{"name": "train_C-41", "title": "Evaluating Adaptive Resource Management for Distributed Real-Time Embedded Systems", "abstract": "A challenging problem faced by researchers and developers of distributed real-time and embedded (DRE) systems is devising and implementing effective adaptive resource management strategies that can meet end-to-end quality of service (QoS) requirements in varying operational conditions. This paper presents two contributions to research in adaptive resource management for DRE systems. First, we describe the structure and functionality of the Hybrid Adaptive Resourcemanagement Middleware (HyARM), which provides adaptive resource management using hybrid control techniques for adapting to workload fluctuations and resource availability. Second, we evaluate the adaptive behavior of HyARM via experiments on a DRE multimedia system that distributes video in real-time. Our results indicate that HyARM yields predictable, stable, and high system performance, even in the face of fluctuating workload and resource availability.", "fulltext": "1. INTRODUCTION\nAchieving end-to-end real-time quality of service (QoS)\nis particularly important for open distributed real-time and\nembedded (DRE) systems that face resource constraints, such\nas limited computing power and network bandwidth.\nOverutilization of these system resources can yield unpredictable\nand unstable behavior, whereas under-utilization can yield\nexcessive system cost. A promising approach to meeting\nthese end-to-end QoS requirements effectively, therefore, is\nto develop and apply adaptive middleware [10, 15], which is\nsoftware whose functional and QoS-related properties can be\nmodified either statically or dynamically. Static\nmodifications are carried out to reduce footprint, leverage\ncapabilities that exist in specific platforms, enable functional\nsubsetting, and/or minimize hardware/software infrastructure\ndependencies. Objectives of dynamic modifications include\noptimizing system responses to changing environments or\nrequirements, such as changing component interconnections,\npower-levels, CPU and network bandwidth availability,\nlatency/jitter, and workload.\nIn open DRE systems, adaptive middleware must make\nsuch modifications dependably, i.e., while meeting\nstringent end-to-end QoS requirements, which requires the\nspecification and enforcement of upper and lower bounds on\nsystem resource utilization to ensure effective use of\nsystem resources. To meet these requirements, we have\ndeveloped the Hybrid Adaptive Resource-management\nMiddleware (HyARM), which is an open-source1\ndistributed\nresource management middleware.\nHyARM is based on hybrid control theoretic techniques [8],\nwhich provide a theoretical framework for designing\ncontrol of complex system with both continuous and discrete\ndynamics. In our case study, which involves a distributed\nreal-time video distribution system, the task of adaptive\nresource management is to control the utilization of the\ndifferent resources, whose utilizations are described by\ncontinuous variables. We achieve this by adapting the resolution\nof the transmitted video, which is modeled as a continuous\nvariable, and by changing the frame-rate and the\ncompression, which are modeled by discrete actions. We have\nimplemented HyARM atop The ACE ORB (TAO) [13], which\nis an implementation of the Real-time CORBA\nspecification [12]. Our results show that (1) HyARM ensures\neffective system resource utilization and (2) end-to-end QoS\nrequirements of higher priority applications are met, even in\nthe face of fluctuations in workload.\nThe remainder of the paper is organized as follows:\nSection 2 describes the architecture, functionality, and resource\nutilization model of our DRE multimedia system case study;\nSection 3 explains the structure and functionality of HyARM;\nSection 4 evaluates the adaptive behavior of HyARM via\nexperiments on our multimedia system case study; Section 5\ncompares our research on HyARM with related work; and\nSection 6 presents concluding remarks.\n1\nThe code and examples for HyARM are available at www.\ndre.vanderbilt.edu/\u223cnshankar/HyARM/.\nArticle 7\n2. CASE STUDY: DRE MULTIMEDIA\nSYSTEM\nThis section describes the architecture and QoS\nrequirements of our DRE multimedia system.\n2.1 Multimedia System Architecture\nWireless Link\nWireless Link\nWireless\nLink\n`\n`\n`\nPhysical Link\nPhysical Link\nPhysical Link\nBase Station\nEnd Receiver\nEnd Receiver\nEnd Receiver`\nPhysical Link\nEnd Receiver\nUAV\nCamera\nVideo\nEncoder\nCamera\nVideo\nEncoder\nCamera\nVideo\nEncoder\nUAV\nCamera\nVideo\nEncoder\nCamera\nVideo\nEncoder\nCamera\nVideo\nEncoder\nUAV\nCamera\nVideo\nEncoder\nCamera\nVideo\nEncoder\nCamera\nVideo\nEncoder\nFigure 1: DRE Multimedia System Architecture\nThe architecture for our DRE multimedia system is shown\nin Figure 1 and consists of the following entities: (1)Data\nsource (video capture by UAV), where video is captured\n(related to subject of interest) by camera(s) on each UAV,\nfollowed by encoding of raw video using a specific encoding\nscheme and transmitting the video to the next stage in the\npipeline. (2)Data distributor (base station), where the\nvideo is processed to remove noise, followed by\nretransmission of the processed video to the next stage in the pipeline.\n(3) Sinks (command and control center), where the\nreceived video is again processed to remove noise, then\ndecoded and finally rendered to end user via graphical displays.\nSignificant improvements in video encoding/decoding and\n(de)compression techniques have been made as a result of\nrecent advances in video encoding and compression\ntechniques [14]. Common video compression schemes are\nMPEG1, MPEG-2, Real Video, and MPEG-4. Each compression\nscheme is characterized by its resource requirement, e.g., the\ncomputational power to (de)compress the video signal and\nthe network bandwidth required to transmit the compressed\nvideo signal. Properties of the compressed video, such as\nresolution and frame-rate determine both the quality and the\nresource requirements of the video.\nOur multimedia system case study has the following\nendto-end real-time QoS requirements: (1) latency, (2)\ninterframe delay (also know as jitter), (3) frame rate, and (4)\npicture resolution. These QoS requirements can be\nclassified as being either hard or soft. Hard QoS requirements\nshould be met by the underlying system at all times, whereas\nsoft QoS requirements can be missed occasionally.2\nFor our\ncase study, we treat QoS requirements such as latency and\njitter as harder QoS requirements and strive to meet these\nrequirements at all times. In contrast, we treat QoS\nrequirements such as video frame rate and picture resolution as\nsofter QoS requirements and modify these video properties\nadaptively to handle dynamic changes in resource\navailabil2\nAlthough hard and soft are often portrayed as two discrete\nrequirement sets, in practice they are usually two ends of\na continuum ranging from softer to harder rather than\ntwo disjoint points.\nity effectively.\n2.2 DRE Multimedia System Rresources\nThere are two primary types of resources in our DRE\nmultimedia system: (1) processors that provide\ncomputational power available at the UAVs, base stations, and end\nreceivers and (2) network links that provide communication\nbandwidth between UAVs, base stations, and end receivers.\nThe computing power required by the video capture and\nencoding tasks depends on dynamic factors, such as speed\nof the UAV, speed of the subject (if the subject is mobile),\nand distance between UAV and the subject. The wireless\nnetwork bandwidth available to transmit video captured by\nUAVs to base stations also depends on the wireless\nconnectivity between the UAVs and the base station, which in-turn\ndepend on dynamic factors such as the speed of the UAVs\nand the relative distance between UAVs and base stations.\nThe bandwidth of the link between the base station and\nthe end receiver is limited, but more stable than the\nbandwidth of the wireless network. Resource requirements and\navailability of resources are subjected to dynamic changes.\nTwo classes of applications - QoS-enabled and best-effort\n- use the multimedia system infrastructure described above\nto transmit video to their respective receivers. QoS-enabled\nclass of applications have higher priority over best-effort\nclass of application. In our study, emergency response\napplications belong to QoS-enabled and surveillance applications\nbelong to best-effort class. For example, since a stream from\nan emergency response application is of higher importance\nthan a video stream from a surveillance application, it\nreceives more resources end-to-end.\nSince resource availability significantly affects QoS, we use\ncurrent resource utilization as the primary indicator of\nsystem performance. We refer to the current level of system\nresource utilization as the system condition. Based on this\ndefinition, we can classify system conditions as being either\nunder, over, or effectively utilized.\nUnder-utilization of system resources occurs when the\ncurrent resource utilization is lower than the desired lower bound\non resource utilization. In this system condition, residual\nsystem resources (i.e., network bandwidth and\ncomputational power) are available in large amounts after meeting\nend-to-end QoS requirements of applications. These\nresidual resources can be used to increase the QoS of the\napplications. For example, residual CPU and network bandwidth\ncan be used to deliver better quality video (e.g., with greater\nresolution and higher frame rate) to end receivers.\nOver-utilization of system resources occurs when the\ncurrent resource utilization is higher than the desired upper\nbound on resource utilization. This condition can arise\nfrom loss of resources - network bandwidth and/or\ncomputing power at base station, end receiver or at UAV - or\nmay be due to an increase in resource demands by\napplications. Over-utilization is generally undesirable since the\nquality of the received video (such as resolution and frame\nrate) and timeliness properties (such as latency and jitter)\nare degraded and may result in an unstable (and thus\nineffective) system.\nEffective resource utilization is the desired system\ncondition since it ensures that end-to-end QoS requirements of\nthe UAV-based multimedia system are met and utilization of\nboth system resources, i.e., network bandwidth and\ncomputational power, are within their desired utilization bounds.\nArticle 7\nSection 3 describes techniques we applied to achieve effective\nutilization, even in the face of fluctuating resource\navailability and/or demand.\n3. OVERVIEW OF HYARM\nThis section describes the architecture of the Hybrid\nAdaptive Resource-management Middleware (HyARM). HyARM\nensures efficient and predictable system performance by\nproviding adaptive resource management, including monitoring\nof system resources and enforcing bounds on application\nresource utilization.\n3.1 HyARM Structure and Functionality\nResource Utilization\nLegend\nResource Allocation\nApplication Parameters\nFigure 2: HyARM Architecture\nHyARM is composed of three types of entities shown in\nFigure 2 and described below:\nResource monitors observe the overall resource\nutilization for each type of resource and resource utilization per\napplication. In our multimedia system, there are resource\nmonitors for CPU utilization and network bandwidth. CPU\nmonitors observe the CPU resource utilization of UAVs, base\nstation, and end receivers. Network bandwidth monitors\nobserve the network resource utilization of (1) wireless network\nlink between UAVs and the base station and (2) wired\nnetwork link between the base station and end receivers.\nThe central controller maintains the system resource\nutilization below a desired bound by (1) processing periodic\nupdates it receives from resource monitors and (2)\nmodifying the execution of applications accordingly, e.g., by\nusing different execution algorithms or operating the\napplication with increased/decreased QoS. This adaptation\nprocess ensures that system resources are utilized efficiently and\nend-to-end application QoS requirements are met. In our\nmultimedia system, the HyARM controller determines the\nvalue of application parameters such as (1) video\ncompression schemes, such as Real Video and MPEG-4, and/or (2)\nframe rate, and (3) picture resolution. From the perspective\nof hybrid control theoretic techniques [8], the different video\ncompression schemes and frame rate form the discrete\nvariables of application execution and picture resolution forms\nthe continuous variables.\nApplication adapters modify application execution\naccording to parameters recommended by the controller and\nensures that the operation of the application is in accordance\nwith the recommended parameters. In the current\nmplementation of HyARM, the application adapter modifies the\ninput parameters to the application that affect application\nQoS and resource utilization - compression scheme, frame\nrate, and picture resolution. In our future implementations,\nwe plan to use resource reservation mechanisms such as\nDifferentiated Service [7, 3] and Class-based Kernel Resource\nManagement [4] to provision/reserve network and CPU\nresources. In our multimedia system, the application adapter\nensures that the video is encoded at the recommended frame\nrate and resolution using the specified compression scheme.\n3.2 Applying HyARM to the Multimedia\nSystem Case Study\nHyARM is built atop TAO [13], a widely used open-source\nimplementation of Real-time CORBA [12]. HyARM can be\napplied to ensure efficient, predictable and adaptive resource\nmanagement of any DRE system where resource availability\nand requirements are subject to dynamic change.\nFigure 3 shows the interaction of various parts of the\nDRE multimedia system developed with HyARM, TAO,\nand TAO\"s A/V Streaming Service. TAO\"s A/V Streaming\nservice is an implementation of the CORBA A/V\nStreaming Service specification. TAO\"s A/V Streaming Service is\na QoS-enabled video distribution service that can transfer\nvideo in real-time to one or more receivers. We use the A/V\nStreaming Service to transmit the video from the UAVs to\nthe end receivers via the base station. Three entities of\nReceiver\nUAV\nTAO\nResource\nUtilization\nHyARM\nCentral\nController\nA/V Streaming\nService : Sender\nMPEG1\nMPEG4\nReal\nVideo\nHyARM\nResource\nMonitor\nA/V Streaming\nService : Receiver\nCompressed\nVideo Compressed\nVideo\nApplication\nHyARM\nApplication\nAdapter\nRemote Object Call\nControl\nInputs Resource\nUtilization\nResource\nUtilization /\nControl Inputs\nControl\nInputs\nLegend\nFigure 3: Developing the DRE Multimedia System\nwith HyARM\nHyARM, namely the resource monitors, central controller,\nand application adapters are built as CORBA servants, so\nthey can be distributed throughout a DRE system.\nResource monitors are remote CORBA objects that update\nthe central controller periodically with the current resource\nutilization. Application adapters are collocated with\napplications since the two interact closely.\nAs shown in Figure 3, UAVs compress the data using\nvarious compression schemes, such as MPEG1, MPEG4, and\nReal Video, and uses TAO\"s A/V streaming service to\ntransmit the video to end receivers. HyARM\"s resource monitors\ncontinuously observe the system resource utilization and\nnotify the central controller with the current utilization. 3\nThe interaction between the controller and the resource\nmonitors uses the Observer pattern [5]. When the controller\nreceives resource utilization updates from monitors, it\ncomputes the necessary modifications to application(s)\nparameters and notifies application adapter(s) via a remote\noperation call. Application adapter(s), that are collocated with\nthe application, modify the input parameters to the\napplication - in our case video encoder - to modify the application\nresource utilization and QoS.\n3\nThe base station is not included in the figure since it only\nretransmits the video received from UAVs to end receivers.\nArticle 7\n4. PERFORMANCE RESULTS AND\nANALYSIS\nThis section first describes the testbed that provides the\ninfrastructure for our DRE multimedia system, which was\nused to evaluate the performance of HyARM. We then\ndescribe our experiments and analyze the results obtained to\nempirically evaluate how HyARM behaves during\nunderand over-utilization of system resources.\n4.1 Overview of the Hardware and Software\nTestbed\nOur experiments were performed on the Emulab testbed\nat University of Utah. The hardware configuration consists\nof two nodes acting as UAVs, one acting as base station,\nand one as end receiver. Video from the two UAVs were\ntransmitted to a base station via a LAN configured with\nthe following properties: average packet loss ratio of 0.3 and\nbandwidth 1 Mbps. The network bandwidth was chosen to\nbe 1 Mbps since each UAV in the DRE multimedia system\nis allocated 250 Kbps. These parameters were chosen to\nemulate an unreliable wireless network with limited bandwidth\nbetween the UAVs and the base station. From the base\nstation, the video was retransmitted to the end receiver via a\nreliable wireline link of 10 Mbps bandwidth with no packet\nloss.\nThe hardware configuration of all the nodes was chosen as\nfollows: 600 MHz Intel Pentium III processor, 256 MB\nphysical memory, 4 Intel EtherExpress Pro 10/100 Mbps Ethernet\nports, and 13 GB hard drive. A real-time version of Linux\n- TimeSys Linux/NET 3.1.214 based on RedHat Linux\n9was used as the operating system for all nodes. The\nfollowing software packages were also used for our experiments: (1)\nFfmpeg 0.4.9-pre1, which is an open-source library (http:\n//www.ffmpeg.sourceforge.net/download.php) that\ncompresses video into MPEG-2, MPEG-4, Real Video, and many\nother video formats. (2) Iftop 0.16, which is an\nopensource library (http://www.ex-parrot.com/\u223cpdw/iftop/)\nwe used for monitoring network activity and bandwidth\nutilization. (3) ACE 5.4.3 + TAO 1.4.3, which is an\nopensource (http://www.dre.vanderbilt.edu/TAO)\nimplementation of the Real-time CORBA [12] specification upon which\nHyARM is built. TAO provides the CORBA Audio/Video\n(A/V) Streaming Service that we use to transmit the video\nfrom the UAVs to end receivers via the base station.\n4.2 Experiment Configuration\nOur experiment consisted of two (emulated) UAVs that\nsimultaneously send video to the base station using the\nexperimentation setup described in Section 4.1. At the base\nstation, video was retransmitted to the end receivers (without\nany modifications), where it was stored to a file. Each UAV\nhosted two applications, one QoS-enabled application\n(emergency response), and one best-effort application\n(surveillance). Within each UAV, computational power is shared\nbetween the applications, while the network bandwidth is\nshared among all applications.\nTo evaluate the QoS provided by HyARM, we monitored\nCPU utilization at the two UAVs, and network bandwidth\nutilization between the UAV and the base station. CPU\nresource utilization was not monitored at the base station and\nthe end receiver since they performed no\ncomputationallyintensive operations. The resource utilization of the 10 Mpbs\nphysical link between the base station and the end receiver\ndoes not affect QoS of applications and is not monitored by\nHyARM since it is nearly 10 times the 1 MB bandwidth\nof the LAN between the UAVs and the base station. The\nexperiment also monitors properties of the video that affect\nthe QoS of the applications, such as latency, jitter, frame\nrate, and resolution.\nThe set point on resource utilization for each resource was\nspecified at 0.69, which is the upper bound typically\nrecommended by scheduling techniques, such as rate monotonic\nalgorithm [9]. Since studies [6] have shown that human eyes\ncan perceive delays more than 200ms, we use this as the\nupper bound on jitter of the received video. QoS\nrequirements for each class of application is specified during system\ninitialization and is shown in Table 1.\n4.3 Empirical Results and Analysis\nThis section presents the results obtained from running\nthe experiment described in Section 4.2 on our DRE\nmultimedia system testbed. We used system resource utilization\nas a metric to evaluate the adaptive resource management\ncapabilities of HyARM under varying input work loads. We\nalso used application QoS as a metric to evaluate HyARM\"s\ncapabilities to support end-to-end QoS requirements of the\nvarious classes of applications in the DRE multimedia\nsystem. We analyze these results to explain the significant\ndifferences in system performance and application QoS.\nComparison of system performance is decomposed into\ncomparison of resource utilization and application QoS. For\nsystem resource utilization, we compare (1) network\nbandwidth utilization of the local area network and (2) CPU\nutilization at the two UAV nodes. For application QoS, we\ncompare mean values of video parameters, including (1)\npicture resolution, (2) frame rate, (3) latency, and (4) jitter.\nComparison of resource utilization. Over-utilization\nof system resources in DRE systems can yield an unstable\nsystem. In contrast, under-utilization of system resources\nincreases system cost. Figure 4 and Figure 5 compare the\nsystem resource utilization with and without HyARM.\nFigure 4 shows that HyARM maintains system utilization close\nto the desired utilization set point during fluctuation in\ninput work load by transmitting video of higher (or lower) QoS\nfor QoS-enabled (or best-effort) class of applications during\nover (or under) utilization of system resources.\nFigure 5 shows that without HyARM, network\nutilization was as high as 0.9 during increase in workload\nconditions, which is greater than the utilization set point of 0.7\nby 0.2. As a result of over-utilization of resources, QoS of\nthe received video, such as average latency and jitter, was\naffected significantly. Without HyARM, system resources\nwere either under-utilized or over-utilized, both of which\nare undesirable. In contrast, with HyARM, system resource\nutilization is always close to the desired set point, even\nduring fluctuations in application workload. During\nsudden fluctuation in application workload, system conditions\nmay be temporarily undesirable, but are restored to the\ndesired condition within several sampling periods. Temporary\nover-utilization of resources is permissible in our multimedia\nsystem since the quality of the video may be degraded for\na short period of time, though application QoS will be\ndegraded significantly if poor quality video is transmitted for\na longer period of time.\nComparison of application QoS. Figures 6, Figure 7,\nand Table 2 compare latency, jitter, resolution, and\nframeArticle 7\nClass Resolution Frame Rate Latency (msec ) Jitter (msec)\nQoS Enabled 1024 x 768 25 200 200\nBest-effort 320 x 240 15 300 250\nTable 1: Application QoS Requirements\nFigure 4: Resource utilization with HyARM Figure 5: Resource utilization without HyARM\nrate of the received video, respectively. Table 2 shows that\nHyARM increases the resolution and frame video of\nQoSenabled applications, but decreases the resolution and frame\nrate of best effort applications. During over utilization of\nsystem resources, resolution and frame rate of lower priority\napplications are reduced to adapt to fluctuations in\napplication workload and to maintain the utilization of resources\nat the specified set point.\nIt can be seen from Figure 6 and Figure 7 that HyARM\nreduces the latency and jitter of the received video\nsignificantly. These figures show that the QoS of QoS-enabled\napplications is greatly improved by HyARM. Although\napplication parameters, such as frame rate and resolutions,\nwhich affect the soft QoS requirements of best-effort\napplications may be compromised, the hard QoS requirements,\nsuch as latency and jitter, of all applications are met.\nHyARM responds to fluctuation in resource availability\nand/or demand by constant monitoring of resource\nutilization. As shown in Figure 4, when resources utilization\nincreases above the desired set point, HyARM lowers the\nutilization by reducing the QoS of best-effort applications. This\nadaptation ensures that enough resources are available for\nQoS-enabled applications to meet their QoS needs.\nFigures 6 and 7 show that the values of latency and jitter of\nthe received video of the system with HyARM are nearly half\nof the corresponding value of the system without HyARM.\nWith HyARM, values of these parameters are well below\nthe specified bounds, whereas without HyARM, these value\nare significantly above the specified bounds due to\noverutilization of the network bandwidth, which leads to network\ncongestion and results in packet loss. HyARM avoids this\nby reducing video parameters such as resolution, frame-rate,\nand/or modifying the compression scheme used to compress\nthe video.\nOur conclusions from analyzing the results described above\nare that applying adaptive middleware via hybrid control to\nDRE system helps to (1) improve application QoS, (2)\nincrease system resource utilization, and (3) provide better\npredictability (lower latency and inter-frame delay) to\nQoSenabled applications. These improvements are achieved largely\ndue to monitoring of system resource utilization, efficient\nsystem workload management, and adaptive resource\nprovisioning by means of HyARM\"s network/CPU resource\nmonitors, application adapter, and central controller,\nrespectively.\n5. RELATED WORK\nA number of control theoretic approaches have been\napplied to DRE systems recently. These techniques aid in\novercoming limitations with traditional scheduling approaches\nthat handle dynamic changes in resource availability poorly\nand result in a rigidly scheduled system that adapts poorly\nto change. A survey of these techniques is presented in [1].\nOne such approach is feedback control scheduling (FCS) [2,\n11]. FCS algorithms dynamically adjust resource allocation\nby means of software feedback control loops. FCS\nalgorithms are modeled and designed using rigorous\ncontroltheoretic methodologies. These algorithms provide robust\nand analytical performance assurances despite uncertainties\nin resource availability and/or demand. Although existing\nFCS algorithms have shown promise, these algorithms often\nassume that the system has continuous control variable(s)\nthat can continuously be adjusted. While this assumption\nholds for certain classes of systems, there are many classes\nof DRE systems, such as avionics and total-ship computing\nenvironments that only support a finite a priori set of\ndiscrete configurations. The control variables in such systems\nare therefore intrinsically discrete.\nHyARM handles both continuous control variables, such\nas picture resolution, and discrete control variable, such as\ndiscrete set of frame rates. HyARM can therefore be applied\nto system that support continuous and/or discrete set of\ncontrol variables. The DRE multimedia system as described\nin Section 2 is an example DRE system that offers both\ncontinuous (picture resolution) and discrete set (frame-rate) of\ncontrol variables. These variables are modified by HyARM\nto achieve efficient resource utilization and improved\napplication QoS.\n6. CONCLUDING REMARKS\nArticle 7\nFigure 6: Comparison of Video Latency Figure 7: Comparison of Video Jitter\nSource Picture Size / Frame Rate\nWith HyARM Without HyARM\nUAV1 QoS Enabled Application 1122 X 1496 / 25 960 X 720 / 20\nUAV1 Best-effort Application 288 X 384 / 15 640 X 480 / 20\nUAV2 QoS Enabled Application 1126 X 1496 / 25 960 X 720 / 20\nUAV2 Best-effort Application 288 X 384 / 15 640 X 480 / 20\nTable 2: Comparison of Video Quality\nMany distributed real-time and embedded (DRE) systems\ndemand end-to-end quality of service (QoS) enforcement\nfrom their underlying platforms to operate correctly. These\nsystems increasingly run in open environments, where\nresource availability is subject to dynamic change. To meet\nend-to-end QoS in dynamic environments, DRE systems can\nbenefit from an adaptive middleware that monitors system\nresources, performs efficient application workload\nmanagement, and enables efficient resource provisioning for\nexecuting applications.\nThis paper described HyARM, an adaptive middleware,\nthat provides effective resource management to DRE\nsystems. HyARM employs hybrid control techniques to\nprovide the adaptive middleware capabilities, such as resource\nmonitoring and application adaptation that are key to\nproviding the dynamic resource management capabilities for\nopen DRE systems. We employed HyARM to a\nrepresentative DRE multimedia system that is implemented using\nReal-time CORBA and CORBA A/V Streaming Service.\nWe evaluated the performance of HyARM in a system\ncomposed of three distributed resources and two classes of\napplications with two applications each. Our empirical\nresults indicate that HyARM ensures (1) efficient resource\nutilization by maintaining the resource utilization of system\nresources within the specified utilization bounds, (2) QoS\nrequirements of QoS-enabled applications are met at all times.\nOverall, HyARM ensures efficient, predictable, and adaptive\nresource management for DRE systems.\n7. REFERENCES\n[1] T. F. Abdelzaher, J. Stankovic, C. Lu, R. Zhang, and Y. Lu.\nFeddback Performance Control in Software Services. IEEE:\nControl Systems, 23(3), June 2003.\n[2] L. Abeni, L. Palopoli, G. Lipari, and J. Walpole. Analysis of a\nreservation-based feedback scheduler. In IEEE Real-Time\nSystems Symposium, Dec. 2002.\n[3] S. Blake, D. Black, M. Carlson, E. Davies, Z. Wang, and\nW. Weiss. An architecture for differentiated services. Network\nInformation Center RFC 2475, Dec. 1998.\n[4] H. Franke, S. Nagar, C. Seetharaman, and V. Kashyap.\nEnabling Autonomic Workload Management in Linux. 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The Design and\nPerformance of Real-Time Object Request Brokers. Computer\nCommunications, 21(4):294-324, Apr. 1998.\n[14] Thomas Sikora. Trends and Perspectives in Image and Video\nCoding. In Proceedings of the IEEE, Jan. 2005.\n[15] X. Wang, H.-M. Huang, V. Subramonian, C. Lu, and C. Gill.\nCAMRIT: Control-based Adaptive Middleware for Real-time\nImage Transmission. In Proc. of the 10th IEEE Real-Time and\nEmbedded Tech. and Applications Symp. (RTAS), Toronto,\nCanada, May 2004.\nArticle 7", "keywords": "real-time video distribution system;dynamic environment;hybrid system;video encoding/decoding;quality of service;streaming service;hybrid adaptive resourcemanagement middleware;distributed real-time embedded system;distribute real-time embed system;adaptive resource management;service end-to-end quality;hybrid control technique;service quality;real-time corba specification;end-to-end quality of service;resource reservation mechanism"}
{"name": "train_C-42", "title": "Demonstration of Grid-Enabled Ensemble Kalman Filter Data Assimilation Methodology for Reservoir Characterization", "abstract": "Ensemble Kalman filter data assimilation methodology is a popular approach for hydrocarbon reservoir simulations in energy exploration. In this approach, an ensemble of geological models and production data of oil fields is used to forecast the dynamic response of oil wells. The Schlumberger ECLIPSE software is used for these simulations. Since models in the ensemble do not communicate, message-passing implementation is a good choice. Each model checks out an ECLIPSE license and therefore, parallelizability of reservoir simulations depends on the number licenses available. We have Grid-enabled the ensemble Kalman filter data assimilation methodology for the TIGRE Grid computing environment. By pooling the licenses and computing resources across the collaborating institutions using GridWay metascheduler and TIGRE environment, the computational accuracy can be increased while reducing the simulation runtime. In this paper, we provide an account of our efforts in Gridenabling the ensemble Kalman Filter data assimilation methodology. Potential benefits of this approach, observations and lessons learned will be discussed.", "fulltext": "1. INTRODUCTION\nGrid computing [1] is an emerging collaborative\ncomputing paradigm to extend institution/organization\nspecific high performance computing (HPC) capabilities\ngreatly beyond local resources. Its importance stems from\nthe fact that ground breaking research in strategic\napplication areas such as bioscience and medicine, energy\nexploration and environmental modeling involve strong\ninterdisciplinary components and often require intercampus\ncollaborations and computational capabilities beyond\ninstitutional limitations.\nThe Texas Internet Grid for Research and Education\n(TIGRE) [2,3] is a state funded cyberinfrastructure\ndevelopment project carried out by five (Rice, A&M, TTU,\nUH and UT Austin) major university systems - collectively\ncalled TIGRE Institutions. The purpose of TIGRE is to\ncreate a higher education Grid to sustain and extend\nresearch and educational opportunities across Texas.\nTIGRE is a project of the High Performance Computing\nacross Texas (HiPCAT) [4] consortium. The goal of\nHiPCAT is to support advanced computational technologies\nto enhance research, development, and educational\nactivities.\nThe primary goal of TIGRE is to design and deploy\nstate-of-the-art Grid middleware that enables integration of\ncomputing systems, storage systems and databases,\nvisualization laboratories and displays, and even\ninstruments and sensors across Texas. The secondary goal\nis to demonstrate the TIGRE capabilities to enhance\nresearch and educational opportunities in strategic\napplication areas of interest to the State of Texas. These are\nbioscience and medicine, energy exploration and air quality\nmodeling. Vision of the TIGRE project is to foster\ninterdisciplinary and intercampus collaborations, identify\nnovel approaches to extend academic-government-private\npartnerships, and become a competitive model for external\nfunding opportunities. The overall goal of TIGRE is to\nsupport local, campus and regional user interests and offer\navenues to connect with national Grid projects such as\nOpen Science Grid [5], and TeraGrid [6].\nWithin the energy exploration strategic application area,\nwe have Grid-enabled the ensemble Kalman Filter (EnKF)\n[7] approach for data assimilation in reservoir modeling and\ndemonstrated the extensibility of the application using the\nTIGRE environment and the GridWay [8] metascheduler.\nSection 2 provides an overview of the TIGRE environment\nand capabilities. Application description and the need for\nGrid-enabling EnKF methodology is provided in Section 3.\nThe implementation details and merits of our approach are\ndiscussed in Section 4. Conclusions are provided in Section\n5. Finally, observations and lessons learned are documented\nin Section 6.\n2. TIGRE ENVIRONMENT\nThe TIGRE Grid middleware consists of minimal set of\ncomponents derived from a subset of the Virtual Data\nToolkit (VDT) [9] which supports a variety of operating\nsystems. The purpose of choosing a minimal software stack\nis to support applications at hand, and to simplify\ninstallation and distribution of client/server stacks across\nTIGRE sites. Additional components will be added as they\nbecome necessary. The PacMan [10] packaging and\ndistribution mechanism is employed for TIGRE\nclient/server installation and management. The PacMan\ndistribution mechanism involves retrieval, installation, and\noften configuration of the packaged software. This\napproach allows the clients to keep current, consistent\nversions of TIGRE software. It also helps TIGRE sites to\ninstall the needed components on resources distributed\nthroughout the participating sites. The TIGRE client/server\nstack consists of an authentication and authorization layer,\nGlobus GRAM4-based job submission via web services\n(pre-web services installations are available up on request).\nThe tools for handling Grid proxy generation, Grid-enabled\nfile transfer and Grid-enabled remote login are supported.\nThe pertinent details of TIGRE services and tools for job\nscheduling and management are provided below.\n2.1. Certificate Authority\nThe TIGRE security infrastructure includes a certificate\nauthority (CA) accredited by the International Grid Trust\nFederation (IGTF) for issuing X. 509 user and resource\nGrid certificates [11]. The Texas Advanced Computing\nCenter (TACC), University of Texas at Austin is the\nTIGRE\"s shared CA. The TIGRE Institutions serve as\nRegistration Authorities (RA) for their respective local user\nbase. For up-to-date information on securing user and\nresource certificates and their installation instructions see\nref [2]. The users and hosts on TIGRE are identified by\ntheir distinguished name (DN) in their X.509 certificate\nprovided by the CA. A native Grid-mapfile that contains a\nlist of authorized DNs is used to authenticate and authorize\nuser job scheduling and management on TIGRE site\nresources. At Texas Tech University, the users are\ndynamically allocated one of the many generic pool\naccounts. This is accomplished through the Grid User\nManagement System (GUMS) [12].\n2.2. Job Scheduling and Management\nThe TIGRE environment supports GRAM4-based job\nsubmission via web services. The job submission scripts are\ngenerated using XML. The web services GRAM translates\nthe XML scripts into target cluster specific batch schedulers\nsuch as LSF, PBS, or SGE. The high bandwidth file transfer\nprotocols such as GridFTP are utilized for staging files in\nand out of the target machine. The login to remote hosts for\ncompilation and debugging is only through GSISSH service\nwhich requires resource authentication through X.509\ncertificates. The authentication and authorization of Grid\njobs are managed by issuing Grid certificates to both users\nand hosts. The certificate revocation lists (CRL) are\nupdated on a daily basis to maintain high security standards\nof the TIGRE Grid services. The TIGRE portal [2]\ndocumentation area provides a quick start tutorial on\nrunning jobs on TIGRE.\n2.3. Metascheduler\nThe metascheduler interoperates with the cluster level\nbatch schedulers (such as LSF, PBS) in the overall Grid\nworkflow management. In the present work, we have\nemployed GridWay [8] metascheduler - a Globus incubator\nproject - to schedule and manage jobs across TIGRE.\nThe GridWay is a light-weight metascheduler that fully\nutilizes Globus functionalities. It is designed to provide\nefficient use of dynamic Grid resources by multiple users\nfor Grid infrastructures built on top of Globus services. The\nTIGRE site administrator can control the resource sharing\nthrough a powerful built-in scheduler provided by GridWay\nor by extending GridWay\"s external scheduling module to\nprovide their own scheduling policies. Application users\ncan write job descriptions using GridWay\"s simple and\ndirect job template format (see Section 4 for details) or\nstandard Job Submission Description Language (JSDL).\nSee section 4 for implementation details.\n2.4. Customer Service Management System\nA TIGRE portal [2] was designed and deployed to interface\nusers and resource providers. It was designed using\nGridPort [13] and is maintained by TACC. The TIGRE\nenvironment is supported by open source tools such as the\nOpen Ticket Request System (OTRS) [14] for servicing\ntrouble tickets, and MoinMoin [15] Wiki for TIGRE\ncontent and knowledge management for education, outreach\nand training. The links for OTRS and Wiki are consumed\nby the TIGRE portal [2] - the gateway for users and\nresource providers. The TIGRE resource status and loads\nare monitored by the Grid Port Information Repository\n(GPIR) service of the GridPort toolkit [13] which interfaces\nwith local cluster load monitoring service such as Ganglia.\nThe GPIR utilizes cron jobs on each resource to gather\nsite specific resource characteristics such as jobs that are\nrunning, queued and waiting for resource allocation.\n3. ENSEMBLE KALMAN FILTER\nAPPLICATION\nThe main goal of hydrocarbon reservoir simulations is to\nforecast the production behavior of oil and gas field\n(denoted as field hereafter) for its development and optimal\nmanagement. In reservoir modeling, the field is divided into\nseveral geological models as shown in Figure 1. For\naccurate performance forecasting of the field, it is necessary\nto reconcile several geological models to the dynamic\nresponse of the field through history matching [16-20].\nFigure 1. Cross-sectional view of the Field. Vertical\nlayers correspond to different geological models and the\nnails are oil wells whose historical information will be\nused for forecasting the production behavior.\n(Figure Ref:http://faculty.smu.edu/zchen/research.html).\nThe EnKF is a Monte Carlo method that works with an\nensemble of reservoir models. This method utilizes\ncrosscovariances [21] between the field measurements and the\nreservoir model parameters (derived from several models)\nto estimate prediction uncertainties. The geological model\nparameters in the ensemble are sequentially updated with a\ngoal to minimize the prediction uncertainties. Historical\nproduction response of the field for over 50 years is used in\nthese simulations. The main advantage of EnKF is that it\ncan be readily linked to any reservoir simulator, and can\nassimilate latest production data without the need to re-run\nthe simulator from initial conditions. Researchers in Texas\nare large subscribers of the Schlumberger ECLIPSE [22]\npackage for reservoir simulations. In the reservoir\nmodeling, each geological model checks out an ECLIPSE\nlicense. The simulation runtime of the EnKF methodology\ndepends on the number of geological models used, number\nof ECLIPSE licenses available, production history of the\nfield, and propagated uncertainties in history matching.\nThe overall EnKF workflow is shown Figure 2.\nFigure 2. Ensemble Kaman Filter Data Assimilation\nWorkflow. Each site has L licenses.\nAt START, the master/control process (EnKF main\nprogram) reads the simulation configuration file for number\n(N) of models, and model-specific input files. Then, N\nworking directories are created to store the output files. At\nthe end of iteration, the master/control process collects the\noutput files from N models and post processes\ncrosscovariances [21] to estimate the prediction uncertainties.\nThis information will be used to update models (or input\nfiles) for the next iteration. The simulation continues until\nthe production histories are exhausted.\nTypical EnKF simulation with N=50 and field histories\nof 50-60 years, in time steps ranging from three months to a\nyear, takes about three weeks on a serial computing\nenvironment.\nIn parallel computing environment, there is no\ninterprocess communication between the geological models\nin the ensemble. However, at the end of each simulation\ntime-step, model-specific output files are to be collected for\nanalyzing cross covariances [21] and to prepare next set of\ninput files. Therefore, master-slave model in\nmessagepassing (MPI) environment is a suitable paradigm. In this\napproach, the geological models are treated as slaves and\nare distributed across the available processors. The master\nCluster or (TIGRE/GridWay)\nSTART\nRead Configuration File\nCreate N Working Directories\nCreate N Input files\nModel l Model 2 Model N. . .\nECLIPSE\non site A\nECLIPSE\non Site B\nECLIPSE\non Site Z\nCollect N Model Outputs,\nPost-process Output files\nEND\n. . .\nprocess collects model-specific output files, analyzes and\nprepares next set of input files for the simulation. Since\neach geological model checks out an ECLIPSE license,\nparallelizability of the simulation depends on the number of\nlicenses available. When the available number of licenses is\nless than the number of models in the ensemble, one or\nmore of the nodes in the MPI group have to handle more\nthan one model in a serial fashion and therefore, it takes\nlonger to complete the simulation.\nA Petroleum Engineering Department usually procures\n10-15 ECLIPSE licenses while at least ten-fold increase in\nthe number of licenses would be necessary for industry\nstandard simulations. The number of licenses can be\nincreased by involving several Petroleum Engineering\nDepartments that support ECLIPSE package.\nSince MPI does not scale very well for applications that\ninvolve remote compute clusters, and to get around the\nfirewall issues with license servers across administrative\ndomains, Grid-enabling the EnKF workflow seems to be\nnecessary. With this motivation, we have implemented\nGrid-enabled EnKF workflow for the TIGRE environment\nand demonstrated parallelizability of the application across\nTIGRE using GridWay metascheduler. Further details are\nprovided in the next section.\n4. IMPLEMENTATION DETAILS\nTo Grid-enable the EnKF approach, we have eliminated\nthe MPI code for parallel processing and replaced with N\nsingle processor jobs (or sub-jobs) where, N is the number\nof geological models in the ensemble. These model-specific\nsub-jobs were distributed across TIGRE sites that support\nECLIPSE package using the GridWay [8] metascheduler.\nFor each sub-job, we have constructed a GridWay job\ntemplate that specifies the executable, input and output\nfiles, and resource requirements. Since the TIGRE compute\nresources are not expected to change frequently, we have\nused static resource discovery policy for GridWay and the\nsub-jobs were scheduled dynamically across the TIGRE\nresources using GridWay. Figure 3 represents the sub-job\ntemplate file for the GridWay metascheduler.\nFigure 3. GridWay Sub-Job Template\nIn Figure 3, REQUIREMENTS flag is set to choose the\nresources that satisfy the application requirements. In the\ncase of EnKF application, for example, we need resources\nthat support ECLIPSE package. ARGUMENTS flag\nspecifies the model in the ensemble that will invoke\nECLIPSE at a remote site. INPUT_FILES is prepared by\nthe EnKF main program (or master/control process) and is\ntransferred by GridWay to the remote site where it is\nuntared and is prepared for execution. Finally,\nOUTPUT_FILES specifies the name and location where the\noutput files are to be written.\nThe command-line features of GridWay were used to\ncollect and process the model-specific outputs to prepare\nnew set of input files. This step mimics MPI process\nsynchronization in master-slave model. At the end of each\niteration, the compute resources and licenses are committed\nback to the pool. Table 1 shows the sub-jobs in TIGRE\nGrid via GridWay using gwps command and for clarity,\nonly selected columns were shown\n.\nUSER JID DM EM NAME HOST\npingluo 88 wrap pend enkf.jt antaeus.hpcc.ttu.edu/LSF\npingluo 89 wrap pend enkf.jt antaeus.hpcc.ttu.edu/LSF\npingluo 90 wrap actv enkf.jt minigar.hpcc.ttu.edu/LSF\npingluo 91 wrap pend enkf.jt minigar.hpcc.ttu.edu/LSF\npingluo 92 wrap done enkf.jt cosmos.tamu.edu/PBS\npingluo 93 wrap epil enkf.jt cosmos.tamu.edu/PBS\nTable 1. Job scheduling across TIGRE using GridWay\nMetascheduler. DM: Dispatch state, EM: Execution state,\nJID is the job id and HOST corresponds to site specific\ncluster and its local batch scheduler.\nWhen a job is submitted to GridWay, it will go through a\nseries of dispatch (DM) and execution (EM) states. For\nDM, the states include pend(ing), prol(og), wrap(per),\nepil(og), and done. DM=prol means the job has been\nscheduled to a resource and the remote working directory is\nin preparation. DM=warp implies that GridWay is\nexecuting the wrapper which in turn executes the\napplication. DM=epil implies the job has finished\nrunning at the remote site and results are being transferred\nback to the GridWay server. Similarly, when EM=pend\nimplies the job is waiting in the queue for resource and the\njob is running when EM=actv. For complete list of\nmessage flags and their descriptions, see the documentation\nin ref [8].\nWe have demonstrated the Grid-enabled EnKF runs\nusing GridWay for TIGRE environment. The jobs are so\nchosen that the runtime doesn\"t exceed more than a half\nhour. The simulation runs involved up to 20 jobs between\nA&M and TTU sites with TTU serving 10 licenses. For\nresource information, see Table I.\nOne of the main advantages of Grid-enabled EnKF\nsimulation is that both the resources and licenses are\nreleased back to the pool at the end of each simulation time\nstep unlike in the case of MPI implementation where\nlicenses and nodes are locked until the completion of entire\nsimulation. However, the fact that each sub-job gets\nscheduled independently via GridWay could possibly incur\nanother time delay caused by waiting in queue for execution\nin each simulation time step. Such delays are not expected\nEXECUTABLE=runFORWARD\nREQUIREMENTS=HOSTNAME=cosmos.tamu.edu |\nHOSTNAME=antaeus.hpcc.ttu.edu |\nHOSTNAME=minigar.hpcc.ttu.edu |\nARGUMENTS=001\nINPUT_FILES=001.in.tar\nOUTPUT_FILES=001.out.tar\nin MPI implementation where the node is blocked for\nprocessing sub-jobs (model-specific calculation) until the\nend of the simulation. There are two main scenarios for\ncomparing Grid and cluster computing approaches.\nScenario I: The cluster is heavily loaded. The conceived\naverage waiting time of job requesting large number of\nCPUs is usually longer than waiting time of jobs requesting\nsingle CPU. Therefore, overall waiting time could be\nshorter in Grid approach which requests single CPU for\neach sub-job many times compared to MPI implementation\nthat requests large number of CPUs at a single time. It is\napparent that Grid scheduling is beneficial especially when\ncluster is heavily loaded and requested number of CPUs for\nthe MPI job is not readily available.\nScenario II: The cluster is relatively less loaded or\nlargely available. It appears the MPI implementation is\nfavorable compared to the Grid scheduling. However,\nparallelizability of the EnKF application depends on the\nnumber of ECLIPSE licenses and ideally, the number of\nlicenses should be equal to the number of models in the\nensemble. Therefore, if a single institution does not have\nsufficient number of licenses, the cluster availability doesn\"t\nhelp as much as it is expected.\nSince the collaborative environment such as TIGRE can\naddress both compute and software resource requirements\nfor the EnKF application, Grid-enabled approach is still\nadvantageous over the conventional MPI implementation in\nany of the above scenarios.\n5. CONCLUSIONS AND FUTURE WORK\nTIGRE is a higher education Grid development project\nand its purpose is to sustain and extend research and\neducational opportunities across Texas. Within the energy\nexploration application area, we have Grid-enabled the MPI\nimplementation of the ensemble Kalman filter data\nassimilation methodology for reservoir characterization.\nThis task was accomplished by removing MPI code for\nparallel processing and replacing with single processor jobs\none for each geological model in the ensemble. These\nsingle processor jobs were scheduled across TIGRE via\nGridWay metascheduler. We have demonstrated that by\npooling licenses across TIGRE sites, more geological\nmodels can be handled in parallel and therefore conceivably\nbetter simulation accuracy. This approach has several\nadvantages over MPI implementation especially when a site\nspecific cluster is heavily loaded and/or the number licenses\nrequired for the simulation is more than those available at a\nsingle site.\nTowards the future work, it would be interesting to\ncompare the runtime between MPI, and Grid\nimplementations for the EnKF application. This effort could\nshed light on quality of service (QoS) of Grid environments\nin comparison with cluster computing.\nAnother aspect of interest in the near future would be\nmanaging both compute and license resources to address\nthe job (or processor)-to-license ratio management.\n6. OBSERVATIONS AND LESSIONS\nLEARNED\nThe Grid-enabling efforts for EnKF application have\nprovided ample opportunities to gather insights on the\nvisibility and promise of Grid computing environments for\napplication development and support. The main issues are\nindustry standard data security and QoS comparable to\ncluster computing.\nSince the reservoir modeling research involves\nproprietary data of the field, we had to invest substantial\nefforts initially in educating the application researchers on\nthe ability of Grid services in supporting the industry\nstandard data security through role- and privilege-based\naccess using X.509 standard.\nWith respect to QoS, application researchers expect\ncluster level QoS with Grid environments. Also, there is a\nsteep learning curve in Grid computing compared to the\nconventional cluster computing. Since Grid computing is\nstill an emerging technology, and it spans over several\nadministrative domains, Grid computing is still premature\nespecially in terms of the level of QoS although, it offers\nbetter data security standards compared to commodity\nclusters.\nIt is our observation that training and outreach programs\nthat compare and contrast the Grid and cluster computing\nenvironments would be a suitable approach for enhancing\nuser participation in Grid computing. This approach also\nhelps users to match their applications and abilities Grids\ncan offer.\nIn summary, our efforts through TIGRE in Grid-enabling\nthe EnKF data assimilation methodology showed\nsubstantial promise in engaging Petroleum Engineering\nresearchers through intercampus collaborations. Efforts are\nunder way to involve more schools in this effort. These\nefforts may result in increased collaborative research,\neducational opportunities, and workforce development\nthrough graduate/faculty research programs across TIGRE\nInstitutions.\n7. ACKNOWLEDGMENTS\nThe authors acknowledge the State of Texas for supporting\nthe TIGRE project through the Texas Enterprise Fund, and\nTIGRE Institutions for providing the mechanism, in which\nthe authors (Ravi Vadapalli, Taesung Kim, and Ping Luo)\nare also participating. The authors thank the application\nresearchers Prof. Akhil Datta-Gupta of Texas A&M\nUniversity and Prof. Lloyd Heinze of Texas Tech\nUniversity for their discussions and interest to exploit the\nTIGRE environment to extend opportunities in research and\ndevelopment.\n8. REFERENCES\n[1] Foster, I. and Kesselman, C. (eds.) 2004. The Grid: Blueprint\nfor a new computing infrastructure (The Elsevier series in\nGrid computing)\n[2] TIGRE Portal: http://tigreportal.hipcat.net\n[3] Vadapalli, R. Sill, A., Dooley, R., Murray, M., Luo, P., Kim,\nT., Huang, M., Thyagaraja, K., and Chaffin, D. 2007.\nDemonstration of TIGRE environment for Grid\nenabled/suitable applications. 8th\nIEEE/ACM Int. Conf. on\nGrid Computing, Sept 19-21, Austin\n[4] The High Performance Computing across Texas Consortium\nhttp://www.hipcat.net\n[5] Pordes, R. Petravick, D. Kramer, B. Olson, D. Livny, M.\nRoy, A. Avery, P. Blackburn, K. Wenaus, T. W\u00fcrthwein, F.\nFoster, I. Gardner, R. Wilde, M. Blatecky, A. McGee, J. and\nQuick, R. 2007. The Open Science Grid, J. Phys Conf Series\nhttp://www.iop.org/EJ/abstract/1742-6596/78/1/012057 and\nhttp://www.opensciencegrid.org\n[6] Reed, D.A. 2003. Grids, the TeraGrid and Beyond,\nComputer, vol 30, no. 1 and http://www.teragrid.org\n[7] Evensen, G. 2006. Data Assimilation: The Ensemble Kalman\nFilter, Springer\n[8] Herrera, J. Huedo, E. Montero, R. S. and Llorente, I. M.\n2005. 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History matching\nwith an ensemble Kalman filter and discrete cosine\nparameterization, SPE 108761, Proc of the Annual Technical\nConf and Exhibition, Nov 11-14, Anaheim, CA\n[20] Li, G. and Reynolds, A. C. 2007. An iterative ensemble\nKalman filter for data assimilation, SPE 109808, Proc of the\nSPE Annual Technical Conf and Exhibition, Nov 11-14,\nAnaheim, CA\n[21] Arroyo-Negrete, E. Devagowda, D. Datta-Gupta, A. 2006.\nStreamline assisted ensemble Kalman filter for rapid and\ncontinuous reservoir model updating. Proc of the Int. Oil &\nGas Conf and Exhibition, SPE 104255, Dec 5-7, China\n[22] ECLIPSE Reservoir Engineering Software\nhttp://www.slb.com/content/services/software/reseng/index.a\nsp", "keywords": "pooling license;grid-enabling;ensemble kalman filter;and gridway;cyberinfrastructure development project;tigre grid computing environment;grid computing;hydrocarbon reservoir simulation;gridway metascheduler;enkf;datum assimilation methodology;high performance computing;tigre;energy exploration;tigre grid middleware;strategic application area;reservoir model"}
{"name": "train_C-44", "title": "MSP: Multi-Sequence Positioning of Wireless Sensor Nodes\u2217", "abstract": "Wireless Sensor Networks have been proposed for use in many location-dependent applications. Most of these need to identify the locations of wireless sensor nodes, a challenging task because of the severe constraints on cost, energy and effective range of sensor devices. To overcome limitations in existing solutions, we present a Multi-Sequence Positioning (MSP) method for large-scale stationary sensor node localization in outdoor environments. The novel idea behind MSP is to reconstruct and estimate two-dimensional location information for each sensor node by processing multiple one-dimensional node sequences, easily obtained through loosely guided event distribution. Starting from a basic MSP design, we propose four optimizations, which work together to increase the localization accuracy. We address several interesting issues, such as incomplete (partial) node sequences and sequence flip, found in the Mirage test-bed we built. We have evaluated the MSP system through theoretical analysis, extensive simulation as well as two physical systems (an indoor version with 46 MICAz motes and an outdoor version with 20 MICAz motes). This evaluation demonstrates that MSP can achieve an accuracy within one foot, requiring neither additional costly hardware on sensor nodes nor precise event distribution. It also provides a nice tradeoff between physical cost (anchors) and soft cost (events), while maintaining localization accuracy.", "fulltext": "1 Introduction\nAlthough Wireless Sensor Networks (WSN) have shown\npromising prospects in various applications [5], researchers\nstill face several challenges for massive deployment of such\nnetworks. One of these is to identify the location of\nindividual sensor nodes in outdoor environments. Because of\nunpredictable flow dynamics in airborne scenarios, it is not currently\nfeasible to localize sensor nodes during massive UVA-based\ndeployment. On the other hand, geometric information is\nindispensable in these networks, since users need to know where\nevents of interest occur (e.g., the location of intruders or of a\nbomb explosion).\nPrevious research on node localization falls into two\ncategories: range-based approaches and range-free approaches.\nRange-based approaches [13, 17, 19, 24] compute per-node\nlocation information iteratively or recursively based on\nmeasured distances among target nodes and a few anchors which\nprecisely know their locations. These approaches generally\nrequire costly hardware (e.g., GPS) and have limited\neffective range due to energy constraints (e.g., ultrasound-based\nTDOA [3, 17]). Although range-based solutions can be\nsuitably used in small-scale indoor environments, they are\nconsidered less cost-effective for large-scale deployments. On the\nother hand, range-free approaches [4, 8, 10, 13, 14, 15] do not\nrequire accurate distance measurements, but localize the node\nbased on network connectivity (proximity) information.\nUnfortunately, since wireless connectivity is highly influenced by the\nenvironment and hardware calibration, existing solutions fail\nto deliver encouraging empirical results, or require substantial\nsurvey [2] and calibration [24] on a case-by-case basis.\nRealizing the impracticality of existing solutions for the\nlarge-scale outdoor environment, researchers have recently\nproposed solutions (e.g., Spotlight [20] and Lighthouse [18])\nfor sensor node localization using the spatiotemporal\ncorrelation of controlled events (i.e., inferring nodes\" locations based\non the detection time of controlled events). These solutions\ndemonstrate that long range and high accuracy localization can\nbe achieved simultaneously with little additional cost at\nsensor nodes. These benefits, however, come along with an\nimplicit assumption that the controlled events can be precisely\ndistributed to a specified location at a specified time. We argue\nthat precise event distribution is difficult to achieve, especially\nat large scale when terrain is uneven, the event distribution\ndevice is not well calibrated and its position is difficult to\nmaintain (e.g., the helicopter-mounted scenario in [20]).\nTo address these limitations in current approaches, in this\npaper we present a multi-sequence positioning (MSP) method\n15\nfor large-scale stationary sensor node localization, in\ndeployments where an event source has line-of-sight to all sensors.\nThe novel idea behind MSP is to estimate each sensor node\"s\ntwo-dimensional location by processing multiple easy-to-get\none-dimensional node sequences (e.g., event detection order)\nobtained through loosely-guided event distribution.\nThis design offers several benefits. First, compared to a\nrange-based approach, MSP does not require additional costly\nhardware. It works using sensors typically used by sensor\nnetwork applications, such as light and acoustic sensors, both of\nwhich we specifically consider in this work. Second, compared\nto a range-free approach, MSP needs only a small number of\nanchors (theoretically, as few as two), so high accuracy can be\nachieved economically by introducing more events instead of\nmore anchors. And third, compared to Spotlight, MSP does not\nrequire precise and sophisticated event distribution, an\nadvantage that significantly simplifies the system design and reduces\ncalibration cost.\nThis paper offers the following additional intellectual\ncontributions:\n\u2022 We are the first to localize sensor nodes using the concept\nof node sequence, an ordered list of sensor nodes, sorted\nby the detection time of a disseminated event. We\ndemonstrate that making full use of the information embedded\nin one-dimensional node sequences can significantly\nimprove localization accuracy. Interestingly, we discover\nthat repeated reprocessing of one-dimensional node\nsequences can further increase localization accuracy.\n\u2022 We propose a distribution-based location estimation\nstrategy that obtains the final location of sensor nodes using\nthe marginal probability of joint distribution among\nadjacent nodes within the sequence. This new algorithm\noutperforms the widely adopted Centroid estimation [4, 8].\n\u2022 To the best of our knowledge, this is the first work to\nimprove the localization accuracy of nodes by adaptive\nevents. The generation of later events is guided by\nlocalization results from previous events.\n\u2022 We evaluate line-based MSP on our new Mirage test-bed,\nand wave-based MSP in outdoor environments. Through\nsystem implementation, we discover and address several\ninteresting issues such as partial sequence and sequence\nflips. To reveal MSP performance at scale, we provide\nanalytic results as well as a complete simulation study.\nAll the simulation and implementation code is available\nonline at http://www.cs.umn.edu/\u223czhong/MSP.\nThe rest of the paper is organized as follows. Section 2\nbriefly surveys the related work. Section 3 presents an\noverview of the MSP localization system. In sections 4 and 5,\nbasic MSP and four advanced processing methods are\nintroduced. Section 6 describes how MSP can be applied in a wave\npropagation scenario. Section 7 discusses several\nimplementation issues. Section 8 presents simulation results, and Section 9\nreports an evaluation of MSP on the Mirage test-bed and an\noutdoor test-bed. Section 10 concludes the paper.\n2 Related Work\nMany methods have been proposed to localize wireless\nsensor devices in the open air. Most of these can be\nclassified into two categories: range-based and range-free\nlocalization. Range-based localization systems, such as GPS [23],\nCricket [17], AHLoS [19], AOA [16], Robust\nQuadrilaterals [13] and Sweeps [7], are based on fine-grained\npoint-topoint distance estimation or angle estimation to identify\npernode location. Constraints on the cost, energy and hardware\nfootprint of each sensor node make these range-based\nmethods undesirable for massive outdoor deployment. In addition,\nranging signals generated by sensor nodes have a very limited\neffective range because of energy and form factor concerns.\nFor example, ultrasound signals usually effectively propagate\n20-30 feet using an on-board transmitter [17]. Consequently,\nthese range-based solutions require an undesirably high\ndeployment density. Although the received signal strength\nindicator (RSSI) related [2, 24] methods were once considered\nan ideal low-cost solution, the irregularity of radio\npropagation [26] seriously limits the accuracy of such systems. The\nrecently proposed RIPS localization system [11] superimposes\ntwo RF waves together, creating a low-frequency envelope that\ncan be accurately measured. This ranging technique performs\nvery well as long as antennas are well oriented and\nenvironmental factors such as multi-path effects and background noise\nare sufficiently addressed.\nRange-free methods don\"t need to estimate or measure\naccurate distances or angles. Instead, anchors or controlled-event\ndistributions are used for node localization. Range-free\nmethods can be generally classified into two types: anchor-based\nand anchor-free solutions.\n\u2022 For anchor-based solutions such as Centroid [4], APIT\n[8], SeRLoc [10], Gradient [13] , and APS [15], the main\nidea is that the location of each node is estimated based on\nthe known locations of the anchor nodes. Different anchor\ncombinations narrow the areas in which the target nodes\ncan possibly be located. Anchor-based solutions normally\nrequire a high density of anchor nodes so as to achieve\ngood accuracy. In practice, it is desirable to have as few\nanchor nodes as possible so as to lower the system cost.\n\u2022 Anchor-free solutions require no anchor nodes. Instead,\nexternal event generators and data processing platforms\nare used. The main idea is to correlate the event detection\ntime at a sensor node with the known space-time\nrelationship of controlled events at the generator so that detection\ntime-stamps can be mapped into the locations of sensors.\nSpotlight [20] and Lighthouse [18] work in this fashion.\nIn Spotlight [20], the event distribution needs to be\nprecise in both time and space. Precise event distribution\nis difficult to achieve without careful calibration,\nespecially when the event-generating devices require certain\nmechanical maneuvers (e.g., the telescope mount used in\nSpotlight). All these increase system cost and reduce\nlocalization speed. StarDust [21], which works much faster,\nuses label relaxation algorithms to match light spots\nreflected by corner-cube retro-reflectors (CCR) with sensor\nnodes using various constraints. Label relaxation\nalgorithms converge only when a sufficient number of robust\nconstraints are obtained. Due to the environmental impact\non RF connectivity constraints, however, StarDust is less\naccurate than Spotlight.\nIn this paper, we propose a balanced solution that avoids\nthe limitations of both anchor-based and anchor-free solutions.\nUnlike anchor-based solutions [4, 8], MSP allows a flexible\ntradeoff between the physical cost (anchor nodes) with the soft\n16\n1\nA\nB\n2\n3\n4\n5\nTarget nodeAnchor node\n1A 5 3 B2 4\n1 B2 5A 43\n1A25B4 3\n1 52 AB 4 3\n1\n2\n3\n5\n4\n(b)\n(c)(d)\n(a)\nEvent 1\nNode Sequence generated by event 1\nEvent 3\nNode Sequence generated by event 2\nNode Sequence generated by event 3\nNode Sequence generated by event 4\nEvent 2 Event 4\nFigure 1. The MSP System Overview\ncost (localization events). MSP uses only a small number of\nanchors (theoretically, as few as two). Unlike anchor-free\nsolutions, MSP doesn\"t need to maintain rigid time-space\nrelationships while distributing events, which makes system design\nsimpler, more flexible and more robust to calibration errors.\n3 System Overview\nMSP works by extracting relative location information from\nmultiple simple one-dimensional orderings of nodes.\nFigure 1(a) shows a layout of a sensor network with anchor nodes\nand target nodes. Target nodes are defined as the nodes to be\nlocalized. Briefly, the MSP system works as follows. First,\nevents are generated one at a time in the network area (e.g.,\nultrasound propagations from different locations, laser scans\nwith diverse angles). As each event propagates, as shown in\nFigure 1(a), each node detects it at some particular time\ninstance. For a single event, we call the ordering of nodes, which\nis based on the sequential detection of the event, a node\nsequence. Each node sequence includes both the targets and the\nanchors as shown in Figure 1(b). Second, a multi-sequence\nprocessing algorithm helps to narrow the possible location of\neach node to a small area (Figure 1(c)). Finally, a\ndistributionbased estimation method estimates the exact location of each\nsensor node, as shown in Figure 1(d).\nFigure 1 shows that the node sequences can be obtained\nmuch more economically than accurate pair-wise distance\nmeasurements between target nodes and anchor nodes via\nranging methods. In addition, this system does not require a rigid\ntime-space relationship for the localization events, which is\ncritical but hard to achieve in controlled event distribution\nscenarios (e.g., Spotlight [20]).\nFor the sake of clarity in presentation, we present our system\nin two cases:\n\u2022 Ideal Case, in which all the node sequences obtained\nfrom the network are complete and correct, and nodes are\ntime-synchronized [12, 9].\n\u2022 Realistic Deployment, in which (i) node sequences can\nbe partial (incomplete), (ii) elements in sequences could\nflip (i.e., the order obtained is reversed from reality), and\n(iii) nodes are not time-synchronized.\nTo introduce the MSP algorithm, we first consider a simple\nstraight-line scan scenario. Then, we describe how to\nimplement straight-line scans as well as other event types, such as\nsound wave propagation.\n1\nA\n2\n3\n4\n5\nB\nC\n6\n7\n8\n9\nStraight-line Scan 1\nStraight-lineScan2\n8\n1\n5 A\n6\nC\n4\n3\n7\n2\nB\n9\n3\n1\nC 5\n9\n2 A 4 6\nB\n7 8\nTarget node\nAnchor node\nFigure 2. Obtaining Multiple Node Sequences\n4 Basic MSP\nLet us consider a sensor network with N target nodes and\nM anchor nodes randomly deployed in an area of size S. The\ntop-level idea for basic MSP is to split the whole sensor\nnetwork area into small pieces by processing node sequences.\nBecause the exact locations of all the anchors in a node sequence\nare known, all the nodes in this sequence can be divided into\nO(M +1) parts in the area.\nIn Figure 2, we use numbered circles to denote target nodes\nand numbered hexagons to denote anchor nodes. Basic MSP\nuses two straight lines to scan the area from different directions,\ntreating each scan as an event. All the nodes react to the event\nsequentially generating two node sequences. For vertical scan\n1, the node sequence is (8,1,5,A,6,C,4,3,7,2,B,9), as shown\noutside the right boundary of the area in Figure 2; for\nhorizontal scan 2, the node sequence is (3,1,C,5,9,2,A,4,6,B,7,8),\nas shown under the bottom boundary of the area in Figure 2.\nSince the locations of the anchor nodes are available, the\nanchor nodes in the two node sequences actually split the area\nvertically and horizontally into 16 parts, as shown in Figure 2.\nTo extend this process, suppose we have M anchor nodes and\nperform d scans from different angles, obtaining d node\nsequences and dividing the area into many small parts.\nObviously, the number of parts is a function of the number of\nanchors M, the number of scans d, the anchors\" location as well as\nthe slop k for each scan line. According to the pie-cutting\ntheorem [22], the area can be divided into O(M2d2) parts. When\nM and d are appropriately large, the polygon for each target\nnode may become sufficiently small so that accurate\nestimation can be achieved. We emphasize that accuracy is affected\nnot only by the number of anchors M, but also by the number\nof events d. In other words, MSP provides a tradeoff between\nthe physical cost of anchors and the soft cost of events.\nAlgorithm 1 depicts the computing architecture of basic\nMSP. Each node sequence is processed within line 1 to 8. For\neach node, GetBoundaries() in line 5 searches for the\npredecessor and successor anchors in the sequence so as to\ndetermine the boundaries of this node. Then in line 6 UpdateMap()\nshrinks the location area of this node according to the newly\nobtained boundaries. After processing all sequences, Centroid\nEstimation (line 11) set the center of gravity of the final\npolygon as the estimated location of the target node.\nBasic MSP only makes use of the order information\nbetween a target node and the anchor nodes in each sequence.\nActually, we can extract much more location information from\n17\nAlgorithm 1 Basic MSP Process\nOutput: The estimated location of each node.\n1: repeat\n2: GetOneUnprocessedSeqence();\n3: repeat\n4: GetOneNodeFromSequenceInOrder();\n5: GetBoundaries();\n6: UpdateMap();\n7: until All the target nodes are updated;\n8: until All the node sequences are processed;\n9: repeat\n10: GetOneUnestimatedNode();\n11: CentroidEstimation();\n12: until All the target nodes are estimated;\neach sequence. Section 5 will introduce advanced MSP, in\nwhich four novel optimizations are proposed to improve the\nperformance of MSP significantly.\n5 Advanced MSP\nFour improvements to basic MSP are proposed in this\nsection. The first three improvements do not need additional\nsensing and communication in the networks but require only\nslightly more off-line computation. The objective of all these\nimprovements is to make full use of the information embedded\nin the node sequences. The results we have obtained\nempirically indicate that the implementation of the first two methods\ncan dramatically reduce the localization error, and that the third\nand fourth methods are helpful for some system deployments.\n5.1 Sequence-Based MSP\nAs shown in Figure 2, each scan line and M anchors, splits\nthe whole area into M + 1 parts. Each target node falls into\none polygon shaped by scan lines. We noted that in basic MSP,\nonly the anchors are used to narrow down the polygon of each\ntarget node, but actually there is more information in the node\nsequence that we can made use of.\nLet\"s first look at a simple example shown in Figure 3. The\nprevious scans narrow the locations of target node 1 and node\n2 into two dashed rectangles shown in the left part of Figure 3.\nThen a new scan generates a new sequence (1, 2). With\nknowledge of the scan\"s direction, it is easy to tell that node 1 is\nlocated to the left of node 2. Thus, we can further narrow the\nlocation area of node 2 by eliminating the shaded part of node\n2\"s rectangle. This is because node 2 is located on the right of\nnode 1 while the shaded area is outside the lower boundary of\nnode 1. Similarly, the location area of node 1 can be narrowed\nby eliminating the shaded part out of node 2\"s right boundary.\nWe call this procedure sequence-based MSP which means that\nthe whole node sequence needs to be processed node by node\nin order. Specifically, sequence-based MSP follows this exact\nprocessing rule:\n1\n2\n1 2\n1\n2\nLower boundary of 1 Upper boundary of 1\nLower boundary of 2 Upper boundary of 2\nNew sequence\nNew upper boundary of 1\nNew Lower boundary of 2\nEventPropagation\nFigure 3. Rule Illustration in Sequence Based MSP\nAlgorithm 2 Sequence-Based MSP Process\nOutput: The estimated location of each node.\n1: repeat\n2: GetOneUnprocessedSeqence();\n3: repeat\n4: GetOneNodeByIncreasingOrder();\n5: ComputeLowbound();\n6: UpdateMap();\n7: until The last target node in the sequence;\n8: repeat\n9: GetOneNodeByDecreasingOrder();\n10: ComputeUpbound();\n11: UpdateMap();\n12: until The last target node in the sequence;\n13: until All the node sequences are processed;\n14: repeat\n15: GetOneUnestimatedNode();\n16: CentroidEstimation();\n17: until All the target nodes are estimated;\nElimination Rule: Along a scanning direction, the lower\nboundary of the successor\"s area must be equal to or larger\nthan the lower boundary of the predecessor\"s area, and the\nupper boundary of the predecessor\"s area must be equal to or\nsmaller than the upper boundary of the successor\"s area.\nIn the case of Figure 3, node 2 is the successor of node 1,\nand node 1 is the predecessor of node 2. According to the\nelimination rule, node 2\"s lower boundary cannot be smaller\nthan that of node 1 and node 1\"s upper boundary cannot exceed\nnode 2\"s upper boundary.\nAlgorithm 2 illustrates the pseudo code of sequence-based\nMSP. Each node sequence is processed within line 3 to 13. The\nsequence processing contains two steps:\nStep 1 (line 3 to 7): Compute and modify the lower\nboundary for each target node by increasing order in the node\nsequence. Each node\"s lower boundary is determined by the\nlower boundary of its predecessor node in the sequence, thus\nthe processing must start from the first node in the sequence\nand by increasing order. Then update the map according to the\nnew lower boundary.\nStep 2 (line 8 to 12): Compute and modify the upper\nboundary for each node by decreasing order in the node sequence.\nEach node\"s upper boundary is determined by the upper\nboundary of its successor node in the sequence, thus the processing\nmust start from the last node in the sequence and by\ndecreasing order. Then update the map according to the new upper\nboundary.\nAfter processing all the sequences, for each node, a polygon\nbounding its possible location has been found. Then,\ncenter-ofgravity-based estimation is applied to compute the exact\nlocation of each node (line 14 to 17).\nAn example of this process is shown in Figure 4. The third\nscan generates the node sequence (B,9,2,7,4,6,3,8,C,A,5,1). In\naddition to the anchor split lines, because nodes 4 and 7 come\nafter node 2 in the sequence, node 4 and 7\"s polygons could\nbe narrowed according to node 2\"s lower boundary (the lower\nright-shaded area); similarly, the shaded area in node 2\"s\nrectangle could be eliminated since this part is beyond node 7\"s\nupper boundary indicated by the dotted line. Similar\neliminating can be performed for node 3 as shown in the figure.\n18\n1\nA\n2\n3\n4\n5\nB\nC\n6\n7\n8\n9\nStraight-line Scan 1\nStraight-lineScan2\nStraight-line Scan 3\nTarget node\nAnchor node\nFigure 4. Sequence-Based MSP Example\n1\nA\n2\n3\n4\n5\nB\nC\n6\n7\n8\n9\nStraight-line Scan 1\nStraight-lineScan2\nStraight-line Scan 3\nReprocessing Scan 1\nTarget node\nAnchor node\nFigure 5. Iterative MSP: Reprocessing Scan 1\nFrom above, we can see that the sequence-based MSP\nmakes use of the information embedded in every sequential\nnode pair in the node sequence. The polygon boundaries of\nthe target nodes obtained in prior could be used to further split\nother target nodes\" areas. Our evaluation in Sections 8 and 9\nshows that sequence-based MSP considerably enhances system\naccuracy.\n5.2 Iterative MSP\nSequence-based MSP is preferable to basic MSP because it\nextracts more information from the node sequence. In fact,\nfurther useful information still remains! In sequence-based MSP,\na sequence processed later benefits from information produced\nby previously processed sequences (e.g., the third scan in\nFigure 5). However, the first several sequences can hardly benefit\nfrom other scans in this way. Inspired by this phenomenon,\nwe propose iterative MSP. The basic idea of iterative MSP is\nto process all the sequences iteratively several times so that the\nprocessing of each single sequence can benefit from the results\nof other sequences.\nTo illustrate the idea more clearly, Figure 4 shows the results\nof three scans that have provided three sequences. Now if we\nprocess the sequence (8,1,5,A,6,C,4,3,7,2,B,9) obtained from\nscan 1 again, we can make progress, as shown in Figure 5.\nThe reprocessing of the node sequence 1 provides information\nin the way an additional vertical scan would. From\nsequencebased MSP, we know that the upper boundaries of nodes 3 and\n4 along the scan direction must not extend beyond the upper\nboundary of node 7, therefore the grid parts can be eliminated\n(a) Central of Gravity (b) Joint Distribution\n1 2\n2\n1 1\n2\n1\n2 2\n1\n1 2\n2\n1 1\n2\nFigure 6. Example of Joint Distribution Estimation\n\u2026...\nvm\nap[0]\nvm\nap[1]\nvm\nap[2]\nvm\nap[3]\nCombine\nm\nap\nFigure 7. Idea of DBE MSP for Each Node\nfor the nodes 3 and node 4, respectively, as shown in Figure 5.\nFrom this example, we can see that iterative processing of the\nsequence could help further shrink the polygon of each target\nnode, and thus enhance the accuracy of the system.\nThe implementation of iterative MSP is straightforward:\nprocess all the sequences multiple times using sequence-based\nMSP. Like sequence-based MSP, iterative MSP introduces no\nadditional event cost. In other words, reprocessing does not\nactually repeat the scan physically. Evaluation results in\nSection 8 will show that iterative MSP contributes noticeably to\na lower localization error. Empirical results show that after 5\niterations, improvements become less significant. In summary,\niterative processing can achieve better performance with only\na small computation overhead.\n5.3 Distribution-Based Estimation\nAfter determining the location area polygon for each node,\nestimation is needed for a final decision. Previous research\nmostly applied the Center of Gravity (COG) method [4] [8]\n[10] which minimizes average error. If every node is\nindependent of all others, COG is the statistically best solution. In\nMSP, however, each node may not be independent. For\nexample, two neighboring nodes in a certain sequence could have\noverlapping polygon areas. In this case, if the marginal\nprobability of joint distribution is used for estimation, better\nstatistical results are achieved.\nFigure 6 shows an example in which node 1 and node 2 are\nlocated in the same polygon. If COG is used, both nodes are\nlocalized at the same position (Figure 6(a)). However, the node\nsequences obtained from two scans indicate that node 1 should\nbe to the left of and above node 2, as shown in Figure 6(b).\nThe high-level idea of distribution-based estimation\nproposed for MSP, which we call DBE MSP, is illustrated in\nFigure 7. The distributions of each node under the ith scan (for the\nith node sequence) are estimated in node.vmap[i], which is a\ndata structure for remembering the marginal distribution over\nscan i. Then all the vmaps are combined to get a single map\nand weighted estimation is used to obtain the final location.\nFor each scan, all the nodes are sorted according to the gap,\nwhich is the diameter of the polygon along the direction of the\nscan, to produce a second, gap-based node sequence. Then,\nthe estimation starts from the node with the smallest gap. This\nis because it is statistically more accurate to assume a uniform\ndistribution of the node with smaller gap. For each node\nprocessed in order from the gap-based node sequence, either if\n19\nPred. node\"s area\nPredecessor node exists:\nconditional distribution\nbased on pred. node\"s area\nAlone: Uniformly Distributed\nSucc. node\"s area\nSuccessor node exists:\nconditional distribution\nbased on succ. node\"s area\nSucc. node\"s area\nBoth predecessor and successor\nnodes exist: conditional distribution\nbased on both of them\nPred. node\"s area\nFigure 8. Four Cases in DBE Process\nno neighbor node in the original event-based node sequence\nshares an overlapping area, or if the neighbors have not been\nprocessed due to bigger gaps, a uniform distribution Uniform()\nis applied to this isolated node (the Alone case in Figure 8).\nIf the distribution of its neighbors sharing overlapped areas has\nbeen processed, we calculate the joint distribution for the node.\nAs shown in Figure 8, there are three possible cases\ndepending on whether the distribution of the overlapping predecessor\nand/or successor nodes have/has already been estimated.\nThe estimation\"s strategy of starting from the most accurate\nnode (smallest gap node) reduces the problem of estimation\nerror propagation. The results in the evaluation section indicate\nthat applying distribution-based estimation could give\nstatistically better results.\n5.4 Adaptive MSP\nSo far, all the enhancements to basic MSP focus on\nimproving the multi-sequence processing algorithm given a fixed set\nof scan directions. All these enhancements require only more\ncomputing time without any overhead to the sensor nodes.\nObviously, it is possible to have some choice and optimization on\nhow events are generated. For example, in military situations,\nartillery or rocket-launched mini-ultrasound bombs can be used\nfor event generation at some selected locations. In adaptive\nMSP, we carefully generate each new localization event so as\nto maximize the contribution of the new event to the refinement\nof localization, based on feedback from previous events.\nFigure 9 depicts the basic architecture of adaptive MSP.\nThrough previous localization events, the whole map has been\npartitioned into many small location areas. The idea of\nadaptive MSP is to generate the next localization event to achieve\nbest-effort elimination, which ideally could shrink the location\narea of individual node as much as possible.\nWe use a weighted voting mechanism to evaluate candidate\nlocalization events. Every node wants the next event to split its\narea evenly, which would shrink the area fast. Therefore, every\nnode votes for the parameters of the next event (e.g., the scan\nangle k of the straight-line scan). Since the area map is\nmaintained centrally, the vote is virtually done and there is no need\nfor the real sensor nodes to participate in it. After gathering all\nthe voting results, the event parameters with the most votes win\nthe election. There are two factors that determine the weight of\neach vote:\n\u2022 The vote for each candidate event is weighted according\nto the diameter D of the node\"s location area. Nodes with\nbigger location areas speak louder in the voting, because\nMap Partitioned by the Localization Events\nDiameter of Each\nArea\nCandidate\nLocalization Events\nEvaluation\nTrigger Next\nLocalization Evet\nFigure 9. Basic Architecture of Adaptive MSP\n2\n3\nDiameter D3\n1\n1\n3k\n2\n3k\n3\n3k\n4\n3k\n5\n3k\n6\n3k\n1\n3k 2\n3k 3\n3k\n6\n3k4\n3k 5\n3k\nWeight\nel\nsmall\ni\nopt\ni\nj\nii\nj\ni\nS\nS\nDkkDfkWeight\narg\n),(,()( \u22c5=\u2206=\n1\n3\nopt\nk\nTarget node\nAnchor node\nCenter of Gravity\nNode 3's area\nFigure 10. Candidate Slops for Node 3 at Anchor 1\noverall system error is reduced mostly by splitting the\nlarger areas.\n\u2022 The vote for each candidate event is also weighted\naccording to its elimination efficiency for a location area, which\nis defined as how equally in size (or in diameter) an event\ncan cut an area. In other words, an optimal scan event\ncuts an area in the middle, since this cut shrinks the area\nquickly and thus reduces localization uncertainty quickly.\nCombining the above two aspects, the weight for each vote\nis computed according to the following equation (1):\nWeight(k\nj\ni ) = f(Di,\u25b3(k\nj\ni ,k\nopt\ni )) (1)\nk\nj\ni is node i\"s jth supporting parameter for next event\ngeneration; Di is diameter of node i\"s location area; \u25b3(k\nj\ni ,k\nopt\ni ) is the\ndistance between k\nj\ni and the optimal parameter k\nopt\ni for node i,\nwhich should be defined to fit the specific application.\nFigure 10 presents an example for node 1\"s voting for the\nslopes of the next straight-line scan. In the system, there\nare a fixed number of candidate slopes for each scan (e.g.,\nk1,k2,k3,k4...). The location area of target node 3 is shown\nin the figure. The candidate events k1\n3,k2\n3,k3\n3,k4\n3,k5\n3,k6\n3 are\nevaluated according to their effectiveness compared to the optimal\nideal event which is shown as a dotted line with appropriate\nweights computed according to equation (1). For this\nspecific example, as is illustrated in the right part of Figure 10,\nf(Di,\u25b3(k\nj\ni ,kopt\ni )) is defined as the following equation (2):\nWeight(kj\ni ) = f(Di,\u25b3(kj\ni ,kopt\ni )) = Di \u00b7\nSsmall\nSlarge\n(2)\nSsmall and Slarge are the sizes of the smaller part and larger\npart of the area cut by the candidate line respectively. In this\ncase, node 3 votes 0 for the candidate lines that do not cross its\narea since Ssmall = 0.\nWe show later that adaptive MSP improves localization\naccuracy in WSNs with irregularly shaped deployment areas.\n20\n5.5 Overhead and MSP Complexity Analysis\nThis section provides a complexity analysis of the MSP\ndesign. We emphasize that MSP adopts an asymmetric design in\nwhich sensor nodes need only to detect and report the events.\nThey are blissfully oblivious to the processing methods\nproposed in previous sections. In this section, we analyze the\ncomputational cost on the node sequence processing side, where\nresources are plentiful.\nAccording to Algorithm 1, the computational complexity of\nBasic MSP is O(d \u00b7 N \u00b7 S), and the storage space required is\nO(N \u00b7 S), where d is the number of events, N is the number of\ntarget nodes, and S is the area size.\nAccording to Algorithm 2, the computational complexity of\nboth sequence-based MSP and iterative MSP is O(c\u00b7d \u00b7N \u00b7S),\nwhere c is the number of iterations and c = 1 for\nsequencebased MSP, and the storage space required is O(N \u00b7S). Both the\ncomputational complexity and storage space are equal within a\nconstant factor to those of basic MSP.\nThe computational complexity of the distribution-based\nestimation (DBE MSP) is greater. The major overhead comes\nfrom the computation of joint distributions when both\npredecessor and successor nodes exit. In order to compute the\nmarginal probability, MSP needs to enumerate the locations of\nthe predecessor node and the successor node. For example,\nif node A has predecessor node B and successor node C, then\nthe marginal probability PA(x,y) of node A\"s being at location\n(x,y) is:\nPA(x,y) = \u2211\ni\n\u2211\nj\n\u2211\nm\n\u2211\nn\n1\nNB,A,C\n\u00b7PB(i, j)\u00b7PC(m,n) (3)\nNB,A,C is the number of valid locations for A satisfying the\nsequence (B, A, C) when B is at (i, j) and C is at (m,n);\nPB(i, j) is the available probability of node B\"s being located\nat (i, j); PC(m,n) is the available probability of node C\"s\nbeing located at (m,n). A naive algorithm to compute equation\n(3) has complexity O(d \u00b7 N \u00b7 S3). However, since the marginal\nprobability indeed comes from only one dimension along the\nscanning direction (e.g., a line), the complexity can be reduced\nto O(d \u00b7 N \u00b7 S1.5) after algorithm optimization. In addition, the\nfinal location areas for every node are much smaller than the\noriginal field S; therefore, in practice, DBE MSP can be\ncomputed much faster than O(d \u00b7N \u00b7S1.5).\n6 Wave Propagation Example\nSo far, the description of MSP has been solely in the\ncontext of straight-line scan. However, we note that MSP is\nconceptually independent of how the event is propagated as long\nas node sequences can be obtained. Clearly, we can also\nsupport wave-propagation-based events (e.g., ultrasound\npropagation, air blast propagation), which are polar coordinate\nequivalences of the line scans in the Cartesian coordinate system.\nThis section illustrates the effects of MSP\"s implementation in\nthe wave propagation-based situation. For easy modelling, we\nhave made the following assumptions:\n\u2022 The wave propagates uniformly in all directions,\ntherefore the propagation has a circle frontier surface. Since\nMSP does not rely on an accurate space-time relationship,\na certain distortion in wave propagation is tolerable. If any\ndirectional wave is used, the propagation frontier surface\ncan be modified accordingly.\n1\n3\n5\n9\nTarget node\nAnchor node\nPrevious Event location\nA\n2\nCenter of Gravity\n4\n8\n7\nB\n6\nC\nA line of preferred locations for next event\nFigure 11. Example of Wave Propagation Situation\n\u2022 Under the situation of line-of-sight, we allow obstacles to\nreflect or deflect the wave. Reflection and deflection are\nnot problems because each node reacts only to the first\ndetected event. Those reflected or deflected waves come\nlater than the line-of-sight waves. The only thing the\nsystem needs to maintain is an appropriate time interval\nbetween two successive localization events.\n\u2022 We assume that background noise exists, and therefore we\nrun a band-pass filter to listen to a particular wave\nfrequency. This reduces the chances of false detection.\nThe parameter that affects the localization event generation\nhere is the source location of the event. The different\ndistances between each node and the event source determine the\nrank of each node in the node sequence. Using the node\nsequences, the MSP algorithm divides the whole area into many\nnon-rectangular areas as shown in Figure 11. In this figure,\nthe stars represent two previous event sources. The previous\ntwo propagations split the whole map into many areas by those\ndashed circles that pass one of the anchors. Each node is\nlocated in one of the small areas. Since sequence-based MSP,\niterative MSP and DBE MSP make no assumptions about the\ntype of localization events and the shape of the area, all three\noptimization algorithms can be applied for the wave\npropagation scenario.\nHowever, adaptive MSP needs more explanation. Figure 11\nillustrates an example of nodes\" voting for next event source\nlocations. Unlike the straight-line scan, the critical parameter\nnow is the location of the event source, because the distance\nbetween each node and the event source determines the rank of\nthe node in the sequence. In Figure 11, if the next event breaks\nout along/near the solid thick gray line, which perpendicularly\nbisects the solid dark line between anchor C and the center of\ngravity of node 9\"s area (the gray area), the wave would reach\nanchor C and the center of gravity of node 9\"s area at roughly\nthe same time, which would relatively equally divide node 9\"s\narea. Therefore, node 9 prefers to vote for the positions around\nthe thick gray line.\n7 Practical Deployment Issues\nFor the sake of presentation, until now we have described\nMSP in an ideal case where a complete node sequence can be\nobtained with accurate time synchronization. In this section\nwe describe how to make MSP work well under more realistic\nconditions.\n21\n7.1 Incomplete Node Sequence\nFor diverse reasons, such as sensor malfunction or natural\nobstacles, the nodes in the network could fail to detect\nlocalization events. In such cases, the node sequence will not be\ncomplete. This problem has two versions:\n\u2022 Anchor nodes are missing in the node sequence\nIf some anchor nodes fail to respond to the localization\nevents, then the system has fewer anchors. In this case,\nthe solution is to generate more events to compensate for\nthe loss of anchors so as to achieve the desired accuracy\nrequirements.\n\u2022 Target nodes are missing in the node sequence\nThere are two consequences when target nodes are\nmissing. First, if these nodes are still be useful to sensing\napplications, they need to use other backup localization\napproaches (e.g., Centroid) to localize themselves with help\nfrom their neighbors who have already learned their own\nlocations from MSP. Secondly, since in advanced MSP\neach node in the sequence may contribute to the overall\nsystem accuracy, dropping of target nodes from sequences\ncould also reduce the accuracy of the localization. Thus,\nproper compensation procedures such as adding more\nlocalization events need to be launched.\n7.2 Localization without Time Synchronization\nIn a sensor network without time synchronization support,\nnodes cannot be ordered into a sequence using timestamps. For\nsuch cases, we propose a listen-detect-assemble-report\nprotocol, which is able to function independently without time\nsynchronization.\nlisten-detect-assemble-report requires that every node\nlistens to the channel for the node sequence transmitted from its\nneighbors. Then, when the node detects the localization event,\nit assembles itself into the newest node sequence it has heard\nand reports the updated sequence to other nodes. Figure 12\n(a) illustrates an example for the listen-detect-assemble-report\nprotocol. For simplicity, in this figure we did not differentiate\nthe target nodes from anchor nodes. A solid line between two\nnodes stands for a communication link. Suppose a straight line\nscans from left to right. Node 1 detects the event, and then it\nbroadcasts the sequence (1) into the network. Node 2 and node\n3 receive this sequence. When node 2 detects the event, node\n2 adds itself into the sequence and broadcasts (1, 2). The\nsequence propagates in the same direction with the scan as shown\nin Figure 12 (a). Finally, node 6 obtains a complete sequence\n(1,2,3,5,7,4,6).\nIn the case of ultrasound propagation, because the event\npropagation speed is much slower than that of radio, the\nlistendetect-assemble-report protocol can work well in a situation\nwhere the node density is not very high. For instance, if the\ndistance between two nodes along one direction is 10 meters,\nthe 340m/s sound needs 29.4ms to propagate from one node\nto the other. While normally the communication data rate is\n250Kbps in the WSN (e.g., CC2420 [1]), it takes only about\n2 \u223c 3 ms to transmit an assembled packet for one hop.\nOne problem that may occur using the\nlisten-detectassemble-report protocol is multiple partial sequences as\nshown in Figure 12 (b). Two separate paths in the network may\nresult in two sequences that could not be further combined. In\nthis case, since the two sequences can only be processed as\nseparate sequences, some order information is lost. Therefore the\n1,2,5,4\n1,3,7,4\n1,2,3,5 1,2,3,5,7,4\n1,2,3,5,7\n1,2,3,5\n1,3\n1,2\n1\n2\n3\n5\n7\n4\n6\n1\n1\n1,3 1,2,3,5,7,4,6\n1,2,5\n1,3,7\n1,3\n1,2\n1\n2\n3\n5\n7\n4\n6\n1\n1\n1,3,7,4,6\n1,2,5,4,6\n(a)\n(b)\n(c)\n1,3,2,5 1,3,2,5,7,4\n1,3,2,5,7\n1,3,2,5\n1,3\n1,2\n1\n2\n3\n5\n7\n4\n6\n1\n1\n1,3 1,3,2,5,7,4,6\nEvent Propagation\nEvent Propagation\nEvent Propagation\nFigure 12. Node Sequence without Time Synchronization\naccuracy of the system would decrease.\nThe other problem is the sequence flip problem. As shown\nin Figure 12 (c), because node 2 and node 3 are too close to\neach other along the scan direction, they detect the scan\nalmost simultaneously. Due to the uncertainty such as media\naccess delay, two messages could be transmitted out of order.\nFor example, if node 3 sends out its report first, then the order\nof node 2 and node 3 gets flipped in the final node sequence.\nThe sequence flip problem would appear even in an accurately\nsynchronized system due to random jitter in node detection if\nan event arrives at multiple nodes almost simultaneously. A\nmethod addressing the sequence flip is presented in the next\nsection.\n7.3 Sequence Flip and Protection Band\nSequence flip problems can be solved with and without\ntime synchronization. We firstly start with a scenario\napplying time synchronization. Existing solutions for time\nsynchronization [12, 6] can easily achieve sub-millisecond-level\naccuracy. For example, FTSP [12] achieves 16.9\u00b5s (microsecond)\naverage error for a two-node single-hop case. Therefore, we\ncan comfortably assume that the network is synchronized with\nmaximum error of 1000\u00b5s. However, when multiple nodes are\nlocated very near to each other along the event propagation\ndirection, even when time synchronization with less than 1ms\nerror is achieved in the network, sequence flip may still occur.\nFor example, in the sound wave propagation case, if two nodes\nare less than 0.34 meters apart, the difference between their\ndetection timestamp would be smaller than 1 millisecond.\nWe find that sequence flip could not only damage system\naccuracy, but also might cause a fatal error in the MSP algorithm.\nFigure 13 illustrates both detrimental results. In the left side of\nFigure 13(a), suppose node 1 and node 2 are so close to each\nother that it takes less than 0.5ms for the localization event to\npropagate from node 1 to node 2. Now unfortunately, the node\nsequence is mistaken to be (2,1). So node 1 is expected to be\nlocated to the right of node 2, such as at the position of the\ndashed node 1. According to the elimination rule in\nsequencebased MSP, the left part of node 1\"s area is cut off as shown in\nthe right part of Figure 13(a). This is a potentially fatal error,\nbecause node 1 is actually located in the dashed area which has\nbeen eliminated by mistake. During the subsequent\neliminations introduced by other events, node 1\"s area might be cut off\ncompletely, thus node 1 could consequently be erased from the\nmap! Even in cases where node 1 still survives, its area actually\ndoes not cover its real location.\n22\n1\n2\n12\n2\nLower boundary of 1 Upper boundary of 1\nFlipped Sequence Fatal Elimination Error\nEventPropagation\n1 1\nFatal Error\n1\n1\n2\n12\n2\nLower boundary of 1 Upper boundary of 1\nFlipped Sequence Safe Elimination\nEventPropagation\n1 1\nNew lower boundary of 1\n1\nB\n(a)\n(b)\nB: Protection band\nFigure 13. Sequence Flip and Protection Band\nAnother problem is not fatal but lowers the localization\naccuracy. If we get the right node sequence (1,2), node 1 has a\nnew upper boundary which can narrow the area of node 1 as in\nFigure 3. Due to the sequence flip, node 1 loses this new upper\nboundary.\nIn order to address the sequence flip problem, especially to\nprevent nodes from being erased from the map, we propose\na protection band compensation approach. The basic idea of\nprotection band is to extend the boundary of the location area\na little bit so as to make sure that the node will never be erased\nfrom the map. This solution is based on the fact that nodes\nhave a high probability of flipping in the sequence if they are\nnear to each other along the event propagation direction. If\ntwo nodes are apart from each other more than some distance,\nsay, B, they rarely flip unless the nodes are faulty. The width\nof a protection band B, is largely determined by the maximum\nerror in system time synchronization and the localization event\npropagation speed.\nFigure 13(b) presents the application of the protection band.\nInstead of eliminating the dashed part in Figure 13(a) for node\n1, the new lower boundary of node 1 is set by shifting the\noriginal lower boundary of node 2 to the left by distance B. In this\ncase, the location area still covers node 1 and protects it from\nbeing erased. In a practical implementation, supposing that the\nultrasound event is used, if the maximum error of system time\nsynchronization is 1ms, two nodes might flip with high\nprobability if the timestamp difference between the two nodes is\nsmaller than or equal to 1ms. Accordingly, we set the\nprotection band B as 0.34m (the distance sound can propagate within\n1 millisecond). By adding the protection band, we reduce the\nchances of fatal errors, although at the cost of localization\naccuracy. Empirical results obtained from our physical test-bed\nverified this conclusion.\nIn the case of using the listen-detect-assemble-report\nprotocol, the only change we need to make is to select the protection\nband according to the maximum delay uncertainty introduced\nby the MAC operation and the event propagation speed. To\nbound MAC delay at the node side, a node can drop its report\nmessage if it experiences excessive MAC delay. This converts\nthe sequence flip problem to the incomplete sequence problem,\nwhich can be more easily addressed by the method proposed in\nSection 7.1.\n8 Simulation Evaluation\nOur evaluation of MSP was conducted on three platforms:\n(i) an indoor system with 46 MICAz motes using straight-line\nscan, (ii) an outdoor system with 20 MICAz motes using sound\nwave propagation, and (iii) an extensive simulation under\nvarious kinds of physical settings.\nIn order to understand the behavior of MSP under\nnumerous settings, we start our evaluation with simulations.\nThen, we implemented basic MSP and all the advanced\nMSP methods for the case where time synchronization is\navailable in the network. The simulation and\nimplementation details are omitted in this paper due to space\nconstraints, but related documents [25] are provided online at\nhttp://www.cs.umn.edu/\u223czhong/MSP. Full implementation and\nevaluation of system without time synchronization are yet to be\ncompleted in the near future.\nIn simulation, we assume all the node sequences are perfect\nso as to reveal the performance of MSP achievable in the\nabsence of incomplete node sequences or sequence flips. In our\nsimulations, all the anchor nodes and target nodes are assumed\nto be deployed uniformly. The mean and maximum errors are\naveraged over 50 runs to obtain high confidence. For legibility\nreasons, we do not plot the confidence intervals in this paper.\nAll the simulations are based on the straight-line scan example.\nWe implement three scan strategies:\n\u2022 Random Scan: The slope of the scan line is randomly\nchosen at each time.\n\u2022 Regular Scan: The slope is predetermined to rotate\nuniformly from 0 degree to 180 degrees. For example, if the\nsystem scans 6 times, then the scan angles would be: 0,\n30, 60, 90, 120, and 150.\n\u2022 Adaptive Scan: The slope of each scan is determined\nbased on the localization results from previous scans.\nWe start with basic MSP and then demonstrate the\nperformance improvements one step at a time by adding (i)\nsequencebased MSP, (ii) iterative MSP, (iii) DBE MSP and (iv) adaptive\nMSP.\n8.1 Performance of Basic MSP\nThe evaluation starts with basic MSP, where we compare the\nperformance of random scan and regular scan under different\nconfigurations. We intend to illustrate the impact of the number\nof anchors M, the number of scans d, and target node density\n(number of target nodes N in a fixed-size region) on the\nlocalization error. Table 1 shows the default simulation parameters.\nThe error of each node is defined as the distance between the\nestimated location and the real position. We note that by\ndefault we only use three anchors, which is considerably fewer\nthan existing range-free solutions [8, 4].\nImpact of the Number of Scans: In this experiment, we\ncompare regular scan with random scan under a different number\nof scans from 3 to 30 in steps of 3. The number of anchors\nTable 1. Default Configuration Parameters\nParameter Description\nField Area 200\u00d7200 (Grid Unit)\nScan Type Regular (Default)/Random Scan\nAnchor Number 3 (Default)\nScan Times 6 (Default)\nTarget Node Number 100 (Default)\nStatistics Error Mean/Max\nRandom Seeds 50 runs\n23\n0 5 10 15 20 25 30\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\nMean Error and Max Error VS Scan Time\nScan Time\nError Max Error of Random Scan\nMax Error of Regular Scan\nMean Error of Random Scan\nMean Error of Regular Scan\n(a) Error vs. Number of Scans\n0 5 10 15 20 25 30\n0\n10\n20\n30\n40\n50\n60\nMean Error and Max Error VS Anchor Number\nAnchor Number\nError\nMax Error of Random Scan\nMax Error of Regular Scan\nMean Error of Random Scan\nMean Error of Regular Scan\n(b) Error vs. Anchor Number\n0 50 100 150 200\n10\n20\n30\n40\n50\n60\n70\nMean Error and Max Error VS Target Node Number\nTarget Node Number\nError\nMax Error of Random Scan\nMax Error of Regular Scan\nMean Error of Random Scan\nMean Error of Regular Scan\n(c) Error vs. Number of Target Nodes\nFigure 14. Evaluation of Basic MSP under Random and Regular Scans\n0 5 10 15 20 25 30\n0\n10\n20\n30\n40\n50\n60\n70\nBasic MSP VS Sequence Based MSP II\nScan Time\nError\nMax Error of Basic MSP\nMax Error of Seq MSP\nMean Error of Basic MSP\nMean Error of Seq MSP\n(a) Error vs. Number of Scans\n0 5 10 15 20 25 30\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\nBasic MSP VS Sequence Based MSP I\nAnchor Number\nError\nMax Error of Basic MSP\nMax Error of Seq MSP\nMean Error of Basic MSP\nMean Error of Seq MSP\n(b) Error vs. Anchor Number\n0 50 100 150 200\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\n55\nBasic MSP VS Sequence Based MSP III\nTarget Node Number\nError\nMax Error of Basic MSP\nMax Error of Seq MSP\nMean Error of Basic MSP\nMean Error of Seq MSP\n(c) Error vs. Number of Target Nodes\nFigure 15. Improvements of Sequence-Based MSP over Basic MSP\nis 3 by default. Figure 14(a) indicates the following: (i) as\nthe number of scans increases, the localization error decreases\nsignificantly; for example, localization errors drop more than\n60% from 3 scans to 30 scans; (ii) statistically, regular scan\nachieves better performance than random scan under identical\nnumber of scans. However, the performance gap reduces as\nthe number of scans increases. This is expected since a large\nnumber of random numbers converges to a uniform\ndistribution. Figure 14(a) also demonstrates that MSP requires only\na small number of anchors to perform very well, compared to\nexisting range-free solutions [8, 4].\nImpact of the Number of Anchors: In this experiment, we\ncompare regular scan with random scan under different\nnumber of anchors from 3 to 30 in steps of 3. The results shown in\nFigure 14(b) indicate that (i) as the number of anchor nodes\nincreases, the localization error decreases, and (ii)\nstatistically, regular scan obtains better results than random scan with\nidentical number of anchors. By combining Figures 14(a)\nand 14(b), we can conclude that MSP allows a flexible tradeoff\nbetween physical cost (anchor nodes) and soft cost\n(localization events).\nImpact of the Target Node Density: In this experiment, we\nconfirm that the density of target nodes has no impact on the\naccuracy, which motivated the design of sequence-based MSP.\nIn this experiment, we compare regular scan with random scan\nunder different number of target nodes from 10 to 190 in steps\nof 20. Results in Figure 14(c) show that mean localization\nerrors remain constant across different node densities. However,\nwhen the number of target nodes increases, the average\nmaximum error increases.\nSummary: From the above experiments, we can conclude that\nin basic MSP, regular scan are better than random scan under\ndifferent numbers of anchors and scan events. This is because\nregular scans uniformly eliminate the map from different\ndirections, while random scans would obtain sequences with\nredundant overlapping information, if two scans choose two similar\nscanning slopes.\n8.2 Improvements of Sequence-Based MSP\nThis section evaluates the benefits of exploiting the order\ninformation among target nodes by comparing sequence-based\nMSP with basic MSP. In this and the following sections,\nregular scan is used for straight-line scan event generation. The\npurpose of using regular scan is to keep the scan events and\nthe node sequences identical for both sequence-based MSP and\nbasic MSP, so that the only difference between them is the\nsequence processing procedure.\nImpact of the Number of Scans: In this experiment, we\ncompare sequence-based MSP with basic MSP under different\nnumber of scans from 3 to 30 in steps of 3. Figure 15(a)\nindicates significant performance improvement in sequence-based\nMSP over basic MSP across all scan settings, especially when\nthe number of scans is large. For example, when the number\nof scans is 30, errors in sequence-based MSP are about 20%\nof that of basic MSP. We conclude that sequence-based MSP\nperforms extremely well when there are many scan events.\nImpact of the Number of Anchors: In this experiment, we\nuse different number of anchors from 3 to 30 in steps of 3. As\nseen in Figure 15(b), the mean error and maximum error of\nsequence-based MSP is much smaller than that of basic MSP.\nEspecially when there is limited number of anchors in the\nsystem, e.g., 3 anchors, the error rate was almost halved by\nusing sequence-based MSP. This phenomenon has an interesting\nexplanation: the cutting lines created by anchor nodes are\nexploited by both basic MSP and sequence-based MSP, so as the\n24\n0 2 4 6 8 10\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\nBasic MSP VS Iterative MSP\nIterative Times\nError\nMax Error of Iterative Seq MSP\nMean Error of Iterative Seq MSP\nMax Error of Basic MSP\nMean Error of Basic MSP\nFigure 16. Improvements of Iterative MSP\n0 2 4 6 8 10 12 14 16\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nDBE VS Non\u2212DBE\nError\nCumulativeDistrubutioinFunctions(CDF)\nMean Error CDF of DBE MSP\nMean Error CDF of Non\u2212DBE MSP\nMax Error CDF of DBE MSP\nMax Error CDF of Non\u2212DBE MSP\nFigure 17. Improvements of DBE MSP\n0 20 40 60 80 100\n0\n10\n20\n30\n40\n50\n60\n70\nAdaptive MSP for 500by80\nTarget Node Number\nError\nMax Error of Regualr Scan\nMax Error of Adaptive Scan\nMean Error of Regualr Scan\nMean Error of Adaptive Scan\n(a) Adaptive MSP for 500 by 80 field\n0 10 20 30 40 50\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nMean Error CDF at Different Angle Steps in Adaptive Scan\nMean Error\nCumulativeDistrubutioinFunctions(CDF)\n5 Degree Angle Step Adaptive\n10 Degree Angle Step Adaptive\n20 Degree Angle Step Adaptive\n30 Degree Step Regular Scan\n(b) Impact of the Number of Candidate Events\nFigure 18. The Improvements of Adaptive MSP\nnumber of anchor nodes increases, anchors tend to dominate\nthe contribution. Therefore the performance gaps lessens.\nImpact of the Target Node Density: Figure 15(c)\ndemonstrates the benefits of exploiting order information among\ntarget nodes. Since sequence-based MSP makes use of the\ninformation among the target nodes, having more target nodes\ncontributes to the overall system accuracy. As the number of\ntarget nodes increases, the mean error and maximum error of\nsequence-based MSP decreases. Clearly the mean error in\nbasic MSP is not affected by the number of target nodes, as shown\nin Figure 15(c).\nSummary: From the above experiments, we can conclude that\nexploiting order information among target nodes can improve\naccuracy significantly, especially when the number of events is\nlarge but with few anchors.\n8.3 Iterative MSP over Sequence-Based MSP\nIn this experiment, the same node sequences were processed\niteratively multiple times. In Figure 16, the two single marks\nare results from basic MSP, since basic MSP doesn\"t perform\niterations. The two curves present the performance of\niterative MSP under different numbers of iterations c. We note that\nwhen only a single iteration is used, this method degrades to\nsequence-based MSP. Therefore, Figure 16 compares the three\nmethods to one another.\nFigure 16 shows that the second iteration can reduce the\nmean error and maximum error dramatically. After that, the\nperformance gain gradually reduces, especially when c > 5.\nThis is because the second iteration allows earlier scans to\nexploit the new boundaries created by later scans in the first\niteration. Such exploitation decays quickly over iterations.\n8.4 DBE MSP over Iterative MSP\nFigure 17, in which we augment iterative MSP with\ndistribution-based estimation (DBE MSP), shows that DBE\nMSP could bring about statistically better performance.\nFigure 17 presents cumulative distribution localization errors. In\ngeneral, the two curves of the DBE MSP lay slightly to the left\nof that of non-DBE MSP, which indicates that DBE MSP has\na smaller statistical mean error and averaged maximum error\nthan non-DBE MSP. We note that because DBE is augmented\non top of the best solution so far, the performance\nimprovement is not significant. When we apply DBE on basic MSP\nmethods, the improvement is much more significant. We omit\nthese results because of space constraints.\n8.5 Improvements of Adaptive MSP\nThis section illustrates the performance of adaptive MSP\nover non-adaptive MSP. We note that feedback-based\nadaptation can be applied to all MSP methods, since it affects only\nthe scanning angles but not the sequence processing. In this\nexperiment, we evaluated how adaptive MSP can improve the\nbest solution so far. The default angle granularity (step) for\nadaptive searching is 5 degrees.\nImpact of Area Shape: First, if system settings are regular,\nthe adaptive method hardly contributes to the results. For a\nsquare area (regular), the performance of adaptive MSP and\nregular scans are very close. However, if the shape of the area\nis not regular, adaptive MSP helps to choose the appropriate\nlocalization events to compensate. Therefore, adaptive MSP\ncan achieve a better mean error and maximum error as shown\nin Figure 18(a). For example, adaptive MSP improves\nlocalization accuracy by 30% when the number of target nodes is\n10.\nImpact of the Target Node Density: Figure 18(a) shows that\nwhen the node density is low, adaptive MSP brings more\nbenefit than when node density is high. This phenomenon makes\nstatistical sense, because the law of large numbers tells us that\nnode placement approaches a truly uniform distribution when\nthe number of nodes is increased. Adaptive MSP has an edge\n25\nFigure 19. The Mirage Test-bed (Line Scan) Figure 20. The 20-node Outdoor Experiments (Wave)\nwhen layout is not uniform.\nImpact of Candidate Angle Density: Figure 18(b) shows that\nthe smaller the candidate scan angle step, the better the\nstatistical performance in terms of mean error. The rationale is clear,\nas wider candidate scan angles provide adaptive MSP more\nopportunity to choose the one approaching the optimal angle.\n8.6 Simulation Summary\nStarting from basic MSP, we have demonstrated\nstep-bystep how four optimizations can be applied on top of each other\nto improve localization performance. In other words, these\noptimizations are compatible with each other and can jointly\nimprove the overall performance. We note that our simulations\nwere done under assumption that the complete node sequence\ncan be obtained without sequence flips. In the next section, we\npresent two real-system implementations that reveal and\naddress these practical issues.\n9 System Evaluation\nIn this section, we present a system implementation of MSP\non two physical test-beds. The first one is called Mirage, a\nlarge indoor test-bed composed of six 4-foot by 8-foot boards,\nillustrated in Figure 19. Each board in the system can be used\nas an individual sub-system, which is powered, controlled and\nmetered separately. Three Hitachi CP-X1250 projectors,\nconnected through a Matorx Triplehead2go graphics expansion\nbox, are used to create an ultra-wide integrated display on six\nboards. Figure 19 shows that a long tilted line is generated by\nthe projectors. We have implemented all five versions of MSP\non the Mirage test-bed, running 46 MICAz motes. Unless\nmentioned otherwise, the default setting is 3 anchors and 6 scans at\nthe scanning line speed of 8.6 feet/s. In all of our graphs, each\ndata point represents the average value of 50 trials. In the\noutdoor system, a Dell A525 speaker is used to generate 4.7KHz\nsound as shown in Figure 20. We place 20 MICAz motes in the\nbackyard of a house. Since the location is not completely open,\nsound waves are reflected, scattered and absorbed by various\nobjects in the vicinity, causing a multi-path effect. In the\nsystem evaluation, simple time synchronization mechanisms are\napplied on each node.\n9.1 Indoor System Evaluation\nDuring indoor experiments, we encountered several\nrealworld problems that are not revealed in the simulation. First,\nsequences obtained were partial due to misdetection and\nmessage losses. Second, elements in the sequences could flip due\nto detection delay, uncertainty in media access, or error in time\nsynchronization. We show that these issues can be addressed\nby using the protection band method described in Section 7.3.\n9.1.1 On Scanning Speed and Protection Band\nIn this experiment, we studied the impact of the scanning\nspeed and the length of protection band on the performance of\nthe system. In general, with increasing scanning speed, nodes\nhave less time to respond to the event and the time gap between\ntwo adjacent nodes shrinks, leading to an increasing number of\npartial sequences and sequence flips.\nFigure 21 shows the node flip situations for six scans with\ndistinct angles under different scan speeds. The x-axis shows\nthe distance between the flipped nodes in the correct node\nsequence. y-axis shows the total number of flips in the six scans.\nThis figure tells us that faster scan brings in not only\nincreasing number of flips, but also longer-distance flips that require\nwider protection band to prevent from fatal errors.\nFigure 22(a) shows the effectiveness of the protection band\nin terms of reducing the number of unlocalized nodes. When\nwe use a moderate scan speed (4.3feet/s), the chance of flipping\nis rare, therefore we can achieve 0.45 feet mean accuracy\n(Figure 22(b)) with 1.6 feet maximum error (Figure 22(c)). With\nincreasing speeds, the protection band needs to be set to a larger\nvalue to deal with flipping. Interesting phenomena can be\nobserved in Figures 22: on one hand, the protection band can\nsharply reduce the number of unlocalized nodes; on the other\nhand, protection bands enlarge the area in which a target would\npotentially reside, introducing more uncertainty. Thus there is\na concave curve for both mean and maximum error when the\nscan speed is at 8.6 feet/s.\n9.1.2 On MSP Methods and Protection Band\nIn this experiment, we show the improvements resulting\nfrom three different methods. Figure 23(a) shows that a\nprotection band of 0.35 feet is sufficient for the scan speed of\n8.57feet/s. Figures 23(b) and 23(c) show clearly that iterative\nMSP (with adaptation) achieves best performance. For\nexample, Figures 23(b) shows that when we set the protection band\nat 0.05 feet, iterative MSP achieves 0.7 feet accuracy, which\nis 42% more accurate than the basic design. Similarly,\nFigures 23(b) and 23(c) show the double-edged effects of\nprotection band on the localization accuracy.\n0 5 10 15 20\n0\n20\n40\n(3) Flip Distribution for 6 Scans at Line Speed of 14.6feet/s\nFlips\nNode Distance in the Ideal Node Sequence\n0 5 10 15 20\n0\n20\n40\n(2) Flip Distribution for 6 Scans at Line Speed of 8.6feet/s\nFlips\n0 5 10 15 20\n0\n20\n40\n(1) Flip Distribution for 6 Scans at Line Speed of 4.3feet/s\nFlips\nFigure 21. Number of Flips for Different Scan Speeds\n26\n0 0.2 0.4 0.6 0.8 1\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\nUnlocalized Node Number(Line Scan at Different Speed)\nProtection Band (in feet)\nUnlocalizedNodeNumber\nScan Line Speed: 14.6feet/s\nScan Line Speed: 8.6feet/s\nScan Line Speed: 4.3feet/s\n(a) Number of Unlocalized Nodes\n0 0.2 0.4 0.6 0.8 1\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n1.1\nMean Error(Line Scan at Different Speed)\nProtection Band (in feet)\nError(infeet)\nScan Line Speed:14.6feet/s\nScan Line Speed: 8.6feet/s\nScan Line Speed: 4.3feet/s\n(b) Mean Localization Error\n0 0.2 0.4 0.6 0.8 1\n1.5\n2\n2.5\n3\n3.5\n4\nMax Error(Line Scan at Different Speed)\nProtection Band (in feet)\nError(infeet)\nScan Line Speed: 14.6feet/s\nScan Line Speed: 8.6feet/s\nScan Line Speed: 4.3feet/s\n(c) Max Localization Error\nFigure 22. Impact of Protection Band and Scanning Speed\n0 0.2 0.4 0.6 0.8 1\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\nUnlocalized Node Number(Scan Line Speed 8.57feet/s)\nProtection Band (in feet)\nNumberofunlocalizednodeoutof46\nUnlocalized node of Basic MSP\nUnlocalized node of Sequence Based MSP\nUnlocalized node of Iterative MSP\n(a) Number of Unlocalized Nodes\n0 0.2 0.4 0.6 0.8 1\n0.7\n0.8\n0.9\n1\n1.1\n1.2\n1.3\n1.4\nMean Error(Scan Line Speed 8.57feet/s)\nProtection Band (in feet)\nError(infeet)\nMean Error of Basic MSP\nMean Error of Sequence Based MSP\nMean Error of Iterative MSP\n(b) Mean Localization Error\n0 0.2 0.4 0.6 0.8 1\n1.5\n2\n2.5\n3\n3.5\n4\nMax Error(Scan Line Speed 8.57feet/s)\nProtection Band (in feet)\nError(infeet)\nMax Error of Basic MSP\nMax Error of Sequence Based MSP\nMax Error of Iterative MSP\n(c) Max Localization Error\nFigure 23. Impact of Protection Band under Different MSP Methods\n3 4 5 6 7 8 9 10 11\n0\n0.5\n1\n1.5\n2\n2.5\nUnlocalized Node Number(Protection Band: 0.35 feet)\nAnchor Number\nUnlocalizedNodeNumber\n4 Scan Events at Speed 8.75feet/s\n6 Scan Events at Speed 8.75feet/s\n8 Scan Events at Speed 8.75feet/s\n(a) Number of Unlocalized Nodes\n3 4 5 6 7 8 9 10 11\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nMean Error(Protection Band: 0.35 feet)\nAnchor Number\nError(infeet)\nMean Error of 4 Scan Events at Speed 8.75feet/s\nMean Error of 6 Scan Events at Speed 8.75feet/s\nMean Error of 8 Scan Events at Speed 8.75feet/s\n(b) Mean Localization Error\n3 4 5 6 7 8 9 10 11\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\n2.2\n2.4\n2.6\n2.8\nMax Error(Protection Band: 0.35 feet)\nAnchor Number\nError(infeet)\nMax Error of 4 Scan Events at Speed 8.75feet/s\nMax Error of 6 Scan Events at Speed 8.75feet/s\nMax Error of 8 Scan Events at Speed 8.75feet/s\n(c) Max Localization Error\nFigure 24. Impact of the Number of Anchors and Scans\n9.1.3 On Number of Anchors and Scans\nIn this experiment, we show a tradeoff between hardware\ncost (anchors) with soft cost (events). Figure 24(a) shows that\nwith more cutting lines created by anchors, the chance of\nunlocalized nodes increases slightly. We note that with a 0.35 feet\nprotection band, the percentage of unlocalized nodes is very\nsmall, e.g., in the worst-case with 11 anchors, only 2 out of 46\nnodes are not localized due to flipping. Figures 24(b) and 24(c)\nshow the tradeoff between number of anchors and the number\nof scans. Obviously, with the number of anchors increases, the\nerror drops significantly. With 11 anchors we can achieve a\nlocalization accuracy as low as 0.25 \u223c 0.35 feet, which is nearly a\n60% improvement. Similarly, with increasing number of scans,\nthe accuracy drops significantly as well. We can observe about\n30% across all anchor settings when we increase the number of\nscans from 4 to 8. For example, with only 3 anchors, we can\nachieve 0.6-foot accuracy with 8 scans.\n9.2 Outdoor System Evaluation\nThe outdoor system evaluation contains two parts: (i)\neffective detection distance evaluation, which shows that the\nnode sequence can be readily obtained, and (ii) sound\npropagation based localization, which shows the results of\nwavepropagation-based localization.\n9.2.1 Effective Detection Distance Evaluation\nWe firstly evaluate the sequence flip phenomenon in wave\npropagation. As shown in Figure 25, 20 motes were placed as\nfive groups in front of the speaker, four nodes in each group\nat roughly the same distances to the speaker. The gap between\neach group is set to be 2, 3, 4 and 5 feet respectively in four\nexperiments. Figure 26 shows the results. The x-axis in each\nsubgraph indicates the group index. There are four nodes in each\ngroup (4 bars). The y-axis shows the detection rank (order)\nof each node in the node sequence. As distance between each\ngroup increases, number of flips in the resulting node sequence\n27\nFigure 25. Wave Detection\n1 2 3 4 5\n0\n5\n10\n15\n20\n2 feet group distance\nRank\nGroup Index\n1 2 3 4 5\n0\n5\n10\n15\n20\n3 feet group distance\nRank\nGroup Index\n1 2 3 4 5\n0\n5\n10\n15\n20\n4 feet group distance\nRank\nGroup Index\n1 2 3 4 5\n0\n5\n10\n15\n20\n5 feet group distance\nRank\nGroup Index\nFigure 26. Ranks vs. Distances\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\n22\n24\n0 2 4 6 8 10 12 14\nY-Dimension(feet)\nX-Dimension (feet)\nNode\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\n22\n24\n0 2 4 6 8 10 12 14\nY-Dimension(feet)\nX-Dimension (feet)\nAnchor\nFigure 27. Localization Error (Sound)\ndecreases. For example, in the 2-foot distance subgraph, there\nare quite a few flips between nodes in adjacent and even\nnonadjacent groups, while in the 5-foot subgraph, flips between\ndifferent groups disappeared in the test.\n9.2.2 Sound Propagation Based Localization\nAs shown in Figure 20, 20 motes are placed as a grid\nincluding 5 rows with 5 feet between each row and 4 columns with\n4 feet between each column. Six 4KHz acoustic wave\npropagation events are generated around the mote grid by a speaker.\nFigure 27 shows the localization results using iterative MSP\n(3 times iterative processing) with a protection band of 3 feet.\nThe average error of the localization results is 3 feet and the\nmaximum error is 5 feet with one un-localized node.\nWe found that sequence flip in wave propagation is more\nsevere than that in the indoor, line-based test. This is expected\ndue to the high propagation speed of sound. Currently we use\nMICAz mote, which is equipped with a low quality\nmicrophone. We believe that using a better speaker and more events,\nthe system can yield better accuracy. Despite the hardware\nconstrains, the MSP algorithm still successfully localized most of\nthe nodes with good accuracy.\n10 Conclusions\nIn this paper, we present the first work that exploits the\nconcept of node sequence processing to localize sensor nodes. We\ndemonstrated that we could significantly improve localization\naccuracy by making full use of the information embedded in\nmultiple easy-to-get one-dimensional node sequences. We\nproposed four novel optimization methods, exploiting order and\nmarginal distribution among non-anchor nodes as well as the\nfeedback information from early localization results.\nImportantly, these optimization methods can be used together, and\nimprove accuracy additively. The practical issues of partial\nnode sequence and sequence flip were identified and addressed\nin two physical system test-beds. We also evaluated\nperformance at scale through analysis as well as extensive\nsimulations. Results demonstrate that requiring neither costly\nhardware on sensor nodes nor precise event distribution, MSP can\nachieve a sub-foot accuracy with very few anchor nodes\nprovided sufficient events.\n11 References\n[1] CC2420 Data Sheet. Avaiable at http://www.chipcon.com/.\n[2] P. Bahl and V. N. Padmanabhan. Radar: An In-Building RF-Based User\nLocation and Tracking System. In IEEE Infocom \"00.\n[3] M. Broxton, J. Lifton, and J. Paradiso. Localizing A Sensor Network via\nCollaborative Processing of Global Stimuli. In EWSN \"05.\n[4] N. Bulusu, J. Heidemann, and D. Estrin. GPS-Less Low Cost Outdoor\nLocalization for Very Small Devices. IEEE Personal Communications\nMagazine, 7(4), 2000.\n[5] D. Culler, D. Estrin, and M. Srivastava. Overview of Sensor Networks.\nIEEE Computer Magazine, 2004.\n[6] J. Elson, L. Girod, and D. Estrin. Fine-Grained Network Time\nSynchronization Using Reference Broadcasts. In OSDI \"02.\n[7] D. K. Goldenberg, P. Bihler, M. Gao, J. Fang, B. D. Anderson, A. Morse,\nand Y. Yang. Localization in Sparse Networks Using Sweeps. In\nMobiCom \"06.\n[8] T. He, C. Huang, B. M. Blum, J. A. Stankovic, and T. Abdelzaher.\nRangeFree Localization Schemes in Large-Scale Sensor Networks. In\nMobiCom \"03.\n[9] B. Kusy, P. Dutta, P. Levis, M. Mar, A. Ledeczi, and D. Culler. Elapsed\nTime on Arrival: A Simple and Versatile Primitive for Canonical Time\nSynchronization Services. International Journal of ad-hoc and\nUbiquitous Computing, 2(1), 2006.\n[10] L. Lazos and R. Poovendran. SeRLoc: Secure Range-Independent\nLocalization for Wireless Sensor Networks. In WiSe \"04.\n[11] M. Maroti, B. Kusy, G. Balogh, P. Volgyesi, A. Nadas, K. Molnar,\nS. Dora, and A. Ledeczi. Radio Interferometric Geolocation. In\nSenSys \"05.\n[12] M. Maroti, B. Kusy, G. Simon, and A. Ledeczi. The Flooding Time\nSynchronization Protocol. In SenSys \"04.\n[13] D. Moore, J. Leonard, D. Rus, and S. Teller. Robust Distributed Network\nLocalization with Noise Range Measurements. In SenSys \"04.\n[14] R. Nagpal and D. Coore. An Algorithm for Group Formation in an\nAmorphous Computer. In PDCS \"98.\n[15] D. Niculescu and B. Nath. ad-hoc Positioning System. In GlobeCom\n\"01.\n[16] D. Niculescu and B. Nath. ad-hoc Positioning System (APS) Using\nAOA. In InfoCom \"03.\n[17] N. B. Priyantha, A. Chakraborty, and H. Balakrishnan. The Cricket\nLocation-Support System. In MobiCom \"00.\n[18] K. R\u00a8omer. The Lighthouse Location System for Smart Dust. In MobiSys\n\"03.\n[19] A. Savvides, C. C. Han, and M. B. Srivastava. Dynamic Fine-Grained\nLocalization in ad-hoc Networks of Sensors. In MobiCom \"01.\n[20] R. Stoleru, T. He, J. A. Stankovic, and D. Luebke. A High-Accuracy,\nLow-Cost Localization System for Wireless Sensor Networks. In SenSys\n\"05.\n[21] R. Stoleru, P. Vicaire, T. He, and J. A. Stankovic. StarDust: a Flexible\nArchitecture for Passive Localization in Wireless Sensor Networks. In\nSenSys \"06.\n[22] E. W. Weisstein. Plane Division by Lines. mathworld.wolfram.com.\n[23] B. H. Wellenhoff, H. Lichtenegger, and J. Collins. Global Positions\nSystem: Theory and Practice,Fourth Edition. Springer Verlag, 1997.\n[24] K. Whitehouse. The Design of Calamari: an ad-hoc Localization System\nfor Sensor Networks. In University of California at Berkeley, 2002.\n[25] Z. Zhong. MSP Evaluation and Implementation Report. Avaiable at\nhttp://www.cs.umn.edu/\u223czhong/MSP.\n[26] G. Zhou, T. He, and J. A. Stankovic. Impact of Radio Irregularity on\nWireless Sensor Networks. In MobiSys \"04.\n28", "keywords": "marginal distribution;node localization;multi-sequence positioning;listen-detect-assemble-report protocol;event distribution;range-based approach;spatiotemporal correlation;localization;node sequence process;distribution-based location estimation;massive uva-based deploment;wireless sensor network"}
{"name": "train_C-45", "title": "StarDust: A Flexible Architecture for Passive Localization in Wireless Sensor Networks", "abstract": "The problem of localization in wireless sensor networks where nodes do not use ranging hardware, remains a challenging problem, when considering the required location accuracy, energy expenditure and the duration of the localization phase. In this paper we propose a framework, called StarDust, for wireless sensor network localization based on passive optical components. In the StarDust framework, sensor nodes are equipped with optical retro-reflectors. An aerial device projects light towards the deployed sensor network, and records an image of the reflected light. An image processing algorithm is developed for obtaining the locations of sensor nodes. For matching a node ID to a location we propose a constraint-based label relaxation algorithm. We propose and develop localization techniques based on four types of constraints: node color, neighbor information, deployment time for a node and deployment location for a node. We evaluate the performance of a localization system based on our framework by localizing a network of 26 sensor nodes deployed in a 120 \u00d7 60 ft2 area. The localization accuracy ranges from 2 ft to 5 ft while the localization time ranges from 10 milliseconds to 2 minutes.", "fulltext": "1 Introduction\nWireless Sensor Networks (WSN) have been envisioned\nto revolutionize the way humans perceive and interact with\nthe surrounding environment. One vision is to embed tiny\nsensor devices in outdoor environments, by aerial\ndeployments from unmanned air vehicles. The sensor nodes form\na network and collaborate (to compensate for the extremely\nscarce resources available to each of them: computational\npower, memory size, communication capabilities) to\naccomplish the mission. Through collaboration, redundancy and\nfault tolerance, the WSN is then able to achieve\nunprecedented sensing capabilities.\nA major step forward has been accomplished by\ndeveloping systems for several domains: military surveillance [1]\n[2] [3], habitat monitoring [4] and structural monitoring [5].\nEven after these successes, several research problems remain\nopen. Among these open problems is sensor node\nlocalization, i.e., how to find the physical position of each sensor\nnode. Despite the attention the localization problem in WSN\nhas received, no universally acceptable solution has been\ndeveloped. There are several reasons for this. On one hand,\nlocalization schemes that use ranging are typically high end\nsolutions. GPS ranging hardware consumes energy, it is\nrelatively expensive (if high accuracy is required) and poses\nform factor challenges that move us away from the vision\nof dust size sensor nodes. Ultrasound has a short range and\nis highly directional. Solutions that use the radio transceiver\nfor ranging either have not produced encouraging results (if\nthe received signal strength indicator is used) or are sensitive\nto environment (e.g., multipath). On the other hand,\nlocalization schemes that only use the connectivity information\nfor inferring location information are characterized by low\naccuracies: \u2248 10 ft in controlled environments, 40\u221250 ft in\nrealistic ones.\nTo address these challenges, we propose a framework for\nWSN localization, called StarDust, in which the\ncomplexity associated with the node localization is completely\nremoved from the sensor node. The basic principle of the\nframework is localization through passivity: each sensor\nnode is equipped with a corner-cube retro-reflector and\npossibly an optical filter (a coloring device). An aerial\nvehicle projects light onto the deployment area and records\nimages containing retro-reflected light beams (they appear as\nluminous spots). Through image processing techniques, the\nlocations of the retro-reflectors (i.e., sensor nodes) is\ndeter57\nmined. For inferring the identity of the sensor node present\nat a particular location, the StarDust framework develops a\nconstraint-based node ID relaxation algorithm.\nThe main contributions of our work are the following. We\npropose a novel framework for node localization in WSNs\nthat is very promising and allows for many future extensions\nand more accurate results. We propose a constraint-based\nlabel relaxation algorithm for mapping node IDs to the\nlocations, and four constraints (node, connectivity, time and\nspace), which are building blocks for very accurate and very\nfast localization systems. We develop a sensor node\nhardware prototype, called a SensorBall. We evaluate the\nperformance of a localization system for which we obtain location\naccuracies of 2 \u2212 5 ft with a localization duration ranging\nfrom 10 milliseconds to 2 minutes. We investigate the range\nof a system built on our framework by considering realities\nof physical phenomena that occurs during light propagation\nthrough the atmosphere.\nThe rest of the paper is structured as follows. Section 2\nis an overview of the state of art. The design of the\nStarDust framework is presented in Section 3. One\nimplementation and its performance evaluation are in Sections 4 and\n5, followed by a suite of system optimization techniques, in\nSection 6. In Section 7 we present our conclusions.\n2 Related Work\nWe present the prior work in localization in two major\ncategories: the range-based, and the range-free schemes.\nThe range-based localization techniques have been\ndesigned to use either more expensive hardware (and hence\nhigher accuracy) or just the radio transceiver. Ranging\ntechniques dependent on hardware are the time-of-flight (ToF)\nand the time-difference-of-arrival(TDoA). Solutions that use\nthe radio are based on the received signal strength indicator\n(RSSI) and more recently on radio interferometry.\nThe ToF localization technique that is most widely used is\nthe GPS. GPS is a costly solution for a high accuracy\nlocalization of a large scale sensor network. AHLoS [6] employs\na TDoA ranging technique that requires extensive hardware\nand solves relatively large nonlinear systems of equations.\nThe Cricket location-support system (TDoA) [7] can achieve\na location granularity of tens of inches with highly\ndirectional and short range ultrasound transceivers. In [2] the\nlocation of a sniper is determined in an urban terrain, by\nusing the TDoA between an acoustic wave and a radio beacon.\nThe PushPin project [8] uses the TDoA between ultrasound\npulses and light flashes for node localization. The RADAR\nsystem [9] uses the RSSI to build a map of signal strengths\nas emitted by a set of beacon nodes. A mobile node is\nlocated by the best match, in the signal strength space, with a\npreviously acquired signature. In MAL [10], a mobile node\nassists in measuring the distances (acting as constraints)\nbetween nodes until a rigid graph is generated. The localization\nproblem is formulated as an on-line state estimation in a\nnonlinear dynamic system [11]. A cooperative ranging that\nattempts to achieve a global positioning from distributed local\noptimizations is proposed in [12]. A very recent, remarkable,\nlocalization technique is based on radio interferometry, RIPS\n[13], which utilizes two transmitters to create an interfering\nsignal. The frequencies of the emitters are very close to each\nother, thus the interfering signal will have a low frequency\nenvelope that can be easily measured. The ranging technique\nperforms very well. The long time required for localization\nand multi-path environments pose significant challenges.\nReal environments create additional challenges for the\nrange based localization schemes. These have been\nemphasized by several studies [14] [15] [16]. To address these\nchallenges, and others (hardware cost, the energy expenditure,\nthe form factor, the small range, localization time), several\nrange-free localization schemes have been proposed. Sensor\nnodes use primarily connectivity information for inferring\nproximity to a set of anchors. In the Centroid localization\nscheme [17], a sensor node localizes to the centroid of its\nproximate beacon nodes. In APIT [18] each node decides its\nposition based on the possibility of being inside or outside of\na triangle formed by any three beacons within node\"s\ncommunication range. The Gradient algorithm [19], leverages\nthe knowledge about the network density to infer the average\none hop length. This, in turn, can be transformed into\ndistances to nodes with known locations. DV-Hop [20] uses the\nhop by hop propagation capability of the network to forward\ndistances to landmarks. More recently, several localization\nschemes that exploit the sensing capabilities of sensor nodes,\nhave been proposed. Spotlight [21] creates well controlled\n(in time and space) events in the network while the sensor\nnodes detect and timestamp this events. From the\nspatiotemporal knowledge for the created events and the temporal\ninformation provided by sensor nodes, nodes\" spatial\ninformation can be obtained. In a similar manner, the Lighthouse\nsystem [22] uses a parallel light beam, that is emitted by an\nanchor which rotates with a certain period. A sensor node\ndetects the light beam for a period of time, which is\ndependent on the distance between it and the light emitting device.\nMany of the above localization solutions target specific\nsets of requirements and are useful for specific applications.\nStarDust differs in that it addresses a particular demanding\nset of requirements that are not yet solved well. StarDust is\nmeant for localizing air dropped nodes where node\npassiveness, high accuracy, low cost, small form factor and rapid\nlocalization are all required. Many military applications have\nsuch requirements.\n3 StarDust System Design\nThe design of the StarDust system (and its name) was\ninspired by the similarity between a deployed sensor network,\nin which sensor nodes indicate their presence by emitting\nlight, and the Universe consisting of luminous and\nilluminated objects: stars, galaxies, planets, etc.\nThe main difficulty when applying the above ideas to the\nreal world is the complexity of the hardware that needs to\nbe put on a sensor node so that the emitted light can be\ndetected from thousands of feet. The energy expenditure for\nproducing an intense enough light beam is also prohibitive.\nInstead, what we propose to use for sensor node\nlocalization is a passive optical element called a retro-reflector.\nThe most common retro-reflective optical component is a\nCorner-Cube Retroreflector (CCR), shown in Figure 1(a). It\nconsists of three mutually perpendicular mirrors. The\ninter58\n(a) (b)\nFigure 1. Corner-Cube Retroreflector (a) and an array of\nCCRs molded in plastic (b)\nesting property of this optical component is that an incoming\nbeam of light is reflected back, towards the source of the\nlight, irrespective of the angle of incidence. This is in\ncontrast with a mirror, which needs to be precisely positioned to\nbe perpendicular to the incident light. A very common and\ninexpensive implementation of an array of CCRs is the\nretroreflective plastic material used on cars and bicycles for night\ntime detection, shown in Figure 1(b).\nIn the StarDust system, each node is equipped with a\nsmall (e.g. 0.5in2) array of CCRs and the enclosure has\nself-righting capabilities that orient the array of CCRs\npredominantly upwards. It is critical to understand that the\nupward orientation does not need to be exact. Even when large\nangular variations from a perfectly upward orientation are\npresent, a CCR will return the light in the exact same\ndirection from which it came.\nIn the remaining part of the section, we present the\narchitecture of the StarDust system and the design of its main\ncomponents.\n3.1 System Architecture\nThe envisioned sensor network localization scenario is as\nfollows:\n\u2022 The sensor nodes are released, possibly in a controlled\nmanner, from an aerial vehicle during the night.\n\u2022 The aerial vehicle hovers over the deployment area and\nuses a strobe light to illuminate it. The sensor nodes,\nequipped with CCRs and optical filters (acting as\ncoloring devices) have self-righting capabilities and\nretroreflect the incoming strobe light. The retro-reflected\nlight is either white, as the originating source light,\nor colored, due to optical filters.\n\u2022 The aerial vehicle records a sequence of two images\nvery close in time (msec level). One image is taken\nwhen the strobe light is on, the other when the strobe\nlight is off. The acquired images are used for obtaining\nthe locations of sensor nodes (which appear as luminous\nspots in the image).\n\u2022 The aerial vehicle executes the mapping of node IDs to\nthe identified locations in one of the following ways: a)\nby using the color of a retro-reflected light, if a sensor\nnode has a unique color; b) by requiring sensor nodes\nto establish neighborhood information and report it to\na base station; c) by controlling the time sequence of\nsensor nodes deployment and recording additional\nimLight Emitter\nSensor Node i\nTransfer Function\n\u03a6i(\u03bb)\n\u03a8(\u03bb)\n\u03a6(\u03a8(\u03bb))\nImage\nProcessing\nNode ID Matching\nRadio Model\nR\nG(\u039b,E)\nCentral Device\nV\"\nV\"\nFigure 2. The StarDust system architecture\nages; d) by controlling the location where a sensor node\nis deployed.\n\u2022 The computed locations are disseminated to the sensor\nnetwork.\nThe architecture of the StarDust system is shown in\nFigure 2. The architecture consists of two main components:\nthe first is centralized and it is located on a more powerful\ndevice. The second is distributed and it resides on all\nsensor nodes. The Central Device consists of the following: the\nLight Emitter, the Image Processing module, the Node ID\nMapping module and the Radio Model. The distributed\ncomponent of the architecture is the Transfer Function, which\nacts as a filter for the incoming light. The aforementioned\nmodules are briefly described below:\n\u2022 Light Emitter - It is a strobe light, capable of producing\nvery intense, collimated light pulses. The emitted light\nis non-monochromatic (unlike a laser) and it is\ncharacterized by a spectral density \u03a8(\u03bb), a function of the\nwavelength. The emitted light is incident on the CCRs\npresent on sensor nodes.\n\u2022 Transfer Function \u03a6(\u03a8(\u03bb)) - This is a bandpass filter\nfor the incident light on the CCR. The filter allows a\nportion of the original spectrum, to be retro-reflected.\nFrom here on, we will refer to the transfer function as\nthe color of a sensor node.\n\u2022 Image Processing - The Image Processing module\nacquires high resolution images. From these images the\nlocations and the colors of sensor nodes are obtained.\nIf only one set of pictures can be taken (i.e., one\nlocation of the light emitter/image analysis device), then the\nmap of the field is assumed to be known as well as the\ndistance between the imaging device and the field. The\naforementioned assumptions (field map and distance to\nit) are not necessary if the images can be simultaneously\ntaken from different locations. It is important to remark\nhere that the identity of a node can not be directly\nobtained through Image Processing alone, unless a\nspecific characteristic of a sensor node can be identified in\nthe image.\n\u2022 Node ID Matching - This module uses the detected\nlocations and through additional techniques (e.g., sensor\nnode coloring and connectivity information (G(\u039b,E))\nfrom the deployed network) to uniquely identify the\nsensor nodes observed in the image. The connectivity\ninformation is represented by neighbor tables sent from\n59\nAlgorithm 1 Image Processing\n1: Background filtering\n2: Retro-reflected light recognition through intensity\nfiltering\n3: Edge detection to obtain the location of sensor nodes\n4: Color identification for each detected sensor node\neach sensor node to the Central Device.\n\u2022 Radio Model - This component provides an estimate of\nthe radio range to the Node ID Matching module. It\nis only used by node ID matching techniques that are\nbased on the radio connectivity in the network. The\nestimate of the radio range R is based on the sensor node\ndensity (obtained through the Image Processing\nmodule) and the connectivity information (i.e., G(\u039b,E)).\nThe two main components of the StarDust architecture\nare the Image Processing and the Node ID Mapping. Their\ndesign and analysis is presented in the sections that follow.\n3.2 Image Processing\nThe goal of the Image Processing Algorithm (IPA) is to\nidentify the location of the nodes and their color. Note that\nIPA does not identify which node fell where, but only what\nis the set of locations where the nodes fell.\nIPA is executed after an aerial vehicle records two\npictures: one in which the field of deployment is illuminated and\none when no illuminations is present. Let Pdark be the\npicture of the deployment area, taken when no light was emitted\nand Plight be the picture of the same deployment area when a\nstrong light beam was directed towards the sensor nodes.\nThe proposed IPA has several steps, as shown in\nAlgorithm 1. The first step is to obtain a third picture Pfilter where\nonly the differences between Pdark and Plight remain. Let us\nassume that Pdark has a resolution of n \u00d7 m, where n is the\nnumber of pixels in a row of the picture, while m is the\nnumber of pixels in a column of the picture. Then Pdark is\ncomposed of n \u00d7 m pixels noted Pdark(i, j), i \u2208 1 \u2264 i \u2264 n,1 \u2264\nj \u2264 m. Similarly Plight is composed of n \u00d7 m pixels noted\nPlight(i, j), 1 \u2264 i \u2264 n,1 \u2264 j \u2264 m.\nEach pixel P is described by an RGB value where the R\nvalue is denoted by PR, the G value is denoted by PG, and\nthe B value is denoted by PB. IPA then generates the third\npicture, Pfilter, through the following transformations:\nPR\nfilter(i, j) = PR\nlight(i, j)\u2212PR\ndark(i, j)\nPG\nfilter(i, j) = PG\nlight(i, j)\u2212PG\ndark(i, j)\nPB\nfilter(i, j) = PB\nlight(i, j)\u2212PB\ndark(i, j)\n(1)\nAfter this transformation, all the features that appeared in\nboth Pdark and Plight are removed from Pfilter. This simplifies\nthe recognition of light retro-reflected by sensor nodes.\nThe second step consists of identifying the elements\ncontained in Pfilter that retro-reflect light. For this, an intensity\nfilter is applied to Pfilter. First IPA converts Pfilter into a\ngrayscale picture. Then the brightest pixels are identified and\nused to create Preflect. This step is eased by the fact that the\nreflecting nodes should appear much brighter than any other\nilluminated object in the picture.\nSupport: Q(\u03bbk)\nni\nP1\n...\nP2\n...\nPN\n\u03bb1\n...\n\u03bbk\n...\n\u03bbN\nFigure 3. Probabilistic label relaxation\nThe third step runs an edge detection algorithm on Preflect\nto identify the boundary of the nodes present. A tool such as\nMatlab provides a number of edge detection techniques. We\nused the bwboundaries function. For the obtained edges, the\nlocation (x,y) (in the image) of each node is determined by\ncomputing the centroid of the points constituting its edges.\nStandard computer graphics techniques [23] are then used\nto transform the 2D locations of sensor nodes detected in\nmultiple images into 3D sensor node locations. The color of\nthe node is obtained as the color of the pixel located at (x,y)\nin Plight.\n3.3 Node ID Matching\nThe goal of the Node ID Matching module is to\nobtain the identity (node ID) of a luminous spot in the\nimage, detected to be a sensor node. For this, we define V =\n{(x1,y1),(x2,y2),...,(xm,ym)} to be the set of locations of\nthe sensor nodes, as detected by the Image Processing\nmodule and \u039b = {\u03bb1,\u03bb2,...,\u03bbm} to be the set of unique node IDs\nassigned to the m sensor nodes, before deployment. From\nhere on, we refer to node IDs as labels.\nWe model the problem of finding the label \u03bbj of a node ni\nas a probabilistic label relaxation problem, frequently used\nin image processing/understanding. In the image processing\ndomain, scene labeling (i.e., identifying objects in an\nimage) plays a major role. The goal of scene labeling is to\nassign a label to each object detected in an image, such that\nan appropriate image interpretation is achieved. It is\nprohibitively expensive to consider the interactions among all\nthe objects in an image. Instead, constraints placed among\nnearby objects generate local consistencies and through\niteration, global consistencies can be obtained.\nThe main idea of the sensor node localization through\nprobabilistic label relaxation is to iteratively compute the\nprobability of each label being the correct label for a\nsensor node, by taking into account, at each iteration, the\nsupport for a label. The support for a label can be understood\nas a hint or proof, that a particular label is more likely to be\nthe correct one, when compared with the other potential\nlabels for a sensor node. We pictorially depict this main idea\nin Figure 3. As shown, node ni has a set of candidate\nlabels {\u03bb1,...,\u03bbk}. Each of the labels has a different value\nfor the Support function Q(\u03bbk). We defer the explanation\nof how the Support function is implemented until the\nsubsections that follow, where we provide four concrete\ntechniques. Formally, the algorithm is outlined in Algorithm 2,\nwhere the equations necessary for computing the new\nprobability Pni(\u03bbk) for a label \u03bbk of a node ni, are expressed by the\n60\nAlgorithm 2 Label Relaxation\n1: for each sensor node ni do\n2: assign equal prob. to all possible labels\n3: end for\n4: repeat\n5: converged \u2190 true\n6: for each sensor node ni do\n7: for each each label \u03bbj of ni do\n8: compute the Support label \u03bbj: Equation 4\n9: end for\n10: compute K for the node ni: Equation 3\n11: for each each label \u03bbj do\n12: update probability of label \u03bbj: Equation 2\n13: if |new prob.\u2212old prob.| \u2265 \u03b5 then\n14: converged \u2190 false\n15: end if\n16: end for\n17: end for\n18: until converged = true\nfollowing equations:\nPs+1\nni\n(\u03bbk) =\n1\nKni\nPs\nni\n(\u03bbk)Qs\nni\n(\u03bbk) (2)\nwhere Kni is a normalizing constant, given by:\nKni =\nN\n\u2211\nk=1\nPs\nni\n(\u03bbk)Qs\nni\n(\u03bbk) (3)\nand Qs\nni\n(\u03bbk) is:\nQs\nni\n(\u03bbk) = support for label \u03bbk of node ni (4)\nThe label relaxation algorithm is iterative and it is\npolynomial in the size of the network(number of nodes). The\npseudo-code is shown in Algorithm 2. It initializes the\nprobabilities associated with each possible label, for a node ni,\nthrough a uniform distribution. At each iteration s, the\nalgorithm updates the probability associated with each label, by\nconsidering the Support Qs\nni\n(\u03bbk) for each candidate label of\na sensor node.\nIn the sections that follow, we describe four different\ntechniques for implementing the Support function: based on\nnode coloring, radio connectivity, the time of deployment\n(time) and the location of deployment (space). While some\nof these techniques are simplistic, they are primitives which,\nwhen combined, can create powerful localization systems.\nThese design techniques have different trade-offs, which we\nwill present in Section 3.3.6.\n3.3.1 Relaxation with Color Constraints\nThe unique mapping between a sensor node\"s position\n(identified by the image processing) and a label can be\nobtained by assigning a unique color to each sensor node. For\nthis we define C = {c1,c2,...,cn} to be the set of unique\ncolors available and M : \u039b \u2192 C to be a one-to-one mapping of\nlabels to colors. This mapping is known prior to the sensor\nnode deployment (from node manufacturing).\nIn the case of color constrained label relaxation, the\nsupport for label \u03bbk is expressed as follows:\nQs\nni\n(\u03bbk) = 1 (5)\nAs a result, the label relaxation algorithm (Algorithm 2)\nconsists of the following steps: one label is assigned to each\nsensor node (lines 1-3 of the algorithm), implicitly having\na probability Pni(\u03bbk) = 1 ; the algorithm executes a single\niteration, when the support function, simply, reiterates the\nconfidence in the unique labeling.\nHowever, it is often the case that unique colors for each\nnode will not be available. It is interesting to discuss here the\ninfluence that the size of the coloring space (i.e., |C|) has on\nthe accuracy of the localization algorithm. Several cases are\ndiscussed below:\n\u2022 If |C| = 0, no colors are used and the sensor nodes are\nequipped with simple CCRs that reflect back all the\nincoming light (i.e., no filtering, and no coloring of the\nincoming light). From the image processing system, the\nposition of sensor nodes can still be obtained. Since\nall nodes appear white, no single sensor node can be\nuniquely identified.\n\u2022 If |C| = m \u2212 1 then there are enough unique colors for\nall nodes (one node remains white, i.e. no coloring), the\nproblem is trivially solved. Each node can be identified,\nbased on its unique color. This is the scenario for the\nrelaxation with color constraints.\n\u2022 If |C| \u2265 1, there are several options for how to\npartition the coloring space. If C = {c1} one possibility is\nto assign the color c1 to a single node, and leave the\nremaining m\u22121 sensor nodes white, or to assign the color\nc1 to more than one sensor node. One can observe that\nonce a color is assigned uniquely to a sensor node, in\neffect, that sensor node is given the status of anchor,\nor node with known location.\nIt is interesting to observe that there is an entire spectrum\nof possibilities for how to partition the set of sensor nodes\nin equivalence classes (where an equivalence class is\nrepresented by one color), in order to maximize the success of the\nlocalization algorithm. One of the goals of this paper is to\nunderstand how the size of the coloring space and its\npartitioning affect localization accuracy.\nDespite the simplicity of this method of constraining the\nset of labels that can be assigned to a node, we will show that\nthis technique is very powerful, when combined with other\nrelaxation techniques.\n3.3.2 Relaxation with Connectivity Constraints\nConnectivity information, obtained from the sensor\nnetwork through beaconing, can provide additional information\nfor locating sensor nodes. In order to gather connectivity\ninformation, the following need to occur: 1) after deployment,\nthrough beaconing of HELLO messages, sensor nodes build\ntheir neighborhood tables; 2) each node sends its neighbor\ntable information to the Central device via a base station.\nFirst, let us define G = (\u039b,E) to be the weighted\nconnectivity graph built by the Central device from the received\nneighbor table information. In G the edge (\u03bbi,\u03bbj) has a\n61\n\u03bb1\n\u03bb2\n...\n\u03bbN\nni nj\ngi2,j2\n\u03bb1\n\u03bb2\n...\n\u03bbN\nPj,\u03bb1\nPj,\u03bb2\n...\nPj,\u03bbN\nPi,\u03bb1\nPi,\u03bb1\n...\nPi,\u03bbN gi2,jm\nFigure 4. Label relaxation with connectivity constraints\nweight gij represented by the number of beacons sent by \u03bbj\nand received by \u03bbi. In addition, let R be the radio range of\nthe sensor nodes.\nThe main idea of the connectivity constrained label\nrelaxation is depicted in Figure 4 in which two nodes ni and\nnj have been assigned all possible labels. The confidence in\neach of the candidate labels for a sensor node, is represented\nby a probability, shown in a dotted rectangle.\nIt is important to remark that through beaconing and the\nreporting of neighbor tables to the Central Device, a global\nview of all constraints in the network can be obtained. It\nis critical to observe that these constraints are among labels.\nAs shown in Figure 4 two constraints exist between nodes ni\nand nj. The constraints are depicted by gi2,j2 and gi2,jM, the\nnumber of beacons sent the labels \u03bbj2 and \u03bbjM and received\nby the label \u03bbi2.\nThe support for the label \u03bbk of sensor node ni, resulting\nfrom the interaction (i.e., within radio range) with sensor\nnode nj is given by:\nQs\nni\n(\u03bbk) =\nM\n\u2211\nm=1\ng\u03bbk\u03bbm\nPs\nnj\n(\u03bbm) (6)\nAs a result, the localization algorithm (Algorithm 3\nconsists of the following steps: all labels are assigned to each\nsensor node (lines 1-3 of the algorithm), and implicitly each\nlabel has a probability initialized to Pni(\u03bbk) = 1/|\u039b|; in each\niteration, the probabilities for the labels of a sensor node are\nupdated, when considering the interaction with the labels of\nsensor nodes within R. It is important to remark that the\nidentity of the nodes within R is not known, only the candidate\nlabels and their probabilities. The relaxation algorithm\nconverges when, during an iteration, the probability of no label\nis updated by more than \u03b5.\nThe label relaxation algorithm based on connectivity\nconstraints, enforces such constraints between pairs of sensor\nnodes. For a large scale sensor network deployment, it is not\nfeasible to consider all pairs of sensor nodes in the network.\nHence, the algorithm should only consider pairs of sensor\nnodes that are within a reasonable communication range (R).\nWe assume a circular radio range and a symmetric\nconnectivity. In the remaining part of the section we propose a\nsimple analytical model that estimates the radio range R for\nmedium-connected networks (less than 20 neighbors per R).\nWe consider the following to be known: the size of the\ndeployment field (L), the number of sensor nodes deployed (N)\nAlgorithm 3 Localization\n1: Estimate the radio range R\n2: Execute the Label Relaxation Algorithm with Support\nFunction given by Equation 6 for neighbors less than R\napart\n3: for each sensor node ni do\n4: node identity is \u03bbk with max. prob.\n5: end for\nand the total number of unidirectional (i.e., not symmetric)\none-hop radio connections in the network (k). For our\nanalysis, we uniformly distribute the sensor nodes in a square area\nof length L, by using a grid of unit length L/\n\u221a\nN. We use the\nsubstitution u = L/\n\u221a\nN to simplify the notation, in order to\ndistinguish the following cases: if u \u2264 R \u2264\n\u221a\n2u each node\nhas four neighbors (the expected k = 4N); if\n\u221a\n2u \u2264 R \u2264 2u\neach node has eight neighbors (the expected k = 8N); if\n2u \u2264 R \u2264\n\u221a\n5u each node has twelve neighbors ( the expected\nk = 12N); if\n\u221a\n5u \u2264 R \u2264 3u each node has twenty neighbors\n(the expected k = 20N)\nFor a given t = k/4N we take R to be the middle of the\ninterval. As an example, if t = 5 then R = (3 +\n\u221a\n5)u/2. A\nquadratic fitting for R over the possible values of t, produces\nthe following closed-form solution for the communication\nrange R, as a function of network connectivity k, assuming L\nand N constant:\nR(k) =\nL\n\u221a\nN\n\u22120.051\nk\n4N\n2\n+0.66\nk\n4N\n+0.6 (7)\nWe investigate the accuracy of our model in Section 5.2.1.\n3.3.3 Relaxation with Time Constraints\nTime constraints can be treated similarly with color\nconstraints. The unique identification of a sensor node can be\nobtained by deploying sensor nodes individually, one by one,\nand recording a sequence of images. The sensor node that is\nidentified as new in the last picture (it was not identified in\nthe picture before last) must be the last sensor node dropped.\nIn a similar manner with color constrained label\nrelaxation, the time constrained approach is very simple, but may\ntake too long, especially for large scale systems. While it\ncan be used in practice, it is unlikely that only a time\nconstrained label relaxation is used. As we will see, by\ncombining constrained-based primitives, realistic localization\nsystems can be implemented.\nThe support function for the label relaxation with time\nconstraints is defined identically with the color constrained\nrelaxation:\nQs\nni\n(\u03bbk) = 1 (8)\nThe localization algorithm (Algorithm 2 consists of the\nfollowing steps: one label is assigned to each sensor node\n(lines 1-3 of the algorithm), and implicitly having a\nprobability Pni(\u03bbk) = 1 ; the algorithm executes a single iteration,\n62\nD1\nD2\nD4\nD\n3Node\nLabel-1\nLabel-2\nLabel-3\nLabel-4\n0.2\n0.1\n0.5\n0.2\nFigure 5. Relaxation with space\nconstraints\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n1.4\n0 1 2 3 4 5 6 7 8\nPDF\nDistance D\n\u03c3 = 0.5\n\u03c3 = 1\n\u03c3 = 2\nFigure 6. Probability distribution of\ndistances\n-4\n-3\n-2\n-1\n0\n1\n2\n3\n4\nX\n-4\n-3\n-2\n-1\n0\n1\n2\n3\n4\nY\n0\n0.2\n0.4\n0.6\n0.8\n1\nNode Density\nFigure 7. Distribution of nodes\nwhen the support function, simply, reiterates the confidence\nin the unique labeling.\n3.3.4 Relaxation with Space Constraints\nSpatial information related to sensor deployment can also\nbe employed as another input to the label relaxation\nalgorithm. To do that, we use two types of locations: the node\nlocation pn and the label location pl. The former pn is defined\nas the position of nodes (xn,yn,zn) after deployment, which\ncan be obtained through Image Processing as mentioned in\nSection 3.3. The latter pl is defined as the location (xl,yl,zl)\nwhere a node is dropped. We use Dni\n\u03bbm\nto denote the\nhorizontal distance between the location of the label \u03bbm and the\nlocation of the node ni. Clearly, Dni\n\u03bbm\n= (xn \u2212xl)2 +(yn \u2212yl)2.\nAt the time of a sensor node release, the one-to-one\nmapping between the node and its label is known. In other words,\nthe label location is the same as the node location at the\nrelease time. After release, the label location information is\npartially lost due to the random factors such as wind and\nsurface impact. However, statistically, the node locations are\ncorrelated with label locations. Such correlation depends on\nthe airdrop methods employed and environments. For the\nsake of simplicity, let\"s assume nodes are dropped from the\nair through a helicopter hovering in the air. Wind can be\ndecomposed into three components X,Y and Z. Only X and\nY affect the horizontal distance a node can travel.\nAccording to [24], we can assume that X and Y follow an\nindependent normal distribution. Therefore, the absolute value of\nthe wind speed follows a Rayleigh distribution. Obviously\nthe higher the wind speed is, the further a node would land\naway horizontally from the label location. If we assume that\nthe distance D is a function of the wind speed V [25] [26],\nwe can obtain the probability distribution of D under a given\nwind speed distribution. Without loss of generality, we\nassume that D is proportional to the wind speed. Therefore,\nD follows the Rayleigh distribution as well. As shown in\nFigure 5, the spatial-based relaxation is a recursive process\nto assign the probability that a nodes has a certain label by\nusing the distances between the location of a node with\nmultiple label locations.\nWe note that the distribution of distance D affects the\nprobability with which a label is assigned. It is not\nnecessarily true that the nearest label is always chosen. For example,\nif D follows the Rayleigh(\u03c32) distribution, we can obtain the\nProbability Density Function (PDF) of distances as shown\nin Figure 6. This figure indicates that the possibility of a\nnode to fall vertically is very small under windy conditions\n(\u03c3 > 0), and that the distance D is affected by the \u03c3. The\nspatial distribution of nodes for \u03c3 = 1 is shown in Figure 7.\nStrong wind with a high \u03c3 value leads to a larger node\ndispersion. More formally, given a probability density function\nPDF(D), the support for label \u03bbk of sensor node ni can be\nformulated as:\nQs\nni\n(\u03bbk) = PDF(Dni\n\u03bbk\n) (9)\nIt is interesting to point out two special cases. First, if all\nnodes are released at once (i.e., only one label location for\nall released nodes), the distance D from a node to all labels\nis the same. In this case, Ps+1\nni\n(\u03bbk) = Ps\nni\n(\u03bbk), which indicates\nthat we can not use the spatial-based relaxation to recursively\nnarrow down the potential labels for a node. Second, if nodes\nare released at different locations that are far away from each\nother, we have: (i) If node ni has label \u03bbk, Ps\nni\n(\u03bbk) \u2192 1 when\ns \u2192 \u221e, (ii) If node ni does not have label \u03bbk, Ps\nni\n(\u03bbk) \u2192 0\nwhen s \u2192 \u221e. In this second scenario, there are multiple\nlabels (one label per release), hence it is possible to correlate\nrelease times (labels) with positions on the ground. These\nresults indicate that spatial-based relaxation can label the node\nwith a very high probability if the physical separation among\nnodes is large.\n3.3.5 Relaxation with Color and Connectivity\nConstraints\nOne of the most interesting features of the StarDust\narchitecture is that it allows for hybrid localization solutions to be\nbuilt, depending on the system requirements. One example\nis a localization system that uses the color and connectivity\nconstraints. In this scheme, the color constraints are used for\nreducing the number of candidate labels for sensor nodes,\nto a more manageable value. As a reminder, in the\nconnectivity constrained relaxation, all labels are candidate labels\nfor each sensor node. The color constraints are used in the\ninitialization phase of Algorithm 3 (lines 1-3). After the\ninitialization, the standard connectivity constrained relaxation\nalgorithm is used.\nFor a better understanding of how the label relaxation\nalgorithm works, we give a concrete example, exemplified in\nFigure 8. In part (a) of the figure we depict the data structures\n63\n11\n8\n4\n1\n12\n9\n7\n5\n3\nni nj\n12\n8\n10\n11\n10\n0.2\n0.2\n0.2\n0.2\n0.2\n0.25\n0.25\n0.25\n0.25\n(a)\n11\n8\n4\n1\n12\n9\n7\n5\n3\nni nj\n12\n8\n10\n11\n10\n0.2\n0.2\n0.2\n0.2\n0.2\n0.32\n0\n0.68\n0\n(b)\nFigure 8. A step through the algorithm. After\ninitialization (a) and after the 1st iteration for node ni (b)\nassociated with nodes ni and nj after the initialization steps\nof the algorithm (lines 1-6), as well as the number of beacons\nbetween different labels (as reported by the network, through\nG(\u039b,E)). As seen, the potential labels (shown inside the\nvertical rectangles) are assigned to each node. Node ni can be\nany of the following: 11,8,4,1. Also depicted in the figure\nare the probabilities associated with each of the labels. After\ninitialization, all probabilities are equal.\nPart (b) of Figure 8 shows the result of the first iteration\nof the localization algorithm for node ni, assuming that node\nnj is the first wi chosen in line 7 of Algorithm 3. By using\nEquation 6, the algorithm computes the support Q(\u03bbi) for\neach of the possible labels for node ni. Once the Q(\u03bbi)\"s\nare computed, the normalizing constant, given by Equation\n3 can be obtained. The last step of the iteration is to update\nthe probabilities associated with all potential labels of node\nni, as given by Equation 2.\nOne interesting problem, which we explore in the\nperformance evaluation section, is to assess the impact the\npartitioning of the color set C has on the accuracy of\nlocalization. When the size of the coloring set is smaller than the\nnumber of sensor nodes (as it is the case for our hybrid\nconnectivity/color constrained relaxation), the system designer\nhas the option of allowing one node to uniquely have a color\n(acting as an anchor), or multiple nodes. Intuitively, by\nassigning one color to more than one node, more constraints\n(distributed) can be enforced.\n3.3.6 Relaxation Techniques Analysis\nThe proposed label relaxation techniques have different\ntrade-offs. For our analysis of the trade-offs, we consider\nthe following metrics of interest: the localization time\n(duration), the energy consumed (overhead), the network size\n(scale) that can be handled by the technique and the\nlocalization accuracy. The parameters of interest are the following:\nthe number of sensor nodes (N), the energy spent for one\naerial drop (\u03b5d), the energy spent in the network for\ncollecting and reporting neighbor information \u03b5b and the time Td\ntaken by a sensor node to reach the ground after being\naerially deployed. The cost comparison of the different label\nrelaxation techniques is shown in Table 1.\nAs shown, the relaxation techniques based on color and\nspace constraints have the lowest localization duration, zero,\nfor all practical purposes. The scalability of the color based\nrelaxation technique is, however, limited to the number of\n(a) (b)\nFigure 9. SensorBall with self-righting capabilities (a)\nand colored CCRs (b)\nunique color filters that can be built. The narrower the\nTransfer Function \u03a8(\u03bb), the larger the number of unique colors\nthat can be created. The manufacturing costs, however, are\nincreasing as well. The scalability issue is addressed by all\nother label relaxation techniques. Most notably, the time\nconstrained relaxation, which is very similar to the\ncolorconstrained relaxation, addresses the scale issue, at a higher\ndeployment cost.\nCriteria Color Connectivity Time Space\nDuration 0 NTb NTd 0\nOverhead \u03b5d \u03b5d +N\u03b5b N\u03b5d \u03b5d\nScale |C| |N| |N| |N|\nAccuracy High Low High Medium\nTable 1. Comparison of label relaxation techniques\n4 System Implementation\nThe StarDust localization framework, depicted in Figure\n2, is flexible in that it enables the development of new\nlocalization systems, based on the four proposed label\nrelaxation schemes, or the inclusion of other, yet to be invented,\nschemes. For our performance evaluation we implemented a\nversion of the StarDust framework, namely the one proposed\nin Section 3.3.5, where the constraints are based on color and\nconnectivity.\nThe Central device of the StarDust system consists of the\nfollowing: the Light Emitter - we used a\ncommon-off-theshelf flash light (QBeam, 3 million candlepower); the\nimage acquisition was done with a 3 megapixel digital camera\n(Sony DSC-S50) which provided the input to the Image\nProcessing algorithm, implemented in Matlab.\nFor sensor nodes we built a custom sensor node, called\nSensorBall, with self-righting capabilities, shown in Figure\n9(a). The self-righting capabilities are necessary in order to\norient the CCR predominantly upwards. The CCRs that we\nused were inexpensive, plastic molded, night time warning\nsigns commonly available on bicycles, as shown in Figure\n9(b). We remark here the low quality of the CCRs we used.\nThe reflectivity of each CCR (there are tens molded in the\nplastic container) is extremely low, and each CCR is not built\nwith mirrors. A reflective effect is achieved by employing\nfinely polished plastic surfaces. We had 5 colors available,\nin addition to the standard CCR, which reflects all the\nincoming light (white CCR). For a slightly higher price (ours\nwere 20cents/piece), better quality CCRs can be employed.\n64\nFigure 10. The field in the dark Figure 11. The illuminated field Figure 12. The difference: Figure\n10Figure 11\nHigher quality (better mirrors) would translate in more\naccurate image processing (better sensor node detection) and\nsmaller form factor for the optical component (an array of\nCCRs with a smaller area can be used).\nThe sensor node platform we used was the micaZ mote.\nThe code that runs on each node is a simple application\nwhich broadcasts 100 beacons, and maintains a neighbor\ntable containing the percentage of successfully received\nbeacons, for each neighbor. On demand, the neighbor table is\nreported to a base station, where the node ID mapping is\nperformed.\n5 System Evaluation\nIn this section we present the performance evaluation of\na system implementation of the StarDust localization\nframework. The three major research questions that our evaluation\ntries to answer are: the feasibility of the proposed framework\n(can sensor nodes be optically detected at large distances),\nthe localization accuracy of one actual implementation of the\nStarDust framework, and whether or not atmospheric\nconditions can affect the recognition of sensor nodes in an\nimage. The first two questions are investigated by evaluating\nthe two main components of the StarDust framework: the\nImage Processing and the Node ID Matching. These\ncomponents have been evaluated separately mainly because of\nlack of adequate facilities. We wanted to evaluate the\nperformance of the Image Processing Algorithm in a long range,\nrealistic, experimental set-up, while the Node ID Matching\nrequired a relatively large area, available for long periods of\ntime (for connectivity data gathering). The third research\nquestion is investigated through a computer modeling of\natmospheric phenomena.\nFor the evaluation of the Image Processing module, we\nperformed experiments in a football stadium where we\ndeploy 6 sensor nodes in a 3\u00d72 grid. The distance between the\nCentral device and the sensor nodes is approximately 500 ft.\nThe metrics of interest are the number of false positives and\nfalse negatives in the Image Processing Algorithm.\nFor the evaluation of the Node ID Mapping component,\nwe deploy 26 sensor nodes in an 120 \u00d7 60 ft2 flat area of\na stadium. In order to investigate the influence the radio\nconnectivity has on localization accuracy, we vary the height\nabove ground of the deployed sensor nodes. Two set-ups are\nused: one in which the sensor nodes are on the ground, and\nthe second one, in which the sensor nodes are raised 3 inches\nabove ground. From here on, we will refer to these two\nexperimental set-ups as the low connectivity and the high\nconnectivity networks, respectively because when nodes are\non the ground the communication range is low resulting in\nless neighbors than when the nodes are elevated and have a\ngreater communication range. The metrics of interest are:\nthe localization error (defined as the distance between the\ncomputed location and the true location - known from the\nmanual placement), the percentage of nodes correctly\nlocalized, the convergence of the label relaxation algorithm, the\ntime to localize and the robustness of the node ID mapping\nto errors in the Image Processing module.\nThe parameters that we vary experimentally are: the\nangle under which images are taken, the focus of the camera,\nand the degree of connectivity. The parameters that we vary\nin simulations (subsequent to image acquisition and\nconnectivity collection) the number of colors, the number of\nanchors, the number of false positives or negatives as input\nto the Node ID Matching component, the distance between\nthe imaging device and sensor network (i.e., range),\natmospheric conditions (light attenuation coefficient) and CCR\nreflectance (indicative of its quality).\n5.1 Image Processing\nFor the IPA evaluation, we deploy 6 sensor nodes in a\n3 \u00d7 2 grid. We take 13 sets of pictures using different\norientations of the camera and different zooming factors. All\npictures were taken from the same location. Each set is\ncomposed of a picture taken in the dark and of a picture taken\nwith a light beam pointed at the nodes. We process the\npictures offline using a Matlab implementation of IPA. Since we\nare interested in the feasibility of identifying colored sensor\nnodes at large distance, the end result of our IPA is the 2D\nlocation of sensor nodes (position in the image). The\ntransformation to 3D coordinates can be done through standard\ncomputer graphics techniques [23].\nOne set of pictures obtained as part of our experiment is\nshown in Figures 10 and 11. The execution of our IPA\nalgorithm results in Figure 12 which filters out the background,\nand Figure 13 which shows the output of the edge detection\nstep of IPA. The experimental results are depicted in\nFigure 14. For each set of pictures the graph shows the number\nof false positives (the IPA determines that there is a node\n65\nFigure 13. Retroreflectors detected in Figure 12\n0\n1\n2\n3\n1 2 3 4 5 6 7 8 9 10 11\nExperiment Number\nCount\nFalse Positives\nFalse Negatives\nFigure 14. False Positives and Negatives for the 6 nodes\nwhile there is none), and the number of false negatives (the\nIPA determines that there is no node while there is one). In\nabout 45% of the cases, we obtained perfect results, i.e., no\nfalse positives and no false negatives. In the remaining cases,\nwe obtained a number of false positives of at most one, and\na number of false negatives of at most two.\nWe exclude two pairs of pictures from Figure 14. In the\nfirst excluded pair, we obtain 42 false positives and in the\nsecond pair 10 false positives and 7 false negatives. By\ncarefully examining the pictures, we realized that the first pair\nwas taken out of focus and that a car temporarily appeared\nin one of the pictures of the second pair. The anomaly in\nthe second set was due to the fact that we waited too long to\ntake the second picture. If the pictures had been taken a few\nmilliseconds apart, the car would have been represented on\neither both or none of the pictures and the IPA would have\nfiltered it out.\n5.2 Node ID Matching\nWe evaluate the Node ID Matching component of our\nsystem by collecting empirical data (connectivity information)\nfrom the outdoor deployment of 26 nodes in the 120\u00d760 ft2\narea. We collect 20 sets of data for the high connectivity\nand low connectivity network deployments. Off-line we\ninvestigate the influence of coloring on the metrics of interest,\nby randomly assigning colors to the sensor nodes. For one\nexperimental data set we generate 50 random assignments\nof colors to sensor nodes. It is important to observe that, for\nthe evaluation of the Node ID Matching algorithm (color and\nconnectivity constrained), we simulate the color assignment\nto sensor nodes. As mentioned in Section 4 the size of the\ncoloring space available to us was 5 (5 colors). Through\nsimulations of color assignment (not connectivity) we are able\nto investigate the influence that the size of the coloring space\nhas on the accuracy of localization. The value of the\nparam0\n10\n20\n30\n40\n50\n60\n0 10 20 30 40 50 60 70 80 90\nDistance [feet]\nCount\nConnected\nNot Connected\nFigure 15. The number of existing and missing radio\nconnections in the sparse connectivity experiment\n0\n10\n20\n30\n40\n50\n60\n70\n0 10 20 30 40 50 60 70 80 90 10 11 12\nDistance [feet]\nCount\nConnected\nNot Connected\nFigure 16. The number of existing and missing radio\nconnections in the high connectivity experiment\neter \u03b5 used in Algorithm 2 was 0.001. The results presented\nhere represent averages over the randomly generated\ncolorings and over all experimental data sets.\nWe first investigate the accuracy of our proposed Radio\nModel, and subsequently use the derived values for the radio\nrange in the evaluation of the Node ID matching component.\n5.2.1 Radio Model\nFrom experiments, we obtain the average number of\nobserved beacons (k, defined in Section 3.3.2) for the low\nconnectivity network of 180 beacons and for the high\nconnectivity network of 420 beacons. From our Radio Model\n(Equation 7, we obtain a radio range R = 25 ft for the low\nconnectivity network and R = 40 ft for the high connectivity\nnetwork.\nTo estimate the accuracy of our simple model, we plot\nthe number of radio links that exist in the networks, and the\nnumber of links that are missing, as functions of the distance\nbetween nodes. The results are shown in Figures 15 and 16.\nWe define the average radio range R to be the distance over\nwhich less than 20% of potential radio links, are missing.\nAs shown in Figure 15, the radio range is between 20 ft and\n25 ft. For the higher connectivity network, the radio range\nwas between 30 ft and 40 ft.\nWe choose two conservative estimates of the radio range:\n20 ft for the low connectivity case and 35 ft for the high\nconnectivity case, which are in good agreement with the values\npredicted by our Radio Model.\n5.2.2 Localization Error vs. Coloring Space Size\nIn this experiment we investigate the effect of the number\nof colors on the localization accuracy. For this, we randomly\nassign colors from a pool of a given size, to the sensor nodes.\n66\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\n0 5 10 15 20\nNumber of Colors\nLocalizationError[feet]\nR=15feet\nR=20feet\nR=25feet\nFigure 17. Localization error\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\n100\n0 5 10 15 20\nNumber of Colors\n%CorrectLocalized[x100]\nR=15feet\nR=20feet\nR=25feet\nFigure 18. Percentage of nodes correctly localized\nWe then execute the localization algorithm, which uses the\nempirical data. The algorithm is run for three different radio\nranges: 15, 20 and 25 ft, to investigate its influence on the\nlocalization error.\nThe results are depicted in Figure 17 (localization error)\nand Figure 18 (percentage of nodes correctly localized). As\nshown, for an estimate of 20 ft for the radio range (as\npredicted by our Radio Model) we obtain the smallest\nlocalization errors, as small as 2 ft, when enough colors are used.\nBoth Figures 17 and 18 confirm our intuition that a larger\nnumber of colors available significantly decrease the error in\nlocalization.\nThe well known fact that relaxation algorithms do not\nalways converge, was observed during our experiments. The\npercentage of successful runs (when the algorithm\nconverged) is depicted in Figure 19. As shown, in several\nsituations, the algorithm failed to converge (the algorithm\nexecution was stopped after 100 iterations per node). If the\nalgorithm does not converge in a predetermined number of steps,\nit will terminate and the label with the highest probability\nwill provide the identity of the node. It is very probable that\nthe chosen label is incorrect, since the probabilities of some\nof labels are constantly changing (with each iteration).The\nconvergence of relaxation based algorithms is a well known\nissue.\n5.2.3 Localization Error vs. Color Uniqueness\nAs mentioned in the Section 3.3.1, a unique color gives a\nsensor node the statute of an anchor. A sensor node that is\nan anchor can unequivocally be identified through the Image\nProcessing module. In this section we investigate the effect\nunique colors have on the localization accuracy. Specifically,\nwe want to experimentally verify our intuition that assigning\nmore nodes to a color can benefit the localization accuracy,\nby enforcing more constraints, as opposed to uniquely\nassigning a color to a single node.\n90\n95\n100\n105\n0 5 10 15 20\nNumber of Colors\nConvergenceRate[x100]\nR=15feet\nR=20feet\nR=25feet\nFigure 19. Convergence error\n0\n2\n4\n6\n8\n10\n12\n14\n16\n4 6 8\nNumber of Colors\nLocalizationError[feet]\n0 anchors\n2 anchors\n4 anchors\n6 anchors\n8 anchors\nFigure 20. Localization error vs. number of colors\nFor this, we fix the number of available colors to either 4,\n6 or 8 and vary the number of nodes that are given unique\ncolors, from 0, up to the maximum number of colors (4, 6 or\n8). Naturally, if we have a maximum number of colors of 4,\nwe can assign at most 4 anchors. The experimental results\nare depicted in Figure 20 (localization error) and Figure 21\n(percentage of sensor node correctly localized). As expected,\nthe localization accuracy increases with the increase in the\nnumber of colors available (larger coloring space). Also, for\na given size of the coloring space (e.g., 6 colors available), if\nmore colors are uniquely assigned to sensor nodes then the\nlocalization accuracy decreases. It is interesting to observe\nthat by assigning colors uniquely to nodes, the benefit of\nhaving additional colors is diminished. Specifically, if 8 colors\nare available and all are assigned uniquely, the system would\nbe less accurately localized (error \u2248 7 ft), when compared\nto the case of 6 colors and no unique assignments of colors\n(\u2248 5 ft localization error).\nThe same trend, of a less accurate localization can be\nobserved in Figure 21, which shows the percentage of nodes\ncorrectly localized (i.e., 0 ft localization error). As shown, if\nwe increase the number of colors that are uniquely assigned,\nthe percentage of nodes correctly localized decreases.\n5.2.4 Localization Error vs. Connectivity\nWe collected empirical data for two network deployments\nwith different degrees of connectivity (high and low) in\norder to assess the influence of connectivity on location\naccuracy. The results obtained from running our localization\nalgorithm are depicted in Figure 22 and Figure 23. We\nvaried the number of colors available and assigned no anchors\n(i.e., no unique assignments of colors).\nIn both scenarios, as expected, localization error decrease\nwith an increase in the number of colors. It is interesting\nto observe, however, that the low connectivity scenario\nim67\n0\n20\n40\n60\n80\n100\n120\n140\n4 6 8\nNumber of Colors\n%CorrectLocalized[x100]\n0 anchors\n2 anchors\n4 anchors\n6 anchors\n8 anchors\nFigure 21. Percentage of nodes correctly localized vs.\nnumber of colors\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\n0 2 4 6 8 10 12\nNumber of Colors\nLocalizationError[feet]\nLow Connectivity\nHigh Connectivity\nFigure 22. Localization error vs. number of colors\nproves the localization accuracy quicker, from the additional\nnumber of colors available. When the number of colors\nbecomes relatively large (twelve for our 26 sensor node\nnetwork), both scenarios (low and high connectivity) have\ncomparable localization errors, of less that 2 ft. The same trend\nof more accurate location information is evidenced by\nFigure 23 which shows that the percentage of nodes that are\nlocalized correctly grows quicker for the low connectivity\ndeployment.\n5.3 Localization Error vs. Image Processing\nErrors\nSo far we investigated the sources for error in\nlocalization that are intrinsic to the Node ID Matching component.\nAs previously presented, luminous objects can be\nmistakenly detected to be sensor nodes during the location\ndetection phase of the Image Processing module. These false\npositives can be eliminated by the color recognition procedure\nof the Image Processing module. More problematic are false\nnegatives (when a sensor node does not reflect back enough\nlight to be detected). They need to be handled by the\nlocalization algorithm. In this case, the localization algorithm\nis presented with two sets of nodes of different sizes, that\nneed to be matched: one coming from the Image Processing\n(which misses some nodes) and one coming from the\nnetwork, with the connectivity information (here we assume a\nfully connected network, so that all sensor nodes report their\nconnectivity information). In this experiment we investigate\nhow Image Processing errors (false negatives) influence the\nlocalization accuracy.\nFor this evaluation, we ran our localization algorithm with\nempirical data, but dropped a percentage of nodes from the\nlist of nodes detected by the Image Processing algorithm (we\nartificially introduced false negatives in the Image\nProcess0\n10\n20\n30\n40\n50\n60\n70\n80\n90\n100\n0 2 4 6 8 10 12\nNumber of Colors\n%CorrectLocalized[x100]\nLow Connectivity\nHigh Connectivity\nFigure 23. Percentage of nodes correctly localized\n0\n2\n4\n6\n8\n10\n12\n14\n0 4 8 12 16\n% False Negatives [x100]\nLocalizationError[feet]\n4 colors\n8 colors\n12 colors\nFigure 24. Impact of false negatives on the localization\nerror\ning). The effect of false negatives on localization accuracy is\ndepicted in Figure 24. As seen in the figure if the number of\nfalse negatives is 15%, the error in position estimation\ndoubles when 4 colors are available. It is interesting to observe\nthat the scenario when more colors are available (e.g., 12\ncolors) is being affected more drastically than the scenario with\nless colors (e.g., 4 colors). The benefit of having more colors\navailable is still being maintained, at least for the range of\ncolors we investigated (4 through 12 colors).\n5.4 Localization Time\nIn this section we look more closely at the duration for\neach of the four proposed relaxation techniques and two\ncombinations of them: color-connectivity and color-time.\nWe assume that 50 unique color filters can be manufactured,\nthat the sensor network is deployed from 2,400 ft\n(necessary for the time-constrained relaxation) and that the time\nrequired for reporting connectivity grows linearly, with an\ninitial reporting period of 160sec, as used in a real world\ntracking application [1]. The localization duration results, as\npresented in Table 1, are depicted in Figure 25.\nAs shown, for all practical purposes the time required\nby the space constrained relaxation techniques is 0sec. The\nsame applies to the color constrained relaxation, for which\nthe localization time is 0sec (if the number of colors is\nsufficient). Considering our assumptions, only for a network of\nsize 50 the color constrained relaxation works. The\nlocalization duration for all other network sizes (100, 150 and 200)\nis infinite (i.e., unique color assignments to sensor nodes\ncan not be made, since only 50 colors are unique), when\nonly color constrained relaxation is used. Both the\nconnectivity constrained and time constrained techniques increase\nlinearly with the network size (for the time constrained, the\nCentral device deploys sensor nodes one by one, recording\nan image after the time a sensor node is expected to reach the\n68\n0\n500\n1000\n1500\n2000\n2500\n3000\nColor Connectivity Time Space\nColorConenctivity\nColor-Time\nLocalization technique\nLocalizationtime[sec]\n50 nodes\n100 nodes\n150 nodes\n200 nodes\nFigure 25. Localization time for different\nlabel relaxation schemes\n0 2000 4000 6000 8000\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\nr [feet]\nC\nr\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1.0\nFigure 26. Apparent contrast in a\nclear atmosphere\n0 2000 4000 6000 8000\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\nr [feet]\nC\nr\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1.0\nFigure 27. Apparent contrast in a\nhazing atmosphere\nground).\nIt is interesting to notice in Figure 25 the improvement in\nthe localization time obtained by simply combining the color\nand the connectivity constrained techniques. The\nlocalization duration in this case is identical with the connectivity\nconstrained technique.\nThe combination of color and time constrained\nrelaxations is even more interesting. For a reasonable\nlocalization duration of 52seconds a perfect (i.e., 0 ft localization\nerror) localization system can be built. In this scenario, the\nset of sensor nodes is split in batches, with each batch\nhaving a set of unique colors. It would be very interesting to\nconsider other scenarios, where the strength of the space\nconstrained relaxation (0sec for any sensor network size) is\nused for improving the other proposed relaxation techniques.\nWe leave the investigation and rigorous classification of such\ntechnique combination for future work.\n5.5 System Range\nIn this section we evaluate the feasibility of the\nStarDust localization framework when considering the realities\nof light propagation through the atmosphere.\nThe main factor that determines the range of our system is\nlight scattering, which redirects the luminance of the source\ninto the medium (in essence equally affecting the luminosity\nof the target and of the background). Scattering limits the\nvisibility range by reducing the apparent contrast between\nthe target and its background (approaches zero, as the\ndistance increases). The apparent contrast Cr is quantitatively\nexpressed by the formula:\nCr = (Nt\nr \u2212Nb\nr )/Nb\nr (10)\nwhere Nt\nr and Nb\nr are the apparent target radiance and\napparent background radiance at distance r from the light source,\nrespectively. The apparent radiance Nt\nr of a target at a\ndistance r from the light source, is given by:\nNt\nr = Na +\nI\u03c1te\u22122\u03c3r\n\u03c0r2\n(11)\nwhere I is the intensity of the light source, \u03c1t is the\ntarget reflectance, \u03c3 is the spectral attenuation coefficient (\u2248\n0.12km\u22121 and \u2248 0.60km\u22121 for a clear and a hazy\natmosphere, respectively) and Na is the radiance of the\natmospheric backscatter, and it can be expressed as follows:\nNa =\nG\u03c32I\n2\u03c0\n2\u03c3rZ\n0.02\u03c3r\ne\u2212x\nx2\ndx (12)\nwhere G = 0.24 is a backscatter gain. The apparent\nbackground radiance Nb\nr is given by formulas similar with\nEquations 11 and 12, where only the target reflectance \u03c1t is\nsubstituted with the background reflectance \u03c1b. It is important\nto remark that when Cr reaches its lower limit, no increase\nin the source luminance or receiver sensitivity will increase\nthe range of the system. From Equations 11 and 12 it can be\nobserved that the parameter which can be controlled and can\ninfluence the range of the system is \u03c1t, the target reflectance.\nFigures 26 and 27 depict the apparent contrast Cr as a\nfunction of the distance r for a clear and for a hazy\natmosphere, respectively. The apparent contrast is investigated for\nreflectance coefficients \u03c1t ranging from 0.3 to 1.0 (perfect\nreflector). For a contrast C of at least 0.5, as it can be seen in\nFigure 26 a range of approximately 4,500 ft can be achieved\nif the atmosphere is clear. The performance dramatically\ndeteriorates, when the atmospheric conditions are problematic.\nAs shown in Figure 27 a range of up to 1,500 ft is\nachievable, when using highly reflective CCR components.\nWhile our light source (3 million candlepower) was\nsufficient for a range of a few hundred feet, we remark that there\nexist commercially available light sources (20 million\ncandlepower) or military (150 million candlepower [27]),\npowerful enough for ranges of a few thousand feet.\n6 StarDust System Optimizations\nIn this section we describe extensions of the proposed\narchitecture that can constitute future research directions.\n6.1 Chained Constraint Primitives\nIn this paper we proposed four primitives for\nconstraintbased relaxation algorithms: color, connectivity, time and\nspace. To demonstrate the power that can be obtained by\ncombining them, we proposed and evaluated one\ncombination of such primitives: color and connectivity. An\ninteresting research direction to pursue could be to chain more than\ntwo of these primitives. An example of such chain is: color,\ntemporal, spatial and connectivity. Other research directions\ncould be to use voting scheme for deciding which primitive\nto use or assign different weights to different relaxation\nalgorithms.\n69\n6.2 Location Learning\nIf after several iterations of the algorithm, none of the\nlabel probabilities for a node ni converges to a higher value, the\nconfidence in our labeling of that node is relatively low. It\nwould be interesting to associate with a node, more than one\nlabel (implicitly more than one location) and defer the label\nassignment decision until events are detected in the network\n(if the network was deployed for target tracking).\n6.3 Localization in Rugged Environments\nThe initial driving force for the StarDust localization\nframework was to address the sensor node localization in\nextremely rugged environments. Canopies, dense vegetation,\nextremely obstructing environments pose significant\nchallenges for sensor nodes localization. The hope, and our\noriginal idea, was to consider the time period between the aerial\ndeployment and the time when the sensor node disappears\nunder the canopy. By recording the last visible position of a\nsensor node (as seen from the aircraft) a reasonable estimate\nof the sensor node location can be obtained. This would\nrequire that sensor nodes posses self-righting capabilities,\nwhile in mid-air. Nevertheless, we remark on the suitability\nof our localization framework for rugged, non-line-of-sight\nenvironments.\n7 Conclusions\nStarDust solves the localization problem for aerial\ndeployments where passiveness, low cost, small form factor\nand rapid localization are required. Results show that\naccuracy can be within 2 ft and localization time within\nmilliseconds. StarDust also shows robustness with respect to errors.\nWe predict the influence the atmospheric conditions can have\non the range of a system based on the StarDust framework,\nand show that hazy environments or daylight can pose\nsignificant challenges.\nMost importantly, the properties of StarDust support\nthe potential for even more accurate localization solutions\nas well as solutions for rugged, non-line-of-sight\nenvironments.\n8 References\n[1] T. He, S. Krishnamurthy, J. A. Stankovic, T. Abdelzaher, L. Luo,\nR. Stoleru, T. Yan, L. Gu, J. Hui, and B. Krogh, An energy-efficient\nsurveillance system using wireless sensor networks, in MobiSys, 2004.\n[2] G. Simon, M. Maroti, A. Ledeczi, G. Balogh, B. Kusy, A. Nadas,\nG. Pap, J. Sallai, and K. Frampton, Sensor network-based\ncountersniper system, in SenSys, 2004.\n[3] A. Arora, P. Dutta, and B. Bapat, A line in the sand: A wireless sensor\nnetwork for trage detection, classification and tracking, in Computer\nNetworks, 2004.\n[4] R. Szewczyk, A. Mainwaring, J. Polastre, J. Anderson, and D. Culler,\nAn analysis of a large scale habitat monitoring application, in ACM\nSenSys, 2004.\n[5] N. Xu, S. Rangwala, K. K. Chintalapudi, D. Ganesan, A. Broad,\nR. Govindan, and D. Estrin, A wireless sensor network for structural\nmonitoring, in ACM SenSys, 2004.\n[6] A. Savvides, C. Han, and M. Srivastava, Dynamic fine-grained\nlocalization in ad-hoc networks of sensors, in Mobicom, 2001.\n[7] N. Priyantha, A. Chakraborty, and H. Balakrishnan, The cricket\nlocation-support system, in Mobicom, 2000.\n[8] M. Broxton, J. Lifton, and J. Paradiso, Localizing a sensor network\nvia collaborative processing of global stimuli, in EWSN, 2005.\n[9] P. Bahl and V. N. Padmanabhan, Radar: An in-building rf-based user\nlocation and tracking system, in IEEE Infocom, 2000.\n[10] N. Priyantha, H. Balakrishnan, E. Demaine, and S. Teller,\nMobileassisted topology generation for auto-localization in sensor networks,\nin IEEE Infocom, 2005.\n[11] P. N. Pathirana, A. Savkin, S. Jha, and N. Bulusu, Node localization\nusing mobile robots in delay-tolerant sensor networks, IEEE\nTransactions on Mobile Computing, 2004.\n[12] C. Savarese, J. M. Rabaey, and J. Beutel, Locationing in distribued\nad-hoc wireless sensor networks, in ICAASSP, 2001.\n[13] M. Maroti, B. Kusy, G. Balogh, P. Volgyesi, A. Nadas, K. Molnar,\nS. Dora, and A. Ledeczi, Radio interferometric geolocation, in ACM\nSenSys, 2005.\n[14] K. Whitehouse, A. Woo, C. Karlof, F. Jiang, and D. Culler, The\neffects of ranging noise on multi-hop localization: An empirical study,\nin IPSN, 2005.\n[15] Y. Kwon, K. Mechitov, S. Sundresh, W. Kim, and G. Agha, Resilient\nlocalization for sensor networks in outdoor environment, UIUC, Tech.\nRep., 2004.\n[16] R. Stoleru and J. A. Stankovic, Probability grid: A location\nestimation scheme for wireless sensor networks, in SECON, 2004.\n[17] N. Bulusu, J. Heidemann, and D. Estrin, GPS-less low cost outdoor\nlocalization for very small devices, IEEE Personal Communications\nMagazine, 2000.\n[18] T. He, C. Huang, B. Blum, J. A. Stankovic, and T. Abdelzaher,\nRange-Free localization schemes in large scale sensor networks, in\nACM Mobicom, 2003.\n[19] R. Nagpal, H. Shrobe, and J. Bachrach, Organizing a global\ncoordinate system from local information on an ad-hoc sensor network, in\nIPSN, 2003.\n[20] D. Niculescu and B. Nath, ad-hoc positioning system, in IEEE\nGLOBECOM, 2001.\n[21] R. Stoleru, T. He, J. A. Stankovic, and D. Luebke, A high-accuracy\nlow-cost localization system for wireless sensor networks, in ACM\nSenSys, 2005.\n[22] K. R\u00a8omer, The lighthouse location system for smart dust, in\nACM/USENIX MobiSys, 2003.\n[23] R. Y. Tsai, A versatile camera calibration technique for\nhighaccuracy 3d machine vision metrology using off-the-shelf tv cameras\nand lenses, IEEE JRA, 1987.\n[24] C. L. Archer and M. Z. Jacobson, Spatial and temporal distributions\nof U.S. winds and wind power at 80m derived from measurements,\nGeophysical Research Jrnl., 2003.\n[25] Team for advanced flow simulation and modeling. [Online].\nAvailable: http://www.mems.rice.edu/TAFSM/RES/\n[26] K. Stein, R. Benney, T. Tezduyar, V. Kalro, and J. Leonard, 3-D\ncomputation of parachute fluid-structure interactions - performance and\ncontrol, in Aerodynamic Decelerator Systems Conference, 1999.\n[27] Headquarters Department of the Army, Technical manual for\nsearchlight infrared AN/GSS-14(V)1, 1982.\n70", "keywords": "range;unique mapping;performance;image processing;connectivity;localization;scene labeling;probability;sensor node;aerial vehicle;consistency;wireless sensor network;corner-cube retro-reflector"}
{"name": "train_C-46", "title": "TSAR: A Two Tier Sensor Storage Architecture Using Interval Skip Graphs", "abstract": "Archival storage of sensor data is necessary for applications that query, mine, and analyze such data for interesting features and trends. We argue that existing storage systems are designed primarily for flat hierarchies of homogeneous sensor nodes and do not fully exploit the multi-tier nature of emerging sensor networks, where an application can comprise tens of tethered proxies, each managing tens to hundreds of untethered sensors. We present TSAR, a fundamentally different storage architecture that envisions separation of data from metadata by employing local archiving at the sensors and distributed indexing at the proxies. At the proxy tier, TSAR employs a novel multi-resolution ordered distributed index structure, the Interval Skip Graph, for efficiently supporting spatio-temporal and value queries. At the sensor tier, TSAR supports energy-aware adaptive summarization that can trade off the cost of transmitting metadata to the proxies against the overhead of false hits resulting from querying a coarse-grain index. We implement TSAR in a two-tier sensor testbed comprising Stargatebased proxies and Mote-based sensors. Our experiments demonstrate the benefits and feasibility of using our energy-efficient storage architecture in multi-tier sensor networks.", "fulltext": "1. Introduction\n1.1 Motivation\nMany different kinds of networked data-centric sensor\napplications have emerged in recent years. Sensors in these applications\nsense the environment and generate data that must be processed,\nfiltered, interpreted, and archived in order to provide a useful\ninfrastructure to its users. To achieve its goals, a typical sensor\napplication needs access to both live and past sensor data. Whereas\naccess to live data is necessary in monitoring and surveillance\napplications, access to past data is necessary for applications such as\nmining of sensor logs to detect unusual patterns, analysis of\nhistorical trends, and post-mortem analysis of particular events. Archival\nstorage of past sensor data requires a storage system, the key\nattributes of which are: where the data is stored, whether it is indexed,\nand how the application can access this data in an energy-efficient\nmanner with low latency.\nThere have been a spectrum of approaches for constructing\nsensor storage systems. In the simplest, sensors stream data or events\nto a server for long-term archival storage [3], where the server\noften indexes the data to permit efficient access at a later time. Since\nsensors may be several hops from the nearest base station, network\ncosts are incurred; however, once data is indexed and archived,\nsubsequent data accesses can be handled locally at the server without\nincurring network overhead. In this approach, the storage is\ncentralized, reads are efficient and cheap, while writes are expensive.\nFurther, all data is propagated to the server, regardless of whether\nit is ever used by the application.\nAn alternate approach is to have each sensor store data or events\nlocally (e.g., in flash memory), so that all writes are local and incur\nno communication overheads. A read request, such as whether an\nevent was detected by a particular sensor, requires a message to\nbe sent to the sensor for processing. More complex read requests\nare handled by flooding. For instance, determining if an intruder\nwas detected over a particular time interval requires the request to\nbe flooded to all sensors in the system. Thus, in this approach,\nthe storage is distributed, writes are local and inexpensive, while\nreads incur significant network overheads. Requests that require\nflooding, due to the lack of an index, are expensive and may waste\nprecious sensor resources, even if no matching data is stored at\nthose sensors. Research efforts such as Directed Diffusion [17]\nhave attempted to reduce these read costs, however, by intelligent\nmessage routing.\nBetween these two extremes lie a number of other sensor storage\nsystems with different trade-offs, summarized in Table 1. The\ngeographic hash table (GHT) approach [24, 26] advocates the use of\nan in-network index to augment the fully distributed nature of\nsensor storage. In this approach, each data item has a key associated\nwith it, and a distributed or geographic hash table is used to map\nkeys to nodes that store the corresponding data items. Thus, writes\ncause data items to be sent to the hashed nodes and also trigger\nupdates to the in-network hash table. A read request requires a lookup\nin the in-network hash table to locate the node that stores the data\n39\nitem; observe that the presence of an index eliminates the need for\nflooding in this approach.\nMost of these approaches assume a flat, homogeneous\narchitecture in which every sensor node is energy-constrained. In this\npaper, we propose a novel storage architecture called TSAR1\nthat\nreflects and exploits the multi-tier nature of emerging sensor\nnetworks, where the application is comprised of tens of tethered\nsensor proxies (or more), each controlling tens or hundreds of\nuntethered sensors. TSAR is a component of our PRESTO [8] predictive\nstorage architecture, which combines archival storage with caching\nand prediction. We believe that a fundamentally different storage\narchitecture is necessary to address the multi-tier nature of future\nsensor networks. Specifically, the storage architecture needs to\nexploit the resource-rich nature of proxies, while respecting resource\nconstraints at the remote sensors. No existing sensor storage\narchitecture explicitly addresses this dichotomy in the resource\ncapabilities of different tiers.\nAny sensor storage system should also carefully exploit current\ntechnology trends, which indicate that the capacities of flash\nmemories continue to rise as per Moore\"s Law, while their costs continue\nto plummet. Thus it will soon be feasible to equip each sensor with\n1 GB of flash storage for a few tens of dollars. An even more\ncompelling argument is the energy cost of flash storage, which can be\nas much as two orders of magnitude lower than that for\ncommunication. Newer NAND flash memories offer very low write and\nerase energy costs - our comparison of a 1GB Samsung NAND\nflash storage [16] and the Chipcon CC2420 802.15.4 wireless radio\n[4] in Section 6.2 indicates a 1:100 ratio in per-byte energy cost\nbetween the two devices, even before accounting for network protocol\noverheads. These trends, together with the energy-constrained\nnature of untethered sensors, indicate that local storage offers a viable,\nenergy-efficient alternative to communication in sensor networks.\nTSAR exploits these trends by storing data or events locally on\nthe energy-efficient flash storage at each sensor. Sensors send\nconcise identifying information, which we term metadata, to a nearby\nproxy; depending on the representation used, this metadata may be\nan order of magnitude or more smaller than the data itself,\nimposing much lower communication costs. The resource-rich proxies\ninteract with one another to construct a distributed index of the\nmetadata reported from all sensors, and thus an index of the\nassociated data stored at the sensors. This index provides a unified,\nlogical view of the distributed data, and enables an application to\nquery and read past data efficiently - the index is used to\npinpoint all data that match a read request, followed by messages to\nretrieve that data from the corresponding sensors. In-network\nindex lookups are eliminated, reducing network overheads for read\nrequests. This separation of data, which is stored at the sensors,\nand the metadata, which is stored at the proxies, enables TSAR to\nreduce energy overheads at the sensors, by leveraging resources at\ntethered proxies.\n1.2 Contributions\nThis paper presents TSAR, a novel two-tier storage architecture\nfor sensor networks. To the best of our knowledge, this is the first\nsensor storage system that is explicitly tailored for emerging\nmultitier sensor networks. Our design and implementation of TSAR has\nresulted in four contributions.\nAt the core of the TSAR architecture is a novel distributed index\nstructure based on interval skip graphs that we introduce in this\npaper. This index structure can store coarse summaries of sensor\ndata and organize them in an ordered manner to be easily\nsearch1\nTSAR: Tiered Storage ARchitecture for sensor networks.\nable. This data structure has O(log n) expected search and update\ncomplexity. Further, the index provides a logically unified view of\nall data in the system.\nSecond, at the sensor level, each sensor maintains a local archive\nthat stores data on flash memory. Our storage architecture is fully\nstateless at each sensor from the perspective of the metadata index;\nall index structures are maintained at the resource-rich proxies, and\nonly direct requests or simple queries on explicitly identified\nstorage locations are sent to the sensors. Storage at the remote sensor\nis in effect treated as appendage of the proxy, resulting in low\nimplementation complexity, which makes it ideal for small,\nresourceconstrained sensor platforms. Further, the local store is optimized\nfor time-series access to archived data, as is typical in many\napplications. Each sensor periodically sends a summary of its data to a\nproxy. TSAR employs a novel adaptive summarization technique\nthat adapts the granularity of the data reported in each summary to\nthe ratio of false hits for application queries. More fine grain\nsummaries are sent whenever more false positives are observed, thereby\nbalancing the energy cost of metadata updates and false positives.\nThird, we have implemented a prototype of TSAR on a multi-tier\ntestbed comprising Stargate-based proxies and Mote-based sensors.\nOur implementation supports spatio-temporal, value, and\nrangebased queries on sensor data.\nFourth, we conduct a detailed experimental evaluation of TSAR\nusing a combination of EmStar/EmTOS [10] and our prototype.\nWhile our EmStar/EmTOS experiments focus on the scalability of\nTSAR in larger settings, our prototype evaluation involves latency\nand energy measurements in a real setting. Our results demonstrate\nthe logarithmic scaling property of the sparse skip graph and the\nlow latency of end-to-end queries in a duty-cycled multi-hop\nnetwork .\nThe remainder of this paper is structured as follows. Section 2\npresents key design issues that guide our work. Section 3 and 4\npresent the proxy-level index and the local archive and\nsummarization at a sensor, respectively. Section 5 discusses our prototype\nimplementation, and Section 6 presents our experimental results. We\npresent related work in Section 7 and our conclusions in Section 8.\n2. Design Considerations\nIn this section, we first describe the various components of a\nmulti-tier sensor network assumed in our work. We then present a\ndescription of the expected usage models for this system, followed\nby several principles addressing these factors which guide the\ndesign of our storage system.\n2.1 System Model\nWe envision a multi-tier sensor network comprising multiple tiers\n- a bottom tier of untethered remote sensor nodes, a middle tier of\ntethered sensor proxies, and an upper tier of applications and user\nterminals (see Figure 1).\nThe lowest tier is assumed to form a dense deployment of\nlowpower sensors. A canonical sensor node at this tier is equipped\nwith low-power sensors, a micro-controller, and a radio as well as\na significant amount of flash memory (e.g., 1GB). The common\nconstraint for this tier is energy, and the need for a long lifetime\nin spite of a finite energy constraint. The use of radio, processor,\nRAM, and the flash memory all consume energy, which needs to\nbe limited. In general, we assume radio communication to be\nsubstantially more expensive than accesses to flash memory.\nThe middle tier consists of power-rich sensor proxies that have\nsignificant computation, memory and storage resources and can use\n40\nTable 1: Characteristics of sensor storage systems\nSystem Data Index Reads Writes Order preserving\nCentralized store Centralized Centralized index Handled at store Send to store Yes\nLocal sensor store Fully distributed No index Flooding, diffusion Local No\nGHT/DCS [24] Fully distributed In-network index Hash to node Send to hashed node No\nTSAR/PRESTO Fully distributed Distributed index at proxies Proxy lookup + sensor query Local plus index update Yes\nUser\nUnified Logical Store\nQueries\n(time, space, value)\nQuery\nResponse\nCache\nQuery forwarding\nProxy\nRemote\nSensors\nLocal Data Archive\non Flash Memory\nInterval\nSkip Graph\nQuery\nforwarding\nsummaries\nstart index\nend index\nlinear\ntraversal\nQuery\nResponse\nCache-miss\ntriggered\nquery forwarding\nsummaries\nFigure 1: Architecture of a multi-tier sensor network.\nthese resources continuously. In urban environments, the proxy tier\nwould comprise a tethered base-station class nodes (e.g., Crossbow\nStargate), each with with multiple radios-an 802.11 radio that\nconnects it to a wireless mesh network and a low-power radio (e.g.\n802.15.4) that connects it to the sensor nodes. In remote sensing\napplications [10], this tier could comprise a similar Stargate node\nwith a solar power cell. Each proxy is assumed to manage several\ntens to hundreds of lower-tier sensors in its vicinity. A typical\nsensor network deployment will contain multiple geographically\ndistributed proxies. For instance, in a building monitoring application,\none sensor proxy might be placed per floor or hallway to monitor\ntemperature, heat and light sensors in their vicinity.\nAt the highest tier of our infrastructure are applications that query\nthe sensor network through a query interface[20]. In this work, we\nfocus on applications that require access to past sensor data. To\nsupport such queries, the system needs to archive data on a\npersistent store. Our goal is to design a storage system that exploits the\nrelative abundance of resources at proxies to mask the scarcity of\nresources at the sensors.\n2.2 Usage Models\nThe design of a storage system such as TSAR is affected by the\nqueries that are likely to be posed to it. A large fraction of queries\non sensor data can be expected to be spatio-temporal in nature.\nSensors provide information about the physical world; two key\nattributes of this information are when a particular event or activity\noccurred and where it occurred. Some instances of such queries\ninclude the time and location of target or intruder detections (e.g.,\nsecurity and monitoring applications), notifications of specific types\nof events such as pressure and humidity values exceeding a\nthreshold (e.g., industrial applications), or simple data collection queries\nwhich request data from a particular time or location (e.g., weather\nor environment monitoring).\nExpected queries of such data include those requesting ranges\nof one or more attributes; for instance, a query for all image data\nfrom cameras within a specified geographic area for a certain\nperiod of time. In addition, it is often desirable to support efficient\naccess to data in a way that maintains spatial and temporal\nordering. There are several ways of supporting range queries, such as\nlocality-preserving hashes such as are used in DIMS [18].\nHowever, the most straightforward mechanism, and one which naturally\nprovides efficient ordered access, is via the use of order-preserving\ndata structures. Order-preserving structures such as the well-known\nB-Tree maintain relationships between indexed values and thus\nallow natural access to ranges, as well as predecessor and successor\noperations on their key values.\nApplications may also pose value-based queries that involve\ndetermining if a value v was observed at any sensor; the query\nreturns a list of sensors and the times at which they observed this\nvalue. Variants of value queries involve restricting the query to a\ngeographical region, or specifying a range (v1, v2) rather than a\nsingle value v. Value queries can be handled by indexing on the\nvalues reported in the summaries. Specifically, if a sensor reports\na numerical value, then the index is constructed on these values. A\nsearch involves finding matching values that are either contained in\nthe search range (v1, v2) or match the search value v exactly.\nHybrid value and spatio-temporal queries are also possible. Such\nqueries specify a time interval, a value range and a spatial region\nand request all records that match these attributes - find all\ninstances where the temperature exceeded 100o\nF at location R\nduring the month of August. These queries require an index on both\ntime and value.\nIn TSAR our focus is on range queries on value or time, with\nplanned extensions to include spatial scoping.\n2.3 Design Principles\nOur design of a sensor storage system for multi-tier networks is\nbased on the following set of principles, which address the issues\narising from the system and usage models above.\n\u2022 Principle 1: Store locally, access globally: Current\ntechnology allows local storage to be significantly more\nenergyefficient than network communication, while technology\ntrends show no signs of erasing this gap in the near future.\nFor maximum network life a sensor storage system should\nleverage the flash memory on sensors to archive data locally,\nsubstituting cheap memory operations for expensive radio\ntransmission. But without efficient mechanisms for retrieval,\nthe energy gains of local storage may be outweighed by\ncommunication costs incurred by the application in searching for\ndata. We believe that if the data storage system provides\nthe abstraction of a single logical store to applications, as\n41\ndoes TSAR, then it will have additional flexibility to\noptimize communication and storage costs.\n\u2022 Principle 2: Distinguish data from metadata: Data must\nbe identified so that it may be retrieved by the application\nwithout exhaustive search. To do this, we associate\nmetadata with each data record - data fields of known syntax\nwhich serve as identifiers and may be queried by the storage\nsystem. Examples of this metadata are data attributes such as\nlocation and time, or selected or summarized data values. We\nleverage the presence of resource-rich proxies to index\nmetadata for resource-constrained sensors. The proxies share this\nmetadata index to provide a unified logical view of all data in\nthe system, thereby enabling efficient, low-latency lookups.\nSuch a tier-specific separation of data storage from metadata\nindexing enables the system to exploit the idiosyncrasies of\nmulti-tier networks, while improving performance and\nfunctionality.\n\u2022 Principle 3: Provide data-centric query support: In a sensor\napplication the specific location (i.e. offset) of a record in a\nstream is unlikely to be of significance, except if it conveys\ninformation concerning the location and/or time at which the\ninformation was generated. We thus expect that applications\nwill be best served by a query interface which allows them\nto locate data by value or attribute (e.g. location and time),\nrather than a read interface for unstructured data. This in turn\nimplies the need to maintain metadata in the form of an index\nthat provides low cost lookups.\n2.4 System Design\nTSAR embodies these design principles by employing local\nstorage at sensors and a distributed index at the proxies. The key\nfeatures of the system design are as follows:\nIn TSAR, writes occur at sensor nodes, and are assumed to\nconsist of both opaque data as well as application-specific metadata.\nThis metadata is a tuple of known types, which may be used by the\napplication to locate and identify data records, and which may be\nsearched on and compared by TSAR in the course of locating data\nfor the application. In a camera-based sensing application, for\ninstance, this metadata might include coordinates describing the field\nof view, average luminance, and motion values, in addition to basic\ninformation such as time and sensor location. Depending on the\napplication, this metadata may be two or three orders of magnitude\nsmaller than the data itself, for instance if the metadata consists of\nfeatures extracted from image or acoustic data.\nIn addition to storing data locally, each sensor periodically sends\na summary of reported metadata to a nearby proxy. The summary\ncontains information such as the sensor ID, the interval (t1, t2)\nover which the summary was generated, a handle identifying the\ncorresponding data record (e.g. its location in flash memory),\nand a coarse-grain representation of the metadata associated with\nthe record. The precise data representation used in the summary\nis application-specific; for instance, a temperature sensor might\nchoose to report the maximum and minimum temperature values\nobserved in an interval as a coarse-grain representation of the\nactual time series.\nThe proxy uses the summary to construct an index; the index\nis global in that it stores information from all sensors in the\nsystem and it is distributed across the various proxies in the system.\nThus, applications see a unified view of distributed data, and can\nquery the index at any proxy to get access to data stored at any\nsensor. Specifically, each query triggers lookups in this distributed\nindex and the list of matches is then used to retrieve the\ncorresponding data from the sensors. There are several distributed index and\nlookup methods which might be used in this system; however, the\nindex structure described in Section 3 is highly suited for the task.\nSince the index is constructed using a coarse-grain summary,\ninstead of the actual data, index lookups will yield approximate\nmatches. The TSAR summarization mechanism guarantees that\nindex lookups will never yield false negatives - i.e. it will never miss\nsummaries which include the value being searched for. However,\nindex lookups may yield false positives, where a summary matches\nthe query but when queried the remote sensor finds no matching\nvalue, wasting network resources. The more coarse-grained the\nsummary, the lower the update overhead and the greater the\nfraction of false positives, while finer summaries incur update overhead\nwhile reducing query overhead due to false positives. Remote\nsensors may easily distinguish false positives from queries which result\nin search hits, and calculate the ratio between the two; based on this\nratio, TSAR employs a novel adaptive technique that dynamically\nvaries the granularity of sensor summaries to balance the metadata\noverhead and the overhead of false positives.\n3. Data Structures\nAt the proxy tier, TSAR employs a novel index structure called\nthe Interval Skip Graph, which is an ordered, distributed data\nstructure for finding all intervals that contain a particular point or range\nof values. Interval skip graphs combine Interval Trees [5], an\ninterval-based binary search tree, with Skip Graphs [1], a ordered,\ndistributed data structure for peer-to-peer systems [13]. The\nresulting data structure has two properties that make it ideal for\nsensor networks. First, it has O(log n) search complexity for\naccessing the first interval that matches a particular value or range, and\nconstant complexity for accessing each successive interval.\nSecond, indexing of intervals rather than individual values makes the\ndata structure ideal for indexing summaries over time or value.\nSuch summary-based indexing is a more natural fit for\nenergyconstrained sensor nodes, since transmitting summaries incurs less\nenergy overhead than transmitting all sensor data.\nDefinitions: We assume that there are Np proxies and Ns\nsensors in a two-tier sensor network. Each proxy is responsible for\nmultiple sensor nodes, and no assumption is made about the\nnumber of sensors per proxy. Each sensor transmits interval summaries\nof data or events regularly to one or more proxies that it is\nassociated with, where interval i is represented as [lowi, highi]. These\nintervals can correspond to time or value ranges that are used for\nindexing sensor data. No assumption is made about the size of an\ninterval or about the amount of overlap between intervals.\nRange queries on the intervals are posed by users to the network\nof proxies and sensors; each query q needs to determine all index\nvalues that overlap the interval [lowq, highq]. The goal of the\ninterval skip graph is to index all intervals such that the set that overlaps\na query interval can be located efficiently. In the rest of this section,\nwe describe the interval skip graph in greater detail.\n3.1 Skip Graph Overview\nIn order to inform the description of the Interval Skip Graph, we\nfirst provide a brief overview of the Skip Graph data structure; for\na more extensive description the reader is referred to [1]. Figure 2\nshows a skip graph which indexes 8 keys; the keys may be seen\nalong the bottom, and above each key are the pointers associated\nwith that key. Each data element, consisting of a key and its\nassociated pointers, may reside on a different node in the network,\n42\n7 9 13 17 21 25 311\nlevel 0\nlevel 1\nlevel 2\nkey\nsingle skip graph element\n(each may be on different node)\nfind(21)\nnode-to-node messages\nFigure 2: Skip Graph of 8 Elements\n[6,14] [9,12] [14,16] [15,23] [18,19] [20,27] [21,30][2,5]\n5 14 14 16 23 23 27 30\n[low,high]\nmax\ncontains(13)\nmatch\nno\nmatch\nhalt\nFigure 3: Interval Skip Graph\n[6,14]\n[9,12]\n[14,16]\n[15,23]\n[18,19]\n[20,27]\n[21,30]\n[2,5]\nNode 1\nNode 2\nNode 3\nlevel 2\nlevel 1\nlevel 0\nFigure 4: Distributed Interval Skip Graph\nand pointers therefore identify both a remote node as well as a data\nelement on that node. In this figure we may see the following\nproperties of a skip graph:\n\u2022 Ordered index: The keys are members of an ordered data\ntype, for instance integers. Lookups make use of ordered\ncomparisons between the search key and existing index\nentries. In addition, the pointers at the lowest level point\ndirectly to the successor of each item in the index.\n\u2022 In-place indexing: Data elements remain on the nodes\nwhere they were inserted, and messages are sent between\nnodes to establish links between those elements and others\nin the index.\n\u2022 Log n height: There are log2 n pointers associated with each\nelement, where n is the number of data elements indexed.\nEach pointer belongs to a level l in [0... log2 n \u2212 1], and\ntogether with some other pointers at that level forms a chain\nof n/2l\nelements.\n\u2022 Probabilistic balance: Rather than relying on re-balancing\noperations which may be triggered at insert or delete, skip\ngraphs implement a simple random balancing mechanism\nwhich maintains close to perfect balance on average, with\nan extremely low probability of significant imbalance.\n\u2022 Redundancy and resiliency: Each data element forms an\nindependent search tree root, so searches may begin at any\nnode in the network, eliminating hot spots at a single search\nroot. In addition the index is resilient against node failure;\ndata on the failed node will not be accessible, but remaining\ndata elements will be accessible through search trees rooted\non other nodes.\nIn Figure 2 we see the process of searching for a particular value\nin a skip graph. The pointers reachable from a single data element\nform a binary tree: a pointer traversal at the highest level skips over\nn/2 elements, n/4 at the next level, and so on. Search consists\nof descending the tree from the highest level to level 0, at each\nlevel comparing the target key with the next element at that level\nand deciding whether or not to traverse. In the perfectly balanced\ncase shown here there are log2 n levels of pointers, and search will\ntraverse 0 or 1 pointers at each level. We assume that each data\nelement resides on a different node, and measure search cost by the\nnumber messages sent (i.e. the number of pointers traversed); this\nwill clearly be O(log n).\nTree update proceeds from the bottom, as in a B-Tree, with the\nroot(s) being promoted in level as the tree grows. In this way, for\ninstance, the two chains at level 1 always contain n/2 entries each,\nand there is never a need to split chains as the structure grows. The\nupdate process then consists of choosing which of the 2l\nchains to\ninsert an element into at each level l, and inserting it in the proper\nplace in each chain.\nMaintaining a perfectly balanced skip graph as shown in\nFigure 2 would be quite complex; instead, the probabilistic balancing\nmethod introduced in Skip Lists [23] is used, which trades off a\nsmall amount of overhead in the expected case in return for simple\nupdate and deletion. The basis for this method is the observation\nthat any element which belongs to a particular chain at level l can\nonly belong to one of two chains at level l+1. To insert an element\nwe ascend levels starting at 0, randomly choosing one of the two\npossible chains at each level, an stopping when we reach an empty\nchain.\nOne means of implementation (e.g. as described in [1]) is to\nassign each element an arbitrarily long random bit string. Each\nchain at level l is then constructed from those elements whose bit\nstrings match in the first l bits, thus creating 2l\npossible chains\nat each level and ensuring that each chain splits into exactly two\nchains at the next level. Although the resulting structure is not\nperfectly balanced, following the analysis in [23] we can show that\nthe probability of it being significantly out of balance is extremely\nsmall; in addition, since the structure is determined by the random\nnumber stream, input data patterns cannot cause the tree to become\nimbalanced.\n3.2 Interval Skip Graph\nA skip graph is designed to store single-valued entries. In this\nsection, we introduce a novel data structure that extends skip graphs\nto store intervals [lowi, highi] and allows efficient searches for all\nintervals covering a value v, i.e. {i : lowi \u2264 v \u2264 highi}. Our data\nstructure can be extended to range searches in a straightforward\nmanner.\nThe interval skip graph is constructed by applying the method of\naugmented search trees, as described by Cormen, Leiserson, and\nRivest [5] and applied to binary search trees to create an Interval\nTree. The method is based on the observation that a search structure\nbased on comparison of ordered keys, such as a binary tree, may\nalso be used to search on a secondary key which is non-decreasing\nin the first key.\nGiven a set of intervals sorted by lower bound - lowi \u2264\nlowi+1 - we define the secondary key as the cumulative maximum,\nmaxi = maxk=0...i (highk). The set of intervals intersecting a\nvalue v may then be found by searching for the first interval (and\nthus the interval with least lowi) such that maxi \u2265 v. We then\n43\ntraverse intervals in increasing order lower bound, until we find the\nfirst interval with lowi > v, selecting those intervals which\nintersect v.\nUsing this approach we augment the skip graph data structure, as\nshown in Figure 3, so that each entry stores a range (lower bound\nand upper bound) and a secondary key (cumulative maximum of\nupper bound). To efficiently calculate the secondary key maxi for\nan entry i, we take the greatest of highi and the maximum values\nreported by each of i\"s left-hand neighbors.\nTo search for those intervals containing the value v, we first\nsearch for v on the secondary index, maxi, and locate the first entry\nwith maxi \u2265 v. (by the definition of maxi, for this data element\nmaxi = highi.) If lowi > v, then this interval does not contain\nv, and no other intervals will, either, so we are done. Otherwise we\ntraverse the index in increasing order of mini, returning matching\nintervals, until we reach an entry with mini > v and we are done.\nSearches for all intervals which overlap a query range, or which\ncompletely contain a query range, are straightforward extensions\nof this mechanism.\nLookup Complexity: Lookup for the first interval that matches\na given value is performed in a manner very similar to an interval\ntree. The complexity of search is O(log n). The number of\nintervals that match a range query can vary depending on the amount of\noverlap in the intervals being indexed, as well as the range specified\nin the query.\nInsert Complexity: In an interval tree or interval skip list, the\nmaximum value for an entry need only be calculated over the\nsubtree rooted at that entry, as this value will be examined only when\nsearching within the subtree rooted at that entry. For a simple\ninterval skip graph, however, this maximum value for an entry must be\ncomputed over all entries preceding it in the index, as searches may\nbegin anywhere in the data structure, rather than at a distinguished\nroot element. It may be easily seen that in the worse case the\ninsertion of a single interval (one that covers all existing intervals in\nthe index) will trigger the update of all entries in the index, for a\nworst-case insertion cost of O(n).\n3.3 Sparse Interval Skip Graph\nThe final extensions we propose take advantage of the\ndifference between the number of items indexed in a skip graph and the\nnumber of systems on which these items are distributed. The cost\nin network messages of an operation may be reduced by\narranging the data structure so that most structure traversals occur locally\non a single node, and thus incur zero network cost. In addition,\nsince both congestion and failure occur on a per-node basis, we\nmay eliminate links without adverse consequences if those links\nonly contribute to load distribution and/or resiliency within a\nsingle node. These two modifications allow us to achieve reductions\nin asymptotic complexity of both update and search.\nAs may be in Section 3.2, insert and delete cost on an\ninterval skip graph has a worst case complexity of O(n), compared to\nO(log n) for an interval tree. The main reason for the difference\nis that skip graphs have a full search structure rooted at each\nelement, in order to distribute load and provide resilience to system\nfailures in a distributed setting. However, in order to provide load\ndistribution and failure resilience it is only necessary to provide a\nfull search structure for each system. If as in TSAR the number\nof nodes (proxies) is much smaller than the number of data\nelements (data summaries indexed), then this will result in significant\nsavings.\nImplementation: To construct a sparse interval skip graph, we\nensure that there is a single distinguished element on each system,\nthe root element for that system; all searches will start at one of\nthese root elements. When adding a new element, rather than\nsplitting lists at increasing levels l until the element is in a list with no\nothers, we stop when we find that the element would be in a list\ncontaining no root elements, thus ensuring that the element is reachable\nfrom all root elements. An example of applying this optimization\nmay be seen in Figure 5. (In practice, rather than designating\nexisting data elements as roots, as shown, it may be preferable to insert\nnull values at startup.)\nWhen using the technique of membership vectors as in [1], this\nmay be done by broadcasting the membership vectors of each root\nelement to all other systems, and stopping insertion of an element\nat level l when it does not share an l-bit prefix with any of the Np\nroot elements. The expected number of roots sharing a log2Np-bit\nprefix is 1, giving an expected expected height for each element of\nlog2Np +O(1). An alternate implementation, which distributes\ninformation concerning root elements at pointer establishment time,\nis omitted due to space constraints; this method eliminates the need\nfor additional messages.\nPerformance: In a (non-interval) sparse skip graph, since the\nexpected height of an inserted element is now log2 Np + O(1),\nexpected insertion complexity is O(log Np), rather than O(log n),\nwhere Np is the number of root elements and thus the number of\nseparate systems in the network. (In the degenerate case of a\nsingle system we have a skip list; with splitting probability 0.5 the\nexpected height of an individual element is 1.) Note that since\nsearches are started at root elements of expected height log2 n,\nsearch complexity is not improved.\nFor an interval sparse skip graph, update performance is\nimproved considerably compared to the O(n) worst case for the\nnonsparse case. In an augmented search structure such as this, an\nelement only stores information for nodes which may be reached from\nthat element-e.g. the subtree rooted at that element, in the case of\na tree. Thus, when updating the maximum value in an interval tree,\nthe update is only propagated towards the root. In a sparse interval\nskip graph, updates to a node only propagate towards the Np root\nelements, for a worst-case cost of Np log2 n.\nShortcut search: When beginning a search for a value v, rather\nthan beginning at the root on that proxy, we can find the element\nthat is closest to v (e.g. using a secondary local index), and then\nbegin the search at that element. The expected distance between\nthis element and the search terminus is log2 Np, and the search\nwill now take on average log2 Np + O(1) steps. To illustrate this\noptimization, in Figure 4 depending on the choice of search root, a\nsearch for [21, 30] beginning at node 2 may take 3 network hops,\ntraversing to node 1, then back to node 2, and finally to node 3\nwhere the destination is located, for a cost of 3 messages. The\nshortcut search, however, locates the intermediate data element on\nnode 2, and then proceeds directly to node 3 for a cost of 1 message.\nPerformance: This technique may be applied to the primary key\nsearch which is the first of two insertion steps in an interval skip\ngraph. By combining the short-cut optimization with sparse\ninterval skip graphs, the expected cost of insertion is now O(log Np),\nindependent of the size of the index or the degree of overlap of the\ninserted intervals.\n3.4 Alternative Data Structures\nThus far we have only compared the sparse interval skip graph\nwith similar structures from which it is derived. A comparison with\nseveral other data structures which meet at least some of the\nrequirements for the TSAR index is shown in Table 2.\n44\nTable 2: Comparison of Distributed Index Structures\nRange Query Support Interval Representation Re-balancing Resilience Small Networks Large Networks\nDHT, GHT no no no yes good good\nLocal index, flood query yes yes no yes good bad\nP-tree, RP* (distributed B-Trees) yes possible yes no good good\nDIMS yes no yes yes yes yes\nInterval Skipgraph yes yes no yes good good\n[6,14] [9,12] [14,16] [15,23] [18,19] [20,27] [21,30][2,5]\nRoots Node 1\nNode 2\nFigure 5: Sparse Interval Skip Graph\nThe hash-based systems, DHT [25] and GHT [26], lack the\nability to perform range queries and are thus not well-suited to indexing\nspatio-temporal data. Indexing locally using an appropriate\nsinglenode structure and then flooding queries to all proxies is a\ncompetitive alternative for small networks; for large networks the linear\ndependence on the number of proxies becomes an issue. Two\ndistributed B-Trees were examined - P-Trees [6] and RP* [19]. Each\nof these supports range queries, and in theory could be modified\nto support indexing of intervals; however, they both require\ncomplex re-balancing, and do not provide the resilience characteristics\nof the other structures. DIMS [18] provides the ability to perform\nspatio-temporal range queries, and has the necessary resilience to\nfailures; however, it cannot be used index intervals, which are used\nby TSAR\"s data summarization algorithm.\n4. Data Storage and Summarization\nHaving described the proxy-level index structure, we turn to the\nmechanisms at the sensor tier. TSAR implements two key\nmechanisms at the sensor tier. The first is a local archival store at each\nsensor node that is optimized for resource-constrained devices. The\nsecond is an adaptive summarization technique that enables each\nsensor to adapt to changing data and query characteristics. The rest\nof this section describes these mechanisms in detail.\n4.1 Local Storage at Sensors\nInterval skip graphs provide an efficient mechanism to lookup\nsensor nodes containing data relevant to a query. These queries are\nthen routed to the sensors, which locate the relevant data records\nin the local archive and respond back to the proxy. To enable such\nlookups, each sensor node in TSAR maintains an archival store of\nsensor data. While the implementation of such an archival store\nis straightforward on resource-rich devices that can run a database,\nsensors are often power and resource-constrained. Consequently,\nthe sensor archiving subsystem in TSAR is explicitly designed to\nexploit characteristics of sensor data in a resource-constrained\nsetting.\nTimestamp\nCalibration\nParameters\nOpaque DataData/Event Attributes size\nFigure 6: Single storage record\nSensor data has very distinct characteristics that inform our\ndesign of the TSAR archival store. Sensors produce time-series data\nstreams, and therefore, temporal ordering of data is a natural and\nsimple way of storing archived sensor data. In addition to\nsimplicity, a temporally ordered store is often suitable for many sensor data\nprocessing tasks since they involve time-series data processing.\nExamples include signal processing operations such as FFT, wavelet\ntransforms, clustering, similarity matching, and target detection.\nConsequently, the local archival store is a collection of records,\ndesigned as an append-only circular buffer, where new records are\nappended to the tail of the buffer. The format of each data record is\nshown in Figure 6. Each record has a metadata field which includes\na timestamp, sensor settings, calibration parameters, etc. Raw\nsensor data is stored in the data field of the record. The data field\nis opaque and application-specific-the storage system does not\nknow or care about interpreting this field. A camera-based sensor,\nfor instance, may store binary images in this data field. In order\nto support a variety of applications, TSAR supports variable-length\ndata fields; as a result, record sizes can vary from one record to\nanother.\nOur archival store supports three operations on records: create,\nread, and delete. Due to the append-only nature of the store,\ncreation of records is simple and efficient. The create operation simply\ncreates a new record and appends it to the tail of the store. Since\nrecords are always written at the tail, the store need not maintain\na free space list. All fields of the record need to be specified at\ncreation time; thus, the size of the record is known a priori and the\nstore simply allocates the the corresponding number of bytes at the\ntail to store the record. Since writes are immutable, the size of a\nrecord does not change once it is created.\nproxy\nproxy\nproxy\nrecord\n3 record\nsummary\nlocal archive in\nflash memory\ndata summary\nstart,end offset\ntime interval\nsensor\nsummary\nsent to proxy\nInsert summaries\ninto interval skip graph\nFigure 7: Sensor Summarization\n45\nThe read operation enables stored records to be retrieved in\norder to answer queries. In a traditional database system, efficient\nlookups are enabled by maintaining a structure such as a B-tree that\nindexes certain keys of the records. However, this can be quite\ncomplex for a small sensor node with limited resources. Consequently,\nTSAR sensors do not maintain any index for the data stored in their\narchive. Instead, they rely on the proxies to maintain this metadata\nindex-sensors periodically send the proxy information\nsummarizing the data contained in a contiguous sequence of records, as well\nas a handle indicating the location of these records in flash memory.\nThe mechanism works as follows: In addition to the summary\nof sensor data, each node sends metadata to the proxy containing\nthe time interval corresponding to the summary, as well as the start\nand end offsets of the flash memory location where the raw data\ncorresponding is stored (as shown in Figure 7). Thus, random\naccess is enabled at granularity of a summary-the start offset of each\nchunk of records represented by a summary is known to the proxy.\nWithin this collection, records are accessed sequentially. When a\nquery matches a summary in the index, the sensor uses these offsets\nto access the relevant records on its local flash by sequentially\nreading data from the start address until the end address. Any\nqueryspecific operation can then be performed on this data. Thus, no\nindex needs to be maintained at the sensor, in line with our goal\nof simplifying sensor state management. The state of the archive\nis captured in the metadata associated with the summaries, and is\nstored and maintained at the proxy.\nWhile we anticipate local storage capacity to be large, eventually\nthere might be a need to overwrite older data, especially in high\ndata rate applications. This may be done via techniques such as\nmulti-resolution storage of data [9], or just simply by overwriting\nolder data. When older data is overwritten, a delete operation is\nperformed, where an index entry is deleted from the interval skip\ngraph at the proxy and the corresponding storage space in flash\nmemory at the sensor is freed.\n4.2 Adaptive Summarization\nThe data summaries serve as glue between the storage at the\nremote sensor and the index at the proxy. Each update from a sensor\nto the proxy includes three pieces of information: the summary, a\ntime period corresponding to the summary, and the start and end\noffsets for the flash archive. In general, the proxy can index the\ntime interval representing a summary or the value range reported\nin the summary (or both). The former index enables quick lookups\non all records seen during a certain interval, while the latter index\nenables quick lookups on all records matching a certain value.\nAs described in Section 2.4, there is a trade-off between the\nenergy used in sending summaries (and thus the frequency and\nresolution of those summaries) and the cost of false hits during queries.\nThe coarser and less frequent the summary information, the less\nenergy required, while false query hits in turn waste energy on\nrequests for non-existent data.\nTSAR employs an adaptive summarization technique that\nbalances the cost of sending updates against the cost of false positives.\nThe key intuition is that each sensor can independently identify the\nfraction of false hits and true hits for queries that access its local\narchive. If most queries result in true hits, then the sensor\ndetermines that the summary can be coarsened further to reduce update\ncosts without adversely impacting the hit ratio. If many queries\nresult in false hits, then the sensor makes the granularity of each\nsummary finer to reduce the number and overhead of false hits.\nThe resolution of the summary depends on two\nparametersthe interval over which summaries of the data are constructed and\ntransmitted to the proxy, as well as the size of the\napplicationspecific summary. Our focus in this paper is on the interval over\nwhich the summary is constructed. Changing the size of the data\nsummary can be performed in an application-specific manner (e.g.\nusing wavelet compression techniques as in [9]) and is beyond the\nscope of this paper. Currently, TSAR employs a simple\nsummarization scheme that computes the ratio of false and true hits and\ndecreases (increases) the interval between summaries whenever this\nratio increases (decreases) beyond a threshold.\n5. TSAR Implementation\nWe have implemented a prototype of TSAR on a multi-tier\nsensor network testbed. Our prototype employs Crossbow Stargate\nnodes to implement the proxy tier. Each Stargate node employs a\n400MHz Intel XScale processor with 64MB RAM and runs the\nLinux 2.4.19 kernel and EmStar release 2.1. The proxy nodes\nare equipped with two wireless radios, a Cisco Aironet 340-based\n802.11b radio and a hostmote bridge to the Mica2 sensor nodes\nusing the EmStar transceiver. The 802.11b wireless network is\nused for inter-proxy communication within the proxy tier, while\nthe wireless bridge enables sensor-proxy communication. The\nsensor tier consists of Crossbow Mica2s and Mica2dots, each\nconsisting of a 915MHz CC1000 radio, a BMAC protocol stack, a 4 Mb\non-board flash memory and an ATMega 128L processor. The\nsensor nodes run TinyOS 1.1.8. In addition to the on-board flash, the\nsensor nodes can be equipped with external MMC/SD flash cards\nusing a custom connector. The proxy nodes can be equipped with\nexternal storage such as high-capacity compact flash (up to 4GB),\n6GB micro-drives, or up to 60GB 1.8inch mobile disk drives.\nSince sensor nodes may be several hops away from the nearest\nproxy, the sensor tier employs multi-hop routing to communicate\nwith the proxy tier. In addition, to reduce the power consumption\nof the radio while still making the sensor node available for queries,\nlow power listening is enabled, in which the radio receiver is\nperiodically powered up for a short interval to sense the channel for\ntransmissions, and the packet preamble is extended to account for\nthe latency until the next interval when the receiving radio wakes\nup. Our prototype employs the MultiHopLEPSM routing protocol\nwith the BMAC layer configured in the low-power mode with a\n11% duty cycle (one of the default BMAC [22] parameters)\nOur TSAR implementation on the Mote involves a data\ngathering task that periodically obtains sensor readings and logs these\nreading to flash memory. The flash memory is assumed to be a\ncircular append-only store and the format of the logged data is\ndepicted in Figure 6. The Mote sends a report to the proxy every N\nreadings, summarizing the observed data. The report contains: (i)\nthe address of the Mote, (ii) a handle that contains an offset and the\nlength of the region in flash memory containing data referred to by\nthe summary, (iii) an interval (t1, t2) over which this report is\ngenerated, (iv) a tuple (low, high) representing the minimum and the\nmaximum values observed at the sensor in the interval, and (v) a\nsequence number. The sensor updates are used to construct a sparse\ninterval skip graph that is distributed across proxies, via network\nmessages between proxies over the 802.11b wireless network.\nOur current implementation supports queries that request records\nmatching a time interval (t1, t2) or a value range (v1, v2). Spatial\nconstraints are specified using sensor IDs. Given a list of matching\nintervals from the skip graph, TSAR supports two types of\nmessages to query the sensor: lookup and fetch. A lookup message\ntriggers a search within the corresponding region in flash memory\nand returns the number of matching records in that memory region\n(but does not retrieve data). In contrast, a fetch message not only\n46\n0\n10\n20\n30\n40\n50\n60\n70\n80\n128512 1024 2048 4096\nNumberofMessages\nIndex size (entries)\nInsert (skipgraph)\nInsert (sparse skipgraph)\nInitial lookup\n(a) James Reserve Data\n0\n10\n20\n30\n40\n50\n60\n70\n80\n512 1024 2048 4096\nNumberofMessages\nIndex size (entries)\nInsert (skipgraph)\nInsert (sparse skipgraph)\nInitial lookup\n(b) Synthetic Data\nFigure 8: Skip Graph Insert Performance\ntriggers a search but also returns all matching data records to the\nproxy. Lookup messages are useful for polling a sensor, for\ninstance, to determine if a query matches too many records.\n6. Experimental Evaluation\nIn this section, we evaluate the efficacy of TSAR using our\nprototype and simulations. The testbed for our experiments consists\nof four Stargate proxies and twelve Mica2 and Mica2dot sensors;\nthree sensors each are assigned to each proxy. Given the limited\nsize of our testbed, we employ simulations to evaluate the\nbehavior of TSAR in larger settings. Our simulation employs the EmTOS\nemulator [10], which enables us to run the same code in simulation\nand the hardware platform.\nRather than using live data from a real sensor, to ensure\nrepeatable experiments, we seed each sensor node with a dataset\n(i.e., a trace) that dictates the values reported by that node to the\nproxy. One section of the flash memory on each sensor node is\nprogrammed with data points from the trace; these observations\nare then replayed during an experiment, logged to the local archive\n(located in flash memory, as well), and reported to the proxy. The\nfirst dataset used to evaluate TSAR is a temperature dataset from\nJames Reserve [27] that includes data from eleven temperature\nsensor nodes over a period of 34 days. The second dataset is\nsynthetically generated; the trace for each sensor is generated using a\nuniformly distributed random walk though the value space.\nOur experimental evaluation has four parts. First, we run\nEmTOS simulations to evaluate the lookup, update and delete overhead\nfor sparse interval skip graphs using the real and synthetic datasets.\nSecond, we provide summary results from micro-benchmarks of\nthe storage component of TSAR, which include empirical\ncharacterization of the energy costs and latency of reads and writes for the\nflash memory chip as well as the whole mote platform, and\ncomparisons to published numbers for other storage and\ncommunication technologies. These micro-benchmarks form the basis for our\nfull-scale evaluation of TSAR on a testbed of four Stargate proxies\nand twelve Motes. We measure the end-to-end query latency in our\nmulti-hop testbed as well as the query processing overhead at the\nmote tier. Finally, we demonstrate the adaptive summarization\ncapability at each sensor node. The remainder of this section presents\nour experimental results.\n6.1 Sparse Interval Skip Graph Performance\nThis section evaluates the performance of sparse interval skip\ngraphs by quantifying insert, lookup and delete overheads.\nWe assume a proxy tier with 32 proxies and construct sparse\ninterval skip graphs of various sizes using our datasets. For each skip\n0\n5\n10\n15\n20\n25\n30\n35\n409620481024512\nNumberofMessages\nIndex size (entries)\nInitial lookup\nTraversal\n(a) James Reserve Data\n0\n2\n4\n6\n8\n10\n12\n14\n409620481024512\nNumberofMessages\nIndex size (entries)\nInitial lookup\nTraversal\n(b) Synthetic Data\nFigure 9: Skip Graph Lookup Performance\n0\n10\n20\n30\n40\n50\n60\n70\n1 4 8 16 24 32 48\nNumberofmessages\nNumber of proxies\nSkipgraph insert\nSparse skipgraph insert\nInitial lookup\n(a) Impact of Number of\nProxies\n0\n20\n40\n60\n80\n100\n120\n512 1024 2048 4096\nNumberofMessages\nIndex size (entries)\nInsert (redundant)\nInsert (non-redundant)\nLookup (redundant)\nLookup (non-redundant)\n(b) Impact of Redundant\nSummaries\nFigure 10: Skip Graph Overheads\ngraph, we evaluate the cost of inserting a new value into the index.\nEach entry was deleted after its insertion, enabling us to quantify\nthe delete overhead as well. Figure 8(a) and (b) quantify the insert\noverhead for our two datasets: each insert entails an initial traversal\nthat incurs log n messages, followed by neighbor pointer update at\nincreasing levels, incurring a cost of 4 log n messages. Our results\ndemonstrate this behavior, and show as well that performance of\ndelete-which also involves an initial traversal followed by pointer\nupdates at each level-incurs a similar cost.\nNext, we evaluate the lookup performance of the index\nstructure. Again, we construct skip graphs of various sizes using our\ndatasets and evaluate the cost of a lookup on the index structure.\nFigures 9(a) and (b) depict our results. There are two components\nfor each lookup-the lookup of the first interval that matches the\nquery and, in the case of overlapping intervals, the subsequent\nlinear traversal to identify all matching intervals. The initial lookup\ncan be seen to takes log n messages, as expected. The costs of\nthe subsequent linear traversal, however, are highly data dependent.\nFor instance, temperature values for the James Reserve data exhibit\nsignificant spatial correlations, resulting in significant overlap\nbetween different intervals and variable, high traversal cost (see\nFigure 9(a)). The synthetic data, however, has less overlap and incurs\nlower traversal overhead as shown in Figure 9(b).\nSince the previous experiments assumed 32 proxies, we evaluate\nthe impact of the number of proxies on skip graph performance. We\nvary the number of proxies from 10 to 48 and distribute a skip graph\nwith 4096 entries among these proxies. We construct regular\ninterval skip graphs as well as sparse interval skip graphs using these\nentries and measure the overhead of inserts and lookups. Thus, the\nexperiment also seeks to demonstrate the benefits of sparse skip\ngraphs over regular skip graphs. Figure 10(a) depicts our results.\nIn regular skip graphs, the complexity of insert is O(log2n) in the\n47\nexpected case (and O(n) in the worst case) where n is the number\nof elements. This complexity is unaffected by changing the\nnumber of proxies, as indicated by the flat line in the figure. Sparse\nskip graphs require fewer pointer updates; however, their overhead\nis dependent on the number of proxies, and is O(log2Np) in the\nexpected case, independent of n. This can be seen to result in\nsignificant reduction in overhead when the number of proxies is small,\nwhich decreases as the number of proxies increases.\nFailure handling is an important issue in a multi-tier sensor\narchitecture since it relies on many components-proxies, sensor nodes\nand routing nodes can fail, and wireless links can fade. Handling\nof many of these failure modes is outside the scope of this\npaper; however, we consider the case of resilience of skip graphs\nto proxy failures. In this case, skip graph search (and subsequent\nrepair operations) can follow any one of the other links from a\nroot element. Since a sparse skip graph has search trees rooted\nat each node, searching can then resume once the lookup request\nhas routed around the failure. Together, these two properties\nensure that even if a proxy fails, the remaining entries in the skip\ngraph will be reachable with high probability-only the entries on\nthe failed proxy and the corresponding data at the sensors becomes\ninaccessible.\nTo ensure that all data on sensors remains accessible, even in the\nevent of failure of a proxy holding index entries for that data, we\nincorporate redundant index entries. TSAR employs a simple\nredundancy scheme where additional coarse-grain summaries are used\nto protect regular summaries. Each sensor sends summary data\nperiodically to its local proxy, but less frequently sends a\nlowerresolution summary to a backup proxy-the backup summary\nrepresents all of the data represented by the finer-grained summaries,\nbut in a lossier fashion, thus resulting in higher read overhead (due\nto false hits) if the backup summary is used. The cost of\nimplementing this in our system is low - Figure 10(b) shows the overhead of\nsuch a redundancy scheme, where a single coarse summary is send\nto a backup for every two summaries sent to the primary proxy.\nSince a redundant summary is sent for every two summaries, the\ninsert cost is 1.5 times the cost in the normal case. However, these\nredundant entries result in only a negligible increase in lookup\noverhead, due the logarithmic dependence of lookup cost on the index\nsize, while providing full resilience to any single proxy failure.\n6.2 Storage Microbenchmarks\nSince sensors are resource-constrained, the energy consumption\nand the latency at this tier are important measures for evaluating the\nperformance of a storage architecture. Before performing an\nendto-end evaluation of our system, we provide more detailed\ninformation on the energy consumption of the storage component used\nto implement the TSAR local archive, based on empirical\nmeasurements. In addition we compare these figures to those for other\nlocal storage technologies, as well as to the energy consumption of\nwireless communication, using information from the literature. For\nempirical measurements we measure energy usage for the storage\ncomponent itself (i.e. current drawn by the flash chip), as well as\nfor the entire Mica2 mote.\nThe power measurements in Table 3 were performed for the\nAT45DB041 [15] flash memory on a Mica2 mote, which is an older\nNOR flash device. The most promising technology for low-energy\nstorage on sensing devices is NAND flash, such as the Samsung\nK9K4G08U0M device [16]; published power numbers for this\ndevice are provided in the table. Published energy requirements for\nwireless transmission using the Chipcon [4] CC2420 radio (used\nin MicaZ and Telos motes) are provided for comparison, assuming\nEnergy Energy/byte\nMote flash\nRead 256 byte page 58\u00b5J* /\n136\u00b5J* total\n0.23\u00b5J*\nWrite 256 byte page 926\u00b5J* /\n1042\u00b5J* total\n3.6\u00b5J*\nNAND Flash\nRead 512 byte page 2.7\u00b5J 1.8nJ\nWrite 512 byte page 7.8\u00b5J 15nJ\nErase 16K byte sector 60\u00b5J 3.7nJ\nCC2420 radio\nTransmit 8 bits\n(-25dBm)\n0.8\u00b5J 0.8\u00b5J\nReceive 8 bits 1.9\u00b5J 1.9\u00b5J\nMote AVR processor\nIn-memory search,\n256 bytes\n1.8\u00b5J 6.9nJ\nTable 3: Storage and Communication Energy Costs (*measured\nvalues)\n0\n200\n400\n600\n800\n1000\n1 2 3\nLatency(ms)\nNumber of hops\n(a) Multi-hop query\nperformance\n0\n100\n200\n300\n400\n500\n1 5121024 2048 4096\nLatency(ms)\nIndex size (entries)\nSensor communication\nProxy communication\nSensor lookup, processing\n(b) Query Performance\nFigure 11: Query Processing Latency\nzero network and protocol overhead. Comparing the total energy\ncost for writing flash (erase + write) to the total cost for\ncommunication (transmit + receive), we find that the NAND flash is almost\n150 times more efficient than radio communication, even assuming\nperfect network protocols.\n6.3 Prototype Evaluation\nThis section reports results from an end-to-end evaluation of the\nTSAR prototype involving both tiers. In our setup, there are four\nproxies connected via 802.11 links and three sensors per proxy. The\nmulti-hop topology was preconfigured such that sensor nodes were\nconnected in a line to each proxy, forming a minimal tree of depth\n0\n400\n800\n1200\n1600\n0 20 40 60 80 100 120 140 160\nRetrievallatency(ms)\nArchived data retrieved (bytes)\n(a) Data Query and Fetch\nTime\n0\n2\n4\n6\n8\n10\n12 4 8 16 32\nLatency(ms)\nNumber of 34-byte records searched\n(b) Sensor query\nprocessing delay\nFigure 12: Query Latency Components\n48\n3. Due to resource constraints we were unable to perform\nexperiments with dozens of sensor nodes, however this topology ensured\nthat the network diameter was as large as for a typical network of\nsignificantly larger size.\nOur evaluation metric is the end-to-end latency of query\nprocessing. A query posed on TSAR first incurs the latency of a sparse\nskip graph lookup, followed by routing to the appropriate sensor\nnode(s). The sensor node reads the required page(s) from its local\narchive, processes the query on the page that is read, and transmits\nthe response to the proxy, which then forwards it to the user. We\nfirst measure query latency for different sensors in our multi-hop\ntopology. Depending on which of the sensors is queried, the total\nlatency increases almost linearly from about 400ms to 1 second, as\nthe number of hops increases from 1 to 3 (see Figure 11(a)).\nFigure 11(b) provides a breakdown of the various components\nof the end-to-end latency. The dominant component of the total\nlatency is the communication over one or more hops. The\ntypical time to communicate over one hop is approximately 300ms.\nThis large latency is primarily due to the use of a duty-cycled MAC\nlayer; the latency will be larger if the duty cycle is reduced (e.g.\nthe 2% setting as opposed to the 11.5% setting used in this\nexperiment), and will conversely decrease if the duty cycle is increased.\nThe figure also shows the latency for varying index sizes; as\nexpected, the latency of inter-proxy communication and skip graph\nlookups increases logarithmically with index size. Not surprisingly,\nthe overhead seen at the sensor is independent of the index size.\nThe latency also depends on the number of packets transmitted\nin response to a query-the larger the amount of data retrieved by a\nquery, the greater the latency. This result is shown in Figure 12(a).\nThe step function is due to packetization in TinyOS; TinyOS sends\none packet so long as the payload is smaller than 30 bytes and splits\nthe response into multiple packets for larger payloads. As the data\nretrieved by a query is increased, the latency increases in steps,\nwhere each step denotes the overhead of an additional packet.\nFinally, Figure 12(b) shows the impact of searching and\nprocessing flash memory regions of increasing sizes on a sensor. Each\nsummary represents a collection of records in flash memory, and\nall of these records need to be retrieved and processed if that\nsummary matches a query. The coarser the summary, the larger the\nmemory region that needs to be accessed. For the search sizes\nexamined, amortization of overhead when searching multiple flash\npages and archival records, as well as within the flash chip and its\nassociated driver, results in the appearance of sub-linear increase\nin latency with search size. In addition, the operation can be seen\nto have very low latency, in part due to the simplicity of our query\nprocessing, requiring only a compare operation with each stored\nelement. More complex operations, however, will of course incur\ngreater latency.\n6.4 Adaptive Summarization\nWhen data is summarized by the sensor before being reported\nto the proxy, information is lost. With the interval summarization\nmethod we are using, this information loss will never cause the\nproxy to believe that a sensor node does not hold a value which it in\nfact does, as all archived values will be contained within the interval\nreported. However, it does cause the proxy to believe that the sensor\nmay hold values which it does not, and forward query messages to\nthe sensor for these values. These false positives constitute the cost\nof the summarization mechanism, and need to be balanced against\nthe savings achieved by reducing the number of reports. The goal\nof adaptive summarization is to dynamically vary the summary size\nso that these two costs are balanced.\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0 5 10 15 20 25 30\nFractionoftruehits\nSummary size (number of records)\n(a) Impact of summary\nsize\n0\n5\n10\n15\n20\n25\n30\n35\n0 5000 10000 15000 20000 25000 30000\nSummarizationsize(num.records)\nNormalized time (units)\nquery rate 0.2\nquery rate 0.03\nquery rate 0.1\n(b) Adaptation to query\nrate\nFigure 13: Impact of Summarization Granularity\nFigure 13(a) demonstrates the impact of summary granularity\non false hits. As the number of records included in a summary\nis increased, the fraction of queries forwarded to the sensor which\nmatch data held on that sensor (true positives) decreases. Next,\nin Figure 13(b) we run the a EmTOS simulation with our\nadaptive summarization algorithm enabled. The adaptive algorithm\nincreases the summary granularity (defined as the number of records\nper summary) when Cost(updates)\nCost(falsehits)\n> 1 + and reduces it if\nCost(updates)\nCost(falsehits)\n> 1 \u2212 , where is a small constant. To\ndemonstrate the adaptive nature of our technique, we plot a time series\nof the summarization granularity. We begin with a query rate of 1\nquery per 5 samples, decrease it to 1 every 30 samples, and then\nincrease it again to 1 query every 10 samples. As shown in\nFigure 13(b), the adaptive technique adjusts accordingly by sending\nmore fine-grain summaries at higher query rates (in response to the\nhigher false hit rate), and fewer, coarse-grain summaries at lower\nquery rates.\n7. Related Work\nIn this section, we review prior work on storage and indexing\ntechniques for sensor networks. While our work addresses both\nproblems jointly, much prior work has considered them in isolation.\nThe problem of archival storage of sensor data has received\nlimited attention in sensor network literature. ELF [7] is a\nlogstructured file system for local storage on flash memory that\nprovides load leveling and Matchbox is a simple file system that is\npackaged with the TinyOS distribution [14]. Both these systems\nfocus on local storage, whereas our focus is both on storage at the\nremote sensors as well as providing a unified view of distributed\ndata across all such local archives. Multi-resolution storage [9] is\nintended for in-network storage and search in systems where there\nis significant data in comparison to storage resources. In contrast,\nTSAR addresses the problem of archival storage in two-tier systems\nwhere sufficient resources can be placed at the edge sensors. The\nRISE platform [21] being developed as part of the NODE project\nat UCR addresses the issues of hardware platform support for large\namounts of storage in remote sensor nodes, but not the indexing\nand querying of this data.\nIn order to efficiently access a distributed sensor store, an index\nneeds to be constructed of the data. Early work on sensor networks\nsuch as Directed Diffusion [17] assumes a system where all useful\nsensor data was stored locally at each sensor, and spatially scoped\nqueries are routed using geographic co-ordinates to locations where\nthe data is stored. Sources publish the events that they detect, and\nsinks with interest in specific events can subscribe to these events.\nThe Directed Diffusion substrate routes queries to specific locations\n49\nif the query has geographic information embedded in it (e.g.: find\ntemperature in the south-west quadrant), and if not, the query is\nflooded throughout the network.\nThese schemes had the drawback that for queries that are not\ngeographically scoped, search cost (O(n) for a network of n nodes)\nmay be prohibitive in large networks with frequent queries.\nLocal storage with in-network indexing approaches address this\nissue by constructing indexes using frameworks such as Geographic\nHash Tables [24] and Quad Trees [9]. Recent research has seen\na growing body of work on data indexing schemes for sensor\nnetworks[26][11][18]. One such scheme is DCS [26], which provides\na hash function for mapping from event name to location. DCS\nconstructs a distributed structure that groups events together\nspatially by their named type. Distributed Index of Features in\nSensornets (DIFS [11]) and Multi-dimensional Range Queries in Sensor\nNetworks (DIM [18]) extend the data-centric storage approach to\nprovide spatially distributed hierarchies of indexes to data.\nWhile these approaches advocate in-network indexing for sensor\nnetworks, we believe that indexing is a task that is far too\ncomplicated to be performed at the remote sensor nodes since it involves\nmaintaining significant state and large tables. TSAR provides a\nbetter match between resource requirements of storage and indexing\nand the availability of resources at different tiers. Thus complex\noperations such as indexing and managing metadata are performed\nat the proxies, while storage at the sensor remains simple.\nIn addition to storage and indexing techniques specific to sensor\nnetworks, many distributed, peer-to-peer and spatio-temporal index\nstructures are relevant to our work. DHTs [25] can be used for\nindexing events based on their type, quad-tree variants such as\nRtrees [12] can be used for optimizing spatial searches, and K-D\ntrees [2] can be used for multi-attribute search. While this paper\nfocuses on building an ordered index structure for range queries, we\nwill explore the use of other index structures for alternate queries\nover sensor data.\n8. Conclusions\nIn this paper, we argued that existing sensor storage systems\nare designed primarily for flat hierarchies of homogeneous sensor\nnodes and do not fully exploit the multi-tier nature of emerging\nsensor networks. We presented the design of TSAR, a fundamentally\ndifferent storage architecture that envisions separation of data from\nmetadata by employing local storage at the sensors and distributed\nindexing at the proxies. At the proxy tier, TSAR employs a novel\nmulti-resolution ordered distributed index structure, the Sparse\nInterval Skip Graph, for efficiently supporting spatio-temporal and\nrange queries. At the sensor tier, TSAR supports energy-aware\nadaptive summarization that can trade-off the energy cost of\ntransmitting metadata to the proxies against the overhead of false hits\nresulting from querying a coarser resolution index structure. We\nimplemented TSAR in a two-tier sensor testbed comprising\nStargatebased proxies and Mote-based sensors. Our experimental\nevaluation of TSAR demonstrated the benefits and feasibility of\nemploying our energy-efficient low-latency distributed storage architecture\nin multi-tier sensor networks.\n9. REFERENCES\n[1] James Aspnes and Gauri Shah. Skip graphs. In Fourteenth Annual ACM-SIAM\nSymposium on Discrete Algorithms, pages 384-393, Baltimore, MD, USA,\n12-14 January 2003.\n[2] Jon Louis Bentley. Multidimensional binary search trees used for associative\nsearching. Commun. ACM, 18(9):509-517, 1975.\n[3] Philippe Bonnet, J. E. Gehrke, and Praveen Seshadri. Towards sensor database\nsystems. In Proceedings of the Second International Conference on Mobile\nData Management., January 2001.\n[4] Chipcon. CC2420 2.4 GHz IEEE 802.15.4 / ZigBee-ready RF transceiver, 2004.\n[5] Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein.\nIntroduction to Algorithms. The MIT Press and McGraw-Hill, second edition\nedition, 2001.\n[6] Adina Crainiceanu, Prakash Linga, Johannes Gehrke, and Jayavel\nShanmugasundaram. Querying Peer-to-Peer Networks Using P-Trees.\nTechnical Report TR2004-1926, Cornell University, 2004.\n[7] Hui Dai, Michael Neufeld, and Richard Han. ELF: an efficient log-structured\nflash file system for micro sensor nodes. In SenSys \"04: Proceedings of the 2nd\ninternational conference on Embedded networked sensor systems, pages\n176-187, New York, NY, USA, 2004. ACM Press.\n[8] Peter Desnoyers, Deepak Ganesan, Huan Li, and Prashant Shenoy. PRESTO: A\npredictive storage architecture for sensor networks. In Tenth Workshop on Hot\nTopics in Operating Systems (HotOS X)., June 2005.\n[9] Deepak Ganesan, Ben Greenstein, Denis Perelyubskiy, Deborah Estrin, and\nJohn Heidemann. An evaluation of multi-resolution storage in sensor networks.\nIn Proceedings of the First ACM Conference on Embedded Networked Sensor\nSystems (SenSys)., 2003.\n[10] L. Girod, T. Stathopoulos, N. Ramanathan, J. Elson, D. Estrin, E. Osterweil,\nand T. Schoellhammer. A system for simulation, emulation, and deployment of\nheterogeneous sensor networks. In Proceedings of the Second ACM Conference\non Embedded Networked Sensor Systems, Baltimore, MD, 2004.\n[11] B. Greenstein, D. Estrin, R. Govindan, S. Ratnasamy, and S. Shenker. DIFS: A\ndistributed index for features in sensor networks. Elsevier Journal of ad-hoc\nNetworks, 2003.\n[12] Antonin Guttman. R-trees: a dynamic index structure for spatial searching. In\nSIGMOD \"84: Proceedings of the 1984 ACM SIGMOD international\nconference on Management of data, pages 47-57, New York, NY, USA, 1984.\nACM Press.\n[13] Nicholas Harvey, Michael B. Jones, Stefan Saroiu, Marvin Theimer, and Alec\nWolman. Skipnet: A scalable overlay network with practical locality properties.\nIn In proceedings of the 4th USENIX Symposium on Internet Technologies and\nSystems (USITS \"03), Seattle, WA, March 2003.\n[14] Jason Hill, Robert Szewczyk, Alec Woo, Seth Hollar, David Culler, and\nKristofer Pister. System architecture directions for networked sensors. In\nProceedings of the Ninth International Conference on Architectural Support for\nProgramming Languages and Operating Systems (ASPLOS-IX), pages 93-104,\nCambridge, MA, USA, November 2000. ACM.\n[15] Atmel Inc. 4-megabit 2.5-volt or 2.7-volt DataFlash AT45DB041B, 2005.\n[16] Samsung Semiconductor Inc. K9W8G08U1M, K9K4G08U0M: 512M x 8 bit /\n1G x 8 bit NAND flash memory, 2003.\n[17] Chalermek Intanagonwiwat, Ramesh Govindan, and Deborah Estrin. Directed\ndiffusion: A scalable and robust communication paradigm for sensor networks.\nIn Proceedings of the Sixth Annual International Conference on Mobile\nComputing and Networking, pages 56-67, Boston, MA, August 2000. ACM\nPress.\n[18] Xin Li, Young-Jin Kim, Ramesh Govindan, and Wei Hong. Multi-dimensional\nrange queries in sensor networks. In Proceedings of the First ACM Conference\non Embedded Networked Sensor Systems (SenSys)., 2003. to appear.\n[19] Witold Litwin, Marie-Anne Neimat, and Donovan A. Schneider. RP*: A family\nof order preserving scalable distributed data structures. In VLDB \"94:\nProceedings of the 20th International Conference on Very Large Data Bases,\npages 342-353, San Francisco, CA, USA, 1994.\n[20] Samuel Madden, Michael Franklin, Joseph Hellerstein, and Wei Hong. TAG: a\ntiny aggregation service for ad-hoc sensor networks. In OSDI, Boston, MA,\n2002.\n[21] A. Mitra, A. Banerjee, W. Najjar, D. Zeinalipour-Yazti, D.Gunopulos, and\nV. Kalogeraki. High performance, low power sensor platforms featuring\ngigabyte scale storage. In SenMetrics 2005: Third International Workshop on\nMeasurement, Modeling, and Performance Analysis of Wireless Sensor\nNetworks, July 2005.\n[22] J. Polastre, J. Hill, and D. Culler. Versatile low power media access for wireless\nsensor networks. In Proceedings of the Second ACM Conference on Embedded\nNetworked Sensor Systems (SenSys), November 2004.\n[23] William Pugh. Skip lists: a probabilistic alternative to balanced trees. Commun.\nACM, 33(6):668-676, 1990.\n[24] S. Ratnasamy, D. Estrin, R. Govindan, B. Karp, L. Yin S. Shenker, and F. Yu.\nData-centric storage in sensornets. In ACM First Workshop on Hot Topics in\nNetworks, 2001.\n[25] S. Ratnasamy, P. Francis, M. Handley, R. Karp, and S. Shenker. A scalable\ncontent addressable network. In Proceedings of the 2001 ACM SIGCOMM\nConference, 2001.\n[26] S. Ratnasamy, B. Karp, L. Yin, F. Yu, D. Estrin, R. Govindan, and S. Shenker.\nGHT - a geographic hash-table for data-centric storage. In First ACM\nInternational Workshop on Wireless Sensor Networks and their Applications,\n2002.\n[27] N. Xu, E. Osterweil, M. Hamilton, and D. Estrin.\nhttp://www.lecs.cs.ucla.edu/\u02dcnxu/ess/. James Reserve Data.\n50", "keywords": "analysis;archival storage;datum separation;sensor datum;index method;homogeneous architecture;flash storage;metada;distributed index structure;interval skip graph;interval tree;spatial scoping;geographic hash table;separation of datum;flooding;multi-tier sensor network;wireless sensor network;archive"}
{"name": "train_C-48", "title": "Multi-dimensional Range Queries in Sensor Networks\u2217", "abstract": "In many sensor networks, data or events are named by attributes. Many of these attributes have scalar values, so one natural way to query events of interest is to use a multidimensional range query. An example is: List all events whose temperature lies between 50\u25e6 and 60\u25e6 , and whose light levels lie between 10 and 15. Such queries are useful for correlating events occurring within the network. In this paper, we describe the design of a distributed index that scalably supports multi-dimensional range queries. Our distributed index for multi-dimensional data (or DIM) uses a novel geographic embedding of a classical index data structure, and is built upon the GPSR geographic routing algorithm. Our analysis reveals that, under reasonable assumptions about query distributions, DIMs scale quite well with network size (both insertion and query costs scale as O( \u221a N)). In detailed simulations, we show that in practice, the insertion and query costs of other alternatives are sometimes an order of magnitude more than the costs of DIMs, even for moderately sized network. Finally, experiments on a small scale testbed validate the feasibility of DIMs.", "fulltext": "1. INTRODUCTION\nIn wireless sensor networks, data or events will be named\nby attributes [15] or represented as virtual relations in a\ndistributed database [18, 3]. Many of these attributes will\nhave scalar values: e.g., temperature and light levels, soil\nmoisture conditions, etc. In these systems, we argue, one\nnatural way to query for events of interest will be to use\nmulti-dimensional range queries on these attributes. For\nexample, scientists analyzing the growth of marine\nmicroorganisms might be interested in events that occurred within\ncertain temperature and light conditions: List all events\nthat have temperatures between 50\u25e6\nF and 60\u25e6\nF, and light\nlevels between 10 and 20.\nSuch range queries can be used in two distinct ways. They\ncan help users efficiently drill-down their search for events of\ninterest. The query described above illustrates this, where\nthe scientist is presumably interested in discovering, and\nperhaps mapping the combined effect of temperature and\nlight on the growth of marine micro-organisms. More\nimportantly, they can be used by application software running\nwithin a sensor network for correlating events and triggering\nactions. For example, if in a habitat monitoring application,\na bird alighting on its nest is indicated by a certain range\nof thermopile sensor readings, and a certain range of\nmicrophone readings, a multi-dimensional range query on those\nattributes enables higher confidence detection of the arrival\nof a flock of birds, and can trigger a system of cameras.\nIn traditional database systems, such range queries are\nsupported using pre-computed indices. Indices trade-off some\ninitial pre-computation cost to achieve a significantly more\nefficient querying capability. For sensor networks, we\nassert that a centralized index for multi-dimensional range\nqueries may not be feasible for energy-efficiency reasons (as\nwell as the fact that the access bandwidth to this central\nindex will be limited, particularly for queries emanating\nfrom within the network). Rather, we believe, there will\nbe situations when it is more appropriate to build an\ninnetwork distributed data structure for efficiently answering\nmulti-dimensional range queries.\nIn this paper, we present just such a data structure, that\nwe call a DIM1\n. DIMs are inspired by classical database\nindices, and are essentially embeddings of such indices within\nthe sensor network. DIMs leverage two key ideas: in-network\n1\nDistributed Index for Multi-dimensional data.\n63\ndata centric storage, and a novel locality-preserving\ngeographic hash (Section 3). DIMs trace their lineage to\ndatacentric storage systems [23]. The underlying mechanism in\nthese systems allows nodes to consistently hash an event to\nsome location within the network, which allows efficient\nretrieval of events. Building upon this, DIMs use a technique\nwhereby events whose attribute values are close are likely\nto be stored at the same or nearby nodes. DIMs then use\nan underlying geographic routing algorithm (GPSR [16]) to\nroute events and queries to their corresponding nodes in an\nentirely distributed fashion.\nWe discuss the design of a DIM, presenting algorithms for\nevent insertion and querying, for maintaining a DIM in the\nevent of node failure, and for making DIMs robust to data or\npacket loss (Section 3). We then extensively evaluate DIMs\nusing analysis (Section 4), simulation (Section 5), and actual\nimplementation (Section 6). Our analysis reveals that,\nunder reasonable assumptions about query distributions, DIMs\nscale quite well with network size (both insertion and query\ncosts scale as O(\n\u221a\nN)). In detailed simulations, we show\nthat in practice, the event insertion and querying costs of\nother alternatives are sometimes an order of magnitude the\ncosts of DIMs, even for moderately sized network.\nExperiments on a small scale testbed validate the feasibility of\nDIMs (Section 6). Much work remains, including efficient\nsupport for skewed data distributions, existential queries,\nand node heterogeneity.\nWe believe that DIMs will be an essential, but perhaps\nnot necessarily the only, distributed data structure\nsupporting efficient queries in sensor networks. DIMs will be part\nof a suite of such systems that enable feature extraction [7],\nsimple range querying [10], exact-match queries [23], or\ncontinuous queries [15, 18]. All such systems will likely be\nintegrated to a sensor network database system such as\nTinyDB [17]. Application designers could then choose the\nappropriate method of information access. For instance,\na fire tracking application would use DIM to detect the\nhotspots, and would then use mechanisms that enable\ncontinuous queries [15, 18] to track the spatio-temporal progress\nof the hotspots. Finally, we note that DIMs are applicable\nnot just to sensor networks, but to other deeply distributed\nsystems (embedded networks for home and factory\nautomation) as well.\n2. RELATED WORK\nThe basic problem that this paper addresses -\nmultidimensional range queries - is typically solved in database\nsystems using indexing techniques. The database\ncommunity has focused mostly on centralized indices, but distributed\nindexing has received some attention in the literature.\nIndexing techniques essentially trade-off some data\ninsertion cost to enable efficient querying. Indexing has, for long,\nbeen a classical research problem in the database\ncommunity [5, 2]. Our work draws its inspiration from the class\nof multi-key constant branching index structures,\nexemplified by k-d trees [2], where k represents the dimensionality\nof the data space. Our approach essentially represents a\ngeographic embedding of such structures in a sensor field.\nThere is one important difference. The classical indexing\nstructures are data-dependent (as are some indexing schemes\nthat use locality preserving hashes, and developed in the\ntheory literature [14, 8, 13]). The index structure is decided\nnot only by the data, but also by the order in which data\nis inserted. Our current design is not data dependent.\nFinally, tangentially related to our work is the class of spatial\nindexing systems [21, 6, 11].\nWhile there has been some work on distributed indexing,\nthe problem has not been extensively explored. There\nexist distributed indices of a restricted kind-those that allow\nexact match or partial prefix match queries. Examples of\nsuch systems, of course, are the Internet Domain Name\nSystem, and the class of distributed hash table (DHT) systems\nexemplified by Freenet[4], Chord[24], and CAN[19]. Our\nwork is superficially similar to CAN in that both construct\na zone-based overlay atop of the underlying physical\nnetwork. The underlying details make the two systems very\ndifferent: CAN\"s overlay is purely logical while our overlay\nis consistent with the underlying physical topology. More\nrecent work in the Internet context has addressed support\nfor range queries in DHT systems [1, 12], but it is unclear if\nthese directly translate to the sensor network context.\nSeveral research efforts have expressed the vision of a\ndatabase interface to sensor networks [9, 3, 18], and there\nare examples of systems that contribute to this vision [18,\n3, 17]. Our work is similar in spirit to this body of\nliterature. In fact, DIMs could become an important component\nof a sensor network database system such as TinyDB [17].\nOur work departs from prior work in this area in two\nsignificant respects. Unlike these approaches, in our work the data\ngenerated at a node are hashed (in general) to different\nlocations. This hashing is the key to scaling multi-dimensional\nrange searches. In all the other systems described above,\nqueries are flooded throughout the network, and can\ndominate the total cost of the system. Our work avoids query\nflooding by an appropriate choice of hashing. Madden et\nal. [17] also describe a distributed index, called Semantic\nRouting Trees (SRT). This index is used to direct queries\nto nodes that have detected relevant data. Our work\ndiffers from SRT in three key aspects. First, SRT is built on\nsingle attributes while DIM supports mulitple attributes.\nSecond, SRT constructs a routing tree based on historical\nsensor readings, and therefore works well only for\nslowlychanging sensor values. Finally, in SRT queries are issued\nfrom a fixed node while in DIM queries can be issued from\nany node.\nA similar differentiation applies with respect to work on\ndata-centric routing in sensor networks [15, 25], where data\ngenerated at a node is assumed to be stored at the node,\nand queries are either flooded throughout the network [15],\nor each source sets up a network-wide overlay announcing its\npresence so that mobile sinks can rendezvous with sources\nat the nearest node on the overlay [25]. These approaches\nwork well for relatively long-lived queries.\nFinally, our work is most close related to data-centric\nstorage [23] systems, which include geographic hash-tables\n(GHTs) [20], DIMENSIONS [7], and DIFS [10].In a GHT,\ndata is hashed by name to a location within the network,\nenabling highly efficient rendezvous. GHTs are built upon the\nGPSR [16] protocol and leverage some interesting properties\nof that protocol, such as the ability to route to a node nearest\nto a given location. We also leverage properties in GPSR (as\nwe describe later), but we use a locality-preserving hash to\nstore data, enabling efficient multi-dimensional range queries.\nDIMENSIONS and DIFS can be thought of as using the\nsame set of primitives as GHT (storage using consistent\nhashing), but for different ends: DIMENSIONS allows\ndrill64\ndown search for features within a sensor network, while\nDIFS allows range queries on a single key in addition to\nother operations.\n3. THE DESIGN OF DIMS\nMost sensor networks are deployed to collect data from\nthe environment. In these networks, nodes (either\nindividually or collaboratively) will generate events. An event\ncan generally be described as a tuple of attribute values,\nA1, A2, \u00b7 \u00b7 \u00b7 , Ak , where each attribute Ai represents a\nsensor reading, or some value corresponding to a detection\n(e.g., a confidence level). The focus of this paper is the\ndesign of systems to efficiently answer multi-dimensional range\nqueries of the form: x1 \u2212 y1, x2 \u2212 y2, \u00b7 \u00b7 \u00b7 , xk \u2212 yk . Such a\nquery returns all events whose attribute values fall into the\ncorresponding ranges. Notice that point queries, i.e., queries\nthat ask for events with specified values for each attribute,\nare a special case of range queries.\nAs we have discussed in Section 1, range queries can\nenable efficient correlation and triggering within the network.\nIt is possible to implement range queries by flooding a query\nwithin the network. However, as we show in later sections,\nthis alternative can be inefficient, particularly as the system\nscales, and if nodes within the network issue such queries\nrelatively frequently. The other alternative, sending all events\nto an external storage node results in the access link being\na bottleneck, especially if nodes within the network issue\nqueries. Shenker et al. [23] also make similar arguments with\nrespect to data-centric storage schemes in general; DIMs are\nan instance of such schemes.\nThe system we present in this paper, the DIM, relies upon\ntwo foundations: a locality-preserving geographic hash, and\nan underlying geographic routing scheme.\nThe key to resolving range queries efficiently is data\nlocality: i.e., events with comparable attribute values are stored\nnearby. The basic insight underlying DIM is that data\nlocality can be obtained by a locality-preserving geographic\nhash function. Our geographic hash function finds a\nlocalitypreserving mapping from the multi-dimensional space\n(described by the set of attributes) to a 2-d geographic space;\nthis mapping is inspired by k-d trees [2] and is described\nlater. Moreover, each node in the network self-organizes\nto claim part of the attribute space for itself (we say that\neach node owns a zone), so events falling into that space are\nrouted to and stored at that node.\nHaving established the mapping, and the zone structure,\nDIMs use a geographic routing algorithm previously\ndeveloped in the literature to route events to their corresponding\nnodes, or to resolve queries. This algorithm, GPSR [16],\nessentially enables the delivery of a packet to a node at a\nspecified location. The routing mechanism is simple: when\na node receives a packet destined to a node at location X, it\nforwards the packet to the neighbor closest to X. In GPSR,\nthis is called greedy-mode forwarding. When no such\nneighbor exists (as when there exists a void in the network), the\nnode starts the packet on a perimeter mode traversal,\nusing the well known right-hand rule to circumnavigate voids.\nGPSR includes efficient techniques for perimeter traversal\nthat are based on graph planarization algorithms amenable\nto distributed implementation.\nFor all of this to work, DIMs make two assumptions that\nare consistent with the literature [23]. First, all nodes know\nthe approximate geographic boundaries of the network. These\nboundaries may either be configured in nodes at the time of\ndeployment, or may be discovered using a simple protocol.\nSecond, each node knows its geographic location. Node\nlocations can be automatically determined by a localization\nsystem or by other means.\nAlthough the basic idea of DIMs may seem\nstraightforward, it is challenging to design a completely distributed\ndata structure that must be robust to packet losses and\nnode failures, yet must support efficient query distribution\nand deal with communication voids and obstacles. We now\ndescribe the complete design of DIMs.\n3.1 Zones\nThe key idea behind DIMs, as we have discussed, is a\ngeographic locality-preserving hash that maps a multi-attribute\nevent to a geographic zone. Intuitively, a zone is a\nsubdivision of the geographic extent of a sensor field.\nA zone is defined by the following constructive procedure.\nConsider a rectangle R on the x-y plane. Intuitively, R is\nthe bounding rectangle that contains all sensors withing the\nnetwork. We call a sub-rectangle Z of R a zone, if Z is\nobtained by dividing R k times, k \u2265 0, using a procedure\nthat satisfies the following property:\nAfter the i-th division, 0 \u2264 i \u2264 k, R is\npartitioned into 2i\nequal sized rectangles. If i is an\nodd (even) number, the i-th division is parallel\nto the y-axis (x-axis).\nThat is, the bounding rectangle R is first sub-divided into\ntwo zones at level 0 by a vertical line that splits R into two\nequal pieces, each of these sub-zones can be split into two\nzones at level 1 by a horizontal line, and so on. We call the\nnon-negative integer k the level of zone Z, i.e. level(Z) = k.\nA zone can be identified either by a zone code code(Z)\nor by an address addr(Z). The code code(Z) is a 0-1 bit\nstring of length level(Z), and is defined as follows. If Z lies\nin the left half of R, the first (from the left) bit of code(Z)\nis 0, else 1. If Z lies in the bottom half of R, the second\nbit of code(Z) is 0, else 1. The remaining bits of code(Z)\nare then recursively defined on each of the four quadrants of\nR. This definition of the zone code matches the definition\nof zones given above, encoding divisions of the sensor field\ngeography by bit strings. Thus, in Figure 2, the zone in the\ntop-right corner of the rectangle R has a zone code of 1111.\nNote that the zone codes collectively define a zone tree such\nthat individual zones are at the leaves of this tree.\nThe address of a zone Z, addr(Z), is defined to be the\ncentroid of the rectangle defined by Z. The two representations\nof a zone (its code and its address) can each be computed\nfrom the other, assuming the level of the zone is known.\nTwo zones are called sibling zones if their zone codes are\nthe same except for the last bit. For example, if code(Z1) =\n01101 and code(Z2) = 01100, then Z1 and Z2 are sibling\nzones. The sibling subtree of a zone is the subtree rooted\nat the left or right sibling of the zone in the zone tree. We\nuniquely define a backup zone for each zone as follows: if\nthe sibling subtree of the zone is on the left, the backup\nzone is the right-most zone in the sibling subtree;\notherwise, the backup zone is the left-most zone in the sibling\nsubtree. For a zone Z, let p be the first level(Z) \u2212 1 digits\nof code(Z). Let backup(Z) be the backup zone of zone Z.\nIf code(Z) = p1, code(backup(Z)) = p01\u2217 with the most\nnumber of trailing 1\"s (\u2217 means 0 or 1 occurrences). If\n65\ncode(Z) = p0, code(backup(Z)) = p10\u2217 with the most\nnumber of trailing 0\"s.\n3.2 Associating Zones with Nodes\nOur definition of a zone is independent of the actual\ndistribution of nodes in the sensor field, and only depends upon\nthe geographic extent (the bounding rectangle) of the sensor\nfield. Now we describe how zones are mapped to nodes.\nConceptually, the sensor field is logically divided into zones\nand each zone is assigned to a single node. If the sensor\nnetwork were deployed in a grid-like (i.e., very regular) fashion,\nthen it is easy to see that there exists a k such that each\nnode maps into a distinct level-k zone. In general, however,\nthe node placements within a sensor field are likely to be less\nregular than the grid. For some k, some zones may be empty\nand other zones might have more than one node situated\nwithin them. One alternative would have been to choose\na fixed k for the overall system, and then associate nodes\nwith the zones they are in (and if a zone is empty, associate\nthe nearest node with it, for some definition of nearest).\nBecause it makes our overall query routing system simpler,\nwe allow nodes in a DIM to map to different-sized zones.\nTo precisely understand the associations between zones\nand nodes, we define the notion of zone ownership. For any\ngiven placement of network nodes, consider a node A. Let\nZA to be the largest zone that includes only node A and no\nother node. Then, we say that A owns ZA. Notice that this\ndefinition of ownership may leave some sections of the sensor\nfield un-associated with a node. For example, in Figure 2,\nthe zone 110 does not contain any nodes and would not have\nan owner. To remedy this, for any empty zone Z, we define\nthe owner to be the owner of backup(Z). In our example,\nthat empty zone\"s owner would also be the node that owns\n1110, its backup zone.\nHaving defined the association between nodes and zones,\nthe next problem we tackle is: given a node placement, does\nthere exist a distributed algorithm that enables each node\nto determine which zones it owns, knowing only the overall\nboundary of the sensor network? In principle, this should\nbe relatively straightforward, since each node can simply\ndetermine the location of its neighbors, and apply simple\ngeometric methods to determine the largest zone around it\nsuch that no other node resides in that zone. In practice,\nhowever, communication voids and obstacles make the\nalgorithm much more challenging. In particular, resolving the\nownership of zones that do not contain any nodes is\ncomplicated. Equally complicated is the case where the zone\nof a node is larger than its communication radius and the\nnode cannot determine the boundaries of its zone by local\ncommunication alone.\nOur distributed zone building algorithm defers the\nresolution of such zones until when either a query is initiated, or\nwhen an event is inserted. The basic idea behind our\nalgorithm is that each node tentatively builds up an idea of the\nzone it resides in just by communicating with its neighbors\n(remembering which boundaries of the zone are undecided\nbecause there is no radio neighbor that can help resolve that\nboundary). These undecided boundaries are later resolved\nby a GPSR perimeter traversal when data messages are\nactually routed.\nWe now describe the algorithm, and illustrate it using\nexamples. In our algorithm, each node uses an array bound[0..3]\nto maintain the four boundaries of the zone it owns\n(rememFigure 1: A network, where circles represent sensor\nnodes and dashed lines mark the network boundary.\n1111\n011\n00\n110\n100\n101\n1110\n010\nFigure 2: The zone code and boundaries.\n0 1\n0 1\n10\n10\n1 1\n10\n00\nFigure 3: The Corresponding Zone Tree\nber that in this algorithm, the node only tries to determine\nthe zone it resides in, not the other zones it might own\nbecause those zones are devoid of nodes). When a node\nstarts up, each node initializes this array to be the network\nboundary, i.e., initially each node assumes its zone contains\nthe whole network. The zone boundary algorithm now\nrelies upon GPSR\"s beacon messages to learn the locations of\nneighbors within radio range. Upon hearing of such a\nneighbor, the node calls the algorithm in Figure 4 to update its\nzone boundaries and its code accordingly. In this algorithm,\nwe assume that A is the node at which the algorithm is\nexecuted, ZA is its zone, and a is a newly discovered neighbor\nof A. (Procedure Contain(ZA, a) is used to decide if node\na is located within the current zone boundaries of node A).\nUsing this algorithm, then, each node can independently\nand asynchronously decide its own tentative zone based on\nthe location of its neighbors. Figure 2 illustrates the results\nof applying this algorithm for the network in Figure 1.\nFigure 3 describes the corresponding zone tree. Each zone\nresides at a leaf node and the code of a zone is the path from\nthe root to the zone if we represent the branch to the left\n66\nBuild-Zone(a)\n1 while Contain(ZA, a)\n2 do if length(code(ZA)) mod 2 = 0\n3 then new bound \u2190 (bound[0] + bound[1])/2\n4 if A.x < new bound\n5 then bound[1] \u2190 new bound\n6 else bound[0] \u2190 new bound\n7 else new bound \u2190 (bound[2] + bound[3])/2\n8 if A.y < new bound\n9 then bound[3] \u2190 new bound\n10 else bound[2] \u2190 new bound\n11 Update zone code code(ZA)\nFigure 4: Zone Boundary Determination, where A.x\nand A.y represent the geographic coordinate of node\nA.\nInsert-Event(e)\n1 c \u2190 Encode(e)\n2 if Contain(ZA, c) = true and is Internal() = true\n3 then Store e and exit\n4 Send-Message(c, e)\nSend-Message(c, m)\n1 if \u2203 neighbor Y, Closer(Y, owner(m), m) = true\n2 then addr(m) \u2190 addr(Y )\n3 else if length(c) > length(code(m))\n4 then Update code(m) and addr(m)\n5 source(m) \u2190 caller\n6 if is Owner(msg) = true\n7 then owner(m) \u2190 caller\"s code\n8 Send(m)\nFigure 5: Inserting an event in a DIM. Procedure\nCloser(A, B, m) returns true if code(A) is closer to\ncode(m) than code(B). source(m) is used to set the source\naddress of message m.\nchild by 0 and the branch to the right child by 1. This binary\ntree forms the index that we will use in the following event\nand query processing procedures.\nWe see that the zone sizes are different and depend on\nthe local densities and so are the lengths of zone codes for\ndifferent nodes. Notice that in Figure 2, there is an empty\nzone whose code should be 110. In this case, if the node in\nzone 1111 can only hear the node in zone 1110, it sets its\nboundary with the empty zone to undecided, because it did\nnot hear from any neighboring nodes from that direction.\nAs we have mentioned before, the undecided boundaries are\nresolved using GPSR\"s perimeter mode when an event is\ninserted, or a query sent. We describe event insertion in the\nnext step.\nFinally, this description does not describe how a node\"s\nzone codes are adjusted when neighboring nodes fail, or new\nnodes come up. We return to this in Section 3.5.\n3.3 Inserting an Event\nIn this section, we describe how events are inserted into\na DIM. There are two algorithms of interest: a consistent\nhashing technique for mapping an event to a zone, and a\nrouting algorithm for storing the event at the appropriate\nzone. As we shall see, these two algorithms are inter-related.\n3.3.1 Hashing an Event to a Zone\nIn Section 3.1, we described a recursive tessellation of\nthe geographic extent of a sensor field. We now describe\na consistent hashing scheme for a DIM that supports range\nqueries on m distinct attributes2\nLet us denote these attributes A1 . . . Am. For simplicity,\nassume for now that the depth of every zone in the network\nis k, k is a multiple of m, and that this value of k is known\nto every node. We will relax this assumption shortly.\nFurthermore, for ease of discussion, we assume that all attribute\nvalues have been normalized to be between 0 and 1.\nOur hashing scheme assigns a k bit zone code to an event\nas follows. For i between 1 and m, if Ai < 0.5, the i-th\nbit of the zone code is assigned 0, else 1. For i between\nm + 1 and 2m, if Ai\u2212m < 0.25 or Ai\u2212m \u2208 [0.5, 0.75), the\ni-th bit of the zone is assigned 0, else 1, because the next\nlevel divisions are at 0.25 and 0.75 which divide the ranges\nto [0, 0.25), [0.25, 0.5), [0.5, 0.75), and [0.75, 1). We repeat\nthis procedure until all k bits have been assigned. As an\nexample, consider event E = 0.3, 0.8 . For this event, the\n5-bit zone code is code(ZA) = 01110.\nEssentially, our hashing scheme uses the values of the\nattributes in round-robin fashion on the zone tree (such as\nthe one in Figure 3), in order to map an m-attribute event\nto a zone code. This is reminiscent of k-d trees [2], but\nis quite different from that data structure: zone trees are\nspatial embeddings and do not incorporate the re-balancing\nalgorithms in k-d trees.\nIn our design of DIMs, we do not require nodes to have\nzone codes of the same length, nor do we expect a node to\nknow the zone codes of other nodes. Rather, suppose the\nencoding node is A and its own zone code is of length kA.\nThen, given an event E, node A only hashes E to a zone\ncode of length kA. We denote the zone code assigned to an\nevent E by code(E). As we describe below, as the event is\nrouted, code(E) is refined by intermediate nodes. This lazy\nevaluation of zone codes allows different nodes to use\ndifferent length zone codes without any explicit coordination.\n3.3.2 Routing an Event to its Owner\nThe aim of hashing an event to a zone code is to store the\nevent at the node within the network node that owns that\nzone. We call this node the owner of the event. Consider\nan event E that has just been generated at a node A. After\nencoding event E, node A compares code(E) with code(A).\nIf the two are identical, node A store event E locally;\notherwise, node A will attempt to route the event to its owner.\nTo do this, note that code(E) corresponds to some zone\nZ , which is A\"s current guess for the zone at which event E\nshould be stored. A now invokes GPSR to send a message\nto addr(Z ) (the centroid of Z , Section 3.1). The message\ncontains the event E, code(E), and the target geographic\nlocation for storing the event. In the message, A also marks\nitself as the owner of event E. As we will see later, the\nguessed zone Z , the address addr(Z ), and the owner of\nE, all of them contained in the message, will be refined by\nintermediate forwarding nodes.\nGPSR now delivers this message to the next hop towards\naddr(Z ) from A. This next hop node (call it B) does not\nimmediately forward the message. Rather, it attempts to\ncom2\nDIM does not assume that all nodes are homogeneous in\nterms of the sensors they have. Thus, in an m dimensional\nDIM, a node that does not possess all m sensors can use NULL\nvalues for the corresponding readings. DIM treats NULL as\nan extreme value for range comparisons. As an aside, a\nnetwork may have many DIM instances running concurrently.\n67\npute a new zone code for E to get a new code codenew(E).\nB will update the code contained in the message (and also\nthe geographic destination of the message) if codenew(E) is\nlonger than the event code in the message. In this manner,\nas the event wends its way to its owner, its zone code gets\nrefined. Now, B compares its own code code(B) against the\nowner code owner(E) contained in the incoming message.\nIf code(B) has a longer match with code(E) than the\ncurrent owner owner(E), then B sets itself to be the current\nowner of E, meaning that if nobody is eligible to store E,\nthen B will store the event (we shall see how this happens\nnext). If B\"s zone code does not exactly match code(E), B\nwill invoke GPSR to deliver E to the next hop.\n3.3.3 Resolving undecided zone boundaries during\ninsertion\nSuppose that some node, say C, finds itself to be the\ndestination (or eventual owner) of an event E. It does so by\nnoticing that code code(C) equals code(E) after locally\nrecomputing a code for E. In that case, C stores E locally, but\nonly if all four of C\"s zone boundaries are decided. When\nthis condition holds, C knows for sure that no other nodes\nhave overlapped zones with it. In this case, we call C an\ninternal node.\nRecall, though, that because the zone discovery algorithm\nSection 3.2 only uses information from immediate neighbors,\none or more of C\"s boundaries may be undecided. If so, C\nassumes that some other nodes have a zone that overlaps\nwith its own, and sets out to resolve this overlap. To do\nthis, C now sets itself to be the owner of E and continues\nforwarding the message. Here we rely on GPSR\"s\nperimeter mode routing to probe around the void that causes the\nundecided boundary. Since the message starts from C and\nis destined for a geographic location near C, GPSR\nguarantees that the message will be delivered back to C if no\nother nodes will update the information in the message. If\nthe message comes back to C with itself to be the owner, C\ninfers that it must be the true owner of the zone and stores\nE locally.\nIf this does not happen, there are two possibilities. The\nfirst is that as the event traverses the perimeter, some\nintermediate node, say B whose zone overlaps with C\"s marks\nitself to be the owner of the event, but otherwise does not\nchange the event\"s zone code. This node also recognizes that\nits own zone overlaps with C\"s and initiates a message\nexchange which causes each of them to appropriately shrink\ntheir zone.\nFigures 6 through 8 show an example of this data-driven\nzone shrinking. Initially, both node A and node B have\nclaimed the same zone 0 because they are out of radio range\nof each other. Suppose that A inserts an event E = 0.4, 0.8, 0.9 .\nA encodes E to 0 and claims itself to be the owner of E.\nSince A is not an internal node, it sends out E, looking for\nother owner candidates of E. Once E gets to node B, B will\nsee in the message\"s owner field A\"s code that is the same as\nits own. B then shrinks its zone from 0 to 01 according to\nA\"s location which is also recorded in the message and send\na shrink request to A. Upon receiving this request, A also\nshrinks its zone from 0 to 00.\nA second possibility is if some intermediate node changes\nthe destination code of E to a more specific value (i.e.,\nlonger zone code). Let us label this node D. D now tries\nto initiate delivery to the centroid of the new zone. This\nA\nB\n0\n0\n110\n100\n1111\n1110\n101\nFigure 6: Nodes A and B have claimed the same zone.\nA\nB\n<0.4,0.8,0.9>\nFigure 7: An event/query message (filled arrows)\ntriggers zone shrinking (hollow arrows).\nA\nB\n01\n00\n110\n100\n1111\n1110\n101\nFigure 8: The zone layout after shrinking. Now node\nA and B have been mapped to different zones.\nmight result in a new perimeter walk that returns to D (if,\nfor example, D happens to be geographically closest to the\ncentroid of the zone). However, D would not be the owner\nof the event, which would still be C. In routing to the\ncentroid of this zone, the message may traverse the perimeter\nand return to D. Now D notices that C was the original\nowner, so it encapsulates the event and directs it to C. In\ncase that there indeed is another node, say X, that owns\nan overlapped zone with C, X will notice this fact by\nfinding in the message the same prefix of the code of one of\nits zones, but with a different geographic location from its\nown. X will shrink its zone to resolve the overlap. If X\"s\nzone is smaller than or equal to C\"s zone, X will also send\na shrink request to C. Once C receives a shrink request,\nit will reduce its zone appropriately and fix its undecided\nboundary. In this manner, the zone formation process is\nresolved on demand in a data-driven way.\n68\nThere are several interesting effects with respect to\nperimeter walking that arise in our algorithm. The first is that\nthere are some cases where an event insertion might cause\nthe entire outer perimeter of the network to be traversed3\n.\nFigure 6 also works as an example where the outer\nperimeter is traversed. Event E inserted by A will eventually be\nstored in node B. Before node B stores event E, if B\"s\nnominal radio range does not intersect the network boundary, it\nneeds to send out E again as A did, because B in this case\nis not an internal node. But if B\"s nominal radio range\nintersects the network boundary, it then has two choices. It\ncan assume that there will not be any nodes outside the\nnetwork boundary and so B is an internal node. This is an\naggressive approach. On the other hand, B can also make\na conservative decision assuming that there might be some\nother nodes it have not heard of yet. B will then force the\nmessage walking another perimeter before storing it.\nIn some situations, especially for large zones where the\nnode that owns a zone is far away from the centroid of the\nowned zone, there might exist a small perimeter around the\ndestination that does not include the owner of the zone. The\nevent will end up being stored at a different node than the\nreal owner. In order to deal with this problem, we add an\nextra operation in event forwarding, called efficient neighbor\ndiscovery. Before invoking GPSR, a node needs to check if\nthere exists a neighbor who is eligible to be the real owner of\nthe event. To do this, a node C, say, needs to know the zone\ncodes of its neighboring nodes. We deploy GPSR\"s\nbeaconing message to piggyback the zone codes for nodes. So by\nsimply comparing the event\"s code and neighbor\"s code, a\nnode can decide whether there exists a neighbor Y which\nis more likely to be the owner of event E. C delivers E\nto Y , which simply follows the decision making procedure\ndiscussed above.\n3.3.4 Summary and Pseudo-code\nIn summary, our event insertion procedure is designed to\nnicely interact with the zone discovery mechanism, and the\nevent hashing mechanism. The latter two mechanisms are\nkept simple, while the event insertion mechanism uses lazy\nevaluation at each hop to refine the event\"s zone code, and it\nleverages GPSR\"s perimeter walking mechanism to fix\nundecided zone boundaries. In Section 3.5, we address robustness\nof event insertion to packet loss or to node failures.\nFigure 5 shows the pseudo-code for inserting and\nforwarding an event e. In this pseudo code, we have omitted a\ndescription of the zone shrinking procedure. In the pseudo\ncode, procedure is Internal() is used to determine if the\ncaller is an internal node and procedure is Owner() is used\nto determine if the caller is more eligible to be the owner of\nthe event than is currently claimed owner as recorded in the\nmessage. Procedure Send-Message is used to send either\nan event message or a query message. If the message\ndestination address has been changed, the packet source address\nneeds also to be changed in order to avoid being dropped by\nGPSR, since GPSR does not allow a node to see the same\npacket in greedy mode twice.\n3\nThis happens less frequently than for GHTs, where\ninserting an event to a location outside the actual (but inside\nthe nominal) boundary of the network will always invoke an\nexternal perimeter walk.\n3.4 Resolving and Routing Queries\nDIMs support both point queries4\nand range queries.\nRouting a point query is identical to routing an event. Thus, the\nrest of this section details how range queries are routed.\nThe key challenge in routing zone queries is brought out\nby the following strawman design. If the entire network was\ndivided evenly into zones of depth k (for some pre-defined\nconstant k), then the querier (the node issuing the query)\ncould subdivide a given range query into the relevant\nsubzones and route individual requests to each of the zones.\nThis can be inefficient for large range queries and also hard\nto implement in our design where zone sizes are not\npredefined. Accordingly, we use a slightly different technique\nwhere a range query is initially routed to a zone\ncorresponding to the entire range, and is then progressively split into\nsmaller subqueries. We describe this algorithm here.\nThe first step of the algorithm is to map a range query to\na zone code prefix. Conceptually, this is easy; in a zone tree\n(Figure 3), there exists some node which contains the entire\nrange query in its sub-tree, and none of its children in the\ntree do. The initial zone code we choose for the query is the\nzone code corresponding to that tree node, and is a prefix of\nthe zone codes of all zones (note that these zones may not\nbe geographically contiguous) in the subtree. The querier\ncomputes the zone code of Q, denoted by code(Q) and then\nstarts routing a query to addr(code(Q)).\nUpon receiving a range query Q, a node A (where A is any\nnode on the query propagation path) divides it into multiple\nsmaller sized subqueries if there is an overlap between the\nzone of A, zone(A) and the zone code associated with Q,\ncode(Q). Our approach to split a query Q into subqueries\nis as follows. If the range of Q\"s first attribute contains\nthe value 0.5, A divides Q into two sub-queries one of whose\nfirst attribute ranges from 0 to 0.5, and the other from 0.5 to\n1. Then A decides the half that overlaps with its own zone.\nLet\"s call it QA. If QA does not exist, then A stops splitting;\notherwise, it continues splitting (using the second attribute\nrange) and recomputing QA until QA is small enough so\nthat it completely falls into zone(A) and hence A can now\nresolve it. For example, suppose that node A, whose code\nis 0110, is to split a range query Q = 0.3 \u2212 0.8, 0.6 \u2212 0.9 .\nThe splitting steps is shown in Figure 2. After splitting,\nwe obtain three smaller queries q0 = 0.3 \u2212 0.5, 0.6 \u2212 0.75 ,\nq1 = 0.3 \u2212 0.5, 0.75 \u2212 0.9 , and q2 = 0.5 \u2212 0.8, 0.6 \u2212 0.9 .\nThis splitting procedure is illustrated in Figure 9 which\nalso shows the codes of each subquery after splitting.\nA then replies to subquery q0 with data stored locally\nand sends subqueries q1 and q2 using the procedure outlined\nabove. More generally, if node A finds itself to be inside\nthe zone subtree that maximally covers Q, it will send the\nsubqueries that resulted from the split. Otherwise, if there\nis no overlap between A and Q, then A forwards Q as is (in\nthis case Q is either the original query, or a product of an\nearlier split).\nFigure 10 describes the pseudo-code for the zone splitting\nalgorithm. As shown in the above algorithm, once a\nsubquery has been recognized as belonging to the caller\"s zone,\nprocedure Resolve is invoked to resolve the subquery and\nsend a reply to the querier. Every query message contains\n4\nBy point queries, we mean the equality condition on all\nindexed keys. DIM index attributes are not necessarily\nprimary keys.\n69\nthe geographic location of its initiator, so the corresponding\nreply message can be delivered directly back to the\ninitiator. Finally, in the process of query resolution, zones might\nshrink similar to shrinkage during inserting. We omit this\nin the pseudo code.\n3.5 Robustness\nUntil now, we have not discussed the impact of node\nfailures and packet losses, or node arrivals and departures on\nour algorithms. Packet losses can affect query and event\ninsertion, and node failures can result in lost data, while node\narrivals and departures can impact the zone structure. We\nnow discuss how DIMs can be made robust to these kinds\nof dynamics.\n3.5.1 Maintaining Zones\nIn previous sections, we described how the zone discovery\nalgorithm could leave zone boundaries undecided. These\nundecided boundaries are resolved during insertion or\nquerying, using the zone shrinking procedure describe above.\nWhen a new node joins the network, the zone discovery\nmechanism (Section 3.2) will cause neighboring zones to\nappropriately adjust their zone boundaries. At this time, those\nzones can also transfer to the new node those events they\nstore but which should belong to the new node.\nBefore a node turns itself off (if this is indeed possible), it\nknows that its backup node (Section 3.1) will take over its\nzone, and will simply send all its events to its backup node.\nNode deletion may also cause zone expansion. In order to\nkeep the mapping between the binary zone tree\"s leaf nodes\nand zones, we allow zone expansion to only occur among\nsibling zones (Section 3.1). The rule is: if zone(A)\"s sibling\nzone becomes empty, then A can expand its own zone to\ninclude its sibling zone.\nNow, we turn our attention to node failures. Node failures\nare just like node deletions except that a failed node does\nnot have a chance to move its events to another node. But\nhow does a node decide if its sibling has failed? If the\nsibling is within radio range, the absence of GPSR beaconing\nmessages can detect this. Once it detects this, the node can\nexpand its zone. A different approach is needed for\ndetecting siblings who are not within radio range. These are the\ncases where two nodes own their zones after exchanging a\nshrink message; they do not periodically exchange messages\nthereafter to maintain this zone relationship. In this case,\nwe detect the failure in a data-driven fashion, with obvious\nefficiency benefits compared to periodic keepalives. Once a\nnode B has failed, an event or query message that previously\nshould have been owned by the failed node will now be\ndelivered to the node A that owns the empty zone left by node\nB. A can see this message because A stands right around\nthe empty area left by B and is guaranteed to be visited in a\nGPSR perimeter traversal. A will set itself to be the owner\nof the message, and any node which would have dropped this\nmessage due to a perimeter loop will redirect the message to\nA instead. If A\"s zone happens to be the sibling of B\"s zone,\nA can safely expand its own zone and notify its expanded\nzone to its neighbors via GPSR beaconing messages.\n3.5.2 Preventing Data Loss from Node Failure\nThe algorithms described above are robust in terms of\nzone formation, but node failure can erase data. To avoid\nthis, DIMs can employ two kinds of replication: local\nreplication to be resilient to random node failures, and mirror\nreplication for resilience to concurrent failure of\ngeographically contiguous nodes.\nMirror replication is conceptually easy. Suppose an event\nE has a zone code code(E). Then, the node that inserts\nE would store two copies of E; one at the zone denoted\nby code(E), and the other at the zone corresponding to the\none\"s complement of code(E). This technique essentially\ncreates a mirror DIM. A querier would need, in parallel, to\nquery both the original DIM and its mirror since there is no\nway of knowing if a collection of nodes has failed. Clearly,\nthe trade-off here is an approximate doubling of both\ninsertion and query costs.\nThere exists a far cheaper technique to ensure resilience\nto random node failures. Our local replication technique\nrests on the observation that, for each node A, there exists\na unique node which will take over its zone when A fails.\nThis node is defined as the node responsible for A\"s zone\"s\nbackup zone (see Section 3.1). The basic idea is that A\nreplicates each data item it has in this node. We call this\nnode A\"s local replica. Let A\"s local replica be B. Often\nB will be a radio neighbor of A and can be detected from\nGPSR beacons. Sometimes, however, this is not the case,\nand B will have to be explicitly discovered.\nWe use an explicit message for discovering the local replica.\nDiscovering the local replica is data-driven, and uses a\nmechanism similar to that of event insertion. Node A sends a\nmessage whose geographic destination is a random nearby\nlocation chosen by A. The location is close enough to A such\nthat GPSR will guarantee that the message will delivered\nback to A. In addition, the message has three fields, one for\nthe zone code of A, code(A), one for the owner owner(A) of\nzone(A) which is set to be empty, and one for the geographic\nlocation of owner(A). Then the packet will be delivered in\nGPSR perimeter mode. Each node that receives this\nmessage will compare its zone code and code(A) in the message,\nand if it is more eligible to be the owner of zone(A) than\nthe current owner(A) recorded in the message, it will\nupdate the field owner(A) and the corresponding geographic\nlocation. Once the packet comes back to A, it will know the\nlocation of its local replica and can start to send replicas.\nIn a dense sensor network, the local replica of a node\nis usually very near to the node, either its direct neighbor\nor 1-2 hops away, so the cost of sending replicas to local\nreplication will not dominate the network traffic. However,\na node\"s local replica itself may fail. There are two ways to\ndeal with this situation; periodic refreshes, or repeated\ndatadriven discovery of local replicas. The former has higher\noverhead, but more quickly discovers failed replicas.\n3.5.3 Robustness to Packet Loss\nFinally, the mechanisms for querying and event insertion\ncan be easily made resilient to packet loss. For event\ninsertion, a simple ACK scheme suffices.\nOf course, queries and responses can be lost as well. In\nthis case, there exists an efficient approach for error\nrecovery. This rests on the observation that the querier knows\nwhich zones fall within its query and should have responded\n(we assume that a node that has no data matching a query,\nbut whose zone falls within the query, responds with a\nnegative acknowledgment). After a conservative timeout, the\nquerier can re-issue the queries selectively to these zones.\nIf DIM cannot get any answers (positive or negative) from\n70\n<0.3-0.8, 0.6-0.9>\n<0.5-0.8, 0.6-0.9><0.3-0.5, 0.6-0.9>\n<0.3-0.5, 0.6-0.9>\n<0.3-0.5, 0.6-0.9>\n<0.3-0.5, 0.6-0.75> <0.3-0.5, 0.75-0.9>\n0\n0\n1\n1\n1\n1\nFigure 9: An example of range query splitting\nResolve-Range-Query(Q)\n1 Qsub \u2190 nil\n2 q0, Qsub \u2190 Split-Query(Q)\n3 if q0 = nil\n4 then c \u2190 Encode(Q)\n5 if Contain(c, code(A)) = true\n6 then go to step 12\n7 else Send-Message(c, q0)\n8 else Resolve(q0)\n9 if is Internal() = true\n10 then Absorb (q0)\n11 else Append q0 to Qsub\n12 if Qsub = nil\n13 then for each subquery q \u2208 Qsub\n14 do c \u2190 Encode(q)\n15 Send-Message(c, q)\nFigure 10: Query resolving algorithm\ncertain zones after repeated timeouts, it can at least return\nthe partial query results to the application together with the\ninformation about the zones from which data is missing.\n4. DIMS: AN ANALYSIS\nIn this section, we present a simple analytic performance\nevaluation of DIMs, and compare their performance against\nother possible approaches for implementing multi-dimensional\nrange queries in sensor networks. In the next section, we\nvalidate these analyses using detailed packet-level simulations.\nOur primary metrics for the performance of a DIM are:\nAverage Insertion Cost measures the average number of\nmessages required to insert an event into the network.\nAverage Query Delivery Cost measures the average\nnumber of messages required to route a query message to\nall the relevant nodes in the network.\nIt does not measure the number of messages required to\ntransmit responses to the querier; this latter number\ndepends upon the precise data distribution and is the same\nfor many of the schemes we compare DIMs against.\nIn DIMs, event insertion essentially uses geographic\nrouting. In a dense N-node network where the likelihood of\ntraversing perimeters is small, the average event insertion\ncost proportional to\n\u221a\nN [23].\nOn the other hand, the query delivery cost depends upon\nthe size of ranges specified in the query. Recall that our\nquery delivery mechanism is careful about splitting a query\ninto sub-queries, doing so only when the query nears the\nzone that covers the query range. Thus, when the querier is\nfar from the queried zone, there are two components to the\nquery delivery cost. The first, which is proportional to\n\u221a\nN,\nis the cost to deliver the query near the covering zone. If\nwithin this covering zone, there are M nodes, the message\ndelivery cost of splitting the query is proportional to M.\nThe average cost of query delivery depends upon the\ndistribution of query range sizes. Now, suppose that query sizes\nfollow some density function f(x), then the average cost of\nresolve a query can be approximated by\n\u00ca N\n1\nxf(x)dx. To\ngive some intuition for the performance of DIMs, we\nconsider four different forms for f(x): the uniform distribution\nwhere a query range encompassing the entire network is as\nlikely as a point query; a bounded uniform distribution where\nall sizes up to a bound B are equally likely; an algebraic\ndistribution in which most queries are small, but large queries\nare somewhat likely; and an exponential distribution where\nmost queries are small and large queries are unlikely. In all\nour analyses, we make the simplifying assumption that the\nsize of a query is proportional to the number of nodes that\ncan answer that query.\nFor the uniform distribution P(x) \u221d c for some constant c.\nIf each query size from 1 . . . N is equally likely, the average\nquery delivery cost of uniformly distributed queries is O(N).\nThus, for uniformly distributed queries, the performance of\nDIMs is comparable to that of flooding. However, for the\napplications we envision, where nodes within the network\nare trying to correlate events, the uniform distribution is\nhighly unrealistic.\nSomewhat more realistic is a situation where all query\nsizes are bounded by a constant B. In this case, the average\ncost for resolving such a query is approximately\n\u00ca B\n1\nxf(x)dx =\nO(B). Recall now that all queries have to pay an\napproximate cost of O(\n\u221a\nN) to deliver the query near the covering\nzone. Thus, if DIM limited queries to a size proportional to\u221a\nN, the average query cost would be O(\n\u221a\nN).\nThe algebraic distribution, where f(x) \u221d x\u2212k\n, for some\nconstant k between 1 and 2, has an average query resolution\ncost given by\n\u00ca N\n1\nxf(x)dx = O(N2\u2212k\n). In this case, if k >\n1.5, the average cost of query delivery is dominated by the\ncost to deliver the query to near the covering zone, given by\nO(\n\u221a\nN).\nFinally, for the exponential distribution, f(x) = ce\u2212cx\nfor\nsome constant c, and the average cost is just the mean of the\ncorresponding distribution, i.e., O(1) for large N.\nAsymptotically, then, the cost of the query for the exponential\ndistribution is dominated by the cost to deliver the query\nnear the covering zone (O(\n\u221a\nN)).\nThus, we see that if queries follow either the bounded\nuniform distribution, the algebraic distribution, or the\nexponential distribution, the query cost scales as the insertion\ncost (for appropriate choice of constants for the bounded\nuniform and the algebraic distributions).\nHow well does the performance of DIMs compare against\nalternative choices for implementing multi-dimensional queries?\nA simple alternative is called external storage [23], where all\nevents are stored centrally in a node outside the sensor\nnetwork. This scheme incurs an insertion cost of O(\n\u221a\nN), and\na zero query cost. However, as [23] points out, such systems\nmay be impractical in sensor networks since the access link\nto the external node becomes a hotspot.\nA second alternative implementation would store events\nat the node where they are generated. Queries are flooded\n71\nthroughout the network, and nodes that have matching data\nrespond. Examples of systems that can be used for this\n(although, to our knowledge, these systems do not implement\nmulti-dimensional range queries) are Directed Diffusion [15]\nand TinyDB [17]. The flooding scheme incurs a zero\ninsertion cost, but an O(N) query cost. It is easy to show that\nDIMs outperform flooding as long as the ratio of the number\nof insertions to the number of queries is less than\n\u221a\nN.\nA final alternative would be to use a geographic hash table\n(GHT [20]). In this approach, attribute values are assumed\nto be integers (this is actually quite a reasonable\nassumption since attribute values are often quantized), and events\nare hashed on some (say, the first) attribute. A range query\nis sub-divided into several sub-queries, one for each integer\nin the range of the first attribute. Each sub-query is then\nhashed to the appropriate location. The nodes that receive a\nsub-query only return events that match all other attribute\nranges. In this approach, which we call GHT-R (GHT\"s for\nrange queries) the insertion cost is O(\n\u221a\nN). Suppose that\nthe range of the first attribute contains r discrete values.\nThen the cost to deliver queries is O(r\n\u221a\nN). Thus,\nasymptotically, GHT-R\"s perform similarly to DIMs. In practice,\nhowever, the proportionality constants are significantly\ndifferent, and DIMs outperform GHT-Rs, as we shall show\nusing detailed simulations.\n5. DIMS: SIMULATION RESULTS\nOur analysis gives us some insight into the asymptotic\nbehavior of various approaches for multi-dimensional range\nqueries. In this section, we use simulation to compare DIMs\nagainst flooding and GHT-R; this comparison gives us a\nmore detailed understanding of these approaches for\nmoderate size networks, and gives us a nuanced view of the\nmechanistic differences between some of these approaches.\n5.1 Simulation Methodology\nWe use ns-2 for our simulations. Since DIMs are\nimplemented on top of GPSR, we first ported an earlier GPSR\nimplementation to the latest version of ns-2. We modified\nthe GPSR module to call our DIM implementation when\nit receives any data message in transit or when it is about\nto drop a message because that message traversed the entire\nperimeter. This allows a DIM to modify message zone codes\nin flight (Section 3), and determine the actual owner of an\nevent or query.\nIn addition, to this, we implemented in ns-2 most of the\nDIM mechanisms described in Section 3. Of those\nmechanisms, the only one we did not implement is mirror\nreplication. We have implemented selective query retransmission\nfor resiliency to packet loss, but have left the evaluation of\nthis mechanism to future work. Our DIM implementation\nin ns-2 is 2800 lines of code.\nFinally, we implemented GHT-R, our GHT-based\nmultidimensional range query mechanism in ns-2. This\nimplementation was relatively straightforward, given that we had\nported GPSR, and modified GPSR to detect the completion\nof perimeter mode traversals.\nUsing this implementation, we conducted a fairly\nextensive evaluation of DIM and two alternatives (flooding, and\nour GHT-R). For all our experiments, we use uniformly\nplaced sensor nodes with network sizes ranging from 50\nnodes to 300 nodes. Each node has a radio range of 40m.\nFor the results presented here, each node has on average 20\nnodes within its nominal radio range. We have conducted\nexperiments at other node densities; they are in agreement\nwith the results presented here.\nIn all our experiments, each node first generates 3 events5\non average (more precisely, for a topology of size N, we have\n3N events, and each node is equally likely to generate an\nevent). We have conducted experiments for three different\nevent value distributions. Our uniform event distribution\ngenerates 2-dimensional events and, for each dimension,\nevery attribute value is equally likely. Our normal event\ndistribution generates 2-dimensional events and, for each\ndimension, the attribute value is normally distributed with a\nmean corresponding to the mid-point of the attribute value\nrange. The normal event distribution represents a skewed\ndata set. Finally, our trace event distribution is a collection\nof 4-dimensional events obtained from a habitat monitoring\nnetwork. As we shall see, this represents a fairly skewed\ndata set.\nHaving generated events, for each simulation we\ngenerate queries such that, on average, each node generates 2\nqueries. The query sizes are determined using the four size\ndistributions we discussed in Section 4: uniform,\nboundeduniform, algebraic and exponential. Once a query size has\nbeen determined, the location of the query (i.e., the actual\nboundaries of the zone) are uniformly distributed. For our\nGHT-R experiments, the dynamic range of the attributes\nhad 100 discrete values, but we restricted the query range\nfor any one attribute to 50 discrete values to allow those\nsimulations to complete in reasonable time.\nFinally, using one set of simulations we evaluate the\nefficacy of local replication by turning off random fractions of\nnodes and measuring the fidelity of the returned results.\nThe primary metrics for our simulations are the average\nquery and insertion costs, as defined in Section 4.\n5.2 Results\nAlthough we have examined almost all the combinations\nof factors described above, we discuss only the most salient\nones here, for lack of space.\nFigure 11 plots the average insertion costs for DIM and\nGHT-R (for flooding, of course, the insertion costs are zero).\nDIM incurs less per event overhead in inserting events\n(regardless of the actual event distribution; Figure 11 shows the\ncost for uniformly distributed events). The reason for this is\ninteresting. In GHT-R, storing almost every event incurs a\nperimeter traversal, and storing some events require\ntraversing the outer perimeter of the network [20]. By contrast, in\nDIM, storing an event incurs a perimeter traversal only when\na node\"s boundaries are undecided. Furthermore, an\ninsertion or a query in a DIM can traverse the outer perimeter\n(Section 3.3), but less frequently than in GHTs.\nFigure 13 plots the average query cost for a bounded\nuniform query size distribution. For this graph (and the next)\nwe use a uniform event distribution, since the event\ndistribution does not affect the query delivery cost. For this\nsimulation, our bound was 1\n4\nth the size of the largest possible\n5\nOur metrics are chosen so that the exact number of events\nand queries is unimportant for our discussion. Of course,\nthe overall performance of the system will depend on the\nrelative frequency of events and queries, as we discuss in\nSection 4. Since we don\"t have realistic ratios for these, we\nfocus on the microscopic costs, rather than on the overall\nsystem costs.\n72\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\n50 100 150 200 250 300\nAverageCostperInsertion\nNetwork Size\nDIM\nGHT-R\nFigure 11: Average insertion cost for DIM and\nGHT.\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n5 10 15 20 25 30\nFractionofrepliescomparedwithnon-failurecase\nFraction of failed nodes (%)\nNo Replication\nLocal Replication\nFigure 12: Local replication performance.\nquery (e.g., a query of the form 0 \u2212 0.5, 0 \u2212 0.5 . Even for\nthis generous query size, DIMs perform quite well (almost\na third the cost of flooding). Notice, however, that\nGHTRs incur high query cost since almost any query requires as\nmany subqueries as the width of the first attribute\"s range.\nFigure 14 plots the average query cost for the exponential\ndistribution (the average query size for this distribution was\nset to be 1\n16\nth the largest possible query). The superior\nscaling of DIMs is evident in these graphs. Clearly, this is\nthe regime in which one might expect DIMs to perform best,\nwhen most of the queries are small and large queries are\nrelatively rare. This is also the regime in which one would\nexpect to use multi-dimensional range queries: to perform\nrelatively tight correlations. As with the bounded uniform\ndistribution, GHT query cost is dominated by the cost of\nsending sub-queries; for DIMs, the query splitting strategy\nworks quite well in keep overall query delivery costs low.\nFigure 12 describes the efficacy of local replication. To\nobtain this figure, we conducted the following experiment.\nOn a 100-node network, we inserted a number of events\nuniformly distributed throughout the network, then issued\na query covering the entire network and recorded the\nanswers. Knowing the expected answers for this query, we\nthen successively removed a fraction f of nodes randomly,\nand re-issued the same query. The figure plots the fraction\nof expected responses actually received, with and without\nreplication. As the graph shows, local replication performs\nwell for random failures, returning almost 90% of the\nresponses when up to 30% of the nodes have failed\nsimultaneously 6\n.In the absence of local replication, of course, when\n6\nIn practice, the performance of local replication is likely to\n0\n100\n200\n300\n400\n500\n600\n700\n50 100 150 200 250 300\nAverageCostperQueryinBoundedUnifDistribution\nNetwork Size\nDIM\nflooding\nGHT-R\nFigure 13: Average query cost with a bounded\nuniform query distribution\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n50 100 150 200 250 300\nAverageCostperQueryinExponentialDistribution\nNetwork Size\nDIM\nflooding\nGHT-R\nFigure 14: Average query cost with an exponential\nquery distribution\n30% of the nodes fail, the response rate is only 70% as one\nwould expect.\nWe note that DIMs (as currently designed) are not\nperfect. When the data is highly skewed-as it was for our trace\ndata set from the habitat monitoring application where most\nof the event values fell into within 10% of the attribute\"s\nrange-a few DIM nodes will clearly become the bottleneck.\nThis is depicted in Figure 15, which shows that for DIMs,\nand GHT-Rs, the maximum number of transmissions at any\nnetwork node (the hotspots) is rather high. (For less skewed\ndata distributions, and reasonable query size distributions,\nthe hotspot curves for all three schemes are comparable.)\nThis is a standard problem that the database indices have\ndealt with by tree re-balancing. In our case, simpler\nsolutions might be possible (and we discuss this in Section 7).\nHowever, our use of the trace data demonstrates that\nDIMs work for events which have more than two dimensions.\nIncreasing the number of dimensions does not noticeably\ndegrade DIMs query cost (omitted for lack of space).\nAlso omitted are experiments examining the impact of\nseveral other factors, as they do not affect our conclusions\nin any way. As we expected, DIMs are comparable in\nperformance to flooding when all sizes of queries are equally\nlikely. For an algebraic distribution of query sizes, the\nrelative performance is close to that for the exponential\ndistribution. For normally distributed events, the insertion costs\nbe much better than this. Assuming a node and its replica\ndon\"t simultaneously fail often, a node will almost always\ndetect a replica failure and re-replicate, leading to near 100%\nresponse rates.\n73\n0\n2000\n4000\n6000\n8000\n10000\n12000\n50 100 150 200 250 300\nMaximumHotspotonTraceDataSet\nNetwork Size\nDIM\nflooding\nGHT-R\nFigure 15: Hotspot usage\nDIM\nZone\nManager\nQuery\nRouter\nQuery\nProcessor\nEvent\nManager\nEvent\nRouter\nGPSR interface(Event driven/Thread based)\nupdate\nuseuse\nupdate\nGPSR\nUpper interface(Event driven/Thread based)\nLower interface(Event driven/Thread based)\nGreedy\nForwarding\nPerimeter\nForwarding\nBeaconing\nNeighbor\nList\nManager\nupdate\nuse\nMoteNIC (MicaRadio) IP Socket (802.11b/Ethernet)\nFigure 16: Software architecture of DIM over GPSR\nare comparable to that for the uniform distribution.\nFinally, we note that in all our evaluations we have only\nused list queries (those that request all events matching the\nspecified range). We expect that for summary queries (those\nthat expect an aggregate over matching events), the overall\ncost of DIMs could be lower because the matching data are\nlikely to be found in one or a small number of zones. We\nleave an understanding of this to future work. Also left to\nfuture work is a detailed understanding of the impact of\nlocation error on DIM\"s mechanisms. Recent work [22] has\nexamined the impact of imprecise location information on\nother data-centric storage mechanisms such as GHTs, and\nfound that there exist relatively simple fixes to GPSR that\nameliorate the effects of location error.\n6. IMPLEMENTATION\nWe have implemented DIMs on a Linux platform suitable\nfor experimentation on PDAs and PC-104 class machines.\nTo implement DIMs, we had to develop and test an\nindependent implementation of GPSR. Our GPSR implementation\nis full-featured, while our DIM implementation has most of\nthe algorithms discussed in Section 3; some of the robustness\nextensions have only simpler variants implemented.\nThe software architecture of DIM/GPSR system is shown\nin Figure 16. The entire system (about 5000 lines of code)\nis event-driven and multi-threaded. The DIM subsystem\nconsists of six logical components: zone management, event\nmaintenance, event routing, query routing, query\nprocessing, and GPSR interactions. The GPSR system is\nimplemented as user-level daemon process. Applications are\nexecuted as clients. For the DIM subsystem, the GPSR module\n0\n2\n4\n6\n8\n10\n12\n14\n16\n0.25x0.25 0.50x0.50 0.75x0.75 1.0x1.0\nQuery size\nAverage#ofreceivedresponses\nperquery\nFigure 17: Number of events received for different\nquery sizes\n0\n2\n4\n6\n8\n10\n12\n14\n16\n0.25x0.25 0.50x0.50 0.75x0.75 1.0x1.0\nQuery sizeTotalnumberofmessages\nonlyforsendingthequery\nFigure 18: Query distribution cost\nprovides several extensions: it exports information about\nneighbors, and provides callbacks during packet forwarding\nand perimeter-mode termination.\nWe tested our implementation on a testbed consisting of 8\nPC-104 class machines. Each of these boxes runs Linux and\nuses a Mica mote (attached through a serial cable) for\ncommunication. These boxes are laid out in an office building\nwith a total spatial separation of over a hundred feet. We\nmanually measured the locations of these nodes relative to\nsome coordinate system and configured the nodes with their\nlocation. The network topology is approximately a chain.\nOn this testbed, we inserted queries and events from a\nsingle designated node. Our events have two attributes which\nspan all combinations of the four values [0, 0.25, 0.75, 1]\n(sixteen events in all). Our queries span four sizes, returning 1,\n4, 9 and 16 events respectively.\nFigure 17 plots the number of events received for different\nsized queries. It might appear that we received fewer events\nthan expected, but this graph doesn\"t count the events that\nwere already stored at the querier. With that adjustment,\nthe number of responses matches our expectation. Finally,\nFigure 18 shows the total number of messages required for\ndifferent query sizes on our testbed.\nWhile these experiments do not reveal as much about the\nperformance range of DIMs as our simulations do, they\nnevertheless serve as proof-of-concept for DIMs. Our next step\nin the implementation is to port DIMs to the Mica motes,\nand integrate them into the TinyDB [17] sensor database\nengine on motes.\n74\n7. CONCLUSIONS\nIn this paper, we have discussed the design and evaluation\nof a distributed data structure called DIM for efficiently\nresolving multi-dimensional range queries in sensor networks.\nOur design of DIMs relies upon a novel locality-preserving\nhash inspired by early work in database indexing, and is\nbuilt upon GPSR. We have a working prototype, both of\nGPSR and DIM, and plan to conduct larger scale\nexperiments in the future.\nThere are several interesting future directions that we\nintend to pursue. One is adaptation to skewed data\ndistributions, since these can cause storage and transmission\nhotspots. Unlike traditional database indices that re-balance\ntrees upon data insertion, in sensor networks it might be\nfeasible to re-structure the zones on a much larger timescale\nafter obtaining a rough global estimate of the data\ndistribution. Another direction is support for node heterogeneity\nin the zone construction process; nodes with larger storage\nspace assert larger-sized zones for themselves. A third is\nsupport for efficient resolution of existential queries-whether\nthere exists an event matching a multi-dimensional range.\nAcknowledgments\nThis work benefited greatly from discussions with Fang Bian,\nHui Zhang and other ENL lab members, as well as from\ncomments provided by the reviewers and our shepherd Feng\nZhao.\n8. REFERENCES\n[1] J. Aspnes and G. Shah. Skip Graphs. 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In Proceedings of the Sixth\nAnnual ACM/IEEE International Conference on Mobile\nComputing and Networking (Mobicom 2000), Boston, MA,\nAugust 2000.\n[16] B. Karp and H. T. Kung. GPSR: Greedy Perimeter\nStateless Routing for Wireless Networks. In Proceedings of\nthe Sixth Annual ACM/IEEE International Conference on\nMobile Computing and Networking (Mobicom 2000),\nBoston, MA, August 2000.\n[17] S. Madden, M. Franklin, J. Hellerstein, and W. Hong. The\nDesign of an Acquisitional Query Processor for Sensor\nNetworks. In Proceedings of ACM SIGCMOD, San Diego,\nCA, June 2003.\n[18] S. Madden, M. J. Franklin, J. M. Hellerstein, and W. Hong.\nTAG: a Tiny AGregation Service for ad-hoc Sensor\nNetworks. In Proceedings of 5th Annual Symposium on\nOperating Systems Design and Implementation (OSDI),\nBoston, MA, December 2002.\n[19] S. Ratnasamy, P. Francis, M. Handley, R. Karp, and\nS. Shenker. A Scalable Content-Addressable Network. In\nProceedings of the ACM SIGCOMM, San Diego, CA,\nAugust 2001.\n[20] S. Ratnasamy, B. Karp, L. Yin, F. Yu, D. Estrin,\nR. Govindan, and S. Shenker. GHT: A Geographic Hash\nTable for Data-Centric Storage. In Proceedings of the First\nACM International Workshop on Wireless Sensor\nNetworks and Applications, Atlanta, GA, September 2002.\n[21] H. Samet. Spatial Data Structures. In W. Kim, editor,\nModern Database Systems: The Object Model,\nInteroperability and Beyond, pages 361-385. Addison\nWesley/ACM, 1995.\n[22] K. Sead, A. Helmy, and R. Govindan. On the Effect of\nLocalization Errors on Geographic Face Routing in Sensor\nNetworks. In Under submission, 2003.\n[23] S. Shenker, S. Ratnasamy, B. Karp, R. Govindan, and\nD. Estrin. Data-Centric Storage in Sensornets. In Proc.\nACM SIGCOMM Workshop on Hot Topics In Networks,\nPrinceton, NJ, 2002.\n[24] I. Stoica, R. Morris, D. Karger, M. F. Kaashoek, and\nH. Balakrishnan. Chord: A Scalable Peer-To-Peer Lookup\nService for Internet Applications. In Proceedings of the\nACM SIGCOMM, San Diego, CA, August 2001.\n[25] F. Ye, H. Luo, J. Cheng, S. Lu, and L. Zhang. A Two-Tier\nData Dissemination Model for Large-scale Wireless Sensor\nNetworks. In Proceedings of the Eighth Annual ACM/IEEE\nInternational Conference on Mobile Computing and\nNetworking (Mobicom\"02), Atlanta, GA, September 2002.\n75", "keywords": "datacentric storage system;multi-dimensional range query;multidimensional range query;event insertion;querying cost;query flooding;indexing technique;dim;distributed datum structure;asymptotic behavior;locality-preserving geographic hash;sensor network;geographic routing;centralized index;normal event distribution;efficient correlation;distributed index"}
{"name": "train_C-49", "title": "Evaluating Opportunistic Routing Protocols with Large Realistic Contact Traces", "abstract": "Traditional mobile ad-hoc network (MANET) routing protocols assume that contemporaneous end-to-end communication paths exist between data senders and receivers. In some mobile ad-hoc networks with a sparse node population, an end-to-end communication path may break frequently or may not exist at any time. Many routing protocols have been proposed in the literature to address the problem, but few were evaluated in a realistic opportunistic network setting. We use simulation and contact traces (derived from logs in a production network) to evaluate and compare five existing protocols: direct-delivery, epidemic, random, PRoPHET, and Link-State, as well as our own proposed routing protocol. We show that the direct delivery and epidemic routing protocols suffer either low delivery ratio or high resource usage, and other protocols make tradeoffs between delivery ratio and resource usage.", "fulltext": "1. INTRODUCTION\nMobile opportunistic networks are one kind of delay-tolerant\nnetwork (DTN) [6]. Delay-tolerant networks provide service\ndespite long link delays or frequent link breaks. Long link delays\nhappen in networks with communication between nodes at a great\ndistance, such as interplanetary networks [2]. Link breaks are caused\nby nodes moving out of range, environmental changes, interference\nfrom other moving objects, radio power-offs, or failed nodes. For\nus, mobile opportunistic networks are those DTNs with sparse node\npopulation and frequent link breaks caused by power-offs and the\nmobility of the nodes.\nMobile opportunistic networks have received increasing interest\nfrom researchers. In the literature, these networks include mobile\nsensor networks [25], wild-animal tracking networks [11],\npocketswitched networks [8], and transportation networks [1, 14]. We\nexpect to see more opportunistic networks when the\none-laptopper-child (OLPC) project [18] starts rolling out inexpensive\nlaptops with wireless networking capability for children in developing\ncountries, where often no infrastructure exits. Opportunistic\nnetworking is one promising approach for those children to exchange\ninformation.\nOne fundamental problem in opportunistic networks is how to\nroute messages from their source to their destination. Mobile\nopportunistic networks differ from the Internet in that disconnections\nare the norm instead of the exception. In mobile opportunistic\nnetworks, communication devices can be carried by people [4],\nvehicles [1] or animals [11]. Some devices can form a small mobile\nad-hoc network when the nodes move close to each other. But a\nnode may frequently be isolated from other nodes. Note that\ntraditional Internet routing protocols and ad-hoc routing protocols, such\nas AODV [20] or DSDV [19], assume that a contemporaneous\nendto-end path exists, and thus fail in mobile opportunistic networks.\nIndeed, there may never exist an end-to-end path between two given\ndevices.\nIn this paper, we study protocols for routing messages between\nwireless networking devices carried by people. We assume that\npeople send messages to other people occasionally, using their\ndevices; when no direct link exists between the source and the\ndestination of the message, other nodes may relay the message to the\ndestination. Each device represents a unique person (it is out of the\nscope of this paper when a device maybe carried by multiple\npeople). Each message is destined for a specific person and thus for\na specific node carried by that person. Although one person may\ncarry multiple devices, we assume that the sender knows which\ndevice is the best to receive the message. We do not consider\nmulticast or geocast in this paper.\nMany routing protocols have been proposed in the literature.\nFew of them were evaluated in realistic network settings, or even in\nrealistic simulations, due to the lack of any realistic people\nmobility model. Random walk or random way-point mobility models are\noften used to evaluate the performance of those routing protocols.\nAlthough these synthetic mobility models have received extensive\ninterest by mobile ad-hoc network researchers [3], they do not\nreflect people\"s mobility patterns [9]. Realising the limitations of\nusing random mobility models in simulations, a few researchers have\nstudied routing protocols in mobile opportunistic networks with\nrealistic mobility traces. Chaintreau et al. [5] theoretically analyzed\nthe impact of routing algorithms over a model derived from a\nrealistic mobility data set. Su et al. [22] simulated a set of routing\n35\nprotocols in a small experimental network. Those studies help\nresearchers better understand the theoretical limits of opportunistic\nnetworks, and the routing protocol performance in a small network\n(20-30 nodes).\nDeploying and experimenting large-scale mobile opportunistic\nnetworks is difficult, we too resort to simulation. Instead of\nusing a complex mobility model to mimic people\"s mobility patterns,\nwe used mobility traces collected in a production wireless\nnetwork at Dartmouth College to drive our simulation. Our\nmessagegeneration model, however, was synthetic.\nTo the best of our knowledge, we are the first to simulate the\neffect of routing protocols in a large-scale mobile opportunistic\nnetwork, using realistic contact traces derived from real traces of\na production network with more than 5, 000 users.\nUsing realistic contact traces, we evaluate the performance of\nthree naive routing protocols (direct-delivery, epidemic, and\nrandom) and two prediction-based routing protocols, PRoPHET [16]\nand Link-State [22]. We also propose a new prediction-based\nrouting protocol, and compare it to the above in our evaluation.\n2. ROUTING PROTOCOL\nA routing protocol is designed for forwarding messages from one\nnode (source) to another node (destination). Any node may\ngenerate messages for any other node, and may carry messages destined\nfor other nodes. In this paper, we consider only messages that are\nunicast (single destination).\nDTN routing protocols could be described in part by their\ntransfer probability and replication probability; that is, when one node\nmeets another node, what is the probability that a message should\nbe transfered and if so, whether the sender should retain its copy.\nTwo extremes are the direct-delivery protocol and the epidemic\nprotocol. The former transfers with probability 1 when the node\nmeets the destination, 0 for others, and no replication. The latter\nuses transfer probability 1 for all nodes and unlimited replication.\nBoth these protocols have their advantages and disadvantages. All\nother protocols are between the two extremes.\nFirst, we define the notion of contact between two nodes. Then\nwe describe five existing protocols before presenting our own\nproposal.\nA contact is defined as a period of time during which two nodes\nhave the opportunity to communicate. Although we are aware that\nwireless technologies differ, we assume that a node can reliably\ndetect the beginning and end time of a contact with nearby nodes.\nA node may be in contact with several other nodes at the same time.\nThe contact history of a node is a sequence of contacts with other\nnodes. Node i has a contact history Hi(j), for each other node j,\nwhich denotes the historical contacts between node i and node j.\nWe record the start and end time for each contact; however, the last\ncontacts in the node\"s contact history may not have ended.\n2.1 Direct Delivery Protocol\nIn this simple protocol, a message is transmitted only when the\nsource node can directly communicate with the destination node\nof the message. In mobile opportunistic networks, however, the\nprobability for the sender to meet the destination may be low, or\neven zero.\n2.2 Epidemic Routing Protocol\nThe epidemic routing protocol [23] floods messages into the\nnetwork. The source node sends a copy of the message to every node\nthat it meets. The nodes that receive a copy of the message also\nsend a copy of the message to every node that they meet.\nEventually, a copy of the message arrives at the destination of the message.\nThis protocol is simple, but may use significant resources;\nexcessive communication may drain each node\"s battery quickly.\nMoreover, since each node keeps a copy of each message, storage is not\nused efficiently, and the capacity of the network is limited.\nAt a minimum, each node must expire messages after some amount\nof time or stop forwarding them after a certain number of hops.\nAfter a message expires, the message will not be transmitted and will\nbe deleted from the storage of any node that holds the message.\nAn optimization to reduce the communication cost is to\ntransfer index messages before transferring any data message. The\nindex messages contain IDs of messages that a node currently holds.\nThus, by examining the index messages, a node only transfers\nmessages that are not yet contained on the other nodes.\n2.3 Random Routing\nAn obvious approach between the above two extremes is to\nselect a transfer probability between 0 and 1 to forward messages at\neach contact. We use a simple replication strategy that allows only\nthe source node to make replicas, and limits the replication to a\nspecific number of copies. The message has some chance of\nbeing transferred to a highly mobile node, and thus may have a better\nchance to reach its destination before the message expires.\n2.4 PRoPHET Protocol\nPRoPHET [16] is a Probabilistic Routing Protocol using History\nof past Encounters and Transitivity to estimate each node\"s delivery\nprobability for each other node. When node i meets node j, the\ndelivery probability of node i for j is updated by\npij = (1 \u2212 pij)p0 + pij, (1)\nwhere p0 is an initial probability, a design parameter for a given\nnetwork. Lindgren et al. [16] chose 0.75, as did we in our\nevaluation. When node i does not meet j for some time, the delivery\nprobability decreases by\npij = \u03b1k\npij, (2)\nwhere \u03b1 is the aging factor (\u03b1 < 1), and k is the number of time\nunits since the last update.\nThe PRoPHET protocol exchanges index messages as well as\ndelivery probabilities. When node i receives node j\"s delivery\nprobabilities, node i may compute the transitive delivery probability\nthrough j to z with\npiz = piz + (1 \u2212 piz)pijpjz\u03b2, (3)\nwhere \u03b2 is a design parameter for the impact of transitivity; we\nused \u03b2 = 0.25 as did Lindgren [16].\n2.5 Link-State Protocol\nSu et al. [22] use a link-state approach to estimate the weight of\neach path from the source of a message to the destination. They\nuse the median inter-contact duration or exponentially aged\nintercontact duration as the weight on links. The exponentially aged\ninter-contact duration of node i and j is computed by\nwij = \u03b1wij + (1 \u2212 \u03b1)I, (4)\nwhere I is the new inter-contact duration and \u03b1 is the aging factor.\nNodes share their link-state weights when they can communicate\nwith each other, and messages are forwarded to the node that have\nthe path with the lowest link-state weight.\n36\n3. TIMELY-CONTACT PROBABILITY\nWe also use historical contact information to estimate the\nprobability of meeting other nodes in the future. But our method differs\nin that we estimate the contact probability within a period of time.\nFor example, what is the contact probability in the next hour?\nNeither PRoPHET nor Link-State considers time in this way.\nOne way to estimate the timely-contact probability is to use the\nratio of the total contact duration to the total time. However, this\napproach does not capture the frequency of contacts. For example,\none node may have a long contact with another node, followed by\na long non-contact period. A third node may have a short contact\nwith the first node, followed by a short non-contact period. Using\nthe above estimation approach, both examples would have similar\ncontact probability. In the second example, however, the two nodes\nhave more frequent contacts.\nWe design a method to capture the contact frequency of mobile\nnodes. For this purpose, we assume that even short contacts are\nsufficient to exchange messages.1\nThe probability for node i to meet node j is computed by the\nfollowing procedure. We divide the contact history Hi(j) into a\nsequence of n periods of \u0394T starting from the start time (t0) of the\nfirst contact in history Hi(j) to the current time. We number each\nof the n periods from 0 to n \u2212 1, then check each period. If node\ni had any contact with node j during a given period m, which is\n[t0 + m\u0394T, t0 + (m + 1)\u0394T), we set the contact status Im to be\n1; otherwise, the contact status Im is 0. The probability p\n(0)\nij that\nnode i meets node j in the next \u0394T can be estimated as the average\nof the contact status in prior intervals:\np\n(0)\nij =\n1\nn\nn\u22121X\nm=0\nIm. (5)\nTo adapt to the change of contact patterns, and reduce the storage\nspace for contact histories, a node may discard old history contacts;\nin this situation, the estimate would be based on only the retained\nhistory.\nThe above probability is the direct contact probability of two\nnodes. We are also interested in the probability that we may be\nable to pass a message through a sequence of k nodes. We define\nthe k-order probability inductively,\np\n(k)\nij = p\n(0)\nij +\nX\n\u03b1\np\n(0)\ni\u03b1 p\n(k\u22121)\n\u03b1j , (6)\nwhere \u03b1 is any node other than i or j.\n3.1 Our Routing Protocol\nWe first consider the case of a two-hop path, that is, with only\none relay node. We consider two approaches: either the receiving\nneighbor decides whether to act as a relay, or the source decides\nwhich neighbors to use as relay.\n3.1.1 Receiver Decision\nWhenever a node meets other nodes, they exchange all their\nmessages (or as above, index messages). If the destination of a\nmessage is the receiver itself, the message is delivered. Otherwise, if\nthe probability of delivering the message to its destination through\nthis receiver node within \u0394T is greater than or equal to a certain\nthreshold, the message is stored in the receiver\"s storage to forward\n1\nIn our simulation, however, we accurately model the\ncommunication costs and some short contacts will not succeed in transfer of\nall messages.\nto the destination. If the probability is less than the threshold, the\nreceiver discards the message. Notice that our protocol replicates\nthe message whenever a good-looking relay comes along.\n3.1.2 Sender Decision\nTo make decisions, a sender must have the information about its\nneighbors\" contact probability with a message\"s destination.\nTherefore, meta-data exchange is necessary.\nWhen two nodes meet, they exchange a meta-message,\ncontaining an unordered list of node IDs for which the sender of the\nmetamessage has a contact probability greater than the threshold.\nAfter receiving a meta-message, a node checks whether it has\nany message that destined to its neighbor, or to a node in the node\nlist of the neighbor\"s meta-message. If it has, it sends a copy of the\nmessage.\nWhen a node receives a message, if the destination of the\nmessage is the receiver itself, the message is delivered. Otherwise, the\nmessage is stored in the receiver\"s storage for forwarding to the\ndestination.\n3.1.3 Multi-node Relay\nWhen we use more than two hops to relay a message, each node\nneeds to know the contact probabilities along all possible paths to\nthe message destination.\nEvery node keeps a contact probability matrix, in which each cell\npij is a contact probability between to nodes i and j. Each node\ni computes its own contact probabilities (row i) with other nodes\nusing Equation (5) whenever the node ends a contact with other\nnodes. Each row of the contact probability matrix has a version\nnumber; the version number for row i is only increased when node i\nupdates the matrix entries in row i. Other matrix entries are updated\nthrough exchange with other nodes when they meet.\nWhen two nodes i and j meet, they first exchange their contact\nprobability matrices. Node i compares its own contact matrix with\nnode j\"s matrix. If node j\"s matrix has a row l with a higher version\nnumber, then node i replaces its own row l with node j\"s row l.\nLikewise node j updates its matrix. After the exchange, the two\nnodes will have identical contact probability matrices.\nNext, if a node has a message to forward, the node estimates\nits neighboring node\"s order-k contact probability to contact the\ndestination of the message using Equation (6). If p\n(k)\nij is above a\nthreshold, or if j is the destination of the message, node i will send\na copy of the message to node j.\nAll the above effort serves to determine the transfer probability\nwhen two nodes meet. The replication decision is orthogonal to\nthe transfer decision. In our implementation, we always replicate.\nAlthough PRoPHET [16] and Link-State [22] do no replication, as\ndescribed, we added replication to those protocols for better\ncomparison to our protocol.\n4. EVALUATION RESULTS\nWe evaluate and compare the results of direct delivery, epidemic,\nrandom, PRoPHET, Link-State, and timely-contact routing\nprotocols.\n4.1 Mobility traces\nWe use real mobility data collected at Dartmouth College.\nDartmouth College has collected association and disassociation\nmessages from devices on its wireless network wireless users since\nspring 2001 [13]. Each message records the wireless card MAC\naddress, the time of association/disassociation, and the name of the\naccess point. We treat each unique MAC address as a node. For\n37\nmore information about Dartmouth\"s network and the data\ncollection, see previous studies [7, 12].\nOur data are not contacts in a mobile ad-hoc network. We can\napproximate contact traces by assuming that two users can\ncommunicate with each other whenever they are associated with the same\naccess point. Chaintreau et al. [5] used Dartmouth data traces and\nmade the same assumption to theoretically analyze the impact of\nhuman mobility on opportunistic forwarding algorithms. This\nassumption may not be accurate,2\nbut it is a good first approximation.\nIn our simulation, we imagine the same clients and same mobility\nin a network with no access points. Since our campus has full WiFi\ncoverage, we assume that the location of access points had little\nimpact on users\" mobility.\nWe simulated one full month of trace data (November 2003)\ntaken from CRAWDAD [13], with 5, 142 users. Although\npredictionbased protocols require prior contact history to estimate each node\"s\ndelivery probability, our preliminary results show that the\nperformance improvement of warming-up over one month of trace was\nmarginal. Therefore, for simplicity, we show the results of all\nprotocols without warming-up.\n4.2 Simulator\nWe developed a custom simulator.3\nSince we used contact traces\nderived from real mobility data, we did not need a mobility model\nand omitted physical and link-layer details for node discovery. We\nwere aware that the time for neighbor discovery in different\nwireless technologies vary from less than one seconds to several\nseconds. Furthermore, connection establishment also takes time, such\nas DHCP. In our simulation, we assumed the nodes could discover\nand connect each other instantly when they were associated with a\nsame AP. To accurately model communication costs, however, we\nsimulated some MAC-layer behaviors, such as collision.\nThe default settings of the network of our simulator are listed in\nTable 1, using the values recommended by other papers [22, 16].\nThe message probability was the probability of generating\nmessages, as described in Section 4.3. The default transmission\nbandwidth was 11 Mb/s. When one node tried to transmit a message, it\nfirst checked whether any nearby node was transmitting. If it was,\nthe node backed off a random number of slots. Each slot was 1\nmillisecond, and the maximum number of backoff slots was 30. The\nsize of messages was uniformly distributed between 80 bytes and\n1024 bytes. The hop count limit (HCL) was the maximum number\nof hops before a message should stop forwarding. The time to live\n(TTL) was the maximum duration that a message may exist before\nexpiring. The storage capacity was the maximum space that a node\ncan use for storing messages. For our routing method, we used a\ndefault prediction window \u0394T of 10 hours and a probability\nthreshold of 0.01. The replication factor r was not limited by default, so\nthe source of a message transferred the messages to any other node\nthat had a contact probability with the message destination higher\nthan the probability threshold.\n4.3 Message generation\nAfter each contact event in the contact trace, we generated a\nmessage with a given probability; we choose a source node and a\ndes2\nTwo nodes may not have been able to directly communicate while\nthey were at two far sides of an access point, or two nodes may\nhave been able to directly communicate if they were between two\nadjacent access points.\n3\nWe tried to use a general network simulator (ns2), which was\nextremely slow when simulating a large number of mobile nodes (in\nour case, more than 5000 nodes), and provided unnecessary detail\nin modeling lower-level network protocols.\nTable 1: Default Settings of the Simulation\nParameter Default value\nmessage probability 0.001\nbandwidth 11 Mb/s\ntransmission slot 1 millisecond\nmax backoff slots 30\nmessage size 80-1024 bytes\nhop count limit (HCL) unlimited\ntime to live (TTL) unlimited\nstorage capacity unlimited\nprediction window \u0394T 10 hours\nprobability threshold 0.01\ncontact history length 20\nreplication always\naging factor \u03b1 0.9 (0.98 PRoPHET)\ninitial probability p0 0.75 (PRoPHET)\ntransitivity impact \u03b2 0.25 (PRoPHET)\n0\n20000\n40000\n60000\n80000\n100000\n120000\n0 5 10 15 20\nNumberofoccurrence\nhour\nmovements\ncontacts\nFigure 1: Movements and contacts duration each hour\ntination node randomly using a uniform distribution across nodes\nseen in the contact trace up to the current time. When there were\nmore contacts during a certain period, there was a higher likelihood\nthat a new message was generated in that period. This correlation\nis not unreasonable, since there were more movements during the\nday than during the night, and so the number of contacts. Figure 1\nshows the statistics of the numbers of movements and the numbers\nof contacts during each hour of the day, summed across all users\nand all days. The plot shows a clear diurnal activity pattern. The\nactivities reached lowest around 5am and peaked between 4pm and\n5pm. We assume that in some applications, network traffic exhibits\nsimilar patterns, that is, people send more messages during the day,\ntoo.\nMessages expire after a TTL. We did not use proactive methods\nto notify nodes the delivery of messages, so that the messages can\nbe removed from storage.\n4.4 Metrics\nWe define a set of metrics that we use in evaluating routing\nprotocols in opportunistic networks:\n\u2022 delivery ratio, the ratio of the number of messages delivered\nto the number of total messages generated.\n\u2022 message transmissions, the total number of messages\ntransmitted during the simulation across all nodes.\n38\n\u2022 meta-data transmissions, the total number of meta-data units\ntransmitted during the simulation across all nodes.\n\u2022 message duplications, the number of times a message copy\noccurred, due to replication.\n\u2022 delay, the duration between a message\"s generation time and\nthe message\"s delivery time.\n\u2022 storage usage, the max and mean of maximum storage (bytes)\nused across all nodes.\n4.5 Results\nHere we compare simulation results of the six routing protocols.\n0.001\n0.01\n0.1\n1\nunlimited 100 24 10 1\nDeliveryratio\nMessage time-to-live (TTL) (hour)\ndirect\nrandom\nprediction\nstate\nprophet\nepidemic\nFigure 2: Delivery ratio (log scale). The direct and random\nprotocols for one-hour TTL had delivery ratios that were too\nlow to be visible in the plot.\nFigure 2 shows the delivery ratio of all the protocols, with\ndifferent TTLs. (In all the plots in the paper, prediction stands for our\nmethod, state stands for the Link-State protocol, and prophet\nrepresents PRoPHET.) Although we had 5,142 users in the\nnetwork, the direct-delivery and random protocols had low delivery\nratios (note the log scale). Even for messages with an unlimited\nlifetime, only 59 out of 2077 messages were delivered during this\none-month simulation. The delivery ratio of epidemic routing was\nthe best. The three prediction-based approaches had low delivery\nratio, compared to epidemic routing. Although our method was\nslightly better than the other two, the advantage was marginal.\nThe high delivery ratio of epidemic routing came with a price:\nexcessive transmissions. Figure 3 shows the number of message\ndata transmissions. The number of message transmissions of\nepidemic routing was more than 10 times higher than for the\npredictionbased routing protocols. Obviously, the direct delivery protocol\nhad the lowest number of message transmissions - the number of\nmessage delivered. Among the three prediction-based methods,\nthe PRoPHET transmitted fewer messages, but had comparable\ndelivery-ratio as seen in Figure 2.\nFigure 4 shows that epidemic and all prediction-based methods\nhad substantial meta-data transmissions, though epidemic routing\nhad relatively more, with shorter TTLs. Because epidemic\nprotocol transmitted messages at every contact, in turn, more nodes had\nmessages that required meta-data transmission during contact. The\ndirect-delivery and random protocols had no meta-data\ntransmissions.\nIn addition to its message transmissions and meta-data\ntransmissions, the epidemic routing protocol also had excessive message\n1\n10\n100\n1000\n10000\n100000\n1e+06\n1e+07\n1e+08\nunlimited 100 24 10 1\nNumberofmessagetransmitted\nMessage time-to-live (TTL) (hour)\ndirect\nrandom\nprediction\nstate\nprophet\nepidemic\nFigure 3: Message transmissions (log scale)\n1\n10\n100\n1000\n10000\n100000\n1e+06\n1e+07\n1e+08\nunlimited 100 24 10 1\nNumberofmeta-datatransmissions\nMessage time-to-live (TTL) (hour)\ndirect\nrandom\nprediction\nstate\nprophet\nepidemic\nFigure 4: Meta-data transmissions (log scale). Direct and\nrandom protocols had no meta-data transmissions.\nduplications, spreading replicas of messages over the network.\nFigure 5 shows that epidemic routing had one or two orders more\nduplication than the prediction-based protocols. Recall that the\ndirectdelivery and random protocols did not replicate, thus had no data\nduplications.\nFigure 6 shows both the median and mean delivery delays. All\nprotocols show similar delivery delays in both mean and median\nmeasures for medium TTLs, but differ for long and short TTLs.\nWith a 100-hour TTL, or unlimited TTL, epidemic routing had the\nshortest delays. The direct-delivery had the longest delay for\nunlimited TTL, but it had the shortest delay for the one-hour TTL.\nThe results seem contrary to our intuition: the epidemic routing\nprotocol should be the fastest routing protocol since it spreads\nmessages all over the network. Indeed, the figures show only the delay\ntime for delivered messages. For direct delivery, random, and the\nprobability-based routing protocols, relatively few messages were\ndelivered for short TTLs, so many messages expired before they\ncould reach their destination; those messages had infinite delivery\ndelay and were not included in the median or mean measurements.\nFor longer TTLs, more messages were delivered even for the\ndirectdelivery protocol. The statistics of longer TTLs for comparison are\nmore meaningful than those of short TTLs.\nSince our message generation rate was low, the storage usage\nwas also low in our simulation. Figure 7 shows the maximum\nand average of maximum volume (in KBytes) of messages stored\n39\n1\n10\n100\n1000\n10000\n100000\n1e+06\n1e+07\n1e+08\nunlimited 100 24 10 1\nNumberofmessageduplications\nMessage time-to-live (TTL) (hour)\ndirect\nrandom\nprediction\nstate\nprophet\nepidemic\nFigure 5: Message duplications (log scale). Direct and random\nprotocols had no message duplications.\n1\n10\n100\n1000\n10000\nunlimited100 24 10 1 unlimited100 24 10 1\nDelay(minute)\nMessage time-to-live (TTL) (hour)\ndirect\nrandom\nprediction\nstate\nprophet\nepidemic\nMean delayMedian delay\nFigure 6: Median and mean delays (log scale).\nin each node. The epidemic routing had the most storage usage.\nThe message time-to-live parameter was the big factor affecting the\nstorage usage for epidemic and prediction-based routing protocols.\nWe studied the impact of different parameters of our\npredictionbased routing protocol. Our prediction-based protocol was\nsensitive to several parameters, such as the probability threshold and the\nprediction window \u0394T. Figure 8 shows the delivery ratios when\nwe used different probability thresholds. (The leftmost value 0.01\nis the value used for the other plots.) A higher probability threshold\nlimited the transfer probability, so fewer messages were delivered.\nIt also required fewer transmissions as shown in Figure 9. With\na larger prediction window, we got a higher contact probability.\nThus, for the same probability threshold, we had a slightly higher\ndelivery ratio as shown in Figure 10, and a few more transmissions\nas shown in Figure 11.\n5. RELATED WORK\nIn addition to the protocols that we evaluated in our simulation,\nseveral other opportunistic network routing protocols have been\nproposed in the literature. We did not implement and evaluate these\nrouting protocols, because either they require domain-specific\ninformation (location information) [14, 15], assume certain mobility\npatterns [17], present orthogonal approaches [10, 24] to other\nrouting protocols.\n0.1\n1\n10\n100\n1000\n10000\nunlimited100 24 10 1 unlimited100 24 10 1\nStorageusage(KB)\nMessage time-to-live (TTL) (hour)\ndirect\nrandom\nprediction\nstate\nprophet\nepidemic\nMean of maximumMax of maximum\nFigure 7: Max and mean of maximum storage usage across all\nnodes (log scale).\n0\n0.2\n0.4\n0.6\n0.8\n1\n0 0.2 0.4 0.6 0.8 1\nDeliveryratio\nProbability threshold\nFigure 8: Probability threshold impact on delivery ratio of\ntimely-contact routing.\nLeBrun et al. [14] propose a location-based delay-tolerant\nnetwork routing protocol. Their algorithm assumes that every node\nknows its own position, and the destination is stationary at a known\nlocation. A node forwards data to a neighbor only if the\nneighbor is closer to the destination than its own position. Our protocol\ndoes not require knowledge of the nodes\" locations, and learns their\ncontact patterns.\nLeguay et al. [15] use a high-dimensional space to represent a\nmobility pattern, then routes messages to nodes that are closer to\nthe destination node in the mobility pattern space. Location\ninformation of nodes is required to construct mobility patterns.\nMusolesi et al. [17] propose an adaptive routing protocol for\nintermittently connected mobile ad-hoc networks. They use a Kalman\nfilter to compute the probability that a node delivers messages. This\nprotocol assumes group mobility and cloud connectivity, that is,\nnodes move as a group, and among this group of nodes a\ncontemporaneous end-to-end connection exists for every pair of nodes. When\ntwo nodes are in the same connected cloud, DSDV [19] routing is\nused.\nNetwork coding also draws much interest from DTN research.\nErasure-coding [10, 24] explores coding algorithms to reduce\nmessage replicas. The source node replicates a message m times, then\nuses a coding scheme to encode them in one big message.\nAfter replicas are encoded, the source divides the big message into k\n40\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n0 0.2 0.4 0.6 0.8 1\nNumberofmessagetransmitted(million)\nProbability threshold\nFigure 9: Probability threshold impact on message\ntransmission of timely-contact routing.\n0\n0.2\n0.4\n0.6\n0.8\n1\n0.01 0.1 1 10 100\nDeliveryratio\nPrediction window (hour)\nFigure 10: Prediction window impact on delivery ratio of\ntimely-contact routing (semi-log scale).\nblocks of the same size, and transmits a block to each of the first k\nencountered nodes. If m of the blocks are received at the\ndestination, the message can be restored, where m < k. In a uniformly\ndistributed mobility scenario, the delivery probability increases\nbecause the probability that the destination node meets m relays is\ngreater than it meets k relays, given m < k.\n6. SUMMARY\nWe propose a prediction-based routing protocol for\nopportunistic networks. We evaluate the performance of our protocol using\nrealistic contact traces, and compare to five existing routing\nprotocols.\nOur simulation results show that direct delivery had the\nlowest delivery ratio, the fewest data transmissions, and no meta-data\ntransmission or data duplication. Direct delivery is suitable for\ndevices that require an extremely low power consumption. The\nrandom protocol increased the chance of delivery for messages\notherwise stuck at some low mobility nodes. Epidemic routing delivered\nthe most messages. The excessive transmissions, and data\nduplication, however, consume more resources than portable devices may\nbe able to provide.\nNone of these protocols (direct-delivery, random and epidemic\nrouting) are practical for real deployment of opportunistic networks,\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n0.01 0.1 1 10 100\nNumberofmessagetransmitted(million)\nPrediction window (hour)\nFigure 11: Prediction window impact on message transmission\nof timely-contact routing (semi-log scale).\nbecause they either had an extremely low delivery ratio, or had an\nextremely high resource consumption. The prediction-based\nrouting protocols had a delivery ratio more than 10 times better than\nthat for direct-delivery and random routing, and fewer\ntransmissions and less storage usage than epidemic routing. They also had\nfewer data duplications than epidemic routing.\nAll the prediction-based routing protocols that we have\nevaluated had similar performance. Our method had a slightly higher\ndelivery ratio, but more transmissions and higher storage usage.\nThere are many parameters for prediction-based routing protocols,\nhowever, and different parameters may produce different results.\nIndeed, there is an opportunity for some adaptation; for example,\nhigh priority messages may be given higher transfer and\nreplication probabilities to increase the chance of delivery and reduce the\ndelay, or a node with infrequent contact may choose to raise its\ntransfer probability.\nWe only studied the impact of predicting peer-to-peer contact\nprobability for routing in unicast messages. In some applications,\ncontext information (such as location) may be available for the\npeers. One may also consider other messaging models, for\nexample, where messages are sent to a location, such that every node at\nthat location will receive a copy of the message. Location\nprediction [21] may be used to predict nodes\" mobility, and to choose as\nrelays those nodes moving toward the destined location.\nResearch on routing in opportunistic networks is still in its early\nstage. Many other issues of opportunistic networks, such as\nsecurity and privacy, are mainly left open. We anticipate studying these\nissues in future work.\n7. ACKNOWLEDGEMENT\nThis research is a project of the Center for Mobile\nComputing and the Institute for Security Technology Studies at Dartmouth\nCollege. It was supported by DoCoMo Labs USA, the\nCRAWDAD archive at Dartmouth College (funded by NSF CRI Award\n0454062), NSF Infrastructure Award EIA-9802068, and by Grant\nnumber 2005-DD-BX-1091 awarded by the Bureau of Justice\nAssistance. Points of view or opinions in this document are those of\nthe authors and do not represent the official position or policies of\nany sponsor.\n8. REFERENCES\n[1] John Burgess, Brian Gallagher, David Jensen, and Brian Neil\nLevine. 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{"name": "train_C-50", "title": "CenWits: A Sensor-Based Loosely Coupled Search and Rescue System Using Witnesses", "abstract": "This paper describes the design, implementation and evaluation of a search and rescue system called CenWits. CenWits uses several small, commonly-available RF-based sensors, and a small number of storage and processing devices. It is designed for search and rescue of people in emergency situations in wilderness areas. A key feature of CenWits is that it does not require a continuously connected sensor network for its operation. It is designed for an intermittently connected network that provides only occasional connectivity. It makes a judicious use of the combined storage capability of sensors to filter, organize and store important information, combined battery power of sensors to ensure that the system remains operational for longer time periods, and intermittent network connectivity to propagate information to a processing center. A prototype of CenWits has been implemented using Berkeley Mica2 motes. The paper describes this implementation and reports on the performance measured from it.", "fulltext": "1. INTRODUCTION\nSearch and rescue of people in emergency situation in a\ntimely manner is an extremely important service. It has\nbeen difficult to provide such a service due to lack of timely\ninformation needed to determine the current location of a\nperson who may be in an emergency situation. With the\nemergence of pervasive computing, several systems [12, 19,\n1, 5, 6, 4, 11] have been developed over the last few years\nthat make use of small devices such as cell phones,\nsensors, etc. All these systems require a connected network\nvia satellites, GSM base stations, or mobile devices. This\nrequirement severely limits their applicability, particularly\nin remote wilderness areas where maintaining a connected\nnetwork is very difficult.\nFor example, a GSM transmitter has to be in the range\nof a base station to transmit. As a result, it cannot operate\nin most wilderness areas. While a satellite transmitter is\nthe only viable solution in wilderness areas, it is typically\nexpensive and cumbersome. Furthermore, a line of sight is\nrequired to transmit to satellite, and that makes it\ninfeasible to stay connected in narrow canyons, large cities with\nskyscrapers, rain forests, or even when there is a roof or some\nother obstruction above the transmitter, e.g. in a car. An\nRF transmitter has a relatively smaller range of\ntransmission. So, while an in-situ sensor is cheap as a single unit, it is\nexpensive to build a large network that can provide\nconnectivity over a large wilderness area. In a mobile environment\nwhere sensors are carried by moving people, power-efficient\nrouting is difficult to implement and maintain over a large\nwilderness area. In fact, building an adhoc sensor network\nusing only the sensors worn by hikers is nearly impossible\ndue to a relatively small number of sensors spread over a\nlarge wilderness area.\nIn this paper, we describe the design, implementation\nand evaluation of a search and rescue system called\nCenWits (Connection-less Sensor-Based Tracking System\nUsing Witnesses). CenWits is comprised of mobile, in-situ\nsensors that are worn by subjects (people, wild animals, or\nin-animate objects), access points (AP) that collect\ninformation from these sensors, and GPS receivers and location\npoints (LP) that provide location information to the\nsensors. A subject uses GPS receivers (when it can connect to\na satellite) and LPs to determine its current location. The\nkey idea of CenWits is that it uses a concept of witnesses\nto convey a subject\"s movement and location information\nto the outside world. This averts a need for maintaining a\nconnected network to transmit location information to the\noutside world. In particular, there is no need for\nexpensive GSM or satellite transmitters, or maintaining an adhoc\nnetwork of in-situ sensors in CenWits.\n180\nCenWits employs several important mechanisms to\naddress the key problem of resource constraints (low signal\nstrength, low power and limited memory) in sensors. In\nparticular, it makes a judicious use of the combined\nstorage capability of sensors to filter, organize and store\nimportant information, combined battery power of sensors to\nensure that the system remains operational for longer time\nperiods, and intermittent network connectivity to propagate\ninformation to a processing center.\nThe problem of low signal strengths (short range RF\ncommunication) is addressed by avoiding a need for maintaining\na connected network. Instead, CenWits propagates the\nlocation information of sensors using the concept of witnesses\nthrough an intermittently connected network. As a result,\nthis system can be deployed in remote wilderness areas, as\nwell as in large urban areas with skyscrapers and other tall\nstructures. Also, this makes CenWits cost-effective. A\nsubject only needs to wear light-weight and low-cost sensors\nthat have GPS receivers but no expensive GSM or satellite\ntransmitters. Furthermore, since there is no need for a\nconnected sensor network, there is no need to deploy sensors in\nvery large numbers.\nThe problem of limited battery life and limited memory of\na sensor is addressed by incorporating the concepts of groups\nand partitions. Groups and partitions allow sensors to stay\nin sleep or receive modes most of the time. Using groups and\npartitions, the location information collected by a sensor can\nbe distributed among several sensors, thereby reducing the\namount of memory needed in one sensor to store that\ninformation. In fact, CenWits provides an adaptive tradeoff\nbetween memory and power consumption of sensors. Each\nsensor can dynamically adjust its power and memory\nconsumption based on its remaining power or available memory.\nIt has amply been noted that the strength of sensor\nnetworks comes from the fact that several sensor nodes can\nbe distributed over a relatively large area to construct a\nmultihop network. This paper demonstrates that important\nlarge-scale applications can be built using sensors by\njudiciously integrating the storage, communication and\ncomputation capabilities of sensors. The paper describes\nimportant techniques to combine memory, transmission and\nbattery power of many sensors to address resource constraints\nin the context of a search and rescue application. However,\nthese techniques are quite general. We discuss several other\nsensor-based applications that can employ these techniques.\nWhile CenWits addresses the general location tracking\nand reporting problem in a wide-area network, there are\ntwo important differences from the earlier work done in this\narea. First, unlike earlier location tracking solutions,\nCenWits does not require a connected network. Second, unlike\nearlier location tracking solutions, CenWits does not aim for\na very high accuracy of localization. Instead, the main goal\nis to provide an approximate, small area where search and\nrescue efforts can be concentrated.\nThe rest of this paper is organized as follows. In Section\n2, we overview some of the recent projects and technologies\nrelated to movement and location tracking, and search and\nrescue systems. In Section 3, we describe the overall\narchitecture of CenWits, and provide a high-level description of\nits functionality. In the next section, Section 4, we discuss\npower and memory management in CenWits. To simplify\nour presentation, we will focus on a specific application of\ntracking lost/injured hikers in all these sections. In\nSection 6, we describe a prototype implementation of CenWits\nand present performance measured from this\nimplementation. We discuss how the ideas of CenWits can be used\nto build several other applications in Section 7. Finally, in\nSection 8, we discuss some related issues and conclude the\npaper.\n2. RELATED WORK\nA survey of location systems for ubiquitous computing\nis provided in [11]. A location tracking system for adhoc\nsensor networks using anchor sensors as reference to gain\nlocation information and spread it out to outer node is\nproposed in [17]. Most location tracking systems in adhoc\nsensor networks are for benefiting geographic-aware routing.\nThey don\"t fit well for our purposes. The well-known\nactive badge system [19] lets a user carry a badge around.\nAn infrared sensor in the room can detect the presence of\na badge and determine the location and identification of\nthe person. This is a useful system for indoor environment,\nwhere GPS doesn\"t work. Locationing using 802.11 devices\nis probably the cheapest solution for indoor position\ntracking [8]. Because of the popularity and low cost of 802.11\ndevices, several business solutions based on this technology\nhave been developed[1].\nA system that combines two mature technologies and is\nviable in suburban area where a user can see clear sky and\nhas GSM cellular reception at the same time is currently\navailable[5]. This system receives GPS signal from a\nsatellite and locates itself, draws location on a map, and sends\nlocation information through GSM network to the others\nwho are interested in the user\"s location.\nA very simple system to monitor children consists an RF\ntransmitter and a receiver. The system alarms the holder\nof the receiver when the transmitter is about to run out of\nrange [6].\nPersonal Locater Beacons (PLB) has been used for avalanche\nrescuing for years. A skier carries an RF transmitter that\nemits beacons periodically, so that a rescue team can find\nhis/her location based on the strength of the RF signal.\nLuxury version of PLB combines a GPS receiver and a\nCOSPASSARSAT satellite transmitter that can transmit user\"s\nlocation in latitude and longitude to the rescue team whenever\nan accident happens [4]. However, the device either is turned\non all the time resulting in fast battery drain, or must be\nturned on after the accident to function.\nAnother related technology in widespread use today is the\nONSTAR system [3], typically used in several luxury cars.\nIn this system, a GPS unit provides position information,\nand a powerful transmitter relays that information via\nsatellite to a customer service center. Designed for emergencies,\nthe system can be triggered either by the user with the push\nof a button, or by a catastrophic accident. Once the system\nhas been triggered, a human representative attempts to gain\ncommunication with the user via a cell phone built as an\nincar device. If contact cannot be made, emergency services\nare dispatched to the location provided by GPS. Like PLBs,\nthis system has several limitations. First, it is heavy and\nexpensive. It requires a satellite transmitter and a connected\nnetwork. If connectivity with either the GPS network or a\ncommunication satellite cannot be maintained, the system\nfails. Unfortunately, these are common obstacles\nencountered in deep canyons, narrow streets in large cities, parking\ngarages, and a number of other places.\n181\nThe Lifetch system uses GPS receiver board combined\nwith a GSM/GPRS transmitter and an RF transmitter in\none wireless sensor node called Intelligent Communication\nUnit (ICU). An ICU first attempts to transmit its location\nto a control center through GSM/GPRS network. If that\nfails, it connects with other ICUs (adhoc network) to\nforward its location information until the information reaches\nan ICU that has GSM/GPRS reception. This ICU then\ntransmits the location information of the original ICU via\nthe GSM/GPRS network.\nZebraNet is a system designed to study the moving\npatterns of zebras [13]. It utilizes two protocols: History-based\nprotocol and flooding protocol. History-based protocol is\nused when the zebras are grazing and not moving around\ntoo much. While this might be useful for tracking zebras,\nit\"s not suitable for tracking hikers because two hikers are\nmost likely to meet each other only once on a trail. In\nthe flooding protocol, a node dumps its data to a neighbor\nwhenever it finds one and doesn\"t delete its own copy until\nit finds a base station. Without considering routing loops,\npacket filtering and grouping, the size of data on a node will\ngrow exponentially and drain the power and memory of a\nsensor node with in a short time. Instead, Cenwits uses a\nfour-phase hand-shake protocol to ensure that a node\ntransmits only as much information as the other node is willing\nto receive. While ZebraNet is designed for a big group of\nsensors moving together in the same direction with same\nspeed, Cenwits is designed to be used in the scenario where\nsensors move in different directions at different speeds.\nDelay tolerant network architecture addresses some\nimportant problems in challenged (resource-constrained)\nnetworks [9]. While this work is mainly concerned with\ninteroperability of challenged networks, some problems related\nto occasionally-connected networks are similar to the ones\nwe have addressed in CenWits.\nAmong all these systems, luxury PLB and Lifetch are\ndesigned for location tracking in wilderness areas. However,\nboth of these systems require a connected network. Luxury\nPLB requires the user to transmit a signal to a satellite,\nwhile Lifetch requires connection to GSM/GPRS network.\nLuxury PLB transmits location information, only when an\naccident happens. However, if the user is buried in the snow\nor falls into a deep canyon, there is almost no chance for the\nsignal to go through and be relayed to the rescue team. This\nis because satellite transmission needs line of sight.\nFurthermore, since there is no known history of user\"s location, it is\nnot possible for the rescue team to infer the current location\nof the user. Another disadvantage of luxury PLB is that a\nsatellite transmitter is very expensive, costing in the range\nof $750. Lifetch attempts to transmit the location\ninformation by GSM/GPRS and adhoc sensor network that uses\nAODV as the routing protocol. However, having a cellular\nreception in remote areas in wilderness areas, e.g.\nAmerican national parks is unlikely. Furthermore, it is extremely\nunlikely that ICUs worn by hikers will be able to form an\nadhoc network in a large wilderness area. This is because\nthe hikers are mobile and it is very unlikely to have several\nICUs placed dense enough to forward packets even on a very\npopular hike route.\nCenWits is designed to address the limitations of systems\nsuch as luxury PLB and Lifetch. It is designed to\nprovide hikers, skiers, and climbers who have their activities\nmainly in wilderness areas a much higher chance to convey\ntheir location information to a control center. It is not\nreliant upon constant connectivity with any communication\nmedium. Rather, it communicates information along from\nuser to user, finally arriving at a control center. Unlike\nseveral of the systems discussed so far, it does not require that\na user\"s unit is constantly turned on. In fact, it can discover\na victim\"s location, even if the victim\"s sensor was off at the\ntime of accident and has remained off since then. CenWits\nsolves one of the greatest problems plaguing modern search\nand rescue systems: it has an inherent on-site storage\ncapability. This means someone within the network will have\naccess to the last-known-location information of a victim,\nand perhaps his bearing and speed information as well.\nFigure 1: Hiker A and Hiker B are are not in the\nrange of each other\n3. CENWITS\nWe describe CenWits in the context of locating lost/injured\nhikers in wilderness areas. Each hiker wears a sensor (MICA2\nmotes in our prototype) equipped with a GPS receiver and\nan RF transmitter. Each sensor is assigned a unique ID and\nmaintains its current location based on the signal received by\nits GPS receiver. It also emits beacons periodically. When\nany two sensors are in the range of one another, they record\nthe presence of each other (witness information), and also\nexchange the witness information they recorded earlier. The\nkey idea here is that if two sensors come with in range of\neach other at any time, they become each other\"s witnesses.\nLater on, if the hiker wearing one of these sensors is lost, the\nother sensor can convey the last known (witnessed) location\nof the lost hiker. Furthermore, by exchanging the witness\ninformation that each sensor recorded earlier, the witness\ninformation is propagated beyond a direct contact between\ntwo sensors.\nTo convey witness information to a processing center or to\na rescue team, access points are established at well-known\nlocations that the hikers are expected to pass through, e.g.\nat the trail heads, trail ends, intersection of different trails,\nscenic view points, resting areas, and so on. Whenever a\nsensor node is in the vicinity of an access point, all witness\ninformation stored in that sensor is automatically dumped\nto the access point. Access points are connected to a\nprocessing center via satellite or some other network1\n. The\nwitness information is downloaded to the processing center\nfrom various access points at regular intervals. In case,\nconnection to an access point is lost, the information from that\n1\nA connection is needed only between access points and a\nprocessing center. There is no need for any connection\nbetween different access points.\n182\naccess point can be downloaded manually, e.g. by UAVs.\nTo estimate the speed, location and direction of a hiker at\nany point in time, all witness information of that hiker that\nhas been collected from various access points is processed.\nFigure 2: Hiker A and Hiker B are in the range\nof each other. A records the presence of B and B\nrecords the presence of A. A and B become each\nother\"s witnesses.\nFigure 3: Hiker A is in the range of an access\npoint. It uploads its recorded witness information\nand clears its memory.\nAn example of how CenWits operates is illustrated in\nFigures 1, 2 and 3. First, hikers A and B are on two close\ntrails, but out of range of each other (Figure 1). This is\na very common scenario during a hike. For example, on a\npopular four-hour hike, a hiker might run into as many as\n20 other hikers. This accounts for one encounter every 12\nminutes on average. A slow hiker can go 1 mile (5,280 feet)\nper hour. Thus in 12 minutes a slow hiker can go as far as\n1056 feet. This implies that if we were to put 20 hikers on a\n4-hour, one-way hike evenly, the range of each sensor node\nshould be at least 1056 feet for them to communicate with\none another continuously. The signal strength starts\ndropping rapidly for two Mica2 nodes to communicate with each\nother when they are 180 feet away, and is completely lost\nwhen they are 230 feet away from each other[7]. So, for the\nsensors to form a sensor network on a 4-hour hiking trail,\nthere should be at least 120 hikers scattered evenly. Clearly,\nthis is extremely unlikely. In fact, in a 4-hour, less-popular\nhiking trail, one might only run into say five other hikers.\nCenWits takes advantage of the fact that sensors can\ncommunicate with one another and record their presence. Given\na walking speed of one mile per hour (88 feet per minute)\nand Mica2 range of about 150 feet for non-line-of-sight radio\ntransmission, two hikers have about 150/88 = 1.7 minutes to\ndiscover the presence of each other and exchange their\nwitness information. We therefore design our system to have\neach sensor emit a beacon every one-and-a-half minute. In\nFigure 2, hiker B\"s sensor emits a beacon when A is in range,\nthis triggers A to exchange data with B. A communicates\nthe following information to B: My ID is A; I saw C at 1:23\nPM at (39\u25e6\n49.3277655\", 105\u25e6\n39.1126776\"), I saw E at 3:09\nPM at (40\u25e6\n49.2234879\", 105\u25e6\n20.3290168\"). B then replies\nwith My ID is B; I saw K at 11:20 AM at (39\u25e6\n51.4531655\",\n105\u25e6\n41.6776223\"). In addition, A records I saw B at 4:17\nPM at (41\u25e6\n29.3177354\", 105\u25e6\n04.9106211\") and B records I\nsaw A at 4:17 PM at (41\u25e6\n29.3177354\", 105\u25e6\n04.9106211\").\nB goes on his way to overnight camping while A heads\nback to trail head where there is an AP, which emits beacon\nevery 5 seconds to avoid missing any hiker. A dumps all\nwitness information it has collected to the access point. This\nis shown in Figure 3.\n3.1 Witness Information: Storage\nA critical concern is that there is limited amount of\nmemory available on motes (4 KB SDRAM memory, 128 KB\nflash memory, and 4-512 KB EEPROM). So, it is important\nto organize witness information efficiently. CenWits stores\nwitness information at each node as a set of witness records\n(Format is shown in Figure 4.\n1 B\nNode ID Record Time X, Y Location Time Hop Count\n1 B 3 B 8 B 3 B\nFigure 4: Format of a witness record.\nWhen two nodes i and j encounter each other, each node\ngenerates a new witness record. In the witness record\ngenerated by i, Node ID is j, Record Time is the current time\nin i\"s clock, (X,Y) are the coordinates of the location of i\nthat i recorded most recently (either from satellite or an\nLP), Location Time is the time when the this location was\nrecorded, and Hop Count is 0.\nEach node is assigned a unique Node Id when it enters a\ntrail. In our current prototype, we have allocated one byte\nfor Node Id, although this can be increased to two or more\nbytes if a large number of hikers are expected to be present\nat the same time. We can represent time in 17 bits to a\nsecond precision. So, we have allocated 3 bytes each for Record\nTime and Location Time. The circumference of the Earth\nis approximately 40,075 KM. If we use a 32-bit number to\nrepresent both longitude and latitude, the precision we get\nis 40,075,000/232\n= 0.0093 meter = 0.37 inches, which is\nquite precise for our needs. So, we have allocated 4 bytes\neach for X and Y coordinates of the location of a node. In\nfact, a foot precision can be achieved by using only 27 bits.\n3.2 Location Point and Location Inference\nAlthough a GPS receiver provides an accurate location\ninformation, it has it\"s limitation. In canyons and rainy\nforests, a GPS receiver does not work. When there is a\nheavy cloud cover, GPS users have experienced inaccuracy\nin the reported location as well. Unfortunately, a lot of\nhiking trails are in dense forests and canyons, and it\"s not that\nuncommon to rain after hikers start hiking. To address this,\nCenWits incorporates the idea of location points (LP). A\nlocation point can update a sensor node with its current\nlocation whenever the node is near that LP. LPs are placed at\ndifferent locations in a wilderness area where GPS receivers\ndon\"t work. An LP is a very simple device that emits\nprerecorded location information at some regular time interval.\nIt can be placed in difficult-to-reach places such as deep\ncanyons and dense rain forests by simply dropping them\nfrom an airplane. LPs allow a sensor node to determine\nits current location more accurately. However, they are not\n183\nan essential requirement of CenWits. If an LP runs out of\npower, the CenWits will continue to work correctly.\nFigure 5: GPS receiver not working correctly.\nSensors then have to rely on LP to provide coordination\nIn Figure 5, B cannot get GPS reception due to bad\nweather. It then runs into A on the trail who doesn\"t have\nGPS reception either. Their sensors record the presence of\neach other. After 10 minutes, A is in range of an LP that\nprovides an accurate location information to A. When A\nreturns to trail head and uploads its data (Figure 6), the\nsystem can draw a circle centered at the LP from which A\nfetched location information for the range of encounter\nlocation of A and B. By Overlapping this circle with the trail\nmap, two or three possible location of encounter can be\ninferred. Thus when a rescue is required, the possible location\nof B can be better inferred (See Figures 7 and 8).\nFigure 6: A is back to trail head, It reports the\ntime of encounter with B to AP, but no location\ninformation to AP\nFigure 7: B is still missing after sunset. CenWits\ninfers the last contact point and draws the circle of\npossible current locations based on average hiking\nspeed\nCenWits requires that the clocks of different sensor nodes\nbe loosely synchronized with one another. Such a\nsynchronization is trivial when GPS coverage is available. In\naddition, sensor nodes in CenWits synchronize their clocks\nwhenever they are in the range of an AP or an LP. The\nFigure 8: Based on overlapping landscape, B might\nhave hiked to wrong branch and fallen off a cliff. Hot\nrescue areas can thus be determined\nsynchronization accuracy Cenwits needs is of the order of a\nsecond or so. As long as the clocks are synchronized with in\none second range, whether A met B at 12:37\"45 or 12:37\"46\ndoesn\"t matter in the ordering of witness events and\ninferring the path.\n4. MEMORY AND POWER MANAGEMENT\nCenWits employs several important mechanisms to\nconserve power and memory. It is important to note while\ncurrent sensor nodes have limited amount of memory,\nfuture sensor nodes are expected to have much more memory.\nWith this in mind, the main focus in our design is to\nprovide a tradeoff between the amount of memory available and\namount of power consumption.\n4.1 Memory Management\nThe size of witness information stored at a node can get\nvery large. This is because the node may come across several\nother nodes during a hike, and may end up accumulating a\nlarge amount of witness information over time. To address\nthis problem, CenWits allows a node to pro-actively free up\nsome parts of its memory periodically. This raises an\ninteresting question of when and which witness record should be\ndeleted from the memory of a node? CenWits uses three\ncriteria to determine this: record count, hop count, and record\ngap.\nRecord count refers to the number of witness records with\nsame node id that a node has stored in its memory. A node\nmaintains an integer parameter MAX RECORD COUNT.\nIt stores at most MAX RECORD COUNT witness records\nof any node.\nEvery witness record has a hop count field that stores the\nnumber times (hops) this record has been transferred since\nbeing created. Initially this field is set to 0. Whenever a\nnode receives a witness record from another node, it\nincrements the hop count of that record by 1. A node maintains\nan integer parameter called MAX HOP COUNT. It keeps\nonly those witness records in its memory, whose hop count\nis less than MAX HOP COUNT. The MAX HOP COUNT\nparameter provides a balance between two conflicting goals:\n(1) To ensure that a witness record has been propagated to\nand thus stored at as many nodes as possible, so that it has\na high probability of being dumped at some AP as quickly\nas possible; and (2) To ensure that a witness record is stored\nonly at a few nodes, so that it does not clog up too much of\nthe combined memory of all sensor nodes. We chose to use\nhop count instead of time-to-live to decide when to drop a\npacket. The main reason for this is that the probability of\na packet reaching an AP goes up as the hop count adds up.\nFor example, when the hop count if 5 for a specific record,\n184\nthe record is in at least 5 sensor nodes. On the other hand,\nif we discard old records, without considering hop count,\nthere is no guarantee that the record is present in any other\nsensor node.\nRecord gap refers to the time difference between the record\ntimes of two witness records with the same node id. To\nsave memory, a node n ensures the the record gap between\nany two witness records with the same node id is at least\nMIN RECORD GAP. For each node id i, n stores the\nwitness record with the most recent record time rti, the witness\nwith most recent record time that is at least MIN RECORD GAP\ntime units before rti, and so on until the record count limit\n(MAX RECORD COUNT) is reached.\nWhen a node is tight in memory, it adjusts the three\nparameters, MAX RECORD COUNT, MAX HOP COUNT and\nMIN RECORD GAP to free up some memory. It\ndecrements MAX RECORD COUNT and MAX HOP COUNT,\nand increments MIN RECORD GAP. It then first erases\nall witness records whose hop count exceeds the reduced\nMAX HOP COUNT value, and then erases witness records\nto satisfy the record gap criteria. Also, when a node has\nextra memory space available, e.g. after dumping its witness\ninformation at an access point, it resets MAX RECORD COUNT,\nMAX HOP COUNT and MIN RECORD GAP to some\npredefined values.\n4.2 Power Management\nAn important advantage of using sensors for tracking\npurposes is that we can regulate the behavior of a sensor node\nbased on current conditions. For example, we mentioned\nearlier that a sensor should emit a beacon every 1.7 minute,\ngiven a hiking speed of 1 mile/hour. However, if a user is\nmoving 10 feet/sec, a beacon should be emitted every 10\nseconds. If a user is not moving at all, a beacon can be\nemitted every 10 minutes. In the night, a sensor can be put\ninto sleep mode to save energy, when a user is not likely to\nmove at all for a relatively longer period of time. If a user\nis active for only eight hours in a day, we can put the sensor\ninto sleep mode for the other 16 hours and thus save 2/3rd\nof the energy.\nIn addition, a sensor node can choose to not send any\nbeacons during some time intervals. For example, suppose\nhiker A has communicated its witness information to three\nother hikers in the last five minutes. If it is running low\non power, it can go to receive mode or sleep mode for the\nnext ten minutes. It goes to receive mode if it is still willing\nto receive additional witness information from hikers that it\nencounters in the next ten minutes. It goes to sleep mode if\nit is extremely low on power.\nThe bandwidth and energy limitations of sensor nodes\nrequire that the amount of data transferred among the nodes\nbe reduced to minimum. It has been observed that in some\nscenarios 3000 instructions could be executed for the same\nenergy cost of sending a bit 100m by radio [15]. To reduce\nthe amount of data transfer, CenWits employs a handshake\nprotocol that two nodes execute when they encounter one\nanother. The goal of this protocol is to ensure that a node\ntransmits only as much witness information as the other\nnode is willing to receive. This protocol is initiated when\na node i receives a beacon containing the node ID of the\nsender node j and i has not exchanged witness information\nwith j in the last \u03b4 time units. Assume that i < j. The\nprotocol consists of four phases (See Figure 9):\n1. Phase I: Node i sends its receive constraints and the\nnumber of witness records it has in its memory.\n2. Phase II: On receiving this message from i, j sends its\nreceive constraints and the number of witness records\nit has in its memory.\n3. Phase III: On receiving the above message from j, i\nsends its witness information (filtered based on receive\nconstraints received in phase II).\n4. Phase IV: After receiving the witness records from\ni, j sends its witness information (filtered based on\nreceive constraints received in phase I).\nj\n<Constaints, Witness info size>\n<Constaints, Witness info size>\n<Filtered Witness info>\n<Filtered Witness info>\ni j\nj\nj\ni\ni\ni\nFigure 9: Four-Phase Hand Shake Protocol (i < j)\nReceive constraints are a function of memory and power.\nIn the most general case, they are comprised of the three\nparameters (record count, hop count and record gap) used\nfor memory management. If i is low on memory, it specifies\nthe maximum number of records it is willing to accept from\nj. Similarly, i can ask j to send only those records that\nhave hop count value less than MAX HOP COUNT \u2212 1.\nFinally, i can include its MIN RECORD GAP value in its\nreceive constraints. Note that the handshake protocol is\nbeneficial to both i and j. They save memory by receiving\nonly as much information as they are willing to accept and\nconserve energy by sending only as many witness records as\nneeded.\nIt turns out that filtering witness records based on\nMIN RECORD GAP is complex. It requires that the\nwitness records of any given node be arranged in an order sorted\nby their record time values. Maintaining this sorted order is\ncomplex in memory, because new witness records with the\nsame node id can arrive later that may have to be inserted\nin between to preserve the sorted order. For this reason, the\nreceive constraints in the current CenWits prototype do not\ninclude record gap.\nSuppose i specifies a hop count value of 3. In this case,\nj checks the hop count field of every witness record before\nsending them. If the hop count value is greater than 3, the\nrecord is not transmitted.\n4.3 Groups and Partitions\nTo further reduce communication and increase the\nlifetime of our system, we introduce the notion of groups. The\nidea is based on the concept of abstract regions presented\nin [20]. A group is a set of n nodes that can be defined\nin terms of radio connectivity, geographic location, or other\nproperties of nodes. All nodes within a group can\ncommunicate directly with one another and they share information\nto maintain their view of the external world. At any point\nin time, a group has exactly one leader that communicates\n185\nwith external nodes on behalf of the entire group. A group\ncan be static, meaning that the group membership does not\nchange over the period of time, or it could be dynamic in\nwhich case nodes can leave or join the group. To make our\nanalysis simple and to explain the advantages of group, we\nfirst discuss static groups.\nA static group is formed at the start of a hiking trail or ski\nslope. Suppose there are five family members who want to\ngo for a hike in the Rocky Mountain National Park. Before\nthese members start their hike, each one of them is given\na sensor node and the information is entered in the system\nthat the five nodes form a group. Each group member is\ngiven a unique id and every group member knows about\nother members of the group. The group, as a whole, is also\nassigned an id to distinguish it from other groups in the\nsystem.\nFigure 10: A group of five people. Node 2 is the\ngroup leader and it is communicating on behalf of\nthe group with an external node 17. All other\n(shown in a lighter shade) are in sleep mode.\nAs the group moves through the trail, it exchanges\ninformation with other nodes or groups that it comes across. At\nany point in time, only one group member, called the leader,\nsends and receives information on behalf of the group and\nall other n \u2212 1 group members are put in the sleep mode\n(See Figure 10). It is this property of groups that saves\nus energy. The group leadership is time-multiplexed among\nthe group members. This is done to make sure that a single\nnode does not run out of battery due to continuous exchange\nof information. Thus after every t seconds, the leadership\nis passed on to another node, called the successor, and the\nleader (now an ordinary member) is put to sleep. Since\nenergy is dear, we do not implement an extensive election\nalgorithm for choosing the successor. Instead, we choose the\nsuccessor on the basis of node id. The node with the next\nhighest id in the group is chosen as the successor. The last\nnode, of course, chooses the node with the lowest id as its\nsuccessor.\nWe now discuss the data storage schemes for groups.\nMemory is a scarce resource in sensor nodes and it is therefore\nimportant that witness information be stored efficiently among\ngroup members. Efficient data storage is not a trivial task\nwhen it comes to groups. The tradeoff is between simplicity\nof the scheme and memory savings. A simpler scheme\nincurs lesser energy cost as compared to a more sophisticated\nscheme, but offers lesser memory savings as well. This is\nbecause in a more complicated scheme, the group members\nhave to coordinate to update and store information. After\nconsidering a number of different schemes, we have come\nto a conclusion that there is no optimal storage scheme for\ngroups. The system should be able to adapt according to\nits requirements. If group members are low on battery, then\nthe group can adapt a scheme that is more energy efficient.\nSimilarly, if the group members are running out of memory,\nthey can adapt a scheme that is more memory efficient. We\nfirst present a simple scheme that is very energy efficient but\ndoes not offer significant memory savings. We then present\nan alternate scheme that is much more memory efficient.\nAs already mentioned a group can receive information\nonly through the group leader. Whenever the leader comes\nacross an external node e, it receives information from that\nnode and saves it. In our first scheme, when the timeslot for\nthe leader expires, the leader passes this new information it\nreceived from e to its successor. This is important because\nduring the next time slot, if the new leader comes across\nanother external node, it should be able to pass\ninformation about all the external nodes this group has witnessed\nso far. Thus the information is fully replicated on all nodes\nto maintain the correct view of the world.\nOur first scheme does not offer any memory savings but is\nhighly energy efficient and may be a good choice when the\ngroup members are running low on battery. Except for the\ntime when the leadership is switched, all n \u2212 1 members are\nasleep at any given time. This means that a single member\nis up for t seconds once every n\u2217t seconds and therefore has\nto spend approximately only 1/nth\nof its energy. Thus, if\nthere are 5 members in a group, we save 80% energy, which\nis huge. More energy can be saved by increasing the group\nsize.\nWe now present an alternate data storage scheme that\naims at saving memory at the cost of energy. In this scheme\nwe divide the group into what we call partitions. Partitions\ncan be thought of as subgroups within a group. Each\npartition must have at least two nodes in it. The nodes within a\npartition are called peers. Each partition has one peer\ndesignated as partition leader. The partition leader stays in\nreceive mode at all times, while all others peers a partition stay\nin the sleep mode. Partition leadership is time-multiplexed\namong the peers to make sure that a single node does not\nrun out of battery. Like before, a group has exactly one\nleader and the leadership is time-multiplexed among\npartitions. The group leader also serves as the partition leader\nfor the partition it belongs to (See Figure 11).\nIn this scheme, all partition leaders participate in\ninformation exchange. Whenever a group comes across an external\nnode e, every partition leader receives all witness\ninformation, but it only stores a subset of that information after\nfiltering. Information is filtered in such a way that each\npartition leader has to store only B/K bytes of data, where\nK is the number of partitions and B is the total number\nof bytes received from e. Similarly when a group wants to\nsend witness information to e, each partition leader sends\nonly B/K bytes that are stored in the partition it belongs\nto. However, before a partition leader can send information,\nit must switch from receive mode to send mode. Also,\npartition leaders must coordinate with one another to ensure\nthat they do not send their witness information at the same\ntime, i.e. their message do not collide. All this is achieved\nby having the group leader send a signal to every partition\nleader in turn.\n186\nFigure 11: The figure shows a group of eight nodes\ndivided into four partitions of 2 nodes each. Node\n1 is the group leader whereas nodes 2, 9, and 7 are\npartition leaders. All other nodes are in the sleep\nmode.\nSince the partition leadership is time-multiplexed, it is\nimportant that any information received by the partition\nleader, p1, be passed on to the next leader, p2. This has\nto be done to make sure that p2 has all the information\nthat it might need to send when it comes across another\nexternal node during its timeslot. One way of achieving this\nis to wake p2 up just before p1\"s timeslot expires and then\nhave p1 transfer information only to p2. An alternate is to\nwake all the peers up at the time of leadership change, and\nthen have p1 broadcast the information to all peers. Each\npeer saves the information sent by p1 and then goes back\nto sleep. In both cases, the peers send acknowledgement to\nthe partition leader after receiving the information. In the\nformer method, only one node needs to wake up at the time\nof leadership change, but the amount of information that\nhas to be transmitted between the nodes increases as time\npasses. In the latter case, all nodes have to be woken up at\nthe time of leadership change, but small piece of information\nhas to be transmitted each time among the peers. Since\ncommunication is much more expensive than bringing the\nnodes up, we prefer the second method over the first one.\nA group can be divided into partitions in more than one\nway. For example, suppose we have a group of six members.\nWe can divide this group into three partitions of two peers\neach, or two partitions with three peers each. The choice\nonce again depends on the requirements of the system. A\nfew big partitions will make the system more energy efficient.\nThis is because in this configuration, a greater number of\nnodes will stay in sleep mode at any given point in time.\nOn the other hand, several small partitions will make the\nsystem memory efficient, since each node will have to store\nlesser information (See Figure 12).\nA group that is divided into partitions must be able to\nreadjust itself when a node leaves or runs out of battery.\nThis is crucial because a partition must have at least two\nnodes at any point in time to tolerate failure of one node.\nFor example, in figure 3 (a), if node 2 or node 5 dies, the\npartition is left with only one node. Later on, if that single\nnode in the partition dies, all witness information stored in\nthat partition will be lost. We have devised a very simple\nprotocol to solve this problem. We first explain how\npartiFigure 12: The figure shows two different ways of\npartitioning a group of six nodes. In (a), a group\nis divided into three partitions of two nodes. Node\n1 is the group leader, nodes 9 and 5 are partition\nleaders, and nodes 2, 3, and 6 are in sleep mode. In\n(b) the group is divided into two partitions of three\nnodes. Node 1 is the group leader, node 9 is the\npartition leader and nodes 2, 3, 5, and 6 are in sleep\nmode.\ntions are adjusted when a peer dies, and then explain what\nhappens if a partition leader dies.\nSuppose node 2 in figure 3 (a) dies. When node 5, the\npartition leader, sends information to node 2, it does not\nreceive an acknowledgement from it and concludes that node\n2 has died2\n. At this point, node 5 contacts other partition\nleaders (nodes 1 ... 9) using a broadcast message and\ninforms them that one of its peers has died. Upon hearing\nthis, each partition leader informs node 5 (i) the number of\nnodes in its partition, (ii) a candidate node that node 5 can\ntake if the number of nodes in its partition is greater than\n2, and (iii) the amount of witness information stored in its\npartition. Upon hearing from every leader, node 5 chooses\nthe candidate node from the partition with maximum\nnumber (must be greater than 2) of peers, and sends a message\nback to all leaders. Node 5 then sends data to its new peer\nto make sure that the information is replicated within the\npartition.\nHowever, if all partitions have exactly two nodes, then\nnode 5 must join another partition. It chooses the partition\nthat has the least amount of witness information to join. It\nsends its witness information to the new partition leader.\nWitness information and membership update is propagated\nto all peers during the next partition leadership change.\nWe now consider the case where the partition leader dies.\nIf this happens, then we wait for the partition leadership to\nchange and for the new partition leader to eventually find\nout that a peer has died. Once the new partition leader finds\nout that it needs more peers, it proceeds with the protocol\nexplained above. However, in this case, we do lose\ninformation that the previous partition leader might have received\njust before it died. This problem can be solved by\nimplementing a more rigorous protocol, but we have decided to\ngive up on accuracy to save energy.\nOur current design uses time-division multiplexing to\nschedule wakeup and sleep modes in the sensor nodes. However,\nrecent work on radio wakeup sensors [10] can be used to do\nthis scheduling more efficiently. we plan to incorporate radio\nwakeup sensors in CenWits when the hardware is mature.\n2\nThe algorithm to conclude that a node has died can be\nmade more rigorous by having the partition leader query\nthe suspected node a few times.\n187\n5. SYSTEM EVALUATION\nA sensor is constrained in the amount of memory and\npower. In general, the amount of memory needed and power\nconsumption depends on a variety of factors such as node\ndensity, number of hiker encounters, and the number of\naccess points. In this Section, we provide an estimate of how\nlong the power of a MICA2 mote will last under certain\nassumtions.\nFirst, we assume that each sensor node carries about 100\nwitness records. On encountering another hiker, a sensor\nnode transmits 50 witness records and receives 50 new\nwitness records. Since, each record is 16 bytes long, it will take\n0.34 seconds to transmit 50 records and another 0.34\nseconds to receive 50 records over a 19200 bps link. The power\nconsumption of MICA2 due to CPU processing,\ntransmission and reception are approximately 8.0 mA, 7.0 mA and\n8.5 mA per hour respectively [18], and the capacity of an\nalkaline battery is 2500mAh.\nSince the radio module of Mica2 is half-duplex and\nassuming that the CPU is always active when a node is awake,\npower consumption due to transmission is 8 + 8.5 = 16.5\nmA per hour and due to reception is 8 + 7 = 15mA per\nhour. So, average power consumtion due to transmission\nand reception is (16.5 + 15)/2 = 15.75 mA per hour.\nGiven that the capacity of an alkaline battery is 2500\nmAh, a battery should last for 2500/15.75 = 159 hours of\ntransmission and reception. An encounter between two\nhikers results in exchange of about 50 witness records that takes\nabout 0.68 seconds as calculated above. Thus, a single\nalkaline battery can last for (159 \u2217 60 \u2217 60)/0.68 = 841764 hiker\nencounters.\nAssuming that a node emits a beacon every 90 seconds\nand a hiker encounter occurs everytime a beacon is emitted\n(worst-case scenario), a single alkaline battery will last for\n(841764 \u2217 90)/(30 \u2217 24 \u2217 60 \u2217 60) = 29 days. Since, a Mica2\nis equipped with two batteries, a Mica2 sensor can remain\noperation for about two months. Notice that this\ncalculation is preliminary, because it assumes that hikers are active\n24 hours of the day and a hiker encounter occurs every 90\nseconds. In a more realistic scenario, power is expected to\nlast for a much longer time period. Also, this time period\nwill significantly increase when groups of hikers are moving\ntogether.\nFinally, the lifetime of a sensor running on two\nbatteries can definitely be increased significantly by using energy\nscavenging techniques and energy harvesting techniques [16,\n14].\n6. PROTOTYPE IMPLEMENTATION\nWe have implemented a prototype of CenWits on MICA2\nsensor 900MHz running Mantis OS 0.9.1b. One of the sensor\nis equipped with MTS420CA GPS module, which is capable\nof barometric pressure and two-axis acceleration sensing in\naddition to GPS location tracking. We use SiRF, the serial\ncommunication protocol, to control GPS module. SiRF has\na rich command set, but we record only X and Y coordinates.\nA witness record is 16 bytes long. When a node starts up, it\nstores its current location and emits a beacon\nperiodicallyin the prototype, a node emits a beacon every minute.\nWe have conducted a number of experiments with this\nprototype. A detailed report on these experiments with the\nraw data collected and photographs of hikers, access points\netc. is available at http://csel.cs.colorado.edu/\u223chuangjh/\nCenwits.index.htm. Here we report results from three of\nthem. In all these experiments, there are three access points\n(A, B and C) where nodes dump their witness information.\nThese access points also provide location information to the\nnodes that come with in their range. We first show how\nCenWits can be used to determine the hiking trail a hiker is most\nlikely on and the speed at which he is hiking, and identify\nhot search areas in case he is reported missing. Next, we\nshow the results of power and memory management\ntechniques of CenWits in conserving power and memory of a\nsensor node in one of our experiments.\n6.1 Locating Lost Hikers\nThe first experiment is called Direct Contact. It is a very\nsimple experiment in which a single hiker starts from A,\ngoes to B and then C, and finally returns to A (See Figure\n13). The goal of this experiment is to illustrate that\nCenWits can deduce the trail a hiker takes by processing witness\ninformation.\nFigure 13: Direct Contact Experiment\nNode Id Record (X,Y) Location Hop\nTime Time Count\n1 15 (12,7) 15 0\n1 33 (31,17) 33 0\n1 46 (12,23) 46 0\n1 10 (12,7) 10 0\n1 48 (12,23) 48 0\n1 16 (12,7) 16 0\n1 34 (31,17) 34 0\nTable 1: Witness information collected in the direct\ncontact experiment.\nThe witness information dumped at the three access points\nwas then collected and processed at a control center. Part\nof the witness information collected at the control center is\nshown in Table 1. The X,Y locations in this table\ncorrespond to the location information provided by access points\nA, B, and C. A is located at (12,7), B is located at (31,17)\nand C is located at (12,23). Three encounter points\n(between hiker 1 and the three access points) extracted from\n188\nthis witness information are shown in Figure 13 (shown in\nrectangular boxes). For example, A,1 at 16 means 1 came in\ncontact with A at time 16. Using this information, we can\ninfer the direction in which hiker 1 was moving and speed at\nwhich he was moving. Furthermore, given a map of hiking\ntrails in this area, it is clearly possible to identify the hiking\ntrail that hiker 1 took.\nThe second experiment is called Indirect Inference. This\nexperiment is designed to illustrate that the location,\ndirection and speed of a hiker can be inferred by CenWits, even\nif the hiker never comes in the range of any access point. It\nillustrates the importance of witness information in search\nand rescue applications. In this experiment, there are three\nhikers, 1, 2 and 3. Hiker 1 takes a trail that goes along\naccess points A and B, while hiker 3 takes trail that goes along\naccess points C and B. Hiker 2 takes a trail that does not\ncome in the range of any access points. However, this hiker\nmeets hiker 1 and 3 during his hike. This is illustrated in\nFigure 14.\nFigure 14: Indirect Inference Experiment\nNode Id Record (X,Y) Location Hop\nTime Time Count\n2 16 (12,7) 6 0\n2 15 (12,7) 6 0\n1 4 (12,7) 4 0\n1 6 (12,7) 6 0\n1 29 (31,17) 29 0\n1 31 (31,17) 31 0\nTable 2: Witness information collected from hiker 1\nin indirect inference experiment.\nPart of the witness information collected at the control\ncenter from access points A, B and C is shown in Tables\n2 and 3. There are some interesting data in these tables.\nFor example, the location time in some witness records is\nnot the same as the record time. This means that the node\nthat generated that record did not have its most up-to-date\nlocation at the encounter time. For example, when hikers\n1 and 2 meet at time 16, the last recorded location time of\nNode Id Record (X,Y) Location Hop\nTime Time Count\n3 78 (12,23) 78 0\n3 107 (31,17) 107 0\n3 106 (31,17) 106 0\n3 76 (12,23) 76 0\n3 79 (12,23) 79 0\n2 94 (12,23) 79 0\n1 16 (?,?) ? 1\n1 15 (?,?) ? 1\nTable 3: Witness information collected from hiker 3\nin indirect inference experiment.\nhiker 1 is (12,7) recorded at time 6. So, node 1 generates\na witness record with record time 16, location (12,7) and\nlocation time 6. In fact, the last two records in Table 3\nhave (?,?) as their location. This has happened because\nthese witness records were generate by hiker 2 during his\nencounter with 1 at time 15 and 16. Until this time, hiker\n2 hadn\"t come in contact with any location points.\nInterestingly, a more accurate location information of 1\nand 2 encounter or 2 and 3 encounter can be computed by\nprocess the witness information at the control center. It\ntook 25 units of time for hiker 1 to go from A (12,7) to B\n(31,17). Assuming a constant hiking speed and a relatively\nstraight-line hike, it can be computed that at time 16, hiker\n1 must have been at location (18,10). Thus (18,10) is a more\naccurate location of encounter between 1 and 2.\nFinally, our third experiment called Identifying Hot Search\nAreas is designed to determine the trail a hiker has taken\nand identify hot search areas for rescue after he is reported\nmissing. There are six hikers (1, 2, 3, 4, 5 and 6) in this\nexperiment. Figure 15 shows the trails that hikers 1, 2,\n3, 4 and 5 took, along with the encounter points obtained\nfrom witness records collected at the control center. For\nbrevity, we have not shown the entire witness information\ncollected at the control center. This information is available\nat http://csel.cs.colorado.edu/\u223chuangjh/Cenwits/index.htm.\nFigure 15: Identifying Hot Search Area Experiment\n(without hiker 6)\n189\nNow suppose hiker 6 is reported missing at time 260. To\ndetermine the hot search areas, the witness records of hiker\n6 are processed to determine the trail he is most likely on,\nthe speed at which he had been moving, direction in which\nhe had been moving, and his last known location. Based on\nthis information and the hiking trail map, hot search areas\nare identified. The hiking trail taken by hiker 6 as inferred\nby CenWits is shown by a dotted line and the hot search\nareas identified by CenWits are shown by dark lines inside\nthe dotted circle in Figure 16.\nFigure 16: Identifying Hot Search Area Experiment\n(with hiker 6)\n6.2 Results of Power and Memory\nManagement\nThe witness information shown in Tables 1, 2 and 3 has\nnot been filtered using the three criteria described in\nSection 4.1. For example, the witness records generated by 3 at\nrecord times 76, 78 and 79 (see Table 3) have all been\ngenerated due a single contact between access point C and node\n3. By applying the record gap criteria, two of these three\nrecords will be erased. Similarly, the witness records\ngenerated by 1 at record times 10, 15 and 16 (see Table 1) have\nall been generated due a single contact between access point\nA and node 1. Again, by applying the record gap criteria,\ntwo of these three records will be erased. Our experiments\ndid not generate enough data to test the impact of record\ncount or hop count criteria.\nTo evaluate the impact of these criteria, we simulated\nCenWits to generate a significantly large number of records for a\ngiven number of hikers and access points. We generated\nwitness records by having the hikers walk randomly. We applied\nthe three criteria to measure the amount of memory savings\nin a sensor node. The results are shown in Table 4. The\nnumber of hikers in this simulation was 10 and the number\nof access points was 5. The number of witness records\nreported in this table is an average number of witness records\na sensor node stored at the time of dump to an access point.\nThese results show that the three memory management\ncriteria significantly reduces the memory consumption of\nsensor nodes in CenWits. For example, they can reduce\nMAX MIN MAX # of\nRECORD RECORD HOP Witness\nCOUNT GAP COUNT Records\n5 5 5 628\n4 5 5 421\n3 5 5 316\n5 10 5 311\n5 20 5 207\n5 5 4 462\n5 5 3 341\n3 20 3 161\nTable 4: Impact of memory management techniques.\nthe memory consumption by up to 75%. However, these\nresults are premature at present for two reasons: (1) They\nare generated via simulation of hikers walking at random;\nand (2) It is not clear what impact the erasing of witness\nrecords has on the accuracy of inferred location/hot search\nareas of lost hikers. In our future work, we plan to undertake\na major study to address these two concerns.\n7. OTHER APPLICATIONS\nIn addition to the hiking in wilderness areas, CenWits can\nbe used in several other applications, e.g. skiing, climbing,\nwild life monitoring, and person tracking. Since CenWits\nrelies only on intermittent connectivity, it can take advantage\nof the existing cheap and mature technologies, and thereby\nmake tracking cheaper and fairly accurate. Since CenWits\ndoesn\"t rely on keeping track of a sensor holder all time,\nbut relies on maintaining witnesses, the system is relatively\ncheaper and widely applicable. For example, there are some\ndangerous cliffs in most ski resorts. But it is too expensive\nfor a ski resort to deploy a connected wireless sensor network\nthrough out the mountain. Using CenWits, we can deploy\nsome sensors at the cliff boundaries. These boundary\nsensors emit beacons quite frequently, e.g. every second, and\nso can record presence of skiers who cross the boundary and\nfall off the cliff. Ski patrols can cruise the mountains every\nhour, and automatically query the boundary sensor when in\nrange using PDAs. If a PDA shows that a skier has been\nclose to the boundary sensor, the ski patrol can use a long\nrange walkie-talkie to query control center at the resort base\nto check the witness record of the skier. If there is no\nwitness record after the recorded time in the boundary sensor,\nthere is a high chance that a rescue is needed.\nIn wildlife monitoring, a very popular method is to attach\na GPS receiver on the animals. To collect data, either a\nsatellite transmitter is used, or the data collector has to\nwait until the GPS receiver brace falls off (after a year or so)\nand then search for the GPS receiver. GPS transmitters are\nvery expensive, e.g. the one used in geese tracking is $3,000\neach [2]. Also, it is not yet known if continuous radio signal\nis harmful to the birds. Furthermore, a GPS transmitter is\nquite bulky and uncomfortable, and as a result, birds always\ntry to get rid of it. Using CenWits, not only can we record\nthe presence of wildlife, we can also record the behavior\nof wild animals, e.g. lions might follow the migration of\ndeers. CenWits does nor require any bulky and expensive\nsatellite transmitters, nor is there a need to wait for a year\nand search for the braces. CenWits provides a very simple\nand cost-effective solution in this case. Also, access points\n190\ncan be strategically located, e.g. near a water source, to\nincrease chances of collecting up-to-date data. In fact, the\naccess points need not be statically located. They can be\nplaced in a low-altitude plane (e.g a UAV) and be flown over\na wilderness area to collect data from wildlife.\nIn large cities, CenWits can be used to complement GPS,\nsince GPS doesn\"t work indoor and near skyscrapers. If a\nperson A is reported missing, and from the witness records\nwe find that his last contacts were C and D, we can trace\nan approximate location quickly and quite efficiently.\n8. DISCUSSION AND FUTURE WORK\nThis paper presents a new search and rescue system called\nCenWits that has several advantages over the current search\nand rescue systems. These advantages include a\nlooselycoupled system that relies only on intermittent network\nconnectivity, power and storage efficiency, and low cost. It\nsolves one of the greatest problems plaguing modern search\nand rescue systems: it has an inherent on-site storage\ncapability. This means someone within the network will have\naccess to the last-known-location information of a victim,\nand perhaps his bearing and speed information as well. It\nutilizes the concept of witnesses to propagate information,\ninfer current possible location and speed of a subject, and\nidentify hot search and rescue areas in case of emergencies.\nA large part of CenWits design focuses on addressing the\npower and memory limitations of current sensor nodes. In\nfact, power and memory constraints depend on how much\nweight (of sensor node) a hiker is willing to carry and the\ncost of these sensors. An important goal of CenWits is build\nsmall chips that can be implanted in hiking boots or ski\njackets. This goal is similar to the avalanche beacons that\nare currently implanted in ski jackets. We anticipate that\npower and memory will continue to be constrained in such\nan environment.\nWhile the paper focuses on the development of a search\nand rescue system, it also provides some innovative,\nsystemlevel ideas for information processing in a sensor network\nsystem.\nWe have developed and experimented with a basic\nprototype of CenWits at present. Future work includes\ndeveloping a more mature prototype addressing important issues\nsuch as security, privacy, and high availability. There are\nseveral pressing concerns regarding security, privacy, and\nhigh availability in CenWits. For example, an adversary\ncan sniff the witness information to locate endangered\nanimals, females, children, etc. He may inject false information\nin the system. An individual may not be comfortable with\nproviding his/her location and movement information, even\nthough he/she is definitely interested in being located in a\ntimely manner at the time of emergency. In general, people\nin hiking community are friendly and usually trustworthy.\nSo, a bullet-proof security is not really required. However,\nwhen CenWits is used in the context of other applications,\nsecurity requirements may change. Since the sensor nodes\nused in CenWits are fragile, they can fail. In fact, the nature\nand level of security, privacy and high availability support\nneeded in CenWits strongly depends on the application for\nwhich it is being used and the individual subjects involved.\nAccordingly, we plan to design a multi-level support for\nsecurity, privacy and high availability in CenWits.\nSo far, we have experimented with CenWits in a very\nrestricted environment with a small number of sensors. Our\nnext goal is to deploy this system in a much larger and more\nrealistic environment. In particular, discussions are currenly\nunderway to deploy CenWits in the Rocky Mountain and\nYosemite National Parks.\n9. 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Jaskowski, K. Jedrzejek, B. Nyczkowski, and\nS. Skowronek. Lifetch life saving system. CSIDC, 2004.\n[13] P. Juang, H. Oki, Y. Wang, M. Martonosi, L. Peh,\nand D. Rubenstein. Energy-efficient computing for\nwildlife tracking: design tradeoffs and early\nexperiences with ZebraNet. In ASPLOS, 2002.\n[14] K. Kansal and M. Srivastava. Energy harvesting aware\npower management. In Wireless Sensor Networks: A\nSystems Perspective, 2005.\n[15] G. J. Pottie and W. J. Kaiser. Embedding the\ninternet: wireless integrated network sensors.\nCommunications of the ACM, 43(5), May 2000.\n[16] S. Roundy, P. K. Wright, and J. Rabaey. A study of\nlow-level vibrations as a power source for wireless\nsensor networks. Computer Communications, 26(11),\n2003.\n[17] C. Savarese, J. M. Rabaey, and J. Beutel. Locationing\nin distributed ad-hoc wireless sensor networks.\nICASSP, 2001.\n[18] V. Shnayder, M. Hempstead, B. Chen, G. Allen, and\nM. Welsh. Simulating the power consumption of\nlarge-scale sensor network applications. In Sensys,\n2004.\n[19] R. Want and A. Hopper. Active badges and personal\ninteractive computing objects. IEEE Transactions of\nConsumer Electronics, 1992.\n[20] M. Welsh and G. Mainland. Programming sensor\nnetworks using abstract regions. First USENIX/ACM\nSymposium on Networked Systems Design and\nImplementation (NSDI \"04), 2004.\n191", "keywords": "intermittent network connectivity;gp receiver;pervasive computing;connected network;satellite transmitter;emergency situation;search and rescue;witness;beacon;location tracking system;rf transmitter;group and partition;sensor network;hiker"}
{"name": "train_C-52", "title": "Fairness in Dead-Reckoning based Distributed Multi-Player Games", "abstract": "In a distributed multi-player game that uses dead-reckoning vectors to exchange movement information among players, there is inaccuracy in rendering the objects at the receiver due to network delay between the sender and the receiver. The object is placed at the receiver at the position indicated by the dead-reckoning vector, but by that time, the real position could have changed considerably at the sender. This inaccuracy would be tolerable if it is consistent among all players; that is, at the same physical time, all players see inaccurate (with respect to the real position of the object) but the same position and trajectory for an object. But due to varying network delays between the sender and different receivers, the inaccuracy is different at different players as well. This leads to unfairness in game playing. In this paper, we first introduce an error measure for estimating this inaccuracy. Then we develop an algorithm for scheduling the sending of dead-reckoning vectors at a sender that strives to make this error equal at different receivers over time. This algorithm makes the game very fair at the expense of increasing the overall mean error of all players. To mitigate this effect, we propose a budget based algorithm that provides improved fairness without increasing the mean error thereby maintaining the accuracy of game playing. We have implemented both the scheduling algorithm and the budget based algorithm as part of BZFlag, a popular distributed multi-player game. We show through experiments that these algorithms provide fairness among players in spite of widely varying network delays. An additional property of the proposed algorithms is that they require less number of DRs to be exchanged (compared to the current implementation of BZflag) to achieve the same level of accuracy in game playing.", "fulltext": "1. INTRODUCTION\nIn a distributed multi-player game, players are normally\ndistributed across the Internet and have varying delays to each other\nor to a central game server. Usually, in such games, the players are\npart of the game and in addition they may control entities that make\nup the game. During the course of the game, the players and the\nentities move within the game space. A player sends information\nabout her movement as well as the movement of the entities she\ncontrols to the other players using a Dead-Reckoning (DR) vector.\nA DR vector contains information about the current position of the\nplayer/entity in terms of x, y and z coordinates (at the time the DR\nvector was sent) as well as the trajectory of the entity in terms of\nthe velocity component in each of the dimensions. Each of the\nparticipating players receives such DR vectors from one another and\nrenders the other players/entities on the local consoles until a new\nDR vector is received for that player/entity. In a peer-to-peer game,\nplayers send DR vectors directly to each other; in a client-server\ngame, these DR vectors may be forwarded through a game server.\nThe idea of DR is used because it is almost impossible for\nplayers/entities to exchange their current positions at every time unit.\nDR vectors are quantization of the real trajectory (which we refer\nto as real path) at a player. Normally, a new DR vector is computed\nand sent whenever the real path deviates from the path extrapolated\nusing the previous DR vector (say, in terms of distance in the x, y,\nz plane) by some amount specified by a threshold. We refer to the\ntrajectory that can be computed using the sequence of DR vectors\nas the exported path. Therefore, at the sending player, there is a\ndeviation between the real path and the exported path. The error due\nto this deviation can be removed if each movement of player/entity\nis communicated to the other players at every time unit; that is a\nDR vector is generated at every time unit thereby making the real\nand exported paths the same. Given that it is not feasible to\nsatisfy this due to bandwidth limitations, this error is not of practical\ninterest. Therefore, the receiving players can, at best, follow the\nexported path. Because of the network delay between the sending\nand receiving players, when a DR vector is received and rendered\nat a player, the original trajectory of the player/entity may have\nalready changed. Thus, in physical time, there is a deviation at the\nreceiving player between the exported path and the rendered\ntrajectory (which we refer to as placed path). We refer to this error\nas the export error. Note that the export error, in turn, results in a\ndeviation between the real and the placed paths.\nThe export error manifests itself due to the deviation between the\nexported path at the sender and the placed path at the receiver (i)\n1\nbefore the DR vector is received at the receiver (referred to as the\nbefore export error, and (ii) after the DR vector is received at the\nreceiver (referred to as the after export error). In an earlier paper [1],\nwe showed that by synchronizing the clocks at all the players and\nby using a technique based on time-stamping messages that carry\nthe DR vectors, we can guarantee that the after export error is made\nzero. That is, the placed and the exported paths match after the DR\nvector is received. We also showed that the before export error can\nnever be eliminated since there is always a non-zero network delay,\nbut can be significantly reduced using our technique [1].\nHenceforth we assume that the players use such a technique which results\nin unavoidable but small overall export error.\nIn this paper we consider the problem of different and varying\nnetwork delays between each sender-receiver pair of a DR vector,\nand consequently, the different and varying export errors at the\nreceivers. Due to the difference in the export errors among the\nreceivers, the same entity is rendered at different physical time at\ndifferent receivers. This brings in unfairness in game playing. For\ninstance a player with a large delay would always see an entity\nlate in physical time compared to the other players and,\ntherefore, her action on the entity would be delayed (in physical time)\neven if she reacted instantaneously after the entity was rendered.\nOur goal in this paper is to improve the fairness of these games in\nspite of the varying network delays by equalizing the export error\nat the players. We explore whether the time-average of the export\nerrors (which is the cumulative export error over a period of time\naveraged over the time period) at all the players can be made the\nsame by scheduling the sending of the DR vectors appropriately at\nthe sender. We propose two algorithms to achieve this.\nBoth the algorithms are based on delaying (or dropping) the\nsending of DR vectors to some players on a continuous basis to\ntry and make the export error the same at all the players. At an\nabstract level, the algorithm delays sending DR vectors to players\nwhose accumulated error so far in the game is smaller than others;\nthis would mean that the export error due to this DR vector at these\nplayers will be larger than that of the other players, thereby making\nthem the same. The goal is to make this error at least approximately\nequal at every DR vector with the deviation in the error becoming\nsmaller as time progresses.\nThe first algorithm (which we refer to as the scheduling\nalgorithm) is based on estimating the delay between players and\nrefining the sending of DR vectors by scheduling them to be sent\nto different players at different times at every DR generation point.\nThrough an implementation of this algorithm using the open source\ngame BZflag, we show that this algorithm makes the game very fair\n(we measure fairness in terms of the standard deviation of the\nerror). The drawback of this algorithm is that it tends to push the\nerror of all the players towards that of the player with the worst\nerror (which is the error at the farthest player, in terms of delay,\nfrom the sender of the DR). To alleviate this effect, we propose\na budget based algorithm which budgets how the DRs are sent to\ndifferent players. At a high level, the algorithm is based on the\nidea of sending more DRs to players who are farther away from\nthe sender compared to those who are closer. Experimental results\nfrom BZflag illustrates that the budget based algorithm follows a\nmore balanced approach. It improves the fairness of the game but\nat the same time does so without pushing up the mean error of the\nplayers thereby maintaining the accuracy of the game. In addition,\nthe budget based algorithm is shown to achieve the same level of\naccuracy of game playing as the current implementation of BZflag\nusing much less number of DR vectors.\n2. PREVIOUS WORK\nEarlier work on network games to deal with network latency has\nmostly focussed on compensation techniques for packet delay and\nloss [2, 3, 4]. These methods are aimed at making large delays and\nmessage loss tolerable for players but does not consider the\nproblems that may be introduced by varying delays from the server to\ndifferent players or from the players to one another. For example,\nthe concept of local lag has been used in [3] where each player\ndelays every local operation for a certain amount of time so that\nremote players can receive information about the local operation and\nexecute the same operation at the about same time, thus reducing\nstate inconsistencies. The online multi-player game MiMaze [2, 5,\n6], for example, takes a static bucket synchronization approach to\ncompensate for variable network delays. In MiMaze, each player\ndelays all events by 100 ms regardless of whether they are\ngenerated locally or remotely. Players with a network delay larger\nthan 100 ms simply cannot participate in the game. In general,\ntechniques based on bucket synchronization depend on imposing a\nworst case delay on all the players.\nThere have been a few papers which have studied the problem of\nfairness in a distributed game by more sophisticated message\ndelivery mechanisms. But these works [7, 8] assume the existence of\na global view of the game where a game server maintains a view\n(or state) of the game. Players can introduce objects into the game\nor delete objects that are already part of the game (for example, in\na first-person shooter game, by shooting down the object). These\nadditions and deletions are communicated to the game server\nusing action messages. Based on these action messages, the state\nof the game is changed at the game server and these changes are\ncommunicated to the players using update messages. Fairness is\nachieved by ordering the delivery of action and update messages at\nthe game server and players respectively based on the notion of a\nfair-order which takes into account the delays between the game\nserver and the different players. Objects that are part of the game\nmay move but how this information is communicated to the players\nseems to be beyond the scope of these works. In this sense, these\nworks are very limited in scope and may be applicable only to\nfirstperson shooter games and that too to only games where players are\nnot part of the game.\nDR vectors can be exchanged directly among the players\n(peerto-peer model) or using a central server as a relay (client-server\nmodel). It has been shown in [9] that multi-player games that\nuse DR vectors together with bucket synchronization are not\ncheatproof unless additional mechanisms are put in place. Both the\nscheduling algorithm and the budget-based algorithm described in\nour paper use DR vectors and hence are not cheat-proof. For\nexample, a receiver could skew the delay estimate at the sender to\nmake the sender believe that the delay between the sender and the\nreceiver is high thereby gaining undue advantage. We emphasize\nthat the focus of this paper is on fairness without addressing the\nissue of cheating.\nIn the next section, we describe the game model that we use\nand illustrate how senders and receivers exchange DR vectors and\nhow entities are rendered at the receivers based on the time-stamp\naugmented DR vector exchange as described in [1]. In Section 4,\nwe describe the DR vector scheduling algorithm that aims to make\nthe export error equal across the players with varying delays from\nthe sender of a DR vector, followed by experimental results\nobtained from instrumentation of the scheduling algorithm on the\nopen source game BZFlag. Section 5, describes the budget based\nalgorithm that achieves improved fairness but without reducing the\nlevel accuracy of game playing. Conclusions are presented in\nSection 6.\n2\n3. GAME MODEL\nThe game architecture is based on players distributed across the\nInternet and exchanging DR vectors to each other. The DR\nvectors could either be sent directly from one player to another\n(peerto-peer model) or could be sent through a game server which\nreceives the DR vector from a player and forwards it to other players\n(client-server model). As mentioned before, we assume\nsynchronized clocks among the participating players.\nEach DR vector sent from one player to another specifies the\ntrajectory of exactly one player/entity. We assume a linear DR vector\nin that the information contained in the DR vector is only enough at\nthe receiving player to compute the trajectory and render the entity\nin a straight line path. Such a DR vector contains information about\nthe starting position and velocity of the player/entity where the\nvelocity is constant1\n. Thus, the DR vectors sent by a player specifies\nthe current time at the player when the DR vector is computed (not\nthe time at which this DR vector is sent to the other players as we\nwill explain later), the current position of the player/entity in terms\nof the x, y, z coordinates and the velocity vector in the direction\nof x, y and z coordinates. Specifically, the ith\nDR vector sent by\nplayer j about the kth\nentity is denoted by DRj\nik and is represented\nby the following tuple (Tj\nik, xj\nik, yj\nik, zj\nik, vxj\nik, vyj\nik, vzj\nik).\nWithout loss of generality, in the rest of the discussion, we\nconsider a sequence of DR vectors sent by only one player and for\nonly one entity. For simplicity, we consider a two dimensional\ngame space rather than a three dimensional one. Hence we use\nDRi to denote the ith\nsuch DR vector represented as the tuple\n(Ti, xi, yi, vxi, vyi). The receiving player computes the starting\nposition for the entity based on xi, yi and the time difference\nbetween when the DR vector is received and the time Ti at which it\nwas computed. Note that the computation of time difference is\nfeasible since all the clocks are synchronized. The receiving player\nthen uses the velocity components to project and render the\ntrajectory of the entity. This trajectory is followed until a new DR vector\nis received which changes the position and/or velocity of the entity.\ntimeT1\nReal\nExported\nPlaced\ndt1\nA\nB\nC\nD\nDR1\n= (T1, x1, y1, vx1, vy1)\ncomputed at time T1 and\nsent to the receiver\nDR0\n= (T0, x0, y0, vx0, vy0)\ncomputed at time T0 and\nsent to the receiver\nT0\ndt0\nPlaced\nE\nFigure 1: Trajectories and deviations.\nBased on this model, Figure 1 illustrates the sending and\nreceiv1\nOther type of DR vectors include quadratic DR vectors which\nspecify the acceleration of the entity and cubic spline DR vectors\nthat consider the starting position and velocity and the ending\nposition and velocity of the entity.\ning of DR vectors and the different errors that are encountered. The\nfigure shows the reception of DR vectors at a player (henceforth\ncalled the receiver). The horizontal axis shows the time which is\nsynchronized among all the players. The vertical axis tries to\nconceptually capture the two-dimensional position of an entity.\nAssume that at time T0 a DR vector DR0 is computed by the sender\nand immediately sent to the receiver. Assume that DR0 is received\nat the receiver after a delay of dt0 time units. The receiver\ncomputes the initial position of the entity as (x0 + vx0 \u00d7 dt0, y0 +\nvy0 \u00d7 dt0) (shown as point E). The thick line EBD represents the\nprojected and rendered trajectory at the receiver based on the\nvelocity components vx0 and vy0 (placed path). At time T1 a DR vector\nDR1 is computed for the same entity and immediately sent to the\nreceiver2\n. Assume that DR1 is received at the receiver after a delay\nof dt1 time units. When this DR vector is received, assume that the\nentity is at point D. A new position for the entity is computed as\n(x1 + vx1 \u00d7 dt1, y1 + vy0 \u00d7 dt1) and the entity is moved to this\nposition (point C). The velocity components vx1 and vy1 are used\nto project and render this entity further.\nLet us now consider the error due to network delay. Although\nDR1 was computed at time T1 and sent to the receiver, it did not\nreach the receiver until time T1 + dt1. This means, although the\nexported path based on DR1 at the sender at time T1 is the\ntrajectory AC, until time T1 + dt1, at the receiver, this entity was being\nrendered at trajectory BD based on DR0. Only at time T1 + dt1\ndid the entity get moved to point C from which point onwards the\nexported and the placed paths are the same. The deviation between\nthe exported and placed paths creates an error component which we\nrefer to as the export error. A way to represent the export error is\nto compute the integral of the distance between the two trajectories\nover the time when they are out of sync. We represent the integral\nof the distances between the placed and exported paths due to some\nDR DRi over a time interval [t1, t2] as Err(DRi, t1, t2). In the\nfigure, the export error due to DR1 is computed as the integral of\nthe distance between the trajectories AC and BD over the time\ninterval [T1, T1 + dt1]. Note that there could be other ways of\nrepresenting this error as well, but in this paper, we use the integral of\nthe distance between the two trajectories as a measure of the export\nerror. Note that there would have been an export error created due\nto the reception of DR0 at which time the placed path would have\nbeen based on a previous DR vector. This is not shown in the figure\nbut it serves to remind the reader that the export error is cumulative\nwhen a sequence of DR vectors are received. Starting from time\nT1 onwards, there is a deviation between the real and the exported\npaths. As we discussed earlier, this export error is unavoidable.\nThe above figure and example illustrates one receiver only. But\nin reality, DR vectors DR0 and DR1 are sent by the sender to all\nthe participating players. Each of these players receives DR0 and\nDR1 after varying delays thereby creating different export error\nvalues at different players. The goal of the DR vector scheduling\nalgorithm to be described in the next section is to make this\n(cumulative) export error equal at every player independently for each of\nthe entities that make up the game.\n4. SCHEDULING ALGORITHM\nFORSENDING DR VECTORS\nIn Section 3 we showed how delay from the sender of a new DR\n2\nNormally, DR vectors are not computed on a periodic basis but\non an on-demand basis where the decision to compute a new DR\nvector is based on some threshold being exceeded on the deviation\nbetween the real path and the path exported by the previous DR\nvector.\n3\nvector to the receiver of the DR vector could lead to export error\nbecause of the deviation of the placed path from the exported path\nat the receiver until this new DR vector is received. We also\nmentioned that the goal of the DR vector scheduling algorithm is to\nmake the export error equal at all receivers over a period of time.\nSince the game is played in a distributed environment, it makes\nsense for the sender of an entity to keep track of all the errors at the\nreceivers and try to make them equal. However, the sender cannot\nknow the actual error at a receiver till it gets some information\nregarding the error back from the receiver. Our algorithm estimates\nthe error to compute a schedule to send DR vectors to the receivers\nand corrects the error when it gets feedbacks from the receivers. In\nthis section we provide motivations for the algorithm and describe\nthe steps it goes through. Throughout this section, we will use the\nfollowing example to illustrate the algorithm.\ntimeT1\nExported path\nPlaced path\nat receiver 2\ndt1\nA\nB\nC\nD\nE\nF\nT0\nG2\nG1\ndt2\nDR1 sent\nto receiver 1\nDR1 sent\nto receiver 2\nT1\n1 T1\n2\nda1\nda2\nG\nH\nI\nJ\nK\nL\nN\nM\nDR1 estimated\nto be received\nby receiver 2\nDR1 estimated\nto be received\nby receiver 1\nDR1 actually\nreceived by\nreceiver 1\nDR1 actually\nreceived by\nreceiver 2\nDR0 sent to\nboth receivers\nDR1 computed\nby sender\nPlaced path\nat receiver 1\nFigure 2: DR vector flow between a sender and two receivers\nand the evolution of estimated and actual placed paths at the\nreceivers. DR0 = (T0, T0, x0, y0, vx0, vy0), sent at time T0 to\nboth receivers. DR1 = (T1, T1\n1 , x1, y1, vx1, vy1) sent at time\nT1\n1 = T1+\u03b41 to receiver 1 and DR1 = (T1, T2\n1 , x1, y1, vx1, vy1)\nsent at time T2\n1 = T1 + \u03b42 to receiver 2.\nConsider the example in Figure 2. The figure shows a single\nsender sending DR vectors for an entity to two different receivers\n1 and 2. DR0 computed at T0 is sent and received by the receivers\nsometime between T0 and T1 at which time they move the location\nof the entity to match the exported path. Thus, the path of the\nentity is shown only from the point where the placed path matches\nthe exported path for DR0. Now consider DR1. At time T1, DR1\nis computed by the sender but assume that it is not immediately\nsent to the receivers and is only sent after time \u03b41 to receiver 1\n(at time T1\n1 = T1 + \u03b41) and after time \u03b42 to receiver 2 (at time\nT2\n1 = T1 + \u03b42). Note that the sender includes the sending\ntimestamp with the DR vector as shown in the figure. Assume that\nthe sender estimates (it will be clear shortly why the sender has to\nestimate the delay) that after a delay of dt1, receiver 1 will receive\nit, will use the coordinate and velocity parameters to compute the\nentity\"s current location and move it there (point C) and from this\ntime onwards, the exported and the placed paths will become the\nsame. However, in reality, receiver 1 receives DR1 after a delay\nof da1 (which is less than sender\"s estimates of dt1), and moves\nthe corresponding entity to point H. Similarly, the sender estimates\nthat after a delay of dt2, receiver 2 will receive DR1, will compute\nthe current location of the entity and move it to that point (point\nE), while in reality it receives DR1 after a delay of da2 > dt2 and\nmoves the entity to point N. The other points shown on the placed\nand exported paths will be used later in the discussion to describe\ndifferent error components.\n4.1 Computation of Relative Export Error\nReferring back to the discussion from Section 3, from the sender\"s\nperspective, the export error at receiver 1 due to DR1 is given\nby Err(DR1, T1, T1 + \u03b41 + dt1) (the integral of the distance\nbetween the trajectories AC and DB over the time interval [T1, T1 +\n\u03b41 + dt1]) of Figure 2. This is due to the fact that the sender uses\nthe estimated delay dt1 to compute this error. Similarly, the\nexport error from the sender\"s perspective at received 2 due to DR1\nis given by Err(DR1, T1, T1 + \u03b42 + dt2) (the integral of the\ndistance between the trajectories AE and DF over the time interval\n[T1, T1 + \u03b42 + dt2]). Note that the above errors from the sender\"s\nperspective are only estimates. In reality, the export error will be\neither smaller or larger than the estimated value, based on whether\nthe delay estimate was larger or smaller than the actual delay that\nDR1 experienced. This difference between the estimated and the\nactual export error is the relative export error (which could either\nbe positive or negative) which occurs for every DR vector that is\nsent and is accumulated at the sender.\nThe concept of relative export error is illustrated in Figure 2.\nSince the actual delay to receiver 1 is da1, the export error\ninduced by DR1 at receiver 1 is Err(DR1, T1, T1 + \u03b41 + da1).\nThis means, there is an error in the estimated export error and the\nsender can compute this error only after it gets a feedback from the\nreceiver about the actual delay for the delivery of DR1, i.e., the\nvalue of da1. We propose that once receiver 1 receives DR1, it\nsends the value of da1 back to the sender. The receiver can\ncompute this information as it knows the time at which DR1 was sent\n(T1\n1 = T1 + \u03b41, which is appended to the DR vector as shown in\nFigure 2) and the local receiving time (which is synchronized with\nthe sender\"s clock). Therefore, the sender computes the relative\nexport error for receiver 1, represented using R1 as\nR1 = Err(DR1, T1, T1 + \u03b41 + dt1)\n\u2212 Err(DR1, T1, T1 + \u03b41 + da1)\n= Err(DR1, T1 + \u03b41 + dt1, T1 + \u03b41 + da1)\nSimilarly the relative export error for receiver 2 is computed as\nR2 = Err(DR1, T1, T1 + \u03b42 + dt2)\n\u2212 Err(DR1, T1, T1 + \u03b42 + da2)\n= Err(DR1, T1 + \u03b42 + dt2, T1 + \u03b42 + da2)\nNote that R1 > 0 as da1 < dt1, and R2 < 0 as da2 > dt2.\nRelative export errors are computed by the sender as and when it\nreceives the feedback from the receivers. This example shows the\n4\nrelative export error values after DR1 is sent and the corresponding\nfeedbacks are received.\n4.2 Equalization of Error Among Receivers\nWe now explain what we mean by making the errors equal\nat all the receivers and how this can be achieved. As stated\nbefore the sender keeps estimates of the delays to the receivers, dt1\nand dt2 in the example of Figure 2. This says that at time T1\nwhen DR1 is computed, the sender already knows how long it may\ntake messages carrying this DR vector to reach the receivers. The\nsender uses this information to compute the export errors, which are\nErr(DR1, T1, T1 + \u03b41 + dt1) and Err(DR1, T1, T1 + \u03b42 + dt2)\nfor receivers 1 and 2, respectively. Note that the areas of these error\ncomponents are a function of \u03b41 and \u03b42 as well as the network\ndelays dt1 and dt2. If we are to make the exports errors due to DR1\nthe same at both receivers, the sender needs to choose \u03b41 and \u03b42\nsuch that\nErr(DR1, T1, T1 + \u03b41 + dt1) = Err(DR1, T1, T1 + \u03b42 + dt2).\nBut when T1 was computed there could already have been\naccumulated relative export errors due to previous DR vectors (DR0 and\nthe ones before). Let us represent the accumulated relative error up\nto DRi for receiver j as Ri\nj. To accommodate these accumulated\nrelative errors, the sender should now choose \u03b41 and \u03b42 such that\nR0\n1 + Err(DR1, T1, T1 + \u03b41 + dt1) =\nR0\n2 + Err(DR1, T1, T1 + \u03b42 + dt2)\nThe \u03b4i determines the scheduling instant of the DR vector at the\nsender for receiver i. This method of computation of \u03b4\"s ensures\nthat the accumulated export error (i.e., total actual error) for each\nreceiver equalizes at the transmission of each DR vector.\nIn order to establish this, assume that the feedback for DR vector\nDi from a receiver comes to the sender before schedule for Di+1 is\ncomputed. Let Si\nm and Ai\nm denote the estimated error for receiver\nm used for computing schedule for Di and accumulated error for\nreceiver m computed after receiving feedback for Di, respectively.\nThen Ri\nm = Ai\nm \u2212Si\nm. In order to compute the schedule instances\n(i.e., \u03b4\"s) for Di, for any pair of receivers m and n, we do Ri\u22121\nm +\nSi\nm = Ri\u22121\nn + Si\nn. The following theorem establishes the fact\nthat the accumulated export error is equalized at every scheduling\ninstant.\nTHEOREM 4.1. When the schedule instances for sending Di\nare computed for any pair of receivers m and n, the following\ncondition is satisfied:\ni\u22121\nk=1\nAk\nm + Si\nm =\ni\u22121\nk=1\nAk\nn + Si\nn.\nProof: By induction. Assume that the premise holds for some i.\nWe show that it holds for i+1. The base case for i = 1 holds since\ninitially R0\nm = R0\nn = 0, and the S1\nm = S1\nn is used to compute the\nscheduling instances.\nIn order to compute the schedule for Di+1, the we first compute\nthe relative errors as\nRi\nm = Ai\nm \u2212 Si\nm, and Ri\nn = Ai\nn \u2212 Si\nn.\nThen to compute \u03b4\"s we execute\nRi\nm + Si+1\nm = Ri\nn + Si+1\nn\nAi\nm \u2212 Si\nm + Si+1\nm = Ai\nn \u2212 Si\nn + Si+1\nn .\nAdding the condition of the premise on both sides we get,\ni\nk=1\nAk\nm + Si+1\nm =\ni\nk=1\nAk\nn + Si+1\nn .\n4.3 Computation of the Export Error\nLet us now consider how the export errors can be computed.\nFrom the previous section, to find \u03b41 and \u03b42 we need to find\nErr(DR1, T1, T1 +\u03b41 +dt1) and Err(DR1, T1, T1 +\u03b42 +dt2).\nNote that the values of R0\n1 and R0\n2 are already known at the sender.\nConsider the computation of Err(DR1, T1, T1 +\u03b41 +dt1). This is\nthe integral of the distance between the trajectories AC due to DR1\nand BD due to DR0. From DR0 and DR1, point A is (X1, Y1) =\n(x1, y1) and point B is (X0, Y0) = (x0 + (T1 \u2212 T0) \u00d7 vx0, y0 +\n(T1 \u2212 T0) \u00d7 vy0). The trajectory AC can be represented as a\nfunction of time as (X1(t), Y1(t) = (X1 + vx1 \u00d7 t, Y1 + vy1 \u00d7 t)\nand the trajectory of BD can be represented as (X0(t), Y0(t) =\n(X0 + vx0 \u00d7 t, Y0 + vy0 \u00d7 t).\nThe distance between the two trajectories as a function of time\nthen becomes,\ndist(t) = (X1(t) \u2212 X0(t))2 + (Y1(t) \u2212 Y0(t))2\n= ((X1 \u2212 X0) + (vx1 \u2212 vx0)t)2\n+((Y1 \u2212 Y0) + (vy1 \u2212 vy0)t)2\n= ((vx1 \u2212 vx0)2 + (vy1 \u2212 vy0)2)t2\n+2((X1 \u2212 X0)(vx1 \u2212 vx0)\n+(Y1 \u2212 Y0)(vy1 \u2212 vy0))t\n+(X1 \u2212 X0)2 + (Y1 \u2212 Y0)2\nLet\na = (vx1 \u2212 vx0)2\n+ (vy1 \u2212 vy0)2\nb = 2((X1 \u2212 X0)(vx1 \u2212 vx0)\n+(Y1 \u2212 Y0)(vy1 \u2212 vy0))\nc = (X1 \u2212 X0)2\n+ (Y1 \u2212 Y0)2\nThen dist(t) can be written as\ndist(t) = a \u00d7 t2 + b \u00d7 t + c.\nThen Err(DR1, t1, t2) for some time interval [t1, t2] becomes\nt2\nt1\ndist(t) dt =\nt2\nt1\na \u00d7 t2 + b \u00d7 t + c dt.\nA closed form solution for the indefinite integral\na \u00d7 t2 + b \u00d7 t + c dt =\n(2at + b)\n\u221a\nat2 + bt + c\n4a\n+\n1\n2\nln\n1\n2b\n+ at\n\u221a\na\n+ at2 + bt + c c\n1\n\u221a\na\n\u2212\n1\n8\nln\n1\n2b\n+ at\n\u221a\na\n+ at2 + bt + c b2\na\u2212 3\n2\nErr(DR1, T1, T1 +\u03b41 +dt1) and Err(DR1, T1, T1 +\u03b42 +dt2)\ncan then be calculated by applying the appropriate limits to the\nabove solution. In the next section, we consider the computation\nof the \u03b4\"s for N receivers.\n5\n4.4 Computation of Scheduling Instants\nWe again look at the computation of \u03b4\"s by referring to Figure 2.\nThe sender chooses \u03b41 and \u03b42 such that R0\n1 + Err(DR1, T1, T1 +\n\u03b41 +dt1) = R0\n2 +Err(DR1, T1, T1 +\u03b42 +dt2). If R0\n1 and R0\n2 both\nare zero, then \u03b41 and \u03b42 should be chosen such that Err(DR1, T1, T1+\n\u03b41 +dt1) = Err(DR1, T1, T1 +\u03b42 +dt2). This equality will hold\nif \u03b41 + dt1 = \u03b42 + dt2. Thus, if there is no accumulated relative\nexport error, all that the sender needs to do is to choose the \u03b4\"s in\nsuch a way that they counteract the difference in the delay to the\ntwo receivers, so that they receive the DR vector at the same time.\nAs discussed earlier, because the sender is not able to a priori learn\nthe delay, there will always be an accumulated relative export error\nfrom a previous DR vector that does have to be taken into account.\nTo delve deeper into this, consider the computation of the\nexport error as illustrated in the previous section. To compute the\n\u03b4\"s we require that R0\n1 + Err(DR1, T1, T1 + \u03b41 + dt1) = R0\n2 +\nErr(DR1, T1, T1 + \u03b42 + dt2). That is,\nR0\n1 +\nT1+\u03b41+dt1\nT1\ndist(t) dt = R0\n2 +\nT1+\u03b42+dt2\nT1\ndist(t) dt.\nThat is\nR0\n1 +\nT1+dt1\nT1\ndist(t) dt +\nT1+dt1+\u03b41\nT1+dt1\ndist(t) dt =\nR0\n2 +\nT1+dt2\nT1\ndist(t) dt +\nT1+dt2+\u03b42\nT1+dt2\ndist(t) dt.\nThe components R0\n1, R0\n2, are already known to (or estimated by)\nthe sender. Further, the error components\nT1+dt1\nT1\ndist(t) dt and\nT1+dt2\nT1\ndist(t) dt can be a priori computed by the sender using\nestimated values of dt1 and dt2. Let us use E1 to denote R0\n1 +\nT1+dt1\nT1\ndist(t) dt and E2 to denote R0\n2 +\nT1+dt2\nT1\ndist(t) dt.\nThen, we require that\nE1 +\nT1+dt1+\u03b41\nT1+dt1\ndist(t) dt = E2 +\nT1+dt2+\u03b42\nT1+dt2\ndist(t) dt.\nAssume that E1 > E2. Then, for the above equation to hold, we\nrequire that\nT1+dt1+\u03b41\nT1+dt1\ndist(t) dt <\nT1+dt2+\u03b42\nT1+dt2\ndist(t) dt.\nTo make the game as fast as possible within this framework, the \u03b4\nvalues should be made as small as possible so that DR vectors are\nsent to the receivers as soon as possible subject to the fairness\nrequirement. Given this, we would choose \u03b41 to be zero and compute\n\u03b42 from the equation\nE1 = E2 +\nT1+dt2+\u03b42\nT1+dt2\ndist(t) dt.\nIn general, if there are N receivers 1, . . . , N, when a sender\ngenerates a DR vector and decides to schedule them to be sent, it first\ncomputes the Ei values for all of them from the accumulated\nrelative export errors and estimates of delays. Then, it finds the smallest\nof these values. Let Ek be the smallest value. The sender makes \u03b4k\nto be zero and computes the rest of the \u03b4\"s from the equality\nEi +\nT1+dti+\u03b4i\nT1+dti\ndist(t) dt = Ek,\n\u2200i 1 \u2264 i \u2264 N, i = k. (1)\nThe \u03b4\"s thus obtained gives the scheduling instants of the DR\nvector for the receivers.\n4.5 Steps of the Scheduling Algorithm\nFor the purpose of the discussion below, as before let us denote\nthe accumulated relative export error at a sender for receiver k up\nuntil DRi to be Ri\nk. Let us denote the scheduled delay at the sender\nbefore DRi is sent to receiver k as \u03b4i\nk. Given the above discussion,\nthe algorithm steps are as follows:\n1. The sender computes DRi at (say) time Ti and then\ncomputes \u03b4i\nk, and Ri\u22121\nk , \u2200k, 1 \u2264 k \u2264 N based on the estimation\nof delays dtk, \u2200k, 1 \u2264 k \u2264 N as per Equation (1). It\nschedules, DRi to be sent to receiver k at time Ti + \u03b4i\nk.\n2. The DR vectors are sent to the receivers at the scheduled\ntimes which are received after a delay of dak, \u2200k, 1 \u2264 k \u2264\nN where dak \u2264 or > dtk. The receivers send the value of\ndak back to the sender (the receiver can compute this value\nbased on the time stamps on the DR vector as described\nearlier).\n3. The sender computes Ri\nk as described earlier and illustrated\nin Figure 2. The sender also recomputes (using exponential\naveraging method similar to round-trip time estimation by\nTCP [10]) the estimate of delay dtk from the new value of\ndak for receiver k.\n4. Go back to Step 1 to compute DRi+1 when it is required\nand follow the steps of the algorithm to schedule and send\nthis DR vector to the receivers.\n4.6 Handling Cases in Practice\nSo far we implicity assumed that DRi is sent out to all receivers\nbefore a decision is made to compute the next DR vector DRi+1,\nand the receivers send the value of dak corresponding to DRi and\nthis information reaches the sender before it computes DRi+1 so\nthat it can compute Ri+1\nk and then use it in the computation of \u03b4i+1\nk .\nTwo issues need consideration with respect to the above algorithm\nwhen it is used in practice.\n\u2022 It may so happen that a new DR vector is computed even\nbefore the previous DR vector is sent out to all receivers.\nHow will this situation be handled?\n\u2022 What happens if the feedback does not arrive before DRi+1\nis computed and scheduled to be sent?\nLet us consider the first scenario. We assume that DRi has been\nscheduled to be sent and the scheduling instants are such that \u03b4i\n1 <\n\u03b4i\n2 < \u00b7 \u00b7 \u00b7 < \u03b4i\nN . Assume that DRi+1 is to be computed (because\nthe real path has deviated exceeding a threshold from the path\nexported by DRi) at time Ti+1 where Ti + \u03b4i\nk < Ti+1 < Ti + \u03b4i\nk+1.\nThis means, DRi has been sent only to receivers up to k in the\nscheduled order. In our algorithm, in this case, the scheduled delay\nordering queue is flushed which means DRi is not sent to receivers\nstill queued to receive it, but a new scheduling order is computed\nfor all the receivers to send DRi+1.\nFor those receivers who have been sent DRi, assume for now\nthat daj, 1 \u2264 j \u2264 k has been received from all receivers (the\nscenario where daj has not been received will be considered as a part\nof the second scenario later). For these receivers, Ei\nj, 1 \u2264 j \u2264 k\ncan be computed. For those receivers j, k + 1 \u2264 j \u2264 N to\nwhom DRi was not sent Ei\nj does not apply. Consider a receiver\nj, k + 1 \u2264 j \u2264 N to whom DRi was not sent. Refer to\nFigure 3. For such a receiver j, when DRi+1 is to be scheduled and\n6\ntimeTi\nExported path\ndtj\nA\nB\nC\nD\nTi-1\nGi\nj\nDRi+1 computed by sender\nand DRi for receiver k+1 to\nN is removed from queue\nDRi+1 scheduled\nfor receiver k+1\nTi+1\nG\nH\nE\nF\nDRi scheduled\nfor receiver j\nDRi computed\nby sender\nPlaced path\nat receiver k+1\nGi+1\nj\nFigure 3: Schedule computation when DRi is not sent to\nreceiver j, k + 1 \u2264 j \u2264 N.\n\u03b4i+1\nj needs to be computed, the total export error is the accumulated\nrelative export error at time Ti when schedule for DRi was\ncomputed, plus the integral of the distance between the two trajectories\nAC and BD of Figure 3 over the time interval [Ti, Ti+1 + \u03b4i+1\nj +\ndtj]. Note that this integral is given by Err(DRi, Ti, Ti+1) +\nErr(DRi+1, Ti+1, Ti+1 + \u03b4i+1\nj + dtj). Therefore, instead of Ei\nj\nof Equation (1), we use the value Ri\u22121\nj + Err(DRi, Ti, Ti+1) +\nErr(DRi+1, Ti+1, Ti+1 + \u03b4i+1\nj + dtj) where Ri\u22121\nj is relative\nexport error used when the schedule for DRi was computed.\nNow consider the second scenario. Here the feedback dak\ncorresponding to DRi has not arrived before DRi+1 is computed and\nscheduled. In this case, Ri\nk cannot be computed. Thus, in the\ncomputation of \u03b4k for DRi+1, this will be assumed to be zero. We\ndo assume that a reliable mechanism is used to send dak back to\nthe sender. When this information arrives at a later time, Ri\nk will\nbe computed and accumulated to future relative export errors (for\nexample Ri+1\nk if dak is received before DRi+2 is computed) and\nused in the computation of \u03b4k when a future DR vector is to be\nscheduled (for example DRi+2).\n4.7 Experimental Results\nIn order to evaluate the effectiveness and quantify benefits\nobtained through the use of the scheduling algorithm, we implemented\nthe proposed algorithm in BZFlag (Battle Zone Flag) [11] game.\nIt is a first-person shooter game where the players in teams drive\ntanks and move within a battle field. The aim of the players is to\nnavigate and capture flags belonging to the other team and bring\nthem back to their own area. The players shoot each other\"s tanks\nusing shooting bullets. The movement of the tanks as well as that\nof the shots are exchanged among the players using DR vectors.\nWe have modified the implementation of BZFlag to\nincorporate synchronized clocks among the players and the server and\nexchange time-stamps with the DR vector. We set up a testbed with\nfour players running the instrumented version of BZFlag, with one\nas a sender and the rest as receivers. The scheduling approach and\nthe base case where each DR vector was sent to all the receivers\nconcurrently at every trigger point were implemented in the same\nrun by tagging the DR vectors according to the type of approach\nused to send the DR vector. NISTNet [12] was used to introduce\ndelays across the sender and the three receivers. Mean delays of\n800ms, 500ms and 200ms were introduced between the sender and\nfirst, second and the third receiver, respectively. We introduce a\nvariance of 100 msec (to the mean delay of each receiver) to model\nvariability in delay. The sender logged the errors of each receiver\nevery 100 milliseconds for both the scheduling approach and the\nbase case. The sender also calculated the standard deviation and\nthe mean of the accumulated export error of all the receivers every\n100 milliseconds. Figure 4 plots the mean and standard deviation\nof the accumulated export error of all the receivers in the\nscheduling case against the base case. Note that the x-axis of these graphs\n(and the other graphs that follow) represents the system time when\nthe snapshot of the game was taken.\nObserve that the standard deviation of the error with scheduling\nis much lower as compared to the base case. This implies that the\naccumulated errors of the receivers in the scheduling case are closer\nto one another. This shows that the scheduling approach achieves\nfairness among the receivers even if they are at different distances\n(i.e, latencies) from the sender.\nObserve that the mean of the accumulated error increased\nmultifold with scheduling in comparison to the base case. Further\nexploration for the reason for the rise in the mean led to the conclusion\nthat every time the DR vectors are scheduled in a way to equalize\nthe total error, it pushes each receivers total error higher. Also, as\nthe accumulated error has an estimated component, the schedule is\nnot accurate to equalize the errors for the receivers, leading to the\nDR vector reaching earlier or later than the actual schedule. In\neither case, the error is not equalized and if the DR vector reaches\nlate, it actually increases the error for a receiver beyond the highest\naccumulated error. This means that at the next trigger, this receiver\nwill be the one with highest error and every other receiver\"s error\nwill be pushed to this error value. This flip-flop effect leads to\nthe increase in the accumulated error for all the receivers.\nThe scheduling for fairness leads to the decrease in standard\ndeviation (i.e., increases the fairness among different players), but it\ncomes at the cost of higher mean error, which may not be a\ndesirable feature. This led us to explore different ways of equalizing the\naccumulated errors. The approach discussed in the following\nsection is a heuristic approach based on the following idea. Using the\nsame amount of DR vectors over time as in the base case, instead\nof sending the DR vectors to all the receivers at the same frequency\nas in the base case, if we can increase the frequency of sending\nthe DR vectors to the receiver with higher accumulated error and\ndecrease the frequency of sending DR vectors to the receiver with\nlower accumulated error, we can equalize the export error of all\nreceivers over time. At the same time we wish to decrease the\nerror of the receiver with the highest accumulated error in the base\ncase (of course, this receiver would be sent more DR vectors than\nin the base case). We refer to such an algorithm as a budget based\nalgorithm.\n5. BUDGET BASED ALGORITHM\nIn a game, the sender of an entity sends DR vectors to all the\nreceivers every time a threshold is crossed by the entity. Lower\nthe threshold, more DR vectors are generated during a given time\nperiod. Since the DR vectors are sent to all the receivers and the\nnetwork delay between the sender-receiver pairs cannot be avoided,\nthe before export error 3\nwith the most distant player will always\n3\nNote that after export error is eliminated by using synchronized\nclock among the players.\n7\n0\n1000\n2000\n3000\n4000\n5000\n15950 16000 16050 16100 16150 16200 16250 16300\nMeanAccumulatedError\nTime in Seconds\nBase Case\nScheduling Algorithm #1\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\n15950 16000 16050 16100 16150 16200 16250 16300\nStandardDeviationofAccumulatedError\nTime in Seconds\nBase Case\nScheduling Algorithm #1\nFigure 4: Mean and standard deviation of error with scheduling and without (i.e., base case).\nbe higher than the rest. In order to mitigate the imbalance in the\nerror, we propose to send DR vectors selectively to different\nplayers based on the accumulated errors of these players. The budget\nbased algorithm is based on this idea and there are two variations\nof it. One is a probabilistic budget based scheme and the other, a\ndeterministic budget base scheme.\n5.1 Probabilistic budget based scheme\nThe probabilistic budget based scheme has three main steps: a)\nlower the dead reckoning threshold but at the same time keep the\ntotal number of DRs sent the same as the base case, b) at every\ntrigger, probabilistically pick a player to send the DR vector to,\nand c) send the DR vector to the chosen player. These steps are\ndescribed below.\nThe lowering of DR threshold is implemented as follows.\nLowering the threshold is equivalent to increasing the number of trigger\npoints where DR vectors are generated. Suppose the threshold is\nsuch that the number of triggers caused by it in the base case is t\nand at each trigger n DR vectors sent by the sender, which results\nin a total of nt DR vectors. Our goal is to keep the total number of\nDR vectors sent by the sender fixed at nt, but lower the number of\nDR vectors sent at each trigger (i.e., do not send the DR vector to\nall the receivers). Let n and t be the number of DR vectors sent\nat each trigger and number of triggers respectively in the modified\ncase. We want to ensure n t = nt. Since we want to increase the\nnumber of trigger points, i.e, t > t, this would mean that n < n.\nThat is, not all receivers will be sent the DR vector at every trigger.\nIn the probabilistic budget based scheme, at each trigger, a\nprobability is calculated for each receiver to be sent a DR vector and\nonly one receiver is sent the DR (n = 1). This probability is based\non the relative weights of the receivers\" accumulated errors. That\nis, a receiver with a higher accumulated error will have a higher\nprobability of being sent the DR vector. Consider that the\naccumulated error for three players are a1, a2 and a3 respectively.\nThen the probability of player 1 receiving the DR vector would\nbe a1\na1+a2+a3\n. Similarly for the other players. Once the player is\npicked, the DR vector is sent to that player.\nTo compare the probabilistic budget based algorithm with the\nbase case, we needed to lower the threshold for the base case (for\nfair comparison). As the dead reckoning threshold in the base\ncase was already very fine, it was decided that instead of\nlowering the threshold, the probabilistic budget based approach would\nbe compared against a modified base case that would use the\nnormal threshold as the budget based algorithm but the base case was\nmodified such that every third trigger would be actually used to\nsend out a DR vector to all the three receivers used in our\nexperiments. This was called as the 1/3 base case as it resulted in 1/3\nnumber of DR vectors being sent as compared to the base case.\nThe budget per trigger for the probability based approach was\ncalculated as one DR vector at each trigger as compared to three DR\nvectors at every third trigger in the 1/3 base case; thus the two cases\nlead to the same number of DR vectors being sent out over time.\nIn order to evaluate the effectiveness of the probabilistic budget\nbased algorithm, we instrumented the BZFlag game to use this\napproach. We used the same testbed consisting of one sender and\nthree receivers with delays of 800ms, 500ms and 200ms from the\nsender and with low delay variance (100ms) and moderate delay\nvariance (180ms). The results are shown in Figures 5 and 6. As\nmentioned earlier, the x-axis of these graphs represents the system\ntime when the snapshot of the game was taken. Observe from the\nfigures that the standard deviation of the accumulated error among\nthe receivers with the probabilistic budget based algorithm is less\nthan the 1/3 base case and the mean is a little higher than the 1/3\nbase case. This implies that the game is fairer as compared to the\n1/3 base case at the cost of increasing the mean error by a small\namount as compared to the 1/3 base case.\nThe increase in mean error in the probabilistic case compared to\nthe 1/3 base case can be attributed to the fact that the even though\nthe probabilistic approach on average sends the same number of\nDR vectors as the 1/3 base case, it sometimes sends DR vectors to\na receiver less frequently and sometimes more frequently than the\n1/3 base case due to its probabilistic nature. When a receiver does\nnot receive a DR vector for a long time, the receiver\"s trajectory\nis more and more off of the sender\"s trajectory and hence the rate\nof buildup of the error at the receiver is higher. At times when\na receiver receives DR vectors more frequently, it builds up error\nat a lower rate but there is no way of reversing the error that was\nbuilt up when it did not receive a DR vector for a long time. This\nleads the receivers to build up more error in the probabilistic case\nas compared to the 1/3 base case where the receivers receive a DR\nvector almost periodically.\n8\n0\n200\n400\n600\n800\n1000\n15950 16000 16050 16100 16150 16200 16250 16300\nMeanAccumulatedError\nTime in Seconds\n1/3 Base Case\nDeterministic Algorithm\nProbabilistic Algorithm\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n500\n15950 16000 16050 16100 16150 16200 16250 16300\nStandardDeviationofAccumulatedError\nTime in Seconds\n1/3 Base Case\nDeterministic Algorithm\nProbabilistic Algorithm\nFigure 5: Mean and standard deviation of error for different algorithms (including budget based algorithms) for low delay variance.\n0\n200\n400\n600\n800\n1000\n16960 16980 17000 17020 17040 17060 17080 17100 17120 17140 17160 17180\nMeanAccumulatedError\nTime in Seconds\n1/3 Base Case\nDeterministic Algorithm\nProbabilistic Algorithm\n0\n50\n100\n150\n200\n250\n300\n16960 16980 17000 17020 17040 17060 17080 17100 17120 17140 17160 17180\nStandardDeviationofAccumulatedError\nTime in Seconds\n1/3 Base Case\nDeterministic Algorithm\nProbabilistic Algorithm\nFigure 6: Mean and standard deviation of error for different algorithms (including budget based algorithms) for moderate delay\nvariance.\n5.2 Deterministic budget based scheme\nTo bound the increase in mean error we decided to modify the\nbudget based algorithm to be deterministic. The first two steps\nof the algorithm are the same as in the probabilistic algorithm; the\ntrigger points are increased to lower the threshold and accumulated\nerrors are used to compute the probability that a receiver will\nreceiver a DR vector. Once these steps are completed, a deterministic\nschedule for the receiver is computed as follows:\n1. If there is any receiver(s) tagged to receive a DR vector at\nthe current trigger, the sender sends out the DR vector to the\nrespective receiver(s). If at least one receiver was sent a DR\nvector, the sender calculates the probabilities of each receiver\nreceiving a DR vector as explained before and follows steps\n2 to 6, else it does not do anything.\n2. For each receiver, the probability value is multiplied with the\nbudget available at each trigger (which is set to 1 as explained\nbelow) to give the frequency of sending the DR vector to each\nreceiver.\n3. If any of the receiver\"s frequency after multiplying with the\nbudget goes over 1, the receiver\"s frequency is set as 1 and\nthe surplus amount is equally distributed to all the receivers\nby adding the amount to their existing frequencies. This\nprocess is repeated until all the receivers have a frequency of\nless than or equal to 1. This is due to the fact that at a trigger\nwe cannot send more than one DR vector to the respective\nreceiver. That will be wastage of DR vectors by sending\nredundant information.\n4. (1/frequency) gives us the schedule at which the sender should\nsend DR vectors to the respective receiver. Credit obtained\npreviously (explained in step 5) if any is subtracted from the\nschedule. Observe that the resulting value of the schedule\nmight not be an integer; hence, the value is rounded off by\ntaking the ceiling of the schedule. For example, if the\nfrequency is 1/3.5, this implies that we would like to have a DR\nvector sent every 3.5 triggers. However, we are constrained\nto send it at the 4th trigger giving us a credit of 0.5. When we\ndo send the DR vector next time, we would be able to send it\n9\non the 3rd trigger because of the 0.5 credit.\n5. The difference between the schedule and the ceiling of the\nschedule is the credit that the receiver has obtained which\nis remembered for the future and used at the next time as\nexplained in step 4.\n6. For each of those receivers who were sent a DR vector at\nthe current trigger, the receivers are tagged to receive the\nnext DR vector at the trigger that happens exactly schedule\n(the ceiling of the schedule) number of times away from the\ncurrent trigger. Observe that no other receiver\"s schedule is\nmodified at this point as they all are running a schedule\ncalculated at some previous point of time. Those schedules will\nbe automatically modified at the trigger when they are\nscheduled to receive the next DR vector. At the first trigger, the\nsender sends the DR vector to all the receivers and uses a\nrelative probability of 1/n for each receiver and follows the\nsteps 2 to 6 to calculate the next schedule for each receiver\nin the same way as mentioned for other triggers. This\nalgorithm ensures that every receiver has a guaranteed schedule\nof receiving DR vectors and hence there is no irregularity in\nsending the DR vector to any receiver as was observed in the\nbudget based probabilistic algorithm.\nWe used the testbed described earlier (three receivers with\nvarying delays) to evaluate the deterministic algorithm using the budget\nof 1 DR vector per trigger so as to use the same number of DR\nvectors as in the 1/3 base case. Results from our experiments are\nshown in Figures 5 and 6. It can be observed that the standard\ndeviation of error in the deterministic budget based algorithm is less\nthan the 1/3 base case and also has the same mean error as the 1/3\nbase case. This indicates that the deterministic algorithm is more\nfair than the 1/3 base case and at the same time does not increase\nthe mean error thereby leading to a better game quality compared\nto the probabilistic algorithm.\nIn general, when comparing the deterministic approach to the\nprobabilistic approach, we found that the mean accumulated\nerror was always less in the deterministic approach. With respect to\nstandard deviation of the accumulated error, we found that in the\nfixed or low variance cases, the deterministic approach was\ngenerally lower, but in higher variance cases, it was harder to draw\nconclusions as the probabilistic approach was sometimes better than\nthe deterministic approach.\n6. CONCLUSIONS AND FUTURE WORK\nIn distributed multi-player games played across the Internet,\nobject and player trajectory within the game space are exchanged in\nterms of DR vectors. Due to the variable delay between players,\nthese DR vectors reach different players at different times. There is\nunfair advantage gained by receivers who are closer to the sender\nof the DR as they are able to render the sender\"s position more\naccurately in real time. In this paper, we first developed a model\nfor estimating the error in rendering player trajectories at the\nreceivers. We then presented an algorithm based on scheduling the\nDR vectors to be sent to different players at different times thereby\nequalizing the error at different players. This algorithm is aimed\nat making the game fair to all players, but tends to increase the\nmean error of the players. To counter this effect, we presented\nbudget based algorithms where the DR vectors are still\nscheduled to be sent at different players at different times but the\nalgorithm balances the need for fairness with the requirement that the\nerror of the worst case players (who are furthest from the sender)\nare not increased compared to the base case (where all DR vectors\nare sent to all players every time a DR vector is generated). We\npresented two variations of the budget based algorithms and through\nexperimentation showed that the algorithms reduce the standard\ndeviation of the error thereby making the game more fair and at the\nsame time has comparable mean error to the base case.\n7. REFERENCES\n[1] S.Aggarwal, H. Banavar, A. Khandelwal, S. Mukherjee, and\nS. Rangarajan, Accuracy in Dead-Reckoning based\nDistributed Multi-Player Games, Proceedings of ACM\nSIGCOMM 2004 Workshop on Network and System Support\nfor Games (NetGames 2004), Aug. 2004.\n[2] L. Gautier and C. Diot, Design and Evaluation of MiMaze,\na Multiplayer Game on the Internet, in Proc. of IEEE\nMultimedia (ICMCS\"98), 1998.\n[3] M. Mauve, Consistency in Replicated Continuous\nInteractive Media, in Proc. of the ACM Conference on\nComputer Supported Cooperative Work (CSCW\"00), 2000,\npp. 181-190.\n[4] S.K. Singhal and D.R. Cheriton, Exploiting Position\nHistory for Efficient Remote Rendering in Networked\nVirtual Reality, Presence: Teleoperators and Virtual\nEnvironments, vol. 4, no. 2, pp. 169-193, 1995.\n[5] C. Diot and L. Gautier, A Distributed Architecture for\nMultiplayer Interactive Applications on the Internet, in\nIEEE Network Magazine, 1999, vol. 13, pp. 6-15.\n[6] L. Pantel and L.C. Wolf, On the Impact of Delay on\nReal-Time Multiplayer Games, in Proc. of ACM\nNOSSDAV\"02, May 2002.\n[7] Y. Lin, K. Guo, and S. Paul, Sync-MS: Synchronized\nMessaging Service for Real-Time Multi-Player Distributed\nGames, in Proc. of 10th IEEE International Conference on\nNetwork Protocols (ICNP), Nov 2002.\n[8] K. Guo, S. Mukherjee, S. Rangarajan, and S. Paul, A Fair\nMessage Exchange Framework for Distributed Multi-Player\nGames, in Proc. of NetGames2003, May 2003.\n[9] N. E. Baughman and B. N. Levine, Cheat-Proof Playout for\nCentralized and Distributed Online Games, in Proc. of IEEE\nINFOCOM\"01, April 2001.\n[10] M. Allman and V. Paxson, On Estimating End-to-End\nNetwork Path Properties, in Proc. of ACM SIGCOMM\"99,\nSept. 1999.\n[11] BZFlag Forum, BZFlag Game, URL:\nhttp://www.bzflag.org.\n[12] Nation Institute of Standards and Technology, NIST Net,\nURL: http://snad.ncsl.nist.gov/nistnet/.\n10", "keywords": "fairness;dead-reckoning vector;export error;network delay;budget based algorithm;clock synchronization;distribute multi-player game;bucket synchronization;mean error;distributed multi-player game;quantization;dead-reckon;scheduling algorithm;accuracy"}
{"name": "train_C-53", "title": "Globally Synchronized Dead-Reckoning with Local Lag for Continuous Distributed Multiplayer Games", "abstract": "Dead-Reckoning (DR) is an effective method to maintain consistency for Continuous Distributed Multiplayer Games (CDMG). Since DR can filter most unnecessary state updates and improve the scalability of a system, it is widely used in commercial CDMG. However, DR cannot maintain high consistency, and this constrains its application in highly interactive games. With the help of global synchronization, DR can achieve higher consistency, but it still cannot eliminate before inconsistency. In this paper, a method named Globally Synchronized DR with Local Lag (GS-DR-LL), which combines local lag and Globally Synchronized DR (GS-DR), is presented. Performance evaluation shows that GS-DR-LL can effectively decrease before inconsistency, and the effects increase with the lag.", "fulltext": "1. INTRODUCTION\nNowadays, many distributed multiplayer games adopt replicated\narchitectures. In such games, the states of entities are changed not\nonly by the operations of players, but also by the passing of time\n[1, 2]. These games are referred to as Continuous Distributed\nMultiplayer Games (CDMG). Like other distributed applications,\nCDMG also suffer from the consistency problem caused by\nnetwork transmission delay. Although new network techniques\n(e.g. QoS) can reduce or at least bound the delay, they can not\ncompletely eliminate it, as there exists the physical speed\nlimitation of light, for instance, 100 ms is needed for light to\npropagate from Europe to Australia [3]. There are many studies\nabout the effects of network transmission delay in different\napplications [4, 5, 6, 7]. In replication based games, network\ntransmission delay makes the states of local and remote sites to be\ninconsistent, which can cause serious problems, such as reducing\nthe fairness of a game and leading to paradoxical situations etc. In\norder to maintain consistency for distributed systems, many\ndifferent approaches have been proposed, among which local lag\nand Dead-Reckoning (DR) are two representative approaches.\nMauve et al [1] proposed local lag to maintain high consistency\nfor replicated continuous applications. It synchronizes the\nphysical clocks of all sites in a system. After an operation is\nissued at local site, it delays the execution of the operation for a\nshort time. During this short time period the operation is\ntransmitted to remote sites, and all sites try to execute the\noperation at a same physical time. In order to tackle the\ninconsistency caused by exceptional network transmission delay,\na time warp based mechanism is proposed to repair the state.\nLocal lag can achieve significant high consistency, but it is based\non operation transmission, which forwards every operation on a\nshared entity to remote sites. Since operation transmission\nmechanism requests that all operations should be transmitted in a\nreliable way, message filtering is difficult to be deployed and the\nscalability of a system is limited.\nDR is based on state transmission mechanism. In addition to the\nhigh fidelity model that maintains the accurate states of its own\nentities, each site also has a DR model that estimates the states of\nall entities (including its own entities). After each update of its\nown entities, a site compares the accurate state with the estimated\none. If the difference exceeds a pre-defined threshold, a state\nupdate would be transmitted to all sites and all DR models would\nbe corrected. Through state estimation, DR can not only maintain\nconsistency but also decrease the number of transmitted state\nupdates. Compared with aforementioned local lag, DR cannot\nmaintain high consistency. Due to network transmission delay,\nwhen a remote site receives a state update of an entity the state of\nthe entity might have changed at the site sending the state update.\nIn order to make DR maintain high consistency, Aggarwal et al [8]\nproposed Globally Synchronized DR (GS-DR), which\nsynchronizes the physical clocks of all sites in a system and adds\ntime stamps to transmitted state updates. Detailed description of\nGS-DR can be found in Section 3.\nWhen a state update is available, GS-DR immediately updates the\nstate of local site and then transmits the state update to remote\nsites, which causes the states of local site and remote sites to be\ninconsistent in the transmission procedure. Thus with the\nsynchronization of physical clocks, GS-DR can eliminate after\ninconsistency, but it cannot tackle before inconsistency [8]. In this\npaper, we propose a new method named globally synchronized\nDR with Local Lag (GS-DR-LL), which combines local lag and\nGS-DR. By delaying the update to local site, GS-DR-LL can\nachieve higher consistency than GS-DR. The rest of this paper is\norganized as follows: Section 2 gives the definition of consistency\nand corresponding metrics; the cause of the inconsistency of DR\nis analyzed in Section 3; Section 4 describes how GS-DR-LL\nworks; performance evaluation is presented in Section 5; Section\n6 concludes the paper.\n2. CONSISTENCY DEFINITIONS AND\nMETRICS\nThe consistency of replicated applications has already been well\ndefined in discrete domain [9, 10, 11, 12], but few related work\nhas been done in continuous domain. Mauve et al [1] have given a\ndefinition of consistency for replicated applications in continuous\ndomain, but the definition is based on operation transmission and\nit is difficult for the definition to describe state transmission based\nmethods (e.g. DR). Here, we present an alternative definition of\nconsistency in continuous domain, which suits state transmission\nbased methods well.\nGiven two distinct sites i and j, which have replicated a shared\nentity e, at a given time t, the states of e at sites i and j are Si(t)\nand Sj(t).\nDEFINITION 1: the states of e at sites i and j are consistent at\ntime t, iff:\nDe(i, j, t) = |Si(t) - Sj(t)| = 0 (1)\nDEFINITION 2: the states of e at sites i and j are consistent\nbetween time t1 and t2 (t1 < t2), iff:\nDe(i, j, t1, t2) = dt|)t(S)t(S|\nt2\nt1\nji = 0 (2)\nIn this paper, formulas (1) and (2) are used to determine whether\nthe states of shared entities are consistent between local and\nremote sites. Due to network transmission delay, it is difficult to\nmaintain the states of shared entities absolutely consistent.\nCorresponding metrics are needed to measure the consistency of\nshared entities between local and remote sites.\nDe(i, j, t) can be used as a metric to measure the degree of\nconsistency at a certain time point. If De(i, j, t1) > De(i, j, t2), it\ncan be stated that between sites i and j, the consistency of the\nstates of entity e at time point t1 is lower than that at time point t2.\nIf De(i, j, t) > De(l, k, t), it can be stated that, at time point t, the\nconsistency of the states of entity e between sites i and j is lower\nthan that between sites l and k.\nSimilarly, De(i, j, t1, t2) can been used as a metric to measure the\ndegree of consistency in a certain time period. If De(i, j, t1, t2) >\nDe(i, j, t3, t4) and |t1 - t2| = |t3 - t4|, it can be stated that between\nsites i and j, the consistency of the states of entity e between time\npoints t1 and t2 is lower than that between time points t3 and t4. If\nDe(i, j, t1, t2) > De(l, k, t1, t2), it can be stated that between time\npoints t1 and t2, the consistency of the states of entity e between\nsites i and j is lower than that between sites l and k.\nIn DR, the states of entities are composed of the positions and\norientations of entities and some prediction related parameters\n(e.g. the velocities of entities). Given two distinct sites i and j,\nwhich have replicated a shared entity e, at a given time point t, the\npositions of e at sites i and j are (xit, yit, zit) and (xjt, yjt, zjt), De(i, j,\nt) and D (i, j, t1, t2) could be calculated as:\nDe(i, j, t) = )zz()yy()xx( jtit\n2\njtit\n2\njtit\n2\n(3)\nDe(i, j, t1, t2)\n= dt)zz()yy()xx(\n2t\n1t jtit\n2\njtit\n2\njtit\n2\n(4)\nIn this paper, formulas (3) and (4) are used as metrics to measure\nthe consistency of shared entities between local and remote sites.\n3. INCONSISTENCY IN DR\nThe inconsistency in DR can be divided into two sections by the\ntime point when a remote site receives a state update. The\ninconsistency before a remote site receives a state update is\nreferred to as before inconsistency, and the inconsistency after a\nremote site receives a state update is referred to as after\ninconsistency. Before inconsistency and after inconsistency are\nsimilar with the terms before export error and after export error\n[8].\nAfter inconsistency is caused by the lack of synchronization\nbetween the physical clocks of all sites in a system. By employing\nphysical clock synchronization, GS-DR can accurately calculate\nthe states of shared entities after receiving state updates, and it\ncan eliminate after inconsistency. Before inconsistency is caused\nby two reasons. The first reason is the delay of sending state\nupdates, as local site does not send a state update unless the\ndifference between accurate state and the estimated one is larger\nthan a predefined threshold. The second reason is network\ntransmission delay, as a shared entity can be synchronized only\nafter remote sites receiving corresponding state update.\nFigure 1. The paths of a shared entity by using GS-DR.\nFor example, it is assumed that the velocity of a shared entity is\nthe only parameter to predict the entity\"s position, and current\nposition of the entity can be calculated by its last position and\ncurrent velocity. To simplify the description, it is also assumed\nthat there are only two sites i and j in a game session, site i acts as\n2 The 5th Workshop on Network & System Support for Games 2006 - NETGAMES 2006\nlocal site and site j acts as remote site, and t1 is the time point the\nlocal site updates the state of the shared entity. Figure 1 illustrates\nthe paths of the shared entity at local site and remote site in x axis\nby using GS-DR. At the beginning, the positions of the shared\nentity are the same at sites i and j and the velocity of the shared\nentity is 0. Before time point t0, the paths of the shared entity at\nsites i and j in x coordinate are exactly the same. At time point t0,\nthe player at site i issues an operation, which changes the velocity\nin x axis to v0. Site i first periodically checks whether the\ndifference between the accurate position of the shared entity and\nthe estimated one, 0 in this case, is larger than a predefined\nthreshold. At time point t1, site i finds that the difference is larger\nthan the threshold and it sends a state update to site j. The state\nupdate contains the position and velocity of the shared entity at\ntime point t1 and time point t1 is also attached as a timestamp. At\ntime point t2, the state update reaches site j, and the received state\nand the time deviation between time points t1 and t2 are used to\ncalculate the current position of the shared entity. Then site j\nupdates its replicated entity\"s position and velocity, and the paths\nof the shared entity at sites i and j overlap again.\nFrom Figure 1, it can be seen that the after inconsistency is 0, and\nthe before consistency is composed of two parts, D1 and D2. D1\nis De(i, j, t0, t1) and it is caused by the state filtering mechanism\nof DR. D2 is De(i, j, t1, t2) and it is caused by network\ntransmission delay.\n4. GLOBALLY SYNCHRONIZED DR\nWITH LOCAL LAG\nFrom the analysis in Section 3, It can be seen that GS-DR can\neliminate after inconsistency, but it cannot effectively tackle\nbefore inconsistency. In order to decrease before inconsistency,\nwe propose GS-DR-LL, which combines GS-DR with local lag\nand can effectively decrease before inconsistency.\nIn GS-DR-LL, the state of a shared entity at a certain time point t\nis notated as S = (t, pos, par 1, par 2, \u2026\u2026, par n), in which pos\nmeans the position of the entity and par 1 to par n means the\nparameters to calculate the position of the entity. In order to\nsimplify the description of GS-DR-LL, it is assumed that there are\nonly one shared entity and one remote site.\nAt the beginning of a game session, the states of the shared entity\nare the same at local and remote sites, with the same position p0\nand parameters pars0 (pars represents all the parameters). Local\nsite keeps three states: the real state of the entity Sreal, the\npredicted state at remote site Sp-remote, and the latest state updated\nto remote site Slate. Remote site keep only one state Sremote, which\nis the real state of the entity at remote site. Therefore, at the\nbeginning of a game session Sreal = Sp-remote = Slate = Sremote = (t0,\np0, pars0). In GS-DR-LL, it is assumed that the physical clocks of\nall sites are synchronized with a deviation of less than 50 ms\n(using NTP or GPS clock). Furthermore, it is necessary to make\ncorrections to a physical clock in a way that does not result in\ndecreasing the value of the clock, for example by slowing down\nor halting the clock for a period of time. Additionally it is\nassumed that the game scene is updated at a fixed frequency and\nT stands for the time interval between two consecutive updates,\nfor example, if the scene update frequency is 50 Hz, T would be\n20 ms. n stands for the lag value used by local lag, and t stands for\ncurrent physical time.\nAfter updating the scene, local site waits for a constant amount of\ntime T. During this time period, local site receives the operations\nof the player and stores them in a list L. All operations in L are\nsorted by their issue time. At the end of time period T, local site\nexecutes all stored operations, whose issue time is between t - T\nand t, on Slate to get the new Slate, and it also executes all stored\noperations, whose issue time is between t - (n + T) and t - n, on\nSreal to get the new Sreal. Additionally, local site uses Sp-remote and\ncorresponding prediction methods to estimate the new Sp-remote.\nAfter new Slate, Sreal, and Sp-remote are calculated, local site\ncompares whether the difference between the new Slate and\nSpremote exceeds the predefined threshold. If YES, local site sends\nnew Slate to remote site and Sp-remote is updated with new Slate. Note\nthat the timestamp of the sent state update is t. After that, local\nsite uses Sreal to update local scene and deletes the operations,\nwhose issue time is less than t - n, from L.\nAfter updating the scene, remote site waits for a constant amount\nof time T. During this time period, remote site stores received\nstate update(s) in a list R. All state updates in R are sorted by their\ntimestamps. At the end of time period T, remote site checks\nwhether R contains state updates whose timestamps are less than t\n- n. Note that t is current physical time and it increases during the\ntransmission of state updates. If YES, it uses these state updates\nand corresponding prediction methods to calculate the new Sremote,\nelse they use Sremote and corresponding prediction methods to\nestimate the new Sremote. After that, local site uses Sremote to update\nlocal scene and deletes the sate updates, whose timestamps are\nless than t - n, from R.\nFrom the above description, it can been see that the main\ndifference between GS-DR and GS-DR-LL is that GS-DR-LL\nuses the operations, whose issue time is less than t - n, to\ncalculate Sreal. That means that the scene seen by local player is\nthe results of the operations issued a period of time (i.e. n) ago.\nMeanwhile, if the results of issued operations make the difference\nbetween Slate and Sp-remote exceed a predefined threshold,\ncorresponding state updates are sent to remote sites immediately.\nThe aforementioned is the basic mechanism of GS-DR-LL. In the\ncase with multiple shared entities and remote sites, local site\ncalculates Slate, Sreal, and Sp-remote for different shared entities\nrespectively, if there are multiple Slate need to be transmitted, local\nsite packets them in one state update and then send it to all remote\nsites.\nFigure 2 illustrates the paths of a shared entity at local site and\nremote site while using GS-DR and GS-DR-LL. All conditions\nare the same with the conditions used in the aforementioned\nexample describing GS-DR. Compared with t1, t2, and n, T (i.e.\nthe time interval between two consecutive updates) is quite small\nand it is ignored in the following description.\nAt time point t0, the player at site i issues an operation, which\nchanges the velocity of the shared entity form 0 to v0. By using\nGS-DR-LL, the results of the operation are updated to local scene\nat time point t0 + n. However the operation is immediately used\nto calculate Slate, thus in spite of GS-DR or GS-DR-LL, at time\npoint t1 site i finds that the difference between accurate position\nand the estimated one is larger than the threshold and it sends a\nstate update to site j. At time point t2, the state update is received\nby remote site j. Assuming that the timestamp of the state update\nis less than t - n, site j uses it to update local scene immediately.\nThe 5th Workshop on Network & System Support for Games 2006 - NETGAMES 2006 3\nWith GS-DR, the time period of before inconsistency is (t2 - t1) +\n(t1 - t0), whereas it decreases to (t2 - t1 - n) + (t1 - t0) with the\nhelp of GS-DR-LL. Note that t2 - t1 is caused by network\ntransmission delay and t1 - t0 is caused by the state filtering\nmechanism of DR. If n is larger than t2 - t1, GS-DR-LL can\neliminate the before inconsistency caused by network\ntransmission delay, but it cannot eliminate the before\ninconsistency caused by the state filtering mechanism of DR\n(unless the threshold is set to 0). In highly interactive games,\nwhich request high consistency and GS-DR-LL might be\nemployed, the results of operations are quite difficult to be\nestimated and a small threshold must be used. Thus, in practice,\nmost before inconsistency is caused by network transmission\ndelay and GS-DR-LL has the capability to eliminate such before\ninconsistency.\nFigure 2. The paths of a shared entity by using GS-DR and\nGS-DR-LL.\nTo GS-DR-LL, the selection of lag value n is very important, and\nboth network transmission delay and the effects of local lag on\ninteraction should be considered. According to the results of HCI\nrelated researches, humans cannot perceive the delay imposed on\na system when it is smaller than a specific value, and the specific\nvalue depends on both the system and the task. For example, in a\ngraphical user interface a delay of approximately 150 ms cannot\nbe noticed for keyboard interaction and the threshold increases to\n195 ms for mouse interaction [13], and a delay of up to 50 ms is\nuncritical for a car-racing game [5]. Thus if network transmission\ndelay is less than the specific value of a game system, n can be set\nto the specific value. Else n can be set in terms of the effects of\nlocal lag on the interaction of a system [14]. In the case that a\nlarge n must be used, some HCI methods (e.g. echo [15]) can be\nused to relieve the negative effects of the large lag. In the case\nthat n is larger than the network transmission delay, GS-DR-LL\ncan eliminate most before inconsistency. Traditional local lag\nrequests that the lag value must be larger than typical network\ntransmission delay, otherwise state repairs would flood the system.\nHowever GS-DR-LL allows n to be smaller than typical network\ntransmission delay. In this case, the before inconsistency caused\nby network transmission delay still exists, but it can be decreased.\n5. PERFORMANCE EVALUATION\nIn order to evaluate GS-DR-LL and compare it with GS-DR in a\nreal application, we had implemented both two methods in a\nnetworked game named spaceship [1]. Spaceship is a very simple\nnetworked computer game, in which players can control their\nspaceships to accelerate, decelerate, turn, and shoot spaceships\ncontrolled by remote players with laser beams. If a spaceship is\nhit by a laser beam, its life points decrease one. If the life points\nof a spaceship decrease to 0, the spaceship is removed from the\ngame and the player controlling the spaceship loses the game.\nIn our practical implementation, GS-DR-LL and GS-DR\ncoexisted in the game system, and the test bed was composed of\ntwo computers connected by 100 M switched Ethernet, with one\ncomputer acted as local site and the other acted as remote site. In\norder to simulate network transmission delay, a specific module\nwas developed to delay all packets transmitted between the two\ncomputers in terms of a predefined delay value.\nThe main purpose of performance evaluation is to study the\neffects of GS-DR-LL on decreasing before inconsistency in a\nparticular game system under different thresholds, lags, and\nnetwork transmission delays. Two different thresholds were used\nin the evaluation, one is 10 pixels deviation in position or 15\ndegrees deviation in orientation, and the other is 4 pixels or 5\ndegrees. Six different combinations of lag and network\ntransmission delay were used in the evaluation and they could be\ndivided into two categories. In one category, the lag was fixed at\n300 ms and three different network transmission delays (100 ms,\n300 ms, and 500 ms) were used. In the other category, the\nnetwork transmission delay was fixed at 800 ms and three\ndifferent lags (100 ms, 300 ms, and 500 ms) were used. Therefore\nthe total number of settings used in the evaluation was 12 (2 \u00d7 6).\nThe procedure of performance evaluation was composed of three\nsteps. In the first step, two participants were employed to play the\ngame, and the operation sequences were recorded. Based on the\nrecords, a sub operation sequence, which lasted about one minute\nand included different operations (e.g. accelerate, decelerate, and\nturn), was selected. In the second step, the physical clocks of the\ntwo computers were synchronized first. Under different settings\nand consistency maintenance approaches, the selected sub\noperation sequence was played back on one computer, and it\ndrove the two spaceships, one was local and the other was remote,\nto move. Meanwhile, the tracks of the spaceships on the two\ncomputers were recorded separately and they were called as a\ntrack couple. Since there are 12 settings and 2 consistency\nmaintenance approaches, the total number of recorded track\ncouples was 24. In the last step, to each track couple, the\ninconsistency between them was calculated, and the unit of\ninconsistency was pixel. Since the physical clocks of the two\ncomputers were synchronized, the calculation of inconsistency\nwas quite simple. The inconsistency at a particular time point was\nthe distance between the positions of the two spaceships at that\ntime point (i.e. formula (3)).\nIn order to show the results of inconsistency in a clear way, only\nparts of the results, which last about 7 seconds, are used in the\nfollowing figures, and the figures show almost the same parts of\nthe results. Figures 3, 4, and 5 show the results of inconsistency\nwhen the lag is fixed at 300 ms and the network transmission\ndelays are 100, 300, and 500 ms. It can been seen that\ninconsistency does exist, but in most of the time it is 0.\nAdditionally, inconsistency increases with the network\ntransmission delay, but decreases with the threshold. Compared\nwith GS-DR, GS-DR-LL can decrease more inconsistency, and it\neliminates most inconsistency when the network transmission\ndelay is 100 ms and the threshold is 4 pixels or 5 degrees.\n4 The 5th Workshop on Network & System Support for Games 2006 - NETGAMES 2006\nAccording to the prediction and state filtering mechanisms of DR,\ninconsistency cannot be completely eliminated if the threshold is\nnot 0. With the definitions of before inconsistency and after\ninconsistency, it can be indicated that GS-DR and GS-DR-LL\nboth can eliminate after inconsistency, and GS-DR-LL can\neffectively decrease before inconsistency. It can be foreseen that\nwith proper lag and threshold (e.g. the lag is larger than the\nnetwork transmission delay and the threshold is 0), GS-DR-LL\neven can eliminate before inconsistency.\n0\n10\n20\n30\n40\n0.0 1.5 3.1 4.6 6.1\nTime (seconds)\nInconsistency(pixels)\nGS-DR-LL GS-DR\nThe threshold is 10 pixels or 15degrees\n0\n10\n20\n30\n40\n0.0 1.5 3.1 4.6 6.1\nTime (seconds)\nInconsistency(pixels)\nGS-DR-LL GS-DR\nThe threshold is 4 pixels or 5degrees\nFigure 3. Inconsistency when the network transmission delay is 100 ms and the lag is 300 ms.\n0\n10\n20\n30\n40\n0.0 1.5 3.1 4.6 6.1\nTime (seconds)\nInconsistency(pixels)\nGS-DR-LL GS-DR\nThe threshold is 10 pixels or 15degrees\n0\n10\n20\n30\n40\n0.0 1.5 3.1 4.6 6.1\nTime (seconds)\nInconsistency(pixels) GS-DR-LL GS-DR\nThe threshold is 4 pixels or 5degrees\nFigure 4. Inconsistency when the network transmission delay is 300 ms and the lag is 300 ms.\n0\n10\n20\n30\n40\n0.0 1.5 3.1 4.6 6.2\nTime (seconds)\nInconsistency(pixels)\nGS-DR-LL GS-DR\nThe threshold is 10 pixels or 15degrees\n0\n10\n20\n30\n40\n0.0 1.5 3.1 4.6 6.1\nTime (seconds)\nInconsistency(pixels)\nGS-DR-LL GS-DR\nThe threshold is 4 pixels or 5degrees\nFigure 5. Inconsistency when the network transmission delay is 500 ms and the lag is 300 ms.\nFigures 6, 7, and 8 show the results of inconsistency when the\nnetwork transmission delay is fixed at 800 ms and the lag are 100,\n300, and 500 ms. It can be seen that with GS-DR-LL before\ninconsistency decreases with the lag. In traditional local lag, the\nlag must be set to a value larger than typical network transmission\ndelay, otherwise the state repairs would flood the system. From\nthe above results it can be seen that there does not exist any\nconstraint on the selection of the lag, with GS-DR-LL a system\nwould work fine even if the lag is much smaller than the network\ntransmission delay.\nThe 5th Workshop on Network & System Support for Games 2006 - NETGAMES 2006 5\nFrom all above results, it can be indicated that GS-DR and\nGSDR-LL both can eliminate after inconsistency, and GS-DR-LL\ncan effectively decrease before inconsistency, and the effects\nincrease with the lag.\n0\n10\n20\n30\n40\n0.0 1.5 3.1 4.7 6.2\nTime (seconds)\nInconsistency(pixels)\nGS-DR-LL GS-DR\nThe threshold is 10 pixels or 15degrees\n0\n10\n20\n30\n40\n0.0 1.5 3.1 4.6 6.1\nTime (seconds)\nInconsistency(pixels)\nGS-DR-LL GS-DR\nThe threshold is 4 pixels or 5degrees\nFigure 6. Inconsistency when the network transmission delay is 800 ms and the lag is 100 ms.\n0\n10\n20\n30\n40\n0.0 1.5 3.1 4.6 6.1\nTime (seconds)\nInconsistency(pixels)\nGS-DR-LL GS-DR\nThe threshold is 10 pixels or 15degrees\n0\n10\n20\n30\n40\n0.0 1.5 3.1 4.6 6.1\nTime (seconds)\nInconsistency(pixels)\nGS-DR-LL GS-DR\nThe threshold is 4 pixels or 5degrees\nFigure 7. Inconsistency when the network transmission delay is 800 ms and the lag is 300 ms.\n0\n10\n20\n30\n40\n0.0 1.5 3.1 4.6 6.1\nTime (seconds)\nInconsistency(pixels)\nGS-DR-LL GS-DR\nThe threshold is 10 pixels or 15degrees\n0\n10\n20\n30\n40\n0.0 1.5 3.1 4.6 6.1\nTime (seconds)\nInconsistency(pixels)\nGS-DR-LL GS-DR\nThe threshold is 4 pixels or 5degrees\nFigure 8. Inconsistency when the network transmission delay is 800 ms and the lag is 500 ms.\n6. CONCLUSIONS\nCompared with traditional DR, GS-DR can eliminate after\ninconsistency through the synchronization of physical clocks, but\nit cannot tackle before inconsistency, which would significantly\ninfluence the usability and fairness of a game. In this paper, we\nproposed a method named GS-DR-LL, which combines local lag\nand GS-DR, to decrease before inconsistency through delaying\nupdating the execution results of local operations to local scene.\nPerformance evaluation indicates that GS-DR-LL can effectively\ndecrease before inconsistency, and the effects increase with the\nlag.\nGS-DR-LL has significant implications to consistency\nmaintenance approaches. First, GS-DR-LL shows that improved\nDR can not only eliminate after inconsistency but also decrease\n6 The 5th Workshop on Network & System Support for Games 2006 - NETGAMES 2006\nbefore inconsistency, with proper lag and threshold, it would even\neliminate before inconsistency. As a result, the application of DR\ncan be greatly broadened and it could be used in the systems\nwhich request high consistency (e.g. highly interactive games).\nSecond, GS-DR-LL shows that by combining local lag and\nGSDR, the constraint on selecting lag value is removed and a lag,\nwhich is smaller than typical network transmission delay, could\nbe used. As a result, the application of local lag can be greatly\nbroadened and it could be used in the systems which have large\ntypical network transmission delay (e.g. Internet based games).\n7. REFERENCES\n[1] Mauve, M., Vogel, J., Hilt, V., and Effelsberg, W. Local-Lag\nand Timewarp: Providing Consistency for Replicated\nContinuous Applications. IEEE Transactions on Multimedia,\nVol. 6, No.1, 2004, 47-57.\n[2] Li, F.W., Li, L.W., and Lau, R.W. Supporting Continuous\nConsistency in Multiplayer Online Games. In Proc. of ACM\nMultimedia, 2004, 388-391.\n[3] Pantel, L. and Wolf, L. On the Suitability of Dead\nReckoning Schemes for Games. In Proc. of NetGames, 2002,\n79-84.\n[4] Alhalabi, M.O., Horiguchi, S., and Kunifuji, S. An\nExperimental Study on the Effects of Network Delay in\nCooperative Shared Haptic Virtual Environment. Computers\nand Graphics, Vol. 27, No. 2, 2003, 205-213.\n[5] Pantel, L. and Wolf, L.C. On the Impact of Delay on\nRealTime Multiplayer Games. In Proc. of NOSSDAV, 2002,\n2329.\n[6] Meehan, M., Razzaque, S., Whitton, M.C., and Brooks, F.P.\nEffect of Latency on Presence in Stressful Virtual\nEnvironments. In Proc. of IEEE VR, 2003, 141-148.\n[7] Bernier, Y.W. Latency Compensation Methods in\nClient/Server In-Game Protocol Design and Optimization. In\nProc. of Game Developers Conference, 2001.\n[8] Aggarwal, S., Banavar, H., and Khandelwal, A. Accuracy in\nDead-Reckoning based Distributed Multi-Player Games. In\nProc. of NetGames, 2004, 161-165.\n[9] Raynal, M. and Schiper, A. From Causal Consistency to\nSequential Consistency in Shared Memory Systems. In Proc.\nof Conference on Foundations of Software Technology and\nTheoretical Computer Science, 1995, 180-194.\n[10] Ahamad, M., Burns, J.E., Hutto, P.W., and Neiger, G. Causal\nMemory. In Proc. of International Workshop on Distributed\nAlgorithms, 1991, 9-30.\n[11] Herlihy, M. and Wing, J. Linearizability: a Correctness\nCondition for Concurrent Objects. ACM Transactions on\nProgramming Languages and Systems, Vol. 12, No. 3, 1990,\n463-492.\n[12] Misra, J. Axioms for Memory Access in Asynchronous\nHardware Systems. ACM Transactions on Programming\nLanguages and Systems, Vol. 8, No. 1, 1986, 142-153.\n[13] Dabrowski, J.R. and Munson, E.V. Is 100 Milliseconds too\nFast. In Proc. of SIGCHI Conference on Human Factors in\nComputing Systems, 2001, 317-318.\n[14] Chen, H., Chen, L., and Chen, G.C. Effects of Local-Lag\nMechanism on Cooperation Performance in a Desktop CVE\nSystem. Journal of Computer Science and Technology, Vol.\n20, No. 3, 2005, 396-401.\n[15] Chen, L., Chen, H., and Chen, G.C. Echo: a Method to\nImprove the Interaction Quality of CVEs. In Proc. of IEEE\nVR, 2005, 269-270.\nThe 5th Workshop on Network & System Support for Games 2006 - NETGAMES 2006 7", "keywords": "local lag;physical clock;time warp;usability and fairness;continuous replicate application;network transmission delay;distribute multi-player game;accurate state;gs-dr-ll;dead-reckon;multiplayer game;consistency;correction"}
{"name": "train_C-54", "title": "Remote Access to Large Spatial Databases", "abstract": "Enterprises in the public and private sectors have been making their large spatial data archives available over the Internet. However, interactive work with such large volumes of online spatial data is a challenging task. We propose two efficient approaches to remote access to large spatial data. First, we introduce a client-server architecture where the work is distributed between the server and the individual clients for spatial query evaluation, data visualization, and data management. We enable the minimization of the requirements for system resources on the client side while maximizing system responsiveness as well as the number of connections one server can handle concurrently. Second, for prolonged periods of access to large online data, we introduce APPOINT (an Approach for Peer-to-Peer O\ufb04oading the INTernet). This is a centralized peer-to-peer approach that helps Internet users transfer large volumes of online data efficiently. In APPOINT, active clients of the clientserver architecture act on the server\"s behalf and communicate with each other to decrease network latency, improve service bandwidth, and resolve server congestions.", "fulltext": "1. INTRODUCTION\nIn recent years, enterprises in the public and private\nsectors have provided access to large volumes of spatial data\nover the Internet. Interactive work with such large volumes\nof online spatial data is a challenging task. We have been\ndeveloping an interactive browser for accessing spatial online\ndatabases: the SAND (Spatial and Non-spatial Data)\nInternet Browser. Users of this browser can interactively and\nvisually manipulate spatial data remotely. Unfortunately,\ninteractive remote access to spatial data slows to a crawl\nwithout proper data access mechanisms. We developed two\nseparate methods for improving the system performance,\ntogether, form a dynamic network infrastructure that is highly\nscalable and provides a satisfactory user experience for\ninteractions with large volumes of online spatial data.\nThe core functionality responsible for the actual database\noperations is performed by the server-based SAND system.\nSAND is a spatial database system developed at the\nUniversity of Maryland [12]. The client-side SAND Internet\nBrowser provides a graphical user interface to the facilities\nof SAND over the Internet. Users specify queries by\nchoosing the desired selection conditions from a variety of menus\nand dialog boxes.\nSAND Internet Browser is Java-based, which makes it\ndeployable across many platforms. In addition, since Java has\noften been installed on target computers beforehand, our\nclients can be deployed on these systems with little or no\nneed for any additional software installation or\ncustomization. The system can start being utilized immediately\nwithout any prior setup which can be extremely beneficial in\ntime-sensitive usage scenarios such as emergencies.\nThere are two ways to deploy SAND. First, any standard\nWeb browser can be used to retrieve and run the client piece\n(SAND Internet Browser) as a Java application or an applet.\nThis way, users across various platforms can continuously\naccess large spatial data on a remote location with little or\n15\nno need for any preceding software installation. The second\noption is to use a stand-alone SAND Internet Browser along\nwith a locally-installed Internet-enabled database\nmanagement system (server piece). In this case, the SAND Internet\nBrowser can still be utilized to view data from remote\nlocations. However, frequently accessed data can be downloaded\nto the local database on demand, and subsequently accessed\nlocally. Power users can also upload large volumes of spatial\ndata back to the remote server using this enhanced client.\nWe focused our efforts in two directions. We first aimed at\ndeveloping a client-server architecture with efficient caching\nmethods to balance local resources on one side and the\nsignificant latency of the network connection on the other. The\nlow bandwidth of this connection is the primary concern in\nboth cases. The outcome of this research primarily addresses\nthe issues of our first type of usage (i.e., as a remote browser\napplication or an applet) for our browser and other similar\napplications. The second direction aims at helping users\nthat wish to manipulate large volumes of online data for\nprolonged periods. We have developed a centralized\npeerto-peer approach to provide the users with the ability to\ntransfer large volumes of data (i.e., whole data sets to the\nlocal database) more efficiently by better utilizing the\ndistributed network resources among active clients of a\nclientserver architecture. We call this architecture\nAPPOINTApproach for Peer-to-Peer O\ufb04oading the INTernet. The\nresults of this research addresses primarily the issues of the\nsecond type of usage for our SAND Internet Browser (i.e.,\nas a stand-alone application).\nThe rest of this paper is organized as follows. Section 2\ndescribes our client-server approach in more detail. Section 3\nfocuses on APPOINT, our peer-to-peer approach. Section 4\ndiscusses our work in relation to existing work. Section 5\noutlines a sample SAND Internet Browser scenario for both\nof our remote access approaches. Section 6 contains\nconcluding remarks as well as future research directions.\n2. THE CLIENT-SERVER APPROACH\nTraditionally, Geographic Information Systems (GIS)\nsuch as ArcInfo from ESRI [2] and many spatial databases\nare designed to be stand-alone products. The spatial\ndatabase is kept on the same computer or local area network\nfrom where it is visualized and queried. This architecture\nallows for instantaneous transfer of large amounts of data\nbetween the spatial database and the visualization module\nso that it is perfectly reasonable to use large-bandwidth\nprotocols for communication between them. There are however\nmany applications where a more distributed approach is\ndesirable. In these cases, the database is maintained in one\nlocation while users need to work with it from possibly distant\nsites over the network (e.g., the Internet). These connections\ncan be far slower and less reliable than local area networks\nand thus it is desirable to limit the data flow between the\ndatabase (server) and the visualization unit (client) in order\nto get a timely response from the system.\nOur client-server approach (Figure 1) allows the actual\ndatabase engine to be run in a central location maintained\nby spatial database experts, while end users acquire a\nJavabased client component that provides them with a gateway\ninto the SAND spatial database engine.\nOur client is more than a simple image viewer. Instead, it\noperates on vector data allowing the client to execute many\noperations such as zooming or locational queries locally. In\nFigure 1: SAND Internet Browser - Client-Server\narchitecture.\nessence, a simple spatial database engine is run on the client.\nThis database keeps a copy of a subset of the whole database\nwhose full version is maintained on the server. This is a\nconcept similar to \u2018caching\". In our case, the client acts as\na lightweight server in that given data, it evaluates queries\nand provides the visualization module with objects to be\ndisplayed. It initiates communication with the server only\nin cases where it does not have enough data stored locally.\nSince the locally run database is only updated when\nadditional or newer data is needed, our architecture allows the\nsystem to minimize the network traffic between the client\nand the server when executing the most common user-side\noperations such as zooming and panning. In fact, as long\nas the user explores one region at a time (i.e., he or she is\nnot panning all over the database), no additional data needs\nto be retrieved after the initial population of the client-side\ndatabase. This makes the system much more responsive\nthan the Web mapping services. Due to the complexity of\nevaluating arbitrary queries (i.e., more complex queries than\nwindow queries that are needed for database visualization),\nwe do not perform user-specified queries on the client. All\nuser queries are still evaluated on the server side and the\nresults are downloaded onto the client for display. However,\nassuming that the queries are selective enough (i.e., there are\nfar fewer elements returned from the query than the number\nof elements in the database), the response delay is usually\nwithin reasonable limits.\n2.1 Client-Server Communication\nAs mentioned above, the SAND Internet Browser is a\nclient piece of the remotely accessible spatial database server\nbuilt around the SAND kernel. In order to communicate\nwith the server, whose application programming interface\n(API) is a Tcl-based scripting language, a servlet specifically\ndesigned to interface the SAND Internet Browser with the\nSAND kernel is required on the server side. This servlet\nlistens on a given port of the server for incoming requests from\nthe client. It translates these requests into the SAND-Tcl\nlanguage. Next, it transmits these SAND-Tcl commands or\nscripts to the SAND kernel. After results are provided by\nthe kernel, the servlet fetches and processes them, and then\nsends those results back to the originating client.\nOnce the Java servlet is launched, it waits for a client to\ninitiate a connection. It handles both requests for the actual\nclient Java code (needed when the client is run as an applet)\nand the SAND traffic. When the client piece is launched,\nit connects back to the SAND servlet, the communication\nis driven by the client piece; the server only responds to\nthe client\"s queries. The client initiates a transaction by\n6\nsending a query. The Java servlet parses the query and\ncreates a corresponding SAND-Tcl expression or script in\nthe SAND kernel\"s native format. It is then sent to the\nkernel for evaluation or execution. The kernel\"s response\nnaturally depends on the query and can be a boolean value,\na number or a string representing a value (e.g., a default\ncolor) or, a whole tuple (e.g., in response to a nearest tuple\nquery). If a script was sent to the kernel (e.g., requesting\nall the tuples matching some criteria), then an arbitrary\namount of data can be returned by the SAND server. In this\ncase, the data is first compressed before it is sent over the\nnetwork to the client. The data stream gets decompressed\nat the client before the results are parsed.\nNotice, that if another spatial database was to be used\ninstead of the SAND kernel, then only a simple\nmodification to the servlet would need to be made in order for the\nSAND Internet Browser to function properly. In\nparticular, the queries sent by the client would need to be recoded\ninto another query language which is native to this different\nspatial database. The format of the protocol used for\ncommunication between the servlet and the client is unaffected.\n3. THE PEER-TO-PEER APPROACH\nMany users may want to work on a complete spatial data\nset for a prolonged period of time. In this case, making an\ninitial investment of downloading the whole data set may be\nneeded to guarantee a satisfactory session. Unfortunately,\nspatial data tends to be large. A few download requests\nto a large data set from a set of idle clients waiting to be\nserved can slow the server to a crawl. This is due to the fact\nthat the common client-server approach to transferring data\nbetween the two ends of a connection assumes a designated\nrole for each one of the ends (i.e, some clients and a server).\nWe built APPOINT as a centralized peer-to-peer system\nto demonstrate our approach for improving the common\nclient-server systems. A server still exists. There is a\ncentral source for the data and a decision mechanism for the\nservice. The environment still functions as a client-server\nenvironment under many circumstances. Yet, unlike many\ncommon client-server environments, APPOINT maintains\nmore information about the clients. This includes,\ninventories of what each client downloads, their availabilities, etc.\nWhen the client-server service starts to perform poorly or\na request for a data item comes from a client with a poor\nconnection to the server, APPOINT can start appointing\nappropriate active clients of the system to serve on behalf\nof the server, i.e., clients who have already volunteered their\nservices and can take on the role of peers (hence, moving\nfrom a client-server scheme to a peer-to-peer scheme). The\ndirectory service for the active clients is still performed by\nthe server but the server no longer serves all of the requests.\nIn this scheme, clients are used mainly for the purpose of\nsharing their networking resources rather than introducing\nnew content and hence they help o\ufb04oad the server and scale\nup the service. The existence of a server is simpler in terms\nof management of dynamic peers in comparison to pure\npeerto-peer approaches where a flood of messages to discover\nwho is still active in the system should be used by each peer\nthat needs to make a decision. The server is also the main\nsource of data and under regular circumstances it may not\nforward the service.\nData is assumed to be formed of files. A single file forms\nthe atomic means of communication. APPOINT optimizes\nrequests with respect to these atomic requests. Frequently\naccessed data sets are replicated as a byproduct of having\nbeen requested by a large number of users. This opens up\nthe potential for bypassing the server in future downloads for\nthe data by other users as there are now many new points of\naccess to it. Bypassing the server is useful when the server\"s\nbandwidth is limited. Existence of a server assures that\nunpopular data is also available at all times. The service\ndepends on the availability of the server. The server is now\nmore resilient to congestion as the service is more scalable.\nBackups and other maintenance activities are already\nbeing performed on the server and hence no extra\nadministrative effort is needed for the dynamic peers. If a peer goes\ndown, no extra precautions are taken. In fact, APPOINT\ndoes not require any additional resources from an already\nexisting client-server environment but, instead, expands its\ncapability. The peers simply get on to or get off from a table\non the server.\nUploading data is achieved in a similar manner as\ndownloading data. For uploads, the active clients can again be\nutilized. Users can upload their data to a set of peers other\nthan the server if the server is busy or resides in a distant\nlocation. Eventually the data is propagated to the server.\nAll of the operations are performed in a transparent\nfashion to the clients. Upon initial connection to the server,\nthey can be queried as to whether or not they want to share\ntheir idle networking time and disk space. The rest of the\noperations follow transparently after the initial contact.\nAPPOINT works on the application layer but not on lower\nlayers. This achieves platform independence and easy\ndeployment of the system. APPOINT is not a replacement but\nan addition to the current client-server architectures. We\ndeveloped a library of function calls that when placed in a\nclient-server architecture starts the service. We are\ndeveloping advanced peer selection schemes that incorporate the\nlocation of active clients, bandwidth among active clients,\ndata-size to be transferred, load on active clients, and\navailability of active clients to form a complete means of selecting\nthe best clients that can become efficient alternatives to the\nserver.\nWith APPOINT we are defining a very simple API that\ncould be used within an existing client-server system easily.\nInstead of denial of service or a slow connection, this API\ncan be utilized to forward the service appropriately. The\nAPI for the server side is:\nstart(serverPortNo)\nmakeFileAvailable(file,location,boolean)\ncallback receivedFile(file,location)\ncallback errorReceivingFile(file,location,error)\nstop()\nSimilarly the API for the client side is:\nstart(clientPortNo,serverPortNo,serverAddress)\nmakeFileAvailable(file,location,boolean)\nreceiveFile(file,location)\nsendFile(file,location)\nstop()\nThe server, after starting the APPOINT service, can make\nall of the data files available to the clients by using the\nmakeFileAvailable method. This will enable APPOINT\nto treat the server as one of the peers.\nThe two callback methods of the server are invoked when\na file is received from a client, or when an error is\nencountered while receiving a file from a client. APPOINT\nguar7\nFigure 2: The localization operation in APPOINT.\nantees that at least one of the callbacks will be called so\nthat the user (who may not be online anymore) can always\nbe notified (i.e., via email). Clients localizing large data\nfiles can make these files available to the public by using the\nmakeFileAvailable method on the client side.\nFor example, in our SAND Internet Browser, we have the\nlocalization of spatial data as a function that can be chosen\nfrom our menus. This functionality enables users to\ndownload data sets completely to their local disks before starting\ntheir queries or analysis. In our implementation, we have\ncalls to the APPOINT service both on the client and the\nserver sides as mentioned above. Hence, when a localization\nrequest comes to the SAND Internet Browser, the browser\nleaves the decisions to optimally find and localize a data set\nto the APPOINT service. Our server also makes its data\nfiles available over APPOINT. The mechanism for the\nlocalization operation is shown with more details from the\nAPPOINT protocols in Figure 2. The upload operation is\nperformed in a similar fashion.\n4. RELATED WORK\nThere has been a substantial amount of research on\nremote access to spatial data. One specific approach has\nbeen adopted by numerous Web-based mapping services\n(MapQuest [5], MapsOnUs [6], etc.). The goal in this\napproach is to enable remote users, typically only equipped\nwith standard Web browsers, to access the company\"s\nspatial database server and retrieve information in the form of\npictorial maps from them. The solution presented by most\nof these vendors is based on performing all the calculations\non the server side and transferring only bitmaps that\nrepresent results of user queries and commands. Although the\nadvantage of this solution is the minimization of both\nhardware and software resources on the client site, the resulting\nproduct has severe limitations in terms of available\nfunctionality and response time (each user action results in a new\nbitmap being transferred to the client).\nWork described in [9] examines a client-server\narchitecture for viewing large images that operates over a\nlowbandwidth network connection. It presents a technique\nbased on wavelet transformations that allows the\nminimization of the amount of data needed to be transferred over\nthe network between the server and the client. In this case,\nwhile the server holds the full representation of the large\nimage, only a limited amount of data needs to be transferred\nto the client to enable it to display a currently requested\nview into the image. On the client side, the image is\nreconstructed into a pyramid representation to speed up zooming\nand panning operations. Both the client and the server keep\na common mask that indicates what parts of the image are\navailable on the client and what needs to be requested. This\nalso allows dropping unnecessary parts of the image from the\nmain memory on the server.\nOther related work has been reported in [16] where a\nclient-server architecture is described that is designed to\nprovide end users with access to a server. It is assumed that\nthis data server manages vast databases that are impractical\nto be stored on individual clients. This work blends raster\ndata management (stored in pyramids [22]) with vector data\nstored in quadtrees [19, 20].\nFor our peer-to-peer transfer approach (APPOINT),\nNapster is the forefather where a directory service is centralized\non a server and users exchange music files that they have\nstored on their local disks. Our application domain, where\nthe data is already freely available to the public, forms a\nprime candidate for such a peer-to-peer approach. Gnutella\nis a pure (decentralized) peer-to-peer file exchange system.\nUnfortunately, it suffers from scalability issues, i.e., floods of\nmessages between peers in order to map connectivity in the\nsystem are required. Other systems followed these popular\nsystems, each addressing a different flavor of sharing over\nthe Internet. Many peer-to-peer storage systems have also\nrecently emerged. PAST [18], Eternity Service [7], CFS [10],\nand OceanStore [15] are some peer-to-peer storage systems.\nSome of these systems have focused on anonymity while\nothers have focused on persistence of storage. Also, other\napproaches, like SETI@Home [21], made other resources, such\nas idle CPUs, work together over the Internet to solve large\nscale computational problems. Our goal is different than\nthese approaches. With APPOINT, we want to improve\nexisting client-server systems in terms of performance by using\nidle networking resources among active clients. Hence, other\nissues like anonymity, decentralization, and persistence of\nstorage were less important in our decisions. Confirming\nthe authenticity of the indirectly delivered data sets is not\nyet addressed with APPOINT. We want to expand our\nresearch, in the future, to address this issue.\nFrom our perspective, although APPOINT employs some\nof the techniques used in peer-to-peer systems, it is also\nclosely related to current Web caching architectures.\nSquirrel [13] forms the middle ground. It creates a pure\npeer-topeer collaborative Web cache among the Web browser caches\nof the machines in a local-area network. Except for this\nrecent peer-to-peer approach, Web caching is mostly a\nwellstudied topic in the realm of server/proxy level caching [8,\n11, 14, 17]. Collaborative Web caching systems, the most\nrelevant of these for our research, focus on creating\neither a hierarchical, hash-based, central directory-based, or\nmulticast-based caching schemes. We do not compete with\nthese approaches. In fact, APPOINT can work in\ntandem with collaborative Web caching if they are deployed\ntogether. We try to address the situation where a request\narrives at a server, meaning all the caches report a miss.\nHence, the point where the server is reached can be used to\ntake a central decision but then the actual service request\ncan be forwarded to a set of active clients, i.e., the\ndown8\nload and upload operations. Cache misses are especially\ncommon in the type of large data-based services on which\nwe are working. Most of the Web caching schemes that are\nin use today employ a replacement policy that gives a\npriority to replacing the largest sized items over smaller-sized\nones. Hence, these policies would lead to the immediate\nreplacement of our relatively large data files even though they\nmay be used frequently. In addition, in our case, the user\ncommunity that accesses a certain data file may also be very\ndispersed from a network point of view and thus cannot take\nadvantage of any of the caching schemes. Finally, none of\nthe Web caching methods address the symmetric issue of\nlarge data uploads.\n5. A SAMPLE APPLICATION\nFedStats [1] is an online source that enables ordinary\ncitizens access to official statistics of numerous federal agencies\nwithout knowing in advance which agency produced them.\nWe are using a FedStats data set as a testbed for our work.\nOur goal is to provide more power to the users of FedStats\nby utilizing the SAND Internet Browser. As an example,\nwe looked at two data files corresponding to\nEnvironmental Protection Agency (EPA)-regulated facilities that have\nchlorine and arsenic, respectively. For each file, we had the\nfollowing information available: EPA-ID, name, street, city,\nstate, zip code, latitude, longitude, followed by flags to\nindicate if that facility is in the following EPA programs:\nHazardous Waste, Wastewater Discharge, Air Emissions,\nAbandoned Toxic Waste Dump, and Active Toxic Release.\nWe put this data into a SAND relation where the spatial\nattribute \u2018location\" corresponds to the latitude and\nlongitude. Some queries that can be handled with our system on\nthis data include:\n1. Find all EPA-regulated facilities that have arsenic and\nparticipate in the Air Emissions program, and:\n(a) Lie in Georgia to Illinois, alphabetically.\n(b) Lie within Arkansas or 30 miles within its border.\n(c) Lie within 30 miles of the border of Arkansas (i.e.,\nboth sides of the border).\n2. For each EPA-regulated facility that has arsenic, find\nall EPA-regulated facilities that have chlorine and:\n(a) That are closer to it than to any other\nEPAregulated facility that has arsenic.\n(b) That participate in the Air Emissions program\nand are closer to it than to any other\nEPAregulated facility which has arsenic. In order to\navoid reporting a particular facility more than\nonce, we use our \u2018group by EPA-ID\" mechanism.\nFigure 3 illustrates the output of an example query that\nfinds all arsenic sites within a given distance of the border of\nArkansas. The sites are obtained in an incremental manner\nwith respect to a given point. This ordering is shown by\nusing different color shades.\nWith this example data, it is possible to work with the\nSAND Internet Browser online as an applet (connecting to\na remote server) or after localizing the data and then\nopening it locally. In the first case, for each action taken, the\nclient-server architecture will decide what to ask for from\nthe server. In the latter case, the browser will use the\npeerto-peer APPOINT architecture for first localizing the data.\n6. CONCLUDING REMARKS\nAn overview of our efforts in providing remote access to\nlarge spatial data has been given. We have outlined our\napproaches and introduced their individual elements. Our\nclient-server approach improves the system performance by\nusing efficient caching methods when a remote server is\naccessed from thin-clients. APPOINT forms an alternative\napproach that improves performance under an existing\nclientserver system by using idle client resources when individual\nusers want work on a data set for longer periods of time\nusing their client computers.\nFor the future, we envision development of new efficient\nalgorithms that will support large online data transfers within\nour peer-to-peer approach using multiple peers\nsimultaneously. We assume that a peer (client) can become\nunavailable at any anytime and hence provisions need to be in place\nto handle such a situation. To address this, we will augment\nour methods to include efficient dynamic updates. Upon\ncompletion of this step of our work, we also plan to run\ncomprehensive performance studies on our methods.\nAnother issue is how to access data from different sources\nin different formats. In order to access multiple data sources\nin real time, it is desirable to look for a mechanism that\nwould support data exchange by design. The XML\nprotocol [3] has emerged to become virtually a standard for\ndescribing and communicating arbitrary data. GML [4] is\nan XML variant that is becoming increasingly popular for\nexchange of geographical data. We are currently working\non making SAND XML-compatible so that the user can\ninstantly retrieve spatial data provided by various agencies in\nthe GML format via their Web services and then explore,\nquery, or process this data further within the SAND\nframework. This will turn the SAND system into a universal tool\nfor accessing any spatial data set as it will be deployable on\nmost platforms, work efficiently given large amounts of data,\nbe able to tap any GML-enabled data source, and provide\nan easy to use graphical user interface. This will also\nconvert the SAND system from a research-oriented prototype\ninto a product that could be used by end users for\naccessing, viewing, and analyzing their data efficiently and with\nminimum effort.\n7. REFERENCES\n[1] Fedstats: The gateway to statistics from over 100 U.S.\nfederal agencies. http://www.fedstats.gov/, 2001.\n[2] Arcinfo: Scalable system of software for geographic\ndata creation, management, integration, analysis, and\ndissemination. http://www.esri.com/software/\narcgis/arcinfo/index.html, 2002.\n[3] Extensible markup language (xml).\nhttp://www.w3.org/XML/, 2002.\n[4] Geography markup language (gml) 2.0.\nhttp://opengis.net/gml/01-029/GML2.html, 2002.\n[5] Mapquest: Consumer-focused interactive mapping site\non the web. http://www.mapquest.com, 2002.\n[6] Mapsonus: Suite of online geographic services.\nhttp://www.mapsonus.com, 2002.\n[7] R. Anderson. The Eternity Service. In Proceedings of\nthe PRAGOCRYPT\"96, pages 242-252, Prague, Czech\nRepublic, September 1996.\n[8] L. Breslau, P. Cao, L. Fan, G. Phillips, and\nS. Shenker. Web caching and Zipf-like distributions:\n9\nFigure 3: Sample output from the SAND Internet Browser - Large dark dots indicate the result of a query\nthat looks for all arsenic sites within a given distance from Arkansas. Different color shades are used to\nindicate ranking order by the distance from a given point.\nEvidence and implications. In Proceedings of the IEEE\nInfocom\"99, pages 126-134, New York, NY, March\n1999.\n[9] E. Chang, C. Yap, and T. Yen. Realtime visualization\nof large images over a thinwire. In R. Yagel and\nH. Hagen, editors, Proceedings IEEE Visualization\"97\n(Late Breaking Hot Topics), pages 45-48, Phoenix,\nAZ, October 1997.\n[10] F. Dabek, M. F. Kaashoek, D. Karger, R. Morris, and\nI. Stoica. Wide-area cooperative storage with CFS. In\nProceedings of the ACM SOSP\"01, pages 202-215,\nBanff, AL, October 2001.\n[11] A. Dingle and T. Partl. Web cache coherence.\nComputer Networks and ISDN Systems,\n28(7-11):907-920, May 1996.\n[12] C. Esperan\u00b8ca and H. Samet. Experience with\nSAND/Tcl: a scripting tool for spatial databases.\nJournal of Visual Languages and Computing,\n13(2):229-255, April 2002.\n[13] S. Iyer, A. Rowstron, and P. Druschel. Squirrel: A\ndecentralized peer-to-peer Web cache. Rice\nUniversity/Microsoft Research, submitted for\npublication, 2002.\n[14] D. Karger, A. Sherman, A. Berkheimer, B. Bogstad,\nR. Dhanidina, K. Iwamoto, B. Kim, L. Matkins, and\nY. Yerushalmi. Web caching with consistent hashing.\nComputer Networks, 31(11-16):1203-1213, May 1999.\n[15] J. Kubiatowicz, D. Bindel, Y. Chen, S. Czerwinski,\nP. Eaton, D. Geels, R. Gummadi, S. Rhea,\nH. Weatherspoon, W. Weimer, C. Wells, and B. Zhao.\nOceanStore: An architecture for global-scale persistent\nstore. In Proceedings of the ACM ASPLOS\"00, pages\n190-201, Cambridge, MA, November 2000.\n[16] M. Potmesil. Maps alive: viewing geospatial\ninformation on the WWW. Computer Networks and\nISDN Systems, 29(8-13):1327-1342, September 1997.\nAlso Hyper Proceedings of the 6th International World\nWide Web Conference, Santa Clara, CA, April 1997.\n[17] M. Rabinovich, J. Chase, and S. Gadde. Not all hits\nare created equal: Cooperative proxy caching over a\nwide-area network. Computer Networks and ISDN\nSystems, 30(22-23):2253-2259, November 1998.\n[18] A. Rowstron and P. Druschel. Storage management\nand caching in PAST, a large-scale, persistent\npeer-to-peer storage utility. In Proceedings of the ACM\nSOSP\"01, pages 160-173, Banff, AL, October 2001.\n[19] H. Samet. Applications of Spatial Data Structures:\nComputer Graphics, Image Processing, and GIS.\nAddison-Wesley, Reading, MA, 1990.\n[20] H. Samet. The Design and Analysis of Spatial Data\nStructures. Addison-Wesley, Reading, MA, 1990.\n[21] SETI@Home. http://setiathome.ssl.berkeley.edu/,\n2001.\n[22] L. J. Williams. Pyramidal parametrics. Computer\nGraphics, 17(3):1-11, July 1983. Also Proceedings of\nthe SIGGRAPH\"83 Conference, Detroit, July 1983.\n10", "keywords": "large spatial datum;sand;datum visualization;remote access;internet;datum management;web browser;gi;dynamic network infrastructure;client/server;spatial query evaluation;client-server architecture;peer-to-peer;centralized peer-to-peer approach;internet-enabled database management system;network latency"}
{"name": "train_C-55", "title": "Context Awareness for Group Interaction Support", "abstract": "In this paper, we present an implemented system for supporting group interaction in mobile distributed computing environments. First, an introduction to context computing and a motivation for using contextual information to facilitate group interaction is given. We then present the architecture of our system, which consists of two parts: a subsystem for location sensing that acquires information about the location of users as well as spatial proximities between them, and one for the actual context-aware application, which provides services for group interaction.", "fulltext": "1. INTRODUCTION\nToday\"s computing environments are characterized by an\nincreasing number of powerful, wirelessly connected mobile\ndevices. Users can move throughout an environment while\ncarrying their computers with them and having remote access to\ninformation and services, anytime and anywhere. New situations\nappear, where the user\"s context - for example his current\nlocation or nearby people - is more dynamic; computation does\nnot occur at a single location and in a single context any longer,\nbut comprises a multitude of situations and locations. This\ndevelopment leads to a new class of applications, which are\naware of the context in which they run in and thus bringing virtual\nand real worlds together.\nMotivated by this and the fact, that only a few studies have been\ndone for supporting group communication in such computing\nenvironments [12], we have developed a system, which we refer\nto as Group Interaction Support System (GISS). It supports group\ninteraction in mobile distributed computing environments in a\nway that group members need not to at the same place any longer\nin order to interact with each other or just to be aware of the\nothers situation.\nIn the following subchapters, we will give a short overview on\ncontext aware computing and motivate its benefits for supporting\ngroup interaction. A software framework for developing\ncontextsensitive applications is presented, which serves as middleware\nfor GISS. Chapter 2 presents the architecture of GISS, and chapter\n3 and 4 discuss the location sensing and group interaction\nconcepts of GISS in more detail. Chapter 5 gives a final summary\nof our work.\n1.1 What is Context Computing?\nAccording to Merriam-Webster\"s Online Dictionary1\n, context is\ndefined as the interrelated conditions in which something exists\nor occurs. Because this definition is very general, many\napproaches have been made to define the notion of context with\nrespect to computing environments.\nMost definitions of context are done by enumerating examples or\nby choosing synonyms for context. The term context-aware has\nbeen introduced first in [10] where context is referred to as\nlocation, identities of nearby people and objects, and changes to\nthose objects. In [2], context is also defined by an enumeration of\nexamples, namely location, identities of the people around the\nuser, the time of the day, season, temperature etc. [9] defines\ncontext as the user\"s location, environment, identity and time.\nHere we conform to a widely accepted and more formal\ndefinition, which defines context as any information than can be\nused to characterize the situation of an entity. An entity is a\nperson, place, or object that is considered relevant to the\ninteraction between a user and an application, including the user\nand applications themselves. [4]\n[4] identifies four primary types of context information\n(sometimes referred to as context dimensions), that are - with\nrespect to characterizing the situation of an entity - more\nimportant than others. These are location, identity, time and\nactivity, which can also be used to derive other sources of\ncontextual information (secondary context types). For example, if\nwe know a person\"s identity, we can easily derive related\ninformation about this person from several data sources (e.g. day\nof birth or e-mail address).\nAccording to this definition, [4] defines a system to be\ncontextaware if it uses context to provide relevant information and/or\nservices to the user, where relevancy depends on the user\"s task.\n[4] also gives a classification of features for context-aware\napplications, which comprises presentation of information and\nservices to a user, automatic execution of a service and tagging of\ncontext to information for later retrieval.\nFigure 1. Layers of a context-aware system\nContext computing is based on two major issues, namely\nidentifying relevant context (identity, location, time, activity) and\nusing obtained context (automatic execution, presentation,\ntagging). In order to do this, there are a few layers between (see\nFigure 1). First, the obtained low-level context information has to\nbe transformed, aggregated and interpreted (context\ntransformation) and represented in an abstract context world\nmodel (context representation), either centralized or\ndecentralized. Finally, the stored context information is used to\ntrigger certain context events (context triggering). [7]\n1.2 Group Interaction in Context\nAfter these abstract and formal definitions about what context and\ncontext computing is, we will now focus on the main goal of this\nwork, namely how the interaction of mobile group members can\nbe supported by using context information.\nIn [6] we have identified organizational systems to be crucial for\nsupporting mobile groups (see Figure 2). First, there has to be an\nInformation and Knowledge Management System, which is\ncapable of supporting a team with its information processing- and\nknowledge gathering needs. The next part is the Awareness\nSystem, which is dedicated to the perceptualisation of the effects\nof team activity. It does this by communicating work context,\nagenda and workspace information to the users. The Interaction\nSystems provide support for the communication among team\nmembers, either synchronous or asynchronous, and for the shared\naccess to artefacts, such as documents. Mobility Systems deploy\nmechanisms to enable any-place access to team memory as well\nas the capturing and delivery of awareness information from and\nto any places. Finally yet importantly, the organisational\ninnovation system integrates aspects of the team itself, like roles,\nleadership and shared facilities.\nWith respect to these five aspects of team support, we focus on\ninteraction and partly cover mobility- and awareness-support.\nGroup interaction includes all means that enable group members\nto communicate freely with all the other members. At this point,\nthe question how context information can be used for supporting\ngroup interaction comes up. We believe that information about\nthe current situation of a person provides a surplus value to\nexisting group interaction systems. Context information facilitates\ngroup interaction by allowing each member to be aware of the\navailability status or the current location of each other group\nmember, which again makes it possible to form groups\ndynamically, to place virtual post-its in the real world or to\ndetermine which people are around.\nFigure 2. Support for Mobile Groups [6]\nMost of today\"s context-aware applications use location and time\nonly, and location is referred to as a crucial type of context\ninformation [3]. We also see the importance of location\ninformation in mobile and ubiquitous environments, wherefore a\nmain focus of our work is on the utilization of location\ninformation and information about users in spatial proximity.\nNevertheless, we believe that location, as the only used type of\ncontext information, is not sufficient to support group interaction,\nwherefore we also take advantage of the other three primary\ntypes, namely identity, time and activity. This provides a\ncomprehensive description of a user\"s current situation and thus\nenabling numerous means for supporting group interaction, which\nare described in detail in chapter 4.4.\nWhen we look at the types of context information stated above,\nwe can see that all of them are single user-centred, taking into\naccount only the context of the user itself. We believe, that for the\nsupport of group interaction, the status of the group itself has also\nbe taken into account. Therefore, we have added a fifth\ncontextdimension group-context, which comprises more than the sum of\nthe individual member\"s contexts. Group context includes any\ninformation about the situation of a whole group, for example\nhow many members a group currently has or if a certain group\nmeets right now.\n1.3 Context Middleware\nThe Group Interaction Support System (GISS) uses the\nsoftwareframework introduced in [1], which serves as a middleware for\ndeveloping context-sensitive applications. This so-called Context\nFramework is based on a distributed communication architecture\nand it supports different kinds of transport protocols and message\ncoding mechanisms.\n89\nA main feature of the framework is the abstraction of context\ninformation retrieval via various sensors and its delivery to a level\nwhere no difference appears, for the application designer,\nbetween these different kinds of context retrieval mechanisms; the\ninformation retrieval is hidden from the application developer.\nThis is achieved by so-called entities, which describe\nobjectse.g. a human user - that are important for a certain context\nscenario.\nEntities express their functionality by the use of so-called\nattributes, which can be loaded into the entity. These attributes\nare complex pieces of software, which are implemented as Java\nclasses. Typical attributes are encapsulations of sensors, but they\ncan also be used to implement context services, for example to\nnotify other entities about location changes of users.\nEach entity can contain a collection of such attributes, where an\nentity itself is an attribute. The initial set of attributes an entity\ncontains can change dynamically at runtime, if an entity loads or\nunloads attributes from the local storage or over the network. In\norder to load and deploy new attributes, an entity has to reference\na class loader and a transport and lookup layer, which manages\nthe lookup mechanism for discovering other entities and the\ntransport. XML configuration files specify which initial set of\nentities should be loaded and which attributes these entities own.\nThe communication between entities and attributes is based on\ncontext events. Each attribute is able to trigger events, which are\naddressed to other attributes and entities respectively,\nindependently on which physical computer they are running.\nAmong other things, and event contains the name of the event and\na list of parameters delivering information about the event itself.\nRelated with this event-based architecture is the use of ECA\n(Event-Condition-Action)-rules for defining the behaviour of the\ncontext system. Therefore, every entity has a rule-interpreter,\nwhich catches triggered events, checks conditions associated with\nthem and causes certain actions. These rules are referenced by the\nentity\"s XML configuration. A rule itself is even able to trigger\nthe insertion of new rules or the unloading of existing rules at\nruntime in order to change the behaviour of the context system\ndynamically.\nTo sum up, the context framework provides a flexible, distributed\narchitecture for hiding low-level sensor data from high-level\napplications and it hides external communication details from the\napplication developer. Furthermore, it is able to adapt its\nbehaviour dynamically by loading attributes, entities or\nECArules at runtime.\n2. ARCHITECTURE OVERVIEW\nAs GISS uses the Context Framework described in chapter 1.3 as\nmiddleware, every user is represented by an entity, as well as the\ncentral server, which is responsible for context transformation,\ncontext representation and context triggering (cf. Figure 1).\nA main part of our work is about the automated acquisition of\nposition information and its sensor-independent provision at\napplication level. We do not only sense the current location of\nusers, but also determine spatial proximities between them.\nDeveloping the architecture, we focused on keeping the client as\nsimple as possible and reducing the communication between\nclient and server to a minimum.\nEach client may have various location and/or proximity sensors\nattached, which are encapsulated by respective Context\nFramework-attributes (Sensor Encapsulation). These attributes\nare responsible for integrating native sensor-implementations into\nthe Context Framework and sending sensor-dependent position\ninformation to the server. We consider it very important to\nsupport different types of sensors even at the same time, in order\nto improve location accuracy on the one hand, while providing a\npervasive location-sensing environment with seamless transition\nbetween different location sensing techniques on the other hand.\nAll location- and proximity-sensors supported are represented by\nserver-side context-attributes, which correspond to the client-side\nsensor encapsulation-attributes and abstract the sensor-dependent\nposition information received from all users via the wireless\nnetwork (sensor abstraction). This requires a context repository,\nwhere the mapping of diverse physical positions to standardized\nlocations is stored.\nThe standardized location- and proximity-information of each\nuser is then passed to the so-called Sensor Fusion-attributes,\none for symbolic locations and a second one for spatial\nproximities. Their job is to merge location- and\nproximityinformation of clients, respectively, which is described in detail in\nChapter 3.3. Every time the symbolic location of a user or the\nspatial proximity between two users changes, the Sensor\nFusion-attributes notify the GISS Core-attribute, which\ncontrols the application.\nBecause of the abstraction of sensor-dependent position\ninformation, the system can easily be extended by additional\nsensors, just by implementing the (typically two) attributes for\nencapsulating sensors (some sensors may not need a client-side\npart), abstracting physical positions and observing the interface to\nGISS Core.\nFigure 3. Architecture of the Group Interaction Support\nSystem (GISS)\nThe GISS Core-attribute is the central coordinator of the\napplication as it shows to the user. It not only serves as an\ninterface to the location-sensing subsystem, but also collects\nfurther context information in other dimensions (time, identity or\nactivity).\n90\nEvery time a change in the context of one or more users is\ndetected, GISS Core evaluates the effect of these changes on\nthe user, on the groups he belongs to and on the other members of\nthese groups. Whenever necessary, events are thrown to the\naffected clients to trigger context-aware activities, like changing\nthe presentation of awareness information or the execution of\nservices.\nThe client-side part of the application is kept as simple as\npossible. Furthermore, modular design was not only an issue on\nthe sensor side but also when designing the user interface\narchitecture. Thus, the complete user interface can be easily\nexchanged, if all of the defined events are taken into account and\nunderstood by the new interface-attribute.\nThe currently implemented user interface is split up in two parts,\nwhich are also represented by two attributes. The central attribute\non client-side is the so-called Instant Messenger Encapsulation,\nwhich on the one hand interacts with the server through events\nand on the other hand serves as a proxy for the external\napplication the user interface is built on.\nAs external application, we use an existing open source instant\nmessenger - the ICQ2\n-compliant Simple Instant Messenger\n(SIM)3\n. We have chosen and instant messenger as front-end\nbecause it provides a well-known interface for most users and\nfacilitates a seamless integration of group interaction support, thus\nincreasing acceptance and ease of use. As the basic functionality\nof the instant messenger - to serve as a client in an instant\nmessenger network - remains fully functional, our application is\nable to use the features already provided by the messenger. For\nexample, the contexts activity and identity are derived from the\nmessenger network as it is described later.\nThe Instant Messenger Encapsulation is also responsible for\nsupporting group communication. Through the interface of the\nmessenger, it provides means of synchronous and asynchronous\ncommunication as well as a context-aware reminder system and\ntools for managing groups and the own availability status.\nThe second part of the user interface is a visualisation of the\nuser\"s locations, which is implemented in the attribute Viewer.\nThe current implementation provides a two-dimensional map of\nthe campus, but it can easily be replaced by other visualisations, a\nthree-dimensional VRML-model for example. Furthermore, this\nvisualisation is used to show the artefacts for asynchronous\ncommunication. Based on a floor plan-view of the geographical\narea the user currently resides in, it gives a quick overview of\nwhich people are nearby, their state and provides means to\ninteract with them.\nIn the following chapters 3 and 4, we describe the location\nsensing-backend and the application front-end for supporting\ngroup interaction in more detail.\n3. LOCATION SENSING\nIn the following chapter, we will introduce a location model,\nwhich is used for representing locations; afterwards, we will\ndescribe the integration of location- and proximity-sensors in\n2\nhttp://www.icq.com/\n3\nhttp://sim-icq.sourceforge.net\nmore detail. Finally, we will have a closer look on the fusion of\nlocation- and proximity-information, acquired by various sensors.\n3.1 Location Model\nA location model (i.e. a context representation for the\ncontextinformation location) is needed to represent the locations of users,\nin order to be able to facilitate location-related queries like given\na location, return a list of all the objects there or given an\nobject, return its current location. In general, there are two\napproaches [3,5]: symbolic models, which represent location as\nabstract symbols, and a geometric model, which represent\nlocation as coordinates.\nWe have chosen a symbolic location model, which refers to\nlocations as abstract symbols like Room P111 or Physics\nBuilding, because we do not require geometric location data.\nInstead, abstract symbols are more convenient for human\ninteraction at application level. Furthermore, we use a symbolic\nlocation containment hierarchy similar to the one introduced in\n[11], which consists of top-level regions, which contain buildings,\nwhich contain floors, and the floors again contain rooms. We also\ndistinguish four types, namely region (e.g. a whole campus),\nsection (e.g. a building or an outdoor section), level (e.g. a certain\nfloor in a building) and area (e.g. a certain room). We introduce a\nfifth type of location, which we refer to as semantic. These\nsocalled semantic locations can appear at any level in the hierarchy\nand they can be nested, but they do not necessarily have a\ngeographic representation. Examples for such semantic locations\nare tagged objects within a room (e.g. a desk and a printer on this\ndesk) or the name of a department, which contains certain rooms.\nFigure 4. Symbolic Location Containment Hierarchy\nThe hierarchy of symbolic locations as well as the type of each\nposition is stored in the context repository.\n3.2 Sensors\nOur architecture supports two different kinds of sensors: location\nsensors, which acquire location information, and proximity\nsensors, which detect spatial proximities between users.\nAs described above, each sensor has a server- and in most cases a\ncorresponding client-side-implementation, too. While the\nclientattributes (Sensor Abstraction) are responsible for acquiring\nlow-level sensor-data and transmitting it to the server, the\ncorresponding Sensor Encapsulation-attributes transform them\ninto a uniform and sensor-independent format, namely symbolic\nlocations and IDs of users in spatial proximity, respectively.\n91\nAfterwards, the respective attribute Sensor Fusion is being\ntriggered with this sensor-independent information of a certain\nuser, detected by a particular sensor. Such notifications are\nperformed every time the sensor acquired new information.\nAccordingly, Sensor Abstraction-attributes are responsible to\ndetect when a certain sensor is no longer available on the client\nside (e.g. if it has been unplugged by the user) or when position\nrespectively proximity could not be determined any longer (e.g.\nRFID reader cannot detect tags) and notify the corresponding\nsensor fusion about this.\n3.2.1 Location Sensors\nIn order to sense physical positions, the Sensor\nEncapsulationattributes asynchronously transmit sensor-dependent position\ninformation to the server. The corresponding location Sensor\nAbstraction-attributes collect these physical positions delivered\nby the sensors of all users, and perform a repository-lookup in\norder to get the associated symbolic location. This requires certain\ntables for each sensor, which map physical positions to symbolic\nlocations. One physical position may have multiple symbolic\nlocations at different accuracy-levels in the location hierarchy\nassigned to, for example if a sensor covers several rooms. If such\na mapping could be found, an event is thrown in order to notify\nthe attribute Location Sensor Fusion about the symbolic\nlocations a certain sensor of a particular user determined.\nWe have prototypically implemented three kinds of location\nsensors, which are based on WLAN (IEEE 802.11), Bluetooth and\nRFID (Radio Frequency Identification). We have chosen these\nthree completely different sensors because of their differences\nconcerning accuracy, coverage and administrative effort, in order\nto evaluate the flexibility of our system (see Table 1).\nThe most accurate one is an RFID sensor, which is based on an\nactive RFID-reader. As soon as the reader is plugged into the\nclient, it scans for active RFID tags in range and transmits their\nserial numbers to the server, where they are mapped to symbolic\nlocations. We also take into account RSSI (Radio Signal Strength\nInformation), which provides position accuracy of few\ncentimetres and thus enables us to determine which RFID-tag is\nnearest. Due to this high accuracy, RFID is used for locating users\nwithin rooms. The administration is quite simple; once a new\nRFID tag is placed, its serial number simply has to be assigned to\na single symbolic location. A drawback is the poor availability,\nwhich can be traced back to the fact that RFID readers are still\nvery expensive.\nThe second one is an 802.11 WLAN sensor. Therefore, we\nintegrated a purely software-based, commercial WLAN\npositioning system for tracking clients on the university\ncampuswide WLAN infrastructure. The reached position accuracy is in\nthe range of few meters and thus is suitable for location sensing at\nthe granularity of rooms. A big disadvantage is that a map of the\nwhole area has to be calibrated with measuring points at a\ndistance of 5 meters each. Because most mobile computers are\nequipped with WLAN technology and the positioning-system is a\nsoftware-only solution, nearly everyone is able to use this kind of\nsensor.\nFinally, we have implemented a Bluetooth sensor, which detects\nBluetooth tags (i.e. Bluetooth-modules with known position) in\nrange and transmits them to the server that maps to symbolic\nlocations. Because of the fact that we do not use signal\nstrengthinformation in the current implementation, the accuracy is above\n10 meters and therefore a single Bluetooth MAC address is\nassociated with several symbolic locations, according to the\nphysical locations such a Bluetooth module covers. This leads to\nthe disadvantage that the range of each Bluetooth-tag has to be\ndetermined and mapped to symbolic locations within this range.\nTable 1. Comparison of implemented sensors\nSensor Accuracy Coverage Administration\nRFID < 10 cm poor easy\nWLAN 1-4 m very well\nvery\ntimeconsuming\nBluetooth ~ 10 m well time-consuming\n3.2.2 Proximity Sensors\nAny sensor that is able to detect whether two users are in spatial\nproximity is referred to as proximity sensor. Similar to the\nlocation sensors, the Proximity Sensor Abstraction-attributes\ncollect physical proximity information of all users and transform\nthem to mappings of user-IDs.\nWe have implemented two types of proximity-sensors, which are\nbased on Bluetooth on the one hand and on fused symbolic\nlocations (see chapter 3.3.1) on the other hand.\nThe Bluetooth-implementation goes along with the\nimplementation of the Bluetooth-based location sensor. The\nalready determined Bluetooth MAC addresses in range of a\ncertain client are being compared with those of all other clients,\nand each time the attribute Bluetooth Sensor Abstraction\ndetects congruence, it notifies the proximity sensor fusion about\nthis.\nThe second sensor is based on symbolic locations processed by\nLocation Sensor Fusion, wherefore it does not need a client-side\nimplementation. Each time the fused symbolic location of a\ncertain user changes, it checks whether he is at the same symbolic\nlocation like another user and again notifies the proximity sensor\nfusion about the proximity between these two users. The range\ncan be restricted to any level of the location containment\nhierarchy, for example to room granularity.\nA currently unresolved issue is the incomparable granularity of\ndifferent proximity sensors. For example, the symbolic locations\nat same level in the location hierarchy mostly do not cover the\nsame geographic area.\n3.3 Sensor Fusion\nCore of the location sensing subsystem is the sensor fusion. It\nmerges data of various sensors, while coping with differences\nconcerning accuracy, coverage and sample-rate. According to the\ntwo kinds of sensors described in chapter 3.2, we distinguish\nbetween fusion of location sensors on the one hand, and fusion of\nproximity sensors on the other hand.\nThe fusion of symbolic locations as well as the fusion of spatial\nproximities operates on standardized information (cf. Figure 3).\nThis has the advantage, that additional position- and\nproximitysensors can be added easily or the fusion algorithms can be\nreplaced by ones that are more sophisticated.\n92\nFusion is performed for each user separately and takes into\naccount the measurements at a single point in time only (i.e. no\nhistory information is used for determining the current location of\na certain user). The algorithm collects all events thrown by the\nSensor Abstraction-attributes, performs fusion and triggers the\nGISS Core-attribute if the symbolic location of a certain user or\nthe spatial proximity between users changed.\nAn important feature is the persistent storage of location- and\nproximity-history in a database in order to allow future retrieval.\nThis enables applications to visualize the movement of users for\nexample.\n3.3.1 Location Sensor Fusion\nGoal of the fusion of location information is to improve precision\nand accuracy by merging the set of symbolic locations supplied\nby various location sensors, in order to reduce the number of\nthese locations to a minimum, ideally to a single symbolic\nlocation per user. This is quite difficult, because different sensors\nmay differ in accuracy and sample rate as well.\nThe Location Sensor Fusion-attribute is triggered by events,\nwhich are thrown by the Location Sensor\nAbstractionattributes. These events contain information about the identity of\nthe user concerned, his current location and the sensor by which\nthe location has been determined.\nIf the attribute Location Sensor Fusion receives such an event,\nit checks if the amount of symbolic locations of the user\nconcerned has changed (compared with the last event). If this is\nthe case, it notifies the GISS Core-attribute about all symbolic\nlocations this user is currently associated with.\nHowever, this information is not very useful on its own if a\ncertain user is associated with several locations. As described in\nchapter 3.2.1, a single location sensor may deliver multiple\nsymbolic locations. Moreover, a certain user may have several\nlocation sensors, which supply symbolic locations differing in\naccuracy (i.e. different levels in the location containment\nhierarchy). To cope with this challenge, we implemented a fusion\nalgorithm in order to reduce the number of symbolic locations to a\nminimum (ideally to a single location).\nIn a first step, each symbolic location is associated with its\nnumber of occurrences. A symbolic location may occur several\ntimes if it is referred to by more than one sensor or if a single\nsensor detects multiple tags, which again refer to several\nlocations. Furthermore, this number is added to the previously\ncalculated number of occurrences of each symbolic location,\nwhich is a child-location of the considered one in the location\ncontainment hierarchy. For example, if - in Figure 4 - room2\noccurs two times and desk occurs a single time, the value 2 of\nroom2 is added to the value 1 of desk, whereby desk finally\ngets the value 3. In a final step, only those symbolic locations are\nleft which are assigned with the highest number of occurrences.\nA further reduction can be achieved by assigning priorities to\nsensors (based on accuracy and confidence) and cumulating these\npriorities for each symbolic location instead of just counting the\nnumber of occurrences.\nIf the remaining fused locations have changed (i.e. if they differ\nfrom the fused locations the considered user is currently\nassociated with), they are provided with the current timestamp,\nwritten to the database and the GISS-attribute is notified about\nwhere the user is probably located.\nFinally, the most accurate, common location in the location\nhierarchy is calculated (i.e. the least upper bound of these\nsymbolic locations) in order to get a single symbolic location. If it\nchanges, the GISS Core-attribute is triggered again.\n3.3.2 Proximity Sensor Fusion\nProximity sensor fusion is much simpler than the fusion of\nsymbolic locations. The corresponding proximity sensor\nfusionattribute is triggered by events, which are thrown by the\nProximity Sensor Abstraction-attributes. These special events\ncontain information about the identity of the two users concerned,\nif they are currently in spatial proximity or if proximity no longer\npersists, and by which proximity-sensor this has been detected.\nIf the sensor fusion-attribute is notified by a certain Proximity\nSensor Abstraction-attribute about an existing spatial proximity,\nit first checks if these two users are already known to be in\nproximity (detected either by another user or by another\nproximity-sensor of the user, which caused the event). If not, this\nchange in proximity is written to the context repository with\ncurrent timestamp. Similarly, if the attribute Proximity Fusion\nis notified about an ended proximity, it checks if the users are still\nknown to be in proximity, and writes this change to the repository\nif not.\nFinally, if spatial proximity between the two users actually\nchanged, an event is thrown to notify the GISS Core-attribute\nabout this.\n4. CONTEXTSENSITIVE INTERACTION\n4.1 Overview\nIn most of today\"s systems supporting interaction in groups, the\nprovided means lack any awareness of the user\"s current context,\nthus being unable to adapt to his needs.\nIn our approach, we use context information to enhance\ninteraction and provide further services, which offer new\npossibilities to the user. Furthermore, we believe that interaction\nin groups also has to take into account the current context of the\ngroup itself and not only the context of individual group\nmembers. For this reason, we also retrieve information about the\ngroup\"s current context, derived from the contexts of the group\nmembers together with some sort of meta-information (see\nchapter 4.3).\nThe sources of context used for our application correspond with\nthe four primary context types given in chapter 1.1 - identity (I),\nlocation (L), time (T) and activity (A). As stated before, we also\ntake into account the context of the group the user is interaction\nwith, so that we could add a fifth type of context\ninformationgroup awareness (G) - to the classification. Using this context\ninformation, we can trigger context-aware activities in all of the\nthree categories described in chapter 1.1 - presentation of\ninformation (P), automatic execution of services (A) and tagging\nof context to information for later retrieval (T).\nTable 2 gives an overview of activities we have already\nimplemented; they are described comprehensively in chapter 4.4.\nThe table also shows which types of context information are used\nfor each activity and the category the activity could be classified\nin.\n93\nTable 2. Classification of implemented context-aware\nactivities\nService L T I A G P A T\nLocation Visualisation X X X\nGroup Building Support X X X X\nSupport for Synchronous\nCommunication\nX X X X\nSupport for Asynchronous\nCommunication\nX X X X X X X\nAvailability Management X X X\nTask Management Support X X X X\nMeeting Support X X X X X X\nReasons for implementing these very features are to take\nadvantage of all four types of context information in order to\nsupport group interaction by utilizing a comprehensive knowledge\nabout the situation a single user or a whole group is in.\nA critical issue for the user acceptance of such a system is the\nusability of its interface. We have evaluated several ways of\npresenting context-aware means of interaction to the user, until\nwe came to the solution we use right now. Although we think that\nthe user interface that has been implemented now offers the best\ntrade-off between seamless integration of features and ease of use,\nit would be no problem to extend the architecture with other user\ninterfaces, even on different platforms.\nThe chosen solution is based on an existing instant messenger,\nwhich offers several possibilities to integrate our system (see\nchapter 4.2). The biggest advantage of this approach is that the\nuser is confronted with a graphical user interface he is already\nused to in most cases. Furthermore, our system uses an instant\nmessenger account as an identifier, so that the user does not have\nto register a further account anywhere else (for example, the user\ncan use his already existing ICQ2\n-account).\n4.2 Instant Messenger Integration\nOur system is based upon an existing instant messenger, the\nsocalled Simple Instant Messenger (SIM)3\n. The implementation of\nthis messenger is carried out as a project at Sourceforge4\n.\nSIM supports multiple messenger protocols such as AIM5\n, ICQ2\nand MSN6\n. It also supports connections to multiple accounts at\nthe same time. Furthermore, full support for SMS-notification\n(where provided from the used protocol) is given.\nSIM is based on a plug-in concept. All protocols as well as parts\nof the user-interface are implemented as plug-ins. Its architecture\nis also used to extend the application\"s abilities to communicate\nwith external applications. For this purpose, a remote control\nplug-in is provided, by which SIM can be controlled from\nexternal applications via socket connection. This remote control\ninterface is extensively used by GISS for retrieving the contact\nlist, setting the user\"s availability-state or sending messages. The\n4\nhttp://sourceforge.net/\n5\nhttp://www.aim.com/\n6\nhttp://messenger.msn.com/\nfunctionality of the plug-in was extended in several ways, for\nexample to accept messages for an account (as if they would have\nbeen sent via the messenger network).\nThe messenger, more exactly the contact list (i.e. a list of profiles\nof all people registered with the instant messenger, which is\nvisualized by listing their names as it can be seen in Figure 5), is\nalso used to display locations of other members of the groups a\nuser belongs to. This provides location awareness without taking\ntoo much space or requesting the user\"s full attention. A more\ncomprehensive description of these features is given in chapter\n4.4.\n4.3 Sources of Context Information\nWhile the location-context of a user is obtained from our location\nsensing subsystem described in chapter 3, we consider further\ntypes of context than location relevant for the support of group\ninteraction, too.\nLocal time as a very important context dimension can be easily\nretrieved from the real time clock of the user\"s system. Besides\nlocation and time, we also use context information of user\"s\nactivity and identity, where we exploit the functionality provided\nby the underlying instant messenger system. Identity (or more\nexactly, the mapping of IDs to names as well as additional\ninformation from the user\"s profile) can be distilled out of the\ncontents of the user\"s contact list.\nInformation about the activity or a certain user is only available in\na very restricted area, namely the activity at the computer itself.\nOther activities like making a phone call or something similar,\ncannot be recognized with the current implementation of the\nactivity sensor. The only context-information used is the instant\nmessenger\"s availability state, thus only providing a very coarse\nclassification of the user\"s activity (online, offline, away, busy\netc.). Although this may not seem to be very much information, it\nis surely relevant and can be used to improve or even enable\nseveral services.\nHaving collected the context information from all available users,\nit is now possible to distil some information about the context of a\ncertain group. Information about the context of a group includes\nhow many members the group currently has, if the group meets\nright now, which members are participating at a meeting, how\nmany members have read which of the available posts from other\nteam members and so on.\nTherefore, some additional information like a list of members for\neach group is needed. These lists can be assembled manually (by\nusers joining and leaving groups) or retrieved automatically. The\ncontext of a group is secondary context and is aggregated from\nthe available contexts of the group members. Every time the\ncontext of a single group member changes, the context of the\nwhole group is changing and has to be recalculated.\nWith knowledge about a user\"s context and the context of the\ngroups he belongs to, we can provide several context-aware\nservices to the user, which enhance his interaction abilities. A\nbrief description of these services is given in chapter 4.4.\n94\n4.4 Group Interaction Support\n4.4.1 Visualisation of Location Information\nAn important feature is the visualisation of location information,\nthus allowing users to be aware of the location of other users and\nmembers of groups he joined, respectively.\nAs already described in chapter 2, we use two different forms of\nvisualisation. The maybe more important one is to display\nlocation information in the contact list of the instant messenger,\nright beside the name, thus being always visible while not\ndrawing the user\"s attention on it (compared with a\ntwodimensional view for example, which requires a own window for\ndisplaying a map of the environment).\nDue to the restricted space in the contact list, it has been\nnecessary to implement some sort of level-of-detail concept. As\nwe use a hierarchical location model, we are able to determine the\nmost accurate common location of two users. In the contact list,\nthe current symbolic location one level below the previously\ncalculated common location is then displayed. If, for example,\nuser A currently resides in room P121 at the first floor of a\nbuilding and user B, which has to be displayed in the contact list\nof user A, is in room P304 at the third floor, the most accurate\ncommon location of these two users is the building they are in.\nFor that reason, the floor (i.e. one level beyond the common\nlocation, namely the building) of user B is displayed in the\ncontact list of user A. If both people reside on the same floor or\neven in the same room, the room would be taken.\nFigure 5 shows a screenshot of the Simple Instant Messenger3\n,\nwhere the current location of those people, whose location is\nknown by GISS, is displayed in brackets right beside their name.\nOn top of the image, the heightened, integrated GISS-toolbar is\nshown, which currently contains the following, implemented\nfunctionality (from left to right): Asynchronous communication\nfor groups (see chapter 4.4.4), context-aware reminders (see\nchapter 4.4.6), two-dimensional visualisation of\nlocationinformation, forming and managing groups (see chapter 4.4.2),\ncontext-aware availability-management (see chapter 4.4.5) and\nfinally a button for terminating GISS.\nFigure 5. GISS integration in Simple Instant Messenger3\nAs displaying just this short form of location may not be enough\nfor the user, because he may want to see the most accurate\nposition available, a fully qualified position is shown if a name\nin the contact-list is clicked (e.g. in the form of\ndesk@room2@department1@1stfloor@building 1@campus).\nThe second possible form of visualisation is a graphical one. We\nhave evaluated a three-dimensional view, which was based on a\nVRML model of the respective area (cf. Figure 6). Due to lacks in\nnavigational and usability issues, we decided to use a\ntwodimensional view of the floor (it is referred to as level in the\nlocation hierarchy, cf. Figure 4). Other levels of granularity like\nsection (e.g. building) and region (e.g. campus) are also provided.\nIn this floor-plan-based view, the current locations are shown in\nthe manner of ICQ2\ncontacts, which are placed at the currently\nsensed location of the respective person. The availability-status of\na user, for example away if he is not on the computer right now,\nor busy if he does not want to be disturbed, is visualized by\ncolour-coding the ICQ2\n-flower left beside the name. Furthermore,\nthe floor-plan-view shows so-called the virtual post-its, which are\nvirtual counterparts of real-life post-its and serve as our means of\nasynchronous communication (more about virtual post-its can be\nfound in chapter 4.4.4).\nFigure 6. 3D-view of the floor (VRML)\nFigure 7 shows the two-dimensional map of a certain floor, where\nseveral users are currently located (visualized by their name and\nthe flower left beside). The location of the client, on which the\nmap is displayed, is visualized by a green circle. Down to the\nright, two virtual post-its can be seen.\nFigure 7. 2D view of the floor\nAnother feature of the 2D-view is the visualisation of\nlocationhistory of users. As we store the complete history of a user\"s\nlocations together with a timestamp, we are able to provide\ninformation about the locations he has been back in time. When\nthe mouse is moved over the name of a certain user in the\n2Dview, footprints of a user, placed at the locations he has been,\nare faded out the stronger, the older the location information is.\n95\n4.4.2 Forming and Managing Groups\nTo support interaction in groups, it is first necessary to form\ngroups. As groups can have different purposes, we distinguish two\ntypes of groups.\nSo-called static groups are groups, which are built up manually\nby people joining and leaving them. Static groups can be further\ndivided into two subtypes. In open static groups, everybody can\njoin and leave anytime, useful for example to form a group of\nlecture attendees of some sort of interest group. Closed static\ngroups have an owner, who decides, which persons are allowed to\njoin, although everybody could leave again at any time. Closed\ngroups enable users for example to create a group of their friends,\nthus being able to communicate with them easily.\nIn contrast to that, we also support the creation of dynamic\ngroups. They are formed among persons, who are at the same\nlocation at the same time. The creation of dynamic groups is only\nperformed at locations, where it makes sense to form groups, for\nexample in lecture halls or meeting rooms, but not on corridors or\noutdoor. It would also be not very meaningful to form a group\nonly of the people residing in the left front sector of a hall;\ninstead, the complete hall should be considered. For these\nreasons, all the defined locations in the hierarchy are tagged,\nwhether they allow the formation of groups or not. Dynamic\ngroups are also not only formed granularity of rooms, but also on\nhigher levels in the hierarchy, for example with the people\ncurrently residing in the area of a department.\nAs the members of dynamic groups constantly change, it is\npossible to create an open static group out of them.\n4.4.3 Synchronous Communication for Groups\nThe most important form of synchronous communication on\ncomputers today is instant messaging; some people even see\ninstant messaging to be the real killer application on the Internet.\nThis has also motivated the decision to build GISS upon an\ninstant messaging system.\nIn today\"s messenger systems, peer-to-peer-communication is\nextensively supported. However, when it comes to\ncommunication in groups, the support is rather poor most of the\ntime. Often, only sending a message to multiple recipients is\nsupported, lacking means to take into account the current state of\nthe recipients. Furthermore, groups can only be formed of\nmembers in one\"s contact list, thus being not able to send\nmessages to a group, where not all of its members are known\n(which may be the case in settings, where the participants of a\nlecture form a group).\nOur approach does not have the mentioned restrictions. We\nintroduce group-entries in the user\"s contact list; enable him or\nhis to send messages to this group easily, without knowing who\nexactly is currently a member of this group. Furthermore, group\nmessages are only delivered to persons, who are currently not\nbusy, thus preventing a disturbance by a message, which is\npossibly unimportant for the user.\nThese features cannot be carried out in the messenger network\nitself, so whenever a message to a group account is sent, we\nintercept it and route it through our system to all the recipients,\nwhich are available at a certain time. Communication via a group\naccount is also stored centrally, enabling people to query missed\nmessages or simply viewing the message history.\n4.4.4 Asynchronous Communication for Groups\nAsynchronous communication in groups is not a new idea. The\ngoal of this approach is not to reinvent the wheel, as email is\nmaybe the most widely used form of asynchronous\ncommunication on computers and is broadly accepted and\nstandardized. In out work, we aim at the combination of\nasynchronous communication with location awareness.\nFor this reason, we introduce the concept of so-called virtual\npostits (cp. [13]), which are messages that are bound to physical\nlocations. These virtual post-its could be either visible for all\nusers that are passing by or they can be restricted to be visible for\ncertain groups of people only. Moreover, a virtual post-it can also\nhave an expiry date after which it is dropped and not displayed\nanymore. Virtual post-its can also be commented by others, thus\nproviding some from of forum-like interaction, where each post-it\nforms a thread.\nVirtual post-its are displayed automatically, whenever a user\n(available) passes by the first time. Afterwards, post-its can be\naccessed via the 2D-viewer, where all visible post-its are shown.\nAll readers of a post-it are logged and displayed when viewing it,\nproviding some sort of awareness about the group members\"\nactivities in the past.\n4.4.5 Context-aware Availability Management\nInstant messengers in general provide some kind of availability\ninformation about a user. Although this information can be only\ndefined in a very coarse granularity, we have decided to use these\nmeans of gathering activity context, because the introduction of\nan additional one would strongly decrease the usability of the\nsystem.\nTo support the user managing his availability, we provide an\ninterface that lets the user define rules to adapt his availability to\nthe current context. These rules follow the form on event (E) if\ncondition (C) then action (A), which is directly supported by the\nECA-rules of the Context Framework described in chapter 1.3.\nThe testing of conditions is periodically triggered by throwing\nevents (whenever the context of a user changes). The condition\nitself is defined by the user, who can demand the change of his\navailability status as the action in the rule. As a condition, the user\ncan define his location, a certain time (also triggering daily, every\nweek or every month) or any logical combination of these criteria.\n4.4.6 Context-Aware Reminders\nReminders [14] are used to give the user the opportunity of\ndefining tasks and being reminded of those, when certain criteria\nare fulfilled. Thus, a reminder can be seen as a post-it to oneself,\nwhich is only visible in certain cases. Reminders can be bound to\na certain place or time, but also to spatial proximity of users or\ngroups. These criteria can be combined with Boolean operators,\nthus providing a powerful means to remind the user of tasks that\nhe wants to carry out when a certain context occurs.\nA reminder will only pop up the first time the actual context\nmeets the defined criterion. On showing up the reminder, the user\nhas the chance to resubmit it to be reminded again, for example\nfive minutes later or the next time a certain user is in spatial\nproximity.\n96\n4.4.7 Context-Aware Recognition and Notification of\nGroup Meetings\nWith the available context information, we try to recognize\nmeetings of a group. The determination of the criteria, when the\nsystem recognizes a group having a meeting, is part of the\nongoing work. In a first approach, we use the location- and\nactivity-context of the group members to determine a meeting.\nWhenever more than 50 % of the members of a group are\navailable at a location, where a meeting is considered to make\nsense (e.g. not on a corridor), a meeting minutes post-it is created\nat this location and all absent group members are notified of the\nmeeting and the location it takes place.\nDuring the meeting, the comment-feature of virtual post-its\nprovides a means to take notes for all of the participants. When\nmembers are joining or leaving the meeting, this is automatically\nadded as a note to the list of comments.\nLike the recognition of the beginning of a meeting, the\nrecognition of its end is still part of ongoing work. If the end of\nthe meeting is recognized, all group members get the complete list\nof comments as a meeting protocol at the end of the meeting.\n5. CONCLUSIONS\nThis paper discussed the potentials of support for group\ninteraction by using context information. First, we introduced the\nnotions of context and context computing and motivated their\nvalue for supporting group interaction.\nAn architecture is presented to support context-aware group\ninteraction in mobile, distributed environments. It is built upon a\nflexible and extensible framework, thus enabling an easy adoption\nto available context sources (e.g. by adding additional sensors) as\nwell as the required form of representation.\nWe have prototypically developed a set of services, which\nenhance group interaction by taking into account the current\ncontext of the users as well as the context of groups itself.\nImportant features are dynamic formation of groups, visualization\nof location on a two-dimensional map as well as unobtrusively\nintegrated in an instant-messenger, asynchronous communication\nby virtual post-its, which are bound to certain locations, and a\ncontext-aware availability-management, which adapts the\navailability-status of a user to his current situation.\nTo provide location information, we have implemented a\nsubsystem for automated acquisition of location- and\nproximityinformation provided by various sensors, which provides a\ntechnology-independent presentation of locations and spatial\nproximities between users and merges this information using\nsensor-independent fusion algorithms. A history of locations as\nwell as of spatial proximities is stored in a database, thus enabling\ncontext history-based services.\n6. REFERENCES\n[1] Beer, W., Christian, V., Ferscha, A., Mehrmann, L.\nModeling Context-aware Behavior by Interpreted ECA\nRules. In Proceedings of the International Conference on\nParallel and Distributed Computing (EUROPAR\"03).\n(Klagenfurt, Austria, August 26-29, 2003). Springer Verlag,\nLNCS 2790, 1064-1073.\n[2] Brown, P.J., Bovey, J.D., Chen X. Context-Aware\nApplications: From the Laboratory to the Marketplace.\nIEEE Personal Communications, 4(5) (1997), 58-64.\n[3] Chen, H., Kotz, D. A Survey of Context-Aware Mobile\nComputing Research. Technical Report TR2000-381,\nComputer Science Department, Dartmouth College,\nHanover, New Hampshire, November 2000.\n[4] Dey, A. Providing Architectural Support for Building\nContext-Aware Applications. 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Ph.D. Thesis, Department of\nComputing, Imperial College, London, May 1998.\n[9] Ryan, N., Pascoe, J., Morse, D. Enhanced Reality\nFieldwork: the Context-Aware Archaeological Assistant.\nGaffney, V., Van Leusen, M., Exxon, S. (eds.) Computer\nApplications in Archaeology (1997)\n[10] Schilit, B.N., Theimer, M. Disseminating Active Map\nInformation to Mobile Hosts. IEEE Network, 8(5) (1994),\n22-32.\n[11] Schilit, B.N. A System Architecture for Context-Aware\nMobile Computing. Ph.D. Thesis, Columbia University,\nDepartment of Computer Science, May 1995.\n[12] Wang, B., Bodily, J., Gupta, S.K.S. Supporting Persistent\nSocial Groups in Ubiquitous Computing Environments\nUsing Context-Aware Ephemeral Group Service. In\nProceedings of the Second IEEE International Conference\non Pervasive Computing and Communications\n(PerCom\"04). (March 14-17, 2004). IEEE Computer Society\nPress, 287-296.\n[13] Pascoe, J. The Stick-e Note Architecture: Extending the\nInterface Beyond the User. Proceedings of the 2nd\nInternational Conference of Intelligent User Interfaces\n(IUI\"97). (Orlando, USA, 1997), 261-264.\n[14] Dey, A., Abowd, G. CybreMinder: A Context-Aware System\nfor Supporting Re-minders. Proceedings of the 2nd\nInternational Symposium on Handheld and Ubiquitous\nComputing (HUC\"00). (Bristol, UK, 2000), 172-186.\n97", "keywords": "software framework;xml configuration file;context awareness;location sense;event-condition-action;fifth contextdimension group-context;contextaware;group interaction;sensor fusion;mobility system"}
{"name": "train_C-56", "title": "A Hierarchical Process Execution Support for Grid Computing", "abstract": "Grid is an emerging infrastructure used to share resources among virtual organizations in a seamless manner and to provide breakthrough computing power at low cost. Nowadays there are dozens of academic and commercial products that allow execution of isolated tasks on grids, but few products support the enactment of long-running processes in a distributed fashion. In order to address such subject, this paper presents a programming model and an infrastructure that hierarchically schedules process activities using available nodes in a wide grid environment. Their advantages are automatic and structured distribution of activities and easy process monitoring and steering.", "fulltext": "1. INTRODUCTION\nGrid computing is a model for wide-area distributed and\nparallel computing across heterogeneous networks in\nmultiple administrative domains. This research field aims to\npromote sharing of resources and provides breakthrough\ncomputing power over this wide network of virtual\norganizations in a seamless manner [8]. Traditionally, as in Globus\n[6], Condor-G [9] and Legion [10], there is a minimal\ninfrastructure that provides data resource sharing, computational\nresource utilization management, and distributed execution.\nSpecifically, considering distributed execution, most of the\nexisting grid infrastructures supports execution of isolated\ntasks, but they do not consider their task interdependencies\nas in processes (workflows) [12]. This deficiency restricts\nbetter scheduling algorithms, distributed execution\ncoordination and automatic execution recovery.\nThere are few proposed middleware infrastructures that\nsupport process execution over the grid. In general, they\nmodel processes by interconnecting their activities through\ncontrol and data dependencies. Among them, WebFlow\n[1] emphasizes an architecture to construct distributed\nprocesses; Opera-G [3] provides execution recovering and\nsteering, GridFlow [5] focuses on improved scheduling algorithms\nthat take advantage of activity dependencies, and SwinDew\n[13] supports totally distributed execution on peer-to-peer\nnetworks. However, such infrastructures contain\nscheduling algorithms that are centralized by process [1, 3, 5], or\ncompletely distributed, but difficult to monitor and control\n[13].\nIn order to address such constraints, this paper proposes a\nstructured programming model for process description and a\nhierarchical process execution infrastructure. The\nprogramming model employs structured control flow to promote\ncontrolled and contextualized activity execution.\nComplementary, the support infrastructure, which executes a process\nspecification, takes advantage of the hierarchical structure\nof a specified process in order to distribute and schedule\nstrong dependent activities as a unit, allowing a better\nexecution performance and fault-tolerance and providing\nlocalized communication.\nThe programming model and the support infrastructure,\nnamed X avantes, are under implementation in order to show\nthe feasibility of the proposed model and to demonstrate its\ntwo major advantages: to promote widely distributed\nprocess execution and scheduling, but in a controlled,\nstructured and localized way.\nNext Section describes the programming model, and\nSection 3, the support infrastructure for the proposed grid\ncomputing model. Section 4 demonstrates how the support\ninfrastructure executes processes and distributes activities.\nRelated works are presented and compared to the proposed\nmodel in Section 5. The last Section concludes this paper\nencompassing the advantages of the proposed hierarchical\nprocess execution support for the grid computing area and\nlists some future works.\n87 Middleware 2004 Companion\nProcessElement\nProcess Activity Controller\n1\n*\n1\n*\nFigure 1: High-level framework of the programming\nmodel\n2. PROGRAMMING MODEL\nThe programming model designed for the grid computing\narchitecture is very similar to the specified to the Business\nProcess Execution Language (BPEL) [2]. Both describe\nprocesses in XML [4] documents, but the former specifies\nprocesses strictly synchronous and structured, and has more\nconstructs for structured parallel control. The rationale\nbehind of its design is the possibility of hierarchically distribute\nthe process control and coordination based on structured\nconstructs, differently from BPEL, which does not allow\nhierarchical composition of processes.\nIn the proposed programming model, a process is a set of\ninterdependent activities arranged to solve a certain\nproblem. In detail, a process is composed of activities,\nsubprocesses, and controllers (see Figure 1). Activities represent\nsimple tasks that are executed on behalf of a process;\nsubprocesses are processes executed in the context of a\nparent process; and controllers are control elements used to\nspecify the execution order of these activities and\nsubprocesses. Like structured languages, controllers can be nested\nand then determine the execution order of other controllers.\nData are exchanged among process elements through\nparameters. They are passed by value, in case of simple\nobjects, or by reference, if they are remote objects shared\namong elements of the same controller or process. External\ndata can be accessed through data sources, such as relational\ndatabases or distributed objects.\n2.1 Controllers\nControllers are structured control constructs used to\ndefine the control flow of processes. There are sequential and\nparallel controllers.\nThe sequential controller types are: block, switch, for\nand while. The block controller is a simple sequential\nconstruct, and the others mimic equivalent structured\nprogramming language constructs. Similarly, the parallel types are:\npar, parswitch, parfor and parwhile. They extend the\nrespective sequential counterparts to allow parallel execution\nof process elements.\nAll parallel controller types fork the execution of one or\nmore process elements, and then, wait for each execution to\nfinish. Indeed, they contain a fork and a join of execution.\nAiming to implement a conditional join, all parallel\ncontroller types contain an exit condition, evaluated all time\nthat an element execution finishes, in order to determine\nwhen the controller must end.\nThe parfor and parwhile are the iterative versions of\nthe parallel controller types. Both fork executions while\nthe iteration condition is true. This provides flexibility to\ndetermine, at run-time, the number of process elements to\nexecute simultaneously.\nWhen compared to workflow languages, the parallel\ncontroller types represent structured versions of the workflow\ncontrol constructors, because they can nest other controllers\nand also can express fixed and conditional forks and joins,\npresent in such languages.\n2.2 Process Example\nThis section presents an example of a prime number search\napplication that receives a certain range of integers and\nreturns a set of primes contained in this range. The whole\ncomputation is made by a process, which uses a parallel\ncontroller to start and dispatch several concurrent activities\nof the same type, in order to find prime numbers. The\nportion of the XML document that describes the process and\nactivity types is shown below.\n<PROCESS_TYPE NAME=\"FindPrimes\">\n<IN_PARAMETER TYPE=\"int\" NAME=\"min\"/>\n<IN_PARAMETER TYPE=\"int\" NAME=\"max\"/>\n<IN_PARAMETER TYPE=\"int\" NAME=\"numPrimes\"/>\n<IN_PARAMETER TYPE=\"int\" NAME=\"numActs\"/>\n<BODY>\n<PRE_CODE>\nsetPrimes(new RemoteHashSet());\nparfor.setMin(getMin());\nparfor.setMax(getMax());\nparfor.setNumPrimes(getNumPrimes());\nparfor.setNumActs(getNumActs());\nparfor.setPrimes(getPrimes());\nparfor.setCounterBegin(0);\nparfor.setCounterEnd(getNumActs()-1);\n</PRE_CODE>\n<PARFOR NAME=\"parfor\">\n<IN_PARAMETER TYPE=\"int\" NAME=\"min\"/>\n<IN_PARAMETER TYPE=\"int\" NAME=\"max\"/>\n<IN_PARAMETER TYPE=\"int\" NAME=\"numPrimes\"/>\n<IN_PARAMETER TYPE=\"int\" NAME=\"numActs\"/>\n<IN_PARAMETER\nTYPE=\"RemoteCollection\" NAME=\"primes\"/>\n<ITERATE>\n<PRE_CODE>\nint range=\n(getMax()-getMin()+1)/getNumActs();\nint minNum = range*getCounter()+getMin();\nint maxNum = minNum+range-1;\nif (getCounter() == getNumActs()-1)\nmaxNum = getMax();\nfindPrimes.setMin(minNum);\nfindPrimes.setMax(maxNum);\nfindPrimes.setNumPrimes(getNumPrimes());\nfindPrimes.setPrimes(getPrimes());\n</PRE_CODE>\n<ACTIVITY\nTYPE=\"FindPrimes\" NAME=\"findPrimes\"/>\n</ITERATE>\n</PARFOR>\n</BODY>\n<OUT_PARAMETER\nTYPE=\"RemoteCollection\" NAME=\"primes\"/>\n</PROCESS_TYPE>\nMiddleware for Grid Computing 88\n<ACTIVITY_TYPE NAME=\"FindPrimes\">\n<IN_PARAMETER TYPE=\"int\" NAME=\"min\"/>\n<IN_PARAMETER TYPE=\"int\" NAME=\"max\"/>\n<IN_PARAMETER TYPE=\"int\" NAME=\"numPrimes\"/>\n<IN_PARAMETER\nTYPE=\"RemoteCollection\" NAME=\"primes\"/>\n<CODE>\nfor (int num=getMin(); num<=getMax(); num++) {\n// stop, required number of primes was found\nif (primes.size() >= getNumPrimes())\nbreak;\nboolean prime = true;\nfor (int i=2; i<num; i++) {\nif (num % i == 0) {\nprime = false;\nbreak;\n}\n}\nif (prime) {\nprimes.add(new Integer(num));\n}\n}\n</CODE>\n</ACTIVITY_TYPE>\nFirstly, a process type that finds prime numbers, named\nFindPrimes, is defined. It receives, through its input\nparameters, a range of integers in which prime numbers have\nto be found, the number of primes to be returned, and the\nnumber of activities to be executed in order to perform this\nwork. At the end, the found prime numbers are returned as\na collection through its output parameter.\nThis process contains a PARFOR controller aiming to\nexecute a determined number of parallel activities. It iterates\nfrom 0 to getNumActs() - 1, which determines the number\nof activities, starting a parallel activity in each iteration. In\nsuch case, the controller divides the whole range of numbers\nin subranges of the same size, and, in each iteration, starts a\nparallel activity that finds prime numbers in a specific\nsubrange. These activities receive a shared object by reference\nin order to store the prime numbers just found and control\nif the required number of primes has been reached.\nFinally, it is defined the activity type, FindPrimes, used\nto find prime numbers in each subrange. It receives, through\nits input parameters, the range of numbers in which it has\nto find prime numbers, the total number of prime numbers\nto be found by the whole process, and, passed by reference,\na collection object to store the found prime numbers.\nBetween its CODE markers, there is a simple code to find prime\nnumbers, which iterates over the specified range and\nverifies if the current integer is a prime. Additionally, in each\niteration, the code verifies if the required number of primes,\ninserted in the primes collection by all concurrent activities,\nhas been reached, and exits if true.\nThe advantage of using controllers is the possibility of the\nsupport infrastructure determines the point of execution the\nprocess is in, allowing automatic recovery and monitoring,\nand also the capability of instantiating and dispatching\nprocess elements only when there are enough computing\nresources available, reducing unnecessary overhead. Besides,\ndue to its structured nature, they can be easily composed\nand the support infrastructure can take advantage of this\nin order to distribute hierarchically the nested controllers to\nGroup Server\nGroup\nJava Virtual Machine\nRMI JDBC\nGroup Manager\nProcess Server\nJava Virtual Machine\nRMI JDBC\nProcess Coordinator\nWorker\nJava Virtual Machine\nRMI\nActivity Manager\nRepository\nFigure 2: Infrastructure architecture\ndifferent machines over the grid, allowing enhanced\nscalability and fault-tolerance.\n3. SUPPORT INFRASTRUCTURE\nThe support infrastructure comprises tools for\nspecification, and services for execution and monitoring of\nstructured processes in highly distributed, heterogeneous and\nautonomous grid environments. It has services to monitor\navailability of resources in the grid, to interpret processes\nand schedule activities and controllers, and to execute\nactivities.\n3.1 Infrastructure Architecture\nThe support infrastructure architecture is composed of\ngroups of machines and data repositories, which preserves\nits administrative autonomy. Generally, localized machines\nand repositories, such as in local networks or clusters, form\na group. Each machine in a group must have a Java Virtual\nMachine (JVM) [11], and a Java Runtime Library, besides\na combination of the following grid support services: group\nmanager (GM), process coordinator (PC) and activity\nmanager (AM). This combination determines what kind of group\nnode it represents: a group server, a process server, or\nsimply a worker (see Figure 2).\nIn a group there are one or more group managers, but\nonly one acts as primary and the others, as replicas. They\nare responsible to maintain availability information of group\nmachines. Moreover, group managers maintain references to\ndata resources of the group. They use group repositories to\npersist and recover the location of nodes and their\navailability.\nTo control process execution, there are one or more\nprocess coordinators per group. They are responsible to\ninstantiate and execute processes and controllers, select resources,\nand schedule and dispatch activities to workers. In order\nto persist and recover process execution and data, and also\nload process specification, they use group repositories.\nFinally, in several group nodes there is an activity\nmanager. It is responsible to execute activities in the hosted\nmachine on behalf of the group process coordinators, and to\ninform the current availability of the associated machine to\ngroup managers. They also have pendent activity queues,\ncontaining activities to be executed.\n3.2 Inter-group Relationships\nIn order to model real grid architecture, the infrastructure\nmust comprise several, potentially all, local networks, like\nInternet does. Aiming to satisfy this intent, local groups are\n89 Middleware 2004 Companion\nGM\nGM\nGM\nGM\nFigure 3: Inter-group relationships\nconnected to others, directly or indirectly, through its group\nmanagers (see Figure 3).\nEach group manager deals with requests of its group\n(represented by dashed ellipses), in order to register local\nmachines and maintain correspondent availability.\nAdditionally, group managers communicate to group managers of\nother groups. Each group manager exports coarse\navailability information to group managers of adjacent groups and\nalso receives requests from other external services to\nfurnish detailed availability information. In this way, if there\nare resources available in external groups, it is possible to\nsend processes, controllers and activities to these groups in\norder to execute them in external process coordinators and\nactivity managers, respectively.\n4. PROCESS EXECUTION\nIn the proposed grid architecture, a process is specified\nin XML, using controllers to determine control flow;\nreferencing other processes and activities; and passing objects to\ntheir parameters in order to define data flow. After specified,\nthe process is compiled in a set of classes, which represent\nspecific process, activity and controller types. At this time,\nit can be instantiated and executed by a process coordinator.\n4.1 Dynamic Model\nTo execute a specified process, it must be instantiated by\nreferencing its type on a process coordinator service of a\nspecific group. Also, the initial parameters must be passed\nto it, and then it can be started.\nThe process coordinator carries out the process by\nexecuting the process elements included in its body sequentially.\nIf the element is a process or a controller, the process\ncoordinator can choose to execute it in the same machine or to\npass it to another process coordinator in a remote machine,\nif available. Else, if the element is an activity, it passes to\nan activity manager of an available machine.\nProcess coordinators request the local group manager to\nfind available machines that contain the required service,\nprocess coordinator or activity manager, in order to\nexecute a process element. Then, it can return a local\nmachine, a machine in another group or none, depending on\nthe availability of such resource in the grid. It returns an\nexternal worker (activity manager machine) if there are no\navailable workers in the local group; and, it returns an\nexternal process server (process coordinator machine), if there\nare no available process servers or workers in the local group.\nObeying this rule, group managers try to find process servers\nin the same group of the available workers.\nSuch procedure is followed recursively by all process\ncoGM\nFindPrimes\nActivity\nAM\nFindPrimes\nActivity\nAM\nFindPrimes\nActivity\nAM\nFindPrimes\nProcess\nPC\nFigure 4: FindPrimes process execution\nordinators that execute subprocesses or controllers of a\nprocess. Therefore, because processes are structured by\nnesting process elements, the process execution is automatically\ndistributed hierarchically through one or more grid groups\naccording to the availability and locality of computing\nresources.\nThe advantage of this distribution model is wide area\nexecution, which takes advantage of potentially all grid\nresources; and localized communication of process elements,\nbecause strong dependent elements, which are under the\nsame controller, are placed in the same or near groups.\nBesides, it supports easy monitoring and steering, due to its\nstructured controllers, which maintain state and control over\nits inner elements.\n4.2 Process Execution Example\nRevisiting the example shown in Section 2.2, a process\ntype is specified to find prime numbers in a certain range of\nnumbers. In order to solve this problem, it creates a number\nof activities using the parfor controller. Each activity, then,\nfinds primes in a determined part of the range of numbers.\nFigure 4 shows an instance of this process type executing\nover the proposed infrastructure. A FindPrimes process\ninstance is created in an available process coordinator (PC),\nwhich begins executing the parfor controller. In each\niteration of this controller, the process coordinator requests\nto the group manager (GM) an available activity manager\n(AM) in order to execute a new instance of the FindPrimes\nactivity. If there is any AM available in this group or in an\nexternal one, the process coordinator sends the activity class\nand initial parameters to this activity manager and requests\nits execution. Else, if no activity manager is available, then\nthe controller enters in a wait state until an activity manager\nis made available, or is created.\nIn parallel, whenever an activity finishes, its result is sent\nback to the process coordinator, which records it in the\nparfor controller. Then, the controller waits until all\nactivities that have been started are finished, and it ends. At\nthis point, the process coordinator verifies that there is no\nother process element to execute and finishes the process.\n5. RELATED WORK\nThere are several academic and commercial products that\npromise to support grid computing, aiming to provide\ninterfaces, protocols and services to leverage the use of widely\nMiddleware for Grid Computing 90\ndistributed resources in heterogeneous and autonomous\nnetworks. Among them, Globus [6], Condor-G [9] and Legion\n[10] are widely known. Aiming to standardize interfaces\nand services to grid, the Open Grid Services Architecture\n(OGSA) [7] has been defined.\nThe grid architectures generally have services that\nmanage computing resources and distribute the execution of\nindependent tasks on available ones. However, emerging\narchitectures maintain task dependencies and automatically\nexecute tasks in a correct order. They take advantage of\nthese dependencies to provide automatic recovery, and\nbetter distribution and scheduling algorithms.\nFollowing such model, WebFlow [1] is a process\nspecification tool and execution environment constructed over\nCORBA that allows graphical composition of activities and\ntheir distributed execution in a grid environment. Opera-G\n[3], like WebFlow, uses a process specification language\nsimilar to the data flow diagram and workflow languages, but\nfurnishes automatic execution recovery and limited steering\nof process execution.\nThe previously referred architectures and others that\nenact processes over the grid have a centralized coordination.\nIn order to surpass this limitation, systems like SwinDew [13]\nproposed a widely distributed process execution, in which\neach node knows where to execute the next activity or join\nactivities in a peer-to-peer environment.\nIn the specific area of activity distribution and scheduling,\nemphasized in this work, GridFlow [5] is remarkable. It uses\na two-level scheduling: global and local. In the local level,\nit has services that predict computing resource utilization\nand activity duration. Based on this information, GridFlow\nemploys a PERT-like technique that tries to forecast the\nactivity execution start time and duration in order to better\nschedule them to the available resources.\nThe architecture proposed in this paper, which\nencompasses a programming model and an execution support\ninfrastructure, is widely decentralized, differently from WebFlow\nand Opera-G, being more scalable and fault-tolerant. But,\nlike the latter, it is designed to support execution recovery.\nComparing to SwinDew, the proposed architecture\ncontains widely distributed process coordinators, which\ncoordinate processes or parts of them, differently from SwinDew\nwhere each node has a limited view of the process: only the\nactivity that starts next. This makes easier to monitor and\ncontrol processes.\nFinally, the support infrastructure breaks the process and\nits subprocesses for grid execution, allowing a group to\nrequire another group for the coordination and execution of\nprocess elements on behalf of the first one. This is\ndifferent from GridFlow, which can execute a process in at most\ntwo levels, having the global level as the only responsible to\nschedule subprocesses in other groups. This can limit the\noverall performance of processes, and make the system less\nscalable.\n6. CONCLUSION AND FUTURE WORK\nGrid computing is an emerging research field that intends\nto promote distributed and parallel computing over the wide\narea network of heterogeneous and autonomous\nadministrative domains in a seamless way, similar to what Internet\ndoes to the data sharing. There are several products that\nsupport execution of independent tasks over grid, but only a\nfew supports the execution of processes with interdependent\ntasks.\nIn order to address such subject, this paper proposes a\nprogramming model and a support infrastructure that\nallow the execution of structured processes in a widely\ndistributed and hierarchical manner. This support\ninfrastructure provides automatic, structured and recursive\ndistribution of process elements over groups of available machines;\nbetter resource use, due to its on demand creation of\nprocess elements; easy process monitoring and steering, due to\nits structured nature; and localized communication among\nstrong dependent process elements, which are placed under\nthe same controller. These features contribute to better\nscalability, fault-tolerance and control for processes execution\nover the grid. Moreover, it opens doors for better scheduling\nalgorithms, recovery mechanisms, and also, dynamic\nmodification schemes.\nThe next work will be the implementation of a recovery\nmechanism that uses the execution and data state of\nprocesses and controllers to recover process execution. After\nthat, it is desirable to advance the scheduling algorithm to\nforecast machine use in the same or other groups and to\nforesee start time of process elements, in order to use this\ninformation to pre-allocate resources and, then, obtain a\nbetter process execution performance. Finally, it is\ninteresting to investigate schemes of dynamic modification of\nprocesses over the grid, in order to evolve and adapt long-term\nprocesses to the continuously changing grid environment.\n7. ACKNOWLEDGMENTS\nWe would like to thank Paulo C. Oliveira, from the State\nTreasury Department of Sao Paulo, for its deeply revision\nand insightful comments.\n8. REFERENCES\n[1] E. Akarsu, G. C. Fox, W. Furmanski, and T. Haupt.\nWebFlow: High-Level Programming Environment and\nVisual Authoring Toolkit for High Performance\nDistributed Computing. In Proceedings of\nSupercom puting (SC98), 1998.\n[2] T. Andrews and F. Curbera. Specification: Business\nProcess Execution Language for W eb Services V ersion\n1.1. IBM DeveloperWorks, 2003. Available at\n\nhttp://www-106.ibm.com/developerworks/library/wsbpel.\n[3] W. Bausch. O PERA -G :A M icrokernelfor\nCom putationalG rids. PhD thesis, Swiss Federal\nInstitute of Technology, Zurich, 2004.\n[4] T. Bray and J. Paoli. Extensible M arkup Language\n(X M L) 1.0. XML Core WG, W3C, 2004. Available at\nhttp://www.w3.org/TR/2004/REC-xml-20040204.\n[5] J. Cao, S. A. Jarvis, S. Saini, and G. R. Nudd.\nGridFlow: Workflow Management for Grid\nComputing. In Proceedings ofthe International\nSym posium on Cluster Com puting and the G rid\n(CCG rid 2003), 2003.\n[6] I. Foster and C. Kesselman. Globus: A\nMetacomputing Infrastructure Toolkit. Intl.J.\nSupercom puter A pplications, 11(2):115-128, 1997.\n[7] I. Foster, C. Kesselman, J. M. Nick, and S. Tuecke.\nThe Physiology ofthe G rid: A n O pen G rid Services\nA rchitecture for D istributed System s Integration.\n91 Middleware 2004 Companion\nOpen Grid Service Infrastructure WG, Global Grid\nForum, 2002.\n[8] I. Foster, C. Kesselman, and S. Tuecke. The Anatomy\nof the Grid: Enabling Scalable Virtual Organization.\nThe Intl.JournalofH igh Perform ance Com puting\nA pplications, 15(3):200-222, 2001.\n[9] J. Frey, T. Tannenbaum, M. Livny, I. Foster, and\nS. Tuecke. Condor-G: A Computational Management\nAgent for Multi-institutional Grids. In Proceedings of\nthe Tenth Intl.Sym posium on H igh Perform ance\nD istributed Com puting (H PD C-10). IEEE, 2001.\n[10] A. S. Grimshaw and W. A. Wulf. Legion - A View\nfrom 50,000 Feet. In Proceedings ofthe Fifth Intl.\nSym posium on H igh Perform ance D istributed\nCom puting. IEEE, 1996.\n[11] T. Lindholm and F. Yellin. The Java V irtualM achine\nSpecification. Sun Microsystems, Second Edition\nedition, 1999.\n[12] B. R. Schulze and E. R. M. Madeira. Grid Computing\nwith Active Services. Concurrency and Com putation:\nPractice and Experience Journal, 5(16):535-542, 2004.\n[13] J. Yan, Y. Yang, and G. K. Raikundalia. Enacting\nBusiness Processes in a Decentralised Environment\nwith P2P-Based Workflow Support. In Proceedings of\nthe Fourth Intl.Conference on W eb-Age Inform ation\nM anagem ent(W A IM 2003), 2003.\nMiddleware for Grid Computing 92", "keywords": "distributed computing;parallel computing;distribute middleware;parallel execution;grid computing;process support;hierarchical process execution;grid architecture;process execution;distributed system;process description;distributed scheduling;scheduling algorithm;distributed application;distributed process;distributed execution"}
{"name": "train_C-57", "title": "Congestion Games with Load-Dependent Failures: Identical Resources", "abstract": "We define a new class of games, congestion games with loaddependent failures (CGLFs), which generalizes the well-known class of congestion games, by incorporating the issue of resource failures into congestion games. In a CGLF, agents share a common set of resources, where each resource has a cost and a probability of failure. Each agent chooses a subset of the resources for the execution of his task, in order to maximize his own utility. The utility of an agent is the difference between his benefit from successful task completion and the sum of the costs over the resources he uses. CGLFs possess two novel features. It is the first model to incorporate failures into congestion settings, which results in a strict generalization of congestion games. In addition, it is the first model to consider load-dependent failures in such framework, where the failure probability of each resource depends on the number of agents selecting this resource. Although, as we show, CGLFs do not admit a potential function, and in general do not have a pure strategy Nash equilibrium, our main theorem proves the existence of a pure strategy Nash equilibrium in every CGLF with identical resources and nondecreasing cost functions.", "fulltext": "1. INTRODUCTION\nWe study the effects of resource failures in congestion\nsettings. This study is motivated by a variety of situations\nin multi-agent systems with unreliable components, such as\nmachines, computers etc. We define a model for congestion\ngames with load-dependent failures (CGLFs) which provides\nsimple and natural description of such situations. In this\nmodel, we are given a finite set of identical resources (service\nproviders) where each element possesses a failure\nprobability describing the probability of unsuccessful completion of\nits assigned tasks as a (nondecreasing) function of its\ncongestion. There is a fixed number of agents, each having\na task which can be carried out by any of the resources.\nFor reliability reasons, each agent may decide to assign his\ntask, simultaneously, to a number of resources. Thus, the\ncongestion on the resources is not known in advance, but\nis strategy-dependent. Each resource is associated with a\ncost, which is a (nonnegative) function of the congestion\nexperienced by this resource. The objective of each agent is to\nmaximize his own utility, which is the difference between his\nbenefit from successful task completion and the sum of the\ncosts over the set of resources he uses. The benefits of the\nagents from successful completion of their tasks are allowed\nto vary across the agents.\nThe resource cost function describes the cost suffered by\nan agent for selecting that resource, as a function of the\nnumber of agents who have selected it. Thus, it is natural\nto assume that these functions are nonnegative. In addition,\nin many real-life applications of our model the resource cost\nfunctions have a special structure. In particular, they can\nmonotonically increase or decrease with the number of the\nusers, depending on the context. The former case is\nmotivated by situations where high congestion on a resource\ncauses longer delay in its assigned tasks execution and as\na result, the cost of utilizing this resource might be higher.\nA typical example of such situation is as follows. Assume\nwe need to deliver an important package. Since there is no\nguarantee that a courier will reach the destination in time,\nwe might send several couriers to deliver the same package.\nThe time required by each courier to deliver the package\nincreases with the congestion on his way. In addition, the\npayment to a courier is proportional to the time he spends\nin delivering the package. Thus, the payment to the courier\nincreases when the congestion increases. The latter case\n(decreasing cost functions) describes situations where a group\nof agents using a particular resource have an opportunity to\nshare its cost among the group\"s members, or, the cost of\n210\nusing a resource decreases with the number of users,\naccording to some marketing policy.\nOur results\nWe show that CGLFs and, in particular, CGLFs with\nnondecreasing cost functions, do not admit a\npotential function. Therefore, the CGLF model can not be\nreduced to congestion games. Nevertheless, if the\nfailure probabilities are constant (do not depend on the\ncongestion) then a potential function is guaranteed to\nexist.\nWe show that CGLFs and, in particular, CGLFs with\ndecreasing cost functions, do not possess pure\nstrategy Nash equilibria. However, as we show in our main\nresult, there exists a pure strategy Nash\nequilibrium in any CGLF with nondecreasing cost\nfunctions.\nRelated work\nOur model extends the well-known class of congestion games\n[11]. In a congestion game, every agent has to choose from a\nfinite set of resources, where the utility (or cost) of an agent\nfrom using a particular resource depends on the number of\nagents using it, and his total utility (cost) is the sum of\nthe utilities (costs) obtained from the resources he uses. An\nimportant property of these games is the existence of pure\nstrategy Nash equilibria. Monderer and Shapley [9]\nintroduced the notions of potential function and potential game\nand proved that the existence of a potential function implies\nthe existence of a pure strategy Nash equilibrium. They\nobserved that Rosenthal [11] proved his theorem on\ncongestion games by constructing a potential function (hence,\nevery congestion game is a potential game). Moreover, they\nshowed that every finite potential game is isomorphic to a\ncongestion game; hence, the classes of finite potential games\nand congestion games coincide.\nCongestion games have been extensively studied and\ngeneralized. In particular, Leyton-Brown and Tennenholtz [5]\nextended the class of congestion games to the class of\nlocaleffect games. In a local-effect game, each agent\"s payoff is\neffected not only by the number of agents who have chosen\nthe same resources as he has chosen, but also by the number\nof agents who have chosen neighboring resources (in a given\ngraph structure). Monderer [8] dealt with another type of\ngeneralization of congestion games, in which the resource\ncost functions are player-specific (PS-congestion games). He\ndefined PS-congestion games of type q (q-congestion games),\nwhere q is a positive number, and showed that every game\nin strategic form is a q-congestion game for some q.\nPlayerspecific resource cost functions were discussed for the first\ntime by Milchtaich [6]. He showed that simple and\nstrategysymmetric PS-congestion games are not potential games,\nbut always possess a pure strategy Nash equilibrium.\nPScongestion games were generalized to weighted congestion\ngames [6] (or, ID-congestion games [7]), in which the\nresource cost functions are not only player-specific, but also\ndepend on the identity of the users of the resource.\nAckermann et al. [1] showed that weighted congestion games\nadmit pure strategy Nash equilibria if the strategy space of\neach player consists of the bases of a matroid on the set of\nresources.\nMuch of the work on congestion games has been inspired\nby the fact that every such game has a pure strategy Nash\nequilibrium. In particular, Fabrikant et al. [3] studied\nthe computational complexity of finding pure strategy Nash\nequilibria in congestion games. Intensive study has also\nbeen devoted to quantify the inefficiency of equilibria in\ncongestion games. Koutsoupias and Papadimitriou [4]\nproposed the worst-case ratio of the social welfare achieved\nby a Nash equilibrium and by a socially optimal strategy\nprofile (dubbed the price of anarchy) as a measure of the\nperformance degradation caused by lack of coordination.\nChristodoulou and Koutsoupias [2] considered the price of\nanarchy of pure equilibria in congestion games with linear\ncost functions. Roughgarden and Tardos [12] used this\napproach to study the cost of selfish routing in networks with\na continuum of users.\nHowever, the above settings do not take into\nconsideration the possibility that resources may fail to execute their\nassigned tasks. In the computer science context of\ncongestion games, where the alternatives of concern are machines,\ncomputers, communication lines etc., which are obviously\nprone to failures, this issue should not be ignored.\nPenn, Polukarov and Tennenholtz were the first to\nincorporate the issue of failures into congestion settings [10].\nThey introduced a class of congestion games with failures\n(CGFs) and proved that these games, while not being\nisomorphic to congestion games, always possess Nash equilibria\nin pure strategies. The CGF-model significantly differs from\nours. In a CGF, the authors considered the delay associated\nwith successful task completion, where the delay for an agent\nis the minimum of the delays of his successful attempts and\nthe aim of each agent is to minimize his expected delay. In\ncontrast with the CGF-model, in our model we consider the\ntotal cost of the utilized resources, where each agent wishes\nto maximize the difference between his benefit from a\nsuccessful task completion and the sum of his costs over the\nresources he uses.\nThe above differences imply that CGFs and CGLFs\npossess different properties. In particular, if in our model the\nresource failure probabilities were constant and known in\nadvance, then a potential function would exist. This, however,\ndoes not hold for CGFs; in CGFs, the failure probabilities\nare constant but there is no potential function.\nFurthermore, the procedures proposed by the authors in [10] for\nthe construction of a pure strategy Nash equilibrium are\nnot valid in our model, even in the simple, agent-symmetric\ncase, where all agents have the same benefit from successful\ncompletion of their tasks.\nOur work provides the first model of congestion settings\nwith resource failures, which considers the sum of\ncongestiondependent costs over utilized resources, and therefore, does\nnot extend the CGF-model, but rather generalizes the classic\nmodel of congestion games. Moreover, it is the first model\nto consider load-dependent failures in the above context.\n211\nOrganization\nThe rest of the paper is organized as follows. In Section 2\nwe define our model. In Section 3 we present our results.\nIn 3.1 we show that CGLFs, in general, do not have pure\nstrategy Nash equilibria. In 3.2 we focus on CGLFs with\nnondecreasing cost functions (nondecreasing CGLFs). We\nshow that these games do not admit a potential function.\nHowever, in our main result we show the existence of pure\nstrategy Nash equilibria in nondecreasing CGLFs. Section\n4 is devoted to a short discussion. Many of the proofs are\nomitted from this conference version of the paper, and will\nappear in the full version.\n2. THE MODEL\nThe scenarios considered in this work consist of a finite set\nof agents where each agent has a task that can be carried\nout by any element of a set of identical resources (service\nproviders). The agents simultaneously choose a subset of\nthe resources in order to perform their tasks, and their aim\nis to maximize their own expected payoff, as described in\nthe sequel.\nLet N be a set of n agents (n \u2208 N), and let M be a set\nof m resources (m \u2208 N). Agent i \u2208 N chooses a\nstrategy \u03c3i \u2208 \u03a3i which is a (potentially empty) subset of the\nresources. That is, \u03a3i is the power set of the set of\nresources: \u03a3i = P(M). Given a subset S \u2286 N of the agents,\nthe set of strategy combinations of the members of S is\ndenoted by \u03a3S = \u00d7i\u2208S\u03a3i, and the set of strategy\ncombinations of the complement subset of agents is denoted by\n\u03a3\u2212S (\u03a3\u2212S = \u03a3N S = \u00d7i\u2208N S\u03a3i). The set of pure strategy\nprofiles of all the agents is denoted by \u03a3 (\u03a3 = \u03a3N ).\nEach resource is associated with a cost, c(\u00b7), and a\nfailure probability, f(\u00b7), each of which depends on the\nnumber of agents who use this resource. We assume that the\nfailure probabilities of the resources are independent. Let\n\u03c3 = (\u03c31, . . . , \u03c3n) \u2208 \u03a3 be a pure strategy profile. The\n(m-dimensional) congestion vector that corresponds to \u03c3 is\nh\u03c3\n= (h\u03c3\ne )e\u2208M , where h\u03c3\ne =\n\u02db\n\u02db{i \u2208 N : e \u2208 \u03c3i}\n\u02db\n\u02db. The\nfailure probability of a resource e is a monotone nondecreasing\nfunction f : {1, . . . , n} \u2192 [0, 1) of the congestion\nexperienced by e. The cost of utilizing resource e is a function\nc : {1, . . . , n} \u2192 R+ of the congestion experienced by e.\nThe outcome for agent i \u2208 N is denoted by xi \u2208 {S, F},\nwhere S and F, respectively, indicate whether the task\nexecution succeeded or failed. We say that the execution of\nagent\"s i task succeeds if the task of agent i is successfully\ncompleted by at least one of the resources chosen by him.\nThe benefit of agent i from his outcome xi is denoted by\nVi(xi), where Vi(S) = vi, a given (nonnegative) value, and\nVi(F) = 0.\nThe utility of agent i from strategy profile \u03c3 and his\noutcome xi, ui(\u03c3, xi), is the difference between his benefit from\nthe outcome (Vi(xi)) and the sum of the costs of the\nresources he has used:\nui(\u03c3, xi) = Vi(xi) \u2212\nX\ne\u2208\u03c3i\nc(h\u03c3\ne ) .\nThe expected utility of agent i from strategy profile \u03c3, Ui(\u03c3),\nis, therefore:\nUi(\u03c3) = 1 \u2212\nY\ne\u2208\u03c3i\nf(h\u03c3\ne )\n!\nvi \u2212\nX\ne\u2208\u03c3i\nc(h\u03c3\ne ) ,\nwhere 1 \u2212\nQ\ne\u2208\u03c3i\nf(h\u03c3\ne ) denotes the probability of successful\ncompletion of agent i\"s task. We use the convention thatQ\ne\u2208\u2205 f(h\u03c3\ne ) = 1. Hence, if agent i chooses an empty set\n\u03c3i = \u2205 (does not assign his task to any resource), then his\nexpected utility, Ui(\u2205, \u03c3\u2212i), equals zero.\n3. PURE STRATEGY NASH EQUILIBRIA\nIN CGLFS\nIn this section we present our results on CGLFs. We\ninvestigate the property of the (non-)existence of pure strategy\nNash equilibria in these games. We show that this class of\ngames does not, in general, possess pure strategy equilibria.\nNevertheless, if the resource cost functions are\nnondecreasing then such equilibria are guaranteed to exist, despite the\nnon-existence of a potential function.\n3.1 Decreasing Cost Functions\nWe start by showing that the class of CGLFs and, in\nparticular, the subclass of CGLFs with decreasing cost\nfunctions, does not, in general, possess Nash equilibria in pure\nstrategies.\nConsider a CGLF with two agents (N = {1, 2}) and two\nresources (M = {e1, e2}). The cost function of each resource\nis given by c(x) = 1\nxx , where x \u2208 {1, 2}, and the failure\nprobabilities are f(1) = 0.01 and f(2) = 0.26. The benefits\nof the agents from successful task completion are v1 = 1.1\nand v2 = 4. Below we present the payoff matrix of the game.\n\u2205 {e1} {e2} {e1, e2}\n\u2205 U1 = 0 U1 = 0 U1 = 0 U1 = 0\nU2 = 0 U2 = 2.96 U2 = 2.96 U2 = 1.9996\n{e1} U1 = 0.089 U1 = 0.564 U1 = 0.089 U1 = 0.564\nU2 = 0 U2 = 2.71 U2 = 2.96 U2 = 2.7396\n{e2} U1 = 0.089 U1 = 0.089 U1 = 0.564 U1 = 0.564\nU2 = 0 U2 = 2.96 U2 = 2.71 U2 = 2.7396\n{e1, e2} U1 = \u22120.90011 U1 = \u22120.15286 U1 = \u22120.15286 U1 = 0.52564\nU2 = 0 U2 = 2.71 U2 = 2.71 U2 = 3.2296\nTable 1: Example for non-existence of pure strategy Nash\nequilibria in CGLFs.\nIt can be easily seen that for every pure strategy profile \u03c3\nin this game there exist an agent i and a strategy \u03c3i \u2208 \u03a3i\nsuch that Ui(\u03c3\u2212i, \u03c3i) > Ui(\u03c3). That is, every pure strategy\nprofile in this game is not in equilibrium.\nHowever, if the cost functions in a given CGLF do not\ndecrease in the number of users, then, as we show in the\nmain result of this paper, a pure strategy Nash equilibrium\nis guaranteed to exist.\n212\n3.2 Nondecreasing Cost Functions\nThis section focuses on the subclass of CGLFs with\nnondecreasing cost functions (henceforth, nondecreasing CGLFs).\nWe show that nondecreasing CGLFs do not, in general,\nadmit a potential function. Therefore, these games are not\ncongestion games. Nevertheless, we prove that all such games\npossess pure strategy Nash equilibria.\n3.2.1 The (Non-)Existence of a Potential Function\nRecall that Monderer and Shapley [9] introduced the\nnotions of potential function and potential game, where\npotential game is defined to be a game that possesses a potential\nfunction. A potential function is a real-valued function over\nthe set of pure strategy profiles, with the property that the\ngain (or loss) of an agent shifting to another strategy while\nthe other agents\" strategies are kept unchanged, equals to\nthe corresponding increment of the potential function. The\nauthors [9] showed that the classes of finite potential games\nand congestion games coincide.\nHere we show that the class of CGLFs and, in particular,\nthe subclass of nondecreasing CGLFs, does not admit a\npotential function, and therefore is not included in the class of\ncongestion games. However, for the special case of constant\nfailure probabilities, a potential function is guaranteed to\nexist. To prove these statements we use the following\ncharacterization of potential games [9].\nA path in \u03a3 is a sequence \u03c4 = (\u03c30\n\u2192 \u03c31\n\u2192 \u00b7 \u00b7 \u00b7 ) such\nthat for every k \u2265 1 there exists a unique agent, say agent\ni, such that \u03c3k\n= (\u03c3k\u22121\n\u2212i , \u03c3i) for some \u03c3i = \u03c3k\u22121\ni in \u03a3i. A\nfinite path \u03c4 = (\u03c30\n\u2192 \u03c31\n\u2192 \u00b7 \u00b7 \u00b7 \u2192 \u03c3K\n) is closed if \u03c30\n= \u03c3K\n.\nIt is a simple closed path if in addition \u03c3l\n= \u03c3k\nfor every\n0 \u2264 l = k \u2264 K \u2212 1. The length of a simple closed path is\ndefined to be the number of distinct points in it; that is, the\nlength of \u03c4 = (\u03c30\n\u2192 \u03c31\n\u2192 \u00b7 \u00b7 \u00b7 \u2192 \u03c3K\n) is K.\nTheorem 1. [9] Let G be a game in strategic form with\na vector U = (U1, . . . , Un) of utility functions. For a finite\npath \u03c4 = (\u03c30\n\u2192 \u03c31\n\u2192 \u00b7 \u00b7 \u00b7 \u2192 \u03c3K\n), let U(\u03c4) =\nPK\nk=1[Uik (\u03c3k\n)\u2212\nUik (\u03c3k\u22121\n)], where ik is the unique deviator at step k. Then,\nG is a potential game if and only if U(\u03c4) = 0 for every\nsimple closed path \u03c4 of length 4.\nLoad-Dependent Failures\nBased on Theorem 1, we present the following\ncounterexample that demonstrates the non-existence of a potential\nfunction in CGLFs.\nWe consider the following agent-symmetric game G in\nwhich two agents (N = {1, 2}) wish to assign a task to two\nresources (M = {e1, e2}). The benefit from a successful task\ncompletion of each agent equals v, and the failure\nprobability function strictly increases with the congestion. Consider\nthe simple closed path of length 4 which is formed by\n\u03b1 = (\u2205, {e2}) , \u03b2 = ({e1}, {e2}) ,\n\u03b3 = ({e1}, {e1, e2}) , \u03b4 = (\u2205, {e1, e2}) :\n{e2} {e1, e2}\n\u2205 U1 = 0 U1 = 0\nU2 = (1 \u2212 f(1)) v \u2212 c(1) U2 =\n`\n1 \u2212 f(1)2\n\u00b4\nv \u2212 2c(1)\n{e1} U1 = (1 \u2212 f(1)) v \u2212 c(1) U1 = (1 \u2212 f(2)) v \u2212 c(2)\nU2 = (1 \u2212 f(1)) v \u2212 c(1) U2 = (1 \u2212 f(1)f(2)) v \u2212 c(1) \u2212 c(2)\nTable 2: Example for non-existence of potentials in CGLFs.\nTherefore,\nU1(\u03b1) \u2212 U1(\u03b2) + U2(\u03b2) \u2212 U2(\u03b3) + U1(\u03b3) \u2212 U1(\u03b4)\n+U2(\u03b4) \u2212 U2(\u03b1) = v (1 \u2212 f(1)) (f(1) \u2212 f(2)) = 0.\nThus, by Theorem 1, nondecreasing CGLFs do not\nadmit potentials. As a result, they are not congestion games.\nHowever, as presented in the next section, the special case\nin which the failure probabilities are constant, always\npossesses a potential function.\nConstant Failure Probabilities\nWe show below that CGLFs with constant failure\nprobabilities always possess a potential function. This follows from\nthe fact that the expected benefit (revenue) of each agent in\nthis case does not depend on the choices of the other agents.\nIn addition, for each agent, the sum of the costs over his\nchosen subset of resources, equals the payoff of an agent\nchoosing the same strategy in the corresponding congestion game.\nAssume we are given a game G with constant failure\nprobabilities. Let \u03c4 = (\u03b1 \u2192 \u03b2 \u2192 \u03b3 \u2192 \u03b4 \u2192 \u03b1) be an arbitrary\nsimple closed path of length 4. Let i and j denote the active\nagents (deviators) in \u03c4 and z \u2208 \u03a3\u2212{i,j} be a fixed\nstrategy profile of the other agents. Let \u03b1 = (xi, xj, z), \u03b2 =\n(yi, xj, z), \u03b3 = (yi, yj, z), \u03b4 = (xi, yj, z), where xi, yi \u2208 \u03a3i\nand xj, yj \u2208 \u03a3j. Then,\nU(\u03c4) = Ui(xi, xj, z) \u2212 Ui(yi, xj, z)\n+Uj(yi, xj, z) \u2212 Uj(yi, yj, z)\n+Ui(yi, yj, z) \u2212 Ui(xi, yj, z)\n+Uj(xi, yj, z) \u2212 Uj(xi, xj, z)\n=\n\n1 \u2212 f|xi|\n\nvi \u2212\nX\ne\u2208xi\nc(h\n(xi,xj ,z)\ne ) \u2212 . . .\n\u2212\n\n1 \u2212 f|xj |\n\nvj +\nX\ne\u2208xj\nc(h\n(xi,xj ,z)\ne )\n=\n\u00bb\n1 \u2212 f|xi|\n\nvi \u2212 . . . \u2212\n\n1 \u2212 f|xj |\n\nvj\n\n\u2212\n\u00bb X\ne\u2208xi\nc(h\n(xi,xj ,z)\ne ) \u2212 . . . \u2212\nX\ne\u2208xj\nc(h\n(xi,xj ,z)\ne )\n\n.\nNotice that\n\u00bb\n1 \u2212 f|xi|\n\nvi \u2212 . . . \u2212\n\n1 \u2212 f|xj |\n\nvj\n\n= 0, as\na sum of a telescope series. The remaining sum equals 0, by\napplying Theorem 1 to congestion games, which are known\nto possess a potential function. Thus, by Theorem 1, G is a\npotential game.\n213\nWe note that the above result holds also for the more\ngeneral settings with non-identical resources (having\ndifferent failure probabilities and cost functions) and general cost\nfunctions (not necessarily monotone and/or nonnegative).\n3.2.2 The Existence of a Pure Strategy Nash\nEquilibrium\nIn the previous section, we have shown that CGLFs and,\nin particular, nondecreasing CGLFs, do not admit a\npotential function, but this fact, in general, does not contradict\nthe existence of an equilibrium in pure strategies. In this\nsection, we present and prove the main result of this\npaper (Theorem 2) which shows the existence of pure strategy\nNash equilibria in nondecreasing CGLFs.\nTheorem 2. Every nondecreasing CGLF possesses a Nash\nequilibrium in pure strategies.\nThe proof of Theorem 2 is based on Lemmas 4, 7 and\n8, which are presented in the sequel. We start with some\ndefinitions and observations that are needed for their proofs.\nIn particular, we present the notions of A-, D- and S-stability\nand show that a strategy profile is in equilibrium if and only\nif it is A-, D- and S- stable. Furthermore, we prove the\nexistence of such a profile in any given nondecreasing CGLF.\nDefinition 3. For any strategy profile \u03c3 \u2208 \u03a3 and for any\nagent i \u2208 N, the operation of adding precisely one resource\nto his strategy, \u03c3i, is called an A-move of i from \u03c3.\nSimilarly, the operation of dropping a single resource is called a\nD-move, and the operation of switching one resource with\nanother is called an S-move.\nClearly, if agent i deviates from strategy \u03c3i to strategy \u03c3i\nby applying a single A-, D- or S-move, then max {|\u03c3i \u03c3i|,\n|\u03c3i \u03c3i|} = 1, and vice versa, if max {|\u03c3i \u03c3i|, |\u03c3i \u03c3i|} =\n1 then \u03c3i is obtained from \u03c3i by applying exactly one such\nmove. For simplicity of exposition, for any pair of sets A\nand B, let \u00b5(A, B) = max {|A B|, |B A|}.\nThe following lemma implies that any strategy profile, in\nwhich no agent wishes unilaterally to apply a single A-,\nDor S-move, is a Nash equilibrium. More precisely, we show\nthat if there exists an agent who benefits from a unilateral\ndeviation from a given strategy profile, then there exists a\nsingle A-, D- or S-move which is profitable for him as well.\nLemma 4. Given a nondecreasing CGLF, let \u03c3 \u2208 \u03a3 be a\nstrategy profile which is not in equilibrium, and let i \u2208 N\nsuch that \u2203xi \u2208 \u03a3i for which Ui(\u03c3\u2212i, xi) > Ui(\u03c3). Then,\nthere exists yi \u2208 \u03a3i such that Ui(\u03c3\u2212i, yi) > Ui(\u03c3) and \u00b5(yi, \u03c3i)\n= 1.\nTherefore, to prove the existence of a pure strategy Nash\nequilibrium, it suffices to look for a strategy profile for which\nno agent wishes to unilaterally apply an A-, D- or S-move.\nBased on the above observation, we define A-, D- and\nSstability as follows.\nDefinition 5. A strategy profile \u03c3 is said to be A-stable\n(resp., D-stable, S-stable) if there are no agents with a\nprofitable A- (resp., D-, S-) move from \u03c3. Similarly, we\ndefine a strategy profile \u03c3 to be DS-stable if there are no\nagents with a profitable D- or S-move from \u03c3.\nThe set of all DS-stable strategy profiles is denoted by\n\u03a30\n. Obviously, the profile (\u2205, . . . , \u2205) is DS-stable, so \u03a30\nis not empty. Our goal is to find a DS-stable profile for\nwhich no profitable A-move exists, implying this profile is\nin equilibrium. To describe how we achieve this, we define\nthe notions of light (heavy) resources and (nearly-) even\nstrategy profiles, which play a central role in the proof of\nour main result.\nDefinition 6. Given a strategy profile \u03c3, resource e is\ncalled \u03c3-light if h\u03c3\ne \u2208 arg mine\u2208M h\u03c3\ne and \u03c3-heavy otherwise.\nA strategy profile \u03c3 with no heavy resources will be termed\neven. A strategy profile \u03c3 satisfying |h\u03c3\ne \u2212 h\u03c3\ne | \u2264 1 for all\ne, e \u2208 M will be termed nearly-even.\nObviously, every even strategy profile is nearly-even. In\naddition, in a nearly-even strategy profile, all heavy resources\n(if exist) have the same congestion. We also observe that the\nprofile (\u2205, . . . , \u2205) is even (and DS-stable), so the subset of\neven, DS-stable strategy profiles is not empty.\nBased on the above observations, we define two types of\nan A-move that are used in the sequel. Suppose \u03c3 \u2208 \u03a30\nis a nearly-even DS-stable strategy profile. For each agent\ni \u2208 N, let ei \u2208 arg mine\u2208M \u03c3i h\u03c3\ne . That is, ei is a\nlightest resource not chosen previously by i. Then, if there\nexists any profitable A-move for agent i, then the A-move\nwith ei is profitable for i as well. This is since if agent i\nwishes to unilaterally add a resource, say a \u2208 M \u03c3i, then\nUi (\u03c3\u2212i, (\u03c3i \u222a {a})) > Ui(\u03c3). Hence,\n1 \u2212\nY\ne\u2208\u03c3i\nf(h\u03c3\ne )f(h\u03c3\na + 1)\n!\nvi \u2212\nX\ne\u2208\u03c3i\nc(h\u03c3\ne ) \u2212 c(h\u03c3\na + 1)\n> 1 \u2212\nY\ne\u2208\u03c3i\nf(h\u03c3\ne )\n!\nvi \u2212\nX\ne\u2208\u03c3i\nc(h\u03c3\ne )\n\u21d2 vi\nY\ne\u2208\u03c3i\nf(h\u03c3\ne ) >\nc(h\u03c3\na + 1)\n1 \u2212 f(h\u03c3\na + 1)\n\u2265\nc(h\u03c3\nei\n+ 1)\n1 \u2212 f(h\u03c3\nei\n+ 1)\n\u21d2 Ui (\u03c3\u2212i, (\u03c3i \u222a {ei})) > Ui(\u03c3) .\nIf no agent wishes to change his strategy in this\nmanner, i.e. Ui(\u03c3) \u2265 Ui(\u03c3\u2212i, \u03c3i \u222a{ei}) for all i \u2208 N, then by the\nabove Ui(\u03c3) \u2265 Ui(\u03c3\u2212i, \u03c3i \u222a{a}) for all i \u2208 N and a \u2208 M \u03c3i.\nHence, \u03c3 is A-stable and by Lemma 4, \u03c3 is a Nash\nequilibrium strategy profile. Otherwise, let N(\u03c3) denote the subset\nof all agents for which there exists ei such that a unilateral\naddition of ei is profitable. Let a \u2208 arg minei : i\u2208N(\u03c3) h\u03c3\nei\n. Let\nalso i \u2208 N(\u03c3) be the agent for which ei = a. If a is \u03c3-light,\nthen let \u03c3 = (\u03c3\u2212i, \u03c3i \u222a {a}). In this case we say that \u03c3 is\nobtained from \u03c3 by a one-step addition of resource a, and a\nis called an added resource. If a is \u03c3-heavy then there exists\na \u03c3-light resource b and an agent j such that a \u2208 \u03c3j and\nb /\u2208 \u03c3j. Then let \u03c3 =\n`\n\u03c3\u2212{i,j}, \u03c3i \u222a {a}, (\u03c3j {a}) \u222a {b}\n\u00b4\n.\nIn this case we say that \u03c3 is obtained from \u03c3 by a two-step\naddition of resource b, and b is called an added resource.\nWe notice that, in both cases, the congestion of each\nresource in \u03c3 is the same as in \u03c3, except for the added\nresource, for which its congestion in \u03c3 increased by 1. Thus,\nsince the added resource is \u03c3-light and \u03c3 is nearly-even, \u03c3\nis nearly-even. Then, the following lemma implies the\nSstability of \u03c3 .\n214\nLemma 7. In a nondecreasing CGLF, every nearly-even\nstrategy profile is S-stable.\nCoupled with Lemma 7, the following lemma shows that\nif \u03c3 is a nearly-even and DS-stable strategy profile, and \u03c3 is\nobtained from \u03c3 by a one- or two-step addition of resource\na, then the only potential cause for a non-DS-stability of \u03c3\nis the existence of an agent k \u2208 N with \u03c3k = \u03c3k, who wishes\nto drop the added resource a.\nLemma 8. Let \u03c3 be a nearly-even DS-stable strategy\nprofile of a given nondecreasing CGLF, and let \u03c3 be obtained\nfrom \u03c3 by a one- or two-step addition of resource a. Then,\nthere are no profitable D-moves for any agent i \u2208 N with\n\u03c3i = \u03c3i. For an agent i \u2208 N with \u03c3i = \u03c3i, the only possible\nprofitable D-move (if exists) is to drop the added resource a.\nWe are now ready to prove our main result - Theorem\n2. Let us briefly describe the idea behind the proof. By\nLemma 4, it suffices to prove the existence of a strategy\nprofile which is A-, D- and S-stable. We start with the set\nof even and DS-stable strategy profiles which is obviously\nnot empty. In this set, we consider the subset of strategy\nprofiles with maximum congestion and maximum sum of the\nagents\" utilities. Assuming on the contrary that every\nDSstable profile admits a profitable A-move, we show the\nexistence of a strategy profile x in the above subset, such that a\n(one-step) addition of some resource a to x results in a\nDSstable strategy. Then by a finite series of one- or two-step\naddition operations we obtain an even, DS-stable strategy\nprofile with strictly higher congestion on the resources,\ncontradicting the choice of x. The full proof is presented below.\nProof of Theorem 2: Let \u03a31\n\u2286 \u03a30\nbe the subset of\nall even, DS-stable strategy profiles. Observe that since\n(\u2205, . . . , \u2205) is an even, DS-stable strategy profile, then \u03a31\nis not empty, and min\u03c3\u2208\u03a30\n\u02db\n\u02db{e \u2208 M : e is \u03c3\u2212heavy}\n\u02db\n\u02db = 0.\nThen, \u03a31\ncould also be defined as\n\u03a31\n= arg min\n\u03c3\u2208\u03a30\n\u02db\n\u02db{e \u2208 M : e is \u03c3\u2212heavy}\n\u02db\n\u02db ,\nwith h\u03c3\nbeing the common congestion.\nNow, let \u03a32\n\u2286 \u03a31\nbe the subset of \u03a31\nconsisting of all\nthose profiles with maximum congestion on the resources.\nThat is,\n\u03a32\n= arg max\n\u03c3\u2208\u03a31\nh\u03c3\n.\nLet UN (\u03c3) =\nP\ni\u2208N Ui(\u03c3) denotes the group utility of the\nagents, and let \u03a33\n\u2286 \u03a32\nbe the subset of all profiles in \u03a32\nwith maximum group utility. That is,\n\u03a33\n= arg max\n\u03c3\u2208\u03a32\nX\ni\u2208N\nUi(\u03c3) = arg max\n\u03c3\u2208\u03a32\nUN (\u03c3) .\nConsider first the simple case in which max\u03c3\u2208\u03a31 h\u03c3\n= 0.\nObviously, in this case, \u03a31\n= \u03a32\n= \u03a33\n= {x = (\u2205, . . . , \u2205)}.\nWe show below that by performing a finite series of\n(onestep) addition operations on x, we obtain an even,\nDSstable strategy profile y with higher congestion, that is with\nhy\n> hx\n= 0, in contradiction to x \u2208 \u03a32\n. Let z \u2208 \u03a30\nbe\na nearly-even (not necessarily even) DS-stable profile such\nthat mine\u2208M hz\ne = 0, and note that the profile x satisfies\nthe above conditions. Let N(z) be the subset of agents for\nwhich a profitable A-move exists, and let i \u2208 N(z).\nObviously, there exists a z-light resource a such that Ui(z\u2212i, zi \u222a\n{a}) > Ui(z) (otherwise, arg mine\u2208M hz\ne \u2286 zi, in\ncontradiction to mine\u2208M hz\ne = 0). Consider the strategy profile\nz = (z\u2212i, zi \u222a {a}) which is obtained from z by a (one-step)\naddition of resource a by agent i. Since z is nearly-even and\na is z-light, we can easily see that z is nearly-even. Then,\nLemma 7 implies that z is S-stable. Since i is the only agent\nusing resource a in z , by Lemma 8, no profitable D-moves\nare available. Thus, z is a DS-stable strategy profile.\nTherefore, since the number of resources is finite, there is a finite\nseries of one-step addition operations on x = (\u2205, . . . , \u2205) that\nleads to strategy profile y \u2208 \u03a31\nwith hy\n= 1 > 0 = hx\n, in\ncontradiction to x \u2208 \u03a32\n.\nWe turn now to consider the other case where max\u03c3\u2208\u03a31 h\u03c3\n\u2265 1. In this case we select from \u03a33\na strategy profile x,\nas described below, and use it to contradict our contrary\nassumption. Specifically, we show that there exists x \u2208 \u03a33\nsuch that for all j \u2208 N,\nvjf(hx\n)|xj |\u22121\n\u2265\nc(hx\n+ 1)\n1 \u2212 f(hx + 1)\n. (1)\nLet x be a strategy profile which is obtained from x by\na (one-step) addition of some resource a \u2208 M by some\nagent i \u2208 N(x) (note that x is nearly-even). Then, (1)\nis derived from and essentially equivalent to the inequality\nUj(x ) \u2265 Uj(x\u2212j, xj {a}), for all a \u2208 xj. That is, after\nperforming an A-move with a by i, there is no profitable\nD-move with a. Then, by Lemmas 7 and 8, x is DS-stable.\nFollowing the same lines as above, we construct a procedure\nthat initializes at x and achieves a strategy profile y \u2208 \u03a31\nwith hy\n> hx\n, in contradiction to x \u2208 \u03a32\n.\nNow, let us confirm the existence of x \u2208 \u03a33\nthat\nsatisfies (1). Let x \u2208 \u03a33\nand let M(x) be the subset of all\nresources for which there exists a profitable (one-step)\naddition. First, we show that (1) holds for all j \u2208 N such that\nxj \u2229M(x) = \u2205, that is, for all those agents with one of their\nresources being desired by another agent.\nLet a \u2208 M(x), and let x be the strategy profile that is\nobtained from x by the (one-step) addition of a by agent i.\nAssume on the contrary that there is an agent j with a \u2208 xj\nsuch that\nvjf(hx\n)|xj |\u22121\n<\nc(hx\n+ 1)\n1 \u2212 f(hx + 1)\n.\nLet x = (x\u2212j, xj {a}). Below we demonstrate that x\nis a DS-stable strategy profile and, since x and x\ncorrespond to the same congestion vector, we conclude that x\nlies in \u03a32\n. In addition, we show that UN (x ) > UN (x),\ncontradicting the fact that x \u2208 \u03a33\n.\nTo show that x \u2208 \u03a30\nwe note that x is an even strategy\nprofile, and thus no S-moves may be performed for x . In\naddition, since hx\n= hx\nand x \u2208 \u03a30\n, there are no profitable\nD-moves for any agent k = i, j. It remains to show that\nthere are no profitable D-moves for agents i and j as well.\n215\nSince Ui(x ) > Ui(x), we get\nvif(hx\n)|xi|\n>\nc(hx\n+ 1)\n1 \u2212 f(hx + 1)\n\u21d2 vif(hx\n)|xi |\u22121\n= vif(hx\n)|xi|\n>\nc(hx\n+ 1)\n1 \u2212 f(hx + 1)\n>\nc(hx\n)\n1 \u2212 f(hx)\n=\nc(hx\n)\n1 \u2212 f(hx )\n,\nwhich implies Ui(x ) > Ui(x\u2212i, xi {b}), for all b \u2208 xi .\nThus, there are no profitable D-moves for agent i. By the\nDS-stability of x, for agent j and for all b \u2208 xj, we have\nUj(x) \u2265 Uj(x\u2212j, xj {b}) \u21d2 vjf(hx\n)|xj |\u22121\n\u2265\nc(hx\n)\n1 \u2212 f(hx)\n.\nThen,\nvjf(hx\n)|xj |\u22121\n> vjf(hx\n)|xj |\n= vjf(hx\n)|xj |\u22121\n\u2265\nc(hx\n)\n1 \u2212 f(hx)\n=\nc(hx\n)\n1 \u2212 f(hx )\n\u21d2 Uj(x ) > Uj(x\u2212j, xj {b}), for all b \u2208 xi. Therefore, x\nis DS-stable and lies in \u03a32\n.\nTo show that UN (x ), the group utility of x , satisfies\nUN (x ) > UN (x), we note that hx\n= hx\n, and thus Uk(x ) =\nUk(x), for all k \u2208 N {i, j}. Therefore, we have to show\nthat Ui(x ) + Uj(x ) > Ui(x) + Uj(x), or Ui(x ) \u2212 Ui(x) >\nUj(x) \u2212 Uj(x ). Observe that\nUi(x ) > Ui(x) \u21d2 vif(hx\n)|xi|\n>\nc(hx\n+ 1)\n1 \u2212 f(hx + 1)\nand\nUj(x ) < Uj(x ) \u21d2 vjf(hx\n)|xj |\u22121\n<\nc(hx\n+ 1)\n1 \u2212 f(hx + 1)\n,\nwhich yields\nvif(hx\n)|xi|\n> vjf(hx\n)|xj |\u22121\n.\nThus, Ui(x ) \u2212 Ui(x)\n=\n\n1 \u2212 f(hx\n)|xi|+1\n\nvi \u2212 (|xi| + 1) c(hx\n)\n\u2212\nh\n1 \u2212 f(hx\n)|xi|\n\nvi \u2212 |xi|c(hx\n)\ni\n= vif(hx\n)|xi|\n(1 \u2212 f(hx\n)) \u2212 c(hx\n)\n> vjf(hx\n)|xj |\u22121\n(1 \u2212 f(hx\n)) \u2212 c(hx\n)\n=\n\n1 \u2212 f(hx\n)|xj |\n\nvj \u2212 |xj|c(hx\n)\n\u2212\nh\n1 \u2212 f(hx\n)|xj |\u22121\n\nvj \u2212 (|xi| \u2212 1) c(hx\n)\ni\n= Uj(x) \u2212 Uj(x ) .\nTherefore, x lies in \u03a32\nand satisfies UN (x ) > UN (x), in\ncontradiction to x \u2208 \u03a33\n.\nHence, if x \u2208 \u03a33\nthen (1) holds for all j \u2208 N such that\nxj \u2229M(x) = \u2205. Now let us see that there exists x \u2208 \u03a33\nsuch\nthat (1) holds for all the agents. For that, choose an agent\ni \u2208 arg mink\u2208N vif(hx\n)|xk|\n. If there exists a \u2208 xi \u2229 M(x)\nthen i satisfies (1), implying by the choice of agent i, that\nthe above obviously yields the correctness of (1) for any\nagent k \u2208 N. Otherwise, if no resource in xi lies in M(x),\nthen let a \u2208 xi and a \u2208 M(x). Since a \u2208 xi, a /\u2208 xi,\nand hx\na = hx\na , then there exists agent j such that a \u2208 xj\nand a /\u2208 xj. One can easily check that the strategy\nprofile x =\n`\nx\u2212{i,j}, (xi {a}) \u222a {a }, (xj {a }) \u222a {a}\n\u00b4\nlies\nin \u03a33\n. Thus, x satisfies (1) for agent i, and therefore, for\nany agent k \u2208 N.\nNow, let x \u2208 \u03a33\nsatisfy (1). We show below that by\nperforming a finite series of one- and two-step addition\noperations on x, we can achieve a strategy profile y that lies\nin \u03a31\n, such that hy\n> hx\n, in contradiction to x \u2208 \u03a32\n. Let\nz \u2208 \u03a30\nbe a nearly-even (not necessarily even), DS-stable\nstrategy profile, such that\nvi\nY\ne\u2208zi {b}\nf(hz\ne) \u2265\nc(hz\nb + 1)\n1 \u2212 f(hz\nb + 1)\n, (2)\nfor all i \u2208 N and for all z-light resource b \u2208 zi. We note that\nfor profile x \u2208 \u03a33\n\u2286 \u03a31\n, with all resources being x-light,\nconditions (2) and (1) are equivalent. Let z be obtained\nfrom z by a one- or two-step addition of a z-light resource\na. Obviously, z is nearly-even. In addition, hz\ne \u2265 hz\ne for\nall e \u2208 M, and mine\u2208M hz\ne \u2265 mine\u2208M hz\ne. To complete the\nproof we need to show that z is DS-stable, and, in addition,\nthat if mine\u2208M hz\ne = mine\u2208M hz\ne then z has property (2).\nThe DS-stability of z follows directly from Lemmas 7 and 8,\nand from (2) with respect to z. It remains to prove property\n(2) for z with mine\u2208M hz\ne = mine\u2208M hz\ne. Using (2) with\nrespect to z, for any agent k with zk = zk and for any\nzlight resource b \u2208 zk, we get\nvk\nY\ne\u2208zk\n{b}\nf(hz\ne ) \u2265 vk\nY\ne\u2208zk {b}\nf(hz\ne)\n\u2265\nc(hz\nb + 1)\n1 \u2212 f(hz\nb + 1)\n=\nc(hz\nb + 1)\n1 \u2212 f(hz\nb + 1)\n,\nas required. Now let us consider the rest of the agents.\nAssume z is obtained by the one-step addition of a by agent\ni. In this case, i is the only agent with zi = zi. The required\nproperty for agent i follows directly from Ui(z ) > Ui(z). In\nthe case of a two-step addition, let z =\n`\nz\u2212{i,j}, zi \u222a {b},\n(zj {b}) \u222a {a}), where b is a z-heavy resource. For agent\ni, from Ui(z\u2212i, zi \u222a {b}) > Ui(z) we get\n1 \u2212\nY\ne\u2208zi\nf(hz\ne)f(hz\nb + 1)\n!\nvi \u2212\nX\ne\u2208zi\nc(hz\ne) \u2212 c(hz\nb + 1)\n> 1 \u2212\nY\ne\u2208zi\nf(hz\ne)\n!\nvi \u2212\nX\ne\u2208zi\nc(hz\ne)\n\u21d2 vi\nY\ne\u2208zi\nf(hz\ne) >\nc(hz\nb + 1)\n1 \u2212 f(hz\nb + 1)\n, (3)\nand note that since hz\nb \u2265 hz\ne for all e \u2208 M and, in\nparticular, for all z -light resources, then\nc(hz\nb + 1)\n1 \u2212 f(hz\nb + 1)\n\u2265\nc(hz\ne + 1)\n1 \u2212 f(hz\ne + 1)\n, (4)\nfor any z -light resource e .\n216\nNow, since hz\ne \u2265 hz\ne for all e \u2208 M and b is z-heavy, then\nvi\nY\ne\u2208zi {e }\nf(hz\ne ) \u2265 vi\nY\ne\u2208zi {e }\nf(hz\ne)\n= vi\nY\ne\u2208(zi\u222a{b}) {e }\nf(hz\ne) \u2265 vi\nY\ne\u2208zi\nf(hz\ne) ,\nfor any z -light resource e . The above, coupled with (3)\nand (4), yields the required. For agent j we just use (2)\nwith respect to z and the equality hz\nb = hz\na . For any z -light\nresource e ,\nvj\nY\ne\u2208zj {e }\nf(hz\ne ) \u2265 vi\nY\ne\u2208zi {e }\nf(hz\ne)\n\u2265\nc(hz\ne + 1)\n1 \u2212 f(hz\ne + 1)\n=\nc(hz\ne + 1)\n1 \u2212 f(hz\ne + 1)\n.\nThus, since the number of resources is finite, there is a finite\nseries of one- and two-step addition operations on x that\nleads to strategy profile y \u2208 \u03a31\nwith hy\n> hx\n, in\ncontradiction to x \u2208 \u03a32\n. This completes the proof.\n4. DISCUSSION\nIn this paper, we introduce and investigate congestion\nsettings with unreliable resources, in which the probability of a\nresource\"s failure depends on the congestion experienced by\nthis resource. We defined a class of congestion games with\nload-dependent failures (CGLFs), which generalizes the\nwellknown class of congestion games. We study the existence of\npure strategy Nash equilibria and potential functions in the\npresented class of games. We show that these games do not,\nin general, possess pure strategy equilibria. Nevertheless,\nif the resource cost functions are nondecreasing then such\nequilibria are guaranteed to exist, despite the non-existence\nof a potential function.\nThe CGLF-model can be modified to the case where the\nagents pay only for non-faulty resources they selected. Both\nthe model discussed in this paper and the modified one are\nreasonable. In the full version we will show that the\nmodified model leads to similar results. In particular, we can\nshow the existence of a pure strategy equilibrium for\nnondecreasing CGLFs also in the modified model.\nIn future research we plan to consider various extensions\nof CGLFs. In particular, we plan to consider CGLFs where\nthe resources may have different costs and failure\nprobabilities, as well as CGLFs in which the resource failure\nprobabilities are mutually dependent. In addition, it is of\ninterest to develop an efficient algorithm for the computation of\npure strategy Nash equilibrium, as well as discuss the social\n(in)efficiency of the equilibria.\n5. REFERENCES\n[1] H. Ackermann, H. R\u00a8oglin, and B. V\u00a8ocking. Pure nash\nequilibria in player-specific and weighted congestion\ngames. In WINE-06, 2006.\n[2] G. Christodoulou and E. Koutsoupias. The price of\nanarchy of finite congestion games. In Proceedings of\nthe 37th Annual ACM Symposium on Theory and\nComputing (STOC-05), 2005.\n[3] A. Fabrikant, C. Papadimitriou, and K. Talwar. The\ncomplexity of pure nash equilibria. In STOC-04, pages\n604-612, 2004.\n[4] E. Koutsoupias and C. Papadimitriou. Worst-case\nequilibria. In Proceedings of the 16th Annual\nSymposium on Theoretical Aspects of Computer\nScience, pages 404-413, 1999.\n[5] K. Leyton-Brown and M. Tennenholtz. Local-effect\ngames. In IJCAI-03, 2003.\n[6] I. Milchtaich. Congestion games with player-specific\npayoff functions. 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Journal of the ACM, 49(2):236-259, 2002.\n217", "keywords": "potential function;nash equilibrium;nondecreasing cost function;resource cost function;pure strategy nash equilibrium;load-dependent failure;load-dependent resource failure;identical resource;real-valued function;failure probability;localeffect game;congestion game"}
{"name": "train_C-58", "title": "A Scalable Distributed Information Management System\u2217", "abstract": "We present a Scalable Distributed Information Management System (SDIMS) that aggregates information about large-scale networked systems and that can serve as a basic building block for a broad range of large-scale distributed applications by providing detailed views of nearby information and summary views of global information. To serve as a basic building block, a SDIMS should have four properties: scalability to many nodes and attributes, flexibility to accommodate a broad range of applications, administrative isolation for security and availability, and robustness to node and network failures. We design, implement and evaluate a SDIMS that (1) leverages Distributed Hash Tables (DHT) to create scalable aggregation trees, (2) provides flexibility through a simple API that lets applications control propagation of reads and writes, (3) provides administrative isolation through simple extensions to current DHT algorithms, and (4) achieves robustness to node and network reconfigurations through lazy reaggregation, on-demand reaggregation, and tunable spatial replication. Through extensive simulations and micro-benchmark experiments, we observe that our system is an order of magnitude more scalable than existing approaches, achieves isolation properties at the cost of modestly increased read latency in comparison to flat DHTs, and gracefully handles failures.", "fulltext": "1. INTRODUCTION\nThe goal of this research is to design and build a Scalable\nDistributed Information Management System (SDIMS) that aggregates\ninformation about large-scale networked systems and that can serve\nas a basic building block for a broad range of large-scale distributed\napplications. Monitoring, querying, and reacting to changes in\nthe state of a distributed system are core components of\napplications such as system management [15, 31, 37, 42], service\nplacement [14, 43], data sharing and caching [18, 29, 32, 35, 46], sensor\nmonitoring and control [20, 21], multicast tree formation [8, 9, 33,\n36, 38], and naming and request routing [10, 11]. We therefore\nspeculate that a SDIMS in a networked system would provide a\ndistributed operating systems backbone and facilitate the\ndevelopment and deployment of new distributed services.\nFor a large scale information system, hierarchical aggregation\nis a fundamental abstraction for scalability. Rather than expose all\ninformation to all nodes, hierarchical aggregation allows a node to\naccess detailed views of nearby information and summary views of\nglobal information. In a SDIMS based on hierarchical aggregation,\ndifferent nodes can therefore receive different answers to the query\nfind a [nearby] node with at least 1 GB of free memory or find\na [nearby] copy of file foo. A hierarchical system that aggregates\ninformation through reduction trees [21, 38] allows nodes to access\ninformation they care about while maintaining system scalability.\nTo be used as a basic building block, a SDIMS should have\nfour properties. First, the system should be scalable: it should\naccommodate large numbers of participating nodes, and it should\nallow applications to install and monitor large numbers of data\nattributes. Enterprise and global scale systems today might have tens\nof thousands to millions of nodes and these numbers will increase\nover time. Similarly, we hope to support many applications, and\neach application may track several attributes (e.g., the load and\nfree memory of a system\"s machines) or millions of attributes (e.g.,\nwhich files are stored on which machines).\nSecond, the system should have flexibility to accommodate a\nbroad range of applications and attributes. For example,\nreaddominated attributes like numCPUs rarely change in value, while\nwrite-dominated attributes like numProcesses change quite often.\nAn approach tuned for read-dominated attributes will consume high\nbandwidth when applied to write-dominated attributes. Conversely,\nan approach tuned for write-dominated attributes will suffer from\nunnecessary query latency or imprecision for read-dominated\nattributes. Therefore, a SDIMS should provide mechanisms to handle\ndifferent types of attributes and leave the policy decision of tuning\nreplication to the applications.\nThird, a SDIMS should provide administrative isolation. In a\nlarge system, it is natural to arrange nodes in an organizational or\nan administrative hierarchy. A SDIMS should support\nadministraSession 10: Distributed Information Systems\n379\ntive isolation in which queries about an administrative domain\"s\ninformation can be satisfied within the domain so that the system can\noperate during disconnections from other domains, so that an\nexternal observer cannot monitor or affect intra-domain queries, and\nto support domain-scoped queries efficiently.\nFourth, the system must be robust to node failures and\ndisconnections. A SDIMS should adapt to reconfigurations in a timely\nfashion and should also provide mechanisms so that applications\ncan tradeoff the cost of adaptation with the consistency level in the\naggregated results when reconfigurations occur.\nWe draw inspiration from two previous works: Astrolabe [38]\nand Distributed Hash Tables (DHTs).\nAstrolabe [38] is a robust information management system.\nAstrolabe provides the abstraction of a single logical aggregation tree\nthat mirrors a system\"s administrative hierarchy. It provides a\ngeneral interface for installing new aggregation functions and provides\neventual consistency on its data. Astrolabe is robust due to its use\nof an unstructured gossip protocol for disseminating information\nand its strategy of replicating all aggregated attribute values for a\nsubtree to all nodes in the subtree. This combination allows any\ncommunication pattern to yield eventual consistency and allows\nany node to answer any query using local information. This high\ndegree of replication, however, may limit the system\"s ability to\naccommodate large numbers of attributes. Also, although the\napproach works well for read-dominated attributes, an update at one\nnode can eventually affect the state at all nodes, which may limit\nthe system\"s flexibility to support write-dominated attributes.\nRecent research in peer-to-peer structured networks resulted in\nDistributed Hash Tables (DHTs) [18, 28, 29, 32, 35, 46]-a data\nstructure that scales with the number of nodes and that distributes\nthe read-write load for different queries among the participating\nnodes. It is interesting to note that although these systems export\na global hash table abstraction, many of them internally make use\nof what can be viewed as a scalable system of aggregation trees\nto, for example, route a request for a given key to the right DHT\nnode. Indeed, rather than export a general DHT interface, Plaxton\net al.\"s [28] original application makes use of hierarchical\naggregation to allow nodes to locate nearby copies of objects. It seems\nappealing to develop a SDIMS abstraction that exposes this internal\nfunctionality in a general way so that scalable trees for aggregation\ncan be a basic system building block alongside the DHTs.\nAt a first glance, it might appear to be obvious that simply\nfusing DHTs with Astrolabe\"s aggregation abstraction will result in a\nSDIMS. However, meeting the SDIMS requirements forces a\ndesign to address four questions: (1) How to scalably map different\nattributes to different aggregation trees in a DHT mesh? (2) How to\nprovide flexibility in the aggregation to accommodate different\napplication requirements? (3) How to adapt a global, flat DHT mesh\nto attain administrative isolation property? and (4) How to provide\nrobustness without unstructured gossip and total replication?\nThe key contributions of this paper that form the foundation of\nour SDIMS design are as follows.\n1. We define a new aggregation abstraction that specifies both\nattribute type and attribute name and that associates an\naggregation function with a particular attribute type. This\nabstraction paves the way for utilizing the DHT system\"s internal\ntrees for aggregation and for achieving scalability with both\nnodes and attributes.\n2. We provide a flexible API that lets applications control the\npropagation of reads and writes and thus trade off update\ncost, read latency, replication, and staleness.\n3. We augment an existing DHT algorithm to ensure path\nconvergence and path locality properties in order to achieve\nadministrative isolation.\n4. We provide robustness to node and network reconfigurations\nby (a) providing temporal replication through lazy\nreaggregation that guarantees eventual consistency and (b)\nensuring that our flexible API allows demanding applications gain\nadditional robustness by using tunable spatial replication of\ndata aggregates or by performing fast on-demand\nreaggregation to augment the underlying lazy reaggregation or by\ndoing both.\nWe have built a prototype of SDIMS. Through simulations and\nmicro-benchmark experiments on a number of department machines\nand PlanetLab [27] nodes, we observe that the prototype achieves\nscalability with respect to both nodes and attributes through use\nof its flexible API, inflicts an order of magnitude lower maximum\nnode stress than unstructured gossiping schemes, achieves isolation\nproperties at a cost of modestly increased read latency compared to\nflat DHTs, and gracefully handles node failures.\nThis initial study discusses key aspects of an ongoing system\nbuilding effort, but it does not address all issues in building a SDIMS.\nFor example, we believe that our strategies for providing robustness\nwill mesh well with techniques such as supernodes [22] and other\nongoing efforts to improve DHTs [30] for further improving\nrobustness. Also, although splitting aggregation among many trees\nimproves scalability for simple queries, this approach may make\ncomplex and multi-attribute queries more expensive compared to\na single tree. Additional work is needed to understand the\nsignificance of this limitation for real workloads and, if necessary, to\nadapt query planning techniques from DHT abstractions [16, 19]\nto scalable aggregation tree abstractions.\nIn Section 2, we explain the hierarchical aggregation\nabstraction that SDIMS provides to applications. In Sections 3 and 4, we\ndescribe the design of our system for achieving the flexibility,\nscalability, and administrative isolation requirements of a SDIMS. In\nSection 5, we detail the implementation of our prototype system.\nSection 6 addresses the issue of adaptation to the topological\nreconfigurations. In Section 7, we present the evaluation of our\nsystem through large-scale simulations and microbenchmarks on real\nnetworks. Section 8 details the related work, and Section 9\nsummarizes our contribution.\n2. AGGREGATION ABSTRACTION\nAggregation is a natural abstraction for a large-scale distributed\ninformation system because aggregation provides scalability by\nallowing a node to view detailed information about the state near it\nand progressively coarser-grained summaries about progressively\nlarger subsets of a system\"s data [38].\nOur aggregation abstraction is defined across a tree spanning all\nnodes in the system. Each physical node in the system is a leaf and\neach subtree represents a logical group of nodes. Note that logical\ngroups can correspond to administrative domains (e.g., department\nor university) or groups of nodes within a domain (e.g., 10\nworkstations on a LAN in CS department). An internal non-leaf node,\nwhich we call virtual node, is simulated by one or more physical\nnodes at the leaves of the subtree for which the virtual node is the\nroot. We describe how to form such trees in a later section.\nEach physical node has local data stored as a set of (attributeType,\nattributeName, value) tuples such as (configuration, numCPUs,\n16), (mcast membership, session foo, yes), or (file stored, foo,\nmyIPaddress). The system associates an aggregation function ftype\nwith each attribute type, and for each level-i subtree Ti in the\nsystem, the system defines an aggregate value Vi,type,name for each\n(at380\ntributeType, attributeName) pair as follows. For a (physical) leaf\nnode T0 at level 0, V0,type,name is the locally stored value for the\nattribute type and name or NULL if no matching tuple exists. Then\nthe aggregate value for a level-i subtree Ti is the aggregation\nfunction for the type, ftype computed across the aggregate values of\neach of Ti\"s k children:\nVi,type,name = ftype(V0\ni\u22121,type,name,V1\ni\u22121,type,name,...,Vk\u22121\ni\u22121,type,name).\nAlthough SDIMS allows arbitrary aggregation functions, it is\noften desirable that these functions satisfy the hierarchical\ncomputation property [21]: f(v1,...,vn)= f(f(v1,...,vs1 ), f(vs1+1,...,vs2 ),\n..., f(vsk+1,...,vn)), where vi is the value of an attribute at node\ni. For example, the average operation, defined as avg(v1,...,vn) =\n1/n.\u2211n\ni=0 vi, does not satisfy the property. Instead, if an attribute\nstores values as tuples (sum,count), the attribute satisfies the\nhierarchical computation property while still allowing the applications\nto compute the average from the aggregate sum and count values.\nFinally, note that for a large-scale system, it is difficult or\nimpossible to insist that the aggregation value returned by a probe\ncorresponds to the function computed over the current values at the\nleaves at the instant of the probe. Therefore our system provides\nonly weak consistency guarantees - specifically eventual\nconsistency as defined in [38].\n3. FLEXIBILITY\nA major innovation of our work is enabling flexible aggregate\ncomputation and propagation. The definition of the aggregation\nabstraction allows considerable flexibility in how, when, and where\naggregate values are computed and propagated. While previous\nsystems [15, 29, 38, 32, 35, 46] implement a single static strategy,\nwe argue that a SDIMS should provide flexible computation and\npropagation to efficiently support wide variety of applications with\ndiverse requirements. In order to provide this flexibility, we\ndevelop a simple interface that decomposes the aggregation\nabstraction into three pieces of functionality: install, update, and probe.\nThis definition of the aggregation abstraction allows our system\nto provide a continuous spectrum of strategies ranging from lazy\naggregate computation and propagation on reads to aggressive\nimmediate computation and propagation on writes. In Figure 1, we\nillustrate both extreme strategies and an intermediate strategy.\nUnder the lazy Update-Local computation and propagation strategy,\nan update (or write) only affects local state. Then, a probe (or read)\nthat reads a level-i aggregate value is sent up the tree to the issuing\nnode\"s level-i ancestor and then down the tree to the leaves. The\nsystem then computes the desired aggregate value at each layer up\nthe tree until the level-i ancestor that holds the desired value.\nFinally, the level-i ancestor sends the result down the tree to the\nissuing node. In the other extreme case of the aggressive Update-All\nimmediate computation and propagation on writes [38], when an\nupdate occurs, changes are aggregated up the tree, and each new\naggregate value is flooded to all of a node\"s descendants. In this\ncase, each level-i node not only maintains the aggregate values for\nthe level-i subtree but also receives and locally stores copies of all\nof its ancestors\" level- j ( j > i) aggregation values. Also, a leaf\nsatisfies a probe for a level-i aggregate using purely local data. In an\nintermediate Update-Up strategy, the root of each subtree maintains\nthe subtree\"s current aggregate value, and when an update occurs,\nthe leaf node updates its local state and passes the update to its\nparent, and then each successive enclosing subtree updates its\naggregate value and passes the new value to its parent. This strategy\nsatisfies a leaf\"s probe for a level-i aggregate value by sending the\nprobe up to the level-i ancestor of the leaf and then sending the\naggregate value down to the leaf. Finally, notice that other strategies\nexist. In general, an Update-Upk-Downj strategy aggregates up to\nparameter description optional\nattrType Attribute Type\naggrfunc Aggregation Function\nup How far upward each update is\nsent (default: all)\nX\ndown How far downward each\naggregate is sent (default: none)\nX\ndomain Domain restriction (default: none) X\nexpTime Expiry Time\nTable 1: Arguments for the install operation\nthe kth level and propagates the aggregate values of a node at level\nl (s.t. l \u2264 k) downward for j levels.\nA SDIMS must provide a wide range of flexible computation and\npropagation strategies to applications for it to be a general\nabstraction. An application should be able to choose a particular\nmechanism based on its read-to-write ratio that reduces the bandwidth\nconsumption while attaining the required responsiveness and\nprecision. Note that the read-to-write ratio of the attributes that\napplications install vary extensively. For example, a read-dominated\nattribute like numCPUs rarely changes in value, while a\nwritedominated attribute like numProcesses changes quite often. An\naggregation strategy like Update-All works well for read-dominated\nattributes but suffers high bandwidth consumption when applied for\nwrite-dominated attributes. Conversely, an approach like\nUpdateLocal works well for write-dominated attributes but suffers from\nunnecessary query latency or imprecision for read-dominated\nattributes.\nSDIMS also allows non-uniform computation and propagation\nacross the aggregation tree with different up and down parameters\nin different subtrees so that applications can adapt with the\nspatial and temporal heterogeneity of read and write operations. With\nrespect to spatial heterogeneity, access patterns may differ for\ndifferent parts of the tree, requiring different propagation strategies\nfor different parts of the tree. Similarly with respect to temporal\nheterogeneity, access patterns may change over time requiring\ndifferent strategies over time.\n3.1 Aggregation API\nWe provide the flexibility described above by splitting the\naggregation API into three functions: Install() installs an aggregation\nfunction that defines an operation on an attribute type and\nspecifies the update strategy that the function will use, Update() inserts\nor modifies a node\"s local value for an attribute, and Probe()\nobtains an aggregate value for a specified subtree. The install\ninterface allows applications to specify the k and j parameters of the\nUpdate-Upk-Downj strategy along with the aggregation function.\nThe update interface invokes the aggregation of an attribute on the\ntree according to corresponding aggregation function\"s aggregation\nstrategy. The probe interface not only allows applications to obtain\nthe aggregated value for a specified tree but also allows a probing\nnode to continuously fetch the values for a specified time, thus\nenabling an application to adapt to spatial and temporal heterogeneity.\nThe rest of the section describes these three interfaces in detail.\n3.1.1 Install\nThe Install operation installs an aggregation function in the\nsystem. The arguments for this operation are listed in Table 1. The\nattrType argument denotes the type of attributes on which this\naggregation function is invoked. Installed functions are soft state that\nmust be periodically renewed or they will be garbage collected at\nexpTime.\nThe arguments up and down specify the aggregate computation\n381\nUpdate Strategy On Update On Probe for Global Aggregate Value On Probe for Level-1 Aggregate Value\nUpdate-Local\nUpdate-Up\nUpdate-All\nFigure 1: Flexible API\nparameter description optional\nattrType Attribute Type\nattrName Attribute Name\nmode Continuous or One-shot (default:\none-shot)\nX\nlevel Level at which aggregate is sought\n(default: at all levels)\nX\nup How far up to go and re-fetch the\nvalue (default: none)\nX\ndown How far down to go and\nreaggregate (default: none)\nX\nexpTime Expiry Time\nTable 2: Arguments for the probe operation\nand propagation strategy Update-Upk-Downj. The domain\nargument, if present, indicates that the aggregation function should be\ninstalled on all nodes in the specified domain; otherwise the\nfunction is installed on all nodes in the system.\n3.1.2 Update\nThe Update operation takes three arguments attrType, attrName,\nand value and creates a new (attrType, attrName, value) tuple or\nupdates the value of an old tuple with matching attrType and\nattrName at a leaf node.\nThe update interface meshes with installed aggregate\ncomputation and propagation strategy to provide flexibility. In particular,\nas outlined above and described in detail in Section 5, after a leaf\napplies an update locally, the update may trigger re-computation\nof aggregate values up the tree and may also trigger propagation\nof changed aggregate values down the tree. Notice that our\nabstraction associates an aggregation function with only an attrType\nbut lets updates specify an attrName along with the attrType. This\ntechnique helps achieve scalability with respect to nodes and\nattributes as described in Section 4.\n3.1.3 Probe\nThe Probe operation returns the value of an attribute to an\napplication. The complete argument set for the probe operation is shown\nin Table 2. Along with the attrName and the attrType arguments, a\nlevel argument specifies the level at which the answers are required\nfor an attribute. In our implementation we choose to return results\nat all levels k < l for a level-l probe because (i) it is inexpensive as\nthe nodes traversed for level-l probe also contain level k aggregates\nfor k < l and as we expect the network cost of transmitting the\nadditional information to be small for the small aggregates which we\nfocus and (ii) it is useful as applications can efficiently get several\naggregates with a single probe (e.g., for domain-scoped queries as\nexplained in Section 4.2).\nProbes with mode set to continuous and with finite expTime\nenable applications to handle spatial and temporal heterogeneity. When\nnode A issues a continuous probe at level l for an attribute, then\nregardless of the up and down parameters, updates for the attribute\nat any node in A\"s level-l ancestor\"s subtree are aggregated up to\nlevel l and the aggregated value is propagated down along the path\nfrom the ancestor to A. Note that continuous mode enables SDIMS\nto support a distributed sensor-actuator mechanism where a\nsensor monitors a level-i aggregate with a continuous mode probe and\ntriggers an actuator upon receiving new values for the probe.\nThe up and down arguments enable applications to perform\nondemand fast re-aggregation during reconfigurations, where a forced\nre-aggregation is done for the corresponding levels even if the\naggregated value is available, as we discuss in Section 6. When\npresent, the up and down arguments are interpreted as described\nin the install operation.\n3.1.4 Dynamic Adaptation\nAt the API level, the up and down arguments in install API can be\nregarded as hints, since they suggest a computation strategy but do\nnot affect the semantics of an aggregation function. A SDIMS\nimplementation can dynamically adjust its up/down strategies for an\nattribute based on its measured read/write frequency. But a virtual\nintermediate node needs to know the current up and down\npropagation values to decide if the local aggregate is fresh in order to\nanswer a probe. This is the key reason why up and down need to be\nstatically defined at the install time and can not be specified in the\nupdate operation. In dynamic adaptation, we implement a\nleasebased mechanism where a node issues a lease to a parent or a child\ndenoting that it will keep propagating the updates to that parent or\nchild. We are currently evaluating different policies to decide when\nto issue a lease and when to revoke a lease.\n4. SCALABILITY\nOur design achieves scalability with respect to both nodes and\nattributes through two key ideas. First, it carefully defines the\naggregation abstraction to mesh well with its underlying scalable DHT\nsystem. Second, it refines the basic DHT abstraction to form an\nAutonomous DHT (ADHT) to achieve the administrative isolation\nproperties that are crucial to scaling for large real-world systems.\nIn this section, we describe these two ideas in detail.\n4.1 Leveraging DHTs\nIn contrast to previous systems [4, 15, 38, 39, 45], SDIMS\"s\naggregation abstraction specifies both an attribute type and attribute\nname and associates an aggregation function with a type rather than\njust specifying and associating a function with a name. Installing a\nsingle function that can operate on many different named attributes\nmatching a type improves scalability for sparse attribute types\nwith large, sparsely-filled name spaces. For example, to construct\na file location service, our interface allows us to install a single\nfunction that computes an aggregate value for any named file. A\nsubtree\"s aggregate value for (FILELOC, name) would be the ID of\na node in the subtree that stores the named file. Conversely,\nAstrolabe copes with sparse attributes by having aggregation functions\ncompute sets or lists and suggests that scalability can be improved\nby representing such sets with Bloom filters [6]. Supporting sparse\nnames within a type provides at least two advantages. First, when\nthe value associated with a name is updated, only the state\nassoci382\n001 010100\n000\n011 101\n111\n110\n011 111 001 101 000 100 110010\nL0\nL1\nL2\nL3\nFigure 2: The DHT tree corresponding to key 111 (DHTtree111)\nand the corresponding aggregation tree.\nated with that name needs to be updated and propagated to other\nnodes. Second, splitting values associated with different names\ninto different aggregation values allows our system to leverage\nDistributed Hash Tables (DHTs) to map different names to different\ntrees and thereby spread the function\"s logical root node\"s load and\nstate across multiple physical nodes.\nGiven this abstraction, scalably mapping attributes to DHTs is\nstraightforward. DHT systems assign a long, random ID to each\nnode and define an algorithm to route a request for key k to a\nnode rootk such that the union of paths from all nodes forms a tree\nDHTtreek rooted at the node rootk. Now, as illustrated in Figure 2,\nby aggregating an attribute along the aggregation tree\ncorresponding to DHTtreek for k =hash(attribute type, attribute name),\ndifferent attributes will be aggregated along different trees.\nIn comparison to a scheme where all attributes are aggregated\nalong a single tree, aggregating along multiple trees incurs lower\nmaximum node stress: whereas in a single aggregation tree\napproach, the root and the intermediate nodes pass around more\nmessages than leaf nodes, in a DHT-based multi-tree, each node acts as\nan intermediate aggregation point for some attributes and as a leaf\nnode for other attributes. Hence, this approach distributes the onus\nof aggregation across all nodes.\n4.2 Administrative Isolation\nAggregation trees should provide administrative isolation by\nensuring that for each domain, the virtual node at the root of the\nsmallest aggregation subtree containing all nodes of that domain is\nhosted by a node in that domain. Administrative isolation is\nimportant for three reasons: (i) for security - so that updates and probes\nflowing in a domain are not accessible outside the domain, (ii) for\navailability - so that queries for values in a domain are not affected\nby failures of nodes in other domains, and (iii) for efficiency - so\nthat domain-scoped queries can be simple and efficient.\nTo provide administrative isolation to aggregation trees, a DHT\nshould satisfy two properties:\n1. Path Locality: Search paths should always be contained in\nthe smallest possible domain.\n2. Path Convergence: Search paths for a key from different\nnodes in a domain should converge at a node in that domain.\nExisting DHTs support path locality [18] or can easily support it\nby using the domain nearness as the distance metric [7, 17], but they\ndo not guarantee path convergence as those systems try to optimize\nthe search path to the root to reduce response latency. For example,\nPastry [32] uses prefix routing in which each node\"s routing table\ncontains one row per hexadecimal digit in the nodeId space where\nthe ith row contains a list of nodes whose nodeIds differ from the\ncurrent node\"s nodeId in the ith digit with one entry for each\npossible digit value. Given a routing topology, to route a packet to\nan arbitrary destination key, a node in Pastry forwards a packet to\nthe node with a nodeId prefix matching the key in at least one more\ndigit than the current node. If such a node is not known, the\ncurrent node uses an additional data structure, the leaf set containing\n110XX\n010XX\n011XX\n100XX\n101XX\nuniv\ndep1 dep2\nkey = 111XX\n011XX 100XX 101XX 110XX 010XX\nL1\nL0\nL2\nFigure 3: Example shows how isolation property is violated\nwith original Pastry. We also show the corresponding\naggregation tree.\n110XX\n010XX\n011XX\n100XX\n101XX\nuniv\ndep1 dep2\nkey = 111XX\nX\n011XX 100XX 101XX 110XX 010XX\nL0\nL1\nL2\nFigure 4: Autonomous DHT satisfying the isolation property.\nAlso the corresponding aggregation tree is shown.\nL immediate higher and lower neighbors in the nodeId space, and\nforwards the packet to a node with an identical prefix but that is\nnumerically closer to the destination key in the nodeId space. This\nprocess continues until the destination node appears in the leaf set,\nafter which the message is routed directly. Pastry\"s expected\nnumber of routing steps is logn, where n is the number of nodes, but\nas Figure 3 illustrates, this algorithm does not guarantee path\nconvergence: if two nodes in a domain have nodeIds that match a key\nin the same number of bits, both of them can route to a third node\noutside the domain when routing for that key.\nSimple modifications to Pastry\"s route table construction and\nkey-routing protocols yield an Autonomous DHT (ADHT) that\nsatisfies the path locality and path convergence properties. As Figure 4\nillustrates, whenever two nodes in a domain share the same prefix\nwith respect to a key and no other node in the domain has a longer\nprefix, our algorithm introduces a virtual node at the boundary of\nthe domain corresponding to that prefix plus the next digit of the\nkey; such a virtual node is simulated by the existing node whose id\nis numerically closest to the virtual node\"s id. Our ADHT\"s routing\ntable differs from Pastry\"s in two ways. First, each node maintains\na separate leaf set for each domain of which it is a part. Second,\nnodes use two proximity metrics when populating the routing tables\n- hierarchical domain proximity is the primary metric and network\ndistance is secondary. Then, to route a packet to a global root for a\nkey, ADHT routing algorithm uses the routing table and the leaf set\nentries to route to each successive enclosing domain\"s root (the\nvirtual or real node in the domain matching the key in the maximum\nnumber of digits). Additional details about the ADHT algorithm\nare available in an extended technical report [44].\nProperties. Maintaining a different leaf set for each\nadministrative hierarchy level increases the number of neighbors that each\nnode tracks to (2b)\u2217lgb n+c.l from (2b)\u2217lgb n+c in unmodified\nPastry, where b is the number of bits in a digit, n is the number of\nnodes, c is the leaf set size, and l is the number of domain levels.\nRouting requires O(lgbn + l) steps compared to O(lgbn) steps in\nPastry; also, each routing hop may be longer than in Pastry because\nthe modified algorithm\"s routing table prefers same-domain nodes\nover nearby nodes. We experimentally quantify the additional\nrouting costs in Section 7.\nIn a large system, the ADHT topology allows domains to\nim383\nA1 A2 B1\n((B1.B.,1),\n(B.,1),(.,1))\n((B1.B.,1),\n(B.,1),(.,1))\nL2\nL1\nL0\n((B1.B.,1),\n(B.,1),(.,3))\n((A1.A.,1),\n(A.,2),(.,2))\n((A1.A.,1),\n(A.,1),(.,1))\n((A2.A.,1),\n(A.,1),(.,1))\nFigure 5: Example for domain-scoped queries\nprove security for sensitive attribute types by installing them only\nwithin a specified domain. Then, aggregation occurs entirely within\nthe domain and a node external to the domain can neither observe\nnor affect the updates and aggregation computations of the attribute\ntype. Furthermore, though we have not implemented this feature\nin the prototype, the ADHT topology would also support\ndomainrestricted probes that could ensure that no one outside of a domain\ncan observe a probe for data stored within the domain.\nThe ADHT topology also enhances availability by allowing the\ncommon case of probes for data within a domain to depend only on\na domain\"s nodes. This, for example, allows a domain that becomes\ndisconnected from the rest of the Internet to continue to answer\nqueries for local data.\nAggregation trees that provide administrative isolation also\nenable the definition of simple and efficient domain-scoped\naggregation functions to support queries like what is the average load\non machines in domain X? For example, consider an\naggregation function to count the number of machines in an example\nsystem with three machines illustrated in Figure 5. Each leaf node\nl updates attribute NumMachines with a value vl containing a set\nof tuples of form (Domain, Count) for each domain of which the\nnode is a part. In the example, the node A1 with name A1.A.\nperforms an update with the value ((A1.A.,1),(A.,1),(.,1)). An\naggregation function at an internal virtual node hosted on node N with\nchild set C computes the aggregate as a set of tuples: for each\ndomain D that N is part of, form a tuple (D,\u2211c\u2208C(count|(D,count) \u2208\nvc)). This computation is illustrated in the Figure 5. Now a query\nfor NumMachines with level set to MAX will return the\naggregate values at each intermediate virtual node on the path to the\nroot as a set of tuples (tree level, aggregated value) from which\nit is easy to extract the count of machines at each enclosing\ndomain. For example, A1 would receive ((2, ((B1.B.,1),(B.,1),(.,3))),\n(1, ((A1.A.,1),(A.,2),(.,2))), (0, ((A1.A.,1),(A.,1),(.,1)))). Note that\nsupporting domain-scoped queries would be less convenient and\nless efficient if aggregation trees did not conform to the system\"s\nadministrative structure. It would be less efficient because each\nintermediate virtual node will have to maintain a list of all values at\nthe leaves in its subtree along with their names and it would be less\nconvenient as applications that need an aggregate for a domain will\nhave to pick values of nodes in that domain from the list returned\nby a probe and perform computation.\n5. PROTOTYPE IMPLEMENTATION\nThe internal design of our SDIMS prototype comprises of two\nlayers: the Autonomous DHT (ADHT) layer manages the overlay\ntopology of the system and the Aggregation Management Layer\n(AML) maintains attribute tuples, performs aggregations, stores\nand propagates aggregate values. Given the ADHT construction\ndescribed in Section 4.2, each node implements an Aggregation\nManagement Layer (AML) to support the flexible API described in\nSection 3. In this section, we describe the internal state and\noperation of the AML layer of a node in the system.\nlocal\nMIB\nMIBs\nancestor\nreduction MIB\n(level 1)MIBs\nancestor\nMIB from\nchild 0X...\nMIB from\nchild 0X...\nLevel 2\nLevel 1\nLevel 3\nLevel 0\n1XXX...\n10XX...\n100X...\nFrom parents0X..\nTo parent 0X...\n\u2212\u2212 aggregation functions\nFrom parents\nTo parent 10XX...\n1X..\n1X..\n1X..\nTo parent 11XX...\nNode Id: (1001XXX)\n1001X..\n100X..\n10X..\n1X..\nVirtual Node\nFigure 6: Example illustrating the data structures and the\norganization of them at a node.\nWe refer to a store of (attribute type, attribute name, value) tuples\nas a Management Information Base or MIB, following the\nterminology from Astrolabe [38] and SNMP [34]. We refer an (attribute\ntype, attribute name) tuple as an attribute key.\nAs Figure 6 illustrates, each physical node in the system acts as\nseveral virtual nodes in the AML: a node acts as leaf for all attribute\nkeys, as a level-1 subtree root for keys whose hash matches the\nnode\"s ID in b prefix bits (where b is the number of bits corrected\nin each step of the ADHT\"s routing scheme), as a level-i subtree\nroot for attribute keys whose hash matches the node\"s ID in the\ninitial i \u2217 b bits, and as the system\"s global root for attribute keys\nwhose hash matches the node\"s ID in more prefix bits than any\nother node (in case of a tie, the first non-matching bit is ignored\nand the comparison is continued [46]).\nTo support hierarchical aggregation, each virtual node at the root\nof a level-i subtree maintains several MIBs that store (1) child MIBs\ncontaining raw aggregate values gathered from children, (2) a\nreduction MIB containing locally aggregated values across this raw\ninformation, and (3) an ancestor MIB containing aggregate values\nscattered down from ancestors. This basic strategy of maintaining\nchild, reduction, and ancestor MIBs is based on Astrolabe [38],\nbut our structured propagation strategy channels information that\nflows up according to its attribute key and our flexible propagation\nstrategy only sends child updates up and ancestor aggregate results\ndown as far as specified by the attribute key\"s aggregation\nfunction. Note that in the discussion below, for ease of explanation, we\nassume that the routing protocol is correcting single bit at a time\n(b = 1). Our system, built upon Pastry, handles multi-bit correction\n(b = 4) and is a simple extension to the scheme described here.\nFor a given virtual node ni at level i, each child MIB contains the\nsubset of a child\"s reduction MIB that contains tuples that match\nni\"s node ID in i bits and whose up aggregation function attribute is\nat least i. These local copies make it easy for a node to recompute\na level-i aggregate value when one child\"s input changes. Nodes\nmaintain their child MIBs in stable storage and use a simplified\nversion of the Bayou log exchange protocol (sans conflict detection\nand resolution) for synchronization after disconnections [26].\nVirtual node ni at level i maintains a reduction MIB of tuples\nwith a tuple for each key present in any child MIB containing the\nattribute type, attribute name, and output of the attribute type\"s\naggregate functions applied to the children\"s tuples.\nA virtual node ni at level i also maintains an ancestor MIB to\nstore the tuples containing attribute key and a list of aggregate\nvalues at different levels scattered down from ancestors. Note that the\n384\nlist for a key might contain multiple aggregate values for a same\nlevel but aggregated at different nodes (see Figure 4). So, the\naggregate values are tagged not only with level information, but are\nalso tagged with ID of the node that performed the aggregation.\nLevel-0 differs slightly from other levels. Each level-0 leaf node\nmaintains a local MIB rather than maintaining child MIBs and a\nreduction MIB. This local MIB stores information about the local\nnode\"s state inserted by local applications via update() calls. We\nenvision various sensor programs and applications insert data into\nlocal MIB. For example, one program might monitor local\nconfiguration and perform updates with information such as total memory,\nfree memory, etc., A distributed file system might perform update\nfor each file stored on the local node.\nAlong with these MIBs, a virtual node maintains two other\ntables: an aggregation function table and an outstanding probes\ntable. An aggregation function table contains the aggregation\nfunction and installation arguments (see Table 1) associated with an\nattribute type or an attribute type and name. Each aggregate\nfunction is installed on all nodes in a domain\"s subtree, so the aggregate\nfunction table can be thought of as a special case of the ancestor\nMIB with domain functions always installed up to a root within a\nspecified domain and down to all nodes within the domain. The\noutstanding probes table maintains temporary information\nregarding in-progress probes.\nGiven these data structures, it is simple to support the three API\nfunctions described in Section 3.1.\nInstall The Install operation (see Table 1) installs on a domain an\naggregation function that acts on a specified attribute type.\nExecution of an install operation for function aggrFunc on attribute type\nattrType proceeds in two phases: first the install request is passed\nup the ADHT tree with the attribute key (attrType, null) until it\nreaches the root for that key within the specified domain. Then, the\nrequest is flooded down the tree and installed on all intermediate\nand leaf nodes.\nUpdate When a level i virtual node receives an update for an\nattribute from a child below: it first recomputes the level-i\naggregate value for the specified key, stores that value in its reduction\nMIB and then, subject to the function\"s up and domain parameters,\npasses the updated value to the appropriate parent based on the\nattribute key. Also, the level-i (i \u2265 1) virtual node sends the updated\nlevel-i aggregate to all its children if the function\"s down parameter\nexceeds zero. Upon receipt of a level-i aggregate from a parent,\na level k virtual node stores the value in its ancestor MIB and, if\nk \u2265 i\u2212down, forwards this aggregate to its children.\nProbe A Probe collects and returns the aggregate value for a\nspecified attribute key for a specified level of the tree. As Figure 1\nillustrates, the system satisfies a probe for a level-i aggregate value\nusing a four-phase protocol that may be short-circuited when\nupdates have previously propagated either results or partial results up\nor down the tree. In phase 1, the route probe phase, the system\nroutes the probe up the attribute key\"s tree to either the root of the\nlevel-i subtree or to a node that stores the requested value in its\nancestor MIB. In the former case, the system proceeds to phase 2 and\nin the latter it skips to phase 4. In phase 2, the probe scatter phase,\neach node that receives a probe request sends it to all of its children\nunless the node\"s reduction MIB already has a value that matches\nthe probe\"s attribute key, in which case the node initiates phase 3\non behalf of its subtree. In phase 3, the probe aggregation phase,\nwhen a node receives values for the specified key from each of its\nchildren, it executes the aggregate function on these values and\neither (a) forwards the result to its parent (if its level is less than i)\nor (b) initiates phase 4 (if it is at level i). Finally, in phase 4, the\naggregate routing phase the aggregate value is routed down to the\nnode that requested it. Note that in the extreme case of a function\ninstalled with up = down = 0, a level-i probe can touch all nodes\nin a level-i subtree while in the opposite extreme case of a\nfunction installed with up = down = ALL, probe is a completely local\noperation at a leaf.\nFor probes that include phases 2 (probe scatter) and 3 (probe\naggregation), an issue is how to decide when a node should stop\nwaiting for its children to respond and send up its current\naggregate value. A node stops waiting for its children when one of three\nconditions occurs: (1) all children have responded, (2) the ADHT\nlayer signals one or more reconfiguration events that mark all\nchildren that have not yet responded as unreachable, or (3) a watchdog\ntimer for the request fires. The last case accounts for nodes that\nparticipate in the ADHT protocol but that fail at the AML level.\nAt a virtual node, continuous probes are handled similarly as\none-shot probes except that such probes are stored in the\noutstanding probe table for a time period of expTime specified in the probe.\nThus each update for an attribute triggers re-evaluation of\ncontinuous probes for that attribute.\nWe implement a lease-based mechanism for dynamic adaptation.\nA level-l virtual node for an attribute can issue the lease for\nlevell aggregate to a parent or a child only if up is greater than l or it\nhas leases from all its children. A virtual node at level l can issue\nthe lease for level-k aggregate for k > l to a child only if down\u2265\nk \u2212l or if it has the lease for that aggregate from its parent. Now a\nprobe for level-k aggregate can be answered by level-l virtual node\nif it has a valid lease, irrespective of the up and down values. We\nare currently designing different policies to decide when to issue a\nlease and when to revoke a lease and are also evaluating them with\nthe above mechanism.\nOur current prototype does not implement access control on\ninstall, update, and probe operations but we plan to implement\nAstrolabe\"s [38] certificate-based restrictions. Also our current\nprototype does not restrict the resource consumption in executing the\naggregation functions; but, \u2018techniques from research on resource\nmanagement in server systems and operating systems [2, 3] can be\napplied here.\n6. ROBUSTNESS\nIn large scale systems, reconfigurations are common. Our two\nmain principles for robustness are to guarantee (i) read availability\n- probes complete in finite time, and (ii) eventual consistency -\nupdates by a live node will be visible to probes by connected nodes\nin finite time. During reconfigurations, a probe might return a stale\nvalue for two reasons. First, reconfigurations lead to incorrectness\nin the previous aggregate values. Second, the nodes needed for\naggregation to answer the probe become unreachable. Our\nsystem also provides two hooks that applications can use for improved\nend-to-end robustness in the presence of reconfigurations: (1)\nOndemand re-aggregation and (2) application controlled replication.\nOur system handles reconfigurations at two levels - adaptation at\nthe ADHT layer to ensure connectivity and adaptation at the AML\nlayer to ensure access to the data in SDIMS.\n6.1 ADHT Adaptation\nOur ADHT layer adaptation algorithm is same as Pastry\"s\nadaptation algorithm [32] - the leaf sets are repaired as soon as a\nreconfiguration is detected and the routing table is repaired lazily. Note\nthat maintaining extra leaf sets does not degrade the fault-tolerance\nproperty of the original Pastry; indeed, it enhances the resilience\nof ADHTs to failures by providing additional routing links. Due\nto redundancy in the leaf sets and the routing table, updates can be\nrouted towards their root nodes successfully even during failures.\n385\nReconfig\nreconfig\nnotices\nDHT\npartial\nDHT\ncomplete\nDHT\nends\nLazy\nTime\nData\n3 7 81 2 4 5 6starts\nLazy\nData\nstarts\nLazy\nData\nstarts\nLazy\nData\nrepairrepair\nreaggr reaggr reaggr reaggr\nhappens\nFigure 7: Default lazy data re-aggregation time line\nAlso note that the administrative isolation property satisfied by our\nADHT algorithm ensures that the reconfigurations in a level i\ndomain do not affect the probes for level i in a sibling domain.\n6.2 AML Adaptation\nBroadly, we use two types of strategies for AML adaptation in\nthe face of reconfigurations: (1) Replication in time as a\nfundamental baseline strategy, and (2) Replication in space as an\nadditional performance optimization that falls back on replication in\ntime when the system runs out of replicas. We provide two\nmechanisms for replication in time. First, lazy re-aggregation propagates\nalready received updates to new children or new parents in a lazy\nfashion over time. Second, applications can reduce the probability\nof probe response staleness during such repairs through our flexible\nAPI with appropriate setting of the down parameter.\nLazy Re-aggregation: The DHT layer informs the AML layer\nabout reconfigurations in the network using the following three\nfunction calls - newParent, failedChild, and newChild. On\nnewParent(parent, prefix), all probes in the outstanding-probes table\ncorresponding to prefix are re-evaluated. If parent is not null, then\naggregation functions and already existing data are lazily transferred\nin the background. Any new updates, installs, and probes for this\nprefix are sent to the parent immediately. On failedChild(child,\nprefix), the AML layer marks the child as inactive and any outstanding\nprobes that are waiting for data from this child are re-evaluated.\nOn newChild(child, prefix), the AML layer creates space in its data\nstructures for this child.\nFigure 7 shows the time line for the default lazy re-aggregation\nupon reconfiguration. Probes initiated between points 1 and 2 and\nthat are affected by reconfigurations are reevaluated by AML upon\ndetecting the reconfiguration. Probes that complete or start between\npoints 2 and 8 may return stale answers.\nOn-demand Re-aggregation: The default lazy aggregation\nscheme lazily propagates the old updates in the system.\nAdditionally, using up and down knobs in the Probe API, applications can\nforce on-demand fast re-aggregation of updates to avoid staleness\nin the face of reconfigurations. In particular, if an application\ndetects or suspects an answer as stale, then it can re-issue the probe\nincreasing the up and down parameters to force the refreshing of\nthe cached data. Note that this strategy will be useful only after the\nDHT adaptation is completed (Point 6 on the time line in Figure 7).\nReplication in Space: Replication in space is more\nchallenging in our system than in a DHT file location application because\nreplication in space can be achieved easily in the latter by just\nreplicating the root node\"s contents. In our system, however, all internal\nnodes have to be replicated along with the root.\nIn our system, applications control replication in space using up\nand down knobs in the Install API; with large up and down values,\naggregates at the intermediate virtual nodes are propagated to more\nnodes in the system. By reducing the number of nodes that have to\nbe accessed to answer a probe, applications can reduce the\nprobability of incorrect results occurring due to the failure of nodes that\ndo not contribute to the aggregate. For example, in a file location\napplication, using a non-zero positive down parameter ensures that\na file\"s global aggregate is replicated on nodes other than the root.\n0.1\n1\n10\n100\n1000\n10000\n0.0001 0.01 1 100 10000\nAvg.numberofmessagesperoperation\nRead to Write ratio\nUpdate-All\nUp=ALL, Down=9\nUp=ALL, Down=6\nUpdate-Up\nUpdate-Local\nUp=2, Down=0\nUp=5, Down=0\nFigure 8: Flexibility of our approach. With different UP and\nDOWN values in a network of 4096 nodes for different\nreadwrite ratios.\nProbes for the file location can then be answered without accessing\nthe root; hence they are not affected by the failure of the root.\nHowever, note that this technique is not appropriate in some cases. An\naggregated value in file location system is valid as long as the node\nhosting the file is active, irrespective of the status of other nodes\nin the system; whereas an application that counts the number of\nmachines in a system may receive incorrect results irrespective of\nthe replication. If reconfigurations are only transient (like a node\ntemporarily not responding due to a burst of load), the replicated\naggregate closely or correctly resembles the current state.\n7. EVALUATION\nWe have implemented a prototype of SDIMS in Java using the\nFreePastry framework [32] and performed large-scale simulation\nexperiments and micro-benchmark experiments on two real\nnetworks: 187 machines in the department and 69 machines on the\nPlanetLab [27] testbed. In all experiments, we use static up and\ndown values and turn off dynamic adaptation. Our evaluation\nsupports four main conclusions. First, flexible API provides different\npropagation strategies that minimize communication resources at\ndifferent read-to-write ratios. For example, in our simulation we\nobserve Update-Local to be efficient for read-to-write ratios\nbelow 0.0001, Update-Up around 1, and Update-All above 50000.\nSecond, our system is scalable with respect to both nodes and\nattributes. In particular, we find that the maximum node stress in\nour system is an order lower than observed with an Update-All,\ngossiping approach. Third, in contrast to unmodified Pastry which\nviolates path convergence property in upto 14% cases, our system\nconforms to the property. Fourth, the system is robust to\nreconfigurations and adapts to failures with in a few seconds.\n7.1 Simulation Experiments\nFlexibility and Scalability: A major innovation of our system\nis its ability to provide flexible computation and propagation of\naggregates. In Figure 8, we demonstrate the flexibility exposed by the\naggregation API explained in Section 3. We simulate a system with\n4096 nodes arranged in a domain hierarchy with branching factor\n(bf) of 16 and install several attributes with different up and down\nparameters. We plot the average number of messages per operation\nincurred for a wide range of read-to-write ratios of the operations\nfor different attributes. Simulations with other sizes of networks\nwith different branching factors reveal similar results. This graph\nclearly demonstrates the benefit of supporting a wide range of\ncomputation and propagation strategies. Although having a small UP\n386\n1\n10\n100\n1000\n10000\n100000\n1e+06\n1e+07\n1 10 100 1000 10000 100000\nMaximumNodeStress\nNumber of attributes installed\nGossip 256\nGossip 4096\nGossip 65536\nDHT 256\nDHT 4096\nDHT 65536\nFigure 9: Max node stress for a gossiping approach vs. ADHT\nbased approach for different number of nodes with increasing\nnumber of sparse attributes.\nvalue is efficient for attributes with low read-to-write ratios (write\ndominated applications), the probe latency, when reads do occur,\nmay be high since the probe needs to aggregate the data from all\nthe nodes that did not send their aggregate up. Conversely,\napplications that wish to improve probe overheads or latencies can increase\ntheir UP and DOWN propagation at a potential cost of increase in\nwrite overheads.\nCompared to an existing Update-all single aggregation tree\napproach [38], scalability in SDIMS comes from (1) leveraging DHTs\nto form multiple aggregation trees that split the load across nodes\nand (2) flexible propagation that avoids propagation of all updates\nto all nodes. Figure 9 demonstrates the SDIMS\"s scalability with\nnodes and attributes. For this experiment, we build a simulator to\nsimulate both Astrolabe [38] (a gossiping, Update-All approach)\nand our system for an increasing number of sparse attributes. Each\nattribute corresponds to the membership in a multicast session with\na small number of participants. For this experiment, the session\nsize is set to 8, the branching factor is set to 16, the propagation\nmode for SDIMS is Update-Up, and the participant nodes perform\ncontinuous probes for the global aggregate value. We plot the\nmaximum node stress (in terms of messages) observed in both schemes\nfor different sized networks with increasing number of sessions\nwhen the participant of each session performs an update operation.\nClearly, the DHT based scheme is more scalable with respect to\nattributes than an Update-all gossiping scheme. Observe that at some\nconstant number of attributes, as the number of nodes increase in\nthe system, the maximum node stress increases in the gossiping\napproach, while it decreases in our approach as the load of\naggregation is spread across more nodes. Simulations with other session\nsizes (4 and 16) yield similar results.\nAdministrative Hierarchy and Robustness: Although the\nrouting protocol of ADHT might lead to an increased number of\nhops to reach the root for a key as compared to original Pastry, the\nalgorithm conforms to the path convergence and locality properties\nand thus provides administrative isolation property. In Figure 10,\nwe quantify the increased path length by comparisons with\nunmodified Pastry for different sized networks with different branching\nfactors of the domain hierarchy tree. To quantify the path\nconvergence property, we perform simulations with a large number of\nprobe pairs - each pair probing for a random key starting from two\nrandomly chosen nodes. In Figure 11, we plot the percentage of\nprobe pairs for unmodified pastry that do not conform to the path\nconvergence property. When the branching factor is low, the\ndomain hierarchy tree is deeper resulting in a large difference between\n0\n1\n2\n3\n4\n5\n6\n7\n10 100 1000 10000 100000\nPathLength\nNumber of Nodes\nADHT bf=4\nADHT bf=16\nADHT bf=64\nPASTRY bf=4,16,64\nFigure 10: Average path length to root in Pastry versus ADHT\nfor different branching factors. Note that all lines\ncorresponding to Pastry overlap.\n0\n2\n4\n6\n8\n10\n12\n14\n16\n10 100 1000 10000 100000\nPercentageofviolations\nNumber of Nodes\nbf=4\nbf=16\nbf=64\nFigure 11: Percentage of probe pairs whose paths to the root\ndid not conform to the path convergence property with Pastry.\nU\npdate-All\nU\npdate-U\np\nU\npdate-Local\n0\n200\n400\n600\n800\nLatency(inms)\nAverage Latency\nU\npdate-All\nU\npdate-U\np\nU\npdate-Local\n0\n1000\n2000\n3000\nLatency(inms) Average Latency\n(a) (b)\nFigure 12: Latency of probes for aggregate at global root level\nwith three different modes of aggregate propagation on (a)\ndepartment machines, and (b) PlanetLab machines\nPastry and ADHT in the average path length; but it is at these small\ndomain sizes, that the path convergence fails more often with the\noriginal Pastry.\n7.2 Testbed experiments\nWe run our prototype on 180 department machines (some\nmachines ran multiple node instances, so this configuration has a\ntotal of 283 SDIMS nodes) and also on 69 machines of the\nPlanetLab [27] testbed. We measure the performance of our system with\ntwo micro-benchmarks. In the first micro-benchmark, we install\nthree aggregation functions of types Update-Local, Update-Up, and\nUpdate-All, perform update operation on all nodes for all three\naggregation functions, and measure the latencies incurred by probes\nfor the global aggregate from all nodes in the system. Figure 12\n387\n0\n20\n40\n60\n80\n100\n120\n140\n0 5 10 15 20 25\n2700\n2720\n2740\n2760\n2780\n2800\n2820\n2840\nLatency(inms)\nValuesObserved\nTime(in sec)\nValues\nlatency\nNode Killed\nFigure 13: Micro-benchmark on department network showing\nthe behavior of the probes from a single node when failures are\nhappening at some other nodes. All 283 nodes assign a value of\n10 to the attribute.\n10\n100\n1000\n10000\n100000\n0 50 100 150 200 250 300 350 400 450 500\n500\n550\n600\n650\n700\nLatency(inms)\nValuesObserved\nTime(in sec)\nValues\nlatency\nNode Killed\nFigure 14: Probe performance during failures on 69 machines\nof PlanetLab testbed\nshows the observed latencies for both testbeds. Notice that the\nlatency in Update-Local is high compared to the Update-UP policy.\nThis is because latency in Update-Local is affected by the presence\nof even a single slow machine or a single machine with a high\nlatency network connection.\nIn the second benchmark, we examine robustness. We install one\naggregation function of type Update-Up that performs sum\noperation on an integer valued attribute. Each node updates the attribute\nwith the value 10. Then we monitor the latencies and results\nreturned on the probe operation for global aggregate on one chosen\nnode, while we kill some nodes after every few probes. Figure 13\nshows the results on the departmental testbed. Due to the nature\nof the testbed (machines in a department), there is little change in\nthe latencies even in the face of reconfigurations. In Figure 14, we\npresent the results of the experiment on PlanetLab testbed. The\nroot node of the aggregation tree is terminated after about 275\nseconds. There is a 5X increase in the latencies after the death of the\ninitial root node as a more distant node becomes the root node after\nrepairs. In both experiments, the values returned on probes start\nreflecting the correct situation within a short time after the failures.\nFrom both the testbed benchmark experiments and the\nsimulation experiments on flexibility and scalability, we conclude that (1)\nthe flexibility provided by SDIMS allows applications to tradeoff\nread-write overheads (Figure 8), read latency, and sensitivity to\nslow machines (Figure 12), (2) a good default aggregation\nstrategy is Update-Up which has moderate overheads on both reads and\nwrites (Figure 8), has moderate read latencies (Figure 12), and is\nscalable with respect to both nodes and attributes (Figure 9), and\n(3) small domain sizes are the cases where DHT algorithms fail to\nprovide path convergence more often and SDIMS ensures path\nconvergence with only a moderate increase in path lengths (Figure 11).\n7.3 Applications\nSDIMS is designed as a general distributed monitoring and\ncontrol infrastructure for a broad range of applications. Above, we\ndiscuss some simple microbenchmarks including a multicast\nmembership service and a calculate-sum function. Van Renesse et al. [38]\nprovide detailed examples of how such a service can be used for a\npeer-to-peer caching directory, a data-diffusion service, a\npublishsubscribe system, barrier synchronization, and voting.\nAdditionally, we have initial experience using SDIMS to construct two\nsignificant applications: the control plane for a large-scale distributed\nfile system [12] and a network monitor for identifying heavy\nhitters that consume excess resources.\nDistributed file system control: The PRACTI (Partial\nReplication, Arbitrary Consistency, Topology Independence) replication\nsystem provides a set of mechanisms for data replication over which\narbitrary control policies can be layered. We use SDIMS to provide\nseveral key functions in order to create a file system over the\nlowlevel PRACTI mechanisms.\nFirst, nodes use SDIMS as a directory to handle read misses.\nWhen a node n receives an object o, it updates the (ReadDir, o)\nattribute with the value n; when n discards o from its local store,\nit resets (ReadDir, o) to NULL. At each virtual node, the ReadDir\naggregation function simply selects a random non-null child value\n(if any) and we use the Update-Up policy for propagating updates.\nFinally, to locate a nearby copy of an object o, a node n1 issues a\nseries of probe requests for the (ReadDir, o) attribute, starting with\nlevel = 1 and increasing the level value with each repeated probe\nrequest until a non-null node ID n2 is returned. n1 then sends a\ndemand read request to n2, and n2 sends the data if it has it.\nConversely, if n2 does not have a copy of o, it sends a nack to n1,\nand n1 issues a retry probe with the down parameter set to a value\nlarger than used in the previous probe in order to force on-demand\nre-aggregation, which will yield a fresher value for the retry.\nSecond, nodes subscribe to invalidations and updates to interest\nsets of files, and nodes use SDIMS to set up and maintain\nperinterest-set network-topology-sensitive spanning trees for\npropagating this information. To subscribe to invalidations for interest\nset i, a node n1 first updates the (Inval, i) attribute with its\nidentity n1, and the aggregation function at each virtual node selects\none non-null child value. Finally, n1 probes increasing levels of the\nthe (Inval, i) attribute until it finds the first node n2 = n1; n1 then\nuses n2 as its parent in the spanning tree. n1 also issues a\ncontinuous probe for this attribute at this level so that it is notified of any\nchange to its spanning tree parent. Spanning trees for streams of\npushed updates are maintained in a similar manner.\nIn the future, we plan to use SDIMS for at least two additional\nservices within this replication system. First, we plan to use SDIMS\nto track the read and write rates to different objects; prefetch\nalgorithms will use this information to prioritize replication [40, 41].\nSecond, we plan to track the ranges of invalidation sequence\nnumbers seen by each node for each interest set in order to augment\nthe spanning trees described above with additional hole filling to\nallow nodes to locate specific invalidations they have missed.\nOverall, our initial experience with using SDIMS for the\nPRACTII replication system suggests that (1) the general aggregation\ninterface provided by SDIMS simplifies the construction of\ndistributed applications-given the low-level PRACTI mechanisms,\n388\nwe were able to construct a basic file system that uses SDIMS for\nseveral distinct control tasks in under two weeks and (2) the weak\nconsistency guarantees provided by SDIMS meet the requirements\nof this application-each node\"s controller effectively treats\ninformation from SDIMS as hints, and if a contacted node does not have\nthe needed data, the controller retries, using SDIMS on-demand\nreaggregation to obtain a fresher hint.\nDistributed heavy hitter problem: The goal of the heavy hitter\nproblem is to identify network sources, destinations, or protocols\nthat account for significant or unusual amounts of traffic. As noted\nby Estan et al. [13], this information is useful for a variety of\napplications such as intrusion detection (e.g., port scanning), denial of\nservice detection, worm detection and tracking, fair network\nallocation, and network maintenance. Significant work has been done\non developing high-performance stream-processing algorithms for\nidentifying heavy hitters at one router, but this is just a first step;\nideally these applications would like not just one router\"s views of\nthe heavy hitters but an aggregate view.\nWe use SDIMS to allow local information about heavy hitters\nto be pooled into a view of global heavy hitters. For each\ndestination IP address IPx, a node updates the attribute (DestBW,IPx)\nwith the number of bytes sent to IPx in the last time window. The\naggregation function for attribute type DestBW is installed with the\nUpdate-UP strategy and simply adds the values from child nodes.\nNodes perform continuous probe for global aggregate of the\nattribute and raise an alarm when the global aggregate value goes\nabove a specified limit. Note that only nodes sending data to a\nparticular IP address perform probes for the corresponding attribute.\nAlso note that techniques from [25] can be extended to hierarchical\ncase to tradeoff precision for communication bandwidth.\n8. RELATED WORK\nThe aggregation abstraction we use in our work is heavily\ninfluenced by the Astrolabe [38] project. Astrolabe adopts a\nPropagateAll and unstructured gossiping techniques to attain robustness [5].\nHowever, any gossiping scheme requires aggressive replication of\nthe aggregates. While such aggressive replication is efficient for\nread-dominated attributes, it incurs high message cost for attributes\nwith a small read-to-write ratio. Our approach provides a\nflexible API for applications to set propagation rules according to their\nread-to-write ratios. Other closely related projects include\nWillow [39], Cone [4], DASIS [1], and SOMO [45]. Willow, DASIS\nand SOMO build a single tree for aggregation. Cone builds a tree\nper attribute and requires a total order on the attribute values.\nSeveral academic [15, 21, 42] and commercial [37] distributed\nmonitoring systems have been designed to monitor the status of\nlarge networked systems. Some of them are centralized where all\nthe monitoring data is collected and analyzed at a central host.\nGanglia [15, 23] uses a hierarchical system where the attributes are\nreplicated within clusters using multicast and then cluster\naggregates are further aggregated along a single tree. Sophia [42] is\na distributed monitoring system designed with a declarative logic\nprogramming model where the location of query execution is both\nexplicit in the language and can be calculated during evaluation.\nThis research is complementary to our work. TAG [21] collects\ninformation from a large number of sensors along a single tree.\nThe observation that DHTs internally provide a scalable forest\nof reduction trees is not new. Plaxton et al.\"s [28] original paper\ndescribes not a DHT, but a system for hierarchically aggregating and\nquerying object location data in order to route requests to nearby\ncopies of objects. Many systems-building upon both Plaxton\"s\nbit-correcting strategy [32, 46] and upon other strategies [24, 29,\n35]-have chosen to hide this power and export a simple and\ngeneral distributed hash table abstraction as a useful building block for\na broad range of distributed applications. Some of these systems\ninternally make use of the reduction forest not only for routing but\nalso for caching [32], but for simplicity, these systems do not\ngenerally export this powerful functionality in their external interface.\nOur goal is to develop and expose the internal reduction forest of\nDHTs as a similarly general and useful abstraction.\nAlthough object location is a predominant target application for\nDHTs, several other applications like multicast [8, 9, 33, 36] and\nDNS [11] are also built using DHTs. All these systems implicitly\nperform aggregation on some attribute, and each one of them must\nbe designed to handle any reconfigurations in the underlying DHT.\nWith the aggregation abstraction provided by our system, designing\nand building of such applications becomes easier.\nInternal DHT trees typically do not satisfy domain locality\nproperties required in our system. Castro et al. [7] and Gummadi et\nal. [17] point out the importance of path convergence from the\nperspective of achieving efficiency and investigate the performance of\nPastry and other DHT algorithms, respectively. SkipNet [18]\nprovides domain restricted routing where a key search is limited to the\nspecified domain. This interface can be used to ensure path\nconvergence by searching in the lowest domain and moving up to the next\ndomain when the search reaches the root in the current domain.\nAlthough this strategy guarantees path convergence, it loses the\naggregation tree abstraction property of DHTs as the domain constrained\nrouting might touch a node more than once (as it searches forward\nand then backward to stay within a domain).\n9. CONCLUSIONS\nThis paper presents a Scalable Distributed Information\nManagement System (SDIMS) that aggregates information in large-scale\nnetworked systems and that can serve as a basic building block\nfor a broad range of applications. For large scale systems,\nhierarchical aggregation is a fundamental abstraction for scalability.\nWe build our system by extending ideas from Astrolabe and DHTs\nto achieve (i) scalability with respect to both nodes and attributes\nthrough a new aggregation abstraction that helps leverage DHT\"s\ninternal trees for aggregation, (ii) flexibility through a simple API\nthat lets applications control propagation of reads and writes, (iii)\nadministrative isolation through simple augmentations of current\nDHT algorithms, and (iv) robustness to node and network\nreconfigurations through lazy reaggregation, on-demand reaggregation,\nand tunable spatial replication.\nAcknowlegements\nWe are grateful to J.C. Browne, Robert van Renessee, Amin\nVahdat, Jay Lepreau, and the anonymous reviewers for their helpful\ncomments on this work.\n10. REFERENCES\n[1] K. Albrecht, R. Arnold, M. Gahwiler, and R. Wattenhofer.\nJoin and Leave in Peer-to-Peer Systems: The DASIS\napproach. 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Directed\ndiffusion: a scalable and robust communication paradigm for\nsensor networks. In MobiCom, 2000.\n[21] S. R. Madden, M. J. Franklin, J. M. Hellerstein, and\nW. Hong. TAG: a Tiny AGgregation Service for ad-hoc\nSensor Networks. In OSDI, 2002.\n[22] D. Malkhi. Dynamic Lookup Networks. In FuDiCo, 2002.\n[23] M. L. Massie, B. N. Chun, and D. E. Culler. The ganglia\ndistributed monitoring system: Design, implementation, and\nexperience. In submission.\n[24] P. Maymounkov and D. Mazieres. Kademlia: A Peer-to-peer\nInformation System Based on the XOR Metric. In\nProceesings of the IPTPS, March 2002.\n[25] C. Olston and J. Widom. Offering a precision-performance\ntradeoff for aggregation queries over replicated data. In\nVLDB, pages 144-155, Sept. 2000.\n[26] K. Petersen, M. Spreitzer, D. Terry, M. Theimer, and\nA. Demers. Flexible Update Propagation for Weakly\nConsistent Replication. In Proc. SOSP, Oct. 1997.\n[27] Planetlab. http://www.planet-lab.org.\n[28] C. G. Plaxton, R. Rajaraman, and A. W. Richa. Accessing\nNearby Copies of Replicated Objects in a Distributed\nEnvironment. In ACM SPAA, 1997.\n[29] S. Ratnasamy, P. Francis, M. Handley, R. Karp, and\nS. Shenker. A Scalable Content Addressable Network. In\nProceedings of ACM SIGCOMM, 2001.\n[30] S. Ratnasamy, S. Shenker, and I. Stoica. Routing Algorithms\nfor DHTs: Some Open Questions. In IPTPS, March 2002.\n[31] T. Roscoe, R. Mortier, P. Jardetzky, and S. Hand. InfoSpect:\nUsing a Logic Language for System Health Monitoring in\nDistributed Systems. In Proceedings of the SIGOPS\nEuropean Workshop, 2002.\n[32] A. Rowstron and P. Druschel. Pastry: Scalable, Distributed\nObject Location and Routing for Large-scale Peer-to-peer\nSystems. In Middleware, 2001.\n[33] S.Ratnasamy, M.Handley, R.Karp, and S.Shenker.\nApplication-level Multicast using Content-addressable\nNetworks. In Proceedings of the NGC, November 2001.\n[34] W. Stallings. SNMP, SNMPv2, and CMIP. Addison-Wesley,\n1993.\n[35] I. Stoica, R. Morris, D. Karger, F. Kaashoek, and\nH. Balakrishnan. Chord: A scalable Peer-To-Peer lookup\nservice for internet applications. In ACM SIGCOMM, 2001.\n[36] S.Zhuang, B.Zhao, A.Joseph, R.Katz, and J.Kubiatowicz.\nBayeux: An Architecture for Scalable and Fault-tolerant\nWide-Area Data Dissemination. In NOSSDAV, 2001.\n[37] IBM Tivoli Monitoring.\nwww.ibm.com/software/tivoli/products/monitor.\n[38] R. VanRenesse, K. P. Birman, and W. Vogels. Astrolabe: A\nRobust and Scalable Technology for Distributed System\nMonitoring, Management, and Data Mining. TOCS, 2003.\n[39] R. VanRenesse and A. Bozdog. Willow: DHT, Aggregation,\nand Publish/Subscribe in One Protocol. In IPTPS, 2004.\n[40] A. Venkataramani, P. Weidmann, and M. Dahlin. Bandwidth\nconstrained placement in a wan. In PODC, Aug. 2001.\n[41] A. Venkataramani, P. Yalagandula, R. Kokku, S. Sharif, and\nM. Dahlin. Potential costs and benefits of long-term\nprefetching for content-distribution. Elsevier Computer\nCommunications, 25(4):367-375, Mar. 2002.\n[42] M. Wawrzoniak, L. Peterson, and T. Roscoe. Sophia: An\nInformation Plane for Networked Systems. In HotNets-II,\n2003.\n[43] R. Wolski, N. Spring, and J. Hayes. The network weather\nservice: A distributed resource performance forecasting\nservice for metacomputing. Journal of Future Generation\nComputing Systems, 15(5-6):757-768, Oct 1999.\n[44] P. Yalagandula and M. Dahlin. SDIMS: A scalable\ndistributed information management system. Technical\nReport TR-03-47, Dept. of Computer Sciences, UT Austin,\nSep 2003.\n[45] Z. Zhang, S.-M. Shi, and J. Zhu. SOMO: Self-Organized\nMetadata Overlay for Resource Management in P2P DHT. In\nIPTPS, 2003.\n[46] B. Y. Zhao, J. D. Kubiatowicz, and A. D. Joseph. Tapestry:\nAn Infrastructure for Fault-tolerant Wide-area Location and\nRouting. Technical Report UCB/CSD-01-1141, UC\nBerkeley, Apr. 2001.\n390", "keywords": "autonomous dht;temporal heterogeneity;administrative isolation;distribute hash table;lazy re-aggregation;write-dominated attribute;large-scale networked system;update-upk-downj strategy;information management system;freepastry framework;tunable spatial replication;distributed hash table;aggregation management layer;distributed operating system backbone;availability;read-dominated attribute;network system monitor;virtual node;networked system monitoring;eventual consistency"}
{"name": "train_C-61", "title": "Authority Assignment in Distributed Multi-Player Proxy-based Games", "abstract": "We present a proxy-based gaming architecture and authority assignment within this architecture that can lead to better game playing experience in Massively Multi-player Online games. The proposed game architecture consists of distributed game clients that connect to game proxies (referred to as communication proxies) which forward game related messages from the clients to one or more game servers. Unlike proxy-based architectures that have been proposed in the literature where the proxies replicate all of the game state, the communication proxies in the proposed architecture support clients that are in proximity to it in the physical network and maintain information about selected portions of the game space that are relevant only to the clients that they support. Using this architecture, we propose an authority assignment mechanism that divides the authority for deciding the outcome of different actions/events that occur within the game between client and servers on a per action/event basis. We show that such division of authority leads to a smoother game playing experience by implementing this mechanism in a massively multi-player online game called RPGQuest. In addition, we argue that cheat detection techniques can be easily implemented at the communication proxies if they are made aware of the game-play mechanics.", "fulltext": "1. INTRODUCTION\nIn Massively Multi-player On-line Games (MMOG), game\nclients who are positioned across the Internet connect to\na game server to interact with other clients in order to be\npart of the game. In current architectures, these\ninteractions are direct in that the game clients and the servers\nexchange game messages with each other. In addition, current\nMMOGs delegate all authority to the game server to make\ndecisions about the results pertaining to the actions that\ngame clients take and also to decide upon the result of other\ngame related events. Such centralized authority has been\nimplemented with the claim that this improves the security\nand consistency required in a gaming environment.\nA number of works have shown the effect of network latency\non distributed multi-player games [1, 2, 3, 4]. It has been\nshown that network latency has real impact on practical\ngame playing experience [3, 5]. Some types of games can\nfunction quite well even in the presence of large delays. For\nexample, [4] shows that in a modern RPG called Everquest\n2, the breakpoint of the game when adding artificial\nlatency was 1250ms. This is accounted to the fact that the\ncombat system used in Everquest 2 is queueing based and\nhas very low interaction. For example, a player queues up\n4 or 5 spells they wish to cast, each of these spells take 1-2\nseconds to actually perform, giving the server plenty of time\nto validate these actions. But there are other games such as\nFPS games that break even in the presence of moderate\nnetwork latencies [3, 5]. Latency compensation techniques have\nbeen proposed to alleviate the effect of latency [1, 6, 7] but\nit is obvious that if MMOGs are to increase in\ninteractivity and speed, more architectures will have to be developed\nthat address responsiveness, accuracy and consistency of the\ngamestate.\nIn this paper, we propose two important features that would\nmake game playing within MMOGs more responsive for\nmovement and scalable. First, we propose that centralized\nserver-based architectures be made hierarchical through the\nintroduction of communication proxies so that game updates\nmade by clients that are time sensitive, such as movement,\ncan be more efficiently distributed to other players within\ntheir game-space. Second, we propose that assignment of\nauthority in terms of who makes the decision on client\nactions such as object pickups and hits, and collisions between\nplayers, be distributed between the clients and the servers in\norder to distribute the computing load away from the central\nserver. In order to move towards more complex real-time\nnetworked games, we believe that definitions of authority\nmust be refined.\nMost currently implemented MMOGs have game servers\nthat have almost absolute authority. We argue that there is\nno single consistent view of the virtual game space that can\nbe maintained on any one component within a network that\nhas significant latency, such as the one that many MMOG\nplayers would experience. We believe that in most cases, the\nclient with the most accurate view of an entity is the best\nsuited to make decisions for that entity when the causality\nof that action will not immediately affect any other\nplayers. In this paper we define what it means to have authority\nwithin the context of events and objects in a virtual game\nspace. We then show the benefits of delegating authority\nfor different actions and game events between the clients\nand server.\nIn our model, the game space consists of game clients\n(representing the players) and objects that they control. We\ndivide the client actions and game events (we will\ncollectively refer to these as events) such as collisions, hits etc.\ninto three different categories, a) events for which the game\nclient has absolute authority, b) events for which the game\nserver has absolute authority, and c) events for which the\nauthority changes dynamically from client to the server and\nvice-versa. Depending on who has the authority, that\nentity will make decisions on the events that happen within a\ngame space. We propose that authority for all decisions that\npertain to a single player or object in the game that neither\naffects the other players or objects, nor are affected by the\nactions of other players be delegated to that player\"s game\nclient. These type of decisions would include collision\ndetection with static objects within the virtual game space and\nhit detection with linear path bullets (whose trajectory is\nfixed and does not change with time) fired by other players.\nAuthority for decisions that could be affected by two or more\nplayers should be delegated to the impartial central server,\nin some cases, to ensure that no conflicts occur and in other\ncases can be delegated to the clients responsible for those\nplayers. For example, collision detection of two players that\ncollide with each other and hit detection of non-linear\nbullets (that changes trajectory with time) should be delegated\nto the server. Decision on events such as item pickup (for\nexample, picking up items in a game to accumulate points)\nshould be delegated to a server if there are multiple\nplayers within close proximity of an item and any one of the\nplayers could succeed in picking the item; for item pick-up\ncontention where the client realizes that no other player,\nexcept its own player, is within a certain range of the item,\nthe client could be delegated the responsibility to claim the\nitem. The client\"s decision can always be accurately verified\nby the server.\nIn summary, we argue that while current authority models\nthat only delegate responsibility to the server to make\nauthoritative decisions on events is more secure than allowing\nthe clients to make the decisions, these types of models add\nundesirable delays to events that could very well be decided\nby the clients without any inconsistency being introduced\ninto the game. As networked games become more complex,\nour architecture will become more applicable. This\narchitecture is applicable for massively multiplayer games where\nthe speed and accuracy of game-play are a major concern\nwhile consistency between player game-states is still desired.\nWe propose that a mixed authority assignment mechanism\nsuch as the one outlined above be implemented in high\ninteraction MMOGs.\nOur paper has the following contributions. First we propose\nan architecture that uses communication proxies to enable\nclients to connect to the game server. A communication\nproxy in the proposed architecture maintains information\nonly about portions of the game space that are relevant to\nclients connected to it and is able to process the movement\ninformation of objects and players within these portions.\nIn addition, it is capable of multicasting this information\nonly to a relevant subset of other communication proxies.\nThese functionalities of a communication proxy leads to a\ndecrease in latency of event update and subsequently, better\ngame playing experience. Second, we propose a mixed\nauthority assignment mechanism as described above that\nimproves game playing experience. Third, we implement the\nproposed mixed authority assignment mechanism within a\nMMOG called RPGQuest [8] to validate its viability within\nMMOGs.\nIn Section 2, we describe the proxy-based game\narchitecture in more detail and illustrate its advantages. In\nSection 3, we provide a generic description of the mixed\nauthority assignment mechanism and discuss how it improves\ngame playing experience. In Section 4, we show the\nfeasibility of implementing the proposed mixed authority\nassignment mechanism within existing MMOGs by describing a\nproof-of-concept implementation within an existing MMOG\ncalled RPGQuest. Section 5 discusses related work. In\nSection 6, we present our conclusions and discuss future work.\n2. PROXY-BASED GAME ARCHITECTURE\nMassively Multi-player Online Games (MMOGs) usually\nconsist of a large game space in which the players and\ndifferent game objects reside and move around and interact with\neach-other. State information about the whole game space\ncould be kept in a single central server which we would\nrefer to as a Central-Server Architecture. But to alleviate\nthe heavy demand on the processing for handling the large\nplayer population and the objects in the game in real-time, a\nMMOG is normally implemented using a distributed server\narchitecture where the game space is further sub-divided\ninto regions so that each region has relatively smaller\nnumber of players and objects that can be handled by a single\nserver. In other words, the different game regions are hosted\nby different servers in a distributed fashion. When a player\nmoves out of one game region to another adjacent one, the\nplayer must communicate with a different server (than it was\ncurrently communicating with) hosting the new region. The\nservers communicate with one another to hand off a player\nor an object from one region to another. In this model, the\nplayer on the client machine has to establish multiple\ngaming sessions with different servers so that it can roam in the\nentire game space.\nWe propose a communication proxy based architecture where\na player connects to a (geographically) nearby proxy instead\nof connecting to a central server in the case of a\ncentralserver architecture or to one of the servers in case of\ndis2 The 5th Workshop on Network & System Support for Games 2006 - NETGAMES 2006\ntributed server architecture. In the proposed architecture,\nplayers who are close by geographically join a particular\nproxy. The proxy then connects to one or more game servers,\nas needed by the set of players that connect to it and\nmaintains persistent transport sessions with these server. This\nalleviates the problem of each player having to connect\ndirectly to multiple game servers, which can add extra\nconnection setup delay. Introduction of communication proxies\nalso mitigates the overhead of a large number of transport\nsessions that must be managed and reduces required network\nbandwidth [9] and processing at the game servers both with\ncentral server and distributed server architectures. With\ncentral server architectures, communication proxies reduce\nthe overhead at the server by not requiring the server to\nterminate persistent transport sessions from every one of the\nclients. With distributed-server architectures, additionally,\ncommunication proxies eliminate the need for the clients to\nmaintain persistent transport sessions to every one of the\nservers. Figure 1 shows the proposed architecture.\nFigure 1: Architecture of the gaming environment.\nNote that the communication proxies need not be cognizant\nof the game. They host a number of players and inform the\nservers which players are hosted by the proxy in question.\nAlso note that the players hosted by a proxy may not be in\nthe same game space. That is, a proxy hosts players that\nare geographically close to it, but the players themselves\ncan reside in different parts of the game space. The proxy\ncommunicates with the servers responsible for maintaining\nthe game spaces subscribed by the different players. The\nproxies communicate with one another in a peer-to-peer to\nfashion. The responsiveness of the game can be improved\nfor updates that do not need to wait on processing at a\ncentral authority. In this way, information about players can\nbe disseminated faster before even the game server gets to\nknow about it. This definitely improves the responsiveness\nof the game. However, it ignores consistency that is critical\nin MMORPGs. The notion that an architecture such as this\none can still maintain temporal consistency will be discussed\nin detail in Section 3.\nFigure 2 shows and example of the working principle of the\nproposed architecture. Assume that the game space is\ndivided into 9 regions and there are three servers responsible\nfor managing the regions. Server S1 owns regions 1 and 2,\nS2 manages 4, 5, 7, and 8, and S3 is responsible for 3, 6 and\n9.\nFigure 2: An example.\nThere are four communication proxies placed in\ngeographically distant locations. Players a, b, c join proxy P1, proxy P2\nhosts players d, e, f, players g, h are with proxy P3, whereas\nplayers i, j, k, l are with proxy P4. Underneath each player,\nthe figure shows which game region the player is located\ncurrently. For example, players a, b, c are in regions 1, 2, 6,\nrespectively. Therefore, proxy P1 must communicate with\nservers S1 and S3. The reader can verify the rest of the links\nbetween the proxies and the servers.\nPlayers can move within the region and between regions.\nPlayer movement within a region will be tracked by the\nproxy hosting the player and this movement information\n(for example, the player\"s new coordinates) will be\nmulticast to a subset of other relevant communication proxies\ndirectly. At the same time, this information will be sent\nto the server responsible for that region with the indication\nthat this movement has already been communicated to all\nthe other relevant communication proxies (so that the server\ndoes not have to relay this information to all the proxies).\nFor example, if player a moves within region 1, this\ninformation will be communicated by proxy P1 to server S1 and\nmulticast to proxies P3 and P4. Note that proxies that do\nnot keep state information about this region at this point\nin time (because they do not have any clients within that\nregion) such as P2 do not have to receive this movement\ninformation.\nIf a player is at the boundary of a region and moves into\na new region, there are two possibilities. The first\npossibility is that the proxy hosting the player can identify the\nregion into which the player is moving (based on the\ntrajectory information) because it is also maintaining state\ninformation about the new region at that point in time. In\nthis case, the proxy can update movement information\ndirectly at the other relevant communication proxies and also\nsend information to the appropriate server informing of the\nmovement (this may require handoff between servers as we\nwill describe). Consider the scenario where player a is at\nthe boundary of region 1 and proxy P1 can identify that the\nplayer is moving into region 2. Because proxy P1 is currently\nkeeping state information about region 2, it can inform all\nThe 5th Workshop on Network & System Support for Games 2006 - NETGAMES 2006 3\nthe other relevant communication proxies (in this example,\nno other proxy maintains information about region 2 at this\npoint and so no update needs to be sent to any of the other\nproxies) about this movement and then inform the server\nindependently. In this particular case, server S1 is responsible\nfor region 2 as well and so no handoff between servers would\nbe needed. Now consider another scenario where player j\nmoves from region 9 to region 8 and that proxy P4 is able\nto identify this movement. Again, because proxy P4\nmaintains state information about region 8, it can inform any\nother relevant communication proxies (again, none in this\nexample) about this movement. But now, regions 9 and 8\nare managed by different servers (servers S3 and S2\nrespectively) and thus a hand-off between these servers is needed.\nWe propose that in this particular scenario, the handoff be\nmanaged by the proxy P4 itself. When the proxy sends\nmovement update to server S3 (informing the server that\nthe player is moving out of its region), it would also send\na message to server S2 informing the server of the presence\nand location of the player in one of its region.\nIn the intra-region and inter-region scenarios described above,\nthe proxy is able to manage movement related information,\nupdate only the relevant communication proxies about the\nmovement, update the servers with the movement and\nenable handoff of a player between the servers if needed. In\nthis way, the proxy performs movement updates without\ninvolving the servers in any way in this time-critical function\nthereby speeding up the game and improving game\nplaying experience for the players. We consider this the fast\npath for movement update. We envision the proxies to be\njust communication proxies in that they do not know about\nthe workings of specific games. They merely process\nmovement information of players and objects and communicate\nthis information to the other proxies and the servers. If the\nproxies are made more intelligent in that they understand\nmore of the game logic, it is possible for them to quickly\ncheck on claims made by the clients and mitigate cheating.\nThe servers could perform the same functionality but with\nmore delay. Even without being aware of game logic, the\nproxies can provide additional functionalities such as\ntimestamping messages to make the game playing experience\nmore accurate [10] and fair [11].\nThe second possibility that should be considered is when\nplayers move between regions. It is possible that a player\nmoves from one region to another but the proxy that is\nhosting the player is not able to determine the region into\nwhich the player is moving, a) the proxy does not\nmaintain state information about all the regions into which the\nplayer could potentially move, or b) the proxy is not able\nto determine which region the player may move into (even if\nmaintains state information about all these regions). In this\ncase, we propose that the proxy be not responsible for\nmaking the movement decision, but instead communicate the\nmovement indication to the server responsible for the region\nwithin which the player is currently located. The server will\nthen make the movement decision and then a) inform all\nthe proxies including the proxy hosting the player, and b)\ninitiate handoff with another server if the player moves into\na region managed by another server. We consider this the\nslow path for movement update in that the servers need\nto be involved in determining the new position of the player.\nIn the example, assume that player a moves from region 1\nto region 4. Proxy P1 does not maintain state information\nabout region 4 and thus would pass the movement\ninformation to server S1. The server will identify that the player\nhas moved into region 4 and would inform proxy P1 as well\nas proxy P2 (which is the only other proxy that maintains\ninformation about region 4 at this point in time). Server S1\nwill also initiate a handoff of player a with server S2. Proxy\nP1 will now start maintaining state information about\nregion 4 because one of its hosted players, player a has moved\ninto this region. It will do so by requesting and receiving\nthe current state information about region 4 from server S2\nwhich is responsible for this region.\nThus, a proxy architecture allows us to make use of faster\nmovement updates through the fast path through a proxy if\nand when possible as opposed to conventional server-based\narchitectures that always have to use the slow path through\nthe server for movement updates. By selectively maintaining\nrelevant regional game state information at the proxies, we\nare able to achieve this capability in our architecture without\nthe need for maintaining the complete game state at every\nproxy.\n3. ASSIGNMENT OF AUTHORITY\nAs a MMOG is played, the players and the game objects that\nare part of the game, continually change their state. For\nexample, consider a player who owns a tank in a battlefield\ngame. Based on action of the player, the tank changes its\nposition in the game space, the amount of ammunition the\ntank contains changes as it fires at other tanks, the tank\ncollects bonus firing power based on successful hits, etc.\nSimilarly objects in the battlefield, such as flags, buildings etc.\nchange their state when a flag is picked up by a player (i.e.\ntank) or a building is destroyed by firing at it. That is,\nsome decision has to be made on the state of each player\nand object as the game progresses. Note that the state of\na player and/or object can contain several parameters (e.g.,\nposition, amount of ammunition, fuel storage, points\ncollected, etc), and if any of the parameters changes, the state\nof the player/object changes.\nIn a client-server based game, the server controls all the\nplayers and the objects. When a player at a client machine\nmakes a move, the move is transmitted to the server over\nthe network. The server then analyzes the move, and if\nthe move is a valid one, changes the state of the player at\nthe server and informs the client of the change. The client\nsubsequently updates the state of the player and renders\nthe player at the new location. In this case the authority to\nchange the state of the player resides with the server entirely\nand the client simply follows what the server instructs it to\ndo.\nMost of the current first person shooter (FPS) games and\nrole playing games (RPG) fall under this category. In\ncurrent FPS games, much like in RPG games, the client is not\ntrusted. All moves and actions that it makes are validated.\nIf a client detects that it has hit another player with a bullet,\nit proceeds assuming that it is a hit. Meanwhile, an update\nis sent to the server and the server will send back a message\neither affirming or denying that the player was hit. If the\nremote player was not hit, then the client will know that it\n4 The 5th Workshop on Network & System Support for Games 2006 - NETGAMES 2006\ndid not actually make the shot. If it did make the hit, an\nupdate will also be sent from the server to the other clients\ninforming them that the other player was hit. A difference\nthat occurs in some RPGs is that they use very dumb client\nprograms. Some RPGs do not maintain state information\nat the client and therefore, cannot predict anything such as\nhits at the client. State information is not maintained\nbecause the client is not trusted with it. In RPGs, a cheating\nplayer with a hacked game client can use state information\nstored at the client to gain an advantage and find things\nsuch as hidden treasure or monsters lurking around the\ncorner. This is a reason why most MMORPGs do not send a\nlot of state information to the client and causes the game\nto be less responsive and have lower interaction game-play\nthan FPS games.\nIn a peer-to-peer game, each peer controls the player and\nobject that it owns. When a player makes a move, the\npeer machine analyzes the move and if it is a valid one,\nchanges the state of the player and places the player in new\nposition. Afterwards, the owner peer informs all other peers\nabout the new state of the player and the rest of the peers\nupdate the state of the player. In this scenario, the authority\nto change the state of the player is given to the owning peer\nand all other peers simply follow the owner.\nFor example, Battle Zone Flag (BzFlag) [12] is a\nmultiplayer client-server game where the client has all authority\nfor making decisions. It was built primarily with LAN play\nin mind and cheating as an afterthought. Clients in BzFlag\nare completely authoritative and when they detect that they\nwere hit by a bullet, they send an update to the server which\nsimply forwards the message along to all other players. The\nserver does no sort of validation.\nEach of the above two traditional approaches has its own set\nof advantages and disadvantages. The first approach, which\nwe will refer to as server authoritative henceforth, uses a\ncentralized method to assign authority. While a centralized\napproach can keep the state of the game (i.e., state of all the\nplayers and objects) consistent across any number of client\nmachines, it suffers from delayed response in game-play as\nany move that a player at the client machine makes must go\nthrough one round-trip delay to the server before it can take\neffect on the client\"s screen. In addition to the round-trip\ndelay, there is also queuing delay in processing the state change\nrequest at the server. This can result in additional\nprocessing delay, and can also bring in severe scalability problems\nif there are large number of clients playing the game. One\ndefinite advantage of the server authoritative approach is\nthat it can easily detect if a client is cheating and can take\nappropriate action to prevent cheating.\nThe peer-to-peer approach, henceforth referred to as client\nauthoritative, can make games very responsive. However,\nit can make the game state inconsistent for a few players\nand tie break (or roll back) has to be performed to bring the\ngame back to a consistent state. Neither tie break nor roll\nback is a desirable feature of online gaming. For example,\nassume that for a game, the goal of each player is to collect\nas many flags as possible from the game space (e.g. BzFlag).\nWhen two players in proximity try to collect the same flag\nat the same time, depending on the algorithm used at the\nclient-side, both clients may determine that it is the winner,\nalthough in reality only one player can pick the flag up. Both\nplayers will see on their screen that it is the winner. This\nmakes the state of the game inconsistent. Ways to recover\nfrom this inconsistency are to give the flag to only one player\n(using some tie break rule) or roll the game back so that the\nplayers can try again. Neither of these two approaches is\na pleasing experience for online gaming. Another problem\nwith client authoritative approach is that of cheating by\nclients as there is no cross checking of the validation of the\nstate changes authorized by the owner client.\nWe propose to use a hybrid approach to assign the authority\ndynamically between the client and the server. That is, we\nassign the authority to the client to make the game\nresponsive, and use the server\"s authority only when the client\"s\nindividual authoritative decisions can make the game state\ninconsistent. By moving the authority of time critical\nupdates to the client, we avoid the added delay caused by\nrequiring the server to validate these updates. For example,\nin the flag pickup game, the clients will be given the\nauthority to pickup flags only when other players are not within\na range that they could imminently pickup a flag. Only\nwhen two or more players are close by so that more than\none player may claim to have picked up a flag, the authority\nfor movement and flag pickup would go to the central server\nso that the game state does not become inconsistent. We\nbelieve that in a large game-space where a player is often\nin a very wide open and sparsely populated area such as\nthose often seen in the game Second Life [13], this hybrid\narchitecture would be very beneficial because of the long\nperiods that the client would have authority to send movement\nupdates for itself. This has two advantages over the\ncentralauthority approach, it distributes the processing load down\nto the clients for the majority of events and it allows for a\nmore responsive game that does not need to wait on a server\nfor validation.\nWe believe that our notion of authority can be used to\ndevelop a globally consistent state model of the evolution of\na game. Fundamentally, the consistent state of the system\nis the one that is defined by the server. However, if local\nauthority is delegated to the client, in this case, the client\"s\nstate is superimposed on the server\"s state to determine the\ncorrect global state. For example, if the client is\nauthoritative with respect to movement of a player, then the\ntrajectory of the player is the true trajectory and must\nreplace the server\"s view of the player\"s trajectory. Note that\nthis could be problematic and lead to temporal\ninconsistency only if, for example, two or more entities are moving\nin the same region and can interact with each other. In\nthis situation, the client authority must revert to the server\nand the sever would then make decisions. Thus, the client\nis only authoritative in situations where there is no\npotential to imminently interact with other players. We believe\nthat in complex MMOGs, when allowing more rapid\nmovement, it will still be the case that local authority is possible\nfor significant spans of game time. Note that it might also\nbe possible to minimize the occurrences of the Dead Man\nShooting problem described in [14]. This could be done by\nallowing the client to be authoritative for more actions such\nas its player\"s own death and disallowing other players from\nmaking preemptive decisions based on a remote player.\nThe 5th Workshop on Network & System Support for Games 2006 - NETGAMES 2006 5\nOne reason why the client-server based architecture has gained\npopularity is due to belief that the fastest route to the other\nclients is through the server. While this may be true, we aim\nto create a new architecture where decisions do not always\nhave to be made at the game server and the fastest route to\na client is actually through a communication proxy located\nclose to the client. That is, the shortest distance in our\narchitecture is not through the game server but through the\ncommunication proxy. After a client makes an action such\nas movement, it will simultaneously distribute it directly to\nthe clients and the game server by way of the\ncommunications proxy. We note that our architecture however is not\npractical for a game where game players setup their own\nservers in an ad-hoc fashion and do not have access to\nproxies at the various ISPs. This proxy and distributed authority\narchitecture can be used to its full potential only when the\nproxies can be placed at strategic places within the main\nISPs and evenly distributed geographically.\nOur game architecture does not assume that the client is\nnot to be trusted. We are designing our architecture on the\nfact that there will be sufficient cheat deterring and\ndetection mechanisms present so that it will be both undesirable\nand very difficult to cheat [15]. In our proposed approach,\nwe can make the games cheat resilient by using the\nproxybased architecture when client authoritative decisions take\nplace. In order to achieve this, the proxies have to be game\ncognizant so that decisions made by a client can be cross\nchecked by a proxy that the client connects to. For\nexample, assume that in a game a plane controlled by a client\nmoves in the game space. It is not possible for the plane to\ngo through a building unharmed. In a client authoritative\nmode, it is possible for the client to cheat by maneuvering\nthe plane through a building and claiming the plane to be\nunharmed. However, when such move is published by the\nclient, the proxy, being aware of the game space that the\nplane is in, can quickly check that the client has misused\nthe authority and then can block such move. This allows us\nto distribute authority to make decisions about the clients.\nIn the following section we use a multiplayer game called\nRPGQuest to implement different authoritative schemes and\ndiscuss our experience with the implementation. Our\nimplementation shows the viability of our proposed solution.\n4. IMPLEMENTATION EXPERIENCE\nWe have experimented with the authority assignment\nmechanism described in the last section by implementing the\nmechanisms in a game called RPGQuest. A screen shot from\nthis game is shown in Figure 3. The purpose of the\nimplementation is to test its feasibility in a real game. RPGQuest\nis a basic first person game where the player can move\naround a three dimensional environment. Objects are placed\nwithin the game world and players gain points for each\nobject that is collected. The game clients connect to a game\nserver which allows many players to coexist in the same\ngame world. The basic functionality of this game is\nrepresentative of current online first person shooter and role playing\ngames. The game uses the DirectX 8 graphics API and\nDirectPlay networking API. In this section we will discuss the\nthree different versions of the game that we experimented\nwith.\nFigure 3: The RPGQuest Game.\nThe first version of the game, which is the original\nimplementation of RPGQuest, was created with a completely\nauthoritative server and a non-authoritative client. Authority\ngiven to the server includes decisions of when a player\ncollides with static objects and other players and when a player\npicks up an object. This version of the game performs well\nup to 100ms round-trip latency between the client and the\nserver. There is little lag between the time player hits a\nwall and the time the server corrects the player\"s position.\nHowever, as more latency is induced between the client and\nserver, the game becomes increasingly difficult to play. With\nthe increased latency, the messages coming from the server\ncorrecting the player when it runs into a wall are not\nreceived fast enough. This causes the player to pass through\nthe wall for the period that it is waiting for the server to\nresolve the collision.\nWhen studying the source code of the original version of\nthe RPGQuest game, there is a substantial delay that is\nunavoidable each time an action must be validated by the\nserver. Whenever a movement update is sent to the server,\nthe client must then wait whatever the round trip delay is,\nplus some processing time at the server in order to receive\nits validated or corrected position. This is obviously\nunacceptable in any game where movement or any other rapidly\nchanging state information must be validated and\ndisseminated to the other clients rapidly.\nIn order to get around this problem, we developed a second\nversion of the game, which gives all authority to the client.\nThe client was delegated the authority to validate its own\nmovement and the authority to pick up objects without\nvalidation from the server. In this version of the game when\na player moves around the game space, the client validates\nthat the player\"s new position does not intersect with any\nwalls or static objects. A position update is then sent to the\nserver which then immediately forwards the update to the\nother clients within the region. The update does not have\nto go through any extra processing or validation.\nThis game model of complete authority given to the client\nis beneficial with respect to movement. When latencies of\n6 The 5th Workshop on Network & System Support for Games 2006 - NETGAMES 2006\n100ms and up are induced into the link between the client\nand server, the game is still playable since time critical\naspects of the game like movement do not have to wait on a\nreply from the server. When a player hits a wall, the\ncollision is processed locally and does not have to wait on the\nserver to resolve the collision.\nAlthough game playing experience with respect to\nresponsiveness is improved when the authority for movement is\ngiven to the client, there are still aspects of games that do\nnot benefit from this approach. The most important of these\nis consistency. Although actions such as movement are time\ncritical, other actions are not as time critical, but instead\nrequire consistency among the player states. An example of\na game aspect that requires consistency is picking up objects\nthat should only be possessed by a single player.\nIn our client authoritative version of RPGQuest clients send\ntheir own updates to all other players whenever they pick up\nan object. From our tests we have realized this is a problem\nbecause when there is a realistic amount of latency between\nthe client and server, it is possible for two players to pick\nup the same object at the same time. When two players\nattempt to pick up an object at physical times which are\nclose to each other, the update sent by the player who picked\nup the object first will not reach the second player in time\nfor it to see that the object has already been claimed. The\ntwo players will now both think that they own the object.\nThis is why a server is still needed to be authoritative in this\nsituation and maintain consistency throughout the players.\nThese two versions of the RPGQuest game has showed us\nwhy it is necessary to mix the two absolute models of\nauthority. It is better to place authority on the client for quickly\nchanging actions such as movement. It is not desirable to\nhave to wait for server validation on a movement that could\nchange before the reply is even received. It is also sometimes\nnecessary to place consistency over efficiency in aspects of\nthe game that cannot tolerate any inconsistencies such as\nobject ownership. We believe that as the interactivity of\ngames increases, our architecture of mixed authority that\ndoes not rely on server validation will be necessary.\nTo test the benefits and show the feasibility of our\narchitecture of mixed authority, we developed a third version of\nthe RPGQuest game that distributed authority for\ndifferent actions between the client and server. In this version,\nin the interest of consistency, the server remained\nauthoritative for deciding who picked up an object. The client\nwas given full authority to send positional updates to other\nclients and verify its own position without the need to\nverify its updates with the server. When the player tries to\nmove their avatar, the client verifies that the move will not\ncause it to move through a wall. A positional update is then\nsent to the server which then simply forwards it to the other\nclients within the region. This eliminates any extra\nprocessing delay that would occur at the server and is also a more\naccurate means of verification since the client has a more\naccurate view of its own state than the server.\nThis version of the RPGQuest game where authority is\ndistributed between the client and server is an improvement\nfrom the server authoritative version. The client has no\ndelay in waiting for an update for its own position and other\nclients do not have to wait on the server to verify the update.\nThe inconsistencies where two clients can pick up the same\nobject in the client authoritative architecture are not present\nin this version of the client. However, the benefits of mixed\nauthority will not truly be seen until an implementation of\nour communication proxy is integrated into the game. With\nthe addition of the communication proxy, after the client\nverifies its own positional updates it will be able to send the\nupdate to all clients within its region through a low latency\nlink instead of having to first go through the game server\nwhich could possibly be in a very remote location.\nThe coding of the different versions of the game was very\nsimple. The complexity of the client increased very slightly\nin the client authoritative and hybrid models. The\noriginal dumb clients of RPGQuest know the position of other\nplayers; it is not just sent a screen snapshot from the server.\nThe server updates each client with the position of all nearby\nclients. The dumb clients use client side prediction to fill\nin the gaps between the updates they receive. The only\nextra processing the client has to do in the hybrid architecture\nis to compare its current position to the positions of all\nobjects (walls, boxes, etc.) in its area. This obviously means\nthat each client will have to already have downloaded the\nlocations of all static objects within its current region.\n5. RELATED WORK\nIt has been noted that in addition to latency, bandwidth\nrequirements also dictate the type of gaming architecture to\nbe used. In [16], different types of architectures are\nstudied with respect to bandwidth efficiencies and latency. It is\npointed out that Central Server architectures are not\nscalable because of bandwidth requirements at the server but\nthe overhead for consistency checks are limited as they are\nperformed at the server. A Peer-to-Peer architecture, on the\nother hand, is scalable but there is a significant overhead\nfor consistency checks as this is required at every player.\nThe paper proposes a hybrid architecture which is\nPeer-toPeer in terms of message exchange (and thereby is scalable)\nwhere a Central Server is used for off-line consistency checks\n(thereby mitigating consistency check overhead). The paper\nprovides an implementation example of BZFlag which is a\npeer-to-peer game which is modified to transfer all\nauthority to a central server. In essence, this paper advocates an\nauthority architecture which is server based even for\npeerto-peer games, but does not consider division of authority\nbetween a client and a server to minimize latency which\ncould affect game playing experience even with the type of\nlatency found in server based games (where all authority is\nwith the server).\nThere is also previous work that has suggested that proxy\nbased architectures be used to alleviate the latency\nproblem and in addition use proxies to provide congestion\ncontrol and cheat-proof mechanisms in distributed multi-player\ngames [17]. In [18], a proxy server-network architecture is\npresented that is aimed at improving scalability of\nmultiplayer games and lowering latency in server-client data\ntransmission. The main goal of this work is to improve scalability\nof First-Person Shooter (FPS) and RPG games. The further\nobjective is to improve the responsiveness MMOGs by\nproviding low latency communications between the client and\nThe 5th Workshop on Network & System Support for Games 2006 - NETGAMES 2006 7\nserver. The architecture uses interconnected proxy servers\nthat each have a full view of the global game state. Proxy\nservers are located at various different ISPs. It is mentioned\nin this work that dividing the game space among multiple\ngames servers such as the federated model presented in [19]\nis inefficient for a relatively fast game flow and that the\nproposed architecture alleviates this problem because users\ndo not have to connect to a different server whenever they\ncross the server boundary. This architecture still requires all\nproxies to be aware of the overall game state over the whole\ngame space unlike our work where we require the proxies\nto maintain only partial state information about the game\nspace.\nFidelity based agent architectures have been proposed in [20,\n21]. These works propose a distributed client-server\narchitecture for distributed interactive simulations where\ndifferent servers are responsible for different portions of the game\nspace. When an object moves from one portion to another,\nthere is a handoff from one server to another. Although\nthese works propose an architecture where different portions\nof the simulation space are managed by different servers,\nthey do not address the issue of decreasing the bandwidth\nrequired through the use of communication proxies.\nOur work differs from the above discussed previous works by\nproposing a) a distributed proxy-based architecture to\ndecrease bandwidth requirements at the clients and the servers\nwithout requiring the proxies to keep state information about\nthe whole game space, b) a dynamic authority assignment\ntechnique to reduce latency (by performing consistency checks\nlocally at the client whenever possible) by splitting the\nauthority between the clients and servers on a per object basis,\nand c) proposing that cheat detection can be built into the\nproxies if they are provided more information about the\nspecific game instead of using them purely as communication\nproxies (although this idea has not been implemented yet\nand is part of our future work).\n6. CONCLUSIONS AND FUTURE WORK\nIn this paper, we first proposed a proxy-based\narchitecture for MMOGs that enables MMOGs to scale to a large\nnumber of users by mitigating the need for a large\nnumber of transport sessions to be maintained and decreasing\nboth bandwidth overhead and latency of event update.\nSecond, we proposed a mixed authority assignment mechanism\nthat divides authority for making decisions on actions and\nevents within the game between the clients and server and\nargued how such an authority assignment leads to better\ngame playing experience without sacrificing the consistency\nof the game. Third, to validate the viability of the mixed\nauthority assignment mechanism, we implemented it within\na MMOG called RPGQuest and described our\nimplementation experience.\nIn future work, we propose to implement the\ncommunications proxy architecture described in this paper and\nintegrate the mixed authority mechanism within this\narchitecture. We propose to evaluate the benefits of the proxy-based\narchitecture in terms of scalability, accuracy and\nresponsiveness. We also plan to implement a version of the RPGQuest\ngame with dynamic assignment of authority to allow players\nthe authority to pickup objects when no other players are\nnear. As discussed earlier, this will allow for a more efficient\nand responsive game in certain situations and alleviate some\nof the processing load from the server.\nAlso, since so much trust is put into the clients of our\narchitecture, it will be necessary to integrate into the\narchitecture many of the cheat detection schemes that have been\nproposed in the literature. Software such as Punkbuster [22]\nand a reputation system like those proposed by [23] and [15]\nwould be integral to the operation of an architecture such as\nours which has a lot of trust placed on the client. We further\npropose to make the proxies in our architecture more game\ncognizant so that cheat detection mechanisms can be built\ninto the proxies themselves.\n7. REFERENCES\n[1] Y. W. Bernier. Latency Compensation Methods in\nClient/Server In-game Protocol Design and\nOptimization. In Proc. of Game Developers\nConference\"01, 2001.\n[2] Lothar Pantel and Lars C. Wolf. On the impact of\ndelay on real-time multiplayer games. In NOSSDAV\n\"02: Proceedings of the 12th international workshop on\nNetwork and operating systems support for digital\naudio and video, pages 23-29, New York, NY, USA,\n2002. ACM Press.\n[3] G. Armitage. Sensitivity of Quake3 Players to Network\nLatency. In Proc. of IMW2001, Workshop Poster\nSession, November 2001. http://www.geocities.com/\ngj armitage/q3/quake-results.html.\n[4] Tobias Fritsch, Hartmut Ritter, and Jochen Schiller.\nThe effect of latency and network limitations on\nmmorpgs: a field study of everquest2. In NetGames\n\"05: Proceedings of 4th ACM SIGCOMM workshop on\nNetwork and system support for games, pages 1-9,\nNew York, NY, USA, 2005. ACM Press.\n[5] Tom Beigbeder, Rory Coughlan, Corey Lusher, John\nPlunkett, Emmanuel Agu, and Mark Claypool. The\neffects of loss and latency on user performance in\nunreal tournament 2003. In NetGames \"04:\nProceedings of 3rd ACM SIGCOMM workshop on\nNetwork and system support for games, pages\n144-151, New York, NY, USA, 2004. ACM Press.\n[6] Y. Lin, K. Guo, and S. Paul. Sync-MS: Synchronized\nMessaging Service for Real-Time Multi-Player\nDistributed Games. In Proc. of 10th IEEE\nInternational Conference on Network Protocols\n(ICNP), Nov 2002.\n[7] Katherine Guo, Sarit Mukherjee, Sampath\nRangarajan, and Sanjoy Paul. A fair message\nexchange framework for distributed multi-player\ngames. In NetGames \"03: Proceedings of the 2nd\nworkshop on Network and system support for games,\npages 29-41, New York, NY, USA, 2003. ACM Press.\n[8] T. Barron. Multiplayer Game Programming, chapter\n16-17, pages 672-731. Prima Tech\"s Game\nDevelopment Series. Prima Publishing, 2001.\n8 The 5th Workshop on Network & System Support for Games 2006 - NETGAMES 2006\n[9] Carsten Griwodz and P\u02daal Halvorsen. The fun of using\ntcp for an mmorpg. In NOSSDAV \"06: Proceedings of\nthe International Workshop on Network and Operating\nSystems Support for Digital Audio and VIdeo, New\nYork, NY, USA, 2006. ACM Press.\n[10] Sudhir Aggarwal, Hemant Banavar, Amit Khandelwal,\nSarit Mukherjee, and Sampath Rangarajan. Accuracy\nin dead-reckoning based distributed multi-player\ngames. In NetGames \"04: Proceedings of 3rd ACM\nSIGCOMM workshop on Network and system support\nfor games, pages 161-165, New York, NY, USA, 2004.\nACM Press.\n[11] Sudhir Aggarwal, Hemant Banavar, Sarit Mukherjee,\nand Sampath Rangarajan. Fairness in dead-reckoning\nbased distributed multi-player games. In NetGames\n\"05: Proceedings of 4th ACM SIGCOMM workshop on\nNetwork and system support for games, pages 1-10,\nNew York, NY, USA, 2005. ACM Press.\n[12] Riker, T. et al. Bzflag. http://www.bzflag.org,\n2000-2006.\n[13] Linden Lab. Second life. http://secondlife.com,\n2003.\n[14] Martin Mauve. How to keep a dead man from\nshooting. In IDMS \"00: Proceedings of the 7th\nInternational Workshop on Interactive Distributed\nMultimedia Systems and Telecommunication Services,\npages 199-204, London, UK, 2000. Springer-Verlag.\n[15] Max Skibinsky. Massively Multiplayer Game\nDevelopment 2, chapter The Quest for Holy\nScalePart 2: P2P Continuum, pages 355-373. Charles River\nMedia, 2005.\n[16] Joseph D. Pellegrino and Constantinos Dovrolis.\nBandwidth requirement and state consistency in three\nmultiplayer game architectures. In NetGames \"03:\nProceedings of the 2nd workshop on Network and\nsystem support for games, pages 52-59, New York,\nNY, USA, 2003. ACM Press.\n[17] M. Mauve J. Widmer and S. Fischer. A Generic Proxy\nSystems for Networked Computer Games. In Proc. of\nthe Workshop on Network Games, Netgames 2002,\nApril 2002.\n[18] S. Gorlatch J. Muller, S. Fischer and M.Mauve. A\nProxy Server Network Architecture for Real-Time\nComputer Games. In Euor-Par 2004 Parallel\nProcessing: 10th International EURO-PAR\nConference, August-September 2004.\n[19] H. Hazeyama T. Limura and Y. Kadobayashi. Zoned\nFederation of Game Servers: A Peer-to-Peer Approach\nto Scalable Multiplayer On-line Games. In Proc. of\nACM Workshop on Network Games, Netgames 2004,\nAugust-September 2004.\n[20] B. Kelly and S. Aggarwal. A Framework for a Fidelity\nBased Agent Architecture for Distributed Interactive\nSimulation. In Proc. 14th Workshop on Standards for\nDistributed Interactive Simulation, pages 541-546,\nMarch 1996.\n[21] S. Aggarwal and B. Kelly. Hierarchical Structuring for\nDistributed Interactive Simulation. In Proc. 13th\nWorkshop on Standards for Distributed Interactive\nSimulation, pages 125-132, Sept 1995.\n[22] Even Balance, Inc. Punkbuster.\nhttp://www.evenbalance.com/, 2001-2006.\n[23] Y. Wang and J. Vassileva. Trust and Reputation\nModel in Peer-to-Peer Networks. In Third\nInternational Conference on Peer-to-Peer Computing,\n2003.\nThe 5th Workshop on Network & System Support for Games 2006 - NETGAMES 2006 9", "keywords": "cheat-proof mechanism;latency compensation;role playing game;artificial latency;mmog;central-server architecture;assignment of authority;authority;proxy-based game architecture;first person shooter;communication proxy;distribute multi-player game;client authoritative approach;authority assignment;multi-player online game"}
{"name": "train_C-62", "title": "Network Monitors and Contracting Systems: Competition and Innovation", "abstract": "Today\"s Internet industry suffers from several well-known pathologies, but none is as destructive in the long term as its resistance to evolution. Rather than introducing new services, ISPs are presently moving towards greater commoditization. It is apparent that the network\"s primitive system of contracts does not align incentives properly. In this study, we identify the network\"s lack of accountability as a fundamental obstacle to correcting this problem: Employing an economic model, we argue that optimal routes and innovation are impossible unless new monitoring capability is introduced and incorporated with the contracting system. Furthermore, we derive the minimum requirements a monitoring system must meet to support first-best routing and innovation characteristics. Our work does not constitute a new protocol; rather, we provide practical and specific guidance for the design of monitoring systems, as well as a theoretical framework to explore the factors that influence innovation.", "fulltext": "1. INTRODUCTION\nMany studies before us have noted the Internet\"s resistance to new\nservices and evolution. In recent decades, numerous ideas have\nbeen developed in universities, implemented in code, and even\nwritten into the routers and end systems of the network, only to\nlanguish as network operators fail to turn them on on a large scale.\nThe list includes Multicast, IPv6, IntServ, and DiffServ. Lacking\nthe incentives just to activate services, there seems to be little hope\nof ISPs devoting adequate resources to developing new ideas. In the\nlong term, this pathology stands out as a critical obstacle to the\nnetwork\"s continued success (Ratnasamy, Shenker, and McCanne\nprovide extensive discussion in [11]).\nOn a smaller time scale, ISPs shun new services in favor of cost\ncutting measures. Thus, the network has characteristics of a\ncommodity market. Although in theory, ISPs have a plethora of\nrouting policies at their disposal, the prevailing strategy is to route in\nthe cheapest way possible [2]. On one hand, this leads directly to\nsuboptimal routing. More importantly, commoditization in the short\nterm is surely related to the lack of innovation in the long term.\nWhen the routing decisions of others ignore quality characteristics,\nISPs are motivated only to lower costs. There is simply no reward\nfor introducing new services or investing in quality improvements.\nIn response to these pathologies and others, researchers have put\nforth various proposals for improving the situation. These can be\ndivided according to three high-level strategies: The first attempts\nto improve the status quo by empowering end-users. Clark, et al.,\nsuggest that giving end-users control over routing would lead to\ngreater service diversity, recognizing that some payment mechanism\nmust also be provided [5]. Ratnasamy, Shenker, and McCanne\npostulate a link between network evolution and user-directed\nrouting [11]. They propose a system of Anycast to give end-users\nthe ability to tunnel their packets to an ISP that introduces a\ndesirable protocol. The extra traffic to the ISP, the authors suggest,\nwill motivate the initial investment.\nThe second strategy suggests a revision of the contracting system.\nThis is exemplified by MacKie-Mason and Varian, who propose a\nsmart market to control access to network resources [10]. Prices\nare set to the market-clearing level based on bids that users associate\nto their traffic. In another direction, Afergan and Wroclawski\nsuggest that prices should be explicitly encoded in the routing\nprotocols [2]. They argue that such a move would improve stability\nand align incentives.\nThe third high-level strategy calls for greater network\naccountability. In this vein, Argyraki, et al., propose a system of\npacket obituaries to provide feedback as to which ISPs drop packets\n[3]. They argue that such feedback would help reveal which ISPs\nwere adequately meeting their contractual obligations. Unlike the\nfirst two strategies, we are not aware of any previous studies that\nhave connected accountability with the pathologies of\ncommoditization or lack of innovation.\nIt is clear that these three strategies are closely linked to each other\n(for example, [2], [5], and [9] each argue that giving end-users\nrouting control within the current contracting system is\nproblematic). Until today, however, the relationship between them\nhas been poorly understood. There is currently little theoretical\nfoundation to compare the relative merits of each proposal, and a\nparticular lack of evidence linking accountability with innovation\nand service differentiation. This paper will address both issues.\nWe will begin by introducing an economic network model that\nrelates accountability, contracts, competition, and innovation. Our\nmodel is highly stylized and may be considered preliminary: it is\nbased on a single source sending data to a single destination.\nNevertheless, the structure is rich enough to expose previously\nunseen features of network behavior. We will use our model for\ntwo main purposes:\nFirst, we will use our model to argue that the lack of accountability\nin today\"s network is a fundamental obstacle to overcoming the\npathologies of commoditization and lack of innovation. In other\nwords, unless new monitoring capabilities are introduced, and\nintegrated with the system of contracts, the network cannot achieve\noptimal routing and innovation characteristics. This result provides\nmotivation for the remainder of the paper, in which we explore how\naccountability can be leveraged to overcome these pathologies and\ncreate a sustainable industry. We will approach this problem from a\nclean-slate perspective, deriving the level of accountability needed\nto sustain an ideal competitive structure.\nWhen we say that today\"s Internet has poor accountability, we mean\nthat it reveals little information about the behavior - or misbehavior\n- of ISPs. This well-known trait is largely rooted in the network\"s\nhistory. In describing the design philosophy behind the Internet\nprotocols, Clark lists accountability as the least important among\nseven second level goals. [4] Accordingly, accountability\nreceived little attention during the network\"s formative years. Clark\nrelates this to the network\"s military context, and finds that had the\nnetwork been designed for commercial development, accountability\nwould have been a top priority.\nArgyraki, et al., conjecture that applying the principles of layering\nand transparency may have led to the network\"s lack of\naccountability [3]. According to these principles, end hosts should\nbe informed of network problems only to the extent that they are\nrequired to adapt. They notice when packet drops occur so that they\ncan perform congestion control and retransmit packets. Details of\nwhere and why drops occur are deliberately concealed.\nThe network\"s lack of accountability is highly relevant to a\ndiscussion of innovation because it constrains the system of\ncontracts. This is because contracts depend upon external\ninstitutions to function - the judge in the language of incomplete\ncontract theory, or simply the legal system. Ultimately, if a judge\ncannot verify that some condition holds, she cannot enforce a\ncontract based on that condition. Of course, the vast majority of\ncontracts never end up in court. Especially when a judge\"s ruling is\neasily predicted, the parties will typically comply with the contract\nterms on their own volition. This would not be possible, however,\nwithout the judge acting as a last resort.\nAn institution to support contracts is typically complex, but we\nabstract it as follows: We imagine that a contract is an algorithm\nthat outputs a payment transfer among a set of ISPs (the parties) at\nevery time. This payment is a function of the past and present\nbehaviors of the participants, but only those that are verifiable.\nHence, we imagine that a contract only accepts proofs as inputs.\nWe will call any process that generates these proofs a contractible\nmonitor. Such a monitor includes metering or sensing devices on\nthe physical network, but it is a more general concept. Constructing\na proof of a particular behavior may require readings from various\ndevices distributed among many ISPs. The contractible monitor\nincludes whatever distributed algorithmic mechanism is used to\nmotivate ISPs to share this private information.\nFigure 1 demonstrates how our model of contracts fits together. We\nmake the assumption that all payments are mediated by contracts.\nThis means that without contractible monitors that attest to, say,\nlatency, payments cannot be conditioned on latency.\nFigure 1: Relationship between monitors and contracts\nWith this model, we may conclude that the level of accountability in\ntoday\"s Internet only permits best effort contracts. Nodes cannot\ncondition payments on either quality or path characteristics.\nIs there anything wrong with best-effort contracts? The reader\nmight wonder why the Internet needs contracts at all. After all, in\nnon-network industries, traditional firms invest in research and\ndifferentiate their products, all in the hopes of keeping their\ncustomers and securing new ones. One might believe that such\nmarket forces apply to ISPs as well. We may adopt this as our null\nhypothesis:\nNull hypothesis: Market forces are sufficient to maintain service\ndiversity and innovation on a network, at least to the same extent\nas they do in traditional markets.\nThere is a popular intuitive argument that supports this hypothesis,\nand it may be summarized as follows:\nIntuitive argument supporting null hypothesis:\n1. Access providers try to increase their quality to get more\nconsumers.\n2. Access providers are themselves customers for second hop\nISPs, and the second hops will therefore try to provide\nhighquality service in order to secure traffic from access\nproviders. Access providers try to select high quality transit\nbecause that increases their quality.\n3. The process continues through the network, giving every\nISP a competitive reason to increase quality.\nWe are careful to model our network in continuous time, in order to\ncapture the essence of this argument. We can, for example, specify\nequilibria in which nodes switch to a new next hop in the event of a\nquality drop.\nMoreover, our model allows us to explore any theoretically possible\npunishments against cheaters, including those that are costly for\nend-users to administer. By contrast, customers in the real world\nrarely respond collectively, and often simply seek the best deal\ncurrently offered. These constraints limit their ability to punish\ncheaters.\nEven with these liberal assumptions, however, we find that we must\nreject our null hypothesis. Our model will demonstrate that\nidentifying a cheating ISP is difficult under low accountability,\nlimiting the threat of market driven punishment. We will define an\nindex of commoditization and show that it increases without bound\nas data paths grow long. Furthermore, we will demonstrate a\nframework in which an ISP\"s maximum research investment\ndecreases hyperbolically with its distance from the end-user.\nNetwork\nBehavior\nMonitor Contract\nProof\nPayments\n184\nTo summarize, we argue that the Internet\"s lack of accountability\nmust be addressed before the pathologies of commoditization and\nlack of innovation can be resolved. This leads us to our next topic:\nHow can we leverage accountability to overcome these pathologies?\nWe approach this question from a clean-slate perspective. Instead\nof focusing on incremental improvements, we try to imagine how an\nideal industry would behave, then derive the level of accountability\nneeded to meet that objective. According to this approach, we first\ncraft a new equilibrium concept appropriate for network\ncompetition. Our concept includes the following requirements:\nFirst, we require that punishing ISPs that cheat is done without\nrerouting the path. Rerouting is likely to prompt end-users to switch\nproviders, punishing access providers who administer punishments\ncorrectly. Next, we require that the equilibrium cannot be\nthreatened by a coalition of ISPs that exchanges illicit side\npayments. Finally, we require that the punishment mechanism that\nenforces contracts does not punish innocent nodes that are not in the\ncoalition.\nThe last requirement is somewhat unconventional from an economic\nperspective, but we maintain that it is crucial for any reasonable\nsolution. Although ISPs provide complementary services when they\nform a data path together, they are likely to be horizontal\ncompetitors as well. If innocent nodes may be punished, an ISP\nmay decide to deliberately cheat and draw punishment onto itself\nand its neighbors. By cheating, the ISP may save resources, thereby\nensuring that the punishment is more damaging to the other ISPs,\nwhich probably compete with the cheater directly for some\ncustomers. In the extreme case, the cheater may force the other\nISPs out of business, thereby gaining a monopoly on some routes.\nApplying this equilibrium concept, we derive the monitors needed\nto maintain innovation and optimize routes. The solution is\nsurprisingly simple: contractible monitors must report the quality of\nthe rest of the path, from each ISP to the destination. It turns out\nthat this is the correct minimum accountability requirement, as\nopposed to either end-to-end monitors or hop-by-hop monitors, as\none might initially suspect.\nRest of path monitors can be implemented in various ways. They\nmay be purely local algorithms that listen for packet echoes.\nAlternately, they can be distributed in nature. We describe a way to\nconstruct a rest of path monitor out of monitors for individual ISP\nquality and for the data path. This requires a mechanism to\nmotivate ISPs to share their monitor outputs with each other. The\nrest of path monitor then includes the component monitors and the\ndistributed algorithmic mechanism that ensures that information is\nshared as required. This example shows that other types of monitors\nmay be useful as building blocks, but must be combined to form rest\nof path monitors in order to achieve ideal innovation characteristics.\nOur study has several practical implications for future protocol\ndesign. We show that new monitors must be implemented and\nintegrated with the contracting system before the pathologies of\ncommoditization and lack of innovation can be overcome.\nMoreover, we derive exactly what monitors are needed to optimize\nroutes and support innovation. In addition, our results provide\nuseful input for clean-slate architectural design, and we use several\nnovel techniques that we expect will be applicable to a variety of\nfuture research.\nThe rest of this paper is organized as follows: In section 2, we lay\nout our basic network model. In section 3, we present a\nlowaccountability network, modeled after today\"s Internet. We\ndemonstrate how poor monitoring causes commoditization and a\nlack of innovation. In section 4, we present verifiable monitors, and\nshow that proofs, even without contracts, can improve the status\nquo. In section 5, we turn our attention to contractible monitors.\nWe show that rest of path monitors can support competition games\nwith optimal routing and innovation. We further show that rest of\npath monitors are required to support such competition games. We\ncontinue by discussing how such monitors may be constructed using\nother monitors as building blocks. In section 6, we conclude and\npresent several directions for future research.\n2. BASIC NETWORK MODEL\nA source, S, wants to send data to destination, D. S and D are nodes\non a directed, acyclic graph, with a finite set of intermediate nodes,\n{ }NV ,...2,1= , representing ISPs. All paths lead to D, and every\nnode not connected to D has at least two choices for next hop.\nWe will represent quality by a finite dimensional vector space, Q,\ncalled the quality space. Each dimension represents a distinct\nnetwork characteristic that end-users care about. For example,\nlatency, loss probability, jitter, and IP version can each be assigned\nto a dimension.\nTo each node, i, we associate a vector in the quality space, Qqi \u2208 .\nThis corresponds to the quality a user would experience if i were the\nonly ISP on the data path. Let N\nQ\u2208q be the vector of all node\nqualities.\nOf course, when data passes through multiple nodes, their qualities\ncombine in some way to yield a path quality. We represent this by\nan associative binary operation, *: QQQ \u2192\u00d7 . For path\n( )nvvv ,...,, 21 , the quality is given by nvvv qqq \u2217\u2217\u2217 ...21\n. The *\noperation reflects the characteristics of each dimension of quality.\nFor example, * can act as an addition in the case of latency,\nmultiplication in the case of loss probability, or a\nminimumargument function in the case of security.\nWhen data flows along a complete path from S to D, the source and\ndestination, generally regarded as a single player, enjoy utility given\nby a function of the path quality, \u2192Qu : . Each node along the\npath, i, experiences some cost of transmission, ci.\n2.1 Game Dynamics\nUltimately, we are most interested in policies that promote\ninnovation on the network. In this study, we will use innovation in\na fairly general sense. Innovation describes any investment by an\nISP that alters its quality vector so that at least one potential data\npath offers higher utility. This includes researching a new routing\nalgorithm that decreases the amount of jitter users experience. It\nalso includes deploying a new protocol that supports quality of\nservice. Even more broadly, buying new equipment to decrease\nS D\n185\nlatency may also be regarded as innovation. Innovation\nmay be thought of as the micro-level process by which\nthe network evolves.\nOur analysis is limited in one crucial respect: We focus\non inventions that a single ISP can implement to improve\nthe end-user experience. This excludes technologies that\nrequire adoption by all ISPs on the network to function.\nBecause such technologies do not create a competitive\nadvantage, rewarding them is difficult and may require\nintellectual property or some other market distortion. We\ndefer this interesting topic to future work.\nAt first, it may seem unclear how a large-scale distributed process\nsuch as innovation can be influenced by mechanical details like\nnetworks monitors. Our model must draw this connection in a\nrealistic fashion.\nThe rate of innovation depends on the profits that potential\ninnovators expect in the future. The reward generated by an\ninvention must exceed the total cost to develop it, or the inventor\nwill not rationally invest. This reward, in turn, is governed by the\ncompetitive environment in which the firm operates, including the\nprocess by which firms select prices, and agree upon contracts with\neach other. Of course, these decisions depend on how routes are\nestablished, and how contracts determine actual monetary\nexchanges.\nAny model of network innovation must therefore relate at least three\ndistinct processes: innovation, competition, and routing. We select\na game dynamics that makes the relation between these processes as\nexplicit as possible. This is represented schematically in Figure 2.\nThe innovation stage occurs first, at time 2\u2212=t . In this stage, each\nagent decides whether or not to make research investments. If she\nchooses not to, her quality remains fixed. If she makes an\ninvestment, her quality may change in some way. It is not\nnecessary for us to specify how such changes take place. The\nagents\" choices in this stage determine the vector of qualities, q,\ncommon knowledge for the rest of the game.\nNext, at time 1\u2212=t , agents participate in the competition stage, in\nwhich contracts are agreed upon. In today\"s industry, these\ncontracts include prices for transit access, and peering agreements.\nSince access is provided on a best-effort basis, a transit agreement\ncan simply be represented by its price. Other contracting systems\nwe will explore will require more detail.\nFinally, beginning at 0=t , firms participate in the routing stage.\nOther research has already employed repeated games to study\nrouting, for example [1], [12]. Repetition reveals interesting effects\nnot visible in a single stage game, such as informal collusion to\nelevate prices in [12]. We use a game in continuous time in order to\nstudy such properties. For example, we will later ask whether a\nplayer will maintain higher quality than her contracts require, in the\nhope of keeping her customer base or attracting future customers.\nOur dynamics reflect the fact that ISPs make innovation decisions\ninfrequently. Although real firms have multiple opportunities to\ninnovate, each opportunity is followed by a substantial length of\ntime in which qualities are fixed. The decision to invest focuses on\nhow the firm\"s new quality will improve the contracts it can enter\ninto. Hence, our model places innovation at the earliest stage,\nattempting to capture a single investment decision. Contracting\ndecisions are made on an intermediate time scale, thus appearing\nnext in the dynamics. Routing decisions are made very frequently,\nmainly to maximize immediate profit flows, so they appear in the\nlast stage.\nBecause of this ordering, our model does not allow firms to route\nstrategically to affect future innovation or contracting decisions. In\nopposition, Afergan and Wroclawski argue that contracts are formed\nin response to current traffic patterns, in a feedback loop [2].\nAlthough we are sympathetic to their observation, such an addition\nwould make our analysis intractable. Our model is most realistic\nwhen contracting decisions are infrequent.\nThroughout this paper, our solution concept will be a subgame\nperfect equilibrium (SPE). An SPE is a strategy point that is a Nash\nequilibrium when restricted to each subgame. Three important\nsubgames have been labeled in Figure 2. The innovation game\nincludes all three stages. The competition game includes only the\ncompetition stage and the routing stage. The routing game includes\nonly the routing stage.\nAn SPE guarantees that players are forward-looking. This means,\nfor example, that in the competition stage, firms must act rationally,\nmaximizing their expected profits in the routing stage. They cannot\ncarry out threats they made in the innovation stage if it lowers their\nexpected payoff.\nOur schematic already suggests that the routing game is crucial for\npromoting innovation. To support innovation, the competition\ngame must somehow reward ISPs with high quality. But that\nmeans that the routing game must tend to route to nodes with high\nquality. If the routing game always selects the lowest-cost routes,\nfor example, innovation will not be supported. We will support this\nobservation with analysis later.\n2.2 The Routing Game\nThe routing game proceeds in continuous time, with all players\ndiscounting by a common factor, r. The outputs from previous\nstages, q and the set of contracts, are treated as exogenous\nparameters for this game. For each time 0\u2265t , each node must\nselect a next hop to route data to. Data flows across the resultant\npath, causing utility flow to S and D, and a flow cost to the nodes on\nthe path, as described above. Payment flows are also created, based\non the contracts in place.\nRelating our game to the familiar repeated prisoners\" dilemma,\nimagine that we are trying to impose a high quality, but costly path.\nAs we argued loosely above, such paths must be sustainable in order\nto support innovation. Each ISP on the path tries to maximize her\nown payment, net of costs, so she may not want to cooperate with\nour plan. Rather, if she can find a way to save on costs, at the\nexpense of the high quality we desire, she will be tempted to do so.\nInnovation Game Competition Game Routing Game\nInnovation\nstage\nCompetition\nstage\nRouting\nstageQualities\n(q)\nContracts\n(prices)\nProfits\nt = -2 t = -1 t \u2208 [ 0 , )\nFigure 2: Game Dynamics\n186\nAnalogously to the prisoners\" dilemma, we will call such a decision\ncheating. A little more formally,\nCheating refers to any action that an ISP can take, contrary to\nsome target strategy point that we are trying to impose, that\nenhances her immediate payoff, but compromises the quality of\nthe data path.\nOne type of cheating relates to the data path. Each node on the path\nhas to pay the next node to deliver its traffic. If the next node offers\nhigh quality transit, we may expect that a lower quality node will\noffer a lower price. Each node on the path will be tempted to route\nto a cheaper next hop, increasing her immediate profits, but\nlowering the path quality. We will call this type of action cheating\nin route.\nAnother possibility we can model, is that a node finds a way to save\non its internal forwarding costs, at the expense of its own quality.\nWe will call this cheating internally to distinguish it from cheating\nin route. For example, a node might drop packets beyond the rate\nrequired for congestion control, in order to throttle back TCP flows\nand thus save on forwarding costs [3]. Alternately, a node\nemploying quality of service could give high priority packets a\nlower class of service, thus saving on resources and perhaps\nallowing itself to sell more high priority service.\nIf either cheating in route or cheating internally is profitable, the\nspecified path will not be an equilibrium. We assume that cheating\ncan never be caught instantaneously. Rather, a cheater can always\nenjoy the payoff from cheating for some positive time, which we\nlabel 0t . This includes the time for other players to detect and react\nto the cheating. If the cheater has a contract which includes a\ncustomer lock-in period, 0t also includes the time until customers\nare allowed to switch to a new ISP. As we will see later, it is\nsocially beneficial to decrease 0t , so such lock-in is detrimental to\nwelfare.\n3. PATHOLOGIES OF A\nLOWACCOUNTABILITY NETWORK\nIn order to motivate an exploration of monitoring systems, we begin\nin this section by considering a network with a poor degree of\naccountability, modeled after today\"s Internet. We will show how\nthe lack of monitoring necessarily leads to poor routing and\ndiminishes the rate of innovation. Thus, the network\"s lack of\naccountability is a fundamental obstacle to resolving these\npathologies.\n3.1 Accountability in the Current Internet\nFirst, we reflect on what accountability characteristics the present\nInternet has. Argyraki, et al., point out that end hosts are given\nminimal information about packet drops [3]. Users know when\ndrops occur, but not where they occur, nor why. Dropped packets\nmay represent the innocent signaling of congestion, or, as we\nmentioned above, they may be a form of cheating internally. The\nproblem is similar for other dimensions of quality, or in fact more\nacute. Finding an ISP that gives high priority packets a lower class\nof service, for example, is further complicated by the lack of even\nbasic diagnostic tools.\nIn fact, it is similarly difficult to identify an ISP that cheats in route.\nHuston notes that Internet traffic flows do not always correspond to\nrouting information [8]. An ISP may hand a packet off to a\nneighbor regardless of what routes that neighbor has advertised.\nFurthermore, blocks of addresses are summarized together for\ndistant hosts, so a destination may not even be resolvable until\npackets are forwarded closer.\nOne might argue that diagnostic tools like ping and traceroute can\nidentify cheaters. Unfortunately, Argyraki, et al., explain that these\ntools only reveal whether probe packets are echoed, not the fate of\npast packets [3]. Thus, for example, they are ineffective in detecting\nlow-frequency packet drops. Even more fundamentally, a\nsophisticated cheater can always spot diagnostic packets and give\nthem special treatment.\nAs a further complication, a cheater may assume different aliases\nfor diagnostic packets arriving over different routes. As we will see\nbelow, this gives the cheater a significant advantage in escaping\npunishment for bad behavior, even if the data path is otherwise\nobservable.\n3.2 Modeling Low-Accountability\nAs the above evidence suggests, the current industry allows for very\nlittle insight into the behavior of the network. In this section, we\nattempt to capture this lack of accountability in our model. We\nbegin by defining a monitor, our model of the way that players\nreceive external information about network behavior,\nA monitor is any distributed algorithmic mechanism that runs on\nthe network graph, and outputs, to specific nodes, informational\nstatements about current or past network behavior.\nWe assume that all external information about network behavior is\nmediated in this way. The accountability properties of the Internet\ncan be represented by the following monitors:\nE2E (End to End): A monitor that informs S/D about what the\ntotal path quality is at any time (this is the quality they\nexperience).\nROP (Rest of Path): A monitor that informs each node along the\ndata path what the quality is for the rest of the path to the\ndestination.\nPRc (Packets Received): A monitor that tells nodes how much\ndata they accept from each other, so that they can charge by\nvolume. It is important to note, however, that this information is\naggregated over many source-destination pairs. Hence, for the\nsake of realism, it cannot be used to monitor what the data path is.\nPlayers cannot measure the qualities of other, single nodes, just the\nrest of the path. Nodes cannot see the path past the next hop. This\nlast assumption is stricter than needed for our results. The critical\ningredient is that nodes cannot verify that the path avoids a specific\nhop. This holds, for example, if the path is generally visible, except\nnodes can use different aliases for different parents. Similar results\nalso hold if alternate paths always converge after some integer\nnumber, m, of hops.\nIt is important to stress that E2E and ROP are not the contractible\nmonitors we described in the introduction - they do not generate\nproofs. Thus, even though a player observes certain information,\nshe generally cannot credibly share it with another player. For\nexample, if a node after the first hop starts cheating, the first hop\nwill detect the sudden drop in quality for the rest of the path, but the\nfirst hop cannot make the source believe this observation - the\n187\nsource will suspect that the first hop was the cheater, and fabricated\nthe claim against the rest of the path.\nTypically, E2E and ROP are envisioned as algorithms that run on a\nsingle node, and listen for packet echoes. This is not the only way\nthat they could be implemented, however; an alternate strategy is to\naggregate quality measurements from multiple points in the\nnetwork. These measurements can originate in other monitors,\nlocated at various ISPs. The monitor then includes the component\nmonitors as well as whatever mechanisms are in place to motivate\nnodes to share information honestly as needed. For example, if the\nsource has monitors that reveal the qualities of individual nodes,\nthey could be combined with path information to create an ROP\nmonitor.\nSince we know that contracts only accept proofs as input, we can\ninfer that payments in this environment can only depend on the\nnumber of packets exchanged between players. In other words,\ncontracts are best-effort. For the remainder of this section, we will\nassume that contracts are also linear - there is a constant payment\nflow so long as a node accepts data, and all conditions of the\ncontract are met. Other, more complicated tariffs are also possible,\nand are typically used to generate lock-in. We believe that our\nparameter t0 is sufficient to describe lock-in effects, and we believe\nthat the insights in this section apply equally to any tariffs that are\nbounded so that the routing game remains continuous at infinity.\nRestricting attention to linear contracts allows us to represent some\nnode i\"s contract by its price, pi.\nBecause we further know that nodes cannot observe the path after\nthe next hop, we can infer that contracts exist only between\nneighboring nodes on the graph. We will call this arrangement of\ncontracts bilateral. When a competition game exclusively uses\nbilateral contracts, we will call it a bilateral contract competition\ngame.\nWe first focus on the routing game and ask whether a high quality\nroute can be maintained, even when a low quality route is cheaper.\nRecall that this is a requirement in order for nodes to have any\nincentive to innovate. If nodes tend to route to low price next hops,\nregardless of quality, we say that the network is commoditized. To\nmeasure this tendency, we define an index of commoditization as\nfollows:\nFor a node on the data path, i, define its quality premium,\nminppd ji \u2212= , where pj is the flow payment to the next hop in\nequilibrium, and pmin is the price of the lowest cost next hop.\nDefinition: The index of commoditization, CI , is the average,\nover each node on the data path, i, of i\"s flow profit as a fraction\nof i\"s quality premium, ( ) ijii dpcp /\u2212\u2212 .\nCI ranges from 0, when each node spends all of its potential profit\non its quality premium, to infinite, when a node absorbs positive\nprofit, but uses the lowest price next hop. A high value for CI\nimplies that nodes are spending little of their money inflow on\npurchasing high quality for the rest of the path. As the next claim\nshows, this is exactly what happens as the path grows long:\nClaim 1. If the only monitors are E2E, ROP, and PRc, \u221e\u2192CI\nas \u221e\u2192n , where n is the number of nodes on the data path.\nTo show that this is true, we first need the following lemma, which\nwill establish the difficulty of punishing nodes in the network.\nFirst a bit of notation: Recall that a cheater can benefit from its\nactions for 00 >t before other players can react. When a node\ncheats, it can expect a higher profit flow, at least until it is caught\nand other players react, perhaps by diverting traffic. Let node i\"s\nnormal profit flow be i\u03c0 , and her profit flow during cheating be\nsome greater value, yi. We will call the ratio, iiy \u03c0/ , the\ntemptation to cheat.\nLemma 1. If the only monitors are E2E, ROP, and PRc, the\ndiscounted time, \u2212nt\nrt\ne\n0\n, needed to punish a cheater increases at\nleast as fast as the product of the temptations to cheat along the data\npath,\n\u220f \u2212\u2212\n\u2265\n0\n0\npathdataon\n0\nt\nrt\ni i\ni\nt\nrt\ne\ny\ne\nn\n\u03c0\n(1)\nCorollary. If nodes share a minimum temptation to cheat, \u03c0/y ,\nthe discounted time needed to punish cheating increases at least\nexponentially in the length of the data path, n,\n\u2212\u2212\n\u2265\n0\n00\nt\nrt\nnt\nrt\ne\ny\ne\nn\n\u03c0\n(2)\nSince it is the discounted time that increases exponentially, the\nactual time increases faster than exponentially. If n is so large that\ntn is undefined, the given path cannot be maintained in equilibrium.\nProof. The proof proceeds by induction on the number of nodes on\nthe equilibrium data path, n. For 1=n , there is a single node, say i.\nBy cheating, the node earns extra profit ( ) \u2212\n\u2212\n0\n0\nt\nrt\nii ey \u03c0 . If node i\nis then punished until time 1t , the extra profit must be cancelled out\nby the lost profit between time 0t and 1t , \u22121\n0\nt\nt\nrt\ni e\u03c0 . A little\nmanipulation gives \u2212\u2212\n=\n01\n00\nt\nrt\ni\ni\nt\nrt\ne\ny\ne\n\u03c0\n, as required.\nFor 1>n , assume for induction that the claim holds for 1\u2212n . The\nsource does not know whether the cheater is the first hop, or after\nthe first hop. Because the source does not know the data path after\nthe first hop, it is unable to punish nodes beyond it. If it chooses a\nnew first hop, it might not affect the rest of the data path. Because\nof this, the source must rely on the first hop to punish cheating\nnodes farther along the path. The first hop needs discounted time,\n\u220f \u22120\n0\nhopfirstafter\nt\nrt\ni i\ni e\ny\n\u03c0\n, to accomplish this by assumption. So\nthe source must give the first hop this much discounted time in order\nto punish defectors further down the line (and the source will expect\npoor quality during this period).\nNext, the source must be protected against a first hop that cheats,\nand pretends that the problem is later in the path. The first hop can\n188\ndo this for the full discounted time, \u220f \u22120\n0\nhopfirstafter\nt\nrt\ni i\ni e\ny\n\u03c0\n, so\nthe source must punish the first hop long enough to remove the extra\nprofit it can make. Following the same argument as for 1=n , we\ncan show that the full discounted time is \u220f \u22120\n0\npathdataon\nt\nrt\ni i\ni e\ny\n\u03c0\n,\nwhich completes the proof.\nThe above lemma and its corollary show that punishing cheaters\nbecomes more and more difficult as the data path grows long, until\ndoing so is impossible. To capture some intuition behind this result,\nimagine that you are an end user, and you notice a sudden drop in\nservice quality. If your data only travels through your access\nprovider, you know it is that provider\"s fault. You can therefore\ntake your business elsewhere, at least for some time. This threat\nshould motivate your provider to maintain high quality.\nSuppose, on the other hand, that your data traverses two providers.\nWhen you complain to your ISP, he responds, yes, we know your\nquality went down, but it\"s not our fault, it\"s the next ISP. Give us\nsome time to punish them and then normal quality will resume. If\nyour access provider is telling the truth, you will want to listen,\nsince switching access providers may not even route around the\nactual offender. Thus, you will have to accept lower quality service\nfor some longer time. On the other hand, you may want to punish\nyour access provider as well, in case he is lying. This means you\nhave to wait longer to resume normal service. As more ISPs are\nadded to the path, the time increases in a recursive fashion.\nWith this lemma in hand, we can return to prove Claim 1.\nProof of Claim 1. Fix an equilibrium data path of length n. Label\nthe path nodes 1,2,\u2026,n. For each node i, let i\"s quality premium be\n'11 ++ \u2212= iii ppd . Then we have,\n[ ]\n=\n\u2212\n=\n\u2212\n+\n+\n=\n\u2212\n+\n++\n=\n+\n\u2212=\u2212\n\u2212\u2212\n\u2212\u2212\n=\n\u2212\u2212\n\u2212\n=\n\u2212\u2212\n=\nn\ni\ni\nn\ni iii\niii\nn\ni iii\nii\nn\ni i\niii\nC\ng\nnpcp\npcp\nn\npcp\npp\nnd\npcp\nn\nI\n1\n1\n1\n1\n1\n1\n1\n1\n1\n11\n1\n1\n1\n1\n1\n'1\n'11\n, (3)\nwhere gi is node i\"s temptation to cheat by routing to the lowest\nprice next hop. Lemma 1 tells us that Tg\nn\ni\ni <\u220f\n=1\n, where\n( )01 rt\neT \u2212\n\u2212= . It requires a bit of calculus to show that IC is\nminimized by setting each gi equal to n\nT /1\n. However, as \u221e\u2192n ,\nwe have 1/1\n\u2192n\nT , which shows that \u221e\u2192CI .\nAccording to the claim, as the data path grows long, it increasingly\nresembles a lowest-price path. Since lowest-price routing does not\nsupport innovation, we may speculate that innovation degrades with\nthe length of the data path. Though we suspect stronger claims are\npossible, we can demonstrate one such result by including an extra\nassumption:\nAvailable Bargain Path: A competitive market exists for\nlowcost transit, such that every node can route to the destination for\nno more than flow payment, lp .\nClaim 2. Under the available bargain path assumption, if node i , a\ndistance n from S, can invest to alter its quality, and the source will\nspend no more than sP for a route including node i\"s new quality,\nthen the payment to node i, p, decreases hyperbolically with n,\n( )\n( ) s\nn\nl P\nn\nT\npp\n1\n1/1\n\u2212\n+\u2264\n\u2212\n, (4)\nwhere ( )01 rt\neT \u2212\n\u2212= is the bound on the product of temptations\nfrom the previous claim. Thus, i will spend no more than\n( )\n( )\u2212\n+\n\u2212\ns\nn\nl P\nn\nT\np\nr 1\n1 1/1\non this quality improvement, which\napproaches the bargain path\"s payment,\nr\npl\n, as \u221e\u2192n .\nThe proof is given in the appendix. As a node gets farther from the\nsource, its maximum payment approaches the bargain price, pl.\nHence, the reward for innovation is bounded by the same amount.\nLarge innovations, meaning substantially more expensive than\nrpl / , will not be pursued deep into the network.\nClaim 2 can alternately be viewed as a lower bound on how much it\ncosts to elicit innovation in a network. If the source S wants node i\nto innovate, it needs to get a motivating payment, p, to i during the\nrouting stage. However, it must also pay the nodes on the way to i a\npremium in order to motivate them to route properly. The claim\nshows that this premium increases with the distance to i, until it\ndwarfs the original payment, p.\nOur claims stand in sharp contrast to our null hypothesis from the\nintroduction. Comparing the intuitive argument that supported our\nhypothesis with these claims, we can see that we implicitly used an\noversimplified model of market pressure (as either present or not).\nAs is now clear, market pressure relies on the decisions of\ncustomers, but these are limited by the lack of information. Hence,\ncompetitive forces degrade as the network deepens.\n4. VERIFIABLE MONITORS\nIn this section, we begin to introduce more accountability into the\nnetwork. Recall that in the previous section, we assumed that\nplayers couldn\"t convince each other of their private information.\nWhat would happen if they could? If a monitor\"s informational\nsignal can be credibly conveyed to others, we will call it a verifiable\nmonitor. The monitor\"s output in this case can be thought of as a\nstatement accompanied by a proof, a string that can be processed by\nany player to determine that the statement is true.\nA verifiable monitor is a distributed algorithmic mechanism that\nruns on the network graph, and outputs, to specific nodes, proofs\nabout current or past network behavior.\nAlong these lines, we can imagine verifiable counterparts to E2E\nand ROP. We will label these E2Ev and ROPv. With these\nmonitors, each node observes the quality of the rest of the path and\ncan also convince other players of these observations by giving\nthem a proof.\n189\nBy adding verifiability to our monitors, identifying a single cheater\nis straightforward. The cheater is the node that cannot produce\nproof that the rest of path quality decreased. This means that the\nnegative results of the previous section no longer hold. For\nexample, the following lemma stands in contrast to Lemma 1.\nLemma 2. With monitors E2Ev, ROPv, and PRc, and provided that\nthe node before each potential cheater has an alternate next hop that\nisn\"t more expensive, it is possible to enforce any data path in SPE\nso long as the maximum temptation is less than what can be deterred\nin finite time,\n\u2212\n\u2264\n0\n0\nmax\n1\nt\nrt\ner\ny\n\u03c0\n(5)\nProof. This lemma follows because nodes can share proofs to\nidentify who the cheater is. Only that node must be punished in\nequilibrium, and the preceding node does not lose any payoff in\nadministering the punishment.\nWith this lemma in mind, it is easy to construct counterexamples to\nClaim 1 and Claim 2 in this new environment.\nUnfortunately, there are at least four reasons not to be satisfied with\nthis improved monitoring system. The first, and weakest reason is\nthat the maximum temptation remains finite, causing some\ndistortion in routes or payments. Each node along a route must\nextract some positive profit unless the next hop is also the cheapest.\nOf course, if t0 is small, this effect is minimal.\nThe second, and more serious reason is that we have always given\nour source the ability to commit to any punishment. Real world\nusers are less likely to act collectively, and may simply search for\nthe best service currently offered. Since punishment phases are\ngenerally characterized by a drop in quality, real world end-users\nmay take this opportunity to shop for a new access provider. This\nwill make nodes less motivated to administer punishments.\nThe third reason is that Lemma 2 does not apply to cheating by\ncoalitions. A coalition node may pretend to punish its successor,\nbut instead enjoy a secret payment from the cheating node.\nAlternately, a node may bribe its successor to cheat, if the\npunishment phase is profitable, and so forth. The required\ndiscounted time for punishment may increase exponentially in the\nnumber of coalition members, just as in the previous section!\nThe final reason not to accept this monitoring system is that when a\ncheater is punished, the path will often be routed around not just the\noffender, but around other nodes as well. Effectively, innocent\nnodes will be punished along with the guilty. In our abstract model,\nthis doesn\"t cause trouble since the punishment falls off the\nequilibrium path. The effects are not so benign in the real world.\nWhen ISPs lie in sequence along a data path, they contribute\ncomplementary services, and their relationship is vertical. From the\nperspective of other source-destination pairs, however, these same\nfirms are likely to be horizontal competitors. Because of this, a\nnode might deliberately cheat, in order to trigger punishment for\nitself and its neighbors. By cheating, the node will save money to\nsome extent, so the cheater is likely to emerge from the punishment\nphase better off than the innocent nodes. This may give the cheater\na strategic advantage against its competitors. In the extreme, the\ncheater may use such a strategy to drive neighbors out of business,\nand thereby gain a monopoly on some routes.\n5. CONTRACTIBLE MONITORS\nAt the end of the last section, we identified several drawbacks that\npersist in an environment with E2Ev, ROPv, and PRc. In this\nsection, we will show how all of these drawbacks can be overcome.\nTo do this, we will require our third and final category of monitor:\nA contractible monitor is simply a verifiable monitor that generates\nproofs that can serve as input to a contract. Thus, contractible is\njointly a property of the monitor and the institutions that must verify\nits proofs. Contractibility requires that a court,\n1. Can verify the monitor\"s proofs.\n2. Can understand what the proofs and contracts represent to\nthe extent required to police illegal activity.\n3. Can enforce payments among contracting parties.\nUnderstanding the agreements between companies has traditionally\nbeen a matter of reading contracts on paper. This may prove to be a\nharder task in a future network setting. Contracts may plausibly be\nnegotiated by machine, be numerous, even per-flow, and be further\ncomplicated by the many dimensions of quality.\nWhen a monitor (together with institutional infrastructure) meets\nthese criteria, we will label it with a subscript c, for contractible.\nThe reader may recall that this is how we labeled the packets\nreceived monitor, PRc, which allows ISPs to form contracts with\nper-packet payments. Similarly, E2Ec and ROPc are contractible\nversions of the monitors we are now familiar with.\nAt the end of the previous section, we argued for some desirable\nproperties that we\"d like our solution to have. Briefly, we would\nlike to enforce optimal data paths with an equilibrium concept that\ndoesn\"t rely on re-routing for punishment, is coalition proof, and\ndoesn\"t punish innocent nodes when a coalition cheats. We will call\nsuch an equilibrium a fixed-route coalition-proof\nprotect-theinnocent equilibrium.\nAs the next claim shows, ROPc allows us to create a system of\nlinear (price, quality) contracts under just such an equilibrium.\nClaim 3. With ROPc, for any feasible and consistent assignment of\nrest of path qualities to nodes, and any corresponding payment\nschedule that yields non-negative payoffs, these qualities can be\nmaintained with bilateral contracts in a fixed-route coalition-proof\nprotect-the-innocent equilibrium.\nProof: Fix any data path consistent with the given rest of path\nqualities. Select some monetary punishment, P, large enough to\nprevent any cheating for time t0 (the discounted total payment from\nthe source will work). Let each node on the path enter into a\ncontract with its parent, which fixes an arbitrary payment schedule\nso long as the rest of path quality is as prescribed. When the parent\nnode, which has ROPc, submits a proof that the rest of path quality\nis less than expected, the contract awards her an instantaneous\ntransfer, P, from the downstream node. Such proofs can be\nsubmitted every 0t for the previous interval.\nSuppose now that a coalition, C, decides to cheat. The source\nmeasures a decrease in quality, and according to her contract, is\nawarded P from the first hop. This means that there is a net outflow\nof P from the ISPs as a whole. Suppose that node i is not in C. In\norder for the parent node to claim P from i, it must submit proof that\nthe quality of the path starting at i is not as prescribed. This means\n190\nthat there is a cheater after i. Hence, i would also have detected a\nchange in quality, so i can claim P from the next node on the path.\nThus, innocent nodes are not punished. The sequence of payments\nmust end by the destination, so the net outflow of P must come from\nthe nodes in C. This establishes all necessary conditions of the\nequilibrium.\nEssentially, ROPc allows for an implementation of (price, quality)\ncontracts. Building upon this result, we can construct competition\ngames in which nodes offer various qualities to each other at\nspecified prices, and can credibly commit to meet these\nperformance targets, even allowing for coalitions and a desire to\ndamage other ISPs.\nExample 1. Define a Stackelberg price-quality competition game\nas follows: Extend the partial order of nodes induced by the graph\nto any complete ordering, such that downstream nodes appear\nbefore their parents. In this order, each node selects a contract to\noffer to its parents, consisting of a rest of path quality, and a linear\nprice. In the routing game, each node selects a next hop at every\ntime, consistent with its advertised rest of path quality. The\nStackelberg price-quality competition game can be implemented in\nour model with ROPc monitors, by using the strategy in the proof,\nabove. It has the following useful property:\nClaim 4. The Stackelberg price-quality competition game yields\noptimal routes in SPE.\nThe proof is given in the appendix. This property is favorable from\nan innovation perspective, since firms that invest in high quality will\ntend to fall on the optimal path, gaining positive payoff. In general,\nhowever, investments may be over or under rewarded. Extra\nconditions may be given under which innovation decisions approach\nperfect efficiency for large innovations. We omit the full analysis\nhere.\nExample 2. Alternately, we can imagine that players report their\nprivate information to a central authority, which then assigns all\ncontracts. For example, contracts could be computed to implement\nthe cost-minimizing VCG mechanism proposed by Feigenbaum, et\nal. in [7]. With ROPc monitors, we can adapt this mechanism to\nmaximize welfare. For node, i, on the optimal path, L, the net\npayment must equal, essentially, its contribution to the welfare of S,\nD, and the other nodes. If L\" is an optimal path in the graph with i\nremoved, the profit flow to i is,\n( ) ( )\n\u2208\u2260\u2208\n+\u2212\u2212\n',\n'\nLj\nj\nijLj\njLL ccququ , (6)\nwhere Lq and 'Lq are the qualities of the two paths. Here, (price,\nquality) contracts ensure that nodes report their qualities honestly.\nThe incentive structure of the VCG mechanism is what motivates\nnodes to report their costs accurately.\nA nice feature of this game is that individual innovation decisions\nare efficient, meaning that a node will invest in an innovation\nwhenever the investment cost is less than the increased welfare of\nthe optimal data path. Unfortunately, the source may end up paying\nmore than the utility of the path.\nNotice that with just E2Ec, a weaker version of Claim 3 holds.\nBilateral (price, quality) contracts can be maintained in an\nequilibrium that is fixed-route and coalition-proof, but not\nprotectthe-innocent. This is done by writing contracts to punish everyone\non the path when the end to end quality drops. If the path length is\nn, the first hop pays nP to the source, the second hop pays ( )Pn 1\u2212\nto the first, and so forth. This ensures that every node is punished\nsufficiently to make cheating unprofitable. For the reasons we gave\npreviously, we believe that this solution concept is less than ideal,\nsince it allows for malicious nodes to deliberately trigger\npunishments for potential competitors.\nUp to this point, we have adopted fixed-route coalition-proof\nprotect-the-innocent equilibrium as our desired solution concept,\nand shown that ROPc monitors are sufficient to create some\ncompetition games that are desirable in terms of service diversity\nand innovation. As the next claim will show, rest of path\nmonitoring is also necessary to construct such games under our\nsolution concept.\nBefore we proceed, what does it mean for a game to be desirable\nfrom the perspective of service diversity and innovation? We will\nuse a very weak assumption, essentially, that the game is not fully\ncommoditized for any node. The claim will hold for this entire class\nof games.\nDefinition: A competition game is nowhere-commoditized if for\neach node, i, not adjacent to D, there is some assignment of qualities\nand marginal costs to nodes, such that the optimal data path includes\ni, and i has a positive temptation to cheat.\nIn the case of linear contracts, it is sufficient to require that \u221e<CI ,\nand that every node make positive profit under some assignment of\nqualities and marginal costs.\nStrictly speaking, ROPc monitors are not the only way to construct\nthese desirable games. To prove the next claim, we must broaden\nour notion of rest of path monitoring to include the similar ROPc\"\nmonitor, which attests to the quality starting at its own node,\nthrough the end of the path. Compare the two monitors below:\nROPc: gives a node proof that the path quality from the next node\nto the destination is not correct.\nROPc\": gives a node proof that the path quality from that node to\nthe destination is correct.\nWe present a simplified version of this claim, by including an\nassumption that only one node on the path can cheat at a time\n(though conspirators can still exchange side payments). We will\ndiscuss the full version after the proof.\nClaim 5. Assume a set of monitors, and a nowhere-commoditized\nbilateral contract competition game that always maintains the\noptimal quality in fixed-route coalition-proof protect-the-innocent\nequilibrium, with only one node allowed to cheat at a time. Then\nfor each node, i, not adjacent to D, either i has an ROPc monitor, or\ni\"s children each have an ROPc\" monitor.\nProof: First, because of the fixed-route assumption, punishments\nmust be purely monetary.\nNext, when cheating occurs, if the payment does not go to the\nsource or destination, it may go to another coalition member,\nrendering it ineffective. Thus, the source must accept some\nmonetary compensation, net of its normal flow payment, when\ncheating occurs. Since the source only contracts with the first hop,\nit must accept this money from the first hop. The source\"s contract\nmust therefore distinguish when the path quality is normal from\nwhen it is lowered by cheating. To do so, it can either accept proofs\n191\nfrom the source, that the quality is lower than required, or it can\naccept proofs from the first hop, that the quality is correct. These\nnodes will not rationally offer the opposing type of proof.\nBy definition, any monitor that gives the source proof that the path\nquality is wrong is an ROPc monitor. Any monitor that gives the\nfirst hop proof that the quality is correct is a ROPc\" monitor. Thus,\nat least one of these monitors must exist.\nBy the protect-the-innocent assumption, if cheating occurs, but the\nfirst hop is not a cheater, she must be able to claim the same size\nreward from the next ISP on the path, and thus pass on the\npunishment. The first hop\"s contract with the second must then\ndistinguish when cheating occurs after the first hop. By argument\nsimilar to that for the source, either the first hop has a ROPc\nmonitor, or the second has a ROPc\" monitor. This argument can be\niterated along the entire path to the penultimate node before D.\nSince the marginal costs and qualities can be arranged to make any\npath the optimal path, these statements must hold for all nodes and\ntheir children, which completes the proof.\nThe two possibilities for monitor correspond to which node has the\nburden of proof. In one case, the prior node must prove the\nsuboptimal quality to claim its reward. In the other, the subsequent\nnode must prove that the quality was correct to avoid penalty.\nBecause the two monitors are similar, it seems likely that they\nrequire comparable costs to implement. If submitting the proofs is\ncostly, it seems natural that nodes would prefer to use the ROPc\nmonitor, placing the burden of proof on the upstream node.\nFinally, we note that it is straightforward to derive the full version of\nthe claim, which allows for multiple cheaters. The only\ncomplication is that cheaters can exchange side payments, which\nmakes any money transfers between them redundant. Because of\nthis, we have to further generalize our rest of path monitors, so they\nare less constrained in the case that there are cheaters on either side.\n5.1 Implementing Monitors\nClaim 5 should not be interpreted as a statement that each node must\ncompute the rest of path quality locally, without input from other\nnodes. Other monitors, besides ROPc and ROPc\" can still be used,\nloosely speaking, as building blocks. For instance, network\ntomography is concerned with measuring properties of the network\ninterior with tools located at the edge. Using such techniques, our\nsource might learn both individual node qualities and the data path.\nThis is represented by the following two monitors:\nSHOPc\ni\n: (source-based hop quality) A monitor that gives the\nsource proof of what the quality of node i is.\nSPATHc: (source-based path) A monitor that gives the source\nproof of what the data path is at any time, at least as far as it\nmatches the equilibrium path.\nWith these monitors, a punishment mechanism can be designed to\nfulfill the conditions of Claim 5. It involves the source sharing the\nproofs it generates with nodes further down the path, which use\nthem to determine bilateral payments. Ultimately however, the\nproof of Claim 5 shows us that each node i\"s bilateral contracts\nrequire proof of the rest of path quality. This means that node i (or\npossibly its children) will have to combine the proofs that they\nreceive to generate a proof of the rest of path quality. Thus, the\ncombined process is itself a rest of path monitor.\nWhat we have done, all in all, is constructed a rest of path monitor\nusing SPATHc and SHOPc\ni\nas building blocks. Our new monitor\nincludes both the component monitors and whatever distributed\nalgorithmic mechanism exists to make sure nodes share their proofs\ncorrectly.\nThis mechanism can potentially involve external institutions. For a\nconcrete example, suppose that when node i suspects it is getting\npoor rest of path quality from its successor, it takes the downstream\nnode to court. During the discovery process, the court subpoenas\nproofs of the path and of node qualities from the source (ultimately,\nthere must be some threat to ensure the source complies). Finally,\nfor the court to issue a judgment, one party or the other must\ncompile a proof of what the rest of path quality was. Hence, the\nentire discovery process acts as a rest of path monitor, albeit a rather\ncostly monitor in this case.\nOf course, mechanisms can be designed to combine these monitors\nat much lower cost. Typically, such mechanisms would call for\nautomatic sharing of proofs, with court intervention only as a last\nresort. We defer these interesting mechanisms to future work.\nAs an aside, intuition might dictate that SHOPc\ni\ngenerates more\ninformation than ROPc; after all, inferring individual node qualities\nseems a much harder problem. Yet, without path information,\nSHOPc\ni\nis not sufficient for our first-best innovation result. The\nproof of this demonstrates a useful technique:\nClaim 6. With monitors E2E, ROP, SHOPc\ni\nand PRc, and a\nnowhere-commoditized bilateral contract competition game, the\noptimal quality cannot be maintained for all assignments of quality\nand marginal cost, in fixed-route coalition-proof\nprotect-theinnocent equilibrium.\nProof: Because nodes cannot verify the data path, they cannot form\na proof of what the rest of path quality is. Hence, ROPc monitors do\nnot exist, and therefore the requirements of Claim 5 cannot hold.\n6. CONCLUSIONS AND FUTURE WORK\nIt is our hope that this study will have a positive impact in at least\nthree different ways. The first is practical: we believe our analysis\nhas implications for the design of future monitoring protocols and\nfor public policy.\nFor protocol designers, we first provide fresh motivation to create\nmonitoring systems. We have argued that the poor accountability of\nthe Internet is a fundamental obstacle to alleviating the pathologies\nof commoditization and lack of innovation. Unless accountability\nimproves, these pathologies are guaranteed to remain.\nSecondly, we suggest directions for future advances in monitoring.\nWe have shown that adding verifiability to monitors allows for\nsome improvements in the characteristics of competition. At the\nsame time, this does not present a fully satisfying solution. This\npaper has suggested a novel standard for monitors to aspire to - one\nof supporting optimal routes in innovative competition games under\nfixed-route coalition-proof protect-the-innocent equilibrium. We\nhave shown that under bilateral contracts, this specifically requires\ncontractible rest of path monitors.\nThis is not to say that other types of monitors are unimportant. We\nincluded an example in which individual hop quality monitors and a\npath monitor can also meet our standard for sustaining competition.\nHowever, in order for this to happen, a mechanism must be included\n192\nto combine proofs from these monitors to form a proof of rest of\npath quality. In other words, the monitors must ultimately be\ncombined to form contractible rest of path monitors. To support\nservice differentiation and innovation, it may be easier to design rest\nof path monitors directly, thereby avoiding the task of designing\nmechanisms for combining component monitors.\nAs far as policy implications, our analysis points to the need for\nlegal institutions to enforce contracts based on quality. These\ninstitutions must be equipped to verify proofs of quality, and police\nillegal contracting behavior. As quality-based contracts become\nnumerous and complicated, and possibly negotiated by machine,\nthis may become a challenging task, and new standards and\nregulations may have to emerge in response. This remains an\ninteresting and unexplored area for research.\nThe second area we hope our study will benefit is that of clean-slate\narchitectural design. Traditionally, clean-slate design tends to focus\non creating effective and elegant networks for a static set of\nrequirements. Thus, the approach is often one of engineering,\nwhich tends to neglect competitive effects. We agree with\nRatnasamy, Shenker, and McCanne, that designing for evolution\nshould be a top priority [11]. We have demonstrated that the\nnetwork\"s monitoring ability is critical to supporting innovation, as\nare the institutions that support contracting. These elements should\nfeature prominently in new designs. Our analysis specifically\nsuggests that architectures based on bilateral contracts should\ninclude contractible rest of path monitoring. From a clean-slate\nperspective, these monitors can be transparently and fully integrated\nwith the routing and contracting systems.\nFinally, the last contribution our study makes is methodological.\nWe believe that the mathematical formalization we present is\napplicable to a variety of future research questions. While a\nsignificant literature addresses innovation in the presence of\nnetwork effects, to the best of our knowledge, ours is the first model\nof innovation in a network industry that successfully incorporates\nthe actual topological structure as input. This allows the discovery\nof new properties, such as the weakening of market forces with the\nnumber of ISPs on a data path that we observe with\nlowaccountability.\nOur method also stands in contrast to the typical approach of\ndistributed algorithmic mechanism design. Because this field is\nbased on a principle-agent framework, contracts are usually\nproposed by the source, who is allowed to make a take it or leave it\noffer to network nodes. Our technique allows contracts to emerge\nfrom a competitive framework, so the source is limited to selecting\nthe most desirable contract. We believe this is a closer reflection of\nthe industry.\nBased on the insights in this study, the possible directions for future\nresearch are numerous and exciting. To some degree, contracting\nbased on quality opens a Pandora\"s Box of pressing questions: Do\nquality-based contracts stand counter to the principle of network\nneutrality? Should ISPs be allowed to offer a choice of contracts at\ndifferent quality levels? What anti-competitive behaviors are\nenabled by quality-based contracts? Can a contracting system\nsupport optimal multicast trees?\nIn this study, we have focused on bilateral contracts. This system\nhas seemed natural, especially since it is the prevalent system on the\ncurrent network. Perhaps its most important benefit is that each\ncontract is local in nature, so both parties share a common, familiar\nlegal jurisdiction. There is no need to worry about who will enforce\na punishment against another ISP on the opposite side of the planet,\nnor is there a dispute over whose legal rules to apply in interpreting\na contract.\nAlthough this benefit is compelling, it is worth considering other\nsystems. The clearest alternative is to form a contract between the\nsource and every node on the path. We may call these source\ncontracts. Source contracting may present surprising advantages.\nFor instance, since ISPs do not exchange money with each other, an\nISP cannot save money by selecting a cheaper next hop.\nAdditionally, if the source only has contracts with nodes on the\nintended path, other nodes won\"t even be willing to accept packets\nfrom this source since they won\"t receive compensation for carrying\nthem. This combination seems to eliminate all temptation for a\nsingle cheater to cheat in route. Because of this and other\nencouraging features, we believe source contracts are a fertile topic\nfor further study.\nAnother important research task is to relax our assumption that\nquality can be measured fully and precisely. One possibility is to\nassume that monitoring is only probabilistic or suffers from noise.\nEven more relevant is the possibility that quality monitors are\nfundamentally incomplete. A quality monitor can never anticipate\nevery dimension of quality that future applications will care about,\nnor can it anticipate a new and valuable protocol that an ISP\nintroduces. We may define a monitor space as a subspace of the\nquality space that a monitor can measure, QM \u2282 , and a\ncorresponding monitoring function that simply projects the full\nrange of qualities onto the monitor space, MQm \u2192: .\nClearly, innovations that leave quality invariant under m are not\neasy to support - they are invisible to the monitoring system. In this\nenvironment, we expect that path monitoring becomes more\nimportant, since it is the only way to ensure data reaches certain\ninnovator ISPs. Further research is needed to understand this\nprocess.\n7. ACKNOWLEDGEMENTS\nWe would like to thank the anonymous reviewers, Jens Grossklags,\nMoshe Babaioff, Scott Shenker, Sylvia Ratnasamy, and Hal Varian\nfor their comments. This work is supported in part by the National\nScience Foundation under ITR award ANI-0331659.\n8. REFERENCES\n[1] Afergan, M. Using Repeated Games to Design\nIncentiveBased Routing Systems. In Proceedings of IEEE INFOCOM\n(April 2006).\n[2] Afergan, M. and Wroclawski, J. On the Benefits and\nFeasibility of Incentive Based Routing Infrastructure. In ACM\nSIGCOMM'04 Workshop on Practice and Theory of Incentives\nin Networked Systems (PINS) (August 2004).\n[3] Argyraki, K., Maniatis, P., Cheriton, D., and Shenker, S.\nProviding Packet Obituaries. In Third Workshop on Hot Topics\nin Networks (HotNets) (November 2004).\n[4] Clark, D. D. The Design Philosophy of the DARPA Internet\nProtocols. In Proceedings of ACM SIGCOMM (1988).\n193\n[5] Clark, D. D., Wroclawski, J., Sollins, K. R., and Braden, R.\nTussle in cyberspace: Defining tomorrow's internet. In\nProceedings of ACM SIGCOMM (August 2002).\n[6] Dang-Nguyen, G. and P\u00e9nard, T. Interconnection Agreements:\nStrategic Behaviour and Property Rights. In Brousseau, E. and\nGlachant, J.M. Eds. The Economics of Contracts: Theories and\nApplications, Cambridge University Press, 2002.\n[7] Feigenbaum, J., Papadimitriou, C., Sami, R., and Shenker, S.\nA BGP-based Mechanism for Lowest-Cost Routing.\nDistributed Computing 18 (2005), pp. 61-72.\n[8] Huston, G. Interconnection, Peering, and Settlements. Telstra,\nAustralia.\n[9] Liu, Y., Zhang, H., Gong, W., and Towsley, D. On the\nInteraction Between Overlay Routing and Traffic Engineering.\nIn Proceedings of IEEE INFOCOM (2005).\n[10] MacKie-Mason, J. and Varian, H. Pricing the Internet. In\nKahin, B. and Keller, J. Eds. Public access to the Internet.\nEnglewood Cliffs, NJ; Prentice-Hall, 1995.\n[11] Ratnasamy, S., Shenker, S., and McCanne, S. Towards an\nEvolvable Internet Architecture. In Proceeding of ACM\nSIGCOMM (2005).\n[12] Shakkottai, S., and Srikant, R. Economics of Network Pricing\nwith Multiple ISPs. In Proceedings of IEEE INFOCOM\n(2005).\n9. APPENDIX\nProof of Claim 2. Node i must fall on the equilibrium data path to\nreceive any payment. Let the prices along the data path be\nppppP nS == ,..., 21 , with marginal costs, ncc ,...,1 . We may\nassume the prices on the path are greater than lp or the claim\nfollows trivially. Each node along the data path can cheat in route\nby giving data to the bargain path at price no more than lp . So\nnode j\"s temptation to cheat is at least\n11 ++ \u2212\n\u2212\n\u2265\n\u2212\u2212\n\u2212\u2212\njj\nl\njjj\nljj\npp\npp\npcp\npcp\n. Then Lemma 1 gives,\n1\n13221\n1...\n\u2212\n\u2212\n\u2212\n\u2212>\n\u2212\n\u2212\n\u22c5\u22c5\n\u2212\n\u2212\n\u2212\n\u2212\n\u2265\nn\nS\nl\nn\nlll\nP\npp\nn\npp\npp\npp\npp\npp\npp\nT (7)\nThis can be rearranged to give\n( )\n( ) s\nn\nl P\nn\nT\npp\n1\n1/1\n\u2212\n+\u2264\n\u2212\n, as required.\nThe rest of the claim simply recognizes that rp / is the greatest\nreward node i can receive for its investment, so it will not invest\nsums greater than this.\nProof of Claim 4. Label the nodes 1,2,.. N in the order in which\nthey select contracts. Let subgame n be the game that begins with n\nchoosing its contract. Let Ln be the set of possible paths restricted to\nnodes n,\u2026,N. That is, Ln is the set of possible routes from S to\nreach some node that has already moved.\nFor subgame n, define the local welfare over paths nLl \u2208 , and their\npossible next hops, nj < as follows,\n( ) ( ) j\nli\nipathjl pcqqujlV \u2212\u2212=\n\u2208\n*, , (8)\nwhere ql is the quality of path l in the set {n,\u2026,N}, and pathjq and\npj are the quality and price of the contract j has offered.\nFor induction, assume that subgame n + 1 maximizes local welfare.\nWe show that subgame n does as well. If node n selects next hop k,\nwe can write the following relation,\n( ) ( )( ) ( )( ) nknn knlVpcpknlVnlV \u03c0\u2212=++\u2212= ,,,,, , (9)\nwhere n is node n\"s profit if the path to n is chosen. This path is\nchosen whenever ( )nlV , is maximal over Ln+1 and possible next\nhops. If ( )( )knlV ,, is maximal over Ln, it is also maximal over the\npaths in Ln+1 that don\"t lead to n. This means that node n can choose\nsome n small enough so that ( )nlV , is maximal over Ln+1, so the\nroute will lead to k.\nConversely, if ( )( )knlV ,, is not maximal over Ln, either V is greater\nfor another of n\"s next hops, in which case n will select that one in\norder to increase n, or V is greater for some path in Ln+1 that don\"t\nlead to n, in which case ( )nlV , cannot be maximal for any\nnonnegative n.\nThus, we conclude that subgame n maximizes local welfare. For the\ninitial case, observe that this assumption holds for the source.\nFinally, we deduce that subgame 1, which is the entire game,\nmaximizes local welfare, which is equivalent to actual welfare.\nHence, the Stackelberg price-quality game yields an optimal route.\n194", "keywords": "monitor;clean-slate architectural design;contracting system;verifiable monitor;innovation;contract;routing policy;network monitor;routing stagequality;contractible monitor;commoditization;smart market;incentive"}
{"name": "train_C-65", "title": "Shooter Localization and Weapon Classification with Soldier-Wearable Networked Sensors", "abstract": "The paper presents a wireless sensor network-based mobile countersniper system. A sensor node consists of a helmetmounted microphone array, a COTS MICAz mote for internode communication and a custom sensorboard that implements the acoustic detection and Time of Arrival (ToA) estimation algorithms on an FPGA. A 3-axis compass provides self orientation and Bluetooth is used for communication with the soldier\"s PDA running the data fusion and the user interface. The heterogeneous sensor fusion algorithm can work with data from a single sensor or it can fuse ToA or Angle of Arrival (AoA) observations of muzzle blasts and ballistic shockwaves from multiple sensors. The system estimates the trajectory, the range, the caliber and the weapon type. The paper presents the system design and the results from an independent evaluation at the US Army Aberdeen Test Center. The system performance is characterized by 1degree trajectory precision and over 95% caliber estimation accuracy for all shots, and close to 100% weapon estimation accuracy for 4 out of 6 guns tested.", "fulltext": "1. INTRODUCTION\nThe importance of countersniper systems is underscored\nby the constant stream of news reports coming from the\nMiddle East. In October 2006 CNN reported on a new\ntactic employed by insurgents. A mobile sniper team moves\naround busy city streets in a car, positions itself at a good\nstandoff distance from dismounted US military personnel,\ntakes a single well-aimed shot and immediately melts in the\ncity traffic. By the time the soldiers can react, they are\ngone. A countersniper system that provides almost\nimmediate shooter location to every soldier in the vicinity would\nprovide clear benefits to the warfigthers.\nOur team introduced PinPtr, the first sensor\nnetworkbased countersniper system [17, 8] in 2003. The system is\nbased on potentially hundreds of inexpensive sensor nodes\ndeployed in the area of interest forming an ad-hoc multihop\nnetwork. The acoustic sensors measure the Time of Arrival\n(ToA) of muzzle blasts and ballistic shockwaves, pressure\nwaves induced by the supersonic projectile, send the data to\na base station where a sensor fusion algorithm determines\nthe origin of the shot. PinPtr is characterized by high\nprecision: 1m average 3D accuracy for shots originating within\nor near the sensor network and 1 degree bearing precision\nfor both azimuth and elevation and 10% accuracy in range\nestimation for longer range shots. The truly unique\ncharacteristic of the system is that it works in such reverberant\nenvironments as cluttered urban terrain and that it can\nresolve multiple simultaneous shots at the same time. This\ncapability is due to the widely distributed sensing and the\nunique sensor fusion approach [8]. The system has been\ntested several times in US Army MOUT (Military\nOperations in Urban Terrain) facilities.\nThe obvious disadvantage of such a system is its static\nnature. Once the sensors are distributed, they cover a\ncertain area. Depending on the operation, the deployment may\nbe needed for an hour or a month, but eventually the area\nlooses its importance. It is not practical to gather and reuse\nthe sensors, especially under combat conditions. Even if the\nsensors are cheap, it is still a waste and a logistical problem\nto provide a continuous stream of sensors as the operations\nmove from place to place. As it is primarily the soldiers that\nthe system protects, a natural extension is to mount the\nsensors on the soldiers themselves. While there are\nvehiclemounted countersniper systems [1] available commercially,\nwe are not aware of a deployed system that protects\ndismounted soldiers. A helmet-mounted system was developed\nin the mid 90s by BBN [3], but it was not continued beyond\nthe Darpa program that funded it.\n113\nTo move from a static sensor network-based solution to a\nhighly mobile one presents significant challenges. The sensor\npositions and orientation need to be constantly monitored.\nAs soldiers may work in groups of as little as four people,\nthe number of sensors measuring the acoustic phenomena\nmay be an order of magnitude smaller than before.\nMoreover, the system should be useful to even a single soldier.\nFinally, additional requirements called for caliber estimation\nand weapon classification in addition to source localization.\nThe paper presents the design and evaluation of our\nsoldierwearable mobile countersniper system. It describes the\nhardware and software architecture including the custom sensor\nboard equipped with a small microphone array and\nconnected to a COTS MICAz mote [12]. Special emphasis is\npaid to the sensor fusion technique that estimates the\ntrajectory, range, caliber and weapon type simultaneously. The\nresults and analysis of an independent evaluation of the\nsystem at the US Army Aberdeen Test Center are also\npresented.\n2. APPROACH\nThe firing of a typical military rifle, such as the AK47\nor M16, produces two distinct acoustic phenomena. The\nmuzzle blast is generated at the muzzle of the gun and\ntravels at the speed sound. The supersonic projectile generates\nan acoustic shockwave, a kind of sonic boom. The\nwavefront has a conical shape, the angle of which depends on the\nMach number, the speed of the bullet relative to the speed\nof sound.\nThe shockwave has a characteristic shape resembling a\ncapital N. The rise time at both the start and end of the\nsignal is very fast, under 1 \u03bcsec. The length is determined by\nthe caliber and the miss distance, the distance between the\ntrajectory and the sensor. It is typically a few hundred \u03bcsec.\nOnce a trajectory estimate is available, the shockwave length\ncan be used for caliber estimation.\nOur system is based on four microphones connected to\na sensorboard. The board detects shockwaves and muzzle\nblasts and measures their ToA. If at least three acoustic\nchannels detect the same event, its AoA is also computed.\nIf both the shockwave and muzzle blast AoA are available,\na simple analytical solution gives the shooter location as\nshown in Section 6. As the microphones are close to each\nother, typically 2-4, we cannot expect very high precision.\nAlso, this method does not estimate a trajectory. In fact, an\ninfinite number of trajectory-bullet speed pairs satisfy the\nobservations. However, the sensorboards are also connected\nto COTS MICAz motes and they share their AoA and ToA\nmeasurements, as well as their own location and orientation,\nwith each other using a multihop routing service [9]. A\nhybrid sensor fusion algorithm then estimates the trajectory,\nthe range, the caliber and the weapon type based on all\navailable observations.\nThe sensorboard is also Bluetooth capable for\ncommunication with the soldier\"s PDA or laptop computer. A wired\nUSB connection is also available. The sensorfusion\nalgorithm and the user interface get their data through one of\nthese channels.\nThe orientation of the microphone array at the time of\ndetection is provided by a 3-axis digital compass. Currently\nthe system assumes that the soldier\"s PDA is GPS-capable\nand it does not provide self localization service itself.\nHowever, the accuracy of GPS is a few meters degrading the\nFigure 1: Acoustic sensorboard/mote assembly\n.\noverall accuracy of the system. Refer to Section 7 for an\nanalysis. The latest generation sensorboard features a Texas\nInstruments CC-1000 radio enabling the high-precision radio\ninterferometric self localization approach we have developed\nseparately [7]. However, we leave the integration of the two\ntechnologies for future work.\n3. HARDWARE\nSince the first static version of our system in 2003, the\nsensor nodes have been built upon the UC Berkeley/Crossbow\nMICA product line [11]. Although rudimentary acoustic\nsignal processing can be done on these microcontroller-based\nboards, they do not provide the required computational\nperformance for shockwave detection and angle of arrival\nmeasurements, where multiple signals from different\nmicrophones need to be processed in parallel at a high sampling\nrate. Our 3rd generation sensorboard is designed to be used\nwith MICAz motes-in fact it has almost the same size as\nthe mote itself (see Figure 1).\nThe board utilizes a powerful Xilinx XC3S1000 FPGA\nchip with various standard peripheral IP cores, multiple soft\nprocessor cores and custom logic for the acoustic detectors\n(Figure 2). The onboard Flash (4MB) and PSRAM (8MB)\nmodules allow storing raw samples of several acoustic events,\nwhich can be used to build libraries of various acoustic\nsignatures and for refining the detection cores off-line. Also, the\nexternal memory blocks can store program code and data\nused by the soft processor cores on the FPGA.\nThe board supports four independent analog channels\nsampled at up to 1 MS/s (million samples per seconds). These\nchannels, featuring an electret microphone (Panasonic\nWM64PNT), amplifiers with controllable gain (30-60 dB) and\na 12-bit serial ADC (Analog Devices AD7476), reside on\nseparate tiny boards which are connected to the main\nsensorboard with ribbon cables. This partitioning enables the\nuse of truly different audio channels (eg.: slower sampling\nfrequency, different gain or dynamic range) and also results\nin less noisy measurements by avoiding long analog signal\npaths.\nThe sensor platform offers a rich set of interfaces and can\nbe integrated with existing systems in diverse ways. An\nRS232 port and a Bluetooth (BlueGiga WT12) wireless link\nwith virtual UART emulation are directly available on the\nboard and provide simple means to connect the sensor to\nPCs and PDAs. The mote interface consists of an I2\nC bus\nalong with an interrupt and GPIO line (the latter one is used\n114\nFigure 2: Block diagram of the sensorboard.\nfor precise time synchronization between the board and the\nmote). The motes are equipped with IEEE 802.15.4\ncompliant radio transceivers and support ad-hoc wireless\nnetworking among the nodes and to/from the base station. The\nsensorboard also supports full-speed USB transfers (with\ncustom USB dongles) for uploading recorded audio samples\nto the PC. The on-board JTAG chain-directly accessible\nthrough a dedicated connector-contains the FPGA part\nand configuration memory and provides in-system\nprogramming and debugging facilities.\nThe integrated Honeywell HMR3300 digital compass\nmodule provides heading, pitch and roll information with 1\u25e6\naccuracy, which is essential for calculating and combining\ndirectional estimates of the detected events.\nDue to the complex voltage requirements of the FPGA,\nthe power supply circuitry is implemented on the\nsensorboard and provides power both locally and to the mote. We\nused a quad pack of rechargeable AA batteries as the power\nsource (although any other configuration is viable that meets\nthe voltage requirements). The FPGA core (1.2 V) and I/O\n(3.3 V) voltages are generated by a highly efficient buck\nswitching regulator. The FPGA configuration (2.5 V) and a\nseparate 3.3 V power net are fed by low current LDOs, the\nlatter one is used to provide independent power to the mote\nand to the Bluetooth radio. The regulators-except the last\none-can be turned on/off from the mote or through the\nBluetooth radio (via GPIO lines) to save power.\nThe first prototype of our system employed 10 sensor\nnodes. Some of these nodes were mounted on military kevlar\nhelmets with the microphones directly attached to the\nsurface at about 20 cm separation as shown in Figure 3(a). The\nrest of the nodes were mounted in plastic enclosures\n(Figure 3(b)) with the microphones placed near the corners of\nthe boxes to form approximately 5 cm\u00d710 cm rectangles.\n4. SOFTWARE ARCHITECTURE\nThe sensor application relies on three subsystems\nexploiting three different computing paradigms as they are shown\nin Figure 4. Although each of these execution models suit\ntheir domain specific tasks extremely well, this diversity\n(a) (b)\nFigure 3: Sensor prototypes mounted on a kevlar\nhelmet (a) and in a plastic box on a tripod (b).\npresents a challenge for software development and system\nintegration. The sensor fusion and user interface\nsubsystem is running on PDAs and were implemented in Java.\nThe sensing and signal processing tasks are executed by an\nFPGA, which also acts as a bridge between various wired\nand wireless communication channels. The ad-hoc internode\ncommunication, time synchronization and data sharing are\nthe responsibilities of a microcontroller based radio module.\nSimilarly, the application employs a wide variety of\ncommunication protocols such as Bluetooth and IEEE 802.14.5\nwireless links, as well as optional UARTs, I2\nC and/or USB\nbuses.\nSoldier\nOperated Device\n(PDA/Laptop)\nFPGA\nSensor Board\nMica Radio\nModule\n2.4 GHz Wireless Link\nRadio Control\nMessage Routing\nAcoustic Event Encoder\nSensor Time Synch.\nNetwork Time Synch.Remote Control\nTime\nstamping\nInterrupts\nVirtual\nRegister\nInterface\nC\nO\nO\nR\nD\nI\nN\nA\nT\nO\nR\nA\nn\na\nl\no\ng\nc\nh\na\nn\nn\ne\nl\ns Compass\nPicoBlaze\nComm.\nInterface\nPicoBlaze\nWT12 Bluetooth Radio\nMOTE IF:I2C,Interrupts\nUSB PSRAM\nU\nA\nR\nT\nU\nA\nR\nT\nMB\ndet\nSW\ndet\nREC\nBluetooth Link\nUser\nInterface\nSensor\nFusion\nLocation\nEngine GPS\nMessage (Dis-)AssemblerSensor\nControl\nFigure 4: Software architecture diagram.\nThe sensor fusion module receives and unpacks raw\nmeasurements (time stamps and feature vectors) from the\nsensorboard through the Bluetooth link. Also, it fine tunes\nthe execution of the signal processing cores by setting\nparameters through the same link. Note that measurements\nfrom other nodes along with their location and orientation\ninformation also arrive from the sensorboard which acts as\na gateway between the PDA and the sensor network. The\nhandheld device obtains its own GPS location data and\ndi115\nrectly receives orientation information through the\nsensorboard. The results of the sensor fusion are displayed on the\nPDA screen with low latency. Since, the application is\nimplemented in pure Java, it is portable across different PDA\nplatforms.\nThe border between software and hardware is\nconsiderably blurred on the sensor board. The IP\ncores-implemented in hardware description languages (HDL) on the\nreconfigurable FPGA fabric-closely resemble hardware\nbuilding blocks. However, some of them-most notably the soft\nprocessor cores-execute true software programs. The\nprimary tasks of the sensor board software are 1) acquiring\ndata samples from the analog channels, 2) processing\nacoustic data (detection), and 3) providing access to the results\nand run-time parameters through different interfaces.\nAs it is shown in Figure 4, a centralized virtual register\nfile contains the address decoding logic, the registers for\nstoring parameter values and results and the point to point\ndata buses to and from the peripherals. Thus, it effectively\nintegrates the building blocks within the sensorboard and\ndecouples the various communication interfaces. This\narchitecture enabled us to deploy the same set of sensors in a\ncentralized scenario, where the ad-hoc mote network (using\nthe I2\nC interface) collected and forwarded the results to a\nbase station or to build a decentralized system where the\nlocal PDAs execute the sensor fusion on the data obtained\nthrough the Bluetooth interface (and optionally from other\nsensors through the mote interface). The same set of\nregisters are also accessible through a UART link with a terminal\nemulation program. Also, because the low-level interfaces\nare hidden by the register file, one can easily add/replace\nthese with new ones (eg.: the first generation of motes\nsupported a standard \u03bcP interface bus on the sensor connector,\nwhich was dropped in later designs).\nThe most important results are the time stamps of the\ndetected events. These time stamps and all other timing\ninformation (parameters, acoustic event features) are based\non a 1 MHz clock and an internal timer on the FPGA. The\ntime conversion and synchronization between the sensor\nnetwork and the board is done by the mote by periodically\nrequesting the capture of the current timer value through a\ndedicated GPIO line and reading the captured value from\nthe register file through the I2\nC interface. Based on the the\ncurrent and previous readings and the corresponding mote\nlocal time stamps, the mote can calculate and maintain the\nscaling factor and offset between the two time domains.\nThe mote interface is implemented by the I2\nC slave IP\ncore and a thin adaptation layer which provides a data and\naddress bus abstraction on top of it. The maximum\neffective bandwidth is 100 Kbps through this interface. The\nFPGA contains several UART cores as well: for\ncommunicating with the on-board Bluetooth module, for\ncontrolling the digital compass and for providing a wired RS232\nlink through a dedicated connector. The control, status and\ndata registers of the UART modules are available through\nthe register file. The higher level protocols on these lines are\nimplemented by Xilinx PicoBlaze microcontroller cores [13]\nand corresponding software programs. One of them provides\na command line interface for test and debug purposes, while\nthe other is responsible for parsing compass readings. By\ndefault, they are connected to the RS232 port and to the\non-board digital compass line respectively, however, they\ncan be rewired to any communication interface by changing\nthe register file base address in the programs (e.g. the\ncommand line interface can be provided through the Bluetooth\nchannel).\nTwo of the external interfaces are not accessible through\nthe register file: a high speed USB link and the SRAM\ninterface are tied to the recorder block. The USB module\nimplements a simple FIFO with parallel data lines connected to an\nexternal FT245R USB device controller. The RAM driver\nimplements data read/write cycles with correct timing and\nis connected to the on-board pseudo SRAM. These\ninterfaces provide 1 MB/s effective bandwidth for downloading\nrecorded audio samples, for example.\nThe data acquisition and signal processing paths exhibit\nclear symmetry: the same set of IP cores are instantiated\nfour times (i.e. the number of acoustic channels) and run\nindependently. The signal paths meet only just before\nthe register file. Each of the analog channels is driven by\na serial A/D core for providing a 20 MHz serial clock and\nshifting in 8-bit data samples at 1 MS/s and a digital\npotentiometer driver for setting the required gain. Each channel\nhas its own shockwave and muzzle blast detector, which are\ndescribed in Section 5. The detectors fetch run-time\nparameter values from the register file and store their results there\nas well. The coordinator core constantly monitors the\ndetection results and generates a mote interrupt promptly upon\nfull detection or after a reasonable timeout after partial\ndetection.\nThe recorder component is not used in the final\ndeployment, however, it is essential for development purposes for\nrefining parameter values for new types of weapons or for\nother acoustic sources. This component receives the\nsamples from all channels and stores them in circular buffers in\nthe PSRAM device. If the signal amplitude on one of the\nchannels crosses a predefined threshold, the recorder\ncomponent suspends the sample collection with a predefined delay\nand dumps the contents of the buffers through the USB link.\nThe length of these buffers and delays, the sampling rate,\nthe threshold level and the set of recorded channels can be\n(re)configured run-time through the register file. Note that\nthe core operates independently from the other signal\nprocessing modules, therefore, it can be used to validate the\ndetection results off-line.\nThe FPGA cores are implemented in VHDL, the PicoBlaze\nprograms are written in assembly. The complete\nconfiguration occupies 40% of the resources (slices) of the FPGA and\nthe maximum clock speed is 30 MHz, which is safely higher\nthan the speed used with the actual device (20MHz).\nThe MICAz motes are responsible for distributing\nmeasurement data across the network, which drastically\nimproves the localization and classification results at each node.\nBesides a robust radio (MAC) layer, the motes require two\nessential middleware services to achieve this goal. The\nmessages need to be propagated in the ad-hoc multihop network\nusing a routing service. We successfully integrated the\nDirected Flood-Routing Framework (DFRF) [9] in our\napplication. Apart from automatic message aggregation and\nefficient buffer management, the most unique feature of DFRF\nis its plug-in architecture, which accepts custom routing\npolicies. Routing policies are state machines that govern\nhow received messages are stored, resent or discarded.\nExample policies include spanning tree routing, broadcast,\ngeographic routing, etc. Different policies can be used for\ndifferent messages concurrently, and the application is able to\n116\nchange the underlying policies at run-time (eg.: because of\nthe changing RF environment or power budget). In fact, we\nswitched several times between a simple but lavish broadcast\npolicy and a more efficient gradient routing on the field.\nCorrelating ToA measurements requires a common time\nbase and precise time synchronization in the sensor network.\nThe Routing Integrated Time Synchronization (RITS) [15]\nprotocol relies on very accurate MAC-layer time-stamping\nto embed the cumulative delay that a data message accrued\nsince the time of the detection in the message itself. That\nis, at every node it measures the time the message spent\nthere and adds this to the number in the time delay slot of\nthe message, right before it leaves the current node. Every\nreceiving node can subtract the delay from its current time\nto obtain the detection time in its local time reference. The\nservice provides very accurate time conversion (few \u03bcs per\nhop error), which is more than adequate for this application.\nNote, that the motes also need to convert the sensorboard\ntime stamps to mote time as it is described earlier.\nThe mote application is implemented in nesC [5] and is\nrunning on top of TinyOS [6]. With its 3 KB RAM and\n28 KB program space (ROM) requirement, it easily fits on\nthe MICAz motes.\n5. DETECTION ALGORITHM\nThere are several characteristics of acoustic shockwaves\nand muzzle blasts which distinguish their detection and\nsignal processing algorithms from regular audio applications.\nBoth events are transient by their nature and present very\nintense stimuli to the microphones. This is increasingly\nproblematic with low cost electret microphones-designed\nfor picking up regular speech or music. Although\nmechanical damping of the microphone membranes can mitigate\nthe problem, this approach is not without side effects. The\ndetection algorithms have to be robust enough to handle\nsevere nonlinear distortion and transitory oscillations. Since\nthe muzzle blast signature closely follows the shockwave\nsignal and because of potential automatic weapon bursts, it is\nextremely important to settle the audio channels and the\ndetection logic as soon as possible after an event. Also,\nprecise angle of arrival estimation necessitates high sampling\nfrequency (in the MHz range) and accurate event detection.\nMoreover, the detection logic needs to process multiple\nchannels in parallel (4 channels on our existing hardware).\nThese requirements dictated simple and robust algorithms\nboth for muzzle blast and shockwave detections. Instead of\nusing mundane energy detectors-which might not be able\nto distinguish the two different events-the applied\ndetectors strive to find the most important characteristics of the\ntwo signals in the time-domain using simple state machine\nlogic. The detectors are implemented as independent IP\ncores within the FPGA-one pair for each channel. The\ncores are run-time configurable and provide detection event\nsignals with high precision time stamps and event specific\nfeature vectors. Although the cores are running\nindependently and in parallel, a crude local fusion module integrates\nthem by shutting down those cores which missed their events\nafter a reasonable timeout and by generating a single\ndetection message towards the mote. At this point, the mote can\nread and forward the detection times and features and is\nresponsible to restart the cores afterwards.\nThe most conspicuous characteristics of an acoustic\nshockwave (see Figure 5(a)) are the steep rising edges at the\nbe0 200 400 600 800 1000 1200 1400 1600\n-1\n-0.8\n-0.6\n-0.4\n-0.2\n0\n0.2\n0.4\n0.6\n0.8\n1\nShockwave (M16)\nTime (\u00b5s)\nAmplitude\n1\n3\n5\n2\n4\nlen\n(a)\ns[t] - s[t-D] > E\ntstart\n:= t\ns[t] - s[t-D] < E\ns[t] - s[t-D] > E &\nt - t_start > Lmin\ns[t] - s[t-D] < E\nlen := t - tstart\nIDLE\n1\nFIRST EDGE DONE\n3\nSECOND EDGE\n4\nFIRST EDGE\n2\nFOUND\n5\nt - tstart\n\u2265 Lmax\nt - tstart\n\u2265 Lmax\n(b)\nFigure 5: Shockwave signal generated by a 5.56 \u00d7\n45 mm NATO projectile (a) and the state machine\nof the detection algorithm (b).\nginning and end of the signal. Also, the length of the N-wave\nis fairly predictable-as it is described in Section 6.5-and is\nrelatively short (200-300 \u03bcs). The shockwave detection core\nis continuously looking for two rising edges within a given\ninterval. The state machine of the algorithm is shown in\nFigure 5(b). The input parameters are the minimum\nsteepness of the edges (D, E), and the bounds on the length of\nthe wave (Lmin, Lmax). The only feature calculated by the\ncore is the length of the observed shockwave signal.\nIn contrast to shockwaves, the muzzle blast signatures are\ncharacterized by a long initial period (1-5 ms) where the first\nhalf period is significantly shorter than the second half [4].\nDue to the physical limitations of the analog circuitry\ndescribed at the beginning of this section, irregular oscillations\nand glitches might show up within this longer time window\nas they can be clearly seen in Figure 6(a). Therefore, the real\nchallenge for the matching detection core is to identify the\nfirst and second half periods properly. The state machine\n(Figure 6(b)) does not work on the raw samples directly\nbut is fed by a zero crossing (ZC) encoder. After the initial\ntriggering, the detector attempts to collect those ZC\nsegments which belong to the first period (positive amplitude)\nwhile discarding too short (in our terminology: garbage)\nsegments-effectively implementing a rudimentary low-pass\nfilter in the ZC domain. After it encounters a sufficiently\nlong negative segment, it runs the same collection logic for\nthe second half period. If too much garbage is discarded\nin the collection phases, the core resets itself to prevent the\n(false) detection of the halves from completely different\nperiods separated by rapid oscillation or noise. Finally, if the\nconstraints on the total length and on the length ratio hold,\nthe core generates a detection event along with the actual\nlength, amplitude and energy of the period calculated\nconcurrently. The initial triggering mechanism is based on two\namplitude thresholds: one static (but configurable)\namplitude level and a dynamically computed one. The latter one\nis essential to adapt the sensor to different ambient noise\nenvironments and to temporarily suspend the muzzle blast\ndetector after a shock wave event (oscillations in the analog\nsection or reverberations in the sensor enclosure might\notherwise trigger false muzzle blast detections). The dynamic\nnoise level is estimated by a single pole recursive low-pass\nfilter (cutoff @ 0.5 kHz ) on the FPGA.\n117\n0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000\n-1\n-0.8\n-0.6\n-0.4\n-0.2\n0\n0.2\n0.4\n0.6\n0.8\n1\nTime (\u00b5s)\nAmplitude\nMuzzle blast (M16)\n1\n2\n3\n4 5\nlen2\n+\nlen1\n(a)\nIDLE\n1\nSECOND ZC\n3\nPENDING ZC\n4\nFIRST ZC\n2\nFOUND\n5\namplitude\nthreshold\nlong\npositive ZC\nlong\nnegative ZC\nvalid\nfull period\nmax\ngarbage\nwrong sign\ngarbage\ncollect\nfirst period\ngarbage\ncollect\nfirst period\ngarbage\n(b)\nFigure 6: Muzzle blast signature (a) produced by an\nM16 assault rifle and the corresponding detection\nlogic (b).\nThe detection cores were originally implemented in Java\nand evaluated on pre-recorded signals because of much faster\ntest runs and more convenient debugging facilities. Later\non, they were ported to VHDL and synthesized using the\nXilinx ISE tool suite. The functional equivalence between\nthe two implementations were tested by VHDL test benches\nand Python scripts which provided an automated way to\nexercise the detection cores on the same set of pre-recorded\nsignals and to compare the results.\n6. SENSOR FUSION\nThe sensor fusion algorithm receives detection messages\nfrom the sensor network and estimates the bullet trajectory,\nthe shooter position, the caliber of the projectile and the\ntype of the weapon. The algorithm consists of well separated\ncomputational tasks outlined below:\n1. Compute muzzle blast and shockwave directions of\narrivals for each individual sensor (see 6.1).\n2. Compute range estimates. This algorithm can\nanalytically fuse a pair of shockwave and muzzle blast AoA\nestimates. (see 6.2).\n3. Compute a single trajectory from all shockwave\nmeasurements (see 6.3).\n4. If trajectory available compute range (see 6.4).\nelse compute shooter position first and then trajectory\nbased on it. (see 6.4)\n5. If trajectory available compute caliber (see 6.5).\n6. If caliber available compute weapon type (see 6.6).\nWe describe each step in the following sections in detail.\n6.1 Direction of arrival\nThe first step of the sensor fusion is to calculate the\nmuzzle blast and shockwave AoA-s for each sensorboard. Each\nsensorboard has four microphones that measure the ToA-s.\nSince the microphone spacing is orders of magnitude smaller\nthan the distance to the sound source, we can approximate\nthe approaching sound wave front with a plane (far field\nassumption).\nLet us formalize the problem for 3 microphones first. Let\nP1, P2 and P3 be the position of the microphones ordered by\ntime of arrival t1 < t2 < t3. First we apply a simple\ngeometry validation step. The measured time difference between\ntwo microphones cannot be larger than the sound\npropagation time between the two microphones:\n|ti \u2212 tj| <= |Pi \u2212 Pj |/c + \u03b5\nWhere c is the speed of sound and \u03b5 is the maximum\nmeasurement error. If this condition does not hold, the\ncorresponding detections are discarded. Let v(x, y, z) be the\nnormal vector of the unknown direction of arrival. We also\nuse r1(x1, y1, z1), the vector from P1 to P2 and r2(x2, y2, z2),\nthe vector from P1 to P3. Let\"s consider the projection of\nthe direction of the motion of the wave front (v) to r1\ndivided by the speed of sound (c). This gives us how long it\ntakes the wave front to propagate form P1 to P2:\nvr1 = c(t2 \u2212 t1)\nThe same relationship holds for r2 and v:\nvr2 = c(t3 \u2212 t1)\nWe also know that v is a normal vector:\nvv = 1\nMoving from vectors to coordinates using the dot product\ndefinition leads to a quadratic system:\nxx1 + yy1 + zz1 = c(t2 \u2212 t1)\nxx2 + yy2 + zz2 = c(t3 \u2212 t1)\nx2\n+ y2\n+ z2\n= 1\nWe omit the solution steps here, as they are\nstraightforward, but long. There are two solutions (if the source is on\nthe P1P2P3 plane the two solutions coincide). We use the\nfourth microphone\"s measurement-if there is one-to\neliminate one of them. Otherwise, both solutions are considered\nfor further processing.\n6.2 Muzzle-shock fusion\nu\nv\n11,tP\n22,tP\ntP,\n2P\u2032\nBullet trajectory\nFigure 7: Section plane of a shot (at P) and two\nsensors (at P1 and at P2). One sensor detects the\nmuzzle blast\"s, the other the shockwave\"s time and\ndirection of arrivals.\nConsider the situation in Figure 7. A shot was fired from\nP at time t. Both P and t are unknown. We have one muzzle\nblast and one shockwave detections by two different sensors\n118\nwith AoA and hence, ToA information available. The\nmuzzle blast detection is at position P1 with time t1 and AoA\nu. The shockwave detection is at P2 with time t2 and AoA\nv. u and v are normal vectors. It is shown below that these\nmeasurements are sufficient to compute the position of the\nshooter (P).\nLet P2 be the point on the extended shockwave cone\nsurface where PP2 is perpendicular to the surface. Note that\nPP2 is parallel with v. Since P2 is on the cone surface which\nhits P2, a sensor at P2 would detect the same shockwave\ntime of arrival (t2). The cone surface travels at the speed of\nsound (c), so we can express P using P2:\nP = P2 + cv(t2 \u2212 t).\nP can also be expressed from P1:\nP = P1 + cu(t1 \u2212 t)\nyielding\nP1 + cu(t1 \u2212 t) = P2 + cv(t2 \u2212 t).\nP2P2 is perpendicular to v:\n(P2 \u2212 P2)v = 0\nyielding\n(P1 + cu(t1 \u2212 t) \u2212 cv(t2 \u2212 t) \u2212 P2)v = 0\ncontaining only one unknown t. One obtains:\nt =\n(P1\u2212P2)v\nc\n+uvt1\u2212t2\nuv\u22121\n.\nFrom here we can calculate the shoter position P.\nLet\"s consider the special single sensor case where P1 = P2\n(one sensor detects both shockwave and muzzle blast AoA).\nIn this case:\nt = uvt1\u2212t2\nuv\u22121\n.\nSince u and v are not used separately only uv, the absolute\norientation of the sensor can be arbitrary, we still get t which\ngives us the range.\nHere we assumed that the shockwave is a cone which is\nonly true for constant projectile speeds. In reality, the angle\nof the cone slowly grows; the surface resembles one half of\nan American football. The decelerating bullet results in a\nsmaller time difference between the shockwave and the\nmuzzle blast detections because the shockwave generation slows\ndown with the bullet. A smaller time difference results in a\nsmaller range, so the above formula underestimates the true\nrange. However, it can still be used with a proper\ndeceleration correction function. We leave this for future work.\n6.3 Trajectory estimation\nDanicki showed that the bullet trajectory and speed can\nbe computed analytically from two independent shockwave\nmeasurements where both ToA and AoA are measured [2].\nThe method gets more sensitive to measurement errors as\nthe two shockwave directions get closer to each other. In\nthe special case when both directions are the same, the\ntrajectory cannot be computed. In a real world application,\nthe sensors are typically deployed on a plane approximately.\nIn this case, all sensors located on one side of the\ntrajectory measure almost the same shockwave AoA. To avoid\nthis error sensitivity problem, we consider shockwave\nmeasurement pairs only if the direction of arrival difference is\nlarger than a certain threshold.\nWe have multiple sensors and one sensor can report two\ndifferent directions (when only three microphones detect the\nshockwave). Hence, we typically have several trajectory\ncandidates, i.e. one for each AoA pair over the threshold. We\napplied an outlier filtering and averaging method to fuse\ntogether the shockwave direction and time information and\ncome up with a single trajectory. Assume that we have\nN individual shockwave AoA measurements. Let\"s take all\npossible unordered pairs where the direction difference is\nabove the mentioned threshold and compute the trajectory\nfor each. This gives us at most N(N\u22121)\n2\ntrajectories. A\ntrajectory is represented by one point pi and the normal vector\nvi (where i is the trajectory index). We define the distance\nof two trajectories as the dot product of their normal\nvectors:\nD(i, j) = vivj\nFor each trajectory a neighbor set is defined:\nN(i) := {j|D(i, j) < R}\nwhere R is a radius parameter. The largest neighbor set is\nconsidered to be the core set C, all other trajectories are\noutliers. The core set can be found in O(N2\n) time. The\ntrajectories in the core set are then averaged to get the final\ntrajectory.\nIt can happen that we cannot form any sensor pairs\nbecause of the direction difference threshold. It means all\nsensors are on the same side of the trajectory. In this case,\nwe first compute the shooter position (described in the next\nsection) that fixes p making v the only unknown. To find\nv in this case, we use a simple high resolution grid search\nand minimize an error function based on the shockwave\ndirections.\nWe have made experiments to utilize the measured\nshockwave length in the trajectory estimation. There are some\npromising results, but it needs further research.\n6.4 Shooter position estimation\nThe shooter position estimation algorithm aggregates the\nfollowing heterogenous information generated by earlier\ncomputational steps:\n1. trajectory,\n2. muzzle blast ToA at a sensor,\n3. muzzle blast AoA at a sensor, which is effectively a\nbearing estimate to the shooter, and\n4. range estimate at a sensor (when both shockwave and\nmuzzle blast AoA are available).\nSome sensors report only ToA, some has bearing\nestimate(s) also and some has range estimate(s) as well,\ndepending on the number of successful muzzle blast and shockwave\ndetections by the sensor. For an example, refer to Figure 8.\nNote that a sensor may have two different bearing and range\nestimates. 3 detections gives two possible AoA-s for\nmuzzle blast (i.e. bearing) and/or shockwave. Furthermore, the\ncombination of two different muzzle blast and shockwave\nAoA-s may result in two different ranges.\n119\n11111 ,,,, rrvvt \u2032\u2032\n22 ,vt\n333 ,, vvt \u2032\n4t\n5t\n6t\nbullet trajectory\nshooter position\nFigure 8: Example of heterogenous input data for\nthe shooter position estimation algorithm. All\nsensors have ToA measurements (t1, t2, t3, t4, t5), one\nsensor has a single bearing estimate (v2), one sensor has\ntwo possible bearings (v3, v3) and one sensor has two\nbearing and two range estimates (v1, v1,r1, r1)\nIn a multipath environment, these detections will not only\ncontain gaussian noise, but also possibly large errors due to\nechoes. It has been showed in our earlier work that a similar\nproblem can be solved efficiently with an interval arithmetic\nbased bisection search algorithm [8]. The basic idea is to\ndefine a discrete consistency function over the area of\ninterest and subdivide the space into 3D boxes. For any given\n3D box, this function gives the number of measurements\nsupporting the hypothesis that the shooter was within that\nbox. The search starts with a box large enough to contain\nthe whole area of interest, then zooms in by dividing and\nevaluating boxes. The box with the maximum consistency\nis divided until the desired precision is reached.\nBacktracking is possible to avoid getting stuck in a local maximum.\nThis approach has been shown to be fast enough for\nonline processing. Note, however, that when the trajectory\nhas already been calculated in previous steps, the search\nneeds to be done only on the trajectory making it orders of\nmagnitude faster.\nNext let us describe how the consistency function is\ncalculated in detail. Consider B, a three dimensional box, we\nwould like to compute the consistency value of. First we\nconsider only the ToA information. If one sensor has\nmultiple ToA detections, we use the average of those times, so\none sensor supplies at most one ToA estimate. For each\nToA, we can calculate the corresponding time of the shot,\nsince the origin is assumed to be in box B. Since it is a box\nand not a single point, this gives us an interval for the shot\ntime. The maximum number of overlapping time intervals\ngives us the value of the consistency function for B. For a\ndetailed description of the consistency function and search\nalgorithm, refer to [8].\nHere we extend the approach the following way. We\nmodify the consistency function based on the bearing and range\ndata from individual sensors. A bearing estimate supports\nB if the line segment starting from the sensor with the\nmeasured direction intersects the B box. A range supports B,\nif the sphere with the radius of the range and origin of the\nsensor intersects B. Instead of simply checking whether the\nposition specified by the corresponding bearing-range pairs\nfalls within B, this eliminates the sensor\"s possible\norientation error. The value of the consistency function is\nincremented by one for each bearing and range estimate that is\nconsistent with B.\n6.5 Caliber estimation\nThe shockwave signal characteristics has been studied\nbefore by Whitham [20]. He showed that the shockwave period\nT is related to the projectile diameter d, the length l, the\nperpendicular miss distance b from the bullet trajectory to\nthe sensor, the Mach number M and the speed of sound c.\nT = 1.82Mb1/4\nc(M2\u22121)3/8\nd\nl1/4 \u2248 1.82d\nc\n(Mb\nl\n)1/4\n0\n100\n200\n300\n400\n500\n600\n0 10 20 30\nmiss distance (m)shockwavelength(microseconds)\n.50 cal\n5.56 mm\n7.62 mm\nFigure 9: Shockwave length and miss distance\nrelationship. Each data point represents one\nsensorboard after an aggregation of the individual\nmeasurements of the four acoustic channels. Three\ndifferent caliber projectiles have been tested (196\nshots, 10 sensors).\nTo illustrate the relationship between miss distance and\nshockwave length, here we use all 196 shots with three\ndifferent caliber projectiles fired during the evaluation. (During\nthe evaluation we used data obtained previously using a few\npractice shots per weapon.) 10 sensors (4 microphones by\nsensor) measured the shockwave length. For each sensor,\nwe considered the shockwave length estimation valid if at\nleast three out of four microphones agreed on a value with\nat most 5 microsecond variance. This filtering leads to a\n86% report rate per sensor and gets rid of large\nmeasurement errors. The experimental data is shown in Figure 9.\nWhitham\"s formula suggests that the shockwave length for a\ngiven caliber can be approximated with a power function of\nthe miss distance (with a 1/4 exponent). Best fit functions\non our data are:\n.50 cal: T = 237.75b0.2059\n7.62 mm: T = 178.11b0.1996\n5.56 mm: T = 144.39b0.1757\nTo evaluate a shot, we take the caliber whose\napproximation function results in the smallest RMS error of the\nfiltered sensor readings. This method has less than 1%\ncaliber estimation error when an accurate trajectory estimate\nis available. In other words, caliber estimation only works\nif enough shockwave detections are made by the system to\ncompute a trajectory.\n120\n6.6 Weapon estimation\nWe analyzed all measured signal characteristics to find\nweapon specific information. Unfortunately, we concluded\nthat the observed muzzle blast signature is not characteristic\nenough of the weapon for classification purposes. The\nreflections of the high energy muzzle blast from the environment\nhave much higher impact on the muzzle blast signal shape\nthan the weapon itself. Shooting the same weapon from\ndifferent places caused larger differences on the recorded signal\nthan shooting different weapons from the same place.\n0\n100\n200\n300\n400\n500\n600\n700\n800\n900\n0 100 200 300 400\nrange (m)\nspeed(m/s)\nAK-47\nM240\nFigure 10: AK47 and M240 bullet deceleration\nmeasurements. Both weapons have the same caliber.\nData is approximated using simple linear regression.\n0\n100\n200\n300\n400\n500\n600\n700\n800\n900\n1000\n0 50 100 150 200 250 300 350\nrange (m)\nspeed(m/s)\nM16\nM249\nM4\nFigure 11: M16, M249 and M4 bullet deceleration\nmeasurements. All weapons have the same caliber.\nData is approximated using simple linear regression.\nHowever, the measured speed of the projectile and its\ncaliber showed good correlation with the weapon type. This\nis because for a given weapon type and ammunition pair,\nthe muzzle velocity is nearly constant. In Figures 10 and\n11 we can see the relationship between the range and the\nmeasured bullet speed for different calibers and weapons.\nIn the supersonic speed range, the bullet deceleration can\nbe approximated with a linear function. In case of the\n7.62 mm caliber, the two tested weapons (AK47, M240) can\nbe clearly separated (Figure 10). Unfortunately, this is not\nnecessarily true for the 5.56 mm caliber. The M16 with its\nhigher muzzle speed can still be well classified, but the M4\nand M249 weapons seem practically undistinguishable\n(Figure 11). However, this may be partially due to the limited\nnumber of practice shots we were able to take before the\nactual testing began. More training data may reveal better\nseparation between the two weapons since their published\nmuzzle velocities do differ somewhat.\nThe system carries out weapon classification in the\nfollowing manner. Once the trajectory is known, the speed can be\ncalculated for each sensor based on the shockwave geometry.\nTo evaluate a shot, we choose the weapon type whose\ndeceleration function results in the smallest RMS error of the\nestimated range-speed pairs for the estimated caliber class.\n7. RESULTS\nAn independent evaluation of the system was carried out\nby a team from NIST at the US Army Aberdeen Test Center\nin April 2006 [19]. The experiment was setup on a shooting\nrange with mock-up wooden buildings and walls for\nsupporting elevated shooter positions and generating multipath\neffects. Figure 12 shows the user interface with an aerial\nphotograph of the site. 10 sensor nodes were deployed on\nsurveyed points in an approximately 30\u00d730 m area. There\nwere five fixed targets behind the sensor network. Several\nfiring positions were located at each of the firing lines at\n50, 100, 200 and 300 meters. These positions were known\nto the evaluators, but not to the operators of the system.\nSix different weapons were utilized: AK47 and M240\nfiring 7.62 mm projectiles, M16, M4 and M249 with 5.56mm\nammunition and the .50 caliber M107.\nNote that the sensors remained static during the test. The\nprimary reason for this is that nobody is allowed downrange\nduring live fire tests. Utilizing some kind of remote\ncontrol platform would have been too involved for the limited\ntime the range was available for the test. The experiment,\ntherefore, did not test the mobility aspect of the system.\nDuring the one day test, there were 196 shots fired. The\nresults are summarized in Table 1. The system detected all\nshots successfully. Since a ballistic shockwave is a unique\nacoustic phenomenon, it makes the detection very robust.\nThere were no false positives for shockwaves, but there were\na handful of false muzzle blast detections due to parallel\ntests of artillery at a nearby range.\nShooter Local- Caliber Trajectory Trajectory Distance No.\nRange ization Accu- Azimuth Distance Error of\n(m) Rate racy Error (deg) Error (m) (m) Shots\n50 93% 100% 0.86 0.91 2.2 54\n100 100% 100% 0.66 1.34 8.7 54\n200 96% 100% 0.74 2.71 32.8 54\n300 97% 97% 1.49 6.29 70.6 34\nAll 96% 99.5% 0.88 2.47 23.0 196\nTable 1: Summary of results fusing all available\nsensor observations. All shots were successfully\ndetected, so the detection rate is omitted. Localization\nrate means the percentage of shots that the sensor\nfusion was able to estimate the trajectory of. The\ncaliber accuracy rate is relative to the shots localized\nand not all the shots because caliber estimation\nrequires the trajectory. The trajectory error is broken\ndown to azimuth in degrees and the actual distance\nof the shooter from the trajectory. The distance\nerror shows the distance between the real shooter\nposition and the estimated shooter position. As such,\nit includes the error caused by both the trajectory\nand that of the range estimation. Note that the\ntraditional bearing and range measures are not good\nones for a distributed system such as ours because\nof the lack of a single reference point.\n121\nFigure 12: The user interface of the system\nshowing the experimental setup. The 10 sensor nodes\nare labeled by their ID and marked by dark circles.\nThe targets are black squares marked T-1 through\nT-5. The long white arrows point to the shooter\nposition estimated by each sensor. Where it is\nmissing, the corresponding sensor did not have enough\ndetections to measure the AoA of either the\nmuzzle blast, the shockwave or both. The thick black\nline and large circle indicate the estimated\ntrajectory and the shooter position as estimated by fusing\nall available detections from the network. This shot\nfrom the 100-meter line at target T-3 was localized\nalmost perfectly by the sensor network. The caliber\nand weapon were also identified correctly. 6 out of\n10 nodes were able to estimate the location alone.\nTheir bearing accuracy is within a degree, while the\nrange is off by less than 10% in the worst case.\nThe localization rate characterizes the system\"s ability to\nsuccessfully estimate the trajectory of shots. Since caliber\nestimation and weapon classification relies on the trajectory,\nnon-localized shots are not classified either. There were 7\nshots out of 196 that were not localized. The reason for\nmissed shots is the trajectory ambiguity problem that occurs\nwhen the projectile passes on one side of all the sensors. In\nthis case, two significantly different trajectories can generate\nthe same set of observations (see [8] and also Section 6.3).\nInstead of estimating which one is more likely or displaying\nboth possibilities, we decided not to provide a trajectory at\nall. It is better not to give an answer other than a shot\nalarm than misleading the soldier.\nLocalization accuracy is broken down to trajectory\naccuracy and range estimation precision. The angle of the\nestimated trajectory was better than 1 degree except for the\n300 m range. Since the range should not affect trajectory\nestimation as long as the projectile passes over the network,\nwe suspect that the slightly worse angle precision for 300 m\nis due to the hurried shots we witnessed the soldiers took\nnear the end of the day. This is also indicated by another\ndatapoint: the estimated trajectory distance from the\nactual targets has an average error of 1.3 m for 300 m shots,\n0.75 m for 200 m shots and 0.6 m for all but 300 m shots.\nAs the distance between the targets and the sensor network\nwas fixed, this number should not show a 2\u00d7 improvement\njust because the shooter is closer.\nSince the angle of the trajectory itself does not\ncharacterize the overall error-there can be a translation\nalsoTable 1 also gives the distance of the shooter from the\nestimated trajectory. These indicate an error which is about\n1-2% of the range. To put this into perspective, a\ntrajectory estimate for a 100 m shot will very likely go through or\nvery near the window the shooter is located at. Again, we\nbelieve that the disproportionally larger errors at 300 m are\ndue to human errors in aiming. As the ground truth was\nobtained by knowing the precise location of the shooter and\nthe target, any inaccuracy in the actual trajectory directly\nadds to the perceived error of the system.\nWe call the estimation of the shooter\"s position on the\ncalculated trajectory range estimation due to the lack of a\nbetter term. The range estimates are better than 5%\naccurate from 50 m and 10% for 100 m. However, this goes\nto 20% or worse for longer distances. We did not have a\nfacility to test system before the evaluation for ranges\nbeyond 100 m. During the evaluation, we ran into the\nproblem of mistaking shockwave echoes for muzzle blasts. These\nechoes reached the sensors before the real muzzle blast for\nlong range shots only, since the projectile travels 2-3\u00d7 faster\nthan the speed of sound, so the time between the shockwave\n(and its possible echo from nearby objects) and the muzzle\nblast increases with increasing ranges. This resulted in\nunderestimating the range, since the system measured shorter\ntimes than the real ones. Since the evaluation we finetuned\nthe muzzle blast detection algorithm to avoid this problem.\nDistance M16 AK47 M240 M107 M4 M249 M4-M249\n50m 100% 100% 100% 100% 11% 25% 94%\n100m 100% 100% 100% 100% 22% 33% 100%\n200m 100% 100% 100% 100% 50% 22% 100%\n300m 67% 100% 83% 100% 33% 0% 57%\nAll 96% 100% 97% 100% 23% 23% 93%\nTable 2: Weapon classification results. The\npercentages are relative to the number of shots localized and\nnot all shots, as the classification algorithm needs to\nknow the trajectory and the range. Note that the\ndifference is small; there were 189 shots localized\nout of the total 196.\nThe caliber and weapon estimation accuracy rates are\nbased on the 189 shots that were successfully localized. Note\nthat there was a single shot that was falsely classified by the\ncaliber estimator. The 73% overall weapon classification\naccuracy does not seem impressive. But if we break it down\nto the six different weapons tested, the picture changes\ndramatically as shown in Table 2. For four of the weapons\n(AK14, M16, M240 and M107), the classification rate is\nalmost 100%. There were only two shots out of approximately\n140 that were missed. The M4 and M249 proved to be too\nsimilar and they were mistaken for each other most of the\ntime. One possible explanation is that we had only a limited\nnumber of test shots taken with these weapons right before\nthe evaluation and used the wrong deceleration\napproximation function. Either this or a similar mistake was made\n122\nsince if we simply used the opposite of the system\"s answer\nwhere one of these weapons were indicated, the accuracy\nwould have improved 3x. If we consider these two weapons\na single weapon class, then the classification accuracy for it\nbecomes 93%.\nNote that the AK47 and M240 have the same caliber\n(7.62 mm), just as the M16, M4 and M249 do (5.56 mm).\nThat is, the system is able to differentiate between weapons\nof the same caliber. We are not aware of any system that\nclassifies weapons this accurately.\n7.1 Single sensor performance\nAs was shown previously, a single sensor alone is able\nto localize the shooter if it can determine both the muzzle\nblast and the shockwave AoA, that is, it needs to measure\nthe ToA of both on at least three acoustic channels. While\nshockwave detection is independent of the range-unless the\nprojectile becomes subsonic-, the likelihood of muzzle blast\ndetection beyond 150 meters is not enough for consistently\ngetting at least three per sensor node for AoA estimation.\nHence, we only evaluate the single sensor performance for\nthe 104 shots that were taken from 50 and 100 m. Note that\nwe use the same test data as in the previous section, but we\nevaluate individually for each sensor.\nTable 3 summarizes the results broken down by the ten\nsensors utilized. Since this is now not a distributed system,\nthe results are given relative to the position of the given\nsensor, that is, a bearing and range estimate is provided. Note\nthat many of the common error sources of the networked\nsystem do not play a role here. Time synchronization is\nnot applicable. The sensor\"s absolute location is irrelevant\n(just as the relative location of multiple sensors). The\nsensor\"s orientation is still important though. There are several\ndisadvantages of the single sensor case compared to the\nnetworked system: there is no redundancy to compensate for\nother errors and to perform outlier rejection, the\nlocalization rate is markedly lower, and a single sensor alone is not\nable to estimate the caliber or classify the weapon.\nSensor id 1 2 3 5 7 8 9 10 11 12\nLoc. rate 44% 37% 53% 52% 19% 63% 51% 31% 23% 44%\nBearing (deg) 0.80 1.25 0.60 0.85 1.02 0.92 0.73 0.71 1.28 1.44\nRange (m) 3.2 6.1 4.4 4.7 4.6 4.6 4.1 5.2 4.8 8.2\nTable 3: Single sensor accuracy for 108 shots fired\nfrom 50 and 100 meters. Localization rate refers to\nthe percentage of shots the given sensor alone was\nable to localize. The bearing and range values are\naverage errors. They characterize the accuracy of\nlocalization from the given sensor\"s perspective.\nThe data indicates that the performance of the sensors\nvaried significantly especially considering the localization\nrate. One factor has to be the location of the given\nsensor including how far it was from the firing lines and how\nobstructed its view was. Also, the sensors were hand-built\nprototypes utilizing nowhere near production quality\npackaging/mounting. In light of these factors, the overall\naverage bearing error of 0.9 degrees and range error of 5 m\nwith a microphone spacing of less than 10 cm are excellent.\nWe believe that professional manufacturing and better\nmicrophones could easily achieve better performance than the\nbest sensor in our experiment (>60% localization rate and\n3 m range error).\nInterestingly, the largest error in range was a huge 90 m\nclearly due to some erroneous detection, yet the largest\nbearing error was less than 12 degrees which is still a good\nindication for the soldier where to look.\nThe overall localization rate over all single sensors was\n42%, while for 50 m shots only, this jumped to 61%. Note\nthat the firing range was prepared to simulate an urban\narea to some extent: there were a few single- and two-storey\nwooden structures built both in and around the sensor\ndeployment area and the firing lines. Hence, not all sensors had\nline-of-sight to all shooting positions. We estimate that 10%\nof the sensors had obstructed view to the shooter on\naverage. Hence, we can claim that a given sensor had about 50%\nchance of localizing a shot within 130 m. (Since the sensor\ndeployment area was 30 m deep, 100 m shots correspond to\nactual distances between 100 and 130 m.) Again, we\nemphasize that localization needs at least three muzzle blast and\nthree shockwave detections out of a possible four for each per\nsensor. The detection rate for single sensors-corresponding\nto at least one shockwave detection per sensor-was\npractically 100%.\n0%\n10%\n20%\n30%\n40%\n50%\n60%\n70%\n80%\n90%\n100%\n0 1 2 3 4 5 6 7 8 9 10\nnumber of sensors\npercentageofshots\nFigure 13: Histogram showing what fraction of the\n104 shots taken from 50 and 100 meters were\nlocalized by at most how many individual sensors alone.\n13% of the shots were missed by every single\nsensor, i.e., none of them had both muzzle blast and\nshockwave AoA detections. Note that almost all\nof these shots were still accurately localized by the\nnetworked system, i.e. the sensor fusion using all\navailable observations in the sensor network.\nIt would be misleading to interpret these results as the\nsystem missing half the shots. As soldiers never work alone\nand the sensor node is relatively cheap to afford having\nevery soldier equipped with one, we also need to look at the\noverall detection rates for every shot. Figure 13 shows the\nhistogram of the percentage of shots vs. the number of\nindividual sensors that localized it. 13% of shots were not\nlocalized by any sensor alone, but 87% was localized by at\nleast one sensor out of ten.\n7.2 Error sources\nIn this section, we analyze the most significant sources of\nerror that affect the performance of the networked shooter\nlocalization and weapon classification system. In order to\ncorrelate the distributed observations of the acoustic events,\nthe nodes need to have a common time and space reference.\nHence, errors in the time synchronization, node localization\nand node orientation all degrade the overall accuracy of the\nsystem.\n123\nOur time synchronization approach yields errors\nsignificantly less than 100 microseconds. As the sound travels\nabout 3 cm in that time, time synchronization errors have a\nnegligible effect on the system.\nOn the other hand, node location and orientation can have\na direct effect on the overall system performance. Notice\nthat to analyze this, we do not have to resort to\nsimulation, instead we can utilize the real test data gathered at\nAberdeen. But instead of using the real sensor locations\nknown very accurately and the measured and calibrated\nalmost perfect node orientations, we can add error terms to\nthem and run the sensor fusion. This exactly replicates how\nthe system would have performed during the test using the\nimprecisely known locations and orientations.\nAnother aspect of the system performance that can be\nevaluated this way is the effect of the number of available\nsensors. Instead of using all ten sensors in the data fusion,\nwe can pick any subset of the nodes to see how the accuracy\ndegrades as we decrease the number of nodes.\nThe following experiment was carried out. The number\nof sensors were varied from 2 to 10 in increments of 2. Each\nrun picked the sensors randomly using a uniform\ndistribution. At each run each node was randomly moved to a\nnew location within a circle around its true position with\na radius determined by a zero-mean Gaussian distribution.\nFinally, the node orientations were perturbed using a\nzeromean Gaussian distribution. Each combination of\nparameters were generated 100 times and utilized for all 196 shots.\nThe results are summarized in Figure 14. There is one 3D\nbarchart for each of the experiment sets with the given fixed\nnumber of sensors. The x-axis shows the node location error,\nthat is, the standard deviation of the corresponding\nGaussian distribution that was varied between 0 and 6 meters.\nThe y-axis shows the standard deviation of the node\norientation error that was varied between 0 and 6 degrees. The\nz-axis is the resulting trajectory azimuth error. Note that\nthe elevation angles showed somewhat larger errors than the\nazimuth. Since all the sensors were in approximately a\nhorizontal plane and only a few shooter positions were out of the\nsame plane and only by 2 m or so, the test was not sufficient\nto evaluate this aspect of the system.\nThere are many interesting observation one can make by\nanalyzing these charts. Node location errors in this range\nhave a small effect on accuracy. Node orientation errors, on\nthe other hand, noticeably degrade the performance. Still\nthe largest errors in this experiment of 3.5 degrees for 6\nsensors and 5 degrees for 2 sensors are still very good.\nNote that as the location and orientation errors increase\nand the number of sensors decrease, the most significantly\naffected performance metric is the localization rate. See\nTable 4 for a summary. Successful localization goes down\nfrom almost 100% to 50% when we go from 10 sensors to\n2 even without additional errors. This is primarily caused\nby geometry: for a successful localization, the bullet needs\nto pass over the sensor network, that is, at least one sensor\nshould be on the side of the trajectory other than the rest\nof the nodes. (This is a simplification for illustrative\npurposes. If all the sensors and the trajectory are not coplanar,\nlocalization may be successful even if the projectile passes\non one side of the network. See Section 6.3.) As the\nnumbers of sensors decreased in the experiment by randomly\nselecting a subset, the probability of trajectories abiding by\nthis rule decreased. This also means that even if there are\n0\n2\n4\n6\n0\n2\n4\n6\n0\n1\n2\n3\n4\n5\n6\nazimutherror(degree)\nposition error (m)\norientation error\n(degree)\n2 sensors\n0\n2\n4\n6\n0\n2\n4\n6\n0\n1\n2\n3\n4\n5\n6\nazimutherror(degree)\nposition error (m)\norientation error\n(degree)\n4 sensors\n0\n2\n4\n6\n0\n2\n4\n6\n0\n1\n2\n3\n4\n5\n6\nazimutherror(degree)\nposition error (m)\norientation error\n(degree)\n6 sensors\n0\n2\n4\n6\n0\n2\n4\n6\n0\n1\n2\n3\n4\n5\n6\nazimutherror(degree)\nposition error (m)\norientation error\n(degree)\n8 sensors\nFigure 14: The effect of node localization and\norientation errors on azimuth accuracy with 2, 4, 6 and\n8 nodes. Note that the chart for 10 nodes is almost\nidentical for the 8-node case, hence, it is omitted.\n124\nmany sensors (i.e. soldiers), but all of them are right next to\neach other, the localization rate will suffer. However, when\nthe sensor fusion does provide a result, it is still accurate\neven with few available sensors and relatively large\nindividual errors. A very few consistent observation lead to good\naccuracy as the inconsistent ones are discarded by the\nalgorithm. This is also supported by the observation that for\nthe cases with the higher number of sensors (8 or 10), the\nlocalization rate is hardly affected by even large errors.\nErrors/Sensors 2 4 6 8 10\n0 m, 0 deg 54% 87% 94% 95% 96%\n2 m, 2 deg 53% 80% 91% 96% 96%\n6 m, 0 deg 43% 79% 88% 94% 94%\n0 m, 6 deg 44% 78% 90% 93% 94%\n6 m, 6 deg 41% 73% 85% 89% 92%\nTable 4: Localization rate as a function of the\nnumber of sensors used, the sensor node location and\norientation errors.\nOne of the most significant observations on Figure 14 and\nTable 4 is that there is hardly any difference in the data for\n6, 8 and 10 sensors. This means that there is little advantage\nof adding more nodes beyond 6 sensors as far as the accuracy\nis concerned.\nThe speed of sound depends on the ambient temperature.\nThe current prototype considers it constant that is typically\nset before a test. It would be straightforward to employ\na temperature sensor to update the value of the speed of\nsound periodically during operation. Note also that wind\nmay adversely affect the accuracy of the system. The sensor\nfusion, however, could incorporate wind speed into its\ncalculations. It would be more complicated than temperature\ncompensation, but could be done.\nOther practical issues also need to be looked at before a\nreal world deployment. Silencers reduce the muzzle blast\nenergy and hence, the effective range the system can\ndetect it at. However, silencers do not effect the shockwave\nand the system would still detect the trajectory and caliber\naccurately. The range and weapon type could not be\nestimated without muzzle blast detections. Subsonic weapons\ndo not produce a shockwave. However, this is not of great\nsignificance, since they have shorter range, lower accuracy\nand much less lethality. Hence, their use is not widespread\nand they pose less danger in any case.\nAnother issue is the type of ammunition used. Irregular\narmies may use substandard, even hand manufactured\nbullets. This effects the muzzle velocity of the weapon. For\nweapon classification to work accurately, the system would\nneed to be calibrated with the typical ammunition used by\nthe given adversary.\n8. RELATED WORK\nAcoustic detection and recognition has been under\nresearch since the early fifties. The area has a close\nrelevance to the topic of supersonic flow mechanics [20]. Fansler\nanalyzed the complex near-field pressure waves that occur\nwithin a foot of the muzzle blast. Fansler\"s work gives a\ngood idea of the ideal muzzle blast pressure wave without\ncontamination from echoes or propagation effects [4].\nExperiments with greater distances from the muzzle were\nconducted by Stoughton [18]. The measurements of the ballistic\nshockwaves using calibrated pressure transducers at known\nlocations, measured bullet speeds, and miss distances of\n355 meters for 5.56 mm and 7.62 mm projectiles were made.\nResults indicate that ground interaction becomes a problem\nfor miss distances of 30 meters or larger.\nAnother area of research is the signal processing of gunfire\nacoustics. The focus is on the robust detection and length\nestimation of small caliber acoustic shockwaves and\nmuzzle blasts. Possible techniques for classifying signals as\neither shockwaves or muzzle blasts includes short-time Fourier\nTransform (STFT), the Smoothed Pseudo Wigner-Ville\ndistribution (SPWVD), and a discrete wavelet transformation\n(DWT). Joint time-frequency (JTF) spectrograms are used\nto analyze the typical separation of the shockwave and\nmuzzle blast transients in both time and frequency. Mays\nconcludes that the DWT is the best method for classifying\nsignals as either shockwaves or muzzle blasts because it works\nwell and is less expensive to compute than the SPWVD [10].\nThe edges of the shockwave are typically well defined and\nthe shockwave length is directly related to the bullet\ncharacteristics. A paper by Sadler [14] compares two shockwave\nedge detection methods: a simple gradient-based detector,\nand a multi-scale wavelet detector. It also demonstrates how\nthe length of the shockwave, as determined by the edge\ndetectors, can be used along with Whithams equations [20] to\nestimate the caliber of a projectile. Note that the available\ncomputational performance on the sensor nodes, the limited\nwireless bandwidth and real-time requirements render these\napproaches infeasible on our platform.\nA related topic is the research and development of\nexperimental and prototype shooter location systems. Researchers\nat BBN have developed the Bullet Ears system [3] which has\nthe capability to be installed in a fixed position or worn by\nsoldiers. The fixed system has tetrahedron shaped\nmicrophone arrays with 1.5 meter spacing. The overall system\nconsists of two to three of these arrays spaced 20 to 100\nmeters from each other. The soldier-worn system has 12\nmicrophones as well as a GPS antenna and orientation\nsensors mounted on a helmet. There is a low speed RF\nconnection from the helmet to the processing body. An extensive\ntest has been conducted to measure the performance of both\ntype of systems. The fixed systems performance was one\norder of magnitude better in the angle calculations while their\nrange performance where matched. The angle accuracy of\nthe fixed system was dominantly less than one degree while\nit was around five degrees for the helmet mounted one. The\nrange accuracy was around 5 percent for both of the\nsystems. The problem with this and similar centralized\nsystems is the need of the one or handful of microphone arrays\nto be in line-of-sight of the shooter. A sensor networked\nbased solution has the advantage of widely distributed\nsensing for better coverage, multipath effect compensation and\nmultiple simultaneous shot resolution [8]. This is especially\nimportant for operation in acoustically reverberant urban\nareas. Note that BBN\"s current vehicle-mounted system\ncalled BOOMERANG, a modified version of Bullet Ears,\nis currently used in Iraq [1].\nThe company ShotSpotter specializes in law enforcement\nsystems that report the location of gunfire to police within\nseconds. The goal of the system is significantly different\nthan that of military systems. Shotspotter reports 25 m\ntypical accuracy which is more than enough for police to\n125\nrespond. They are also manufacturing experimental soldier\nwearable and UAV mounted systems for military use [16],\nbut no specifications or evaluation results are publicly\navailable.\n9. CONCLUSIONS\nThe main contribution of this work is twofold. First, the\nperformance of the overall distributed networked system is\nexcellent. Most noteworthy are the trajectory accuracy of\none degree, the correct caliber estimation rate of well over\n90% and the close to 100% weapon classification rate for 4 of\nthe 6 weapons tested. The system proved to be very robust\nwhen increasing the node location and orientation errors and\ndecreasing the number of available sensors all the way down\nto a couple. The key factor behind this is the sensor fusion\nalgorithm\"s ability to reject erroneous measurements. It is\nalso worth mentioning that the results presented here\ncorrespond to the first and only test of the system beyond 100 m\nand with six different weapons. We believe that with the\nlessons learned in the test, a consecutive field experiment\ncould have showed significantly improved results especially\nin range estimation beyond 100 m and weapon classification\nfor the remaining two weapons that were mistaken for each\nother the majority of the times during the test.\nSecond, the performance of the system when used in\nstandalone mode, that is, when single sensors alone provided\nlocalization, was also very good. While the overall\nlocalization rate of 42% per sensor for shots up to 130 m could be\nimproved, the bearing accuracy of less than a degree and\nthe average 5% range error are remarkable using the\nhandmade prototypes of the low-cost nodes. Note that 87% of\nthe shots were successfully localized by at least one of the\nten sensors utilized in standalone mode.\nWe believe that the technology is mature enough that\na next revision of the system could be a commercial one.\nHowever, important aspects of the system would still need\nto be worked on. We have not addresses power\nmanagement yet. A current node runs on 4 AA batteries for about\n12 hours of continuous operation. A deployable version of\nthe sensor node would need to be asleep during normal\noperation and only wake up when an interesting event occurs.\nAn analog trigger circuit could solve this problem, however,\nthe system would miss the first shot. Instead, the acoustic\nchannels would need to be sampled and stored in a circular\nbuffer. The rest of the board could be turned off. When\na trigger wakes up the board, the acoustic data would be\nimmediately available. Experiments with a previous\ngeneration sensor board indicated that this could provide a 10x\nincrease in battery life. Other outstanding issues include\nweatherproof packaging and ruggedization, as well as\nintegration with current military infrastructure.\n10. REFERENCES\n[1] BBN technologies website. http://www.bbn.com.\n[2] E. Danicki. Acoustic sniper localization. Archives of\nAcoustics, 30(2):233-245, 2005.\n[3] G. L. Duckworth et al. Fixed and wearable acoustic\ncounter-sniper systems for law enforcement. In E. M.\nCarapezza and D. B. Law, editors, Proc. SPIE Vol.\n3577, p. 210-230, pages 210-230, Jan. 1999.\n[4] K. Fansler. Description of muzzle blast by modified\nscaling models. Shock and Vibration, 5(1):1-12, 1998.\n[5] D. Gay, P. Levis, R. von Behren, M. Welsh,\nE. Brewer, and D. Culler. The nesC language: a\nholistic approach to networked embedded systems.\nProceedings of Programming Language Design and\nImplementation (PLDI), June 2003.\n[6] J. Hill, R. Szewczyk, A. Woo, S. Hollar, D. Culler, and\nK. Pister. System architecture directions for networked\nsensors. in Proc. of ASPLOS 2000, Nov. 2000.\n[7] B. Kus\u00b4y, G. Balogh, P. V\u00a8olgyesi, J. Sallai, A. N\u00b4adas,\nA. L\u00b4edeczi, M. Mar\u00b4oti, and L. Meertens. Node-density\nindependent localization. Information Processing in\nSensor Networks (IPSN 06) SPOTS Track, Apr. 2006.\n[8] A. L\u00b4edeczi, A. N\u00b4adas, P. V\u00a8olgyesi, G. Balogh,\nB. Kus\u00b4y, J. Sallai, G. Pap, S. D\u00b4ora, K. Moln\u00b4ar,\nM. Mar\u00b4oti, and G. Simon. Countersniper system for\nurban warfare. ACM Transactions on Sensor\nNetworks, 1(1):153-177, Nov. 2005.\n[9] M. Mar\u00b4oti. Directed flood-routing framework for\nwireless sensor networks. In Proceedings of the 5th\nACM/IFIP/USENIX International Conference on\nMiddleware, pages 99-114, New York, NY, USA, 2004.\nSpringer-Verlag New York, Inc.\n[10] B. Mays. Shockwave and muzzle blast classification\nvia joint time frequency and wavelet analysis.\nTechnical report, Army Research Lab Adelphi MD\n20783-1197, Sept. 2001.\n[11] TinyOS Hardware Platforms.\nhttp://tinyos.net/scoop/special/hardware.\n[12] Crossbow MICAz (MPR2400) Radio Module.\nhttp://www.xbow.com/Products/productsdetails.\naspx?sid=101.\n[13] PicoBlaze User Resources.\nhttp://www.xilinx.com/ipcenter/processor_\ncentral/picoblaze/picoblaze_user_resources.htm.\n[14] B. M. Sadler, T. Pham, and L. C. Sadler. Optimal\nand wavelet-based shock wave detection and\nestimation. Acoustical Society of America Journal,\n104:955-963, Aug. 1998.\n[15] J. Sallai, B. Kus\u00b4y, A. L\u00b4edeczi, and P. Dutta. On the\nscalability of routing-integrated time synchronization.\n3rd European Workshop on Wireless Sensor Networks\n(EWSN 2006), Feb. 2006.\n[16] ShotSpotter website. http:\n//www.shotspotter.com/products/military.html.\n[17] G. Simon, M. Mar\u00b4oti, A. L\u00b4edeczi, G. Balogh, B. Kus\u00b4y,\nA. N\u00b4adas, G. Pap, J. Sallai, and K. Frampton. Sensor\nnetwork-based countersniper system. In SenSys \"04:\nProceedings of the 2nd international conference on\nEmbedded networked sensor systems, pages 1-12, New\nYork, NY, USA, 2004. ACM Press.\n[18] R. Stoughton. Measurements of small-caliber ballistic\nshock waves in air. Acoustical Society of America\nJournal, 102:781-787, Aug. 1997.\n[19] B. A. Weiss, C. Schlenoff, M. Shneier, and A. Virts.\nTechnology evaluations and performance metrics for\nsoldier-worn sensors for assist. In Performance Metrics\nfor Intelligent Systems Workshop, Aug. 2006.\n[20] G. Whitham. Flow pattern of a supersonic projectile.\nCommunications on pure and applied mathematics,\n5(3):301, 1952.\n126", "keywords": "1degree trajectory precision;weapon type;weapon classification;range;sensorboard;trajectory;internode communication;datum fusion;acoustic source localization;sensor network;caliber estimation accuracy;helmetmounted microphone array;caliber;caliber estimation;wireless sensor network-based mobile countersniper system;self orientation"}
{"name": "train_C-66", "title": "Heuristics-Based Scheduling of Composite Web Service Workloads", "abstract": "Web services can be aggregated to create composite workflows that provide streamlined functionality for human users or other systems. Although industry standards and recent research have sought to define best practices and to improve end-to-end workflow composition, one area that has not fully been explored is the scheduling of a workflow\"s web service requests to actual service provisioning in a multi-tiered, multi-organisation environment. This issue is relevant to modern business scenarios where business processes within a workflow must complete within QoS-defined limits. Because these business processes are web service consumers, service requests must be mapped and scheduled across multiple web service providers, each with its own negotiated service level agreement. In this paper we provide heuristics for scheduling service requests from multiple business process workflows to web service providers such that a business value metric across all workflows is maximised. We show that a genetic search algorithm is appropriate to perform this scheduling, and through experimentation we show that our algorithm scales well up to a thousand workflows and produces better mappings than traditional approaches.", "fulltext": "1. INTRODUCTION\nWeb services can be composed into workflows to provide\nstreamlined end-to-end functionality for human users or other systems.\nAlthough previous research efforts have looked at ways to\nintelligently automate the composition of web services into workflows\n(e.g. [1, 9]), an important remaining problem is the assignment of\nweb service requests to the underlying web service providers in a\nmulti-tiered runtime scenario within constraints. In this paper we\naddress this scheduling problem and examine means to manage a\nlarge number of business process workflows in a scalable manner.\nThe problem of scheduling web service requests to providers is\nrelevant to modern business domains that depend on multi-tiered\nservice provisioning. Consider the example shown in Figure 1\nthat illustrates our problem space. Workflows comprise multiple\nrelated business processes that are web service consumers; here we\nassume that the workflows represent requested service from\ncustomers or automated systems and that the workflow has already\nbeen composed with an existing choreography toolkit. These\nworkflows are then submitted to a portal (not shown) that acts as a\nscheduling agent between the web service consumers and the web\nservice providers.\nIn this example, a workflow could represent the actions needed to\ninstantiate a vacation itinerary, where one business process requests\nbooking an airline ticket, another business process requests a hotel\nroom, and so forth. Each of these requests target a particular service\ntype (e.g. airline reservations, hotel reservations, car reservations,\netc.), and for each service type, there are multiple instances of\nservice providers that publish a web service interface. An important\nchallenge is that the workflows must meet some quality-of-service\n(QoS) metric, such as end-to-end completion time of all its business\nprocesses, and that meeting or failing this goal results in the\nassignment of a quantitative business value metric for the workflow;\nintuitively, it is desired that all workflows meet their respective QoS\ngoals. We further leverage the notion that QoS service agreements\nare generally agreed-upon between the web service providers and\nthe scheduling agent such that the providers advertise some level\nof guaranteed QoS to the scheduler based upon runtime conditions\nsuch as turnaround time and maximum available concurrency. The\nresulting problem is then to schedule and assign the business\nprocesses\" requests for service types to one of the service providers\nfor that type. The scheduling must be done such that the aggregate\nbusiness value across all the workflows is maximised.\nIn Section 3 we state the scenario as a combinatorial problem and\nutilise a genetic search algorithm [5] to find the best assignment\nof web service requests to providers. This approach converges\ntowards an assignment that maximises the overall business value for\nall the workflows.\nIn Section 4 we show through experimentation that this search\nheuristic finds better assignments than other algorithms (greedy,\nround-robin, and proportional). Further, this approach allows us to\nscale the number of simultaneous workflows (up to one thousand\nworkflows in our experiments) and yet still find effective schedules.\n2. RELATED WORK\nIn the context of service assignment and scheduling, [11] maps\nweb service calls to potential servers using linear programming, but\ntheir work is concerned with mapping only single workflows; our\nprincipal focus is on scalably scheduling multiple workflows (up\n30\nService Type\nSuperHotels.com\nBusiness\nProcess\nBusiness\nProcess\nWorkflow\n...\nBusiness\nProcess\nBusiness\nProcess\n...\nHostileHostels.com\nIncredibleInns.com\nBusiness\nProcess\nBusiness\nProcess\nBusiness\nProcess\n...\nBusiness\nProcess\nService\nProvider\nSkyHighAirlines.com\nSuperCrazyFlights.com\nBusiness\nProcess\n.\n.\n.\n.\n.\n.\nAdvertised QoS\nService Agreement\nCarRentalService.com\nFigure 1: An example scenario demonstrating the interaction between business processes in workflows and web service providers.\nEach business process accesses a service type and is then mapped to a service provider for that type.\nto one thousand as we show later) using different business\nmetrics and a search heuristic. [10] presents a dynamic\nprovisioning approach that uses both predictive and reactive techniques for\nmulti-tiered Internet application delivery. However, the\nprovisioning techniques do not consider the challenges faced when there are\nalternative query execution plans and replicated data sources. [8]\npresents a feedback-based scheduling mechanism for multi-tiered\nsystems with back-end databases, but unlike our work, it assumes\na tighter coupling between the various components of the system.\nOur work also builds upon prior scheduling research. The classic\njob-shop scheduling problem, shown to be NP-complete [4] [3], is\nsimilar to ours in that tasks within a job must be scheduled onto\nmachinery (c.f. our scenario is that business processes within a\nworkflow must be scheduled onto web service providers). The salient\ndifferences are that the machines can process only one job at a time\n(we assume servers can multi-task but with degraded performance\nand a maximum concurrency level), tasks within a job cannot\nsimultaneously run on different machines (we assume business\nprocesses can be assigned to any available server), and the principal\nmetric of performance is the makespan, which is the time for the\nlast task among all the jobs to complete (and as we show later,\noptimising on the makespan is insufficient for scheduling the business\nprocesses, necessitating different metrics).\n3. DESIGN\nIn this section we describe our model and discuss how we can\nfind scheduling assignments using a genetic search algorithm.\n3.1 Model\nWe base our model on the simplified scenario shown in Figure\n1. Specifically, we assume that users or automated systems request\nthe execution of a workflow. The workflows comprise business\nprocesses, each of which makes one web service invocation to a\nservice type. Further, business processes have an ordering in the\nworkflow. The arrangement and execution of the business processes and\nthe data flow between them are all managed by a composition or\nchoreography tool (e.g. [1, 9]). Although composition languages\ncan use sophisticated flow-control mechanisms such as conditional\nbranches, for simplicity we assume the processes execute\nsequentially in a given order.\nThis scenario can be naturally extended to more complex\nrelationships that can be expressed in BPEL [7], which defines how\nbusiness processes interact, messages are exchanged, activities are\nordered, and exceptions are handled. Due to space constraints,\nwe focus on the problem space presented here and will extend our\nmodel to more advanced deployment scenarios in the future.\nEach workflow has a QoS requirement to complete within a\nspecified number of time units (e.g. on the order of seconds, as\ndetailed in the Experiments section). Upon completion (or failure),\nthe workflow is assigned a business value. We extended this\napproach further and considered different types of workflow\ncompletion in order to model differentiated QoS levels that can be applied\nby businesses (for example, to provide tiered customer service).\nWe say that a workflow is successful if it completes within its QoS\nrequirement, acceptable if it completes within a constant factor \u03ba\n31\nof its QoS bound (in our experiments we chose \u03ba=3), or failing\nif it finishes beyond \u03ba times its QoS bound. For each category,\na business value score is assigned to the workflow, with the\nsuccessful category assigned the highest positive score, followed by\nacceptable and then failing. The business value point\ndistribution is non-uniform across workflows, further modelling cases\nwhere some workflows are of higher priority than others.\nEach service type is implemented by a number of different\nservice providers. We assume that the providers make service level\nagreements (SLAs) to guarantee a level of performance defined by\nthe completion time for completing a web service invocation.\nAlthough SLAs can be complex, in this paper we assume for\nsimplicity that the guarantees can take the form of a linear performance\ndegradation under load. This guarantee is defined by several\nparameters: \u03b1 is the expected completion time (for example, on the\norder of seconds) if the assigned workload of web service requests\nis less than or equal to \u03b2, the maximum concurrency, and if the\nworkload is higher than \u03b2, the expected completion for a workload\nof size \u03c9 is \u03b1+ \u03b3(\u03c9 \u2212 \u03b2) where \u03b3 is a fractional coefficient. In our\nexperiments we vary \u03b1, \u03b2, and \u03b3 with different distributions.\nIdeally, all workflows would be able to finish within their QoS\nlimits and thus maximise the aggregate business value across all\nworkflows. However, because we model service providers with\ndegrading performance under load, not all workflows will achieve\ntheir QoS limit: it may easily be the case that business processes\nare assigned to providers who are overloaded and cannot complete\nwithin the respective workflow\"s QoS limit. The key research\nproblem, then, is to assign the business processes to the web service\nproviders with the goal of optimising on the aggregate business\nvalue of all workflows.\nGiven that the scope of the optimisation is the entire set of\nworkflows, it may be that the best scheduling assignments may result in\nsome workflows having to fail in order for more workflows to\nsucceed. This intuitive observation suggests that traditional scheduling\napproaches such as round-robin or proportional assignments will\nnot fare well, which is what we observe and discuss in Section 4.\nOn the other hand, an exhaustive search of all the possible\nassignments will find the best schedule, but the computational complexity\nis prohibitively high. Suppose there are W workflows with an\naverage of B business processes per workflow. Further, in the worst\ncase each business process requests one service type, for which\nthere are P providers. There are thus W \u00b7 PB\ncombinations to\nexplore to find the optimal assignments of business processes to\nproviders. Even for small configurations (e.g. W =10, B=5, P=10),\nthe computational time for exhaustive search is significant, and in\nour work we look to scale these parameters. In the next subsection,\ndiscuss how a genetic search algorithm can be used to converge\ntoward the optimum scheduling assignments.\n3.2 Genetic algorithm\nGiven an exponential search space of business process\nassignments to web service providers, the problem is to find the optimal\nassignment that produces the overall highest aggregate business\nvalue across all workflows. To explore the solution space, we use\na genetic algorithm (GA) search heuristic that simulates Darwinian\nnatural selection by having members of a population compete to\nsurvive in order to pass their genetic chromosomes onto the next\ngeneration; after successive generations, there is a tendency for the\nchromosomes to converge toward the best combination [5] [6].\nAlthough other search heuristics exist that can solve\noptimization problems (e.g. simulated annealing or steepest-ascent\nhillclimbing), the business process scheduling problem fits well with a\nGA because potential solutions can be represented in a matrix form\nand allows us to use prior research in effective GA chromosome\nrecombination to form new members of the population (e.g. [2]).\n0 1 2 3 4\n0 1 2 0 2 1\n1 0 1 0 1 0\n2 1 2 0 0 1\nFigure 2: An example chromosome representing a scheduling\nassignment of (workflow,service type) \u2192 service provider. Each\nrow represents a workflow, and each column represents a\nservice type. For example, here there are 3 workflows (0 to 2) and\n5 service types (0 to 4). In workflow 0, any request for service\ntype 3 goes to provider 2. Note that the service provider\nidentifier is within a range limited to its service type (i.e. its column),\nso the 2 listed for service type 3 is a different server from\nserver 2 in other columns.\nChromosome representation of a solution. In Figure 2 we\nshow an example chromosome that encodes one scheduling\nassignment. The representation is a 2-dimensional matrix that maps\n{workflow, service type} to a service provider. For a business\nprocess in workflow i and utilising service type j, the (i, j)th\nentry in\nthe table is the identifier for the service provider to which the\nbusiness process is assigned. Note that the service provider identifier is\nwithin a range limited to its service type.\nGA execution. A GA proceeds as follows. Initially a random\nset of chromosomes is created for the population. The\nchromosomes are evaluated (hashed) to some metric, and the best ones\nare chosen to be parents. In our problem, the evaluation produces\nthe net business value across all workflows after executing all\nbusiness processes once they are assigned to their respective service\nproviders according to the mapping in the chromosome. The\nparents recombine to produce children, simulating sexual crossover,\nand occasionally a mutation may arise which produces new\ncharacteristics that were not available in either parent. The principal idea\nis that we would like the children to be different from the parents\n(in order to explore more of the solution space) yet not too\ndifferent (in order to contain the portions of the chromosome that result\nin good scheduling assignments). Note that finding the global\noptimum is not guaranteed because the recombination and mutation\nare stochastic.\nGA recombination and mutation. As mentioned, the\nchromosomes are 2-dimensional matrices that represent scheduling\nassignments. To simulate sexual recombination of two chromosomes to\nproduce a new child chromosome, we applied a one-point crossover\nscheme twice (once along each dimension). The crossover is best\nexplained by analogy to Cartesian space as follows. A random\npoint is chosen in the matrix to be coordinate (0, 0). Matrix\nelements from quadrants II and IV from the first parent and elements\nfrom quadrants I and III from the second parent are used to create\nthe new child. This approach follows GA best practices by keeping\ncontiguous chromosome segments together as they are transmitted\nfrom parent to child.\nThe uni-chromosome mutation scheme randomly changes one\nof the service provider assignments to another provider within the\navailable range. Other recombination and mutation schemes are an\narea of research in the GA community, and we look to explore new\noperators in future work.\nGA evaluation function. An important GA component is the\nevaluation function. Given a particular chromosome representing\none scheduling mapping, the function deterministically calculates\nthe net business value across all workloads. The business\nprocesses in each workload are assigned to service providers, and each\nprovider\"s completion time is calculated based on the service\nagreement guarantee using the parameters mentioned in Section 3.1,\nnamely the unloaded completion time \u03b1, the maximum\nconcur32\nrency \u03b2, and a coefficient \u03b3 that controls the linear performance\ndegradation under heavy load. Note that the evaluation function\ncan be easily replaced if desired; for example, other evaluation\nfunctions can model different service provider guarantees or\nparallel workflows.\n4. EXPERIMENTS AND RESULTS\nIn this section we show the benefit of using our GA-based\nscheduler. Because we wanted to scale the scenarios up to a large number\nof workflows (up to 1000 in our experiments), we implemented a\nsimulation program that allowed us to vary parameters and to\nmeasure the results with different metrics. The simulator was written\nin standard C++ and was run on a Linux (Fedora Core) desktop\ncomputer running at 2.8 GHz with 1GB of RAM.\nWe compared our algorithm against alternative candidates:\n\u2022 A well-known round-robin algorithm that assigns each\nbusiness process in circular fashion to the service providers for a\nparticular service type. This approach provides the simplest\nscheme for load-balancing.\n\u2022 A random-proportional algorithm that proportionally assigns\nbusiness processes to the service providers; that is, for a\ngiven service type, the service providers are ranked by their\nguaranteed completion time, and business processes are\nassigned proportionally to the providers based on their\ncompletion time. (We also tried a proportionality scheme based\non both the completion times and maximum concurrency but\nattained the same results, so only the former scheme\"s results\nare shown here.)\n\u2022 A strawman greedy algorithm that always assigns business\nprocesses to the service provider that has the fastest\nguaranteed completion time. This algorithm represents a naive\napproach based on greedy, local observations of each workflow\nwithout taking into consideration all workflows.\nIn the experiments that follow, all results were averaged across\n20 trials, and to help normalise the effects of randomisation used\nduring the GA, each trial started by reading in pre-initialised data\nfrom disk. In Table 1 we list our experimental parameters.\nIn Figure 3 we show the results of running our GA against the\nthree candidate alternatives. The x-axis shows the number for\nworkflows scaled up to 1000, and the y-axis shows the aggregate\nbusiness value for all workflows. As can be seen, the GA consistently\nproduces the highest business value even as the number of\nworkflows grows; at 1000 workflows, the GA produces a 115%\nimprovement over the next-best alternative. (Note that although we\nare optimising against the business value metric we defined earlier,\ngenetic algorithms are able to converge towards the optimal value\nof any metric, as long as the evaluation function can consistently\nmeasure a chromosome\"s value with that metric.)\nAs expected, the greedy algorithm performs very poorly because\nit does the worst job at balancing load: all business processes for\na given service type are assigned to only one server (the one\nadvertised to have the fastest completion time), and as more\nbusiness processes arrive, the provider\"s performance degrades linearly.\nThe round-robin scheme is initially outperformed by the\nrandomproportional scheme up to around 120 workflows (as shown in the\nmagnified graph of Figure 4), but as the number of workflows\nincreases, the round-robin scheme consistently wins over\nrandomproportional. The reason is that although the random-proportional\nscheme assigns business processes to providers proportionally\naccording to the advertised completion times (which is a measure of\nthe power of the service provider), even the best providers will\neventually reach a real-world maximum concurrency for the large\n-2000\n-1000\n0\n1000\n2000\n3000\n4000\n5000\n6000\n7000\n0 200 400 600 800 1000\nAggregatebusinessvalueacrossallworkflows\nTotal number of workflows\nBusiness value scores of scheduling algorithms\nGenetic algorithm\nRound robin\nRandom proportional\nGreedy\nFigure 3: Net business value scores of different scheduling algorithms.\n-500\n0\n500\n1000\n1500\n2000\n2500\n3000\n3500\n4000\n0 50 100 150 200Aggregatebusinessvalueacrossallworkflows\nTotal number of workflows\nBusiness value scores of scheduling algorithms\nGenetic algorithm\nRound robin\nRandom proportional\nGreedy\nFigure 4: Magnification of the left-most region in Figure 3.\nnumber of workflows that we are considering. For a very large\nnumber of workflows, the round-robin scheme is able to better\nbalance the load across all service providers.\nTo better understand the behaviour resulting from the scheduling\nassignments, we show the workflow completion results in Figures\n5, 6, and 7 for 100, 500, and 900 workflows, respectively. These\nfigures show the percentage of workflows that are successful (can\ncomplete with their QoS limit), acceptable (can complete within\n\u03ba=3 times their QoS limit), and failed (cannot complete within \u03ba=3\ntimes their QoS limit). The GA consistently produces the highest\npercentage of successful workflows (resulting in higher business\nvalues for the aggregate set of workflows). Further, the round-robin\nscheme produces better results than the random-proportional for a\nlarge number of workflows but does not perform as well as the GA.\nIn Figure 8 we graph the makespan resulting from the same\nexperiments above. Makespan is a traditional metric from the job\nscheduling community measuring elapsed time for the last job to\ncomplete. While useful, it does not capture the high-level business\nvalue metric that we are optimising against. Indeed, the makespan\nis oblivious to the fact that we provide multiple levels of\ncompletion (successful, acceptable, and failed) and assign business value\nscores accordingly. For completeness, we note that the GA\nprovides the fastest makespan, but it is matched by the round robin\nalgorithm. The GA produces better business values (as shown in\nFigure 3) because it is able to search the solution space to find\nbetter mappings that produce more successful workflows (as shown in\nFigures 5 to 7).\nWe also looked at the effect of the scheduling algorithms on\nbalancing the load. Figure 9 shows the percentage of services\nproviders that were accessed while the workflows ran. As expected,\nthe greedy algorithm always hits one service provider; on the other\nhand, the round-robin algorithm is the fastest to spread the business\n33\nExperimental parameter Comment\nWorkflows 5 to 1000\nBusiness processes per workflow uniform random: 1 - 10\nService types 10\nService providers per service type uniform random: 1 - 10\nWorkflow QoS goal uniform random: 10-30 seconds\nService provider completion time (\u03b1) uniform random: 1 - 12 seconds\nService provider maximum concurrency (\u03b2) uniform random: 1 - 12\nService provider degradation coefficient (\u03b3) uniform random: 0.1 - 0.9\nBusiness value for successful workflows uniform random: 10 - 50 points\nBusiness value for acceptable workflows uniform random: 0 - 10 points\nBusiness value for failed workflows uniform random: -10 - 0 points\nGA: number of parents 20\nGA: number of children 80\nGA: number of generations 1000\nTable 1: Experimental parameters\nFailed\nAcceptable (completed but not within QoS)\nSuccessful (completed within QoS)\n0%\n20%\n40%\n60%\n80%\n100%\nRoundRobinRandProportionalGreedyGeneticAlg\nPercentageofallworkflows\nWorkflow behaviour, 100 workflows\nFigure 5: Workflow behaviour for 100 workflows.\nFailed\nAcceptable (completed but not within QoS)\nSuccessful (completed within QoS)\n0%\n20%\n40%\n60%\n80%\n100%\nRoundRobinRandProportionalGreedyGeneticAlg\nPercentageofallworkflows\nWorkflow behaviour, 500 workflows\nFigure 6: Workflow behaviour for 500 workflows.\nFailed\nAcceptable (completed but not within QoS)\nSuccessful (completed within QoS)\n0%\n20%\n40%\n60%\n80%\n100%\nRoundRobinRandProportionalGreedyGeneticAlg\nPercentageofallworkflows\nWorkflow behaviour, 500 workflows\nFigure 7: Workflow behaviour for 900 workflows.\n0\n50\n100\n150\n200\n250\n300\n0 200 400 600 800 1000\nMakespan[seconds]\nNumber of workflows\nMaximum completion time for all workflows\nGenetic algorithm\nRound robin\nRandom proportional\nGreedy\nFigure 8: Maximum completion time for all workflows. This value\nis the makespan metric used in traditional scheduling research.\nAlthough useful, the makespan does not take into consideration the\nbusiness value scoring in our problem domain.\nprocesses. Figure 10 is the percentage of accessed service providers\n(that is, the percentage of service providers represented in Figure\n9) that had more assigned business processes than their advertised\nmaximum concurrency. For example, in the greedy algorithm only\none service provider is utilised, and this one provider quickly\nbecomes saturated. On the other hand, the random-proportional\nalgorithm uses many service providers, but because business processes\nare proportionally assigned with more assignments going to the\nbetter providers, there is a tendency for a smaller percentage of\nproviders to become saturated.\nFor completeness, we show the performance of the genetic\nalgorithm itself in Figure 11. The algorithm scales linearly with an\nincreasing number of workflows. We note that the round-robin,\nrandom-proportional, and greedy algorithms all finished within 1\nsecond even for the largest workflow configuration. However, we\nfeel that the benefit of finding much higher business value scores\njustifies the running time of the GA; further we would expect that\nthe running time will improve with both software tuning as well as\nwith a computer faster than our off-the-shelf PC.\n5. CONCLUSION\nBusiness processes within workflows can be orchestrated to\naccess web services. In this paper we looked at multi-tiered service\nprovisioning where web service requests to service types can be\nmapped to different service providers. The resulting problem is\nthat in order to support a very large number of workflows, the\nassignment of business process to web service provider must be\nintelligent. We used a business value metric to measure the\nbe34\n0\n0.2\n0.4\n0.6\n0.8\n1\n0 200 400 600 800 1000\nPercentageofallserviceproviders\nNumber of workflows\nService providers utilised\nGenetic algorithm\nRound robin\nRandom proportional\nGreedy\nFigure 9: The percentage of service providers utilized during\nworkload executions. The Greedy algorithm always hits the one service\nprovider, while the Round Robin algorithm spreads requests evenly\nacross the providers.\n0\n0.2\n0.4\n0.6\n0.8\n1\n0 200 400 600 800 1000\nPercentageofallserviceproviders\nNumber of workflows\nService providers saturated\nGenetic algorithm\nRound robin\nRandom proportional\nGreedy\nFigure 10: The percentage of service providers that are saturated\namong those providers who were utilized (that is, percentage of the\nservice providers represented in Figure 9). A saturated service provider\nis one whose workload is greater that its advertised maximum\nconcurrency.\n0\n5\n10\n15\n20\n25\n0 200 400 600 800 1000\nRunningtimeinseconds\nTotal number of workflows\nRunning time of genetic algorithm\nGA running time\nFigure 11: Running time of the genetic algorithm.\nhaviour of workflows meeting or failing QoS values, and we\noptimised our scheduling to maximise the aggregate business value\nacross all workflows. Since the solution space of scheduler\nmappings is exponential, we used a genetic search algorithm to search\nthe space and converge toward the best schedule. With a default\nconfiguration for all parameters and using our business value\nscoring, the GA produced up to 115% business value improvement over\nthe next best algorithm. Finally, because a genetic algorithm will\nconverge towards the optimal value using any metric (even other\nthan the business value metric we used), we believe our approach\nhas strong potential for continuing work.\nIn future work, we look to acquire real-world traces of web\nservice instances in order to get better estimates of service agreement\nguarantees, although we expect that such guarantees between the\nproviders and their consumers are not generally available to the\npublic. We will also look at other QoS metrics such as CPU and\nI/O usage. For example, we can analyse transfer costs with\nvarying bandwidth, latency, data size, and data distribution. Further,\nwe hope to improve our genetic algorithm and compare it to more\nscheduler alternatives. Finally, since our work is complementary\nto existing work in web services choreography (because we rely on\npre-configured workflows), we look to integrate our approach with\navailable web service workflow systems expressed in BPEL.\n6. REFERENCES\n[1] A. Ankolekar, et al. DAML-S: Semantic Markup For Web\nServices, In Proc. of the Int\"l Semantic Web Working\nSymposium, 2001.\n[2] L. Davis. Job Shop Scheduling with Genetic Algorithms,\nIn Proc. of the Int\"l Conference on Genetic Algorithms, 1985.\n[3] H.-L. Fang, P. Ross, and D. Corne. A Promising Genetic\nAlgorithm Approach to Job-Shop Scheduling, Rescheduling,\nand Open-Shop Scheduling Problems , In Proc. on the 5th\nInt\"l Conference on Genetic Algorithms, 1993.\n[4] M. Gary and D. Johnson. Computers and Intractability: A\nGuide to the Theory of NP-Completeness, Freeman, 1979.\n[5] J. Holland. Adaptation in Natural and Artificial Systems:\nAn Introductory Analysis with Applications to Biology,\nControl, and Artificial Intelligence, MIT Press, 1992.\n[6] D. Goldberg. Genetic Algorithms in Search, Optimization\nand Machine Learning, Kluwer Academic Publishers, 1989.\n[7] Business Processes in a Web Services World,\nwww-128.ibm.com/developerworks/\nwebservices/library/ws-bpelwp/.\n[8] G. Soundararajan, K. Manassiev, J. Chen, A. Goel, and C.\nAmza. Back-end Databases in Shared Dynamic Content\nServer Clusters, In Proc. of the IEEE Int\"l Conference on\nAutonomic Computing, 2005.\n[9] B. Srivastava and J. Koehler. Web Service Composition\nCurrent Solutions and Open Problems, ICAP, 2003.\n[10] B. Urgaonkar, P. Shenoy, A. Chandra, and P. Goyal.\nDynamic Provisioning of Multi-Tier Internet Applications,\nIn Proc. of the IEEE Int\"l Conference on Autonomic\nComputing, 2005.\n[11] L. Zeng, B. Benatallah, M. Dumas, J. Kalagnanam, and Q.\nSheng. Quality Driven Web Services Composition, In\nProc. of the WWW Conference, 2003.\n35", "keywords": "qo;service request;scheduling service;qos-defined limit;multi-tiered system;end-to-end workflow composition;work\ufb02ows;multi-organisation environment;business process workflow;web service;streamlined functionality;business value metric;scheduling agent;heuristic;schedule"}
{"name": "train_C-67", "title": "A Holistic Approach to High-Performance Computing: Xgrid Experience", "abstract": "The Ringling School of Art and Design is a fully accredited fouryear college of visual arts and design. With a student to computer ratio of better than 2-to-1, the Ringling School has achieved national recognition for its large-scale integration of technology into collegiate visual art and design education. We have found that Mac OS X is the best operating system to train future artists and designers. Moreover, we can now buy Macs to run high-end graphics, nonlinear video editing, animation, multimedia, web production, and digital video applications rather than expensive UNIX workstations. As visual artists cross from paint on canvas to creating in the digital realm, the demand for a highperformance computing environment grows. In our public computer laboratories, students use the computers most often during the workday; at night and on weekends the computers see only light use. In order to harness the lost processing time for tasks such as video rendering, we are testing Xgrid, a suite of Mac OS X applications recently developed by Apple for parallel and distributed high-performance computing. As with any new technology deployment, IT managers need to consider a number of factors as they assess, plan, and implement Xgrid. Therefore, we would like to share valuable information we learned from our implementation of an Xgrid environment with our colleagues. In our report, we will address issues such as assessing the needs for grid computing, potential applications, management tools, security, authentication, integration into existing infrastructure, application support, user training, and user support. Furthermore, we will discuss the issues that arose and the lessons learned during and after the implementation process.", "fulltext": "1. INTRODUCTION\nGrid computing does not have a single, universally accepted\ndefinition. The technology behind grid computing model is not\nnew. Its roots lie in early distributed computing models that date\nback to early 1980s, where scientists harnessed the computing\npower of idle workstations to let compute intensive applications\nto run on multiple workstations, which dramatically shortening\nprocessing times. Although numerous distributed computing\nmodels were available for discipline-specific scientific\napplications, only recently have the tools became available to use\ngeneral-purpose applications on a grid. Consequently, the grid\ncomputing model is gaining popularity and has become a show\npiece of \"utility computing\". Since in the IT industry, various\ncomputing models are used interchangeably with grid computing,\nwe first sort out the similarities and difference between these\ncomputing models so that grid computing can be placed in\nperspective.\n1.1 Clustering\nA cluster is a group of machines in a fixed configuration united to\noperate and be managed as a single entity to increase robustness\nand performance. The cluster appears as a single high-speed\nsystem or a single highly available system. In this model,\nresources can not enter and leave the group as necessary. There\nare at least two types of clusters: parallel clusters and\nhighavailability clusters. Clustered machines are generally in spatial\nproximity, such as in the same server room, and dedicated solely\nto their task.\nIn a high-availability cluster, each machine provides the same\nservice. If one machine fails, another seamlessly takes over its\nworkload. For example, each computer could be a web server for\na web site. Should one web server \"die,\" another provides the\nservice, so that the web site rarely, if ever, goes down.\nA parallel cluster is a type of supercomputer. Problems are split\ninto many parts, and individual cluster members are given part of\nthe problem to solve. An example of a parallel cluster is\ncomposed of Apple Power Mac G5 computers at Virginia Tech\nUniversity [1].\n1.2 Distributed Computing\nDistributed computing spatially expands network services so that\nthe components providing the services are separated. The major\nobjective of this computing model is to consolidate processing\npower over a network. A simple example is spreading services\nsuch as file and print serving, web serving, and data storage across\nmultiple machines rather than a single machine handling all the\ntasks. Distributed computing can also be more fine-grained, where\neven a single application is broken into parts and each part located\non different machines: a word processor on one server, a spell\nchecker on a second server, etc.\n1.3 Utility Computing\nLiterally, utility computing resembles common utilities such as\ntelephone or electric service. A service provider makes computing\nresources and infrastructure management available to a customer\nas needed, and charges for usage rather than a flat rate. The\nimportant thing to note is that resources are only used as needed,\nand not dedicated to a single customer.\n1.4 Grid Computing\nGrid computing contains aspects of clusters, distributed\ncomputing, and utility computing. In the most basic sense, grid\nturns a group of heterogeneous systems into a centrally managed\nbut flexible computing environment that can work on tasks too\ntime intensive for the individual systems. The grid members are\nnot necessarily in proximity, but must merely be accessible over a\nnetwork; the grid can access computers on a LAN, WAN, or\nanywhere in the world via the Internet. In addition, the computers\ncomprising the grid need not be dedicated to the grid; rather, they\ncan function as normal workstations, and then advertise their\navailability to the grid when not in use.\nThe last characteristic is the most fundamental to the grid\ndescribed in this paper. A well-known example of such an ad\nhoc grid is the SETI@home project [2] of the University of\nCalifornia at Berkeley, which allows any person in the world with\na computer and an Internet connection to donate unused processor\ntime for analyzing radio telescope data.\n1.5 Comparing the Grid and Cluster\nA computer grid expands the capabilities of the cluster by loosing\nits spatial bounds, so that any computer accessible through the\nnetwork gains the potential to augment the grid. A fundamental\ngrid feature is that it scales well. The processing power of any\nmachine added to the grid is immediately availably for solving\nproblems. In addition, the machines on the grid can be\ngeneralpurpose workstations, which keep down the cost of expanding the\ngrid.\n2. ASSESSING THE NEED FOR GRID\nCOMPUTING\nEffective use of a grid requires a computation that can be divided\ninto independent (i.e., parallel) tasks. The results of each task\ncannot depend on the results of any other task, and so the\nmembers of the grid can solve the tasks in parallel. Once the tasks\nhave been completed, the results can be assembled into the\nsolution. Examples of parallelizable computations are the\nMandelbrot set of fractals, the Monte Carlo calculations used in\ndisciplines such as Solid State Physics, and the individual frames\nof a rendered animation. This paper is concerned with the last\nexample.\n2.1 Applications Appropriate for Grid\nComputing\nThe applications used in grid computing must either be\nspecifically designed for grid use, or scriptable in such a way that\nthey can receive data from the grid, process the data, and then\nreturn results. In other words, the best candidates for grid\ncomputing are applications that run the same or very similar\ncomputations on a large number of pieces of data without any\ndependencies on the previous calculated results. Applications\nheavily dependent on data handling rather than processing power\nare generally more suitable to run on a traditional environment\nthan on a grid platform. Of course, the applications must also run\non the computing platform that hosts the grid. Our interest is in\nusing the Alias Maya application [3] with Apple\"s Xgrid [4] on\nMac OS X.\nCommercial applications usually have strict license requirements.\nThis is an important concern if we install a commercial\napplication such as Maya on all members of our grid. By its\nnature, the size of the grid may change as the number of idle\ncomputers changes. How many licenses will be required? Our\nresolution of this issue will be discussed in a later section.\n2.2 Integration into the Existing\nInfrastructure\nThe grid requires a controller that recognizes when grid members\nare available, and parses out job to available members. The\ncontroller must be able to see members on the network. This does\nnot require that members be on the same subnet as the controller,\nbut if they are not, any intervening firewalls and routers must be\nconfigured to allow grid traffic.\n3. XGRID\nXgrid is Apple\"s grid implementation. It was inspired by Zilla, a\ndesktop clustering application developed by NeXT and acquired\nby Apple. In this report we describe the Xgrid Technology\nPreview 2, a free download that requires Mac OS X 10.2.8 or later\nand a minimum 128 MB RAM [5].\nXgrid, leverages Apple\"s traditional ease of use and configuration.\nIf the grid members are on the same subnet, by default Xgrid\nautomatically discovers available resources through Rendezvous\n[6]. Tasks are submitted to the grid through a GUI interface or by\nthe command line. A System Preference Pane controls when each\ncomputer is available to the grid.\nIt may be best to view Xgrid as a facilitator. The Xgrid\narchitecture handles software and data distribution, job execution,\nand result aggregation. However, Xgrid does not perform the\nactual calculations.\n3.1 Xgrid Components\nXgrid has three major components: the client, controller, and the\nagent. Each component is included in the default installation, and\nany computer can easily be configured to assume any role. In\n120\nfact, for testing purposes, a computer can simultaneously assume\nall roles in local mode. The more typical production use is\ncalled cluster mode.\nThe client submits jobs to the controller through the Xgrid GUI or\ncommand line. The client defines how the job will be broken into\ntasks for the grid. If any files or executables must be sent as part\nof a job, they must reside on the client or at a location accessible\nto the client. When a job is complete, the client can retrieve the\nresults from the controller. A client can only connect to a single\ncontroller at a time.\nThe controller runs the GridServer process. It queues tasks\nreceived from clients, distributes those tasks to the agents, and\nhandles failover if an agent cannot complete a task. In Xgrid\nTechnology Preview 2, a controller can handle a maximum of\n10,000 agent connections. Only one controller can exist per\nlogical grid.\nThe agents run the GridAgent process. When the GridAgent\nprocess starts, it registers with a controller; an agent can only be\nconnected to one controller at a time. Agents receive tasks from\ntheir controller, perform the specified computations, and then\nsend the results back to the controller. An agent can be configured\nto always accept tasks, or to just accept them when the computer\nis not otherwise busy.\n3.2 Security and Authentication\nBy default, Xgrid requires two passwords. First, a client needs a\npassword to access a controller. Second, the controller needs a\npassword to access an agent. Either password requirement can be\ndisabled. Xgrid uses two-way-random mutual authentication\nprotocol with MD5 hashes. At this time, data encryption is only\nused for passwords.\nAs mentioned earlier, an agent registers with a controller when the\nGridAgent process starts. There is no native method for the\ncontroller to reject agents, and so it must accept any agent that\nregisters. This means that any agent could submit a job that\nconsumes excessive processor and disk space on the agents. Of\ncourse, since Mac OS X is a BSD-based operating system, the\ncontroller could employ Unix methods of restricting network\nconnections from agents.\nThe Xgrid daemons run as the user nobody, which means the\ndaemons can read, write, or execute any file according to world\npermissions. Thus, Xgrid jobs can execute many commands and\nwrite to /tmp and /Volumes. In general, this is not a major security\nrisk, but is does require a level of trust between all members of the\ngrid.\n3.3 Using Xgrid\n3.3.1 Installation\nBasic Xgrid installation and configuration is described both in\nApple documentation [5] and online at the University of Utah web\nsite [8]. The installation is straightforward and offers no options\nfor customization. This means that every computer on which\nXgrid is installed has the potential to be a client, controller, or\nagent.\n3.3.2 Agent and Controller Configuration\nThe agents and controllers can be configured through the Xgrid\nPreference Pane in the System Preferences or XML files in\n/Library/Preferences. Here the GridServer and GridAgent\nprocesses are started, passwords set, and the controller discovery\nmethod used by agents is selected. By default, agents use\nRendezvous to find a controller, although the agents can also be\nconfigured to look for a specific host.\nThe Xgrid Preference Pane also sets whether the Agents will\nalways accept jobs, or only accept jobs when idle. In Xgrid terms,\nidle either means that the Xgrid screen saver has activated, or the\nmouse and keyboard have not been used for more than 15\nminutes. Even if the agent is configured to always accept tasks, if\nthe computer is being used these tasks will run in the background\nat a low priority.\nHowever, if an agent only accepts jobs when idle, any unfinished\ntask being performed when the computer ceases being idle are\nimmediately stopped and any intermediary results lost. Then the\ncontroller assigns the task to another available member of the\ngrid.\nAdvertising the controller via Rendezvous can be disabled by\nediting /Library/Preferences/com.apple.xgrid.controller.plist. This,\nhowever, will not prevent an agent from connecting to the\ncontroller by hostname.\n3.3.3 Sending Jobs from an Xgrid Client\nThe client sends jobs to the controller either through the Xgrid\nGUI or the command line. The Xgrid GUI submits jobs via small\napplications called plug-ins. Sample plug-ins are provided by\nApple, but they are only useful as simple testing or as examples of\nhow to create a custom plug-in. If we are to employ Xgrid for\nuseful work, we will require a custom plug-in.\nJames Reynolds details the creation of custom plug-ins on the\nUniversity of Utah Mac OS web site [8]. Xgrid stores plug-ins in\n/Library/Xgrid/Plug-ins or ~/Library/Xgrid/Plug-ins, depending\non whether the plug-in was installed with Xgrid or created by a\nuser.\nThe core plug-in parameter is the command, which includes the\nexecutable the agents will run. Another important parameter is the\nworking directory. This directory contains necessary files that\nare not installed on the agents or available to them over a network.\nThe working directory will always be copied to each agent, so it is\nbest to keep this directory small. If the files are installed on the\nagents or available over a network, the working directory\nparameter is not needed.\nThe command line allows the options available with the GUI\nplug-in, but it can be slightly more cumbersome. However, the\ncommand line probably will be the method of choice for serious\nwork. The command arguments must be included in a script\nunless they are very basic. This can be a shell, perl, or python\nscript, as long as the agent can interpret it.\n3.3.4 Running the Xgrid Job\nWhen the Xgrid job is started, the command tells the controller\nhow to break the job into tasks for the agents. Then the command\nis tarred and gzipped and sent to each agent; if there is a working\ndirectory, this is also tarred and gzipped and sent to the agents.\n121\nThe agents extract these files into /tmp and run the task. Recall\nthat since the GridAgent process runs as the user nobody,\neverything associated with the command must be available to\nnobody.\nExecutables called by the command should be installed on the\nagents unless they are very simple. If the executable depends on\nlibraries or other files, it may not function properly if transferred,\neven if the dependent files are referenced in the working directory.\nWhen the task is complete, the results are available to the client.\nIn principle, the results are sent to the client, but whether this\nactually happens depends on the command. If the results are not\nsent to the client, they will be in /tmp on each agent. When\navailable, a better solution is to direct the results to a network\nvolume accessible to the client.\n3.4 Limitations and Idiosyncrasies\nSince Xgrid is only in its second preview release, there are some\nrough edges and limitations. Apple acknowledges some\nlimitations [7]. For example, the controller cannot determine\nwhether an agent is trustworthy and the controller always copies\nthe command and working directory to the agent without checking\nto see if these exist on the agent.\nOther limitations are likely just a by-product of an unfinished\nwork. Neither the client nor controller can specify which agents\nwill receive the tasks, which is particularly important if the agents\ncontain a variety of processor types and speeds and the user wants\nto optimize the calculations. At this time, the best solution to this\nproblem may be to divide the computers into multiple logical\ngrids. There is also no standard way to monitor the progress of a\nrunning job on each agent. The Xgrid GUI and command line\nindicate which agents are working on tasks, but gives no\nindication of progress.\nFinally, at this time only Mac OS X clients can submit jobs to the\ngrid. The framework exists to allow third parties to write plug-ins\nfor other Unix flavors, but Apple has not created them.\n4. XGRID IMPLEMENTATION\nOur goal is an Xgrid render farm for Alias Maya. The Ringling\nSchool has about 400 Apple Power Mac G4\"s and G5\"s in 13\ncomputer labs. The computers range from 733 MHz\nsingleprocessor G4\"s and 500 MHz and 1 GHz dual-processor G4\"s to\n1.8 GHz dual-processor G5\"s. All of these computers are lightly\nused in the evening and on weekends and represent an enormous\nprocessing resource for our student rendering projects.\n4.1 Software Installation\nDuring our Xgrid testing, we loaded software on each computer\nmultiple times, including the operating systems. We saved time by\nfacilitating our installations with the remote administration\ndaemon (radmind) software developed at the University of\nMichigan [9], [10].\nEverything we installed for testing was first created as a radmind\nbase load or overload. Thus, Mac OS X, Mac OS X Developer\nTools, Xgrid, POV-Ray [11], and Alias Maya were stored on a\nradmind server and then installed on our test computers when\nneeded.\n4.2 Initial Testing\nWe used six 1.8 GHz dual-processor Apple Power Mac G5\"s for\nour Xgrid tests. Each computer ran Mac OS X 10.3.3 and\ncontained 1 GB RAM. As shown in Figure 1, one computer\nserved as both client and controller, while the other five acted as\nagents.\nBefore attempting Maya rendering with Xgrid, we performed\nbasic calculations to cement our understanding of Xgrid. Apple\"s\nXgrid documentation is sparse, so finding helpful web sites\nfacilitated our learning.\nWe first ran the Mandelbrot set plug-in provided by Apple, which\nallowed us to test the basic functionality of our grid. Then we\nperformed benchmark rendering with the Open Source\nApplication POV-Ray, as described by Daniel C\u00f4t\u00e9 [12] and\nJames Reynolds [8]. Our results showed that one dual-processor\nG5 rendering the benchmark POV-Ray image took 104 minutes.\nBreaking the image into three equal parts and using Xgrid to send\nthe parts to three agents required 47 minutes. However, two\nagents finished their rendering in 30 minutes, while the third\nagent used 47 minutes; the entire render was only as fast as the\nslowest agent.\nThese results gave us two important pieces of information. First,\nthe much longer rendering time for one of the tasks indicated that\nwe should be careful how we split jobs into tasks for the agents.\nAll portions of the rendering will not take equal amounts of time,\neven if the pixel size is the same. Second, since POV-Ray cannot\ntake advantage of both processors in a G5, neither can an Xgrid\ntask running POV-Ray. Alias Maya does not have this limitation.\n4.3 Rendering with Alias Maya 6\nWe first installed Alias Maya 6 for Mac OS X on the\nclient/controller and each agent. Maya 6 requires licenses for use\nas a workstation application. However, if it is just used for\nrendering from the command line or a script, no license is needed.\nWe thus created a minimal installation of Maya as a radmind\noverload. The application was installed in a hidden directory\ninside /Applications. This was done so that normal users of the\nworkstations would not find and attempt to run Maya, which\nwould fail because these installations are not licensed for such\nuse.\nIn addition, Maya requires the existence of a directory ending in\nthe path /maya. The directory must be readable and writable by\nthe Maya user. For a user running Maya on a Mac OS X\nworkstation, the path would usually be ~/Documents/maya.\nUnless otherwise specified, this directory will be the default\nlocation for Maya data and output files. If the directory does not\nFigure 1. Xgrid test grid.\nClient/\nController\nAgent 1\nAgent 2\nAgent 3\nAgent 4\nAgent 5\nNetwork\nVolume\nJobs\nData\nData\n122\nexist, Maya will try to create it, even if the user specifies that the\ndata and output files exist in other locations.\nHowever, Xgrid runs as the user nobody, which does not have a\nhome directory. Maya is unable to create the needed directory,\nand looks instead for /Alias/maya. This directory also does not\nexist, and the user nobody has insufficient rights to create it. Our\nsolution was to manually create /Alias/maya and give the user\nnobody read and write permissions.\nWe also created a network volume for storage of both the\nrendering data and the resulting rendered frames. This avoided\nsending the Maya files and associated textures to each agent as\npart of a working directory. Such a solution worked well for us\nbecause our computers are geographically close on a LAN; if\ngreater distance had separated the agents from the\nclient/controller, specifying a working directory may have been a\nbetter solution.\nFinally, we created a custom GUI plug-in for Xgrid. The plug-in\ncommand calls a Perl script with three arguments. Two arguments\nspecify the beginning and end frames of the render and the third\nargument the number of frames in each job (which we call the\ncluster size). The script then calculates the total number of jobs\nand parses them out to the agents. For example, if we begin at\nframe 201 and end at frame 225, with 5 frames for each job, the\nplug-in will create 5 jobs and send them out to the agents.\nOnce the jobs are sent to the agents, the script executes the\n/usr/sbin/Render command on each agent with the parameters\nappropriate for the particular job. The results are sent to the\nnetwork volume.\nWith the setup described, we were able to render with Alias Maya\n6 on our test grid. Rendering speed was not important at this time;\nour first goal was to implement the grid, and in that we succeeded.\n4.3.1 Pseudo Code for Perl Script in Custom Xgrid\nPlug-in\nIn this section we summarize in simplified pseudo code format the\nPerl script used in our Xgrig plug-in.\nagent_jobs{\n\u2022 Read beginning frame, end frame, and cluster size of\nrender.\n\u2022 Check whether the render can be divided into an integer\nnumber of jobs based on the cluster size.\n\u2022 If there are not an integer number of jobs, reduce the cluster\nsize of the last job and set its last frame to the end frame of\nthe render.\n\u2022 Determine the start frame and end frame for each job.\n\u2022 Execute the Render command.\n}\n4.4 Lessons Learned\nRendering with Maya from the Xgrid GUI was not trivial. The\nlack of Xgrid documentation and the requirements of Maya\ncombined into a confusing picture, where it was difficult to decide\nthe true cause of the problems we encountered. Trial and error\nwas required to determine the best way to set up our grid.\nThe first hurdle was creating the directory /Alias/maya with read\nand write permissions for the user nobody. The second hurdle was\nlearning that we got the best performance by storing the rendering\ndata on a network volume.\nThe last major hurdle was retrieving our results from the agents.\nUnlike the POV-Ray rendering tests, our initial Maya results were\nnever returned to the client; instead, Maya stored the results in\n/tmp on each agent. Specifying in the plug-in where to send the\nresults would not change this behavior. We decided this was\nlikely a Maya issue rather than an Xgrid issue, and the solution\nwas to send the results to the network volume via the Perl script.\n5. FUTURE PLANS\nMaya on Xgrid is not yet ready to be used by the students of\nRingling School. In order to do this, we must address at least the\nfollowing concerns.\n\u2022 Continue our rendering tests through the command line\nrather than the GUI plug-in. This will be essential for the\nfollowing step.\n\u2022 Develop an appropriate interface for users to send jobs to the\nXgrid controller. This will probably be an extension to the\nweb interface of our existing render farm, where the student\nspecifies parameters that are placed in a script that issues the\nRender command.\n\u2022 Perform timed Maya rendering tests with Xgrid. Part of this\nshould compare the rendering times for Power Mac G4\"s and\nG5\"s.\n6. CONCLUSION\nGrid computing continues to advance. Recently, the IT industry\nhas witnessed the emergence of numerous types of contemporary\ngrid applications in addition to the traditional grid framework for\ncompute intensive applications. For instance, peer-to-peer\napplications such as Kazaa, are based on storage grids that do not\nshare processing power but instead an elegant protocol to swap\nfiles between systems. Although in our campuses we discourage\nstudents from utilizing peer-to-peer applications from music\nsharing, the same protocol can be utilized on applications such as\ndecision support and data mining. The National Virtual\nCollaboratory grid project [13] will link earthquake researchers\nacross the U.S. with computing resources, allowing them to share\nextremely large data sets, research equipment, and work together\nas virtual teams over the Internet.\nThere is an assortment of new grid players in the IT world\nexpanding the grid computing model and advancing the grid\ntechnology to the next level. SAP [14] is piloting a project to\ngrid-enable SAP ERP applications, Dell [15] has partnered with\nPlatform Computing to consolidate computing resources and\nprovide grid-enabled systems for compute intensive applications,\nOracle has integrated support for grid computing in their 10g\nrelease [16], United Devices [17] offers hosting service for\ngridon-demand, and Sun Microsystems continues their research and\ndevelopment of Sun\"s N1 Grid engine [18] which combines grid\nand clustering platforms.\nSimply, the grid computing is up and coming. The potential\nbenefits of grid computing are colossal in higher education\nlearning while the implementation costs are low. Today, it would\nbe difficult to identify an application with as high a return on\ninvestment as grid computing in information technology divisions\nin higher education institutions. It is a mistake to overlook this\ntechnology with such a high payback.\n123\n7. ACKNOWLEDGMENTS\nThe authors would like to thank Scott Hanselman of the IT team\nat the Ringling School of Art and Design for providing valuable\ninput in the planning of our Xgrid testing. We would also like to\nthank the posters of the Xgrid Mailing List [13] for providing\ninsight into many areas of Xgrid.\n8. REFERENCES\n[1] Apple Academic Research,\nhttp://www.apple.com/education/science/profiles/vatech/.\n[2] SETI@home: Search for Extraterrestrial Intelligence at\nhome. http://setiathome.ssl.berkeley.edu/.\n[3] Alias, http://www.alias.com/.\n[4] Apple Computer, Xgrid, http://www.apple.com/acg/xgrid/.\n[5] Xgrid Guide, http://www.apple.com/acg/xgrid/, 2004.\n[6] Apple Mac OS X Features,\nhttp://www.apple.com/macosx/features/rendezvous/.\n[7] Xgrid Manual Page, 2004.\n[8] James Reynolds, Xgrid Presentation, University of Utah,\nhttp://www.macos.utah.edu:16080/xgrid/, 2004.\n[9] Research Systems Unix Group, Radmind, University of\nMichigan, http://rsug.itd.umich.edu/software/radmind.\n[10]Using the Radmind Command Line Tools to Maintain\nMultiple Mac OS X Machines,\n\nhttp://rsug.itd.umich.edu/software/radmind/files/radmindtutorial-0.8.1.pdf.\n[11]POV-Ray, http://www.povray.org/.\n[12]Daniel C\u00f4t\u00e9, Xgrid example: Parallel graphics rendering in\nPOVray, http://unu.novajo.ca/simple/, 2004.\n[13]NEESgrid, http://www.neesgrid.org/.\n[14]SAP, http://www.sap.com/.\n[15]Platform Computing, http://platform.com/.\n[16]Grid, http://www.oracle.com/technologies/grid/.\n[17]United Devices, Inc., http://ud.com/.\n[18]N1 Grid Engine 6, http://www.sun.com/\nsoftware/gridware/index.html/.\n[19]Xgrig Users Mailing List,\n\nhttp://www.lists.apple.com/mailman/listinfo/xgridusers/.\n124", "keywords": "render;multimedia;xgrid environment;xgrid;nonlinear video editing;macintosh os x;grid computing;large-scale integration of technology;web production;animation;digital video application;rendezvous;design;visual art;highperformance computing;design education;high-end graphic;mac os x;operating system;cluster"}
{"name": "train_C-68", "title": "An Evaluation of Availability Latency in Carrier-based Vehicular ad-hoc Networks", "abstract": "On-demand delivery of audio and video clips in peer-to-peer vehicular ad-hoc networks is an emerging area of research. Our target environment uses data carriers, termed zebroids, where a mobile device carries a data item on behalf of a server to a client thereby minimizing its availability latency. In this study, we quantify the variation in availability latency with zebroids as a function of a rich set of parameters such as car density, storage per device, repository size, and replacement policies employed by zebroids. Using analysis and extensive simulations, we gain novel insights into the design of carrier-based systems. Significant improvements in latency can be obtained with zebroids at the cost of a minimal overhead. These improvements occur even in scenarios with lower accuracy in the predictions of the car routes. Two particularly surprising findings are: (1) a naive random replacement policy employed by the zebroids shows competitive performance, and (2) latency improvements obtained with a simplified instantiation of zebroids are found to be robust to changes in the popularity distribution of the data items.", "fulltext": "1. INTRODUCTION\nTechnological advances in areas of storage and wireless\ncommunications have now made it feasible to envision on-demand delivery\nof data items, for e.g., video and audio clips, in vehicular\npeer-topeer networks. In prior work, Ghandeharizadeh et al. [10]\nintroduce the concept of vehicles equipped with a\nCar-to-Car-Peer-toPeer device, termed AutoMata, for in-vehicle entertainment. The\nnotable features of an AutoMata include a mass storage device\noffering hundreds of gigabytes (GB) of storage, a fast processor, and\nseveral types of networking cards. Even with today\"s 500 GB disk\ndrives, a repository of diverse entertainment content may exceed\nthe storage capacity of a single AutoMata. Such repositories\nconstitute the focus of this study. To exchange data, we assume each\nAutoMata is configured with two types of networking cards: 1) a\nlow-bandwidth networking card with a long radio-range in the\norder of miles that enables an AutoMata device to communicate with\na nearby cellular or WiMax station, 2) a high-bandwidth\nnetworking card with a limited radio-range in the order of hundreds of feet.\nThe high bandwidth connection supports data rates in the\norder of tens to hundreds of Megabits per second and represents the\nad-hoc peer to peer network between the vehicles. This is\nlabelled as the data plane and is employed to exchange data items\nbetween devices. The low-bandwidth connection serves as the\ncontrol plane, enabling AutoMata devices to exchange meta-data with\none or more centralized servers. This connection offers bandwidths\nin the order of tens to hundreds of Kilobits per second. The\ncentralized servers, termed dispatchers, compute schedules of data\ndelivery along the data plane using the provided meta-data. These\nschedules are transmitted to the participating vehicles using the\ncontrol plane. The technical feasibility of such a two-tier\narchitecture is presented in [7], with preliminary results to demonstrate the\nbandwidth of the control plane is sufficient for exchange of control\ninformation needed for realizing such an application.\nIn a typical scenario, an AutoMata device presents a passenger\nwith a list of data items1\n, showing both the name of each data item\nand its availability latency. The latter, denoted as \u03b4, is defined as\nthe earliest time at which the client encounters a copy of its\nrequested data item. A data item is available immediately when it\nresides in the local storage of the AutoMata device serving the\nrequest. Due to storage constraints, an AutoMata may not store the\nentire repository. In this case, availability latency is the time from\nwhen the user issues a request until when the AutoMata encounters\nanother car containing the referenced data item. (The terms car and\nAutoMata are used interchangeably in this study.)\nThe availability latency for an item is a function of the current\nlocation of the client, its destination and travel path, the mobility\nmodel of the AutoMata equipped vehicles, the number of replicas\nconstructed for the different data items, and the placement of data\nitem replicas across the vehicles. A method to improve the\navailability latency is to employ data carriers which transport a replica\nof the requested data item from a server car containing it to a client\nthat requested it. These data carriers are termed \u2018zebroids\".\nSelection of zebroids is facilitated by the two-tiered architecture.\nThe control plane enables centralized information gathering at a\ndispatcher present at a base-station.2\nSome examples of control\nin1\nWithout loss of generality, the term data item might be either\ntraditional media such as text or continuous media such as an audio or\nvideo clip.\n2\nThere may be dispatchers deployed at a subset of the base-stations\nfor fault-tolerance and robustness. Dispatchers between\nbasestations may communicate via the wired infrastructure.\n75\nformation are currently active requests, travel path of the clients and\ntheir destinations, and paths of the other cars. For each client\nrequest, the dispatcher may choose a set of z carriers that collaborate\nto transfer a data item from a server to a client (z-relay zebroids).\nHere, z is the number of zebroids such that 0 \u2264 z < N, where\nN is the total number of cars. When z = 0 there are no carriers,\nrequiring a server to deliver the data item directly to the client.\nOtherwise, the chosen relay team of z zebroids hand over the data item\ntransitively to one another to arrive at the client, thereby reducing\navailability latency (see Section 3.1 for details). To increase\nrobustness, the dispatcher may employ multiple relay teams of z-carriers\nfor every request. This may be useful in scenarios where the\ndispatcher has lower prediction accuracy in the information about the\nroutes of the cars. Finally, storage constraints may require a zebroid\nto evict existing data items from its local storage to accommodate\nthe client requested item.\nIn this study, we quantify the following main factors that affect\navailability latency in the presence of zebroids: (i) data item\nrepository size, (ii) car density, (iii) storage capacity per car, (iv) client\ntrip duration, (v) replacement scheme employed by the zebroids,\nand (vi) accuracy of the car route predictions. For a significant\nsubset of these factors, we address some key questions pertaining to\nuse of zebroids both via analysis and extensive simulations.\nOur main findings are as follows. A naive random replacement\npolicy employed by the zebroids shows competitive performance\nin terms of availability latency. With such a policy, substantial\nimprovements in latency can be obtained with zebroids at a minimal\nreplacement overhead. In more practical scenarios, where the\ndispatcher has inaccurate information about the car routes, zebroids\ncontinue to provide latency improvements. A surprising result is\nthat changes in popularity of the data items do not impact the\nlatency gains obtained with a simple instantiation of z-relay zebroids\ncalled one-instantaneous zebroids (see Section 3.1). This study\nsuggests a number of interesting directions to be pursued to gain\nbetter understanding of design of carrier-based systems that\nimprove availability latency.\nRelated Work: Replication in mobile ad-hoc networks has been\na widely studied topic [11, 12, 15]. However, none of these\nstudies employ zebroids as data carriers to reduce the latency of the\nclient\"s requests. Several novel and important studies such as\nZebraNet [13], DakNet [14], Data Mules [16], Message Ferries [20],\nand Seek and Focus [17] have analyzed factors impacting\nintermittently connected networks consisting of data carriers similar in\nspirit to zebroids. Factors considered by each study are dictated by\ntheir assumed environment and target application. A novel\ncharacteristic of our study is the impact on availability latency for a\ngiven database repository of items. A detailed description of\nrelated works can be obtained in [9].\nThe rest of this paper is organized as follows. Section 2\nprovides an overview of the terminology along with the factors that\nimpact availability latency in the presence of zebroids. Section 3\ndescribes how the zebroids may be employed. Section 4 provides\ndetails of the analysis methodology employed to capture the\nperformance with zebroids. Section 5 describes the details of the\nsimulation environment used for evaluation. Section 6 enlists the key\nquestions examined in this study and answers them via analysis\nand simulations. Finally, Section 7 presents brief conclusions and\nfuture research directions.\n2. OVERVIEW AND TERMINOLOGY\nTable 1 summarizes the notation of the parameters used in the\npaper. Below we introduce some terminology used in the paper.\nAssume a network of N AutoMata-equipped cars, each with\nstorage capacity of \u03b1 bytes. The total storage capacity of the\nsystem is ST =N \u00b7\u03b1. There are T data items in the database, each with\nDatabase Parameters\nT Number of data items.\nSi Size of data item i\nfi Frequency of access to data item i.\nReplication Parameters\nRi Normalized frequency of access to data item i\nri Number of replicas for data item i\nn Characterizes a particular replication scheme.\n\u03b4i Average availability latency of data item i\n\u03b4agg Aggregate availability latency, \u03b4agg = T\nj=1 \u03b4j \u00b7 fj\nAutoMata System Parameters\nG Number of cells in the map (2D-torus).\nN Number of AutoMata devices in the system.\n\u03b1 Storage capacity per AutoMata.\n\u03b3 Trip duration of the client AutoMata.\nST Total storage capacity of the AutoMata system, ST = N \u00b7 \u03b1.\nTable 1: Terms and their definitions\nsize Si. The frequency of access to data item i is denoted as fi,\nwith T\nj=1 fj = 1. Let the trip duration of the client AutoMata\nunder consideration be \u03b3.\nWe now define the normalized frequency of access to the data\nitem i, denoted by Ri, as:\nRi =\n(fi)n\nT\nj=1(fj)n\n; 0 \u2264 n \u2264 \u221e (1)\nThe exponent n characterizes a particular replication technique.\nA square-root replication scheme is realized when n = 0.5 [5].\nThis serves as the base-line for comparison with the case when\nzebroids are deployed. Ri is normalized to a value between 0 and\n1. The number of replicas for data item i, denoted as ri, is: ri =\nmin (N, max (1, Ri\u00b7N\u00b7\u03b1\nSi\n)). This captures the case when at least\none copy of every data item must be present in the ad-hoc network\nat all times. In cases where a data item may be lost from the ad-hoc\nnetwork, this equation becomes ri = min (N, max (0, Ri\u00b7N\u00b7\u03b1\nSi\n)).\nIn this case, a request for the lost data item may need to be satisfied\nby fetching the item from a remote server.\nThe availability latency for a data item i, denoted as \u03b4i, is defined\nas the earliest time at which a client AutoMata will find the first\nreplica of the item accessible to it. If this condition is not satisfied,\nthen we set \u03b4i to \u03b3. This indicates that data item i was not available\nto the client during its journey. Note that since there is at least one\nreplica in the system for every data item i, by setting \u03b3 to a large\nvalue we ensure that the client\"s request for any data item i will be\nsatisfied. However, in most practical circumstances \u03b3 may not be\nso large as to find every data item.\nWe are interested in the availability latency observed across all\ndata items. Hence, we augment the average availability latency\nfor every data item i with its fi to obtain the following weighted\navailability latency (\u03b4agg) metric: \u03b4agg = T\ni=1 \u03b4i \u00b7 fi\nNext, we present our solution approach describing how zebroids\nare selected.\n3. SOLUTION APPROACH\n3.1 Zebroids\nWhen a client references a data item missing from its local\nstorage, the dispatcher identifies all cars with a copy of the data item\nas servers. Next, the dispatcher obtains the future routes of all cars\nfor a finite time duration equivalent to the maximum time the client\nis willing to wait for its request to be serviced. Using this\ninformation, the dispatcher schedules the quickest delivery path from any\nof the servers to the client using any other cars as intermediate\ncarriers. Hence, it determines the optimal set of forwarding decisions\n76\nthat will enable the data item to be delivered to the client in the\nminimum amount of time. Note that the latency along the quickest\ndelivery path that employs a relay team of z zebroids is similar to\nthat obtained with epidemic routing [19] under the assumptions of\ninfinite storage and no interference.\nA simple instantiation of z-relay zebroids occurs when z = 1\nand the client\"s request triggers a transfer of a copy of the requested\ndata item from a server to a zebroid in its vicinity. Such a\nzebroid is termed one-instantaneous zebroid. In some cases, the\ndispatcher might have inaccurate information about the routes of\nthe cars. Hence, a zebroid scheduled on the basis of this inaccurate\ninformation may not rendezvous with its target client. To minimize\nthe likelihood of such scenarios, the dispatcher may schedule\nmultiple zebroids. This may incur additional overhead due to redundant\nresource utilization to obtain the same latency improvements.\nThe time required to transfer a data item from a server to a\nzebroid depends on its size and the available link bandwidth. With\nsmall data items, it is reasonable to assume that this transfer time is\nsmall, especially in the presence of the high bandwidth data plane.\nLarge data items may be divided into smaller chunks enabling the\ndispatcher to schedule one or more zebroids to deliver each chunk\nto a client in a timely manner. This remains a future research\ndirection.\nInitially, number of replicas for each data item replicas might be\ncomputed using Equation 1. This scheme computes the number\nof data item replicas as a function of their popularity. It is static\nbecause number of replicas in the system do not change and no\nreplacements are performed. Hence, this is referred to as the\n\u2018nozebroids\" environment. We quantify the performance of the various\nreplacement policies with reference to this base-line that does not\nemploy zebroids.\nOne may assume a cold start phase, where initially only one or\nfew copies of every data item exist in the system. Many storage\nslots of the cars may be unoccupied. When the cars encounter one\nanother they construct new replicas of some selected data items to\noccupy the empty slots. The selection procedure may be to choose\nthe data items uniformly at random. New replicas are created as\nlong as a car has a certain threshold of its storage unoccupied.\nEventually, majority of the storage capacity of a car will be\nexhausted.\n3.2 Carrier-based Replacement policies\nThe replacement policies considered in this paper are reactive\nsince a replacement occurs only in response to a request issued for a\ncertain data item. When the local storage of a zebroid is completely\noccupied, it needs to replace one of its existing items to carry the\nclient requested data item. For this purpose, the zebroid must\nselect an appropriate candidate for eviction. This decision process\nis analogous to that encountered in operating system paging where\nthe goal is to maximize the cache hit ratio to prevent disk access\ndelay [18]. The carrier-based replacement policies employed in our\nstudy are Least Recently Used (LRU), Least Frequently Used\n(LFU) and Random (where a eviction candidate is chosen\nuniformly at random). We have considered local and global variants\nof the LRU/LFU policies which determine whether local or global\nknowledge of contents of the cars known at the dispatcher is used\nfor the eviction decision at a zebroid (see [9] for more details).\nThe replacement policies incur the following overheads. First,\nthe complexity associated with the implementation of a policy.\nSecond, the bandwidth used to transfer a copy of a data item from a\nserver to the zebroid. Third, the average number of replacements\nincurred by the zebroids. Note that in the no-zebroids case neither\noverhead is incurred.\nThe metrics considered in this study are aggregate availability\nlatency, \u03b4agg, percentage improvement in \u03b4agg with zebroids as\ncompared to the no-zebroids case and average number of replacements\nincurred per client request which is an indicator of the overhead\nincurred by zebroids.\nNote that the dispatchers with the help of the control plane may\nensure that no data item is lost from the system. In other words,\nat least one replica of every data item is maintained in the ad-hoc\nnetwork at all times. In such cases, even though a car may meet a\nrequesting client earlier than other servers, if its local storage\ncontains data items with only a single copy in the system, then such a\ncar is not chosen as a zebroid.\n4. ANALYSIS METHODOLOGY\nHere, we present the analytical evaluation methodology and some\napproximations as closed-form equations that capture the\nimprovements in availability latency that can be obtained with both\noneinstantaneous and z-relay zebroids. First, we present some\npreliminaries of our analysis methodology.\n\u2022 Let N be the number of cars in the network performing a 2D\nrandom walk on a\n\u221a\nG\u00d7\n\u221a\nG torus. An additional car serves\nas a client yielding a total of N + 1 cars. Such a mobility\nmodel has been used widely in the literature [17, 16] chiefly\nbecause it is amenable to analysis and provides a baseline\nagainst which performance of other mobility models can be\ncompared. Moreover, this class of Markovian mobility\nmodels has been used to model the movements of vehicles [3,\n21].\n\u2022 We assume that all cars start from the stationary distribution\nand perform independent random walks. Although for sparse\ndensity scenarios, the independence assumption does hold, it\nis no longer valid when N approaches G.\n\u2022 Let the size of data item repository of interest be T. Also,\ndata item i has ri replicas. This implies ri cars, identified as\nservers, have a copy of this data item when the client requests\nitem i.\nAll analysis results presented in this section are obtained\nassuming that the client is willing to wait as long as it takes for its request\nto be satisfied (unbounded trip duration \u03b3 = \u221e). With the random\nwalk mobility model on a 2D-torus, there is a guarantee that as\nlong as there is at least one replica of the requested data item in the\nnetwork, the client will eventually encounter this replica [2].\nExtensions to the analysis that also consider finite trip durations can\nbe obtained in [9].\nConsider a scenario where no zebroids are employed. In this\ncase, the expected availability latency for the data item is the\nexpected meeting time of the random walk undertaken by the client\nwith any of the random walks performed by the servers. Aldous et\nal. [2] show that the the meeting time of two random walks in such\na setting can be modelled as an exponential distribution with the\nmean C = c \u00b7 G \u00b7 log G, where the constant c 0.17 for G \u2265 25.\nThe meeting time, or equivalently the availability latency \u03b4i, for\nthe client requesting data item i is the time till it encounters any of\nthese ri replicas for the first time. This is also an exponential\ndistribution with the following expected value (note that this formulation\nis valid only for sparse cases when G >> ri): \u03b4i = cGlogG\nri\nThe aggregate availability latency without employing zebroids is\nthen this expression averaged over all data items, weighted by their\nfrequency of access:\n\u03b4agg(no \u2212 zeb) =\nT\ni=1\nfi \u00b7 c \u00b7 G \u00b7 log G\nri\n=\nT\ni=1\nfi \u00b7 C\nri\n(2)\n77\n4.1 One-instantaneous zebroids\nRecall that with one-instantaneous zebroids, for a given request,\na new replica is created on a car in the vicinity of the server,\nprovided this car meets the client earlier than any of the ri servers.\nMoreover, this replica is spawned at the time step when the client\nissues the request. Let Nc\ni be the expected total number of nodes\nthat are in the same cell as any of the ri servers. Then, we have\nNc\ni = (N \u2212 ri) \u00b7 (1 \u2212 (1 \u2212\n1\nG\n)ri\n) (3)\nIn the analytical model, we assume that Nc\ni new replicas are\ncreated, so that the total number of replicas is increased to ri +Nc\ni .\nThe availability latency is reduced since the client is more likely to\nmeet a replica earlier. The aggregated expected availability latency\nin the case of one-instantaneous zebroids is then given by,\n\u03b4agg(zeb) =\nT\ni=1\nfi \u00b7 c \u00b7 G \u00b7 log G\nri + Nc\ni\n=\nT\ni=1\nfi \u00b7 C\nri + Nc\ni\n(4)\nNote that in obtaining this expression, for ease of analysis, we\nhave assumed that the new replicas start from random locations\nin the torus (not necessarily from the same cell as the original ri\nservers). It thus treats all the Nc\ni carriers independently, just like\nthe ri original servers. As we shall show below by comparison\nwith simulations, this approximation provides an upper-bound on\nthe improvements that can be obtained because it results in a lower\nexpected latency at the client.\nIt should be noted that the procedure listed above will yield a\nsimilar latency to that employed by a dispatcher employing\noneinstantaneous zebroids (see Section 3.1). Since the dispatcher is\naware of all future car movements it would only transfer the\nrequested data item on a single zebroid, if it determines that the\nzebroid will meet the client earlier than any other server. This selected\nzebroid is included in the Nc\ni new replicas.\n4.2 z-relay zebroids\nTo calculate the expected availability latency with z-relay\nzebroids, we use a coloring problem analog similar to an approach\nused by Spyropoulos et al. [17]. Details of the procedure to obtain\na closed-form expression are given in [9]. The aggregate\navailability latency (\u03b4agg) with z-relay zebroids is given by,\n\u03b4agg(zeb) =\nT\ni=1\n[fi \u00b7\nC\nN + 1\n\u00b7\n1\nN + 1 \u2212 ri\n\u00b7\n(N \u00b7 log\nN\nri\n\u2212 log (N + 1 \u2212 ri))] (5)\n5. SIMULATION METHODOLOGY\nThe simulation environment considered in this study comprises\nof vehicles such as cars that carry a fraction of the data item\nrepository. A prediction accuracy parameter inherently provides a certain\nprobabilistic guarantee on the confidence of the car route\npredictions known at the dispatcher. A value of 100% implies that the\nexact routes of all cars are known at all times. A 70% value for this\nparameter indicates that the routes predicted for the cars will match\nthe actual ones with probability 0.7. Note that this probability is\nspread across the car routes for the entire trip duration. We now\nprovide the preliminaries of the simulation study and then describe\nthe parameter settings used in our experiments.\n\u2022 Similar to the analysis methodology, the map used is a 2D\ntorus. A Markov mobility model representing a unbiased 2D\nrandom walk on the surface of the torus describes the\nmovement of the cars across this torus.\n\u2022 Each grid/cell is a unique state of this Markov chain. In each\ntime slot, every car makes a transition from a cell to any of\nits neighboring 8 cells. The transition is a function of the\ncurrent location of the car and a probability transition matrix\nQ = [qij] where qij is the probability of transition from state\ni to state j. Only AutoMata equipped cars within the same\ncell may communicate with each other.\n\u2022 The parameters \u03b3, \u03b4 have been discretized and expressed in\nterms of the number of time slots.\n\u2022 An AutoMata device does not maintain more than one replica\nof a data item. This is because additional replicas occupy\nstorage without providing benefits.\n\u2022 Either one-instantaneous or z-relay zebroids may be employed\nper client request for latency improvement.\n\u2022 Unless otherwise mentioned, the prediction accuracy\nparameter is assumed to be 100%. This is because this study\naims to quantify the effect of a large number of parameters\nindividually on availability latency.\nHere, we set the size of every data item, Si, to be 1. \u03b1 represents\nthe number of storage slots per AutoMata. Each storage slot stores\none data item. \u03b3 represents the duration of the client\"s journey in\nterms of the number of time slots. Hence the possible values of\navailability latency are between 0 and \u03b3. \u03b4 is defined as the number\nof time slots after which a client AutoMata device will encounter a\nreplica of the data item for the first time. If a replica for the data\nitem requested was encountered by the client in the first cell then\nwe set \u03b4 = 0. If \u03b4 > \u03b3 then we set \u03b4 = \u03b3 indicating that no copy\nof the requested data item was encountered by the client during its\nentire journey. In all our simulations, for illustration we consider a\n5 \u00d7 5 2D-torus with \u03b3 set to 10. Our experiments indicate that the\ntrends in the results scale to maps of larger size.\nWe simulated a skewed distribution of access to the T data items\nthat obeys Zipf\"s law with a mean of 0.27. This distribution is\nshown to correspond to sale of movie theater tickets in the United\nStates [6]. We employ a replication scheme that allocates replicas\nfor a data item as a function of the square-root of the frequency of\naccess of that item. The square-root replication scheme is shown\nto have competitive latency performance over a large parameter\nspace [8]. The data item replicas are distributed uniformly across\nthe AutoMata devices. This serves as the base-line no-zebroids\ncase. The square-root scheme also provides the initial replica\ndistribution when zebroids are employed. Note that the replacements\nperformed by the zebroids will cause changes to the data item replica\ndistribution. Requests generated as per the Zipf distribution are\nissued one at a time. The client car that issues the request is chosen\nin a round-robin manner. After a maximum period of \u03b3, the latency\nencountered by this request is recorded.\nIn all the simulation results, each point is an average of 200,000\nrequests. Moreover, the 95% confidence intervals determined for\nthe results are quite tight for the metrics of latency and\nreplacement overhead. Hence, we only present them for the metric that\ncaptures the percentage improvement in latency with respect to the\nno-zebroids case.\n6. RESULTS\nIn this section, we describe our evaluation results where the\nfollowing key questions are addressed. With a wide choice of\nreplacement schemes available for a zebroid, what is their effect on\navailability latency? A more central question is: Do zebroids provide\n78\n0 20 40 60 80 100\n1.5\n2\n2.5\n3\n3.5\nNumber of cars\nAggregate availability latency (\u03b4\nagg\n)\nlru_global\nlfu_global\nlru_local\nlfu_local\nrandom\nFigure 1: Figure 1 shows the availability latency when\nemploying one-instantaneous zebroids as a function of (N,\u03b1) values,\nwhen the total storage in the system is kept fixed, ST = 200.\nsignificant improvements in availability latency? What is the\nassociated overhead incurred in employing these zebroids? What\nhappens to these improvements in scenarios where a dispatcher may\nhave imperfect information about the car routes? What inherent\ntrade-offs exist between car density and storage per car with\nregards to their combined as well as individual effect on availability\nlatency in the presence of zebroids? We present both simple\nanalysis and detailed simulations to provide answers to these questions\nas well as gain insights into design of carrier-based systems.\n6.1 How does a replacement scheme employed\nby a zebroid impact availability latency?\nFor illustration, we present \u2018scale-up\" experiments where\noneinstantaneous zebroids are employed (see Figure 1). By scale-up,\nwe mean that \u03b1 and N are changed proportionally to keep the total\nsystem storage, ST , constant. Here, T = 50 and ST = 200. We\nchoose the following values of (N,\u03b1) = {(20,10), (25,8), (50,4),\n(100,2)}. The figure indicates that a random replacement scheme\nshows competitive performance. This is because of several reasons.\nRecall that the initial replica distribution is set as per the\nsquareroot replication scheme. The random replacement scheme does not\nalter this distribution since it makes replacements blind to the\npopularity of a data item. However, the replacements cause dynamic\ndata re-organization so as to better serve the currently active\nrequest. Moreover, the mobility pattern of the cars is random, hence,\nthe locations from which the requests are issued by clients are also\nrandom and not known a priori at the dispatcher. These findings\nare significant because a random replacement policy can be\nimplemented in a simple decentralized manner.\nThe lru-global and lfu-global schemes provide a latency\nperformance that is worse than random. This is because these\npolicies rapidly develop a preference for the more popular data items\nthereby creating a larger number of replicas for them. During\neviction, the more popular data items are almost never selected as a\nreplacement candidate. Consequently, there are fewer replicas for\nthe less popular items. Hence, the initial distribution of the data\nitem replicas changes from square-root to that resembling linear\nreplication. The higher number of replicas for the popular data\nitems provide marginal additional benefits, while the lower number\nof replicas for the other data items hurts the latency performance of\nthese global policies. The lfu-local and lru-local schemes have\nsimilar performance to random since they do not have enough history\nof local data item requests. We speculate that the performance of\nthese local policies will approach that of their global variants for a\nlarge enough history of data item requests. On account of the\ncompetitive performance shown by a random policy, for the remainder\nof the paper, we present the performance of zebroids that employ a\nrandom replacement policy.\n6.2 Do zebroids provide significant\nimprovements in availability latency?\nWe find that in many scenarios employing zebroids provides\nsubstantial improvements in availability latency.\n6.2.1 Analysis\nWe first consider the case of one-instantaneous zebroids.\nFigure 2.a shows the variation in \u03b4agg as a function of N for T = 10\nand \u03b1 = 1 with a 10 \u00d7 10 torus using Equation 4. Both the x and y\naxes are drawn to a log-scale. Figure 2.b show the % improvement\nin \u03b4agg obtained with one-instantaneous zebroids. In this case, only\nthe x-axis is drawn to a log-scale. For illustration, we assume that\nthe T data items are requested uniformly.\nInitially, when the network is sparse the analytical approximation\nfor improvements in latency with zebroids, obtained from\nEquations 2 and 4, closely matches the simulation results. However, as\nN increases, the sparseness assumption for which the analysis is\nvalid, namely N << G, is no longer true. Hence, the two curves\nrapidly diverge. The point at which the two curves move away from\neach other corresponds to a value of \u03b4agg \u2264 1. Moreover, as\nmentioned earlier, the analysis provides an upper bound on the latency\nimprovements, as it treats the newly created replicas given by Nc\ni\nindependently. However, these Nc\ni replicas start from the same cell\nas one of the server replicas ri. Finally, the analysis captures a\noneshot scenario where given an initial data item replica distribution,\nthe availability latency is computed. The new replicas created do\nnot affect future requests from the client.\nOn account of space limitations, here, we summarize the\nobservations in the case when z-relay zebroids are employed. The\ninterested reader can obtain further details in [9]. Similar observations,\nlike the one-instantaneous zebroid case, apply since the simulation\nand analysis curves again start diverging when the analysis\nassumptions are no longer valid. However, the key observation here is that\nthe latency improvement with z-relay zebroids is significantly\nbetter than the one-instantaneous zebroids case, especially for lower\nstorage scenarios. This is because in sparse scenarios, the\ntransitive hand-offs between the zebroids creates higher number of\nreplicas for the requested data item, yielding lower availability latency.\nMoreover, it is also seen that the simulation validation curve for the\nimprovements in \u03b4agg with z-relay zebroids approaches that of the\none-instantaneous zebroid case for higher storage (higher N\nvalues). This is because one-instantaneous zebroids are a special case\nof z-relay zebroids.\n6.2.2 Simulation\nWe conduct simulations to examine the entire storage spectrum\nobtained by changing car density N or storage per car \u03b1 to also\ncapture scenarios where the sparseness assumptions for which the\nanalysis is valid do not hold. We separate the effect of N and \u03b1\nby capturing the variation of N while keeping \u03b1 constant (case\n1) and vice-versa (case 2) both with z-relay and one-instantaneous\nzebroids. Here, we set the repository size as T = 25. Figure 3\ncaptures case 1 mentioned above. Similar trends are observed with\ncase 2, a complete description of those results are available in [9].\nWith Figure 3.b, keeping \u03b1 constant, initially increasing car\ndensity has higher latency benefits because increasing N introduces\nmore zebroids in the system. As N is further increased, \u03c9 reduces\nbecause the total storage in the system goes up. Consequently, the\nnumber of replicas per data item goes up thereby increasing the\n79\nnumber of servers. Hence, the replacement policy cannot find a\nzebroid as often to transport the requested data item to the client\nearlier than any of the servers. On the other hand, the increased\nnumber of servers benefits the no-zebroids case in bringing \u03b4agg\ndown. The net effect results in reduction in \u03c9 for larger values of\nN.\n10\n1\n10\n2\n10\n3\n10\n\u22121\n10\n0\n10\n1\n10\n2\nNumber of cars\nno\u2212zebroidsanal\nno\u2212zebroids\nsim\none\u2212instantaneous\nanal\none\u2212instantaneoussim\nAggregate Availability latency (\u03b4agg\n)\n2.a) \u03b4agg\n10\n1\n10\n2\n10\n3\n0\n10\n20\n30\n40\n50\n60\n70\n80\n90\n100\nNumber of cars\n% Improvement in \u03b4agg\nwrt no\u2212zebroids (\u03c9)\nanalytical upper\u2212bound\nsimulation\n2.b) \u03c9\nFigure 2: Figure 2 shows the latency performance with\noneinstantaneous zebroids via simulations along with the\nanalytical approximation for a 10 \u00d7 10 torus with T = 10.\nThe trends mentioned above are similar to that obtained from the\nanalysis. However, somewhat counter-intuitively with relatively\nhigher system storage, z-relay zebroids provide slightly lower\nimprovements in latency as compared to one-instantaneous zebroids.\nWe speculate that this is due to the different data item replica\ndistributions enforced by them. Note that replacements performed by\nthe zebroids cause fluctuations in these replica distributions which\nmay effect future client requests. We are currently exploring\nsuitable choices of parameters that can capture these changing replica\ndistributions.\n6.3 What is the overhead incurred with\nimprovements in latency with zebroids?\nWe find that the improvements in latency with zebroids are\nobtained at a minimal replacement overhead (< 1 per client request).\n6.3.1 Analysis\nWith one-instantaneous zebroids, for each client request a\nmaximum of one zebroid is employed for latency improvement. Hence,\nthe replacement overhead per client request can amount to a\nmaximum of one. Recall that to calculate the latency with one-instantaneous\n0 50 100 150 200 250 300 350 400\n0\n1\n2\n3\n4\n5\n6\nNumber of cars\nAggregate availability latency (\u03b4agg\n)\nno\u2212zebroids\none\u2212instantaneous\nz\u2212relays\n3.a\n0 50 100 150 200 250 300 350 400\n0\n10\n20\n30\n40\n50\n60\nNumber of cars\n% Improvement in \u03b4agg\nwrt no\u2212zebroids (\u03c9)\none\u2212instantaneous\nz\u2212relays\n3.b\nFigure 3: Figure 3 depicts the latency performance with both\none-instantaneous and z-relay zebroids as a function of the car\ndensity when \u03b1 = 2 and T = 25.\nzebroids, Nc\ni new replicas are created in the same cell as the servers.\nNow a replacement is only incurred if one of these Nc\ni newly\ncreated replicas meets the client earlier than any of the ri servers.\nLet Xri and XNc\ni\nrespectively be random variables that capture\nthe minimum time till any of the ri and Nc\ni replicas meet the client.\nSince Xri and XNc\ni\nare assumed to be independent, by the property\nof exponentially distributed random variables we have,\nOverhead/request = 1 \u00b7 P(XNc\ni\n< Xri ) + 0 \u00b7 P(Xri \u2264 XNc\ni\n)\n(6)\nOverhead/request =\nri\nC\nri\nC\n+\nNc\ni\nC\n=\nri\nri + Nc\ni\n(7)\nRecall that the number of replicas for data item i, ri, is a function\nof the total storage in the system i.e., ri = k\u00b7N \u00b7\u03b1 where k satisfies\nthe constraint 1 \u2264 ri \u2264 N. Using this along with Equation 2, we\nget\nOverhead/request = 1 \u2212\nG\nG + N \u00b7 (1 \u2212 k \u00b7 \u03b1)\n(8)\nNow if we keep the total system storage N \u00b7 \u03b1 constant since\nG and T are also constant, increasing N increases the replacement\noverhead. However, if N \u00b7\u03b1 is constant then increasing N causes \u03b1\n80\n0 20 40 60 80 100\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\n0.45\n0.5\nNumber of cars\none\u2212instantaneous\nzebroids\nAverage number of replacements per request\n(N=20,\u03b1=10)\n(N=25,\u03b1=8)\n(N=50,\u03b1=4)\n(N=100,\u03b1=2)\nFigure 4: Figure 4 captures replacement overhead when\nemploying one-instantaneous zebroids as a function of (N,\u03b1)\nvalues, when the total storage in the system is kept fixed, ST =\n200.\nto go down. This implies that a higher replacement overhead is\nincurred for higher N and lower \u03b1 values. Moreover, when ri = N,\nthis means that every car has a replica of data item i. Hence, no\nzebroids are employed when this item is requested, yielding an\noverhead/request for this item as zero. Next, we present\nsimulation results that validate our analysis hypothesis for the overhead\nassociated with deployment of one-instantaneous zebroids.\n6.3.2 Simulation\nFigure 4 shows the replacement overhead with one-instantaneous\nzebroids when (N,\u03b1) are varied while keeping the total system\nstorage constant. The trends shown by the simulation are in agreement\nwith those predicted by the analysis above. However, the total\nsystem storage can be changed either by varying car density (N) or\nstorage per car (\u03b1). On account of similar trends, here we present\nthe case when \u03b1 is kept constant and N is varied (Figure 5). We\nrefer the reader to [9] for the case when \u03b1 is varied and N is held\nconstant.\nWe present an intuitive argument for the behavior of the\nperrequest replacement overhead curves. When the storage is extremely\nscarce so that only one replica per data item exists in the AutoMata\nnetwork, the number of replacements performed by the zebroids is\nzero since any replacement will cause a data item to be lost from\nthe system. The dispatcher ensures that no data item is lost from\nthe system. At the other end of the spectrum, if storage becomes\nso abundant that \u03b1 = T then the entire data item repository can\nbe replicated on every car. The number of replacements is again\nzero since each request can be satisfied locally. A similar scenario\noccurs if N is increased to such a large value that another car with\nthe requested data item is always available in the vicinity of the\nclient. However, there is a storage spectrum in the middle where\nreplacements by the scheduled zebroids result in improvements in\n\u03b4agg (see Figure 3).\nMoreover, we observe that for sparse storage scenarios, the higher\nimprovements with z-relay zebroids are obtained at the cost of a\nhigher replacement overhead when compared to the one-instantaneous\nzebroids case. This is because in the former case, each of these z\nzebroids selected along the lowest latency path to the client needs\nto perform a replacement. However, the replacement overhead is\nstill less than 1 indicating that on an average less than one\nreplacement per client request is needed even when z-relay zebroids are\nemployed.\n0 50 100 150 200 250 300 350 400\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nNumber of cars\nz\u2212relays\none\u2212instantaneous\nAverage number of replacements per request\nFigure 5: Figure 5 shows the replacement overhead with\nzebroids for the cases when N is varied keeping \u03b1 = 2.\n10 20 30 40 50 60 70 80 90 100\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\nPrediction percentage\nno\u2212zebroids (N=50)\none\u2212instantaneous (N=50)\nz\u2212relays (N=50)\nno\u2212zebroids (N=200)\none\u2212instantaneous (N=200) z\u2212relays (N=200)\nAggregate Availability Latency (\u03b4agg\n)\nFigure 6: Figure 6 shows \u03b4agg for different car densities as a\nfunction of the prediction accuracy metric with \u03b1 = 2 and T =\n25.\n6.4 What happens to the availability latency\nwith zebroids in scenarios with\ninaccuracies in the car route predictions?\nWe find that zebroids continue to provide improvements in\navailability latency even with lower accuracy in the car route\npredictions. We use a single parameter p to quantify the accuracy of the\ncar route predictions.\n6.4.1 Analysis\nSince p represents the probability that a car route predicted by the\ndispatcher matches the actual one, hence, the latency with zebroids\ncan be approximated by,\n\u03b4err\nagg = p \u00b7 \u03b4agg(zeb) + (1 \u2212 p) \u00b7 \u03b4agg(no \u2212 zeb) (9)\n\u03b4err\nagg = p \u00b7 \u03b4agg(zeb) + (1 \u2212 p) \u00b7\nC\nri\n(10)\nExpressions for \u03b4agg(zeb) can be obtained from Equations 4\n(one-instantaneous) or 5 (z-relay zebroids).\n6.4.2 Simulation\nFigure 6 shows the variation in \u03b4agg as a function of this route\nprediction accuracy metric. We observe a smooth reduction in the\n81\nimprovement in \u03b4agg as the prediction accuracy metric reduces. For\nzebroids that are scheduled but fail to rendezvous with the client\ndue to the prediction error, we tag any such replacements made by\nthe zebroids as failed. It is seen that failed replacements gradually\nincrease as the prediction accuracy reduces.\n6.5 Under what conditions are the\nimprovements in availability latency with zebroids\nmaximized?\nSurprisingly, we find that the improvements in latency obtained\nwith one-instantaneous zebroids are independent of the input\ndistribution of the popularity of the data items.\n6.5.1 Analysis\nThe fractional difference (labelled \u03c9) in the latency between the\nno-zebroids and one-instantaneous zebroids is obtained from\nequations 2, 3, and 4 as\n\u03c9 =\nT\ni=1\nfi\u00b7C\nri\n\u2212 T\ni=1\nfi\u00b7C\nri+(N\u2212ri)\u00b7(1\u2212(1\u2212 1\nG )ri\n)\nT\ni=1\nfi\u00b7C\nri\n(11)\nHere C = c\u00b7G\u00b7log G. This captures the fractional improvement\nin the availability latency obtained by employing one-instantaneous\nzebroids. Let \u03b1 = 1, making the total storage in the system ST =\nN. Assuming the initial replica distribution is as per the\nsquareroot replication scheme, we have, ri =\n\u221a\nfi\u00b7N\nT\nj=1\n\u221a\nfj\n. Hence, we get\nfi =\nK2\n\u00b7r2\ni\nN2 , where K = T\nj=1 fj. Using this, along with the\napproximation (1 \u2212 x)n\n1 \u2212 n \u00b7 x for small x, we simplify the\nabove equation to get, \u03c9 = 1 \u2212\nT\ni=1\nri\n1+\nN\u2212ri\nG\nT\ni=1 ri\nIn order to determine when the gains with one-instantaneous\nzebroids are maximized, we can frame an optimization problem as\nfollows: Maximize \u03c9, subject to T\ni=1 ri = ST\nTHEOREM 1. With a square-root replication scheme,\nimprovements obtained with one-instantaneous zebroids are independent\nof the input popularity distribution of the data items. (See [9] for\nproof)\n6.5.2 Simulation\nWe perform simulations with two different frequency\ndistribution of data items: Uniform and Zipfian (with mean= 0.27).\nSimilar latency improvements with one-instantaneous zebroids are\nobtained in both cases. This result has important implications. In\ncases with biased popularity toward certain data items, the\naggregate improvements in latency across all data item requests still\nremain the same. Even in scenarios where the frequency of access\nto the data items changes dynamically, zebroids will continue to\nprovide similar latency improvements.\n7. CONCLUSIONS AND\nFUTURE RESEARCH DIRECTIONS\nIn this study, we examined the improvements in latency that can\nbe obtained in the presence of carriers that deliver a data item from\na server to a client. We quantified the variation in availability\nlatency as a function of a rich set of parameters such as car density,\nstorage per car, title database size, and replacement policies\nemployed by zebroids.\nBelow we summarize some key future research directions we\nintend to pursue. To better reflect reality we would like to validate the\nobservations obtained from this study with some real world\nsimulation traces of vehicular movements (for example using\nCORSIM [1]). This will also serve as a validation for the utility of the\nMarkov mobility model used in this study. We are currently\nanalyzing the performance of zebroids on a real world data set\ncomprising of an ad-hoc network of buses moving around a small\nneighborhood in Amherst [4]. Zebroids may also be used for delivery\nof data items that carry delay sensitive information with a certain\nexpiry. Extensions to zebroids that satisfy such application\nrequirements presents an interesting future research direction.\n8. ACKNOWLEDGMENTS\nThis research was supported in part by an Annenberg fellowship and NSF\ngrants numbered CNS-0435505 (NeTS NOSS), CNS-0347621 (CAREER),\nand IIS-0307908.\n9. REFERENCES\n[1] Federal Highway Administration. Corridor simulation. Version 5.1,\nhttp://www.ops.fhwa.dot.gov/trafficanalysistools/cors im.htm.\n[2] D. Aldous and J. Fill. Reversible markov chains and random walks\non graphs. Under preparation.\n[3] A. Bar-Noy, I. Kessler, and M. Sidi. Mobile Users: To Update or Not\nto Update. In IEEE Infocom, 1994.\n[4] J. Burgess, B. Gallagher, D. Jensen, and B. Levine. MaxProp:\nRouting for Vehicle-Based Disruption-Tolerant Networking. In IEEE\nInfocom, April 2006.\n[5] E. Cohen and S. Shenker. Replication Strategies in Unstructured\nPeer-to-Peer Networks. In SIGCOMM, 2002.\n[6] A. Dan, D. Dias, R. Mukherjee, D. Sitaram, and R. Tewari. Buffering\nand Caching in Large-Scale Video Servers. In COMPCON, 1995.\n[7] S. Ghandeharizadeh, S. Kapadia, and B. Krishnamachari. PAVAN: A\nPolicy Framework for Content Availabilty in Vehicular ad-hoc\nNetworks. In VANET, New York, NY, USA, 2004. ACM Press.\n[8] S. Ghandeharizadeh, S. Kapadia, and B. Krishnamachari.\nComparison of Replication Strategies for Content Availability in\nC2P2 networks. In MDM, May 2005.\n[9] S. Ghandeharizadeh, S. Kapadia, and B. Krishnamachari. An\nEvaluation of Availability Latency in Carrier-based Vehicular ad-hoc\nNetworks. Technical report, Department of Computer Science,\nUniversity of Southern California,CENG-2006-1, 2006.\n[10] S. Ghandeharizadeh and B. Krishnamachari. C2p2: A peer-to-peer\nnetwork for on-demand automobile information services. In Globe.\nIEEE, 2004.\n[11] T. Hara. Effective Replica Allocation in ad-hoc Networks for\nImproving Data Accessibility. In IEEE Infocom, 2001.\n[12] H. Hayashi, T. Hara, and S. Nishio. A Replica Allocation Method\nAdapting to Topology Changes in ad-hoc Networks. In DEXA, 2005.\n[13] P. Juang, H. Oki, Y. Wang, M. Martonosi, L. Peh, and D. Rubenstein.\nEnergy-efficient computing for wildlife tracking: design tradeoffs\nand early experiences with ZebraNet. SIGARCH Comput. Archit.\nNews, 2002.\n[14] A. Pentland, R. Fletcher, and A. Hasson. DakNet: Rethinking\nConnectivity in Developing Nations. Computer, 37(1):78-83, 2004.\n[15] F. Sailhan and V. Issarny. Cooperative Caching in ad-hoc Networks.\nIn MDM, 2003.\n[16] R. Shah, S. Roy, S. Jain, and W. Brunette. Data mules: Modeling and\nanalysis of a three-tier architecture for sparse sensor networks.\nElsevier ad-hoc Networks Journal, 1, September 2003.\n[17] T. Spyropoulos, K. Psounis, and C. Raghavendra. Single-Copy\nRouting in Intermittently Connected Mobile Networks. In SECON,\nApril 2004.\n[18] A. Tanenbaum. Modern Operating Systems, 2nd Edition, Chapter 4,\nSection 4.4 . Prentice Hall, 2001.\n[19] A. Vahdat and D. Becker. Epidemic routing for partially-connected\nad-hoc networks. Technical report, Department of Computer Science,\nDuke University, 2000.\n[20] W. Zhao, M. Ammar, and E. Zegura. A message ferrying approach\nfor data delivery in sparse mobile ad-hoc networks. In MobiHoc,\npages 187-198, New York, NY, USA, 2004. ACM Press.\n[21] M. Zonoozi and P. Dassanayake. User Mobility Modeling and\nCharacterization of Mobility Pattern. IEEE Journal on Selected\nAreas in Communications, 15:1239-1252, September 1997.\n82", "keywords": "naive random replacement policy;zebroid;vehicular network;termed zebroid;audio and video clip;mobility;car density;storage per device;datum carrier;latency;simplified instantiation of zebroid;automaton;availability latency;repository size;markov model;zebroid simplified instantiation;mobile device;peer-to-peer vehicular ad-hoc network;replacement policy"}
{"name": "train_C-69", "title": "pTHINC: A Thin-Client Architecture for Mobile Wireless Web", "abstract": "Although web applications are gaining popularity on mobile wireless PDAs, web browsers on these systems can be quite slow and often lack adequate functionality to access many web sites. We have developed pTHINC, a PDA thinclient solution that leverages more powerful servers to run full-function web browsers and other application logic, then sends simple screen updates to the PDA for display. pTHINC uses server-side screen scaling to provide high-fidelity display and seamless mobility across a broad range of different clients and screen sizes, including both portrait and landscape viewing modes. pTHINC also leverages existing PDA control buttons to improve system usability and maximize available screen resolution for application display. We have implemented pTHINC on Windows Mobile and evaluated its performance on mobile wireless devices. Our results compared to local PDA web browsers and other thin-client approaches demonstrate that pTHINC provides superior web browsing performance and is the only PDA thin client that effectively supports crucial browser helper applications such as video playback.", "fulltext": "1. INTRODUCTION\nThe increasing ubiquity of wireless networks and\ndecreasing cost of hardware is fueling a proliferation of mobile\nwireless handheld devices, both as standalone wireless Personal\nDigital Assistants (PDA) and popular integrated PDA/cell\nphone devices. These devices are enabling new forms of\nmobile computing and communication. Service providers are\nleveraging these devices to deliver pervasive web access, and\nmobile web users already often use these devices to access\nweb-enabled information such as news, email, and localized\ntravel guides and maps. It is likely that within a few years,\nmost of the devices accessing the web will be mobile.\nUsers typically access web content by running a web browser\nand associated helper applications locally on the PDA.\nAlthough native web browsers exist for PDAs, they deliver\nsubpar performance and have a much smaller feature set\nand more limited functionality than their desktop\ncomputing counterparts [10]. As a result, PDA web browsers are\noften not able to display web content from web sites that\nleverage more advanced web technologies to deliver a richer web\nexperience. This fundamental problem arises for two\nreasons. First, because PDAs have a completely different\nhardware/software environment from traditional desktop\ncomputers, web applications need to be rewritten and customized\nfor PDAs if at all possible, duplicating development costs.\nBecause the desktop application market is larger and more\nmature, most development effort generally ends up being\nspent on desktop applications, resulting in greater\nfunctionality and performance than their PDA counterparts.\nSecond, PDAs have a more resource constrained environment\nthan traditional desktop computers to provide a smaller\nform factor and longer battery life. Desktop web browsers\nare large, complex applications that are unable to run on a\nPDA. Instead, developers are forced to significantly strip\ndown these web browsers to provide a usable PDA web\nbrowser, thereby crippling PDA browser functionality.\nThin-client computing provides an alternative approach\nfor enabling pervasive web access from handheld devices.\nA thin-client computing system consists of a server and a\nclient that communicate over a network using a remote\ndisplay protocol. The protocol enables graphical displays to be\nvirtualized and served across a network to a client device,\nwhile application logic is executed on the server. Using the\nremote display protocol, the client transmits user input to\nthe server, and the server returns screen updates of the\napplications from the server to the client. Using a thin-client\nmodel for mobile handheld devices, PDAs can become\nsimple stateless clients that leverage the remote server\ncapabilities to execute web browsers and other helper applications.\nThe thin-client model provides several important\nbenefits for mobile wireless web. First, standard desktop web\napplications can be used to deliver web content to PDAs\nwithout rewriting or adapting applications to execute on\na PDA, reducing development costs and leveraging existing\nsoftware investments. Second, complex web applications can\nbe executed on powerful servers instead of running stripped\ndown versions on more resource constrained PDAs,\nproviding greater functionality and better performance [10]. Third,\nweb applications can take advantage of servers with faster\nnetworks and better connectivity, further boosting\napplication performance. Fourth, PDAs can be even simpler\ndevices since they do not need to perform complex application\nlogic, potentially reducing energy consumption and\nextend143\ning battery life. Finally, PDA thin clients can be essentially\nstateless appliances that do not need to be backed up or\nrestored, require almost no maintenance or upgrades, and do\nnot store any sensitive data that can be lost or stolen. This\nmodel provides a viable avenue for medical organizations to\ncomply with HIPAA regulations [6] while embracing mobile\nhandhelds in their day to day operations.\nDespite these potential advantages, thin clients have been\nunable to provide the full range of these benefits in delivering\nweb applications to mobile handheld devices. Existing thin\nclients were not designed for PDAs and do not account for\nimportant usability issues in the context of small form factor\ndevices, resulting in difficulty in navigating displayed web\ncontent. Furthermore, existing thin clients are ineffective at\nproviding seamless mobility across the heterogeneous mix\nof device display sizes and resolutions. While existing thin\nclients can already provide faster performance than native\nPDA web browsers in delivering HTML web content, they\ndo not effectively support more display-intensive web helper\napplications such as multimedia video, which is increasingly\nan integral part of available web content.\nTo harness the full potential of thin-client computing in\nproviding mobile wireless web on PDAs, we have developed\npTHINC (PDA THin-client InterNet Computing). pTHINC\nbuilds on our previous work on THINC [1] to provide a\nthinclient architecture for mobile handheld devices. pTHINC\nvirtualizes and resizes the display on the server to efficiently\ndeliver high-fidelity screen updates to a broad range of\ndifferent clients, screen sizes, and screen orientations, including\nboth portrait and landscape viewing modes. This enables\npTHINC to provide the same persistent web session across\ndifferent client devices. For example, pTHINC can provide\nthe same web browsing session appropriately scaled for\ndisplay on a desktop computer and a PDA so that the same\ncookies, bookmarks, and other meta-data are continuously\navailable on both machines simultaneously. pTHINC\"s\nvirtual display approach leverages semantic information\navailable in display commands, and client-side video hardware to\nprovide more efficient remote display mechanisms that are\ncrucial for supporting more display-intensive web\napplications. Given limited display resolution on PDAs, pTHINC\nmaximizes the use of screen real estate for remote display\nby moving control functionality from the screen to readily\navailable PDA control buttons, improving system usability.\nWe have implemented pTHINC on Windows Mobile and\ndemonstrated that it works transparently with existing\napplications, window systems, and operating systems, and does\nnot require modifying, recompiling, or relinking existing\nsoftware. We have quantitatively evaluated pTHINC against\nlocal PDA web browsers and other thin-client approaches on\nPocket PC devices. Our experimental results demonstrate\nthat pTHINC provides superior web browsing performance\nand is the only PDA thin client that effectively supports\ncrucial browser helper applications such as video playback.\nThis paper presents the design and implementation of\npTHINC. Section 2 describes the overall usage model and\nusability characteristics of pTHINC. Section 3 presents the\ndesign and system architecture of pTHINC. Section 4 presents\nexperimental results measuring the performance of pTHINC\non web applications and comparing it against native PDA\nbrowsers and other popular PDA thin-client systems.\nSection 5 discusses related work. Finally, we present some\nconcluding remarks.\n2. PTHINC USAGE MODEL\npTHINC is a thin-client system that consists of a simple\nclient viewer application that runs on the PDA and a server\nthat runs on a commodity PC. The server leverages more\npowerful PCs to to run web browsers and other application\nlogic. The client takes user input from the PDA stylus and\nvirtual keyboard and sends them to the server to pass to\nthe applications. Screen updates are then sent back from\nthe server to the client for display to the user.\nWhen the pTHINC PDA client is started, the user is\npresented with a simple graphical interface where information\nsuch as server address and port, user authentication\ninformation, and session settings can be provided. pTHINC first\nattempts to connect to the server and perform the\nnecessary handshaking. Once this process has been completed,\npTHINC presents the user with the most recent display of\nhis session. If the session does not exist, a new session is\ncreated. Existing sessions can be seamlessly continued without\nchanges in the session setting or server configuration.\nUnlike other thin-client systems, pTHINC provides a user\nwith a persistent web session model in which a user can\nlaunch a session running a web browser and associated\napplications at the server, then disconnect from that session\nand reconnect to it again anytime. When a user reconnects\nto the session, all of the applications continue running where\nthe user left off, so that the user can continue working as\nthough he or she never disconnected. The ability to\ndisconnect and reconnect to a session at anytime is an important\nbenefit for mobile wireless PDA users which may have\nintermittent network connectivity.\npTHINC\"s persistent web session model enables a user to\nreconnect to a web session from devices other than the one\non which the web session was originally initiated. This\nprovides users with seamless mobility across different devices.\nIf a user loses his PDA, he can easily use another PDA to\naccess his web session. Furthermore, pTHINC allows users\nto use non-PDA devices to access web sessions as well. A\nuser can access the same persistent web session on a\ndesktop PC as on a PDA, enabling a user to use the same web\nsession from any computer.\npTHINC\"s persistent web session model addresses a key\nproblem encountered by mobile web users, the lack of a\ncommon web environment across computers. Web browsers\noften store important information such as bookmarks, cookies,\nand history, which enable them to function in a much more\nuseful manner. The problem that occurs when a user moves\nbetween computers is that this data, which is specific to a\nweb browser installation, cannot move with the user.\nFurthermore, web browsers often need helper applications to\nprocess different media content, and those applications may\nnot be consistently available across all computers. pTHINC\naddresses this problem by enabling a user to remotely use\nthe exact same web browser environment and helper\napplications from any computer. As a result, pTHINC can\nprovide a common, consistent web browsing environment for\nmobile users across different devices without requiring them\nto attempt to repeatedly synchronize different web browsing\nenvironments across multiple machines.\nTo enable a user to access the same web session on\ndifferent devices, pTHINC must provide mechanisms to\nsupport different display sizes and resolutions. Toward this end,\npTHINC provides a zoom feature that enables a user to\nzoom in and out of a display and allows the display of a web\n144\nFigure 1: pTHINC shortcut keys\nsession to be resized to fit the screen of the device being\nused. For example, if the server is running a web session at\n1024\u00d7768 but the client is a PDA with a display resolution\nof 640\u00d7480, pTHINC will resize the desktop display to fit\nthe full display in the smaller screen of the PDA. pTHINC\nprovides the PDA user with the option to increase the size\nof the display by zooming in to different parts of the display.\nUsers are often familiar with the general layout of commonly\nvisited websites, and are able to leverage this resizing\nfeature to better navigate through web pages. For example,\na user can zoom out of the display to view the entire page\ncontent and navigate hyperlinks, then zoom in to a region\nof interest for a better view.\nTo enable a user to access the same web session on\ndifferent devices, pTHINC must also provide mechanisms to\nsupport different display orientations. In a desktop\nenvironment, users are typically accustomed to having displays\npresented in landscape mode where the screen width is larger\nthan its height. However, in a PDA environment, the choice\nis not always obvious. Some users may prefer having the\ndisplay in portrait mode, as it is easier to hold the device\nin their hands, while others may prefer landscape mode in\norder to minimize the amount of side-scrolling necessary\nto view a web page. To accommodate PDA user\npreferences, pTHINC provides an orientation feature that enables\nit to seamless rotate the display between landscape and\nportrait mode. The landscape mode is particularly useful for\npTHINC users who frequently access their web sessions on\nboth desktop and PDA devices, providing those users with\nthe same familiar landscape setting across different devices.\nBecause screen space is a relatively scarce resource on\nPDAs, pTHINC runs in fullscreen mode to maximize the\nscreen area available to display the web session. To be able\nto use all of the screen on the PDA and still allow the user\nto control and interact with it, pTHINC reuses the typical\nshortcut buttons found on PDAs to perform all the\ncontrol functions available to the user. The buttons used by\npTHINC do not require any OS environment changes; they\nare simply intercepted by the pTHINC client application\nwhen they are pressed. Figure 1 shows how pTHINC\nutilizes the shortcut buttons to provide easy navigation and\nimprove the overall user experience. These buttons are not\ndevice specific, and the layout shown is common to\nwidelyused PocketPC devices. pTHINC provides six shortcuts to\nsupport its usage model:\n\u2022 Rotate Screen: The record button on the left edge is\nused to rotate the screen between portrait and\nlandscape mode each time the button is pressed.\n\u2022 Zoom Out: The leftmost button on the bottom front\nis used to zoom out the display of the web session\nproviding a bird\"s eye view of the web session.\n\u2022 Zoom In: The second leftmost button on the bottom\nfront is used to zoom in the display of the web session\nto more clearly view content of interest.\n\u2022 Directional Scroll: The middle button on the bottom\nfront is used to scroll around the display using a single\ncontrol button in a way that is already familiar to PDA\nusers. This feature is particularly useful when the user\nhas zoomed in to a region of the display such that only\npart of the display is visible on the screen.\n\u2022 Show/Hide Keyboard: The second rightmost button on\nthe bottom front is used to bring up a virtual keyboard\ndrawn on the screen for devices which have no physical\nkeyboard. The virtual keyboard uses standard PDA\nOS mechanisms, providing portability across different\nPDA environments.\n\u2022 Close Session: The rightmost button on the bottom\nfront is used to disconnect from the pTHINC session.\npTHINC uses the PDA touch screen, stylus, and standard\nuser interface mechanisms to provide a user interface\npointand-click metaphor similar to that provided by the mouse\nin a traditional desktop computing environment. pTHINC\ndoes not use a cursor since PDA environments do not\nprovide one. Instead, a user can use the stylus to tap on\ndifferent sections of the touch screen to indicate input focus. A\nsingle tap on the touch screen generates a corresponding\nsingle click mouse event. A double tap on the touch screen\ngenerates a corresponding double click mouse event. pTHINC\nprovides two-button mouse emulation by using the stylus to\npress down on the screen for one second to generate a right\nmouse click. All of these actions are identical to the way\nusers already interact with PDA applications in the common\nPocketPC environment. In web browsing, users can click on\nhyperlinks and focus on input boxes by simply tapping on\nthe desired screen area of interest. Unlike local PDA web\nbrowsers and other PDA applications, pTHINC leverages\nmore powerful desktop user interface metaphors to enable\nusers to manipulate multiple open application windows\ninstead of being limited to a single application window at any\ngiven moment. This provides increased browsing flexibility\nbeyond what is currently available on PDA devices. Similar\nto a desktop environment, browser windows and other\napplication windows can be moved around by pressing down\nand dragging the stylus similar to a mouse.\n3. PTHINC SYSTEM ARCHITECTURE\npTHINC builds on the THINC [1] remote display\narchitecture to provide a thin-client system for PDAs. pTHINC\nvirtualizes the display at the server by leveraging the video\ndevice abstraction layer, which sits below the window server\nand above the framebuffer. This is a well-defined, low-level,\ndevice-dependent layer that exposes the video hardware to\nthe display system. pTHINC accomplishes this through a\nsimple virtual display driver that intercepts drawing\ncommands, packetizes, and sends them over the network.\n145\nWhile other thin-client approaches intercept display\ncommands at other layers of the display subsystem, pTHINC\"s\ndisplay virtualization approach provides some key benefits\nin efficiently supporting PDA clients. For example,\nintercepting display commands at a higher layer between\napplications and the window system as is done by X [17] requires\nreplicating and running a great deal of functionality on the\nPDA that is traditionally provided by the desktop window\nsystem. Given both the size and complexity of traditional\nwindow systems, attempting to replicate this functionality\nin the restricted PDA environment would have proven to\nbe a daunting, and perhaps unfeasible task. Furthermore,\napplications and the window system often require tight\nsynchronization in their operation and imposing a wireless\nnetwork between them by running the applications on the server\nand the window system on the client would significantly\ndegrade performance. On the other hand, intercepting at a\nlower layer by extracting pixels out of the framebuffer as\nthey are rendered provides a simple solution that requires\nvery little functionality on the PDA client, but can also\nresult in degraded performance. The reason is that by the\ntime the remote display server attempts to send screen\nupdates, it has lost all semantic information that may have\nhelped it encode efficiently, and it must resort to using a\ngeneric and expensive encoding mechanism on the server,\nas well as a potentially expensive decoding mechanism on\nthe limited PDA client. In contrast to both the high and\nlow level interception approaches, pTHINC\"s approach of\nintercepting at the device driver provides an effective\nbalance between client and server simplicity, and the ability to\nefficiently encode and decode screen updates.\nBy using a low-level virtual display approach, pTHINC\ncan efficiently encode application display commands using\nonly a small set of low-level commands. In a PDA\nenvironment, this set of commands provides a crucial component\nin maintaining the simplicity of the client in the\nresourceconstrained PDA environment. The display commands are\nshown in Table 1, and work as follows. COPY instructs the\nclient to copy a region of the screen from its local framebuffer\nto another location. This command improves the user\nexperience by accelerating scrolling and opaque window\nmovement without having to resend screen data from the server.\nSFILL, PFILL, and BITMAP are commands that paint a\nfixed-size region on the screen. They are useful for\naccelerating the display of solid window backgrounds, desktop\npatterns, backgrounds of web pages, text drawing, and\ncertain operations in graphics manipulation programs. SFILL\nfills a sizable region on the screen with a single color. PFILL\nreplicates a tile over a screen region. BITMAP performs a\nfill using a bitmap of ones and zeros as a stipple to apply\na foreground and background color. Finally, RAW is used\nto transmit unencoded pixel data to be displayed verbatim\non a region of the screen. This command is invoked as a\nlast resort if the server is unable to employ any other\ncommand, and it is the only command that may be compressed\nto mitigate its impact on network bandwidth.\npTHINC delivers its commands using a non-blocking,\nserverpush update mechanism, where as soon as display updates\nare generated on the server, they are sent to the client.\nClients are not required to explicitly request display\nupdates, thus minimizing the impact that the typical\nvarying network latency of wireless links may have on the\nresponsiveness of the system. Keeping in mind that resource\nCommand Description\nCOPY Copy a frame buffer area to specified\ncoordinates\nSFILL Fill an area with a given pixel color value\nPFILL Tile an area with a given pixel pattern\nBITMAP Fill a region using a bit pattern\nRAW Display raw pixel data at a given location\nTable 1: pTHINC Protocol Display Commands\nconstrained PDAs and wireless networks may not be able\nto keep up with a fast server generating a large number of\nupdates, pTHINC is able to coalesce, clip, and discard\nupdates automatically if network loss or congestion occurs, or\nthe client cannot keep up with the rate of updates. This\ntype of behavior proves crucial in a web browsing\nenvironment, where for example, a page may be redrawn multiple\ntimes as it is rendered on the fly by the browser. In this\ncase, the PDA will only receive and render the final result,\nwhich clearly is all the user is interesting in seeing.\npTHINC prioritizes the delivery of updates to the PDA\nusing a Shortest-Remaining-Size-First (SRSF) preemptive\nupdate scheduler. SRSF is analogous to\nShortest-RemainingProcessing-Time scheduling, which is known to be optimal\nfor minimizing mean response time in an interactive system.\nIn a web browsing environment, short jobs are associated\nwith text and basic page layout components such as the\npage\"s background, which are critical web content for the\nuser. On the other hand, large jobs are often lower priority\nbeautifying elements, or, even worse, web page banners\nand advertisements, which are of questionable value to the\nuser as he or she is browsing the page. Using SRSF, pTHINC\nis able to maximize the utilization of the relatively scarce\nbandwidth available on the wireless connection between the\nPDA and the server.\n3.1 Display Management\nTo enable users to just as easily access their web browser\nand helper applications from a desktop computer at home\nas from a PDA while on the road, pTHINC provides a\nresize mechanism to zoom in and out of the display of a web\nsession. pTHINC resizing is completely supported by the\nserver, not the client. The server resamples updates to fit\nwithin the PDAs viewport before they are transmitted over\nthe network. pTHINC uses Fant\"s resampling algorithm to\nresize pixel updates. This provides smooth, visually\npleasing updates with properly antialiasing and has only modest\ncomputational requirements.\npTHINC\"s resizing approach has a number of advantages.\nFirst, it allows the PDA to leverage the vastly superior\ncomputational power of the server to use high quality resampling\nalgorithms and produce higher quality updates for the PDA\nto display. Second, resizing the screen does not translate into\nadditional resource requirements for the PDA, since it does\nnot need to perform any additional work. Finally, better\nutilization of the wireless network is attained since rescaling\nthe updates reduces their bandwidth requirements.\nTo enable users to orient their displays on a PDA to\nprovide a viewing experience that best accommodates user\npreferences and the layout of web pages or applications,\npTHINC provides a display rotation mechanism to switch\nbetween landscape and portrait viewing modes. pTHINC\ndisplay rotation is completely supported by the client, not\nthe server. pTHINC does not explicitly recalculate the\nge146\nometry of display updates to perform rotation, which would\nbe computationally expensive. Instead, pTHINC simply\nchanges the way data is copied into the framebuffer to switch\nbetween display modes. When in portrait mode, data is\ncopied along the rows of the framebuffer from left to right.\nWhen in landscape mode, data is copied along the columns\nof the framebuffer from top to bottom. These very fast and\nsimple techniques replace one set of copy operations with\nanother and impose no performance overhead. pTHINC\nprovides its own rotation mechanism to support a wide range of\ndevices without imposing additional feature requirements on\nthe PDA. Although some newer PDA devices provide native\nsupport for different orientations, this mechanism is not\ndynamic and requires the user to rotate the PDA\"s entire user\ninterface before starting the pTHINC client. Windows\nMobile provides native API mechanisms for PDA applications\nto rotate their UI on the fly, but these mechanisms deliver\npoor performance and display quality as the rotation is\nperformed naively and is not completely accurate.\n3.2 Video Playback\nVideo has gradually become an integral part of the World\nWide Web, and its presence will only continue to increase.\nWeb sites today not only use animated graphics and flash\nto deliver web content in an attractive manner, but also\nutilize streaming video to enrich the web interface. Users are\nable to view pre-recorded and live newscasts on CNN, watch\nsports highlights on ESPN, and even search through large\ncollection of videos on Google Video. To allow applications\nto provide efficient video playback, interfaces have been\ncreated in display systems that allow video device drivers to\nexpose their hardware capabilities back to the applications.\npTHINC takes advantage of these interfaces and its virtual\ndevice driver approach to provide a virtual bridge between\nthe remote client and its hardware and the applications, and\ntransparently support video playback.\nOn top of this architecture, pTHINC uses the YUV\ncolorspace to encode the video content, which provides a\nnumber of benefits. First, it has become increasingly common\nfor PDA video hardware to natively support YUV and be\nable to perform the colorspace conversion and scaling\nautomatically. As a result, pTHINC is able to provide fullscreen\nvideo playback without any performance hits. Second, the\nuse of YUV allows for a more efficient representation of RGB\ndata without loss of quality, by taking advantage of the\nhuman eye\"s ability to better distinguish differences in\nbrightness than in color. In particular, pTHINC uses the YV12\nformat, which allows full color RGB data to be encoded\nusing just 12 bits per pixel. Third, YUV data is produced\nas one of the last steps of the decoding process of most\nvideo codecs, allowing pTHINC to provide video playback\nin a manner that is format independent. Finally, even if the\nPDA\"s video hardware is unable to accelerate playback, the\ncolorspace conversion process is simple enough that it does\nnot impose unreasonable requirements on the PDA.\nA more concrete example of how pTHINC leverages the\nPDA video hardware to support video playback can be seen\nin our prototype implementation on the popular Dell Axim\nX51v PDA, which is equipped with the Intel 2700G\nmultimedia accelerator. In this case, pTHINC creates an\noffscreen buffer in video memory and writes and reads from\nthis memory region data on the YV12 format. When a new\nvideo frame arrives, video data is copied from the buffer to\nFigure 2: Experimental Testbed\nan overlay surface in video memory, which is independent\nof the normal surface used for traditional drawing. As the\nYV12 data is put onto the overlay, the Intel accelerator\nautomatically performs both colorspace conversion and scaling.\nBy using the overlay surface, pTHINC has no need to redraw\nthe screen once video playback is over since the overlapped\nsurface is unaffected. In addition, specific overlay regions\ncan be manipulated by leveraging the video hardware, for\nexample to perform hardware linear interpolation to smooth\nout the frame and display it fullscreen, and to do automatic\nrotation when the client runs in landscape mode.\n4. EXPERIMENTAL RESULTS\nWe have implemented a pTHINC prototype that runs the\nclient on widely-used Windows Mobile-based Pocket PC\ndevices and the server on both Windows and Linux operating\nsystems. To demonstrate its effectiveness in supporting\nmobile wireless web applications, we have measured its\nperformance on web applications. We present experimental results\non different PDA devices for two popular web applications,\nbrowsing web pages and playing video content from the web.\nWe compared pTHINC against native web applications\nrunning locally on the PDA to demonstrate the improvement\nthat pTHINC can provide over the traditional fat-client\napproach. We also compared pTHINC against three of the\nmost widely used thin clients that can run on PDAs, Citrix\nMeta-FrameXP [2], Microsoft Remote Desktop [3] and VNC\n(Virtual Network Computing) [16]. We follow common\npractice and refer to Citrix MetaFrameXP and Microsoft Remote\nDesktop by their respective remote display protocols, ICA\n(Independent Computing Architecture) and RDP (Remote\nDesktop Protocol).\n4.1 Experimental Testbed\nWe conducted our web experiments using two different\nwireless Pocket PC PDAs in an isolated Wi-Fi network\ntestbed, as shown in Figure 2. The testbed consisted of two\nPDA client devices, a packet monitor, a thin-client server,\nand a web server. Except for the PDAs, all of the other\nmachines were IBM Netfinity 4500R servers with dual 933 MHz\nIntel PIII CPUs and 512 MB RAM and were connected on\na switched 100 Mbps FastEthernet network. The web server\nused was Apache 1.3.27, the network emulator was\nNISTNet 2.0.12, and the packet monitor was Ethereal 0.10.9. The\nPDA clients connected to the testbed through a 802.11b\nLucent Orinoco AP-2000 wireless access point. All experiments\nusing the wireless network were conducted within ten feet\nof the access point, so we considered the amount of packet\nloss to be negligible in our experiments.\nTwo Pocket PC PDAs were used to provide results across\nboth older, less powerful models and newer higher\nperformance models. The older model was a Dell Axim X5 with\n147\nClient 1024\u00d7768 640\u00d7480 Depth Resize Clip\nRDP no yes 8-bit no yes\nVNC yes yes 16-bit no no\nICA yes yes 16-bit yes no\npTHINC yes yes 24-bit yes no\nTable 2: Thin-client Testbed Configuration Setting\na 400 MHz Intel XScale PXA255 CPU and 64 MB RAM\nrunning Windows Mobile 2003 and a Dell TrueMobile 1180\n2.4Ghz CompactFlash card for wireless networking. The\nnewer model was a Dell Axim X51v with a 624 MHz Intel\nXScale XPA270 CPU and 64 MB RAM running Windows\nMobile 5.0 and integrated 802.11b wireless networking. The\nX51v has an Intel 2700G multimedia accelerator with 16MB\nvideo memory. Both PDAs are capable of 16-bit color but\nhave different screen sizes and display resolutions. The X5\nhas a 3.5 inch diagonal screen with 240\u00d7320 resolution. The\nX51v has a 3.7 inch diagonal screen with 480\u00d7640.\nThe four thin clients that we used support different\nlevels of display quality as summarized in Table 2. The RDP\nclient only supports a fixed 640\u00d7480 display resolution on\nthe server with 8-bit color depth, while other platforms\nprovide higher levels of display quality. To provide a fair\ncomparison across all platforms, we conducted our experiments\nwith thin-client sessions configured for two possible\nresolutions, 1024\u00d7768 and 640\u00d7480. Both ICA and VNC were\nconfigured to use the native PDA resolution of 16-bit color\ndepth. The current pTHINC prototype uses 24-bit color\ndirectly and the client downsamples updates to the 16-bit color\ndepth available on the PDA. RDP was configured using only\n8-bit color depth since it does not support any better color\ndepth. Since both pTHINC and ICA provide the ability to\nview the display resized to fit the screen, we measured both\nclients with and without the display resized to fit the PDA\nscreen. Each thin client was tested using landscape rather\nthan portrait mode when available. All systems run on the\nX51v could run in landscape mode because the hardware\nprovides a landscape mode feature. However, the X5 does\nnot provide this functionality. Only pTHINC directly\nsupports landscape mode, so it was the only system that could\nrun in landscape mode on both the X5 and X51v.\nTo provide a fair comparison, we also standardized on\ncommon hardware and operating systems whenever possible.\nAll of the systems used the Netfinity server as the thin-client\nserver. For the two systems designed for Windows servers,\nICA and RDP, we ran Windows 2003 Server on the server.\nFor the other systems which support X-based servers, VNC\nand pTHINC, we ran the Debian Linux Unstable\ndistribution with the Linux 2.6.10 kernel on the server. We used the\nlatest thin-client server versions available on each platform\nat the time of our experiments, namely Citrix MetaFrame\nXP Server for Windows Feature Release 3, Microsoft\nRemote Desktop built into Windows XP and Windows 2003\nusing RDP 5.2, and VNC 4.0.\n4.2 Application Benchmarks\nWe used two web application benchmarks for our\nexperiments based on two common application scenarios, browsing\nweb pages and playing video content from the web. Since\nmany thin-client systems including two of the ones tested\nare closed and proprietary, we measured their performance\nin a noninvasive manner by capturing network traffic with\na packet monitor and using a variant of slow-motion\nbenchmarking [13] previously developed to measure thin-client\nperformance in PDA environments [10]. This measurement\nmethodology accounts for both the display decoupling that\ncan occur between client and server in thin-client systems\nas well as client processing time, which may be significant\nin the case of PDAs.\nTo measure web browsing performance, we used a web\nbrowsing benchmark based on the Web Text Page Load Test\nfrom the Ziff-Davis i-Bench benchmark suite [7]. The\nbenchmark consists of JavaScript controlled load of 55 pages from\nthe web server. The pages contain both text and\ngraphics with pages varying in size. The graphics are embedded\nimages in GIF and JPEG formats. The original i-Bench\nbenchmark was modified for slow-motion benchmarking by\nintroducing delays of several seconds between the pages\nusing JavaScript. Then two tests were run, one where\ndelays where added between each page, and one where pages\nwhere loaded continuously without waiting for them to be\ndisplayed on the client. In the first test, delays were\nsufficiently adjusted in each case to ensure that each page could\nbe received and displayed on the client completely without\ntemporal overlap in transferring the data belonging to two\nconsecutive pages. We used the packet monitor to record\nthe packet traffic for each run of the benchmark, then used\nthe timestamps of the first and last packet in the trace to\nobtain our latency measures [10]. The packet monitor also\nrecorded the amount of data transmitted between the client\nand the server. The ratio between the data traffic in the two\ntests yields a scale factor. This scale factor shows the loss\nof data between the server and the client due to inability of\nthe client to process the data quickly enough. The product\nof the scale factor with the latency measurement produces\nthe true latency accounting for client processing time.\nTo run the web browsing benchmark, we used Mozilla\nFirefox 1.0.4 running on the thin-client server for the thin\nclients, and Windows Internet Explorer (IE) Mobile for 2003\nand Mobile for 5.0 for the native browsers on the X5 and\nX51v PDAs, respectively. In all cases, the web browser used\nwas sized to fill the entire display region available.\nTo measure video playback performance, we used a video\nbenchmark that consisted of playing a 34.75s MPEG-1 video\nclip containing a mix of news and entertainment\nprogramming at full-screen resolution. The video clip is 5.11 MB and\nconsists of 834 352x240 pixel frames with an ideal frame rate\nof 24 frames/sec. We measured video performance using\nslow-motion benchmarking by monitoring resulting packet\ntraffic at two playback rates, 1 frames/second (fps) and 24\nfps, and comparing the results to determine playback\ndelays and frame drops that occur at 24 fps to measure overall\nvideo quality [13]. For example, 100% quality means that all\nvideo frames were played at real-time speed. On the other\nhand, 50% quality could mean that half the video data was\ndropped, or that the clip took twice as long to play even\nthough all of the video data was displayed.\nTo run the video benchmark, we used Windows Media\nPlayer 9 for Windows-based thin-client servers, MPlayer 1.0\npre 6 for X-based thin-client servers, and Windows Media\nPlayer 9 Mobile and 10 Mobile for the native video players\nrunning locally on the X5 and X51v PDAs, respectively. In\nall cases, the video player used was sized to fill the entire\ndisplay region available.\n4.3 Measurements\nFigures 3 and 4 show the results of running the web\nbrows148\n0\n1\n10\n100\npTHINC\nResized\npTHINCICA\nResized\nICAVNCRDPLOCAL\nLatency(s)\nPlatform\nAxim X5 (640x480 or less)\nAxim X51v (640x480)\nAxim X5 (1024x768)\nAxim X51v (1024x768)\nFigure 3: Browsing Benchmark: Average Page Latency\ning benchmark. For each platform, we show results for up to\nfour different configurations, two on the X5 and two on the\nX51v, depending on whether each configuration was\nsupported. However, not all platforms could support all\nconfigurations. The local browser only runs at the display\nresolution of the PDA, 480\u00d7680 or less for the X51v and the\nX5. RDP only runs at 640\u00d7480. Neither platform could\nsupport 1024\u00d7768 display resolution. ICA only ran on the\nX5 and could not run on the X51v because it did not work\non Windows Mobile 5.\nFigure 3 shows the average latency per web page for each\nplatform. pTHINC provides the lowest average web\nbrowsing latency on both PDAs. On the X5, pTHINC performs\nup to 70 times better than other thin-client systems and 8\ntimes better than the local browser. On the X51v, pTHINC\nperforms up to 80 times better than other thin-client\nsystems and 7 times better than the native browser. In fact,\nall of the thin clients except VNC outperform the local\nPDA browser, demonstrating the performance benefits of\nthe thin-client approach. Usability studies have shown that\nweb pages should take less than one second to download\nfor the user to experience an uninterrupted web browsing\nexperience [14]. The measurements show that only the thin\nclients deliver subsecond web page latencies. In contrast, the\nlocal browser requires more than 3 seconds on average per\nweb page. The local browser performs worse since it needs\nto run a more limited web browser to process the HTML,\nJavaScript, and do all the rendering using the limited\ncapabilities of the PDA. The thin clients can take advantage of\nfaster server hardware and a highly tuned web browser to\nprocess the web content much faster.\nFigure 3 shows that RDP is the next fastest platform after\npTHINC. However, RDP is only able to run at a fixed\nresolution of 640\u00d7480 and 8-bit color depth. Furthermore, RDP\nalso clips the display to the size of the PDA screen so that\nit does not need to send updates that are not visible on the\nPDA screen. This provides a performance benefit\nassuming the remaining web content is not viewed, but degrades\nperformance when a user scrolls around the display to view\nother web content. RDP achieves its performance with\nsignificantly lower display quality compared to the other thin\nclients and with additional display clipping not used by other\nsystems. As a result, RDP performance alone does not\nprovide a complete comparison with the other platforms. In\ncontrast, pTHINC provides the fastest performance while\nat the same time providing equal or better display quality\nthan the other systems.\n0\n1\n10\n100\n1000\npTHINC\nResized\npTHINCICA\nResized\nICAVNCRDPLOCAL\nDataSize(KB)\nPlatform\nAxim X5 (640x480 or less)\nAxim X51v (640x480)\nAxim X5 (1024x768)\nAxim X51v (1024x768)\nFigure 4: Browsing Benchmark: Average Page Data\nTransferred\nSince VNC and ICA provide similar display quality to\npTHINC, these systems provide a more fair comparison of\ndifferent thin-client approaches. ICA performs worse in part\nbecause it uses higher-level display primitives that require\nadditional client processing costs. VNC performs worse in\npart because it loses display data due to its client-pull\ndelivery mechanism and because of the client processing costs\nin decompressing raw pixel primitives. In both cases, their\nperformance was limited in part because their PDA clients\nwere unable to keep up with the rate at which web pages\nwere being displayed.\nFigure 3 also shows measurements for those thin clients\nthat support resizing the display to fit the PDA screen,\nnamely ICA and pTHINC. Resizing requires additional\nprocessing, which results in slower average web page latencies.\nThe measurements show that the additional delay incurred\nby ICA when resizing versus not resizing is much more\nsubstantial than for pTHINC. ICA performs resizing on the\nslower PDA client. In contrast, pTHINC leverage the more\npowerful server to do resizing, reducing the performance\ndifference between resizing and not resizing. Unlike ICA,\npTHINC is able to provide subsecond web page download\nlatencies in both cases.\nFigure 4 shows the data transferred in KB per page when\nrunning the slow-motion version of the tests. All of the\nplatforms have modest data transfer requirements of roughly\n100 KB per page or less. This is well within the\nbandwidth capacity of Wi-Fi networks. The measurements show\nthat the local browser does not transfer the least amount of\ndata. This is surprising as HTML is often considered to be\na very compact representation of content. Instead, RDP is\nthe most bandwidth efficient platform, largely as a result of\nusing only 8-bit color depth and screen clipping so that it\ndoes not transfer the entire web page to the client. pTHINC\noverall has the largest data requirements, slightly more than\nVNC. This is largely a result of the current pTHINC\nprototype\"s lack of native support for 16-bit color data in the wire\nprotocol. However, this result also highlights pTHINC\"s\nperformance as it is faster than all other systems even while\ntransferring more data. Furthermore, as newer PDA models\nsupport full 24-bit color, these results indicate that pTHINC\nwill continue to provide good web browsing performance.\nSince display usability and quality are as important as\nperformance, Figures 5 to 8 compare screenshots of the\ndifferent thin clients when displaying a web page, in this case\nfrom the popular BBC news website. Except for ICA, all of\nthe screenshots were taken on the X51v in landscape mode\n149\nFigure 5: Browser Screenshot: RDP 640x480 Figure 6: Browser Screenshot: VNC 1024x768\nFigure 7: Browser Screenshot: ICA Resized 1024x768 Figure 8: Browser Screenshot: pTHINC Resized 1024x768\nusing the maximum display resolution settings for each\nplatform given in Table 2. The ICA screenshot was taken on the\nX5 since ICA does not run on the X51v. While the\nscreenshots lack the visual fidelity of the actual device display,\nseveral observations can be made. Figure 5 shows that RDP\ndoes not support fullscreen mode and wastes lots of screen\nspace for controls and UI elements, requiring the user to\nscroll around in order to access the full contents of the web\nbrowsing session. Figure 6 shows that VNC makes better\nuse of the screen space and provides better display quality,\nbut still forces the user to scroll around to view the web\npage due to its lack of resizing support. Figure 7 shows\nICA\"s ability to display the full web page given its resizing\nsupport, but that its lack of landscape capability and poorer\nresize algorithm significantly compromise display quality. In\ncontrast, Figure 8 shows pTHINC using resizing to provide\na high quality fullscreen display of the full width of the web\npage. pTHINC maximizes the entire viewing region by\nmoving all controls to the PDA buttons. In addition, pTHINC\nleverages the server computational power to use a high\nquality resizing algorithm to resize the display to fit the PDA\nscreen without significant overhead.\nFigures 9 and 10 show the results of running the video\nplayback benchmark. For each platform except ICA, we\nshow results for an X5 and X51v configuration. ICA could\nnot run on the X51v as noted earlier. The measurements\nwere done using settings that reflected the environment a\nuser would have to access a web session from both a\ndesktop computer and a PDA. As such, a 1024\u00d7768 server\ndisplay resolution was used whenever possible and the video\nwas shown at fullscreen. RDP was limited to 640\u00d7480\ndisplay resolution as noted earlier. Since viewing the entire\nvideo display is the only really usable option, we resized\nthe display to fit the PDA screen for those platforms that\nsupported this feature, namely ICA and pTHINC.\nFigure 9 shows the video quality for each platform. pTHINC\nis the only thin client able to provide perfect video playback\nquality, similar to the native PDA video player. All of the\nother thin clients deliver very poor video quality. With the\nexception of RDP on the X51v which provided unacceptable\n35% video quality, none of the other systems were even able\nto achieve 10% video quality. VNC and ICA have the worst\nquality at 8% on the X5 device.\npTHINC\"s native video support enables superior video\nperformance, while other thin clients suffer from their\ninability to distinguish video from normal display updates.\nThey attempt to apply ineffective and expensive\ncompression algorithms on the video data and are unable to keep up\nwith the stream of updates generated, resulting in dropped\nframes or long playback times. VNC suffers further from\nits client-pull update model because video frames are\ngenerated faster than the rate at which the client can process\nand send requests to the server to obtain the next display\nupdate. Figure 10 shows the total data transferred during\n150\n0%\n20%\n40%\n60%\n80%\n100%\npTHINCICAVNCRDPLOCAL\nVideoQuality\nPlatform\nAxim X5\nAxim X51v\nFigure 9: Video Benchmark: Fullscreen Video Quality\n0\n1\n10\n100\npTHINCICAVNCRDPLOCAL\nVideoDataSize(MB)\nPlatform\nAxim X5\nAxim X51v\nFigure 10: Video Benchmark: Fullscreen Video Data\nvideo playback for each system. The native player is the\nmost bandwidth efficient platform, sending less than 6 MB\nof data, which corresponds to about 1.2 Mbps of bandwidth.\npTHINC\"s 100% video quality requires about 25 MB of data\nwhich corresponds to a bandwidth usage of less than 6 Mbps.\nWhile the other thin clients send less data than THINC,\nthey do so because they are dropping video data, resulting\nin degraded video quality.\nFigures 11 to 14 compare screenshots of the different thin\nclients when displaying the video clip. Except for ICA, all of\nthe screenshots were taken on the X51v in landscape mode\nusing the maximum display resolution settings for each\nplatform given in Table 2. The ICA screenshot was taken on the\nX5 since ICA does not run on the X51v. Figures 11 and 12\nshow that RDP and VNC are unable to display the entire\nvideo frame on the PDA screen. RDP wastes screen space\nfor UI elements and VNC only shows the top corner of the\nvideo frame on the screen. Figure 13 shows that ICA\nprovides resizing to display the entire video frame, but did not\nproportionally resize the video data, resulting in strange\ndisplay artifacts. In contrast, Figure 14 shows pTHINC using\nresizing to provide a high quality fullscreen display of the\nentire video frame. pTHINC provides visually more appealing\nvideo display than RDP, VNC, or ICA.\n5. RELATED WORK\nSeveral studies have examined the web browsing\nperformance of thin-client computing [13, 19, 10]. The ability for\nthin clients to improve web browsing performance on\nwireless PDAs was first quantitatively demonstrated in a\nprevious study by one of the authors [10]. This study\ndemonstrated that thin clients can provide both faster web\nbrowsing performance and greater web browsing functionality.\nThe study considered a wide range of web content including\ncontent from medical information systems. Our work builds\non this previous study and consider important issues such as\nhow usable existing thin clients are in PDA environments,\nthe trade-offs between thin-client usability and performance,\nperformance across different PDA devices, and the\nperformance of thin clients on common web-related applications\nsuch as video.\nMany thin clients have been developed and some have\nPDA clients, including Microsoft\"s Remote Desktop [3],\nCitrix MetraFrame XP [2], Virtual Network Computing [16,\n12], GoToMyPC [5], and Tarantella [18]. These systems\nwere first designed for desktop computing and retrofitted\nfor PDAs. Unlike pTHINC, they do not address key\nsystem architecture and usability issues important for PDAs.\nThis limits their display quality, system performance,\navailable screen space, and overall usability on PDAs. pTHINC\nbuilds on previous work by two of the authors on THINC [1],\nextending the server architecture and introducing a client\ninterface and usage model to efficiently support PDA devices\nfor mobile web applications.\nOther approaches to improve the performance of mobile\nwireless web browsing have focused on using transcoding\nand caching proxies in conjunction with the fat client model\n[11, 9, 4, 8]. They work by pushing functionality to external\nproxies, and using specialized browsing applications on the\nPDA device that communicate with the proxy. Our\nthinclient approach differs fundamentally from these fat-client\napproaches by pushing all web browser logic to the server,\nleveraging existing investments in desktop web browsers and\nhelper applications to work seamlessly with production\nsystems without any additional proxy configuration or web\nbrowser modifications.\nWith the emergence of web browsing on small display\ndevices, web sites have been redesigned using mechanisms like\nWAP and specialized native web browsers have been\ndeveloped to tailor the needs of these devices. Recently, Opera\nhas developed the Opera Mini [15] web browser, which uses\nan approach similar to the thin-client model to provide\naccess across a number of mobile devices that would normally\nbe incapable of running a web browser. Instead of requiring\nthe device to process web pages, it uses a remote server to\npre-process the page before sending it to the phone.\n6. CONCLUSIONS\nWe have introduced pTHINC, a thin-client architecture\nfor wireless PDAs. pTHINC provides key architectural and\nusability mechanisms such as server-side screen resizing,\nclientside screen rotation using simple copy techniques, YUV video\nsupport, and maximizing screen space for display updates\nand leveraging existing PDA control buttons for UI\nelements. pTHINC transparently supports traditional\ndesktop browsers and their helper applications on PDA devices\nand desktop machines, providing mobile users with\nubiquitous access to a consistent, personalized, and full-featured\nweb environment across heterogeneous devices. We have\nimplemented pTHINC and measured its performance on\nweb applications compared to existing thin-client systems\nand native web applications. Our results on multiple\nmobile wireless devices demonstrate that pTHINC delivers web\nbrowsing performance up to 80 times better than existing\nthin-client systems, and 8 times better than a native PDA\nbrowser. In addition, pTHINC is the only PDA thin client\n151\nFigure 11: Video Screenshot: RDP 640x480 Figure 12: Video Screenshot: VNC 1024x768\nFigure 13: Video Screenshot: ICA Resized 1024x768\nFigure 14: Video Screenshot: pTHINC Resized 1024x768\nthat transparently provides full-screen, full frame rate video\nplayback, making web sites with multimedia content\naccessible to mobile web users.\n7. ACKNOWLEDGEMENTS\nThis work was supported in part by NSF ITR grants\nCCR0219943 and CNS-0426623, and an IBM SUR Award.\n8. REFERENCES\n[1] R. Baratto, L. Kim, and J. Nieh. THINC: A Virtual\nDisplay Architecture for Thin-Client Computing. In\nProceedings of the 20th ACM Symposium on Operating\nSystems Principles (SOSP), Oct. 2005.\n[2] Citrix Metaframe. http://www.citrix.com.\n[3] B. C. Cumberland, G. Carius, and A. Muir. Microsoft\nWindows NT Server 4.0, Terminal Server Edition:\nTechnical Reference. Microsoft Press, Redmond, WA, 1999.\n[4] A. Fox, I. Goldberg, S. D. Gribble, and D. C. Lee.\nExperience With Top Gun Wingman: A Proxy-Based\nGraphical Web Browser for the 3Com PalmPilot. In\nProceedings of Middleware \"98, Lake District, England,\nSeptember 1998, 1998.\n[5] GoToMyPC. http://www.gotomypc.com/.\n[6] Health Insurance Portability and Accountability Act.\nhttp://www.hhs.gov/ocr/hipaa/.\n[7] i-Bench version 1.5. http:\n//etestinglabs.com/benchmarks/i-bench/i-bench.asp.\n[8] A. Joshi. On proxy agents, mobility, and web access.\nMobile Networks and Applications, 5(4):233-241, 2000.\n[9] J. Kangasharju, Y. G. Kwon, and A. Ortega. Design and\nImplementation of a Soft Caching Proxy. Computer\nNetworks and ISDN Systems, 30(22-23):2113-2121, 1998.\n[10] A. Lai, J. Nieh, B. Bohra, V. Nandikonda, A. P. Surana,\nand S. Varshneya. Improving Web Browsing on Wireless\nPDAs Using Thin-Client Computing. In Proceedings of the\n13th International World Wide Web Conference (WWW),\nMay 2004.\n[11] A. Maheshwari, A. Sharma, K. Ramamritham, and\nP. Shenoy. TranSquid: Transcoding and caching proxy for\nheterogenous ecommerce environments. In Proceedings of\nthe 12th IEEE Workshop on Research Issues in Data\nEngineering (RIDE \"02), Feb. 2002.\n[12] .NET VNC Viewer for PocketPC.\nhttp://dotnetvnc.sourceforge.net/.\n[13] J. Nieh, S. J. Yang, and N. Novik. Measuring Thin-Client\nPerformance Using Slow-Motion Benchmarking. ACM\nTrans. Computer Systems, 21(1):87-115, Feb. 2003.\n[14] J. Nielsen. Designing Web Usability. New Riders\nPublishing, Indianapolis, IN, 2000.\n[15] Opera Mini Browser.\nhttp://www.opera.com/products/mobile/operamini/.\n[16] T. Richardson, Q. Stafford-Fraser, K. R. Wood, and\nA. Hopper. Virtual Network Computing. IEEE Internet\nComputing, 2(1), Jan./Feb. 1998.\n[17] R. W. Scheifler and J. Gettys. The X Window System.\nACM Trans. Gr., 5(2):79-106, Apr. 1986.\n[18] Sun Secure Global Desktop.\nhttp://www.sun.com/software/products/sgd/.\n[19] S. J. Yang, J. Nieh, S. Krishnappa, A. Mohla, and\nM. Sajjadpour. Web Browsing Performance of Wireless\nThin-Client Computing. In Proceedings of the 12th\nInternational World Wide Web Conference (WWW), May\n2003.\n152", "keywords": "pervasive web;remote display;pda thinclient solution;system usability;web browser;thin-client computing;mobility;full-function web browser;pthinc;seamless mobility;functionality;thin-client;local pda web browser;web application;video playback;screen resolution;web browsing performance;high-fidelity display;mobile wireless pda;crucial browser helper application"}
{"name": "train_C-71", "title": "A Point-Distribution Index and Its Application to Sensor-Grouping in Wireless Sensor Networks", "abstract": "We propose \u03b9, a novel index for evaluation of point-distribution. \u03b9 is the minimum distance between each pair of points normalized by the average distance between each pair of points. We find that a set of points that achieve a maximum value of \u03b9 result in a honeycomb structure. We propose that \u03b9 can serve as a good index to evaluate the distribution of the points, which can be employed in coverage-related problems in wireless sensor networks (WSNs). To validate this idea, we formulate a general sensorgrouping problem for WSNs and provide a general sensing model. We show that locally maximizing \u03b9 at sensor nodes is a good approach to solve this problem with an algorithm called Maximizing\u03b9 Node-Deduction (MIND). Simulation results verify that MIND outperforms a greedy algorithm that exploits sensor-redundancy we design. This demonstrates a good application of employing \u03b9 in coverage-related problems for WSNs.", "fulltext": "1. INTRODUCTION\nA wireless sensor network (WSN) consists of a large number of\nin-situ battery-powered sensor nodes. A WSN can collect the data\nabout physical phenomena of interest [1]. There are many\npotential applications of WSNs, including environmental monitoring and\nsurveillance, etc. [1][11].\nIn many application scenarios, WSNs are employed to conduct\nsurveillance tasks in adverse, or even worse, in hostile working\nenvironments. One major problem caused is that sensor nodes are\nsubjected to failures. Therefore, fault tolerance of a WSN is\ncritical.\nOne way to achieve fault tolerance is that a WSN should contain\na large number of redundant nodes in order to tolerate node\nfailures. It is vital to provide a mechanism that redundant nodes can be\nworking in sleeping mode (i.e., major power-consuming units such\nas the transceiver of a redundant sensor node can be shut off) to\nsave energy, and thus to prolong the network lifetime. Redundancy\nshould be exploited as much as possible for the set of sensors that\nare currently taking charge in the surveillance work of the network\narea [6].\nWe find that the minimum distance between each pair of points\nnormalized by the average distance between each pair of points\nserves as a good index to evaluate the distribution of the points. We\ncall this index, denoted by \u03b9, the normalized minimum distance. If\npoints are moveable, we find that maximizing \u03b9 results in a\nhoneycomb structure. The honeycomb structure poses that the coverage\nefficiency is the best if each point represents a sensor node that\nis providing surveillance work. Employing \u03b9 in coverage-related\nproblems is thus deemed promising.\nThis enlightens us that maximizing \u03b9 is a good approach to\nselect a set of sensors that are currently taking charge in the\nsurveillance work of the network area. To explore the effectiveness of\nemploying \u03b9 in coverage-related problems, we formulate a\nsensorgrouping problem for high-redundancy WSNs. An algorithm called\nMaximizing-\u03b9 Node-Deduction (MIND) is proposed in which\nredundant sensor nodes are removed to obtain a large \u03b9 for each set of\nsensors that are currently taking charge in the surveillance work of\nthe network area. We also introduce another greedy solution called\nIncremental Coverage Quality Algorithm (ICQA) for this problem,\nwhich serves as a benchmark to evaluate MIND.\nThe main contribution of this paper is twofold. First, we\nintroduce a novel index \u03b9 for evaluation of point-distribution. We show\nthat maximizing \u03b9 of a WSN results in low redundancy of the\nnetwork. Second, we formulate a general sensor-grouping problem\nfor WSNs and provide a general sensing model. With the MIND\nalgorithm we show that locally maximizing \u03b9 among each sensor\nnode and its neighbors is a good approach to solve this problem.\nThis demonstrates a good application of employing \u03b9 in\ncoveragerelated problems.\nThe rest of the paper is organized as follows. In Section 2, we\nintroduce our point-distribution index \u03b9. We survey related work\nand formulate a sensor-grouping problem together with a general\nsensing model in Section 3. Section 4 investigates the application\nof \u03b9 in this grouping problem. We propose MIND for this problem\n1171\nand introduce ICQA as a benchmark. In Section 5, we present\nour simulation results in which MIND and ICQA are compared.\nSection 6 provides conclusion remarks.\n2. THE NORMALIZED MINIMUM DISTANCE\n\u03b9: A POINT-DISTRIBUTION INDEX\nSuppose there are n points in a Euclidean space \u2126. The\ncoordinates of these points are denoted by xi (i = 1, ..., n).\nIt may be necessary to evaluate how the distribution of these\npoints is. There are many metrics to achieve this goal. For\nexample, the Mean Square Error from these points to their mean value\ncan be employed to calculate how these points deviate from their\nmean (i.e., their central). In resource-sharing evaluation, the Global\nFairness Index (GFI) is often employed to measure how even the\nresource distributes among these points [8], when xi represents the\namount of resource that belong to point i. In WSNs, GFI is usually\nused to calculate how even the remaining energy of sensor nodes\nis.\nWhen n is larger than 2 and the points do not all overlap (That\npoints all overlap means xi = xj, \u2200 i, j = 1, 2, ..., n). We propose\na novel index called the normalized minimum distance, namely \u03b9,\nto evaluate the distribution of the points. \u03b9 is the minimum distance\nbetween each pair of points normalized by the average distance\nbetween each pair of points. It is calculated by:\n\u03b9 =\nmin(||xi \u2212 xj||)\n\u00b5\n(\u2200 i, j = 1, 2, ..., n; and i = j) (1)\nwhere ||xi \u2212 xj|| denotes the Euclidean distance between point\ni and point j in \u2126, the min(\u00b7) function calculates the minimum\ndistance between each pair of points, and \u00b5 is the average distance\nbetween each pair of points, which is:\n\u00b5 =\n(\nPn\ni=1\nPn\nj=1,j=i ||xi \u2212 xj||)\nn(n \u2212 1)\n(2)\n\u03b9 measures how well the points separate from one another.\nObviously, \u03b9 is in interval [0, 1]. \u03b9 is equal to 1 if and only if n is equal\nto 3 and these three points forms an equilateral triangle. \u03b9 is equal\nto zero if any two points overlap. \u03b9 is a very interesting value of a\nset of points. If we consider each xi (\u2200i = 1, ..., n) is a variable in\n\u2126, how these n points would look like if \u03b9 is maximized?\nAn algorithm is implemented to generate the topology in which\n\u03b9 is locally maximized (The algorithm can be found in [19]). We\nconsider a 2-dimensional space. We select n = 10, 20, 30, ..., 100\nand perform this algorithm. In order to avoid that the algorithm\nconverge to local optimum, we select different random seeds to\ngenerate the initial points for 1000 time and obtain the best one\nthat results in the largest \u03b9 when the algorithm converges. Figure 1\ndemonstrates what the resulting topology looks like when n = 20\nas an example.\nSuppose each point represents a sensor node. If the sensor\ncoverage model is the Boolean coverage model [15][17][18][14] and\nthe coverage radius of each node is the same. It is exciting to see\nthat this topology results in lowest redundancy because the Vonoroi\ndiagram [2] formed by these nodes (A Vonoroi diagram formed by\na set of nodes partitions a space into a set of convex polygons such\nthat points inside a polygon are closest to only one particular node)\nis a honeycomb-like structure1\n.\nThis enlightens us that \u03b9 may be employed to solve problems\nrelated to sensor-coverage of an area. In WSNs, it is desirable\n1\nThis is how base stations of a wireless cellular network are\ndeployed and why such a network is called a cellular one.\n0 20 40 60 80 100 120 140 160\n0\n20\n40\n60\n80\n100\n120\n140\n160\nX\nY\nFigure 1: Node Number = 20, \u03b9 = 0.435376\nthat the active sensor nodes that are performing surveillance task\nshould separate from one another. Under the constraint that the\nsensing area should be covered, the more each node separates from\nthe others, the less the redundancy of the coverage is. \u03b9 indicates\nthe quality of such separation. It should be useful for approaches\non sensor-coverage related problems.\nIn our following discussions, we will show the effectiveness of\nemploying \u03b9 in sensor-grouping problem.\n3. THE SENSOR-GROUPING PROBLEM\nIn many application scenarios, to achieve fault tolerance, a WSN\ncontains a large number of redundant nodes in order to tolerate\nnode failures. A node sleeping-working schedule scheme is\ntherefore highly desired to exploit the redundancy of working sensors\nand let as many nodes as possible sleep.\nMuch work in the literature is on this issue [6]. Yan et al\nintroduced a differentiated service in which a sensor node finds out\nits responsible working duration with cooperation of its neighbors\nto ensure the coverage of sampled points [17]. Ye et al developed\nPEAS in which sensor nodes wake up randomly over time, probe\ntheir neighboring nodes, and decide whether they should begin to\ntake charge of surveillance work [18]. Xing et al exploited a\nprobabilistic distributed detection model with a protocol called\nCoordinating Grid (Co-Grid) [16]. Wang et al designed an approach called\nCoverage Configuration Protocol (CCP) which introduced the\nnotion that the coverage degree of intersection-points of the\nneighboring nodes\" sensing-perimeters indicates the coverage of a convex\nregion [15]. In our recent work [7], we also provided a sleeping\nconfiguration protocol, namely SSCP, in which sleeping eligibility\nof a sensor node is determined by a local Voronoi diagram. SSCP\ncan provide different levels of redundancy to maintain different\nrequirements of fault tolerance.\nThe major feature of the aforementioned protocols is that they\nemploy online distributed and localized algorithms in which a\nsensor node determines its sleeping eligibility and/or sleeping time\nbased on the coverage requirement of its sensing area with some\ninformation provided by its neighbors.\nAnother major approach for sensor node sleeping-working\nscheduling issue is to group sensor nodes. Sensor nodes in a network are\ndivided into several disjoint sets. Each set of sensor nodes are able\nto maintain the required area surveillance work. The sensor nodes\nare scheduled according to which set they belong to. These sets\nwork successively. Only one set of sensor nodes work at any time.\nWe call the issue sensor-grouping problem.\nThe major advantage of this approach is that it avoids the\noverhead caused by the processes of coordination of sensor nodes to\nmake decision on whether a sensor node is a candidate to sleep or\n1172\nwork and how long it should sleep or work. Such processes should\nbe performed from time to time during the lifetime of a network in\nmany online distributed and localized algorithms. The large\noverhead caused by such processes is the main drawback of the\nonline distributed and localized algorithms. On the contrary, roughly\nspeaking, this approach groups sensor nodes in one time and\nschedules when each set of sensor nodes should be on duty. It does not\nrequire frequent decision-making on working/sleeping eligibility2\n.\nIn [13] by Slijepcevic et al, the sensing area is divided into\nregions. Sensor nodes are grouped with the most-constrained\nleastconstraining algorithm. It is a greedy algorithm in which the\npriority of selecting a given sensor is determined by how many\nuncovered regions this sensor covers and the redundancy caused by\nthis sensor. In [5] by Cardei et al, disjoint sensor sets are\nmodeled as disjoint dominating sets. Although maximum dominating\nsets computation is NP-complete, the authors proposed a\ngraphcoloring based algorithm. Cardei et al also studied similar problem\nin the domain of covering target points in [4]. The NP-completeness\nof the problem is proved and a heuristic that computes the sets are\nproposed. These algorithms are centralized solutions of\nsensorgrouping problem.\nHowever, global information (e.g., the location of each in-network\nsensor node) of a large scale WSN is also very expensive to\nobtained online. Also it is usually infeasible to obtain such\ninformation before sensor nodes are deployed. For example, sensor nodes\nare usually deployed in a random manner and the location of each\nin-network sensor node is determined only after a node is deployed.\nThe solution of sensor-grouping problem should only base on\nlocally obtainable information of a sensor node. That is to say, nodes\nshould determine which group they should join in a fully\ndistributed way. Here locally obtainable information refers to a node\"s\nlocal information and the information that can be directly obtained\nfrom its adjacent nodes, i.e., nodes within its communication range.\nIn Subsection 3.1, we provide a general problem formulation of\nthe sensor-grouping problem. Distributed-solution requirement is\nformulated in this problem. It is followed by discussion in\nSubsection 3.2 on a general sensing model, which serves as a given\ncondition of the sensor-grouping problem formulation.\nTo facilitate our discussions, the notations in our following\ndiscussions are described as follows.\n\u2022 n: The number in-network sensor nodes.\n\u2022 S(j) (j = 1, 2, ..., m): The jth set of sensor nodes where m\nis the number of sets.\n\u2022 L(i) (i = 1, 2, ..., n): The physical location of node i.\n\u2022 \u03c6: The area monitored by the network: i.e., the sensing area\nof the network.\n\u2022 R: The sensing radius of a sensor node. We assume that\na sensor node can only be responsible to monitor a circular\narea centered at the node with a radius equal to R. This is\na usual assumption in work that addresses sensor-coverage\nrelated problems. We call this circular area the sensing area\nof a node.\n3.1 Problem Formulation\nWe assume that each sensor node can know its approximate\nphysical location. The approximate location information is obtainable\nif each sensor node carries a GPS receiver or if some localization\nalgorithms are employed (e.g., [3]).\n2\nNote that if some nodes die, a re-grouping process might also be\nperformed to exploit the remaining nodes in a set of sensor nodes.\nHow to provide this mechanism is beyond the scope of this paper\nand yet to be explored.\nProblem 1. Given:\n\u2022 The set of each sensor node i\"s sensing neighbors N(i) and\nthe location of each member in N(i);\n\u2022 A sensing model which quantitatively describes how a point\nP in area \u03c6 is covered by sensor nodes that are responsible to\nmonitor this point. We call this quantity the coverage quality\nof P.\n\u2022 The coverage quality requirement in \u03c6, denoted by s. When\nthe coverage of a point is larger than this threshold, we say\nthis point is covered.\nFor each sensor node i, make a decision on which group S(j) it\nshould join so that:\n\u2022 Area \u03c6 can be covered by sensor nodes in each set S(j)\n\u2022 m, the number of sets S(j) is maximized.\nIn this formulation, we call sensor nodes within a circular area\ncentered at a sensor node i with a radius equal to 2 \u00b7 R the sensing\nneighbors of node i. This is because sensors nodes in this area,\ntogether with node i, may be cooperative to ensure the coverage of\na point inside node i\"s sensing area.\nWe assume that the communication range of a sensor node is\nlarger than 2 \u00b7 R, which is also a general assumption in work that\naddresses sensor-coverage related problems. That is to say, the first\ngiven condition in Problem 1 is the information that can be obtained\ndirectly from a node\"s adjacent nodes. It is therefore locally\nobtainable information. The last two given conditions in this problem\nformulation can be programmed into a node before it is deployed\nor by a node-programming protocol (e.g., [9]) during network\nruntime. Therefore, the given conditions can all be easily obtained by\na sensor-grouping scheme with fully distributed implementation.\nWe reify this problem with a realistic sensing model in next\nsubsection.\n3.2 A General Sensing Model\nAs WSNs are usually employed to monitor possible events in a\ngiven area, it is therefore a design requirement that an event\noccurring in the network area must/may be successfully detected by\nsensors.\nThis issue is usually formulated as how to ensure that an event\nsignal omitted in an arbitrary point in the network area can be\ndetected by sensor nodes. Obviously, a sensing model is required to\naddress this problem so that how a point in the network area is\ncovered can be modeled and quantified. Thus the coverage quality of\na WSN can be evaluated.\nDifferent applications of WSNs employ different types of\nsensors, which surely have widely different theoretical and physical\ncharacteristics. Therefore, to fulfill different application\nrequirements, different sensing models should be constructed based on the\ncharacteristics of the sensors employed.\nA simple theoretical sensing model is the Boolean sensing model\n[15][18][17][14]. Boolean sensing model assumes that a sensor\nnode can always detect an event occurring in its responsible\nsensing area. But most sensors detect events according to the signal\nstrength sensed. Event signals usually fade in relation to the\nphysical distance between an event and the sensor. The larger the\ndistance, the weaker the event signals that can be sensed by the sensor,\nwhich results in a reduction of the probability that the event can be\nsuccessfully detected by the sensor.\nAs in WSNs, event signals are usually electromagnetic, acoustic,\nor photic signals, they fade exponentially with the increasing of\n1173\ntheir transmit distance. Specifically, the signal strength E(d) of an\nevent that is received by a sensor node satisfies:\nE(d) =\n\u03b1\nd\u03b2\n(3)\nwhere d is the physical distance from the event to the sensor node;\n\u03b1 is related to the signal strength omitted by the event; and \u03b2 is\nsignal fading factor which is typically a positive number larger than\nor equal to 2. Usually, \u03b1 and \u03b2 are considered as constants.\nBased on this notion, to be more reasonable, researchers propose\ncollaborative sensing model to capture application requirements:\nArea coverage can be maintained by a set of collaborative sensor\nnodes: For a point with physical location L, the point is considered\ncovered by the collaboration of i sensors (denoted by k1, ..., ki) if\nand only if the following two equations holds [7][10][12].\n\u2200j = 1, ..., i; L(kj) \u2212 L < R. (4)\nC(L) =\niX\nj=1\n(E( L(kj) \u2212 L ) > s. (5)\nC(L) is regarded as the coverage quality of location L in the\nnetwork area [7][10][12].\nHowever, we notice that defining the sensibility as the sum of the\nsensed signal strength by each collaborative sensor implies a very\nspecial application: Applications must employ the sum of the\nsignal strength to achieve decision-making. To capture generally\nrealistic application requirement, we modify the definition described\nin Equation (5). The model we adopt in this paper is described in\ndetails as follows.\nWe consider the probability P(L, kj ) that an event located at L\ncan be detected by sensor kj is related to the signal strength sensed\nby kj. Formally,\nP(L, kj) = \u03b3E(d) =\n\u03b4\n( L(kj) \u2212 L / + 1)\u03b2\n, (6)\nwhere \u03b3 is a constant and \u03b4 = \u03b3\u03b1 is a constant too. normalizes\nthe distance to a proper scale and the +1 item is to avoid infinite\nvalue of P(L, kj).\nThe probability that an event located at L can be detected by any\ncollaborative sensors that satisfied Equation (4) is:\nP (L) = 1 \u2212\niY\nj=1\n(1 \u2212 P(L, kj )). (7)\nAs the detection probability P (L) reasonably determines how\nan event occurring at location L can be detected by the networks, it\nis a good measure of the coverage quality of location L in a WSN.\nSpecifically, Equation (5) is modified to:\nC(L) = P (L)\n= 1 \u2212\niY\nj=1\n[1 \u2212\n\u03b4\n( L(kj) \u2212 L / + 1)\u03b2\n] > s. (8)\nTo sum it up, we consider a point at location L is covered if\nEquation (4) and (8) hold.\n4. MAXIMIZING-\u03b9 NODE-DEDUCTION\nALGORITHM FOR SENSOR-GROUPING\nPROBLEM\nBefore we process to introduce algorithms to solve the sensor\ngrouping problem, let us define the margin (denoted by \u03b8) of an\narea \u03c6 monitored by the network as the band-like marginal area\nof \u03c6 and all the points on the outer perimeter of \u03b8 is \u03c1 distance\naway from all the points on the inner perimeter of \u03b8. \u03c1 is called the\nmargin length.\nIn a practical network, sensor nodes are usually evenly deployed\nin the network area. Obviously, the number of sensor nodes that\ncan sense an event occurring in the margin of the network is smaller\nthan the number of sensor nodes that can sense an event occurring\nin other area of the network. Based on this consideration, in our\nalgorithm design, we ensure the coverage quality of the network\narea except the margin. The information on \u03c6 and \u03c1 is\nnetworkbased. Each in-network sensor node can be pre-programmed or\non-line informed about \u03c6 and \u03c1, and thus calculate whether a point\nin its sensing area is in the margin or not.\n4.1 Maximizing-\u03b9 Node-Deduction Algorithm\nThe node-deduction process of our Maximizing-\u03b9 Node-Deduction\nAlgorithm (MIND) is simple. A node i greedily maximizes \u03b9 of the\nsub-network composed by itself, its ungrouped sensing neighbors,\nand the neighbors that are in the same group of itself. Under the\nconstraint that the coverage quality of its sensing area should be\nensured, node i deletes nodes in this sub-network one by one. The\ncandidate to be pruned satisfies that:\n\u2022 It is an ungrouped node.\n\u2022 The deletion of the node will not result in uncovered-points\ninside the sensing area of i.\nA candidate is deleted if the deletion of the candidate results in\nlargest \u03b9 of the sub-network compared to the deletion of other\ncandidates. This node-deduction process continues until no candidate\ncan be found. Then all the ungrouped sensing neighbors that are\nnot deleted are grouped into the same group of node i. We call the\nsensing neighbors that are in the same group of node i the group\nsensing neighbors of node i. We then call node i a finished node,\nmeaning that it has finished the above procedure and the sensing\narea of the node is covered. Those nodes that have not yet finished\nthis procedure are called unfinished nodes.\nThe above procedure initiates at a random-selected node that is\nnot in the margin. The node is grouped to the first group. It\ncalculates the resulting group sensing neighbors of it based on the above\nprocedure. It informs these group sensing neighbors that they are\nselected in the group. Then it hands over the above procedure to\nan unfinished group sensing neighbors that is the farthest from\nitself. This group sensing neighbor continues this procedure until no\nunfinished neighbor can be found. Then the first group is formed\n(Algorithmic description of this procedure can be found at [19]).\nAfter a group is formed, another random-selected ungrouped\nnode begins to group itself to the second group and initiates the\nabove procedure. In this way, groups are formed one by one. When\na node that involves in this algorithm found out that the coverage\nquality if its sensing area, except what overlaps the network margin,\ncannot be ensured even if all its ungrouped sensing neighbors are\ngrouped into the same group as itself, the algorithm stops. MIND\nis based on locally obtainable information of sensor nodes. It is\na distributed algorithm that serves as an approximate solution of\nProblem 1.\n4.2 Incremental Coverage Quality Algorithm:\nA Benchmark for MIND\nTo evaluate the effectiveness of introducing \u03b9 in the sensor-group\nproblem, another algorithm for sensor-group problem called\nIncremental Coverage Quality Algorithm (ICQA) is designed. Our aim\n1174\nis to evaluate how an idea, i.e., MIND, based on locally maximize\n\u03b9 performs.\nIn ICQA, a node-selecting process is as follows. A node i\ngreedily selects an ungrouped sensing neighbor in the same group as\nitself one by one, and informs the neighbor it is selected in the group.\nThe criterion is:\n\u2022 The selected neighbor is responsible to provide surveillance\nwork for some uncovered parts of node i\"s sensing area. (i.e.,\nthe coverage quality requirement of the parts is not fulfilled\nif this neighbor is not selected.)\n\u2022 The selected neighbor results in highest improvement of the\ncoverage quality of the neighbor\"s sensing area.\nThe improvement of the coverage quality, mathematically, should\nbe the integral of the the improvements of all points inside the\nneighbor\"s sensing area. A numerical approximation is employed\nto calculate this improvement. Details are presented in our\nsimulation study.\nThis node-selecting process continues until the sensing area of\nnode i is entirely covered. In this way, node i\"s group sensing\nneighbors are found. The above procedure is handed over as what\nMIND does and new groups are thus formed one by one. And\nthe condition that ICQA stops is the same as MIND. ICQA is also\nbased on locally obtainable information of sensor nodes. ICQA is\nalso a distributed algorithm that serves as an approximate solution\nof Problem 1.\n5. SIMULATION RESULTS\nTo evaluate the effectiveness of employing \u03b9 in sensor-grouping\nproblem, we build simulation surveillance networks. We employ\nMIND and ICQA to group the in-network sensor nodes. We\ncompare the grouping results with respect to how many groups both\nalgorithms find and how the performance of the resulting groups\nare.\nDetailed settings of the simulation networks are shown in Table\n1. In simulation networks, sensor nodes are randomly deployed in\na uniform manner in the network area.\nTable 1: The settings of the simulation networks\nArea of sensor field 400m*400m\n\u03c1 20m\nR 80m\n\u03b1, \u03b2, \u03b3 and 1.0, 2.0, 1.0 and 100.0\ns 0.6\nFor evaluating the coverage quality of the sensing area of a node,\nwe divide the sensing area of a node into several regions and regard\nthe coverage quality of the central point in each region as a\nrepresentative of the coverage quality of the region. This is a numerical\napproximation. Larger number of such regions results in better\napproximation. As sensor nodes are with low computational\ncapacity, there is a tradeoff between the number of such regions and the\nprecision of the resulting coverage quality of the sensing area of a\nnode. In our simulation study, we set this number 12. For\nevaluating the improvement of coverage quality in ICQA, we sum up all\nthe improvements at each region-center as the total improvement.\n5.1 Number of Groups Formed by MIND and\nICQA\nWe set the total in-network node number to different values and\nlet the networks perform MIND and ICQA. For each n,\nsimulations run with several random seeds to generate different networks.\nResults are averaged. Figure 2 shows the group numbers found in\nnetworks with different n\"s.\n500 1000 1500 2000\n0\n5\n10\n15\n20\n25\n30\n35\n40\n45\n50\nTotal in\u2212network node number\nTotalnumberofgroupsfound\nICQA\nMMNP\nFigure 2: The number of groups found by MIND and ICQA\nWe can see that MIND always outperforms ICQA in terms of\nthe number of groups formed. Obviously, the larger the number of\ngroups can be formed, the more the redundancy of each group is\nexploited. This output shows that an approach like MIND that aim\nto maximize \u03b9 of the resulting topology can exploits redundancy\nwell.\nAs an example, in case that n = 1500, the results of five\nnetworks are listed in Table 2.\nTable 2: The grouping results of five networks with n = 1500\nNet MIND ICQA MIND ICQA\nGroup Number Group Number Average \u03b9 Average \u03b9\n1 34 31 0.145514 0.031702\n2 33 30 0.145036 0.036649\n3 33 31 0.156483 0.033578\n4 32 31 0.152671 0.029030\n5 33 32 0.146560 0.033109\nThe difference between the average \u03b9 of the groups in each\nnetwork shows that groups formed by MIND result in topologies with\nlarger \u03b9\"s. It demonstrates that \u03b9 is good indicator of redundancy in\ndifferent networks.\n5.2 The Performance of the Resulting Groups\nAlthough MIND forms more groups than ICQA does, which\nimplies longer lifetime of the networks, another importance\nconsideration is how these groups formed by MIND and ICQA perform.\nWe let 10000 events randomly occur in the network area except\nthe margin. We compare how many events happen at the locations\nwhere the quality is less than the requirement s = 0.6 when each\nresulting group is conducting surveillance work (We call the\nnumber of such events the failure number of group). Figure 3 shows\nthe average failure numbers of the resulting groups when different\nnode numbers are set.\nWe can see that the groups formed by MIND outperform those\nformed by ICQA because the groups formed by MIND result in\nlower failure numbers. This further demonstrates that MIND is a\ngood approach for sensor-grouping problem.\n1175\n500 1000 1500 2000\n0\n10\n20\n30\n40\n50\n60\nTotal in\u2212network node number\naveragefailurenumbers\nICQA\nMMNP\nFigure 3: The failure numbers of MIND and ICQA\n6. CONCLUSION\nThis paper proposes \u03b9, a novel index for evaluation of\npointdistribution. \u03b9 is the minimum distance between each pair of points\nnormalized by the average distance between each pair of points.\nWe find that a set of points that achieve a maximum value of \u03b9\nresult in a honeycomb structure. We propose that \u03b9 can serve as a\ngood index to evaluate the distribution of the points, which can be\nemployed in coverage-related problems in wireless sensor networks\n(WSNs). We set out to validate this idea by employing \u03b9 to a\nsensorgrouping problem. We formulate a general sensor-grouping\nproblem for WSNs and provide a general sensing model. With an\nalgorithm called Maximizing-\u03b9 Node-Deduction (MIND), we show that\nmaximizing \u03b9 at sensor nodes is a good approach to solve this\nproblem. Simulation results verify that MIND outperforms a greedy\nalgorithm that exploits sensor-redundancy we design in terms of the\nnumber and the performance of the groups formed. This\ndemonstrates a good application of employing \u03b9 in coverage-related\nproblems.\n7. ACKNOWLEDGEMENT\nThe work described in this paper was substantially supported by\ntwo grants, RGC Project No. CUHK4205/04E and UGC Project\nNo. AoE/E-01/99, of the Hong Kong Special Administrative\nRegion, China.\n8. REFERENCES\n[1] I. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cayirci.\nA survey on wireless sensor networks. IEEE\nCommunications Magazine, 40(8):102-114, 2002.\n[2] F. Aurenhammer. Vononoi diagram - a survey of a\nfundamental geometric data structure. ACM Computing\nSurveys, 23(2):345-405, September 1991.\n[3] N. Bulusu, J. Heidemann, and D. 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{"name": "train_C-72", "title": "GUESS: Gossiping Updates for Efficient Spectrum Sensing", "abstract": "Wireless radios of the future will likely be frequency-agile, that is, supporting opportunistic and adaptive use of the RF spectrum. Such radios must coordinate with each other to build an accurate and consistent map of spectral utilization in their surroundings. We focus on the problem of sharing RF spectrum data among a collection of wireless devices. The inherent requirements of such data and the time-granularity at which it must be collected makes this problem both interesting and technically challenging. We propose GUESS, a novel incremental gossiping approach to coordinated spectral sensing. It (1) reduces protocol overhead by limiting the amount of information exchanged between participating nodes, (2) is resilient to network alterations, due to node movement or node failures, and (3) allows exponentially-fast information convergence. We outline an initial solution incorporating these ideas and also show how our approach reduces network overhead by up to a factor of 2.4 and results in up to 2.7 times faster information convergence than alternative approaches.", "fulltext": "1. INTRODUCTION\nThere has recently been a huge surge in the growth of\nwireless technology, driven primarily by the availability of\nunlicensed spectrum. However, this has come at the cost\nof increased RF interference, which has caused the Federal\nCommunications Commission (FCC) in the United States to\nre-evaluate its strategy on spectrum allocation. Currently,\nthe FCC has licensed RF spectrum to a variety of public and\nprivate institutions, termed primary users. New spectrum\nallocation regimes implemented by the FCC use dynamic\nspectrum access schemes to either negotiate or\nopportunistically allocate RF spectrum to unlicensed secondary users\nPermission to make digital or hard copies of all or part of this work for\npersonal or classroom use is granted without fee provided that copies are\nnot made or distributed for profit or commercial advantage and that copies\nbear this notice and the full citation on the first page. To copy otherwise, to\nrepublish, to post on servers or to redistribute to lists, requires prior specific\nD1\nD2\nD5\nD3\nD4\nPrimary User\nShadowed\nSecondary Users\nSecondary Users detect\nPrimary's Signal\nShadowed\nSecondary User\nFigure 1: Without cooperation, shadowed users are not\nable to detect the presence of the primary user.\nthat can use it when the primary user is absent. The second\ntype of allocation scheme is termed opportunistic spectrum\nsharing. The FCC has already legislated this access method\nfor the 5 GHz band and is also considering the same for\nTV broadcast bands [1]. As a result, a new wave of\nintelligent radios, termed cognitive radios (or software defined\nradios), is emerging that can dynamically re-tune their\nradio parameters based on interactions with their surrounding\nenvironment.\nUnder the new opportunistic allocation strategy,\nsecondary users are obligated not to interfere with primary\nusers (senders or receivers). This can be done by sensing\nthe environment to detect the presence of primary users.\nHowever, local sensing is not always adequate, especially in\ncases where a secondary user is shadowed from a primary\nuser, as illustrated in Figure 1. Here, coordination between\nsecondary users is the only way for shadowed users to\ndetect the primary. In general, cooperation improves sensing\naccuracy by an order of magnitude when compared to not\ncooperating at all [5].\nTo realize this vision of dynamic spectrum access, two\nfundamental problems must be solved: (1) Efficient and\ncoordinated spectrum sensing and (2) Distributed spectrum\nallocation. In this paper, we propose strategies for coordinated\nspectrum sensing that are low cost, operate on timescales\ncomparable to the agility of the RF environment, and are\nresilient to network failures and alterations. We defer the\nproblem of spectrum allocation to future work.\nSpectrum sensing techniques for cognitive radio networks\n[4, 17] are broadly classified into three regimes; (1)\ncentralized coordinated techniques, (2) decentralized coordinated\ntechniques, and (3) decentralized uncoordinated techniques.\nWe advocate a decentralized coordinated approach, similar\nin spirit to OSPF link-state routing used in the Internet.\nThis is more effective than uncoordinated approaches\nbecause making decisions based only on local information is\nfallible (as shown in Figure 1). Moreover, compared to\ncen12\ntralized approaches, decentralized techniques are more\nscalable, robust, and resistant to network failures and security\nattacks (e.g. jamming).\nCoordinating sensory data between cognitive radio devices\nis technically challenging because accurately assessing\nspectrum usage requires exchanging potentially large amounts of\ndata with many radios at very short time scales. Data size\ngrows rapidly due to the large number (i.e. thousands) of\nspectrum bands that must be scanned. This data must also\nbe exchanged between potentially hundreds of neighboring\nsecondary users at short time scales, to account for rapid\nchanges in the RF environment.\nThis paper presents GUESS, a novel approach to\ncoordinated spectrum sensing for cognitive radio networks. Our\napproach is motivated by the following key observations:\n1. Low-cost sensors collect approximate data: Most\ndevices have limited sensing resolution because they are\nlow-cost and low duty-cycle devices and thus cannot\nperform complex RF signal processing (e.g. matched\nfiltering). Many are typically equipped with simple\nenergy detectors that gather only approximate\ninformation.\n2. Approximate summaries are sufficient for coordination:\nApproximate statistical summaries of sensed data are\nsufficient for correlating sensed information between\nradios, as relative usage information is more\nimportant than absolute usage data. Thus, exchanging\nexact RF information may not be necessary, and more\nimportantly, too costly for the purposes of spectrum\nsensing.\n3. RF spectrum changes incrementally: On most bands,\nRF spectrum utilization changes infrequently.\nMoreover, utilization of a specific RF band affects only that\nband and not the entire spectrum. Therefore, if the\nusage pattern of a particular band changes\nsubstantially, nodes detecting that change can initiate an\nupdate protocol to update the information for that band\nalone, leaving in place information already collected\nfor other bands. This allows rapid detection of change\nwhile saving the overhead of exchanging unnecessary\ninformation.\nBased on these observations, GUESS makes the following\ncontributions:\n1. A novel approach that applies randomized gossiping\nalgorithms to the problem of coordinated spectrum\nsensing. These algorithms are well suited to coordinated\nspectrum sensing due to the unique characteristics of\nthe problem: i.e. radios are power-limited, mobile and\nhave limited bandwidth to support spectrum sensing\ncapabilities.\n2. An application of in-network aggregation for\ndissemination of spectrum summaries. We argue that\napproximate summaries are adequate for performing accurate\nradio parameter tuning.\n3. An extension of in-network aggregation and\nrandomized gossiping to support incremental maintenance of\nspectrum summaries. Compared to standard\ngossiping approaches, incremental techniques can further\nreduce overhead and protocol execution time by\nrequiring fewer radio resources.\nThe rest of the paper is organized as follows. Section 2\nmotivates the need for a low cost and efficient approach to\ncoordinated spectrum sensing. Section 3 discusses related\nwork in the area, while Section 4 provides a background on\nin-network aggregation and randomized gossiping. Sections\n5 and 6 discuss extensions and protocol details of these\ntechniques for coordinated spectrum sensing. Section 7 presents\nsimulation results showcasing the benefits of GUESS, and\nSection 8 presents a discussion and some directions for\nfuture work.\n2. MOTIVATION\nTo estimate the scale of the problem, In-stat predicts that\nthe number of WiFi-enabled devices sold annually alone will\ngrow to 430 million by 2009 [2]. Therefore, it would be\nreasonable to assume that a typical dense urban environment\nwill contain several thousand cognitive radio devices in range\nof each other. As a result, distributed spectrum sensing and\nallocation would become both important and fundamental.\nCoordinated sensing among secondary radios is essential\ndue to limited device sensing resolution and physical RF\neffects such as shadowing. Cabric et al. [5] illustrate the gains\nfrom cooperation and show an order of magnitude reduction\nin the probability of interference with the primary user when\nonly a small fraction of secondary users cooperate.\nHowever, such coordination is non-trivial due to: (1) the\nlimited bandwidth available for coordination, (2) the need to\ncommunicate this information on short timescales, and (3)\nthe large amount of sensory data that needs to be exchanged.\nLimited Bandwidth: Due to restrictions of cost and\npower, most devices will likely not have dedicated hardware\nfor supporting coordination. This implies that both data\nand sensory traffic will need to be time-multiplexed onto a\nsingle radio interface. Therefore, any time spent\ncommunicating sensory information takes away from the device\"s\nability to perform its intended function. Thus, any such\ncoordination must incur minimal network overhead.\nShort Timescales: Further compounding the problem\nis the need to immediately propagate updated RF sensory\ndata, in order to allow devices to react to it in a timely\nfashion. This is especially true due to mobility, as rapid changes\nof the RF environment can occur due to device and obstacle\nmovements. Here, fading and multi-path interference\nheavily impact sensing abilities. Signal level can drop to a deep\nnull with just a \u03bb/4 movement in receiver position (3.7 cm\nat 2 GHz), where \u03bb is the wavelength [14]. Coordination\nwhich does not support rapid dissemination of information\nwill not be able to account for such RF variations.\nLarge Sensory Data: Because cognitive radios can\npotentially use any part of the RF spectrum, there will be\nnumerous channels that they need to scan. Suppose we wish to\ncompute the average signal energy in each of 100 discretized\nfrequency bands, and each signal can have up to 128 discrete\nenergy levels. Exchanging complete sensory information\nbetween nodes would require 700 bits per transmission (for\n100 channels, each requiring seven bits of information).\nExchanging this information among even a small group of 50\ndevices each second would require (50 time-steps \u00d7 50\ndevices \u00d7 700 bits per transmission) = 1.67 Mbps of aggregate\nnetwork bandwidth.\nContrast this to the use of a randomized gossip protocol to\ndisseminate such information, and the use of FM bit vectors\nto perform in-network aggregation. By applying gossip and\nFM aggregation, aggregate bandwidth requirements drop to\n(c\u00b7logN time-steps \u00d7 50 devices \u00d7 700 bits per transmission)\n= 0.40 Mbps, since 12 time-steps are needed to propagate\nthe data (with c = 2, for illustrative purpoes1\n). This is\nexplained further in Section 4.\nBased on these insights, we propose GUESS, a low-overhead\napproach which uses incremental extensions to FM\naggregation and randomized gossiping for efficient coordination\nwithin a cognitive radio network. As we show in Section 7,\n1\nConvergence time is correlated with the connectivity topology\nof the devices, which in turn depends on the environment.\n13\nX\nA\nA\nX\nB\nB\nX\nFigure 2: Using FM aggregation to compute average signal level measured by a group of devices.\nthese incremental extensions can further reduce bandwidth\nrequirements by up to a factor of 2.4 over the standard\napproaches discussed above.\n3. RELATED WORK\nResearch in cognitive radio has increased rapidly [4, 17]\nover the years, and it is being projected as one of the leading\nenabling technologies for wireless networks of the future [9].\nAs mentioned earlier, the FCC has already identified new\nregimes for spectrum sharing between primary users and\nsecondary users and a variety of systems have been proposed\nin the literature to support such sharing [4, 17].\nDetecting the presence of a primary user is non-trivial,\nespecially a legacy primary user that is not cognitive\nradio aware. Secondary users must be able to detect the\nprimary even if they cannot properly decode its signals. This\nhas been shown by Sahai et al. [16] to be extremely\ndifficult even if the modulation scheme is known. Sophisticated\nand costly hardware, beyond a simple energy detector, is\nrequired to improve signal detection accuracy [16]. Moreover,\na shadowed secondary user may not even be able to detect\nsignals from the primary. As a result, simple local\nsensing approaches have not gained much momentum. This has\nmotivated the need for cooperation among cognitive radios\n[16].\nMore recently, some researchers have proposed approaches\nfor radio coordination. Liu et al. [11] consider a centralized\naccess point (or base station) architecture in which\nsensing information is forwarded to APs for spectrum allocation\npurposes. APs direct mobile clients to collect such\nsensing information on their behalf. However, due to the need\nof a fixed AP infrastructure, such a centralized approach is\nclearly not scalable.\nIn other work, Zhao et al. [17] propose a distributed\ncoordination approach for spectrum sensing and allocation.\nCognitive radios organize into clusters and coordination\noccurs within clusters. The CORVUS [4] architecture proposes\na similar clustering method that can use either a centralized\nor decentralized approach to manage clusters. Although an\nimprovement over purely centralized approaches, these\ntechniques still require a setup phase to generate the clusters,\nwhich not only adds additional delay, but also requires many\nof the secondary users to be static or quasi-static. In\ncontrast, GUESS does not place such restrictions on secondary\nusers, and can even function in highly mobile environments.\n4. BACKGROUND\nThis section provides the background for our approach.\nWe present the FM aggregation scheme that we use to\ngenerate spectrum summaries and perform in-network\naggregation. We also discuss randomized gossiping techniques for\ndisseminating aggregates in a cognitive radio network.\n4.1 FM Aggregation\nAggregation is the process where nodes in a distributed\nnetwork combine data received from neighboring nodes with\ntheir local value to generate a combined aggregate. This\naggregate is then communicated to other nodes in the\nnetwork and this process repeats until the aggregate at all\nnodes has converged to the same value, i.e. the global\naggregate. Double-counting is a well known problem in this\nprocess, where nodes may contribute more than once to the\naggregate, causing inaccuracy in the final result. Intuitively,\nnodes can tag the aggregate value they transmit with\ninformation about which nodes have contributed to it. However,\nthis approach is not scalable. Order and Duplicate\nInsensitive (ODI) techniques have been proposed in the literature\n[10, 15]. We adopt the ODI approach pioneered by Flajolet\nand Martin (FM) for the purposes of aggregation. Next we\noutline the FM approach; for full details, see [7].\nSuppose we want to compute the number of nodes in the\nnetwork, i.e. the COUNT query. To do so, each node\nperforms a coin toss experiment as follows: toss an unbiased\ncoin, stopping after the first head is seen. The node then\nsets the ith bit in a bit vector (initially filled with zeros),\nwhere i is the number of coin tosses it performed. The\nintuition is that as the number of nodes doing coin toss\nexperiments increases, the probability of a more significant bit\nbeing set in one of the nodes\" bit vectors increases.\nThese bit vectors are then exchanged among nodes. When\na node receives a bit vector, it updates its local bit vector\nby bitwise OR-ing it with the received vector (as shown in\nFigure 2 which computes AVERAGE). At the end of the\naggregation process, every node, with high probability, has\nthe same bit vector. The actual value of the count aggregate\nis then computed using the following formula, AGGF M =\n2j\u22121\n/0.77351, where j represents the bit position of the least\nsignificant zero in the aggregate bit vector [7].\nAlthough such aggregates are very compact in nature,\nrequiring only O(logN) state space (where N is the number\nof nodes), they may not be very accurate as they can only\napproximate values to the closest power of 2, potentially\ncausing errors of up to 50%. More accurate aggregates can\nbe computed by maintaining multiple bit vectors at each\nnode, as explained in [7]. This decreases the error to within\nO(1/\n\u221a\nm), where m is the number of such bit vectors.\nQueries other than count can also be computed using\nvariants of this basic counting algorithm, as discussed in [3] (and\nshown in Figure 2). Transmitting FM bit vectors between\nnodes is done using randomized gossiping, discussed next.\n4.2 Gossip Protocols\nGossip-based protocols operate in discrete time-steps; a\ntime-step is the required amount of time for all\ntransmissions in that time-step to complete. At every time-step, each\nnode having something to send randomly selects one or more\nneighboring nodes and transmits its data to them. The\nrandomized propagation of information provides fault-tolerance\nand resilience to network failures and outages. We\nemphasize that this characteristic of the protocol also allows it to\noperate without relying on any underlying network\nstructure. Gossip protocols have been shown to provide\nexponentially fast convergence2\n, on the order of O(log N)\n[10], where N is the number of nodes (or radios). These\nprotocols can therefore easily scale to very dense\nenvironments.\n2\nConvergence refers to the state in which all nodes have the most\nup-to-date view of the network.\n14\nTwo types of gossip protocols are:\n\u2022 Uniform Gossip: In uniform gossip, at each\ntimestep, each node chooses a random neighbor and sends\nits data to it. This process repeats for O(log(N)) steps\n(where N is the number of nodes in the network).\nUniform gossip provides exponentially fast convergence,\nwith low network overhead [10].\n\u2022 Random Walk: In random walk, only a subset of\nthe nodes (termed designated nodes) communicate in a\nparticular time-step. At startup, k nodes are randomly\nelected as designated nodes. In each time-step, each\ndesignated node sends its data to a random neighbor,\nwhich becomes designated for the subsequent\ntimestep (much like passing a token). This process repeats\nuntil the aggregate has converged in the network.\nRandom walk has been shown to provide similar\nconvergence bounds as uniform gossip in problems of similar\ncontext [8, 12].\n5. INCREMENTAL PROTOCOLS\n5.1 Incremental FM Aggregates\nOne limitation of FM aggregation is that it does not\nsupport updates. Due to the probabilistic nature of FM, once\nbit vectors have been ORed together, information cannot\nsimply be removed from them as each node\"s contribution\nhas not been recorded. We propose the use of delete vectors,\nan extension of FM to support updates. We maintain a\nseparate aggregate delete vector whose value is subtracted from\nthe original aggregate vector\"s value to obtain the resulting\nvalue as follows.\nAGGINC = (2a\u22121\n/0.77351) \u2212 (2b\u22121\n/0.77351) (1)\nHere, a and b represent the bit positions of the least\nsignificant zero in the original and delete bit vectors respectively.\nSuppose we wish to compute the average signal level\ndetected in a particular frequency. To compute this, we\ncompute the SUM of all signal level measurements and divide\nthat by the COUNT of the number of measurements. A\nSUM aggregate is computed similar to COUNT (explained\nin Section 4.1), except that each node performs s coin toss\nexperiments, where s is the locally measured signal level.\nFigure 2 illustrates the sequence by which the average signal\nenergy is computed in a particular band using FM\naggregation.\nNow suppose that the measured signal at a node changes\nfrom s to s . The vectors are updated as follows.\n\u2022 s > s: We simply perform (s \u2212 s) more coin toss\nexperiments and bitwise OR the result with the original\nbit vector.\n\u2022 s < s: We increase the value of the delete vector by\nperforming (s \u2212 s ) coin toss experiments and bitwise\nOR the result with the current delete vector.\nUsing delete vectors, we can now support updates to the\nmeasured signal level. With the original implementation of\nFM, the aggregate would need to be discarded and a new one\nrecomputed every time an update occurred. Thus, delete\nvectors provide a low overhead alternative for applications\nwhose data changes incrementally, such as signal level\nmeasurements in a coordinated spectrum sensing environment.\nNext we discuss how these aggregates can be communicated\nbetween devices using incremental routing protocols.\n5.2 Incremental Routing Protocol\nWe use the following incremental variants of the routing\nprotocols presented in Section 4.2 to support incremental\nupdates to previously computed aggregates.\nUpdate Received OR\nLocal Update Occurs\nRecovered\nSusceptible\nTime-stamp Expires\nInitial State\nAdditional\nUpdate\nReceived\nInfectious\nClean Up\nFigure 3: State diagram each device passes through as\nupdates proceed in the system\n\u2022 Incremental Gossip Protocol (IGP): When an\nupdate occurs, the updated node initiates the gossiping\nprocedure. Other nodes only begin gossiping once they\nreceive the update. Therefore, nodes receiving the\nupdate become active and continue communicating with\ntheir neighbors until the update protocol terminates,\nafter O(log(N)) time steps.\n\u2022 Incremental Random Walk Protocol (IRWP):\nWhen an update (or updates) occur in the system,\ninstead of starting random walks at k random nodes in\nthe network, all k random walks are initiated from the\nupdated node(s). The rest of the protocol proceeds in\nthe same fashion as the standard random walk\nprotocol. The allocation of walks to updates is discussed\nin more detail in [3], where the authors show that the\nnumber of walks has an almost negligible impact on\nnetwork overhead.\n6. PROTOCOL DETAILS\nUsing incremental routing protocols to disseminate\nincremental FM aggregates is a natural fit for the problem of\ncoordinated spectrum sensing. Here we outline the\nimplementation of such techniques for a cognitive radio network.\nWe continue with the example from Section 5.1, where we\nwish to perform coordination between a group of wireless\ndevices to compute the average signal level in a particular\nfrequency band.\nUsing either incremental random walk or incremental\ngossip, each device proceeds through three phases, in order to\ndetermine the global average signal level for a particular\nfrequency band. Figure 3 shows a state diagram of these\nphases.\nSusceptible: Each device starts in the susceptible state\nand becomes infectious only when its locally measured signal\nlevel changes, or if it receives an update message from a\nneighboring device. If a local change is observed, the device\nupdates either the original or delete bit vector, as described\nin Section 5.1, and moves into the infectious state. If it\nreceives an update message, it ORs the received original\nand delete bit vectors with its local bit vectors and moves\ninto the infectious state.\nNote, because signal level measurements may change\nsporadically over time, a smoothing function, such as an\nexponentially weighted moving average, should be applied to\nthese measurements.\nInfectious: Once a device is infectious it continues to\nsend its up-to-date bit vectors, using either incremental\nrandom walk or incremental gossip, to neighboring nodes. Due\nto FM\"s order and duplicate insensitive (ODI) properties,\nsimultaneously occurring updates are handled seamlessly by\nthe protocol.\nUpdate messages contain a time stamp indicating when\nthe update was generated, and each device maintains a\nlo15\n0\n200\n400\n600\n800\n1000\n1 10 100\nNumber of Measured Signal Changes\nExecutiontime(ms)\nIncremental Gossip Uniform Gossip\n(a) Incremental Gossip and Uniform\nGossip on Clique\n0\n200\n400\n600\n800\n1000\n1 10 100\nNumber of Measured Signal Changes\nExecutionTime(ms).\nIncremental Random Walk Random Walk\n(b) Incremental Random Walk and\nRandom Walk on Clique\n0\n400\n800\n1200\n1600\n2000\n1 10 100\nNumber of Measured Signal Changes\nExecutionTime(ms).\nRandom Walk Incremental Random Walk\n(c) Incremental Random Walk and\nRandom Walk on Power-Law Random Graph\nFigure 4: Execution times of Incremental Protocols\n0.9\n1.4\n1.9\n2.4\n2.9\n1 10 100\nNumber of Measured Signal Changes\nOverheadImprovementRatio.\n(NormalizedtoUniformGossip)\nIncremental Gossip Uniform Gossip\n(a) Incremental Gossip and Uniform\nGossip on Clique\n0.9\n1.4\n1.9\n2.4\n2.9\n1 10 100\nNumber of Measured Signal Changes\nOverheadImprovementRatio.\n(NormalizedtoRandomWalk) Incremental Random Walk Random Walk\n(b) Incremental Random Walk and\nRandom Walk on Clique\n0.9\n1.1\n1.3\n1.5\n1.7\n1.9\n1 10 100\nNumber of Measured Signal Changes\nOverheadImprovementRatio.\n(NormalizedtoRandomWalk)\nRandom Walk Incremental Random Walk\n(c) Incremental Random Walk and\nRandom Walk on Power-Law Random Graph\nFigure 5: Network overhead of Incremental Protocols\ncal time stamp of when it received the most recent update.\nUsing this information, a device moves into the recovered\nstate once enough time has passed for the most recent\nupdate to have converged. As discussed in Section 4.2, this\nhappens after O(log(N)) time steps.\nRecovered: A recovered device ceases to propagate any\nupdate information. At this point, it performs clean-up and\nprepares for the next infection by entering the susceptible\nstate. Once all devices have entered the recovered state, the\nsystem will have converged, and with high probability, all\ndevices will have the up-to-date average signal level. Due\nto the cumulative nature of FM, even if all devices have not\nconverged, the next update will include all previous updates.\nNevertheless, the probability that gossip fails to converge is\nsmall, and has been shown to be O(1/N) [10].\nFor coordinated spectrum sensing, non-incremental\nrouting protocols can be implemented in a similar fashion.\nRandom walk would operate by having devices periodically drop\nthe aggregate and re-run the protocol. Each device would\nperform a coin toss (biased on the number of walks) to\ndetermine whether or not it is a designated node. This is\ndifferent from the protocol discussed above where only\nupdated nodes initiate random walks. Similar techniques can\nbe used to implement standard gossip.\n7. EVALUATION\nWe now provide a preliminary evaluation of GUESS in\nsimulation. A more detailed evaluation of this approach can\nbe found in [3]. Here we focus on how incremental\nextensions to gossip protocols can lead to further improvements\nover standard gossiping techniques, for the problem of\ncoordinated spectrum sensing.\nSimulation Setup: We implemented a custom\nsimulator in C++. We study the improvements of our\nincremental gossip protocols over standard gossiping in two\ndimensions: execution time and network overhead. We use two\ntopologies to represent device connectivity: a clique, to\neliminate the effects of the underlying topology on protocol\nperformance, and a BRITE-generated [13] power-law random\ngraph (PLRG), to illustrate how our results extend to more\nrealistic scenarios. We simulate a large deployment of 1,000\ndevices to analyze protocol scalability.\nIn our simulations, we compute the average signal level in\na particular band by disseminating FM bit vectors. In each\nrun of the simulation, we induce a change in the measured\nsignal at one or more devices. A run ends when the new\naverage signal level has converged in the network.\nFor each data point, we ran 100 simulations and 95%\nconfidence intervals (error bars) are shown.\nSimulation Parameters: Each transmission involves\nsending 70 bits of information to a neighboring node. To\ncompute the AVERAGE aggregate, four bit vectors need to\nbe transmitted: the original SUM vector, the SUM delete\nvector, the original COUNT vector, and the COUNT delete\nvector. Non-incremental protocols do not transmit the delete\nvectors. Each transmission also includes a time stamp of\nwhen the update was generated.\nWe assume nodes communicate on a common control\nchannel at 2 Mbps. Therefore, one time-step of protocol\nexecution corresponds to the time required for 1,000 nodes to\nsequentially send 70 bits at 2 Mbps. Sequential use of the\ncontrol channel is a worst case for our protocols; in practice,\nmultiple control channels could be used in parallel to reduce\nexecution time. We also assume nodes are loosely time\nsynchronized, the implications of which are discussed further in\n[3]. Finally, in order to isolate the effect of protocol\noperation on performance, we do not model the complexities of\nthe wireless channel in our simulations.\nIncremental Protocols Reduce Execution Time:\nFigure 4(a) compares the performance of incremental gossip\n(IGP) with uniform gossip on a clique topology. We observe\nthat both protocols have almost identical execution times.\nThis is expected as IGP operates in a similar fashion to\n16\nuniform gossip, taking O(log(N)) time-steps to converge.\nFigure 4(b) compares the execution times of\nincremental random walk (IRWP) and standard random walk on a\nclique. IRWP reduces execution time by a factor of 2.7 for a\nsmall number of measured signal changes. Although random\nwalk and IRWP both use k random walks (in our simulations\nk = number of nodes), IRWP initiates walks only from\nupdated nodes (as explained in Section 5.2), resulting in faster\ninformation convergence. These improvements carry over to\na PLRG topology as well (as shown in Figure 4(c)), where\nIRWP is 1.33 times faster than random walk.\nIncremental Protocols Reduce Network Overhead:\nFigure 5(a) shows the ratio of data transmitted using\nuniform gossip relative to incremental gossip on a clique. For\na small number of signal changes, incremental gossip incurs\n2.4 times less overhead than uniform gossip. This is because\nin the early steps of protocol execution, only devices which\ndetect signal changes communicate. As more signal changes\nare introduced into the system, gossip and incremental\ngossip incur approximately the same overhead.\nSimilarly, incremental random walk (IRWP) incurs much\nless overhead than standard random walk. Figure 5(b) shows\na 2.7 fold reduction in overhead for small numbers of\nsignal changes on a clique. Although each protocol uses the\nsame number of random walks, IRWP uses fewer network\nresources than random walk because it takes less time to\nconverge. This improvement also holds true on more\ncomplex PLRG topologies (as shown in Figure 5(c)), where we\nobserve a 33% reduction in network overhead.\nFrom these results it is clear that incremental techniques\nyield significant improvements over standard approaches to\ngossip, even on complex topologies. Because spectrum\nutilization is characterized by incremental changes to usage,\nincremental protocols are ideally suited to solve this\nproblem in an efficient and cost effective manner.\n8. DISCUSSION AND FUTURE WORK\nWe have only just scratched the surface in addressing the\nproblem of coordinated spectrum sensing using incremental\ngossiping. Next, we outline some open areas of research.\nSpatial Decay: Devices performing coordinated sensing\nare primarily interested in the spectrum usage of their local\nneighborhood. Therefore, we recommend the use of\nspatially decaying aggregates [6], which limits the impact of an\nupdate on more distant nodes. Spatially decaying\naggregates work by successively reducing (by means of a decay\nfunction) the value of the update as it propagates further\nfrom its origin. One challenge with this approach is that\npropagation distance cannot be determined ahead of time\nand more importantly, exhibits spatio-temporal variations.\nTherefore, finding the optimal decay function is non-trivial,\nand an interesting subject of future work.\nSignificance Threshold: RF spectrum bands\ncontinually experience small-scale changes which may not\nnecessarily be significant. Deciding if a change is significant can be\ndone using a significance threshold \u03b2, below which any\nobserved change is not propagated by the node. Choosing an\nappropriate operating value for \u03b2 is application dependent,\nand explored further in [3].\nWeighted Readings: Although we argued that most\ndevices will likely be equipped with low-cost sensing\nequipment, there may be situations where there are some special\ninfrastructure nodes that have better sensing abilities than\nothers. Weighting their measurements more heavily could\nbe used to maintain a higher degree of accuracy.\nDetermining how to assign such weights is an open area of research.\nImplementation Specifics: Finally, implementing\ngossip for coordinated spectrum sensing is also open. If\nimplemented at the MAC layer, it may be feasible to piggy-back\ngossip messages over existing management frames (e.g.\nnetworking advertisement messages). As well, we also require\nthe use of a control channel to disseminate sensing\ninformation. There are a variety of alternatives for\nimplementing such a channel, some of which are outlined in [4]. The\ntrade-offs of different approaches to implementing GUESS\nis a subject of future work.\n9. CONCLUSION\nSpectrum sensing is a key requirement for dynamic\nspectrum allocation in cognitive radio networks. The nature of\nthe RF environment necessitates coordination between\ncognitive radio devices. We propose GUESS, an approximate\nyet low overhead approach to perform efficient coordination\nbetween cognitive radios. The fundamental contributions of\nGUESS are: (1) an FM aggregation scheme for efficient\ninnetwork aggregation, (2) a randomized gossiping approach\nwhich provides exponentially fast convergence and\nrobustness to network alterations, and (3) incremental variations\nof FM and gossip which we show can reduce the\ncommunication time by up to a factor of 2.7 and reduce network\noverhead by up to a factor of 2.4. Our preliminary\nsimulation results showcase the benefits of this approach and we\nalso outline a set of open problems that make this a new\nand exciting area of research.\n10. REFERENCES\n[1] Unlicensed Operation in the TV Broadcast Bands and\nAdditional Spectrum for Unlicensed Devices Below 900 MHz in\nthe 3 GHz band, May 2004. Notice of Proposed Rule-Making\n04-186, Federal Communications Commission.\n[2] In-Stat: Covering the Full Spectrum of Digital Communications\nMarket Research, from Vendor to End-user, December 2005.\nhttp://www.in-stat.com/catalog/scatalogue.asp?id=28.\n[3] N. Ahmed, D. Hadaller, and S. Keshav. Incremental\nMaintenance of Global Aggregates. UW. Technical Report\nCS-2006-19, University of Waterloo, ON, Canada, 2006.\n[4] R. W. Brodersen, A. Wolisz, D. Cabric, S. M. Mishra, and\nD. Willkomm. CORVUS: A Cognitive Radio Approach for\nUsage of Virtual Unlicensed Spectrum. Technical report, July\n2004.\n[5] D. Cabric, S. M. Mishra, and R. W. Brodersen. Implementation\nIssues in Spectrum Sensing for Cognitive Radios. In Asilomar\nConference, 2004.\n[6] E. Cohen and H. Kaplan. Spatially-Decaying Aggregation Over\na Network: Model and Algorithms. In Proceedings of SIGMOD\n2004, pages 707-718, New York, NY, USA, 2004. ACM Press.\n[7] P. Flajolet and G. N. Martin. Probabilistic Counting\nAlgorithms for Data Base Applications. J. Comput. Syst. Sci.,\n31(2):182-209, 1985.\n[8] C. Gkantsidis, M. Mihail, and A. Saberi. Random Walks in\nPeer-to-Peer Networks. In Proceedings of INFOCOM 2004,\npages 1229-1240, 2004.\n[9] E. Griffith. Previewing Intel\"s Cognitive Radio Chip, June 2005.\nhttp://www.internetnews.com/wireless/article.php/3513721.\n[10] D. Kempe, A. Dobra, and J. Gehrke. Gossip-Based\nComputation of Aggregate Information. In FOCS 2003, page\n482, Washington, DC, USA, 2003. IEEE Computer Society.\n[11] X. Liu and S. Shankar. Sensing-based Opportunistic Channel\nAccess. In ACM Mobile Networks and Applications\n(MONET) Journal, March 2005.\n[12] Q. Lv, P. Cao, E. Cohen, K. Li, and S. Shenker. Search and\nReplication in Unstructured Peer-to-Peer Networks. In\nProceedings of ICS, 2002.\n[13] A. Medina, A. Lakhina, I. Matta, and J. Byers. BRITE: an\nApproach to Universal Topology Generation. In Proceedings of\nMASCOTS conference, Aug. 2001.\n[14] S. M. Mishra, A. Sahai, and R. W. Brodersen. Cooperative\nSensing among Cognitive Radios. In ICC 2006, June 2006.\n[15] S. Nath, P. B. Gibbons, S. Seshan, and Z. R. Anderson.\nSynopsis Diffusion for Robust Aggregation in Sensor Networks.\nIn Proceedings of SenSys 2004, pages 250-262, 2004.\n[16] A. Sahai, N. Hoven, S. M. Mishra, and R. Tandra. Fundamental\nTradeoffs in Robust Spectrum Sensing for Opportunistic\nFrequency Reuse. Technical Report UC Berkeley, 2006.\n[17] J. Zhao, H. Zheng, and G.-H. Yang. Distributed Coordination\nin Dynamic Spectrum Allocation Networks. In Proceedings of\nDySPAN 2005, Baltimore (MD), Nov. 2005.\n17", "keywords": "coordinate spectrum sense;coordinated sensing;cognitive radio;spatially decaying aggregate;rf interference;spectrum allocation;opportunistic spectrum sharing;innetwork aggregation;incremental algorithm;rf spectrum;spectrum sensing;incremental gossip protocol;fm aggregation;gossip protocol"}
{"name": "train_C-74", "title": "Adapting Asynchronous Messaging Middleware to ad-hoc Networking", "abstract": "The characteristics of mobile environments, with the possibility of frequent disconnections and fluctuating bandwidth, have forced a rethink of traditional middleware. In particular, the synchronous communication paradigms often employed in standard middleware do not appear to be particularly suited to ad-hoc environments, in which not even the intermittent availability of a backbone network can be assumed. Instead, asynchronous communication seems to be a generally more suitable paradigm for such environments. Message oriented middleware for traditional systems has been developed and used to provide an asynchronous paradigm of communication for distributed systems, and, recently, also for some specific mobile computing systems. In this paper, we present our experience in designing, implementing and evaluating EMMA (Epidemic Messaging Middleware for ad-hoc networks), an adaptation of Java Message Service (JMS) for mobile ad-hoc environments. We discuss in detail the design challenges and some possible solutions, showing a concrete example of the feasibility and suitability of the application of the asynchronous paradigm in this setting and outlining a research roadmap for the coming years.", "fulltext": "1. INTRODUCTION\nWith the increasing popularity of mobile devices and their\nwidespread adoption, there is a clear need to allow the\ndevelopment of a broad spectrum of applications that operate\neffectively over such an environment. Unfortunately, this is far\nfrom simple: mobile devices are increasingly heterogeneous\nin terms of processing capabilities, memory size, battery\ncapacity, and network interfaces. Each such configuration has\nsubstantially different characteristics that are both statically\ndifferent - for example, there is a major difference in\ncapability between a Berkeley mote and an 802.11g-equipped\nlaptop - and that vary dynamically, as in situations of\nfluctuating bandwidth and intermittent connectivity. Mobile ad\nhoc environments have an additional element of complexity\nin that they are entirely decentralised.\nIn order to craft applications for such complex\nenvironments, an appropriate form of middleware is essential if cost\neffective development is to be achieved. In this paper, we\nexamine one of the foundational aspects of middleware for\nmobile ad-hoc environments: that of the communication\nprimitives.\nTraditionally, the most frequently used middleware\nprimitives for communication assume the simultaneous presence\nof both end points on a network, since the stability and\npervasiveness of the networking infrastructure is not an\nunreasonable assumption for most wired environments. In other\nwords, most communication paradigms are synchronous:\nobject oriented middleware such as CORBA and Java RMI are\ntypical examples of middleware based on synchronous\ncommunication.\nIn recent years, there has been growing interest in\nplatforms based on asynchronous communication paradigms, such\nas publish-subscribe systems [6]: these have been exploited\nvery successfully where there is application level\nasynchronicity. From a Gartner Market Report [7]: Given\nmessageoriented-middleware\"s (MOM) popularity, scalability,\nflexibility, and affinity with mobile and wireless architectures,\nby 2004, MOM will emerge as the dominant form of\ncommunication middleware for linking mobile and enterprise\napplications (0.7 probability).... Moreover, in mobile ad-hoc\nsystems, the likelihood of network fragmentation means that\nsynchronous communication may in any case be\nimpracticable, giving situations in which delay tolerant asynchronous\ntraffic is the only form of traffic that could be supported.\n121 Middleware 2004 Companion\nMiddleware for mobile ad-hoc environments must therefore\nsupport semi-synchronous or completely asynchronous\ncommunication primitives if it is to avoid substantial\nlimitations to its utility. Aside from the intellectual challenge in\nsupporting this model, this work is also interesting because\nthere are a number of practical application domains in\nallowing inter-community communication in undeveloped\nareas of the globe. Thus, for example, projects that have been\ncarried out to help populations that live in remote places of\nthe globe such as Lapland [3] or in poor areas that lack fixed\nconnectivity infrastructure [9].\nThere have been attempts to provide mobile middleware\nwith these properties, including STEAM, LIME,\nXMIDDLE, Bayou (see [11] for a more complete review of mobile\nmiddleware). These models differ quite considerably from\nthe existing traditional middleware in terms of primitives\nprovided. Furthermore, some of them fail in providing a\nsolution for the true ad-hoc scenarios.\nIf the projected success of MOM becomes anything like\na reality, there will be many programmers with experience\nof it. The ideal solution to the problem of middleware for\nad-hoc systems is, then, to allow programmers to utilise the\nsame paradigms and models presented by common forms of\nMOM and to ensure that these paradigms are supportable\nwithin the mobile environment. This approach has clear\nadvantages in allowing applications developed on standard\nmiddleware platforms to be easily deployed on mobile\ndevices. Indeed, some research has already led to the\nadaptation of traditional middleware platforms to mobile settings,\nmainly to provide integration between mobile devices and\nexisting fixed networks in a nomadic (i.e., mixed)\nenvironment [4]. With respect to message oriented middleware, the\ncurrent implementations, however, either assume the\nexistence of a backbone network to which the mobile hosts\nconnect from time to time while roaming [10], or assume that\nnodes are always somehow reachable through a path [18].\nNo adaptation to heterogeneous or completely ad-hoc\nscenarios, with frequent disconnection and periodically isolated\nclouds of hosts, has been attempted.\nIn the remainder of this paper we describe an initial\nattempt to adapt message oriented middleware to suit mobile\nand, more specifically, mobile ad-hoc networks. In our case,\nwe elected to examine JMS, as one of the most widely known\nMOM systems. In the latter part of this paper, we explore\nthe limitations of our results and describe the plans we have\nto take the work further.\n2. MESSAGE ORIENTED MIDDLEWARE\nAND JAVA MESSAGE SERVICE (JMS)\nMessage-oriented middleware systems support\ncommunication between distributed components via message-passing:\nthe sender sends a message to identified queues, which\nusually reside on a server. A receiver retrieves the message from\nthe queue at a different time and may acknowledge the reply\nusing the same asynchronous mechanism. Message-oriented\nmiddleware thus supports asynchronous communication in\na very natural way, achieving de-coupling of senders and\nreceivers. A sender is able to continue processing as soon\nas the middleware has accepted the message; eventually,\nthe receiver will send an acknowledgment message and the\nsender will be able to collect it at a convenient time.\nHowever, given the way they are implemented, these middleware\nsystems usually require resource-rich devices, especially in\nterms of memory and disk space, where persistent queues\nof messages that have been received but not yet processed,\nare stored. Sun Java Message Service [5], IBM WebSphere\nMQ [6], Microsoft MSMQ [12] are examples of very\nsuccessful message-oriented middleware for traditional distributed\nsystems.\nThe Java Messaging Service (JMS) is a collection of\ninterfaces for asynchronous communication between distributed\ncomponents. It provides a common way for Java programs\nto create, send and receive messages. JMS users are usually\nreferred to as clients. The JMS specification further defines\nproviders as the components in charge of implementing the\nmessaging system and providing the administrative and\ncontrol functionality (i.e., persistence and reliability) required\nby the system. Clients can send and receive messages,\nasynchronously, through the JMS provider, which is in charge of\nthe delivery and, possibly, of the persistence of the messages.\nThere are two types of communication supported: point\nto point and publish-subscribe models. In the point to point\nmodel, hosts send messages to queues. Receivers can be\nregistered with some specific queues, and can asynchronously\nretrieve the messages and then acknowledge them. The\npublish-subscribe model is based on the use of topics that\ncan be subscribed to by clients. Messages are sent to topics\nby other clients and are then received in an asynchronous\nmode by all the subscribed clients. Clients learn about the\navailable topics and queues through Java Naming and\nDirectory Interface (JNDI) [14]. Queues and topics are created\nby an administrator on the provider and are registered with\nthe JNDI interface for look-up.\nIn the next section, we introduce the challenges of mobile\nnetworks, and show how JMS can be adapted to cope with\nthese requirements.\n3. JMS FOR MOBILE COMPUTING\nMobile networks vary very widely in their characteristics,\nfrom nomadic networks in which modes relocate whilst\noffline through to ad-hoc networks in which modes move freely\nand in which there is no infrastructure. Mobile ad-hoc\nnetworks are most generally applicable in situations where\nsurvivability and instant deployability are key: most notably in\nmilitary applications and disaster relief. In between these\ntwo types of \"mobile\" networks, there are, however, a number\nof possible heterogeneous combinations, where nomadic and\nad-hoc paradigms are used to interconnect totally unwired\nareas to more structured networks (such as a LAN or the\nInternet).\nWhilst the JMS specification has been extensively\nimplemented and used in traditional distributed systems,\nadaptations for mobile environments have been proposed only\nrecently. The challenges of porting JMS to mobile settings\nare considerable; however, in view of its widespread\nacceptance and use, there are considerable advantages in allowing\nthe adaptation of existing applications to mobile\nenvironments and in allowing the interoperation of applications in\nthe wired and wireless regions of a network.\nIn [10], JMS was adapted to a nomadic mobile setting,\nwhere mobile hosts can be JMS clients and communicate\nthrough the JMS provider that, however, sits on a\nbackbone network, providing reliability and persistence. The\nclient prototype presented in [10] is very lightweight, due\nto the delegation of all the heavyweight functionality to the\nMiddleware for Pervasive and ad-hoc Computing 122\nprovider on the wired network. However, this approach is\nsomewhat limited in terms of widespread applicability and\nscalability as a consequence of the concentration of\nfunctionality in the wired portion of the network.\nIf JMS is to be adapted to completely ad-hoc\nenvironments, where no fixed infrastructure is available, and where\nnodes change location and status very dynamically, more\nissues must be taken into consideration. Firstly, discovery\nneeds to use a resilient but distributed model: in this\nextremely dynamic environment, static solutions are\nunacceptable. As discussed in Section 2, a JMS administrator defines\nqueues and topics on the provider. Clients can then learn\nabout them using the Java Naming and Directory Interface\n(JNDI). However, due to the way JNDI is designed, a JNDI\nnode (or more than one) needs to be in reach in order to\nobtain a binding of a name to an address (i.e., knowing where\na specific queue/topic is). In mobile ad-hoc environments,\nthe discovery process cannot assume the existence of a fixed\nset of discovery servers that are always reachable, as this\nwould not match the dynamicity of ad-hoc networks.\nSecondly, a JMS Provider, as suggested by the JMS\nspecification, also needs to be reachable by each node in the\nnetwork, in order to communicate. This assumes a very\ncentralised architecture, which again does not match the\nrequirements of a mobile ad-hoc setting, in which nodes may\nbe moving and sparse: a more distributed and dynamic\nsolution is needed. Persistence is, however, essential\nfunctionality in asynchronous communication environments as hosts\nare, by definition, connected at different times.\nIn the following section, we will discuss our experience\nin designing and implementing JMS for mobile ad-hoc\nnetworks.\n4. JMSFOR MOBILE ad-hoc NETWORKS\n4.1 Adaptation of JMS for Mobile ad-hoc\nNetworks\nDeveloping applications for mobile networks is yet more\nchallenging: in addition to the same considerations as for\ninfrastructured wireless environments, such as the limited\ndevice capabilities and power constraints, there are issues\nof rate of change of network connectivity, and the lack of a\nstatic routing infrastructure. Consequently, we now describe\nan initial attempt to adapt the JMS specification to target\nthe particular requirements related to ad-hoc scenarios. As\ndiscussed in Section 3, a JMS application can use either the\npoint to point and the publish-subscribe styles of messaging.\nPoint to Point Model The point to point model is based\non the concept of queues, that are used to enable\nasynchronous communication between the producer of a message\nand possible different consumers. In our solution, the\nlocation of queues is determined by a negotiation process that\nis application dependent. For example, let us suppose that\nit is possible to know a priori, or it is possible to determine\ndynamically, that a certain host is the receiver of the most\npart of messages sent to a particular queue. In this case, the\noptimum location of the queue may well be on this\nparticular host. In general, it is worth noting that, according to the\nJMS specification and suggested design patterns, it is\ncommon and preferable for a client to have all of its messages\ndelivered to a single queue.\nQueues are advertised periodically to the hosts that are\nwithin transmission range or that are reachable by means of\nthe underlying synchronous communication protocol, if\nprovided. It is important to note that, at the middleware level,\nit is logically irrelevant whether or not the network layer\nimplements some form of ad-hoc routing (though considerably\nmore efficient if it does); the middleware only considers\ninformation about which nodes are actively reachable at any\npoint in time. The hosts that receive advertisement\nmessages add entries to their JNDI registry. Each entry is\ncharacterized by a lease (a mechanism similar to that present\nin Jini [15]). A lease represents the time of validity of a\nparticular entry. If a lease is not refreshed (i.e, its life is\nnot extended), it can expire and, consequently, the entry\nis deleted from the registry. In other words, the host\nassumes that the queue will be unreachable from that point\nin time. This may be caused, for example, if a host storing\nthe queue becomes unreachable. A host that initiates a\ndiscovery process will find the topics and the queues present\nin its connected portion of the network in a straightforward\nmanner.\nIn order to deliver a message to a host that is not\ncurrently in reach1\n, we use an asynchronous epidemic routing\nprotocol that will be discussed in detail in Section 4.2. If two\nhosts are in the same cloud (i.e., a connected path exists\nbetween them), but no synchronous protocol is available, the\nmessages are sent using the epidemic protocol. In this case,\nthe delivery latency will be low as a result of the rapidity of\npropagation of the infection in the connected cloud (see also\nthe simulation results in Section 5). Given the existence of\nan epidemic protocol, the discovery mechanism consists of\nadvertising the queues to the hosts that are currently\nunreachable using analogous mechanisms.\nPublish-Subscribe Model In the publish-subscribe model,\nsome of the hosts are similarly designated to hold topics and\nstore subscriptions, as before. Topics are advertised through\nthe registry in the same way as are queues, and a client\nwishing to subscribe to a topic must register with the client\nholding the topic. When a client wishes to send a message\nto the topic list, it sends it to the topic holder (in the same\nway as it would send a message to a queue). The topic\nholder then forwards the message to all subscribers, using\nthe synchronous protocol if possible, the epidemic protocol\notherwise. It is worth noting that we use a single message\nwith multiple recipients, instead of multiple messages with\nmultiple recipients. When a message is delivered to one of\nthe subscribers, this recipient is deleted from the list. In\norder to delete the other possible replicas, we employ\nacknowledgment messages (discussed in Section 4.4), returned\nin the same way as a normal message.\nWe have also adapted the concepts of durable and non\ndurable subscriptions for ad-hoc settings. In fixed platforms,\ndurable subscriptions are maintained during the\ndisconnections of the clients, whether these are intentional or are the\nresult of failures. In traditional systems, while a durable\nsubscriber is disconnected from the server, it is responsible\nfor storing messages. When the durable subscriber\nreconnects, the server sends it all unexpired messages. The\nproblem is that, in our scenario, disconnections are the norm\n1\nIn theory, it is not possible to send a message to a peer that\nhas never been reachable in the past, since there can be no\nentry present in the registry. However, to overcome this\npossible limitation, we provide a primitive through which\ninformation can be added to the registry without using the\nnormal channels.\n123 Middleware 2004 Companion\nrather than the exception. In other words, we cannot\nconsider disconnections as failures. For these reasons, we adopt\na slightly different semantics. With respect to durable\nsubscriptions, if a subscriber becomes disconnected,\nnotifications are not stored but are sent using the epidemic\nprotocol rather than the synchronous protocol. In other words,\ndurable notifications remain valid during the possible\ndisconnections of the subscriber.\nOn the other hand, if a non-durable subscriber becomes\ndisconnected, its subscription is deleted; in other words,\nduring disconnections, notifications are not sent using the\nepidemic protocol but exploit only the synchronous protocol. If\nthe topic becomes accessible to this host again, it must make\nanother subscription in order to receive the notifications.\nUnsubscription messages are delivered in the same way\nas are subscription messages. It is important to note that\ndurable subscribers have explicitly to unsubscribe from a\ntopic in order to stop the notification process; however, all\ndurable subscriptions have a predefined expiration time in\norder to cope with the cases of subscribers that do not meet\nagain because of their movements or failures. This feature\nis clearly provided to limit the number of the unnecessary\nmessages sent around the network.\n4.2 Message Delivery using Epidemic Routing\nIn this section, we examine one possible mechanism that\nwill allow the delivery of messages in a partially connected\nnetwork. The mechanism we discuss is intended for the\npurposes of demonstrating feasibility; more efficient\ncommunication mechanisms for this environment are themselves\ncomplex, and are the subject of another paper [13].\nThe asynchronous message delivery described above is\nbased on a typical pure epidemic-style routing protocol [16].\nA message that needs to be sent is replicated on each host in\nreach. In this way, copies of the messages are quickly spread\nthrough connected networks, like an infection. If a host\nbecomes connected to another cloud of mobile nodes, during\nits movement, the message spreads through this collection\nof hosts. Epidemic-style replication of data and messages\nhas been exploited in the past in many fields starting with\nthe distributed database systems area [2].\nWithin epidemic routing, each host maintains a buffer\ncontaining the messages that it has created and the replicas\nof the messages generated by the other hosts. To improve\nthe performance, a hash-table indexes the content of the\nbuffer. When two hosts connect, the host with the smaller\nidentifier initiates a so-called anti-entropy session, sending\na list containing the unique identifiers of the messages that\nit currently stores. The other host evaluates this list and\nsends back a list containing the identifiers it is storing that\nare not present in the other host, together with the messages\nthat the other does not have. The host that has started the\nsession receives the list and, in the same way, sends the\nmessages that are not present in the other host. Should buffer\noverflow occur, messages are dropped.\nThe reliability offered by this protocol is typically best\neffort, since there is no guarantee that a message will\neventually be delivered to its recipient. Clearly, the delivery ratio\nof the protocol increases proportionally to the maximum\nallowed delay time and the buffer size in each host (interesting\nsimulation results may be found in [16]).\n4.3 Adaptation of the JMS Message Model\nIn this section, we will analyse the aspects of our\nadaptation of the specification related to the so-called JMS Message\nModel [5]. According to this, JMS messages are\ncharacterised by some properties defined using the header field,\nwhich contains values that are used by both clients and\nproviders for their delivery. The aspects discussed in the\nremainder of this section are valid for both models (point to\npoint and publish-subscribe).\nA JMS message can be persistent or non-persistent.\nAccording to the JMS specification, persistent messages must\nbe delivered with a higher degree of reliability than the\nnonpersistent ones. However, it is worth noting that it is not\npossible to ensure once-and-only-once reliability for\npersistent messages as defined in the specification, since, as we\ndiscussed in the previous subsection, the underlying epidemic\nprotocol can guarantee only best-effort delivery. However,\nclients maintain a list of the identifiers of the recently\nreceived messages to avoid the delivery of message duplicates.\nIn other words, we provide the applications with\nat-mostonce reliability for both types of messages.\nIn order to implement different levels of reliability, EMMA\ntreats persistent and non-persistent messages differently,\nduring the execution of the anti-entropy epidemic protocol. Since\nthe message buffer space is limited, persistent messages are\npreferentially replicated using the available free space. If\nthis is insufficient and non-persistent messages are present\nin the buffer, these are replaced. Only the successful\ndeliveries of the persistent messages are notified to the senders.\nAccording to the JMS specification, it is possible to assign\na priority to each message. The messages with higher\npriorities are delivered in a preferential way. As discussed above,\npersistent messages are prioritised above the non-persistent\nones. Further selection is based on their priorities. Messages\nwith higher priorities are treated in a preferential way. In\nfact, if there is not enough space to replicate all the\npersistent messages, a mechanism based on priorities is used to\ndelete and replicate non-persistent messages (and, if\nnecessary, persistent messages).\nMessages are deleted from the buffers using the expiration\ntime value that can be set by senders. This is a way to free\nspace in the buffers (one preferentially deletes older\nmessages in cases of conflict); to eliminate stale replicas in the\nsystem; and to limit the time for which destinations must\nhold message identifiers to dispose of duplicates.\n4.4 Reliability and Acknowledgment\nMechanisms\nAs already discussed, at-most-once message delivery is the\nbest that can be achieved in terms of delivery semantics in\npartially connected ad-hoc settings. However, it is\npossible to improve the reliability of the system with efficient\nacknowledgment mechanisms. EMMA provides a\nmechanism for failure notification to applications if the\nacknowledgment is not received within a given timeout (that can\nbe configured by application developers). This mechanism\nis the one that distinguishes the delivery of persistent and\nnon-persistent messages in our JMS implementation: the\ndeliveries of the former are notified to the senders, whereas\nthe latter are not.\nWe use acknowledgment messages not only to inform senders\nabout the successful delivery of messages but also to delete\nthe replicas of the delivered messages that are still present\nin the network. Each host maintains a list of the messages\nMiddleware for Pervasive and ad-hoc Computing 124\nsuccessfully delivered that is updated as part of the normal\nprocess of information exchange between the hosts. The lists\nare exchanged during the first steps of the anti-entropic\nepidemic protocol with a certain predefined frequency. In the\ncase of messages with multiple recipients, a list of the actual\nrecipients is also stored. When a host receives the list, it\nchecks its message buffer and updates it according to the\nfollowing rules: (1) if a message has a single recipient and\nit has been delivered, it is deleted from the buffer; (2) if a\nmessage has multiple recipients, the identifiers of the\ndelivered hosts are deleted from the associated list of recipients.\nIf the resulting length of the list of recipients is zero, the\nmessage is deleted from the buffer.\nThese lists have, clearly, finite dimensions and are\nimplemented as circular queues. This simple mechanism, together\nwith the use of expiration timestamps, guarantees that the\nold acknowledgment notifications are deleted from the\nsystem after a limited period of time.\nIn order to improve the reliability of EMMA, a design\nmechanism for intelligent replication of queues and topics\nbased on the context information could be developed.\nHowever this is not yet part of the current architecture of EMMA.\n5. IMPLEMENTATION AND PRELIMINARY\nEVALUATION\nWe implemented a prototype of our platform using the\nJ2ME Personal Profile. The size of the executable is about\n250KB including the JMS 1.1 jar file; this is a perfectly\nacceptable figure given the available memory of the current\nmobile devices on the market. We tested our prototype on\nHP IPaq PDAs running Linux, interconnected with\nWaveLan, and on a number of laptops with the same network\ninterface.\nWe also evaluated the middleware platform using the\nOMNET++ discrete event simulator [17] in order to explore a\nrange of mobile scenarios that incorporated a more realistic\nnumber of hosts than was achievable experimentally. More\nspecifically, we assessed the performance of the system in\nterms of delivery ratio and average delay, varying the\ndensity of population and the buffer size, and using persistent\nand non-persistent messages with different priorities.\nThe simulation results show that the EMMA\"s\nperformance, in terms of delivery ratio and delay of persistent\nmessages with higher priorities, is good. In general, it is\nevident that the delivery ratio is strongly related to the\ncorrect dimensioning of the buffers to the maximum acceptable\ndelay. Moreover, the epidemic algorithms are able to\nguarantee a high delivery ratio if one evaluates performance over\na time interval sufficient for the dissemination of the replicas\nof messages (i.e., the infection spreading) in a large portion\nof the ad-hoc network.\nOne consequence of the dimensioning problem is that\nscalability may be seriously impacted in peer-to-peer\nmiddleware for mobile computing due to the resource poverty of\nthe devices (limited memory to store temporarily messages)\nand the number of possible interconnections in ad-hoc\nsettings. What is worse is that common forms of commercial\nand social organisation (six degrees of separation) mean that\neven modest TTL values on messages will lead to widespread\nflooding of epidemic messages. This problem arises because\nof the lack of intelligence in the epidemic protocol, and can\nbe addressed by selecting carrier nodes for messages with\ngreater care. The details of this process are, however,\noutside the scope of this paper (but may be found in [13]) and do\nnot affect the foundation on which the EMMA middleware\nis based: the ability to deliver messages asynchronously.\n6. CRITICAL VIEW OF THE STATE OF\nTHE ART\nThe design of middleware platforms for mobile\ncomputing requires researchers to answer new and fundamentally\ndifferent questions; simply assuming the presence of wired\nportions of the network on which centralised functionality\ncan reside is not generalisable. Thus, it is necessary to\ninvestigate novel design principles and to devise architectural\npatterns that differ from those traditionally exploited in the\ndesign of middleware for fixed systems.\nAs an example, consider the recent cross-layering trend in\nad-hoc networking [1]. This is a way of re-thinking software\nsystems design, explicitly abandoning the classical forms of\nlayering, since, although this separation of concerns afford\nportability, it does so at the expense of potential efficiency\ngains. We believe that it is possible to view our approach\nas an instance of cross-layering. In fact, we have added the\nepidemic network protocol at middleware level and, at the\nsame time, we have used the existing synchronous network\nprotocol if present both in delivering messages (traditional\nlayering) and in informing the middleware about when\nmessages may be delivered by revealing details of the forwarding\ntables (layer violation). For this reason, we prefer to\nconsider them jointly as the communication layer of our\nplatform together providing more efficient message delivery.\nAnother interesting aspect is the exploitation of context\nand system information to improve the performance of\nmobile middleware platforms. Again, as a result of adopting\na cross-layering methodology, we are able to build systems\nthat gather information from the underlying operating\nsystem and communication components in order to allow for\nadaptation of behaviour. We can summarise this conceptual\ndesign approach by saying that middleware platforms must\nbe not only context-aware (i.e., they should be able to\nextract and analyse information from the surrounding context)\nbut also system-aware (i.e., they should be able to gather\ninformation from the software and hardware components of\nthe mobile system).\nA number of middleware systems have been developed to\nsupport ad-hoc networking with the use of asynchronous\ncommunication (such as LIME, XMIDDLE, STEAM [11]).\nIn particular, the STEAM platform is an interesting\nexample of event-based middleware for ad-hoc networks,\nproviding location-aware message delivery and an effective solution\nfor event filtering.\nA discussion of JMS, and its mobile realisation, has\nalready been conducted in Sections 4 and 2. The Swiss\ncompany Softwired has developed the first JMS middleware for\nmobile computing, called iBus Mobile [10]. The main\ncomponents of this typically infrastructure-based architecture\nare the JMS provider, the so-called mobile JMS gateway,\nwhich is deployed on a fixed host and a lightweight JMS\nclient library. The gateway is used for the communication\nbetween the application server and mobile hosts. The\ngateway is seen by the JMS provider as a normal JMS client. The\nJMS provider can be any JMS-enabled application server,\nsuch as BEA Weblogic. Pronto [19] is an example of\nmid125 Middleware 2004 Companion\ndleware system based on messaging that is specifically\ndesigned for mobile environments. The platform is composed\nof three classes of components: mobile clients implementing\nthe JMS specification, gateways that control traffic,\nguaranteeing efficiency and possible user customizations using\ndifferent plug-ins and JMS servers. Different configurations\nof these components are possible; with respect to mobile ad\nhoc networks applications, the most interesting is\nServerless JMS. The aim of this configuration is to adapt JMS\nto a decentralized model. The publish-subscribe model\nexploits the efficiency and the scalability of the underlying IP\nmulticast protocol. Unreliable and reliable message delivery\nservices are provided: reliability is provided through a\nnegative acknowledgment-based protocol. Pronto represents a\ngood solution for infrastructure-based mobile networks but\nit does not adequately target ad-hoc settings, since mobile\nnodes rely on fixed servers for the exchange of messages.\nOther MOM implemented for mobile environments exist;\nhowever, they are usually straightforward extensions of\nexisting middleware [8]. The only implementation of MOM\nspecifically designed for mobile ad-hoc networks was\ndeveloped at the University of Newcastle [18]. This work is again\na JMS adaptation; the focus of that implementation is on\ngroup communication and the use of application level\nrouting algorithms for topic delivery of messages. However, there\nare a number of differences in the focus of our work. The\nimportance that we attribute to disconnections makes\npersistence a vital requirement for any middleware that needs\nto be used in mobile ad-hoc networks. The authors of [18]\nsignal persistence as possible future work, not considering\nthe fact that routing a message to a non-connected host will\nresult in delivery failure. This is a remarkable limitation in\nmobile settings where unpredictable disconnections are the\nnorm rather than the exception.\n7. ROADMAP AND CONCLUSIONS\nAsynchronous communication is a useful communication\nparadigm for mobile ad-hoc networks, as hosts are allowed to\ncome, go and pick up messages when convenient, also taking\naccount of their resource availability (e.g., power,\nconnectivity levels). In this paper we have described the state of the\nart in terms of MOM for mobile systems. We have also\nshown a proof of concept adaptation of JMS to the extreme\nscenario of partially connected mobile ad-hoc networks.\nWe have described and discussed the characteristics and\ndifferences of our solution with respect to traditional JMS\nimplementations and the existing adaptations for mobile\nsettings. However, trade-offs between application-level routing\nand resource usage should also be investigated, as mobile\ndevices are commonly power/resource scarce. A key\nlimitation of this work is the poorly performing epidemic\nalgorithm and an important advance in the practicability of\nthis work requires an algorithm that better balances the\nneeds of efficiency and message delivery probability. We\nare currently working on algorithms and protocols that,\nexploiting probabilistic and statistical techniques on the basis\nof small amounts of exchanged information, are able to\nimprove considerably the efficiency in terms of resources\n(memory, bandwidth, etc) and the reliability of our middleware\nplatform [13].\nOne futuristic research development, which may take these\nideas of adaptation of messaging middleware for mobile\nenvironments further is the introduction of more mobility\noriented communication extensions, for instance the support\nof geocast (i.e., the ability to send messages to specific\ngeographical areas).\n8. REFERENCES\n[1] M. Conti, G. Maselli, G. Turi, and S. Giordano.\nCross-layering in Mobile ad-hoc Network Design. IEEE\nComputer, 37(2):48-51, February 2004.\n[2] A. Demers, D. Greene, C. Hauser, W. Irish, J. Larson,\nS. Shenker, H. Sturgis, D. Swinehart, and D. Terry.\nEpidemic Algorithms for Replicated Database\nMaintenance. In Sixth Symposium on Principles of\nDistributed Computing, pages 1-12, August 1987.\n[3] A. Doria, M. Uden, and D. P. Pandey. Providing\nconnectivity to the Saami nomadic community. In\nProceedings of the Second International Conference on\nOpen Collaborative Design for Sustainable Innovation,\nDecember 2002.\n[4] M. Haahr, R. Cunningham, and V. Cahill. Supporting\nCORBA applications in a Mobile Environment. In 5th\nInternational Conference on Mobile Computing and\nNetworking (MOBICOM99), pages 36-47. ACM, August\n1999.\n[5] M. Hapner, R. Burridge, R. Sharma, J. Fialli, and\nK. Stout. Java Message Service Specification Version 1.1.\nSun Microsystems, Inc., April 2002.\nhttp://java.sun.com/products/jms/.\n[6] J. Hart. WebSphere MQ: Connecting your applications\nwithout complex programming. IBM WebSphere Software\nWhite Papers, 2003.\n[7] S. Hayward and M. Pezzini. Marrying Middleware and\nMobile Computing. Gartner Group Research Report,\nSeptember 2001.\n[8] IBM. WebSphere MQ EveryPlace Version 2.0, November\n2002. http://www-3.ibm.com/software/integration/wmqe/.\n[9] ITU. Connecting remote communities. Documents of the\nWorld Summit on Information Society, 2003.\nhttp://www.itu.int/osg/spu/wsis-themes.\n[10] S. Maffeis. Introducing Wireless JMS. Softwired AG,\nwww.sofwired-inc.com, 2002.\n[11] C. Mascolo, L. Capra, and W. Emmerich. Middleware for\nMobile Computing. In E. Gregori, G. Anastasi, and\nS. Basagni, editors, Advanced Lectures on Networking,\nvolume 2497 of Lecture Notes in Computer Science, pages\n20-58. Springer Verlag, 2002.\n[12] Microsoft. Microsoft Message Queuing (MSMQ) Version\n2.0 Documentation.\n[13] M. Musolesi, S. Hailes, and C. Mascolo. Adaptive routing\nfor intermittently connected mobile ad-hoc networks.\nTechnical report, UCL-CS Research Note, July 2004.\nSubmitted for Publication.\n[14] Sun Microsystems. Java Naming and Directory Interface\n(JNDI) Documentation Version 1.2. 2003.\nhttp://java.sun.com/products/jndi/.\n[15] Sun Microsystems. Jini Specification Version 2.0, 2003.\nhttp://java.sun.com/products/jini/.\n[16] A. Vahdat and D. Becker. Epidemic routing for Partially\nConnected ad-hoc Networks. Technical Report CS-2000-06,\nDepartment of Computer Science, Duke University, 2000.\n[17] A. Vargas. The OMNeT++ discrete event simulation\nsystem. In Proceedings of the European Simulation\nMulticonference (ESM\"2001), Prague, June 2001.\n[18] E. Vollset, D. Ingham, and P. Ezhilchelvan. JMS on Mobile\nad-hoc Networks. In Personal Wireless Communications\n(PWC), pages 40-52, Venice, September 2003.\n[19] E. Yoneki and J. Bacon. Pronto: Mobilegateway with\npublish-subscribe paradigm over wireless network.\nTechnical Report 559, University of Cambridge, Computer\nLaboratory, February 2003.\nMiddleware for Pervasive and ad-hoc Computing 126", "keywords": "mobile ad-hoc network;asynchronous messaging middleware;context awareness;epidemic protocol;message-oriented middleware;message orient middleware;asynchronous communication;middleware for mobile computing;mobile ad-hoc environment;cross-layering;group communication;application level routing;java messaging service;epidemic messaging middleware"}
{"name": "train_C-75", "title": "Composition of a DIDS by Integrating Heterogeneous IDSs on Grids", "abstract": "This paper considers the composition of a DIDS (Distributed Intrusion Detection System) by integrating heterogeneous IDSs (Intrusion Detection Systems). A Grid middleware is used for this integration. In addition, an architecture for this integration is proposed and validated through simulation.", "fulltext": "1. INTRODUCTION\nSolutions for integrating heterogeneous IDSs (Intrusion Detection\nSystems) have been proposed by several groups [6],[7],[11],[2].\nSome reasons for integrating IDSs are described by the IDWG\n(Intrusion Detection Working Group) from the IETF (Internet\nEngineering Task Force) [12] as follows:\n\u2022 Many IDSs available in the market have strong and weak\npoints, which generally make necessary the deployment of\nmore than one IDS to provided an adequate solution.\n\u2022 Attacks and intrusions generally originate from multiple\nnetworks spanning several administrative domains; these\ndomains usually utilize different IDSs. The integration of\nIDSs is then needed to correlate information from multiple\nnetworks to allow the identification of distributed attacks and\nor intrusions.\n\u2022 The interoperability/integration of different IDS components\nwould benefit the research on intrusion detection and speed\nup the deployment of IDSs as commercial products.\nDIDSs (Distributed Intrusion Detection Systems) therefore started\nto emerge in early 90s [9] to allow the correlation of intrusion\ninformation from multiple hosts, networks or domains to detect\ndistributed attacks. Research on DIDSs has then received much\ninterest, mainly because centralised IDSs are not able to provide\nthe information needed to prevent such attacks [13].\nHowever, the realization of a DIDS requires a high degree of\ncoordination. Computational Grids are appealing as they enable\nthe development of distributed application and coordination in a\ndistributed environment. Grid computing aims to enable\ncoordinate resource sharing in dynamic groups of individuals\nand/or organizations. Moreover, Grid middleware provides means\nfor secure access, management and allocation of remote resources;\nresource information services; and protocols and mechanisms for\ntransfer of data [4].\nAccording to Foster et al. [4], Grids can be viewed as a set of\naggregate services defined by the resources that they share. OGSA\n(Open Grid Service Architecture) provides the foundation for this\nservice orientation in computational Grids. The services in OGSA\nare specified through well-defined, open, extensible and\nplatformindependent interfaces, which enable the development of\ninteroperable applications.\nThis article proposes a model for integration of IDSs by using\ncomputational Grids. The proposed model enables heterogeneous\nIDSs to work in a cooperative way; this integration is termed\nDIDSoG (Distributed Intrusion Detection System on Grid). Each\nof the integrated IDSs is viewed by others as a resource accessed\nthrough the services that it exposes. A Grid middleware provides\nseveral features for the realization of a DIDSoG, including [3]:\ndecentralized coordination of resources; use of standard protocols\nand interfaces; and the delivery of optimized QoS (Quality of\nService).\nThe service oriented architecture followed by Grids (OGSA)\nallows the definition of interfaces that are adaptable to different\nplatforms. Different implementations can be encapsulated by a\nservice interface; this virtualisation allows the consistent access to\nresources in heterogeneous environments [3]. The virtualisation of\nthe environment through service interfaces allows the use of\nservices without the knowledge of how they are actually\nimplemented. This characteristic is important for the integration\nof IDSs as the same service interfaces can be exposed by different\nIDSs.\nGrid middleware can thus be used to implement a great variety of\nservices. Some functions provided by Grid middleware are [3]: (i)\ndata management services, including access services, replication,\nand localisation; (ii) workflow services that implement coordinate\nexecution of multiple applications on multiple resources; (iii)\nauditing services that perform the detection of frauds or\nintrusions; (iv) monitoring services which implement the\ndiscovery of sensors in a distributed environment and generate\nalerts under determined conditions; (v) services for identification\nof problems in a distributed environment, which implement the\ncorrelation of information from disparate and distributed logs.\nThese services are important for the implementation of a DIDSoG.\nA DIDS needs services for the location of and access to\ndistributed data from different IDSs. Auditing and monitoring\nservices take care of the proper needs of the DIDSs such as:\nsecure storage, data analysis to detect intrusions, discovery of\ndistributed sensors, and sending of alerts. The correlation of\ndistributed logs is also relevant because the detection of\ndistributed attacks depends on the correlation of the alert\ninformation generated by the different IDSs that compose the\nDIDSoG.\nThe next sections of this article are organized as follows. Section\n2 presents related work. The proposed model is presented in\nSection 3. Section 4 describes the development and a case study.\nResults and discussion are presented in Section 5. Conclusions\nand future work are discussed in Section 6.\n2. RELATED WORK\nDIDMA [5] is a flexible, scalable, reliable, and\nplatformindependent DIDS. DIDMA architecture allows distributed\nanalysis of events and can be easily extended by developing new\nagents. However, the integration with existing IDSs and the\ndevelopment of security components are presented as future work\n[5]. The extensibility of DIDS DIDMA and the integration with\nother IDSs are goals pursued by DIDSoG. The flexibility,\nscalability, platform independence, reliability and security\ncomponents discussed in [5] are achieved in DIDSoG by using a\nGrid platform.\nMore efficient techniques for analysis of great amounts of data in\nwide scale networks based on clustering and applicable to DIDSs\nare presented in [13]. The integration of heterogeneous IDSs to\nincrease the variety of intrusion detection techniques in the\nenvironment is mentioned as future work [13] DIDSoG thus aims\nat integrating heterogeneous IDSs [13].\nRef. [10] presents a hierarchical architecture for a DIDS;\ninformation is collected, aggregated, correlated and analysed as it\nis sent up in the hierarchy. The architecture comprises of several\ncomponents for: monitoring, correlation, intrusion detection by\nstatistics, detection by signatures and answers. Components in the\nsame level of the hierarchy cooperate with one another. The\nintegration proposed by DIDSoG also follows a hierarchical\narchitecture. Each IDS integrated to the DIDSoG offers\nfunctionalities at a given level of the hierarchy and requests\nfunctionalities from IDSs from another level. The hierarchy\npresented in [10] integrates homogeneous IDSs whereas the\nhierarchical architecture of DIDSoG integrates heterogeneous\nIDSs.\nThere are proposals on integrating computational Grids and IDSs\n[6],[7],[11],[2]. Ref. [6] and [7] propose the use of Globus\nToolkit for intrusion detection, especially for DoS (Denial of\nService) and DDoS (Distributed Denial of Service) attacks;\nGlobus is used due to the need to process great amounts of data to\ndetect these kinds of attack. A two-phase processing architecture\nis presented. The first phase aims at the detection of momentary\nattacks, while the second phase is concerned with chronic or\nperennial attacks.\nTraditional IDSs or DIDSs are generally coordinated by a central\npoint; a characteristic that leaves them prone to attacks. Leu et al.\n[6] point out that IDSs developed upon Grids platforms are less\nvulnerable to attacks because of the distribution provided for such\nplatforms. Leu et al. [6],[7] have used tools to generate several\ntypes of attacks - including TCP, ICMP and UDP flooding - and\nhave demonstrated through experimental results the advantages of\napplying computational Grids to IDSs.\nThis work proposes the development of a DIDS upon a Grid\nplatform. However, the resulting DIDS integrates heterogeneous\nIDSs whereas the DIDSs upon Grids presented by Leu et al.\n[6][7] do not consider the integration of heterogeneous IDSs. The\nprocessing in phases [6][7] is also contemplated by DIDSoG,\nwhich is enabled by the specification of several levels of\nprocessing allowed by the integration of heterogeneous IDSs.\nThe DIDS GIDA (Grid Intrusion Detection Architecture) targets\nat the detection of intrusions in a Grid environment [11]. GridSim\nGrid simulator was used for the validation of DIDS GIDA.\nHomogeneous resources were used to simplify the development\n[11]. However, the possibility of applying heterogeneous\ndetection systems is left for future work\nAnother DIDS for Grids is presented by Choon and Samsudim\n[2]. Scenarios demonstrating how a DIDS can execute on a Grid\nenvironment are presented.\nDIDSoG does not aim at detecting intrusions in a Grid\nenvironment. In contrast, DIDSoG uses the Grid to compose a\nDIDS by integrating specific IDSs; the resulting DIDS could\nhowever be used to identify attacks in a Grid environment. Local\nand distributed attacks can be detected through the integration of\ntraditional IDSs while attacks particular to Grids can be detected\nthrough the integration of Grid IDSs.\n3. THE PROPOSED MODEL\nDIDSoG presents a hierarchy of intrusion detection services; this\nhierarchy is organized through a two-dimensional vector defined\nby Scope:Complexity. The IDSs composing DIDSoG can be\norganized in different levels of scope or complexity, depending on\nits functionalities, the topology of the target environment and\nexpected results.\nFigure 1 presents a DIDSoG composed by different intrusion\ndetection services (i.e. data gathering, data aggregation, data\ncorrelation, analysis, intrusion response and management)\nprovided by different IDSs. The information flow and the\nrelationship between the levels of scope and complexity are\npresented in this figure.\nInformation about the environment (host, network or application)\nis collected by Sensors located both in user 1\"s and user 2\"s\ncomputers in domain 1. The information is sent to both simple\nAnalysers that act on the information from a single host (level\n1:1), and to aggregation and correlation services that act on\ninformation from multiple hosts from the same domain (level 2:1).\nSimple Analysers in the first scope level send the information to\nmore complex Analysers in the next levels of complexity (level 1:\nN). When an Analyser detects an intrusion, it communicates with\nCountermeasure and Monitoring services registered to its scope.\nAn Analyser can invoke a Countermeasure service that replies to a\ndetected attack, or informs a Monitoring service about the\nongoing attack, so the administrator can act accordingly.\nAggregation and correlation resources in the second scope receive\ninformation from Sensors from different users\" computers (user\n1\"s and user 2\"s) in the domain 1. These resources process the\nreceived information and send it to the analysis resources\nregistered to the first level of complexity in the second scope\n(level 2:1). The information is also sent to the aggregation and\ncorrelation resources registered in the first level of complexity in\nthe next scope (level 3:1).\nUser 1\nDomain 1\nAnalysers\nLevel 1:1\nLocal\nSensors\nAnalysers\nLevel 1:N\nAggreg.\nCorrelation\nLevel 2:1\nUser 2\nDomain 1\nLocal\nSensors\nAnalysers\nLevel 2:1\nAnalysers\nLevel 2:N\nAggreg.\nCorrelation\nLevel 3:1\nDomain 2\nMonitor\nLevel 1\nMonitor\nLevel 2\nAnalysers\nLevel 3:1\nAnalysers\nLevel 3:N\nMonitor\nLevel 3\nResponse\nLevel 1\nResponse\nLevel 2\nResponse\nLevel 3\nFig. 1. How DIDSoG works.\nThe analysis resources in the second scope act like the analysis\nresources in the first scope, directing the information to a more\ncomplex analysis resource and putting the Countermeasure and\nMonitoring resources in action in case of detected attacks.\nAggregation and correlation resources in the third scope receive\ninformation from domains 1 and 2. These resources then carry out\nthe aggregation and correlation of the information from different\ndomains and send it to the analysis resources in the first level of\ncomplexity in the third scope (level 3:1). The information could\nalso be sent to the aggregate service in the next scope in case of\nany resources registered to such level.\nThe analysis resources in the third scope act similar to the analysis\nresources in the first and second scopes, except that the analysis\nresources in the third scope act on information from multiple\ndomains.\nThe functionalities of the registered resources in each of the\nscopes and complexity level can vary from one environment to\nanother. The model allows the development of N levels of scope\nand complexity.\nFigure 2 presents the architecture of a resource participating in the\nDIDSoG. Initially, the resource registers itself to GIS (Grid\nInformation Service) so other participating resources can query\nthe services provided. After registering itself, the resource\nrequests information about other intrusion detection resources\nregistered to the GIS.\nA given resource of DIDSoG interacts with other resources, by\nreceiving data from the Source Resources, processing it, and\nsending the results to the Destination Resources, therefore\nforming a grid of intrusion detection resources.\nGrid Resource\nBaseNative\nIDS\nGrid Origin Resources\nGrid Destination Resources\nGrid Information Service\nDescri\nptor\nConnec\ntor\nFig. 2. Architecture of a resource participating of the DIDSoG.\nA resource is made up of four components: Base, Connector,\nDescriptor and Native IDS. Native IDS corresponds to the IDS\nbeing integrated to the DIDSoG. This component process the data\nreceived from the Origin Resources and generates new data to be\nsent to the Destination Resources. A Native IDS component can\nbe any tool processes information related to intrusion detection,\nincluding analysis, data gathering, data aggregation, data\ncorrelation, intrusion response or management.\nThe Descriptor is responsible for the information that identifies a\nresource and its respective Destination Resources in the DIDSoG.\nFigure 3 presents the class diagram of the stored information by\nthe Descriptor. The ResourceDescriptor class has Feature, Level,\nDataType and Target Resources type members. Feature class\nrepresents the functionalities that a resource has. Type, name and\nversion attributes refer to the functions offered by the Native IDS\ncomponent, its name and version, respectively. Level class\nidentifies the level of target and complexity in which the resource\nacts. DataType class represents the data format that the resource\naccepts to receive. DataType class is specialized by classes Text,\nXML and Binary. Class XML contains the DTDFile attribute to\nspecify the DTD file that validates the received XML.\n-ident\n-version\n-description\nResourceDescriptor\n-featureType\n-name\n-version\nFeature\n1\n1\n-type\n-version\nDataType\n-escope\n-complex\nLevel\n1\n1\nText Binary\n-DTDFile\nXML\n1\n1\nTargetResources\n1\n1 10..*\n-featureType\nResource11\n1\n1\nFig. 3. Class Diagram of the Descriptor component.\nTargetResources class represents the features of the Destination\nResources of a determined resource. This class aggregates\nResource. The Resource class identifies the characteristics of a\nDestination Resource. This identification is made through the\nfeatureType attribute and the Level and DataType classes.\nA given resource analyses the information from Descriptors from\nother resources, and compares this information with the\ninformation specified in TargetResources to know to which\nresources to send the results of its processing.\nThe Base component is responsible for the communication of a\nresource with other resources of the DIDSoG and with the Grid\nInformation Service. It is this component that registers the\nresource and the queries other resources in the GIS.\nThe Connector component is the link between Base and Native\nIDS. The information that Base receives from Origin Resources is\npassed to Connector component. The Connector component\nperforms the necessary changes in the data so that it is understood\nby Native IDS, and sends this data to Native IDS for processing.\nThe Connector component also has the responsibility of collecting\nthe information processed by Native IDS, and making the\nnecessary changes so the information can pass through the\nDIDSoG again. After these changes, Connector sends the\ninformation to the Base, which in turn sends it to the Destination\nResources in accordance with the specifications of the Descriptor\ncomponent.\n4. IMPLEMENTATION\nWe have used GridSim Toolkit 3 [1] for development and\nevaluation of the proposed model. We have used and extended\nGridSim features to model and simulate the resources and\ncomponents of DIDSoG.\nFigure 4 presents the Class diagram of the simulated DIDSoG.\nThe Simulation_DIDSoG class starts the simulation components.\nThe Simulation_User class represents a user of DIDSoG. This\nclass\" function is to initiate the processing of a resource Sensor,\nfrom where the gathered information will be sent to other\nresources. DIDSoG_GIS keeps a registry of the DIDSoG\nresources.The DIDSoG_BaseResource class implements the Base\ncomponent (see Figure 2). DIDSoG_BaseResource interacts with\nDIDSoG_Descriptor class, which represents the Descriptor\ncomponent. The DIDSoG_Descriptor class is created from an\nXML file that specifies a resource descriptor (see Figure 3).\nDIDSoG_BaseResource\nDIDSoG_Descriptor\n11\nDIDSoG_GIS\nSimulation_User\nSimulation_DIDSoG\n1\n*1*\n1\n1\nGridInformationService\nGridSim GridResource\nFig. 4. Class Diagram of the simulatated DIDSoG.\nA Connector component must be developed for each Native IDS\nintegrated to DIDSoG. The Connector component is implemented\nby creating a class derived from DIDSoG_BaseResource. The new\nclass will implement new functionalities in accordance with the\nneeds of the corresponding Native IDS.\nIn the simulation environment, data collection resources, analysis,\naggregation/correlation and generation of answers were\nintegrated. Classes were developed to simulate the processing of\neach Native IDS components associated to the resources. For each\nsimulated Native IDS a class derived from\nDIDSoG_BaseResource was developed. This class corresponds to\nthe Connector component of the Native IDS and aims at the\nintegrating the IDS to DIDSoG.\nA XML file describing each of the integrated resources is chosen\nby using the Connector component. The resulting relationship\nbetween the resources integrated to the DIDSoG, in accordance\nwith the specification of its respective descriptors, is presented in\nFigure 5.\nThe Sensor_1 and Sensor_2 resources generate simulated data in\nthe TCPDump [8] format. The generated data is directed to\nAnalyser_1 and Aggreg_Corr_1 resources, in the case of\nSensor_1, and to Aggreg_Corr_1 in the case of Sensor_2,\naccording to the specification of their descriptors.\nUser_1\nAnalyser_\n1\nLevel 1:1\nSensor_1\nAggreg_\nCorr_1\nLevel 2:1\nUser_2\nSensor_2\nAnalyser_2\nLevel 2:1\nAnalyser_3\nLevel 2:2\nTCPDump\nTCPDump\nTCPDumpAg\nTCPDumpAg\nIDMEF\nIDMEF\nIDMEF\nTCPDump\n\nCountermeasure_1\nLevel 1\n\nCountermeasure_2\nLevel 2\nFig. 5. Flow of the execution of the simulation.\nThe Native IDS of Analyser_1 generates alerts for any attempt of\nconnection to port 23. The data received from Analyser_1 had\npresented such features, generating an IDMEF (Intrusion\nDetection Message Exchange Format) alert [14]. The generated\nalert was sent to Countermeasure_1 resource, where a warning\nwas dispatched to the administrator informing him of the alert\nreceived.\nThe Aggreg_Corr_1 resource received the information generated\nby sensors 1 and 2. Its processing activities consist in correlating\nthe source IP addresses with the received data. The resultant\ninformation of the processing of Aggreg_Corr_1 was directed to\nthe Analyser_2 resource.\nThe Native IDS component of the Analyser_2 generates alerts\nwhen a source tries to connect to the same port number of\nmultiple destinations. This situation is identified by the\nAnalyser_2 in the data received from Aggreg_Corr_1 and an alert\nin IDMEF format is then sent to the Countermeasures_2 resource.\nIn addition to generating alerts in IDMEF format, Analyser_2 also\ndirects the received data to the Analyser_3, in the level of\ncomplexity 2. The Native IDS component of Analyser_3\ngenerates alerts when the transmission of ICMP messages from a\ngiven source to multiple destinations is detected. This situation is\ndetected in the data received from Analyser_2, and an IDMEF\nalert is then sent to the Countermeasure_2 resource.\nThe Countermeasure_2 resource receives the alerts generated by\nanalysers 3 and 2, in accordance with the implementation of its\nNative IDS component. Warnings on alerts received are\ndispatched to the administrator.\nThe simulation carried out demonstrates how DIDSoG works.\nSimulated data was generated to be the input for a grid of\nintrusion detection systems composed by several distinct\nresources. The resources carry out tasks such as data collection,\naggregation and analysis, and generation of alerts and warnings in\nan integrated manner.\n5. EXPERIMENT RESULTS\nThe hierarchic organization of scope and complexity provides a\nhigh degree of flexibility to the model. The DIDSoG can be\nmodelled in accordance with the needs of each environment. The\ndescriptors define data flow desired for the resulting DIDS.\nEach Native IDS is integrated to the DIDSoG through a\nConnector component. The Connector component is also flexible\nin the DIDSoG. Adaptations, conversions of data types and\nauxiliary processes that Native IDSs need are provided by the\nConnector. Filters and generation of Specific logs for each Native\nIDS or environment can also be incorporated to the Connector.\nIf the integration of a new IDS to an environment already\nconfigured is desired, it is enough to develop the Connector for\nthe desired IDS and to specify the resource Descriptor. After the\nspecification of the Connector and the Descriptor the new IDS is\nintegrated to the DIDSoG.\nThrough the definition of scopes, resources can act on data of\ndifferent source groups. For example, scope 1 can be related to a\ngiven set of hosts, scope 2 to another set of hosts, while scope 3\ncan be related to hosts from scopes 1 and 2. Scopes can be defined\naccording to the needs of each environment.\nThe complexity levels allow the distribution of the processing\nbetween several resources inside the same scope. In an analysis\ntask, for example, the search for simple attacks can be made by\nresources of complexity 1, whereas the search for more complex\nattacks, that demands more time, can be performed by resources\nof complexity 2. With this, the analysis of the data is made by two\nresources.\nThe distinction between complexity levels can also be organized\nin order to integrate different techniques of intrusion detection.\nThe complexity level 1 could be defined for analyses based on\nsignatures, which are simpler techniques; the complexity level 2\nfor techniques based on behaviour, that require greater\ncomputational power; and the complexity level 3 for intrusion\ndetection in applications, where the techniques are more specific\nand depend on more data.\nThe division of scopes and the complexity levels make the\nprocessing of the data to be carried out in phases. No resource has\nfull knowledge about the complete data processing flow. Each\nresource only knows the results of its processing and the\ndestination to which it sends the results. Resources of higher\ncomplexity must be linked to resources of lower complexity.\nTherefore, the hierarchic structure of the DIDSoG is maintained,\nfacilitating its extension and integration with other domains of\nintrusion detection.\nBy carrying out a hierarchic relationship between the several\nchosen analysers for an environment, the sensor resource is not\noverloaded with the task to send the data to all the analysers. An\ninitial analyser will exist (complexity level 1) to which the sensor\nwill send its data, and this analyser will then direct the data to the\nnext step of the processing flow. Another feature of the\nhierarchical organization is the easy extension and integration\nwith other domains. If it is necessary to add a new host (sensor) to\nthe DIDSoG, it is enough to plug it to the first hierarchy of\nresources. If it is necessary to add a new analyser, it will be in the\nscope of several domains, it is enough to relate it to another\nresource of same scope.\nThe DIDSoG allows different levels to be managed by different\nentities. For example, the first scope can be managed by the local\nuser of a host. The second scope, comprising several hosts of a\ndomain can be managed by the administrator of the domain. A\nthird entity can be responsible for managing the security of\nseveral domains in a joint way. This entity can act in the scope 3\nindependently from others.\nWith the proposed model for integration of IDSs in Grids, the\ndifferent IDSs of an environment (or multiple IDSs integrated) act\nin a cooperative manner improving the intrusion detection\nservices, mainly in two aspects. First, the information from\nmultiple sources are analysed in an integrated way to search for\ndistributed attacks. This integration can be made under several\nscopes. Second, there is a great diversity of data aggregation\ntechniques, data correlation and analysis, and intrusion response\nthat can be applied to the same environment; these techniques can\nbe organized under several levels of complexity.\n6. CONCLUSION\nThe integration of heterogeneous IDSs is important. However, the\nincompatibility and diversity of IDS solutions make such\nintegration extremely difficult. This work thus proposed a model\nfor composition of DIDS by integrating existing IDSs on a\ncomputational Grid platform (DIDSoG). IDSs in DIDSoG are\nencapsulated as Grid services for intrusion detection. A\ncomputational Grid platform is used for the integration by\nproviding the basic requirements for communication, localization,\nresource sharing and security mechanisms.\nThe components of the architecture of the DIDSoG were\ndeveloped and evaluated using the GridSim Grid simulator.\nServices for communication and localization were used to carry\nout the integration between components of different resources.\nBased on the components of the architecture, several resources\nwere modelled forming a grid of intrusion detection. The\nsimulation demonstrated the usefulness of the proposed model.\nData from the sensor resources was read and this data was used to\nfeed other resources of DIDSoG.\nThe integration of distinct IDSs could be observed through the\nsimulated environment. Resources providing different intrusion\ndetection services were integrated (e.g. analysis, correlation,\naggregation and alert). The communication and localization\nservices provided by GridSim were used to integrate components\nof different resources. Various resources were modelled following\nthe architecture components forming a grid of intrusion detection.\nThe components of DIDSoG architecture have served as base for\nthe integration of the resources presented in the simulation.\nDuring the simulation, the different IDSs cooperated with one\nanother in a distributed manner; however, in a coordinated way\nwith an integrated view of the events, having, thus, the capability\nto detect distributed attacks. This capability demonstrates that the\nIDSs integrated have resulted in a DIDS.\nRelated work presents cooperation between components of a\nspecific DIDS. Some work focus on either the development of\nDIDSs on computational Grids or the application of IDSs to\ncomputational Grids. However, none deals with the integration of\nheterogeneous IDSs. In contrast, the proposed model developed\nand simulated in this work, can shed some light into the question\nof integration of heterogeneous IDSs.\nDIDSoG presents new research opportunities that we would like\nto pursue, including: deployment of the model in a more realistic\nenvironment such as a Grid; incorporation of new security\nservices; parallel analysis of data by Native IDSs in multiple\nhosts.\nIn addition to the integration of IDSs enabled by a grid\nmiddleware, the cooperation of heterogeneous IDSs can be\nviewed as an economic problem. IDSs from different\norganizations or administrative domains need incentives for\njoining a grid of intrusion detection services and for collaborating\nwith other IDSs. The development of distributed strategy proof\nmechanisms for integration of IDSs is a challenge that we would\nlike to tackle.\n7. REFERENCES\n[1] Sulistio, A.; Poduvaly, G.; Buyya, R; and Tham, CK,\nConstructing A Grid Simulation with Differentiated Network\nService Using GridSim, Proc. of the 6th International\nConference on Internet Computing (ICOMP'05), June 27-30,\n2005, Las Vegas, USA.\n[2] Choon, O. T.; Samsudim, A. Grid-based Intrusion Detection\nSystem. The 9th\nIEEE Asia-Pacific Conference\nCommunications, September 2003.\n[3] Foster, I.; Kesselman, C.; Tuecke, S. The Physiology of the\nGrid: An Open Grid Service Architecture for Distributed\nSystem Integration. Draft June 2002. Available at\nhttp://www.globus.org/research/papers/ogsa.pdf. Access Feb.\n2006.\n[4] Foster, Ian; Kesselman, Carl; Tuecke, Steven. The anatomy\nof the Grid: enabling scalable virtual organizations.\nInternational Journal of Supercomputer Applications, 2001.\n[5] Kannadiga, P.; Zulkernine, M. DIDMA: A Distributed\nIntrusion Detection System Using Mobile Agents.\nProceedings of the IEEE Sixth International Conference on\nSoftware Engineering, Artificial Intelligence, Networking\nand Parallel/Distributed Computing, May 2005.\n[6] Leu, Fang-Yie, et al. Integrating Grid with Intrusion\nDetection. Proceedings of 19th\nIEEE AINA\"05, March 2005.\n[7] Leu, Fang-Yie, et al. A Performance-Based Grid Intrusion\nDetection System. Proceedings of the 29th\nIEEE\nCOMPSAC\"05, July 2005.\n[8] McCanne, S.; Leres, C.; Jacobson, V.; TCPdump/Libpcap,\nhttp://www.tcpdump.org/, 1994.\n[9] Snapp, S. R. et al. DIDS (Distributed Intrusion Detection\nSystem) - Motivation, Architecture and An Early Prototype.\nProceeding of the Fifteenth IEEE National Computer\nSecurity Conference. Baltimore, MD, October 1992.\n[10] Sterne, D.; et al. A General Cooperative Intrusion Detection\nArchitecture for MANETs. Proceedings of the Third IEEE\nIWIA\"05, March 2005.\n[11] Tolba, M. F. ; et al. GIDA: Toward Enabling Grid Intrusion\nDetection Systems. 5th IEEE International Symposium on\nCluster Computing and the Grid, May 2005.\n[12] Wood, M. Intrusion Detection message exchange\nrequirements. Draft-ietf-idwg-requirements-10, October\n2002. Available at\nhttp://www.ietf.org/internet-drafts/draftietf-idwg-requirements-10.txt. Access March 2006.\n[13] Zhang, Yu-Fang; Xiong, Z.; Wang, X. Distributed Intrusion\nDetection Based on Clustering. Proceedings of IEEE\nInternational Conference Machine Learning and Cybernetics,\nAugust 2005.\n[14] Curry, D.; Debar, H. Intrusion Detection Message exchange\nformat data model and Extensible Markup Language (XML)\nDocument Type Definition. Draft-ietf-idwg-idmef-xml-10,\nMarch 2006. Available at\nhttp://www.ietf.org/internetdrafts/draft-ietf-idwg-idmef-xml-16.txt.", "keywords": "system integration;gridsim grid simulator;heterogeneous intrusion detection system;distributed intrusion detection system;grid middleware;intrusion detection system;grid service for intrusion detection;ids integration;grid;open grid service architecture;integration of ids;computational grid;grid intrusion detection architecture;intrusion detection service"}
{"name": "train_C-76", "title": "Assured Service Quality by Improved Fault Management Service-Oriented Event Correlation", "abstract": "The paradigm shift from device-oriented to service-oriented management has also implications to the area of event correlation. Today\"s event correlation mainly addresses the correlation of events as reported from management tools. However, a correlation of user trouble reports concerning services should also be performed. This is necessary to improve the resolution time and to reduce the effort for keeping the service agreements. We refer to such a type of correlation as service-oriented event correlation. The necessity to use this kind of event correlation is motivated in the paper. To introduce service-oriented event correlation for an IT service provider, an appropriate modeling of the correlation workflow and of the information is necessary. Therefore, we examine the process management frameworks IT Infrastructure Library (ITIL) and enhanced Telecom Operations Map (eTOM) for their contribution to the workflow modeling in this area. The different kinds of dependencies that we find in our general scenario are then used to develop a workflow for the service-oriented event correlation. The MNM Service Model, which is a generic model for IT service management proposed by the Munich Network Management (MNM) Team, is used to derive an appropriate information modeling. An example scenario, the Web Hosting Service of the Leibniz Supercomputing Center (LRZ), is used to demonstrate the application of service-oriented event correlation.", "fulltext": "1. INTRODUCTION\nIn huge networks a single fault can cause a burst of failure\nevents. To handle the flood of events and to find the root\ncause of a fault, event correlation approaches like rule-based\nreasoning, case-based reasoning or the codebook approach\nhave been developed. The main idea of correlation is to\ncondense and structure events to retrieve meaningful\ninformation. Until now, these approaches address primarily the\ncorrelation of events as reported from management tools or\ndevices. Therefore, we call them device-oriented.\nIn this paper we define a service as a set of functions\nwhich are offered by a provider to a customer at a customer\nprovider interface. The definition of a service is therefore\nmore general than the definition of a Web Service, but a\nWeb Service is included in this service definition. As\na consequence, the results are applicable for Web Services\nas well as for other kinds of services. A service level\nagreement (SLA) is defined as a contract between customer and\nprovider about guaranteed service performance.\nAs in today\"s IT environments the offering of such services\nwith an agreed service quality becomes more and more\nimportant, this change also affects the event correlation. It\nhas become a necessity for providers to offer such\nguarantees for a differentiation from other providers. To avoid SLA\nviolations it is especially important for service providers to\nidentify the root cause of a fault in a very short time or even\nact proactively. The latter refers to the case of recognizing\nthe influence of a device breakdown on the offered services.\nAs in this scenario the knowledge about services and their\nSLAs is used we call it service-oriented. It can be addressed\nfrom two directions.\nTop-down perspective: Several customers report a\nproblem in a certain time interval. Are these trouble\nreports correlated? How to identify a resource as being\nthe problem\"s root cause?\n183\nBottom-up perspective: A device (e.g., router, server)\nbreaks down. Which services, and especially which\ncustomers, are affected by this fault?\nThe rest of the paper is organized as follows. In Section\n2 we describe how event correlation is performed today and\npresent a selection of the state-of-the-art event correlation\ntechniques. Section 3 describes the motivation for\nserviceoriented event correlation and its benefits. After having\nmotivated the need for such type of correlation we use two\nwell-known IT service management models to gain\nrequirements for an appropriate workflow modeling and present\nour proposal for it (see Section 4). In Section 5 we present\nour information modeling which is derived from the MNM\nService Model. An application of the approach for a web\nhosting scenario is performed in Section 6. The last section\nconcludes the paper and presents future work.\n2. TODAY\"S EVENT CORRELATION\nTECHNIQUES\nIn [11] the task of event correlation is defined as a\nconceptual interpretation procedure in the sense that a new\nmeaning is assigned to a set of events that happen in a certain\ntime interval. We can distinguish between three aspects\nfor event correlation.\nFunctional aspect: The correlation focuses on functions\nwhich are provided by each network element. It is also\nregarded which other functions are used to provide a\nspecific function.\nTopology aspect: The correlation takes into account how\nthe network elements are connected to each other and\nhow they interact.\nTime aspect: When explicitly regarding time constraints,\na start and end time has to be defined for each event.\nThe correlation can use time relationships between the\nevents to perform the correlation. This aspect is only\nmentioned in some papers [11], but it has to be treated\nin an event correlation system.\nIn the event correlation it is also important to distinguish\nbetween the knowledge acquisition/representation and the\ncorrelation algorithm. Examples of approaches to\nknowledge acquisition/representation are Gruschke\"s dependency\ngraphs [6] and Ensel\"s dependency detection by neural\nnetworks [3]. It is also possible to find the dependencies by\nanalyzing interactions [7]. In addition, there is an approach\nto manage service dependencies with XML and to define a\nresource description framework [4].\nTo get an overview about device-oriented event correlation\na selection of several event correlation techniques being used\nfor this kind of correlation is presented.\nModel-based reasoning: Model-based reasoning (MBR)\n[15, 10, 20] represents a system by modeling each of its\ncomponents. A model can either represent a physical\nentity or a logical entity (e.g., LAN, WAN, domain,\nservice, business process). The models for physical\nentities are called functional model, while the models\nfor all logical entities are called logical model. A\ndescription of each model contains three categories of\ninformation: attributes, relations to other models, and\nbehavior. The event correlation is a result of the\ncollaboration among models.\nAs all components of a network are represented with\ntheir behavior in the model, it is possible to perform\nsimulations to predict how the whole network will\nbehave.\nA comparison in [20] showed that a large MBR system\nis not in all cases easy to maintain. It can be difficult to\nappropriately model the behavior for all components\nand their interactions correctly and completely.\nAn example system for MBR is NetExpert[16] from\nOSI which is a hybrid MBR/RBR system (in 2000 OSI\nwas acquired by Agilent Technologies).\nRule-based reasoning: Rule-based reasoning (RBR) [15,\n10] uses a set of rules for event correlation. The rules\nhave the form conclusion if condition. The condition\nuses received events and information about the system,\nwhile the conclusion contains actions which can either\nlead to system changes or use system parameters to\nchoose the next rule.\nAn advantage of the approach is that the rules are\nmore or less human-readable and therefore their effect\nis intuitive. The correlation has proved to be very fast\nin practice by using the RETE algorithm.\nIn the literature [20, 1] it is claimed that RBR\nsystems are classified as relatively inflexible. Frequent\nchanges in the modeled IT environment would lead to\nmany rule updates. These changes would have to be\nperformed by experts as no automation has currently\nbeen established. In some systems information about\nthe network topology which is needed for the event\ncorrelation is not used explicitly, but is encoded into the\nrules. This intransparent usage would make rule\nupdates for topology changes quite difficult. The system\nbrittleness would also be a problem for RBR systems.\nIt means that the system fails if an unknown case\noccurs, because the case cannot be mapped onto similar\ncases. The output of RBR systems would also be\ndifficult to predict, because of unforeseen rule interactions\nin a large rule set. According to [15] an RBR system\nis only appropriate if the domain for which it is used\nis small, nonchanging, and well understood.\nThe GTE IMPACT system [11] is an example of a\nrulebased system. It also uses MBR (GTE has merged\nwith Bell Atlantic in 1998 and is now called Verizon\n[19]).\nCodebook approach: The codebook approach [12, 21] has\nsimilarities to RBR, but takes a further step and\nencodes the rules into a correlation matrix.\nThe approach starts using a dependency graph with\ntwo kinds of nodes for the modeling. The first kind\nof nodes are the faults (denoted as problems in the\ncited papers) which have to be detected, while the\nsecond kind of nodes are observable events (symptoms in\nthe papers) which are caused by the faults or other\nevents. The dependencies between the nodes are\ndenoted as directed edges. It is possible to choose weights\nfor the edges, e.g., a weight for the probability that\n184\nfault/event A causes event B. Another possible\nweighting could indicate time dependencies. There are\nseveral possibilities to reduce the initial graph. If, e.g.,\na cyclic dependency of events exists and there are no\nprobabilities for the cycles\" edges, all events can be\ntreated as one event.\nAfter a final input graph is chosen, the graph is\ntransformed into a correlation matrix where the columns\ncontain the faults and the rows contain the events.\nIf there is a dependency in the graph, the weight of\nthe corresponding edge is put into the according\nmatrix cell. In case no weights are used, the matrix cells\nget the values 1 for dependency and 0 otherwise.\nAfterwards, a simplification can be done, where events\nwhich do not help to discriminate faults are deleted.\nThere is a trade-off between the minimization of the\nmatrix and the robustness of the results. If the matrix\nis minimized as much as possible, some faults can only\nbe distinguished by a single event. If this event cannot\nbe reliably detected, the event correlation system\ncannot discriminate between the two faults. A measure\nhow many event observation errors can be\ncompensated by the system is the Hamming distance. The\nnumber of rows (events) that can be deleted from the\nmatrix can differ very much depending on the\nrelationships [15].\nThe codebook approach has the advantage that it uses\nlong-term experience with graphs and coding. This\nexperience is used to minimize the dependency graph\nand to select an optimal group of events with respect\nto processing time and robustness against noise.\nA disadvantage of the approach could be that similar\nto RBR frequent changes in the environment make it\nnecessary to frequently edit the input graph.\nSMARTS InCharge [12, 17] is an example of such a\ncorrelation system.\nCase-based reasoning: In contrast to other approaches\ncase-based reasoning (CBR) [14, 15] systems do not\nuse any knowledge about the system structure. The\nknowledge base saves cases with their values for system\nparameters and successful recovery actions for these\ncases. The recovery actions are not performed by the\nCBR system in the first place, but in most cases by a\nhuman operator.\nIf a new case appears, the CBR system compares the\ncurrent system parameters with the system\nparameters in prior cases and tries to find a similar one. To\nidentify such a match it has to be defined for which\nparameters the cases can differ or have to be the same.\nIf a match is found, a learned action can be performed\nautomatically or the operator can be informed with a\nrecovery proposal.\nAn advantage of this approach is that the ability to\nlearn is an integral part of it which is important for\nrapid changing environments.\nThere are also difficulties when applying the approach\n[15]. The fields which are used to find a similar case\nand their importance have to be defined appropriately.\nIf there is a match with a similar case, an adaptation\nof the previous solution to the current one has to be\nfound.\nAn example system for CBR is SpectroRx from\nCabletron Systems. The part of Cabletron that developed\nSpectroRx became an independent software company\nin 2002 and is now called Aprisma Management\nTechnologies [2].\nIn this section four event correlation approaches were\npresented which have evolved into commercial event correlation\nsystems. The correlation approaches have different focuses.\nMBR mainly deals with the knowledge acquisition and\nrepresentation, while RBR and the codebook approach\npropose a correlation algorithm. The focus of CBR is its ability\nto learn from prior cases.\n3. MOTIVATION OF SERVICE-ORIENTED\nEVENT CORRELATION\nFig. 1 shows a general service scenario upon which we\nwill discuss the importance of a service-oriented correlation.\nSeveral services like SSH, a web hosting service, or a video\nconference service are offered by a provider to its customers\nat the customer provider interface. A customer can allow\nseveral users to use a subscribed service. The quality and\ncost issues of the subscribed services between a customer\nand a provider are agreed in SLAs. On the provider side\nthe services use subservices for their provisioning. In case\nof the services mentioned above such subservices are DNS,\nproxy service, and IP service. Both services and subservices\ndepend on resources upon which they are provisioned. As\ndisplayed in the figure a service can depend on more than\none resource and a resource can be used by one or more\nservices.\nSSH\nDNS\nproxy\nIP\nservice dependency resource dependency\nuser a\nuser b\nuser c\ncustomer SLA\nweb a\nvideo conf.\nSSH sun1\nprovider\nvideo conf.\nweb\nservices\nsubservices\nresources\nFigure 1: Scenario\nTo get a common understanding, we distinguish between\ndifferent types of events:\nResource event: We use the term resource event for\nnetwork events and system events. A network event refers\nto events like node up/down or link up/down whereas\nsystem events refer to events like server down or\nauthentication failure.\nService event: A service event indicates that a service\ndoes not work properly. A trouble ticket which is\ngenerated from a customer report is a kind of such an\n185\nevent. Other service events can be generated by the\nprovider of a service, if the provider himself detects a\nservice malfunction.\nIn such a scenario the provider may receive service events\nfrom customers which indicate that SSH, web hosting\nservice, and video conference service are not available. When\nreferring to the service hierarchy, the provider can conclude\nin such a case that all services depend on DNS. Therefore,\nit seems more likely that a common resource which is\nnecessary for this service does not work properly or is not\navailable than to assume three independent service failures. In\ncontrast to a resource-oriented perspective where all of the\nservice events would have to be processed separately, the\nservice events can be linked together. Their information can\nbe aggregated and processed only once. If, e.g., the problem\nis solved, one common message to the customers that their\nservices are available again is generated and distributed by\nusing the list of linked service events. This is certainly a\nsimplified example. However, it shows the general principle of\nidentifying the common subservices and common resources\nof different services.\nIt is important to note that the service-oriented\nperspective is needed to integrate service aspects, especially QoS\naspects. An example of such an aspect is that a fault does not\nlead to a total failure of a service, but its QoS parameters,\nrespectively agreed service levels, at the customer-provider\ninterface might not be met. A degradation in service\nquality which is caused by high traffic load on the backbone\nis another example. In the resource-oriented perspective it\nwould be possible to define events which indicate that there\nis a link usage higher than a threshold, but no mechanism\nhas currently been established to find out which services are\naffected and whether a QoS violation occurs.\nTo summarize, the reasons for the necessity of a\nserviceoriented event correlation are the following:\nKeeping of SLAs (top-down perspective): The time\ninterval between the first symptom (recognized either\nby provider, network management tools, or customers)\nthat a service does not perform properly and the\nverified fault repair needs to be minimized. This is\nespecially needed with respect to SLAs as such agreements\noften contain guarantees like a mean time to repair.\nEffort reduction (top-down perspective): If several\nuser trouble reports are symptoms of the same fault,\nfault processing should be performed only once and\nnot several times. If the fault has been repaired, the\naffected customers should be informed about this\nautomatically.\nImpact analysis (bottom-up perspective): In case of\na fault in a resource, its influence on the associated\nservices and affected customers can be determined. This\nanalysis can be performed for short term (when there\nis currently a resource failure) or long term (e.g.,\nnetwork optimization) considerations.\n4. WORKFLOW MODELING\nIn the following we examine the established IT process\nmanagement frameworks IT Infrastructure Library (ITIL)\nand enhanced Telecom Operations Map (eTOM). The aim is\nfind out where event correlation can be found in the process\nstructure and how detailed the frameworks currently are.\nAfter that we present our solution for a workflow modeling\nfor the service-oriented event correlation.\n4.1 IT Infrastructure Library (ITIL)\nThe British Office of Government Commerce (OGC) and\nthe IT Service Management Forum (itSMF) [9] provide a\ncollection of best practices for IT processes in the area of\nIT service management which is called ITIL. The service\nmanagement is described by 11 modules which are grouped\ninto Service Support Set (provider internal processes) and\nService Delivery Set (processes at the customer-provider\ninterface). Each module describes processes, functions, roles,\nand responsibilities as well as necessary databases and\ninterfaces. In general, ITIL describes contents, processes, and\naims at a high abstraction level and contains no information\nabout management architectures and tools.\nThe fault management is divided into Incident\nManagement process and Problem Management process.\nIncident Management: The Incident Management\ncontains the service desk as interface to customers (e.g.,\nreceives reports about service problems). In case of\nsevere errors structured queries are transferred to the\nProblem Management.\nProblem Management: The Problem Management\"s\ntasks are to solve problems, take care of keeping\npriorities, minimize the reoccurrence of problems, and to\nprovide management information. After receiving\nrequests from the Incident Management, the problem\nhas to be identified and information about necessary\ncountermeasures is transferred to the Change\nManagement.\nThe ITIL processes describe only what has to be done, but\ncontain no information how this can be actually performed.\nAs a consequence, event correlation is not part of the\nmodeling. The ITIL incidents could be regarded as input for the\nservice-oriented event correlation, while the output could be\nused as a query to the ITIL Problem Management.\n4.2 Enhanced Telecom Operations Map\n(eTOM)\nThe TeleManagement Forum (TMF) [18] is an\ninternational non-profit organization from service providers and\nsuppliers in the area of telecommunications services. Similar\nto ITIL a process-oriented framework has been developed at\nfirst, but the framework was designed for a narrower focus,\ni.e., the market of information and communications service\nproviders. A horizontal grouping into processes for\ncustomer care, service development & operations, network &\nsystems management, and partner/supplier is performed. The\nvertical grouping (fulfillment, assurance, billing) reflects the\nservice life cycle.\nIn the area of fault management three processes have been\ndefined along the horizontal process grouping.\nProblem Handling: The purpose of this process is to\nreceive trouble reports from customers and to solve them\nby using the Service Problem Management. The aim\nis also to keep the customer informed about the\ncurrent status of the trouble report processing as well as\nabout the general network status (e.g., planned\nmaintenance). It is also a task of this process to inform the\n186\nQoS/SLA management about the impact of current\nerrors on the SLAs.\nService Problem Management: In this process reports\nabout customer-affecting service failures are received\nand transformed. Their root causes are identified and\na problem solution or a temporary workaround is\nestablished. The task of the Diagnose Problem\nsubprocess is to find the root cause of the problem by\nperforming appropriate tests. Nothing is said how this\ncan be done (e.g., no event correlation is mentioned).\nResource Trouble Management: A subprocess of the\nResource Trouble Management is responsible for\nresource failure event analysis, alarm correlation &\nfiltering, and failure event detection & reporting.\nAnother subprocess is used to execute different tests to\nfind a resource failure. There is also another\nsubprocess which keeps track about the status of the trouble\nreport processing. This subprocess is similar to the\nfunctionality of a trouble ticket system.\nThe process description in eTOM is not very detailed. It\nis useful to have a check list which aspects for these processes\nhave to be taken into account, but there is no detailed\nmodeling of the relationships and no methodology for applying\nthe framework. Event correlation is only mentioned in the\nresource management, but it is not used in the service level.\n4.3 Workflow Modeling for the\nService-Oriented Event Correlation\nFig. 2 shows a general service scenario which we will use\nas basis for the workflow modeling for the service-oriented\nevent correlation. We assume that the dependencies are\nalready known (e.g., by using the approaches mentioned\nin Section 2). The provider offers different services which\ndepend on other services called subservices (service\ndependency). Another kind of dependency exists between\nservices/subservices and resources. These dependencies are\ncalled resource dependencies. These two kinds of\ndependencies are in most cases not used for the event correlation\nperformed today. This resource-oriented event correlation\ndeals only with relationships on the resource level (e.g.,\nnetwork topology).\nservice dependency\nresources\nsubservices\nprovider\nservices\nresource dependency\nFigure 2: Different kinds of dependencies for the\nservice-oriented event correlation\nThe dependencies depicted in Figure 2 reflect a situation\nwith no redundancy in the service provisioning. The\nrelationships can be seen as AND relationships. In case of\nredundancy, if e.g., a provider has 3 independent web servers,\nanother modeling (see Figure 3) should be used (OR\nrelationship). In such a case different relationships are possible.\nThe service could be seen as working properly if one of the\nservers is working or a certain percentage of them is working.\nservices\n) AND relationship b) OR relationship\nresources\nFigure 3: Modeling of no redundancy (a) and of\nredundancy (b)\nAs both ITIL and eTOM contain no description how event\ncorrelation and especially service-oriented event correlation\nshould actually be performed, we propose the following\ndesign for such a workflow (see Fig. 4). The additional\ncomponents which are not part of a device-oriented event\ncorrelation are depicted with a gray background. The workflow is\ndivided into the phases fault detection, fault diagnosis, and\nfault recovery.\nIn the fault detection phase resource events and service\nevents can be generated from different sources. The\nresource events are issued during the use of a resource, e.g.,\nvia SNMP traps. The service events are originated from\ncustomer trouble reports, which are reported via the Customer\nService Management (see below) access point. In addition\nto these two passive ways to get the events, a provider\ncan also perform active tests. These tests can either deal\nwith the resources (resource active probing) or can assume\nthe role of a virtual customer and test a service or one of its\nsubservices by performing interactions at the service access\npoints (service active probing).\nThe fault diagnosis phase is composed of three event\ncorrelation steps. The first one is performed by the resource\nevent correlator which can be regarded as the event\ncorrelator in today\"s commercial systems. Therefore, it deals only\nwith resource events. The service event correlator does a\ncorrelation of the service events, while the aggregate event\ncorrelator finally performs a correlation of both resource and\nservice events. If the correlation result in one of the\ncorrelation steps shall be improved, it is possible to go back to\nthe fault detection phase and start the active probing to get\nadditional events. These events can be helpful to confirm a\ncorrelation result or to reduce the list of possible root causes.\nAfter the event correlation an ordered list of possible root\ncauses is checked by the resource management. When the\nroot cause is found, the failure repair starts. This last step\nis performed in the fault recovery phase.\nThe next subsections present different elements of the\nevent correlation process.\n4.4 Customer Service Management and\nIntelligent Assistant\nThe Customer Service Management (CSM) access point\nwas proposed by [13] as a single interface between customer\n187\nfault\ndetection\nfault\ndiagnosis\nresource\nactive\nprobing\nresource event\nresource\nevent\ncorrelator\nresource\nmanagement\ncandidate\nlist\nfault\nrecovery\nresource\nusage\nservice\nactive\nprobing\nintelligent\nassistant\nservice\nevent\ncorrelator\naggregate\nevent\ncorrelator\nservice eventCSM AP\nFigure 4: Event correlation workflow\nand provider. Its functionality is to provide information\nto the customer about his subscribed services, e.g., reports\nabout the fulfillment of agreed SLAs. It can also be used to\nsubscribe services or to allow the customer to manage his\nservices in a restricted way. Reports about problems with a\nservice can be sent to the customer via CSM. The CSM is\nalso contained in the MNM Service Model (see Section 5).\nTo reduce the effort for the provider\"s first level support,\nan Intelligent Assistant can be added to the CSM. The\nIntelligent Assistant structures the customer\"s information about\na service problem. The information which is needed for a\npreclassification of the problem is gathered from a list of\nquestions to the customer. The list is not static as the\ncurrent question depends on the answers to prior questions or\nfrom the result of specific tests. A decision tree is used\nto structure the questions and tests. The tests allow the\ncustomer to gain a controlled access to the provider\"s\nmanagement. At the LRZ a customer of the E-Mail Service can,\ne.g., use the Intelligent Assistant to perform ping requests\nto the mail server. But also more complex requests could be\npossible, e.g., requests of a combination of SNMP variables.\n4.5 Active Probing\nActive probing is useful for the provider to check his\noffered services. The aim is to identify and react to problems\nbefore a customer notices them. The probing can be done\nfrom a customer point of view or by testing the resources\nwhich are part of the services. It can also be useful to\nperform tests of subservices (own subservices or subservices\noffered by suppliers).\nDifferent schedules are possible to perform the active\nprobing. The provider could select to test important services\nand resources in regular time intervals. Other tests could\nbe initiated by a user who traverses the decision tree of the\nIntelligent Assistant including active tests. Another\npossibility for the use of active probing is a request from the event\ncorrelator, if the current correlation result needs to be\nimproved. The results of active probing are reported via service\nor resource events to the event correlator (or if the test was\ndemanded by the Intelligent Assistant the result is reported\nto it, too). While the events that are received from\nmanagement tools and customers denote negative events (something\ndoes not work), the events from active probing should also\ncontain positive events for a better discrimination.\n4.6 Event Correlator\nThe event correlation should not be performed by a single\nevent correlator, but by using different steps. The reason\nfor this are the different characteristics of the dependencies\n(see Fig. 1).\nOn the resource level there are only relationships between\nresources (network topology, systems configuration). An\nexample for this could be a switch linking separate LANs. If\nthe switch is down, events are reported that other network\ncomponents which are located behind the switch are also not\nreachable. When correlating these events it can be figured\nout that the switch is the likely error cause. At this stage,\nthe integration of service events does not seem to be helpful.\nThe result of this step is a list of resources which could be\nthe problem\"s root cause. The resource event correlator is\nused to perform this step.\nIn the service-oriented scenario there are also service and\nresource dependencies. As next step in the event\ncorrelation process the service events should be correlated with\neach other using the service dependencies, because the\nservice dependencies have no direct relationship to the resource\nlevel. The result of this step, which is performed by the\nservice event correlator, is a list of services/subservices which\ncould contain a failure in a resource. If, e.g., there are\nservice events from customers that two services do not work\nand both services depend on a common subservice, it seems\nmore likely that the resource failure can be found inside the\nsubservice. The output of this correlation is a list of\nservices/subservices which could be affected by a failure in an\nassociated resource.\nIn the last step the aggregate event correlator matches\nthe lists from resource event correlator and service event\ncorrelator to find the problem\"s possible root cause. This is\ndone by using the resource dependencies.\nThe event correlation techniques presented in Section 2\ncould be used to perform the correlation inside the three\nevent correlators. If the dependencies can be found precisely,\nan RBR or codebook approach seems to be appropriate. A\ncase database (CBR) could be used if there are cases which\ncould not be covered by RBR or the codebook approach.\nThese cases could then be used to improve the modeling in\na way that RBR or the codebook approach can deal with\nthem in future correlations.\n5. INFORMATION MODELING\nIn this section we use a generic model for IT service\nmanagement to derive the information necessary for the event\ncorrelation process.\n5.1 MNM Service Model\nThe MNM Service Model [5] is a generic model for IT\nservice management. A distinction is made between customer\nside and provider side. The customer side contains the\nbasic roles customer and user, while the provider side contains\nthe role provider. The provider makes the service available\nto the customer side. The service as a whole is divided into\nusage which is accessed by the role user and management\nwhich is used by the role customer.\nThe model consists of two main views. The Service View\n(see Fig. 5) shows a common perspective of the service for\ncustomer and provider. Everything that is only important\n188\nfor the service realization is not contained in this view. For\nthese details another perspective, the Realization View, is\ndefined (see Fig. 6).\ncustomer domain\nsupplies supplies\nprovider domain\n\u00abrole\u00bb\nprovider\naccesses uses concludes accesses\nimplements observesrealizes\nprovides directs\nsubstantiates\nusesuses\nmanages\nimplementsrealizes\nmanages\nservice\nconcludes\nQoS\nparameters\nusage\nfunctionality\nservice\naccess point\nmanagement\nfunctionality\nservice implementation service management implementation\nservice\nagreement\ncustomersideprovidersidesideindependent\n\u00abrole\u00bb\nuser\n\u00abrole\u00bb\ncustomer\nCSM\naccess point\nservice\nclient\nCSM\nclient\nFigure 5: Service View\nThe Service View contains the service for which the\nfunctionality is defined for usage as well as for management. There\nare two access points (service access point and CSM access\npoint) where user and customer can access the usage and\nmanagement functionality, respectively. Associated to each\nservice is a list of QoS parameters which have to be met by\nthe service at the service access point. The QoS surveillance\nis performed by the management.\nprovider domain\nimplements observesrealizes\nprovides directs\nimplementsrealizes\naccesses uses concludes accesses\nusesuses\nmanages\nside independent\nside independent\nmanages\nmanages\nconcludes\nacts as\nservice implementation service management implementation\nmanages\nuses\nacts as\nservice\nlogic\nsub-service\nclient\nservice\nclient\nCSM\nclient\nuses\nresources\nusesuses\nservice\nmanagement logic\nsub-service\nmanagement client\nbasic\nmanagement functionality\n\u00abrole\u00bb\ncustomer\n\u00abrole\u00bb\nprovider\n\u00abrole\u00bb\nuser\nFigure 6: Realization View\nIn the Realization View the service implementation and the\nservice management implementation are described in detail.\nFor both there are provider-internal resources and\nsubservices. For the service implementation a service logic uses\ninternal resources (devices, knowledge, staff) and external\nsubservices to provide the service. Analogous, the service\nmanagement implementation includes a service management\nlogic using basic management functionalities [8] and external\nmanagement subservices.\nThe MNM Service Model can be used for a similar\nmodeling of the used subservices, i.e., the model can be applied\nrecursively.\nAs the service-oriented event correlation has to use\ndependencies of a service from subservices and resources, the\nmodel is used in the following to derive the needed\ninformation for service events.\n5.2 Information Modeling for Service Events\nToday\"s event correlation deals mainly with events which\nare originated from resources. Beside a resource identifier\nthese events contain information about the resource status,\ne.g., SNMP variables. To perform a service-oriented event\ncorrelation it is necessary to define events which are related\nto services. These events can be generated from the\nprovider\"s own service surveillance or from customer reports\nat the CSM interface. They contain information about the\nproblems with the agreed QoS. In our information\nmodeling we define an event superclass which contains common\nattributes (e.g., time stamp). Resource event and service\nevent inherit from this superclass.\nDerived from the MNM Service Model we define the\ninformation necessary for a service event.\nService: As a service event shall represent the problems of\na single service, a unique identification of the affected\nservice is contained here.\nEvent description: This field has to contain a description\nof the problem. Depending on the interactions at the\nservice access point (Service View) a classification of\nthe problem into different categories should be defined.\nIt should also be possible to add an informal\ndescription of the problem.\nQoS parameters: For each service QoS parameters\n(Service View) are defined between the provider and the\ncustomer. This field represents a list of these QoS\nparameters and agreed service levels. The list can help\nthe provider to set the priority of a problem with\nrespect to the service levels agreed.\nResource list: This list contains the resources (Realization\nView) which are needed to provide the service. This\nlist is used by the provider to check if one of these\nresources causes the problem.\nSubservice service event identification: In the service\nhierarchy (Realization View) the service, for which this\nservice event has been issued, may depend on\nsubservices. If there is a suspicion that one of these\nsubservices causes the problem, child service events are\nissued from this service event for the subservices. In\nsuch a case this field contains links to the\ncorresponding events.\nOther event identifications: In the event correlation\nprocess the service event can be correlated with other\nservice events or with resource events. This field then\ncontains links to other events which have been\ncorrelated to this service event. This is useful to, e.g., send a\ncommon message to all affected customers when their\nsubscribed services are available again.\nIssuer\"s identification: This field can either contain an\nidentification of the customer who reported the\nproblem, an identification of a service provider\"s employee\n189\n(in case the failure has been detected by the provider\"s\nown service active probing) or a link to a parent\nservice event. The identification is needed, if there are\nambiguities in the service event or the issuer should\nbe informed (e.g., that the service is available again).\nThe possible issuers refer to the basic roles (customer,\nprovider) in the Service Model.\nAssignee: To keep track of the processing the name and\naddress of the provider\"s employee who is solving or\nsolved the problem is also noted. This is a\nspecialization of the provider role in the Service Model.\nDates: This field contains key dates in the processing of the\nservice event such as initial date, problem\nidentification date, resolution date. These dates are important\nto keep track how quick the problems have been solved.\nStatus: This field represents the service event\"s actual\nstatus (e.g., active, suspended, solved).\nPriority: The priority shows which importance the service\nevent has from the provider\"s perspective. The\nimportance is derived from the service agreement, especially\nthe agreed QoS parameters (Service View).\nThe fields date, status, and other service events are not\nderived directly from the Service Model, but are necessary\nfor the event correlation process.\n6. APPLICATION OF\nSERVICE-ORIENTED EVENT CORRELATION FOR A\nWEB HOSTING SCENARIO\nThe Leibniz Supercomputing Center is the joint\ncomputing center for the Munich universities and research\ninstitutions. It also runs the Munich Scientific Network and offers\nrelated services. One of these services is the Virtual WWW\nServer, a web hosting offer for smaller research institutions.\nIt currently has approximately 200 customers.\nA subservice of the Virtual WWW Server is the\nStorage Service which stores the static and dynamic web pages\nand uses caching techniques for a fast access. Other\nsubservices are DNS and IP service. When a user accesses a\nhosted web site via one of the LRZ\"s Virtual Private\nNetworks the VPN service is also used. The resources of the\nVirtual WWW Server include a load balancer and 5\nredundant servers. The network connections are also part of the\nresources as well as the Apache web server application\nrunning on the servers. Figure 7 shows the dependencies of the\nVirtual WWW Server.\n6.1 Customer Service Management and\nIntelligent Assistant\nThe Intelligent Assistant that is available at the Leibniz\nSupercomputing Center can currently be used for\nconnectivity or performance problems or problems with the LRZ\nE-Mail Service. A selection of possible customer problem\nreports for the Virtual WWW Server is given in the\nfollowing:\n\u2022 The hosted web site is not reachable.\n\u2022 The web site access is (too) slow.\n\u2022 The web site contains outdated content.\nserver\nserverserver\nserver\nserver server\nserver\nserver\nserver\noutgoing\nconnection\nhosting of LRZ\"s\nown pages\ncontent\ncaching\nserver\nemergency\nserver\nwebmail\nserver dynamic\nweb pages\nstatic\nweb pages\nDNS ProxyIP Storage\nResources:\nServices:\nVirtual WWW Server\nfive redundant servers\nAFS\nNFS\nDBload balancer\nFigure 7: Dependencies of the Virtual WWW\nServer\n\u2022 The transfer of new content to the LRZ does not\nchange the provided content.\n\u2022 The web site looks strange (e.g., caused by problems\nwith HTML version)\nThis customer reports have to be mapped onto failures\nin resources. For, e.g., an unreachable web site different\nroot causes are possible like a DNS problem, connectivity\nproblem, wrong configuration of the load balancer.\n6.2 Active Probing\nIn general, active probing can be used for services or\nresources. For the service active probing of the Virtual WWW\nServer a virtual customer could be installed. This customer\ndoes typical HTTP requests of web sites and compares the\nanswer with the known content. To check the up-to-dateness\nof a test web site, the content could contain a time stamp.\nThe service active probing could also include the testing of\nsubservices, e.g., sending requests to the DNS.\nThe resource active probing performs tests of the resources.\nExamples are connectivity tests, requests to application\nprocesses, and tests of available disk space.\n6.3 Event Correlation for the Virtual WWW\nServer\nFigure 8 shows the example processing. At first, a\ncustomer who takes a look at his hosted web site reports that\nthe content that he had changed is not displayed correctly.\nThis report is transferred to the service management via\nthe CSM interface. An Intelligent Assistant could be used\nto structure the customer report. The service management\ntranslates the customer report into a service event.\nIndependent from the customer report the service\nprovider\"s own service active probing tries to change the content\nof a test web site. Because this is not possible, a service\nevent is issued.\nMeanwhile, a resource event has been reported to the\nevent correlator, because an access of the content caching\nserver to one of the WWW servers failed. As there are no\nother events at the moment the resource event correlation\n190\ncustomer CSM\nservice\nmgmt\nevent\ncorrelator\nresource\nmgmt\ncustomer reports:\n\"web site content\nnot up\u2212to\u2212date\"\nservice active\nprobing reports:\n\"web site content\nchange not\npossible\"\nevent:\n\"retrieval of server\ncontent failed\"event forward\nresource\nevent\ncorrelation\nservice\nevent\ncorrelation\naggregate\nevent\ncorrelation\nlink failure\nreport\nevent forward\ncheck WWW server\ncheck link\nresult display\nlink repair\nresult display\nresult forward\ncustomer report\nFigure 8: Example processing of a customer report\ncannot correlate this event to other events. At this stage\nit would be possible that the event correlator asks the\nresource management to perform an active probing of related\nresources.\nBoth service events are now transferred to the service\nevent correlator and are correlated. From the correlation\nof these events it seems likely that either the WWW server\nitself or the link to the WWW server is the problem\"s root\ncause. A wrong web site update procedure inside the\ncontent caching server seems to be less likely as this would only\nexplain the customer report and not the service active\nprobing result. At this stage a service active probing could be\nstarted, but this does not seem to be useful as this\ncorrelation only deals with the Web Hosting Service and its\nresources and not with other services.\nAfter the separate correlation of both resource and service\nevents, which can be performed in parallel, the aggregate\nevent correlator is used to correlate both types of events.\nThe additional resource event makes it seem much more\nlikely that the problems are caused by a broken link to the\nWWW server or by the WWW server itself and not by the\ncontent caching server. In this case the event correlator asks\nthe resource management to check the link and the WWW\nserver. The decision between these two likely error causes\ncan not be further automated here.\nLater, the resource management finds out that a broken\nlink is the failure\"s root cause. It informs the event correlator\nabout this and it can be determined that this explains all\nprevious events. Therefore, the event correlation can be\nstopped at this point.\nDepending on the provider\"s customer relationship\nmanagement the finding of the root cause and an expected repair\ntime could be reported to the customers. After the link has\nbeen repaired, it is possible to report this event via the CSM\ninterface.\nEven though many details of this event correlation process\ncould also be performed differently, the example showed an\nimportant advantage of the service-oriented event\ncorrelation. The relationship between the service provisioning and\nthe provider\"s resources is explicitly modeled. This allows a\nmapping of the customer report onto the provider-internal\nresources.\n6.4 Event Correlation for Different Services\nIf a provider like the LRZ offers several services the\nserviceoriented event correlation can be used to reveal relationships\nthat are not obvious in the first place. If the LRZ E-Mail\nService and its events are viewed in relationship with the\nevents for the Virtual WWW Server, it is possible to identify\nfailures in common subservices and resources. Both services\ndepend on the DNS which means that customer reports like\nI cannot retrieve new e-mail and The web site of my\nresearch institute is not available can have a common cause,\ne.g., the DNS does not work properly.\n7. CONCLUSION AND FUTURE WORK\nIn our paper we showed the need for a service-oriented\nevent correlation. For an IT service provider this new kind\nof event correlation makes it possible to automatically map\nproblems with the current service quality onto resource\nfailures. This helps to find the failure\"s root cause earlier and\nto reduce costs for SLA violations. In addition, customer\nreports can be linked together and therefore the processing\neffort can be reduced.\nTo receive these benefits we presented our approach for\nperforming the service-oriented event correlation as well as\na modeling of the necessary correlation information. In the\nfuture we are going to apply our workflow and information\nmodeling for services offered by the Leibniz Supercomputing\nCenter going further into details.\nSeveral issues have not been treated in detail so far, e.g.,\nthe consequences for the service-oriented event correlation if\na subservice is offered by another provider. If a service does\nnot perform properly, it has to be determined whether this\nis caused by the provider himself or by the subservice. In\nthe latter case appropriate information has to be exchanged\nbetween the providers via the CSM interface. Another issue\nis the use of active probing in the event correlation process\nwhich can improve the result, but can also lead to a\ncorrelation delay.\nAnother important point is the precise definition of\ndependency which has also been left out by many other\npublications. To avoid having to much dependencies in a certain\nsituation one could try to check whether the dependencies\ncurrently exist. In case of a download from a web site there\nis only a dependency from the DNS subservice at the\nbeginning, but after the address is resolved a download\nfailure is unlikely to have been caused by the DNS. Another\npossibility to reduce the dependencies is to divide a service\ninto its possible user interactions (e.g., an e-mail service into\ntransactions like get mail, sent mail, etc) and to define the\ndependencies for each user interaction.\nAcknowledgments\nThe authors wish to thank the members of the Munich\nNetwork Management (MNM) Team for helpful discussions and\nvaluable comments on previous versions of the paper. The\nMNM Team, directed by Prof. Dr. Heinz-Gerd Hegering, is a\n191\ngroup of researchers of the Munich Universities and the\nLeibniz Supercomputing Center of the Bavarian Academy of\nSciences. Its web server is located at wwwmnmteam.informatik.\nuni-muenchen.de.\n8. REFERENCES\n[1] K. Appleby, G. Goldszmidt, and M. Steinder.\nYemanja - A Layered Event Correlation Engine for\nMulti-domain Server Farms. 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{"name": "train_C-77", "title": "Tracking Immediate Predecessors in Distributed Computations", "abstract": "A distributed computation is usually modeled as a partially ordered set of relevant events (the relevant events are a subset of the primitive events produced by the computation). An important causality-related distributed computing problem, that we call the Immediate Predecessors Tracking (IPT) problem, consists in associating with each relevant event, on the fly and without using additional control messages, the set of relevant events that are its immediate predecessors in the partial order. So, IPT is the on-the-fly computation of the transitive reduction (i.e., Hasse diagram) of the causality relation defined by a distributed computation. This paper addresses the IPT problem: it presents a family of protocols that provides each relevant event with a timestamp that exactly identifies its immediate predecessors. The family is defined by a general condition that allows application messages to piggyback control information whose size can be smaller than n (the number of processes). In that sense, this family defines message size-efficient IPT protocols. According to the way the general condition is implemented, different IPT protocols can be obtained. Two of them are exhibited.", "fulltext": "1. INTRODUCTION\nA distributed computation consists of a set of processes\nthat cooperate to achieve a common goal. A main\ncharacteristic of these computations lies in the fact that the\nprocesses do not share a common global memory, and\ncommunicate only by exchanging messages over a\ncommunication network. Moreover, message transfer delays are finite\nbut unpredictable. This computation model defines what\nis known as the asynchronous distributed system model. It\nis particularly important as it includes systems that span\nlarge geographic areas, and systems that are subject to\nunpredictable loads. Consequently, the concepts, tools and\nmechanisms developed for asynchronous distributed systems\nreveal to be both important and general.\nCausality is a key concept to understand and master the\nbehavior of asynchronous distributed systems [18]. More\nprecisely, given two events e and f of a distributed\ncomputation, a crucial problem that has to be solved in a lot of\ndistributed applications is to know whether they are causally\nrelated, i.e., if the occurrence of one of them is a consequence\nof the occurrence of the other. The causal past of an event\ne is the set of events from which e is causally dependent.\nEvents that are not causally dependent are said to be\nconcurrent. Vector clocks [5, 16] have been introduced to allow\nprocesses to track causality (and concurrency) between the\nevents they produce. The timestamp of an event produced\nby a process is the current value of the vector clock of the\ncorresponding process. In that way, by associating vector\ntimestamps with events it becomes possible to safely decide\nwhether two events are causally related or not.\nUsually, according to the problem he focuses on, a\ndesigner is interested only in a subset of the events produced by\na distributed execution (e.g., only the checkpoint events are\nmeaningful when one is interested in determining\nconsistent global checkpoints [12]). It follows that detecting causal\ndependencies (or concurrency) on all the events of the\ndistributed computation is not desirable in all applications [7,\n15]. In other words, among all the events that may occur\nin a distributed computation, only a subset of them are\nrelevant. In this paper, we are interested in the restriction of\nthe causality relation to the subset of events defined as being\nthe relevant events of the computation.\nBeing a strict partial order, the causality relation is\ntransitive. As a consequence, among all the relevant events that\ncausally precede a given relevant event e, only a subset are\nits immediate predecessors: those are the events f such that\nthere is no relevant event on any causal path from f to e.\nUnfortunately, given only the vector timestamp associated\nwith an event it is not possible to determine which events of\nits causal past are its immediate predecessors. This comes\nfrom the fact that the vector timestamp associated with e\ndetermines, for each process, the last relevant event\nbelong210\ning to the causal past of e, but such an event is not\nnecessarily an immediate predecessor of e. However, some\napplications [4, 6] require to associate with each relevant event only\nthe set of its immediate predecessors. Those applications are\nmainly related to the analysis of distributed computations.\nSome of those analyses require the construction of the\nlattice of consistent cuts produced by the computation [15, 16].\nIt is shown in [4] that the tracking of immediate\npredecessors allows an efficient on the fly construction of this lattice.\nMore generally, these applications are interested in the very\nstructure of the causal past. In this context, the\ndetermination of the immediate predecessors becomes a major issue\n[6]. Additionally, in some circumstances, this determination\nhas to satisfy behavior constraints. If the communication\npattern of the distributed computation cannot be modified,\nthe determination has to be done without adding control\nmessages. When the immediate predecessors are used to\nmonitor the computation, it has to be done on the fly.\nWe call Immediate Predecessor Tracking (IPT) the\nproblem that consists in determining on the fly and without\nadditional messages the immediate predecessors of relevant\nevents. This problem consists actually in determining the\ntransitive reduction (Hasse diagram) of the causality graph\ngenerated by the relevant events of the computation.\nSolving this problem requires tracking causality, hence using\nvector clocks. Previous works have addressed the efficient\nimplementation of vector clocks to track causal dependence on\nrelevant events. Their aim was to reduce the size of\ntimestamps attached to messages. An efficient vector clock\nimplementation suited to systems with fifo channels is proposed\nin [19]. Another efficient implementation that does not\ndepend on channel ordering property is described in [11]. The\nnotion of causal barrier is introduced in [2, 17] to reduce\nthe size of control information required to implement causal\nmulticast. However, none of these papers considers the\nIPT problem. This problem has been addressed for the first\ntime (to our knowledge) in [4, 6] where an IPT protocol\nis described, but without correctness proof. Moreover, in\nthis protocol, timestamps attached to messages are of size\nn. This raises the following question which, to our\nknowledge, has never been answered: Are there efficient vector\nclock implementation techniques that are suitable for the IPT\nproblem?.\nThis paper has three main contributions: (1) a positive\nanswer to the previous open question, (2) the design of a\nfamily of efficient IPT protocols, and (3) a formal\ncorrectness proof of the associated protocols. From a\nmethodological point of view the paper uses a top-down approach. It\nstates abstract properties from which more concrete\nproperties and protocols are derived. The family of IPT\nprotocols is defined by a general condition that allows\napplication messages to piggyback control information whose size\ncan be smaller than the system size (i.e., smaller than the\nnumber of processes composing the system). In that sense,\nthis family defines low cost IPT protocols when we\nconsider the message size. In addition to efficiency, the proposed\napproach has an interesting design property. Namely, the\nfamily is incrementally built in three steps. The basic\nvector clock protocol is first enriched by adding to each process\na boolean vector whose management allows the processes\nto track the immediate predecessor events. Then, a general\ncondition is stated to reduce the size of the control\ninformation carried by messages. Finally, according to the way this\ncondition is implemented, three IPT protocols are obtained.\nThe paper is composed of seven sections. Sections 2\nintroduces the computation model, vector clocks and the notion\nof relevant events. Section 3 presents the first step of the\nconstruction that results in an IPT protocol in which each\nmessage carries a vector clock and a boolean array, both\nof size n (the number of processes). Section 4 improves\nthis protocol by providing the general condition that allows\na message to carry control information whose size can be\nsmaller than n. Section 5 provides instantiations of this\ncondition. Section 6 provides a simulation study comparing\nthe behaviors of the proposed protocols. Finally, Section 7\nconcludes the paper. (Due to space limitations, proofs of\nlemmas and theorems are omitted. They can be found in\n[1].)\n2. MODEL AND VECTOR CLOCK\n2.1 Distributed Computation\nA distributed program is made up of sequential local\nprograms which communicate and synchronize only by\nexchanging messages. A distributed computation describes the\nexecution of a distributed program. The execution of a local\nprogram gives rise to a sequential process. Let {P1, P2, . . . ,\nPn} be the finite set of sequential processes of the distributed\ncomputation. Each ordered pair of communicating processes\n(Pi, Pj ) is connected by a reliable channel cij through which\nPi can send messages to Pj. We assume that each message\nis unique and a process does not send messages to itself1\n.\nMessage transmission delays are finite but unpredictable.\nMoreover, channels are not necessarily fifo. Process speeds\nare positive but arbitrary. In other words, the underlying\ncomputation model is asynchronous.\nThe local program associated with Pi can include send,\nreceive and internal statements. The execution of such a\nstatement produces a corresponding send/receive/internal\nevent. These events are called primitive events. Let ex\ni\nbe the x-th event produced by process Pi. The sequence\nhi = e1\ni e2\ni . . . ex\ni . . . constitutes the history of Pi, denoted\nHi. Let H = \u222an\ni=1Hi be the set of events produced by a\ndistributed computation. This set is structured as a partial\norder by Lamport\"s happened before relation [14] (denoted\nhb\n\u2192) and defined as follows: ex\ni\nhb\n\u2192 ey\nj if and only if\n(i = j \u2227 x + 1 = y) (local precedence) \u2228\n(\u2203m : ex\ni = send(m) \u2227 ey\nj = receive(m)) (msg prec.) \u2228\n(\u2203 ez\nk : ex\ni\nhb\n\u2192 ez\nk \u2227 e z\nk\nhb\n\u2192 ey\nj ) (transitive closure).\nmax(ex\ni , ey\nj ) is a partial function defined only when ex\ni and\ney\nj are ordered. It is defined as follows: max(ex\ni , ey\nj ) = ex\ni if\ney\nj\nhb\n\u2192 ex\ni , max(ex\ni , ey\nj ) = ey\ni if ex\ni\nhb\n\u2192 ey\nj .\nClearly the restriction of\nhb\n\u2192 to Hi, for a given i, is a total\norder. Thus we will use the notation ex\ni < ey\ni iff x < y.\nThroughout the paper, we will use the following notation:\nif e \u2208 Hi is not the first event produced by Pi, then pred(e)\ndenotes the event immediately preceding e in the sequence\nHi. If e is the first event produced by Pi, then pred(e) is\ndenoted by \u22a5 (meaning that there is no such event), and\n\u2200e \u2208 Hi : \u22a5 < e. The partial order bH = (H,\nhb\n\u2192)\nconstitutes a formal model of the distributed computation it is\nassociated with.\n1\nThis assumption is only in order to get simple protocols.\n211\nP1\nP2\nP3\n[1, 1, 2]\n[1, 0, 0] [3, 2, 1]\n[1, 1, 0]\n(2, 1)\n[0, 0, 1]\n(3, 1)\n[2, 0, 1]\n(1, 1) (1, 3)(1, 2)\n(2, 2) (2, 3)\n(3, 2)\n[2, 2, 1] [2, 3, 1]\n(1, 1) (1, 2) (1, 3)\n(2, 1)\n(2, 2)\n(2, 3)\n(3, 1)\n(3, 2)\nFigure 1: Timestamped Relevant Events and Immediate Predecessors Graph (Hasse Diagram)\n2.2 Relevant Events\nFor a given observer of a distributed computation, only\nsome events are relevant2\n[7, 9, 15]. An interesting example\nof what an observation is, is the detection of predicates\non consistent global states of a distributed computation [3,\n6, 8, 9, 13, 15]. In that case, a relevant event corresponds\nto the modification of a local variable involved in the global\npredicate. Another example is the checkpointing problem\nwhere a relevant event is the definition of a local checkpoint\n[10, 12, 20].\nThe left part of Figure 1 depicts a distributed computation\nusing the classical space-time diagram. In this figure, only\nrelevant events are represented. The sequence of relevant\nevents produced by process Pi is denoted by Ri, and R =\n\u222an\ni=1Ri \u2286 H denotes the set of all relevant events. Let \u2192\nbe the relation on R defined in the following way:\n\u2200 (e, f) \u2208 R \u00d7 R : (e \u2192 f) \u21d4 (e\nhb\n\u2192 f).\nThe poset (R, \u2192) constitutes an abstraction of the\ndistributed computation [7]. In the following we consider a\ndistributed computation at such an abstraction level.\nMoreover, without loss of generality we consider that the set of\nrelevant events is a subset of the internal events (if a\ncommunication event has to be observed, a relevant internal event\ncan be generated just before a send and just after a receive\ncommunication event occurred). Each relevant event is\nidentified by a pair (process id, sequence number) (see Figure 1).\nDefinition 1. The relevant causal past of an event e \u2208\nH is the (partially ordered) subset of relevant events f such\nthat f\nhb\n\u2192 e. It is denoted \u2191 (e). We have \u2191 (e) = {f \u2208\nR | f\nhb\n\u2192 e}.\nNote that, if e \u2208 R then \u2191 (e) = {f \u2208 R | f \u2192 e}. In\nthe computation described in Figure 1, we have, for the\nevent e identified (2, 2): \u2191 (e) = {(1, 1), (1, 2), (2, 1), (3, 1)}.\nThe following properties are immediate consequences of the\nprevious definitions. Let e \u2208 H.\nCP1 If e is not a receive event then\n\u2191 (e) =\n8\n<\n:\n\u2205 if pred(e) = \u22a5,\n\u2191 (pred(e)) \u222a {pred(e)} if pred(e) \u2208 R,\n\u2191 (pred(e)) if pred(e) \u2208 R.\nCP2 If e is a receive event (of a message m) then\n\u2191 (e) =\n8\n>><\n>>:\n\u2191 (send(m)) if pred(e) = \u22a5,\n\u2191 (pred(e))\u222a \u2191 (send(m)) \u222a {pred(e)}\nif pred(e) \u2208 R,\n\u2191 (pred(e))\u222a \u2191 (send(m)) if pred(e) \u2208 R.\n2\nThose events are sometimes called observable events.\nDefinition 2. Let e \u2208 Hi. For every j such that \u2191 (e) \u2229\nRj = \u2205, the last relevant event of Pj with respect to e is:\nlastr(e, j) = max{f | f \u2208\u2191 (e) \u2229 Rj}. When \u2191 (e) \u2229 Rj = \u2205,\nlastr(e, j) is denoted by \u22a5 (meaning that there is no such\nevent).\nLet us consider the event e identified (2,2) in Figure 1. We\nhave lastr(e, 1) = (1, 2), lastr(e, 2) = (2, 1), lastr(e, 3) =\n(3, 1). The following properties relate the events lastr(e, j)\nand lastr(f, j) for all the predecessors f of e in the relation\nhb\n\u2192. These properties follow directly from the definitions.\nLet e \u2208 Hi.\nLR0 \u2200e \u2208 Hi:\nlastr(e, i) =\n8\n<\n:\n\u22a5 if pred(e) = \u22a5,\npred(e) if pred(e) \u2208 R,\nlastr(pred(e),i) if pred(e) \u2208 R.\nLR1 If e is not a receipt event: \u2200j = i :\nlastr(e, j) = lastr(pred(e),j).\nLR2 If e is a receive event of m: \u2200j = i :\nlastr(e, j) = max(lastr(pred(e),j), lastr(send(m),j)).\n2.3 Vector Clock System\nDefinition As a fundamental concept associated with the\ncausality theory, vector clocks have been introduced in 1988,\nsimultaneously and independently by Fidge [5] and Mattern\n[16]. A vector clock system is a mechanism that associates\ntimestamps with events in such a way that the\ncomparison of their timestamps indicates whether the\ncorresponding events are or are not causally related (and, if they are,\nwhich one is the first). More precisely, each process Pi has a\nvector of integers V Ci[1..n] such that V Ci[j] is the number\nof relevant events produced by Pj, that belong to the\ncurrent relevant causal past of Pi. Note that V Ci[i] counts the\nnumber of relevant events produced so far by Pi. When a\nprocess Pi produces a (relevant) event e, it associates with\ne a vector timestamp whose value (denoted e.V C) is equal\nto the current value of V Ci.\nVector Clock Implementation The following\nimplementation of vector clocks [5, 16] is based on the observation\nthat \u2200i, \u2200e \u2208 Hi, \u2200j : e.V Ci[j] = y \u21d4 lastr(e, j) = ey\nj\nwhere e.V Ci is the value of V Ci just after the occurrence\nof e (this relation results directly from the properties LR0,\nLR1, and LR2). Each process Pi manages its vector clock\nV Ci[1..n] according to the following rules:\nVC0 V Ci[1..n] is initialized to [0, . . . , 0].\nVC1 Each time it produces a relevant event e, Pi increments\nits vector clock entry V Ci[i] (V Ci[i] := V Ci[i] + 1) to\n212\nindicate it has produced one more relevant event, then\nPi associates with e the timestamp e.V C = V Ci.\nVC2 When a process Pi sends a message m, it attaches to\nm the current value of V Ci. Let m.V C denote this\nvalue.\nVC3 When Pi receives a message m, it updates its vector\nclock as follows: \u2200k : V Ci[k] := max(V Ci[k], m.V C[k]).\n3. IMMEDIATE PREDECESSORS\nIn this section, the Immediate Predecessor Tracking\n(IPT) problem is stated (Section 3.1). Then, some technical\nproperties of immediate predecessors are stated and proved\n(Section 3.2). These properties are used to design the basic\nIPT protocol and prove its correctness (Section 3.3). This\nIPT protocol, previously presented in [4] without proof, is\nbuilt from a vector clock protocol by adding the\nmanagement of a local boolean array at each process.\n3.1 The IPT Problem\nAs indicated in the introduction, some applications (e.g.,\nanalysis of distributed executions [6], detection of\ndistributed properties [7]) require to determine (on-the-fly and\nwithout additional messages) the transitive reduction of the\nrelation \u2192 (i.e., we must not consider transitive causal\ndependency). Given two relevant events f and e, we say that f\nis an immediate predecessor of e if f \u2192 e and there is no\nrelevant event g such that f \u2192 g \u2192 e.\nDefinition 3. The Immediate Predecessor Tracking\n(IPT) problem consists in associating with each relevant event\ne the set of relevant events that are its immediate\npredecessors. Moreover, this has to be done on the fly and without\nadditional control message (i.e., without modifying the\ncommunication pattern of the computation).\nAs noted in the Introduction, the IPT problem is the\ncomputation of the Hasse diagram associated with the partially\nordered set of the relevant events produced by a distributed\ncomputation.\n3.2 Formal Properties of IPT\nIn order to design a protocol solving the IPT problem, it\nis useful to consider the notion of immediate relevant\npredecessor of any event, whether relevant or not. First, we\nobserve that, by definition, the immediate predecessor on\nPj of an event e is necessarily the lastr(e, j) event.\nSecond, for lastr(e, j) to be immediate predecessor of e, there\nmust not be another lastr(e, k) event on a path between\nlastr(e, j) and e. These observations are formalized in the\nfollowing definition:\nDefinition 4. Let e \u2208 Hi. The set of immediate\nrelevant predecessors of e (denoted IP(e)), is the set of the relevant\nevents lastr(e, j) (j = 1, . . . , n) such that \u2200k : lastr(e, j) \u2208\u2191\n(lastr(e, k)).\nIt follows from this definition that IP(e) \u2286 {lastr(e, j)|j =\n1, . . . , n} \u2282\u2191 (e). When we consider Figure 1, The graph\ndepicted in its right part describes the immediate predecessors\nof the relevant events of the computation defined in its left\npart, more precisely, a directed edge (e, f) means that the\nrelevant event e is an immediate predecessor of the relevant\nevent f (3\n).\nThe following lemmas show how the set of immediate\npredecessors of an event is related to those of its predecessors\nin the relation\nhb\n\u2192. They will be used to design and prove\nthe protocols solving the IPT problem. To ease the reading\nof the paper, their proofs are presented in Appendix A.\nThe intuitive meaning of the first lemma is the following:\nif e is not a receive event, all the causal paths arriving at e\nhave pred(e) as next-to-last event (see CP1). So, if pred(e)\nis a relevant event, all the relevant events belonging to its\nrelevant causal past are separated from e by pred(e), and\npred(e) becomes the only immediate predecessor of e. In\nother words, the event pred(e) constitutes a reset w.r.t.\nthe set of immediate predecessors of e. On the other hand,\nif pred(e) is not relevant, it does not separate its relevant\ncausal past from e.\nLemma 1. If e is not a receive event, IP(e) is equal to:\n\u2205 if pred(e) = \u22a5,\n{pred(e)} if pred(e) \u2208 R,\nIP(pred(e)) if pred(e) \u2208 R.\nThe intuitive meaning of the next lemma is as follows: if\ne is a receive event receive(m), the causal paths arriving\nat e have either pred(e) or send(m) as next-to-last events.\nIf pred(e) is relevant, as explained in the previous lemma,\nthis event hides from e all its relevant causal past and\nbecomes an immediate predecessor of e. Concerning the\nlast relevant predecessors of send(m), only those that are\nnot predecessors of pred(e) remain immediate predecessors\nof e.\nLemma 2. Let e \u2208 Hi be the receive event of a message\nm. If pred(e) \u2208 Ri, then, \u2200j, IP(e) \u2229 Rj is equal to:\n{pred(e)} if j = i,\n\u2205 if lastr(pred(e),j) \u2265 lastr(send(m),j),\nIP(send(m)) \u2229 Rj if lastr(pred(e),j) < lastr(send(m),j).\nThe intuitive meaning of the next lemma is the following:\nif e is a receive event receive(m), and pred(e) is not\nrelevant, the last relevant events in the relevant causal past of e are\nobtained by merging those of pred(e) and those of send(m)\nand by taking the latest on each process. So, the\nimmediate predecessors of e are either those of pred(e) or those\nof send(m). On a process where the last relevant events\nof pred(e) and of send(m) are the same event f, none of\nthe paths from f to e must contain another relevant event,\nand thus, f must be immediate predecessor of both events\npred(e) and send(m).\nLemma 3. Let e \u2208 Hi be the receive event of a message\nm. If pred(e) \u2208 Ri, then, \u2200j, IP(e) \u2229 Rj is equal to:\nIP(pred(e)) \u2229 Rj if lastr(pred(e),j) > lastr(send(m),j),\nIP(send(m)) \u2229 Rj if lastr(pred(e),j) < lastr(send(m),j)\nIP(pred(e))\u2229IP(send(m))\u2229Rj if lastr(pred(e),j) = lastr\n(send(m), j).\n3.3 A Basic IPT Protocol\nThe basic protocol proposed here associates with each\nrelevant event e, an attribute encoding the set IP(e) of its\nimmediate predecessors. From the previous lemmas, the set\n3\nActually, this graph is the Hasse diagram of the partial\norder associated with the distributed computation.\n213\nIP(e) of any event e depends on the sets IP of the events\npred(e) and/or send(m) (when e = receive(m)). Hence the\nidea to introduce a data structure allowing to manage the\nsets IPs inductively on the poset (H,\nhb\n\u2192). To take into\naccount the information from pred(e), each process manages\na boolean array IPi such that, \u2200e \u2208 Hi the value of IPi\nwhen e occurs (denoted e.IPi) is the boolean array\nrepresentation of the set IP(e). More precisely, \u2200j : IPi[j] =\n1 \u21d4 lastr(e, j) \u2208 IP(e). As recalled in Section 2.3, the\nknowledge of lastr(e,j) (for every e and every j) is based\non the management of vectors V Ci. Thus, the set IP(e) is\ndetermined in the following way:\nIP(e) = {ey\nj | e.V Ci[j] = y \u2227 e.IPi[j] = 1, j = 1, . . . , n}\nEach process Pi updates IPi according to the Lemmas 1,\n2, and 3:\n1. It results from Lemma 1 that, if e is not a receive event,\nthe current value of IPi is sufficient to determine e.IPi.\nIt results from Lemmas 2 and 3 that, if e is a receive\nevent (e = receive(m)), then determining e.IPi\ninvolves information related to the event send(m). More\nprecisely, this information involves IP(send(m)) and\nthe timestamp of send(m) (needed to compare the\nevents lastr(send(m),j) and lastr(pred(e),j), for\nevery j). So, both vectors send(m).V Cj and send(m).IPj\n(assuming send(m) produced by Pj ) are attached to\nmessage m.\n2. Moreover, IPi must be updated upon the occurrence\nof each event. In fact, the value of IPi just after an\nevent e is used to determine the value succ(e).IPi. In\nparticular, as stated in the Lemmas, the determination\nof succ(e).IPi depends on whether e is relevant or not.\nThus, the value of IPi just after the occurrence of event\ne must  keep track of this event.\nThe following protocol, previously presented in [4] without\nproof, ensures the correct management of arrays V Ci (as in\nSection 2.3) and IPi (according to the Lemmas of Section\n3.2). The timestamp associated with a relevant event e is\ndenoted e.TS.\nR0 Initialization: Both V Ci[1..n] and IPi[1..n] are\ninitialized to [0, . . . , 0].\nR1 Each time it produces a relevant event e:\n- Pi associates with e the timestamp e.TS defined\nas follows e.TS = {(k, V Ci[k]) | IPi[k] = 1},\n- Pi increments its vector clock entry V Ci[i]\n(namely it executes V Ci[i] := V Ci[i] + 1),\n- Pi resets IPi: \u2200 = i : IPi[ ] := 0; IPi[i] := 1.\nR2 When Pi sends a message m to Pj, it attaches to m\nthe current values of V Ci (denoted m.V C) and the\nboolean array IPi (denoted m.IP).\nR3 When it receives a message m from Pj , Pi executes the\nfollowing updates:\n\u2200k \u2208 [1..n] : case\nV Ci[k] < m.V C[k] thenV Ci[k] := m.V C[k];\nIPi[k] := m.IP[k]\nV Ci[k] = m.V C[k] then IPi[k] := min(IPi[k], m.IP[k])\nV Ci[k] > m.V C[k] then skip\nendcase\nThe proof of the following theorem directly follows from\nLemmas 1, 2 and 3.\nTheorem 1. The protocol described in Section 3.3 solves\nthe IPT problem: for any relevant event e, the timestamp\ne.TS contains the identifiers of all its immediate\npredecessors and no other event identifier.\n4. A GENERAL CONDITION\nThis section addresses a previously open problem,\nnamely, How to solve the IPT problem without requiring each\napplication message to piggyback a whole vector clock and\na whole boolean array?. First, a general condition that\ncharacterizes which entries of vectors V Ci and IPi can be\nomitted from the control information attached to a message\nsent in the computation, is defined (Section 4.1). It is then\nshown (Section 4.2) that this condition is both sufficient and\nnecessary.\nHowever, this general condition cannot be locally\nevaluated by a process that is about to send a message. Thus,\nlocally evaluable approximations of this general condition\nmust be defined. To each approximation corresponds a\nprotocol, implemented with additional local data structures. In\nthat sense, the general condition defines a family of IPT\nprotocols, that solve the previously open problem. This issue\nis addressed in Section 5.\n4.1 To Transmit or Not to Transmit Control\nInformation\nLet us consider the previous IPT protocol (Section 3.3).\nRule R3 shows that a process Pj does not systematically\nupdate each entry V Cj[k] each time it receives a message\nm from a process Pi: there is no update of V Cj[k] when\nV Cj[k] \u2265 m.V C[k]. In such a case, the value m.V C[k] is\nuseless, and could be omitted from the control information\ntransmitted with m by Pi to Pj.\nSimilarly, some entries IPj[k] are not updated when a\nmessage m from Pi is received by Pj. This occurs when\n0 < V Cj[k] = m.V C[k] \u2227 m.IP[k] = 1, or when V Cj [k] >\nm.V C[k], or when m.V C[k] = 0 (in the latest case, as\nm.IP[k] = IPi[k] = 0 then no update of IPj[k] is necessary).\nDifferently, some other entries are systematically reset to 0\n(this occurs when 0 < V Cj [k] = m.V C[k] \u2227 m.IP[k] = 0).\nThese observations lead to the definition of the condition\nK(m, k) that characterizes which entries of vectors V Ci and\nIPi can be omitted from the control information attached\nto a message m sent by a process Pi to a process Pj:\nDefinition 5. K(m, k) \u2261\n(send(m).V Ci[k] = 0)\n\u2228 (send(m).V Ci[k] < pred(receive(m)).V Cj[k])\n\u2228\n;\n(send(m).V Ci[k] = pred(receive(m)).V Cj[k])\n\u2227(send(m).IPi[k] = 1) .\n4.2 A Necessary and Sufficient Condition\nWe show here that the condition K(m, k) is both\nnecessary and sufficient to decide which triples of the form\n(k, send(m).V Ci[k], send(m).IPi[k]) can be omitted in an\noutgoing message m sent by Pi to Pj. A triple attached to\nm will also be denoted (k, m.V C[k], m.IP[k]). Due to space\nlimitations, the proofs of Lemma 4 and Lemma 5 are given\nin [1]. (The proof of Theorem 2 follows directly from these\nlemmas.)\n214\nLemma 4. (Sufficiency) If K(m, k) is true, then the triple\n(k, m.V C[k], m.IP[k]) is useless with respect to the correct\nmanagement of IPj[k] and V Cj [k].\nLemma 5. (Necessity) If K(m, k) is false, then the triple\n(k, m.V C[k], m.IP[k]) is necessary to ensure the correct\nmanagement of IPj[k] and V Cj [k].\nTheorem 2. When a process Pi sends m to a process Pj,\nthe condition K(m, k) is both necessary and sufficient not to\ntransmit the triple (k, send(m).V Ci[k], send(m).IPi[k]).\n5. A FAMILY OF IPT PROTOCOLS BASED\nON EVALUABLE CONDITIONS\nIt results from the previous theorem that, if Pi could\nevaluate K(m, k) when it sends m to Pj, this would\nallow us improve the previous IPT protocol in the following\nway: in rule R2, the triple (k, V Ci[k], IPi[k]) is\ntransmitted with m only if \u00acK(m, k). Moreover, rule R3 is\nappropriately modified to consider only triples carried by m.\nHowever, as previously mentioned, Pi cannot locally\nevaluate K(m, k) when it is about to send m. More\nprecisely, when Pi sends m to Pj , Pi knows the exact values of\nsend(m).V Ci[k] and send(m).IPi[k] (they are the current\nvalues of V Ci[k] and IPi[k]). But, as far as the value of\npred(receive(m)).V Cj[k] is concerned, two cases are\npossible. Case (i): If pred(receive(m))\nhb\n\u2192 send(m), then Pi can\nknow the value of pred(receive(m)).V Cj[k] and\nconsequently can evaluate K(m, k). Case (ii): If pred(receive(m))\nand send(m) are concurrent, Pi cannot know the value of\npred(receive(m)).V Cj[k] and consequently cannot evaluate\nK(m, k). Moreover, when it sends m to Pj , whatever the\ncase (i or ii) that actually occurs, Pi has no way to know\nwhich case does occur. Hence the idea to define evaluable\napproximations of the general condition. Let K (m, k) be\nan approximation of K(m, k), that can be evaluated by a\nprocess Pi when it sends a message m. To be correct, the\ncondition K must ensure that, every time Pi should\ntransmit a triple (k, V Ci[k], IPi[k]) according to Theorem 2 (i.e.,\neach time \u00acK(m, k)), then Pi transmits this triple when it\nuses condition K . Hence, the definition of a correct\nevaluable approximation:\nDefinition 6. A condition K , locally evaluable by a\nprocess when it sends a message m to another process, is\ncorrect if \u2200(m, k) : \u00acK(m, k) \u21d2 \u00acK (m, k) or, equivalently,\n\u2200(m, k) : K (m, k) \u21d2 K(m, k).\nThis definition means that a protocol evaluating K to\ndecide which triples must be attached to messages, does not\nmiss triples whose transmission is required by Theorem 2.\nLet us consider the constant condition (denoted K1),\nthat is always false, i.e., \u2200(m, k) : K1(m, k) = false. This\ntrivially correct approximation of K actually corresponds\nto the particular IPT protocol described in Section 3 (in\nwhich each message carries a whole vector clock and a\nwhole boolean vector). The next section presents a better\napproximation of K (denoted K2).\n5.1 A Boolean Matrix-Based Evaluable\nCondition\nCondition K2 is based on the observation that condition\nK is composed of sub-conditions. Some of them can be\nPj\nsend(m)\nPi\nV Ci[k] = x\nIPi[k] = 1\nV Cj[k] \u2265 x receive(m)\nFigure 2: The Evaluable Condition K2\nlocally evaluated while the others cannot. More\nprecisely, K \u2261 a \u2228 \u03b1 \u2228 (\u03b2 \u2227 b), where a \u2261 send(m).V Ci[k] = 0\nand b \u2261 send(m).IPi[k] = 1 are locally evaluable,\nwhereas \u03b1 \u2261 send(m).V Ci[k] < pred(receive(m)).V Cj[k] and\n\u03b2 \u2261 send(m).V Ci[k] = pred(receive(m)).V Cj[k] are not.\nBut, from easy boolean calculus, a\u2228((\u03b1\u2228\u03b2)\u2227b) =\u21d2 a\u2228\u03b1\u2228\n(\u03b2 \u2227 b) \u2261 K. This leads to condition K \u2261 a \u2228 (\u03b3 \u2227 b), where\n\u03b3 = \u03b1 \u2228 \u03b2 \u2261 send(m).V Ci[k] \u2264 pred(receive(m)).V Cj[k] ,\ni.e., K \u2261 (send(m).V Ci[k] \u2264 pred(receive(m)).V Cj[k] \u2227\nsend(m).IPi[k] = 1) \u2228 send(m).V Ci[k] = 0.\nSo, Pi needs to approximate the predicate send(m).V Ci[k]\n\u2264 pred(receive(m)).V Cj[k]. To be correct, this\napproximation has to be a locally evaluable predicate ci(j, k) such that,\nwhen Pi is about to send a message m to Pj, ci(j, k) \u21d2\n(send(m).V Ci[k] \u2264 pred(receive(m)).V Cj[k]). Informally,\nthat means that, when ci(j, k) holds, the local context of\nPi allows to deduce that the receipt of m by Pj will not\nlead to V Cj[k] update (Pj knows as much as Pi about\nPk). Hence, the concrete condition K2 is the following:\nK2 \u2261 send(m).V Ci[k] = 0 \u2228 (ci(j, k) \u2227 send(m).IPi[k] = 1).\nLet us now examine the design of such a predicate\n(denoted ci). First, the case j = i can be ignored, since it is\nassumed (Section 2.1) that a process never sends a\nmessage to itself. Second, in the case j = k, the relation\nsend(m).V Ci[j] \u2264 pred(receive(m)).V Cj [j] is always true,\nbecause the receipt of m by Pj cannot update V Cj[j]. Thus,\n\u2200j = i : ci(j, j) must be true. Now, let us consider the case\nwhere j = i and j = k (Figure 2). Suppose that there exists\nan event e = receive(m ) with e < send(m), m sent by\nPj and piggybacking the triple (k, m .V C[k], m .IP[k]), and\nm .V C[k] \u2265 V Ci[k] (hence m .V C[k] = receive(m ).V Ci[k]).\nAs V Cj[k] cannot decrease this means that, as long as V Ci[k]\ndoes not increase, for every message m sent by Pi to Pj we\nhave the following: send(m).V Ci[k] = receive(m ).V Ci[k] =\nsend(m ).V Cj[k] \u2264 receive(m).V Cj [k], i.e., ci(j, k) must\nremain true. In other words, once ci(j, k) is true, the only\nevent of Pi that could reset it to false is either the receipt\nof a message that increases V Ci[k] or, if k = i, the\noccurrence of a relevant event (that increases V Ci[i]). Similarly,\nonce ci(j, k) is false, the only event that can set it to true is\nthe receipt of a message m from Pj, piggybacking the triple\n(k, m .V C[k], m .IP[k]) with m .V C[k] \u2265 V Ci[k].\nIn order to implement the local predicates ci(j, k), each\nprocess Pi is equipped with a boolean matrix Mi (as in [11])\nsuch that M[j, k] = 1 \u21d4 ci(j, k). It follows from the\nprevious discussion that this matrix is managed according to the\nfollowing rules (note that its i-th line is not significant (case\nj = i), and that its diagonal is always equal to 1):\nM0 Initialization: \u2200 (j, k) : Mi[j, k] is initialized to 1.\n215\nM1 Each time it produces a relevant event e: Pi resets4\nthe ith column of its matrix: \u2200j = i : Mi[j, i] := 0.\nM2 When Pi sends a message: no update of Mi occurs.\nM3 When it receives a message m from Pj , Pi executes the\nfollowing updates:\n\u2200 k \u2208 [1..n] : case\nV Ci[k] < m.V C[k] then \u2200 = i, j, k : Mi[ , k] := 0;\nMi[j, k] := 1\nV Ci[k] = m.V C[k] then Mi[j, k] := 1\nV Ci[k] > m.V C[k] then skip\nendcase\nThe following lemma results from rules M0-M3. The\ntheorem that follows shows that condition K2(m, k) is correct.\n(Both are proved in [1].)\nLemma 6. \u2200i, \u2200m sent by Pi to Pj, \u2200k, we have:\nsend(m).Mi[j, k] = 1 \u21d2\nsend(m).V Ci[k] \u2264 pred(receive(m)).V Cj [k].\nTheorem 3. Let m be a message sent by Pi to Pj . Let\nK2(m, k) \u2261 ((send(m).Mi[j, k] = 1) \u2227 (send(m).IPi[k] =\n1)\u2228(send(m).V Ci[k] = 0)). We have: K2(m, k) \u21d2 K(m, k).\n5.2 Resulting IPT Protocol\nThe complete text of the IPT protocol based on the\nprevious discussion follows.\nRM0 Initialization:\n- Both V Ci[1..n] and IPi[1..n] are set to [0, . . . , 0],\nand \u2200 (j, k) : Mi[j, k] is set to 1.\nRM1 Each time it produces a relevant event e:\n- Pi associates with e the timestamp e.TS defined\nas follows: e.TS = {(k, V Ci[k]) | IPi[k] = 1},\n- Pi increments its vector clock entry V Ci[i]\n(namely, it executes V Ci[i] := V Ci[i] + 1),\n- Pi resets IPi: \u2200 = i : IPi[ ] := 0; IPi[i] := 1.\n- Pi resets the ith column of its boolean matrix:\n\u2200j = i : Mi[j, i] := 0.\nRM2 When Pi sends a message m to Pj, it attaches to m the\nset of triples (each made up of a process id, an integer\nand a boolean): {(k, V Ci[k], IPi[k]) | (Mi[j, k] = 0 \u2228\nIPi[k] = 0) \u2227 (V Ci[k] > 0)}.\nRM3 When Pi receives a message m from Pj , it executes the\nfollowing updates:\n\u2200(k,m.V C[k], m.IP[k]) carried by m:\ncase\nV Ci[k] < m.V C[k] then V Ci[k] := m.V C[k];\nIPi[k] := m.IP[k];\n\u2200 = i, j, k : Mi[ , k] := 0;\n4\nActually, the value of this column remains constant after\nits first update. In fact, \u2200j, Mi[j, i] can be set to 1 only upon\nthe receipt of a message from Pj, carrying the value V Cj[i]\n(see R3). But, as Mj [i, i] = 1, Pj does not send V Cj[i] to\nPi. So, it is possible to improve the protocol by executing\nthis reset of the column Mi[\u2217, i] only when Pi produces\nits first relevant event.\nMi[j, k] := 1\nV Ci[k] = m.V C[k] then IPi[k] := min(IPi[k], m.IP[k]);\nMi[j, k] := 1\nV Ci[k] > m.V C[k] then skip\nendcase\n5.3 A Tradeoff\nThe condition K2(m, k) shows that a triple has not to be\ntransmitted when (Mi[j, k] = 1 \u2227 IPi[k] = 1) \u2228 (V Ci[k] >\n0). Let us first observe that the management of IPi[k]\nis governed by the application program. More precisely,\nthe IPT protocol does not define which are the\nrelevant events, it has only to guarantee a correct\nmanagement of IPi[k]. Differently, the matrix Mi does not belong\nto the problem specification, it is an auxiliary variable of\nthe IPT protocol, which manages it so as to satisfy the\nfollowing implication when Pi sends m to Pj : (Mi[j, k] =\n1) \u21d2 (pred(receive(m)).V Cj [k] \u2265 send(m).V Ci[k]). The\nfact that the management of Mi is governed by the protocol\nand not by the application program leaves open the\npossibility to design a protocol where more entries of Mi are equal\nto 1. This can make the condition K2(m, k) more often\nsatisfied5\nand can consequently allow the protocol to transmit\nless triples.\nWe show here that it is possible to transmit less triples\nat the price of transmitting a few additional boolean\nvectors. The previous IPT matrix-based protocol (Section 5.2)\nis modified in the following way. The rules RM2 and\nRM3 are replaced with the modified rules RM2\" and RM3\"\n(Mi[\u2217, k] denotes the kth column of Mi).\nRM2\" When Pi sends a message m to Pj, it attaches to m\nthe following set of 4-uples (each made up of a\nprocess id, an integer, a boolean and a boolean vector):\n{(k, V Ci[k], IPi[k], Mi[\u2217, k]) | (Mi[j, k] = 0 \u2228 IPi[k] =\n0) \u2227 V Ci[k] > 0}.\nRM3\" When Pi receives a message m from Pj , it executes the\nfollowing updates:\n\u2200(k,m.V C[k], m.IP[k], m.M[1..n, k]) carried by m:\ncase\nV Ci[k] < m.V C[k] then V Ci[k] := m.V C[k];\nIPi[k] := m.IP[k];\n\u2200 = i : Mi[ , k] := m.M[ , k]\nV Ci[k] = m.V C[k] then IPi[k] := min(IPi[k], m.IP[k]);\n\u2200 =i : Mi[ , k] :=\nmax(Mi[ , k], m.M[ , k])\nV Ci[k] > m.V C[k] then skip\nendcase\nSimilarly to the proofs described in [1], it is possible to\nprove that the previous protocol still satisfies the\nproperty proved in Lemma 6, namely, \u2200i, \u2200m sent by Pi to Pj,\n\u2200k we have (send(m).Mi[j, k] = 1) \u21d2 (send(m).V Ci[k] \u2264\npred(receive(m)).V Cj[k]).\n5\nLet us consider the previously described protocol (Section\n5.2) where the value of each matrix entry Mi[j, k] is always\nequal to 0. The reader can easily verify that this setting\ncorrectly implements the matrix. Moreover, K2(m, k) is then\nalways false: it actually coincides with K1(k, m) (which\ncorresponds to the case where whole vectors have to be\ntransmitted with each message).\n216\nIntuitively, the fact that some columns of matrices M are\nattached to application messages allows a transitive\ntransmission of information. More precisely, the relevant history\nof Pk known by Pj is transmitted to a process Pi via a causal\nsequence of messages from Pj to Pi. In contrast, the\nprotocol described in Section 5.2 used only a direct transmission of\nthis information. In fact, as explained Section 5.1, the\npredicate c (locally implemented by the matrix M) was based on\nthe existence of a message m sent by Pj to Pi, piggybacking\nthe triple (k, m .V C[k], m .IP[k]), and m .V C[k] \u2265 V Ci[k],\ni.e., on the existence of a direct transmission of information\n(by the message m ).\nThe resulting IPT protocol (defined by the rules RM0,\nRM1, RM2\" and RM3\") uses the same condition K2(m, k)\nas the previous one. It shows an interesting tradeoff between\nthe number of triples (k, V Ci[k], IPi[k]) whose transmission\nis saved and the number of boolean vectors that have to\nbe additionally piggybacked. It is interesting to notice that\nthe size of this additional information is bounded while each\ntriple includes a non-bounded integer (namely a vector clock\nvalue).\n6. EXPERIMENTAL STUDY\nThis section compares the behaviors of the previous\nprotocols. This comparison is done with a simulation study.\nIPT1 denotes the protocol presented in Section 3.3 that\nuses the condition K1(m, k) (which is always equal to false).\nIPT2 denotes the protocol presented in Section 5.2 that uses\nthe condition K2(m, k) where messages carry triples.\nFinally, IPT3 denotes the protocol presented in Section 5.3 that\nalso uses the condition K2(m, k) but where messages carry\nadditional boolean vectors.\nThis section does not aim to provide an in-depth\nsimulation study of the protocols, but rather presents a general\nview on the protocol behaviors. To this end, it compares\nIPT2 and IPT3 with regard to IPT1. More precisely, for\nIPT2 the aim was to evaluate the gain in terms of triples\n(k, V Ci[k], IPi[k]) not transmitted with respect to the\nsystematic transmission of whole vectors as done in IPT1. For\nIPT3, the aim was to evaluate the tradeoff between the\nadditional boolean vectors transmitted and the number of saved\ntriples. The behavior of each protocol was analyzed on a set\nof programs.\n6.1 Simulation Parameters\nThe simulator provides different parameters enabling to\ntune both the communication and the processes features.\nThese parameters allow to set the number of processes for\nthe simulated computation, to vary the rate of\ncommunication (send/receive) events, and to alter the time duration\nbetween two consecutive relevant events. Moreover, to be\nindependent of a particular topology of the underlying\nnetwork, a fully connected network is assumed. Internal events\nhave not been considered.\nSince the presence of the triples (k, V Ci[k], IPi[k])\npiggybacked by a message strongly depends on the frequency at\nwhich relevant events are produced by a process, different\ntime distributions between two consecutive relevant events\nhave been implemented (e.g., normal, uniform, and Poisson\ndistributions). The senders of messages are chosen\naccording to a random law. To exhibit particular configurations\nof a distributed computation a given scenario can be\nprovided to the simulator. Message transmission delays follow\na standard normal distribution. Finally, the last parameter\nof the simulator is the number of send events that occurred\nduring a simulation.\n6.2 Parameter Settings\nTo compare the behavior of the three IPT protocols, we\nperformed a large number of simulations using different\nparameters setting. We set to 10 the number of processes\nparticipating to a distributed computation. The number of\ncommunication events during the simulation has been set to\n10 000. The parameter \u03bb of the Poisson time distribution (\u03bb\nis the average number of relevant events in a given time\ninterval) has been set so that the relevant events are generated\nat the beginning of the simulation. With the uniform time\ndistribution, a relevant event is generated (in the average)\nevery 10 communication events. The location parameter of\nthe standard normal time distribution has been set so that\nthe occurrence of relevant events is shifted around the third\npart of the simulation experiment.\nAs noted previously, the simulator can be fed with a\ngiven scenario. This allows to analyze the worst case scenarios\nfor IPT2 and IPT3. These scenarios correspond to the case\nwhere the relevant events are generated at the maximal\nfrequency (i.e., each time a process sends or receives a message,\nit produces a relevant event).\nFinally, the three IPT protocols are analyzed with the\nsame simulation parameters.\n6.3 Simulation Results\nThe results are displayed on the Figures 3.a-3.d. These\nfigures plot the gain of the protocols in terms of the number\nof triples that are not transmitted (y axis) with respect to\nthe number of communication events (x axis). From these\nfigures, we observe that, whatever the time distribution\nfollowed by the relevant events, both IPT2 and IPT3 exhibit\na behavior better than IPT1 (i.e., the total number of\npiggybacked triples is lower in IPT2 and IPT3 than in IPT1),\neven in the worst case (see Figure 3.d).\nLet us consider the worst scenario. In that case, the gain\nis obtained at the very beginning of the simulation and lasts\nas long as it exists a process Pj for which \u2200k : V Cj[k] = 0.\nIn that case, the condition \u2200k : K(m, k) is satisfied. As soon\nas \u2203k : V Cj[k] = 0, both IPT2 and IPT3 behave as IPT1\n(the shape of the curve becomes flat) since the condition\nK(m, k) is no longer satisfied.\nFigure 3.a shows that during the first events of the\nsimulation, the slope of curves IPT2 and IPT3 are steep. The\nsame occurs in Figure 3.d (that depicts the worst case\nscenario). Then the slope of these curves decreases and remains\nconstant until the end of the simulation. In fact, as soon as\nV Cj[k] becomes greater than 0, the condition \u00acK(m, k)\nreduces to (Mi[j, k] = 0 \u2228 IPi[k] = 0).\nFigure 3.b displays an interesting feature. It considers \u03bb =\n100. As the relevant events are taken only during the very\nbeginning of the simulation, this figure exhibits a very steep\nslope as the other figures. The figure shows that, as soon as\nno more relevant events are taken, on average, 45% of the\ntriples are not piggybacked by the messages. This shows\nthe importance of matrix Mi. Furthermore, IPT3 benefits\nfrom transmitting additional boolean vectors to save triple\ntransmissions. The Figures 3.a-3.c show that the average\ngain of IPT3 with respect to IPT2 is close to 10%.\nFinally, Figure 3.c underlines even more the importance\n217\nof matrix Mi. When very few relevant events are taken,\nIPT2 and IPT3 turn out to be very efficient. Indeed, this\nfigure shows that, very quickly, the gain in number of triples\nthat are saved is very high (actually, 92% of the triples are\nsaved).\n6.4 Lessons Learned from the Simulation\nOf course, all simulation results are consistent with the\ntheoretical results. IPT3 is always better than or equal to\nIPT2, and IPT2 is always better than IPT1. The simulation\nresults teach us more:\n\u2022 The first lesson we have learnt concerns the matrix Mi.\nIts use is quite significant but mainly depends on the time\ndistribution followed by the relevant events. On the one\nhand, when observing Figure 3.b where a large number of\nrelevant events are taken in a very short time, IPT2 can save\nup to 45% of the triples. However, we could have\nexpected a more sensitive gain of IPT2 since the boolean vector\nIP tends to stabilize to [1, ..., 1] when no relevant events\nare taken. In fact, as discussed in Section 5.3, the\nmanagement of matrix Mi within IPT2 does not allow a transitive\ntransmission of information but only a direct transmission\nof this information. This explains why some columns of Mi\nmay remain equal to 0 while they could potentially be equal\nto 1. Differently, as IPT3 benefits from transmitting\nadditional boolean vectors (providing a transitive transmission\ninformation) it reaches a gain of 50%.\nOn the other hand, when very few relevant events are\ntaken in a large period of time (see Figure 3.c), the behavior of\nIPT2 and IPT3 turns out to be very efficient since the\ntransmission of up to 92% of the triples is saved. This comes from\nthe fact that very quickly the boolean vector IPi tends to\nstabilize to [1, ..., 1] and that matrix Mi contains very few\n0 since very few relevant events have been taken. Thus, a\ndirect transmission of the information is sufficient to quickly\nget matrices Mi equal to [1, ..., 1], . . . , [1, ..., 1].\n\u2022 The second lesson concerns IPT3, more precisely, the\ntradeoff between the additional piggybacking of boolean\nvectors and the number of triples whose transmission is saved.\nWith n = 10, adding 10 booleans to a triple does not\nsubstantially increases its size. The Figures 3.a-3.c exhibit the\nnumber of triples whose transmission is saved: the average\ngain (in number of triples) of IPT3 with respect to IPT2 is\nabout 10%.\n7. CONCLUSION\nThis paper has addressed an important causality-related\ndistributed computing problem, namely, the Immediate\nPredecessors Tracking problem. It has presented a family of\nprotocols that provide each relevant event with a timestamp\nthat exactly identify its immediate predecessors. The\nfamily is defined by a general condition that allows application\nmessages to piggyback control information whose size can\nbe smaller than n (the number of processes). In that sense,\nthis family defines message size-efficient IPT protocols.\nAccording to the way the general condition is implemented,\ndifferent IPT protocols can be obtained. Three of them have\nbeen described and analyzed with simulation experiments.\nInterestingly, it has also been shown that the efficiency of\nthe protocols (measured in terms of the size of the control\ninformation that is not piggybacked by an application\nmessage) depends on the pattern defined by the communication\nevents and the relevant events.\nLast but not least, it is interesting to note that if one is not\ninterested in tracking the immediate predecessor events, the\nprotocols presented in the paper can be simplified by\nsuppressing the IPi booleans vectors (but keeping the boolean\nmatrices Mi). 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TAPSOFT\"93,\nSpringer-Verlag LNCS 668, pp. 629-643, 1993.\n[5] Fidge C.J., Timestamps in Message-Passing Systems that\nPreserve Partial Ordering, Proc. 11th Australian\nComputing Conference, pp. 56-66, 1988.\n[6] Fromentin E., Jard C., Jourdan G.-V. and Raynal M.,\nOn-the-fly Analysis of Distributed Computations, IPL,\n54:267-274, 1995.\n[7] Fromentin E. and Raynal M., Shared Global States in\nDistributed Computations, JCSS, 55(3):522-528, 1997.\n[8] Fromentin E., Raynal M., Garg V.K. and Tomlinson A.,\nOn-the-Fly Testing of Regular Patterns in Distributed\nComputations. Proc. ICPP\"94, Vol. 2:73-76, 1994.\n[9] Garg V.K., Principles of Distributed Systems, Kluwer\nAcademic Press, 274 pages, 1996.\n[10] H\u00b4elary J.-M., Most\u00b4efaoui A., Netzer R.H.B. and Raynal\nM., Communication-Based Prevention of Useless\nCkeckpoints in Distributed Computations. Distributed\nComputing, 13(1):29-43, 2000.\n[11] H\u00b4elary J.-M., Melideo G. and Raynal M., Tracking\nCausality in Distributed Systems: a Suite of Efficient\nProtocols. Proc. SIROCCO\"00, Carleton University Press,\npp. 181-195, L\"Aquila (Italy), June 2000.\n[12] H\u00b4elary J.-M., Netzer R. and Raynal M., Consistency Issues\nin Distributed Checkpoints. IEEE TSE,\n25(4):274-281, 1999.\n[13] Hurfin M., Mizuno M., Raynal M. and Singhal M., Efficient\nDistributed Detection of Conjunction of Local Predicates\nin Asynch Computations. IEEE TSE, 24(8):664-677, 1998.\n[14] Lamport L., Time, Clocks and the Ordering of Events in a\nDistributed System. Comm. ACM, 21(7):558-565, 1978.\n[15] Marzullo K. and Sabel L., Efficient Detection of a Class of\nStable Properties. Distributed Computing, 8(2):81-91, 1994.\n[16] Mattern F., Virtual Time and Global States of Distributed\nSystems. Proc. Int. Conf. Parallel and Distributed\nAlgorithms, (Cosnard, Quinton, Raynal, Robert Eds),\nNorth-Holland, pp. 215-226, 1988.\n[17] Prakash R., Raynal M. and Singhal M., An Adaptive\nCausal Ordering Algorithm Suited to Mobile Computing\nEnvironment. JPDC, 41:190-204, 1997.\n[18] Raynal M. and Singhal S., Logical Time: Capturing\nCausality in Distributed Systems. IEEE Computer,\n29(2):49-57, 1996.\n[19] Singhal M. and Kshemkalyani A., An Efficient\nImplementation of Vector Clocks. IPL, 43:47-52, 1992.\n[20] Wang Y.M., Consistent Global Checkpoints That Contain\na Given Set of Local Checkpoints. IEEE TOC,\n46(4):456-468, 1997.\n218\n0\n1000\n2000\n3000\n4000\n5000\n6000\n0 2000 4000 6000 8000 10000\ngaininnumberoftriples\ncommunication events number\nIPT1\nIPT2\nIPT3\nrelevant events\n(a) The relevant events follow a uniform distribution\n(ratio=1/10)\n-5000\n0\n5000\n10000\n15000\n20000\n25000\n30000\n35000\n40000\n45000\n50000\n0 2000 4000 6000 8000 10000\ngaininnumberoftriples\ncommunication events number\nIPT1\nIPT2\nIPT3\nrelevant events\n(b) The relevant events follow a Poisson distribution\n(\u03bb = 100)\n0\n10000\n20000\n30000\n40000\n50000\n60000\n70000\n80000\n90000\n100000\n0 2000 4000 6000 8000 10000\ngaininnumberoftriples\ncommunication events number\nIPT1\nIPT2\nIPT3\nrelevant events\n(c) The relevant events follow a normal distribution\n0\n50\n100\n150\n200\n250\n300\n350\n400\n450\n1 10 100 1000 10000\ngaininnumberoftriples\ncommunication events number\nIPT1\nIPT2\nIPT3\nrelevant events\n(d) For each pi, pi takes a relevant event and\nbroadcast to all processes\nFigure 3: Experimental Results\n219", "keywords": "immediate predecessor tracking;relevant event;causality track;transitive reduction;ipt protocol;timestamp;message-pass;hasse diagram;piggybacking;immediate predecessor;tracking causality;common global memory;message transfer delay;checkpointing problem;control information;vector timestamp;distributed computation;vector clock;channel ordering property"}
{"name": "train_C-78", "title": "An Architectural Framework and a Middleware for Cooperating Smart Components", "abstract": "In a future networked physical world, a myriad of smart sensors and actuators assess and control aspects of their environments and autonomously act in response to it. Examples range in telematics, traffic management, team robotics or home automation to name a few. To a large extent, such systems operate proactively and independently of direct human control driven by the perception of the environment and the ability to organize respective computations dynamically. The challenging characteristics of these applications include sentience and autonomy of components, issues of responsiveness and safety criticality, geographical dispersion, mobility and evolution. A crucial design decision is the choice of the appropriate abstractions and interaction mechanisms. Looking to the basic building blocks of such systems we may find components which comprise mechanical components, hardware and software and a network interface, thus these components have different characteristics compared to pure software components. They are able to spontaneously disseminate information in response to events observed in the physical environment or to events received from other component via the network interface. Larger autonomous components may be composed recursively from these building blocks. The paper describes an architectural framework and a middleware supporting a component-based system and an integrated view on events-based communication comprising the real world events and the events generated in the system. It starts by an outline of the component-based system construction. The generic event architecture GEAR is introduced which describes the event-based interaction between the components via a generic event layer. The generic event layer hides the different communication channels including the interactions through the environment. An appropriate middleware is presented which reflects these needs and allows to specify events which have quality attributes to express temporal constraints. This is complemented by the notion of event channels which are abstractions of the underlying network and allow to enforce quality attributes. They are established prior to interaction to reserve the needed computational and network resources for highly predictable event dissemination.", "fulltext": "1. INTRODUCTION\nIn recent years we have seen the continuous improvement\nof technologies that are relevant for the construction of\ndistributed embedded systems, including trustworthy visual,\nauditory, and location sensing [11], communication and\nprocessing. We believe that in a future networked physical\nworld a new class of applications will emerge, composed of\na myriad of smart sensors and actuators to assess and\ncontrol aspects of their environments and autonomously act in\nresponse to it. The anticipated challenging characteristics\nof these applications include autonomy, responsiveness and\nsafety criticality, large scale, geographical dispersion,\nmobility and evolution.\nIn order to deal with these challenges, it is of\nfundamental importance to use adequate high-level models,\nabstractions and interaction paradigms. Unfortunately, when\nfacing the specific characteristics of the target systems, the\nshortcomings of current architectures and middleware\ninteraction paradigms become apparent. Looking to the basic\nbuilding blocks of such systems we may find components\nwhich comprise mechanical parts, hardware, software and\na network interface. However, classical event/object\nmodels are usually software oriented and, as such, when\ntrans28\nported to a real-time, embedded systems setting, their\nharmony is cluttered by the conflict between, on the one side,\nsend/receive of software events (message-based), and on\nthe other side, input/output of hardware or real-world\nevents, register-based. In terms of interaction paradigms,\nand although the use of event-based models appears to be\na convenient solution [10, 22], these often lack the\nappropriate support for non-functional requirements like reliability,\ntimeliness or security.\nThis paper describes an architectural framework and a\nmiddleware, supporting a component-based system and an\nintegrated view on event-based communication comprising\nthe real world events and the events generated in the system.\nWhen choosing the appropriate interaction paradigm it\nis of fundamental importance to address the challenging\nissues of the envisaged sentient applications. Unlike classical\napproaches that confine the possible interactions to the\napplication boundaries, i.e. to its components, we consider\nthat the environment surrounding the application also plays\na relevant role in this respect. Therefore, the paper starts by\nclarifying several issues concerning our view of the system,\nabout the interactions that may take place and about the\ninformation flows. This view is complemented by\nproviding an outline of the component-based system construction\nand, in particular, by showing that it is possible to\ncompose larger applications from basic components, following\nan hierarchical composition approach.\nThis provides the necessary background to introduce the\nGeneric-Events Architecture (GEAR), which describes\nthe event-based interaction between the components via a\ngeneric event layer while allowing the seamless integration\nof physical and computer information flows. In fact, the\ngeneric event layer hides the different communication\nchannels, including the interactions through the environment.\nAdditionally, the event layer abstraction is also adequate\nfor the proper handling of the non-functional requirements,\nnamely reliability and timeliness, which are particularly\nstringent in real-time settings. The paper devotes particular\nattention to this issue by discussing the temporal aspects of\ninteractions and the needs for predictability.\nAn appropriate middleware is presented which reflects\nthese needs and allows to specify events which have quality\nattributes to express temporal constraints. This is\ncomplemented by the notion of Event Channels (EC), which are\nabstractions of the underlying network while being abstracted\nby the event layer. In fact, event channels play a\nfundamental role in securing the functional and non-functional\n(e.g. reliability and timeliness) properties of the envisaged\napplications, that is, in allowing the enforcement of quality\nattributes. They are established prior to interaction to\nreserve the needed computational and network resources for\nhighly predictable event dissemination.\nThe paper is organized as follows. In Section 3 we\nintroduce the fundamental notions and abstractions that we\nadopt in this work to describe the interactions taking place\nin the system. Then, in Section 4, we describe the\ncomponentbased approach that allows composition of objects. GEAR\nis then described in Section 5 and Section 6 focuses on\ntemporal aspects of the interactions. Section 7 describes the\nCOSMIC middleware, which may be used to specify the\ninteraction between sentient objects. A simple example to\nhighlight the ideas presented in the paper appears in\nSection 8 and Section 9 concludes the paper.\n2. RELATED WORK\nOur work considers a wired physical world in which a\nvery large number of autonomous components cooperate.\nIt is inspired by many research efforts in very different\nareas. Event-based systems in general have been introduced to\nmeet the requirements of applications in which entities\nspontaneously generate information and disseminate it [1, 25,\n22]. Intended for large systems and requiring quite complex\ninfrastructures, these event systems do not consider\nstringent quality aspects like timeliness and dependability issues.\nSecondly, they are not created to support inter-operability\nbetween tiny smart devices with substantial resource\nconstraints.\nIn [10] a real-time event system for CORBA has been\nintroduced. The events are routed via a central event server\nwhich provides scheduling functions to support the real-time\nrequirements. Such a central component is not available\nin an infrastructure envisaged in our system architecture\nand the developed middleware TAO (The Ace Orb) is quite\ncomplex and unsuitable to be directly integrated in smart\ndevices.\nThere are efforts to implement CORBA for control\nnetworks, tailored to connect sensor and actuator components [15,\n19]. They are targeted for the CAN-Bus [9], a popular\nnetwork developed for the automotive industry. However, in\nthese approaches the support for timeliness or\ndependability issues does not exist or is only very limited.\nA new scheme to integrate smart devices in a CORBA\nenvironment is proposed in [17] and has lead to the proposal of\na standard by the Object Management Group (OMG) [26].\nSmart transducers are organized in clusters that are\nconnected to a CORBA system by a gateway.\nThe clusters form isolated subnetworks. A special master\nnode enforces the temporal properties in the cluster subnet.\nA CORBA gateway allows to access sensor data and write\nactuator data by means of an interface file system (IFS).\nThe basic structure is similar to the WAN-of-CANs\nstructure which has been introduced in the CORTEX project [4].\nIslands of tight control may be realized by a control network\nand cooperate via wired or wireless networks covering a large\nnumber of these subnetworks. However, in contrast to the\nevent channel model introduced in this paper, all\ncommunication inside a cluster relies on a single technical solution of\na synchronous communication channel. Secondly, although\nthe temporal behaviour of a single cluster is rigorously\ndefined, no model to specify temporal properties for\nclusterto-CORBA or cluster-to-cluster interactions is provided.\n3. INFORMATION FLOW AND\nINTERACTION MODEL\nIn this paper we consider a component-based system model\nthat incorporates previous work developed in the context of\nthe IST CORTEX project [5]. As mentioned above, a\nfundamental idea underlying the approach is that applications can\nbe composed of a large number of smart components that\nare able to sense their surrounding environment and\ninteract with it. These components are referred to as sentient\nobjects, a metaphor elaborated in CORTEX and inspired\non the generic concept of sentient computing introduced in\n[12]. Sentient objects accept input events from a variety of\ndifferent sources (including sensors, but not constrained to\nthat), process them, and produce output events, whereby\n29\nthey actuate on the environment and/or interact with other\nobjects. Therefore, the following kinds of interactions can\ntake place in the system:\nEnvironment-to-object interactions: correspond to a\nflow of information from the environment to\napplication objects, reporting about the state of the former,\nand/or notifying about events taking place therein.\nObject-to-object interactions: correspond to a flow of\ninformation among sentient objects, serving two\npurposes. The first is related with complementing the\nassessment of each individual object about the state\nof the surrounding space. The second is related to\ncollaboration, in which the object tries to influence other\nobjects into contributing to a common goal, or into\nreacting to an unexpected situation.\nObject-to-environment interactions: correspond to a\nflow of information from an object to the environment,\nwith the purpose of forcing a change in the state of the\nlatter.\nBefore continuing, we need to clarify a few issues with\nrespect to these possible forms of interaction. We consider\nthat the environment can be a producer or consumer of\ninformation while interacting with sentient objects. The\nenvironment is the real (physical) world surrounding an\nobject, not necessarily close to the object or limited to certain\nboundaries. Quite clearly, the information produced by the\nenvironment corresponds to the physical representation of\nreal-time entities, of which typical examples include\ntemperature, distance or the state of a door. On the other hand,\nactuation on the environment implies the manipulation of\nthese real-time entities, like increasing the temperature\n(applying more heat), changing the distance (applying some\nmovement) or changing the state of the door (closing or\nopening it). The required transformations between system\nrepresentations of these real-time entities and their physical\nrepresentations is accomplished, generically, by sensors and\nactuators. We further consider that there may exist dumb\nsensors and actuators, which interact with the objects by\ndisseminating or capturing raw transducer information, and\nsmart sensors and actuators, with enhanced processing\ncapabilities, capable of speaking some more elaborate event\ndialect (see Sections 5 and 6.1). Interaction with the\nenvironment is therefore done through sensors and actuators,\nwhich may, or may not be part of sentient objects, as\ndiscussed in Section 4.2.\nState or state changes in the environment are considered\nas events, captured by sensors (in the environment or within\nsentient objects) and further disseminated to other\npotentially interested sentient objects in the system. In\nconsequence, it is quite natural to base the communication and\ninteraction among sentient objects and with the environment\non an event-based communication model. Moreover, typical\nproperties of event-based models, such as anonymous and\nnon-blocking communication, are highly desirable in systems\nwhere sentient objects can be mobile and where interactions\nare naturally very dynamic.\nA distinguishing aspect of our work from many of the\nexisting approaches, is that we consider that sentient objects\nmay indirectly communicate with each other through the\nenvironment, when they act on it. Thus the environment\nconstitutes an interaction and communication channel and\nis in the control and awareness loop of the objects. In other\nwords, when a sentient object actuates on the environment it\nwill be able to observe the state changes in the environment\nby means of events captured by the sensors. Clearly, other\nobjects might as well capture the same events, thus\nestablishing the above-mentioned indirect communication path.\nIn systems that involve interactions with the environment\nit is very important to consider the possibility of\ncommunication through the environment. It has been shown that\nthe hidden channels developing through the latter (e.g.,\nfeedback loops) may hinder software-based algorithms ignoring\nthem [30]. Therefore, any solution to the problem requires\nthe definition of convenient abstractions and appropriate\narchitectural constructs.\nOn the other hand, in order to deal with the information\nflow through the whole computer system and environment in\na seamless way, handling software and hardware events\nuniformly, it is also necessary to find adequate abstractions.\nAs discussed in Section 5, the Generic-Events Architecture\nintroduces the concept of Generic Event and an Event Layer\nabstraction which aim at dealing, among others, with these\nissues.\n4. SENTIENT OBJECT COMPOSITION\nIn this section we analyze the most relevant issues related\nwith the sentient object paradigm and the construction of\nsystems composed of sentient objects.\n4.1 Component-based System Construction\nSentient objects can take several different forms: they\ncan simply be software-based components, but they can also\ncomprise mechanical and/or hardware parts, amongst which\nthe very sensorial apparatus that substantiates sentience,\nmixed with software components to accomplish their task.\nWe refine this notion by considering a sentient object as an\nencapsulating entity, a component with internal logic and\nactive processing elements, able to receive, transform and\nproduce new events. This interface hides the internal\nhardware/software structure of the object, which may be\ncomplex, and shields the system from the low-level functional\nand temporal details of controlling a specific sensor or\nactuator.\nFurthermore, given the inherent complexity of the\nenvisaged applications, the number of simultaneous input events\nand the internal size of sentient objects may become too\nlarge and difficult to handle. Therefore, it should be\npossible to consider the hierarchical composition of sentient\nobjects so that the application logic can be separated across as\nfew or as many of these objects as necessary. On the other\nhand, composition of sentient objects should normally be\nconstrained by the actual hardware component\"s structure,\npreventing the possibility of arbitrarily composing sentient\nobjects. This is illustrated in Figure 1, where a sentient\nobject is internally composed of a few other sentient\nobjects, each of them consuming and producing events, some\nof which only internally propagated.\nObserving the figure, and recalling our previous discussion\nabout the possible interactions, we identify all of them here:\nan object-to-environment interaction occurs between the\nobject controlling a WLAN transmitter and some WLAN\nreceiver in the environment; an environment-to-object\ninteraction takes place when the object responsible for the GPS\n30\nG P S\nr e c e p t i o n\nW i r e l e s s\nt r a n s m i s s i o n\nD o p p l e r\nr a d a r\nP h y s i c a l f e e d b a c k\nO b j e c t ' s b o d y\nI n t e r n a l N e t w o r k\nFigure 1: Component-aware sentient object\ncomposition.\nsignal reception uses the information transmitted by the\nsatellites; finally, explicit object-to-object interactions occur\ninternally to the container object, through an internal\ncommunication network. Additionally, it is interesting to\nobserve that implicit communication can also occur, whether\nthe physical feedback develops through the environment\ninternal to the container object (as depicted) or through the\nenvironment external to this object. However, there is a\nsubtle difference between both cases. While in the former the\nfeedback can only be perceived by objects internal to the\ncontainer, bounding the extent to which consistency must\nbe ensured, such bounds do not exist in the latter. In fact,\nthe notion of sentient object as an encapsulating entity may\nserve other purposes (e.g., the confinement of feedback and\nof the propagation of events), beyond the mere hierarchical\ncomposition of objects.\nTo give a more concrete example of such component-aware\nobject composition we consider a scenario of cooperating\nrobots. Each robot is made of several components,\ncorresponding, for instance, to axis and manipulator controllers.\nTogether with the control software, each of these controllers\nmay be a sentient object. On the other hand, a robot itself\nis a sentient object, composed of the objects materialized\nby the controllers, and the environment internal to its own\nstructure, or body.\nThis means that it should be possible to define\ncooperation activities using the events produced by robot sentient\nobjects, without the need to know the internal structure of\nrobots, or the events produced by body objects or by smart\nsensors within the body. From an engineering point of view,\nhowever, this also means that robot sentient object may\nhave to generate new events that reflect its internal state,\nwhich requires the definition of a gateway to make the bridge\nbetween the internal and external environments.\n4.2 Encapsulation and Scoping\nNow an important question is about how to represent and\ndisseminate events in a large scale networked world. As we\nhave seen above, any event generated by a sentient object\ncould, in principle, be visible anywhere in the system and\nthus received by any other sentient object. However, there\nare substantial obstacles to such universal interactions,\noriginating from the components heterogeneity in such a\nlargescale setting.\nFirstly, the components may have severe performance\nconstraints, particularly because we want to integrate smart\nsensors and actuators in such an architecture. Secondly, the\nbandwidth of the participating networks may vary largely.\nSuch networks may be low power, low bandwidth fieldbuses,\nor more powerful wireless networks as well as high speed\nbackbones. Thirdly, the networks may have widely different\nreliability and timeliness characteristics. Consider a\nplatoon of cooperating vehicles. Inside a vehicle there may be\na field-bus like CAN [8, 9], TTP/A [17] or LIN [20], with a\ncomparatively low bandwidth. On the other hand, the\nvehicles are communicating with others in the platoon via a\ndirect wireless link. Finally, there may be multiple platoons\nof vehicles which are coordinated by an additional wireless\nnetwork layer.\nAt the abstraction level of sentient objects, such\nheterogeneity is reflected by the notion of body-vs-environment.\nAt the network level, we assume the WAN-of-CANs\nstructure [27] to model the different networks. The notion of\nbody and environment is derived from the recursively\ndefined component-based object model. A body is similar to\na cell membrane and represents a quality of service\ncontainer for the sentient objects inside. On the network level,\nit may be associated with the components coupled by a\ncertain CAN. A CAN defines the dissemination quality which\ncan be expected by the cooperating objects.\nIn the above example, a vehicle may be a sentient object,\nwhose body is composed of the respective lower level objects\n(sensors and actuators) which are connected by the internal\nnetwork (see Figure 1). Correspondingly, the platoon can be\nseen itself as an object composed of a collection of\ncooperating vehicles, its body being the environment encapsulated by\nthe platoon zone. At the network level, the wireless network\nrepresents the respective CAN. However, several platoons\nunited by their CANs may interact with each other and\nobjects further away, through some wider-range, possible fixed\nnetworking substrate, hence the concept of WAN-of-CANs.\nThe notions of body-environment and WAN-of-CANs are\nvery useful when defining interaction properties across such\nboundaries. Their introduction obeyed to our belief that\na single mechanism to provide quality measures for\ninteractions is not appropriate. Instead, a high level construct\nfor interaction across boundaries is needed which allows to\nspecify the quality of dissemination and exploits the\nknowledge about body and environment to assess the feasibility of\nquality constraints. As we will see in the following section,\nthe notion of an event channel represents this construct in\nour architecture. It disseminates events and allows the\nnetwork independent specification of quality attributes. These\nattributes must be mapped to the respective properties of\nthe underlying network structure.\n5. A GENERIC EVENTS ARCHITECTURE\nIn order to successfully apply event-based object-oriented\nmodels, addressing the challenges enumerated in the\nintroduction of this paper, it is necessary to use adequate\narchitectural constructs, which allow the enforcement of\nfundamental properties such as timeliness or reliability.\nWe propose the Generic-Events Architecture (GEAR),\ndepicted in Figure 2, which we briefly describe in what\nfollows (for a more detailed description please refer to [29]).\nThe L-shaped structure is crucial to ensure some of the\nproperties described.\nEnvironment: The physical surroundings, remote and close,\nsolid and etherial, of sentient objects.\n31\nC o m m ' sC o m m ' sC o m m ' s\nT r a n s l a t i o n\nL a y e r\nT r a n s l a t i o n\nL a y e r\nB o d y\nE n v i r o n m e n t\nB o d y\nE n v i r o n m e n t\nB o d y\nE n v i r o n m e n t\n( i n c l u d i n g o p e r a t i o n a l n e t w o r k )\n( o f o b j e c t o r o b j e c t c o m p o u n d )\nT r a n s l a t i o n\nL a y e r\nT r a n s l a t i o n\nS e n t i e n t\nO b j e c t\nS e n t i e n t\nO b j e c t\nS e n t i e n t\nO b j e c t\nR e g u l a r N e t w o r k\nc o n s u m ep r o d u c e\nE v e n t\nL a y e r\nE v e n t\nL a y e r\nE v e n t\nL a y e r\nS e n t i e n t\nO b j e c t\nFigure 2: Generic-Events architecture.\nBody: The physical embodiment of a sentient object (e.g.,\nthe hardware where a mechatronic controller resides,\nthe physical structure of a car). Note that due to the\ncompositional approach taken in our model, part of\nwhat is environment to a smaller object seen\nindividually, becomes body for a larger, containing object.\nIn fact, the body is the internal environment of the\nobject. This architecture layering allows composition\nto take place seamlessly, in what concerns information\nflow.\nInside a body there may also be implicit knowledge,\nwhich can be exploited to make interaction more\nefficient, like the knowledge about the number of\ncooperating entities, the existence of a specific\ncommunication network or the simple fact that all components are\nco-located and thus the respective events do not need\nto specify location in their context attributes. Such\nintrinsic information is not available outside a body and,\ntherefore, more explicit information has to be carried\nby an event.\nTranslation Layer: The layer responsible for physical event\ntransformation from/to their native form to event\nchannel dialect, between environment/body and an event\nchannel. Essentially one doing observation and\nactuation operations on the lower side, and doing\ntransactions of event descriptions on the other. On the lower\nside this layer may also interact with dumb sensors or\nactuators, therefore talking the language of the\nspecific device. These interactions are done through\noperational networks (hence the antenna symbol in the\nfigure).\nEvent Layer: The layer responsible for event propagation\nin the whole system, through several Event Channels\n(EC):. In concrete terms, this layer is a kind of\nmiddleware that provides important event-processing services\nwhich are crucial for any realistic event-based system.\nFor example, some of the services that imply the\nprocessing of events may include publishing, subscribing,\ndiscrimination (zoning, filtering, fusion, tracing), and\nqueuing.\nCommunication Layer: The layer responsible for\nwrapping events (as a matter of fact, event descriptions\nin EC dialect) into carrier event-messages, to be\ntransported to remote places. For example, a\nsensing event generated by a smart sensor is wrapped in\nan event-message and disseminated, to be caught by\nwhoever is concerned. The same holds for an\nactuation event produced by a sentient object, to be\ndelivered to a remote smart actuator. Likewise, this may\napply to an event-message from one sentient object\nto another. Dumb sensors and actuators do not send\nevent-messages, since they are unable to understand\nthe EC dialect (they do not have an event layer\nneither a communication layer- they communicate, if\nneeded, through operational networks).\nRegular Network: This is represented in the horizontal\naxis of the block diagram by the communication layer,\nwhich encompasses the usual LAN, TCP/IP, and\nrealtime protocols, desirably augmented with reliable and/or\nordered broadcast and other protocols.\nThe GEAR introduces some innovative ideas in distributed\nsystems architecture. While serving an object model based\non production and consumption of generic events, it treats\nevents produced by several sources (environment, body,\nobjects) in a homogeneous way. This is possible due to the use\nof a common basic dialect for talking about events and due\nto the existence of the translation layer, which performs the\nnecessary translation between the physical representation of\na real-time entity and the EC compliant format. Crucial to\nthe architecture is the event layer, which uses event channels\nto propagate events through regular network infrastructures.\nThe event layer is realized by the COSMIC middleware, as\ndescribed in Section 7.\n5.1 Information Flow in GEAR\nThe flow of information (external environment and\ncomputational part) is seamlessly supported by the L-shaped\narchitecture. It occurs in a number of different ways, which\ndemonstrates the expressiveness of the model with regard to\nthe necessary forms of information encountered in real-time\ncooperative and embedded systems.\nSmart sensors produce events which report on the\nenvironment. Body sensors produce events which report on\nthe body. They are disseminated by the local event layer\nmodule, on an event channel (EC) propagated through the\nregular network, to any relevant remote event layer\nmodules where entities showed an interest on them, normally,\nsentient objects attached to the respective local event layer\nmodules.\nSentient objects consume events they are interested in,\nprocess them, and produce other events. Some of these\nevents are destined to other sentient objects. They are\npublished on an EC using the same EC dialect that serves, e.g.,\nsensor originated events. However, these events are\nsemantically of a kind such that they are to be subscribed by\nthe relevant sentient objects, for example, the sentient\nobjects composing a robot controller system, or, at a higher\nlevel, the sentient objects composing the actual robots in\n32\na cooperative application. Smart actuators, on the other\nhand, merely consume events produced by sentient objects,\nwhereby they accept and execute actuation commands.\nAlternatively to talking to other sentient objects, sentient\nobjects can produce events of a lower level, for example,\nactuation commands on the body or environment. They\npublish these exactly the same way: on an event channel\nthrough the local event layer representative. Now, if these\ncommands are of concern to local actuator units (e.g., body,\nincluding internal operational networks), they are passed on\nto the local translation layer. If they are of concern to a\nremote smart actuator, they are disseminated through the\ndistributed event layer, to reach the former. In any case,\nif they are also of interest to other entities, such as other\nsentient objects that wish to be informed of the actuation\ncommand, then they are also disseminated through the EC\nto these sentient objects.\nA key advantage of this architecture is that event-messages\nand physical events can be globally ordered, if necessary,\nsince they all pass through the event layer. The model also\noffers opportunities to solve a long lasting problem in\nrealtime, computer control, and embedded systems: the\ninconsistency between message passing and the feedback loop\ninformation flow subsystems.\n6. TEMPORAL ASPECTS OF THE\nINTERACTIONS\nAny interaction needs some form of predictability. If safety\ncritical scenarios are considered as it is done in CORTEX,\ntemporal aspects become crucial and have to be made\nexplicit. The problem is how to define temporal constraints\nand how to enforce them by appropriate resource usage in a\ndynamic ad-hoc environment. In an system where\ninteractions are spontaneous, it may be also necessary to determine\ntemporal properties dynamically. To do this, the respective\ntemporal information must be stated explicitly and available\nduring run-time. Secondly, it is not always ensured that\ntemporal properties can be fulfilled. In these cases,\nadaptations and timing failure notification must be provided [2,\n28]. In most real-time systems, the notion of a deadline\nis the prevailing scheme to express and enforce timeliness.\nHowever, a deadline only weakly reflect the temporal\ncharacteristics of the information which is handled. Secondly, a\ndeadline often includes implicit knowledge about the system\nand the relations between activities. In a rather well defined,\nclosed environment, it is possible to make such implicit\nassumptions and map these to execution times and deadlines.\nE.g. the engineer knows how long a vehicle position can be\nused before the vehicle movement outdates this information.\nThus he maps this dependency between speed and position\non a deadline which then assures that the position error\ncan be assumed to be bounded. In a open environment, this\nimplicit mapping is not possible any more because, as an\nobvious reason, the relation between speed and position, and\nthus the error bound, cannot easily be reverse engineered\nfrom a deadline. Therefore, our event model includes\nexplicit quality attributes which allow to specify the temporal\nattributes for every individual event. This is of course an\noverhead compared to the use of implicit knowledge, but in\na dynamic environment such information is needed.\nTo illustrate the problem, consider the example of the\nposition of a vehicle. A position is a typical example for\ntime, value entity [30]. Thus, the position is useful if we\ncan determine an error bound which is related to time, e.g. if\nwe want a position error below 10 meters to establish a safety\nproperty between cooperating cars moving with 5 m/sec,\nthe position has a validity time of 2 seconds. In a time,\nvalue entity entity we can trade time against the precision\nof the value. This is known as value over time and time over\nvalue [18]. Once having established the time-value relation\nand captured in event attributes, subscribers of this event\ncan locally decide about the usefulness of an information. In\nthe GEAR architecture temporal validity is used to reason\nabout safety properties in a event-based system [29]. We\nwill briefly review the respective notions and see how they\nare exploited in our COSMIC event middleware.\nConsider the timeline of generating an event representing\nsome real-time entity [18] from its occurrence to the\nnotification of a certain sentient object (Figure 3). The real-time\nentity is captured at the sensor interface of the system and\nhas to be transformed in a form which can be treated by a\ncomputer. During the time interval t0 the sensor reads the\nreal-time entity and a time stamp is associated with the\nrespective value. The derived time, value entity represents\nan observation. It may be necessary to perform substantial\nlocal computations to derive application relevant\ninformation from the raw sensor data. However, it should be noted\nthat the time stamp of the observation is associated with\nthe capture time and thus independent from further signal\nprocessing and event generation. This close relationship\nbetween capture time and the associated value is supported by\nsmart sensors described above.\nThe processed sensor information is assembled in an event\ndata structure after ts to be published to an event channel.\nAs is described later, the event includes the time stamp of\ngeneration and the temporal validity as attributes.\nThe temporal validity is an application defined measure\nfor the expiration of a time, value . As we explained in\nthe example of a position above, it may vary dependent on\napplication parameters. Temporal validity is a more general\nconcept than that of a deadline. It is independent of a\ncertain technical implementation of a system. While deadlines\nmay be used to schedule the respective steps in an event\ngeneration and dissemination, a temporal validity is an\nintrinsic property of a time, value entity carried in an event.\nA temporal validity allows to reason about the usefulness\nof information and is beneficial even in systems in which\ntimely dissemination of events cannot be enforced because\nit enables timing failure detection at the event consumer. It\nis obvious that deadlines or periods can be derived from the\ntemporal validity of an event. To set a deadline, knowledge\nof an implementation, worst case execution times or\nmessage dissemination latencies is necessary. Thus, in the\ntimeline of Figure 3 every interval may have a deadline. Event\ndissemination through soft real-time channels in COSMIC\nexploits the temporal validity to define dissemination\ndeadlines. Quality attributes can be defined, for instance, in\nterms of validity interval, omission degree pairs. These\nallow to characterize the usefulness of the event for a certain\napplication, in a certain context. Because of that, quality\nattributes of an event clearly depend on higher level issues,\nsuch as the nature of the sentient object or of the smart\nsensor that produced the event. For instance, an event\ncontaining an indication of some vehicle speed must have\ndifferent quality attributes depending on the kind of vehicle\n33\nreal-world\nevent\nobservation:\n<time stamp, value>\nevent generated\nready to be transmitted\nevent\nreceived\nnotification\n, to\nt\nevent\nproducer communication network\nevent\nconsumer\nevent channel\npush <event>\n, ts , tm , tt , tn\n, t o : t i m e t o o b t a i n a n o b s e r v a t i o n\n, t s : t i m e t o p r o c e s s s e n s o r r e a d i n g\n, t m : t i m e t o a s s e m b l e a n e v e n t m e s s a g e\n, t t : t i m e t o t r a n s f e r t h e e v e n t o n t h e r e g u l a r n e t w o r k\n, t n : t i m e f o r n o t i f i c a t i o n o n t h e c o n s u m e r s i t e\nFigure 3: Event processing and dissemination.\nfrom which it originated, or depending on its current speed.\nThe same happens with the position event of the car\nexample above, whose validity depends on the current speed\nand on a predefined required precision. However, since\nquality attributes are strictly related with the semantics of the\napplication or, at least, with some high level knowledge of\nthe purpose of the system (from which the validity of the\ninformation can be derived), the definition of these quality\nattributes may be done by exploiting the information\nprovided at the programming interface. Therefore, it is\nimportant to understand how the system programmer can\nspecify non-functional requirements at the API, and how these\nrequirements translate into quality attributes assigned to\nevents. While temporal validity is identified as an intrinsic\nevent property, which is exploited to decide on the\nusefulness of data at a certain point in time, it is still necessary\nto provide a communication facility which can disseminate\nthe event before the validity is expired.\nIn a WAN-of-CANs network structure we have to cope\nwith very different network characteristics and quality of\nservice properties. Therefore, when crossing the network\nboundaries the quality of service guarantees available in a\ncertain network will be lost and it will be very hard, costly\nand perhaps impossible to achieve these properties in the\nnext larger area of the WAN-of CANs structure. CORTEX\nhas a couple of abstractions to cope with this situation\n(network zones, body/environment) which have been discussed\nabove. From the temporal point of view we need a high\nlevel abstraction like the temporal validity for the\nindividual event now to express our quality requirements of the\ndissemination over the network. The bound, coverage pair,\nintroduced in relation with the TCB [28] seems to be an\nappropriate approach. It considers the inherent uncertainty\nof networks and allows to trade the quality of dissemination\nagainst the resources which are needed. In relation with\nthe event channel model discussed later, the bound,\ncoverage pair allows to specify the quality properties of an event\nchannel independently of specific technical issues. Given\nthe typical environments in which sentient applications will\noperate, where it is difficult or even impossible to provide\ntimeliness or reliability guarantees, we proposed an\nalternative way to handle non-functional application requirements,\nin relation with the TCB approach [28]. The proposed\napproach exploits intrinsic characteristics of applications, such\nas fail-safety, or time-elasticity, in order to secure QoS\nspecifications of the form bound, coverage . Instead of\nconstructing systems that rely on guaranteed bounds, the idea\nis to use (possibly changing) bounds that are secured with a\nconstant probability all over the execution. This obviously\nrequires an application to be able to adapt to changing\nconditions (and/or changing bounds) or, if this is not possible,\nto be able to perform some safety procedures when the\noperational conditions degrade to an unbearable level. The\nbounds we mentioned above refer essentially to timeliness\nbounds associated to the execution of local or distributed\nactivities, or combinations thereof. From these bounds it is\nthen possible to derive the quality attributes, in particular\nvalidity intervals, that characterize the events published in\nthe event channel.\n6.1 The Role of Smart Sensors and Actuators\nSmart devices encapsulate hardware, software and\nmechanical components and provide information and a set of\nwell specified functions and which are closely related to\nthe interaction with the environment. The built-in\ncomputational components and the network interface enable the\nimplementation of a well-defined high level interface that\ndoes not just provide raw transducer data, but a processed,\napplication-related set of events. Moreover, they exhibit an\nautonomous spontaneous behaviour. They differ from\ngeneral purpose nodes because they are dedicated to a certain\nfunctionality which complies to their sensing and\nactuating capabilities while general purpose node may execute any\nprogram.\nConcerning the sentient object model, smart sensors and\nactuators may be basic sentient objects themselves,\nconsuming events from the real-world environment and producing\nthe respective generic events for the system\"s event layer or,\n34\nvice versa consuming a generic event and converting it to a\nreal-world event by an actuation. Smart components\ntherefore constitute the periphery, i.e. the real-world interface of\na more complex sentient object. The model of sentient\nobjects also constitutes the framework to built more complex\nvirtual sensors by relating multiple (primary, i.e. sensors\nwhich directly sense a physical entity) sensors.\nSmart components translate events of the environment\nto an appropriate form available at the event layer or, vice\nversa, transform a system event into an actuation. For smart\ncomponents we can assume that:\n\u2022 Smart components have dedicated resources to\nperform a specific function.\n\u2022 These resources are not used for other purposes during\nnormal real-time operation.\n\u2022 No local temporal conflicts occur that will change the\nobservable temporal behaviour.\n\u2022 The functions of a component can usually only be\nchanged during a configuration procedure which is not\nperformed when the component is involved in critical\noperations.\n\u2022 An observation of the environment as a time,value\npair can be obtained with a bounded jitter in time.\nMany predictability and scheduling problems arise from\nthe fact, that very low level timing behaviours have to be\nhandled on a single processor. Here, temporal\nencapsulation of activities is difficult because of the possible side\neffects when sharing a single processor resource. Consider the\ncontrol of a simple IR-range detector which is used for\nobstacle avoidance. Dependent on its range and the speed of\na vehicle, it has to be polled to prevent the vehicle from\ncrashing into an obstacle. On a single central processor,\nthis critical activity has to be coordinated with many\nsimilar, possibly less critical functions. It means that a very\nfine grained schedule has to be derived based purely on the\nartifacts of the low level device control. In a smart\nsensor component, all this low level timing behaviour can be\noptimized and encapsulated. Thus we can assume temporal\nencapsulation similar to information hiding in the functional\ndomain. Of course, there is still the problem to guarantee\nthat an event will be disseminated and recognized in due\ntime by the respective system components, but this relates\nto application related events rather than the low artifacts of\na device timing. The main responsibility to provide\ntimeliness guarantees is shifted to the event layer where these\nevents are disseminated. Smart sensors thus lead to network\ncentric system model. The network constitute the shared\nresource which has to be scheduled in a predictable way. The\nCOSMIC middleware introduced in the next section is an\napproach to provide predictable event dissemination for a\nnetwork of smart sensors and actuators.\n7. AN EVENT MODEL ANDMIDDLEWARE\nFOR COOPERATING SMART DEVICES\nAn event model and a middleware suitable for smart\ncomponents must support timely and reliable communication\nand also must be resource efficient. COSMIC\n(COoperating Smart devices) is aimed at supporting the\ninteraction between those components according to the concepts\nintroduced so far. Based on the model of a WAN-of-CANs,\nwe assume that the components are connected to some form\nof CAN as a fieldbus or a special wireless sensor network\nwhich provides specific network properties. E.g. a fieldbus\ndeveloped for control applications usually includes\nmechanisms for predictable communication while other networks\nonly support a best effort dissemination. A gateway\nconnects these CANs to the next level in the network hierarchy.\nThe event system should allow the dynamic interaction over\na hierarchy of such networks and comply with the overall\nCORTEX generic event model. Events are typed\ninformation carriers and are disseminated in a publisher/ subscriber\nstyle [24, 7], which is particularly suitable because it\nsupports generative, anonymous communication [3] and does\nnot create any artificial control dependencies between\nproducers of information and the consumers. This decoupling\nin space (no references or names of senders or receivers are\nneeded for communication) and the flow decoupling (no\ncontrol transfer occurs with a data transfer) are well known [24,\n7, 14] and crucial properties to maintain autonomy of\ncomponents and dynamic interactions.\nIt is obvious that not all networks can provide the same\nQoS guarantees and secondly, applications may have widely\ndiffering requirements for event dissemination.\nAdditionally, when striving for predictability, resources have to be\nreserved and data structures must be set up before\ncommunication takes place. Thus, these things can not predictably\nbe made on the fly while disseminating an event. Therefore,\nwe introduced the notion of an event channel to cope with\ndiffering properties and requirements and have an object to\nwhich we can assign resources and reservations. The\nconcept of an event channel is not new [10, 25], however, it has\nnot yet been used to reflect the properties of the underlying\nheterogeneous communication networks and mechanisms as\ndescribed by the GEAR architecture. Rather, existing event\nmiddleware allows to specify the priorities or deadlines of\nevents handled in an event server. Event channels allow\nto specify the communication properties on the level of the\nevent system in a fine grained way. An event channel is\ndefined by:\nevent channel := subject, quality attributeList,\nhandlers\nThe subject determines the types of events event which\nmay be issued to the channel. The quality attributes model\nthe properties of the underlying communication network\nand dissemination scheme. These attributes include latency\nspecifications, dissemination constraints and reliability\nparameters. The notion of zones which represent a guaranteed\nquality of service in a subnetwork support this approach.\nOur goal is to handle the temporal specifications as bound,\ncoverage pairs [28] orthogonal to the more technical\nquestions of how to achieve a certain synchrony property of the\ndissemination infrastructure. Currently, we support\nquality attributes of event channels in a CAN-Bus environment\nrepresented by explicit synchrony classes.\nThe COSMIC middleware maps the channel properties to\nlower level protocols of the regular network. Based on our\nprevious work on predictable protocols for the CAN-Bus,\nCOSMIC defines an abstract network which provides hard,\nsoft and non real-time message classes [21].\nCorrespondingly, we distinguish three event channel classes\naccording to their synchrony properties: hard real-time\nchannels, soft real-time channels and non-real-time channels.\nHard real-time channels (HRTC) guarantee event\npropagation within the defined time constraints in the presence\n35\nof a specified number of omission faults. HRTECs are\nsupported by a reservation scheme which is similar to the scheme\nused in time-triggered protocols like TTP [16][31], TTP/A [17],\nand TTCAN [8]. However, a substantial advantage over a\nTDMA scheme is that due to CAN-Bus properties,\nbandwidth which was reserved but is not needed by a HRTEC\ncan be used by less critical traffic [21].\nSoft real-time channels (SRTC) exploit the temporal\nvalidity interval of events to derive deadlines for scheduling.\nThe validity interval defines the point in time after which\nan event becomes temporally inconsistent. Therefore, in a\nreal-time system an event is useless after this point and may\nme discarded. The transmission deadline (DL) is defined as\nthe latest point in time when a message has to be\ntransmitted and is specified in a time interval which is derived from\nthe expiration time:\ntevent ready < DL < texpiration \u2212 \u2206notification\ntexpiration defines the point in time when the temporal\nvalidity expires. \u2206notification is the expected end-to-end\nlatency which includes the transfer time over the network and\nthe time the event may be delayed by the local event\nhandling in the nodes. As said before, event deadlines are used\nto schedule the dissemination by SRTECs. However,\ndeadlines may be missed in transient overload situations or due\nto arbitrary arrival times of events. On the publisher side\nthe application\"s exception handler is called whenever the\nevent deadline expires before event transmission. At this\npoint in time the event is also not expected to arrive at the\nsubscriber side before the validity expires. Therefore, the\nevent is removed from the sending queue. On the subscriber\nside the expiration time is used to schedule the delivery of\nthe event. If the event cannot be delivered until its\nexpiration time it is removed from the respective queues allocated\nby the COSMIC middleware. This prevents the\ncommunication system to be loaded by outdated messages.\nNon-real-time channels do not assume any temporal\nspecification and disseminate events in a best effort manner. An\ninstance of an event channel is created locally, whenever a\npublisher makes an announcement for publication or a\nsubscriber subscribes for an event notification. When a\npublisher announces publication, the respective data structures\nof an event channel are created by the middleware. When\na subscriber subscribes to an event channel, it may specify\ncontext attributes of an event which are used to filter events\nlocally. E.g. a subscriber may only be interested in events\ngenerated at a certain location. Additionally the subscriber\nspecifies quality properties of the event channel. A more\ndetailed description of the event channels can be found in [13].\nCurrently, COSMIC handles all event channels which\ndisseminate events beyond the CAN network boundary as non\nreal-time event channels. This is mainly because we use the\nTCP/IP protocol to disseminate events over wireless links\nor to the standard Ethernet. However, there are a\nnumber of possible improvements which can easily be integrated\nin the event channel model. The Timely Computing Base\n(TCB) [28] can be exploited for timing failure detection and\nthus would provide awareness for event dissemination in\nenvironments where timely delivery of events cannot be\nenforced. Additionally, there are wireless protocols which can\nprovide timely and reliable message delivery [6, 23] which\nmay be exploited for the respective event channel classes.\nEvents are the information carriers which are exchanged\nbetween sentient objects through event channels. To cope\nwith the requirements of an ad-hoc environment, an event\nincludes the description of the context in which it has been\ngenerated and quality attributes defining requirements for\ndissemination. This is particularly important in an open,\ndynamic environment where an event may travel over\nmultiple networks. An event instance is specified as:\nevent := subject, context attributeList,\nquality attributeList, contents\nA subject defines the type of the event and is related\nto the event contents. It supports anonymous\ncommunication and is used to route an event. The subject has to\nmatch to the subject of the event channel through which\nthe event is disseminated. Attributes are complementary\nto the event contents. They describe individual functional\nand non-functional properties of the event. The context\nattributes describe the environment in which the event has\nbeen generated, e.g. a location, an operational mode or a\ntime of occurrence. The quality attributes specify\ntimeliness and dependability aspects in terms of validity\ninterval, omission degree pairs. The validity interval defines the\npoint in time after which an event becomes temporally\ninconsistent [18]. As described above, the temporal validity\ncan be mapped to a deadline. However, usually a\ndeadline is an engineering artefact which is used for scheduling\nwhile the temporal validity is a general property of a time,\nvalue entity. In a environment where a deadline cannot\nbe enforced, a consumer of an event eventually must decide\nwhether the event still is temporally consistent, i.e.\nrepresents a valid time, value entity.\n7.1 The Architecture of the COSMIC\nMiddleware\nOn the architectural level, COSMIC distinguish three\nlayers roughly depicted in Figure 4. Two of them, the event\nlayer and the abstract network layer are implemented by the\nCOSMIC middleware. The event layer provides the API for\nthe application and realizes the abstraction of event and\nevent channels.\nThe abstract network implements real-time message classes\nand adapts the quality requirements to the underlying real\nnetwork. An event channel handler resides in every node. It\nsupports the programming interface and provides the\nnecessary data structures for event-based communication.\nWhenever an object subscribes to a channel or a publisher\nannounces a channel, the event channel handler is involved. It\ninitiates the binding of the channel\"s subject, which is\nrepresented by a network independent unique identifier to an\naddress of the underlying abstract network to enable\ncommunication [14]. The event channel handler then tightly\ncooperates with the respective handlers of the abstract network\nlayer to disseminate events or receive event notifications. It\nshould be noted that the QoS properties of the event layer\nin general depend on what the abstract network layer can\nprovide. Thus, it may not always be possible to e.g. support\nhard real-time event channels because the abstract network\nlayer cannot provide the respective guarantees. In [13], we\ndescribe the protocols and services of the abstract network\nlayer particularly for the CAN-Bus.\nAs can be seen in Figure 4, the hard real-time (HRT)\nmessage class is supported by a dedicated handler which is\nable to provide the time triggered message dissemination.\n36\n\u0014\nevent\nnotifications\nHRT-msg\nlist\nSRT-msg\nqueue\nNRT-msg\nqueue\nHRT-msg\ncalendar\nHRTC\nHandler\nS/NRTC\nHandler\nAbstract Network\nLayer\nCAN Layer\nRX Buffer TX Buffer\nRX, TX, error\ninterrupts\nEvent Channel\nSpecs.\nEvent Layer\nsend\nmessages\nexception\nnotification\nexceptions,\nnotifications\nECH:\nEvent Channel\nHandler\np u b l i s h a n n o u n c e s u b s c r i b e\nb i n d i n g\np r o t o c o l\nc o n f i g .\np r o t o c o l\nGlobal\nTime\nService\nevent\nnotifications\nHRT-msg\nlist\nSRT-msg\nqueue\nNRT-msg\nqueue\nHRT-msg\ncalendar\nHRTC\nHandler\nS/NRTC\nHandler\nAbstract Network\nLayer\nCAN Layer\nRX Buffer TX Buffer\nRX, TX, error\ninterrupts\nEvent Channel\nSpecs.\nEvent Layer\nsend\nmessages\nexception\nnotification\nexceptions,\nnotifications\nECH:\nEvent Channel\nHandler\np u b l i s h a n n o u n c e s u b s c r i b e\nb i n d i n g\np r o t o c o l\nc o n f i g .\np r o t o c o l\nGlobal\nTime\nService\nFigure 4: Architecture layers of COSMIC.\nThe HRT handler maintains the HRT message list, which\ncontains an entry for each local HRT message to be sent.\nThe entry holds the parameters for the message, the\nactivation status and the binding information. Messages are\nscheduled on the bus according to the HRT message\ncalendar which comprises the precise start time for each time slot\nallocated for a message. Soft real-time message queues order\noutgoing messages according to their transmission deadlines\nderived from the temporal validity interval. If the\ntransmission deadline is exceeded, the event message is purged out of\nthe queue. The respective application is notified via the\nexception notification interface and can take actions like trying\nto publish the event again or publish it to a channel of\nanother class. Incoming event messages are ordered according\nto their temporal validity. If an event message arrive, the\nrespective applications are notified. At the moment, an\noutdated message is deleted from the queue and if the queue\nruns out of space, the oldest message is discarded.\nHowever, there are other policies possible depending on event\nattributes and available memory space. Non real-time\nmessages are FIFO ordered in a fixed size circular buffer.\n7.2 Status of COSMIC\nThe goal for developing COSMIC was to provide a\nplatform to seamlessly integrate smart tiny components in a\nlarge system. Therefore, COSMIC should run also on the\nsmall, resource constraint devices which are built around\n16Bit or even 8-Bit micro-controllers. The distributed\nCOSMIC middleware has been implemented and tested on\nvarious platforms. Under RT-Linux, we support the real-time\nchannels over the CAN Bus as described above. The\nRTLinux version runs on Pentium processors and is currently\nevaluated before we intent to port it to a smart sensor or\nactuator. For the interoperability in a WAN-of-CANs\nenvironment, we only provide non real-time channels at the\nmoment. This version includes a gateway between the\nCANbus and a TCP/IP network. It allows us to use a\nstandard wireless 802.11 network. The non real-time version of\nCOSMIC is available on Linux, RT-Linux and on the\nmicrocontroller families C167 (Infineon) and 68HC908 (Motorola).\nBoth micro-controllers have an on-board CAN controller\nand thus do not require additional hardware components for\nthe network. The memory footprint of COSMIC is about 13\nKbyte on a C167 and slightly more on the 68HC908 where it\nfits into the on-board flash memory without problems.\nBecause only a few channels are required on such a smart sensor\nor actuator component, the requirement of RAM (which is\na scarce resource on many single chip systems) to hold the\ndynamic data structures of a channel is low. The COSMIC\nmiddleware makes it very easy to include new smart sensors\nin an existing system. Particularly, the application running\non a smart sensor to condition and process the raw physical\ndata must not be aware of any low level network specific\ndetails. It seamlessly interacts with other components of the\nsystem exclusively via event channels.\nThe demo example, briefly described in the next chapter,\nis using a distributed infrastructure of tiny smart sensors\nand actuators directly cooperating via event channels over\nheterogeneous networks.\n8. AN ILLUSTRATIVE EXAMPLE\nA simple example for many important properties of the\nproposed system showing the coordination through the\nenvironment and events disseminated over the network is the\ndemo of two cooperating robots depicted in Figure 5.\nEach robot is equipped with smart distance sensors, speed\nsensors, acceleration sensors and one of the robots (the guide\n(KURT2) in front (Figure 5)) has a tracking camera\nallowing to follow a white line. The robots form a WAN-of-CANs\nsystem in which their local CANs are interconnected via a\nwireless 802.11 network. COSMIC provides the event layer\nfor seamless interaction. The blind robot (N.N.) is\nsearching the guide randomly. Whenever the blind robot detects\n(by its front distance sensors) an obstacle, it checks whether\nthis may be the guide. For this purpose, it dynamically\nsubscribes to the event channel disseminating distance events\nfrom rear distance sensors of the guide(s) and compares\nthese with the distance events from its local front sensors.\nIf the distance is approximately the same it infers that it\nis really behind a guide. Now N.N. also subscribes to the\nevent channels of the tracking camera and the speed sensors\n37\nFigure 5: Cooperating robots.\nto follow the guide. The demo application highlights the\nfollowing properties of the system:\n1. Dynamic interaction of robots which is not known in\nadvance. In principle, any two a priori unknown robots\ncan cooperate. All what publishers and subscribers\nhave to know to dynamically interact in this\nenvironment is the subject of the respective event class. A\nproblem will be to receive only the events of the robot\nwhich is closest. A robot identity does not help much\nto solve this problem. Rather, the position of the event\ngeneration entity which is captured in the respective\nattributes can be evaluated to filter the relevant event\nout of the event stream. A suitable wireless protocol\nwhich uses proximity to filter events has been proposed\nby Meier and Cahill [22] in the CORTEX project.\n2. Interaction through the environment. The\ncooperation between the robots is controlled by sensing the\ndistance between the robots. If the guide detects that\nthe distance grows, it slows down. Respectively, if the\nblind robot comes too close it reduces its speed. The\nlocal distance sensors produce events which are\ndisseminated through a low latency, highly predictable event\nchannel. The respective reaction time can be\ncalculated as function of the speed and the distance of the\nrobots and define a dynamic dissemination deadline\nfor events. Thus, the interaction through the\nenvironment will secure the safety properties of the\napplication, i.e. the follower may not crash into the guide and\nthe guide may not loose the follower. Additionally, the\nrobots have remote subscriptions to the respective\ndistance events which are used to check it with the local\nsensor readings to validate that they really follow the\nguide which they detect with their local sensors.\nBecause there may be longer latencies and omissions, this\ncheck occasionally will not be possible. The\nunavailability of the remote events will decrease the quality\nof interaction and probably and slow down the robots,\nbut will not affect safety properties.\n3. Cooperative sensing. The blind robot subscribes to the\nevents of the line tracking camera. Thus it can see\nthrough the eye of the guide. Because it knows the\ndistance to the guide and the speed as well, it can foresee\nthe necessary movements. The proposed system\nprovides the architectural framework for such a\ncooperation. The respective sentient object controlling the\nactuation of the robot receives as input the position\nand orientation of the white line to be tracked. In the\ncase of the guide robot, this information is directly\ndelivered as a body event with a low latency and a high\nreliability over the internal network. For the follower\nrobot, the information comes also via an event channel\nbut with different quality attributes. These quality\nattributes are reflected in the event channel description.\nThe sentient object controlling the actuation of the\nfollower is aware of the increased latency and higher\nprobability of omission.\n9. CONCLUSION AND FUTURE WORK\nThe paper addresses problems of building large distributed\nsystems interacting with the physical environment and\nbeing composed from a huge number of smart components.\nWe cannot assume that the network architecture in such a\nsystem is homogeneous. Rather multiple edge- networks\nare fused to a hierarchical, heterogeneous wide area\nnetwork. They connect the tiny sensors and actuators\nperceiving the environment and providing sentience to the\napplication. Additionally, mobility and dynamic deployment of\ncomponents require the dynamic interaction without fixed,\na priori known addressing and routing schemes. The work\npresented in the paper is a contribution towards the\nseamless interaction in such an environment which should not be\nrestricted by technical obstacles. Rather it should be\npossible to control the flow of information by explicitly specifying\nfunctional and temporal dissemination constraints.\nThe paper presented the general model of a sentient\nobject to describe composition, encapsulation and interaction\nin such an environment and developed the Generic Event\nArchitecture GEAR which integrates the interaction through\nthe environment and the network. While appropriate\nabstractions and interaction models can hide the functional\nheterogeneity of the networks, it is impossible to hide the\nquality differences. Therefore, one of the main concerns is\nto define temporal properties in such an open\ninfrastructure. The notion of an event channel has been introduced\nwhich allows to specify quality aspects explicitly. They can\nbe verified at subscription and define a boundary for event\ndissemination. The COSMIC middleware is a first attempt\nto put these concepts into operation. COSMIC allows the\ninteroperability of tiny components over multiple network\nboundaries and supports the definition of different real-time\nevent channel classes.\nThere are many open questions that emerged from our\nwork. One direction of future research will be the inclusion\nof real-world communication channels established between\nsensors and actuators in the temporal analysis and the\nordering of such events in a cause-effect chain. Additionally,\nthe provision of timing failure detection for the adaptation\nof interactions will be in the focus of our research. To reduce\nnetwork traffic and only disseminate those events to the\nsubscribers which they are really interested in and which have\na chance to arrive timely, the encapsulation and scoping\nschemes have to be transformed into respective multi-level\nfiltering rules. The event attributes which describe aspects\nof the context and temporal constraints for the\ndissemination will be exploited for this purpose. Finally, it is intended\nto integrate the results in the COSMIC middleware to\nenable experimental assessment.\n38\n10. REFERENCES\n[1] J. Bacon, K. Moody, J. Bates, R. Hayton, C. Ma,\nA. McNeil, O. Seidel, and M. Spiteri. Generic support\nfor distributed applications. IEEE Computer,\n33(3):68-76, 2000.\n[2] L. B. Becker, M. Gergeleit, S. Schemmer, and E. Nett.\nUsing a flexible real-time scheduling strategy in a\ndistributed embedded application. 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In Proc. 2003 IEEE Conference on Emerging\nTechnologies and Factory Automation, Lisbon,\nPortugal, Sept. 2003.\n[14] J. Kaiser and M. Mock. Implementing the real-time\npublisher/subscriber model on the controller area\nnetwork (CAN). In Proceedings of the 2nd International\nSymposium on Object-oriented Real-time distributed\nComputing (ISORC99), Saint-Malo, France, May 1999.\n[15] K. Kim, G. Jeon, S. Hong, T. Kim, and S. Kim.\nIntegrating subscription-based and connection-oriented\ncommunications into the embedded CORBA for\nthe CAN Bus. In Proceedings of the IEEE Real-time\nTechnology and Application Symposium, May 2000.\n[16] H. Kopetz and G. Gr\u00a8unsteidl. TTP - A\nTime-Triggered Protocol for Fault-Tolerant Real-Time\nSystems. Technical Report rr-12-92, Institut f\u00a8ur\nTechnische Informatik, Technische Universit\u00a8at Wien,\nTreilstr. 3/182/1, A-1040 Vienna, Austria, 1992.\n[17] H. Kopetz, M. Holzmann, and W. Elmenreich. A\nUniversal Smart Transducer Interface: TTP/A.\nInternational Journal of Computer System, Science\nEngineering, 16(2), Mar. 2001.\n[18] H. Kopetz and P. Ver\u00b4\u0131ssimo. Real-time and\nDependability Concepts. In S. J. Mullender, editor,\nDistributed Systems, 2nd Edition, ACM-Press,\nchapter 16, pages 411-446. Addison-Wesley, 1993.\n[19] S. Lankes, A. Jabs, and T. Bemmerl. Integration of a\nCAN-based connection-oriented communication model\ninto Real-Time CORBA. In Workshop on Parallel and\nDistributed Real-Time Systems, Nice, France, Apr.\n2003.\n[20] Local Interconnect Network: LIN Specification\nPackage Revision 1.2. Technical report, Nov. 2000.\n[21] M. Livani, J. Kaiser, and W. Jia. Scheduling hard and\nsoft real-time communication in the controller area\nnetwork. Control Engineering, 7(12):1515-1523, 1999.\n[22] R. Meier and V. Cahill. Steam: Event-based\nmiddleware for wireless ad-hoc networks. In Proceedings\nof the International Workshop on Distributed\nEvent-Based Systems (ICDCS/DEBS\"02), pages\n639-644, Vienna, Austria, 2002.\n[23] E. Nett and S. Schemmer. Reliable real-time\ncommunication in cooperative mobile applications.\nIEEE Transactions on Computers, 52(2):166-180, Feb.\n2003.\n[24] B. Oki, M. Pfluegl, A. Seigel, and D. Skeen. The\ninformation bus - an architecture for extensible\ndistributed systems. Operating Systems Review,\n27(5):58-68, 1993.\n[25] O. M. G. (OMG). CORBAservices: Common Object\nServices Specification - Notification Service\nSpecification, Version 1.0, 2000.\n[26] O. M. G. (OMG). Smart transducer interface, initial\nsubmission, June 2001.\n[27] P. Ver\u00b4\u0131ssimo, V. Cahill, A. Casimiro, K. Cheverst,\nA. Friday, and J. Kaiser. Cortex: Towards supporting\nautonomous and cooperating sentient entities. In\nProceedings of European Wireless 2002, Florence, Italy,\nFeb. 2002.\n[28] P. Ver\u00b4\u0131ssimo and A. Casimiro. The Timely Computing\nBase model and architecture. Transactions on\nComputers - Special Issue on Asynchronous Real-Time\nSystems, 51(8):916-930, Aug. 2002.\n[29] P. Ver\u00b4\u0131ssimo and A. Casimiro. Event-driven support of\nreal-time sentient objects. In Proceedings of the 8th\nIEEE International Workshop on Object-oriented\nReal-time Dependable Systems, Guadalajara, Mexico,\nJan. 2003.\n[30] P. Ver\u00b4\u0131ssimo and L. Rodrigues. Distributed Systems for\nSystem Architects. Kluwer Academic Publishers, 2001.\n39", "keywords": "smart sensor;sensor and actuator;corba;dissemination quality;sentient object;event channel;real-time entity;generic event architecture;gear architecture;soft real-time channel;temporal constraint;event-based system;cosmic middleware;middleware architecture;cortex;temporal validity;event-base communication;componentbase system;sentient computing"}
{"name": "train_C-79", "title": "A Cross-Layer Approach to Resource Discovery and Distribution in Mobile ad-hoc Networks", "abstract": "This paper describes a cross-layer approach to designing robust P2P system over mobile ad-hoc networks. The design is based on simple functional primitives that allow routing at both P2P and network layers to be integrated to reduce overhead. With these primitives, the paper addresses various load balancing techniques. Preliminary simulation results are also presented.", "fulltext": "1. INTRODUCTION\nMobile ad-hoc networks (MANETs) consist of mobile nodes that\nautonomously establish connectivity via multi-hop wireless\ncommunications. Without relying on any existing, pre-configured\nnetwork infrastructure or centralized control, MANETs are useful\nin situations where impromptu communication facilities are\nrequired, such as battlefield communications and disaster relief\nmissions. As MANET applications demand collaborative\nprocessing and information sharing among mobile nodes, resource\n(service) discovery and distribution have become indispensable\ncapabilities.\nOne approach to designing resource discovery and distribution\nschemes over MANETs is to construct a peer-to-peer (P2P)\nsystem (or an overlay) which organizes peers of the system into a\nlogical structure, on top of the actual network topology. However,\ndeploying such P2P systems over MANETs may result in either a\nlarge number of flooding operations triggered by the reactive\nrouting process, or inefficiency in terms of bandwidth utilization in\nproactive routing schemes. Either way, constructing an overlay\nwill potentially create a scalability problem for large-scale\nMANETs.\nDue to the dynamic nature of MANETs, P2P systems should be\nrobust by being scalable and adaptive to topology changes. These\nsystems should also provide efficient and effective ways for peers\nto interact, as well as other desirable application specific features.\nThis paper describes a design paradigm that uses the following\ntwo functional primitives to design robust resource discovery and\ndistribution schemes over MANETs.\n1. Positive/negative feedback. Query packets are used to\nexplore a route to other peers holding resources of interest.\nOptionally, advertisement packets are sent out to advertise\nroutes from other peers about available resources. When\ntraversing a route, these control packets measure goodness\nof the route and leave feedback information on each node\nalong the way to guide subsequent control packets to\nappropriate directions.\n2. Sporadic random walk. As the network topology and/or\nthe availability of resources change, existing routes may\nbecome stale while better routes become available. Sporadic\nrandom walk allows a control packet to explore different\npaths and opportunistically discover new and/or better\nroutes.\nAdopting this paradigm, the whole MANET P2P system operates\nas a collection of autonomous entities which consist of different\ntypes of control packets such as query and advertisement packets.\nThese packets work collaboratively, but indirectly, to achieve\ncommon tasks, such as resource discovery, routing, and load\nbalancing. With collaboration among these entities, a MANET P2P\nsystem is able to \u2018learn\" the network dynamics by itself and adjust\nits behavior accordingly, without the overhead of organizing peers\ninto an overlay.\nThe remainder of this paper is organized as follows. Related work\nis described in the next section. Section 3 describes the resource\ndiscovery scheme. Section 4 describes the resource distribution\nscheme. The replica invalidation scheme is described in Section 5,\nfollowed by it performance evaluation in Section 6. Section 7\nconcludes the paper.\n2. RELATED WORK\nFor MANETs, P2P systems can be classified based on the design\nprinciple, into layered and cross-layer approaches. A layered\napproach adopts a P2P-like [1] solution, where resource discovery is\nfacilitated as an application layer protocol and query/reply\nmessages are delivered by the underlying MANET routing protocols.\nFor instance, Konark [2] makes use of a underlying multicast\nprotocol such that service providers and queriers advertise and\nsearch services via a predefined multicast group, respectively.\nProem [3] is a high-level mobile computing platform for P2P\nsystems over MANETs. It defines a transport protocol that sits on\ntop of the existing TCP/IP stack, hence relying on an existing\nrouting protocol to operate. With limited control over how control\nand data packets are routed in the network, it is difficult to avoid\nthe inefficiency of the general-purpose routing protocols which\nare often reactive and flooding-based.\nIn contrast, cross-layer approaches either relies on its own routing\nmechanism or augments existing MANET routing algorithms to\nsupport resource discovery. 7DS [4], which is the pioneering\nwork deploying P2P system on mobile devices, exploits data\nlocality and node mobility to dissemination data in a single-hop\nfashion. Hence, long search latency may be resulted as a 7DS\nnode can get data of interest only if the node that holds the data is\nin its radio coverage. Mohan et al. [5] propose an adaptive service\ndiscovery algorithm that combines both push and pull models.\nSpecifically, a service provider/querier broadcasts\nadvertisement/query only when the number of nodes advertising or\nquerying, which is estimated by received control packets, is below a\nthreshold during a period of time. In this way, the number of\ncontrol packets on the network is constrained, thus providing good\nscalability. Despite the mechanism to reduce control packets, high\noverhead may still be unavoidable, especially when there are\nmany clients trying to locate different services, due to the fact that\nthe algorithm relies on flooding,\nFor resource replication, Yin and Cao [6] design and evaluate\ncooperative caching techniques for MANETs. Caching, however,\nis performed reactively by intermediate nodes when a querier\nrequests data from a server. Data items or resources are never\npushed into other nodes proactively. Thanedar et al. [7] propose a\nlightweight content replication scheme using an expanding ring\ntechnique. If a server detects the number of requests exceed a\nthreshold within a time period, it begins to replicate its data onto\nnodes capable of storing replicas, whose hop counts from the\nserver are of certain values. Since data replication is triggered by\nthe request frequency alone, it is possible that there are replicas\nunnecessarily created in a large scope even though only nodes\nwithin a small range request this data. Our proposed resource\nreplication mechanism, in contrast, attempts to replicate a data\nitem in appropriate areas, instead of a large area around the server,\nwhere the item is requested frequently.\n3. RESOURCE DISCOVERY\nWe propose a cross-layer, hybrid resource discovery scheme that\nrelies on the multiple interactions of query, reply and\nadvertisement packets. We assume that each resource is associated with a\nunique ID1\n. Initially, when a node wants to discover a resource, it\ndeploys query packets, which carry the corresponding resource\nID, and randomly explore the network to search for the requested\nresource. Upon receiving such a query packet, a reply packet is\ngenerated by the node providing the requested resource.\nAdvertisement packets can also be used to proactively inform other\nnodes about what resources are available at each node. In addition\nto discovering the \u2018identity\" of the node providing the requested\nresource, it may be also necessary to discover a \u2018route\" leading to\nthis node for further interaction.\nTo allow intermediate nodes to make a decision on where to\nforward query packets, each node maintains two tables: neighbor\n1\nThe assumption of unique ID is made for brevity in exposition,\nand resources could be specified via attribute-value assertions.\ntable and pheromone table. The neighbor table maintains a list of\nall current neighbors obtained via a neighbor discovery protocol.\nThe pheromone table maintains the mapping of a resource ID and\na neighbor ID to a pheromone value. This table is initially empty,\nand is updated by a reply packet generated by a successful query.\nFigure 1 illustrates an example of a neighbor table and a\npheromone table maintained by node A having four neighbors. When\nnode A receives a query packet searching for a resource, it makes\na decision to which neighbor it should forward the query packet\nby computing the desirability of each of the neighbors that have\nnot been visited before by the same query packet. For a resource\nID r, the desirability of choosing a neighbor n, \u03b4(r,n), is obtained\nfrom the pheromone value of the entry whose neighbor and\nresource ID fields are n and r, respectively. If no such entry exists in\nthe pheromone table, \u03b4(r,n) is set to zero.\nOnce the desirabilities of all valid next hops have been calculated,\nthey are normalized to obtain the probability of choosing each\nneighbor. In addition, a small probability is also assigned to those\nneighbors with zero desirability to exercise the sporadic random\nwalk primitive. Based on these probabilities, a next hop is\nselected to forward the query packet to. When a query packet\nencounters a node with a satisfying resource, a reply packet is\nreturned to the querying node. The returning reply packet also\nupdates the pheromone table at each node on its return trip by\nincreasing the pheromone value in the entry whose resource ID and\nneighbor ID fields match the ID of the discovered resource and\nthe previous hop, respectively. If such an entry does not exist, a\nnew entry is added into the table. Therefore, subsequent query\npackets looking for the same resource, when encountering this\npheromone information, are then guided toward the same\ndestination with a small probability of taking an alternate path.\nSince the hybrid discovery scheme neither relies on a MANET\nrouting protocol nor arranges nodes into a logical overlay, query\npackets are to traverse the actual network topology. In dense\nnetworks, relatively large nodal degrees can have potential impacts\non this random exploring mechanism. To address this issue, the\nhybrid scheme also incorporates proactive advertisement in\naddition to the reactive query. To perform proactive advertisement,\neach node periodically deploys an advertising packet containing a\nlist of its available resources\" IDs. These packets will traverse\naway from the advertising node in a random walk manner up to a\nlimited number of hops and advertise resource information to\nsurrounding nodes in the same way as reply packets. In the hybrid\nscheme, an increase of pheromone serves as a positive feedback\nwhich indirectly guides query packets looking for similar\nresources. Intuitively, the amount of pheromone increased is\ninversely proportional to the distance the reply packet has traveled\nback, and other metrics, such as quality of the resource, could\ncontribute to this amount as well. Each node also performs an\nimplicit negative feedback for resources that have not been given\na positive feedback for some time by regularly decreasing the\npheromone in all of its pheromone table entries over time. In\naddition, pheromone can be reduced by an explicit negative response,\nfor instance, a reply packet returning from a node that is not\nwilling to provide a resource due to excessive workload. As a result,\nload balancing can be achieved via positive and negative\nfeedback. A node serving too many nodes can either return fewer\nresponses to query packets or generate negative responses.\n2 The 3rd International Conference on Mobile Technology, Applications and Systems - Mobility 2006\nFigure 1: Example illustrating neighbor and pheromone tables maintained by node A: (a) wireless connectivity around A showing\nthat it currently has four neighbors, (b) A\"s neighbor table, and (c) a possible pheromone table of A\nFigure 2: Sample scenarios illustrating the three mechanisms supporting load-balancing: (a) resource replication, (b) resource\nrelocation, and (c) resource division\n4. RESOURCE DISTRIBUTION\nIn addition to resource discovery, a querying node usually\nattempts to access and retrieve the contents of a resource after a\nsuccessful discovery. In certain situations, it is also beneficial to\nmake a resource readily available at multiple nodes when the\nresource can be relocated and/or replicated, such as data files.\nFurthermore, in MANETs, we should consider not only the amount\nof load handled by a resource provider, but also the load on those\nintermediate nodes that are located on the communication paths\nbetween the provider and other nodes as well. Hence, we describe\na cross-layer, hybrid resource distribution scheme to achieve load\nbalancing by incorporating the functionalities of resource\nrelocation, resource replication, and resource division.\n4.1 Resource Replication\nMultiple replicas of a resource in the network help prevent a\nsingle node, as well as nodes surrounding it, from being overloaded\nby a large number of requests and data transfers. An example is\nwhen a node has obtained a data file from another node, the\nrequesting node and the intermediate nodes can cache the file and\nstart sharing that file with other surrounding nodes right away. In\naddition, replicable resources can also be proactively replicated at\nother nodes which are located in certain strategic areas. For\ninstance, to help nodes find a resource quickly, we could replicate\nthe resource so that it becomes reachable by random walk for a\nspecific number of hops from any node with some probability, as\ndepicted in Figure 2(a).\nTo realize this feature, the hybrid resource distribution scheme\nemploys a different type of control packet, called resource\nreplication packet, which is responsible for finding an appropriate\nplace to create a replica of a resource. A resource replication\npacket of type R is deployed by a node that is providing the\nresource R itself. Unlike a query packet which follows higher\npheromone upstream toward a resource it is looking for, a\nresource replication packet tends to be propelled away from similar\nresources by moving itself downstream toward weaker\npheromone. When a resource replication packet finds itself in an area\nwith sufficiently low pheromone, it makes a decision whether it\nshould continue exploring or turn back. The decision depends on\nconditions such as current workload and/or remaining energy of\nthe node being visited, as well as popularity of the resource itself.\n4.2 Resource Relocation\nIn certain situations, a resource may be required to transfer from\none node to another. For example, a node may no longer want to\npossess a file due to the shortage of storage space, but it cannot\nsimply delete the file since other nodes may still need it in the\nfuture. In this case, the node can choose to create replicas of the\nfile by the aforementioned resource replication mechanism and\nthen delete its own copy. Let us consider a situation where a\nmajority of nodes requesting for a resource are located far away from\na resource provider, as shown on the top of Figure 2(b). If the\nresource R is relocatable, it is preferred to be relocated to another\narea that is closer to those nodes, similar to the bottom of the\nsame figure. Hence network bandwidth is more efficiently\nutilized.\nThe 3rd Conference on Mobile Technology, Applications and Systems - Mobility 2006 3\nThe hybrid resource distribution scheme incorporates resource\nrelocation algorithms that are adaptive to user requests and aim to\nreduce communication overhead. Specifically, by following the\nsame pheromone maintenance concept, the hybrid resource\ndistribution scheme introduces another type of pheromone which\ncorresponds to user requests, instead of resources. This type of\npheromone, called request pheromone, is setup by query packets\nthat are in their exploring phases (not returning ones) to guide a\nresource to a new location.\n4.3 Resource Division\nCertain types of resources can be divided into smaller\nsubresources (e.g., a large file being broken into smaller files) and\ndistributed to multiple locations to avoid overloading a single\nnode, as depicted in Figure 2(c). The hybrid resource distribution\nscheme incorporates a resource division mechanism that operates\nat a thin layer right above all the other mechanisms described\nearlier. The resource division mechanism is responsible for\ndecomposing divisible resources into sub-resources, and then adds\nan extra keyword to distinguish each sub-resource from one\nanother. Therefore, each of these sub-resources will be seen by the\nother mechanisms as one single resource which can be\nindependently discovered, replicated, and relocated. The resource division\nmechanism is also responsible for combining data from these\nsubresources together (e.g., merging pieces of a file) and delivering\nthe final result to the application.\n5. REPLICA INVALIDATION\nAlthough replicas improve accessibility and balance load, replica\ninvalidation becomes a critical issue when nodes caching\nupdatable resources may concurrently update their own replicas,\nwhich renders replicas held by other nodes obsolete. Most\nexisting solutions to the replica invalidation problem either impose\nconstrains that only the data source could perform update and\ninvalidate other replicas, or resort to network-wide flooding which\nresults in heavy network traffic and leads to scalability problem,\nor both. The lack of infrastructure supports and frequent topology\nchanges in MANETs further challenge the issue.\nWe apply the same cross-layer paradigm to invalidating replicas\nin MANETs which allows concurrent updates performed by\nmultiple replicas. To coordinate concurrent updates and disseminate\nreplica invalidations, a special infrastructure, called validation\nmesh or mesh for short, is adaptively maintained among nodes\npossessing \u2018valid\" replicas of a resource. Once a node has updated\nits replica, an invalidation packet will only be disseminated over\nthe validation mesh to inform other replica-possessing nodes that\ntheir replicas become invalid and should be deleted. The structure\n(topology) of the validation mesh keeps evolving (1) when nodes\nrequest and cache a resource, (2) when nodes update their\nrespective replicas and invalidate other replicas, and (3) when nodes\nmove. To accommodate the dynamics, our scheme integrates the\ncomponents of swarm intelligence to adaptively maintain the\nvalidation mesh without relying on any underlying MANET routing\nprotocol. In particular, the scheme takes into account concurrent\nupdates initiated by multiple nodes to ensure the consistency\namong replicas. In addition, version number is used to distinguish\nnew from old replicas when invalidating any stale replica.\nSimulation results show that the proposed scheme effectively facilitates\nconcurrent replica updates and efficiently perform replica\ninvalidation without incurring network-wide flooding.\nFigure 3 depicts the idea of \u2018validation mesh\" which maintains\nconnectivity among nodes holding valid replicas of a resource to\navoid network-wide flooding when invalidating replicas.\nFigure 3: Examples showing maintenance of validation mesh\nThere are eight nodes in the sample network, and we start with\nonly node A holding the valid file, as shown in Figure 3(a). Later\non, node G issues a query packet for the file and eventually\nobtains the file from A via nodes B and D. Since intermediate nodes\nare allowed to cache forwarded data, nodes B, D, and G will now\nhold valid replicas of the file. As a result, a validation mesh is\nestablished among nodes A, B, D, and G, as depicted in Figure\n3(b). In Figure 3(c), another node, H, has issued a query packet\nfor the same file and obtained it from node B\"s cache via node E.\nAt this point, six nodes hold valid replicas and are connected\nthrough the validation mesh. Now we assume node G updates its\nreplica of the file and informs the other nodes by sending an\ninvalidation packet over the validation mesh. Consequently, all\nother nodes except G remove their replicas of the file from their\nstorage and the validation mesh is torn down. However, query\nforwarding pheromone, as denoted by the dotted arrows in Figure\n3(d), is setup at these nodes via the \u2018reverse paths\" in which the\ninvalidation packets have traversed, so that future requests for this\nfile will be forwarded to node G. In Figure 3(e), node H makes a\nnew request for the file again. This time, its query packet follows\nthe pheromone toward node G, where the updated file can be\nobtained. Eventually, a new validation mesh is established over\nnodes G, B, D, E, and H.\nTo maintain a validation mesh among the nodes holding valid\nreplicas, one of them is designated to be the focal node. Initially,\nthe node that originally holds the data is the focal node. As nodes\nupdate replicas, the node that last (or most recently) updates a\n4 The 3rd International Conference on Mobile Technology, Applications and Systems - Mobility 2006\ncorresponding replica assumes the role of focal node. We also\nname nodes, such as G and H, who originate requests to replicate\ndata as clients, and nodes B, D, and E who locally cache passing\ndata as data nodes. For instance, in Figures 3(a), 3(b), and 3(c),\nnode A is the focal node; in Figures 3(d), 3(e), and 3(f), node G\nbecomes the focal node. In addition, to accommodate newly\nparticipating nodes and mobility of nodes, the focal node periodically\nfloods the validation mesh with a keep-alive packet, so that nodes\nwho can hear this packet are considered themselves to be part of\nthe validation mesh. If a node holding a valid/updated replica\ndoesn\"t hear a keep-alive packet for a certain time interval, it will\ndeploy a search packet using the resource discovery mechanism\ndescribed in Section 3 to find another node (termed attachment\npoint) currently on the validation mesh so that it can attach itself\nto. Once an attachment point is found, a search_reply packet is\nreturned to the disconnected node who originated the search.\nIntermediate nodes who forward the search_reply packet will\nbecome part of the validation mesh as well. To illustrate the effect of\nnode mobility, in Figure 3(f), node H has moved to a location\nwhere it is not directly connected to the mesh. Via the resource\ndiscovery mechanism, node H relies on an intermediate node F to\nconnect itself to the mesh. Here, node F, although part of the\nvalidation mesh, doesn\"t hold data replica, and hence is termed\nnondata node.\nClient and data node who keep hearing the keep-alive packets\nfrom the focal node act as if they are holding a valid replica, so\nthat they can reply to query packets, like node B in Figure 3(c)\nreplying a request from node H. While a disconnected node\nattempting to discover an attachment point to reattach itself to the\nmesh, the disconnected node can\"t reply to a query packet. For\ninstance, in Figure 3(f), node H does not reply to any query packet\nbefore it reattaches itself to the mesh.\nAlthough validation mesh provides a conceptual topology that (1)\nconnects all replicas together, (2) coordinates concurrent updates,\nand (3) disseminates invalidation packets, the technical issue is\nhow such a mesh topology could be effectively and efficiently\nmaintained and evolved when (a) nodes request and cache a\nresource, (b) when nodes update their respective replicas and\ninvalidate other replicas, and (c) when nodes move. Without relying\non any MANET routing protocols, the two primitives work\ntogether to facilitate efficient search and adaptive maintenance.\n6. PERFORMANCE EVALUATION\nWe have conducted simulation experiments using the QualNet\nsimulator to evaluate the performance of the described resource\ndiscovery, resource distribution, and replica invalidation schemes.\nHowever, due to space limitation only the performance of the\nreplica invalidation is reported. In our experiments, eighty nodes\nare uniformly distributed over a terrain of size 1000\u00d71000 m2\n.\nEach node has a communication range of approximately 250 m\nover a 2 Mbps wireless channel, using IEEE802.11 as the MAC\nlayer. We use the random-waypoint mobility model with a pause\ntime of 1 second. Nodes may move at the minimum and maximum\nspeeds of 1 m/s and 5 m/s, respectively. Table 1 lists other\nparameter settings used in the simulation. Initially, there is one\nresource server node in network. Two nodes are randomly picked\nup every 10 seconds as clients. Every \u03b2 seconds, we check the\nnumber of nodes, N, which have gotten data. Then we randomly\npickup Min(\u03b3,N) nodes from them to initiate data update. Each\nexperiment is run for 10 minutes.\nTable 1: Simulation Settings\nHOP_LIMIT 10\nADVERTISE_HOP_LIMIT 1\nKEEPALIVE_INTERVAL 3 second\nNUM_SEARCH 1\nADVERTISE_INTERVAL 5 second\nEXPIRATION_INTERVAL 10 second\nAverage Query Generation Rate 2 query/ 10 sec\nMax # of Concurrent Update (\u03b3) 2\nFrequency of Update (\u03b2) 3s\nWe evaluate the performance under different mobility speed, the\ndensity, the maximum number of concurrent update nodes, and\nupdate frequency using two metrics:\n\u2022 Average overhead per update measures the average number of\npackets transmitted per update in the network.\n\u2022 Average delay per update measures how long our approach\ntakes to finish an update on average.\nAll figures shown present the results with a 70% confidence\ninterval.\nFigure 4: Overhead vs. speed\nfor 80 nodes\nFigure 5: Overhead vs. density\nFigure 6: Overhead vs. max\n#concurrent updates\nFigure 7: Overhead vs. freq.\nFigure 8: Delay vs. speed Figure 9: Delay vs. density\nThe 3rd Conference on Mobile Technology, Applications and Systems - Mobility 2006 5\nFigure 10: Delay vs. max\n#concurrent updates\nFigure 11: Delay vs. freq.\nFigures 4, 5, 6, and 7 show the overhead versus various parameter\nvalues. In Figure 4, the overhead increases as the speed increase,\nwhich is due to the fact that as the speed increase, nodes move out\nof mesh more frequently, and will send out more search packets.\nHowever, the overhead is not high, and even in speed 10m/sec,\nthe overhead is below 100 packets. In contrast, the packets will be\nexpected to be more than 200 packets at various speeds when\nflooding is used.\nFigure 5 shows that the overhead almost remains the same under\nvarious densities. That is attributed to only flooding over the mesh\ninstead of the whole network. The size of mesh doesn\"t vary much\non various densities, so that the overhead doesn\"t vary much.\nFigure 6 shows that overhead also almost remains the same under\nvarious maximum number of concurrent updates. That\"s because\none more node just means one more flood over the mesh during\nupdate process so that the impact is limited.\nFigure 7 shows that if updates happen more frequently, the\noverhead is higher. This is because the more quickly updates happen,\n(1) there will be more keep_alive message over the mesh between\ntwo updates, and (2) nodes move out of mesh more frequently and\nsend out more search packets.\nFigures 8, 9, 10, and 11 show the delay versus various parameter\nvalues. From Figure 8, we know the delay increases as the speed\nincreases, which is due to the fact that with increasing speed,\nclients will move out of mesh with higher probability. When these\nclients want to update data, they will spend time to first search the\nmesh. The faster the speed, the more time clients need to spend to\nsearch the mesh.\nFigure 9 shows that delay is negligibly affected by the density.\nDelay decreases slightly as the number of nodes increases, due to\nthe fact that the more nodes in the network, the more nodes\nreceives the advertisement packets which helps the search packet\nfind the target so that the delay of update decreases.\nFigure 10 shows that delay decreases slightly as the maximum\nnumber of concurrent updates increases. The larger the maximum\nnumber of concurrent updates is, the more nodes are picked up to\ndo update. Then with higher probability, one of these nodes is still\nin mesh and finishes the update immediately (don\"t need to search\nmesh first), which decreases the delay.\nFigure 11 shows how the delay varies with the update frequency.\nWhen updates happen more frequently, the delay will higher.\nBecause the less frequently, the more time nodes in mesh have to\nmove out of mesh then they need to take time to search the mesh\nwhen they do update, which increases the delay.\nThe simulation results show that the replica invalidation scheme\ncan significantly reduce the overhead with an acceptable delay.\n7. CONCLUSION\nTo facilitate resource discovery and distribution over MANETs,\none approach is to designing peer-to-peer (P2P) systems over\nMANETs which constructs an overlay by organizing peers of the\nsystem into a logical structure on the top of MANETs\" physical\ntopology. However, deploying overlay over MANETs may result\nin either a large number of flooding operations triggered by the\nrouting process, or inefficiency in terms of bandwidth usage.\nSpecifically, overlay routing relies on the network-layer routing\nprotocols. In the case of a reactive routing protocol, routing on the\noverlay may cause a large number of flooded route discovery\nmessage since the routing path in each routing step must be\ndiscovered on demand. On the other hand, if a proactive routing\nprotocol is adopted, each peer has to periodically broadcast\ncontrol messages, which leads to poor efficiency in terms of\nbandwidth usage. Either way, constructing an overlay will potentially\nsuffer from the scalability problem. The paper describes a design\nparadigm that uses the functional primitives of positive/negative\nfeedback and sporadic random walk to design robust resource\ndiscovery and distribution schemes over MANETs. In particular,\nthe scheme offers the features of (1) cross-layer design of P2P\nsystems, which allows the routing process at both the P2P and the\nnetwork layers to be integrated to reduce overhead, (2) scalability\nand mobility support, which minimizes the use of global flooding\noperations and adaptively combines proactive resource\nadvertisement and reactive resource discovery, and (3) load balancing,\nwhich facilitates resource replication, relocation, and division to\nachieve load balancing.\n8. REFERENCES\n[1] A. Oram, Peer-to-Peer: Harnessing the Power of Disruptive\nTechnologies. O\"Reilly, March 2000.\n[2] S. Helal, N. Desai, V. Verma, and C. Lee, Konark - A\nService Discovery and Delivery Protocol for ad-hoc\nNetworks, in the Third IEEE Conference on Wireless\nCommunication Networks (WCNC), New Orleans, Louisiana, 2003.\n[3] G. Krotuem, Proem: A Peer-to-Peer Computing Platform\nfor Mobile ad-hoc Networks, in Advanced Topic Workshop\nMiddleware for Mobile Computing, Germany, 2001.\n[4] M. Papadopouli and H. Schulzrinne, A Performance\nAnalysis of 7DS a Peer-to-Peer Data Dissemination and\nPrefetching Tool for Mobile Users, in Advances in wired and\nwireless communications, IEEE Sarnoff Symposium Digest,\nEwing, NJ, 2001, (Best student paper & poster award).\n[5] U. Mohan, K. Almeroth, and E. Belding-Royer, Scalable\nService Discovery in Mobile ad-hoc Networks, in IFIP\nNetworking Conference, Athens, Greece, May 2004.\n[6] L. Yin and G. Cao, Supporting Cooperative Caching in Ad\nHoc Networks, in IEEE INFOCOM, 2004.\n[7] V. Thanedar, K. Almeroth, and E. Belding-Royer, A\nLightweight Content Replication Scheme for Mobile ad-hoc\nEnvironments, in IFIP Networking Conference, Athens, Greece,\nMay 2004.\n6 The 3rd International Conference on Mobile Technology, Applications and Systems - Mobility 2006", "keywords": "manet routing protocol;resource discovery;query packet;mobile ad-hoc network;manet p2p system;manet;neighbor discovery protocol;concurrent update;replica invalidation;invalidation packet;route discovery message;validation mesh;hybrid discovery scheme;negative feedback"}
{"name": "train_C-80", "title": "Consistency-preserving Caching of Dynamic Database Content", "abstract": "With the growing use of dynamic web content generated from relational databases, traditional caching solutions for throughput and latency improvements are ineffective. We describe a middleware layer called Ganesh that reduces the volume of data transmitted without semantic interpretation of queries or results. It achieves this reduction through the use of cryptographic hashing to detect similarities with previous results. These benefits do not require any compromise of the strict consistency semantics provided by the back-end database. Further, Ganesh does not require modifications to applications, web servers, or database servers, and works with closed-source applications and databases. Using two benchmarks representative of dynamic web sites, measurements of our prototype show that it can increase end-to-end throughput by as much as twofold for non-data intensive applications and by as much as tenfold for data intensive ones.", "fulltext": "1. INTRODUCTION\nAn increasing fraction of web content is dynamically generated\nfrom back-end relational databases. Even when database content\nremains unchanged, temporal locality of access cannot be exploited\nbecause dynamic content is not cacheable by web browsers or by\nintermediate caching servers such as Akamai mirrors. In a\nmultitiered architecture, each web request can stress the WAN link\nbetween the web server and the database. This causes user\nexperience to be highly variable because there is no caching to\ninsulate the client from bursty loads. Previous attempts in caching\ndynamic database content have generally weakened transactional\nsemantics [3, 4] or required application modifications [15, 34].\nWe report on a new solution that takes the form of a\ndatabaseagnostic middleware layer called Ganesh. Ganesh makes no effort\nto semantically interpret the contents of queries or their results.\nInstead, it relies exclusively on cryptographic hashing to detect\nsimilarities with previous results. Hash-based similarity detection has\nseen increasing use in distributed file systems [26, 36, 37] for\nimproving performance on low-bandwidth networks. However, these\ntechniques have not been used for relational databases. Unlike\nprevious approaches that use generic methods to detect similarity,\nGanesh exploits the structure of relational database results to yield\nsuperior performance improvement.\nOne faces at least three challenges in applying hash-based\nsimilarity detection to back-end databases. First, previous work in this\nspace has traditionally viewed storage content as uninterpreted bags\nof bits with no internal structure. This allows hash-based\ntechniques to operate on long, contiguous runs of data for maximum\neffectiveness. In contrast, relational databases have rich internal\nstructure that may not be as amenable to hash-based similarity\ndetection. Second, relational databases have very tight integrity and\nconsistency constraints that must not be compromised by the use\nof hash-based techniques. Third, the source code of commercial\ndatabases is typically not available. This is in contrast to previous\nwork which presumed availability of source code.\nOur experiments show that Ganesh, while conceptually simple,\ncan improve performance significantly at bandwidths\nrepresentative of today\"s commercial Internet. On benchmarks modeling\nmultitiered web applications, the throughput improvement was as high\nas tenfold for data-intensive workloads. For workloads that were\nnot data-intensive, throughput improvements of up to twofold were\nobserved. Even when bandwidth was not a constraint, Ganesh had\nlow overhead and did not hurt performance. Our experiments also\nconfirm that exploiting the structure present in database results is\ncrucial to this performance improvement.\n2. BACKGROUND\n2.1 Dynamic Content Generation\nAs the World Wide Web has grown, many web sites have\ndecentralized their data and functionality by pushing them to the edges\nof the Internet. Today, eBusiness systems often use a three-tiered\narchitecture consisting of a front-end web server, an application\nserver, and a back-end database server. Figure 1 illustrates this\narchitecture. The first two tiers can be replicated close to a\nconcentration of clients at the edge of the Internet. This improves user\nexperience by lowering end-to-end latency and reducing exposure\nWWW 2007 / Track: Performance and Scalability Session: Scalable Systems for Dynamic Content\n311\nBack-End Database\nServer\nFront-End Web and\nApplication Servers\nFigure 1: Multi-Tier Architecture\nto backbone traffic congestion. It can also increase the availability\nand scalability of web services.\nContent that is generated dynamically from the back-end database\ncannot be cached in the first two tiers. While databases can be\neasily replicated in a LAN, this is infeasible in a WAN because of\nthe difficult task of simultaneously providing strong consistency,\navailability, and tolerance to network partitions [7]. As a result,\ndatabases tend to be centralized to meet the strong consistency\nrequirements of many eBusiness applications such as banking,\nfinance, and online retailing [38]. Thus, the back-end database is\nusually located far from many sets of first and second-tier nodes [2].\nIn the absence of both caching and replication, WAN bandwidth\ncan easily become a limiting factor in the performance and\nscalability of data-intensive applications.\n2.2 Hash-Based Systems\nGanesh\"s focus is on efficient transmission of results by\ndiscovering similarities with the results of previous queries. As SQL queries\ncan generate large results, hash-based techniques lend themselves\nwell to the problem of efficiently transferring these large results\nacross bandwidth constrained links.\nThe use of hash-based techniques to reduce the volume of data\ntransmitted has emerged as a common theme of many recent\nstorage systems, as discussed in Section 8.2. These techniques rely\non some basic assumptions. Cryptographic hash functions are\nassumed to be collision-resistant. In other words, it is\ncomputationally intractable to find two inputs that hash to the same output. The\nfunctions are also assumed to be one-way; that is, finding an\ninput that results in a specific output is computationally infeasible.\nMenezes et al. [23] provide more details about these assumptions.\nThe above assumptions allow hash-based systems to assume that\ncollisions do not occur. Hence, they are able to treat the hash of a\ndata item as its unique identifier. A collection of data items\neffectively becomes content-addressable, allowing a small hash to serve\nas a codeword for a much larger data item in permanent storage or\nnetwork transmission.\nThe assumption that collisions are so rare as to be effectively\nnon-existent has recently come under fire [17]. However, as\nexplained by Black [5], we believe that these issues do not form a\nconcern for Ganesh. All communication is between trusted parts\nof the system and an adversary has no way to force Ganesh to\naccept invalid data. Further, Ganesh does not depend critically on any\nspecific hash function. While we currently use SHA-1, replacing it\nwith a different hash function would be simple. There would be\nno impact on performance as stronger hash functions (e.g.\nSHA256) only add a few extra bytes and the generated hashes are still\norders of magnitude smaller than the data items they represent. No\nre-hashing of permanent storage is required since Ganesh only uses\nhashing on volatile data.\n3. DESIGN AND IMPLEMENTATION\nGanesh exploits redundancy in the result stream to avoid\ntransmitting result fragments that are already present at the query site.\nRedundancy can arise naturally in many different ways. For\nexample, a query repeated after a certain interval may return a different\nresult because of updates to the database; however, there may be\nsignificant commonality between the two results. As another\nexample, a user who is refining a search may generate a sequence\nof queries with overlapping results. When Ganesh detects\nredundancy, it suppresses transmission of the corresponding result\nfragments. Instead, it transmits a much smaller digest of those\nfragments and lets the query site reconstruct the result through hash\nlookup in a cache of previous results. In effect, Ganesh uses\ncomputation at the edges to reduce Internet communication.\nOur description of Ganesh focuses on four aspects. We first\nexplain our approach to detecting similarity in query results. Next,\nwe discuss how the Ganesh architecture is completely invisible to\nall components of a multi-tier system. We then describe Ganesh\"s\nproxy-based approach and the dataflow for detecting similarity.\n3.1 Detecting Similarity\nOne of the key design decisions in Ganesh is how similarity is\ndetected. There are many potential ways to decompose a result into\nfragments. The optimal way is, of course, the one that results in the\nsmallest possible object for transmission for a given query\"s results.\nFinding this optimal decomposition is a difficult problem because\nof the large space of possibilities and because the optimal choice\ndepends on many factors such as the contents of the query\"s result,\nthe history of recent results, and the cache management algorithm.\nWhen an object is opaque, the use of Rabin fingerprints [8, 30]\nto detect common data between two objects has been successfully\nshown in the past by systems such as LBFS [26] and CASPER [37].\nRabin fingerprinting uses a sliding window over the data to\ncompute a rolling hash. Assuming that the hash function is uniformly\ndistributed, a chunk boundary is defined whenever the lower order\nbits of the hash value equal some predetermined value. The\nnumber of lower order bits used defines the average chunk size. These\nsub-divided chunks of the object become the unit of comparison for\ndetecting similarity between different objects.\nAs the locations of boundaries found by using Rabin fingerprints\nis stochastically determined, they usually fail to align with any\nstructural properties of the underlying data. The algorithm\ntherefore deals well with in-place updates, insertions and deletions.\nHowever, it performs poorly in the presence of any reordering of data.\nFigure 2 shows an example where two results, A and B,\nconsisting of three rows, have the same data but have different sort\nattributes. In the extreme case, Rabin fingerprinting might be unable\nto find any similar data due to the way it detects chunk boundaries.\nFortunately, Ganesh can use domain specific knowledge for more\nprecise boundary detection. The information we exploit is that a\nquery\"s result reflects the structure of a relational database where\nall data is organized as tables and rows. It is therefore simple to\ncheck for similarity with previous results at two granularities: first\nthe entire result, and then individual rows. The end of a row in a\nresult serves as a natural chunk boundary. It is important to note that\nusing the tabular structure in results only involves shallow\ninterpretation of the data. Ganesh does not perform any deeper semantic\ninterpretation such as understanding data types, result schema, or\nintegrity constraints.\nTuning Rabin fingerprinting for a workload can also be difficult.\nIf the average chunk size is too large, chunks can span multiple\nresult rows. However, selecting a smaller average chunk size\nincreases the amount of metadata required to the describe the results.\nWWW 2007 / Track: Performance and Scalability Session: Scalable Systems for Dynamic Content\n312\nFigure 2: Rabin Fingerprinting vs. Ganesh\"s Chunking\nThis, in turn, would decrease the savings obtained via its use.\nRabin fingerprinting also needs two computationally-expensive passes\nover the data: once to determine chunk boundaries and one again to\ngenerate cryptographic hashes for the chunks. Ganesh only needs\na single pass for hash generation as the chunk boundaries are\nprovided by the data\"s natural structure.\nThe performance comparison in Section 6 shows that Ganesh\"s\nrow-based algorithm outperforms Rabin fingerprinting. Given that\nprevious work has already shown that Rabin fingerprinting\nperforms better than gzip [26], we do not compare Ganesh to\ncompression algorithms in this paper.\n3.2 Transparency\nThe key factor influencing our design was the need for Ganesh\nto be completely transparent to all components of a typical\neBusiness system: web servers, application servers, and database servers.\nWithout this, Ganesh stands little chance of having a significant\nreal-world impact. Requiring modifications to any of the above\ncomponents would raise the barrier for entry of Ganesh into an\nexisting system, and thus reduce its chances of adoption. Preserving\ntransparency is simplified by the fact that Ganesh is purely a\nperformance enhancement, not a functionality or usability enhancement.\nWe chose agent interposition as the architectural approach to\nrealizing our goal. This approach relies on the existence of a compact\nprogramming interface that is already widely used by target\nsoftware. It also relies on a mechanism to easily add new code without\ndisrupting existing module structure.\nThese conditions are easily met in our context because of the\npopularity of Java as the programming language for eBusiness\nsystems. The Java Database Connectivity (JDBC) API [32] allows\nJava applications to access a wide variety of databases and even\nother tabular data repositories such as flat files. Access to these\ndata sources is provided by JDBC drivers that translate between\nthe JDBC API and the database communication mechanism.\nFigure 3(a) shows how JDBC is typically used in an application.\nAs the JDBC interface is standardized, one can substitute one\nJDBC driver for another without application modifications. The\nJDBC driver thus becomes the natural module to exploit for code\ninterposition. As shown in Figure 3(b), the native JDBC driver is\nreplaced with a Ganesh JDBC driver that presents the same\nstandardized interface. The Ganesh driver maintains an in-memory\ncache of result fragments from previous queries and performs\nreassembly of results. At the database, we add a new process called\nthe Ganesh proxy. This proxy, which can be shared by multiple\nfront-end nodes, consists of two parts: code to detect similarity\nin result fragments and the original native JDBC driver that\ncommunicates with the database. The use of a proxy at the database\nmakes Ganesh database-agnostic and simplifies prototyping and\nexperimentation. Ganesh is thus able to work with a wide range\nof databases and applications, requiring no modifications to either.\n3.3 Proxy-Based Caching\nThe native JDBC driver shown in Figure 3(a) is a lightweight\ncode component supplied by the database vendor. Its main\nfuncClient\nDatabase\nWeb and\nApplication Server\nNative JDBC Driver\nWAN\n(a) Native Architecture\nClient\nDatabase\nGanesh Proxy\nNative JDBC Driver\nWAN\nWeb and\nApplication Server\nGanesh JDBC Driver\n(b) Ganesh\"s Interposition-based Architecture\nFigure 3: Native vs. Ganesh Architecture\ntion is to mediate communication between the application and the\nremote database. It forwards queries, buffers entire results, and\nresponds to application requests to view parts of results.\nThe Ganesh JDBC driver shown in Figure 3(b) presents the\napplication with an interface identical to that provided by the native\ndriver. It provides the ability to reconstruct results from compact\nhash-based descriptions sent by the proxy. To perform this\nreconstruction, the driver maintains an in-memory cache of\nrecentlyreceived results. This cache is only used as a source of result\nfragments in reconstructing results. No attempt is made by the Ganesh\ndriver or proxy to track database updates. The lack of cache\nconsistency does not hurt correctness as a description of the results is\nalways fetched from the proxy - at worst, there will be no\nperformance benefit from using Ganesh. Stale data will simply be paged\nout of the cache over time.\nThe Ganesh proxy accesses the database via the native JDBC\ndriver, which remains unchanged between Figures 3(a) and (b).\nThe database is thus completely unaware of the existence of the\nproxy. The proxy does not examine any queries received from\nthe Ganesh driver but passes them to the native driver. Instead,\nthe proxy is responsible for inspecting database output received\nfrom the native driver, detecting similar results, and generating\nhash-based encodings of these results whenever enough similarity\nis found. While this architecture does not decrease the load on a\ndatabase, as mentioned earlier in Section 2.1, it is much easier to\nreplicate databases for scalability in a LAN than in a WAN.\nTo generate a hash-based encoding, the proxy must be aware of\nwhat result fragments are available in the Ganesh driver\"s cache.\nOne approach is to be optimistic, and to assume that all result\nfragments are available. This will result in the smallest possible initial\ntransmission of a result. However, in cases where there is little\noverlap with previous results, the Ganesh driver will have to make\nmany calls to the proxy during reconstruction to fetch missing\nresult fragments. To avoid this situation, the proxy loosely tracks the\nstate of the Ganesh driver\"s cache. Since both components are\nunder our control, it is relatively simple to do this without resorting\nto gray-box techniques or explicit communication for maintaining\ncache coherence. Instead, the proxy simulates the Ganesh driver\"s\ncache management algorithm and uses this to maintain a list of\nhashes for which the Ganesh driver is likely to possess the result\nfragments. In case of mistracking, there will be no loss of\ncorrectness but there will be extra round-trip delays to fetch the missing\nfragments. If the client detects loss of synchronization with the\nproxy, it can ask the proxy to reset the state shared between them.\nAlso note that the proxy does not need to keep the result fragments\nthemselves, only their hashes. This allows the proxy to remain\nscalable even when it is shared by many front-end nodes.\nWWW 2007 / Track: Performance and Scalability Session: Scalable Systems for Dynamic Content\n313\nObject Output Stream\nConvert ResultSet\nObject Input Stream\nConvert ResultSet\nAll Data\nRecipe\nResultSet\nAll Data\nResultSet\nNetwork\nGanesh Proxy Ganesh JDBC Driver\nResult\nSet\nRecipe\nResult\nSet\nYes\nYes\nNo\nNo\nGaneshInputStream\nGaneshOutputStream\nFigure 4: Dataflow for Result Handling\n3.4 Encoding and Decoding Results\nThe Ganesh proxy receives database output as Java objects from\nthe native JDBC driver. It examines this output to see if a Java\nobject of type ResultSet is present. The JDBC interface uses\nthis data type to store results of database queries. If a ResultSet\nobject is found, it is shrunk as discussed below. All other Java\nobjects are passed through unmodified.\nAs discussed in Section 3.1, the proxy uses the row boundaries\ndefined in the ResultSet to partition it into fragments\nconsisting of single result rows. All ResultSet objects are converted\ninto objects of a new type called RecipeResultSet. We use\nthe term recipe for this compact description of a database\nresult because of its similarity to a file recipe in the CASPER file\nsystem [37]. The conversion replaces each result fragment that is\nlikely to be present in the Ganesh driver\"s cache by a SHA-1 hash\nof that fragment. Previously unseen result fragments are retained\nverbatim. The proxy also retains hashes for the new result\nfragments as they will be present in the driver\"s cache in the future.\nNote that the proxy only caches hashes for result fragments and\ndoes not cache recipes.\nThe proxy constructs a RecipeResultSet by checking for\nsimilarity at the entire result and then the row level. If the entire\nresult is predicted to be present in the Ganesh driver\"s cache, the\nRecipeResultSet is simply a single hash of the entire result.\nOtherwise, it contains hashes for those rows predicted to be present\nin that cache; all other rows are retained verbatim. If the proxy\nestimates an overall space savings, it will transmit the\nRecipeResultSet. Otherwise the original ResultSet is transmitted.\nThe RecipeResultSet objects are transformed back into\nResultSet objects by the Ganesh driver. Figure 4 illustrates\nResultSet handling at both ends. Each SHA-1 hash found in a\nRecipeResultSet is looked up in the local cache of result\nfragments. On a hit, the hash is replaced by the corresponding\nfragment. On a miss, the driver contacts the Ganesh proxy to fetch the\nfragment. All previously unseen result fragments that were retained\nverbatim by the proxy are hashed and added to the result cache.\nThere should be very few misses if the proxy has accurately\ntracked the Ganesh driver\"s cache state. A future optimization would\nbe to batch the fetch of missing fragments. This would be valuable\nwhen there are many small missing fragments in a high-latency\nWAN. Once the transformation is complete, the fully reconstructed\nResultSet object is passed up to the application.\n4. EXPERIMENTAL VALIDATION\nThree questions follow from the goals and design of Ganesh:\n\u2022 First, can performance can be improved significantly by\nexploiting similarity across database results?\nBenchmark Dataset Details\n500,000 Users, 12,000 Stories\nBBOARD 2.0 GB 3,298,000 Comments\nAUCTION 1.3 GB 1,000,000 Users, 34,000 Items\nTable 1: Benchmark Dataset Details\n\u2022 Second, how important is Ganesh\"s structural similarity\ndetection relative to Rabin fingerprinting\"s similarity detection?\n\u2022 Third, is the overhead of the proxy-based design acceptable?\nOur evaluation answers these question through controlled\nexperiments with the Ganesh prototype. This section describes the\nbenchmarks used, our evaluation procedure, and the experimental setup.\nResults of the experiments are presented in Sections 5, 6, and 7.\n4.1 Benchmarks\nOur evaluation is based on two benchmarks [18] that have been\nwidely used by other researchers to evaluate various aspects of\nmulti-tier [27] and eBusiness architectures [9]. The first\nbenchmark, BBOARD, is modeled after Slashdot, a technology-oriented\nnews site. The second benchmark, AUCTION, is modeled after\neBay, an online auction site. In both benchmarks, most content is\ndynamically generated from information stored in a database.\nDetails of the datasets used can be found in Table 1.\n4.1.1 The BBOARD Benchmark\nThe BBOARD benchmark, also known as RUBBoS [18],\nmodels Slashdot, a popular technology-oriented web site. Slashdot\naggregates links to news stories and other topics of interest found\nelsewhere on the web. The site also serves as a bulletin board by\nallowing users to comment on the posted stories in a threaded\nconversation form. It is not uncommon for a story to gather hundreds\nof comments in a matter of hours. The BBOARD benchmark is\nsimilar to the site and models the activities of a user, including\nreadonly operations such as browsing the stories of the day, browsing\nstory categories, and viewing comments as well as write operations\nsuch as new user registration, adding and moderating comments,\nand story submission.\nThe benchmark consists of three different phases: a short\nwarmup phase, a runtime phase representing the main body of the\nworkload, and a short cool-down phase. In this paper we only report\nresults from the runtime phase. The warm-up phase is important\nin establishing dynamic system state, but measurements from that\nphase are not significant for our evaluation. The cool-down phase\nis solely for allowing the benchmark to shut down.\nThe warm-up, runtime, and cool-down phases are 2, 15, and 2\nminutes respectively. The number of simulated clients were 400,\n800, 1200, and 1600. The benchmark is available in a Java Servlets\nand PHP version and has different datasets; we evaluated Ganesh\nusing the Java Servlets version and the Expanded dataset.\nThe BBOARD benchmark defines two different workloads. The\nfirst, the Authoring mix, consists of 70% read-only operations and\n30% read-write operations. The second, the Browsing mix,\ncontains only read-only operations and does not update the database.\n4.1.2 The AUCTION Benchmark\nThe AUCTION benchmark, also known as RUBiS [18], models\neBay, the online auction site. The eBay web site is used to buy\nand sell items via an auction format. The main activities of a user\ninclude browsing, selling, or bidding for items. Modeling the\nactivities on this site, this benchmark includes read-only activities such\nas browsing items by category and by region, as well as read-write\nWWW 2007 / Track: Performance and Scalability Session: Scalable Systems for Dynamic Content\n314\nNetEm\nRouter Ganesh\nProxy\nClients Web and\nApplication Server\nDatabase\nServer\nFigure 5: Experimental Setup\nactivities such as bidding for items, buying and selling items, and\nleaving feedback.\nAs with BBOARD, the benchmark consists of three different phases.\nThe warm-up, runtime, and cool-down phases for this experiment\nare 1.5, 15, and 1 minutes respectively. We tested Ganesh with\nfour client configurations where the number of test clients was set\nto 400, 800, 1200, and 1600. The benchmark is available in a\nEnterprise Java Bean (EJB), Java Servlets, and PHP version and has\ndifferent datasets; we evaluated Ganesh with the Java Servlets\nversion and the Expanded dataset.\nThe AUCTION benchmark defines two different workloads. The\nfirst, the Bidding mix, consists of 70% read-only operations and\n30% read-write operations. The second, the Browsing mix,\ncontains only read-only operations and does not update the database.\n4.2 Experimental Procedure\nBoth benchmarks involve a synthetic workload of clients\naccessing a web server. The number of clients emulated is an\nexperimental parameter. Each emulated client runs an instance of the\nbenchmark in its own thread, using a matrix to transition between\ndifferent benchmark states. The matrix defines a stochastic model\nwith probabilities of transitioning between the different states that\nrepresent typical user actions. An example transition is a user\nlogging into the AUCTION system and then deciding on whether to\npost an item for sale or bid on active auctions. Each client also\nmodels user think time between requests. The think time is\nmodeled as an exponential distribution with a mean of 7 seconds.\nWe evaluate Ganesh along two axes: number of clients and WAN\nbandwidth. Higher loads are especially useful in understanding\nGanesh\"s performance when the CPU or disk of the database server\nor proxy is the limiting factor. A previous study has shown that\napproximately 50% of the wide-area Internet bottlenecks observed\nhad an available bandwidth under 10 Mb/s [1]. Based on this work,\nwe focus our evaluation on the WAN bandwidth of 5 Mb/s with\n66 ms of round-trip latency, representative of severely constrained\nnetwork paths, and 20 Mb/s with 33 ms of round-trip latency,\nrepresentative of a moderately constrained network path. We also report\nGanesh\"s performance at 100 Mb/s with no added round-trip\nlatency. This bandwidth, representative of an unconstrained network,\nis especially useful in revealing any potential overhead of Ganesh\nin situations where WAN bandwidth is not the limiting factor. For\neach combination of number of clients and WAN bandwidth, we\nmeasured results from the two configurations listed below:\n\u2022 Native: This configuration corresponds to Figure 3(a).\nNative avoids Ganesh\"s overhead in using a proxy and\nperforming Java object serialization.\n\u2022 Ganesh: This configuration corresponds to Figure 3(b). For\na given number of clients and WAN bandwidth, comparing\nthese results to the corresponding Native results gives the\nperformance benefit due to the Ganesh middleware system.\nThe metric used to quantify the improvement in throughput is\nthe number of client requests that can be serviced per second. The\nmetric used to quantify Ganesh\"s overhead is the average response\ntime for a client request. For all of the experiments, the Ganesh\ndriver used by the application server used a cache size of 100,000\nitems1\n. The proxy was effective in tracking the Ganesh driver\"s\ncache state; for all of our experiments the miss rate on the driver\nnever exceeded 0.7%.\n4.3 Experimental Setup\nThe experimental setup used for the benchmarks can be seen in\nFigure 5. All machines were 3.2 GHz Pentium 4s (with\nHyperThreading enabled.) With the exception of the database server, all\nmachines had 2 GB of SDRAM and ran the Fedora Core Linux\ndistribution. The database server had 4 GB of SDRAM.\nWe used Apache\"s Tomcat as both the application server that\nhosted the Java Servlets and the web server. Both benchmarks\nused Java Servlets to generate the dynamic content. The database\nserver used the open source MySQL database. For the native JDBC\ndrivers, we used the Connector/J drivers provided by MySQL. The\napplication server used Sun\"s Java Virtual Machine as the runtime\nenvironment for the Java Servlets. The sysstat tool was used to\nmonitor the CPU, network, disk, and memory utilization on all\nmachines.\nThe machines were connected by a switched gigabit Ethernet\nnetwork. As shown in Figure 5, the front-end web and\napplication server was separated from the proxy and database server by a\nNetEm router [16]. This router allowed us to control the bandwidth\nand latency settings on the network. The NetEm router is a\nstandard PC with two network cards running the Linux Traffic Control\nand Network Emulation software. The bandwidth and latency\nconstraints were only applied to the link between the application server\nand the database for the native case and between the application\nserver and the proxy for the Ganesh case. There is no\ncommunication between the application server and the database with Ganesh\nas all data flows through the proxy. As our focus was on the WAN\nlink between the application server and the database, there were no\nconstraints on the link between the simulated test clients and the\nweb server.\n5. THROUGHPUT AND RESPONSE TIME\nIn this section, we address the first question raised in Section 4:\nCan performance can be improved significantly by exploiting\nsimilarity across database results? To answer this question, we use\nresults from the BBOARD and AUCTION benchmarks. We use\ntwo metrics to quantify the performance improvement obtainable\nthrough the use of Ganesh: throughput, from the perspective of the\nweb server, and average response time, from the perspective of the\nclient. Throughput is measured in terms of the number of client\nrequests that can be serviced per second.\n5.1 BBOARD Results and Analysis\n5.1.1 Authoring Mix\nFigures 6 (a) and (b) present the average number of requests\nserviced per second and the average response time for these requests\nas perceived by the clients for BBOARD\"s Authoring Mix.\nAs Figure 6 (a) shows, Native easily saturates the 5 Mb/s link.\nAt 400 clients, the Native solution delivers 29 requests/sec with an\naverage response time of 8.3 seconds. Native\"s throughput drops\nwith an increase in test clients as clients timeout due to\ncongestion at the application server. Usability studies have shown that\nresponse times above 10 seconds cause the user to move on to\n1\nAs Java lacks a sizeof() operator, Java caches therefore limit\ntheir size based on the number of objects. The size of cache dumps\ntaken at the end of the experiments never exceeded 212 MB.\nWWW 2007 / Track: Performance and Scalability Session: Scalable Systems for Dynamic Content\n315\n0\n50\n100\n150\n200\n250\n400\n800\n1200\n1600\n400\n800\n1200\n1600\n400\n800\n1200\n1600\n5 Mb/s 20 Mb/s 100 Mb/s\nTest Clients\nRequests/sec\nNative Ganesh\n0.001\n0.01\n0.1\n1\n10\n100\n400\n800\n1200\n1600\n400\n800\n1200\n1600\n400\n800\n1200\n1600\n5 Mb/s 20 Mb/s 100 Mb/s\nTest Clients\nAvg.Resp.Time(sec)\nNative Ganesh\nNote Logscale\n(a) Throughput: Authoring Mix (b) Response Time: Authoring Mix\n0\n50\n100\n150\n200\n250\n400\n800\n1200\n1600\n400\n800\n1200\n1600\n400\n800\n1200\n1600\n5 Mb/s 20 Mb/s 100 Mb/s\nTest Clients\nRequests/sec\nNative Ganesh\n0.001\n0.01\n0.1\n1\n10\n100\n400\n800\n1200\n1600\n400\n800\n1200\n1600\n400\n800\n1200\n1600\n5 Mb/s 20 Mb/s 100 Mb/s\nTest Clients\nAvg.Resp.Time(sec)\nNative Ganesh\nNote Logscale\n(c) Throughput: Browsing Mix (d) Response Time: Browsing Mix\nMean of three trials. The maximum standard deviation for throughput and response time was 9.8% and 11.9% of the corresponding mean.\nFigure 6: BBOARD Benchmark - Throughput and Average Response Time\nother tasks [24]. Based on these numbers, increasing the\nnumber of test clients makes the Native system unusable. Ganesh at\n5 Mb/s, however, delivers a twofold improvement with 400 test\nclients and a fivefold improvement at 1200 clients. Ganesh\"s\nperformance drops slightly at 1200 and 1600 clients as the network is\nsaturated. Compared to Native, Figure 6 (b) shows that Ganesh\"s\nresponse times are substantially lower with sub-second response\ntimes at 400 clients.\nFigure 6 (a) also shows that for 400 and 800 test clients Ganesh\nat 5 Mb/s has the same throughput and average response time as\nNative at 20 Mb/s. Only at 1200 and 1600 clients does Native at 20\nMb/s deliver higher throughput than Ganesh at 5 Mb/s.\nComparing both Ganesh and Native at 20 Mb/s, we see that\nGanesh is no longer bandwidth constrained and delivers up to a\ntwofold improvement over Native at 1600 test clients. As Ganesh\ndoes not saturate the network with higher test client configurations,\nat 1600 test clients, its average response time is 0.1 seconds rather\nthan Native\"s 7.7 seconds.\nAs expected, there are no visible gains from Ganesh at the higher\nbandwidth of 100 Mb/s where the network is no longer the\nbottleneck. Ganesh, however, still tracks Native in terms of throughput.\n5.1.2 Browsing Mix\nFigures 6 (c) and (d) present the average number of requests\nserviced per second and the average response time for these requests\nas perceived by the clients for BBOARD\"s Browsing Mix.\nRegardless of the test client configuration, Figure 6 (c) shows\nthat Native\"s throughput at 5 Mb/s is limited to 10 reqs/sec. Ganesh\nat 5 Mb/s with 400 test clients, delivers more than a sixfold\nincrease in throughput. The improvement increases to over a\nelevenfold increase at 800 test clients before Ganesh saturates the\nnetwork. Further, Figure 6 (d) shows that Native\"s average response\ntime of 35 seconds at 400 test clients make the system unusable.\nThese high response times further increase with the addition of test\nclients. Even with the 1600 test client configuration Ganesh\ndelivers an acceptable average response time of 8.2 seconds.\nDue to the data-intensive nature of the Browsing mix, Ganesh at\n5 Mb/s surprisingly performs much better than Native at 20 Mb/s.\nFurther, as shown in Figure 6 (d), while the average response time\nfor Native at 20 Mb/s is acceptable at 400 test clients, it is unusable\nwith 800 test clients with an average response time of 15.8 seconds.\nLike the 5 Mb/s case, this response time increases with the addition\nof extra test clients.\nGanesh at 20 Mb/s and both Native and Ganesh at 100 Mb/s are\nnot bandwidth limited. However, performance plateaus out after\n1200 test clients due to the database CPU being saturated.\n5.1.3 Filter Variant\nWe were surprised by the Native performance from the BBOARD\nbenchmark. At the bandwidth of 5 Mb/s, Native performance was\nlower than what we had expected. It turned out the benchmark\ncode that displays stories read all the comments associated with\nthe particular story from the database and only then did some\npostprocessing to select the comments to be displayed. While this is\nexactly the behavior of SlashCode, the code base behind the\nSlashdot web site, we decided to modify the benchmark to perform some\npre-filtering at the database. This modified benchmark, named the\nFilter Variant, models a developer who applies optimizations at the\nSQL level to transfer less data. In the interests of brevity, we only\nbriefly summarize the results from the Authoring mix.\nFor the Authoring mix, at 800 test clients at 5 Mb/s, Figure 7 (a)\nshows that Native\"s throughput increase by 85% when compared\nto the original benchmark while Ganesh\"s improvement is smaller\nat 15%. Native\"s performance drops above 800 clients as the test\nclients time out due to high response times. The most significant\ngain for Native is seen at 20 Mb/s. At 1600 test clients, when\ncompared to the original benchmark, Native sees a 73% improvement\nin throughput and a 77% reduction in average response time. While\nWWW 2007 / Track: Performance and Scalability Session: Scalable Systems for Dynamic Content\n316\n0\n50\n100\n150\n200\n250\n400\n800\n1200\n1600\n400\n800\n1200\n1600\n400\n800\n1200\n1600\n5 Mb/s 20 Mb/s 100 Mb/s\nTest Clients\nRequests/sec\nNative Ganesh\n0.001\n0.01\n0.1\n1\n10\n100\n400\n800\n1200\n1600\n400\n800\n1200\n1600\n400\n800\n1200\n1600\n5 Mb/s 20 Mb/s 100 Mb/s\nTest Clients\nAvg.Resp.Time(sec)\nNative Ganesh\nNote Logscale\n(a) Throughput: Authoring Mix (b) Response Time: Authoring Mix\nMean of three trials. The maximum standard deviation for throughput and response time was 7.2% and 11.5% of the corresponding mean.\nFigure 7: BBOARD Benchmark - Filter Variant - Throughput and Average Response Time\nGanesh sees no improvement when compared to the original, it still\nprocesses 19% more requests/sec than Native. Thus, while the\noptimizations were more helpful to Native, Ganesh still delivers an\nimprovement in performance.\n5.2 AUCTION Results and Analysis\n5.2.1 Bidding Mix\nFigures 8 (a) and (b) present the average number of requests\nserviced per second and the average response time for these requests\nas perceived by the clients for AUCTION\"s Bidding Mix. As\nmentioned earlier, the Bidding mix consists of a mixture of read and\nwrite operations.\nThe AUCTION benchmark is not as data intensive as BBOARD.\nTherefore, most of the gains are observed at the lower bandwidth\nof 5 Mb/s. Figure 8 (a) shows that the increase in throughput due\nto Ganesh ranges from 8% at 400 test clients to 18% with 1600\ntest clients. As seen in Figure 8 (b), the average response times for\nGanesh are significantly lower than Native ranging from a decrease\nof 84% at 800 test clients to 88% at 1600 test clients.\nFigure 8 (a) also shows that with a fourfold increase of\nbandwidth from 5 Mb/s to 20 Mb/s, Native is no longer bandwidth\nconstrained and there is no performance difference between Ganesh\nand Native. With the higher test client configurations, we did\nobserve that the bandwidth used by Ganesh was lower than Native.\nGanesh might still be useful in these non-constrained scenarios if\nbandwidth is purchased on a metered basis. Similar results are seen\nfor the 100 Mb/s scenario.\n5.2.2 Browsing Mix\nFor AUCTION\"s Browsing Mix, Figures 8 (c) and (d) present the\naverage number of requests serviced per second and the average\nresponse time for these requests as perceived by the clients.\nAgain, most of the gains are observed at lower bandwidths. At 5\nMb/s, Native and Ganesh deliver similar throughput and response\ntimes with 400 test clients. While the throughput for both remains\nthe same at 800 test clients, Figure 8 (d) shows that Ganesh\"s\naverage response time is 62% lower than Native. Native saturates the\nlink at 800 clients and adding extra test clients only increases the\naverage response time. Ganesh, regardless of the test client\nconfiguration, is not bandwidth constrained and maintains the same\nresponse time. At 1600 test clients, Figure 8 (c) shows that Ganesh\"s\nthroughput is almost twice that of Native.\nAt the higher bandwidths of 20 and 100 Mb/s, neither Ganesh\nnor Native is bandwidth limited and deliver equivalent throughput\nand response times.\nBenchmark Orig. Size Ganesh Size Rabin Size\nSelectSort1 223.6 MB 5.4 MB 219.3 MB\nSelectSort2 223.6 MB 5.4 MB 223.6 MB\nTable 2: Similarity Microbenchmarks\n6. STRUCTURAL VS. RABIN SIMILARITY\nIn this section, we address the second question raised in\nSection 4: How important is Ganesh\"s structural similarity detection\nrelative to Rabin fingerprinting-based similarity detecting? To\nanswer this question, we used microbenchmarks and the BBOARD and\nAUCTION benchmarks. As Ganesh always performed better than\nRabin fingerprinting, we only present a subset of the results here in\nthe interests of brevity.\n6.1 Microbenchmarks\nTwo microbenchmarks show an example of the effects of data\nreordering on Rabin fingerprinting algorithm. In the first\nmicrobenchmark, SelectSort1, a query with a specified sort order selects\n223.6 MB of data spread over approximately 280 K rows. The\nquery is then repeated with a different sort attribute. While the\nsame number of rows and the same data is returned, the order of\nrows is different. In such a scenario, one would expect a large\namount of similarity to be detected between both results. As\nTable 2 shows, Ganesh\"s row-based algorithm achieves a 97.6%\nreduction while the Rabin fingerprinting algorithm, with the average\nchunk size parameter set to 4 KB, only achieves a 1% reduction.\nThe reason, as shown earlier in Figure 2, is that with Rabin\nfingerprinting, the spans of data between two consecutive boundaries\nusually cross row boundaries. With the order of the rows changing\nin the second result and the Rabin fingerprints now spanning\ndifferent rows, the algorithm is unable to detect significant similarity.\nThe small gain seen is mostly for those single rows that are large\nenough to be broken into multiple chunks.\nSelectSort2, another micro-benchmark executed the same queries\nbut increased the minimum chunk size of the Rabin fingerprinting\nalgorithm. As can be seen in Table 2, even the small gain from the\nprevious microbenchmark disappears as the minimum chunk size\nwas greater than the average row size. While one can partially\naddress these problems by dynamically varying the parameters of the\nRabin fingerprinting algorithm, this can be computationally\nexpensive, especially in the presence of changing workloads.\n6.2 Application Benchmarks\nWe ran the BBOARD benchmark described in Section 4.1.1 on\ntwo versions of Ganesh: the first with Rabin fingerprinting used as\nWWW 2007 / Track: Performance and Scalability Session: Scalable Systems for Dynamic Content\n317\n0\n50\n100\n150\n200\n250\n300\n350\n400\n800\n1200\n1600\n400\n800\n1200\n1600\n400\n800\n1200\n1600\n5 Mb/s 20 Mb/s 100 Mb/s\nTest Clients\nRequests/sec\nNative Ganesh\n0.001\n0.01\n0.1\n1\n10\n400\n800\n1200\n1600\n400\n800\n1200\n1600\n400\n800\n1200\n1600\n5 Mb/s 20 Mb/s 100 Mb/s\nTest Clients\nAvg.Resp.Time(sec)\nNative Ganesh\nNote Logscale\n(a) Throughput: Bidding Mix (b) Response Time: Bidding Mix\n0\n50\n100\n150\n200\n250\n300\n350\n400\n800\n1200\n1600\n400\n800\n1200\n1600\n400\n800\n1200\n1600\n5 Mb/s 20 Mb/s 100 Mb/s\nTest Clients\nRequests/sec\nNative Ganesh\n0.001\n0.01\n0.1\n1\n10\n400\n800\n1200\n1600\n400\n800\n1200\n1600\n400\n800\n1200\n1600\n5 Mb/s 20 Mb/s 100 Mb/s\nTest Clients\nAvg.Resp.Time(sec)\nNative Ganesh\nNote Logscale\n(c) Throughput: Browsing Mix (d) Response Time: Browsing Mix\nMean of three trials. The maximum standard deviation for throughput and response time was 2.2% and 11.8% of the corresponding mean.\nFigure 8: AUCTION Benchmark - Throughput and Average Response Time\nthe chunking algorithm and the second with Ganesh\"s row-based\nalgorithm. Rabin\"s results for the Browsing Mix are normalized to\nGanesh\"s results and presented in Figure 9.\nAs Figure 9 (a) shows, at 5 Mb/s, independent of the test client\nconfiguration, Rabin significantly underperforms Ganesh. This\nhappens because of a combination of two reasons. First, as outlined\nin Section 3.1, Rabin finds less similarity as it does not exploit\nthe result\"s structural information. Second, this benchmark\ncontained some queries that generated large results. In this case,\nRabin, with a small average chunk size, generated a large number of\nobjects that evicted other useful data from the cache. In contrast,\nGanesh was able to detect these large rows and correspondingly\nincrease the size of the chunks. This was confirmed as cache\nstatistics showed that Ganesh\"s hit ratio was roughly three time that of\nRabin. Throughput measurements at 20 Mb/s were similar with\nthe exception of Rabin\"s performance with 400 test clients. In this\ncase, Ganesh was not network limited and, in fact, the throughput\nwas the same as 400 clients at 5 Mb/s. Rabin, however, took\nadvantage of the bandwidth increase from 5 to 20 Mb/s to deliver a\nslightly better performance. At 100 Mb/s, Rabin\"s throughput was\nalmost similar to Ganesh as bandwidth was no longer a bottleneck.\nThe normalized response time, presented in Figure 9 (b), shows\nsimilar trends. At 5 and 20 Mb/s, the addition of test clients\ndecreases the normalized response time as Ganesh\"s average response\ntime increases faster than Rabin\"s. However, at no point does Rabin\noutperform Ganesh. Note that at 400 and 800 clients at 100 Mb/s,\nRabin does have a higher overhead even when it is not bandwidth\nconstrained. As mentioned in Section 3.1, this is due to the fact that\nRabin has to hash each ResultSet twice. The overhead\ndisappears with 1200 and 1600 clients as the database CPU is saturated\nand limits the performance of both Ganesh and Rabin.\n7. PROXY OVERHEAD\nIn this section, we address the third question raised in Section 4:\nIs the overhead of Ganesh\"s proxy-based design acceptable? To\nanswer this question, we concentrate on its performance at the higher\nbandwidths. Our evaluation in Section 5 showed that Ganesh, when\ncompared to Native, can deliver a substantial throughput\nimprovement at lower bandwidths. It is only at higher bandwidths that\nlatency, measured by the average response time for a client request,\nand throughput, measured by the number of client requests that can\nbe serviced per second, overheads would be visible.\nLooking at the Authoring mix of the original BBOARD\nbenchmark, there are no visible gains from Ganesh at 100 Mb/s. Ganesh,\nhowever, still tracks Native in terms of throughput. While the\naverage response time is higher for Ganesh, the absolute difference is\nin between 0.01 and 0.04 seconds and would be imperceptible to\nthe end-user. The Browsing mix shows an even smaller difference\nin average response times. The results from the filter variant of the\nBBOARD benchmarks are similar. Even for the AUCTION\nbenchmark, the difference between Native and Ganesh\"s response time at\n100 Mb/s was never greater than 0.02 seconds. The only exception\nto the above results was seen in the filter variant of the BBOARD\nbenchmark where Ganesh at 1600 test clients added 0.85 seconds\nto the average response time. Thus, even for much faster networks\nwhere the WAN link is not the bottleneck, Ganesh always delivers\nthroughput equivalent to Native. While some extra latency is added\nby the proxy-based design, it is usually imperceptible.\n8. RELATED WORK\nTo the best of our knowledge, Ganesh is the first system that\ncombines the use of hash-based techniques with caching of database\nresults to improve throughput and response times for applications\nwith dynamic content. We also believe that it is also the first\nsystem to demonstrate the benefits of using structural information for\nWWW 2007 / Track: Performance and Scalability Session: Scalable Systems for Dynamic Content\n318\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\n400\n800\n1200\n1600\n400\n800\n1200\n1600\n400\n800\n1200\n1600\n5 Mb/s 20 Mb/s 100 Mb/s\nTest Clients\nNorm.Throughput\n31.8\n3.8\n2.8\n2.3\n23.8\n32.8\n5.8\n3.6\n1.8\n2.1\n1.1\n1.0\n0\n5\n10\n15\n20\n25\n30\n35\n400\n800\n1200\n1600\n400\n800\n1200\n1600\n400\n800\n1200\n1600\n5 Mb/s 20 Mb/s 100 Mb/s\nTest Clients\nNorm.ResponseTime\n(a) Normalized Throughput: Higher is better (b) Normalized Response Time: Higher is worse\nFor throughput, a normalized result greater than 1 implies that Rabin is better, For response time, a normalized result greater than 1 implies\nthat Ganesh is better. Mean of three trials. The maximum standard deviation for throughput and response time was 9.1% and 13.9% of\nthe corresponding mean.\nFigure 9: Normalized Comparison of Ganesh vs. Rabin - BBOARD Browsing Mix\ndetecting similarity. In this section, we first discuss alternative\napproaches to caching dynamic content and then examine other uses\nof hash-based primitives in distributed systems.\n8.1 Caching Dynamic Content\nAt the database layer, a number of systems have advocated\nmiddletier caching where parts of the database are replicated at the edge or\nserver [3, 4, 20]. These systems either cache entire tables in what\nis essentially a replicated database or use materialized views from\nprevious query replies [19]. They require tight integration with the\nback-end database to ensure a time bound on the propagation of\nupdates. These systems are also usually targeted towards\nworkloads that do not require strict consistency and can tolerate stale\ndata. Further, unlike Ganesh, some of these mid-tier caching\nsolutions [2, 3], suffer from the complexity of having to participate in\nquery planing and distributed query processing.\nGao et al. [15] propose using a distributed object replication\narchitecture where the data store\"s consistency requirements are\nadapted on a per-application basis. These solutions require\nsubstantial developer resources and detailed understanding of the\napplication being modified. While systems that attempt to automate\nthe partitioning and replication of an application\"s database\nexist [34], they do not provide full transaction semantics. In\ncomparison, Ganesh does not weaken any of the semantics provided by\nthe underlying database.\nRecent work in the evaluation of edge caching options for\ndynamic web sites [38] has suggested that, without careful planning,\nemploying complex offloading strategies can hurt performance.\nInstead, the work advocates for an architecture in which all tiers\nexcept the database should be offloaded to the edge. Our evaluation of\nGanesh has shown that it would benefit these scenarios. To improve\ndatabase scalability, C-JDBC [10], SSS [22], and Ganymed [28]\nalso advocate the use of an interposition-based architecture to\ntransparently cluster and replicate databases at the middleware level.\nThe approaches of these architectures and Ganesh are\ncomplementary and they would benefit each other.\nMoving up to the presentation layer, there has been widespread\nadoption of fragment-based caching [14], which improves cache\nutilization by separately caching different parts of generated web\npages. While fragment-based caching works at the edge, a recent\nproposal has proposed moving web page assembly to the clients to\noptimize content delivery [31]. While Ganesh is not used at the\npresentation layer, the same principles have been applied in Duplicate\nTransfer Detection [25] to increase web cache efficiency as well as\nfor web access across bandwidth limited links [33].\n8.2 Hash-based Systems\nThe past few years have seen the emergence of many systems\nthat exploit hash-based techniques. At the heart of all these\nsystems is the idea of detecting similarity in data without requiring\ninterpretation of that data. This simple yet elegant idea relies on\ncryptographic hashing, as discussed earlier in Section 2. Successful\napplications of this idea span a wide range of storage systems.\nExamples include peer-to-peer backup of personal computing files [11],\nstorage-efficient archiving of data [29], and finding similar files [21].\nSpring and Wetherall [35] apply similar principles at the network\nlevel. Using synchronized caches at both ends of a network link,\nduplicated data is replaced by smaller tokens for transmission and\nthen restored at the remote end. This and other hash-based systems\nsuch as the CASPER [37] and LBFS [26] filesystems, and Layer-2\nbandwidth optimizers such as Riverbed and Peribit use Rabin\nfingerprinting [30] to discover spans of commonality in data. This\napproach is especially useful when data items are modified in-place\nthrough insertions, deletions, and updates. However, as Section 6\nshows, the performance of this technique can show a dramatic drop\nin the presence of data reordering. Ganesh instead uses row\nboundaries as dividers for detecting similarity.\nThe most aggressive use of hash-based techniques is by systems\nthat use hashes as the primary identifiers for objects in persistent\nstorage. Storage systems such as CFS [12] and PAST [13] that\nhave been built using distributed hash tables fall into this category.\nSingle Instance Storage [6] and Venti [29] are other examples of\nsuch systems. As discussed in Section 2.2, the use of cryptographic\nhashes for addressing persistent data represents a deeper level of\nfaith in their collision-resistance than that assumed by Ganesh. If\ntime reveals shortcomings in the hash algorithm, the effort involved\nin correcting the flaw is much greater. In Ganesh, it is merely a\nmatter of replacing the hash algorithm.\n9. CONCLUSION\nThe growing use of dynamic web content generated from\nrelational databases places increased demands on WAN bandwidth.\nTraditional caching solutions for bandwidth and latency reduction\nare often ineffective for such content. This paper shows that the\nimpact of WAN accesses to databases can be substantially reduced\nthrough the Ganesh architecture without any compromise of the\ndatabase\"s strict consistency semantics. The essence of the Ganesh\narchitecture is the use of computation at the edges to reduce\ncommunication through the Internet. Ganesh is able to use\ncryptographic hashes to detect similarity with previous results and send\nWWW 2007 / Track: Performance and Scalability Session: Scalable Systems for Dynamic Content\n319\ncompact recipes of results rather than full results. Our design uses\ninterposition to achieve complete transparency: clients, application\nservers, and database servers are all unaware of Ganesh\"s presence\nand require no modification.\nOur experimental evaluation confirms that Ganesh, while\nconceptually simple, can be highly effective in improving throughput\nand response time. Our results also confirm that exploiting the\nstructure present in database results to detect similarity is crucial\nto this performance improvement.\n10. REFERENCES\n[1] AKELLA, A., SESHAN, S., AND SHAIKH, A. An empirical\nevaluation of wide-area internet bottlenecks. In Proc. 3rd\nACM SIGCOMM Conference on Internet Measurement\n(Miami Beach, FL, USA, Oct. 2003), pp. 101-114.\n[2] ALTINEL, M., BORNH \u00a8OVD, C., KRISHNAMURTHY, S.,\nMOHAN, C., PIRAHESH, H., AND REINWALD, B. Cache\ntables: Paving the way for an adaptive database cache. In\nProc. of 29th VLDB (Berlin, Germany, 2003), pp. 718-729.\n[3] ALTINEL, M., LUO, Q., KRISHNAMURTHY, S., MOHAN,\nC., PIRAHESH, H., LINDSAY, B. G., WOO, H., AND\nBROWN, L. Dbcache: Database caching for web application\nservers. In Proc. 2002 ACM SIGMOD (2002), pp. 612-612.\n[4] AMIRI, K., PARK, S., TEWARI, R., AND PADMANABHAN,\nS. Dbproxy: A dynamic data cache for web applications. In\nProc. IEEE International Conference on Data Engineering\n(ICDE) (Mar. 2003).\n[5] BLACK, J. Compare-by-hash: A reasoned analysis. In Proc.\n2006 USENIX Annual Technical Conference (Boston, MA,\nMay 2006), pp. 85-90.\n[6] BOLOSKY, W. J., CORBIN, S., GOEBEL, D., , AND\nDOUCEUR, J. R. Single instance storage in windows 2000.\nIn Proc. 4th USENIX Windows Systems Symposium (Seattle,\nWA, Aug. 2000), pp. 13-24.\n[7] BREWER, E. A. Lessons from giant-scale services. IEEE\nInternet Computing 5, 4 (2001), 46-55.\n[8] BRODER, A., GLASSMAN, S., MANASSE, M., AND\nZWEIG, G. Syntactic clustering of the web. In Proc. 6th\nInternational WWW Conference (1997).\n[9] CECCHET, E., CHANDA, A., ELNIKETY, S.,\nMARGUERITE, J., AND ZWAENEPOEL, W. Performance\ncomparison of middleware architectures for generating\ndynamic web content. In Proc. Fourth ACM/IFIP/USENIX\nInternational Middleware Conference (Rio de Janeiro,\nBrazil, June 2003).\n[10] CECCHET, E., MARGUERITE, J., AND ZWAENEPOEL, W.\nC-JDBC: Flexible database clustering middleware. In Proc.\n2004 USENIX Annual Technical Conference (Boston, MA,\nJune 2004).\n[11] COX, L. P., MURRAY, C. D., AND NOBLE, B. D. Pastiche:\nMaking backup cheap and easy. In OSDI: Symposium on\nOperating Systems Design and Implementation (2002).\n[12] DABEK, F., KAASHOEK, M. F., KARGER, D., MORRIS,\nR., AND STOICA, I. Wide-area cooperative storage with\nCFS. In 18th ACM Symposium on Operating Systems\nPrinciples (Banff, Canada, Oct. 2001).\n[13] DRUSCHEL, P., AND ROWSTRON, A. PAST: A large-scale,\npersistent peer-to-peer storage utility. In HotOS VIII (Schloss\nElmau, Germany, May 2001), pp. 75-80.\n[14] Edge side includes. http://www.esi.org.\n[15] GAO, L., DAHLIN, M., NAYATE, A., ZHENG, J., AND\nIYENGAR, A. Application specific data replication for edge\nservices. In WWW \"03: Proc. Twelfth International\nConference on World Wide Web (2003), pp. 449-460.\n[16] HEMMINGER, S. Netem - emulating real networks in the lab.\nIn Proc. 2005 Linux Conference Australia (Canberra,\nAustralia, Apr. 2005).\n[17] HENSON, V. An analysis of compare-by-hash. In Proc. 9th\nWorkshop on Hot Topics in Operating Systems (HotOS IX)\n(May 2003), pp. 13-18.\n[18] Jmob benchmarks. http://jmob.objectweb.org/.\n[19] LABRINIDIS, A., AND ROUSSOPOULOS, N. Balancing\nperformance and data freshness in web database servers. In\nProc. 29th VLDB Conference (Sept. 2003).\n[20] LARSON, P.-A., GOLDSTEIN, J., AND ZHOU, J.\nTransparent mid-tier database caching in sql server. In Proc.\n2003 ACM SIGMOD (2003), pp. 661-661.\n[21] MANBER, U. Finding similar files in a large file system. In\nProc. USENIX Winter 1994 Technical Conference (San\nFransisco, CA, 17-21 1994), pp. 1-10.\n[22] MANJHI, A., AILAMAKI, A., MAGGS, B. M., MOWRY,\nT. C., OLSTON, C., AND TOMASIC, A. Simultaneous\nscalability and security for data-intensive web applications.\nIn Proc. 2006 ACM SIGMOD (June 2006), pp. 241-252.\n[23] MENEZES, A. J., VANSTONE, S. A., AND OORSCHOT, P.\nC. V. Handbook of Applied Cryptography. CRC Press, 1996.\n[24] MILLER, R. B. Response time in man-computer\nconversational transactions. In Proc. AFIPS Fall Joint\nComputer Conference (1968), pp. 267-277.\n[25] MOGUL, J. C., CHAN, Y. M., AND KELLY, T. Design,\nimplementation, and evaluation of duplicate transfer\ndetection in http. In Proc. First Symposium on Networked\nSystems Design and Implementation (San Francisco, CA,\nMar. 2004).\n[26] MUTHITACHAROEN, A., CHEN, B., AND MAZIERES, D. A\nlow-bandwidth network file system. In Proc. 18th ACM\nSymposium on Operating Systems Principles (Banff, Canada,\nOct. 2001).\n[27] PFEIFER, D., AND JAKSCHITSCH, H. Method-based\ncaching in multi-tiered server applications. In Proc. Fifth\nInternational Symposium on Distributed Objects and\nApplications (Catania, Sicily, Italy, Nov. 2003).\n[28] PLATTNER, C., AND ALONSO, G. Ganymed: Scalable\nreplication for transactional web applications. In Proc. 5th\nACM/IFIP/USENIX International Conference on\nMiddleware (2004), pp. 155-174.\n[29] QUINLAN, S., AND DORWARD, S. Venti: A new approach\nto archival storage. In Proc. FAST 2002 Conference on File\nand Storage Technologies (2002).\n[30] RABIN, M. Fingerprinting by random polynomials. In\nHarvard University Center for Research in Computing\nTechnology Technical Report TR-15-81 (1981).\n[31] RABINOVICH, M., XIAO, Z., DOUGLIS, F., AND\nKALMANEK, C. Moving edge side includes to the real edge\n- the clients. In Proc. 4th USENIX Symposium on Internet\nTechnologies and Systems (Seattle, WA, Mar. 2003).\n[32] REESE, G. Database Programming with JDBC and Java,\n1st ed. O\"Reilly, June 1997.\n[33] RHEA, S., LIANG, K., AND BREWER, E. Value-based web\ncaching. In Proc. Twelfth International World Wide Web\nConference (May 2003).\n[34] SIVASUBRAMANIAN, S., ALONSO, G., PIERRE, G., AND\nVAN STEEN, M. Globedb: Autonomic data replication for\nweb applications. In WWW \"05: Proc. 14th International\nWorld-Wide Web conference (May 2005).\n[35] SPRING, N. T., AND WETHERALL, D. A\nprotocol-independent technique for eliminating redundant\nnetwork traffic. In Proc. of ACM SIGCOMM (Aug. 2000).\n[36] TOLIA, N., HARKES, J., KOZUCH, M., AND\nSATYANARAYANAN, M. Integrating portable and distributed\nstorage. In Proc. 3rd USENIX Conference on File and\nStorage Technologies (San Francisco, CA, Mar. 2004).\n[37] TOLIA, N., KOZUCH, M., SATYANARAYANAN, M., KARP,\nB., PERRIG, A., AND BRESSOUD, T. Opportunistic use of\ncontent addressable storage for distributed file systems. In\nProc. 2003 USENIX Annual Technical Conference (San\nAntonio, TX, June 2003), pp. 127-140.\n[38] YUAN, C., CHEN, Y., AND ZHANG, Z. Evaluation of edge\ncaching/offloading for dynamic content delivery. In WWW\n\"03: Proc. Twelfth International Conference on World Wide\nWeb (2003), pp. 461-471.\nWWW 2007 / Track: Performance and Scalability Session: Scalable Systems for Dynamic Content\n320", "keywords": "natural chunk boundary;read-write operation;bboard benchmark;content addressable storage;redundancy;relational database system;database cache;relational database;reciperesultset;temporal locality;caching dynamic database content;jdbc driver;bandwidth optimization;wide area network;database content;proxy;resultset object;hash-based technique"}
{"name": "train_C-81", "title": "Adaptive Duty Cycling for Energy Harvesting Systems", "abstract": "Harvesting energy from the environment is feasible in many applications to ameliorate the energy limitations in sensor networks. In this paper, we present an adaptive duty cycling algorithm that allows energy harvesting sensor nodes to autonomously adjust their duty cycle according to the energy availability in the environment. The algorithm has three objectives, namely (a) achieving energy neutral operation, i.e., energy consumption should not be more than the energy provided by the environment, (b) maximizing the system performance based on an application utility model subject to the above energyneutrality constraint, and (c) adapting to the dynamics of the energy source at run-time. We present a model that enables harvesting sensor nodes to predict future energy opportunities based on historical data. We also derive an upper bound on the maximum achievable performance assuming perfect knowledge about the future behavior of the energy source. Our methods are evaluated using data gathered from a prototype solar energy harvesting platform and we show that our algorithm can utilize up to 58% more environmental energy compared to the case when harvesting-aware power management is not used.", "fulltext": "1. INTRODUCTION\nEnergy supply has always been a crucial issue in designing\nbattery-powered wireless sensor networks because the lifetime and\nutility of the systems are limited by how long the batteries are able to\nsustain the operation. The fidelity of the data produced by a sensor\nnetwork begins to degrade once sensor nodes start to run out of\nbattery power. Therefore, harvesting energy from the environment\nhas been proposed to supplement or completely replace battery\nsupplies to enhance system lifetime and reduce the maintenance cost\nof replacing batteries periodically.\nHowever, metrics for evaluating energy harvesting systems are\ndifferent from those used for battery powered systems.\nEnvironmental energy is distinct from battery energy in two ways.\nFirst it is an inexhaustible supply which, if appropriately used, can\nallow the system to last forever, unlike the battery which is a limited\nresource. Second, there is an uncertainty associated with its\navailability and measurement, compared to the energy stored in the\nbattery which can be known deterministically. Thus, power\nmanagement methods based on battery status are not always\napplicable to energy harvesting systems. In addition, most power\nmanagement schemes designed for battery-powered systems only\naccount for the dynamics of the energy consumers (e.g., CPU, radio)\nbut not the dynamics of the energy supply. Consequently, battery\npowered systems usually operate at the lowest performance level that\nmeets the minimum data fidelity requirement in order to maximize\nthe system life. Energy harvesting systems, on the other hand, can\nprovide enhanced performance depending on the available energy.\nIn this paper, we will study how to adapt the performance of the\navailable energy profile. There exist many techniques to accomplish\nperformance scaling at the node level, such as radio transmit power\nadjustment [1], dynamic voltage scaling [2], and the use of low\npower modes [3]. However, these techniques require hardware\nsupport and may not always be available on resource constrained\nsensor nodes. Alternatively, a common performance scaling\ntechnique is duty cycling. Low power devices typically provide at\nleast one low power mode in which the node is shut down and the\npower consumption is negligible. In addition, the rate of duty cycling\nis directly related to system performance metrics such as network\nlatency and sampling frequency. We will use duty cycle adjustment\nas the primitive performance scaling technique in our algorithms.\n2. RELATED WORK\nEnergy harvesting has been explored for several different types\nof systems, such as wearable computers [4], [5], [6], sensor networks\n[7], etc. Several technologies to extract energy from the environment\nhave been demonstrated including solar, motion-based, biochemical,\nvibration-based [8], [9], [10], [11], and others are being developed\n[12], [13]. While several energy harvesting sensor node platforms\nhave been prototyped [14], [15], [16], there is a need for systematic\npower management techniques that provide performance guarantees\nduring system operation. The first work to take environmental\nenergy into account for data routing was [17], followed by [18].\nWhile these works did demonstrate that environment aware\ndecisions improve performance compared to battery aware decisions,\ntheir objective was not to achieve energy neutral operation. Our\nproposed techniques attempt to maximize system performance while\nmaintaining energy-neutral operation.\n3. SYSTEM MODEL\nThe energy usage considerations in a harvesting system vary\nsignificantly from those in a battery powered system, as mentioned\nearlier. We propose the model shown in Figure 1 for designing\nenergy management methods in a harvesting system. The functions\nof the various blocks shown in the figure are discussed below. The\nprecise methods used in our system to achieve these functions will\nbe discussed in subsequent sections.\nHarvested Energy Tracking: This block represents the mechanisms\nused to measure the energy received from the harvesting device,\nsuch as the solar panel. Such information is useful for determining\nthe energy availability profile and adapting system performance\nbased on it. Collecting this information requires that the node\nhardware be equipped with the facility to measure the power\ngenerated from the environment, and the Heliomote platform [14]\nwe used for evaluating the algorithms has this capability.\nEnergy Generation Model: For wireless sensor nodes with limited\nstorage and processing capabilities to be able to use the harvested\nenergy data, models that represent the essential components of this\ninformation without using extensive storage are required. The\npurpose of this block is to provide a model for the energy available\nto the system in a form that may be used for making power\nmanagement decisions. The data measured by the energy tracking\nblock is used here to predict future energy availability. A good\nprediction model should have a low prediction error and provide\npredicted energy values for durations long enough to make\nmeaningful performance scaling decisions. Further, for energy\nsources that exhibit both long-term and short-term patterns (e.g.,\ndiurnal and climate variations vs. weather patterns for solar energy),\nthe model must be able to capture both characteristics. Such a model\ncan also use information from external sources such as local weather\nforecast service to improve its accuracy.\nEnergy Consumption Model: It is also important to have detailed\ninformation about the energy usage characteristics of the system, at\nvarious performance levels. For general applicability of our design,\nwe will assume that only one sleep mode is available. We assume\nthat the power consumption in the sleep and active modes is known.\nIt may be noted that for low power systems with more advanced\ncapabilities such as dynamic voltage scaling (DVS), multiple low\npower modes, and the capability to shut down system components\nselectively, the power consumption in each of the states and the\nresultant effect on application performance should be known to make\npower management decisions.\nEnergy Storage Model: This block represents the model for the\nenergy storage technology. Since all the generated energy may not be\nused instantaneously, the harvesting system will usually have some\nenergy storage technology. Storage technologies (e.g., batteries and\nultra-capacitors) are non-ideal, in that there is some energy loss while\nstoring and retrieving energy from them. These characteristics must be\nknown to efficiently manage energy usage and storage. This block also\nincludes the system capability to measure the residual stored energy.\nMost low power systems use batteries to store energy and provide\nresidual battery status. This is commonly based on measuring the\nbattery voltage which is then mapped to the residual battery energy\nusing the known charge to voltage relationship for the battery\ntechnology in use. More sophisticated methods which track the flow of\nenergy into and out of the battery are also available.\nHarvesting-aware Power Management: The inputs provided by the\npreviously mentioned blocks are used here to determine the suitable\npower management strategy for the system. Power management\ncould be carried to meet different objectives in different applications.\nFor instance, in some systems, the harvested energy may marginally\nsupplement the battery supply and the objective may be to maximize\nthe system lifetime. A more interesting case is when the harvested\nenergy is used as the primary source of energy for the system with\nthe objective of achieving indefinitely long system lifetime. In such\ncases, the power management objective is to achieve energy neutral\noperation. In other words, the system should only use as much\nenergy as harvested from the environment and attempt to maximize\nperformance within this available energy budget.\n4. THEORETICALLY OPTIMAL POWER\nMANAGEMENT\nWe develop the following theory to understand the energy\nneutral mode of operation. Let us define Ps(t) as the energy harvested\nfrom the environment at time t, and the energy being consumed by\nthe load at that time is Pc(t). Further, we model the non-ideal storage\nbuffer by its round-trip efficiency \u03b7 (strictly less than 1) and a\nconstant leakage power Pleak. Using this notation, applying the rule\nof energy conservation leads to the following inequality:\n0 0 00\n[ ( ) ( )] [ ( ) ( )] 0\nT T T\ns c c s leakP t P t dt P t P t dt P dtB \u03b7\n+ +\n\u2212 \u2212 \u2212 \u2265+ \u2212\u222b \u222b \u222b (1)\nwhere B0 is the initial battery level and the function [X]+\n= X if X > 0\nand zero otherwise.\nDEFINITION 1 (\u03c1,\u03c31,\u03c32) function: A non-negative, continuous and\nbounded function P (t) is said to be a (\u03c1,\u03c31,\u03c32) function if and only if\nfor any value of finite real number T , the following are satisfied:\n2 1( )\nT\nT P t dt T\u03c1 \u03c3 \u03c1 \u03c3\u2212 \u2264 \u2264 +\u222b (2)\nThis function can be used to model both energy sources and loads.\nIf the harvested energy profile Ps(t) is a (\u03c11,\u03c31,\u03c32) function, then the\naverage rate of available energy over long durations becomes \u03c11, and\nthe burstiness is bounded by \u03c31 and \u03c32 . Similarly, Pc(t) can be modeled\nas a (\u03c12,\u03c33) function, when \u03c12 and \u03c33 are used to place an upper bound\non power consumption (the inequality on the right side) while there are\nno minimum power consumption constraints.\nThe condition for energy neutrality, equation (1), leads to the\nfollowing theorem, based on the energy production, consumption, and\nenergy buffer models discussed above.\nTHEOREM 1 (ENERGY NEUTRAL OPERATION): Consider\na harvesting system in which the energy production profile is\ncharacterized by a (\u03c11, \u03c31, \u03c32) function, the load is characterized by\na (\u03c12, \u03c33) function and the energy buffer is characterized by\nparameters \u03b7 for storage efficiency, and Pleak for leakage power. The\nfollowing conditions are sufficient for the system to achieve energy\nneutrality:\n\u03c12 \u2264 \u03b7\u03c11 \u2212 Pleak (3)\nB0 \u2265 \u03b7\u03c32 + \u03c33 (4)\nB \u2265 B0 (5)\nwhere B0 is the initial energy stored in the buffer and provides a\nlower bound on the capacity of the energy buffer B. The proof is\npresented in our prior work [19].\nTo adjust the duty cycle D using our performance scaling\nalgorithm, we assume the following relation between duty cycle and\nthe perceived utility of the system to the user: Suppose the utility of\nthe application to the user is represented by U(D) when the system\noperates at a duty cycle D. Then,\nmin\n1 min max\n2 max\n( ) 0,\n( ) ,\n( ) ,\nU D if D D\nU D k D if D D D\nU D k if D D\n\u03b2\n= <\n= + \u2264 \u2264\n= >\nThis is a fairly general and simple model and the specific values of\nDmin and Dmax may be determined as per application requirements. As\nan example, consider a sensor node designed to detect intrusion across\na periphery. In this case, a linear increase in duty cycle translates into a\nlinear increase in the detection probability. The fastest and the slowest\nspeeds of the intruders may be known, leading to a minimum and\nHarvested Energy\nTracking\nEnergy Consumption\nModel\nEnergy Storage Model\n\nHarvestingaware Power\nMangement\nEnergy Generation\nModel\nLOAD\nFigure 1. System model for an energy harvesting system.\n181\nmaximum sensing delay tolerable, which results in the relevant Dmax\nand Dmin for the sensor node. While there may be cases where the\nrelationship between utility and duty cycle may be non-linear, in this\npaper, we restrict our focus on applications that follow this linear\nmodel. In view of the above models for the system components and\nthe required performance, the objective of our power management\nstrategy is adjust the duty cycle D(i) dynamically so as to maximize\nthe total utility U(D) over a period of time, while ensuring energy\nneutral operation for the sensor node.\nBefore discussing the performance scaling methods for harvesting\naware duty cycle adaptation, let us first consider the optimal power\nmanagement strategy that is possible for a given energy generation\nprofile. For the calculation of the optimal strategy, we assume\ncomplete knowledge of the energy availability profile at the node,\nincluding the availability in the future. The calculation of the optimal is\na useful tool for evaluating the performance of our proposed algorithm.\nThis is particularly useful for our algorithm since no prior algorithms\nare available to serve as a baseline for comparison.\nSuppose the time axis is partitioned into discrete slots of duration\n\u0394T, and the duty cycle adaptation calculation is carried out over a\nwindow of Nw such time slots. We define the following energy profile\nvariables, with the index i ranging over {1,\u2026, Nw}: Ps(i) is the power\noutput from the harvested source in time slot i, averaged over the slot\nduration, Pc is the power consumption of the load in active mode, and\nD(i) is the duty cycle used in slot i, whose value is to be determined.\nB(i) is the residual battery energy at the beginning of slot i. Following\nthis convention, the battery energy left after the last slot in the window\nis represented by B(Nw+1). The values of these variables will depend\non the choice of D(i).\nThe energy used directly from the harvested source and the energy\nstored and used from the battery must be accounted for differently.\nFigure 2 shows two possible cases for Ps(i) in a time slot. Ps(i) may\neither be less than or higher than Pc , as shown on the left and right\nrespectively. When Ps(i) is lower than Pc, some of the energy used by\nthe load comes from the battery, while when Ps(i) is higher than Pc, all\nthe energy used is supplied directly from the harvested source. The\ncrosshatched area shows the energy that is available for storage into\nthe battery while the hashed area shows the energy drawn from the\nbattery. We can write the energy used from the battery in any slot i as:\n( ) ( ) ( ) ( )[ ] ( ) ( ){ } ( ) ( )[ ]1 1c cs s sB i B i TD i P P i TP i D i TD i P i P\u03b7 \u03b7\n+ +\n\u2212 + = \u0394 \u2212 \u2212 \u0394 \u2212 \u2212 \u2212 (6)\nIn equation (6), the first term on the right hand side measures the\nenergy drawn from the battery when Ps(i) < Pc, the next term measures\nthe energy stored into the battery when the node is in sleep mode, and\nthe last term measures the energy stored into the battery in active mode\nif Ps(i) > Pc. For energy neutral operation, we require the battery at the\nend of the window of Nw slots to be greater than or equal to the starting\nbattery. Clearly, battery level will go down when the harvested energy\nis not available and the system is operated from stored energy.\nHowever, the window Nw is judiciously chosen such that over that\nduration, we expect the environmental energy availability to complete\na periodic cycle. For instance, in the case of solar energy harvesting,\nNw could be chosen to be a twenty-four hour duration, corresponding\nto the diurnal cycle in the harvested energy. This is an approximation\nsince an ideal choice of the window size would be infinite, but a finite\nsize must be used for analytical tractability. Further, the battery level\ncannot be negative at any time, and this is ensured by having a large\nenough initial battery level B0 such that node operation is sustained\neven in the case of total blackout during a window period. Stating the\nabove constraints quantitatively, we can express the calculation of the\noptimal duty cycles as an optimization problem below:\n1\nmax ( )\nwN\ni\nD i\n=\n\u2211 (7)\n( ) ( ) ( ) ( ) ( ) ( ){ } ( ) ( )1 1c s s s cB i B i TD i P P i TP i D i TD i P i P\u03b7 \u03b7\n+ +\n\u23a1 \u23a4 \u23a1 \u23a4\u2212 + = \u0394 \u2212 \u2212 \u0394 \u2212 \u2212 \u2212\u23a3 \u23a6 \u23a3 \u23a6\n(8)\n0(1)B B= (9)\n0( 1)wB N B+ \u2265 (10)\nmin w( ) i {1,...,N }D i D\u2265 \u2200 \u2208 (11)\nmax w( ) i {1,...,N }D i D\u2264 \u2200 \u2208 (12)\nThe solution to the optimization problem yields the duty cycles\nthat must be used in every slot and the evolution of residual battery\nover the course of Nw slots. Note that while the constraints above\ncontain the non-linear function [x]+\n, the quantities occurring within\nthat function are all known constants. The variable quantities occur\nonly in linear terms and hence the above optimization problem can\nbe solved using standard linear programming techniques, available\nin popular optimization toolboxes.\n5. HARVESTING-AWARE POWER\nMANAGEMENT\nWe now present a practical algorithm for power management that\nmay be used for adapting the performance based on harvested energy\ninformation. This algorithm attempts to achieve energy neutral\noperation without using knowledge of the future energy availability\nand maximizes the achievable performance within that constraint.\nThe harvesting-aware power management strategy consists of\nthree parts. The first part is an instantiation of the energy generation\nmodel which tracks past energy input profiles and uses them to\npredict future energy availability. The second part computes the\noptimal duty cycles based on the predicted energy, and this step\nuses our computationally tractable method to solve the optimization\nproblem. The third part consists of a method to dynamically adapt\nthe duty cycle in response to the observed energy generation profile\nin real time. This step is required since the observed energy\ngeneration may deviate significantly from the predicted energy\navailability and energy neutral operation must be ensured with the\nactual energy received rather than the predicted values.\n5.1. Energy Prediction Model\nWe use a prediction model based on Exponentially Weighted\nMoving-Average (EWMA). The method is designed to exploit the\ndiurnal cycle in solar energy but at the same time adapt to the seasonal\nvariations. A historical summary of the energy generation profile is\nmaintained for this purpose. While the storage data size is limited to a\nvector length of Nw values in order to minimize the memory overheads\nof the power management algorithm, the window size is effectively\ninfinite as each value in the history window depends on all the\nobserved data up to that instant. The window size is chosen to be 24\nhours and each time slot is taken to be 30 minutes as the variation in\ngenerated power by the solar panel using this setting is less than 10%\nbetween each adjacent slots. This yields Nw = 48. Smaller slot\ndurations may be used at the expense of a higher Nw.\nThe historical summary maintained is derived as follows. On a\ntypical day, we expect the energy generation to be similar to the energy\ngeneration at the same time on the previous days. The value of energy\ngenerated in a particular slot is maintained as a weighted average of the\nenergy received in the same time-slot during all observed days. The\nweights are exponential, resulting in decaying contribution from older\nFigure 2. Two possible cases for energy calculations\nSlot i Slot k\nPc\nPc\nP(i)\nP(i)\nActive Sleep\n182\ndata. More specifically, the historical average maintained for each slot\nis given by:\n1 (1 )k k kx x x\u03b1 \u03b1\u2212= + \u2212\nwhere \u03b1 is the value of the weighting factor, kx is the observed value\nof energy generated in the slot, and 1kx \u2212\nis the previously stored\nhistorical average. In this model, the importance of each day relative to\nthe previous one remains constant because the same weighting factor\nwas used for all days.\nThe average value derived for a slot is treated as an estimate of\npredicted energy value for the slot corresponding to the subsequent\nday. This method helps the historical average values adapt to the\nseasonal variations in energy received on different days. One of the\nparameters to be chosen in the above prediction method is the\nparameter \u03b1, which is a measure of rate of shift in energy pattern over\ntime. Since this parameter is affected by the characteristics of the\nenergy and sensor node location, the system should have a training\nperiod during which this parameter will be determined. To determine a\ngood value of \u03b1, we collected energy data over 72 days and compared\nthe average error of the prediction method for various values of \u03b1. The\nerror based on the different values of \u03b1 is shown in Figure 3. This\ncurve suggests an optimum value of \u03b1 = 0.15 for minimum prediction\nerror and this value will be used in the remainder of this paper.\n5.2. Low-complexity Solution\nThe energy values predicted for the next window of Nw slots are\nused to calculated the desired duty cycles for the next window,\nassuming the predicted values match the observed values in the future.\nSince our objective is to develop a practical algorithm for embedded\ncomputing systems, we present a simplified method to solve the linear\nprogramming problem presented in Section 4. To this end, we define\nthe sets S and D as follows:\n{ }\n{ }\n| ( ) 0\n| ( ) 0\ns c\nc s\nS i P i P\nD i P P i\n= \u2212 \u2265\n= \u2212 >\nThe two sets differ by the condition that whether the node operation\ncan be sustained entirely from environmental energy. In the case that\nenergy produced from the environment is not sufficient, battery will be\ndischarged to supplement the remaining energy. Next we sum up both\nsides of (6) over the entire Nw window and rewrite it with the new\nnotation.\n1\n1 1 1\n( )[ ( )] ( ) ( ) ( ) ( )[ ( ) ]\nNw Nw Nw\ni i c s s s s c\ni i D i i i S\nB B TD i P P i TP i TP i D i TD i P i P\u03b7 \u03b7 \u03b7+\n= \u2208 = = \u2208\n\u2212 = \u0394 \u2212 \u2212 \u0394 + \u0394 \u2212 \u0394 \u2212\u2211 \u2211 \u2211 \u2211 \u2211\nThe term on the left hand side is actually the battery energy used over\nthe entire window of Nw slots, which can be set to 0 for energy neutral\noperation. After some algebraic manipulation, this yields:\n1\n1\n( ) ( ) ( ) 1 ( )\nNw\nc\ns s c\ni i D i S\nP\nP i D i P i P D i\n\u03b7 \u03b7= \u2208 \u2208\n\u239b \u239e\u239b \u239e\n= + \u2212 +\u239c \u239f\u239c \u239f\n\u239d \u23a0\u239d \u23a0\n\u2211 \u2211 \u2211 (13)\nThe term on the left hand side is the total energy received in Nw\nslots. The first term on the right hand side can be interpreted as the\ntotal energy consumed during the D slots and the second term is the\ntotal energy consumed during the S slots. We can now replace three\nconstraints (8), (9), and (10) in the original problem with (13), restating\nthe optimization problem as follows:\n1\nmax ( )\nwN\ni\nD i\n=\n\u2211\n1\n1\n( ) ( ) ( ) 1 ( )\nNw\nc\ns s c\ni i D i S\nP\nP i D i P i P D i\n\u03b7 \u03b7= \u2208 \u2208\n\u239b \u239e\u239b \u239e\n= + \u2212 +\u239c \u239f\u239c \u239f\n\u239d \u23a0\u239d \u23a0\n\u2211 \u2211 \u2211\nmin\nmax\nD(i) D {1,...,Nw)\nD(i) D {1,...,Nw)\ni\ni\n\u2265 \u2200 \u2208\n\u2264 \u2200 \u2208\nThis form facilitates a low complexity solution that doesn\"t require\na general linear programming solver. Since our objective is to\nmaximize the total system utility, it is preferable to set the duty cycle to\nDmin for time slots where the utility per unit energy is the least. On the\nother hand, we would also like the time slots with the highest Ps to\noperate at Dmax because of better efficiency of using energy directly\nfrom the energy source. Combining these two characteristics, we\ndefine the utility co-efficient for each slot i as follows:\n1\n( ) 1\n1 ( ) 1\nc\nc\ns\nP for i S\nW i P\nP i for i D\n\u03b7 \u03b7\n\u2208\u23a7\n\u23aa\n= \u239b \u239e\u239b \u239e\u23a8\n+ \u2212 \u2208\u239c \u239f\u239c \u239f\u23aa\n\u239d \u23a0\u239d \u23a0\u23a9\nwhere W(i) is a representation of how efficient the energy usage in a\nparticular time slot i is. A larger W(i) indicates more system utility per\nunit energy in slot i and vice versa. The algorithm starts by assuming\nD(i) =Dmin for i = {1\u2026NW} because of the minimum duty cycle\nrequirement, and computes the remaining system energy R by:\n1\n1\n( ) ( ) ( ) 1 ( ) (14)\nNw\nc\ns s c\ni i D i S\nP\nR P i D i P i P D i\n\u03b7 \u03b7= \u2208 \u2208\n\u239b \u239e\u239b \u239e\n= \u2212 + \u2212 \u2212\u239c \u239f\u239c \u239f\n\u239d \u23a0\u239d \u23a0\n\u2211 \u2211 \u2211\nA negative R concludes that the optimization problem is infeasible,\nmeaning the system cannot achieve energy neutrality even at the\nminimum duty cycle. In this case, the system designer is responsible\nfor increasing the environment energy availability (e.g., by using larger\nsolar panels). If R is positive, it means the system has excess energy\nthat is not being used, and this may be allocated to increase the duty\ncycle beyond Dmin for some slots. Since our objective is to maximize\nthe total system utility, the most efficient way to allocate the excess\nenergy is to assign duty cycle Dmax to the slots with the highest W(i).\nSo, the coefficients W(i) are arranged in decreasing order and duty\ncycle Dmax is assigned to the slots beginning with the largest\ncoefficients until the excess energy available, R (computed by (14) in\nevery iteration), is insufficient to assign Dmax to another slot. The\nremaining energy, RLast, is used to increase the duty cycle to some\nvalue between Dmin and Dmax in the slot with the next lower coefficient.\nDenoting this slot with index j, the duty cycle is given by:\nD(j)=\nmin\n/\n( ( ) ) / ( )\nLast c\nLast\ns c s\nR P if j D\nDR\nif j S\nP j P P j\u03b7\n\u2208\u23a7 \u23ab\n\u23aa \u23aa\n+\u23a8 \u23ac\n\u2208\u23aa \u23aa\u2212 \u2212\u23a9 \u23ad\nThe above solution to the optimization problem requires only simple\narithmetic calculations and one sorting step which can be easily\nimplemented on an embedded platform, as opposed to implementing a\ngeneral linear program solver.\n5.3. Slot-by-slot continual duty cycle adaptiation.\nThe observed energy values may vary greatly from the predicted\nones, such as due to the effect of clouds or other sudden changes. It is\nthus important to adapt the duty cycles calculated using the predicted\nvalues, to the actual energy measurements in real time to ensure energy\nneutrality. Denote the initial duty cycle assignments for each time slot i\ncomputed using the predicted energy values as D(i) = {1, ...,Nw}. First\nwe compute the difference between predicted power level Ps(i) and\nactual power level observed, Ps\"(i) in every slot i. Then, the excess\nenergy in slot i, denoted by X, can be obtained as follows:\n( ) '( ) '( )\n1\n( ) '( ) ( )[ ( ) '( )](1 ) '( )\ns s s c\ns s s s s c\nP i P i if P i P\nX\nP i P i D i P i P i if P i P\n\u03b7\n\u2212 >\u23a7\n\u23aa\n= \u23a8\n\u2212 \u2212 \u2212 \u2212 \u2264\u23aa\n\u23a9\n0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5\n2.6\n2.7\n2.8\n2.9\n3\nalpha\nAvgError(mA)\nFigure 3. Choice of prediction parameter.\n183\nThe upper term accounts for the energy difference when actual\nreceived energy is more than the power drawn by the load. On the\nother hand, if the energy received is less than Pc, we will need to\naccount for the extra energy used from the battery by the load, which is\na function of duty cycle used in time slot i and battery efficiency factor\n\u03b7. When more energy is received than predicted, X is positive and that\nexcess energy is available for use in the subsequent solutes, while if X\nis negative, that energy must be compensated from subsequent slots.\nCASE I: X<0. In this case, we want to reduce the duty cycles used in\nthe future slots in order to make up for this shortfall of energy. Since\nour objective function is to maximize the total system utility, we have\nto reduce the duty cycles for time slots with the smallest normalized\nutility coefficient, W(i). This is accomplished by first sorting the\ncoefficient W(j) ,where j>i. in decreasing order, and then iteratively\nreducing Dj to Dmin until the total reduction in energy consumption is\nthe same as X.\nCASE II: X>0. Here, we want to increase the duty cycles used in the\nfuture to utilize this excess energy we received in recent time slot. In\ncontrast to Case I, the duty cycles of future time slots with highest\nutility coefficient W(i) should be increased first in order to maximize\nthe total system utility.\nSuppose the duty cycle is changed by d in slot j. Define a quantity\nR(j,d) as follows:\n\u23aa\n\u23a9\n\u23aa\n\u23a8\n\u23a7\n<=\u239f\n\u239f\n\u23a0\n\u239e\n\u239c\n\u239c\n\u239d\n\u239b\n\u239f\u239f\n\u23a0\n\u239e\n\u239c\u239c\n\u239d\n\u239b\n\u2212+\n>\u22c5\n=\nlji\nl\nljl\nPPifP\nP\nd\nPPifP\ndjR\n\n1\n1\nd\n),(\n\u03b7\u03b7\nThe precise procedure to adapt the duty cycle to account for the\nabove factors is presented in Algorithm 1. This calculation is\nperformed at the end of every slot to set the duty cycle for the next\nslot. We claim that our duty cycling algorithm is energy neutral\nbecause an surplus of energy at the previous time slot will always\ntranslate to additional energy opportunity for future time slots, and\nvice versa. The claim may be violated in cases of severe energy\nshortages especially towards the end of window. For example, a large\ndeficit in energy supply can\"t be restored if there is no future energy\ninput until the end of the window. In such case, this offset will be\ncarried over to the next window so that long term energy neutrality is\nstill maintained.\n6. EVALUATION\nOur adaptive duty cycling algorithm was evaluated using an actual\nsolar energy profile measured using a sensor node called Heliomote,\ncapable of harvesting solar energy [14]. This platform not only tracks\nthe generated energy but also the energy flow into and out of the\nbattery to provide an accurate estimate of the stored energy.\nThe energy harvesting platform was deployed in a residential area\nin Los Angeles from the beginning of June through the middle of\nAugust for a total of 72 days. The sensor node used is a Mica2 mote\nrunning at a fixed 40% duty cycle with an initially full battery. Battery\nvoltage and net current from the solar panels are sampled at a period of\n10 seconds. The energy generation profile for that duration, measured\nby tracking the output current from the solar cell is shown in Figure 4,\nboth on continuous and diurnal scales. We can observe that although\nthe energy profile varies from day to day, it still exhibits a general\npattern over several days.\n0 10 20 30 40 50 60 70\n0\n10\n20\n30\n40\n50\n60\n70\nDay\nmA\n0 5 10 15 20\n0\n10\n20\n30\n40\n50\n60\n70\nHour\nmA\n6.1. Prediction Model\nWe first evaluate the performance of the prediction model, which\nis judged by the amount of absolute error it made between the\npredicted and actual energy profile. Figure 5 shows the average error\nof each time slot in mA over the entire 72 days. Generally, the amount\nof error is larger during the day time because that\"s when the factor of\nweather can cause deviations in received energy, while the prediction\nmade for night time is mostly correct.\n6.2. Adaptive Duty cycling algorithm\nPrior methods to optimize performance while achieving energy\nneutral operation using harvested energy are scarce. Instead, we\ncompare the performance of our algorithm against two extremes: the\ntheoretical optimal calculated assuming complete knowledge about\nfuture energy availability and a simple approach which attempts to\nachieve energy neutrality using a fixed duty cycle without accounting\nfor battery inefficiency.\nThe optimal duty cycles are calculated for each slot using the\nfuture knowledge of actual received energy for that slot. For the simple\napproach, the duty cycle is kept constant within each day and is\nFigure 4 Solar Energy Profile (Left: Continuous, Right: Diurnal)\nInput: D: Initial duty cycle, X: Excess energy due to error in the\nprediction, P: Predicted energy profile, i: index of current time slot\nOutput: D: Updated duty cycles in one or more subsequent slots\nAdaptDutyCycle()\nIteration: At each time slot do:\nif X > 0\nWsorted = W{1, ...,Nw} sorted in decending order.\nQ := indices of Wsorted\nfor k = 1 to |Q|\nif Q(k) \u2264 i or D(Q(k)) \u2265 Dmax //slot is already passed\ncontinue\nif R(Q(k), Dmax \u2212 D(Q(k))) < X\nD(Q(k)) = Dmax\nX = X \u2212 R(j, Dmax \u2212 D(Q(k)))\nelse\n//X insufficient to increase duty cycle to Dmax\nif P (Q(k)) > Pl\nD(Q(k)) = D(Q(k)) + X/Pl\nelse\nD(Q(k)) = D(Q(k)) +\n( ( ))(1 1 ))c s\nX\nP P Q k\u03b7 \u03b7+ \u2212\nif X < 0\nWsorted = W{1, ...,Nw} sorted in ascending order.\nQ := indices of Wsorted\nfor k = 1 to |Q|\nif Q(k) \u2264 I or D(Q(k)) \u2264 Dmin\ncontinue\nif R(Q(k), Dmax \u2212 D(Q(k))) > X\nD(Q(k)) = Dmin\nX = X \u2212 R(j, Dmin \u2212 D(Q(k)))\nelse\nif P (Q(k)) > Pc\nD(Q(k)) = D(Q(k)) + X/Pc\nelse\nD(Q(k)) = D(Q(k)) +\n( ( ))(1 1 ))c s\nX\nP P Q k\u03b7 \u03b7+ \u2212\nALGORITHM 1 Pseudocode for the duty-cycle adaptation algorithm\nFigure 5. Average Predictor Error in mA\n0 5 10 15 20 25\n0\n2\n4\n6\n8\n10\n12\nTime(H)\nabserror(mA)\n184\ncomputed by taking the ratio of the predicted energy availability and\nthe maximum usage, and this guarantees that the senor node will never\ndeplete its battery running at this duty cycle.\n{1.. )\n( )s w c\ni Nw\nD P i N P\u03b7\n\u2208\n= \u22c5 \u22c5\u2211\nWe then compare the performance of our algorithm to the two\nextremes with varying battery efficiency. Figure 6 shows the results,\nusing Dmax = 0.8 and Dmin = 0.3. The battery efficiency was varied\nfrom 0.5 to 1 on the x-axis and solar energy utilizations achieved by\nthe three algorithms are shown on the y-axis. It shows the fraction of\nnet received energy that is used to perform useful work rather than lost\ndue to storage inefficiency.\nAs can be seen from the figure, battery efficiency factor has great\nimpact on the performance of the three different approaches. The three\napproaches all converges to 100% utilization if we have a perfect\nbattery (\u03b7=1), that is, energy is not lost by storing it into the batteries.\nWhen battery inefficiency is taken into account, both the adaptive and\noptimal approach have much better solar energy utilization rate than\nthe simple one. Additionally, the result also shows that our adaptive\nduty cycle algorithm performs extremely close to the optimal.\n0.4 0.5 0.6 0.7 0.8 0.9 1\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nEta-batery roundtrip efficiency\nSolarEnergyUtilization(%)\nOptimal\nAdaptive\nSimple\nWe also compare the performance of our algorithm with different\nvalues of Dmin and Dmax for \u03b7=0.7, which is typical of NiMH batteries.\nThese results are shown in Table 1 as the percentage of energy saved\nby the optimal and adaptive approaches, and this is the energy which\nwould normally be wasted in the simple approach. The figures and\ntable indicate that our real time algorithm is able to achieve a\nperformance very close to the optimal feasible. In addition, these\nresults show that environmental energy harvesting with appropriate\npower management can achieve much better utilization of the\nenvironmental energy.\nDmax\nDmin\n0.8\n0.05\n0.8\n0.1\n0.8\n0.3\n0.5\n0.2\n0.9\n0.2\n1.0\n0.2\nAdaptive 51.0% 48.2% 42.3% 29.4% 54.7% 58.7%\nOptimal 52.3% 49.6% 43.7% 36.7% 56.6% 60.8%\n7. CONCLUSIONS\nWe discussed various issues in power management for systems\npowered using environmentally harvested energy. Specifically, we\ndesigned a method for optimizing performance subject to the\nconstraint of energy neutral operation. We also derived a theoretically\noptimal bound on the performance and showed that our proposed\nalgorithm operated very close to the optimal. The proposals were\nevaluated using real data collected using an energy harvesting sensor\nnode deployed in an outdoor environment.\nOur method has significant advantages over currently used\nmethods which are based on a conservative estimate of duty cycle and\ncan only provide sub-optimal performance. However, this work is only\nthe first step towards optimal solutions for energy neutral operation. It\nis designed for a specific power scaling method based on adapting the\nduty cycle. Several other power scaling methods, such as DVS,\nsubmodule power switching and the use of multiple low power modes are\nalso available. It is thus of interest to extend our methods to exploit\nthese advanced capabilities.\n8. ACKNOWLEDGEMENTS\nThis research was funded in part through support provided by\nDARPA under the PAC/C program, the National Science Foundation\n(NSF) under award #0306408, and the UCLA Center for Embedded\nNetworked Sensing (CENS). Any opinions, findings, conclusions or\nrecommendations expressed in this paper are those of the authors and\ndo not necessarily reflect the views of DARPA, NSF, or CENS.\nREFERENCES\n[1] R Ramanathan, and R Hain, Toplogy Control of Multihop Wireless\nNetworks Using Transmit Power Adjustment in Proc. Infocom. Vol 2.\n26-30 pp. 404-413. March 2000\n[2] T.A. Pering, T.D. Burd, and R. W. Brodersen,  The simulation and\nevaluation of dynamic voltage scaling algorithms, in Proc. ACM\nISLPED, pp. 76-81, 1998\n[3] L. Benini and G. De Micheli, Dynamic Power Management: Design\nTechniques and CAD Tools. Kluwer Academic Publishers, Norwell, MA,\n1997.\n[4] John Kymisis, Clyde Kendall, Joseph Paradiso, and Neil Gershenfeld.\nParasitic power harvesting in shoes. In ISWC, pages 132-139. IEEE\nComputer Society press, October 1998.\n[5] Nathan S. Shenck and Joseph A. Paradiso. Energy scavenging with\nshoemounted piezoelectrics. IEEE Micro, 21(3):30\u00f142, May-June 2001.\n[6] T Starner. 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Ambient intelligence: industrial research on a visionary\nconcept. In Proceedings of the 2003 international symposium on Low\npower electronics and design, pages 247-251. ACM Press, 2003.\n[14] V Raghunathan, A Kansal, J Hsu, J Friedman, and MB Srivastava,\n\"Design Considerations for Solar Energy Harvesting Wireless Embedded\nSystems,\" (IPSN/SPOTS), April 2005.\n[15] Xiaofan Jiang, Joseph Polastre, David Culler, Perpetual Environmentally\nPowered Sensor Networks, (IPSN/SPOTS), April 25-27, 2005.\n[16] Chulsung Park, Pai H. Chou, and Masanobu Shinozuka, \"DuraNode:\nWireless Networked Sensor for Structural Health Monitoring,\" to appear\nin Proceedings of the 4th IEEE International Conference on Sensors,\nIrvine, CA, Oct. 31 - Nov. 1, 2005.\n[17] Aman Kansal and Mani B. Srivastava. An environmental energy\nharvesting framework for sensor networks. In International symposium on\nLow power electronicsand design, pages 481-486. ACM Press, 2003.\n[18] Thiemo Voigt, Hartmut Ritter, and Jochen Schiller. Utilizing solar power\nin wireless sensor networks. In LCN, 2003.\n[19] A. Kansal, J. Hsu, S. Zahedi, and M. B. Srivastava. Power management\nin energy harvesting sensor networks. Technical Report\nTR-UCLA-NESL200603-02, Networked and Embedded Systems Laboratory, UCLA,\nMarch 2006.\nFigure 6. Duty Cycles achieved with respect to \u03b7\nTABLE 1. Energy Saved by adaptive and optimal approach.\n185", "keywords": "sampling frequency;energy harvest;energy harvesting system;duty cycling rate;low power design;harvesting-aware power management;solar panel;duty cycle;performance scaling;power scaling;energy neutral operation;sensor network;energy tracking;storage buffer;environmental energy;power management;network latency"}
{"name": "train_C-83", "title": "Concept and Architecture of a Pervasive Document Editing and Managing System", "abstract": "Collaborative document processing has been addressed by many approaches so far, most of which focus on document versioning and collaborative editing. We address this issue from a different angle and describe the concept and architecture of a pervasive document editing and managing system. It exploits database techniques and real-time updating for sophisticated collaboration scenarios on multiple devices. Each user is always served with upto-date documents and can organize his work based on document meta data. For this, we present our conceptual architecture for such a system and discuss it with an example.", "fulltext": "1. INTRODUCTION\nText documents are a valuable resource for virtually any enterprise\nand organization. Documents like papers, reports and general\nbusiness documentations contain a large part of today\"s (business)\nknowledge. Documents are mostly stored in a hierarchical folder\nstructure on file servers and it is difficult to organize them in regard\nto classification, versioning etc., although it is of utmost importance\nthat users can find, retrieve and edit up-to-date versions of\ndocuments whenever they want and, in a user-friendly way.\n1.1 Problem Description\nWith most of the commonly used word-processing applications\ndocuments can be manipulated by only one user at a time: tools for\npervasive collaborative document editing and management, are\nrarely deployed in today\"s world. Despite the fact, that people strive\nfor location- and time- independence, the importance of pervasive\ncollaborative work, i.e. collaborative document editing and\nmanagement is totally neglected. Documents could therefore be\nseen as a vulnerable source in today\"s world, which demands for an\nappropriate solution: The need to store, retrieve and edit these\ndocuments collaboratively anytime, everywhere and with almost\nevery suitable device and with guaranteed mechanisms for security,\nconsistency, availability and access control, is obvious.\nIn addition, word processing systems ignore the fact that the history\nof a text document contains crucial information for its management.\nSuch meta data includes creation date, creator, authors, version,\nlocation-based information such as time and place when/where a\nuser reads/edits a document and so on. Such meta data can be\ngathered during the documents creation process and can be used\nversatilely. Especially in the field of pervasive document\nmanagement, meta data is of crucial importance since it offers\ntotally new ways of organizing and classifying documents: On the\none hand, the user\"s actual situation influences the user\"s objectives.\nMeta data could be used to give the user the best possible view on\nthe documents, dependent of his actual information. On the other\nhand, as soon as the user starts to work, i.e. reads or edits a\ndocument, new meta data can be gathered in order to make the\nsystem more adaptable and in a sense to the users situation and, to\noffer future users a better view on the documents.\nAs far as we know, no system exists, that satisfies the\naforementioned requirements. A very good overview about\nrealtime communication and collaboration system is described in [7].\nWe therefore strive for a pervasive document editing and\nmanagement system, which enables pervasive (and collaborative)\ndocument editing and management: users should be able to read and\nedit documents whenever, wherever, with whomever and with\nwhatever device.\nIn this paper, we present collaborative database-based real-time\nword processing, which provides pervasive document editing and\nmanagement functionality. It enables the user to work on\ndocuments collaboratively and offers sophisticated document\nmanagement facility: the user is always served with up-to-date\ndocuments and can organize and manage documents on the base of\nmeta data. Additionally document data is treated as \u2018first class\ncitizen\" of the database as demanded in [1].\n1.2 Underlying Concepts\nThe concept of our pervasive document editing and management\nsystem requires an appropriate architectural foundation. Our\nconcept and implementation are based on the TeNDaX [3]\ncollaborative database-based document editing and management\nsystem, which enables pervasive document editing and managing.\nTeNDaX is a Text Native Database eXtension. It enables the\nstorage of text in databases in a native form so that editing text is\nfinally represented as real-time transactions. Under the term \u2018text\nediting\" we understand the following: writing and deleting text\n(characters), copying & pasting text, defining text layout &\nstructure, inserting notes, setting access rights, defining business\nprocesses, inserting tables, pictures, and so on i.e. all the actions\nregularly carried out by word processing users. With \u2018real-time\ntransaction\" we mean that editing text (e.g. writing a\ncharacter/word) invokes one or several database transactions so that\neverything, which is typed appears within the editor as soon as these\nobjects are stored persistently. Instead of creating files and storing\nthem in a file system, the content and all of the meta data belonging\nto the documents is stored in a special way in the database, which\nenables very fast real-time transactions for all editing tasks [2].\nThe database schema and the above-mentioned transactions are\ncreated in such a way that everything can be done within a\nmultiuser environment, as is usual done by database technology. As a\nconsequence, many of the achievements (with respect to data\norganization and querying, recovery, integrity and security\nenforcement, multi-user operation, distribution management,\nuniform tool access, etc.) are now, by means of this approach, also\navailable for word processing.\n2. APPROACH\nOur pervasive editing and management system is based on the\nabove-mentioned database-based TeNDaX approach, where\ndocument data is stored natively in the database and supports\npervasive collaborative text editing and document management.\nWe define the pervasive document editing and management system,\nas a system, where documents can easily be accessed and\nmanipulated everywhere (within the network), anytime\n(independently of the number of users working on the same\ndocument) and with any device (desktop, notebook, PDA, mobile\nphone etc.).\nDB 3\nRTSC 4\nRTSC 1\nRTSC 2\nRTSC 3\nAS 1\nAS 3\nDB 1\nDB 2\nAS 2\nAS 4\nDB 4\nA\nB\nC\nD\nE\nF\nG\nFigure 1. TeNDaX Application Architecture\nIn contrast to documents stored locally on the hard drive or on a file\nserver, our system automatically serves the user with the up-to-date\nversion of a document and changes done on the document are stored\npersistently in the database and immediately propagated to all\nclients who are working on the same document. Additionally, meta\ndata gathered during the whole document creation process enables\nsophisticated document management. With the TeXt SQL API as\nabstract interface, this approach can be used by any tool and for any\ndevice.\nThe system is built on the following components (see Figure 1): An\neditor in Java implements the presentation layer (A-G in Figure 1).\nThe aim of this layer is the integration in a well-known\nwordprocessing application such as OpenOffice.\nThe business logic layer represents the interface between the\ndatabase and the word-processing application. It consists of the\nfollowing three components: The application server (marked as AS\n1-4 in Figure 1) enables text editing within the database\nenvironment and takes care of awareness, security, document\nmanagement etc., all within a collaborative, real-time and multi-user\nenvironment. The real-time server component (marked as RTSC\n14 in Figure 1) is responsible for the propagation of information, i.e.\nupdates between all of the connected editors.\nThe storage engine (data layer) primarily stores the content of\ndocuments as well as all related meta data within the database\nDatabases can be distributed in a peer-to-peer network (DB 1-4 in\nFigure 1)..\nIn the following, we will briefly present the database schema, the\neditor and the real-time server component as well as the concept of\ndynamic folders, which enables sophisticated document\nmanagement on the basis of meta data.\n2.1 Application Architecture\nA database-based real-time collaborative editor allows the same\ndocument to be opened and edited simultaneously on the same\ncomputer or over a network of several computers and mobile\ndevices. All concurrency issues, as well as message propagation, are\nsolved within this approach, while multiple instances of the same\ndocument are being opened [3]. Each insert or delete action is a\ndatabase transaction and as such, is immediately stored persistently\nin the database and propagated to all clients working on the same\ndocument.\n2.1.1 Database Schema\nAs it was mentioned earlier that text is stored in a native way. Each\ncharacter of a text document is stored as a single object in the\ndatabase [3]. When storing text in such a native form, the\nperformance of the employed database system is of crucial\nimportance. The concept and performance issues of such a text\ndatabase are described in [3], collaborative layouting in [2],\ndynamic collaborative business processes within documents in [5],\nthe text editing creation time meta data model in [6] and the relation\nto XML databases in [7].\nFigure 2 depicts the core database schema. By connecting a client to\nthe database, a Session instance is created. One important attribute\nof the Session is the DocumentSession. This attribute refers to\nDocumentSession instances, which administrates all opened\ndocuments. For each opened document, a DocumentSession\ninstance is created. The DocumentSession is important for the\nrealtime server component, which, in case of a\n42\nis beforeis after\nChar\n(ID)\nhas\nTextElement\n(ID)\nstarts\nwith\nis used\nby\nInternalFile\n(ID)\nis in includes\ncreated\nat\nhas\ninserted\nby\ninserted\nis active\nir\nir\nCharacterValue\n(Unicode)\nhas\nList\n(ID)\nstarts\nstarts\nwith\nends ends with\nFileSize\nhas\nUser\n(ID)\nlast read by\nlast written by\ncreated\nat\ncreated by\nStyle\nDTD\n(ID)\nis used\nby\nuses\nuses\nis used\nby\nAuthors\narehas\nDescription\nPassword\nPicture\nUserColors\nUserListSecurity\nhas\nhas\nhas\nhas\nhas\nhas\nFileNode\n(ID)\nreferences/isreferencedby\nis dynamic DynStructure\nNodeDetails\nhas\nhas is NodeType\nis parent\nof\nhas\nparent\nhas\nRole\n(ID)\ncreated\nat\ncreated\ncreated\nby\nName\nhas\nDescription\nis user\nName\nhas\nhas\nmain role\nFileNodeAccessMatrix\n(ID)\nhas\nis\nAccessMatrix\nread option\ngrand option\nwrite option\ncontains\nhas\naccess\nTimes\nopened \u2026 times with \u2026 by\ncontains/ispartof\nir\nir\nis...andincludes\nLineage\n(ID)\nreferences\nis after\nis before\nCopyPaste\n(ID)\nreferences\nis in\nis copy\nof\nis a copy\nfrom\nhasCopyPaste\n(ID)\nis activeLength has\nStr (Stream)\nhas\ninserted by / inserted\nRegularChar\nStartChar EndChar\nFile\nExternalFile\nis from\nURL\nType\n(extension)\nis of\nTitle\nhas\nDocumentSession\n(ID)\nis opened\nby\nhas\nopened\nhas\nopened\nSession\n(ID)\nisconnectedwith\nlaunched by\nVersionNumber\nuses\nhas\nread option\ngrand option\nwrite option\nends with\nis used\nby\nis in has\nis unique\nDTD (Stream)\nhas\nhas\nName\nColumn\n(ID)\nhas set on\nOn/off\nisvisible\u2026for\nfalse\nLanguageProfile\n(ID)\nhas\ncontains\nName\nProfile\nMarking\n(ID)\nhas\nparent\ninternal\nis copy\nfrom\nhasRank\nis onPosition\nstarts\nwith\nends with\nis logical style\nis itemized\nis italic\nis enumerated\nis underline\nis\nis part of\nAlignment\nSize has\nFont has\nhasColor\nis bold\nhas\nuses\nElementName\nStylesheetName\nisused\nby\nProcess\n(ID)\nis running by OS\nis web session\nMainRoles\nRoles has\nhas\nTimestamp\n(Date, Time)\ncreated\nat\nTimestamp\n(Date, Time)\nTimestamp\n(Date, Time)\nTimestamp\n(Date, Time)\nTimestamp\n(Date, Time)created\nat\nType\nhas\nPort\nIP\nhas\nhas\nMessagePropagator\n(ID)\nPicture\n(Stream)\nName\nPicture\n(ID)\nhas\ncontains\nLayoutBlock WorkflowBlockLogicalBlock\ncontains\nBlockDataType\nhas\nproperty\nBlockData is of\nWorkflowInstance\n(ID)\nisin\nTaskInstance\n(ID)\nhas\nparent\nTimestamp\n(Date, Time)\nTimestamp\n(Date, Time)\nTimestamp\n(Date, Time)\nTimestamp\n(Date, Time)\nlast modified at\ncompleted at\nstarted at\ncreated\nat\nis on\nhas\nName\ncreated by\nhas\nattached\nComment\nTypeis of\nTimestamp\n(Date, Time)\nTimestamp\n(Date, Time)\nTimestamp\n(Date, Time)\ncreated\nat\nstarted at\n<< last modified at\nis\nCategory\nEditors\nhas\nStatus\nhas\nTimestamp\n(Date, Time)\n<< status last modified\nTimestamp\n(Date, Time)\nis due at\nDueType\nhas\nTimezone\nhas\nNotes\nhas\nSecurityLevel\nhasset\nTimestamp\n(Date, Time)\n<< is completed at\nisfollowedby\nTask\n(Code)\nDescription\nhas\nIndent\nreferences\nhasbeenopenedat...by\nTimestamp\nRedoHistory\nis before\nis after\nreferences\nhasCharCounter\nis inhas\nhas\nOffset\nActionID\n(Code)\nTimestamp\n(Date, Time)\ninvoked\nat\ninvoked\nby\nVersion\n(ID)\nisbuild\nfrom\nhas\ncreated\nbyarchived\nhas\nComment\nTimestamp\n(Date, Time)\n<<createdat\nUndoHistory\n(ID)\nstarts\nends\nhas\nName\ncreated\nby\nName\nhas\nis before\nis after\n<< references\nCharCounter\nhas\nis in\ncreated\nat\nTimestamp\nis active\ncreated\nby\nis used\nby\nOffset\nhas\ncreated\nat\nTimestamp\nIndex\n(ID)\nlastmodifiedby\nLexicon\n(ID)\nisof\nFrequency\nis\noccurring\nis stop word\nTerm\nis\nis in\nends with\nstarts\nwith\n<< original starts with\nWordNumber\nSentenceNumber\nParagraphNumber\nCitatons\nhas\nis in\nis\nis in\nistemporary\nis in\nhas\nStructure\nhas\nElementPath\ncreatedat\nTimestamp\n<< describes\nSpiderBuild\n(ID)\nis updated\nis deleted\nTimestamp\n(Date, Time)\n<<lastupdatedat\nhas validated structure\n<<neededtoindex\nTime\n(ms)\nIndexUpdate\nnextupdatein\nhasindexed\nisrunningbyOS\nlastupdate\nenabled\nTimestamp\nTime\n(s)\nDocuments\nStopCharacter\nDescription\nCharacter\nValue\n(ASCII)\nis sentence stop\nis paragraph stop\nName\nhas\nis\nis\nOptionsSettings\nshow information show warningsshow exceptions\ndo lineage recording\ndo internal lineage recording\nask for unknown source\nshow intra document\nlineage information\nare set\nfor\nX\nX\nX\nVirtualBorder\n(ID)\nisonhas\n{1, 2}\n{1, 2}\nir\nir\nUserMode\n(Code)\nUserMode\n(Code)\nFigure 2. TeNDaX Database Schema (Object Role Modeling Diagram)\nchange on a document done by a client, is responsible for sending\nupdate information to all the clients working on the same\ndocument. The DocumentId in the class DocumentSession points\nto a FileNode instance, and corresponds to the ID of the opened\ndocument. Instances of the class FileNode either represent a\nfolder node or a document node. The folder node corresponds to a\nfolder of a file system and the document node to that of a file.\nInstances of the class Char represent the characters of a\ndocument. The value of a character is stored in the attribute\nCharacterValue. The sequence is defined by the attributes After\nand Before of the class Char. Particular instances of Char mark\nthe beginning and the end of a document. The methods\nInsertChars and RemoveChars are used to add and delete\ncharacters.\n2.1.2 Editor\nAs seen above, each document is natively stored in the database.\nOur editor does not have a replica of one part of the native text\ndatabase in the sense of database replicas. Instead, it has a so-called\nimage as its replica. Even if several authors edit the same text at the\nsame time, they work on one unique document at all times. The\nsystem guarantees this unique view.\nEditing a document involves a number of steps: first, getting the\nrequired information out of the image, secondly, invoking the\ncorresponding methods within the database, thirdly, changing the\nimage, and fourthly, informing all other clients about the changes.\n2.1.3 Real-Time Server Component\nThe real-time server component is responsible for the real-time\npropagation of any changes on a document done within an editor to\nall the editors who are working or have opened the same document.\nWhen an editor connects to the application server, which in turn\nconnects to the database, the database also establishes a connection\nto the real-time server component (if there isn\"t already a\nconnection). The database system informs the real-time server\ncomponent about each new editor session (session), which the\nrealtime server component administrates in his SessionManager. Then,\nthe editor as well connects to the real-time server component. The\nreal-time server component adds the editor socket to the client\"s\ndata structure in the SessionManager and is then ready to\ncommunicate.\nEach time a change on a document from an editor is persistently\nstored in the database, the database sends a message to the real-time\nserver component, which in turns, sends the changes to all the\n43\neditors working on the same document. Therefore, a special\ncommunication protocol is used: the update protocol.\nUpdate Protocol\nThe real-time server component uses the update protocol to\ncommunicate with the database and the editors. Messages are sent\nfrom the database to the real-time server component, which sends\nthe messages to the affected editors. The update protocol consists of\ndifferent message types. Messages consist of two packages:\npackage one contains information for the real-time server\ncomponent whereas package two is passed to the editors and\ncontains the update information, as depicted in Figure 3.\n|| RTSC || Parameter | \u2026 | Parameter|| || Editor Data ||\nProtocol between database system and\nreal-time server component\nProtocol between real -time server\ncomponent and editors\nFigure 3. Update Protocol\nIn the following, two message types are presented:\n||u|sessionId,...,sessionId||||editor data||\nu: update message, sessionId: Id of the client session\nWith this message type the real-time server component sends the\neditor data package to all editors specified in the sessionId list.\n||ud|fileId||||editor data||\nud: update document message, fileId: Id of the file\nWith this message type, the real-time server component sends the\neditor data to all editors who have opened the document with the\nindicated file-Id.\nClass Model\nFigure 4 depicts the class model as well as the environment of the\nreal-time server component. The environment consists mainly of the\neditor and the database, but any other client application that could\nmake use of the real-time server component can connect.\nConnectionListener: This class is responsible for the connection to\nthe clients, i.e. to the database and the editors. Depending on the\nconnection type (database or editor) the connection is passed to an\nEditorWorker instance or DatabaseMessageWorker instance\nrespectively.\nEditorWorker: This class manages the connections of type \u2018editor\".\nThe connection (a socket and its input and output stream) is stored\nin the SessionManager.\nSessionManager: This class is similar to an \u2018in-memory database\":\nall editor session information, e.g. the editor sockets, which editor\nhas opened which document etc. are stored within this data\nstructure.\nDatabaseMessageWorker: This class is responsible for the\nconnections of type \u2018database\". At run-time, only one connection\nexists for each database. Update messages from the database are\nsent to the DatabaseMessageWorker and, with the help of\nadditional information from the SessionManager, sent to the\ncorresponding clients.\nServiceClass: This class offers a set of methods for reading, writing\nand logging messages.\ntdb.mp.editor tdb.mp.database\ntdb.mp.mgmt\nEditorWorker\nDatabaseMessageWorker\nSessionManager\nMessageHandler\nConnectionListener\nServiceClass\nMessageQueue\ntdb.mp.listener tdb.mp.service\njunit.tests\n1\n*\n1\n*\n1 *\n1\n*\n1*\n1\n*\nEditors Datenbanksystem 1\n2\n1\n*\n1\n*\n1\n*\nTCP/IP\nFigure 4. Real-Time Server Component Class Diagram\n2.1.4 Dynamic Folders\nAs mentioned above, every editing action invoked by a user is\nimmediately transferred to the database. At the same time, more\ninformation about the current transaction is gathered.\nAs all information is stored in the database, one character can hold a\nmultitude of information, which can later be used for the retrieval of\ndocuments. Meta data is collected at character level, from document\nstructure (layout, workflow, template, semantics, security,\nworkflow and notes), on the level of a document section and on the\nlevel of the whole document [6].\nAll of the above-mentioned meta data is crucial information for\ncreating content and knowledge out of word processing documents.\nThis meta data can be used to create an alternative storage system\nfor documents. In any case, it is not an easy task to change users\"\nfamiliarity to the well known hierarchical file system. This is also\nthe main reason why we do not completely disregard the classical\nfile system, but rather enhance it. Folders which correspond to the\nclassical hierarchical file system will be called static folders.\nFolders where the documents are organized according to meta data,\nwill be called dynamic folders. As all information is stored in the\ndatabase, the file system, too, is based on the database.\nThe dynamic folders build up sub-trees, which are guided by the\nmeta data selected by the user. Thus, the first step in using a\ndynamic folder is the definition of how it should be built. For each\nlevel of a dynamic folder, exactly one meta data item is used to. The\nfollowing example illustrates the steps which have to be taken in\norder to define a dynamic folder, and the meta data which should be\nused.\nAs a first step, the meta data which will be used for the dynamic\nfolder must be chosen (see Table 1): The sequence of the meta data\ninfluences the structure of the folder. Furthermore, for each meta\ndata used, restrictions and granularity must be defined by the user;\nif no restrictions are defined, all accessible documents are listed.\nThe granularity therefore influences the number of sub-folders\nwhich will be created for the partitioning of the documents.\n44\nAs the user enters the tree structure of the dynamic folder, he can\nnavigate through the branches to arrive at the document(s) he is\nlooking for. The directory names indicate which meta data\ndetermines the content of the sub-folder in question. At each level,\nthe documents, which have so far been found to match the meta\ndata, can be inspected.\nTable 1. Defining dynamic folders (example)\nLevel Meta data Restrictions Granularity\n1 Creator Only show documents\nwhich have been created\nby the users Leone or\nHodel or Gall\nOne folder per\ncreator\n2 Current\nlocation\nOnly show documents\nwhich where read at my\ncurrent location\nOne folder per\ntask status\n3 Authors Only show documents\nwhere at least 40% was\nwritten by user \u2018Leone\"\nEach 20% one\nfolder\nad-hoc changes of granularity and restrictions are possible in order\nto maximize search comfort for the user. It is possible to predefine\ndynamic folders for frequent use, e.g. a location-based folder, as\nwell as to create and modify dynamic folders on an ad-hoc basis.\nFurthermore, the content of such dynamic folders can change from\none second to another, depending on the changes made by other\nusers at that moment.\n3. VALIDATION\nThe proposed architecture is validated on the example of a character\ninsertion. Insert operations are the mostly used operations in a\n(collaborative) editing system. The character insertion is based on\nthe TeNDaX Insert Algorithm which is formally described in the\nfollowing. The algorithm is simplified for this purpose.\n3.1 Insert Characters Algorithm\nThe symbol c stands for the object character, p stands for the\nprevious character, n stands for the next character of a character\nobject c and the symbol l stands for a list of character objects.\nc = character\np=previous character\nn = next character\nl = list of characters\nThe symbol c1 stands for the first character in the list l, ci stands\nfor a character in the list l at the position i, whereas i is a value\nbetween 1 and the length of the list l, and cn stands for the last\ncharacter in the list l.\nc1 = first character in list l\nci = character at position i in list l\ncn = last character in list l\nThe symbol \u03b2 stands for the special character that marks the\nbeginning of a document and \u03b5 stands for the special character\nthat marks the end of a document.\n\u03b2=beginning of document\n\u03b5=end of document\nThe function startTA starts a transaction.\nstartTA = start transaction\nThe function commitTA commits a transaction that was started.\ncommitTA = commit transaction\nThe function checkWriteAccess checks if the write access for a\ndocument session s is granted.\ncheckWriteAccess(s) = check if write access for document session\ns is granted\nThe function lock acquires an exclusive lock for a character c and\nreturns 1 for a success and 0 for no success.\nlock(c) = acquire the lock for character c\nsuccess : return 1, no success : return 0\nThe function releaseLocks releases all locks that a transaction has\nacquired so far.\nreleaseLocks = release all locks\nThe function getPrevious returns the previous character and\ngetNext returns the next character of a character c.\ngetPrevious(c) = return previous character of character c\ngetNext(c) = return next character of character c\nThe function linkBefore links a preceding character p with a\nsucceeding character x and the function linkAfter links a\nsucceeding character n with a preceding character y.\nlinkBefore(p,x) = link character p to character x\nlinkAfter(n,y) = link character n to character y\nThe function updateString links a character p with the first\ncharacter c1 of a character list l and a character n with the last\ncharacter cn of a character list l\nupdateString(l, p, n) = linkBefore(p cl)\u2227 linkAfter(n, cn )\nThe function insertChar inserts a character c in the table Char\nwith the fields After set to a character p and Before set to a\ncharacter n.\ninsertChar(c, p, n) = linkAfter(c,p) \u2227 linkBefore(c,n) \u2227\nlinkBefore(p,c) \u2227 linkAfter(n,c)\nThe function checkPreceding determines the previous character's\nCharacterValue of a character c and if the previous character's\nstatus is active.\ncheckPreceding(c) = return status and CharacterValue of the\nprevious character\nThe function checkSucceeding determines the next character's\nCharacterValue of a character c and if the next character's status is\nactive.\n45\ncheckSucceeding(c) = return status and CharacterValue of the\nnext character\nThe function checkCharValue determines the CharacterValue of a\ncharacter c.\ncheckCharValue(c) = return CharacterValue of character c\nThe function sendUpdate sends an update message\n(UpdateMessage) from the database to the real-time server\ncomponent.\nsendUpdate(UpdateMessage)\nThe function Read is used in the real-time server component to\nread the UpdateMessage.\nRead(UpdateInformationMessage)\nThe function AllocatEditors checks on the base of the\nUpdateMessage and the SessionManager, which editors have to\nbe informed.\nAllocateEditors(UpdateInformationMessage, SessionManager) =\nreturns the affected editors\nThe function SendMessage(EditorData) sends the editor part of\nthe UpdateMessage to the editors\nSendMessage(EditorData)\nIn TeNDaX, the Insert Algorithm is implemented in the class\nmethod InsertChars of the class Char which is depicted in Figure\n2. The relevant parameters for the definitions beneath, are\nintroduced in the following list:\n- nextCharacterOID: OID of the character situated next to the\nstring to be inserted\n- previousCharacterOID: OID of the character situated\npreviously to the string to be inserted\n- characterOIDs (List): List of character which have to be\ninserted\nThus, the insertion of characters can be defined stepwise as\nfollows:\nStart a transaction.\nstartTA\nSelect the character that is situated before the character that\nfollows the string to be inserted.\ngetPrevious(nextCharacterOID) = PrevChar(prevCharOID) \u21d0\n\u03a0 After \u03d1OID = nextCharacterOID(Char))\nAcquire the lock for the character that is situated in the document\nbefore the character that follows the string which shall be inserted.\nlock(prevCharId)\nAt this time the list characterOIDs contains the characters c1 to cn\nthat shall be inserted.\ncharacterOIDs={ c1, \u2026, cn }\nEach character of the string is inserted at the appropriate position\nby linking the preceding and the succeeding character to it.\nFor each character ci of characterOIDs:\ninsertChar(ci, p, n)\nWhereas ci \u2208 { c1,\u2026, cn }\nCheck if the preceding and succeeding characters are active or if it\nis the beginning or the end of the document.\ncheckPreceding(prevCharOID) = IsOK(IsActive,\nCharacterValue) \u21d0 \u03a0 IsActive, CharacterValue (\u03d1 OID =\nnextCharacterOID(Char))\ncheckSucceeding(nextCharacterOID) = IsOK(IsActive,\nCharacterValue)\u21d0 \u03a0 IsActive, CharacterValue (\u03d1 OID =\nnextCharacterOID(Char))\nUpdate characters before and after the string to be inserted.\nupdateString(characterOIDs, prevCharOID, nextCharacterOID)\nRelease all locks and commit Transaction.\nreleaseLocks\ncommitTA\nSend update information to the real-time server component\nsendUpdate(UpdatenMessage)\nRead update message and inform affected editors of the change\nRead(UpdateMessage)\nAllocate Editors(UpdateMessage, SessionManager)\nSendMessage(EditorData)\n3.2 Insert Characters Example\nFigure 1 gives a snapshot the system, i.e. of its architecture: four\ndatabases are distributed over a peer-to-peer network. Each\ndatabase is connected to an application server (AS) and each\napplication server is connected to a real-time server component\n(RTSC). Editors are connected to one or more real-time server\ncomponents and to the corresponding databases.\nConsidering that editor A (connected to database 1 and 4) and\neditor B (connected to database 1 and 2) are working on the same\ndocument stored in database 1. Editor B now inserts a character\ninto this document. The insert operation is passed to application\nserver 1, which in turns, passes it to the database 1, where an\ninsert operation is invoked; the characters are inserted according\nto the algorithm discussed in the previous section. After the\ninsertion, database 1 sends an update message (according to the\nupdate protocol discussed before) to real-time server component 1\n(via AS 1). RTCS 1 combines the received update information\nwith the information in his SessionManager and sends the editor\ndata to the affected editors, in this case to editor A and B, where\nthe changes are immediately shown.\nOccurring collaboration conflicts are solved and described in [3].\n4. SUMMARY\nWith the approach presented in this paper and the implemented\nprototype, we offer real-time collaborative editing and management\nof documents stored in a special way in a database. With this\napproach we provide security, consistency and availability of\ndocuments and consequently offer pervasive document editing and\nmanagement. Pervasive document editing and management is\nenabled due to the proposed architecture with the embedded\nreal46\ntime server component, which propagates changes to a document\nimmediately and consequently offers up-to-date documents.\nDocument editing and managing is consequently enabled anywhere,\nanytime and with any device.\nThe above-descried system is implemented in a running prototype.\nThe system will be tested soon in line with a student workshop next\nautumn.\nREFERENCES\n[1] Abiteboul, S., Agrawal, R., et al.: The Lowell Database\nResearch Self Assessment. Massachusetts, USA, 2003.\n[2] Hodel, T. B., Businger, D., and Dittrich, K. R.: Supporting\nCollaborative Layouting in Word Processing. IEEE\nInternational Conference on Cooperative Information\nSystems (CoopIS), Larnaca, Cyprus, IEEE, 2004.\n[3] Hodel, T. B. and Dittrich, K. R.: \"Concept and prototype of a\ncollaborative business process environment for document\nprocessing.\" Data & Knowledge Engineering 52, Special\nIssue: Collaborative Business Process Technologies(1):\n61120, 2005.\n[4] Hodel, T. B., Dubacher, M., and Dittrich, K. R.: Using\nDatabase Management Systems for Collaborative Text\nEditing. ACM European Conference of\nComputersupported Cooperative Work (ECSCW CEW 2003),\nHelsinki, Finland, 2003.\n[5] Hodel, T. B., Gall, H., and Dittrich, K. R.: Dynamic\nCollaborative Business Processes within Documents. ACM\nSpecial Interest Group on Design of Communication\n(SIGDOC) , Memphis, USA, 2004.\n[6] Hodel, T. B., R. Hacmac, and Dittrich, K. R.: Using Text\nEditing Creation Time Meta Data for Document\nManagement. Conference on Advanced Information\nSystems Engineering (CAiSE'05), Porto, Portugal, Springer\nLecture Notes, 2005.\n[7] Hodel, T. B., Specker, F. and Dittrich, K. R.: Embedded\nSOAP Server on the Operating System Level for ad-hoc\nAutomatic Real-Time Bidirectional Communication.\nInformation Resources Management Association (IRMA),\nSan Diego, USA, 2005.\n[8] O\"Kelly, P.: Revolution in Real-Time Communication and\nCollaboration: For Real This Time. Application Strategies:\nIn-Depth Research Report. Burton Group, 2005.\n47", "keywords": "collaborative layouting;restriction;hierarchical file system;computer support collaborative work;cscw;computer supported collaborative work;real-time server component;text editing;collaborative document;pervasive document edit and management system;real-time transaction;character insertion;granularity;pervasive document editing and managing system;collaborative document processing;business logic layer"}
{"name": "train_C-84", "title": "Selfish Caching in Distributed Systems: A Game-Theoretic Analysis", "abstract": "We analyze replication of resources by server nodes that act selfishly, using a game-theoretic approach. We refer to this as the selfish caching problem. In our model, nodes incur either cost for replicating resources or cost for access to a remote replica. We show the existence of pure strategy Nash equilibria and investigate the price of anarchy, which is the relative cost of the lack of coordination. The price of anarchy can be high due to undersupply problems, but with certain network topologies it has better bounds. With a payment scheme the game can always implement the social optimum in the best case by giving servers incentive to replicate.", "fulltext": "1. INTRODUCTION\nWide-area peer-to-peer file systems [2,5,22,32,33], peer-to-peer\ncaches [15, 16], and web caches [6, 10] have become popular over\nthe last few years. Caching1\nof files in selected servers is widely\nused to enhance the performance, availability, and reliability of\nthese systems. However, most such systems assume that servers\ncooperate with one another by following protocols optimized for\noverall system performance, regardless of the costs incurred by\neach server.\nIn reality, servers may behave selfishly - seeking to maximize\ntheir own benefit. For example, parties in different\nadministrative domains utilize their local resources (servers) to better\nsupport clients in their own domains. They have obvious incentives to\ncache objects2\nthat maximize the benefit in their domains, possibly\nat the expense of globally optimum behavior. It has been an open\nquestion whether these caching scenarios and protocols maintain\ntheir desirable global properties (low total social cost, for example)\nin the face of selfish behavior.\nIn this paper, we take a game-theoretic approach to analyzing\nthe problem of caching in networks of selfish servers through\ntheoretical analysis and simulations. We model selfish caching as a\nnon-cooperative game. In the basic model, the servers have two\npossible actions for each object. If a replica of a requested object\nis located at a nearby node, the server may be better off accessing\nthe remote replica. On the other hand, if all replicas are located too\nfar away, the server is better off caching the object itself. Decisions\nabout caching the replicas locally are arrived at locally, taking into\naccount only local costs. We also define a more elaborate payment\nmodel, in which each server bids for having an object replicated at\nanother site. Each site now has the option of replicating an object\nand collecting the related bids. Once all servers have chosen a\nstrategy, each game specifies a configuration, that is, the set of servers\nthat replicate the object, and the corresponding costs for all servers.\nGame theory predicts that such a situation will end up in a Nash\nequilibrium, that is, a set of (possibly randomized) strategies with\nthe property that no player can benefit by changing its strategy\nwhile the other players keep their strategies unchanged [28].\nFoundational considerations notwithstanding, it is not easy to accept\nrandomized strategies as the behavior of rational agents in a\ndistributed system (see [28] for an extensive discussion) - but this\nis what classical game theory can guarantee. In certain very\nfortunate situations, however (see [9]), the existence of pure (that is,\ndeterministic) Nash equilibria can be predicted.\nWith or without randomization, however, the lack of\ncoordination inherent in selfish decision-making may incur costs well\nbeyond what would be globally optimum. This loss of efficiency is\n1\nWe will use caching and replication interchangeably.\n2\nWe use the term object as an abstract entity that represents files\nand other data objects.\n21\nquantified by the price of anarchy [21]. The price of anarchy is\nthe ratio of the social (total) cost of the worst possible Nash\nequilibrium to the cost of the social optimum. The price of anarchy\nbounds the worst possible behavior of a selfish system, when left\ncompletely on its own. However, in reality there are ways whereby\nthe system can be guided, through seeding or incentives, to a\npreselected Nash equilibrium. This optimistic version of the price of\nanarchy [3] is captured by the smallest ratio between a Nash\nequilibrium and the social optimum.\nIn this paper we address the following questions :\n\u2022 Do pure strategy Nash equilibria exist in the caching game?\n\u2022 If pure strategy Nash equilibria do exist, how efficient are\nthey (in terms of the price of anarchy, or its optimistic\ncounterpart) under different placement costs, network topologies,\nand demand distributions?\n\u2022 What is the effect of adopting payments? Will the Nash\nequilibria be improved?\nWe show that pure strategy Nash equilibria always exist in the\ncaching game. The price of anarchy of the basic game model can\nbe O(n), where n is the number of servers; the intuitive reason is\nundersupply. Under certain topologies, the price of anarchy does\nhave tighter bounds. For complete graphs and stars, it is O(1). For\nD-dimensional grids, it is O(n\nD\nD+1 ). Even the optimistic price of\nanarchy can be O(n). In the payment model, however, the game\ncan always implement a Nash equilibrium that is same as the social\noptimum, so the optimistic price of anarchy is one.\nOur simulation results show several interesting phases. As the\nplacement cost increases from zero, the price of anarchy increases.\nWhen the placement cost first exceeds the maximum distance\nbetween servers, the price of anarchy is at its highest due to\nundersupply problems. As the placement cost further increases, the price\nof anarchy decreases, and the effect of replica misplacement\ndominates the price of anarchy.\nThe rest of the paper is organized as follows. In Section 2 we\ndiscuss related work. Section 3 discusses details of the basic game and\nanalyzes the bounds of the price of anarchy. In Section 4 we discuss\nthe payment game and analyze its price of anarchy. In Section 5 we\ndescribe our simulation methodology and study the properties of\nNash equilibria observed. We discuss extensions of the game and\ndirections for future work in Section 6.\n2. RELATED WORK\nThere has been considerable research on wide-area peer-to-peer\nfile systems such as OceanStore [22], CFS [5], PAST [32],\nFARSITE [2], and Pangaea [33], web caches such as NetCache [6] and\nSummaryCache [10], and peer-to-peer caches such as Squirrel [16].\nMost of these systems use caching for performance, availability,\nand reliability. The caching protocols assume obedience to the\nprotocol and ignore participants\" incentives. Our work starts from the\nassumption that servers are selfish and quantifies the cost of the\nlack of coordination when servers behave selfishly.\nThe placement of replicas in the caching problem is the most\nimportant issue. There is much work on the placement of web\nreplicas, instrumentation servers, and replicated resources. All\nprotocols assume obedience and ignore participants\" incentives. In [14],\nGribble et al. discuss the data placement problem in peer-to-peer\nsystems. Ko and Rubenstein propose a self-stabilizing, distributed\ngraph coloring algorithm for the replicated resource placement [20].\nChen, Katz, and Kubiatowicz propose a dynamic replica\nplacement algorithm exploiting underlying distributed hash tables [4].\nDouceur and Wattenhofer describe a hill-climbing algorithm to\nexchange replicas for reliability in FARSITE [8]. RaDar is a\nsystem that replicates and migrates objects for an Internet hosting\nservice [31]. Tang and Chanson propose a coordinated en-route web\ncaching that caches objects along the routing path [34].\nCentralized algorithms for the placement of objects, web proxies, mirrors,\nand instrumentation servers in the Internet have been studied\nextensively [18,19,23,30].\nThe facility location problem has been widely studied as a\ncentralized optimization problem in theoretical computer science and\noperations research [27]. Since the problem is NP-hard,\napproximation algorithms based on primal-dual techniques, greedy\nalgorithms, and local search have been explored [17, 24, 26]. Our\ncaching game is different from all of these in that the optimization\nprocess is performed among distributed selfish servers.\nThere is little research in non-cooperative facility location games,\nas far as we know. Vetta [35] considers a class of problems where\nthe social utility is submodular (submodularity means decreasing\nmarginal utility). In the case of competitive facility location among\ncorporations he proves that any Nash equilibrium gives an expected\nsocial utility within a factor of 2 of optimal plus an additive term\nthat depends on the facility opening cost. Their results are not\ndirectly applicable to our problem, however, because we consider\neach server to be tied to a particular location, while in their model\nan agent is able to open facilities in multiple locations. Note that in\nthat paper the increase of the price of anarchy comes from\noversupply problems due to the fact that competing corporations can open\nfacilities at the same location. On the other hand, the significant\nproblems in our game are undersupply and misplacement.\nIn a recent paper, Goemans et al. analyze content distribution on\nad-hoc wireless networks using a game-theoretic approach [12]. As\nin our work, they provide monetary incentives to mobile users for\ncaching data items, and provide tight bounds on the price of\nanarchy and speed of convergence to (approximate) Nash equilibria.\nHowever, their results are incomparable to ours because their\npayoff functions neglect network latencies between users, they\nconsider multiple data items (markets), and each node has a limited\nbudget to cache items.\nCost sharing in the facility location problem has been studied\nusing cooperative game theory [7, 13, 29]. Goemans and Skutella\nshow strong connections between fair cost allocations and linear\nprogramming relaxations for facility location problems [13]. P\u00b4al\nand Tardos develop a method for cost-sharing that is approximately\nbudget-balanced and group strategyproof and show that the method\nrecovers 1/3 of the total cost for the facility location game [29].\nDevanur, Mihail, and Vazirani give a strategyproof cost allocation\nfor the facility location problem, but cannot achieve group\nstrategyproofness [7].\n3. BASIC GAME\nThe caching problem we study is to find a configuration that\nmeets certain objectives (e.g., minimum total cost). Figure 1 shows\nexamples of caching among four servers. In network (a), A stores\nan object. Suppose B wants to access the object. If it is cheaper\nto access the remote replica than to cache it, B accesses the remote\nreplica as shown in network (b). In network (c), C wants to access\nthe object. If C is far from A, C caches the object instead of\naccessing the object from A. It is possible that in an optimal configuration\nit would be better to place replicas in A and B. Understanding the\nplacement of replicas by selfish servers is the focus of our study.\nThe caching problem is abstracted as follows. There is a set N of\nn servers and a set M of m objects. The distance between servers\ncan be represented as a distance matrix D (i.e., dij is the distance\n22\nServer\nServer\nServer\nServer\nA\nB\nC\nD\n(a)\nServer\nServer\nServer\nServer\nA\nB\nC\nD\n(b)\nServer\nServer\nServer\nServer\nA\nB\nC\nD\n(c)\nFigure 1: Caching. There are four servers labeled A, B, C, and D. The rectangles are object replicas. In (a), A stores an object. If B incurs less cost\naccessing A\"s replica than it would caching the object itself, it accesses the object from A as in (b). If the distance cost is too high, the server caches\nthe object itself, as C does in (c). This figure is an example of our caching game model.\nfrom server i to server j). D models an underlying network\ntopology. For our analysis we assume that the distances are symmetric\nand the triangle inequality holds on the distances (for all servers\ni, j, k: dij + djk \u2265 dik). Each server has demand from clients\nthat is represented by a demand matrix W (i.e., wij is the demand\nof server i for object j). When a server caches objects, the server\nincurs some placement cost that is represented by a matrix \u03b1 (i.e.,\n\u03b1ij is a placement cost of server i for object j).\nIn this study, we assume that servers have no capacity limit. As\nwe discuss in the next section, this fact means that the caching\nbehavior with respect to each object can be examined separately.\nConsequently, we can talk about configurations of the system with\nrespect to a given object:\nDEFINITION 1. A configuration X for some object O is the set\nof servers replicating this object.\nThe goal of the basic game is to find configurations that are achieved\nwhen servers optimize their cost functions locally.\n3.1 Game Model\nWe take a game-theoretic approach to analyzing the\nuncapacitated caching problem among networked selfish servers. We model\nthe selfish caching problem as a non-cooperative game with n\nplayers (servers/nodes) whose strategies are sets of objects to cache. In\nthe game, each server chooses a pure strategy that minimizes its\ncost. Our focus is to investigate the resulting configuration, which\nis the Nash equilibrium of the game. It should be emphasized that\nwe consider only pure strategy Nash equilibria in this paper.\nThe cost model is an important part of the game. Let Ai be the\nset of feasible strategies for server i, and let Si \u2208 Ai be the strategy\nchosen by server i. Given a strategy profile S = (S1, S2, ..., Sn),\nthe cost incurred by server i is defined as:\nCi(S) =\nj\u2208Si\n\u03b1ij +\nj /\u2208Si\nwij di (i,j). (1)\nwhere \u03b1ij is the placement cost of object j, wij is the demand that\nserver i has for object j, (i, j) is the closest server to i that caches\nobject j, and dik is the distance between i and k. When no server\ncaches the object, we define distance cost di (i,j) to be dM -large\nenough that at least one server will choose to cache the object.\nThe placement cost can be further divided into first-time\ninstallation cost and maintenance cost:\n\u03b1ij = k1i + k2i\nUpdateSizej\nObjectSizej\n1\nT\nPj\nk\nwkj , (2)\nwhere k1i is the installation cost, k2i is the relative weight\nbetween the maintenance cost and the installation cost, Pj is the\nratio of the number of writes over the number of reads and writes,\nUpdateSizej is the size of an update, ObjectSizej is the size of\nthe object, and T is the update period. We see tradeoffs between\ndifferent parameters in this equation. For example, placing replicas\nbecomes more expensive as UpdateSizej increases, Pj increases,\nor T decreases. However, note that by varying \u03b1ij itself we can\ncapture the full range of behaviors in the game. For our analysis,\nwe use only \u03b1ij .\nSince there is no capacity limit on servers, we can look at each\nsingle object as a separate game and combine the pure strategy\nequilibria of these games to obtain a pure strategy equilibrium of\nthe multi-object game. Fabrikant, Papadimitriou, and Talwar\ndiscuss this existence argument: if two games are known to have pure\nequilibria, and their cost functions are cross-monotonic, then their\nunion is also guaranteed to have pure Nash equilibria, by a\ncontinuity argument [9]. A Nash equilibrium for the multi-object game is\nthe cross product of Nash equilibria for single-object games.\nTherefore, we can focus on the single object game in the rest of this paper.\nFor single object selfish caching, each server i has two strategies\n- to cache or not to cache. The object under consideration is j.\nWe define Si to be 1 when server i caches j and 0 otherwise. The\ncost incurred by server i is\nCi(S) = \u03b1ij Si + wij di (i,j)(1 \u2212 Si). (3)\nWe refer to this game as the basic game. The extent to which Ci(S)\nrepresents actual cost incurred by server i is beyond the scope of\nthis paper; we will assume that an appropriate cost function of the\nform of Equation 3 can be defined.\n3.2 Nash Equilibrium Solutions\nIn principle, we can start with a random configuration and let\nthis configuration evolve as each server alters its strategy and\nattempts to minimize its cost. Game theory is interested in stable\nsolutions called Nash equilibria. A pure strategy Nash equilibrium\nis reached when no server can benefit by unilaterally changing its\nstrategy. A Nash equilibrium3\n(S\u2217\ni , S\u2217\n\u2212i) for the basic game\nspecifies a configuration X such that \u2200i \u2208 N, i \u2208 X \u21d4 S\u2217\ni = 1.\nThus, we can consider a set E of all pure strategy Nash equilibrium\nconfigurations:\nX \u2208 E \u21d4 \u2200i \u2208 N,\n\u2200Si \u2208 Ai, Ci(S\u2217\ni , S\u2217\n\u2212i) \u2264 Ci(Si, S\u2217\n\u2212i)\n(4)\nBy this definition, no server has incentive to deviate in the\nconfigurations since it cannot reduce its cost.\nFor the basic game, we can easily see that:\nX \u2208 E \u21d4 \u2200i \u2208 N, \u2203j \u2208 X s.t. dji \u2264 \u03b1\nand \u2200j \u2208 X, \u00ac\u2203k \u2208 X s.t. dkj < \u03b1\n(5)\nThe first condition guarantees that there is a server that places the\nreplica within distance \u03b1 of each server i. If the replica is not placed\n3\nThe notation for strategy profile (S\u2217\ni , S\u2217\n\u2212i) separates node i s\nstrategy (S\u2217\ni ) from the strategies of other nodes (S\u2217\n\u2212i).\n23\nA B1\u2212\u03b1\n0\n0\n0\n0\n0 0\n0\n0\n0\n0\n2\nn\nnodes\n2\nn\nnodes\n(a)\nA B1\u2212\u03b1\n0\n0\n0\n0\n0 0\n0\n0\n0\n0\n2\nn\nnodes\n2\nn\nnodes\n(b)\nA B1\u2212\u03b1\n2\nn\nnodes\n2\nn\nnodes\nn2\nn2\nn2\nn2\nn2 n2\nn2\nn2\nn2\nn2\n(c)\nFigure 2: Potential inefficiency of Nash equilibria illustrated by two clusters of n\n2\nservers. The intra-cluster distances are all zero and the distance\nbetween clusters is \u03b1 \u2212 1, where \u03b1 is the placement cost. The dark nodes replicate the object. Network (a) shows a Nash equilibrium in the basic\ngame, where one server in a cluster caches the object. Network (b) shows the social optimum where two replicas, one for each cluster, are placed. The\nprice of anarchy is O(n) and even the optimistic price of anarchy is O(n). This high price of anarchy comes from the undersupply of replicas due to\nthe selfish nature of servers. Network (c) shows a Nash equilibrium in the payment game, where two replicas, one for each cluster, are placed. Each\nlight node in each cluster pays 2/n to the dark node, and the dark node replicates the object. Here, the optimistic price of anarchy is one.\nat i, then it is placed at another server within distance \u03b1 of i, so i has\nno incentive to cache. If the replica is placed at i, then the second\ncondition ensures there is no incentive to drop the replica because\nno two servers separated by distance less than \u03b1 both place replicas.\n3.3 Social Optimum\nThe social cost of a given strategy profile is defined as the total\ncost incurred by all servers, namely:\nC(S) =\nn\u22121\ni=0\nCi(S) (6)\nwhere Ci(S) is the cost incurred by server i given by Equation 1.\nThe social optimum cost, referred to as C(SO) for the remainder\nof the paper, is the minimum social cost. The social optimum cost\nwill serve as an important base case against which to measure the\ncost of selfish caching. We define C(SO) as:\nC(SO) = min\nS\nC(S) (7)\nwhere S varies over all possible strategy profiles. Note that in the\nbasic game, this means varying configuration X over all possible\nconfigurations. In some sense, C(SO) represents the best possible\ncaching behavior - if only nodes could be convinced to cooperate\nwith one another.\nThe social optimum configuration is a solution of a mini-sum\nfacility location problem, which is NP-hard [11]. To find such\nconfigurations, we formulate an integer programming problem:\nminimize\n\u00c8i\n\u00c8j\n\u00a2\u03b1ij xij +\n\u00c8k wij dikyijk\n\u00a3\nsubject to\n\u2200i, j\n\u00c8k yijk = I(wij)\n\u2200i, j, k xij \u2212 ykji \u2265 0\n\u2200i, j xij \u2208 {0, 1}\n\u2200i, j, k yijk \u2208 {0, 1}\n(8)\nHere, xij is 1 if server i replicates object j and 0 otherwise; yijk\nis 1 if server i accesses object j from server k and 0 otherwise;\nI(w) returns 1 if w is nonzero and 0 otherwise. The first constraint\nspecifies that if server i has demand for object j, then it must access\nj from exactly one server. The second constraint ensures that server\ni replicates object j if any other server accesses j from i.\n3.4 Analysis\nTo analyze the basic game, we first give a proof of the existence\nof pure strategy Nash equilibria. We discuss the price of anarchy in\ngeneral and then on specific underlying topologies. In this analysis\nwe use simply \u03b1 in place of \u03b1ij , since we deal with a single object\nand we assume placement cost is the same for all servers. In\naddition, when we compute the price of anarchy, we assume that all\nnodes have the same demand (i.e., \u2200i \u2208 N wij = 1).\nTHEOREM 1. Pure strategy Nash equilibria exist in the basic\ngame.\nPROOF. We show a constructive proof. First, initialize the set\nV to N. Then, remove all nodes with zero demand from V . Each\nnode x defines \u03b2x, where \u03b2x = \u03b1\nwxj\n. Furthermore, let Z(y) =\n{z : dzy \u2264 \u03b2z, z \u2208 V }; Z(y) represents all nodes z for which y\nlies within \u03b2z from z.\nPick a node y \u2208 V such that \u03b2y \u2264 \u03b2x for all x \u2208 V . Place a\nreplica at y and then remove y and all z \u2208 Z(y) from V . No such z\ncan have incentive to replicate the object because it can access y\"s\nreplica at lower (or equal) cost. Iterate this process of placing\nreplicas until V is empty. Because at each iteration y is the remaining\nnode with minimum \u03b2, no replica will be placed within distance\n\u03b2y of any such y by this process. The resulting configuration is a\npure-strategy Nash equilibrium of the basic game.\nThe Price of Anarchy (POA): To quantify the cost of lack of\ncoordination, we use the price of anarchy [21] and the optimistic\nprice of anarchy [3]. The price of anarchy is the ratio of the social\ncosts of the worst-case Nash equilibrium and the social optimum,\nand the optimistic price of anarchy is the ratio of the social costs of\nthe best-case Nash equilibrium and the social optimum.\nWe show general bounds on the price of anarchy. Throughout\nour discussion, we use C(SW ) to represent the cost of worst case\nNash equilibrium, C(SO) to represent the cost of social optimum,\nand PoA to represent the price of anarchy, which is C(SW )\nC(SO)\n.\nThe worst case Nash equilibrium maximizes the total cost\nunder the constraint that the configuration meets the Nash condition.\nFormally, we can define C(SW ) as follows.\nC(SW ) = max\nX\u2208E\n(\u03b1|X| +\ni\nmin\nj\u2208X\ndij) (9)\nwhere minj\u2208X dij is the distance to the closest replica (including i\nitself) from node i and X varies through Nash equilibrium\nconfigurations.\nBounds on the Price of Anarchy: We show bounds of the price\nof anarchy varying \u03b1. Let dmin = min(i,j)\u2208N\u00d7N,i=j dij and\ndmax = max(i,j)\u2208N\u00d7N dij . We see that if \u03b1 \u2264 dmin, PoA = 1\n24\nTopology PoA\nComplete graph 1\nStar \u2264 2\nLine O(\n\u221a\nn)\nD-dimensional grid O(n\nD\nD+1 )\nTable 1: PoA in the basic game for specific topologies\ntrivially, since every server caches the object for both Nash\nequilibrium and social optimum. When \u03b1 > dmax, there is a transition\nin Nash equilibria: since the placement cost is greater than any\ndistance cost, only one server caches the object and other servers\naccess it remotely. However, the social optimum may still place\nmultiple replicas. Since \u03b1 \u2264 C(SO) \u2264 \u03b1+minj\u2208N\n\u00c8i dij when \u03b1 >\ndmax, we obtain\n\u03b1+maxj\u2208N\n\u00c8i dij\n\u03b1+minj\u2208N\n\u00c8i dij\n\u2264 PoA \u2264\n\u03b1+maxj\u2208N\n\u00c8i dij\n\u03b1\n.\nNote that depending on the underlying topology, even the lower\nbound of PoA can be O(n). Finally, there is a transition when\n\u03b1 > maxj\u2208N\n\u00c8i dij. In this case, PoA =\n\u03b1+maxj\u2208N\n\u00c8i dij\n\u03b1+minj\u2208N\n\u00c8i dij\nand\nit is upper bounded by 2.\nFigure 2 shows an example of the inefficiency of a Nash\nequilibrium. In the network there are two clusters of servers whose\nsize is n\n2\n. The distance between two clusters is \u03b1 \u2212 1 where \u03b1 is\nthe placement cost. Figure 2(a) shows a Nash equilibrium where\none server in a cluster caches the object. In this case, C(SW ) =\n\u03b1 + (\u03b1 \u2212 1)n\n2\n, since all servers in the other cluster accesses the\nremote replica. However, the social optimum places two replicas, one\nfor each cluster, as shown in Figure 2(b). Therefore, C(SO) = 2\u03b1.\nPoA =\n\u03b1+(\u03b1\u22121) n\n2\n2\u03b1\n, which is O(n). This bad price of anarchy\ncomes from an undersupply of replicas due to the selfish nature of\nthe servers. Note that all Nash equilibria have the same cost; thus\neven the optimistic price of anarchy is O(n).\nIn Appendix A, we analyze the price of anarchy with specific\nunderlying topologies and show that PoA can have tighter bounds\nthan O(n) for the complete graph, star, line, and D-dimensional\ngrid. In these topologies, we set the distance between directly\nconnected nodes to one. We describe the case where \u03b1 > 1, since\nPoA = 1 trivially when \u03b1 \u2264 1. A summary of the results is\nshown in Table 1.\n4. PAYMENT GAME\nIn this section, we present an extension to the basic game with\npayments and analyze the price of anarchy and the optimistic price\nof anarchy of the game.\n4.1 Game Model\nThe new game, which we refer to as the payment game, allows\neach player to offer a payment to another player to give the latter\nincentive to replicate the object. The cost of replication is shared\namong the nodes paying the server that replicates the object.\nThe strategy for each player i is specified by a triplet (vi, bi, ti) \u2208\n{N, \u00ca+, \u00ca+}. vi specifies the player to whom i makes a bid,\nbi \u2265 0 is the value of the bid, and ti \u2265 0 denotes a threshold\nfor payments beyond which i will replicate the object. In addition,\nwe use Ri to denote the total amount of bids received by a node i\n(Ri =\n\u00c8j:vj =i bj).\nA node i replicates the object if and only if Ri \u2265 ti, that is, the\namount of bids it receives is greater than or equal to its threshold.\nLet Ii denote the corresponding indicator variable, that is, Ii equals\n1 if i replicates the object, and 0 otherwise. We make the rule that\nif a node i makes a bid to another node j and j replicates the object,\nthen i must pay j the amount bi. If j does not replicate the object,\ni does not pay j.\nGiven a strategy profile, the outcome of the game is the set of\ntuples {(Ii, vi, bi, Ri)}. Ii tells us whether player i replicates the\nobject or not, bi is the payment player i makes to player vi, and\nRi is the total amount of bids received by player i. To compute\nthe payoffs given the outcome, we must now take into account the\npayments a node makes, in addition to the placement costs and\naccess costs of the basic game.\nBy our rules, a server node i pays bi to node vi if vi replicates\nthe object, and receives a payment of Ri if it replicates the object\nitself. Its net payment is biIvi \u2212 RiIi. The total cost incurred by\neach node is the sum of its placement cost, access cost, and net\npayment. It is defined as\nCi(S) = \u03b1ij Ii + wij di (i,j)(1 \u2212 Ii) + biIvi \u2212 RiIi. (10)\nThe cost of social optimum for the payment game is same as that\nfor the basic game, since the net payments made cancel out.\n4.2 Analysis\nIn analyzing the payment model, we first show that a Nash\nequilibrium in the basic game is also a Nash equilibrium in the payment\ngame. We then present an important positive result - in the\npayment game the socially optimal configuration can always be\nimplemented by a Nash equilibrium. We know from the counterexample\nin Figure 2 that this is not guaranteed in the the basic game. In this\nanalysis we use \u03b1 to represent \u03b1ij .\nTHEOREM 2. Any configuration that is a pure strategy Nash\nequilibrium in the basic game is also a pure strategy Nash\nequilibrium in the payment game. Therefore, the price of anarchy of the\npayment game is at least that of the basic game.\nPROOF. Consider any Nash equilibrium configuration in the\nbasic game. For each node i replicating the object, set its threshold ti\nto 0; everyone else has threshold \u03b1. Also, for all i, bi = 0.\nA node that replicates the object does not have incentive to change\nits strategy: changing the threshold does not decrease its cost, and\nit would have to pay at least \u03b1 to access a remote replica or\nincentivize a nearby node to cache. Therefore it is better off keeping its\nthreshold and bid at 0 and replicating the object.\nA node that is not replicating the object can access the object\nremotely at a cost less than or equal to \u03b1. Lowering its threshold does\nnot decrease its cost, since all bi are zero. The payment necessary\nfor another server to place a replica is at least \u03b1.\nNo player has incentive to deviate, so the current configuration\nis a Nash equilibrium.\nIn fact, Appendix B shows that the PoA of the payment game\ncan be more than that of the basic game in a given topology.\nNow let us look at what happens to the example shown in\nFigure 2 in the best case. Suppose node B\"s neighbors each decide\nto pay node B an amount 2/n. B does not have an incentive to\ndeviate, since accessing the remote replica does not decrease its\ncost. The same argument holds for A because of symmetry in the\ngraph. Since no one has an incentive to deviate, the configuration is\na Nash equilibrium. Its total cost is 2\u03b1, the same as in the socially\noptimal configuration shown in Figure 2(b). Next we prove that\nindeed the payment game always has a strategy profile that\nimplements the socially optimal configuration as a Nash equilibrium. We\nfirst present the following observation, which is used in the proof,\nabout thresholds in the payment game.\nOBSERVATION 1. If node i replicates the object, j is the\nnearest node to i among the other nodes that replicate the object, and\ndij < \u03b1 in a Nash equilibrium, then i should have a threshold at\n25\nleast (\u03b1 \u2212 dij). Otherwise, it cannot collect enough payment to\ncompensate for the cost of replicating the object and is better off\naccessing the replica at j.\nTHEOREM 3. In the payment game, there is always a pure\nstrategy Nash equilibrium that implements the social optimum\nconfiguration. The optimistic price of anarchy in the payment game is\ntherefore always one.\nPROOF. Consider the socially optimal configuration \u03c6opt. Let\nNo be the set of nodes that replicate the object and Nc = N \u2212 No\nbe the rest of the nodes. Also, for each i in No, let Qi denote the\nset of nodes that access the object from i, not including i itself. In\nthe socially optimal configuration, dij \u2264 \u03b1 for all j in Qi.\nWe want to find a set of payments and thresholds that makes this\nconfiguration implementable. The idea is to look at each node i in\nNo and distribute the minimum payment needed to make i replicate\nthe object among the nodes that access the object from i. For each\ni in No, and for each j in Qi, we define\n\u03b4j = min{\u03b1, min\nk\u2208No\u2212{i}\ndjk} \u2212 dji (11)\nNote that \u03b4j is the difference between j\"s cost for accessing the\nreplica at i and j\"s next best option among replicating the object\nand accessing some replica other than i. It is clear that \u03b4j \u2265 0.\nCLAIM 1. For each i \u2208 No, let be the nearest node to i in\nNo. Then,\n\u00c8j\u2208Qi\n\u03b4j \u2265 \u03b1 \u2212 di .\nPROOF. (of claim) Assume the contrary, that is,\n\u00c8j\u2208Qi\n\u03b4j <\n\u03b1 \u2212 di . Consider the new configuration \u03c6new wherein i does not\nreplicate and each node in Qi chooses its next best strategy (either\nreplicating or accessing the replica at some node in No \u2212 {i}). In\naddition, we still place replicas at each node in No \u2212 {i}. It is easy\nto see that cost of \u03c6opt minus cost of \u03c6new is at least:\n(\u03b1 +\nj\u2208Qi\ndij) \u2212 (di +\nj\u2208Qi\nmin{\u03b1, min\nk\u2208No\u2212{i}\ndik})\n= \u03b1 \u2212 di \u2212\nj\u2208Qi\n\u03b4j > 0,\nwhich contradicts the optimality of \u03c6opt.\nWe set bids as follows. For each i in No, bi = 0 and for each j\nin Qi, j bids to i (i.e., vj = i) the amount:\nbj = max{0, \u03b4j \u2212 i/(|Qi| + 1)}, j \u2208 Qi (12)\nwhere i =\n\u00c8j\u2208Qi\n\u03b4j \u2212 \u03b1 + di \u2265 0 and |Qi| is the cardinality of\nQi. For the thresholds, we have:\nti =\n\u03b1 if i \u2208 Nc;\u00c8j\u2208Qi\nbj if i \u2208 No.\n(13)\nThis fully specifies the strategy profile of the nodes, and it is easy\nto see that the outcome is indeed the socially optimal configuration.\nNext, we verify that the strategies stipulated constitute a Nash\nequilibrium. Having set ti to \u03b1 for i in Nc means that any node\nin N is at least as well off lowering its threshold and replicating\nas bidding \u03b1 to some node in Nc to make it replicate, so we may\ndisregard the latter as a profitable strategy. By observation 1, to\nensure that each i in No does not deviate, we require that if is the\nnearest node to i in No, then\n\u00c8j\u2208Qi\nbj is at least (\u03b1 \u2212 di ).\nOtherwise, i will raise ti above\n\u00c8j\u2208Qi\nbj so that it does not replicate\nand instead accesses the replica at . We can easily check that\nj\u2208Qi\nbj \u2265\nj\u2208Qi\n\u03b4j \u2212\n|Qi| i\n|Qi| + 1\n= \u03b1 \u2212 di +\ni\n|Qi| + 1\n\u2265 \u03b1 \u2212 di .\n1\n1.5\n2\n2.5\n3\n3.5\n4\n4.5\n5\n5.5\n0 20 40 60 80 100 120 140 160 180 200\n1\n10\n100\nC(NE)/C(SO)\nAverageNumberofReplicas\nalpha\nPoA\nRatio\nOPoA\nReplica (SO)\nReplica (NE)\nFigure 3: We present P oA, Ratio, and OP oA results for the basic\ngame, varying \u03b1 on a 100-node line topology, and we show number\nof replicas placed by the Nash equilibria and by the optimal solution.\nWe see large peaks in P oA and OP oA at \u03b1 = 100, where a phase\ntransition causes an abrupt transition in the lines.\nTherefore, each node i \u2208 No does not have incentive to change\nti since i loses its payments received or there is no change, and i\ndoes not have incentive to bi since it replicates the object. Each\nnode j in Nc has no incentive to change tj since changing tj does\nnot reduce its cost. It also does not have incentive to reduce bj\nsince the node where j accesses does not replicate and j has to\nreplicate the object or to access the next closest replica, which costs\nat least the same from the definition of bj . No player has incentive\nto deviate, so this strategy profile is a Nash equilibrium.\n5. SIMULATION\nWe run simulations to compare Nash equilibria for the\nsingleobject caching game with the social optimum computed by solving\nthe integer linear program described in Equation 8 using Mosek [1].\nWe examine price of anarchy (PoA), optimistic price of anarchy\n(OPoA), and the average ratio of the costs of Nash equilibria and\nsocial optima (Ratio), and when relevant we also show the average\nnumbers of replicas placed by the Nash equilibrium (Replica(NE))\nand the social optimum (Replica(SO)). The PoA and OPoA are\ntaken from the worst and best Nash equilibria, respectively, that we\nobserve over the runs. Each data point in our figures is based on\n1000 runs, randomly varying the initial strategy profile and player\norder. The details of the simulations including protocols and a\ndiscussion of convergence are presented in Appendix C.\nIn our evaluation, we study the effects of variation in four\ncategories: placement cost, underlying topology, demand distribution,\nand payments. As we vary the placement cost \u03b1, we directly\ninfluence the tradeoff between caching and not caching. In order to get\na clear picture of the dependency of PoA on \u03b1 in a simple case, we\nfirst analyze the basic game with a 100-node line topology whose\nedge distance is one.\nWe also explore transit-stub topologies generated using the\nGTITM library [36] and power-law topologies (Router-level\nBarabasiAlbert model) generated using the BRITE topology generator [25].\nFor these topologies, we generate an underlying physical graph of\n3050 physical nodes. Both topologies have similar minimum,\naverage, and maximum physical node distances. The average distance\nis 0.42. We create an overlay of 100 server nodes and use the same\noverlay for all experiments with the given topology.\nIn the game, each server has a demand whose distribution is\nBernoulli(p), where p is the probability of having demand for the\nobject; the default unless otherwise specified is p = 1.0.\n26\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\n2.2\n2.4\n2.6\n2.8\n3\n0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2\n1\n10\n100\nC(NE)/C(SO)\nAverageNumberofReplicas\nalpha\nPoA\nRatio\nOPoA\nReplica (SO)\nReplica (NE)\n(a)\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\n2.2\n2.4\n2.6\n2.8\n3\n0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2\n1\n10\n100\nC(NE)/C(SO)\nAverageNumberofReplicas\nalpha\nPoA\nRatio\nOPoA\nReplica (SO)\nReplica (NE)\n(b)\nFigure 4: Transit-stub topology: (a) basic game, (b) payment game. We show the P oA, Ratio, OP oA, and the number of replicas placed while\nvarying \u03b1 between 0 and 2 with 100 servers on a 3050-physical-node transit-stub topology.\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\n2.2\n2.4\n0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2\n1\n10\n100\nC(NE)/C(SO)\nAverageNumberofReplicas\nalpha\nPoA\nRatio\nOPoA\nReplica (SO)\nReplica (NE)\n(a)\n0.8\n1\n1.2\n1.4\n1.6\n1.8\n2\n2.2\n2.4\n0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2\n1\n10\n100\nC(NE)/C(SO)\nAverageNumberofReplicas\nalpha\nPoA\nRatio\nOPoA\nReplica (SO)\nReplica (NE)\n(b)\nFigure 5: Power-law topology: (a) basic game, (b) payment game. We show the P oA, Ratio, OP oA, and the number of replicas placed while\nvarying \u03b1 between 0 and 2 with 100 servers on a 3050-physical-node power-law topology.\n5.1 Varying Placement Cost\nFigure 3 shows PoA, OPoA, and Ratio, as well as number\nof replicas placed, for the line topology as \u03b1 varies. We observe\ntwo phases. As \u03b1 increases the PoA rises quickly to a peak at\n100. After 100, there is a gradual decline. OPoA and Ratio show\nbehavior similar to PoA.\nThese behaviors can be explained by examining the number of\nreplicas placed by Nash equilibria and by optimal solutions. We see\nthat when \u03b1 is above one, Nash equilibrium solutions place fewer\nreplicas than optimal on average. For example, when \u03b1 is 100,\nthe social optimum places four replicas, but the Nash equilibrium\nplaces only one. The peak in PoA at \u03b1 = 100 occurs at the point\nfor a 100-node line where the worst-case cost of accessing a remote\nreplica is slightly less than the cost of placing a new replica, so\nselfish servers will never place a second replica. The optimal solution,\nhowever, places multiple replicas to decrease the high global cost\nof access. As \u03b1 continues to increase, the undersupply problem\nlessens as the optimal solution places fewer replicas.\n5.2 Different Underlying Topologies\nIn Figure 4(a) we examine an overlay graph on the more realistic\ntransit-stub topology. The trends for the PoA, OPoA, and Ratio\nare similar to the results for the line topology, with a peak in PoA\nat \u03b1 = 0.8 due to maximal undersupply.\nIn Figure 5(a) we examine an overlay graph on the power-law\ntopology. We observe several interesting differences between the\npower-law and transit-stub results. First, the PoA peaks at a lower\nlevel in the power-law graph, around 2.3 (at \u03b1 = 0.9) while the\npeak PoA in the transit-stub topology is almost 3.0 (at \u03b1 = 0.8).\nAfter the peak, PoA and Ratio decrease more slowly as \u03b1\nincreases. OPoA is close to one for the whole range of \u03b1 values.\nThis can be explained by the observation in Figure 5(a) that there\nis no significant undersupply problem here like there was in the\ntransit-stub graph. Indeed the high PoA is due mostly to\nmisplacement problems when \u03b1 is from 0.7 to 2.0, since there is little\ndecrease in PoA when the number of replicas in social optimum\nchanges from two to one. The OPoA is equal to one in the figure\nwhen the same number of replicas are placed.\n5.3 Varying Demand Distribution\nNow we examine the effects of varying the demand distribution.\nThe set of servers with demand is random for p < 1, so we\ncalculate the expected PoA by averaging over 5 trials (each data point\nis based on 5000 runs). We run simulations for demand levels of\np \u2208 {0.2, 0.6, 1.0} as \u03b1 is varied on the 100 servers on top of\nthe transit-stub graph. We observe that as demand falls, so does\nexpected PoA. As p decreases, the number of replicas placed in\nthe social optimum decreases, but the number in Nash equilibria\nchanges little. Furthermore, when \u03b1 exceeds the overlay diameter,\nthe number in Nash equilibria stays constant when p varies.\nTherefore, lower p leads to a lesser undersupply problem, agreeing with\nintuition. We do not present the graph due to space limitations and\nredundancy; the PoA for p = 1.0 is identical to PoA in Figure 4(a),\nand the lines for p = 0.6 and p = 0.2 are similar but lower and flatter.\n27\n5.4 Effects of Payment\nFinally, we discuss the effects of payments on the efficiency of\nNash equilibria. The results are presented in Figure 4(b) and\nFigure 5(b). As shown in the analysis, the simulations achieve OPoA\nclose to one (it is not exactly one because of randomness in the\nsimulations). The Ratio for the payment game is much lower than\nthe Ratio for the basic game, since the protocol for the payment\ngame tends to explore good regions in the space of Nash\nequilibria. We observe in Figure 4 that for \u03b1 \u2265 0.4, the average number\nof replicas of Nash equilibria gets closer with payments to that of\nthe social optimum than it does without. We observe in Figure 5\nthat more replicas are placed with payments than without when \u03b1\nis between 0.7 and 1.3, the only range of significant undersupply in\nthe power-law case. The results confirm that payments give servers\nincentive to replicate the object and this leads to better equilibria.\n6. DISCUSSION AND FUTURE WORK\nWe suggest several interesting extensions and directions. One\nextension is to consider multiple objects in the capacitated caching\ngame, in which servers have capacity limits when placing objects.\nSince caching one object affects the ability to cache another, there\nis no separability of a multi-object game into multiple single object\ngames. As studied in [12], one way to formulate this problem is to\nfind the best response of a server by solving a knapsack problem\nand to compute Nash equilibria.\nIn our analyses, we assume that all nodes have the same demand.\nHowever, nodes could have different demand depending on objects.\nWe intend to examine the effects of heterogeneous demands (or\nheterogeneous placement costs) analytically. We also want to look\nat the following aggregation effect. Suppose there are n \u2212 1\nclustered nodes with distance of \u03b1\u22121 from a node hosting a replica.\nAll nodes have demands of one. In that case, the price of anarchy\nis O(n). However, if we aggregate n \u2212 1 nodes into one node with\ndemand n \u2212 1, the price of anarchy becomes O(1), since \u03b1 should\nbe greater than (n \u2212 1)(\u03b1 \u2212 1) to replicate only one object. Such\naggregation can reduce the inefficiency of Nash equilibria.\nWe intend to compute the bounds of the price of anarchy under\ndifferent underlying topologies such as random graphs or\ngrowthrestricted metrics. We want to investigate whether there are certain\ndistance constraints that guarantee O(1) price of anarchy. In\naddition, we want to run large-scale simulations to observe the change\nin the price of anarchy as the network size increases.\nAnother extension is to consider server congestion. Suppose the\ndistance is the network distance plus \u03b3 \u00d7 (number of accesses)\nwhere \u03b3 is an extra delay when an additional server accesses the\nreplica. Then, when \u03b1 > \u03b3, it can be shown that PoA is bounded\nby \u03b1\n\u03b3\n. As \u03b3 increases, the price of anarchy bound decreases, since\nthe load of accesses is balanced across servers.\nWhile exploring the caching problem, we made several\nobservations that seem counterintuitive. First, the PoA in the payment\ngame can be worse than the PoA in the basic game. Another\nobservation we made was that the number of replicas in a Nash\nequilibrium can be more than the number of replicas in the social\noptimum even without payments. For example, a graph with diameter\nslightly more than \u03b1 may have a Nash equilibrium configuration\nwith two replicas at the two ends. However, the social optimum\nmay place one replica at the center. We leave the investigation of\nmore examples as an open issue.\n7. CONCLUSIONS\nIn this work we introduce a novel non-cooperative game model\nto characterize the caching problem among selfish servers without\nany central coordination. 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Improved Approximation\nAlgorithms for Metric Facility Location Problems. In Proc.\nof Intl. Workshop on Approximation Algorithms for\nCombinatorial Optimization Problems, 2002.\n[25] A. Medina, A. Lakhina, I. Matta, and J. Byers. BRITE:\nUniversal Topology Generation from a User\"s Perspective.\nTechnical Report 2001-003, 1 2001.\n[26] R. R. Mettu and C. G. Plaxton. The Online Median Problem.\nIn Proc. of IEEE FOCS, 2000.\n[27] P. B. Mirchandani and R. L. Francis. Discrete Location\nTheory. Wiley-Interscience Series in Discrete Mathematics\nand Optimization, 1990.\n[28] M. J. Osborne and A. Rubinstein. A Course in Game Theory.\nMIT Press, 1994.\n[29] M. Pal and E. Tardos. Group Strategyproof Mechanisms via\nPrimal-Dual Algorithms. In Proc. of IEEE FOCS, 2003.\n[30] L. Qiu, V. N. Padmanabhan, and G. M. Voelker. On the\nPlacement of Web Server Replicas. In Proc. of IEEE\nINFOCOM, 2001.\n[31] M. Rabinovich, I. Rabinovich, R. Rajaraman, and\nA. Aggarwal. A Dynamic Object Replication and Migration\nProtocol for an Internet Hosting Service. In Proc. of IEEE\nICDCS, 1999.\n[32] A. Rowstron and P. Druschel. Storage Management and\nCaching in PAST, A Large-scale, Persistent Peer-to-peer\nStorage Utility. In Proc. of ACM SOSP, October 2001.\n[33] Y. Saito, C. Karamanolis, M. Karlsson, and M. Mahalingam.\nTaming Aggressive Replication in the Pangaea Wide-Area\nFile System. In Proc. of USENIX OSDI, 2002.\n[34] X. Tang and S. T. Chanson. Coordinated En-route Web\nCaching. In IEEE Trans. Computers, 2002.\n[35] A. Vetta. Nash Equilibria in Competitive Societies, with\nApplications to Facility Location, Traffic Routing, and\nAuctions. In Proc. of IEEE FOCS, 2002.\n[36] E. W. Zegura, K. L. Calvert, and S. Bhattacharjee. How to\nModel an Internetwork. In Proc. of IEEE INFOCOM, 1996.\nAPPENDIX\nA. ANALYZING SPECIFIC TOPOLOGIES\nWe now analyze the price of anarchy (PoA) for the basic game\nwith specific underlying topologies and show that PoA can have\nbetter bounds. We look at complete graph, star, line, and\nDdimensional grid. In all these topologies, we set the distance\nbetween two directly connected nodes to one. We describe the case\nwhere \u03b1 > 1, since PoA = 1 trivially when \u03b1 \u2264 1.\nA BC D3\n\u03b1\n3\n\u03b1\n4\n3\u03b1\n4\n\u03b1\n4\n\u03b1\nFigure 6: Example where the payment game has a Nash equilibrium\nwhich is worse than any Nash equilibrium in the basic game. The\nunlabeled distances between the nodes in the cluster are all 1. The\nthresholds of white nodes are all \u03b1 and the thresholds of dark nodes are all\n\u03b1/4. The two dark nodes replicate the object in this payment game\nNash equilibrium.\nFor a complete graph, PoA = 1, and for a star, PoA \u2264 2.\nFor a complete graph, when \u03b1 > 1, both Nash equilibria and\nsocial optima place one replica at one server, so PoA = 1. For\nstar, when 1 < \u03b1 < 2, the worst case Nash equilibrium places\nreplicas at all leaf nodes. However, the social optimum places\none replica at the center node. Therefore, PoA = (n\u22121)\u03b1+1\n\u03b1+(n\u22121)\n\u2264\n2(n\u22121)+1\n1+(n\u22121)\n\u2264 2. When \u03b1 > 2, the worst case Nash equilibrium\nplaces one replica at a leaf node and the other nodes access the\nremote replica, and the social optimum places one replica at the\ncenter. PoA = \u03b1+1+2(n\u22122)\n\u03b1+(n\u22121)\n= 1 + n\n\u03b1+(n\u22121)\n\u2264 2.\nFor a line, the price of anarchy is O(\n\u221a\nn). When 1 < \u03b1 < n,\nthe worst case Nash equilibrium places replicas every 2\u03b1 so that\nthere is no overlap between areas covered by two adjacent servers\nthat cache the object. The social optimum places replicas at least\nevery\n\u221a\n2\u03b1. The placement of replicas for the social optimum is\nas follows. Suppose there are two replicas separated by distance\nd. By placing an additional replica in the middle, we want to have\nthe reduction of distance to be at least \u03b1. The distance reduction\nis d/2 + 2{((d/2 \u2212 1) \u2212 1) + ((d/2 \u2212 2) \u2212 2) + ... + ((d/2 \u2212\nd/4) \u2212 d/4)} \u2265 d2\n/8. d should be at most 2\n\u221a\n2\u03b1. Therefore, the\ndistance between replicas in the social optimum is at most\n\u221a\n2\u03b1.\nC(SW ) = \u03b1(n\u22121)\n2\u03b1\n+ \u03b1(\u03b1+1)\n2\n(n\u22121)\n2\u03b1\n= \u0398(\u03b1n). C(SO) \u2265 \u03b1 n\u22121\u221a\n2\u03b1\n+\n2\n\u221a\n2\u03b1/2(\n\u221a\n2\u03b1/2+1)\n2\nn\u22121\u221a\n2\u03b1\n. C(SO) = \u2126(\n\u221a\n\u03b1n). Therefore, PoA =\nO(\n\u221a\n\u03b1). When \u03b1 > n \u2212 1, the worst case Nash equilibrium places\none replica at a leaf node and C(SW ) = \u03b1 + (n\u22121)n\n2\n. However,\nthe social optimum still places replicas every\n\u221a\n2\u03b1. If we view\nPoA as a continuous function of \u03b1 and compute a derivative of\nPoA, the derivative becomes 0 when \u03b1 is \u0398(n2\n), which means\nthe function decreases as \u03b1 increases from n. Therefore, PoA is\nmaximum when \u03b1 is n, and PoA = \u0398(n2\n)\n\u2126(\n\u221a\nnn)\n= O(\n\u221a\nn). When\n\u03b1 > (n\u22121)n\n2\n, the social optimum also places only one replica, and\nPoA is trivially bounded by 2. This result holds for the ring and\nit can be generalized to the D-dimensional grid. As the dimension\nin the grid increases, the distance reduction of additional replica\nplacement becomes \u2126(dD+1\n) where d is the distance between two\nadjacent replicas. Therefore, PoA = \u0398(n2)\n\u2126(n\n1\nD+1 n)\n= O(n\nD\nD+1 ).\nB. PAYMENT CAN DO WORSE\nConsider the network in Figure 6 where \u03b1 > 1+\u03b1/3. Any Nash\nequilibrium in the basic game model would have exactly two\nreplicas - one in the left cluster, and one in the right. It is easy to verify\nthat the worst placement (in terms of social cost) of two replicas\noccurs when they are placed at nodes A and B. This placement can\nbe achieved as a Nash equilibrium in the payment game, but not in\nthe basic game since A and B are a distance 3\u03b1/4 apart.\n29\nAlgorithm 1 Initialization for the Basic Game\nL1 = a random subset of servers\nfor each node i in N do\nif i \u2208 L1 then\nSi = 1 ; replicate the object\nelse\nSi = 0\nAlgorithm 2 Move Selection of i for the Basic Game\nCost1 = \u03b1\nCost2 = minj\u2208X\u2212{i} dij ; X is the current configuration\nCostmin = min{Cost1, Cost2}\nif Costnow > Costmin then\nif Costmin == Cost1 then\nSi = 1\nelse\nSi = 0\nC. NASH DYNAMICS PROTOCOLS\nThe simulator initializes the game according to the given\nparameters and a random initial strategy profile and then iterates through\nrounds. Initially the order of player actions is chosen randomly. In\neach round, each server performs the Nash dynamics protocol that\nadjusts its strategies greedily in the chosen order. When a round\npasses without any server changing its strategy, the simulation ends\nand a Nash equilibrium is reached.\nIn the basic game, we pick a random initial subset of servers to\nreplicate the object as shown in Algorithm 1. After the\ninitialization, each player runs the move selection procedure described in\nAlgorithm 2 (in algorithms 2 and 4, Costnow represents the\ncurrent cost for node i). This procedure chooses greedily between\nreplication and non-replication. It is not hard to see that this Nash\ndynamics protocol converges in two rounds.\nIn the payment game, we pick a random initial subset of servers\nto replicate the object by setting their thresholds to 0. In addition,\nwe initialize a second random subset of servers to replicate the\nobject with payments from other servers. The details are shown in\nAlgorithm 3. After the initialization, each player runs the move\nselection procedure described in Algorithm 4. This procedure chooses\ngreedily between replication and accessing a remote replica, with\nthe possibilities of receiving and making payments, respectively.\nIn the protocol, each node increases its threshold value by incr if it\ndoes not replicate the object. By this ramp up procedure, the cost of\nreplicating an object is shared fairly among the nodes that access a\nreplica from a server that does cache. If incr is small, cost is shared\nmore fairly, and the game tends to reach equilibria that encourages\nmore servers to store replicas, though the convergence takes longer.\nIf incr is large, the protocol converges quickly, but it may miss\nefficient equilibria. In the simulations we set incr to 0.1. Most of our\nA\nB C\na\nb\nc\n\u03b1/3+1\n2\u03b1/3\u22121\n2\u03b1/3\nFigure 7: An example where the Nash dynamics protocol does not\nconverge in the payment game.\nAlgorithm 3 Initialization for the Payment Game\nL1 = a random subset of servers\nfor each node i in N do\nbi = 0\nif i \u2208 L1 then\nti = 0 ; replicate the object\nelse\nti = \u03b1\nL2 = {}\nfor each node i in N do\nif coin toss == head then\nMi = {j : d(j, i) < mink\u2208L1\u222aL2 d(j, k)}\nif Mi != \u2205 then\nfor each node j \u2208 Mi do\nbj = max{\n\u03b1+\n\u00c8k\u2208Mi\nd(i,k)\n|Mi|\n\u2212 d(i, j), 0}\nL2 = L2 \u222a {i}\nAlgorithm 4 Move Selection of i for the Payment Game\nCost1 = \u03b1 \u2212 Ri\nCost2 = minj\u2208N\u2212{i}{tj \u2212 Rj + dij }\nCostmin = min{Cost1, Cost2}\nif Costnow > Costmin then\nif Costmin == Cost1 then\nti = Ri\nelse\nti = Ri + incr\nvi = argminj{tj \u2212 Rj + dij}\nbi = tvi \u2212 Rvi\nsimulation runs converged, but there were a very few cases where\nthe simulation did not converge due to the cycles of dynamics. The\nprotocol does not guarantee convergence within a certain number\nof rounds like the protocol for the basic game.\nWe provide an example graph and an initial condition such that\nthe Nash dynamics protocol does not converge in the payment game\nif started from this initial condition. The graph is represented by\na shortest path metric on the network shown in Figure 7. In the\nstarting configuration, only A replicates the object, and a pays it\nan amount \u03b1/3 to do so. The thresholds for A, B and C are \u03b1/3\neach, and the thresholds for a, b and c are 2\u03b1/3. It is not hard to\nverify that the Nash dynamics protocol will never converge if we\nstart with this condition.\nThe Nash dynamics protocol for the payment game needs\nfurther investigation. The dynamics protocol for the payment game\nshould avoid cycles of actions to achieve stabilization of the\nprotocol. Finding a self-stabilizing dynamics protocol is an interesting\nproblem. In addition, a fixed value of incr cannot adapt to changing\nenvironments. A small value of incr can lead to efficient equilibria,\nbut it can take long time to converge. An important area for future\nresearch is looking at adaptively changing incr.\n30", "keywords": "caching problem;nash equilibrium;remote replica;social utility;submodularity;peer-to-peer file system;demand distribution;game-theoretic model;cache;anarchy price;aggregation effect;network topology;game-theoretic approach;distribute system;group strategyproofness;instrumentation server;price of anarchy;primal-dual technique;peer-to-peer system"}
{"name": "train_H-35", "title": "AdaRank: A Boosting Algorithm for Information Retrieval", "abstract": "In this paper we address the issue of learning to rank for document retrieval. In the task, a model is automatically created with some training data and then is utilized for ranking of documents. The goodness of a model is usually evaluated with performance measures such as MAP (Mean Average Precision) and NDCG (Normalized Discounted Cumulative Gain). Ideally a learning algorithm would train a ranking model that could directly optimize the performance measures with respect to the training data. Existing methods, however, are only able to train ranking models by minimizing loss functions loosely related to the performance measures. For example, Ranking SVM and RankBoost train ranking models by minimizing classification errors on instance pairs. To deal with the problem, we propose a novel learning algorithm within the framework of boosting, which can minimize a loss function directly defined on the performance measures. Our algorithm, referred to as AdaRank, repeatedly constructs \u2018weak rankers\" on the basis of re-weighted training data and finally linearly combines the weak rankers for making ranking predictions. We prove that the training process of AdaRank is exactly that of enhancing the performance measure used. Experimental results on four benchmark datasets show that AdaRank significantly outperforms the baseline methods of BM25, Ranking SVM, and RankBoost.", "fulltext": "1. INTRODUCTION\nRecently \u2018learning to rank\" has gained increasing attention in\nboth the fields of information retrieval and machine learning. When\napplied to document retrieval, learning to rank becomes a task as\nfollows. In training, a ranking model is constructed with data\nconsisting of queries, their corresponding retrieved documents, and\nrelevance levels given by humans. In ranking, given a new query, the\ncorresponding retrieved documents are sorted by using the trained\nranking model. In document retrieval, usually ranking results are\nevaluated in terms of performance measures such as MAP (Mean\nAverage Precision) [1] and NDCG (Normalized Discounted\nCumulative Gain) [15]. Ideally, the ranking function is created so that the\naccuracy of ranking in terms of one of the measures with respect to\nthe training data is maximized.\nSeveral methods for learning to rank have been developed and\napplied to document retrieval. For example, Herbrich et al. [13]\npropose a learning algorithm for ranking on the basis of Support\nVector Machines, called Ranking SVM. Freund et al. [8] take a\nsimilar approach and perform the learning by using boosting,\nreferred to as RankBoost. All the existing methods used for\ndocument retrieval [2, 3, 8, 13, 16, 20] are designed to optimize loss\nfunctions loosely related to the IR performance measures, not loss\nfunctions directly based on the measures. For example, Ranking\nSVM and RankBoost train ranking models by minimizing\nclassification errors on instance pairs.\nIn this paper, we aim to develop a new learning algorithm that\ncan directly optimize any performance measure used in document\nretrieval. Inspired by the work of AdaBoost for classification [9],\nwe propose to develop a boosting algorithm for information\nretrieval, referred to as AdaRank. AdaRank utilizes a linear\ncombination of \u2018weak rankers\" as its model. In learning, it repeats the\nprocess of re-weighting the training sample, creating a weak ranker,\nand calculating a weight for the ranker.\nWe show that AdaRank algorithm can iteratively optimize an\nexponential loss function based on any of IR performance measures.\nA lower bound of the performance on training data is given, which\nindicates that the ranking accuracy in terms of the performance\nmeasure can be continuously improved during the training process.\nAdaRank offers several advantages: ease in implementation,\ntheoretical soundness, efficiency in training, and high accuracy in ranking.\nExperimental results indicate that AdaRank can outperform the\nbaseline methods of BM25, Ranking SVM, and RankBoost, on four\nbenchmark datasets including OHSUMED, WSJ, AP, and .Gov.\nTuning ranking models using certain training data and a\nperformance measure is a common practice in IR [1]. As the number of\nfeatures in the ranking model gets larger and the amount of\ntraining data gets larger, the tuning becomes harder. From the viewpoint\nof IR, AdaRank can be viewed as a machine learning method for\nranking model tuning.\nRecently, direct optimization of performance measures in\nlearning has become a hot research topic. Several methods for\nclassification [17] and ranking [5, 19] have been proposed. AdaRank can\nbe viewed as a machine learning method for direct optimization of\nperformance measures, based on a different approach.\nThe rest of the paper is organized as follows. After a summary\nof related work in Section 2, we describe the proposed AdaRank\nalgorithm in details in Section 3. Experimental results and\ndiscussions are given in Section 4. Section 5 concludes this paper and\ngives future work.\n2. RELATED WORK\n2.1 Information Retrieval\nThe key problem for document retrieval is ranking, specifically,\nhow to create the ranking model (function) that can sort documents\nbased on their relevance to the given query. It is a common practice\nin IR to tune the parameters of a ranking model using some labeled\ndata and one performance measure [1]. For example, the\nstate-ofthe-art methods of BM25 [24] and LMIR (Language Models for\nInformation Retrieval) [18, 22] all have parameters to tune. As\nthe ranking models become more sophisticated (more features are\nused) and more labeled data become available, how to tune or train\nranking models turns out to be a challenging issue.\nRecently methods of \u2018learning to rank\" have been applied to\nranking model construction and some promising results have been\nobtained. For example, Joachims [16] applies Ranking SVM to\ndocument retrieval. He utilizes click-through data to deduce\ntraining data for the model creation. Cao et al. [4] adapt Ranking\nSVM to document retrieval by modifying the Hinge Loss function\nto better meet the requirements of IR. Specifically, they introduce\na Hinge Loss function that heavily penalizes errors on the tops of\nranking lists and errors from queries with fewer retrieved\ndocuments. Burges et al. [3] employ Relative Entropy as a loss function\nand Gradient Descent as an algorithm to train a Neural Network\nmodel for ranking in document retrieval. The method is referred to\nas \u2018RankNet\".\n2.2 Machine Learning\nThere are three topics in machine learning which are related to\nour current work. They are \u2018learning to rank\", boosting, and direct\noptimization of performance measures.\nLearning to rank is to automatically create a ranking function\nthat assigns scores to instances and then rank the instances by\nusing the scores. Several approaches have been proposed to tackle\nthe problem. One major approach to learning to rank is that of\ntransforming it into binary classification on instance pairs. This\n\u2018pair-wise\" approach fits well with information retrieval and thus is\nwidely used in IR. Typical methods of the approach include\nRanking SVM [13], RankBoost [8], and RankNet [3]. For other\napproaches to learning to rank, refer to [2, 11, 31].\nIn the pair-wise approach to ranking, the learning task is\nformalized as a problem of classifying instance pairs into two categories\n(correctly ranked and incorrectly ranked). Actually, it is known\nthat reducing classification errors on instance pairs is equivalent to\nmaximizing a lower bound of MAP [16]. In that sense, the\nexisting methods of Ranking SVM, RankBoost, and RankNet are only\nable to minimize loss functions that are loosely related to the IR\nperformance measures.\nBoosting is a general technique for improving the accuracies of\nmachine learning algorithms. The basic idea of boosting is to\nrepeatedly construct \u2018weak learners\" by re-weighting training data\nand form an ensemble of weak learners such that the total\nperformance of the ensemble is \u2018boosted\". Freund and Schapire have\nproposed the first well-known boosting algorithm called AdaBoost\n(Adaptive Boosting) [9], which is designed for binary\nclassification (0-1 prediction). Later, Schapire & Singer have introduced a\ngeneralized version of AdaBoost in which weak learners can give\nconfidence scores in their predictions rather than make 0-1\ndecisions [26]. Extensions have been made to deal with the problems\nof multi-class classification [10, 26], regression [7], and ranking\n[8]. In fact, AdaBoost is an algorithm that ingeniously constructs\na linear model by minimizing the \u2018exponential loss function\" with\nrespect to the training data [26]. Our work in this paper can be\nviewed as a boosting method developed for ranking, particularly\nfor ranking in IR.\nRecently, a number of authors have proposed conducting direct\noptimization of multivariate performance measures in learning. For\ninstance, Joachims [17] presents an SVM method to directly\noptimize nonlinear multivariate performance measures like the F1\nmeasure for classification. Cossock & Zhang [5] find a way to\napproximately optimize the ranking performance measure DCG [15].\nMetzler et al. [19] also propose a method of directly maximizing\nrank-based metrics for ranking on the basis of manifold learning.\nAdaRank is also one that tries to directly optimize multivariate\nperformance measures, but is based on a different approach. AdaRank\nis unique in that it employs an exponential loss function based on\nIR performance measures and a boosting technique.\n3. OUR METHOD: ADARANK\n3.1 General Framework\nWe first describe the general framework of learning to rank for\ndocument retrieval. In retrieval (testing), given a query the system\nreturns a ranking list of documents in descending order of the\nrelevance scores. The relevance scores are calculated with a ranking\nfunction (model). In learning (training), a number of queries and\ntheir corresponding retrieved documents are given. Furthermore,\nthe relevance levels of the documents with respect to the queries are\nalso provided. The relevance levels are represented as ranks (i.e.,\ncategories in a total order). The objective of learning is to construct\na ranking function which achieves the best results in ranking of the\ntraining data in the sense of minimization of a loss function. Ideally\nthe loss function is defined on the basis of the performance measure\nused in testing.\nSuppose that Y = {r1, r2, \u00b7 \u00b7 \u00b7 , r } is a set of ranks, where denotes\nthe number of ranks. There exists a total order between the ranks\nr r \u22121 \u00b7 \u00b7 \u00b7 r1, where \u2018 \" denotes a preference relationship.\nIn training, a set of queries Q = {q1, q2, \u00b7 \u00b7 \u00b7 , qm} is given. Each\nquery qi is associated with a list of retrieved documents di = {di1, di2,\n\u00b7 \u00b7 \u00b7 , di,n(qi)} and a list of labels yi = {yi1, yi2, \u00b7 \u00b7 \u00b7 , yi,n(qi)}, where n(qi)\ndenotes the sizes of lists di and yi, dij denotes the jth\ndocument in\ndi, and yij \u2208 Y denotes the rank of document di j. A feature\nvector xij = \u03a8(qi, di j) \u2208 X is created from each query-document pair\n(qi, di j), i = 1, 2, \u00b7 \u00b7 \u00b7 , m; j = 1, 2, \u00b7 \u00b7 \u00b7 , n(qi). Thus, the training set\ncan be represented as S = {(qi, di, yi)}m\ni=1.\nThe objective of learning is to create a ranking function f : X \u2192\n, such that for each query the elements in its corresponding\ndocument list can be assigned relevance scores using the function and\nthen be ranked according to the scores. Specifically, we create a\npermutation of integers \u03c0(qi, di, f) for query qi, the\ncorresponding list of documents di, and the ranking function f. Let di =\n{di1, di2, \u00b7 \u00b7 \u00b7 , di,n(qi)} be identified by the list of integers {1, 2, \u00b7 \u00b7 \u00b7 , n(qi)},\nthen permutation \u03c0(qi, di, f) is defined as a bijection from {1, 2, \u00b7 \u00b7 \u00b7 ,\nn(qi)} to itself. We use \u03c0( j) to denote the position of item j (i.e.,\ndi j). The learning process turns out to be that of minimizing the\nloss function which represents the disagreement between the\npermutation \u03c0(qi, di, f) and the list of ranks yi, for all of the queries.\nTable 1: Notations and explanations.\nNotations Explanations\nqi \u2208 Q ith\nquery\ndi = {di1, di2, \u00b7 \u00b7 \u00b7 , di,n(qi)} List of documents for qi\nyi j \u2208 {r1, r2, \u00b7 \u00b7 \u00b7 , r } Rank of di j w.r.t. qi\nyi = {yi1, yi2, \u00b7 \u00b7 \u00b7 , yi,n(qi)} List of ranks for qi\nS = {(qi, di, yi)}m\ni=1 Training set\nxij = \u03a8(qi, dij) \u2208 X Feature vector for (qi, di j)\nf(xij) \u2208 Ranking model\n\u03c0(qi, di, f) Permutation for qi, di, and f\nht(xi j) \u2208 tth\nweak ranker\nE(\u03c0(qi, di, f), yi) \u2208 [\u22121, +1] Performance measure function\nIn the paper, we define the rank model as a linear combination of\nweak rankers: f(x) = T\nt=1 \u03b1tht(x), where ht(x) is a weak ranker, \u03b1t\nis its weight, and T is the number of weak rankers.\nIn information retrieval, query-based performance measures are\nused to evaluate the \u2018goodness\" of a ranking function. By query\nbased measure, we mean a measure defined over a ranking list\nof documents with respect to a query. These measures include\nMAP, NDCG, MRR (Mean Reciprocal Rank), WTA (Winners Take\nALL), and Precision@n [1, 15]. We utilize a general function\nE(\u03c0(qi, di, f), yi) \u2208 [\u22121, +1] to represent the performance\nmeasures. The first argument of E is the permutation \u03c0 created using\nthe ranking function f on di. The second argument is the list of\nranks yi given by humans. E measures the agreement between \u03c0\nand yi. Table 1 gives a summary of notations described above.\nNext, as examples of performance measures, we present the\ndefinitions of MAP and NDCG. Given a query qi, the corresponding\nlist of ranks yi, and a permutation \u03c0i on di, average precision for qi\nis defined as:\nAvgPi =\nn(qi)\nj=1 Pi( j) \u00b7 yij\nn(qi)\nj=1 yij\n, (1)\nwhere yij takes on 1 and 0 as values, representing being relevant or\nirrelevant and Pi( j) is defined as precision at the position of dij:\nPi( j) =\nk:\u03c0i(k)\u2264\u03c0i(j) yik\n\u03c0i(j)\n, (2)\nwhere \u03c0i( j) denotes the position of di j.\nGiven a query qi, the list of ranks yi, and a permutation \u03c0i on di,\nNDCG at position m for qi is defined as:\nNi = ni \u00b7\nj:\u03c0i(j)\u2264m\n2yi j \u2212 1\nlog(1 + \u03c0i( j))\n, (3)\nwhere yij takes on ranks as values and ni is a normalization\nconstant. ni is chosen so that a perfect ranking \u03c0\u2217\ni \"s NDCG score at\nposition m is 1.\n3.2 Algorithm\nInspired by the AdaBoost algorithm for classification, we have\ndevised a novel algorithm which can optimize a loss function based\non the IR performance measures. The algorithm is referred to as\n\u2018AdaRank\" and is shown in Figure 1.\nAdaRank takes a training set S = {(qi, di, yi)}m\ni=1 as input and\ntakes the performance measure function E and the number of\niterations T as parameters. AdaRank runs T rounds and at each round it\ncreates a weak ranker ht(t = 1, \u00b7 \u00b7 \u00b7 , T). Finally, it outputs a ranking\nmodel f by linearly combining the weak rankers.\nAt each round, AdaRank maintains a distribution of weights over\nthe queries in the training data. We denote the distribution of weights\nInput: S = {(qi, di, yi)}m\ni=1, and parameters E and T\nInitialize P1(i) = 1/m.\nFor t = 1, \u00b7 \u00b7 \u00b7 , T\n\u2022 Create weak ranker ht with weighted distribution Pt on\ntraining data S .\n\u2022 Choose \u03b1t\n\u03b1t =\n1\n2\n\u00b7 ln\nm\ni=1 Pt(i){1 + E(\u03c0(qi, di, ht), yi)}\nm\ni=1 Pt(i){1 \u2212 E(\u03c0(qi, di, ht), yi)}\n.\n\u2022 Create ft\nft(x) =\nt\nk=1\n\u03b1khk(x).\n\u2022 Update Pt+1\nPt+1(i) =\nexp{\u2212E(\u03c0(qi, di, ft), yi)}\nm\nj=1 exp{\u2212E(\u03c0(qj, dj, ft), yj)}\n.\nEnd For\nOutput ranking model: f(x) = fT (x).\nFigure 1: The AdaRank algorithm.\nat round t as Pt and the weight on the ith\ntraining query qi at round\nt as Pt(i). Initially, AdaRank sets equal weights to the queries. At\neach round, it increases the weights of those queries that are not\nranked well by ft, the model created so far. As a result, the learning\nat the next round will be focused on the creation of a weak ranker\nthat can work on the ranking of those \u2018hard\" queries.\nAt each round, a weak ranker ht is constructed based on training\ndata with weight distribution Pt. The goodness of a weak ranker is\nmeasured by the performance measure E weighted by Pt:\nm\ni=1\nPt(i)E(\u03c0(qi, di, ht), yi).\nSeveral methods for weak ranker construction can be considered.\nFor example, a weak ranker can be created by using a subset of\nqueries (together with their document list and label list) sampled\naccording to the distribution Pt. In this paper, we use single features\nas weak rankers, as will be explained in Section 3.6.\nOnce a weak ranker ht is built, AdaRank chooses a weight \u03b1t > 0\nfor the weak ranker. Intuitively, \u03b1t measures the importance of ht.\nA ranking model ft is created at each round by linearly\ncombining the weak rankers constructed so far h1, \u00b7 \u00b7 \u00b7 , ht with weights\n\u03b11, \u00b7 \u00b7 \u00b7 , \u03b1t. ft is then used for updating the distribution Pt+1.\n3.3 Theoretical Analysis\nThe existing learning algorithms for ranking attempt to minimize\na loss function based on instance pairs (document pairs). In\ncontrast, AdaRank tries to optimize a loss function based on queries.\nFurthermore, the loss function in AdaRank is defined on the basis\nof general IR performance measures. The measures can be MAP,\nNDCG, WTA, MRR, or any other measures whose range is within\n[\u22121, +1]. We next explain why this is the case.\nIdeally we want to maximize the ranking accuracy in terms of a\nperformance measure on the training data:\nmax\nf\u2208F\nm\ni=1\nE(\u03c0(qi, di, f), yi), (4)\nwhere F is the set of possible ranking functions. This is equivalent\nto minimizing the loss on the training data\nmin\nf\u2208F\nm\ni=1\n(1 \u2212 E(\u03c0(qi, di, f), yi)). (5)\nIt is difficult to directly optimize the loss, because E is a\nnoncontinuous function and thus may be difficult to handle. We instead\nattempt to minimize an upper bound of the loss in (5)\nmin\nf\u2208F\nm\ni=1\nexp{\u2212E(\u03c0(qi, di, f), yi)}, (6)\nbecause e\u2212x\n\u2265 1 \u2212 x holds for any x \u2208 . We consider the use of a\nlinear combination of weak rankers as our ranking model:\nf(x) =\nT\nt=1\n\u03b1tht(x). (7)\nThe minimization in (6) then turns out to be\nmin\nht\u2208H,\u03b1t\u2208 +\nL(ht, \u03b1t) =\nm\ni=1\nexp{\u2212E(\u03c0(qi, di, ft\u22121 + \u03b1tht), yi)}, (8)\nwhere H is the set of possible weak rankers, \u03b1t is a positive weight,\nand ( ft\u22121 + \u03b1tht)(x) = ft\u22121(x) + \u03b1tht(x). Several ways of computing\ncoefficients \u03b1t and weak rankers ht may be considered. Following\nthe idea of AdaBoost, in AdaRank we take the approach of \u2018forward\nstage-wise additive modeling\" [12] and get the algorithm in Figure\n1. It can be proved that there exists a lower bound on the ranking\naccuracy for AdaRank on training data, as presented in Theorem 1.\nT\uf768\uf765\uf76f\uf772\uf765\uf76d 1. The following bound holds on the ranking\naccuracy of the AdaRank algorithm on training data:\n1\nm\nm\ni=1\nE(\u03c0(qi, di, fT ), yi) \u2265 1 \u2212\nT\nt=1\ne\u2212\u03b4t\nmin 1 \u2212 \u03d5(t)2,\nwhere \u03d5(t) = m\ni=1 Pt(i)E(\u03c0(qi, di, ht), yi), \u03b4t\nmin = mini=1,\u00b7\u00b7\u00b7 ,m \u03b4t\ni, and\n\u03b4t\ni = E(\u03c0(qi, di, ft\u22121 + \u03b1tht), yi) \u2212 E(\u03c0(qi, di, ft\u22121), yi)\n\u2212\u03b1tE(\u03c0(qi, di, ht), yi),\nfor all i = 1, 2, \u00b7 \u00b7 \u00b7 , m and t = 1, 2, \u00b7 \u00b7 \u00b7 , T.\nA proof of the theorem can be found in appendix. The theorem\nimplies that the ranking accuracy in terms of the performance\nmeasure can be continuously improved, as long as e\u2212\u03b4t\nmin 1 \u2212 \u03d5(t)2 < 1\nholds.\n3.4 Advantages\nAdaRank is a simple yet powerful method. More importantly, it\nis a method that can be justified from the theoretical viewpoint, as\ndiscussed above. In addition AdaRank has several other advantages\nwhen compared with the existing learning to rank methods such as\nRanking SVM, RankBoost, and RankNet.\nFirst, AdaRank can incorporate any performance measure,\nprovided that the measure is query based and in the range of [\u22121, +1].\nNotice that the major IR measures meet this requirement. In\ncontrast the existing methods only minimize loss functions that are\nloosely related to the IR measures [16].\nSecond, the learning process of AdaRank is more efficient than\nthose of the existing learning algorithms. The time complexity of\nAdaRank is of order O((k+T)\u00b7m\u00b7n log n), where k denotes the\nnumber of features, T the number of rounds, m the number of queries\nin training data, and n is the maximum number of documents for\nqueries in training data. The time complexity of RankBoost, for\nexample, is of order O(T \u00b7 m \u00b7 n2\n) [8].\nThird, AdaRank employs a more reasonable framework for\nperforming the ranking task than the existing methods. Specifically in\nAdaRank the instances correspond to queries, while in the existing\nmethods the instances correspond to document pairs. As a result,\nAdaRank does not have the following shortcomings that plague the\nexisting methods. (a) The existing methods have to make a strong\nassumption that the document pairs from the same query are\nindependently distributed. In reality, this is clearly not the case and this\nproblem does not exist for AdaRank. (b) Ranking the most relevant\ndocuments on the tops of document lists is crucial for document\nretrieval. The existing methods cannot focus on the training on the\ntops, as indicated in [4]. Several methods for rectifying the problem\nhave been proposed (e.g., [4]), however, they do not seem to\nfundamentally solve the problem. In contrast, AdaRank can naturally\nfocus on training on the tops of document lists, because the\nperformance measures used favor rankings for which relevant documents\nare on the tops. (c) In the existing methods, the numbers of\ndocument pairs vary from query to query, resulting in creating models\nbiased toward queries with more document pairs, as pointed out in\n[4]. AdaRank does not have this drawback, because it treats queries\nrather than document pairs as basic units in learning.\n3.5 Differences from AdaBoost\nAdaRank is a boosting algorithm. In that sense, it is similar to\nAdaBoost, but it also has several striking differences from AdaBoost.\nFirst, the types of instances are different. AdaRank makes use of\nqueries and their corresponding document lists as instances. The\nlabels in training data are lists of ranks (relevance levels). AdaBoost\nmakes use of feature vectors as instances. The labels in training\ndata are simply +1 and \u22121.\nSecond, the performance measures are different. In AdaRank,\nthe performance measure is a generic measure, defined on the\ndocument list and the rank list of a query. In AdaBoost the\ncorresponding performance measure is a specific measure for binary\nclassification, also referred to as \u2018margin\" [25].\nThird, the ways of updating weights are also different. In\nAdaBoost, the distribution of weights on training instances is\ncalculated according to the current distribution and the performance of\nthe current weak learner. In AdaRank, in contrast, it is calculated\naccording to the performance of the ranking model created so far,\nas shown in Figure 1. Note that AdaBoost can also adopt the weight\nupdating method used in AdaRank. For AdaBoost they are\nequivalent (cf., [12] page 305). However, this is not true for AdaRank.\n3.6 Construction of Weak Ranker\nWe consider an efficient implementation for weak ranker\nconstruction, which is also used in our experiments. In the\nimplementation, as weak ranker we choose the feature that has the optimal\nweighted performance among all of the features:\nmax\nk\nm\ni=1\nPt(i)E(\u03c0(qi, di, xk), yi).\nCreating weak rankers in this way, the learning process turns out\nto be that of repeatedly selecting features and linearly combining\nthe selected features. Note that features which are not selected in\nthe training phase will have a weight of zero.\n4. EXPERIMENTAL RESULTS\nWe conducted experiments to test the performances of AdaRank\nusing four benchmark datasets: OHSUMED, WSJ, AP, and .Gov.\nTable 2: Features used in the experiments on OHSUMED,\nWSJ, and AP datasets. C(w, d) represents frequency of word\nw in document d; C represents the entire collection; n denotes\nnumber of terms in query; | \u00b7 | denotes the size function; and\nid f(\u00b7) denotes inverse document frequency.\n1 wi\u2208q d ln(c(wi, d) + 1) 2 wi\u2208q d ln( |C|\nc(wi,C)\n+ 1)\n3 wi\u2208q d ln(id f(wi)) 4 wi\u2208q d ln(c(wi,d)\n|d|\n+ 1)\n5 wi\u2208q d ln(c(wi,d)\n|d|\n\u00b7 id f(wi) + 1) 6 wi\u2208q d ln(c(wi,d)\u00b7|C|\n|d|\u00b7c(wi,C)\n+ 1)\n7 ln(BM25 score)\n0.2\n0.3\n0.4\n0.5\n0.6\nMAP NDCG@1 NDCG@3 NDCG@5 NDCG@10\nBM25\nRanking SVM\nRarnkBoost\nAdaRank.MAP\nAdaRank.NDCG\nFigure 2: Ranking accuracies on OHSUMED data.\n4.1 Experiment Setting\nRanking SVM [13, 16] and RankBoost [8] were selected as\nbaselines in the experiments, because they are the state-of-the-art\nlearning to rank methods. Furthermore, BM25 [24] was used as a\nbaseline, representing the state-of-the-arts IR method (we actually used\nthe tool Lemur1\n).\nFor AdaRank, the parameter T was determined automatically\nduring each experiment. Specifically, when there is no\nimprovement in ranking accuracy in terms of the performance measure, the\niteration stops (and T is determined). As the measure E, MAP and\nNDCG@5 were utilized. The results for AdaRank using MAP and\nNDCG@5 as measures in training are represented as AdaRank.MAP\nand AdaRank.NDCG, respectively.\n4.2 Experiment with OHSUMED Data\nIn this experiment, we made use of the OHSUMED dataset [14]\nto test the performances of AdaRank. The OHSUMED dataset\nconsists of 348,566 documents and 106 queries. There are in total\n16,140 query-document pairs upon which relevance judgments are\nmade. The relevance judgments are either \u2018d\" (definitely relevant),\n\u2018p\" (possibly relevant), or \u2018n\"(not relevant). The data have been\nused in many experiments in IR, for example [4, 29].\nAs features, we adopted those used in document retrieval [4].\nTable 2 shows the features. For example, tf (term frequency), idf\n(inverse document frequency), dl (document length), and\ncombinations of them are defined as features. BM25 score itself is also a\nfeature. Stop words were removed and stemming was conducted in\nthe data.\nWe randomly divided queries into four even subsets and\nconducted 4-fold cross-validation experiments. We tuned the\nparameters for BM25 during one of the trials and applied them to the other\ntrials. The results reported in Figure 2 are those averaged over four\ntrials. In MAP calculation, we define the rank \u2018d\" as relevant and\n1\nhttp://www.lemurproject.com\nTable 3: Statistics on WSJ and AP datasets.\nDataset # queries # retrieved docs # docs per query\nAP 116 24,727 213.16\nWSJ 126 40,230 319.29\n0.40\n0.45\n0.50\n0.55\n0.60\nMAP NDCG@1 NDCG@3 NDCG@5 NDCG@10\nBM25\nRanking SVM\nRankBoost\nAdaRank.MAP\nAdaRank.NDCG\nFigure 3: Ranking accuracies on WSJ dataset.\nthe other two ranks as irrelevant. From Figure 2, we see that both\nAdaRank.MAP and AdaRank.NDCG outperform BM25, Ranking\nSVM, and RankBoost in terms of all measures. We conducted\nsignificant tests (t-test) on the improvements of AdaRank.MAP over\nBM25, Ranking SVM, and RankBoost in terms of MAP. The\nresults indicate that all the improvements are statistically significant\n(p-value < 0.05). We also conducted t-test on the improvements\nof AdaRank.NDCG over BM25, Ranking SVM, and RankBoost\nin terms of NDCG@5. The improvements are also statistically\nsignificant.\n4.3 Experiment with WSJ and AP Data\nIn this experiment, we made use of the WSJ and AP datasets\nfrom the TREC ad-hoc retrieval track, to test the performances of\nAdaRank. WSJ contains 74,520 articles of Wall Street Journals\nfrom 1990 to 1992, and AP contains 158,240 articles of\nAssociated Press in 1988 and 1990. 200 queries are selected from the\nTREC topics (No.101 \u223c No.300). Each query has a number of\ndocuments associated and they are labeled as \u2018relevant\" or \u2018irrelevant\"\n(to the query). Following the practice in [28], the queries that have\nless than 10 relevant documents were discarded. Table 3 shows the\nstatistics on the two datasets.\nIn the same way as in section 4.2, we adopted the features listed\nin Table 2 for ranking. We also conducted 4-fold cross-validation\nexperiments. The results reported in Figure 3 and 4 are those\naveraged over four trials on WSJ and AP datasets, respectively. From\nFigure 3 and 4, we can see that AdaRank.MAP and AdaRank.NDCG\noutperform BM25, Ranking SVM, and RankBoost in terms of all\nmeasures on both WSJ and AP. We conducted t-tests on the\nimprovements of AdaRank.MAP and AdaRank.NDCG over BM25,\nRanking SVM, and RankBoost on WSJ and AP. The results\nindicate that all the improvements in terms of MAP are statistically\nsignificant (p-value < 0.05). However only some of the improvements\nin terms of NDCG@5 are statistically significant, although overall\nthe improvements on NDCG scores are quite high (1-2 points).\n4.4 Experiment with .Gov Data\nIn this experiment, we further made use of the TREC .Gov data\nto test the performance of AdaRank for the task of web retrieval.\nThe corpus is a crawl from the .gov domain in early 2002, and\nhas been used at TREC Web Track since 2002. There are a total\n0.40\n0.45\n0.50\n0.55\nMAP NDCG@1 NDCG@3 NDCG@5 NDCG@10\nBM25\nRanking SVM\nRankBoost\nAdaRank.MAP\nAdaRank.NDCG\nFigure 4: Ranking accuracies on AP dataset.\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\nMAP NDCG@1 NDCG@3 NDCG@5 NDCG@10\nBM25\nRanking SVM\nRankBoost\nAdaRank.MAP\nAdaRank.NDCG\nFigure 5: Ranking accuracies on .Gov dataset.\nTable 4: Features used in the experiments on .Gov dataset.\n1 BM25 [24] 2 MSRA1000 [27]\n3 PageRank [21] 4 HostRank [30]\n5 Relevance Propagation [23] (10 features)\nof 1,053,110 web pages with 11,164,829 hyperlinks in the data.\nThe 50 queries in the topic distillation task in the Web Track of\nTREC 2003 [6] were used. The ground truths for the queries are\nprovided by the TREC committee with binary judgment: relevant\nor irrelevant. The number of relevant pages vary from query to\nquery (from 1 to 86).\nWe extracted 14 features from each query-document pair.\nTable 4 gives a list of the features. They are the outputs of some\nwell-known algorithms (systems). These features are different from\nthose in Table 2, because the task is different.\nAgain, we conducted 4-fold cross-validation experiments. The\nresults averaged over four trials are reported in Figure 5. From the\nresults, we can see that AdaRank.MAP and AdaRank.NDCG\noutperform all the baselines in terms of all measures. We conducted\nttests on the improvements of AdaRank.MAP and AdaRank.NDCG\nover BM25, Ranking SVM, and RankBoost. Some of the\nimprovements are not statistically significant. This is because we have only\n50 queries used in the experiments, and the number of queries is\ntoo small.\n4.5 Discussions\nWe investigated the reasons that AdaRank outperforms the\nbaseline methods, using the results of the OHSUMED dataset as examples.\nFirst, we examined the reason that AdaRank has higher\nperformances than Ranking SVM and RankBoost. Specifically we\ncom0.58\n0.60\n0.62\n0.64\n0.66\n0.68\nd-n d-p p-n\naccuracy\npair type\nRanking SVM\nRankBoost\nAdaRank.MAP\nAdaRank.NDCG\nFigure 6: Accuracy on ranking document pairs with\nOHSUMED dataset.\n0\n2\n4\n6\n8\n10\n12\nnumberofqueries\nnumber of document pairs per query\nFigure 7: Distribution of queries with different number of\ndocument pairs in training data of trial 1.\npared the error rates between different rank pairs made by\nRanking SVM, RankBoost, AdaRank.MAP, and AdaRank.NDCG on the\ntest data. The results averaged over four trials in the 4-fold cross\nvalidation are shown in Figure 6. We use \u2018d-n\" to stand for the pairs\nbetween \u2018definitely relevant\" and \u2018not relevant\", \u2018d-p\" the pairs\nbetween \u2018definitely relevant\" and \u2018partially relevant\", and \u2018p-n\" the\npairs between \u2018partially relevant\" and \u2018not relevant\". From\nFigure 6, we can see that AdaRank.MAP and AdaRank.NDCG make\nfewer errors for \u2018d-n\" and \u2018d-p\", which are related to the tops of\nrankings and are important. This is because AdaRank.MAP and\nAdaRank.NDCG can naturally focus upon the training on the tops\nby optimizing MAP and NDCG@5, respectively.\nWe also made statistics on the number of document pairs per\nquery in the training data (for trial 1). The queries are clustered into\ndifferent groups based on the the number of their associated\ndocument pairs. Figure 7 shows the distribution of the query groups. In\nthe figure, for example, \u20180-1k\" is the group of queries whose\nnumber of document pairs are between 0 and 999. We can see that the\nnumbers of document pairs really vary from query to query. Next\nwe evaluated the accuracies of AdaRank.MAP and RankBoost in\nterms of MAP for each of the query group. The results are reported\nin Figure 8. We found that the average MAP of AdaRank.MAP\nover the groups is two points higher than RankBoost. Furthermore,\nit is interesting to see that AdaRank.MAP performs particularly\nbetter than RankBoost for queries with small numbers of document\npairs (e.g., \u20180-1k\", \u20181k-2k\", and \u20182k-3k\"). The results indicate that\nAdaRank.MAP can effectively avoid creating a model biased\ntowards queries with more document pairs. For AdaRank.NDCG,\nsimilar results can be observed.\n0.2\n0.3\n0.4\n0.5\nMAP\nquery group\nRankBoost\nAdaRank.MAP\nFigure 8: Differences in MAP for different query groups.\n0.30\n0.31\n0.32\n0.33\n0.34\ntrial 1 trial 2 trial 3 trial 4\nMAP\nAdaRank.MAP\nAdaRank.NDCG\nFigure 9: MAP on training set when model is trained with MAP\nor NDCG@5.\nWe further conducted an experiment to see whether AdaRank has\nthe ability to improve the ranking accuracy in terms of a measure\nby using the measure in training. Specifically, we trained ranking\nmodels using AdaRank.MAP and AdaRank.NDCG and evaluated\ntheir accuracies on the training dataset in terms of both MAP and\nNDCG@5. The experiment was conducted for each trial. Figure\n9 and Figure 10 show the results in terms of MAP and NDCG@5,\nrespectively. We can see that, AdaRank.MAP trained with MAP\nperforms better in terms of MAP while AdaRank.NDCG trained\nwith NDCG@5 performs better in terms of NDCG@5. The results\nindicate that AdaRank can indeed enhance ranking performance in\nterms of a measure by using the measure in training.\nFinally, we tried to verify the correctness of Theorem 1. That is,\nthe ranking accuracy in terms of the performance measure can be\ncontinuously improved, as long as e\u2212\u03b4t\nmin 1 \u2212 \u03d5(t)2 < 1 holds. As\nan example, Figure 11 shows the learning curve of AdaRank.MAP\nin terms of MAP during the training phase in one trial of the cross\nvalidation. From the figure, we can see that the ranking accuracy\nof AdaRank.MAP steadily improves, as the training goes on, until\nit reaches to the peak. The result agrees well with Theorem 1.\n5. CONCLUSION AND FUTURE WORK\nIn this paper we have proposed a novel algorithm for learning\nranking models in document retrieval, referred to as AdaRank. In\ncontrast to existing methods, AdaRank optimizes a loss function\nthat is directly defined on the performance measures. It employs\na boosting technique in ranking model learning. AdaRank offers\nseveral advantages: ease of implementation, theoretical soundness,\nefficiency in training, and high accuracy in ranking. Experimental\nresults based on four benchmark datasets show that AdaRank can\nsignificantly outperform the baseline methods of BM25, Ranking\nSVM, and RankBoost.\n0.49\n0.50\n0.51\n0.52\n0.53\ntrial 1 trial 2 trial 3 trial 4\nNDCG@5\nAdaRank.MAP\nAdaRank.NDCG\nFigure 10: NDCG@5 on training set when model is trained\nwith MAP or NDCG@5.\n0.29\n0.30\n0.31\n0.32\n0 50 100 150 200 250 300 350\nMAP\nnumber of rounds\nFigure 11: Learning curve of AdaRank.\nFuture work includes theoretical analysis on the generalization\nerror and other properties of the AdaRank algorithm, and further\nempirical evaluations of the algorithm including comparisons with\nother algorithms that can directly optimize performance measures.\n6. ACKNOWLEDGMENTS\nWe thank Harry Shum, Wei-Ying Ma, Tie-Yan Liu, Gu Xu, Bin\nGao, Robert Schapire, and Andrew Arnold for their valuable\ncomments and suggestions to this paper.\n7. REFERENCES\n[1] R. Baeza-Yates and B. Ribeiro-Neto. Modern Information\nRetrieval. Addison Wesley, May 1999.\n[2] C. Burges, R. Ragno, and Q. Le. Learning to rank with\nnonsmooth cost functions. In Advances in Neural\nInformation Processing Systems 18, pages 395-402. MIT\nPress, Cambridge, MA, 2006.\n[3] C. Burges, T. Shaked, E. Renshaw, A. Lazier, M. Deeds,\nN. Hamilton, and G. Hullender. Learning to rank using\ngradient descent. In ICML 22, pages 89-96, 2005.\n[4] Y. Cao, J. Xu, T.-Y. Liu, H. Li, Y. Huang, and H.-W. Hon.\nAdapting ranking SVM to document retrieval. In SIGIR 29,\npages 186-193, 2006.\n[5] D. Cossock and T. Zhang. Subset ranking using regression.\nIn COLT, pages 605-619, 2006.\n[6] N. Craswell, D. Hawking, R. Wilkinson, and M. Wu.\nOverview of the TREC 2003 web track. In TREC, pages\n78-92, 2003.\n[7] N. Duffy and D. Helmbold. Boosting methods for regression.\nMach. Learn., 47(2-3):153-200, 2002.\n[8] Y. Freund, R. D. Iyer, R. E. Schapire, and Y. Singer. An\nefficient boosting algorithm for combining preferences.\nJournal of Machine Learning Research, 4:933-969, 2003.\n[9] Y. Freund and R. E. Schapire. A decision-theoretic\ngeneralization of on-line learning and an application to\nboosting. J. Comput. Syst. Sci., 55(1):119-139, 1997.\n[10] J. Friedman, T. Hastie, and R. Tibshirani. Additive logistic\nregression: A statistical view of boosting. The Annals of\nStatistics, 28(2):337-374, 2000.\n[11] G. Fung, R. Rosales, and B. Krishnapuram. Learning\nrankings via convex hull separation. In Advances in Neural\nInformation Processing Systems 18, pages 395-402. MIT\nPress, Cambridge, MA, 2006.\n[12] T. Hastie, R. Tibshirani, and J. H. Friedman. The Elements of\nStatistical Learning. Springer, August 2001.\n[13] R. Herbrich, T. Graepel, and K. Obermayer. Large Margin\nrank boundaries for ordinal regression. MIT Press,\nCambridge, MA, 2000.\n[14] W. Hersh, C. Buckley, T. J. Leone, and D. Hickam.\nOhsumed: an interactive retrieval evaluation and new large\ntest collection for research. In SIGIR, pages 192-201, 1994.\n[15] K. Jarvelin and J. Kekalainen. IR evaluation methods for\nretrieving highly relevant documents. In SIGIR 23, pages\n41-48, 2000.\n[16] T. Joachims. Optimizing search engines using clickthrough\ndata. In SIGKDD 8, pages 133-142, 2002.\n[17] T. Joachims. A support vector method for multivariate\nperformance measures. In ICML 22, pages 377-384, 2005.\n[18] J. Lafferty and C. Zhai. Document language models, query\nmodels, and risk minimization for information retrieval. In\nSIGIR 24, pages 111-119, 2001.\n[19] D. A. Metzler, W. B. Croft, and A. McCallum. Direct\nmaximization of rank-based metrics for information\nretrieval. Technical report, CIIR, 2005.\n[20] R. Nallapati. Discriminative models for information retrieval.\nIn SIGIR 27, pages 64-71, 2004.\n[21] L. Page, S. Brin, R. Motwani, and T. Winograd. The\npagerank citation ranking: Bringing order to the web.\nTechnical report, Stanford Digital Library Technologies\nProject, 1998.\n[22] J. M. Ponte and W. B. Croft. A language modeling approach\nto information retrieval. In SIGIR 21, pages 275-281, 1998.\n[23] T. Qin, T.-Y. Liu, X.-D. Zhang, Z. Chen, and W.-Y. Ma. A\nstudy of relevance propagation for web search. In SIGIR 28,\npages 408-415, 2005.\n[24] S. E. Robertson and D. A. Hull. The TREC-9 filtering track\nfinal report. In TREC, pages 25-40, 2000.\n[25] R. E. Schapire, Y. Freund, P. Barlett, and W. S. Lee. Boosting\nthe margin: A new explanation for the effectiveness of voting\nmethods. In ICML 14, pages 322-330, 1997.\n[26] R. E. Schapire and Y. Singer. Improved boosting algorithms\nusing confidence-rated predictions. Mach. Learn.,\n37(3):297-336, 1999.\n[27] R. Song, J. Wen, S. Shi, G. Xin, T. yan Liu, T. Qin, X. Zheng,\nJ. Zhang, G. Xue, and W.-Y. Ma. Microsoft Research Asia at\nweb track and terabyte track of TREC 2004. In TREC, 2004.\n[28] A. Trotman. Learning to rank. Inf. Retr., 8(3):359-381, 2005.\n[29] J. Xu, Y. Cao, H. Li, and Y. Huang. Cost-sensitive learning\nof SVM for ranking. In ECML, pages 833-840, 2006.\n[30] G.-R. Xue, Q. Yang, H.-J. Zeng, Y. Yu, and Z. Chen.\nExploiting the hierarchical structure for link analysis. In\nSIGIR 28, pages 186-193, 2005.\n[31] H. Yu. SVM selective sampling for ranking with application\nto data retrieval. In SIGKDD 11, pages 354-363, 2005.\nAPPENDIX\nHere we give the proof of Theorem 1.\nP\uf772\uf76f\uf76f\uf766. Set ZT = m\ni=1 exp {\u2212E(\u03c0(qi, di, fT ), yi)} and \u03c6(t) = 1\n2\n(1 +\n\u03d5(t)). According to the definition of \u03b1t, we know that e\u03b1t = \u03c6(t)\n1\u2212\u03c6(t)\n.\nZT =\nm\ni=1\nexp {\u2212E(\u03c0(qi, di, fT\u22121 + \u03b1T hT ), yi)}\n=\nm\ni=1\nexp \u2212E(\u03c0(qi, di, fT\u22121), yi) \u2212 \u03b1T E(\u03c0(qi, di, hT ), yi) \u2212 \u03b4T\ni\n\u2264\nm\ni=1\nexp {\u2212E(\u03c0(qi, di, fT\u22121), yi)} exp {\u2212\u03b1T E(\u03c0(qi, di, hT ), yi)} e\u2212\u03b4T\nmin\n= e\u2212\u03b4T\nmin ZT\u22121\nm\ni=1\nexp {\u2212E(\u03c0(qi, di, fT\u22121), yi)}\nZT\u22121\nexp{\u2212\u03b1T E(\u03c0(qi, di, hT ), yi)}\n= e\u2212\u03b4T\nmin ZT\u22121\nm\ni=1\nPT (i) exp{\u2212\u03b1T E(\u03c0(qi, di, hT ), yi)}.\nMoreover, if E(\u03c0(qi, di, hT ), yi) \u2208 [\u22121, +1] then,\nZT \u2264 e\u2212\u03b4T\nminZT\u22121\nm\ni=1\nPT (i)\n1+E(\u03c0(qi, di, hT ), yi)\n2\ne\u2212\u03b1T\n+\n1\u2212E(\u03c0(qi, di, hT ), yi)\n2\ne\u03b1T\n= e\u2212\u03b4T\nmin ZT\u22121\n\uf8eb\n\uf8ec\uf8ec\uf8ec\uf8ec\uf8ec\uf8ec\uf8ed\u03c6(T)\n1 \u2212 \u03c6(T)\n\u03c6(T)\n+ (1 \u2212 \u03c6(T))\n\u03c6(T)\n1 \u2212 \u03c6(T)\n\uf8f6\n\uf8f7\uf8f7\uf8f7\uf8f7\uf8f7\uf8f7\uf8f8\n= ZT\u22121e\u2212\u03b4T\nmin 4\u03c6(T)(1 \u2212 \u03c6(T))\n\u2264 ZT\u22122\nT\nt=T\u22121\ne\u2212\u03b4t\nmin 4\u03c6(t)(1 \u2212 \u03c6(t))\n\u2264 Z1\nT\nt=2\ne\u2212\u03b4t\nmin 4\u03c6(t)(1 \u2212 \u03c6(t))\n= m\nm\ni=1\n1\nm\nexp{\u2212E(\u03c0(qi, di, \u03b11h1), yi)}\nT\nt=2\ne\u2212\u03b4t\nmin 4\u03c6(t)(1 \u2212 \u03c6(t))\n= m\nm\ni=1\n1\nm\nexp{\u2212\u03b11E(\u03c0(qi, di, h1), yi) \u2212 \u03b41\ni }\nT\nt=2\ne\u2212\u03b4t\nmin 4\u03c6(t)(1 \u2212 \u03c6(t))\n\u2264 me\u2212\u03b41\nmin\nm\ni=1\n1\nm\nexp{\u2212\u03b11E(\u03c0(qi, di, h1), yi)}\nT\nt=2\ne\u2212\u03b4t\nmin 4\u03c6(t)(1 \u2212 \u03c6(t))\n\u2264 m e\u2212\u03b41\nmin 4\u03c6(1)(1 \u2212 \u03c6(1))\nT\nt=2\ne\u2212\u03b4t\nmin 4\u03c6(t)(1 \u2212 \u03c6(t))\n= m\nT\nt=1\ne\u2212\u03b4t\nmin 1 \u2212 \u03d5(t)2.\n\u2234\n1\nm\nm\ni=1\nE(\u03c0(qi, di, fT ), yi) \u2265\n1\nm\nm\ni=1\n{1 \u2212 exp(\u2212E(\u03c0(qi, di, fT ), yi))}\n\u2265 1 \u2212\nT\nt=1\ne\u2212\u03b4t\nmin 1 \u2212 \u03d5(t)2.", "keywords": "support vector machine;trained ranking model;rankboost;weak ranker;ranking model tuning;ranking model;boost;novel learning algorithm;learn to rank;training process;machine learning;new learning algorithm;document retrieval;information retrieval;re-weighted training datum"}
{"name": "train_H-37", "title": "Relaxed Online SVMs for Spam Filtering", "abstract": "Spam is a key problem in electronic communication, including large-scale email systems and the growing number of blogs. Content-based filtering is one reliable method of combating this threat in its various forms, but some academic researchers and industrial practitioners disagree on how best to filter spam. The former have advocated the use of Support Vector Machines (SVMs) for content-based filtering, as this machine learning methodology gives state-of-the-art performance for text classification. However, similar performance gains have yet to be demonstrated for online spam filtering. Additionally, practitioners cite the high cost of SVMs as reason to prefer faster (if less statistically robust) Bayesian methods. In this paper, we offer a resolution to this controversy. First, we show that online SVMs indeed give state-of-the-art classification performance on online spam filtering on large benchmark data sets. Second, we show that nearly equivalent performance may be achieved by a Relaxed Online SVM (ROSVM) at greatly reduced computational cost. Our results are experimentally verified on email spam, blog spam, and splog detection tasks.", "fulltext": "1. INTRODUCTION\nElectronic communication is increasingly plagued by\nunwanted or harmful content known as spam. The most well\nknown form of spam is email spam, which remains a major\nproblem for large email systems. Other forms of spam are\nalso becoming problematic, including blog spam, in which\nspammers post unwanted comments in blogs [21], and splogs,\nwhich are fake blogs constructed to enable link spam with\nthe hope of boosting the measured importance of a given\nwebpage in the eyes of automated search engines [17]. There\nare a variety of methods for identifying these many forms\nof spam, including compiling blacklists of known spammers,\nand conducting link analysis.\nThe approach of content analysis has shown particular\npromise and generality for combating spam. In content\nanalysis, the actual message text (often including hyper-text and\nmeta-text, such as HTML and headers) is analyzed using\nmachine learning techniques for text classification to\ndetermine if the given content is spam. Content analysis has\nbeen widely applied in detecting email spam [11], and has\nalso been used for identifying blog spam [21] and splogs [17].\nIn this paper, we do not explore the related problem of link\nspam, which is currently best combated by link analysis [13].\n1.1 An Anti-Spam Controversy\nThe anti-spam community has been divided on the choice\nof the best machine learning method for content-based spam\ndetection. Academic researchers have tended to favor the\nuse of Support Vector Machines (SVMs), a statistically\nrobust machine learning method [7] which yields\nstate-of-theart performance on general text classification [14]. However,\nSVMs typically require training time that is quadratic in the\nnumber of training examples, and are impractical for\nlargescale email systems. Practitioners requiring content-based\nspam filtering have typically chosen to use the faster (if\nless statistically robust) machine learning method of Naive\nBayes text classification [11, 12, 20]. This Bayesian method\nrequires only linear training time, and is easily implemented\nin an online setting with incremental updates. This allows a\ndeployed system to easily adapt to a changing environment\nover time. Other fast methods for spam filtering include\ncompression models [1] and logistic regression [10]. It has\nnot yet been empirically demonstrated that SVMs give\nimproved performance over these methods in an online spam\ndetection setting [4].\n1.2 Contributions\nIn this paper, we address the anti-spam controversy and\noffer a potential resolution. We first demonstrate that\nonline SVMs do indeed provide state-of-the-art spam detection\nthrough empirical tests on several large benchmark data sets\nof email spam. We then analyze the effect of the tradeoff\nparameter in the SVM objective function, which shows that\nthe expensive SVM methodology may, in fact, be overkill for\nspam detection. We reduce the computational cost of SVM\nlearning by relaxing this requirement on the maximum\nmargin in online settings, and create a Relaxed Online SVM,\nROSVM, appropriate for high performance content-based\nspam filtering in large-scale settings.\n2. SPAM AND ONLINE SVMS\nThe controversy between academics and practitioners in\nspam filtering centers on the use of SVMs. The former\nadvocate their use, but have yet to demonstrate strong\nperformance with SVMs on online spam filtering. Indeed, the\nresults of [4] show that, when used with default parameters,\nSVMs actually perform worse than other methods. In this\nsection, we review the basic workings of SVMs and describe\na simple Online SVM algorithm. We then show that Online\nSVMs indeed achieve state-of-the-art performance on\nfiltering email spam, blog comment spam, and splogs, so long as\nthe tradeoff parameter C is set to a high value. However, the\ncost of Online SVMs turns out to be prohibitive for\nlargescale applications. These findings motivate our proposal of\nRelaxed Online SVMs in the following section.\n2.1 Background: SVMs\nSVMs are a robust machine learning methodology which\nhas been shown to yield state-of-the-art performance on text\nclassification [14]. by finding a hyperplane that separates\ntwo classes of data in data space while maximizing the\nmargin between them.\nWe use the following notation to describe SVMs, which\ndraws from [23]. A data set X contains n labeled example\nvectors {(x1, y1) . . . (xn, yn)}, where each xi is a vector\ncontaining features describing example i, and each yi is the class\nlabel for that example. In spam detection, the classes spam\nand ham (i.e., not spam) are assigned the numerical class\nlabels +1 and \u22121, respectively. The linear SVMs we employ\nin this paper use a hypothesis vector w and bias term b to\nclassify a new example x, by generating a predicted class\nlabel f(x):\nf(x) = sign(< w, x > +b)\nSVMs find the hypothesis w, which defines the separating\nhyperplane, by minimizing the following objective function\nover all n training examples:\n\u03c4(w, \u03be) =\n1\n2\n||w||2\n+ C\nnX\ni=i\n\u03bei\nunder the constraints that\n\u2200i = {1..n} : yi(< w, xi > +b) \u2265 1 \u2212 \u03bei, \u03bei \u2265 0\nIn this objective function, each slack variable \u03bei shows the\namount of error that the classifier makes on a given example\nxi. Minimizing the sum of the slack variables corresponds\nto minimizing the loss function on the training data, while\nminimizing the term 1\n2\n||w||2\ncorresponds to maximizing the\nmargin between the two classes [23]. These two optimization\ngoals are often in conflict; the tradeoff parameter C\ndetermines how much importance to give each of these tasks.\nLinear SVMs exploit data sparsity to classify a new\ninstance in O(s) time, where s is the number of non-zero\nfeatures. This is the same classification time as other linear\nGiven: data set X = (x1, y1), . . . , (xn, yn), C, m:\nInitialize w := 0, b := 0, seenData := { }\nFor Each xi \u2208 X do:\nClassify xi using f(xi) = sign(< w, xi > +b)\nIF yif(xi) < 1\nFind w , b using SMO on seenData,\nusing w, b as seed hypothesis.\nAdd xi to seenData\ndone\nFigure 1: Pseudo code for Online SVM.\nclassifiers, and as Naive Bayesian classification. Training\nSVMs, however, typically takes O(n2\n) time, for n training\nexamples. A variant for linear SVMs was recently proposed\nwhich trains in O(ns) time [15], but because this method\nhas a high constant, we do not explore it here.\n2.2 Online SVMs\nIn many traditional machine learning applications, SVMs\nare applied in batch mode. That is, an SVM is trained on\nan entire set of training data, and is then tested on a\nseparate set of testing data. Spam filtering is typically tested\nand deployed in an online setting, which proceeds\nincrementally. Here, the learner classifies a new example, is told if\nits prediction is correct, updates its hypothesis accordingly,\nand then awaits a new example. Online learning allows a\ndeployed system to adapt itself in a changing environment.\nRe-training an SVM from scratch on the entire set of\npreviously seen data for each new example is cost prohibitive.\nHowever, using an old hypothesis as the starting point for\nre-training reduces this cost considerably. One method of\nincremental and decremental SVM learning was proposed in\n[2]. Because we are only concerned with incremental\nlearning, we apply a simpler algorithm for converting a batch\nSVM learner into an online SVM (see Figure 1 for\npseudocode), which is similar to the approach of [16].\nEach time the Online SVM encounters an example that\nwas poorly classified, it retrains using the old hypothesis as\na starting point. Note that due to the Karush-Kuhn-Tucker\n(KKT) conditions, it is not necessary to re-train on\nwellclassified examples that are outside the margins [23].\nWe used Platt\"s SMO algorithm [22] as a core SVM solver,\nbecause it is an iterative method that is well suited to\nconverge quickly from a good initial hypothesis. Because\nprevious work (and our own initial testing) indicates that binary\nfeature values give the best results for spam filtering [20,\n9], we optimized our implementation of the Online SMO to\nexploit fast inner-products with binary vectors. 1\n2.3 Feature Mapping Spam Content\nExtracting machine learning features from text may be\ndone in a variety of ways, especially when that text may\ninclude hyper-content and meta-content such as HTML and\nheader information. However, previous research has shown\nthat simple methods from text classification, such as bag\nof words vectors, and overlapping character-level n-grams,\ncan achieve strong results [9]. Formally, a bag of words\nvector is a vector x with a unique dimension for each possible\n1\nOur source code is freely available at\nwww.cs.tufts.edu/\u223cdsculley/onlineSMO.\n1\n0.999\n0.995\n0.99\n0.985\n0.98\n0.1 1 10 100 1000\nROCArea\nC\n2-grams\n3-grams\n4-grams\nwords\nFigure 2: Tuning the Tradeoff Parameter C. Tests\nwere conducted with Online SMO, using binary\nfeature vectors, on the spamassassin data set of 6034\nexamples. Graph plots C versus Area under the\nROC curve.\nword, defined as a contiguous substring of non-whitespace\ncharacters. An n-gram vector is a vector x with a unique\ndimension for each possible substring of n total characters.\nNote that n-grams may include whitespace, and are\noverlapping. We use binary feature scoring, which has been shown\nto be most effective for a variety of spam detection\nmethods [20, 9]. We normalize the vectors with the Euclidean\nnorm. Furthermore, with email data, we reduce the impact\nof long messages (for example, with attachments) by\nconsidering only the first 3,000 characters of each string. For blog\ncomments and splogs, we consider the whole text,\nincluding any meta-data such as HTML tags, as given. No other\nfeature selection or domain knowledge was used.\n2.4 Tuning the Tradeoff Parameter, C\nThe SVM tradeoff parameter C must be tuned to balance\nthe (potentially conflicting) goals of maximizing the\nmargin and minimizing the training error. Early work on SVM\nbased spam detection [9] showed that high values of C give\nbest performance with binary features. Later work has not\nalways followed this lead: a (low) default setting of C was\nused on splog detection [17], and also on email spam [4].\nFollowing standard machine learning practice, we tuned C\non separate tuning data not used for later testing. We used\nthe publicly available spamassassin email spam data set,\nand created an online learning task by randomly interleaving\nall 6034 labeled messages to create a single ordered set.\nFor tuning, we performed a coarse parameter search for C\nusing powers of ten from .0001 to 10000. We used the Online\nSVM described above, and tested both binary bag of words\nvectors and n-gram vectors with n = {2, 3, 4}. We used the\nfirst 3000 characters of each message, which included header\ninformation, body of the email, and possibly attachments.\nFollowing the recommendation of [6], we use Area under\nthe ROC curve as our evaluation measure. The results (see\nFigure 2) agree with [9]: there is a plateau of high\nperformance achieved with all values of C \u2265 10, and performance\ndegrades sharply with C < 1. For the remainder of our\nexperiments with SVMs in this paper, we set C = 100. We\nwill return to the observation that very high values of C do\nnot degrade performance as support for the intuition that\nrelaxed SVMs should perform well on spam.\nTable 1: Results for Email Spam filtering with\nOnline SVM on benchmark data sets. Score reported\nis (1-ROCA)%, where 0 is optimal.\ntrec05p-1 trec06p\nOnSVM: words 0.015 (.011-.022) 0.034 (.025-.046)\n3-grams 0.011 (.009-.015) 0.025 (.017-.035)\n4-grams 0.008 (.007-.011) 0.023 (.017-.032)\nSpamProbe 0.059 (.049-.071) 0.092 (.078-.110)\nBogoFilter 0.048 (.038-.062) 0.077 (.056-.105)\nTREC Winners 0.019 (.015-.023) 0.054 (.034-.085)\n53-Ensemble 0.007 (.005-.008) 0.020 (.007-.050)\nTable 2: Results for Blog Comment Spam Detection\nusing SVMs and Leave One Out Cross Validation.\nWe report the same performance measures as in the\nprior work for meaningful comparison.\naccuracy precision recall\nSVM C = 100: words 0.931 0.946 0.954\n3-grams 0.951 0.963 0.965\n4-grams 0.949 0.967 0.956\nPrior best method 0.83 0.874 0.874\n2.5 Email Spam and Online SVMs\nWith C tuned on a separate tuning set, we then tested the\nperformance of Online SVMs in spam detection. We used\ntwo large benchmark data sets of email spam as our test\ncorpora. These data sets are the 2005 TREC public data set\ntrec05p-1 of 92,189 messages, and the 2006 TREC public\ndata sets, trec06p, containing 37,822 messages in English.\n(We do not report our strong results on the trec06c corpus\nof Chinese messages as there have been questions raised over\nthe validity of this test set.) We used the canonical ordering\nprovided with each of these data sets for fair comparison.\nResults for these experiments, with bag of words vectors\nand and n-gram vectors appear in Table 1. To compare our\nresults with previous scores on these data sets, we use the\nsame (1-ROCA)% measure described in [6], which is one\nminus the area under the ROC curve, expressed as a percent.\nThis measure shows the percent chance of error made by\na classifier asserting that one message is more likely to be\nspam than another. These results show that Online SVMs\ndo give state of the art performance on email spam. The\nonly known system that out-performs the Online SVMs on\nthe trec05p-1 data set is a recent ensemble classifier which\ncombines the results of 53 unique spam filters [19]. To\nour knowledge, the Online SVM has out-performed every\nother single filter on these data sets, including those using\nBayesian methods [5, 3], compression models [5, 3], logistic\nregression [10], and perceptron variants [3], the TREC\ncompetition winners [5, 3], and open source email spam filters\nBogoFilter v1.1.5 and SpamProbe v1.4d.\n2.6 Blog Comment Spam and SVMs\nBlog comment spam is similar to email spam in many\nregards, and content-based methods have been proposed for\ndetecting these spam comments [21]. However, large\nbenchmark data sets of labeled blog comment spam do not yet\nexist. Thus, we run experiments on the only publicly available\ndata set we know of, which was used in content-based blog\nTable 3: Results for Splog vs. Blog Detection using\nSVMs and Leave One Out Cross Validation. We\nreport the same evaluation measures as in the prior\nwork for meaningful comparison.\nfeatures precision recall F1\nSVM C = 100: words 0.921 0.870 0.895\n3-grams 0.904 0.866 0.885\n4-grams 0.928 0.876 0.901\nPrior SVM with: words 0.887 0.864 0.875\n4-grams 0.867 0.844 0.855\nwords+urls 0.893 0.869 0.881\ncomment spam detection experiments by [21]. Because of\nthe small size of the data set, and because prior researchers\ndid not conduct their experiments in an on-line setting, we\ntest the performance of linear SVMs using leave-one-out\ncross validation, with SVM-Light, a standard open-source\nSVM implementation [14]. We use the parameter setting\nC = 100, with the same feature space mappings as above.\nWe report accuracy, precision, and recall to compare these to\nthe results given on the same data set by [21]. These results\n(see Table 2) show that SVMs give superior performance on\nthis data set to the prior methodology.\n2.7 Splogs and SVMs\nAs with blog comment spam, there is not yet a large,\npublicly available benchmark corpus of labeled splog detection\ntest data. However, the authors of [17] kindly provided us\nwith the labeled data set of 1,389 blogs and splogs that they\nused to test content-based splog detection using SVMs. The\nonly difference between our methodology and that of [17] is\nthat they used default parameters for C, which SVM-Light\nsets to 1\navg||x||2\n. (For normalized vectors, this default value\nsets C = 1.) They also tested several domain-informed\nfeature mappings, such as giving special features to url tags.\nFor our experiments, we used the same feature mappings\nas above, and tested the effect of setting C = 100. As with\nthe methodology of [17], we performed leave one out cross\nvalidation for apples-to-apples comparison on this data. The\nresults (see Table 3) show that a high value of C produces\nhigher performance for the same feature space mappings,\nand even enables the simple 4-gram mapping to out-perform\nthe previous best mapping which incorporated domain\nknowledge by using words and urls.\n2.8 Computational Cost\nThe results presented in this section demonstrate that\nlinfeatures trec06p trec05p-1\nwords 12196s 66478s\n3-grams 44605s 128924s\n4-grams 87519s 242160s\ncorpus size 32822 92189\nTable 4: Execution time for Online SVMs with email\nspam detection, in CPU seconds. These times do\nnot include the time spent mapping strings to\nfeature vectors. The number of examples in each data\nset is given in the last row as corpus size.\nA\nB\nFigure 3: Visualizing the effect of C.\nHyperplane A maximizes the margin while accepting a\nsmall amount of training error. This corresponds\nto setting C to a low value. Hyperplane B\naccepts a smaller margin in order to reduce\ntraining error. This corresponds to setting C to a high\nvalue. Content-based spam filtering appears to do\nbest with high values of C.\near SVMs give state of the art performance on content-based\nspam filtering. However, this performance comes at a price.\nAlthough the blog comment spam and splog data sets are\ntoo small for the quadratic training time of SVMs to\nappear problematic, the email data sets are large enough to\nillustrate the problems of quadratic training cost.\nTable 4 shows computation time versus data set size for\neach of the online learning tasks (on same system). The\ntraining cost of SVMs are prohibitive for large-scale content\nbased spam detection, or a large blog host. In the\nfollowing section, we reduce this cost by relaxing the expensive\nrequirements of SVMs.\n3. RELAXED ONLINE SVMS (ROSVM)\nOne of the main benefits of SVMs is that they find a\ndecision hyperplane that maximizes the margin between classes\nin the data space. Maximizing the margin is expensive,\ntypically requiring quadratic training time in the number\nof training examples. However, as we saw in the previous\nsection, the task of content-based spam detection is best\nachieved by SVMs with a high value of C. Setting C to a\nhigh value for this domain implies that minimizing\ntraining loss is more important than maximizing the margin (see\nFigure 3).\nThus, while SVMs do create high performance spam\nfilters, applying them in practice is overkill. The full margin\nmaximization feature that they provide is unnecessary, and\nrelaxing this requirement can reduce computational cost.\nWe propose three ways to relax Online SVMs:\n\u2022 Reduce the size of the optimization problem by only\noptimizing over the last p examples.\n\u2022 Reduce the number of training updates by only\ntraining on actual errors.\n\u2022 Reduce the number of iterations in the iterative SVM\nGiven: dataset X = (x1, y1), . . . , (xn, yn), C, m, p:\nInitialize w := 0, b := 0, seenData := { }\nFor Each xi \u2208 X do:\nClassify xi using f(xi) = sign(< w, xi > +b)\nIf yif(xi) < m\nFind w , b with SMO on seenData,\nusing w, b as seed hypothesis.\nset (w, b) := (w\",b\")\nIf size(seenData) > p\nremove oldest example from seenData\nAdd xi to seenData\ndone\nFigure 4: Pseudo-code for Relaxed Online SVM.\nsolver by allowing an approximate solution to the\noptimization problem.\nAs we describe in the remainder of this subsection, all of\nthese methods trade statistical robustness for reduced\ncomputational cost. Experimental results reported in the\nfollowing section show that they equal or approach the\nperformance of full Online SVMs on content-based spam detection.\n3.1 Reducing Problem Size\nIn the full Online SVMs, we re-optimize over the full set\nof seen data on every update, which becomes expensive as\nthe number of seen data points grows. We can bound this\nexpense by only considering the p most recent examples for\noptimization (see Figure 4 for pseudo-code).\nNote that this is not equivalent to training a new SVM\nclassifier from scratch on the p most recent examples,\nbecause each successive optimization problem is seeded with\nthe previous hypothesis w [8]. This hypothesis may contain\nvalues for features that do not occur anywhere in the p most\nrecent examples, and these will not be changed. This allows\nthe hypothesis to remember rare (but informative) features\nthat were learned further than p examples in the past.\nFormally, the optimization problem is now defined most\nclearly in the dual form [23]. In this case, the original\nsoftmargin SVM is computed by maximizing at example n:\nW (\u03b1) =\nnX\ni=1\n\u03b1i \u2212\n1\n2\nnX\ni,j=1\n\u03b1i\u03b1jyiyj < xi, xj >,\nsubject to the previous constraints [23]:\n\u2200i \u2208 {1, . . . , n} : 0 \u2264 \u03b1i \u2264 C and\nnX\ni=1\n\u03b1iyi = 0\nTo this, we add the additional lookback buffer constraint\n\u2200j \u2208 {1, . . . , (n \u2212 p)} : \u03b1j = cj\nwhere cj is a constant, fixed as the last value found for \u03b1j\nwhile j > (n \u2212 p). Thus, the margin found by an\noptimization is not guaranteed to be one that maximizes the margin\nfor the global data set of examples {x1, . . . , xn)}, but rather\none that satisfies a relaxed requirement that the margin be\nmaximized over the examples { x(n\u2212p+1), . . . , xn}, subject\nto the fixed constraints on the hyperplane that were found\nin previous optimizations over examples {x1, . . . , x(n\u2212p)}.\n(For completeness, when p \u2265 n, define (n \u2212 p) = 1.) This\nset of constraints reduces the number of free variables in the\noptimization problem, reducing computational cost.\n3.2 Reducing Number of Updates\nAs noted before, the KKT conditions show that a well\nclassified example will not change the hypothesis; thus it is\nnot necessary to re-train when we encounter such an\nexample. Under the KKT conditions, an example xi is considered\nwell-classified when yif(xi) > 1. If we re-train on every\nexample that is not well-classified, our hyperplane will be\nguaranteed to be optimal at every step.\nThe number of re-training updates can be reduced by\nrelaxing the definition of well classified. An example xi is\nnow considered well classified when yif(xi) > M, for some\n0 \u2264 M \u2264 1. Here, each update still produces an optimal\nhyperplane. The learner may encounter an example that lies\nwithin the margins, but farther from the margins than M.\nSuch an example means the hypothesis is no longer globally\noptimal for the data set, but it is considered good enough\nfor continued use without immediate retraining.\nThis update procedure is similar to that used by\nvariants of the Perceptron algorithm [18]. In the extreme case,\nwe can set M = 0, which creates a mistake driven Online\nSVM. In the experimental section, we show that this\nversion of Online SVMs, which updates only on actual errors,\ndoes not significantly degrade performance on content-based\nspam detection, but does significantly reduce cost.\n3.3 Reducing Iterations\nAs an iterative solver, SMO makes repeated passes over\nthe data set to optimize the objective function. SMO has\none main loop, which can alternate between passing over\nthe entire data set, or the smaller active set of current\nsupport vectors [22]. Successive iterations of this loop bring\nthe hyperplane closer to an optimal value. However, it is\npossible that these iterations provide less benefit than their\nexpense justifies. That is, a close first approximation may\nbe good enough. We introduce a parameter T to control the\nmaximum number of iterations we allow. As we will see in\nthe experimental section, this parameter can be set as low\nas 1 with little impact on the quality of results, providing\ncomputational savings.\n4. EXPERIMENTS\nIn Section 2, we argued that the strong performance on\ncontent-based spam detection with SVMs with a high value\nof C show that the maximum margin criteria is overkill,\nincurring unnecessary computational cost. In Section 3, we\nproposed ROSVM to address this issue, as both of these\nmethods trade away guarantees on the maximum margin\nhyperplane in return for reduced computational cost. In this\nsection, we test these methods on the same benchmark data\nsets to see if state of the art performance may be achieved by\nthese less costly methods. We find that ROSVM is capable\nof achieving these high levels of performance with greatly\nreduced cost. Our main tests on content-based spam\ndetection are performed on large benchmark sets of email data.\nWe then apply these methods on the smaller data sets of\nblog comment spam and blogs, with similar performance.\n4.1 ROSVM Tests\nIn Section 3, we proposed three approaches for reducing\nthe computational cost of Online SMO: reducing the\nprob0.005\n0.01\n0.025\n0.05\n0.1\n10 100 1000 10000 100000\n(1-ROCA)%\nBuffer Size\ntrec05p-1\ntrec06p\n0\n50000\n100000\n150000\n200000\n250000\n10 100 1000 10000 100000\nCPUSec.\nBuffer Size\ntrec05p-1\ntrec06p\nFigure 5: Reduced Size Tests.\nlem size, reducing the number of optimization iterations,\nand reducing the number of training updates. Each of these\napproaches relax the maximum margin criteria on the global\nset of previously seen data. Here we test the effect that each\nof these methods has on both effectiveness and efficiency. In\neach of these tests, we use the large benchmark email data\nsets, trec05p-1 and trec06p.\n4.1.1 Testing Reduced Size\nFor our first ROSVM test, we experiment on the effect\nof reducing the size of the optimization problem by only\nconsidering the p most recent examples, as described in the\nprevious section. For this test, we use the same 4-gram\nmappings as for the reference experiments in Section 2, with the\nsame value C = 100. We test a range of values p in a coarse\ngrid search. Figure 5 reports the effect of the buffer size p in\nrelationship to the (1-ROCA)% performance measure (top),\nand the number of CPU seconds required (bottom).\nThe results show that values of p < 100 do result in\ndegraded performance, although they evaluate very quickly.\nHowever, p values from 500 to 10,000 perform almost as\nwell as the original Online SMO (represented here as p =\n100, 000), at dramatically reduced computational cost.\nThese results are important for making state of the art\nperformance on large-scale content-based spam detection\npractical with online SVMs. Ordinarily, the training time\nwould grow quadratically with the number of seen examples.\nHowever, fixing a value of p ensures that the training time\nis independent of the size of the data set. Furthermore, a\nlookback buffer allows the filter to adjust to concept drift.\n0.005\n0.01\n0.025\n0.05\n0.1\n10521\n(1-ROCA)%\nMax Iters.\ntrec06p\ntrec05p-1\n50000\n100000\n150000\n200000\n250000\n10521\nCPUSec.\nMax Iters.\ntrec06p\ntrec05p-1\nFigure 6: Reduced Iterations Tests.\n4.1.2 Testing Reduced Iterations\nIn the second ROSVM test, we experiment with reducing\nthe number of iterations. Our initial tests showed that the\nmaximum number of iterations used by Online SMO was\nrarely much larger than 10 on content-based spam detection;\nthus we tested values of T = {1, 2, 5, \u221e}. Other parameters\nwere identical to the original Online SVM tests.\nThe results on this test were surprisingly stable (see\nFigure 6). Reducing the maximum number of SMO iterations\nper update had essentially no impact on classification\nperformance, but did result in a moderate increase in speed. This\nsuggests that any additional iterations are spent attempting\nto find improvements to a hyperplane that is already very\nclose to optimal. These results show that for content-based\nspam detection, we can reduce computational cost by\nallowing only a single SMO iteration (that is, T = 1) with\neffectively equivalent performance.\n4.1.3 Testing Reduced Updates\nFor our third ROSVM experiment, we evaluate the impact\nof adjusting the parameter M to reduce the total number of\nupdates. As noted before, when M = 1, the hyperplane is\nglobally optimal at every step. Reducing M allows a slightly\ninconsistent hyperplane to persist until it encounters an\nexample for which it is too inconsistent. We tested values of\nM from 0 to 1, at increments of 0.1. (Note that we used\np = 10000 to decrease the cost of evaluating these tests.)\nThe results for these tests are appear in Figure 7, and\nshow that there is a slight degradation in performance with\nreduced values of M, and that this degradation in\nperformance is accompanied by an increase in efficiency. Values of\n0.005\n0.01\n0.025\n0.05\n0.1\n0 0.2 0.4 0.6 0.8 1\n(1-ROCA)%\nM\ntrec05p-1\ntrec06p\n5000\n10000\n15000\n20000\n25000\n30000\n35000\n40000\n0 0.2 0.4 0.6 0.8 1\nCPUSec.\nM\ntrec05p-1\ntrec06p\nFigure 7: Reduced Updates Tests.\nM > 0.7 give effectively equivalent performance as M = 1,\nand still reduce cost.\n4.2 Online SVMs and ROSVM\nWe now compare ROSVM against Online SVMs on the\nemail spam, blog comment spam, and splog detection tasks.\nThese experiments show comparable performance on these\ntasks, at radically different costs. In the previous section,\nthe effect of the different relaxation methods was tested\nseparately. Here, we tested these methods together to\ncreate a full implementation of ROSVM. We chose the values\np = 10000, T = 1, M = 0.8 for the email spam detection\ntasks. Note that these parameter values were selected as\nthose allowing ROSVM to achieve comparable performance\nresults with Online SVMs, in order to test total difference\nin computational cost. The splog and blog data sets were\nmuch smaller, so we set p = 100 for these tasks to allow\nmeaningful comparisons between the reduced size and full\nsize optimization problems. Because these values were not\nhand-tuned, both generalization performance and runtime\nresults are meaningful in these experiments.\n4.2.1 Experimental Setup\nWe compared Online SVMs and ROSVM on email spam,\nblog comment spam, and splog detection. For the email\nspam, we used the two large benchmark corpora, trec05p-1\nand trec06p, in the standard online ordering. We randomly\nordered both the blog comment spam corpus and the splog\ncorpus to create online learning tasks. Note that this is a\ndifferent setting than the leave-one-out cross validation task\npresented on these corpora in Section 2 - the results are\nnot directly comparable. However, this experimental design\nTable 5: Email Spam Benchmark Data. These\nresults compare Online SVM and ROSVM on email\nspam detection, using binary 4-gram feature space.\nScore reported is (1-ROCA)%, where 0 is optimal.\ntrec05p-1 trec05p-1 trec06p trec06p\n(1-ROC)% CPUs (1-ROC)% CPUs\nOnSVM 0.0084 242,160 0.0232 87,519\nROSVM 0.0090 24,720 0.0240 18,541\nTable 6: Blog Comment Spam. These results\ncomparing Online SVM and ROSVM on blog comment\nspam detection using binary 4-gram feature space.\nAcc. Prec. Recall F1 CPUs\nOnSVM 0.926 0.930 0.962 0.946 139\nROSVM 0.923 0.925 0.965 0.945 11\ndoes allow meaningful comparison between our two online\nmethods on these content-based spam detection tasks.\nWe ran each method on each task, and report the results\nin Tables 5, 6, and 7. Note that the CPU time reported for\neach method was generated on the same computing system.\nThis time reflects only the time needed to complete online\nlearning on tokenized data. We do not report the time taken\nto tokenize the data into binary 4-grams, as this is the same\nadditive constant for all methods on each task. In all cases,\nROSVM was significantly less expensive computationally.\n4.3 Discussion\nThe comparison results shown in Tables 5, 6, and 7 are\nstriking in two ways. First, they show that the performance\nof Online SVMs can be matched and even exceeded by\nrelaxed margin methods. Second, they show a dramatic\ndisparity in computational cost. ROSVM is an order of\nmagnitude more efficient than the normal Online SVM, and gives\ncomparable results. Furthermore, the fixed lookback buffer\nensures that the cost of each update does not depend on the\nsize of the data set already seen, unlike Online SVMs. Note\nthe blog and splog data sets are relatively small, and results\non these data sets must be considered preliminary. Overall,\nthese results show that there is no need to pay the high cost\nof SVMs to achieve this level of performance on\ncontentbased detection of spam. ROSVMs offer a far cheaper\nalternative with little or no performance loss.\n5. CONCLUSIONS\nIn the past, academic researchers and industrial\npractitioners have disagreed on the best method for online\ncontentbased detection of spam on the web. We have presented one\nresolution to this debate. Online SVMs do, indeed,\nproTable 7: Splog Data Set. These results compare\nOnline SVM and ROSVM on splog detection using\nbinary 4-gram feature space.\nAcc. Prec. Recall F1 CPUs\nOnSVM 0.880 0.910 0.842 0.874 29353\nROSVM 0.878 0.902 0.849 0.875 1251\nduce state-of-the-art performance on this task with proper\nadjustment of the tradeoff parameter C, but with cost that\ngrows quadratically with the size of the data set. The high\nvalues of C required for best performance with SVMs show\nthat the margin maximization of Online SVMs is overkill for\nthis task. Thus, we have proposed a less expensive\nalternative, ROSVM, that relaxes this maximum margin\nrequirement, and produces nearly equivalent results. These\nmethods are efficient enough for large-scale filtering of\ncontentbased spam in its many forms.\nIt is natural to ask why the task of content-based spam\ndetection gets strong performance from ROSVM. After all, not\nall data allows the relaxation of SVM requirements. We\nconjecture that email spam, blog comment spam, and splogs all\nshare the characteristic that a subset of features are\nparticularly indicative of content being either spam or not spam.\nThese indicative features may be sparsely represented in the\ndata set, because of spam methods such as word obfuscation,\nin which common spam words are intentionally misspelled in\nan attempt to reduce the effectiveness of word-based spam\ndetection. Maximizing the margin may cause these sparsely\nrepresented features to be ignored, creating an overall\nreduction in performance. It appears that spam data is highly\nseparable, allowing ROSVM to be successful with high\nvalues of C and little effort given to maximizing the margin.\nFuture work will determine how applicable relaxed SVMs\nare to the general problem of text classification.\nFinally, we note that the success of relaxed SVM methods\nfor content-based spam detection is a result that depends\non the nature of spam data, which is potentially subject to\nchange. Although it is currently true that ham and spam\nare linearly separable given an appropriate feature space,\nthis assumption may be subject to attack. While our current\nmethods appear robust against primitive attacks along these\nlines, such as the good word attack [24], we must explore the\nfeasibility of more sophisticated attacks.\n6. REFERENCES\n[1] A. Bratko and B. Filipic. Spam filtering using\ncompression models. Technical Report IJS-DP-9227,\nDepartment of Intelligent Systems, Jozef Stefan\nInstitute, L jubljana, Slovenia, 2005.\n[2] G. Cauwenberghs and T. Poggio. Incremental and\ndecremental support vector machine learning. In\nNIPS, pages 409-415, 2000.\n[3] G. V. Cormack. TREC 2006 spam track overview. In\nTo appear in: The Fifteenth Text REtrieval\nConference (TREC 2006) Proceedings, 2006.\n[4] G. V. Cormack and A. Bratko. Batch and on-line\nspam filter comparison. In Proceedings of the Third\nConference on Email and Anti-Spam (CEAS), 2006.\n[5] G. V. Cormack and T. R. Lynam. TREC 2005 spam\ntrack overview. In The Fourteenth Text REtrieval\nConference (TREC 2005) Proceedings, 2005.\n[6] G. V. Cormack and T. R. Lynam. On-line supervised\nspam filter evaluation. Technical report, David R.\nCheriton School of Computer Science, University of\nWaterloo, Canada, February 2006.\n[7] N. Cristianini and J. Shawe-Taylor. An introduction to\nsupport vector machines. Cambridge University Press,\n2000.\n[8] D. DeCoste and K. Wagstaff. Alpha seeding for\nsupport vector machines. In KDD \"00: Proceedings of\nthe sixth ACM SIGKDD international conference on\nKnowledge discovery and data mining, pages 345-349,\n2000.\n[9] H. Drucker, V. Vapnik, and D. Wu. Support vector\nmachines for spam categorization. IEEE Transactions\non Neural Networks, 10(5):1048-1054, 1999.\n[10] J. Goodman and W. Yin. Online discriminative spam\nfilter training. In Proceedings of the Third Conference\non Email and Anti-Spam (CEAS), 2006.\n[11] P. Graham. A plan for spam. 2002.\n[12] P. Graham. Better bayesian filtering. 2003.\n[13] Z. Gyongi and H. Garcia-Molina. Spam: It\"s not just\nfor inboxes anymore. Computer, 38(10):28-34, 2005.\n[14] T. Joachims. Text categorization with suport vector\nmachines: Learning with many relevant features. In\nECML \"98: Proceedings of the 10th European\nConference on Machine Learning, pages 137-142,\n1998.\n[15] T. Joachims. Training linear svms in linear time. In\nKDD \"06: Proceedings of the 12th ACM SIGKDD\ninternational conference on Knowledge discovery and\ndata mining, pages 217-226, 2006.\n[16] J. Kivinen, A. Smola, and R. Williamson. Online\nlearning with kernels. In Advances in Neural\nInformation Processing Systems 14, pages 785-793.\nMIT Press, 2002.\n[17] P. Kolari, T. Finin, and A. Joshi. SVMs for the\nblogosphere: Blog identification and splog detection.\nAAAI Spring Symposium on Computational\nApproaches to Analyzing Weblogs, 2006.\n[18] W. Krauth and M. M\u00b4ezard. Learning algorithms with\noptimal stability in neural networks. Journal of\nPhysics A, 20(11):745-752, 1987.\n[19] T. Lynam, G. Cormack, and D. Cheriton. On-line\nspam filter fusion. In SIGIR \"06: Proceedings of the\n29th annual international ACM SIGIR conference on\nResearch and development in information retrieval,\npages 123-130, 2006.\n[20] V. Metsis, I. Androutsopoulos, and G. Paliouras.\nSpam filtering with naive bayes - which naive bayes?\nThird Conference on Email and Anti-Spam (CEAS),\n2006.\n[21] G. Mishne, D. Carmel, and R. Lempel. Blocking blog\nspam with language model disagreement. Proceedings\nof the 1st International Workshop on Adversarial\nInformation Retrieval on the Web (AIRWeb), May\n2005.\n[22] J. Platt. Sequenital minimal optimization: A fast\nalgorithm for training support vector machines. In\nB. Scholkopf, C. Burges, and A. Smola, editors,\nAdvances in Kernel Methods - Support Vector\nLearning. MIT Press, 1998.\n[23] B. Scholkopf and A. Smola. Learning with Kernels:\nSupport Vector Machines, Regularization,\nOptimization, and Beyond. MIT Press, 2001.\n[24] G. L. Wittel and S. F. Wu. On attacking statistical\nspam filters. CEAS: First Conference on Email and\nAnti-Spam, 2004.", "keywords": "logistic regression;support vector machine;feature mapping;bayesian method;hyperplane;link spam;spam filter;incremental update;link analysis;machine learning technique;blog;spam filtering;content-based spam detection;splog;content-based filtering"}
{"name": "train_H-38", "title": "DiffusionRank: A Possible Penicillin for Web Spamming", "abstract": "While the PageRank algorithm has proven to be very effective for ranking Web pages, the rank scores of Web pages can be manipulated. To handle the manipulation problem and to cast a new insight on the Web structure, we propose a ranking algorithm called DiffusionRank. DiffusionRank is motivated by the heat diffusion phenomena, which can be connected to Web ranking because the activities flow on the Web can be imagined as heat flow, the link from a page to another can be treated as the pipe of an air-conditioner, and heat flow can embody the structure of the underlying Web graph. Theoretically we show that DiffusionRank can serve as a generalization of PageRank when the heat diffusion coefficient \u03b3 tends to infinity. In such a case 1/\u03b3 = 0, DiffusionRank (PageRank) has low ability of anti-manipulation. When \u03b3 = 0, DiffusionRank obtains the highest ability of anti-manipulation, but in such a case, the web structure is completely ignored. Consequently, \u03b3 is an interesting factor that can control the balance between the ability of preserving the original Web and the ability of reducing the effect of manipulation. It is found empirically that, when \u03b3 = 1, DiffusionRank has a Penicillin-like effect on the link manipulation. Moreover, DiffusionRank can be employed to find group-to-group relations on the Web, to divide the Web graph into several parts, and to find link communities. Experimental results show that the DiffusionRank algorithm achieves the above mentioned advantages as expected.", "fulltext": "1. INTRODUCTION\nWhile the PageRank algorithm [13] has proven to be very\neffective for ranking Web pages, inaccurate PageRank\nresults are induced because of web page manipulations by\npeople for commercial interests. The manipulation problem is\nalso called the Web spam, which refers to hyperlinked pages\non the World Wide Web that are created with the intention\nof misleading search engines [7]. It is reported that\napproximately 70% of all pages in the .biz domain and about 35%\nof the pages in the .us domain belong to the spam category\n[12]. The reason for the increasing amount of Web spam is\nexplained in [12]: some web site operators try to influence\nthe positioning of their pages within search results because\nof the large fraction of web traffic originating from searches\nand the high potential monetary value of this traffic.\nFrom the viewpoint of the Web site operators who want\nto increase the ranking value of a particular page for search\nengines, Keyword Stuffing and Link Stuffing are being used\nwidely [7, 12]. From the viewpoint of the search engine\nmanagers, the Web spam is very harmful to the users\" evaluations\nand thus their preference to choosing search engines because\npeople believe that a good search engine should not return\nirrelevant or low-quality results. There are two methods\nbeing employed to combat the Web spam problem. Machine\nlearning methods are employed to handle the keyword\nstuffing. To successfully apply machine learning methods, we\nneed to dig out some useful textual features for Web pages,\nto mark part of the Web pages as either spam or non-spam,\nthen to apply supervised learning techniques to mark other\npages. For example, see [5, 12]. Link analysis methods are\nalso employed to handle the link stuffing problem. One\nexample is the TrustRank [7], a link-based method, in which\nthe link structure is utilized so that human labelled trusted\npages can propagate their trust scores trough their links.\nThis paper focuses on the link-based method.\nThe rest of the materials are organized as follows. In the\nnext section, we give a brief literature review on various\nrelated ranking techniques. We establish the Heat Diffusion\nModel (HDM) on various cases in Section 3, and propose\nDiffusionRank in Section 4. In Section 5, we describe the\ndata sets that we worked on and the experimental results.\nFinally, we draw conclusions in Section 6.\n2. LITERATURE REVIEW\nThe importance of a Web page is determined by either\nthe textual content of pages or the hyperlink structure or\nboth. As in previous work [7, 13], we focus on ranking\nmethods solely determined by hyperlink structure of the\nWeb graph. All the mentioned ranking algorithms are\nestablished on a graph. For our convenience, we first give some\nnotations. Denote a static graph by G = (V, E), where V =\n{v1, v2, . . . , vn}, E = {(vi, vj) | there is an edge from vi to\nvj}. Ii and di denote the in-degree and the out-degree of\npage i respectively.\n2.1 PageRank\nThe importance of a Web page is an inherently subjective\nmatter, which depends on the reader\"s interests, knowledge\nand attitudes [13]. However, the average importance of all\nreaders can be considered as an objective matter. PageRank\ntries to find such average importance based on the Web link\nstructure, which is considered to contain a large amount of\nstatistical data. The Web is modelled by a directed graph G\nin the PageRank algorithms, and the rank or importance\nxi for page vi \u2208 V is defined recursively in terms of pages\nwhich point to it: xi = (j,i)\u2208E aijxj, where aij is assumed\nto be 1/dj if there is a link from j to i, and 0 otherwise. Or\nin matrix terms, x = Ax. When the concept of random\njump is introduced, the matrix form is changed to\nx = [(1 \u2212 \u03b1)g1T\n+ \u03b1A]x, (1)\nwhere \u03b1 is the probability of following the actual link from a\npage, (1 \u2212 \u03b1) is the probability of taking a random jump,\nand g is a stochastic vector, i.e., 1T\ng = 1. Typically, \u03b1 =\n0.85, and g = 1\nn\n1 is one of the standard settings, where 1 is\nthe vector of all ones [6, 13].\n2.2 TrustRank\nTrustRank [7] is composed of two parts. The first part\nis the seed selection algorithm, in which the inverse\nPageRank was proposed to help an expert of determining a good\nnode. The second part is to utilize the biased PageRank,\nin which the stochastic distribution g is set to be shared by\nall the trusted pages found in the first part. Moreover, the\ninitial input of x is also set to be g. The justification for\nthe inverse PageRank and the solid experiments support its\nadvantage in combating the Web spam. Although there are\nmany variations of PageRank, e.g., a family of link-based\nranking algorithms in [2], TrustRank is especially chosen for\ncomparisons for three reasonss: (1) it is designed for\ncombatting spamming; (2) its fixed parameters make a\ncomparison easy; and (3) it has a strong theoretical relations with\nPageRank and DiffusionRank.\n2.3 Manifold Ranking\nIn [17], the idea of ranking on the data manifolds was\nproposed. The data points represented as vectors in Euclidean\nspace are considered to be drawn from a manifold. From\nthe data points on such a manifold, an undirected weighted\ngraph is created, then the weight matrix is given by the\nGaussian Kernel smoothing. While the manifold ranking\nalgorithm achieves an impressive result on ranking images,\nthe biased vector g and the parameter k in the general\npersonalized PageRank in [17] are unknown in the Web graph\nsetting; therefore we do not include it in the comparisons.\n2.4 Heat Diffusion\nHeat diffusion is a physical phenomena. In a medium,\nheat always flow from position with high temperature to\nposition with low temperature. Heat kernel is used to\ndescribe the amount of heat that one point receives from\nanother point. Recently, the idea of heat kernel on a manifold\nis borrowed in applications such as dimension reduction [3]\nand classification [9, 10, 14]. In these work, the input data\nis considered to lie in a special structure.\nAll the above topics are related to our work. The readers\ncan find that our model is a generalization of PageRank in\norder to resist Web manipulation, that we inherit the first\npart of TrustRank, that we borrow the concept of ranking on\nthe manifold to introduce our model, and that heat diffusion\nis a main scheme in this paper.\n3. HEAT DIFFUSION MODEL\nHeat diffusion provides us with another perspective about\nhow we can view the Web and also a way to calculate\nranking values. In this paper, the Web pages are considered to\nbe drawn from an unknown manifold, and the link structure\nforms a directed graph, which is considered as an\napproximation to the unknown manifold. The heat kernel established\non the Web graph is considered as the representation of the\nrelationship between Web pages. The temperature\ndistribution after a fixed time period, induced by a special initial\ntemperature distribution, is considered as the rank scores on\nthe Web pages. Before establishing the proposed models, we\nfirst show our motivations.\n3.1 Motivations\nThere are two points to explain that PageRank is\nsusceptible to web spam.\n\u2022 Over-democratic. There is a belief behind\nPageRank-all pages are born equal. This can be seen from\nthe equal voting ability of one page: the sum of each\ncolumn is equal to one. This equal voting ability of all\npages gives the chance for a Web site operator to\nincrease a manipulated page by creating a large number\nof new pages pointing to this page since all the newly\ncreated pages can obtain an equal voting right.\n\u2022 Input-independent. For any given non-zero initial\ninput, the iteration will converge to the same stable\ndistribution corresponding to the maximum eigenvalue\n1 of the transition matrix. This input-independent\nproperty makes it impossible to set a special initial\ninput (larger values for trusted pages and less values even\nnegative values for spam pages) to avoid web spam.\nThe input-independent feature of PageRank can be further\nexplained as follows. P = [(1 \u2212 \u03b1)g1T\n+ \u03b1A] is a positive\nstochastic matrix if g is set to be a positive stochastic vector\n(the uniform distribution is one of such settings), and so the\nlargest eigenvalue is 1 and no other eigenvalue whose\nabsolute value is equal to 1, which is guaranteed by the Perron\nTheorem [11]. Let y be the eigenvector corresponding to 1,\nthen we have Py = y. Let {xk} be the sequence generated\nfrom the iterations xk+1 = Pxk, and x0 is the initial input.\nIf {xk} converges to x, then xk+1 = Pxk implies that x\nmust satisfy Px = x. Since the only maximum eigenvalue\nis 1, we have x = cy where c is a constant, and if both x\nand y are normalized by their sums, then c = 1. The above\ndiscussions show that PageRank is independent of the initial\ninput x0.\nIn our opinion, g and \u03b1 are objective parameters\ndetermined by the users\" behaviors and preferences. A, \u03b1 and\ng are the true web structure. While A is obtained by a\ncrawler and the setting \u03b1 = 0.85 is accepted by the people,\nwe think that g should be determined by a user behavior\ninvestigation, something like [1]. Without any prior\nknowledge, g has to be set as g = 1\nn\n1.\nTrustRank model does not follow the true web structure\nby setting a biased g, but the effects of combatting\nspamming are achieved in [7]; PageRank is on the contrary in\nsome ways. We expect a ranking algorithm that has an\neffect of anti-manipulation as TrustRank while respecting the\ntrue web structure as PageRank.\nWe observe that the heat diffusion model is a natural way\nto avoid the over-democratic and input-independent feature\nof PageRank. Since heat always flows from a position with\nhigher temperatures to one with lower temperatures, points\nare not equal as some points are born with high\ntemperatures while others are born with low temperatures. On the\nother hand, different initial temperature distributions will\ngive rise to different temperature distributions after a fixed\ntime period. Based on these considerations, we propose the\nnovel DiffusionRank. This ranking algorithm is also\nmotivated by the viewpoint for the Web structure. We view\nall the Web pages as points drawn from a highly complex\ngeometric structure, like a manifold in a high dimensional\nspace. On a manifold, heat can flow from one point to\nanother through the underlying geometric structure in a given\ntime period. Different geometric structures determine\ndifferent heat diffusion behaviors, and conversely the diffusion\nbehavior can reflect the geometric structure. More\nspecifically, on the manifold, the heat flows from one point to\nanother point, and in a given time period, if one point x\nreceives a large amount of heat from another point y, we\ncan say x and y are well connected, and thus x and y have\na high similarity in the sense of a high mutual connection.\nWe note that on a point with unit mass, the temperature\nand the heat of this point are equivalent, and these two terms\nare interchangeable in this paper. In the following, we first\nshow the HDM on a manifold, which is the origin of HDM,\nbut cannot be employed to the World Wide Web directly,\nand so is considered as the ideal case. To connect the ideal\ncase and the practical case, we then establish HDM on a\ngraph as an intermediate case. To model the real world\nproblem, we further build HDM on a random graph as a\npractical case. Finally we demonstrate the DiffusionRank\nwhich is derived from the HDM on a random graph.\n3.2 Heat Flow On a Known Manifold\nIf the underlying manifold is known, the heat flow\nthroughout a geometric manifold with initial conditions can be\ndescribed by the following second order differential equation:\n\u2202f(x,t)\n\u2202t\n\u2212 \u2206f(x, t) = 0, where f(x, t) is the heat at location x\nat time t, and \u2206f is the Laplace-Beltrami operator on a\nfunction f. The heat diffusion kernel Kt(x, y) is a special\nsolution to the heat equation with a special initial condition-a\nunit heat source at position y when there is no heat in other\npositions. Based on this, the heat kernel Kt(x, y) describes\nthe heat distribution at time t diffusing from the initial unit\nheat source at position y, and thus describes the\nconnectivity (which is considered as a kind of similarity) between x\nand y. However, it is very difficult to represent the World\nWide Web as a regular geometry with a known dimension;\neven the underlying is known, it is very difficult to find the\nheat kernel Kt(x, y), which involves solving the heat\nequation with the delta function as the initial condition. This\nmotivates us to investigate the heat flow on a graph. The\ngraph is considered as an approximation to the underlying\nmanifold, and so the heat flow on the graph is considered as\nan approximation to the heat flow on the manifold.\n3.3 On an Undirected Graph\nOn an undirected graph G, the edge (vi, vj) is considered\nas a pipe that connects nodes vi and vj. The value fi(t)\ndescribes the heat at node vi at time t, beginning from an\ninitial distribution of heat given by fi(0) at time zero. f(t)\n(f(0)) denotes the vector consisting of fi(t) (fi(0)).\nWe construct our model as follows. Suppose, at time t,\neach node i receives M(i, j, t, \u2206t) amount of heat from its\nneighbor j during a period of \u2206t. The heat M(i, j, t, \u2206t)\nshould be proportional to the time period \u2206t and the heat\ndifference fj(t) \u2212 fi(t). Moreover, the heat flows from node\nj to node i through the pipe that connects nodes i and j.\nBased on this consideration, we assume that M(i, j, t, \u2206t) =\n\u03b3(fj(t) \u2212 fi(t))\u2206t. As a result, the heat difference at node\ni between time t + \u2206t and time t will be equal to the sum\nof the heat that it receives from all its neighbors. This is\nformulated as\nfi(t + \u2206t) \u2212 fi(t) =\nj:(j,i)\u2208E\n\u03b3(fj(t) \u2212 fi(t))\u2206t, (2)\nwhere E is the set of edges. To find a closed form solution\nto Eq. (2), we express it in a matrix form: (f(t + \u2206t) \u2212\nf(t))/\u2206t = \u03b3Hf(t), where d(v) denotes the degree of the\nnode v. In the limit \u2206t \u2192 0, it becomes d\ndt\nf(t) = \u03b3Hf(t).\nSolving it, we obtain f(t) = e\u03b3tH\nf(0), especially we have\nf(1) = e\u03b3H\nf(0), Hij =\n\uf8f1\n\uf8f2\n\uf8f3\n\u2212d(vj), j = i,\n1, (vj, vi) \u2208 E,\n0, otherwise,\n(3)\nwhere e\u03b3H\nis defined as e\u03b3H\n= I+\u03b3H+ \u03b32\n2!\nH2\n+ \u03b33\n3!\nH3\n+\u00b7 \u00b7 \u00b7 .\n3.4 On a Directed Graph\nThe above heat diffusion model must be modified to fit the\nsituation where the links between Web pages are directed.\nOn one Web page, when the page-maker creates a link (a, b)\nto another page b, he actually forces the energy flow, for\nexample, people\"s click-through activities, to that page, and\nso there is added energy imposed on the link. As a result,\nheat flows in a one-way manner, only from a to b, not from\nb to a. Based on such consideration, we modified the heat\ndiffusion model on an undirected graph as follows.\nOn a directed graph G, the pipe (vi, vj) is forced by added\nenergy such that heat flows only from vi to vj. Suppose, at\ntime t, each node vi receives RH = RH(i, j, t, \u2206t) amount of\nheat from vj during a period of \u2206t. We have three\nassumptions: (1) RH should be proportional to the time period \u2206t;\n(2) RH should be proportional to the the heat at node vj;\nand (3) RH is zero if there is no link from vj to vi. As a\nresult, vi will receive j:(vj ,vi)\u2208E \u03c3jfj(t)\u2206t amount of heat\nfrom all its neighbors that points to it.\nOn the other hand, node vi diffuses DH(i, t, \u2206t) amount\nof heat to its subsequent nodes. We assume that: (1) The\nheat DH(i, t, \u2206t) should be proportional to the time period\n\u2206t. (2) The heat DH(i, t, \u2206t) should be proportional to the\nthe heat at node vi. (3) Each node has the same ability of\ndiffusing heat. This fits the intuition that a Web surfer only\nhas one choice to find the next page that he wants to browse.\n(4) The heat DH(i, t, \u2206t) should be uniformly distributed\nto its subsequent nodes. The real situation is more complex\nthan what we assume, but we have to make this simple\nassumption in order to make our model concise. As a result,\nnode vi will diffuse \u03b3fi(t)\u2206t/di amount of heat to any of its\nsubsequent nodes, and each of its subsequent node should\nreceive \u03b3fi(t)\u2206t/di amount of heat. Therefore \u03c3j = \u03b3/dj.\nTo sum up, the heat difference at node vi between time\nt+\u2206t and time t will be equal to the sum of the heat that it\nreceives, deducted by what it diffuses. This is formulated as\nfi(t + \u2206t) \u2212 fi(t) = \u2212\u03b3fi(t)\u2206t + j:(vj ,vi)\u2208E \u03b3/djfj(t)\u2206t.\nSimilarly, we obtain\nf(1) = e\u03b3H\nf(0), Hij =\n\uf8f1\n\uf8f2\n\uf8f3\n\u22121, j = i,\n1/dj, (vj, vi) \u2208 E,\n0, otherwise.\n(4)\n3.5 On a Random Directed Graph\nFor real world applications, we have to consider random\nedges. This can be seen in two viewpoints. The first one\nis that in Eq. (1), the Web graph is actually modelled as\na random graph, there is an edge from node vi to node vj\nwith a probability of (1 \u2212 \u03b1)gj (see the item (1 \u2212 \u03b1)g1T\n),\nand that the Web graph is predicted by a random graph\n[15, 16]. The second one is that the Web structure is a\nrandom graph in essence if we consider the content similarity\nbetween two pages, though this is not done in this paper.\nFor these reasons, the model would become more flexible if\nwe extend it to random graphs. The definition of a random\ngraph is given below.\nDefinition 1. A random graph RG = (V, P = (pij)) is\ndefined as a graph with a vertex set V in which the edges are\nchosen independently, and for 1 \u2264 i, j \u2264 |V | the probability\nof (vi, vj) being an edge is exactly pij.\nThe original definition of random graphs in [4], is changed\nslightly to consider the situation of directed graphs. Note\nthat every static graph can be considered as a special\nrandom graph in the sense that pij can only be 0 or 1.\nOn a random graph RG = (V, P), where P = (pij) is\nthe probability of the edge (vi, vj) exists. In such a random\ngraph, the expected heat difference at node i between time\nt + \u2206t and time t will be equal to the sum of the expected\nheat that it receives from all its antecedents, deducted by\nthe expected heat that it diffuses.\nSince the probability of the link (vj, vi) is pji, the\nexpected heat flow from node j to node i should be multiplied\nby pji, and so we have fi(t + \u2206t) \u2212 fi(t) = \u2212\u03b3 fi(t) \u2206t +\nj:(vj ,vi)\u2208E \u03b3pjifj(t)\u2206t/RD+\n(vj), where RD+\n(vi) is the\nexpected out-degree of node vi, it is defined as k pik.\nSimilarly we have\nf(1) = e\u03b3R\nf(0), Rij =\n\uf8f1\n\uf8f2\n\uf8f3\n\u22121, j = i;\npji/RD+\n(vj), j = i.\n(5)\nWhen the graph is large, a direct computation of e\u03b3R\nis\ntime-consuming, and we adopt its discrete approximation:\nf(1) = (I +\n\u03b3\nN\nR)N\nf(0). (6)\nThe matrix (I+ \u03b3\nN\nR)N\nin Eq. (6) and matrix e\u03b3R\nin Eq. (5)\nare called Discrete Diffusion Kernel and the Continuous\nDiffusion Kernel respectively. Based on the Heat Diffusion\nModels and their solutions, DiffusionRank can be\nestablished on undirected graphs, directed graphs, and random\ngraphs. In the next section, we mainly focus on\nDiffusionRank in the random graph setting.\n4. DIFFUSIONRANK\nFor a random graph, the matrix (I + \u03b3\nN\nR)N\nor e\u03b3R\ncan\nmeasure the similarity relationship between nodes. Let fi(0)=\n1, fj(0) = 0 if j = i, then the vector f(0) represent the unit\nheat at node vi while all other nodes has zero heat. For such\nf(0) in a random graph, we can find the heat distribution\nat time 1 by using Eq. (5) or Eq. (6). The heat\ndistribution is exactly the i\u2212th row of the matrix of (I + \u03b3\nN\nR)N\nor\ne\u03b3R\n. So the ith-row jth-column element hij in the matrix\n(I + \u03b3\u2206tR)N\nor e\u03b3R\nmeans the amount of heat that vi can\nreceive from vj from time 0 to 1. Thus the value hij can be\nused to measure the similarity from vj to vi. For a static\ngraph, similarly the matrix (I + \u03b3\nN\nH)N\nor e\u03b3H\ncan measure\nthe similarity relationship between nodes.\nThe intuition behind is that the amount h(i, j) of heat\nthat a page vi receives from a unit heat in a page vj in a\nunit time embodies the extent of the link connections from\npage vj to page vi. Roughly speaking, when there are more\nuncrossed paths from vj to vi, vi will receive more heat from\nvj; when the path length from vj to vi is shorter, vi will\nreceive more heat from vj; and when the pipe connecting\nvj and vi is wide, the heat will flow quickly. The final heat\nthat vi receives will depend on various paths from vj to vi,\ntheir length, and the width of the pipes.\nAlgorithm 1 DiffusionRank Function\nInput: The transition matrix A; the inverse transition\nmatrix U; the decay factor \u03b1I for the inverse PageRank; the\ndecay factor \u03b1B for PageRank; number of iterations MI for\nthe inverse PageRank; the number of trusted pages L; the\nthermal conductivity coefficient \u03b3.\nOutput: DiffusionRank score vector h.\n1: s = 1\n2: for i = 1 TO MI do\n3: s = \u03b1I \u00b7 U \u00b7 s + (1 \u2212 \u03b1I ) \u00b7 1\nn\n\u00b7 1\n4: end for\n5: Sort s in a decreasing order: \u03c0 = Rank({1, . . . , n}, s)\n6: d = 0, Count = 0, i = 0\n7: while Count \u2264 L do\n8: if \u03c0(i) is evaluated as a trusted page then\n9: d(\u03c0(i)) = 1, Count + +\n10: end if\n11: i + +\n12: end while\n13: d = d/|d|\n14: h = d\n15: Find the iteration number MB according to \u03bb\n16: for i = 1 TO MB do\n17: h = (1 \u2212 \u03b3\nMB\n)h + \u03b3\nMB\n(\u03b1B \u00b7 A \u00b7 h + (1 \u2212 \u03b1B) \u00b7 1\nn\n\u00b7 1)\n18: end for\n19: RETURN h\n4.1 Algorithm\nFor the ranking task, we adopt the heat kernel on a\nrandom graph. Formally the DiffusionRank is described in\nAlgorithm 1, in which,the element Uij in the inverse transition\nmatrix U is defined to be 1/Ij if there is a link from i to j,\nand 0 otherwise. This trusted pages selection procedure by\ninverse PageRank is completely borrowed from TrustRank\n[7] except for a fix number of the size of the trusted set.\nAlthough the inverse PageRank is not perfect in its\nability of determining the maximum coverage, it is appealing\nbecause of its polynomial execution time and its\nreasonable intuition-we actually inverse the original link when\nwe try to build the seed set from those pages that point\nto many pages that in turn point to many pages and so\non. In the algorithm, the underlying random graph is set as\nP = \u03b1B \u00b7 A + (1 \u2212 \u03b1B) \u00b7 1\nn\n\u00b7 1n\u00d7n, which is induced by the\nWeb graph. As a result, R = \u2212I + P.\nIn fact, the more general setting for DiffusionRank is P =\n\u03b1B \u00b7A+(1\u2212\u03b1B)\u00b7 1\nn\n\u00b7g\u00b71T\n. By such a setting, DiffusionRank\nis a generalization of TrustRank when \u03b3 tends to infinity\nand when g is set in the same way as TrustRank. However,\nthe second part of TrustRank is not adopted by us. In our\nmodel, g should be the true teleportation determined by\nthe user\"s browse habits, popularity distribution over all the\nWeb pages, and so on; P should be the true model of the\nrandom nature of the World Wide Web. Setting g according\nto the trusted pages will not be consistent with the basic idea\nof Heat Diffusion on a random graph. We simply set g = 1\nonly because we cannot find it without any priori knowledge.\nRemark. In a social network interpretation,\nDiffusionRank first recognizes a group of trusted people, who may\nnot be highly ranked, but they know many other people.\nThe initially trusted people are endowed with the power to\ndecide who can be further trusted, but cannot decide the\nfinal voting results, and so they are not dictators.\n4.2 Advantages\nNext we show the four advantages for DiffusionRank.\n4.2.1 Two closed forms\nFirst, its solutions have two forms, both of which are\nclosed form. One takes the discrete form, and has the\nadvantage of fast computing while the other takes the continuous\nform, and has the advantage of being easily analyzed in\ntheoretical aspects. The theoretical advantage has been shown\nin the proof of theorem in the next section.\n(a) Group to Group Relations (b) An undirected graph\nFigure 1: Two graphs\n4.2.2 Group-group relations\nSecond, it can be naturally employed to detect the\ngroupgroup relation. For example, let G2 and G1 denote two\ngroups, containing pages (j1, j2, . . . , js) and (i1, i2, . . . , it),\nrespectively. Then u,v hiu,jv is the total amounts of heat\nthat G1 receives from G2, where hiu,jv is the iu\u2212th row\njv\u2212th column element of the heat kernel. More specifically,\nwe need to first set f(0) for such an application as follows.\nIn f(0) = (f1(0), f2(0), . . . , fn(0))T\n, if i \u2208 {j1, j2, . . . , js},\nthen fi(0) = 1, and 0 otherwise. Then we employ Eq. (5)\nto calculate f(1) = (f1(1), f2(1), . . . , fn(1))T\n, finally we sum\nthose fj(1) where j \u2208 {i1, i2, . . . , it}. Fig. 1 (a) shows the\nresults generated by the DiffusionRank. We consider five\ngroups-five departments in our Engineering Faculty: CSE,\nMAE, EE, IE, and SE. \u03b3 is set to be 1, the numbers in\nFig. 1 (a) are the amount of heat that they diffuse to each\nother. These results are normalized by the total number of\neach group, and the edges are ignored if the values are less\nthan 0.000001. The group-to-group relations are therefore\ndetected, for example, we can see that the most strong\noverall tie is from EE to IE. While it is a natural application\nfor DiffusionRank because of the easy interpretation by the\namount heat from one group to another group, it is difficult\nto apply other ranking techniques to such an application\nbecause they lack such a physical meaning.\n4.2.3 Graph cut\nThird, it can be used to partition the Web graph into\nseveral parts. A quick example is shown below. The graph\nin Fig. 1 (b) is an undirected graph, and so we employ the\nEq. (3). If we know that node 1 belongs to one\ncommunity and that node 12 belongs to another community, then\nwe can put one unit positive heat source on node 1 and\none unit negative heat source on node 12. After time 1, if\nwe set \u03b3 = 0.5, the heat distribution is [0.25, 0.16, 0.17,\n0.16, 0.15, 0.09, 0.01, -0.04, -0.18 -0.21, -0.21, -0.34], and if\nwe set \u03b3 = 1, it will be [0.17, 0.16, 0.17, 0.16, 0.16, 0.12,\n0.02, -0.07, -0.18, -0.22, -0.24, -0.24]. In both settings, we\ncan easily divide the graph into two parts: {1, 2, 3, 4, 5, 6, 7}\nwith positive temperatures and {8, 9, 10, 11, 12} with\nnegative temperatures. For directed graphs and random graphs,\nsimilarly we can cut them by employing corresponding heat\nsolution.\n4.2.4 Anti-manipulation\nFourth, it can be used to combat manipulation. Let G2\ncontain trusted Web pages (j1, j2, . . . , js), then for each page\ni, v hi,jv is the heat that page i receives from G2, and can\nbe computed by the discrete approximation of Eq. (4) in\nthe case of a static graph or Eq. (6) in the case of a random\ngraph, in which f(0) is set to be a special initial heat\ndistribution so that the trusted Web pages have unit heat while\nall the others have zero heat. In doing so, manipulated Web\npage will get a lower rank unless it has strong in-links from\nthe trusted Web pages directly or indirectly. The situation\nis quite different for PageRank because PageRank is\ninputindependent as we have shown in Section 3.1. Based on the\nfact that the connection from a trusted page to a bad page\nshould be weak-less uncross paths, longer distance and\nnarrower pipe, we can say DiffusionRank can resist web spam if\nwe can select trusted pages. It is fortunate that the trusted\npages selection method in [7]-the first part of TrustRank can\nhelp us to fulfill this task. For such an application of\nDiffusionRank, the computation complexity for Discrete\nDiffusion Kernel is the same as that for PageRank in cases of\nboth a static graph and a random graph. This can be seen\nin Eq. (6), by which we need N iterations and for each\niteration we need a multiplication operation between a matrix\nand a vector, while in Eq. (1) we also need a multiplication\noperation between a matrix and a vector for each iteration.\n4.3 The Physical Meaning of \u03b3\n\u03b3 plays an important role in the anti-manipulation effect\nof DiffusionRank. \u03b3 is the thermal conductivity-the heat\ndiffusion coefficient. If it has a high value, heat will\ndiffuse very quickly. Conversely, if it is small, heat will diffuse\nslowly. In the extreme case, if it is infinitely large, then heat\nwill diffuse from one node to other nodes immediately, and\nthis is exactly the case corresponding to PageRank. Next,\nwe will interpret it mathematically.\nTheorem 1. When \u03b3 tends to infinity and f(0) is not the\nzero vector, e\u03b3R\nf(0) is proportional to the stable distribution\nproduced by PageRank.\nLet g = 1\nn\n1. By the Perron Theorem [11], we have shown\nthat 1 is the largest eigenvalue of P = [(1 \u2212 \u03b1)g1T\n+ \u03b1A],\nand that no other eigenvalue whose absolute value is equal\nto 1. Let x be the stable distribution, and so Px = x. x is\nthe eigenvector corresponding to the eigenvalue 1. Assume\nthe n \u2212 1 other eigenvalues of P are |\u03bb2| < 1, . . . , |\u03bbn| < 1,\nwe can find an invertible matrix S = ( x S1 ) such that\nS\u22121\nPS =\n\uf8eb\n\uf8ec\n\uf8ec\n\uf8ec\n\uf8ed\n1 \u2217 \u2217 \u2217\n0 \u03bb2 \u2217 \u2217\n0 0\n... \u2217\n0 0 0 \u03bbn\n\uf8f6\n\uf8f7\n\uf8f7\n\uf8f7\n\uf8f8\n. (7)\nSince e\u03b3R\n= e\u03b3(\u2212I+P)\n=\nS\u22121\n\uf8eb\n\uf8ec\n\uf8ec\n\uf8ec\n\uf8ed\n1 \u2217 \u2217 \u2217\n0 e\u03b3(\u03bb2\u22121)\n\u2217 \u2217\n0 0\n... \u2217\n0 0 0 e\u03b3(\u03bbn\u22121)\n\uf8f6\n\uf8f7\n\uf8f7\n\uf8f7\n\uf8f8\nS, (8)\nall eigenvalues of the matrix e\u03b3R\nare 1, e\u03b3(\u03bb2\u22121)\n, . . . , e\u03b3(\u03bbn\u22121)\n.\nWhen \u03b3 \u2192 \u221e, they become 1, 0, . . . , 0, which means that 1 is\nthe only nonzero eigenvalue of e\u03b3R\nwhen \u03b3 \u2192 \u221e. We can see\nthat when \u03b3 \u2192 \u221e, e\u03b3R\ne\u03b3R\nf(0) = e\u03b3R\nf(0), and so e\u03b3R\nf(0)\nis an eigenvector of e\u03b3R\nwhen \u03b3 \u2192 \u221e. On the other hand,\ne\u03b3R\nx = (I+\u03b3R+\u03b32\n2!\nR2\n+\u03b33\n3!\nR3\n+. . .)x = Ix+\u03b3Rx+\u03b32\n2!\nR2\nx+\n\u03b33\n3!\nR3\nx + . . . = x since Rx = (\u2212I + P)x = \u2212x + x = 0,\nand hence x is the eigenvector of e\u03b3R\nfor any \u03b3. Therefore\nboth x and e\u03b3R\nf(0) are the eigenvectors corresponding the\nunique eigenvalue 1 of e\u03b3R\nwhen \u03b3 \u2192 \u221e, and consequently\nx = ce\u03b3R\nf(0).\nBy this theorem, we see that DiffusionRank is a\ngeneralization of PageRank. When \u03b3 = 0, the ranking value is\nmost robust to manipulation since no heat is diffused and\nthe system is unchangeable, but the Web structure is\ncompletely ignored since e\u03b3R\nf(0) = e0R\nf(0) = If(0) = f(0);\nwhen \u03b3 = \u221e, DiffusionRank becomes PageRank, it can be\nmanipulated easily. We expect an appropriate setting of\n\u03b3 that can balance both. For this, we have no theoretical\nresult, but in practice we find that \u03b3 = 1 works well in\nSection 5. Next we discuss how to determine the number of\niterations if we employ the discrete heat kernel.\n4.4 The Number of Iterations\nWhile we enjoy the advantage of the concise form of the\nexponential heat kernel, it is better for us to calculate\nDiffusionRank by employing Eq. (6) in an iterative way. Then\nthe problem about determining N-the number of iterations\narises:\nFor a given threshold , find N such that ||((I + \u03b3\nN\nR)N\n\u2212\ne\u03b3R\n)f(0)|| < for any f(0) whose sum is one.\nSince it is difficult to solve this problem, we propose a\nheuristic motivated by the following observations. When\nR = \u2212I+P, by Eq. (7), we have (I+ \u03b3\nN\nR)N\n= (I+ \u03b3\nN\n(\u2212I+\nP))N\n=\nS\u22121\n\uf8eb\n\uf8ec\n\uf8ec\n\uf8ec\n\uf8ed\n1 \u2217 \u2217 \u2217\n0 (1 + \u03b3(\u03bb2\u22121)\nN\n)N\n\u2217 \u2217\n0 0\n... \u2217\n0 0 0 (1 + \u03b3(\u03bbn\u22121)\nN\n)N\n\uf8f6\n\uf8f7\n\uf8f7\n\uf8f7\n\uf8f8\nS. (9)\nComparing Eq. (8) and Eq. (9), we observe that the\neigenvalues of (I + \u03b3\nN\nR)N\n\u2212 e\u03b3R\nare (1 + \u03b3(\u03bbn\u22121)\nN\n)N\n\u2212 e\u03b3(\u03bbn\u22121)\n.\nWe propose a heuristic method to determine N so that the\ndifference between the eigenvalues are less than a threshold\nfor only positive \u03bbs.\nWe also observe that if \u03b3 = 1, \u03bb < 1, then |(1+ \u03b3(\u03bb\u22121)\nN\n)N\n\u2212\ne\u03b3(\u03bb\u22121)\n| < 0.005 if N \u2265 100, and |(1+ \u03b3(\u03bb\u22121)\nN\n)N\n\u2212e\u03b3(\u03bb\u22121)\n| <\n0.01 if N \u2265 30. So we can set N = 30, or N = 100, or others\naccording to different accuracy requirements. In this paper,\nwe use the relatively accurate setting N = 100 to make the\nreal eigenvalues in (I + \u03b3\nN\nR)N\n\u2212 e\u03b3R\nless than 0.005.\n5. EXPERIMENTS\nIn this section, we show the experimental data, the\nmethodology, the setting, and the results.\n5.1 Data Preparation\nOur input data consist of a toy graph, a middle-size\nrealworld graph, and a large-size real-world graph. The toy\ngraph is shown in Fig. 2 (a). The graph below it shows node\n1 is being manipulated by adding new nodes A, B, C, . . .\nsuch that they all point to node 1, and node 1 points to\nthem all. The data of two real Web graph were obtained\nfrom the domain in our institute in October, 2004. The\ntotal number of pages found are 18,542 in the middle-size\ngraph, and 607,170 in the large-size graph respectively. The\nmiddle-size graph is a subgraph of the large-size graph, and\nthey were obtained by the same crawler: one is recorded\nby the crawler in its earlier time, and the other is obtained\nwhen the crawler stopped.\n5.2 Methodology\nThe algorithms we run include PageRank, TrustRank and\nDiffusionRank. All the rank values are multiplied by the\nnumber of nodes so that the sum of the rank values is equal\nto the number of nodes. By this normalization, we can\ncompare the results on graphs with different sizes since the\naverage rank value is one for any graph after such normalization.\nWe will need value difference and pairwise order difference as\ncomparison measures. Their definitions are listed as follows.\nValue Difference. The value difference between A =\n{Ai}n\ni=1 and B = {Bi}n\ni=1 is measured as n\ni=1 |Ai \u2212 Bi|.\nPairwise Order Difference. The order difference between\nA and B is measured as the number of significant order\ndifferences between A and B. The pair (A[i], A[j]) and\n(B[i], B[j]) is considered as a significant order difference if\none of the following cases happens: both A[i] > [ <]A[j]+0.1\nand B[i] \u2264 [ \u2265]A[j]; both A[i] \u2264 [ \u2265]A[j] and B[i] > [ <\n]A[j] + 0.1.\nA\n1\nB\nC\n...\n2\n5\n6 3\n4\n1\n2 5\n6 3 4\n0 1 2 3 4 5 6\n0\n2\n4\n6\n8\n10\n12\nGamma\nValueDifference\nTrust set={1}\nTrust set={2}\nTrust set={3}\nTrust set={4}\nTrust set={5}\nTrust set={6}\n(a) (b)\nFigure 2: (a) The toy graph consisting of six nodes,\nand node 1 is being manipulated by adding new\nnodes A, B, C, . . . (b) The approximation tendency to\nPageRank by DiffusionRank\n5.3 Experimental Set-up\nThe experiments on the middle-size graph and the\nlargesize graphs are conducted on the workstation, whose\nhardware model is Nix Dual Intel Xeon 2.2GHz with 1GB RAM\nand a Linux Kernel 2.4.18-27smp (RedHat7.3). In\ncalculating DiffusionRank, we employ Eq. (6) and the discrete\napproximation of Eq. (4) for such graphs. The related tasks\nare implemented using C language. While in the toy graph,\nwe employ the continuous diffusion kernel in Eq. (4) and\nEq. (5), and implement related tasks using Matlab.\nFor nodes that have zero out-degree (dangling nodes), we\nemploy the method in the modified PageRank algorithm [8],\nin which dangling nodes of are considered to have random\nlinks uniformly to each node. We set \u03b1 = \u03b1I = \u03b1B = 0.85 in\nall algorithms. We also set g to be the uniform distribution\nin both PageRank and DiffusionRank. For DiffusionRank,\nwe set \u03b3 = 1. According to the discussions in Section 4.3 and\nSection 4.4, we set the iteration number to be MB = 100 in\nDiffusionRank, and for accuracy consideration, the iteration\nnumber in all the algorithms is set to be 100.\n5.4 Approximation of PageRank\nWe show that when \u03b3 tends to infinity, the value\ndifferences between DiffusionRank and PageRank tend to zero.\nFig. 2 (b) shows the approximation property of\nDiffusionRank, as proved in Theorem 1, on the toy graph. The\nhorizontal axis of Fig. 2 (b) marks the \u03b3 value, and vertical axis\ncorresponds to the value difference between DiffusionRank\nand PageRank. All the possible trusted sets with L = 1\nare considered. For L > 1, the results should be the linear\ncombination of some of these curves because of the\nlinearity of the solutions to heat equations. On other graphs, the\nsituations are similar.\n5.5 Results of Anti-manipulation\nIn this section, we show how the rank values change as the\nintensity of manipulation increases. We measure the\nintensity of manipulation by the number of newly added points\nthat point to the manipulated point. The horizontal axes\nof Fig. 3 stand for the numbers of newly added points, and\nvertical axes show the corresponding rank values of the\nmanipulated nodes. To be clear, we consider all six situations.\nEvery node in Fig. 2 (a) is manipulated respectively, and its\n0 50 100\n0\n10\n20\n30\n40\n50\nRankoftheManipulatdNode\u22121\nDiffusionRank\u2212Trust 4\nPageRank\nTrustRanl\u2212Trust 4\n0 50 100\n0\n10\n20\n30\n40\n50\nRankoftheManipulatdNode\u22122\nDiffusionRank\u2212Trust 4\nPageRank\nTrustRanl\u2212Trust 4\n0 50 100\n0\n10\n20\n30\n40\n50\nRankoftheManipulatdNode\u22123\nDiffusionRank\u2212Trust 4\nPageRank\nTrustRanl\u2212Trust 4\n0 50 100\n0\n10\n20\n30\n40\n50\nNumber of New Added Nodes\nRankoftheManipulatdNode\u22124\nDiffusionRank\u2212Trust 3\nPageRank\nTrustRanl\u2212Trust 3\n0 50 100\n0\n10\n20\n30\n40\n50\nNumber of New Added Nodes\nRankoftheManipulatdNode\u22125\nDiffusionRank\u2212Trust 4\nPageRank\nTrustRanl\u2212Trust 4\n0 50 100\n0\n10\n20\n30\n40\n50\nNumber of New Added Nodes\nRankoftheManipulatdNode\u22126\nDiffusionRank\u2212Trust 4\nPageRank\nTrustRanl\u2212Trust 4\nFigure 3: The rank values of the manipulated nodes\non the toy graph\n200040006000800010000\n0\n1000\n2000\n3000\n4000\n5000\n6000\n7000\n8000\nNumber of New Added Points\nRankoftheManipulatdNode\nPageRank\nDiffusionRank\u2212uniform\nDiffusionRank0\nDiffusionRank1\nDiffusionRank2\nDiffusionRank3\nTrustRank0\nTrustRank1\nTrustRank2\nTrustRank3\n2000 4000 6000 8000 10000\n0\n20\n40\n60\n80\n100\n120\n140\n160\n180\nNumber of New Added Points\nRankoftheManipulatdNode\nPageRank\nDiffusionRank\nTrustRank\nDiffusionRank\u2212uniform\n(a) (b)\nFigure 4: (a) The rank values of the manipulated\nnodes on the middle-size graph; (b) The rank values\nof the manipulated nodes on the large-size graph\ncorresponding values for PageRank, TrustRank (TR),\nDiffusionRank (DR) are shown in the one of six sub-figures in\nFig. 3. The vertical axes show which node is being\nmanipulated. In each sub-figure, the trusted sets are\ncomputed below. Since the inverse PageRank yields the results\n[1.26, 0.85, 1.31, 1.36, 0.51, 0.71]. Let L = 1. If the\nmanipulated node is not 4, then the trusted set is {4}, and\notherwise {3}. We observe that in all the cases, rank values\nof the manipulated node for DiffusionRank grow slowest as\nthe number of the newly added nodes increases. On the\nmiddle-size graph and the large-size graph, this conclusion\nis also true, see Fig. 4. Note that, in Fig. 4 (a), we choose\nfour trusted sets (L = 1), on which we test DiffusionRank\nand TrustRank, the results are denoted by DiffusionRanki\nand TrustRanki (i = 0, 1, 2, 3 denotes the four trusted set);\nin Fig. 4 (b), we choose one trusted set (L = 1). Moreover,\nin both Fig. 4 (a) and Fig. 4 (b), we show the results for\nDiffusionRank when we have no trusted set, and we trust\nall the pages before some of them are manipulated.\nWe also test the order difference between the ranking\norder A before the page is manipulated and the ranking order\nPA after the page is manipulated. Because after\nmanipulation, the number of pages changes, we only compare the\ncommon part of A and PA. This experiment is used to test\nthe stability of all these algorithms. The less the order\ndifference, the stabler the algorithm, in the sense that only a\nsmaller part of the order relations is affected by the\nmanipulation. Figure 5 (a) shows that the order difference values\nchange when we add new nodes that point to the\nmanipulated node. We give several \u03b3 settings. We find that when\n\u03b3 = 1, the least order difference is achieved by\nDiffusionRank. It is interesting to point out that as \u03b3 increases, the\norder difference will increase first; after reaching a maximum\nvalue, it will decrease, and finally it tends to the PageRank\nresults. We show this tendency in Fig. 5 (b), in which we\nchoose three different settings-the number of manipulated\nnodes are 2,000, 5,000, and 10,000 respectively. From these\nfigures, we can see that when \u03b3 < 2, the values are less than\nthose for PageRank, and that when \u03b3 > 20, the difference\nbetween PageRank and DiffusionRank is very small.\nAfter these investigations, we find that in all the graphs we\ntested, DiffusionRank (when \u03b3 = 1) is most robust to\nmanipulation both in value difference and order difference. The\ntrust set selection algorithm proposed in [7] is effective for\nboth TrustRank and DiffusionRank.\n0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000\n0\n0.5\n1\n1.5\n2\n2.5\n3\nx 10\n5\nNumber of New Added Points\nPairwiseOrderDifference\nPageRank\nDiffusionRank\u2212Gamma=1\nDiffusionRank\u2212Gamma=2\nDiffusionRank\u2212Gamma=3\nDiffusionRank\u2212Gamma=4\nDiffusionRank\u2212Gamma=5\nDiffusionRank\u2212Gamma=15\nTrustRank\n0 5 10 15 20\n0\n0.5\n1\n1.5\n2\n2.5\nx 10\n5\nGamma\nPairwiseOrderDifference\nDiffusionRank: when added 2000 nodes\nDiffusionRank: when added 5000 nodes\nDiffusionRank: when added 10000 nodes\nPageRank\n(a) (b)\nFigure 5: (a) Pairwise order difference on the\nmiddle-size graph, the least it is, the more stable\nthe algorithm; (b) The tendency of varying \u03b3\n6. CONCLUSIONS\nWe conclude that DiffusionRank is a generalization of\nPageRank, which is interesting in that the heat diffusion\ncoefficient \u03b3 can balance the extent that we want to model the\noriginal Web graph and the extent that we want to reduce\nthe effect of link manipulations. The experimental results\nshow that we can actually achieve such a balance by\nsetting \u03b3 = 1, although the best setting including varying \u03b3i\nis still under further investigation. This anti-manipulation\nfeature enables DiffusionRank to be a candidate as a\npenicillin for Web spamming. Moreover, DiffusionRank can be\nemployed to find group-group relations and to partition Web\ngraph into small communities. All these advantages can be\nachieved in the same computational complexity as\nPageRank. For the special application of anti-manipulation,\nDiffusionRank performs best both in reduction effects and in\nits stability among all the three algorithms.\n7. ACKNOWLEDGMENTS\nWe thank Patrick Lau, Zhenjiang Lin and Zenglin Xu\nfor their help. This work is fully supported by two grants\nfrom the Research Grants Council of the Hong Kong Special\nadministrative Region, China (Project No. CUHK4205/04E\nand Project No. CUHK4235/04E).\n8. REFERENCES\n[1] E. Agichtein, E. Brill, and S. T. Dumais. Improving web search\nranking by incorporating user behavior information. In E. N.\nEfthimiadis, S. T. Dumais, D. Hawking, and K. J\u00a8arvelin,\neditors, Proceedings of the 29th Annual International ACM\nSIGIR Conference on Research and Development in\nInformation Retrieval (SIGIR), pages 19-26, 2006.\n[2] R. A. Baeza-Yates, P. Boldi, and C. Castillo. Generalizing\npagerank: damping functions for link-based ranking\nalgorithms. In E. N. Efthimiadis, S. T. Dumais, D. Hawking,\nand K. 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{"name": "train_H-40", "title": "Cross-Lingual Query Suggestion Using Query Logs of Different Languages", "abstract": "Query suggestion aims to suggest relevant queries for a given query, which help users better specify their information needs. Previously, the suggested terms are mostly in the same language of the input query. In this paper, we extend it to cross-lingual query suggestion (CLQS): for a query in one language, we suggest similar or relevant queries in other languages. This is very important to scenarios of cross-language information retrieval (CLIR) and cross-lingual keyword bidding for search engine advertisement. Instead of relying on existing query translation technologies for CLQS, we present an effective means to map the input query of one language to queries of the other language in the query log. Important monolingual and cross-lingual information such as word translation relations and word co-occurrence statistics, etc. are used to estimate the cross-lingual query similarity with a discriminative model. Benchmarks show that the resulting CLQS system significantly outperforms a baseline system based on dictionary-based query translation. Besides, the resulting CLQS is tested with French to English CLIR tasks on TREC collections. The results demonstrate higher effectiveness than the traditional query translation methods.", "fulltext": "1. INTRODUCTION\nQuery suggestion is a functionality to help users of a search\nengine to better specify their information need, by narrowing\ndown or expanding the scope of the search with synonymous\nqueries and relevant queries, or by suggesting related queries that\nhave been frequently used by other users. Search engines, such as\nGoogle, Yahoo!, MSN, Ask Jeeves, all have implemented query\nsuggestion functionality as a valuable addition to their core search\nmethod. In addition, the same technology has been leveraged to\nrecommend bidding terms to online advertiser in the\npay-forperformance search market [12].\nQuery suggestion is closely related to query expansion which\nextends the original query with new search terms to narrow the\nscope of the search. But different from query expansion, query\nsuggestion aims to suggest full queries that have been formulated\nby users so that the query integrity and coherence are preserved in\nthe suggested queries.\nTypical methods for query suggestion exploit query logs and\ndocument collections, by assuming that in the same period of\ntime, many users share the same or similar interests, which can be\nexpressed in different manners [12, 14, 26]. By suggesting the\nrelated and frequently used formulations, it is hoped that the new\nquery can cover more relevant documents. However, all of the\nexisting studies dealt with monolingual query suggestion and to\nour knowledge, there is no published study on cross-lingual query\nsuggestion (CLQS). CLQS aims to suggest related queries but in a\ndifferent language. It has wide applications on World Wide Web:\nfor cross-language search or for suggesting relevant bidding terms\nin a different language. 1\nCLQS can be approached as a query translation problem, i.e., to\nsuggest the queries that are translations of the original query.\nDictionaries, large size of parallel corpora and existing\ncommercial machine translation systems can be used for\ntranslation. However, these kinds of approaches usually rely on\nstatic knowledge and data. It cannot effectively reflect the quickly\nshifting interests of Web users. Moreover, there are some\nproblems with translated queries in target language. For instance,\nthe translated terms can be reasonable translations, but they are\nnot popularly used in the target language. For example, the French\nquery aliment biologique is translated into biologic food by\nGoogle translation tool2\n, yet the correct formulation nowadays\nshould be organic food. Therefore, there exist many mismatch\ncases between the translated terms and the really used terms in\ntarget language. This mismatch makes the suggested terms in the\ntarget language ineffective.\nA natural thinking of solving this mismatch is to map the\nqueries in the source language and the queries in the target\nlanguage, by using the query log of a search engine. We exploit\nthe fact that the users of search engines in the same period of time\nhave similar interests, and they submit queries on similar topics in\ndifferent languages. As a result, a query written in a source\nlanguage likely has an equivalent in a query log in the target\nlanguage. In particular, if the user intends to perform CLIR, then\noriginal query is even more likely to have its correspondent\nincluded in the target language query log. Therefore, if a\ncandidate for CLQS appears often in the query log, then it is more\nlikely the appropriate one to be suggested.\nIn this paper, we propose a method of calculating the similarity\nbetween source language query and the target language query by\nexploiting, in addition to the translation information, a wide\nspectrum of bilingual and monolingual information, such as term\nco-occurrences, query logs with click-through data, etc. A\ndiscriminative model is used to learn the cross-lingual query\nsimilarity based on a set of manually translated queries. The\nmodel is trained by optimizing the cross-lingual similarity to best\nfit the monolingual similarity between one query and the other\nquery\"s translation. Besides being benchmarked as an independent\nmodule, the resulting CLQS system is tested as a new means of\nquery translation in CLIR task on TREC collections. The results\nshow that this new translation method is more effective than the\ntraditional query translation method.\nThe remainder of this paper is organized as follows: Section 2\nintroduces the related work; Section 3 describes in detail the\ndiscriminative model for estimating cross-lingual query similarity;\nSection 4 presents a new CLIR approach using cross-lingual query\nsuggestion as a bridge across language boundaries. Section 5\ndiscusses the experiments and benchmarks; finally, the paper is\nconcluded in Section 6.\n2. RELATED WORK\nMost approaches to CLIR perform a query translation followed by\na monolingual IR. Typically, queries are translated either using a\nbilingual dictionary [22], a machine translation software [9] or a\nparallel corpus [20].\nDespite the various types of resources used, out-of-vocabulary\n(OOV) words and translation disambiguation are the two major\nbottlenecks for CLIR [20]. In [7, 27], OOV term translations are\nmined from the Web using a search engine. In [17], bilingual\nknowledge is acquired based on anchor text analysis. In addition,\nword co-occurrence statistics in the target language has been\nleveraged for translation disambiguation [3, 10, 11, 19].\n2\nhttp://www.google.com/language_tools\nNevertheless, it is arguable that accurate query translation may\nnot be necessary for CLIR. Indeed, in many cases, it is helpful to\nintroduce words even if they are not direct translations of any\nquery word, but are closely related to the meaning of the query.\nThis observation has led to the development of cross-lingual query\nexpansion (CLQE) techniques [2, 16, 18]. [2] reports the\nenhancement on CLIR by post-translation expansion. [16]\ndevelops a cross-lingual relevancy model by leveraging the\ncrosslingual co-occurrence statistics in parallel texts. [18] makes\nperformance comparison on multiple CLQE techniques, including\npre-translation expansion and post-translation expansion.\nHowever, there is lack of a unified framework to combine the\nwide spectrum of resources and recent advances of mining\ntechniques for CLQE.\nCLQS is different from CLQE in that it aims to suggest full\nqueries that have been formulated by users in another language.\nAs CLQS exploits up-to-date query logs, it is expected that for\nmost user queries, we can find common formulations on these\ntopics in the query log in the target language. Therefore, CLQS\nalso plays a role of adapting the original query formulation to the\ncommon formulations of similar topics in the target language.\nQuery logs have been successfully used for monolingual IR [8,\n12, 15, 26], especially in monolingual query suggestions [12] and\nrelating the semantically relevant terms for query expansion [8,\n15]. In [1], the target language query log has been exploited to\nhelp query translation in CLIR.\n3. ESTIMATING CROSS-LINGUAL\nQUERY SIMILARITY\nA search engine has a query log containing user queries in\ndifferent languages within a certain period of time. In addition to\nquery terms, click-through information is also recorded. Therefore,\nwe know which documents have been selected by users for each\nquery. Given a query in the source language, our CLQS task is to\ndetermine one or several similar queries in the target language\nfrom the query log.\nThe key problem with cross-lingual query suggestion is how to\nlearn a similarity measure between two queries in different\nlanguages. Although various statistical similarity measures have\nbeen studied for monolingual terms [8, 26], most of them are\nbased on term co-occurrence statistics, and can hardly be applied\ndirectly in cross-lingual settings.\nIn order to define a similarity measure across languages, one\nhas to use at least one translation tool or resource. So the measure\nis based on both translation relation and monolingual similarity. In\nthis paper, as our purpose is to provide up-to-date query similarity\nmeasure, it may not be sufficient to use only a static translation\nresource. Therefore, we also integrate a method to mine possible\ntranslations on the Web. This method is particularly useful for\ndealing with OOV terms.\nGiven a set of resources of different natures, the next question\nis how to integrate them in a principled manner. In this paper, we\npropose a discriminative model to learn the appropriate similarity\nmeasure. The principle is as follows: we assume that we have a\nreasonable monolingual query similarity measure. For any training\nquery example for which a translation exists, its similarity\nmeasure (with any other query) is transposed to its translation.\nTherefore, we have the desired cross-language similarity value for\nthis example. Then we use a discriminative model to learn the\ncross-language similarity function which fits the best these\nexamples.\nIn the following sections, let us first describe the detail of the\ndiscriminative model for cross-lingual query similarity estimation.\nThen we introduce all the features (monolingual and cross-lingual\ninformation) that we will use in the discriminative model.\n3.1 Discriminative Model for Estimating\nCross-Lingual Query Similarity\nIn this section, we propose a discriminative model to learn\ncrosslingual query similarities in a principled manner. The principle is\nas follows: for a reasonable monolingual query similarity between\ntwo queries, a cross-lingual correspondent can be deduced\nbetween one query and another query\"s translation. In other\nwords, for a pair of queries in different languages, their\ncrosslingual similarity should fit the monolingual similarity between\none query and the other query\"s translation. For example, the\nsimilarity between French query pages jaunes (i.e., yellow\npage in English) and English query telephone directory should\nbe equal to the monolingual similarity between the translation of\nthe French query yellow page and telephone directory. There\nare many ways to obtain a monolingual similarity measure\nbetween terms, e.g., term co-occurrence based mutual information\nand 2\n\u03c7 . Any of them can be used as the target for the cross-lingual\nsimilarity function to fit. In this way, cross-lingual query\nsimilarity estimation is formulated as a regression task as follows:\nGiven a source language query fq , a target language query eq ,\nand a monolingual query similarity MLsim , the corresponding\ncross-lingual query similarity CLsim is defined as follows:\n),(),( eqMLefCL qTsimqqsim f\n= (1)\nwhere fqT is the translation of fq in the target language.\nBased on Equation (1), it would be relatively easy to create a\ntraining corpus. All it requires is a list of query translations. Then\nan existing monolingual query suggestion system can be used to\nautomatically produce similar query to each translation, and create\nthe training corpus for cross-lingual similarity estimation. Another\nadvantage is that it is fairly easy to make use of arbitrary\ninformation sources within a discriminative modeling framework\nto achieve optimal performance.\nIn this paper, support vector machine (SVM) regression\nalgorithm [25] is used to learn the cross-lingual term similarity\nfunction. Given a vector of feature functions f between fq and\neq , ),( efCL ttsim is represented as an inner product between a\nweight vector and the feature vector in a kernel space as follows:\n)),((),( efefCL ttfwttsim \u03c6\u2022= (2)\nwhere \u03c6 is the mapping from the input feature space onto the\nkernel space, and wis the weight vector in the kernel space which\nwill be learned by the SVM regression training. Once the weight\nvector is learned, the Equation (2) can be used to estimate the\nsimilarity between queries of different languages.\nWe want to point out that instead of regression, one can\ndefinitely simplify the task as a binary or ordinal classification, in\nwhich case CLQS can be categorized according to discontinuous\nclass labels, e.g., relevant and irrelevant, or a series of levels of\nrelevancies, e.g., strongly relevant, weakly relevant, and\nirrelevant. In either case, one can resort to discriminative\nclassification approaches, such as an SVM or maximum entropy\nmodel, in a straightforward way. However, the regression\nformalism enables us to fully rank the suggested queries based on\nthe similarity score given by Equation (1).\nThe Equations (1) and (2) construct a regression model for\ncross-lingual query similarity estimation. In the following\nsections, the monolingual query similarity measure (see Section\n3.2) and the feature functions used for SVM regression (see\nSection 3.3) will be presented.\n3.2 Monolingual Query Similarity Measure\nBased on Click-through Information\nAny monolingual term similarity measure can be used as the\nregression target. In this paper, we select the monolingual query\nsimilarity measure presented in [26] which reports good\nperformance by using search users\" click-through information in\nquery logs. The reason to choose this monolingual similarity is\nthat it is defined in a similar context as ours \u2212 according to a user\nlog that reflects users\" intention and behavior. Therefore, we can\nexpect that the cross-language term similarity learned from it can\nalso reflect users\" intention and expectation.\nFollowing [26], our monolingual query similarity is defined by\ncombining both query content-based similarity and click-through\ncommonality in the query log.\nFirst the content similarity between two queries p and q is\ndefined as follows:\n))(),((\n),(\n),(\nqknpknMax\nqpKN\nqpsimilarity content = (3)\nwhere )( xkn is the number of keywords in a query x, ),( qpKN is\nthe number of common keywords in the two queries.\nSecondly, the click-through based similarity is defined as\nfollows,\n))(),((\n),(\n),(\nqrdprdMax\nqpRD\nqpsimilarity throughclick =\u2212\n(4)\nwhere )(xrd is the number of clicked URLs for a query x, and\n),( qpRD is the number of common URLs clicked for two queries.\nFinally, the similarity between two queries is a linear\ncombination of the content-based and click-through-based\nsimilarities, and is presented as follows:\n),(*\n),(*),(\nqpsimilarity\nqpsimilarityqpsimilarity\nthroughclick\ncontent\n\u2212\n+=\n\u03b2\n\u03b1 (5)\nwhere \u03b1 and \u03b2 are the relative importance of the two similarity\nmeasures. In this paper, we set ,4.0=\u03b1 and 6.0=\u03b2 following the\npractice in [26]. Queries with similarity measure higher than a\nthreshold with another query will be regarded as relevant\nmonolingual query suggestions (MLQS) for the latter. In this\npaper, the threshold is set as 0.9 empirically.\n3.3 Features Used for Learning Cross-Lingual\nQuery Similarity Measure\nThis section presents the extraction of candidate relevant queries\nfrom the log with the assistance of various monolingual and\nbilingual resources. Meanwhile, feature functions over source\nquery and the cross-lingual relevant candidates are defined. Some\nof the resources being used here, such as bilingual lexicon and\nparallel corpora, were for query translation in previous work. But\nnote that we employ them here as an assistant means for finding\nrelevant candidates in the log rather than for acquiring accurate\ntranslations.\n3.3.1 Bilingual Dictionary\nIn this subsection, a built-in-house bilingual dictionary containing\n120,000 unique entries is used to retrieve candidate queries. Since\nmultiple translations may be associated with each source word,\nco-occurrence based translation disambiguation is performed [3,\n10]. The process is presented as follows:\nGiven an input query }{ ,2,1 fnfff wwwq K= in the source\nlanguage, for each query term fiw , a set of unique translations are\nprovided by the bilingual dictionary D : },,{)( ,2,1 imiifi tttwD K= .\nThen the cohesion between the translations of two query terms is\nmeasured using mutual information which is computed as follows:\n)()(\n),(\nlog),()( ,\nklij\nklij\nklijklij\ntPtP\nttP\nttPttMI = (6)\nwhere .\n)(\n)(,\n),(\n),(\nN\ntC\ntP\nN\nttC\nttP\nklij\nklij ==\nHere ),( yxC is the number of queries in the log containing both\nx and y , )(xC is the number of queries containing term x , and\nN is the total number of queries in the log.\nBased on the term-term cohesion defined in Equation (6), all the\npossible query translations are ranked using the summation of the\nterm-term cohesion \u2211\u2260\n=\nkiki\nklijqdict ttMITS f\n,,\n),()( . The set of\ntop-4 query translations is denoted as )( fqTS . For each possible\nquery translation )( fqTST\u2208 , we retrieve all the queries containing\nthe same keywords as T from the target language log. The\nretrieved queries are candidate target queries, and are assigned\n)(TSdict\nas the value of the feature Dictionary-based Translation\nScore.\n3.3.2 Parallel Corpora\nParallel corpora are precious resources for bilingual knowledge\nacquisition. Different from the bilingual dictionary, the bilingual\nknowledge learned from parallel corpora assigns probability for\neach translation candidate which is useful in acquiring dominant\nquery translations.\nIn this paper, the Europarl corpus (a set of parallel French and\nEnglish texts from the proceedings of the European Parliament) is\nused. The corpus is first sentence aligned. Then word alignments\nare derived by training an IBM translation model 1 [4] using\nGIZA++ [21]. The learned bilingual knowledge is used to extract\ncandidate queries from the query log. The process is presented as\nfollows:\nGiven a pair of queries, fq in the source language and eq in the\ntarget language, the Bi-Directional Translation Score is defined as\nfollows:\n)|()|(),( 111 feIBMefIBMefIBM qqpqqpqqS = (7)\nwhere )|(1 xypIBM\nis the word sequence translation probability\ngiven by IBM model 1 which has the following form:\n\u220f\u2211= =+\n=\n||\n1\n||\n0\n||1 )|(\n)1|(|\n1\n)|(\ny\nj\nx\ni\nijyIBM xyp\nx\nxyp (8)\nwhere )|( ij xyp is the word to word translation probability\nderived from the word-aligned corpora.\nThe reason to use bidirectional translation probability is to deal\nwith the fact that common words can be considered as possible\ntranslations of many words. By using bidirectional translation, we\ntest whether the translation words can be translated back to the\nsource words. This is helpful to focus on the translation\nprobability onto the most specific translation candidates.\nNow, given an input query fq , the top 10 queries }{ eq with the\nhighest bidirectional translation scores with fq are retrieved from\nthe query log, and ),(1 efIBM qqS in Equation (7) is assigned as the\nvalue for the feature Bi-Directional Translation Score.\n3.3.3 Online Mining for Related Queries\nOOV word translation is a major knowledge bottleneck for query\ntranslation and CLIR. To overcome this knowledge bottleneck,\nweb mining has been exploited in [7, 27] to acquire\nEnglishChinese term translations based on the observation that Chinese\nterms may co-occur with their English translations in the same\nweb page. In this section, this web mining approach is adapted to\nacquire not only translations but semantically related queries in\nthe target language.\nIt is assumed that if a query in the target language co-occurs\nwith the source query in many web pages, they are probably\nsemantically related. Therefore, a simple method is to send the\nsource query to a search engine (Google in our case) for Web\npages in the target language in order to find related queries in the\ntarget language. For instance, by sending a French query pages\njaunes to search for English pages, the English snippets\ncontaining the key words yellow pages or telephone directory\nwill be returned. However, this simple approach may induce\nsignificant amount of noise due to the non-relevant returns from\nthe search engine. In order to improve the relevancy of the\nbilingual snippets, we extend the simple approach by the\nfollowing query modification: the original query is used to search\nwith the dictionary-based query keyword translations, which are\nunified by the \u2227 (and) \u2228 (OR) operators into a single Boolean\nquery. For example, for a given query abcq = where the set of\ntranslation entries in the dictionary of for a is },,{ 321 aaa , b is\n},{ 21 bb and c is }{ 1c , we issue 121321 )()( cbbaaaq \u2227\u2228\u2227\u2228\u2228\u2227 as\none web query.\nFrom the returned top 700 snippets, the most frequent 10 target\nqueries are identified, and are associated with the feature\nFrequency in the Snippets.\nFurthermore, we use Co-Occurrence Double-Check (CODC)\nMeasure to weight the association between the source and target\nqueries. CODC Measure is proposed in [6] as an association\nmeasure based on snippet analysis, named Web Search with\nDouble Checking (WSDC) model. In WSDC model, two objects a\nand b are considered to have an association if b can be found by\nusing a as query (forward process), and a can be found by using b\nas query (backward process) by web search. The forward process\ncounts the frequency of b in the top N snippets of query a, denoted\nas )@( abfreq . Similarly, the backward process count the\nfrequency of a in the top N snippets of query b, denoted\nas )@( bafreq . Then the CODC association score is defined as\nfollows:\n\u23aa\n\u23a9\n\u23aa\n\u23a8\n\u23a7 =\u00d7\n=\n\u23a5\n\u23a5\n\u23a6\n\u23a4\n\u23a2\n\u23a2\n\u23a3\n\u23a1\n\u00d7\notherwise,\n0)@()@(if,0\n),(\n)(\n)@(\n)(\n)@(\nlog\n\u03b1\ne\nef\nf\nfe\nqfreq\nqqfreq\nqfreq\nqqfreq\neffe\nefCODC\ne\nqqfreqqqfreq\nqqS (9)\nCODC measures the association of two terms in the range\nbetween 0 and 1, where under the two extreme cases, eq and fq\nare of no association when 0)@( =fe qqfreq\nor 0)@( =ef qqfreq , and are of the strongest association when\n)()@( ffe qfreqqqfreq = and )()@( eef qfreqqqfreq = . In\nour experiment, \u03b1 is set at 0.15 following the practice in [6].\nAny query eq mined from the Web will be associated with a\nfeature CODC Measure with ),( efCODC qqS as its value.\n3.3.4 Monolingual Query Suggestion\nFor all the candidate queries 0Q being retrieved using dictionary\n(see Section 3.3.1), parallel data (see Section 3.3.2) and web\nmining (see Section 3.3.3), monolingual query suggestion system\n(described in Section 3.1) is called to produce more related\nqueries in the target language. For each target query eq , its\nmonolingual source query )( eML qSQ is defined as the query in\n0Q with the highest monolingual similarity with eq , i.e.,\n),(maxarg)( 0 eeMLQqeML qqsimqSQ e\n\u2032= \u2208\u2032\n(10)\nThen the monolingual similarity between eq and )( eML qSQ is\nused as the value of the eq \"s Monolingual Query Suggestion\nFeature. For any target query 0Qq\u2208 , its Monolingual Query\nSuggestion Feature is set as 1.\nFor any query 0Qqe \u2209 , its values of Dictionary-based\nTranslation Score, Bi-Directional Translation Score, Frequency\nin the Snippet, and CODC Measure are set to be equal to the\nfeature values of )( eML qSQ .\n3.4 Estimating Cross-lingual Query Similarity\nIn summary, four categories of features are used to learn the\ncrosslingual query similarity. SVM regression algorithm [25] is used to\nlearn the weights in Equation (2). In this paper, LibSVM toolkit\n[5] is used for the regression training.\nIn the prediction stage, the candidate queries will be ranked\nusing the cross-lingual query similarity score computed in terms\nof )),((),( efefCL ttfwttsim \u03c6\u2022= , and the queries with\nsimilarity score lower than a threshold will be regarded as\nnonrelevant. The threshold is learned using a development data set by\nfitting MLQS\"s output.\n4. CLIR BASED ON CROSS-LINGUAL\nQUERY SUGGESTION\nIn Section 3, we presented a discriminative model for cross lingual\nquery suggestion. However, objectively benchmarking a query\nsuggestion system is not a trivial task. In this paper, we propose to\nuse CLQS as an alternative to query translation, and test its\neffectiveness in CLIR tasks. The resulting good performance of\nCLIR corresponds to the high quality of the suggested queries.\nGiven a source query fq , a set of relevant queries }{ eq in the\ntarget language are recommended using the cross-lingual query\nsuggestion system. Then a monolingual IR system based on the\nBM25 model [23] is called using each }{ eqq\u2208 as queries to\nretrieve documents. Then the retrieved documents are re-ranked\nbased on the sum of the BM25 scores associated with each\nmonolingual retrieval.\n5. PERFORMACNCE EVALUATION\nIn this section, we will benchmark the cross-lingual query\nsuggestion system, comparing its performance with monolingual\nquery suggestion, studying the contribution of various information\nsources, and testing its effectiveness when being used in CLIR\ntasks.\n5.1 Data Resources\nIn our experiments, French and English are selected as the source\nand target language respectively. Such selection is due to the fact\nthat large scale query logs are readily available for these two\nlanguages. A one-month English query log (containing 7 million\nunique English queries with occurrence frequency more than 5) of\nMSN search engine is used as the target language log. And a\nmonolingual query suggestion system is built based on it. In\naddition, 5,000 French queries are selected randomly from a\nFrench query log (containing around 3 million queries), and are\nmanually translated into English by professional French-English\ntranslators. Among the 5,000 French queries, 4,171 queries have\ntheir translations in the English query log, and are used for CLQS\ntraining and testing. Furthermore, among the 4,171 French\nqueries, 70% are used for cross-lingual query similarity training,\n10% are used as the development data to determine the relevancy\nthreshold, and 20% are used for testing. To retrieve the\ncrosslingual related queries, a built-in-house French-English bilingual\nlexicon (containing 120,000 unique entries) and the Europarl\ncorpus are used.\nBesides benchmarking CLQS as an independent system, the\nCLQS is also tested as a query translation system for CLIR\ntasks. Based on the observation that the CLIR performance\nheavily relies on the quality of the suggested queries, this\nbenchmark measures the quality of CLQS in terms of its\neffectiveness in helping CLIR. To perform such benchmark, we\nuse the documents of TREC6 CLIR data (AP88-90 newswire,\n750MB) with officially provided 25 short French-English queries\npairs (CL1-CL25). The selection of this data set is due to the fact\nthat the average length of the queries are 3.3 words long, which\nmatches the web query logs we use to train CLQS.\n5.2 Performance of Cross-lingual Query\nSuggestion\nMean-square-error (MSE) is used to measure the regression error\nand it is defined as follows:\n( )2\n),(),(\n1\n\u2211 \u2212=\ni\neiqMLeifiCL qTsimqqsim\nl\nMSE fi\nwhere l is the total number of cross-lingual query pairs in the\ntesting data.\nAs described in Section 3.4, a relevancy threshold is learned\nusing the development data, and only CLQS with similarity value\nabove the threshold is regarded as truly relevant to the input\nquery. In this way, CLQS can also be benchmarked as a\nclassification task using precision (P) and recall (R) which are\ndefined as follows:\nCLQS\nMLQSCLQS\nP\nS\nSS I\n= ,\nMLQS\nMLQSCLQS\nR\nS\nSS I\n=\nwhere CLQSS is the set of relevant queries suggested by CLQS,\nMLQSS is the set of relevant queries suggested by MLQS (see\nSection 3.2).\nThe benchmarking results with various feature configurations\nare shown in Table 1.\nRegression Classification\nFeatures\nMSE P R\nDD 0.274 0.723 0.098\nDD+PC 0.224 0.713 0.125\nDD+PC+\nWeb\n0.115 0.808 0.192\nDD+PC+\nWeb+ML\nQS\n0.174 0.796 0.421\nTable 1. CLQS performance with different feature settings\n(DD: dictionary only; DD+PC: dictionary and parallel corpora;\nDD+PC+Web: dictionary, parallel corpora, and web mining;\nDD+PC+Web+MLQS: dictionary, parallel corpora, web mining\nand monolingual query suggestion)\nTable 1 reports the performance comparison with various\nfeature settings. The baseline system (DD) uses a conventional\nquery translation approach, i.e., a bilingual dictionary with\ncooccurrence-based translation disambiguation. The baseline system\nonly covers less than 10% of the suggestions made by MLQS.\nUsing additional features obviously enables CLQS to generate\nmore relevant queries. The most significant improvement on recall\nis achieved by exploiting MLQS. The final CLQS system is able\nto generate 42% of the queries suggested by MLQS. Among all\nthe feature combinations, there is no significant change in\nprecision. This indicates that our methods can improve the recall\nby effectively leveraging various information sources without\nlosing the accuracy of the suggestions.\nBesides benchmarking CLQS by comparing its output with\nMLQS output, 200 French queries are randomly selected from the\nFrench query log. These queries are double-checked to make sure\nthat they are not in the CLQS training corpus. Then CLQS system\nis used to suggest relevant English queries for them. On average,\nfor each French query, 8.7 relevant English queries are suggested.\nThen the total 1,740 suggested English queries are manually\nchecked by two professional English/French translators with\ncross-validation. Among the 1,747 suggested queries, 1,407\nqueries are recognized as relevant to the original ones, hence the\naccuracy is 80.9%. Figure 1 shows an example of CLQS of the\nFrench query terrorisme international (international terrorism\nin English).\n5.3 CLIR Performance\nIn this section, CLQS is tested with French to English CLIR tasks.\nWe conduct CLIR experiments using the TREC 6 CLIR dataset\ndescribed in Section 5.1. The CLIR is performed using a query\ntranslation system followed by a BM25-based [23] monolingual\nIR module. The following three different systems have been used\nto perform query translation: (1) CLQS: our CLQS system; (2)\nMT: Google French to English machine translation system; (3)\nDT: a dictionary based query translation system using\ncooccurrence statistics for translation disambiguation. The\ntranslation disambiguation algorithm is presented in Section 3.3.1.\nBesides, the monolingual IR performance is also reported as a\nreference. The average precision of the four IR systems are\nreported in Table 2, and the 11-point precision-recall curves are\nshown in Figure 2.\nTable 2. Average precision of CLIR on TREC 6 Dataset\n(Monolingual: monolingual IR system; MT: CLIR based on\nmachine translation; DT: CLIR based on dictionary\ntranslation; CLQS: CLQS-based CLIR)\nIR System Average Precision % of Monolingual IR\nMonolingual 0.266 100%\nMT 0.217 81.6%\nDT 0.186 69.9%\nCLQS 0.233 87.6%\nFigure 1. An example of CLQS of the French query\nterrorisme international\ninternational terrorism (0.991); what is terrorism (0.943);\ncounter terrorism (0.920); terrorist (0.911);\nterrorist attacks (0.898); international terrorist (0.853);\nworld terrorism (0.845); global terrorism (0.833);\ntransnational terrorism (0.821); human rights (0.811);\nterrorist groups (0. 777); patterns of global terrorism (0.762)\nseptember 11 (0.734)\n11-point P-R curves (TREC6)\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1\nRecall\nPrecison\nMonolingual\nMT\nDT\nCLQS\nThe benchmark shows that using CLQS as a query translation\ntool outperforms CLIR based on machine translation by 7.4%,\noutperforms CLIR based on dictionary translation by 25.2%, and\nachieves 87.6% of the monolingual IR performance.\nThe effectiveness of CLQS lies in its ability in suggesting\nclosely related queries besides accurate translations. For example,\nfor the query CL14 terrorisme international (international\nterrorism), although the machine translation tool translates the\nquery correctly, CLQS system still achieves higher score by\nrecommending many additional related terms such as global\nterrorism, world terrorism, etc. (as shown in Figure 1). Another\nexample is the query La pollution caus\u00e9e par l'automobile (air\npollution due to automobile) of CL6. The MT tool provides the\ntranslation the pollution caused by the car, while CLQS system\nenumerates all the possible synonyms of car, and suggest the\nfollowing queries car pollution, auto pollution, automobile\npollution. Besides, other related queries such as global\nwarming are also suggested. For the query CL12 La culture\n\u00e9cologique (organic farming), the MT tool fails to generate the\ncorrect translation. Although the correct translation is neither in\nour French-English dictionary, CLQS system generates organic\nfarm as a relevant query due to successful web mining.\nThe above experiment demonstrates the effectiveness of using\nCLQS to suggest relevant queries for CLIR enhancement. A\nrelated research is to perform query expansion to enhance CLIR\n[2, 18]. So it is very interesting to compare the CLQS approach\nwith the conventional query expansion approaches. Following\n[18], post-translation expansion is performed based on\npseudorelevance feedback (PRF) techniques. We first perform CLIR in\nthe same way as before. Then we use the traditional PRF\nalgorithm described in [24] to select expansion terms. In our\nexperiments, the top 10 terms are selected to expand the original\nquery, and the new query is used to search the collection for the\nsecond time. The new CLIR performance in terms of average\nprecision is shown in Table 3. The 11-point P-R curves are drawn\nin Figure 3.\nAlthough being enhanced by pseudo-relevance feedback, the\nCLIR using either machine translation or dictionary-based query\ntranslation still does not perform as well as CLQS-based\napproach. Statistical t-test [13] is conducted to indicate whether\nthe CLQS-based CLIR performs significantly better. Pair-wise\npvalues are shown in Table 4. Clearly, CLQS significantly\noutperforms MT and DT without PRF as well as DT+PRF, but its\nsuperiority over MT+PRF is not significant. However, when\ncombined with PRF, CLQS significant outperforms all the other\nmethods. This indicates the higher effectiveness of CLQS in\nrelated term identification by leveraging a wide spectrum of\nresources. Furthermore, post-translation expansion is capable of\nimproving CLQS-based CLIR. This is due to the fact that CLQS\nand pseudo-relevance feedback are leveraging different categories\nof resources, and both approaches can be complementary.\nIR System AP without PRF AP with PRF\nMonolingual 0.266 (100%) 0.288 (100%)\nMT 0.217 (81.6%) 0.222 (77.1%)\nDT 0.186 (69.9%) 0.220 (76.4%)\nCLQS 0.233 (87.6%) 0.259 (89.9%)\n11-point P-R curves with pseudo relevance feedback (TREC6)\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1\nRecall\nPrecison\nMonolingual\nMT\nDT\nCLQS\nMT DT MT+PRF DT+PRF\nCLQS 0.0298 3.84e-05 0.1472 0.0282\nCLQS+PR\nF\n0.0026 2.63e-05 0.0094 0.0016\n6. CONCLUSIONS\nIn this paper, we proposed a new approach to cross-lingual query\nsuggestion by mining relevant queries in different languages from\nquery logs. The key solution to this problem is to learn a\ncrosslingual query similarity measure by a discriminative model\nexploiting multiple monolingual and bilingual resources. The\nmodel is trained based on the principle that cross-lingual\nsimilarity should best fit the monolingual similarity between one\nquery and the other query\"s translation.\nFigure 2. 11 points precision-recall on TREC6 CLIR data set\nFigure 3. 11 points precision-recall on TREC6 CLIR\ndataset with pseudo relevance feedback\nTable 3. Comparison of average precision (AP) on TREC 6\nwithout and with post-translation expansion. (%) are the\nrelative percentages over the monolingual IR performance\nTable 4. The results of pair-wise significance t-test. Here\npvalue < 0.05 is considered statistically significant\nThe baseline CLQS system applies a typical query translation\napproach, using a bilingual dictionary with co-occurrence-based\ntranslation disambiguation. This approach only covers 10% of the\nrelevant queries suggested by an MLQS system (when the exact\ntranslation of the original query is given). By leveraging\nadditional resources such as parallel corpora, web mining and\nlogbased monolingual query expansion, the final system is able to\ncover 42% of the relevant queries suggested by an MLQS system\nwith precision as high as 79.6%.\nTo further test the quality of the suggested queries, CLQS system\nis used as a query translation system in CLIR tasks.\nBenchmarked using TREC 6 French to English CLIR task, CLQS\ndemonstrates higher effectiveness than the traditional query\ntranslation methods using either bilingual dictionary or\ncommercial machine translation tools.\nThe improvement on TREC French to English CLIR task by\nusing CLQS demonstrates the high quality of the suggested\nqueries. This also shows the strong correspondence between the\ninput French queries and English queries in the log. In the future,\nwe will build CLQS system between languages which may be\nmore loosely correlated, e.g., English and Chinese, and study the\nCLQS performance change due to the less strong correspondence\namong queries in such languages.\n7. REFERENCES\n[1] Ambati, V. and Rohini., U. Using Monolingual Clickthrough\nData to Build Cross-lingual Search Systems. In Proceedings\nof New Directions in Multilingual Information Access\nWorkshop of SIGIR 2006.\n[2] Ballestors, L. A. and Croft, W. B. Phrasal Translation and\nQuery Expansion Techniques for Cross-Language\nInformation Retrieval. In Proc. SIGIR 1997, pp. 84-91.\n[3] Ballestors, L. A. and Croft, W. B. Resolving Ambiguity for\nCross-Language Retrieval. In Proc. SIGIR 1998, pp. 64-71.\n[4] Brown, P. F., Pietra, D. S. A., Pietra, D. V. J., and Mercer, R.\nL. The Mathematics of Statistical Machine Translation:\nParameter Estimation. Computational Linguistics,\n19(2):263311, 1993.\n[5] Chang, C. C. and Lin, C. 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Improving query translation for CLIR using\nstatistical Models. In Proc. SIGIR 2001, pp. 96-104.\n[11] Gao, J. F., Nie, J.-Y., He, H., Chen, W., and Zhou, M.\nResolving Query Translation Ambiguity using a Decaying\nCo-occurrence Model and Syntactic Dependence Relations.\nIn Proc. SIGIR 2002, pp. 183-190.\n[12] Gleich, D., and Zhukov, L. SVD Subspace Projections for\nTerm Suggestion Ranking and Clustering. In Technical\nReport, Yahoo! Research Labs, 2004.\n[13] Hull, D. Using Statistical Testing in the Evaluation of\nRetrieval Experiments. In Proc. SIGIR 1993, pp. 329-338.\n[14] Jeon, J., Croft, W. B., and Lee, J. Finding Similar Questions\nin Large Question and Answer Archives. In Proc. CIKM\n2005, pp. 84-90.\n[15] Joachims, T. Optimizing Search Engines Using Clickthrough\nData. In Proc. SIGKDD 2002, pp. 133-142.\n[16] Lavrenko, V., Choquette, M., and Croft, W. B. Cross-Lingual\nRelevance Models. In Proc. SIGIR 2002, pp. 175-182.\n[17] Lu, W.-H., Chien, L.-F., and Lee, H.-J. Anchor Text Mining\nfor Translation Extraction of Query Terms. In Proc. SIGIR\n2001, pp. 388-389.\n[18] McNamee, P. and Mayfield, J. Comparing Cross-Language\nQuery Expansion Techniques by Degrading Translation\nResources. In Proc. SIGIR 2002, pp. 159-166.\n[19] Monz, C. and Dorr, B. J. Iterative Translation\nDisambiguation for Cross-Language Information Retrieval.\nIn Proc. SIGIR 2005, pp. 520-527.\n[20] Nie, J.-Y., Simard, M., Isabelle, P., and Durand, R.\nCrossLanguage Information Retrieval based on Parallel Text and\nAutomatic Mining of Parallel Text from the Web. In Proc.\nSIGIR 1999, pp. 74-81.\n[21] Och, F. J. and Ney, H. A Systematic Comparison of Various\nStatistical Alignment Models. Computational Linguistics,\n29(1):19-51, 2003.\n[22] Pirkola, A., Hedlund, T., Keshusalo, H., and J\u00e4rvelin, K.\nDictionary-Based Cross-Language Information Retrieval:\nProblems, Methods, and Research Findings. Information\nRetrieval, 4(3/4):209-230, 2001.\n[23] Robertson, S. E., Walker, S., Hancock-Beaulieu, M. M., and\nGatford, M. OKAPI at TREC-3. In Proc.TREC-3, pp.\n200225, 1995.\n[24] Robertson, S. E. and Jones, K. S. Relevance Weighting of\nSearch Terms. Journal of the American Society of\nInformation Science, 27(3):129-146, 1976.\n[25] Smola, A. J. and Sch\u00f6lkopf, B. A. Tutorial on Support Vector\nRegression. Statistics and Computing, 14(3):199-222, 2004.\n[26] Wen, J. R., Nie, J.-Y., and Zhang, H. J. Query Clustering\nUsing User Logs. ACM Trans. Information Systems,\n20(1):59-81, 2002.\n[27] Zhang, Y. and Vines, P. Using the Web for Automated\nTranslation Extraction in Cross-Language Information\nRetrieval. In Proc. SIGIR 2004, pp. 162-169.", "keywords": "bidding term;benchmark;target language query log;map;query expansion;query suggestion;query log;cross-language information retrieval;query translation;search engine advertisement;search engine;keyword bidding;monolingual query suggestion"}
{"name": "train_H-41", "title": "HITS on the Web: How does it Compare?", "abstract": "This paper describes a large-scale evaluation of the effectiveness of HITS in comparison with other link-based ranking algorithms, when used in combination with a state-ofthe-art text retrieval algorithm exploiting anchor text. We quantified their effectiveness using three common performance measures: the mean reciprocal rank, the mean average precision, and the normalized discounted cumulative gain measurements. The evaluation is based on two large data sets: a breadth-first search crawl of 463 million web pages containing 17.6 billion hyperlinks and referencing 2.9 billion distinct URLs; and a set of 28,043 queries sampled from a query log, each query having on average 2,383 results, about 17 of which were labeled by judges. We found that HITS outperforms PageRank, but is about as effective as web-page in-degree. The same holds true when any of the link-based features are combined with the text retrieval algorithm. Finally, we studied the relationship between query specificity and the effectiveness of selected features, and found that link-based features perform better for general queries, whereas BM25F performs better for specific queries.", "fulltext": "1. INTRODUCTION\nLink graph features such as in-degree and PageRank have\nbeen shown to significantly improve the performance of text\nretrieval algorithms on the web. The HITS algorithm is also\nbelieved to be of interest for web search; to some degree,\none may expect HITS to be more informative that other\nlink-based features because it is query-dependent: it tries to\nmeasure the interest of pages with respect to a given query.\nHowever, it remains unclear today whether there are\npractical benefits of HITS over other link graph measures. This\nis even more true when we consider that modern retrieval\nalgorithms used on the web use a document representation\nwhich incorporates the document\"s anchor text, i.e. the text\nof incoming links. This, at least to some degree, takes the\nlink graph into account, in a query-dependent manner.\nComparing HITS to PageRank or in-degree empirically is\nno easy task. There are two main difficulties: scale and\nrelevance. Scale is important because link-based features are\nknown to improve in quality as the document graph grows.\nIf we carry out a small experiment, our conclusions won\"t\ncarry over to large graphs such as the web. However,\ncomputing HITS efficiently on a graph the size of a realistic web\ncrawl is extraordinarily difficult. Relevance is also crucial\nbecause we cannot measure the performance of a feature in\nthe absence of human judgments: what is crucial is ranking\nat the top of the ten or so documents that a user will peruse.\nTo our knowledge, this paper is the first attempt to\nevaluate HITS at a large scale and compare it to other link-based\nfeatures with respect to human evaluated judgment.\nOur results confirm many of the intuitions we have about\nlink-based features and their relationship to text retrieval\nmethods exploiting anchor text. This is reassuring: in the\nabsence of a theoretical model capable of tying these\nmeasures with relevance, the only way to validate our intuitions\nis to carry out realistic experiments. However, we were quite\nsurprised to find that HITS, a query-dependent feature, is\nabout as effective as web page in-degree, the most\nsimpleminded query-independent link-based feature. This\ncontinues to be true when the link-based features are combined\nwith a text retrieval algorithm exploiting anchor text.\nThe remainder of this paper is structured as follows:\nSection 2 surveys related work. Section 3 describes the data\nsets we used in our study. Section 4 reviews the\nperformance measures we used. Sections 5 and 6 describe the\nPageRank and HITS algorithms in more detail, and sketch\nthe computational infrastructure we employed to carry out\nlarge scale experiments. Section 7 presents the results of our\nevaluations, and Section 8 offers concluding remarks.\n2. RELATED WORK\nThe idea of using hyperlink analysis for ranking web search\nresults arose around 1997, and manifested itself in the HITS\n[16, 17] and PageRank [5, 21] algorithms. The popularity\nof these two algorithms and the phenomenal success of the\nGoogle search engine, which uses PageRank, have spawned\na large amount of subsequent research.\nThere are numerous attempts at improving the\neffectiveness of HITS and PageRank. Query-dependent link-based\nranking algorithms inspired by HITS include SALSA [19],\nRandomized HITS [20], and PHITS [7], to name a few.\nQuery-independent link-based ranking algorithms inspired\nby PageRank include TrafficRank [22], BlockRank [14], and\nTrustRank [11], and many others.\nAnother line of research is concerned with analyzing the\nmathematical properties of HITS and PageRank. For\nexample, Borodin et al. [3] investigated various theoretical\nproperties of PageRank, HITS, SALSA, and PHITS, including\ntheir similarity and stability, while Bianchini et al. [2]\nstudied the relationship between the structure of the web graph\nand the distribution of PageRank scores, and Langville and\nMeyer examined basic properties of PageRank such as\nexistence and uniqueness of an eigenvector and convergence of\npower iteration [18].\nGiven the attention that has been paid to improving the\neffectiveness of PageRank and HITS, and the thorough\nstudies of the mathematical properties of these algorithms, it is\nsomewhat surprising that very few evaluations of their\neffectiveness have been published. We are aware of two studies\nthat have attempted to formally evaluate the effectiveness of\nHITS and of PageRank. Amento et al. [1] employed\nquantitative measures, but based their experiments on the result\nsets of just 5 queries and the web-graph induced by topical\ncrawls around the result set of each query. A more recent\nstudy by Borodin et al. [4] is based on 34 queries, result sets\nof 200 pages per query obtained from Google, and a\nneighborhood graph derived by retrieving 50 in-links per result\nfrom Google. By contrast, our study is based on over 28,000\nqueries and a web graph covering 2.9 billion URLs.\n3. OUR DATA SETS\nOur evaluation is based on two data sets: a large web\ngraph and a substantial set of queries with associated results,\nsome of which were labeled by human judges.\nOur web graph is based on a web crawl that was\nconducted in a breadth-first-search fashion, and successfully\nretrieved 463,685,607 HTML pages. These pages contain\n17,672,011,890 hyperlinks (after eliminating duplicate\nhyperlinks embedded in the same web page), which refer to\na total of 2,897,671,002 URLs. Thus, at the end of the\ncrawl there were 2,433,985,395 URLs in the frontier set\nof the crawler that had been discovered, but not yet\ndownloaded. The mean out-degree of crawled web pages is 38.11;\nthe mean in-degree of discovered pages (whether crawled or\nnot) is 6.10. Also, it is worth pointing out that there is a\nlot more variance in in-degrees than in out-degrees; some\npopular pages have millions of incoming links. As we will\nsee, this property affects the computational cost of HITS.\nOur query set was produced by sampling 28,043 queries\nfrom the MSN Search query log, and retrieving a total of\n66,846,214 result URLs for these queries (using commercial\nsearch engine technology), or about 2,838 results per query\non average. It is important to point out that our 2.9 billion\nURL web graph does not cover all these result URLs. In\nfact, only 9,525,566 of the result URLs (about 14.25%) were\ncovered by the graph.\n485,656 of the results in the query set (about 0.73% of\nall results, or about 17.3 results per query) were rated by\nhuman judges as to their relevance to the given query, and\nlabeled on a six-point scale (the labels being definitive,\nexcellent, good, fair, bad and detrimental).\nResults were selected for judgment based on their commercial\nsearch engine placement; in other words, the subset of\nlabeled results is not random, but biased towards documents\nconsidered relevant by pre-existing ranking algorithms.\nInvolving a human in the evaluation process is extremely\ncumbersome and expensive; however, human judgments are\ncrucial for the evaluation of search engines. This is so\nbecause no document features have been found yet that can\neffectively estimate the relevance of a document to a user\nquery. Since content-match features are very unreliable (and\neven more so link features, as we will see) we need to ask\na human to evaluate the results in order to compare the\nquality of features.\nEvaluating the retrieval results from document scores and\nhuman judgments is not trivial and has been the subject of\nmany investigations in the IR community. A good\nperformance measure should correlate with user satisfaction,\ntaking into account that users will dislike having to delve deep\nin the results to find relevant documents. For this reason,\nstandard correlation measures (such as the correlation\ncoefficient between the score and the judgment of a document),\nor order correlation measures (such as Kendall tau between\nthe score and judgment induced orders) are not adequate.\n4. MEASURING PERFORMANCE\nIn this study, we quantify the effectiveness of various\nranking algorithms using three measures: NDCG, MRR, and\nMAP.\nThe normalized discounted cumulative gains (NDCG)\nmeasure [13] discounts the contribution of a document to the\noverall score as the document\"s rank increases (assuming\nthat the best document has the lowest rank). Such a\nmeasure is particularly appropriate for search engines, as studies\nhave shown that search engine users rarely consider anything\nbeyond the first few results [12]. NDCG values are\nnormalized to be between 0 and 1, with 1 being the NDCG of a\nperfect ranking scheme that completely agrees with the\nassessment of the human judges. The discounted\ncumulative gain at a particular rank-threshold T (DCG@T) is\ndefined to be\nPT\nj=1\n1\nlog(1+j)\n\n2r(j)\n\u2212 1\n\n, where r(j) is the\nrating (0=detrimental, 1=bad, 2=fair, 3=good, 4=excellent,\nand 5=definitive) at rank j. The NDCG is computed by\ndividing the DCG of a ranking by the highest possible DCG\nthat can be obtained for that query. Finally, the NDGCs of\nall queries in the query set are averaged to produce a mean\nNDCG.\nThe reciprocal rank (RR) of the ranked result set of a\nquery is defined to be the reciprocal value of the rank of the\nhighest-ranking relevant document in the result set. The RR\nat rank-threshold T is defined to be 0 if none of the\nhighestranking T documents is relevant. The mean reciprocal rank\n(MRR) of a query set is the average reciprocal rank of all\nqueries in the query set.\nGiven a ranked set of n results, let rel(i) be 1 if the result\nat rank i is relevant and 0 otherwise. The precision P(j)\nat rank j is defined to be 1\nj\nPj\ni=1 rel(i), i.e. the fraction\nof the relevant results among the j highest-ranking results.\nThe average precision (AP) at rank-threshold k is defined to\nbe\nPk\ni=1 P (i)rel(i)\nPn\ni=1\nrel(i)\n. The mean average precision (MAP) of a\nquery set is the mean of the average precisions of all queries\nin the query set.\nThe above definitions of MRR and MAP rely on the notion\nof a relevant result. We investigated two definitions of\nrelevance: One where all documents rated fair or better were\ndeemed relevant, and one were all documents rated good\nor better were deemed relevant. For reasons of space, we\nonly report MAP and MRR values computed using the\nlatter definition; using the former definition does not change\nthe qualitative nature of our findings. Similarly, we\ncomputed NDCG, MAP, and MRR values for a wide range of\nrank-thresholds; we report results here at rank 10; again,\nchanging the rank-threshold never led us to different\nconclusions.\nRecall that over 99% of documents are unlabeled. We\nchose to treat all these documents as irrelevant to the query.\nFor some queries, however, not all relevant documents have\nbeen judged. This introduces a bias into our evaluation:\nfeatures that bring new documents to the top of the rank\nmay be penalized. This will be more acute for features less\ncorrelated to the pre-existing commercial ranking algorithms\nused to select documents for judgment. On the other hand,\nmost queries have few perfect relevant documents (i.e. home\npage or item searches) and they will most often be within\nthe judged set.\n5. COMPUTING PAGERANK ON A LARGE\nWEB GRAPH\nPageRank is a query-independent measure of the\nimportance of web pages, based on the notion of peer-endorsement:\nA hyperlink from page A to page B is interpreted as an\nendorsement of page B\"s content by page A\"s author. The\nfollowing recursive definition captures this notion of\nendorsement:\nR(v) =\nX\n(u,v)\u2208E\nR(u)\nOut(u)\nwhere R(v) is the score (importance) of page v, (u, v) is an\nedge (hyperlink) from page u to page v contained in the\nedge set E of the web graph, and Out(u) is the out-degree\n(number of embedded hyperlinks) of page u. However, this\ndefinition suffers from a severe shortcoming: In the\nfixedpoint of this recursive equation, only edges that are part of\na strongly-connected component receive a non-zero score. In\norder to overcome this deficiency, Page et al. grant each page\na guaranteed minimum score, giving rise to the definition\nof standard PageRank:\nR(v) =\nd\n|V |\n+ (1 \u2212 d)\nX\n(u,v)\u2208E\nR(u)\nOut(u)\nwhere |V | is the size of the vertex set (the number of known\nweb pages), and d is a damping factor, typically set to be\nbetween 0.1 and 0.2.\nAssuming that scores are normalized to sum up to 1,\nPageRank can be viewed as the stationary probability\ndistribution of a random walk on the web graph, where at each\nstep of the walk, the walker with probability 1 \u2212 d moves\nfrom its current node u to a neighboring node v, and with\nprobability d selects a node uniformly at random from all\nnodes in the graph and jumps to it. In the limit, the random\nwalker is at node v with probability R(v).\nOne issue that has to be addressed when implementing\nPageRank is how to deal with sink nodes, nodes that do\nnot have any outgoing links. One possibility would be to\nselect another node uniformly at random and transition to\nit; this is equivalent to adding edges from each sink nodes\nto all other nodes in the graph. We chose the alternative\napproach of introducing a single phantom node. Each sink\nnode has an edge to the phantom node, and the phantom\nnode has an edge to itself.\nIn practice, PageRank scores can be computed using power\niteration. Since PageRank is query-independent, the\ncomputation can be performed off-line ahead of query time. This\nproperty has been key to PageRank\"s success, since it is a\nchallenging engineering problem to build a system that can\nperform any non-trivial computation on the web graph at\nquery time.\nIn order to compute PageRank scores for all 2.9 billion\nnodes in our web graph, we implemented a distributed\nversion of PageRank. The computation consists of two distinct\nphases. In the first phase, the link files produced by the web\ncrawler, which contain page URLs and their associated link\nURLs in textual form, are partitioned among the machines\nin the cluster used to compute PageRank scores, and\nconverted into a more compact format along the way.\nSpecifically, URLs are partitioned across the machines in the\ncluster based on a hash of the URLs\" host component, and each\nmachine in the cluster maintains a table mapping the URL\nto a 32-bit integer. The integers are drawn from a densely\npacked space, so as to make suitable indices into the array\nthat will later hold the PageRank scores. The system then\ntranslates our log of pages and their associated hyperlinks\ninto a compact representation where both page URLs and\nlink URLs are represented by their associated 32-bit\nintegers. Hashing the host component of the URLs guarantees\nthat all URLs from the same host are assigned to the same\nmachine in our scoring cluster. Since over 80% of all\nhyperlinks on the web are relative (that is, are between two pages\non the same host), this property greatly reduces the amount\nof network communication required by the second stage of\nthe distributed scoring computation.\nThe second phase performs the actual PageRank power\niteration. Both the link data and the current PageRank\nvector reside on disk and are read in a streaming fashion;\nwhile the new PageRank vector is maintained in memory.\nWe represent PageRank scores as 64-bit floating point\nnumbers. PageRank contributions to pages assigned to remote\nmachines are streamed to the remote machine via a TCP\nconnection.\nWe used a three-machine cluster, each machine equipped\nwith 16 GB of RAM, to compute standard PageRank scores\nfor all 2.9 billion URLs that were contained in our web\ngraph. We used a damping factor of 0.15, and performed 200\npower iterations. Starting at iteration 165, the L\u221e norm of\nthe change in the PageRank vector from one iteration to the\nnext had stopped decreasing, indicating that we had reached\nas much of a fixed point as the limitations of 64-bit floating\npoint arithmetic would allow.\n0.07\n0.08\n0.09\n0.10\n0.11\n1 10 100\nNumber of back-links sampled per result\nNDCG@10\nhits-aut-all\nhits-aut-ih\nhits-aut-id\n0.01\n0.02\n0.03\n0.04\n1 10 100\nNumber of back-links sampled per result\nMAP@10\nhits-aut-all\nhits-aut-ih\nhits-aut-id\n0.07\n0.08\n0.09\n0.10\n0.11\n0.12\n0.13\n0.14\n1 10 100\nNumber of back-links sampled per result\nMRR@10\nhits-aut-all\nhits-aut-ih\nhits-aut-id\nFigure 1: Effectiveness of authority scores computed using different parameterizations of HITS.\nA post-processing phase uses the final PageRank vectors\n(one per machine) and the table mapping URLs to 32-bit\nintegers (representing indices into each PageRank vector) to\nscore the result URL in our query log. As mentioned above,\nour web graph covered 9,525,566 of the 66,846,214 result\nURLs. These URLs were annotated with their computed\nPageRank score; all other URLs received a score of 0.\n6. HITS\nHITS, unlike PageRank, is a query-dependent ranking\nalgorithm. HITS (which stands for Hypertext Induced Topic\nSearch) is based on the following two intuitions: First,\nhyperlinks can be viewed as topical endorsements: A hyperlink\nfrom a page u devoted to topic T to another page v is likely\nto endorse the authority of v with respect to topic T. Second,\nthe result set of a particular query is likely to have a certain\namount of topical coherence. Therefore, it makes sense to\nperform link analysis not on the entire web graph, but rather\non just the neighborhood of pages contained in the result\nset, since this neighborhood is more likely to contain\ntopically relevant links. But while the set of nodes immediately\nreachable from the result set is manageable (given that most\npages have only a limited number of hyperlinks embedded\ninto them), the set of pages immediately leading to the result\nset can be enormous. For this reason, Kleinberg suggests\nsampling a fixed-size random subset of the pages linking to\nany high-indegree page in the result set. Moreover,\nKleinberg suggests considering only links that cross host\nboundaries, the rationale being that links between pages on the\nsame host (intrinsic links) are likely to be navigational or\nnepotistic and not topically relevant.\nGiven a web graph (V, E) with vertex set V and edge\nset E \u2286 V \u00d7 V , and the set of result URLs to a query\n(called the root set R \u2286 V ) as input, HITS computes a\nneighborhood graph consisting of a base set B \u2286 V (the\nroot set and some of its neighboring vertices) and some of\nthe edges in E induced by B. In order to formalize the\ndefinition of the neighborhood graph, it is helpful to first\nintroduce a sampling operator and the concept of a\nlinkselection predicate.\nGiven a set A, the notation Sn[A] draws n elements\nuniformly at random from A; Sn[A] = A if |A| \u2264 n.\nA link section predicate P takes an edge (u, v) \u2208 E. In\nthis study, we use the following three link section predicates:\nall(u, v) \u21d4 true\nih(u, v) \u21d4 host(u) = host(v)\nid(u, v) \u21d4 domain(u) = domain(v)\nwhere host(u) denotes the host of URL u, and domain(u)\ndenotes the domain of URL u. So, all is true for all links,\nwhereas ih is true only for inter-host links, and id is true\nonly for inter-domain links.\nThe outlinked-set OP\nof the root set R w.r.t. a\nlinkselection predicate P is defined to be:\nOP\n=\n[\nu\u2208R\n{v \u2208 V : (u, v) \u2208 E \u2227 P(u, v)}\nThe inlinking-set IP\ns of the root set R w.r.t. a link-selection\npredicate P and a sampling value s is defined to be:\nIP\ns =\n[\nv\u2208R\nSs[{u \u2208 V : (u, v) \u2208 E \u2227 P(u, v)}]\nThe base set BP\ns of the root set R w.r.t. P and s is defined\nto be:\nBP\ns = R \u222a IP\ns \u222a OP\nThe neighborhood graph (BP\ns , NP\ns ) has the base set BP\ns as\nits vertex set and an edge set NP\ns containing those edges in\nE that are covered by BP\ns and permitted by P:\nNP\ns = {(u, v) \u2208 E : u \u2208 BP\ns \u2227 v \u2208 BP\ns \u2227 P(u, v)}\nTo simplify notation, we write B to denote BP\ns , and N to\ndenote NP\ns .\nFor each node u in the neighborhood graph, HITS\ncomputes two scores: an authority score A(u), estimating how\nauthoritative u is on the topic induced by the query, and a\nhub score H(u), indicating whether u is a good reference to\nmany authoritative pages. This is done using the following\nalgorithm:\n1. For all u \u2208 B do H(u) :=\nq\n1\n|B|\n, A(u) :=\nq\n1\n|B|\n.\n2. Repeat until H and A converge:\n(a) For all v \u2208 B : A (v) :=\nP\n(u,v)\u2208N H(u)\n(b) For all u \u2208 B : H (u) :=\nP\n(u,v)\u2208N A(v)\n(c) H := H 2, A := A 2\nwhere X 2 normalizes the vector X to unit length in\neuclidean space, i.e. the squares of its elements sum up to 1.\nIn practice, implementing a system that can compute HITS\nwithin the time constraints of a major search engine (where\nthe peak query load is in the thousands of queries per second,\nand the desired query response time is well below one\nsecond) is a major engineering challenge. Among other things,\nthe web graph cannot reasonably be stored on disk, since\n.221\n.106\n.105\n.104\n.102\n.095\n.092\n.090\n.038\n.036\n.035\n.034\n.032\n.032\n.011\n0.00\n0.05\n0.10\n0.15\n0.20\n0.25\nbm25f\ndegree-in-id\ndegree-in-ih\nhits-aut-id-25\nhits-aut-ih-100\ndegree-in-all\npagerank\nhits-aut-all-100\nhits-hub-all-100\nhits-hub-ih-100\nhits-hub-id-100\ndegree-out-all\ndegree-out-ih\ndegree-out-id\nrandom\nNDCG@10\n.100\n.035\n.033\n.033\n.033\n.029\n.027\n.027\n.008\n.007\n.007\n.006\n.006\n.006\n.002\n0.00\n0.02\n0.04\n0.06\n0.08\n0.10\n0.12\nbm25f\nhits-aut-id-9\ndegree-in-id\nhits-aut-ih-15\ndegree-in-ih\ndegree-in-all\npagerank\nhits-aut-all-100\nhits-hub-all-100\nhits-hub-ih-100\nhits-hub-id-100\ndegree-out-all\ndegree-out-ih\ndegree-out-id\nrandom\nMAP@10\n.273\n.132\n.126\n.117\n.114\n.101\n.101\n.097\n.032\n.032\n.030\n.028\n.027\n.027\n.007\n0.00\n0.05\n0.10\n0.15\n0.20\n0.25\n0.30\nbm25f\nhits-aut-id-9\nhits-aut-ih-15\ndegree-in-id\ndegree-in-ih\ndegree-in-all\nhits-aut-all-100\npagerank\nhits-hub-all-100\nhits-hub-ih-100\nhits-hub-id-100\ndegree-out-all\ndegree-out-ih\ndegree-out-id\nrandom\nMRR@10\nFigure 2: Effectiveness of different features.\nseek times of modern hard disks are too slow to retrieve the\nlinks within the time constraints, and the graph does not fit\ninto the main memory of a single machine, even when using\nthe most aggressive compression techniques.\nIn order to experiment with HITS and other\nquery-dependent link-based ranking algorithms that require non-regular\naccesses to arbitrary nodes and edges in the web graph, we\nimplemented a system called the Scalable Hyperlink Store,\nor SHS for short. SHS is a special-purpose database,\ndistributed over an arbitrary number of machines that keeps a\nhighly compressed version of the web graph in memory and\nallows very fast lookup of nodes and edges. On our\nhardware, it takes an average of 2 microseconds to map a URL\nto a 64-bit integer handle called a UID, 15 microseconds to\nlook up all incoming or outgoing link UIDs associated with\na page UID, and 5 microseconds to map a UID back to a\nURL (the last functionality not being required by HITS).\nThe RPC overhead is about 100 microseconds, but the SHS\nAPI allows many lookups to be batched into a single RPC\nrequest.\nWe implemented the HITS algorithm using the SHS\ninfrastructure. We compiled three SHS databases, one\ncontaining all 17.6 billion links in our web graph (all), one\ncontaining only links between pages that are on different hosts\n(ih, for inter-host), and one containing only links between\npages that are on different domains (id). We consider two\nURLs to belong to different hosts if the host portions of the\nURLs differ (in other words, we make no attempt to\ndetermine whether two distinct symbolic host names refer to\nthe same computer), and we consider a domain to be the\nname purchased from a registrar (for example, we consider\nnews.bbc.co.uk and www.bbc.co.uk to be different hosts\nbelonging to the same domain). Using each of these databases,\nwe computed HITS authority and hub scores for various\nparameterizations of the sampling operator S, sampling\nbetween 1 and 100 back-links of each page in the root set.\nResult URLs that were not covered by our web graph\nautomatically received authority and hub scores of 0, since they\nwere not connected to any other nodes in the neighborhood\ngraph and therefore did not receive any endorsements.\nWe performed forty-five different HITS computations, each\ncombining one of the three link selection predicates (all, ih,\nand id) with a sampling value. For each combination, we\nloaded one of the three databases into an SHS system\nrunning on six machines (each equipped with 16 GB of RAM),\nand computed HITS authority and hub scores, one query\nat a time. The longest-running combination (using the all\ndatabase and sampling 100 back-links of each root set\nvertex) required 30,456 seconds to process the entire query set,\nor about 1.1 seconds per query on average.\n7. EXPERIMENTAL RESULTS\nFor a given query Q, we need to rank the set of documents\nsatisfying Q (the result set of Q). Our hypothesis is that\ngood features should be able to rank relevant documents in\nthis set higher than non-relevant ones, and this should result\nin an increase in each performance measure over the query\nset. We are specifically interested in evaluating the\nusefulness of HITS and other link-based features. In principle, we\ncould do this by sorting the documents in each result set by\ntheir feature value, and compare the resulting NDCGs. We\ncall this ranking with isolated features.\nLet us first examine the relative performance of the\ndifferent parameterizations of the HITS algorithm we\nexamined. Recall that we computed HITS for each combination\nof three link section schemes - all links (all), inter-host links\nonly (ih), and inter-domain links only (id) - with back-link\nsampling values ranging from 1 to 100. Figure 1 shows the\nimpact of the number of sampled back-links on the retrieval\nperformance of HITS authority scores. Each graph is\nassociated with one performance measure. The horizontal axis\nof each graph represents the number of sampled back-links,\nthe vertical axis represents performance under the\nappropriate measure, and each curve depicts a link selection scheme.\nThe id scheme slightly outperforms ih, and both vastly\noutperform the all scheme - eliminating nepotistic links pays\noff. The performance of the all scheme increases as more\nback-links of each root set vertex are sampled, while the\nperformance of the id and ih schemes peaks at between 10\nand 25 samples and then plateaus or even declines,\ndepending on the performance measure.\nHaving compared different parameterizations of HITS, we\nwill now fix the number of sampled back-links at 100 and\ncompare the three link selection schemes against other\nisolated features: PageRank, in-degree and out-degree\ncounting links of all pages, of different hosts only and of different\ndomains only (all, ih and id datasets respectively), and a\ntext retrieval algorithm exploiting anchor text: BM25F[24].\nBM25F is a state-of-the art ranking function solely based on\ntextual content of the documents and their associated\nanchor texts. BM25F is a descendant of BM25 that combines\nthe different textual fields of a document, namely title, body\nand anchor text. This model has been shown to be one of\nthe best-performing web search scoring functions over the\nlast few years [8, 24]. BM25F has a number of free\nparameters (2 per field, 6 in our case); we used the parameter values\ndescribed in [24].\n.341\n.340\n.339\n.337\n.336\n.336\n.334\n.311\n.311\n.310\n.310\n.310\n.310\n.231\n0.22\n0.24\n0.26\n0.28\n0.30\n0.32\n0.34\n0.36\ndegree-in-id\ndegree-in-ih\ndegree-in-all\nhits-aut-ih-100\nhits-aut-all-100\npagerank\nhits-aut-id-10\ndegree-out-all\nhits-hub-all-100\ndegree-out-ih\nhits-hub-ih-100\ndegree-out-id\nhits-hub-id-10\nbm25f\nNDCG@10\n.152\n.152\n.151\n.150\n.150\n.149\n.149\n.137\n.136\n.136\n.128\n.127\n.127\n.100\n0.09\n0.10\n0.11\n0.12\n0.13\n0.14\n0.15\n0.16\ndegree-in-ih\ndegree-in-id\ndegree-in-all\nhits-aut-ih-100\nhits-aut-all-100\nhits-aut-id-10\npagerank\nhits-hub-all-100\ndegree-out-ih\nhits-hub-id-100\ndegree-out-all\ndegree-out-id\nhits-hub-ih-100\nbm25f\nMAP@10\n.398\n.397\n.394\n.394\n.392\n.392\n.391\n.356\n.356\n.356\n.356\n.356\n.355\n.273\n0.25\n0.30\n0.35\n0.40\ndegree-in-id\ndegree-in-ih\ndegree-in-all\nhits-aut-ih-100\nhits-aut-all-100\npagerank\nhits-aut-id-10\ndegree-out-all\nhits-hub-all-100\ndegree-out-ih\nhits-hub-ih-100\ndegree-out-id\nhits-hub-id-10\nbm25f\nMRR@10\nFigure 3: Effectiveness measures for linear combinations of link-based features with BM25F.\nFigure 2 shows the NDCG, MRR, and MAP measures\nof these features. Again all performance measures (and\nfor all rank-thresholds we explored) agree. As expected,\nBM25F outperforms all link-based features by a large\nmargin. The link-based features are divided into two groups,\nwith a noticeable performance drop between the groups.\nThe better-performing group consists of the features that\nare based on the number and/or quality of incoming links\n(in-degree, PageRank, and HITS authority scores); and the\nworse-performing group consists of the features that are\nbased on the number and/or quality of outgoing links\n(outdegree and HITS hub scores). In the group of features based\non incoming links, features that ignore nepotistic links\nperform better than their counterparts using all links.\nMoreover, using only inter-domain (id) links seems to be marginally\nbetter than using inter-host (ih) links.\nThe fact that features based on outgoing links\nunderperform those based on incoming links matches our\nexpectations; if anything, it is mildly surprising that outgoing links\nprovide a useful signal for ranking at all. On the other\nhand, the fact that in-degree features outperform PageRank\nunder all measures is quite surprising. A possible\nexplanation is that link-spammers have been targeting the published\nPageRank algorithm for many years, and that this has led\nto anomalies in the web graph that affect PageRank, but\nnot other link-based features that explore only a distance-1\nneighborhood of the result set. Likewise, it is surprising that\nsimple query-independent features such as in-degree, which\nmight estimate global quality but cannot capture relevance\nto a query, would outperform query-dependent features such\nas HITS authority scores.\nHowever, we cannot investigate the effect of these features\nin isolation, without regard to the overall ranking function,\nfor several reasons. First, features based on the textual\ncontent of documents (as opposed to link-based features) are\nthe best predictors of relevance. Second, link-based features\ncan be strongly correlated with textual features for several\nreasons, mainly the correlation between in-degree and\nnumFeature Transform function\nbm25f T(s) = s\npagerank T(s) = log(s + 3 \u00b7 10\u221212\n)\ndegree-in-* T(s) = log(s + 3 \u00b7 10\u22122\n)\ndegree-out-* T(s) = log(s + 3 \u00b7 103\n)\nhits-aut-* T(s) = log(s + 3 \u00b7 10\u22128\n)\nhits-hub-* T(s) = log(s + 3 \u00b7 10\u22121\n)\nTable 1: Near-optimal feature transform functions.\nber of textual anchor matches.\nTherefore, one must consider the effect of link-based\nfeatures in combination with textual features. Otherwise, we\nmay find a link-based feature that is very good in isolation\nbut is strongly correlated with textual features and results\nin no overall improvement; and vice versa, we may find a\nlink-based feature that is weak in isolation but significantly\nimproves overall performance.\nFor this reason, we have studied the combination of the\nlink-based features above with BM25F. All feature\ncombinations were done by considering the linear combination of two\nfeatures as a document score, using the formula score(d) =Pn\ni=1 wiTi(Fi(d)), where d is a document (or\ndocumentquery pair, in the case of BM25F), Fi(d) (for 1 \u2264 i \u2264 n) is a\nfeature extracted from d, Ti is a transform, and wi is a free\nscalar weight that needs to be tuned. We chose transform\nfunctions that we empirically determined to be well-suited.\nTable 1 shows the chosen transform functions.\nThis type of linear combination is appropriate if we\nassume features to be independent with respect to relevance\nand an exponential model for link features, as discussed\nin [8]. We tuned the weights by selecting a random\nsubset of 5,000 queries from the query set, used an iterative\nrefinement process to find weights that maximized a given\nperformance measure on that training set, and used the\nremaining 23,043 queries to measure the performance of the\nthus derived scoring functions.\nWe explored the pairwise combination of BM25F with\nevery link-based scoring function. Figure 3 shows the NDCG,\nMRR, and MAP measures of these feature combinations,\ntogether with a baseline BM25F score (the right-most bar\nin each graph), which was computed using the same subset\nof 23,045 queries that were used as the test set for the\nfeature combinations. Regardless of the performance measure\napplied, we can make the following general observations:\n1. Combining any of the link-based features with BM25F\nresults in a substantial performance improvement over\nBM25F in isolation.\n2. The combination of BM25F with features based on\nincoming links (PageRank, in-degree, and HITS\nauthority scores) performs substantially better than the\ncombination with features based on outgoing links (HITS\nhub scores and out-degree).\n3. The performance differences between the various\ncombinations of BM25F with features based on incoming\nlinks is comparatively small, and the relative ordering\nof feature combinations is fairly stable across the\n0.00\n0.02\n0.04\n0.06\n0.08\n0.10\n0.12\n0.14\n0 2 4 6 8 10 12 14 16 18 20 22 24\nMAP@10\n26 374 1640 2751 3768 4284 3944 3001 2617 1871 1367 771 1629\nbm25fnorm pagerank degree-in-id hits-aut-id-100\nFigure 4: Effectiveness measures for selected\nisolated features, broken down by query specificity.\nferent performance measures used. However, the\ncombination of BM25F with any in-degree variant, and in\nparticular with id in-degree, consistently outperforms\nthe combination of BM25F with PageRank or HITS\nauthority scores, and can be computed much easier\nand faster.\nFinally, we investigated whether certain features are\nbetter for some queries than for others. Particularly, we are\ninterested in the relationship between the specificity of a query\nand the performance of different ranking features. The most\nstraightforward measure of the specificity of a query Q would\nbe the number of documents in a search engine\"s corpus that\nsatisfy Q. Unfortunately, the query set available to us did\nnot contain this information. Therefore, we chose to\napproximate the specificity of Q by summing up the inverse\ndocument frequencies of the individual query terms\ncomprising Q. The inverse document frequency (IDF) of a term\nt with respect to a corpus C is defined to be logN/doc(t),\nwhere doc(t) is the number of documents in C containing t\nand N is the total number of documents in C. By summing\nup the IDFs of the query terms, we make the (flawed)\nassumption that the individual query terms are independent of\neach other. However, while not perfect, this approximation\nis at least directionally correct.\nWe broke down our query set into 13 buckets, each bucket\nassociated with an interval of query IDF values, and we\ncomputed performance metrics for all ranking functions applied\n(in isolation) to the queries in each bucket. In order to\nkeep the graphs readable, we will not show the performance\nof all the features, but rather restrict ourselves to the four\nmost interesting ones: PageRank, id HITS authority scores,\nid in-degree, and BM25F. Figure 4 shows the MAP@10 for\nall 13 query specificity buckets. Buckets on the far left of\neach graph represent very general queries; buckets on the far\nright represent very specific queries. The figures on the\nupper x axis of each graph show the number of queries in each\nbucket (e.g. the right-most bucket contains 1,629 queries).\nBM25F performs best for medium-specific queries, peaking\nat the buckets representing the IDF sum interval [12,14).\nBy comparison, HITS peaks at the bucket representing the\nIDF sum interval [4,6), and PageRank and in-degree peak at\nthe bucket representing the interval [6,8), i.e. more general\nqueries.\n8. CONCLUSIONS AND FUTURE WORK\nThis paper describes a large-scale evaluation of the\neffectiveness of HITS in comparison with other link-based\nranking algorithms, in particular PageRank and in-degree,\nwhen applied in isolation or in combination with a text\nretrieval algorithm exploiting anchor text (BM25F).\nEvaluation is carried out with respect to a large number of human\nevaluated queries, using three different measures of\neffectiveness: NDCG, MRR, and MAP. Evaluating link-based\nfeatures in isolation, we found that web page in-degree\noutperforms PageRank, and is about as effwective as HITS\nauthority scores. HITS hub scores and web page out-degree are\nmuch less effective ranking features, but still outperform a\nrandom ordering. A linear combination of any link-based\nfeatures with BM25F produces a significant improvement in\nperformance, and there is a clear difference between\ncombining BM25F with a feature based on incoming links\n(indegree, PageRank, or HITS authority scores) and a feature\nbased on outgoing links (HITS hub scores and out-degree),\nbut within those two groups the precise choice of link-based\nfeature matters relatively little.\nWe believe that the measurements presented in this paper\nprovide a solid evaluation of the best well-known link-based\nranking schemes. There are many possible variants of these\nschemes, and many other link-based ranking algorithms have\nbeen proposed in the literature, hence we do not claim this\nwork to be the last word on this subject, but rather the\nfirst step on a long road. Future work includes evaluation\nof different parameterizations of PageRank and HITS. In\nparticular, we would like to study the impact of changes\nto the PageRank damping factor on effectiveness, the\nimpact of various schemes meant to counteract the effects of\nlink spam, and the effect of weighing hyperlinks differently\ndepending on whether they are nepotistic or not. Going\nbeyond PageRank and HITS, we would like to measure the\neffectiveness of other link-based ranking algorithms, such as\nSALSA. Finally, we are planning to experiment with more\ncomplex feature combinations.\n9. REFERENCES\n[1] B. Amento, L. Terveen, and W. Hill. Does authority\nmean quality? Predicting expert quality ratings of\nweb documents. 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Authoritative sources in a\nhyperlinked environment. Journal of the ACM,\n46(5):604-632, 1999.\n[18] A. N. Langville and C. D. Meyer. Deeper inside\nPageRank. Internet Mathematics, 1(3):2005, 335-380.\n[19] R. Lempel and S. Moran. The stochastic approach for\nlink-structure analysis (SALSA) and the TKC effect.\nComputer Networks and ISDN Systems,\n33(1-6):387-401, 2000.\n[20] A. Y. Ng, A. X. Zheng, and M. I. Jordan. Stable\nalgorithms for link analysis. In Proc. of the 24th\nAnnual International ACM SIGIR Conference on\nResearch and Development in Information Retrieval,\npages 258-266, 2001.\n[21] L. Page, S. Brin, R. Motwani, and T. Winograd. The\nPageRank citation ranking: Bringing order to the\nweb. Technical report, Stanford Digital Library\nTechnologies Project, 1998.\n[22] J. A. Tomlin. A new paradigm for ranking pages on\nthe World Wide Web. In Proc. of the 12th\nInternational World Wide Web Conference, pages\n350-355, 2003.\n[23] T. Upstill, N. Craswell, and D. Hawking. 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{"name": "train_H-42", "title": "HITS Hits TRECExploring IR Evaluation Results with Network Analysis", "abstract": "We propose a novel method of analysing data gathered from TREC or similar information retrieval evaluation experiments. We define two normalized versions of average precision, that we use to construct a weighted bipartite graph of TREC systems and topics. We analyze the meaning of well known - and somewhat generalized - indicators from social network analysis on the Systems-Topics graph. We apply this method to an analysis of TREC 8 data; among the results, we find that authority measures systems performance, that hubness of topics reveals that some topics are better than others at distinguishing more or less effective systems, that with current measures a system that wants to be effective in TREC needs to be effective on easy topics, and that by using different effectiveness measures this is no longer the case.", "fulltext": "1. INTRODUCTION\nEvaluation is a primary concern in the Information\nRetrieval (IR) field. TREC (Text REtrieval Conference) [12,\n15] is an annual benchmarking exercise that has become a\nde facto standard in IR evaluation: before the actual\nconference, TREC provides to participants a collection of\ndocuments and a set of topics (representations of information\nneeds). Participants use their systems to retrieve, and\nsubmit to TREC, a list of documents for each topic. After the\nlists have been submitted and pooled, the TREC organizers\nemploy human assessors to provide relevance judgements on\nthe pooled set. This defines a set of relevant documents for\neach topic. System effectiveness is then measured by well\nestablished metrics (Mean Average Precision being the most\nused). Other conferences such as NTCIR, INEX, CLEF\nprovide comparable data.\nNetwork analysis is a discipline that studies features and\nproperties of (usually large) networks, or graphs. Of\nparticular importance is Social Network Analysis [16], that studies\nnetworks made up by links among humans (friendship,\nacquaintance, co-authorship, bibliographic citation, etc.).\nNetwork analysis and IR fruitfully meet in Web Search\nEngine implementation, as is already described in textbooks\n[3,6]. Current search engines use link analysis techniques to\nhelp rank the retrieved documents. Some indicators (and\nthe corresponding algorithms that compute them) have been\nfound useful in this respect, and are nowadays well known:\nInlinks (the number of links to a Web page), PageRank [7],\nand HITS (Hyperlink-Induced Topic Search) [5]. Several\nextensions to these algorithms have been and are being\nproposed. These indicators and algorithms might be quite\ngeneral in nature, and can be used for applications which are\nvery different from search result ranking. One example is\nusing HITS for stemming, as described by Agosti et al. [1].\nIn this paper, we propose and demonstrate a method\nfor constructing a network, specifically a weighted complete\nbidirectional directed bipartite graph, on a set of TREC\ntopics and participating systems. Links represent effectiveness\nmeasurements on system-topic pairs. We then apply\nanalysis methods originally developed for search applications to\nthe resulting network. This reveals phenomena previously\nhidden in TREC data. In passing, we also provide a small\ngeneralization to Kleinberg\"s HITS algorithm, as well as to\nInlinks and PageRank.\nThe paper is organized as follows: Sect. 2 gives some\nmotivations for the work. Sect. 3 presents the basic ideas of\nnormalizing average precision and of constructing a\nsystemstopics graph, whose properties are analyzed in Sect. 4; Sect. 5\npresents some experiments on TREC 8 data; Sect. 6\ndiscusses some issues and Sect. 7 closes the paper.\n2. MOTIVATIONS\nWe are interested in the following hypotheses:\n1. Some systems are more effective than others;\nt1 \u00b7 \u00b7 \u00b7 tn MAP\ns1 AP(s1, t1) \u00b7 \u00b7 \u00b7 AP(s1, tn) MAP(s1)\n...\n...\n...\nsm AP(sm, t1) \u00b7 \u00b7 \u00b7 AP(sm, tn) MAP(sm)\nAAP AAP(t1) \u00b7 \u00b7 \u00b7 AAP(tn)\n(a)\nt1 t2 \u00b7 \u00b7 \u00b7 MAP\ns1 0.5 0.4 \u00b7 \u00b7 \u00b7 0.6\ns2 0.4 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 0.3\n...\n...\n...\n...\nAAP 0.6 0.3 \u00b7 \u00b7 \u00b7\n(b)\nTable 1: AP, MAP and AAP\n2. Some topics are easier than others;\n3. Some systems are better than others at distinguishing\neasy and difficult topics;\n4. Some topics are better than others at distinguishing\nmore or less effective systems.\nThe first of these hypotheses needs no further justification\n- every reported significant difference between any two\nsystems supports it. There is now also quite a lot of evidence\nfor the second, centered on the TREC Robust Track [14].\nOur primary interest is in the third and fourth. The third\nmight be regarded as being of purely academic interest;\nhowever, the fourth has the potential for being of major\npractical importance in evaluation studies. If we could identify\na relatively small number of topics which were really good\nat distinguishing effective and ineffective systems, we could\nsave considerable effort in evaluating systems.\nOne possible direction from this point would be to attempt\ndirect identification of such small sets of topics. However, in\nthe present paper, we seek instead to explore the\nrelationships suggested by the hypotheses, between what different\ntopics tell us about systems and what different systems tell\nus about topics. We seek methods of building and analysing\na matrix of system-topic normalised performances, with a\nview to giving insight into the issue and confirming or\nrefuting the third and fourth hypotheses. It turns out that\nthe obvious symmetry implied by the above formulation of\nthe hypotheses is a property worth investigating, and the\ninvestigation does indeed give us valuable insights.\n3. THE IDEA\n3.1 1st step: average precision table\nFrom TREC results, one can produce an Average\nPrecision (AP) table (see Tab. 1a): each AP(si, tj) value\nmeasures the AP of system si on topic tj.\nBesides AP values, the table shows Mean Average\nPrecision (MAP) values i.e., the mean of the AP values for a\nsingle system over all topics, and what we call Average\nAverage Precision (AAP) values i.e., the average of the AP\nvalues for a single topic over all systems:\nMAP(si) =\n1\nn\nnX\nj=1\nAP(si, tj), (1)\nAAP(tj) =\n1\nm\nmX\ni=1\nAP(si, tj). (2)\nMAPs are indicators of systems performance: higher MAP\nmeans good system. AAP are indicators of the performance\non a topic: higher AAP means easy topic - a topic on which\nall or most systems have good performance.\n3.2 Critique of pure AP\nMAP is a standard, well known, and widely used IR\neffectiveness measure. Single AP values are used too (e.g.,\nin AP histograms). Topic difficulty is often discussed (e.g.,\nin TREC Robust track [14]), although AAP values are not\nused and, to the best of our knowledge, have never been\nproposed (the median, not the average, of AP on a topic\nis used to produce TREC AP histograms [11]). However,\nthe AP values in Tab. 1 present two limitations, which are\nsymmetric in some respect:\n\u2022 Problem 1. They are not reliable to compare the\neffectiveness of a system on different topics, relative\nto the other systems. If, for example, AP(s1, t1) >\nAP(s1, t2), can we infer that s1 is a good system (i.e.,\nhas a good performance) on t1 and a bad system on\nt2? The answer is no: t1 might be an easy topic (with\nhigh AAP) and t2 a difficult one (low AAP). See an\nexample in Tab. 1b: s1 is outperformed (on average)\nby the other systems on t1, and it outperforms the\nother systems on t2.\n\u2022 Problem 2. Conversely, if, for example, AP(s1, t1) >\nAP(s2, t1), can we infer that t1 is considered easier\nby s1 than by s2? No, we cannot: s1 might be a good\nsystem (with high MAP) and s2 a bad one (low MAP);\nsee an example in Tab. 1b.\nThese two problems are a sort of breakdown of the well\nknown high influence of topics on IR evaluation; again, our\nformulation makes explicit the topics / systems symmetry.\n3.3 2nd step: normalizations\nTo avoid these two problems, we can normalize the AP\ntable in two ways. The first normalization removes the\ninfluence of the single topic ease on system performance. Each\nAP(si, tj) value in the table depends on both system\ngoodness and topic ease (the value will increase if a system is\ngood and/or the topic is easy). By subtracting from each\nAP(si, tj) the AAP(tj) value, we obtain normalized AP\nvalues (APA(si, tj), Normalized AP according to AAP):\nAPA(si, tj) = AP(si, tj) \u2212 AAP(tj), (3)\nthat depend on system performance only (the value will\nincrease only if system performance is good). See Tab. 2a.\nThe second normalization removes the influence of the\nsingle system effectiveness on topic ease: by subtracting from\neach AP(si, tj) the MAP(si) value, we obtain normalized\nAP values (APM(si, tj), Normalized AP according to MAP):\nAPM(si, tj) = AP(si, tj) \u2212 MAP(si), (4)\nthat depend on topic ease only (the value will increase only\nif the topic is easy, i.e., all systems perform well on that\ntopic). See Tab. 2b.\nIn other words, APA avoids Problem 1: APA(s, t) values\nmeasure the performance of system s on topic t normalized\nt1 \u00b7 \u00b7 \u00b7 tn MAP\ns1 APA(s1, t1) \u00b7 \u00b7 \u00b7 APA(s1, tn) MAP(s1)\n...\n...\n...\nsm APA(sm, t1) \u00b7 \u00b7 \u00b7 APA(sm, tn) MAP(sm)\n0 \u00b7 \u00b7 \u00b7 0 0\n(a)\nt1 \u00b7 \u00b7 \u00b7 tn\ns1 APM(s1, t1) \u00b7 \u00b7 \u00b7 APM(s1, tn) 0\n...\n...\n...\nsm APM(sm, t1) \u00b7 \u00b7 \u00b7 APM(sm, tn) 0\nAAP AAP(t1) \u00b7 \u00b7 \u00b7 AAP(tn) 0\n(b)\nt1 t2 \u00b7 \u00b7 \u00b7 MAP\ns1 \u22120.1 0.1 \u00b7 \u00b7 \u00b7 . . .\ns2 0.2 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 . . .\n...\n...\n...\n0 0 \u00b7 \u00b7 \u00b7\nt1 t2 \u00b7 \u00b7 \u00b7\ns1 \u22120.1 \u22120.2 \u00b7 \u00b7 \u00b7 0\ns2 0.1 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 0\n...\n...\n...\nAAP . . . . . . \u00b7 \u00b7 \u00b7\n(c) (d)\nTable 2: Normalizations: APA and MAP: normalized\nAP (APA) and MAP (MAP) (a); normalized AP (APM)\nand AAP (AAP) (b); a numeric example (c) and (d)\naccording to the ease of the topic (easy topics will not have\nhigher APA values). Now, if, for example, APA(s1, t2) >\nAPA(s1, t1), we can infer that s1 is a good system on t2 and\na bad system on t1 (see Tab. 2c). Vice versa, APM avoids\nProblem 2: APM(s, t) values measure the ease of topic t\naccording to system s, normalized according to goodness\nof the system (good systems will not lead to higher APM\nvalues). If, for example, APM(s2, t1) > APM(s1, t1), we\ncan infer that t1 is considered easier by s2 than by s1 (see\nTab. 2d).\nOn the basis of Tables 2a and 2b, we can also define two\nnew measures of system effectiveness and topic ease, i.e., a\nNormalized MAP (MAP), obtained by averaging the APA\nvalues on one row in Tab. 2a, and a Normalized AAP (AAP),\nobtained by averaging the APM values on one column in\nTab. 2b:\nMAP(si) =\n1\nn\nnX\nj=1\nAPA(si, tj) (5)\nAAP(tj) =\n1\nm\nmX\ni=1\nAPM(si, tj). (6)\nThus, overall system performance can be measured,\nbesides by means of MAP, also by means of MAP. Moreover,\nMAP is equivalent to MAP, as can be immediately proved\nby using Eqs. (5), (3), and (1):\nMAP(si) =\n1\nn\nnX\nj=1\n(AP(si, tj) \u2212 AAP(tj)) =\n= MAP(si) \u2212\n1\nn\nnX\nj=1\nAAP(tj)\n(and 1\nn\nPn\nj=1 AAP(tj) is the same for all systems). And,\nconversely, overall topic ease can be measured, besides by\nt1 \u00b7 \u00b7 \u00b7 tn\ns1\n... APM\nsm\nt1 \u00b7 \u00b7 \u00b7 tn\ns1\n... APA\nsm\ns1 \u00b7 \u00b7 \u00b7 sm t1 \u00b7 \u00b7 \u00b7 tn\ns1\n... 0 APM 0\nsm\nt1\n... APA\nT\n0 0\ntn\nMAP AAP 0\nFigure 1: Construction of the adjacency matrix.\nAPA\nT\nis the transpose of APA.\nmeans of AAP, also by means of AAP, and this is equivalent\n(the proof is analogous, and relies on Eqs. (6), (4), and (2)).\nThe two Tables 2a and 2b are interesting per se, and can\nbe analyzed in several different ways. In the following we\npropose an analysis based on network analysis techniques,\nmainly Kleinberg\"s HITS algorithm. There is a little further\ndiscussion of these normalizations in Sect. 6.\n3.4 3rd step: Systems-Topics Graph\nThe two tables 2a and 2b can be merged into a single one\nwith the procedure shown in Fig. 1. The obtained matrix\ncan be interpreted as the adjacency matrix of a complete\nweighted bipartite graph, that we call Systems-Topics graph.\nArcs and weights in the graph can be interpreted as follows:\n\u2022 (weight on) arc s \u2192 t: how much the system s thinks\nthat the topic t is easy - assuming that a system has\nno knowledge of the other systems (or in other words,\nhow easy we might think the topic is, knowing only\nthe results for this one system). This corresponds to\nAPM values, i.e., to normalized topic ease (Fig. 2a).\n\u2022 (weight on) arc s \u2190 t: how much the topic t thinks\nthat the system s is good - assuming that a topic has\nno knowledge of the other topics (or in other words,\nhow good we might think the system is, knowing only\nthe results for this one topic). This corresponds to\nAPA (normalized system effectiveness, Fig. 2b).\nFigs. 2c and 2d show the Systems-Topics complete weighted\nbipartite graph, on a toy example with 4 systems and 2\ntopics; the graph is split in two parts to have an understandable\ngraphical representation: arcs in Fig. 2c are labeled with\nAPM values; arcs in Fig. 2d are labeled with APA values.\n4. ANALYSIS OF THE GRAPH\n4.1 Weighted Inlinks, Outlinks, PageRank\nThe sum of weighted outlinks, i.e., the sum of the weights\non the outgoing arcs from each node, is always zero:\n\u2022 The outlinks on each node corresponding to a system\ns (Fig. 2c) is the sum of all the corresponding APM\nvalues on one row of the matrix in Tab. 2b.\n\u2022 The outlinks on each node corresponding to a topic\nt (Fig. 2d) is the sum of all the corresponding APA\n(a) (b)\n(c) (d)\nFigure 2: The relationships between systems and\ntopics (a) and (b); and the Systems-Topics graph for\na toy example (c) and (d). Dashed arcs correspond\nto negative values.\nh\n(a)\ns1\n...\nsm\nt1\n...\ntn\n=\ns1 \u00b7 \u00b7 \u00b7 sm t1 \u00b7 \u00b7 \u00b7 tn\ns1\n... 0 APM\n(APA)\nsm\nt1\n... APA\nT\n0\ntn (APM\nT\n)\n\u00b7\na\n(h)\ns1\n...\nsm\nt1\n...\ntn\nFigure 3: Hub and Authority computation\nvalues on one row of the transpose of the matrix in\nTab. 2a.\nThe average1\nof weighted inlinks is:\n\u2022 MAP for each node corresponding to a system s; this\ncorresponds to the average of all the corresponding\nAPA values on one column of the APA\nT\npart of the\nadjacency matrix (see Fig. 1).\n\u2022 AAP for each node corresponding to a topic t; this\ncorresponds to the average of all the corresponding\nAPM values on one column of the APM part of the\nadjacency matrix (see Fig. 1).\nTherefore, weighted inlinks measure either system\neffectiveness or topic ease; weighted outlinks are not meaningful. We\ncould also apply the PageRank algorithm to the network;\nthe meaning of the PageRank of a node is not quite so\nobvious as Inlinks and Outlinks, but it also seems a sensible\nmeasure of either system effectiveness or topic ease: if a\nsystem is effective, it will have several incoming links with high\n1\nUsually, the sum of the weights on the incoming arcs to\neach node is used in place of the average; since the graph is\ncomplete, it makes no difference.\nweights (APA); if a topic is easy it will have high weights\n(APM) on the incoming links too. We will see experimental\nconfirmation in the following.\n4.2 Hubs and Authorities\nLet us now turn to more sophisticated indicators.\nKleinberg\"s HITS algorithm defines, for a directed graph, two\nindicators: hubness and authority; we reiterate here some of\nthe basic details of the HITS algorithm in order to\nemphasize both the nature of our generalization and the\ninterpretation of the HITS concepts in this context. Usually, hubness\nand authority are defined as h(x) =\nP\nx\u2192y a(y) and a(x) =\nP\ny\u2192x h(y), and described intuitively as a good hub links\nmany good authorities; a good authority is linked from many\ngood hubs. As it is well known, an equivalent formulation\nin linear algebra terms is (see also Fig. 3):\nh = Aa and a = AT\nh (7)\n(where h is the hubness vector, with the hub values for all\nthe nodes; a is the authority vector; A is the adjacency\nmatrix of the graph; and AT\nits transpose). Usually, A\ncontains 0s and 1s only, corresponding to presence and absence\nof unweighted directed arcs, but Eq. (7) can be immediately\ngeneralized to (in fact, it is already valid for) A containing\nany real value, i.e., to weighted graphs.\nTherefore we can have a generalized version (or rather\na generalized interpretation, since the formulation is still\nthe original one) of hubness and authority for all nodes in\na graph. An intuitive formulation of this generalized HITS\nis still available, although slightly more complex: a good\nhub links, by means of arcs having high weights, many good\nauthorities; a good authority is linked, by means of arcs\nhaving high weights, from many good hubs. Since arc weights\ncan be, in general, negative, hub and authority values can be\nnegative, and one could speak of unhubness and unauthority;\nthe intuitive formulation could be completed by adding that\na good hub links good unauthorities by means of links with\nhighly negative weights; a good authority is linked by good\nunhubs by means of links with highly negative weights.\nAnd, also, a good unhub links positively good\nunauthorities and negatively good authorities; a good unauthority\nis linked positively from good unhubs and negatively from\ngood hubs.\nLet us now apply generalized HITS to our Systems-Topics\ngraph. We compute a(s), h(s), a(t), and h(t). Intuitively,\nwe expect that a(s) is somehow similar to Inlinks, so it\nshould be a measure of either systems effectiveness or topic\nease. Similarly, hubness should be more similar to Outlinks,\nthus less meaningful, although the interplay between hub\nand authority might lead to the discovery of something\ndifferent. Let us start by remarking that authority of topics\nand hubness of systems depend only on each other; similarly\nhubness of topics and authority of systems depend only on\neach other: see Figs. 2c, 2d and 3.\nThus the two graphs in Figs. 2c and 2d can be analyzed\nindependently. In fact the entire HITS analysis could be\ndone in one direction only, with just APM(s, t) values or\nalternatively with just APA(s, t). As discussed below,\nprobably most interest resides in the hubness of topics and the\nauthority of systems, so the latter makes sense. However, in\nthis paper, we pursue both analyses together, because the\nsymmetry itself is interesting.\nConsidering Fig. 2c we can state that:\n\u2022 Authority a(t) of a topic node t increases when:\n- if h(si) > 0, APM(si, t) increases\n(or if APM(si, t) > 0, h(si) increases);\n- if h(si) < 0, APM(si, t) decreases\n(or if APM(si, t) < 0, h(si) decreases).\n\u2022 Hubness h(s) of a system node s increases when:\n- if a(tj) > 0, APM(s, tj) increases\n(or, if APM(s, tj) > 0, a(tj) increases);\n- if a(tj) < 0, APM(s, tj) decreases\n(or, if APM(s, tj) < 0, a(tj) decreases).\nWe can summarize this as: a(t) is high if APM(s, t) is high\nfor those systems with high h(s); h(s) is high if APM(s, t)\nis high for those topics with high a(t). Intuitively, authority\na(t) of a topic measures topic ease; hubness h(s) of a system\nmeasures system\"s capability to recognize easy topics. A\nsystem with high unhubness (negative hubness) would tend\nto regard easy topics as hard and hard ones as easy.\nThe situation for Fig. 2d, i.e., for a(s) and h(t), is\nanalogous. Authority a(s) of a system node s measures system\neffectiveness: it increases with the weight on the arc (i.e.,\nAPA(s, tj)) and the hubness of the incoming topic nodes tj.\nHubness h(t) of a topic node t measures topic capability to\nrecognize effective systems: if h(t) > 0, it increases further\nif APA(s, tj) increases; if h(t) < 0, it increases if APA(s, tj)\ndecreases.\nIntuitively, we can state that A system has a higher\nauthority if it is more effective on topics with high hubness;\nand A topic has a higher hubness if it is easier for those\nsystems which are more effective in general. Conversely for\nsystem hubness and topic authority: A topic has a higher\nauthority if it is easier on systems with high hubness; and\nA system has a higher hubness if it is more effective for\nthose topics which are easier in general.\nTherefore, for each system we have two indicators:\nauthority (a(s)), measuring system effectiveness, and hubness\n(h(s)), measuring system capability to estimate topic ease.\nAnd for each topic, we have two indicators: authority (a(t)),\nmeasuring topic ease, and hubness (h(t)), measuring topic\ncapability to estimate systems effectiveness. We can define\nthem formally as\na(s) =\nX\nt\nh(t) \u00b7 APA(s, t), h(t) =\nX\ns\na(s) \u00b7 APA(s, t),\na(t) =\nX\ns\nh(s) \u00b7 APM(s, t), h(s) =\nX\nt\na(t) \u00b7 APM(s, t).\nWe observe that the hubness of topics may be of particular\ninterest for evaluation studies. It may be that we can\nevaluate the effectiveness of systems efficiently by using relatively\nfew high-hubness topics.\n5. EXPERIMENTS\nWe now turn to discuss if these indicators are meaningful\nand useful in practice, and how they correlate with standard\nmeasures used in TREC. We have built the Systems-Topics\ngraph for TREC 8 data (featuring 1282\nsystems - actually,\n2\nActually, TREC 8 data features 129 systems; due to\nsome bug in our scripts, we did not include one system\n(8manexT3D1N0), but the results should not be affected.\n0\n0.1\n0.2\n0.3\n-1 -0.5 0 0.5 1\nNAPM\nNAPA\nAP\nFigure 4: Distributions of AP, APA, and APM values\nin TREC 8 data\nMAP In PR H A\nMAP 1 1.0 1.0 .80 .99\nInlinks 1 1.0 .80 .99\nPageRank 1 .80 .99\nHub 1 .87\n(a)\nAAP In PR H A\nAAP 1 1.0 1.0 .92 1.0\nInlinks 1 1.0 .92 1.0\nPageRank 1 .92 1.0\nHub 1 .93\n(b)\nTable 3: Correlations between network analysis\nmeasures and MAP (a) and AAP (b)\nruns - on 50 topics). This section illustrates the results\nobtained mining these data according to the method presented\nin previous sections.\nFig. 4 shows the distributions of AP, APA, and APM:\nwhereas AP is very skewed, both APA and APM are much\nmore symmetric (as it should be, since they are constructed\nby subtracting the mean). Tables 3a and 3b show the\nPearson\"s correlation values between Inlinks, PageRank, Hub,\nAuthority and, respectively, MAP or AAP (Outlinks\nvalues are not shown since they are always zero, as seen in\nSect. 4). As expected, Inlinks and PageRank have a perfect\ncorrelation with MAP and AAP. Authority has a very high\ncorrelation too with MAP and AAP; Hub assumes slightly\nlower values.\nLet us analyze the correlations more in detail. The\ncorrelations chart in Figs. 5a and 5b demonstrate the high\ncorrelation between Authority and MAP or AAP. Hubness\npresents interesting phenomena: both Fig. 5c (correlation\nwith MAP) and Fig. 5d (correlation with AAP) show that\ncorrelation is not exact, but neither is it random. This, given\nthe meaning of hubness (capability in estimating topic ease\nand system effectiveness), means two things: (i) more\neffective systems are better at estimating topic ease; and (ii)\neasier topics are better at estimating system effectiveness.\nWhereas the first statement is fine (there is nothing against\nit), the second is a bit worrying. It means that system\neffectiveness in TREC is affected more by easy topics than by\ndifficult topics, which is rather undesirable for quite obvious\nreasons: a system capable of performing well on a difficult\ntopic, i.e., on a topic on which the other systems perform\nbadly, would be an important result for IR effectiveness;\ncon-8E-5\n-6E-5\n-4E-5\n-2E-5\n0E+0\n2E-5\n4E-5\n6E-5\n0.0 0.1 0.2 0.3 0.4 0.5\n-3E-1\n-2E-1\n-1E-1\n0E+0\n1E-1\n2E-1\n3E-1\n4E-1\n5E-1\n0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8\n(a) (b)\n0E+0\n2E-2\n4E-2\n6E-2\n8E-2\n1E-1\n1E-1\n1E-1\n0.0 0.1 0.2 0.3 0.4 0.5\n0E+0\n1E-5\n2E-5\n3E-5\n4E-5\n5E-5\n6E-5\n7E-5\n0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8\n(c) (d)\nFigure 5: Correlations: MAP (x axis) and authority (y axis) of systems (a); AAP and authority of topics\n(b); MAP and hub of systems (c) and AAP and hub of topics (d)\nversely, a system capable of performing well on easy topics\nis just a confirmation of the state of the art. Indeed, the\ncorrelation between hubness and AAP (statement (i) above) is\nhigher than the correlation between hubness and MAP\n(corresponding to statement (ii)): 0.92 vs. 0.80. However, this\nphenomenon is quite strong. This is also confirmed by the\nwork being done on the TREC Robust Track [14].\nIn this respect, it is interesting to see what happens if we\nuse a different measure from MAP (and AAP). The GMAP\n(Geometric MAP) metric is defined as the geometric mean of\nAP values, or equivalently as the arithmetic mean of the\nlogarithms of AP values [8]. GMAP has the property of giving\nmore weight to the low end of the AP scale (i.e., to low AP\nvalues), and this seems reasonable, since, intuitively, a\nperformance increase in MAP values from 0.01 to 0.02 should\nbe more important than an increase from 0.81 to 0.82. To\nuse GMAP in place of MAP and AAP, we only need to take\nthe logarithms of initial AP values, i.e., those in Tab. 1a\n(zero values are modified into \u03b5 = 0.00001). We then repeat\nthe same normalization process (with GMAP and GAAP\n- Geometric AAP - replacing MAP and AAP): whereas\nauthority values still perfectly correlate with GMAP (0.99)\nand GAAP (1.00), the correlation with hubness largely\ndisappears (values are \u22120.16 and \u22120.09 - slightly negative but\nnot enough to concern us).\nThis is yet another confirmation that TREC effectiveness\nas measured by MAP depends mainly on easy topics; GMAP\nappears to be a more balanced measure. Note that,\nperhaps surprisingly, GMAP is indeed fairly well balanced, not\nbiased in the opposite direction - that is, it does not\noveremphasize the difficult topics.\nIn Sect. 6.3 below, we discuss another transformation,\nreplacing the log function used in GMAP with logit. This has\na similar effect: the correlation of mean logitAP and average\nlogitAP with hubness are now small positive numbers (0.23\nand 0.15 respectively), still comfortably away from the high\ncorrelations with regular MAP and AAP, i.e., not presenting\nthe problematic phenomenon (ii) above (over-dependency on\neasy topics).\nWe also observe that hub values are positive, whereas\nauthority assumes, as predicted, both positive and negative\nvalues. An intuitive justification is that negative hubness\nwould indicate a node which disagrees with the other nodes,\ne.g., a system which does better on difficult topics, or a\ntopic on which bad systems do better; such systems and\ntopics would be quite strange, and probably do not appear\nin TREC. Finally, although one might think that topics with\nseveral relevant documents are more important and difficult,\nthis is not the case: there is no correlation between hub (or\nany other indicator) and the number of documents relevant\nto a topic.\n6. DISCUSSION\n6.1 Related work\nThere has been considerable interest in recent years in\nquestions of statistical significance of effectiveness\ncomparisons between systems (e.g. [2, 9]), and related questions of\nhow many topics might be needed to establish differences\n(e.g. [13]). We regard some results of the present study as\nin some way complementary to this work, in that we make a\nstep towards answering the question Which topics are best\nfor establishing differences?.\nThe results on evaluation without relevance judgements\nsuch as [10] show that, to some extent, good systems agree\non which are the good documents. We have not addressed\nthe question of individual documents in the present analysis,\nbut this effect is certainly analogous to our results.\n6.2 Are normalizations necessary?\nAt this point it is also worthwhile to analyze what would\nhappen without the MAP- and AAP-normalizations defined\nin Sect. 3.3. Indeed, the process of graph construction\n(Sect. 3.4) is still valid: both the APM and APA matrices\nare replaced by the AP one, and then everything goes on as\nabove. Therefore, one might think that the normalizations\nare unuseful in this setting.\nThis is not the case. From the theoretical point of view,\nthe AP-only graph does not present the interesting\nproperties above discussed: since the AP-only graph is\nsymmetrical (the weight on each incoming link is equal to the weight\non the corresponding outgoing link), Inlinks and Outlinks\nassume the same values. There is symmetry also in\ncomputing hub and authority, that assume the same value for each\nnode since the weights on the incoming and outgoing arcs\nare the same. This could be stated in more precise and\nformal terms, but one might still wonder if on the overall graph\nthere are some sort of counterbalancing effects. It is\ntherefore easier to look at experimental data, which confirm that\nthe normalizations are needed: the correlations between AP,\nInlinks, Outlinks, Hub, and/or Authority are all very close\nto one (none of them is below 0.98).\n6.3 Are these normalizations sufficient?\nIt might be argued that (in the case of APA, for example)\nthe amount we have subtracted from each AP value is\ntopicdependent, therefore the range of the resulting APA value\nis also topic-dependent (e.g. the maximum is 1 \u2212 AAP(tj)\nand the minimum is \u2212 AAP(tj)). This suggests that the\ncross-topic comparisons of these values suggested in Sect. 3.3\nmay not be reliable. A similar issue arises for APM and\ncomparisons across systems.\nOne possible way to overcome this would be to use an\nunconstrained measure whose range is the full real line. Note\nthat in applying the method to GMAP by using log AP, we\navoid the problem with the lower limit but retain it for the\nupper limit. One way to achieve an unconstrainted range\nwould be to use the logit function rather than the log [4,8].\nWe have also run this variant (as already reported in\nSect. 5 above), and it appears to provide very similar\nresults to the GMAP results already given. This is not\nsurprising, since in practice the two functions are very similar\nover most of the operative range. The normalizations thus\nseem reliable.\n6.4 On AAT\nand AT\nA\nIt is well known that h and a vectors are the principal\nleft eigenvectors of AAT\nand AT\nA, respectively (this can\nbe easily derived from Eqs. (7)), and that, in the case of\ncitation graphs, AAT\nand AT\nA represent, respectively,\nbibliographic coupling and co-citations. What is the meaning,\nif any, of AAT\nand AT\nA in our Systems-Topics graph? It\nis easy to derive that:\nAAT\n[i, j] =\n8\n><\n>:\n0\n\uf6be\nif i \u2208 S \u2227 j \u2208 T\nor i \u2208 T \u2227 j \u2208 S\nP\nk A[i, k] \u00b7 A[j, k] otherwise\nAT\nA[i, j] =\n8\n><\n>:\n0\n\uf6be\nif i \u2208 S \u2227 j \u2208 T\nor i \u2208 T \u2227 j \u2208 S\nP\nk A[k, i] \u00b7 A[k, j] otherwise\n(where S is the set of indices corresponding to systems and T\nthe set of indices corresponding to topics). Thus AAT\nand\nAT\nA are block diagonal matrices, with two blocks each, one\nrelative to systems and one relative to topics:\n(a) if i, j \u2208 S, then AAT\n[i, j] =\nP\nk\u2208T APM(i, k)\u00b7APM(j, k)\nmeasures how much the two systems i and j agree in\nestimating topics ease (APM): high values mean that\nthe two systems agree on topics ease.\n(b) if i, j \u2208 T, then AAT\n[i, j] =\nP\nk\u2208S APA(k, i)\u00b7APA(k, j)\nmeasures how much the two topics i and j agree in\nestimating systems effectiveness (APA): high values mean\nthat the two topics agree on systems effectiveness (and\nthat TREC results would not change by leaving out one\nof the two topics).\n(c) if i, j \u2208 S, then AT\nA[i, j] =\nP\nk\u2208T APA(i, k) \u00b7 APA(j, k)\nmeasures how much agreement on the effectiveness of\ntwo systems i and j there is over all topics: high\nvalues mean that many topics quite agree on the two\nsystems effectiveness; low values single out systems that\nare somehow controversial, and that need several topics\nto have a correct effectiveness assessment.\n(d) if i, j \u2208 T, then AT\nA[i, j] =\nP\nk\u2208S APM(k, i)\u00b7APM(k, j)\nmeasures how much agreement on the ease of the two\ntopics i and j there is over all systems: high values mean\nthat many systems quite agree on the two topics ease.\nTherefore, these matrices are meaningful and somehow\ninteresting. For instance, the submatrix (b) corresponds to\na weighted undirected complete graph, whose nodes are the\ntopics and whose arc weights are a measure of how much\ntwo topics agree on systems effectiveness. Two topics that\nare very close on this graph give the same information, and\ntherefore one of them could be discarded without changes in\nTREC results. It would be interesting to cluster the topics\non this graph. Furthermore, the matrix/graph (a) could be\nuseful in TREC pool formation: systems that do not agree\non topic ease would probably find different relevant\ndocuments, and should therefore be complementary in pool\nformation. Note that no notion of single documents is involved\nin the above analysis.\n6.5 Insights\nAs indicated, the primary contribution of this paper has\nbeen a method of analysis. However, in the course of\napplying this method to one set of TREC results, we have\nachieved some insights relating to the hypotheses formulated\nin Sect. 2:\n\u2022 We confirm Hypothesis 2 above, that some topics are\neasier than others.\n\u2022 Differences in the hubness of systems reveal that some\nsystems are better than others at distinguishing easy\nand difficult topics; thus we have some confirmation of\nHypothesis 3.\n\u2022 There are some relatively idiosyncratic systems which\ndo badly on some topics generally considered easy but\nwell on some hard topics. However, on the whole, the\nmore effective systems are better at distinguishing easy\nand difficult topics. This is to be expected: a really\nbad system will do badly on everything, while even a\ngood system may have difficulty with some topics.\n\u2022 Differences in the hubness of topics reveal that some\ntopics are better than others at distinguising more or\nless effective systems; thus we have some confirmation\nof Hypothesis 4.\n\u2022 If we use MAP as the measure of effectiveness, it is\nalso true that the easiest topics are better at\ndistinguishing more or less effective systems. As argued in\nSect. 5, this is an undesirable property. GMAP is more\nbalanced.\nClearly these ideas need to be tested on other data sets.\nHowever, they reveal that the method of analysis proposed\nin this paper can provide valuable information.\n6.6 Selecting topics\nThe confirmation of Hypothesis 4 leads, as indicated, to\nthe idea that we could do reliable system evaluation on a\nmuch smaller set of topics, provided we could select such an\nappropriate set. This selection may not be straightforward,\nhowever. It is possible that simply selecting the high\nhubness topics will achieve this end; however, it is also possible\nthat there are significant interactions between topics which\nwould render such a simple rule ineffective. This\ninvestigation would therefore require serious experimentation. For\nthis reason we have not attempted in this paper to point to\nthe specific high hubness topics as being good for evaluation.\nThis is left for future work.\n7. CONCLUSIONS AND FUTURE\nDEVELOPMENTS\nThe contribution of this paper is threefold:\n\u2022 we propose a novel way of normalizing AP values;\n\u2022 we propose a novel method to analyse TREC data;\n\u2022 the method applied on TREC data does indeed reveal\nsome hidden properties.\nMore particularly, we propose Average Average Precision\n(AAP), a measure of topic ease, and a novel way of\nnormalizing the average precision measure in TREC, on the basis\nof both MAP (Mean Average Precision) and AAP. The\nnormalized measures (APM and APA) are used to build a\nbipartite weighted Systems-Topics graph, that is then\nanalyzed by means of network analysis indicators widely known\nin the (social) network analysis field, but somewhat\ngeneralised. We note that no such approach to TREC data\nanalysis has been proposed so far. The analysis shows that,\nwith current measures, a system that wants to be effective\nin TREC needs to be effective on easy topics. Also, it is\nsuggested that a cluster analysis on topic similarity can lead to\nrelying on a lower number of topics.\nOur method of analysis, as described in this paper, can\nbe applied only a posteriori, i.e., once we have all the\ntopics and all the systems available. Adding (removing) a new\nsystem / topic would mean re-computing hubness and\nauthority indicators. Moreover, we are not explicitly proposing\na change to current TREC methodology, although this could\nbe a by-product of these - and further - analyses.\nThis is an initial work, and further analyses could be\nperformed. For instance, other effectiveness metrics could be\nused, in place of AP. Other centrality indicators, widely\nused in social network analysis, could be computed, although\nprobably with similar results to PageRank. It would be\ninteresting to compute the higher-order eigenvectors of AT\nA\nand AAT\n. The same kind of analysis could be performed at\nthe document level, measuring document ease. Hopefully,\nfurther analyses of the graph defined in this paper,\naccording to the approach described, can be insightful for a better\nunderstanding of TREC or similar data.\nAcknowledgments\nWe would like to thank Nick Craswell for insightful\ndiscussions and the anonymous referees for useful remarks. Part\nof this research has been carried on while the first author\nwas visiting Microsoft Research Cambridge, whose financial\nsupport is acknowledged.\n8. REFERENCES\n[1] M. Agosti, M. Bacchin, N. Ferro, and M. Melucci.\nImproving the automatic retrieval of text documents.\nIn Proceedings of the 3rd CLEF Workshop, volume\n2785 of LNCS, pages 279-290, 2003.\n[2] C. Buckley and E. Voorhees. Evaluating evaluation\nmeasure stability. In 23rd SIGIR, pages 33-40, 2000.\n[3] S. Chakrabarti. Mining the Web. Morgan Kaufmann,\n2003.\n[4] G. V. Cormack and T. R. Lynam. Statistical precision\nof information retrieval evaluation. In 29th SIGIR,\npages 533-540, 2006.\n[5] J. Kleinberg. Authoritative sources in a hyperlinked\nenvironment. J. of the ACM, 46(5):604-632, 1999.\n[6] M. Levene. An Introduction to Search Engines and\nWeb Navigation. Addison Wesley, 2006.\n[7] L. Page, S. Brin, R. Motwani, and T. Winograd. The\nPageRank Citation Ranking: Bringing Order to the\nWeb, 1998.\nhttp://dbpubs.stanford.edu:8090/pub/1999-66.\n[8] S. Robertson. On GMAP - and other transformations.\nIn 13th CIKM, pages 78-83, 2006.\n[9] M. Sanderson and J. Zobel. Information retrieval\nsystem evaluation: effort, sensitivity, and reliability. In\n28th SIGIR, pages 162-169, 2005.\nhttp://doi.acm.org/10.1145/1076034.1076064.\n[10] I. Soboroff, C. Nicholas, and P. Cahan. Ranking\nretrieval systems without relevance judgments. In 24th\nSIGIR, pages 66-73, 2001.\n[11] TREC Common Evaluation Measures, 2005.\nhttp://trec.nist.gov/pubs/trec14/appendices/\nCE.MEASURES05.pdf (Last visit: Jan. 2007).\n[12] Text REtrieval Conference (TREC).\nhttp://trec.nist.gov/ (Last visit: Jan. 2007).\n[13] E. Voorhees and C. Buckley. The effect of topic set\nsize on retrieval experiment error. In 25th SIGIR,\npages 316-323, 2002.\n[14] E. M. Voorhees. Overview of the TREC 2005 Robust\nRetrieval Track. In TREC 2005 Proceedings, 2005.\n[15] E. M. Voorhees and D. K. Harman.\nTRECExperiment and Evaluation in Information Retrieval.\nMIT Press, 2005.\n[16] S. Wasserman and K. Faust. Social Network Analysis.\nCambridge University Press, Cambridge, UK, 1994.", "keywords": "trec;systems-topic graph;hit;social network analysis;mean average precision;link analysis technique;web search engine implementation;pagerank;network analysis;information retrieval evaluation experiment;inlink;ir evaluation;hit algorithm;kleinberg' hit algorithm;human assessor;weighted bipartite graph;stemming"}
{"name": "train_H-43", "title": "Combining Content and Link for Classification using Matrix Factorization", "abstract": "The world wide web contains rich textual contents that are interconnected via complex hyperlinks. This huge database violates the assumption held by most of conventional statistical methods that each web page is considered as an independent and identical sample. It is thus difficult to apply traditional mining or learning methods for solving web mining problems, e.g., web page classification, by exploiting both the content and the link structure. The research in this direction has recently received considerable attention but are still in an early stage. Though a few methods exploit both the link structure or the content information, some of them combine the only authority information with the content information, and the others first decompose the link structure into hub and authority features, then apply them as additional document features. Being practically attractive for its great simplicity, this paper aims to design an algorithm that exploits both the content and linkage information, by carrying out a joint factorization on both the linkage adjacency matrix and the document-term matrix, and derives a new representation for web pages in a low-dimensional factor space, without explicitly separating them as content, hub or authority factors. Further analysis can be performed based on the compact representation of web pages. In the experiments, the proposed method is compared with state-of-the-art methods and demonstrates an excellent accuracy in hypertext classification on the WebKB and Cora benchmarks.", "fulltext": "1. INTRODUCTION\nWith the advance of the World Wide Web, more and more\nhypertext documents become available on the Web. Some examples of\nsuch data include organizational and personal web pages (e.g, the\nWebKB benchmark data set, which contains university web pages),\nresearch papers (e.g., data in CiteSeer), online news articles, and\ncustomer-generated media (e.g., blogs). Comparing to data in\ntraditional information management, in addition to content, these data\non the Web also contain links: e.g., hyperlinks from a student\"s\nhomepage pointing to the homepage of her advisor, paper citations,\nsources of a news article, comments of one blogger on posts from\nanother blogger, and so on. Performing information management\ntasks on such structured data raises many new research challenges.\nIn the following discussion, we use the task of web page\nclassification as an illustrating example, while the techniques we develop\nin later sections are applicable equally well to many other tasks in\ninformation retrieval and data mining.\nFor the classification problem of web pages, a simple approach\nis to treat web pages as independent documents. The advantage\nof this approach is that many off-the-shelf classification tools can\nbe directly applied to the problem. However, this approach\nrelies only on the content of web pages and ignores the structure of\nlinks among them. Link structures provide invaluable information\nabout properties of the documents as well as relationships among\nthem. For example, in the WebKB dataset, the link structure\nprovides additional insights about the relationship among documents\n(e.g., links often pointing from a student to her advisor or from\na faculty member to his projects). Since some links among these\ndocuments imply the inter-dependence among the documents, the\nusual i.i.d. (independent and identical distributed) assumption of\ndocuments does not hold any more. From this point of view, the\ntraditional classification methods that ignore the link structure may\nnot be suitable.\nOn the other hand, a few studies, for example [25], rely solely on\nlink structures. It is however a very rare case that content\ninformation can be ignorable. For example, in the Cora dataset, the content\nof a research article abstract largely determines the category of the\narticle.\nTo improve the performance of web page classification,\ntherefore, both link structure and content information should be taken\ninto consideration. To achieve this goal, a simple approach is to\nconvert one type of information to the other. For example, in spam\nblog classification, Kolari et al. [13] concatenate outlink features\nwith the content features of the blog. In document classification,\nKurland and Lee [14] convert content similarity among documents\ninto weights of links. However, link and content information have\ndifferent properties. For example, a link is an actual piece of\nevidence that represents an asymmetric relationship whereas the\ncontent similarity is usually defined conceptually for every pair of\ndocuments in a symmetric way. Therefore, directly converting one type\nof information to the other usually degrades the quality of\ninformation. On the other hand, there exist some studies, as we will discuss\nin detail in related work, that consider link information and content\ninformation separately and then combine them. We argue that such\nan approach ignores the inherent consistency between link and\ncontent information and therefore fails to combine the two seamlessly.\nSome work, such as [3], incorporates link information using\ncocitation similarity, but this may not fully capture the global link\nstructure. In Figure 1, for example, web pages v6 and v7 co-cite\nweb page v8, implying that v6 and v7 are similar to each other.\nIn turns, v4 and v5 should be similar to each other, since v4 and\nv5 cite similar web pages v6 and v7, respectively. But using\ncocitation similarity, the similarity between v4 and v5 is zero without\nconsidering other information.\nv1\nv2\nv3\nv4\nv5\nv6\nv7\nv8\nFigure 1: An example of link structure\nIn this paper, we propose a simple technique for analyzing\ninter-connected documents, such as web pages, using factor\nanalysis[18]. In the proposed technique, both content information and\nlink structures are seamlessly combined through a single set of\nlatent factors. Our model contains two components. The first\ncomponent captures the content information. This component has a form\nsimilar to that of the latent topics in the Latent Semantic Indexing\n(LSI) [8] in traditional information retrieval. That is, documents\nare decomposed into latent topics/factors, which in turn are\nrepresented as term vectors. The second component captures the\ninformation contained in the underlying link structure, such as links\nfrom homepages of students to those of faculty members. A\nfactor can be loosely considered as a type of documents (e.g., those\nhomepages belonging to students). It is worth noting that we do\nnot explicitly define the semantic of a factor a priori. Instead,\nsimilar to LSI, the factors are learned from the data. Traditional factor\nanalysis models the variables associated with entities through the\nfactors. However, in analysis of link structures, we need to model\nthe relationship of two ends of links, i.e., edges between vertex\npairs. Therefore, the model should involve factors of both vertices\nof the edge. This is a key difference between traditional factor\nanalysis and our model. In our model, we connect two\ncomponents through a set of shared factors, that is, the latent factors in the\nsecond component (for contents) are tied to the factors in the first\ncomponent (for links). By doing this, we search for a unified set\nof latent factors that best explains both content and link structures\nsimultaneously and seamlessly.\nIn the formulation, we perform factor analysis based on matrix\nfactorization: solution to the first component is based on\nfactorizing the term-document matrix derived from content features;\nsolution to the second component is based on factorizing the adjacency\nmatrix derived from links. Because the two factorizations share\na common base, the discovered bases (latent factors) explain both\ncontent information and link structures, and are then used in further\ninformation management tasks such as classification.\nThis paper is organized as follows. Section 2 reviews related\nwork. Section 3 presents the proposed approach to analyze the web\npage based on the combined information of links and content.\nSection 4 extends the basic framework and a few variants for fine tune.\nSection 5 shows the experiment results. Section 6 discusses the\ndetails of this approach and Section 7 concludes.\n2. RELATED WORK\nIn the content analysis part, our approach is closely related to\nLatent Semantic Indexing (LSI) [8]. LSI maps documents into a\nlower dimensional latent space. The latent space implicitly\ncaptures a large portion of information of documents, therefore it is\ncalled the latent semantic space. The similarity between documents\ncould be defined by the dot products of the corresponding vectors\nof documents in the latent space. Analysis tasks, such as\nclassification, could be performed on the latent space. The commonly\nused singular value decomposition (SVD) method ensures that the\ndata points in the latent space can optimally reconstruct the original\ndocuments. Though our approach also uses latent space to\nrepresent web pages (documents), we consider the link structure as well\nas the content of web pages.\nIn the link analysis approach, the framework of hubs and\nauthorities (HITS) [12] puts web page into two categories, hubs and\nauthorities. Using recursive notion, a hub is a web page with many\noutgoing links to authorities, while an authority is a web page with\nmany incoming links from hubs. Instead of using two categories,\nPageRank [17] uses a single category for the recursive notion, an\nauthority is a web page with many incoming links from authorities.\nHe et al. [9] propose a clustering algorithm for web document\nclustering. The algorithm incorporates link structure and the co-citation\npatterns. In the algorithm, all links are treated as undirected edge of\nthe link graph. The content information is only used for weighing\nthe links by the textual similarity of both ends of the links. Zhang\net al. [23] uses the undirected graph regularization framework for\ndocument classification. Achlioptas et al[2] decompose the web\ninto hub and authority attributes then combine them with content.\nZhou et al. [25] and [24] propose a directed graph regularization\nframework for semi-supervised learning. The framework combines\nthe hub and authority information of web pages. But it is difficult\nto combine the content information into that framework. Our\napproach consider the content and the directed linkage between topics\nof source and destination web pages in one step, which implies the\ntopic combines the information of web page as authorities and as\nhubs in a single set of factors.\nCohn and Hofmann [6] construct the latent space from both\ncontent and link information, using content analysis based on\nprobabilistic LSI (PLSI) [10] and link analysis based on PHITS [5]. The\nmajor difference between the approach of [6] (PLSI+PHITS) and\nour approach is in the part of link analysis. In PLSI+PHITS, the\nlink is constructed with the linkage from the topic of the source\nweb page to the destination web page. In the model, the outgoing\nlinks of the destination web page have no effect on the source web\npage. In other words, the overall link structure is not utilized in\nPHITS. In our approach, the link is constructed with the linkage\nbetween the factor of the source web page and the factor of the\ndestination web page, instead of the destination web page itself. The\nfactor of the destination web page contains information of its\noutgoing links. In turn, such information is passed to the factor of the\nsource web page. As the result of matrix factorization, the factor\nforms a factor graph, a miniature of the original graph, preserving\nthe major structure of the original graph.\nTaskar et al. [19] propose relational Markov networks (RMNs)\nfor entity classification, by describing a conditional distribution of\nentity classes given entity attributes and relationships. The model\nwas applied to web page classification, where web pages are\nentities and hyperlinks are treated as relationships. RMNs apply\nconditional random fields to define a set of potential functions on cliques\nof random variables, where the link structure provides hints to form\nthe cliques. However the model does not give an off-the-shelf\nsolution, because the success highly depends on the arts of designing\nthe potential functions. On the other hand, the inference for RMNs\nis intractable and requires belief propagation.\nThe following are some work on combining documents and\nlinks, but the methods are loosely related to our approach. The\nexperiments of [21] show that using terms from the linked\ndocument improves the classification accuracy. Chakrabarti et al.[3] use\nco-citation information in their classification model. Joachims et\nal.[11] combine text kernels and co-citation kernels for\nclassification. Oh et al [16] use the Naive Bayesian frame to combine link\ninformation with content.\n3. OUR APPROACH\nIn this section we will first introduce a novel matrix\nfactorization method, which is more suitable than conventional matrix\nfactorization methods for link analysis. Then we will introduce our\napproach that jointly factorizes the document-term matrix and link\nmatrix and obtains compact and highly indicative factors for\nrepresenting documents or web pages.\n3.1 Link Matrix Factorization\nSuppose we have a directed graph G = (V, E), where the vertex\nset V = {vi}n\ni=1 represents the web pages and the edge set E\nrepresents the hyperlinks between web pages. Let A = {asd} denotes\nthe n\u00d7n adjacency matrix of G, which is also called the link matrix\nin this paper. For a pair of vertices, vs and vd, let asd = 1 when\nthere is an edge from vs to vd, and asd = 0, otherwise. Note that\nA is an asymmetric matrix, because hyperlinks are directed.\nMost machine learning algorithms assume a feature-vector\nrepresentation of instances. For web page classification, however, the\nlink graph does not readily give such a vector representation for\nweb pages. If one directly uses each row or column of A for the job,\nshe will suffer a very high computational cost because the\ndimensionality equals to the number of web pages. On the other hand, it\nwill produces a poor classification accuracy (see our experiments\nin Section 5), because A is extremely sparse1\n.\nThe idea of link matrix factorization is to derive a high-quality\nfeature representation Z of web pages based on analyzing the link\nmatrix A, where Z is an n \u00d7 l matrix, with each row being the\nldimensional feature vector of a web page. The new representation\nof web pages captures the principal factors of the link structure and\nmakes further processing more efficient.\nOne may use a method similar to LSI, to apply the well-known\nprincipal component analysis (PCA) for deriving Z from A. The\ncorresponding optimization problem 2\nis\nmin\nZ,U\nA \u2212 ZU 2\nF + \u03b3 U 2\nF (1)\nwhere \u03b3 is a small positive number, U is an l \u00d7n matrix, and \u00b7 F\nis the Frobenius norm. The optimization aims to approximate A by\nZU , a product of two low-rank matrices, with a regularization on\nU. In the end, the i-th row vector of Z can be thought as the hub\nfeature vector of vertex vi, and the row vector of U can be thought\nas the authority features. A link generation model proposed in [2] is\nsimilar to the PCA approach. Since A is a nonnegative matrix here,\none can also consider to put nonnegative constraints on U and Z,\nwhich produces an algorithm similar to PLSA [10] and NMF [20].\n1\nDue to the sparsity of A, links from two similar pages may not\nshare any common target pages, which makes them to appear\ndissimilar. However the two pages may be indirectly linked to many\ncommon pages via their neighbors.\n2\nAnother equivalent form is minZ,U A \u2212 ZU 2\nF , s. t. U U =\nI. The solution Z is identical subject to a scaling factor.\nHowever, despite its popularity in matrix analysis, PCA (or other\nsimilar methods like PLSA) is restrictive for link matrix\nfactorization. The major problem is that, PCA ignores the fact that the rows\nand columns of A are indexed by exactly the same set of objects\n(i.e., web pages). The approximating matrix \u02dcA = ZU shows no\nevidence that links are within the same set of objects. To see the\ndrawback, let\"s consider a link transitivity situation vi \u2192 vs \u2192 vj,\nwhere page i is linked to page s which itself is linked to page j.\nSince \u02dcA = ZU treats A as links from web pages {vi} to a\ndifferent set of objects, let it be denoted by {oi}, \u02dcA = ZU actually\nsplits an linked object os from vs and breaks down the link path\ninto two parts vi \u2192 os and vs \u2192 oj. This is obviously a miss\ninterpretation to the original link path.\nTo overcome the problem of PCA, in this paper we suggest to\nuse a different factorization:\nmin\nZ,U\nA \u2212 ZUZ 2\nF + \u03b3 U 2\nF (2)\nwhere U is an l \u00d7 l full matrix. Note that U is not symmetric, thus\nZUZ produces an asymmetric matrix, which is the case of A.\nAgain, each row vector of Z corresponds to a feature vector of a\nweb pages. The new approximating form \u02dcA = ZUZ puts a clear\nmeaning that the links are between the same set of objects,\nrepresented by features Z. The factor model actually maps each vertex,\nvi, into a vector zi = {zi,k; 1 \u2264 k \u2264 l} in the Rl\nspace. We call\nthe Rl\nspace the factor space. Then, {zi} encodes the information\nof incoming and outgoing connectivity of vertices {vi}. The\nfactor loadings, U, explain how these observed connections happened\nbased on {zi}. Once we have the vector zi, we can use many\ntraditional classification methods (such as SVMs) or clustering tools\n(such as K-Means) to perform the analysis.\nIllustration Based on a Synthetic Problem\nTo further illustrate the advantages of the proposed link matrix\nfactorization Eq. (2), let us consider the graph in Figure 1. Given\nv1\nv2\nv3\nv4\nv5\nv6\nv7\nv8\nFigure 2: Summarize Figure 1 with a factor graph\nthese observations, we can summarize the graph by grouping as\nfactor graph depicted in Figure 2. In the next we preform the two\nfactorization methods Eq. (2) and Eq. (1) on this link matrix. A\ngood low-rank representation should reveal the structure of the\nfactor graph.\nFirst we try PCA-like decomposition, solving Eq. (1) and\nobtaining\nZ = U =\n2\n6\n6\n6\n6\n6\n6\n6\n6\n6\n6\n6\n6\n6\n6\n6\n6\n4\n1. 1. 0 0 0\n0 0 \u2212.6 \u2212.7 .1\n0 0 .0 .6 \u2212.0\n0 0 .8 \u2212.4 .3\n0 0 .2 \u2212.2 \u2212.9\n.7 .7 0 0 0\n.7 .7 0 0 0\n0 0 0 0 0\n3\n7\n7\n7\n7\n7\n7\n7\n7\n7\n7\n7\n7\n7\n7\n7\n7\n5\n2\n6\n6\n6\n6\n6\n6\n6\n6\n6\n6\n6\n6\n6\n6\n6\n6\n4\n0 0 0 0 0\n.5 \u2212.5 0 0 0\n.5 \u2212.5 0 0 0\n0 0 \u22120.6 \u2212.7 .1\n0 0 .0 .6 \u2212.0\n0 0 .8 \u2212.4 .3\n0 0 .2 \u2212.2 \u2212.9\n.7 .7 0 0 0\n3\n7\n7\n7\n7\n7\n7\n7\n7\n7\n7\n7\n7\n7\n7\n7\n7\n5\nWe can see that the row vectors of v6 and v7 are the same in Z,\nindicating that v6 and v7 have the same hub attributes. The row\nvectors of v2 and v3 are the same in U, indicating that v2 and\nv3 have the same authority attributes. It is not clear to see the\nsimilarity between v4 and v5, because their inlinks (and outlinks)\nare different.\nThen, we factorize A by ZUZ via solving Eq. (2), and obtain\nthe results\nZ = U =\n2\n6\n6\n6\n6\n6\n6\n6\n6\n6\n6\n6\n6\n6\n6\n6\n6\n4\n\u2212.8 \u2212.5 .3 \u2212.1 \u2212.0\n\u2212.0 .4 .6 \u2212.1 \u2212.4\n\u2212.0 .4 .6 \u2212.1 \u2212.4\n.3 \u2212.2 .3 \u2212.4 .3\n.3 \u2212.2 .3 \u2212.4 .3\n\u2212.4 .5 .0 \u2212.2 .6\n\u2212.4 .5 .0 \u2212.2 .6\n\u2212.1 .1 \u2212.4 \u2212.8 \u2212.4\n3\n7\n7\n7\n7\n7\n7\n7\n7\n7\n7\n7\n7\n7\n7\n7\n7\n5\n2\n6\n6\n6\n6\n6\n6\n6\n6\n4\n\u2212.1 \u2212.2 \u2212.4 .6 .7\n.2 \u2212.5 \u2212.5 \u2212.5 .0\n.1 .1 .4 \u2212.4 .3\n.1 \u2212.2 \u2212.0 .3 \u2212.1\n\u2212.3 .3 \u2212.5 \u2212.4 \u2212.2\n3\n7\n7\n7\n7\n7\n7\n7\n7\n5\nThe resultant Z is very consistent with the clustering structure\nof vertices: the row vectors of v2 and v3 are the same, those\nof v4 and v5 are the same, those of v6 and v7 are the same.\nEven interestingly, if we add constraints to ensure Z and U be\nnonnegative, we have\nZ = U =\n2\n6\n6\n6\n6\n6\n6\n6\n6\n6\n6\n6\n6\n6\n6\n6\n6\n4\n1. 0 0 0 0\n0 .9 0 0 0\n0 .9 0 0 0\n0 0 .7 0 0\n0 0 .7 0 0\n0 0 0 .9 0\n0 0 0 .9 0\n0 0 0 0 1.\n3\n7\n7\n7\n7\n7\n7\n7\n7\n7\n7\n7\n7\n7\n7\n7\n7\n5\n2\n6\n6\n6\n6\n6\n6\n6\n6\n4\n0 1. 0 0 0\n0 0 .7 0 0\n0 0 0 .7 0\n0 0 0 0 1.\n0 0 0 0 0\n3\n7\n7\n7\n7\n7\n7\n7\n7\n5\nwhich clearly tells the assignment of vertices to clusters from Z\nand the links of factor graph from U. When the interpretability is\nnot critical in some tasks, for example, classification, we found that\nit achieves better accuracies without the nonnegative constraints.\nGiven our above analysis, it is clear that the factorization ZUZ\nis more expressive than ZU in representing the link matrix A.\n3.2 Content Matrix Factorization\nNow let us consider the content information on the vertices. To\ncombine the link information and content information, we want to\nuse the same latent space to approximate the content as the latent\nspace for the links. Using the bag-of-words approach, we denote\nthe content of web pages by an n\u00d7m matrix C, each of whose rows\nrepresents a document, each column represents a keyword, where\nm is the number of keywords. Like the latent semantic indexing\n(LSI) [8], the l-dimensional latent space for words is denoted by an\nm \u00d7 l matrix V . Therefore, we use ZV to approximate matrix\nC,\nmin\nV,Z\nC \u2212 ZV 2\nF + \u03b2 V 2\nF , (3)\nwhere \u03b2 is a small positive number, \u03b2 V 2\nF serves as a\nregularization term to improve the robustness.\n3.3 Joint Link-Content Matrix Factorization\nThere are many ways to employ both the content and link\ninformation for web page classification. Our idea in this paper is not to\nsimply combine them, but rather to fuse them into a single,\nconsistent, and compact feature representation. To achieve this goal, we\nsolve the following problem,\nmin\nU,V,Z\nn\nJ (U, V, Z)\ndef\n= A \u2212 ZUZ 2\nF +\n\u03b1 C \u2212 ZV 2\nF + \u03b3 U 2\nF + \u03b2 V 2\nF\no\n.\n(4)\nEq. (4) is the joined matrix factorization of A and C with\nregularization. The new representation Z is ensured to capture both the\nstructures of the link matrix A and the content matrix C. Once\nwe find the optimal Z, we can apply the traditional classification\nor clustering methods on vectorial data Z. The relationship among\nthese matrices can be depicted as Figure 3.\nA Y C\nU Z V\nFigure 3: Relationship among the matrices. Node Y is the\ntarget of classification.\nEq. (4) can be solved using gradient methods, such as the\nconjugate gradient method and quasi-Newton methods. Then main\ncomputation of gradient methods is evaluating the object function J\nand its gradients against variables,\n\u2202J\n\u2202U\n=\n\nZ ZUZ Z \u2212 Z AZ\n\n+ \u03b3U,\n\u2202J\n\u2202V\n=\u03b1\n\nV Z Z \u2212 C Z\n\n+ \u03b2V,\n\u2202J\n\u2202Z\n=\n\nZU Z ZU + ZUZ ZU \u2212 A ZU \u2212 AZU\n\n+ \u03b1\n\nZV V \u2212 CV\n\n.\nBecause of the sparsity of A, the computational complexity of\nmultiplication of A and Z is O(\u00b5Al), where \u00b5A is the number of\nnonzero entries in A. Similarly, the computational complexity of\nC Z and CV is O(\u00b5C l), where \u00b5C is the number of nonzero\nentries in C. The computational complexity of the rest\nmultiplications in the gradient computation is O(nl2\n). Therefore, the total\ncomputational complexity in one iteration is O(\u00b5Al + \u00b5C l + nl2\n).\nThe number of links and the number of words in a web page are\nrelatively small comparing to the number of web pages, and are\nalmost constant as the number of web pages/documents increases, i.e.\n\u00b5A = O(n) and \u00b5C = O(n). Therefore, theoretically the\ncomputation time is almost linear to the number of web pages/documents,\nn.\n4. SUPERVISED MATRIX\nFACTORIZATION\nConsider a web page classification problem. We can solve\nEq. (4) to obtain Z as Section 3, then use a traditional classifier\nto perform classification. However, this approach does not take\ndata labels into account in the first step. Believing that using data\nlabels improves the accuracy by obtaining a better Z for the\nclassification, we consider to use the data labels to guide the matrix\nfactorization, called supervised matrix factorization [22]. Because\nsome data used in the matrix factorization have no label\ninformation, the supervised matrix factorization falls into the category of\nsemi-supervised learning.\nLet C be the set of classes. For simplicity, we first consider\nbinary class problem, i.e. C = {\u22121, 1}. Assume we know the\nlabels {yi} for vertices in T \u2282 V. We want to find a hypothesis\nh : V \u2192 R, such that we assign vi to 1 when h(vi) \u2265 0, \u22121\notherwise. We assume a transform from the latent space to R is linear,\ni.e.\nh(vi) = w \u03c6(vi) + b = w zi + b, (5)\nSchool course dept. faculty other project staff student total\nCornell 44 1 34 581 18 21 128 827\nTexas 36 1 46 561 20 2 148 814\nWashington 77 1 30 907 18 10 123 1166\nWisconsin 85 0 38 894 25 12 156 1210\nTable 1: Dataset of WebKB\nwhere w and b are parameters to estimate. Here, w is the norm\nof the decision boundary. Similar to Support Vector Machines\n(SVMs) [7], we can use the hinge loss to measure the loss,\nX\ni:vi\u2208T\n[1 \u2212 yih(vi)]+ ,\nwhere [x]+ is x if x \u2265 0, 0 if x < 0. However, the hinge loss\nis not smooth at the hinge point, which makes it difficult to apply\ngradient methods on the problem. To overcome the difficulty, we\nuse a smoothed version of hinge loss for each data point,\ng(yih(vi)), (6)\nwhere\ng(x) =\n8\n><\n>:\n0 when x \u2265 2,\n1 \u2212 x when x \u2264 0,\n1\n4\n(x \u2212 2)2\nwhen 0 < x < 2.\nWe reduce a multiclass problem into multiple binary ones. One\nsimple scheme of reduction is the one-against-rest coding scheme.\nIn the one-against-rest scheme, we assign a label vector for each\nclass label. The element of a label vector is 1 if the data point\nbelongs the corresponding class, \u22121, if the data point does not belong\nthe corresponding class, 0, if the data point is not labeled. Let Y be\nthe label matrix, each column of which is a label vector. Therefore,\nY is a matrix of n \u00d7 c, where c is the number of classes, |C|. Then\nthe values of Eq. (5) form a matrix\nH = ZW + 1b , (7)\nwhere 1 is a vector of size n, whose elements are all one, W is a\nc \u00d7 l parameter matrix, and b is a parameter vector of size c. The\ntotal loss is proportional to the sum of Eq. (6) over all labeled data\npoints and the classes,\nLY (W, b, Z) = \u03bb\nX\ni:vi\u2208T ,j\u2208C\ng(YijHij),\nwhere \u03bb is the parameter to scale the term.\nTo derive a robust solution, we also use Tikhonov regularization\nfor W,\n\u2126W (W) =\n\u03bd\n2\nW 2\nF ,\nwhere \u03bd is the parameter to scale the term.\nThen the supervised matrix factorization problem becomes\nmin\nU,V,Z,W,b\nJs(U, V, Z, W, b) (8)\nwhere\nJs(U, V, Z, W, b) = J (U, V, Z) + LY (W, b, Z) + \u2126W (W).\nWe can also use gradient methods to solve the problem of Eq. (8).\nThe gradients are\n\u2202Js\n\u2202U\n=\n\u2202J\n\u2202U\n,\n\u2202Js\n\u2202V\n=\n\u2202J\n\u2202V\n,\n\u2202Js\n\u2202Z\n=\n\u2202J\n\u2202Z\n+ \u03bbGW,\n\u2202Js\n\u2202W\n=\u03bbG Z + \u03bdW,\n\u2202Js\n\u2202b\n=\u03bbG 1,\nwhere G is an n\u00d7c matrix, whose ik-th element is Yikg (YikHik),\nand\ng (x) =\n8\n><\n>:\n0 when x \u2265 2,\n\u22121 when x \u2264 0,\n1\n2\n(x \u2212 2) when 0 < x < 2.\nOnce we obtain w, b, and Z, we can apply h on the vertices with\nunknown class labels, or apply traditional classification algorithms\non Z to get the classification results.\n5. EXPERIMENTS\n5.1 Data Description\nIn this section, we perform classification on two datasets, to\ndemonstrate the our approach. The two datasets are the WebKB\ndata set[1] and the Cora data set [15]. The WebKB data set\nconsists of about 6000 web pages from computer science departments\nof four schools (Cornell, Texas, Washington, and Wisconsin). The\nweb pages are classified into seven categories. The numbers of\npages in each category are shown in Table 1. The Cora data set\nconsists of the abstracts and references of about 34,000 computer\nscience research papers. We use part of them to categorize into\none of subfields of data structure (DS), hardware and architecture\n(HA), machine learning (ML), and programing language (PL). We\nremove those articles without reference to other articles in the set.\nThe number of papers and the number of subfields in each area are\nshown in Table 2.\narea # of papers # of subfields\nData structure (DS) 751 9\nHardware and architecture (HA) 400 7\nMachine learning (ML) 1617 7\nPrograming language (PL) 1575 9\nTable 2: Dataset of Cora\n5.2 Methods\nThe task of the experiments is to classify the data based on their\ncontent information and/or link structure. We use the following\nmethods:\n65\n70\n75\n80\n85\n90\n95\n100\nWisconsinWashingtonTexasCornell\naccuracy(%)\ndataset\nSVM on content\nSVM on link\nSVM on link-content\nDirected graph reg.\nPLSI+PHITS\nlink-content MF\nlink-content sup. MF\nmethod Cornell Texas Washington Wisconsin\nSVM on content 81.00 \u00b1 0.90 77.00 \u00b1 0.60 85.20 \u00b1 0.90 84.30 \u00b1 0.80\nSVM on links 70.10 \u00b1 0.80 75.80 \u00b1 1.20 80.50 \u00b1 0.30 74.90 \u00b1 1.00\nSVM on link-content 80.00 \u00b1 0.80 78.30 \u00b1 1.00 85.20 \u00b1 0.70 84.00 \u00b1 0.90\nDirected graph regularization 89.47 \u00b1 1.41 91.28 \u00b1 0.75 91.08 \u00b1 0.51 89.26 \u00b1 0.45\nPLSI+PHITS 80.74 \u00b1 0.88 76.15 \u00b1 1.29 85.12 \u00b1 0.37 83.75 \u00b1 0.87\nlink-content MF 93.50 \u00b1 0.80 96.20 \u00b1 0.50 93.60 \u00b1 0.50 92.60 \u00b1 0.60\nlink-content sup. MF 93.80 \u00b1 0.70 97.07 \u00b1 1.11 93.70 \u00b1 0.60 93.00 \u00b1 0.30\nTable 3: Classification accuracy (mean \u00b1 std-err %) on WebKB data set\n\u2022 SVM on content We apply support vector machines (SVM)\non the content of documents. The features are the\nbag-ofwords and all word are stemmed. This method ignores link\nstructure in the data. Linear SVM is used. The\nregularization parameter of SVM is selected using the cross-validation\nmethod. The implementation of SVM used in the\nexperiments is libSVM[4].\n\u2022 SVM on links We treat links as the features of each\ndocument, i.e. the i-th feature is link-to-pagei. We apply SVM on\nlink features. This method uses link information, but not the\nlink structure.\n\u2022 SVM on link-content We combine the features of the above\ntwo methods. We use different weights for these two set\nof features. The weights are also selected using\ncrossvalidation.\n\u2022 Directed graph regularization This method is described in\n[25] and [24]. This method is solely based on link structure.\n\u2022 PLSI+PHITS This method is described in [6]. This method\ncombines text content information and link structure for\nanalysis. The PHITS algorithm is in spirit similar to Eq.1,\nwith an additional nonnegative constraint. It models the\noutgoing and in-coming structures separately.\n\u2022 Link-content MF This is our approach of matrix\nfactorization described in Section 3. We use 50 latent factors for Z.\nAfter we compute Z, we train a linear SVM using Z as the\nfeature vectors, then apply SVM on testing portion of Z to\nobtain the final result, because of the multiclass output.\n\u2022 Link-content sup. MF This method is our approach of the\nsupervised matrix factorization in Section 4. We use 50 latent\nfactors for Z. After we compute Z, we train a linear SVM\non the training portion of Z, then apply SVM on testing\nportion of Z to obtain the final result, because of the multiclass\noutput.\nWe randomly split data into five folds and repeat the experiment\nfor five times, for each time we use one fold for test, four other\nfolds for training. During the training process, we use the\ncrossvalidation to select all model parameters. We measure the results\nby the classification accuracy, i.e., the percentage of the number\nof correct classified documents in the entire data set. The results\nare shown as the average classification accuracies and it standard\ndeviation over the five repeats.\n5.3 Results\nThe average classification accuracies for the WebKB data set are\nshown in Table 3. For this task, the accuracies of SVM on links\nare worse than that of SVM on content. But the directed graph\nregularization, which is also based on link alone, achieves a much\nhigher accuracy. This implies that the link structure plays an\nimportant role in the classification of this dataset, but individual links\nin a web page give little information. The combination of link and\ncontent using SVM achieves similar accuracy as that of SVM on\ncontent alone, which confirms individual links in a web page give\nlittle information. Since our approach consider the link structure\nas well as the content information, our two methods give results\na highest accuracies among these approaches. The difference\nbetween the results of our two methods is not significant. However in\nthe experiments below, we show the difference between them.\nThe classification accuracies for the Cora data set are shown in\nTable 4. In this experiment, the accuracies of SVM on the\ncombination of links and content are higher than either SVM on content\nor SVM on links. This indicates both content and links are\ninfor45\n50\n55\n60\n65\n70\n75\n80\nPLMLHADS\naccuracy(%)\ndataset\nSVM on content\nSVM on link\nSVM on link-content\nDirected graph reg.\nPLSI+PHITS\nlink-content MF\nlink-content sup. MF\nmethod DS HA ML PL\nSVM on content 53.70 \u00b1 0.50 67.50 \u00b1 1.70 68.30 \u00b1 1.60 56.40 \u00b1 0.70\nSVM on links 48.90 \u00b1 1.70 65.80 \u00b1 1.40 60.70 \u00b1 1.10 58.20 \u00b1 0.70\nSVM on link-content 63.70 \u00b1 1.50 70.50 \u00b1 2.20 70.56 \u00b1 0.80 62.35 \u00b1 1.00\nDirected graph regularization 46.07 \u00b1 0.82 65.50 \u00b1 2.30 59.37 \u00b1 0.96 56.06 \u00b1 0.84\nPLSI+PHITS 53.60 \u00b1 1.78 67.40 \u00b1 1.48 67.51 \u00b1 1.13 57.45 \u00b1 0.68\nlink-content MF 61.00 \u00b1 0.70 74.20 \u00b1 1.20 77.50 \u00b1 0.80 62.50 \u00b1 0.80\nlink-content sup. MF 69.38 \u00b1 1.80 74.20 \u00b1 0.70 78.70 \u00b1 0.90 68.76 \u00b1 1.32\nTable 4: Classification accuracy (mean \u00b1 std-err %) on Cora data set\nmative for classifying the articles into subfields. The method of\ndirected graph regularization does not perform as good as SVM on\nlink-content, which confirms the importance of the article content\nin this task. Though our method of link-content matrix\nfactorization perform slightly better than other methods, our method of\nlinkcontent supervised matrix factorization outperform significantly.\n5.4 The Number of Factors\nAs we discussed in Section 3, the computational complexity of\neach iteration for solving the optimization problem is quadratic to\nthe number of factors. We perform experiments to study how the\nnumber of factors affects the accuracy of predication. We use\ndifferent numbers of factors for the Cornell data of WebKB data set\nand the machine learning (ML) data of Cora data set. The result\nshown in Figure 4(a) and 4(b). The figures show that the accuracy\n88\n89\n90\n91\n92\n93\n94\n95\n0 10 20 30 40 50\naccuracy(%)\nnumber of factors\nlink-content sup. MF\nlink-content MF\n(a) Cornell data\n62\n64\n66\n68\n70\n72\n74\n76\n78\n80\n0 10 20 30 40 50\naccuracy(%)\nnumber of factors\nlink-content sup. MF\nlink-content MF\n(b) ML data\nFigure 4: Accuracy vs number of factors\nincreases as the number of factors increases. It is a different\nconcept from choosing the optimal number of clusters in clustering\napplication. It is how much information to represent in the latent\nvariables. We have considered the regularization over the factors,\nwhich avoids the overfit problem for a large number of factors. To\nchoose of the number of factors, we need to consider the trade-off\nbetween the accuracy and the computation time, which is quadratic\nto the number of factors.\nThe difference between the method of matrix factorization and\nthat of supervised one decreases as the number of factors increases.\nThis indicates that the usefulness of supervised matrix factorization\nat lower number of factors.\n6. DISCUSSIONS\nThe loss functions LA in Eq. (2) and LC in Eq. (3) use squared\nloss due to computationally convenience. Actually, squared loss\ndoes not precisely describe the underlying noise model, because\nthe weights of adjacency matrix can only take nonnegative\nvalues, in our case, zero or one only, and the components of\ncontent matrix C can only take nonnegative integers. Therefore, we\ncan apply other types of loss, such as hinge loss or smoothed\nhinge loss, e.g. LA(U, Z) = \u00b5h(A, ZUZ ), where h(A, B) =P\ni,j [1 \u2212 AijBij]+ .\nIn our paper, we mainly discuss the application of classification.\nA entry of matrix Z means the relationship of a web page and a\nfactor. The values of the entries are the weights of linear model,\ninstead of the probabilities of web pages belonging to latent\ntopics. Therefore, we allow the components take any possible real\nvalues. When we come to the clustering application, we can use this\nmodel to find Z, then apply K-means to partition the web pages\ninto clusters. Actually, we can use the idea of nonnegative matrix\nfactorization for clustering [20] to directly cluster web pages. As\nthe example with nonnegative constraints shown in Section 3, we\nrepresent each cluster by a latent topic, i.e. the dimensionality of\nthe latent space is set to the number of clusters we want. Then the\nproblem of Eq. (4) becomes\nmin\nU,V,Z\nJ (U, V, Z), s.t.Z \u2265 0. (9)\nSolving Eq. (9), we can obtain more interpretable results, which\ncould be used for clustering.\n7. CONCLUSIONS\nIn this paper, we study the problem of how to combine the\ninformation of content and links for web page analysis, mainly on\nclassification application. We propose a simple approach using factors to\nmodel the text content and link structure of web pages/documents.\nThe directed links are generated from the linear combination of\nlinkage of between source and destination factors. By sharing\nfactors between text content and link structure, it is easy to combine\nboth the content information and link structure. Our experiments\nshow our approach is effective for classification. We also discuss\nan extension for clustering application.\nAcknowledgment\nWe would like to thank Dr. Dengyong Zhou for sharing his code\nof his algorithm. Also, thanks to the reviewers for constructive\ncomments.\n8. 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A study of approaches to\nhypertext categorization. Journal of Intelligent Information\nSystems, 18(2-3):219-241, 2002.\n[22] K. Yu, S. Yu, and V. Tresp. Multi-label informed latent\nsemantic indexing. In SIGIR \"05: Proceedings of the 28th\nannual international ACM SIGIR conference on Research\nand development in information retrieval, pages 258-265,\nNew York, NY, USA, 2005. ACM Press.\n[23] T. Zhang, A. Popescul, and B. Dom. Linear prediction\nmodels with graph regularization for web-page\ncategorization. In KDD \"06: Proceedings of the 12th ACM\nSIGKDD international conference on Knowledge discovery\nand data mining, pages 821-826, New York, NY, USA,\n2006. ACM Press.\n[24] D. Zhou, J. Huang, and B. Sch\u00a8olkopf. Learning from labeled\nand unlabeled data on a directed graph. In Proceedings of the\n22nd International Conference on Machine Learning, Bonn,\nGermany, 2005.\n[25] D. Zhou, B. Sch\u00a8olkopf, and T. Hofmann. Semi-supervised\nlearning on directed graphs. Proc. Neural Info. Processing\nSystems, 2004.", "keywords": "low-dimensional factor space;web mining problem;classification;combining content and link;linkage adjacency matrix;content information;authority information;joint factorization;relationship;link structure;factor analysis;asymmetric relationship;document-term matrix;cocitation similarity;webkb and cora benchmark;text content;matrix factorization"}
{"name": "train_H-44", "title": "A Time Machine for Text Search", "abstract": "Text search over temporally versioned document collections such as web archives has received little attention as a research problem. As a consequence, there is no scalable and principled solution to search such a collection as of a specified time t. In this work, we address this shortcoming and propose an efficient solution for time-travel text search by extending the inverted file index to make it ready for temporal search. We introduce approximate temporal coalescing as a tunable method to reduce the index size without significantly affecting the quality of results. In order to further improve the performance of time-travel queries, we introduce two principled techniques to trade off index size for its performance. These techniques can be formulated as optimization problems that can be solved to near-optimality. Finally, our approach is evaluated in a comprehensive series of experiments on two large-scale real-world datasets. Results unequivocally show that our methods make it possible to build an efficient time machine scalable to large versioned text collections.", "fulltext": "1. INTRODUCTION\nIn this work we address time-travel text search over\ntemporally versioned document collections. Given a keyword\nquery q and a time t our goal is to identify and rank\nrelevant documents as if the collection was in its state as of\ntime t.\nAn increasing number of such versioned document\ncollections is available today including web archives,\ncollaborative authoring environments like Wikis, or timestamped\ninformation feeds. Text search on these collections,\nhowever, is mostly time-ignorant: while the searched collection\nchanges over time, often only the most recent version of\na documents is indexed, or, versions are indexed\nindependently and treated as separate documents. Even worse, for\nsome collections, in particular web archives like the\nInternet Archive [18], a comprehensive text-search functionality\nis often completely missing.\nTime-travel text search, as we develop it in this paper,\nis a crucial tool to explore these collections and to unfold\ntheir full potential as the following example demonstrates.\nFor a documentary about a past political scandal, a\njournalist needs to research early opinions and statements made\nby the involved politicians. Sending an appropriate query\nto a major web search-engine, the majority of returned\nresults contains only recent coverage, since many of the early\nweb pages have disappeared and are only preserved in web\narchives. If the query could be enriched with a time point,\nsay August 20th 2003 as the day after the scandal got\nrevealed, and be issued against a web archive, only pages that\nexisted specifically at that time could be retrieved thus better\nsatisfying the journalist\"s information need.\nDocument collections like the Web or Wikipedia [32], as\nwe target them here, are already large if only a single\nsnapshot is considered. Looking at their evolutionary history, we\nare faced with even larger data volumes. As a consequence,\nna\u00a8\u0131ve approaches to time-travel text search fail, and viable\napproaches must scale-up well to such large data volumes.\nThis paper presents an efficient solution to time-travel\ntext search by making the following key contributions:\n1. The popular well-studied inverted file index [35] is\ntransparently extended to enable time-travel text search.\n2. Temporal coalescing is introduced to avoid an\nindexsize explosion while keeping results highly accurate.\n3. We develop two sublist materialization techniques to\nimprove index performance that allow trading off space\nvs. performance.\n4. In a comprehensive experimental evaluation our\napproach is evaluated on the English Wikipedia and parts\nof the Internet Archive as two large-scale real-world\ndatasets with versioned documents.\nThe remainder of this paper is organized as follows. The\npresented work is put in context with related work in\nSection 2. We delineate our model of a temporally versioned\ndocument collection in Section 3. We present our time-travel\ninverted index in Section 4. Building on it, temporal\ncoalescing is described in Section 5. In Section 6 we describe\nprincipled techniques to improve index performance, before\npresenting the results of our experimental evaluation in\nSection 7.\n2. RELATED WORK\nWe can classify the related work mainly into the following\ntwo categories: (i) methods that deal explicitly with\ncollections of versioned documents or temporal databases, and\n(ii) methods for reducing the index size by exploiting either\nthe document-content overlap or by pruning portions of the\nindex. We briefly review work under these categories here.\nTo the best of our knowledge, there is very little prior work\ndealing with historical search over temporally versioned\ndocuments. Anick and Flynn [3], while pioneering this research,\ndescribe a help-desk system that supports historical queries.\nAccess costs are optimized for accesses to the most recent\nversions and increase as one moves farther into the past.\nBurrows and Hisgen [10], in a patent description, delineate\na method for indexing range-based values and mention its\npotential use for searching based on dates associated with\ndocuments. Recent work by N\u00f8rv\u02daag and Nyb\u00f8 [25] and\ntheir earlier proposals concentrate on the relatively simpler\nproblem of supporting text-containment queries only and\nneglect the relevance scoring of results. Stack [29] reports\npractical experiences made when adapting the open source\nsearch-engine Nutch to search web archives. This\nadaptation, however, does not provide the intended time-travel\ntext search functionality. In contrast, research in temporal\ndatabases has produced several index structures tailored for\ntime-evolving databases; a comprehensive overview of the\nstate-of-art is available in [28]. Unlike the inverted file\nindex, their applicability to text search is not well understood.\nMoving on to the second category of related work, Broder\net al. [8] describe a technique that exploits large content\noverlaps between documents to achieve a reduction in index\nsize. Their technique makes strong assumptions about the\nstructure of document overlaps rendering it inapplicable to\nour context. More recent approaches by Hersovici et al. [17]\nand Zhang and Suel [34] exploit arbitrary content overlaps\nbetween documents to reduce index size. None of the\napproaches, however, considers time explicitly or provides the\ndesired time-travel text search functionality. Static\nindexpruning techniques [11, 12] aim to reduce the effective index\nsize, by removing portions of the index that are expected\nto have low impact on the query result. They also do not\nconsider temporal aspects of documents, and thus are\ntechnically quite different from our proposal despite having a\nshared goal of index-size reduction. It should be noted that\nindex-pruning techniques can be adapted to work along with\nthe temporal text index we propose here.\n3. MODEL\nIn the present work, we deal with a temporally versioned\ndocument collection D that is modeled as described in the\nfollowing. Each document d \u2208 D is a sequence of its versions\nd = dt1\n, dt2\n, . . . .\nEach version dti\nhas an associated timestamp ti reflecting\nwhen the version was created. Each version is a vector of\nsearchable terms or features. Any modification to a\ndocument version results in the insertion of a new version with\ncorresponding timestamp. We employ a discrete definition\nof time, so that timestamps are non-negative integers. The\ndeletion of a document at time ti, i.e., its disappearance\nfrom the current state of the collection, is modeled as the\ninsertion of a special tombstone version \u22a5. The validity\ntime-interval val(dti\n) of a version dti\nis [ti, ti+1), if a newer\nversion with associated timestamp ti+1 exists, and [ti, now)\notherwise where now points to the greatest possible value of\na timestamp (i.e., \u2200t : t < now).\nPutting all this together, we define the state Dt\nof the\ncollection at time t (i.e., the set of versions valid at t that\nare not deletions) as\nDt\n=\n[\nd\u2208D\n{dti\n\u2208 d | t \u2208 val(dti\n) \u2227 dti\n= \u22a5} .\nAs mentioned earlier, we want to enrich a keyword query\nq with a timestamp t, so that q be evaluated over Dt\n, i.e.,\nthe state of the collection at time t. The enriched time-travel\nquery is written as q t\nfor brevity.\nAs a retrieval model in this work we adopt Okapi BM25 [27],\nbut note that the proposed techniques are not dependent on\nthis choice and are applicable to other retrieval models like\ntf-idf [4] or language models [26] as well. For our considered\nsetting, we slightly adapt Okapi BM25 as\nw(q t\n, dti\n) =\nX\nv\u2208q\nwtf (v, dti\n) \u00b7 widf (v, t) .\nIn the above formula, the relevance w(q t\n, dti\n) of a\ndocument version dti\nto the time-travel query q t\nis defined.\nWe reiterate that q t\nis evaluated over Dt\nso that only the\nversion dti\nvalid at time t is considered. The first factor\nwtf (v, dti\n) in the summation, further referred to as the\ntfscore is defined as\nwtf (v, dti\n) =\n(k1 + 1) \u00b7 tf(v, dti\n)\nk1 \u00b7 ((1 \u2212 b) + b \u00b7 dl(d ti )\navdl(ti)\n) + tf(v, dti )\n.\nIt considers the plain term frequency tf(v, dti\n) of term v\nin version dti\nnormalizing it, taking into account both the\nlength dl(dti\n) of the version and the average document length\navdl(ti) in the collection at time ti. The length-normalization\nparameter b and the tf-saturation parameter k1 are inherited\nfrom the original Okapi BM25 and are commonly set to\nvalues 1.2 and 0.75 respectively. The second factor widf (v, t),\nwhich we refer to as the idf-score in the remainder, conveys\nthe inverse document frequency of term v in the collection\nat time t and is defined as\nwidf (v, t) = log\nN(t) \u2212 df(v, t) + 0.5\ndf(v, t) + 0.5\nwhere N(t) = |Dt\n| is the collection size at time t and df(v, t)\ngives the number of documents in the collection that contain\nthe term v at time t. While the idf-score depends on the\nwhole corpus as of the query time t, the tf-score is specific\nto each version.\n4. TIME-TRAVELINVERTEDFILEINDEX\nThe inverted file index is a standard technique for text\nindexing, deployed in many systems. In this section, we\nbriefly review this technique and present our extensions to\nthe inverted file index that make it ready for time-travel text\nsearch.\n4.1 Inverted File Index\nAn inverted file index consists of a vocabulary, commonly\norganized as a B+-Tree, that maps each term to its\nidfscore and inverted list. The index list Lv belonging to term\nv contains postings of the form\n( d, p )\nwhere d is a document-identifier and p is the so-called\npayload. The payload p contains information about the term\nfrequency of v in d, but may also include positional\ninformation about where the term appears in the document.\nThe sort-order of index lists depends on which queries are\nto be supported efficiently. For Boolean queries it is\nfavorable to sort index lists in document-order.\nFrequencyorder and impact-order sorted index lists are beneficial for\nranked queries and enable optimized query processing that\nstops early after having identified the k most relevant\ndocuments [1, 2, 9, 15, 31]. A variety of compression techniques,\nsuch as encoding document identifiers more compactly, have\nbeen proposed [33, 35] to reduce the size of index lists. For\nan excellent recent survey about inverted file indexes we\nrefer to [35].\n4.2 Time-Travel Inverted File Index\nIn order to prepare an inverted file index for time travel\nwe extend both inverted lists and the vocabulary structure\nby explicitly incorporating temporal information. The main\nidea for inverted lists is that we include a validity\ntimeinterval [tb, te) in postings to denote when the payload\ninformation was valid. The postings in our time-travel inverted\nfile index are thus of the form\n( d, p, [tb, te) )\nwhere d and p are defined as in the standard inverted file\nindex above and [tb, te) is the validity time-interval.\nAs a concrete example, in our implementation, for a\nversion dti\nhaving the Okapi BM25 tf-score wtf (v, dti\n) for term\nv, the index list Lv contains the posting\n( d, wtf (v, dti\n), [ti, ti+1) ) .\nSimilarly, the extended vocabulary structure maintains\nfor each term a time-series of idf-scores organized as a\nB+Tree. Unlike the tf-score, the idf-score of every term could\nvary with every change in the corpus. Therefore, we take\na simplified approach to idf-score maintenance, by\ncomputing idf-scores for all terms in the corpus at specific (possibly\nperiodic) times.\n4.3 Query Processing\nDuring processing of a time-travel query q t\n, for each query\nterm the corresponding idf-score valid at time t is retrieved\nfrom the extended vocabulary. Then, index lists are\nsequentially read from disk, thereby accumulating the information\ncontained in the postings. We transparently extend the\nsequential reading, which is - to the best of our\nknowledgecommon to all query processing techniques on inverted file\nindexes, thus making them suitable for time-travel\nqueryprocessing. To this end, sequential reading is extended by\nskipping all postings whose validity time-interval does not\ncontain t (i.e., t \u2208 [tb, te)). Whether a posting can be\nskipped can only be decided after the posting has been\ntransferred from disk into memory and therefore still incurs\nsignificant I/O cost. As a remedy, we propose index organization\ntechniques in Section 6 that aim to reduce the I/O overhead\nsignificantly.\nWe note that our proposed extension of the inverted file\nindex makes no assumptions about the sort-order of\nindex lists. As a consequence, existing query-processing\ntechniques and most optimizations (e.g., compression techniques)\nremain equally applicable.\n5. TEMPORAL COALESCING\nIf we employ the time-travel inverted index, as described\nin the previous section, to a versioned document collection,\nwe obtain one posting per term per document version. For\nfrequent terms and large highly-dynamic collections, this\ntime\nscore\nnon-coalesced\ncoalesced\nFigure 1: Approximate Temporal Coalescing\nleads to extremely long index lists with very poor\nqueryprocessing performance.\nThe approximate temporal coalescing technique that we\npropose in this section counters this blowup in index-list\nsize. It builds on the observation that most changes in a\nversioned document collection are minor, leaving large parts\nof the document untouched. As a consequence, the payload\nof many postings belonging to temporally adjacent versions\nwill differ only slightly or not at all. Approximate temporal\ncoalescing reduces the number of postings in an index list by\nmerging such a sequence of postings that have almost equal\npayloads, while keeping the maximal error bounded. This\nidea is illustrated in Figure 1, which plots non-coalesced and\ncoalesced scores of postings belonging to a single document.\nApproximate temporal coalescing is greatly effective given\nsuch fluctuating payloads and reduces the number of\npostings from 9 to 3 in the example. The notion of temporal\ncoalescing was originally introduced in temporal database\nresearch by B\u00a8ohlen et al. [6], where the simpler problem of\ncoalescing only equal information was considered.\nWe next formally state the problem dealt with in\napproximate temporal coalescing, and discuss the computation of\noptimal and approximate solutions. Note that the technique\nis applied to each index list separately, so that the following\nexplanations assume a fixed term v and index list Lv.\nAs an input we are given a sequence of temporally\nadjacent postings\nI = ( d, pi, [ti, ti+1) ), . . . , ( d, pn\u22121, [tn\u22121, tn)) ) .\nEach sequence represents a contiguous time period during\nwhich the term was present in a single document d. If a term\ndisappears from d but reappears later, we obtain multiple\ninput sequences that are dealt with separately. We seek to\ngenerate the minimal length output sequence of postings\nO = ( d, pj, [tj, tj+1) ), . . . , ( d, pm\u22121, [tm\u22121, tm)) ) ,\nthat adheres to the following constraints: First, O and I\nmust cover the same time-range, i.e., ti = tj and tn = tm.\nSecond, when coalescing a subsequence of postings of the\ninput into a single posting of the output, we want the\napproximation error to be below a threshold . In other words, if\n(d, pi, [ti, ti+1)) and (d, pj, [tj, tj+1)) are postings of I and\nO respectively, then the following must hold for a chosen\nerror function and a threshold :\ntj \u2264 ti \u2227 ti+1 \u2264 tj+1 \u21d2 error(pi, pj) \u2264 .\nIn this paper, as an error function we employ the relative\nerror between payloads (i.e., tf-scores) of a document in I\nand O, defined as:\nerrrel(pi, pj) = |pi \u2212 pj| / |pi| .\nFinding an optimal output sequence of postings can be\ncast into finding a piecewise-constant representation for the\npoints (ti, pi) that uses a minimal number of segments while\nretaining the above approximation guarantee. Similar\nproblems occur in time-series segmentation [21, 30] and histogram\nconstruction [19, 20]. Typically dynamic programming is\napplied to obtain an optimal solution in O(n2\nm\u2217\n) [20, 30]\ntime with m\u2217\nbeing the number of segments in an optimal\nsequence. In our setting, as a key difference, only a\nguarantee on the local error is retained - in contrast to a guarantee\non the global error in the aforementioned settings.\nExploiting this fact, an optimal solution is computable by means of\ninduction [24] in O(n2\n) time. Details of the optimal\nalgorithm are omitted here but can be found in the\naccompanying technical report [5].\nThe quadratic complexity of the optimal algorithm makes\nit inappropriate for the large datasets encountered in this\nwork. As an alternative, we introduce a linear-time\napproximate algorithm that is based on the sliding-window\nalgorithm given in [21]. This algorithm produces nearly-optimal\noutput sequences that retain the bound on the relative error,\nbut possibly require a few additional segments more than an\noptimal solution.\nAlgorithm 1 Temporal Coalescing (Approximate)\n1: I = ( d, pi, [ti, ti+1) ), . . . O =\n2: pmin = pi pmax = pi p = pi tb = ti te = ti+1\n3: for ( d, pj, [tj, tj+1) ) \u2208 I do\n4: pmin = min( pmin, pj ) pmax = max( pmax, pj )\n5: p = optrep(pmin, pmax)\n6: if errrel(pmin, p ) \u2264 \u2227 errrel(pmax, p ) \u2264 then\n7: pmin = pmin pmax = pmax p = p te = tj+1\n8: else\n9: O = O \u222a ( d, p, [tb, te) )\n10: pmin = pj pmax = pj p = pj tb = tj te = tj+1\n11: end if\n12: end for\n13: O = O \u222a ( d, p, [tb, te) )\nAlgorithm 1 makes one pass over the input sequence I.\nWhile doing so, it coalesces sequences of postings having\nmaximal length. The optimal representative for a sequence\nof postings depends only on their minimal and maximal\npayload (pmin and pmax) and can be looked up using optrep in\nO(1) (see [16] for details). When reading the next\nposting, the algorithm tries to add it to the current sequence of\npostings. It computes the hypothetical new representative\np and checks whether it would retain the approximation\nguarantee. If this test fails, a coalesced posting bearing the\nold representative is added to the output sequence O and,\nfollowing that, the bookkeeping is reinitialized. The time\ncomplexity of the algorithm is in O(n).\nNote that, since we make no assumptions about the sort\norder of index lists, temporal-coalescing algorithms have an\nadditional preprocessing cost in O(|Lv| log |Lv|) for sorting\nthe index list and chopping it up into subsequences for each\ndocument.\n6. SUBLIST MATERIALIZATION\nEfficiency of processing a query q t\non our time-travel\ninverted index is influenced adversely by the wasted I/O due\nto read but skipped postings. Temporal coalescing\nimplicitly addresses this problem by reducing the overall index list\nsize, but still a significant overhead remains. In this section,\nwe tackle this problem by proposing the idea of materializing\nsublists each of which corresponds to a contiguous\nsubinterval of time spanned by the full index. Each of these sublists\ncontains all coalesced postings that overlap with the\ncorresponding time interval of the sublist. Note that all those\npostings whose validity time-interval spans across the\ntemporal boundaries of several sublists are replicated in each of\nthe spanned sublists. Thus, in order to process the query q t\ntime\nt1 t2 t3 t4 t5 t6 t7 t8 t9 t10\nd1\nd2\nd3\ndocument\n1 2 3 4\n5 6 7\n8 9 10\nFigure 2: Sublist Materialization\nit is sufficient to scan any materialized sublist whose\ntimeinterval contains t.\nWe illustrate the idea of sublist materialization using an\nexample shown in Figure 2. The index list Lv visualized in\nthe figure contains a total of 10 postings from three\ndocuments d1, d2, and d3. For ease of description, we have\nnumbered boundaries of validity time-intervals, in increasing\ntime-order, as t1, . . . , t10 and numbered the postings\nthemselves as 1, . . . , 10. Now, consider the processing of a query\nq t\nwith t \u2208 [t1, t2) using this inverted list. Although only\nthree postings (postings 1, 5 and 8) are valid at time t, the\nwhole inverted list has to be read in the worst case. Suppose\nthat we split the time axis of the list at time t2, forming two\nsublists with postings {1, 5, 8} and {2, 3, 4, 5, 6, 7, 8, 9,\n10} respectively. Then, we can process the above query with\noptimal cost by reading only those postings that existed at\nthis t.\nAt a first glance, it may seem counterintuitive to reduce\nindex size in the first step (using temporal coalescing), and\nthen to increase it again using the sublist materialization\ntechniques presented in this section. However, we reiterate\nthat our main objective is to improve the efficiency of\nprocessing queries, not to reduce the index size alone. The use\nof temporal coalescing improves the performance by\nreducing the index size, while the sublist materialization improves\nperformance by judiciously replicating entries. Further, the\ntwo techniques, can be applied separately and are\nindependent. If applied in conjunction, though, there is a synergetic\neffect - sublists that are materialized from a temporally\ncoalesced index are generally smaller.\nWe employ the notation Lv : [ti, tj) to refer to the\nmaterialized sublist for the time interval [ti, tj), that is formally\ndefined as,\nLv : [ti, tj) = {( d, p, [tb, te) ) \u2208 Lv | tb < tj \u2227 te > ti} .\nTo aid the presentation in the rest of the paper, we first\nprovide some definitions. Let T = t1 . . . tn be the sorted\nsequence of all unique time-interval boundaries of an\ninverted list Lv. Then we define\nE = { [ti, ti+1) | 1 \u2264 i < n}\nto be the set of elementary time intervals. We refer to the\nset of time intervals for which sublists are materialized as\nM \u2286 { [ti, tj) | 1 \u2264 i < j \u2264 n } ,\nand demand\n\u2200 t \u2208 [t1, tn) \u2203 m \u2208 M : t \u2208 m ,\ni.e., the time intervals in M must completely cover the\ntime interval [t1, tn), so that time-travel queries q t\nfor all\nt \u2208 [t1, tn) can be processed. We also assume that\nintervals in M are disjoint. We can make this assumption\nwithout ruling out any optimal solution with regard to space\nor performance defined below. The space required for the\nmaterialization of sublists in a set M is defined as\nS( M ) =\nX\nm\u2208M\n|Lv : m| ,\ni.e., the total length of all lists in M. Given a set M, we let\n\u03c0( [ti, ti+1) ) = [tj, tk) \u2208 M : [ti, ti+1) \u2286 [tj, tk)\ndenote the time interval that is used to process queries q t\nwith t \u2208 [ti, ti+1). The performance of processing queries\nq t\nfor t \u2208 [ti, ti+1) inversely depends on its processing cost\nPC( [ti, ti+1) ) = |Lv : \u03c0( [ti, ti+1) )| ,\nwhich is assumed to be proportional to the length of the\nlist Lv : \u03c0( [ti, ti+1) ). Thus, in order to optimize the\nperformance of processing queries we minimize their processing\ncosts.\n6.1 Performance/Space-Optimal Approaches\nOne strategy to eliminate the problem of skipped\npostings is to eagerly materialize sublists for all elementary time\nintervals, i.e., to choose M = E. In doing so, for every\nquery q t\nonly postings valid at time t are read and thus the\nbest possible performance is achieved. Therefore, we will\nrefer to this approach as Popt in the remainder. The initial\napproach described above that keeps only the full list Lv\nand thus picks M = { [t1, tn) } is referred to as Sopt in the\nremainder. This approach requires minimal space, since it\nkeeps each posting exactly once.\nPopt and Sopt are extremes: the former provides the best\npossible performance but is not space-efficient, the latter\nrequires minimal space but does not provide good\nperformance. The two approaches presented in the rest of this\nsection allow mutually trading off space and performance\nand can thus be thought of as means to explore the\nconfiguration spectrum between the Popt and the Sopt approach.\n6.2 Performance-Guarantee Approach\nThe Popt approach clearly wastes a lot of space\nmaterializing many nearly-identical sublists. In the example\nillustrated in Figure 2 materialized sublists for [t1, t2) and\n[t2, t3) differ only by one posting. If the sublist for [t1, t3)\nwas materialized instead, one could save significant space\nwhile incurring only an overhead of one skipped posting for\nall t \u2208 [t1, t3). The technique presented next is driven by\nthe idea that significant space savings over Popt are\nachievable, if an upper-bounded loss on the performance can be\ntolerated, or to put it differently, if a performance\nguarantee relative to the optimum is to be retained. In detail,\nthe technique, which we refer to as PG (Performance\nGuarantee) in the remainder, finds a set M that has minimal\nrequired space, but guarantees for any elementary time\ninterval [ti, ti+1) (and thus for any query q t\nwith t \u2208 [ti, ti+1))\nthat performance is worse than optimal by at most a factor\nof \u03b3 \u2265 1. Formally, this problem can be stated as\nargmin\nM\nS( M ) s.t.\n\u2200 [ti, ti+1) \u2208 E : PC( [ti, ti+1) ) \u2264 \u03b3 \u00b7 |Lv : [ti, ti+1)| .\nAn optimal solution to the problem can be computed by\nmeans of induction using the recurrence\nC( [t1, tk+1) ) =\nmin {C( [t1, tj) ) + |Lv : [tj, tk+1)| | 1 \u2264 j \u2264 k \u2227 condition} ,\nwhere C( [t1, tj) ) is the optimal cost (i.e., the space\nrequired) for the prefix subproblem\n{ [ti, ti+1) \u2208 E | [ti, ti+1) \u2286 [t1, tj) }\nand condition stands for\n\u2200 [ti, ti+1) \u2208 E : [ti, ti+1) \u2286 [tj, tk+1)\n\u21d2 |Lv : [tj, tk+1)| \u2264 \u03b3 \u00b7 |Lv : [ti, ti+1)|\n.\nIntuitively, the recurrence states that an optimal solution\nfor [t1, tk+1) be combined from an optimal solution to a\nprefix subproblem C( [t1, tj) ) and a time interval [tj, tk+1)\nthat can be materialized without violating the performance\nguarantee.\nPseudocode of the algorithm is omitted for space reasons,\nbut can be found in the accompanying technical report [5].\nThe time complexity of the algorithm is in O(n2\n) - for each\nprefix subproblem the above recurrence must be evaluated,\nwhich is possible in linear time if list sizes |L : [ti, tj)| are\nprecomputed. The space complexity is in O(n2\n) - the cost\nof keeping the precomputed sublist lengths and memoizing\noptimal solutions to prefix subproblems.\n6.3 Space-Bound Approach\nSo far we considered the problem of materializing sublists\nthat give a guarantee on performance while requiring\nminimal space. In many situations, though, the storage space is\nat a premium and the aim would be to materialize a set of\nsublists that optimizes expected performance while not\nexceeding a given space limit. The technique presented next,\nwhich is named SB, tackles this very problem. The space\nrestriction is modeled by means of a user-specified\nparameter \u03ba \u2265 1 that limits the maximum allowed blowup in index\nsize from the space-optimal solution provided by Sopt. The\nSB technique seeks to find a set M that adheres to this\nspace limit but minimizes the expected processing cost (and\nthus optimizes the expected performance). In the definition\nof the expected processing cost, P( [ti, ti+1) ) denotes the\nprobability of a query time-point being in [ti, ti+1).\nFormally, this space-bound sublist-materialization problem can\nbe stated as\nargmin\nM\nX\n[ti, ti+1) \u2208 E\nP( [ti, ti+1) ) \u00b7 PC( [ti, ti+1) ) s.t.\nX\nm\u2208M\n|Lv : m| \u2264 \u03ba |Lv| .\nThe problem can be solved by using dynamic\nprogramming over an increasing number of time intervals: At each\ntime interval in E the algorithms decides whether to start a\nnew materialization time-interval, using the known best\nmaterialization decision from the previous time intervals, and\nkeeping track of the required space consumption for\nmaterialization. A detailed description of the algorithm is omitted\nhere, but can be found in the accompanying technical\nreport [5]. Unfortunately, the algorithm has time complexity\nin O(n3\n|Lv|) and its space complexity is in O(n2\n|Lv|), which\nis not practical for large data sets.\nWe obtain an approximate solution to the problem\nusing simulated annealing [22, 23]. Simulated annealing takes\na fixed number R of rounds to explore the solution space.\nIn each round a random successor of the current solution\nis looked at. If the successor does not adhere to the space\nlimit, it is always rejected (i.e., the current solution is kept).\nA successor adhering to the space limit is always accepted if\nit achieves lower expected processing cost than the current\nsolution. If it achieves higher expected processing cost, it is\nrandomly accepted with probability e\u2212\u2206/r\nwhere \u2206 is the\nincrease in expected processing cost and R \u2265 r \u2265 1 denotes\nthe number of remaining rounds. In addition, throughout\nall rounds, the method keeps track of the best solution seen\nso far. The solution space for the problem at hand can be\nefficiently explored. As we argued above, we solely have\nto look at sets M that completely cover the time interval\n[t1, tn) and do not contain overlapping time intervals. We\nrepresent such a set M as an array of n boolean variables\nb1 . . . bn that convey the boundaries of time intervals in the\nset. Note that b1 and bn are always set to true. Initially,\nall n \u2212 2 intermediate variables assume false, which\ncorresponds to the set M = { [t1, tn) }. A random successor\ncan now be easily generated by switching the value of one\nof the n \u2212 2 intermediate variables. The time complexity of\nthe method is in O(n2\n) - the expected processing cost must\nbe computed in each round. Its space complexity is in O(n)\n- for keeping the n boolean variables.\nAs a side remark note that for \u03ba = 1.0 the SB method\ndoes not necessarily produce the solution that is obtained\nfrom Sopt, but may produce a solution that requires the\nsame amount of space while achieving better expected\nperformance.\n7. EXPERIMENTAL EVALUATION\nWe conducted a comprehensive series of experiments on\ntwo real-world datasets to evaluate the techniques proposed\nin this paper.\n7.1 Setup and Datasets\nThe techniques described in this paper were implemented\nin a prototype system using Java JDK 1.5. All\nexperiments described below were run on a single SUN V40z\nmachine having four AMD Opteron CPUs, 16GB RAM, a large\nnetwork-attached RAID-5 disk array, and running Microsoft\nWindows Server 2003. All data and indexes are kept in an\nOracle 10g database that runs on the same machine. For\nour experiments we used two different datasets.\nThe English Wikipedia revision history (referred to as\nWIKI in the remainder) is available for free download as\na single XML file. This large dataset, totaling 0.7 TBytes,\ncontains the full editing history of the English Wikipedia\nfrom January 2001 to December 2005 (the time of our\ndownload). We indexed all encyclopedia articles excluding\nversions that were marked as the result of a minor edit (e.g.,\nthe correction of spelling errors etc.). This yielded a total of\n892,255 documents with 13,976,915 versions having a mean\n(\u00b5) of 15.67 versions per document at standard deviation (\u03c3)\nof 59.18. We built a time-travel query workload using the\nquery log temporarily made available recently by AOL\nResearch as follows - we first extracted the 300 most frequent\nkeyword queries that yielded a result click on a Wikipedia\narticle (for e.g., french revolution, hurricane season 2005,\nda vinci code etc.). The thus extracted queries contained\na total of 422 distinct terms. For each extracted query, we\nrandomly picked a time point for each month covered by\nthe dataset. This resulted in a total of 18, 000 (= 300 \u00d7 60)\ntime-travel queries.\nThe second dataset used in our experiments was based\non a subset of the European Archive [13], containing weekly\ncrawls of 11 .gov.uk websites throughout the years 2004 and\n2005 amounting close to 2 TBytes of raw data. We filtered\nout documents not belonging to MIME-types text/plain\nand text/html, to obtain a dataset that totals 0.4 TBytes\nand which we refer to as UKGOV in rest of the paper. This\nincluded a total of 502,617 documents with 8,687,108\nversions (\u00b5 = 17.28 and \u03c3 = 13.79). We built a corresponding\nquery workload as mentioned before, this time choosing\nkeyword queries that led to a site in the .gov.uk domain (e.g.,\nminimum wage, inheritance tax , citizenship ceremony\ndates etc.), and randomly sampling a time point for every\nmonth within the two year period spanned by the dataset.\nThus, we obtained a total of 7,200 (= 300 \u00d7 24) time-travel\nqueries for the UKGOV dataset. In total 522 terms appear\nin the extracted queries.\nThe collection statistics (i.e., N and avdl) and term\nstatistics (i.e., DF) were computed at monthly granularity for\nboth datasets.\n7.2 Impact of Temporal Coalescing\nOur first set of experiments is aimed at evaluating the\napproximate temporal coalescing technique, described in\nSection 5, in terms of index-size reduction and its effect on the\nresult quality. For both the WIKI and UKGOV datasets, we\ncompare temporally coalesced indexes for different values of\nthe error threshold computed using Algorithm 1 with the\nnon-coalesced index as a baseline.\nWIKI UKGOV\n# Postings Ratio # Postings Ratio\n- 8,647,996,223 100.00% 7,888,560,482 100.00%\n0.00 7,769,776,831 89.84% 2,926,731,708 37.10%\n0.01 1,616,014,825 18.69% 744,438,831 9.44%\n0.05 556,204,068 6.43% 259,947,199 3.30%\n0.10 379,962,802 4.39% 187,387,342 2.38%\n0.25 252,581,230 2.92% 158,107,198 2.00%\n0.50 203,269,464 2.35% 155,434,617 1.97%\nTable 1: Index sizes for non-coalesced index (-) and\ncoalesced indexes for different values of\nTable 1 summarizes the index sizes measured as the total\nnumber of postings. As these results demonstrate,\napproximate temporal coalescing is highly effective in reducing\nindex size. Even a small threshold value, e.g. = 0.01, has a\nconsiderable effect by reducing the index size almost by an\norder of magnitude. Note that on the UKGOV dataset, even\naccurate coalescing ( = 0) manages to reduce the index size\nto less than 38% of the original size. Index size continues to\nreduce on both datasets, as we increase the value of .\nHow does the reduction in index size affect the query\nresults? In order to evaluate this aspect, we compared the\ntop-k results computed using a coalesced index against the\nground-truth result obtained from the original index, for\ndifferent cutoff levels k. Let Gk and Ck be the top-k documents\nfrom the ground-truth result and from the coalesced index\nrespectively. We used the following two measures for\ncomparison: (i) Relative Recall at cutoff level k (RR@k), that\nmeasures the overlap between Gk and Ck, which ranges in\n[0, 1] and is defined as\nRR@k = |Gk \u2229 Ck|/k .\n(ii) Kendall\"s \u03c4 (see [7, 14] for a detailed definition) at\ncutoff level k (KT@k), measuring the agreement between two\nresults in the relative order of items in Gk \u2229 Ck, with value\n1 (or -1) indicating total agreement (or disagreement).\nFigure 3 plots, for cutoff levels 10 and 100, the mean of\nRR@k and KT@k along with 5% and 95% percentiles, for\ndifferent values of the threshold starting from 0.01. Note\nthat for = 0, results coincide with those obtained by the\noriginal index, and hence are omitted from the graph.\nIt is reassuring to see from these results that approximate\ntemporal coalescing induces minimal disruption to the query\nresults, since RR@k and KT@k are within reasonable limits.\nFor = 0.01, the smallest value of in our experiments,\nRR@100 for WIKI is 0.98 indicating that the results are\n-1\n-0.5\n0\n0.5\n1\n\u03b5\n0.01 0.05 0.10 0.25 0.50\nRelative Recall @ 10 (WIKI)\nKendall's \u03c4 @ 10 (WIKI)\nRelative Recall @ 10 (UKGOV)\nKendall's \u03c4 @ 10 (UKGOV)\n(a) @10\n-1\n-0.5\n0\n0.5\n1\n\u03b5\n0.01 0.05 0.10 0.25 0.50\nRelative Recall @ 100 (WIKI)\nKendall's \u03c4 @ 100 (WIKI)\nRelative Recall @ 100 (UKGOV)\nKendall's \u03c4 @ 100 (UKGOV)\n(b) @100\nFigure 3: Relative recall and Kendall\"s \u03c4 observed on coalesced indexes for different values of\nalmost indistinguishable from those obtained through the\noriginal index. Even the relative order of these common\nresults is quite high, as the mean KT@100 is close to 0.95.\nFor the extreme value of = 0.5, which results in an index\nsize of just 2.35% of the original, the RR@100 and KT@100\nare about 0.8 and 0.6 respectively. On the relatively less\ndynamic UKGOV dataset (as can be seen from the \u03c3 values\nabove), results were even better, with high values of RR and\nKT seen throughout the spectrum of values for both cutoff\nvalues.\n7.3 Sublist Materialization\nWe now turn our attention towards evaluating the\nsublist materialization techniques introduced in Section 6. For\nboth datasets, we started with the coalesced index produced\nby a moderate threshold setting of = 0.10. In order to\nreduce the computational effort, boundaries of elementary\ntime intervals were rounded to day granularity before\ncomputing the sublist materializations. However, note that the\npostings in the materialized sublists still retain their\noriginal timestamps. For a comparative evaluation of the four\napproaches - Popt, Sopt, PG, and SB - we measure space\nand performance as follows. The required space S(M), as\ndefined earlier, is equal to the total number of postings in\nthe materialized sublists. To assess performance we\ncompute the expected processing cost (EPC) for all terms in\nthe respective query workload assuming a uniform\nprobability distribution among query time-points. We report the\nmean EPC, as well as the 5%- and 95%-percentile. In other\nwords, the mean EPC reflects the expected length of the\nindex list (in terms of index postings) that needs to be scanned\nfor a random time point and a random term from the query\nworkload.\nThe Sopt and Popt approaches are, by their definition,\nparameter-free. For the PG approach, we varied its\nparameter \u03b3, which limits the maximal performance degradation,\nbetween 1.0 and 3.0. Analogously, for the SB approach\nthe parameter \u03ba, as an upper-bound on the allowed space\nblowup, was varied between 1.0 and 3.0. Solutions for the\nSB approach were obtained running simulated annealing for\nR = 50, 000 rounds.\nTable 2 lists the obtained space and performance figures.\nNote that EPC values are smaller on WIKI than on\nUKGOV, since terms in the query workload employed for WIKI\nare relatively rarer in the corpus. Based on the depicted\nresults, we make the following key observations. i) As\nexpected, Popt achieves optimal performance at the cost of an\nenormous space consumption. Sopt, to the contrary, while\nconsuming an optimal amount of space, provides only poor\nexpected processing cost. The PG and SB methods, for\ndifferent values of their respective parameter, produce\nsolutions whose space and performance lie in between the\nextremes that Popt and Sopt represent. ii) For the PG method\nwe see that for an acceptable performance degradation of\nonly 10% (i.e., \u03b3 = 1.10) the required space drops by more\nthan one order of magnitude in comparison to Popt on both\ndatasets. iii) The SB approach achieves close-to-optimal\nperformance on both datasets, if allowed to consume at most\nthree times the optimal amount of space (i.e., \u03ba = 3.0),\nwhich on our datasets still corresponds to a space reduction\nover Popt by more than one order of magnitude.\nWe also measured wall-clock times on a sample of the\nqueries with results indicating improvements in execution\ntime by up to a factor of 12.\n8. CONCLUSIONS\nIn this work we have developed an efficient solution for\ntime-travel text search over temporally versioned document\ncollections. Experiments on two real-world datasets showed\nthat a combination of the proposed techniques can reduce\nindex size by up to an order of magnitude while achieving\nnearly optimal performance and highly accurate results.\nThe present work opens up many interesting questions\nfor future research, e.g.: How can we even further improve\nperformance by applying (and possibly extending) encoding,\ncompression, and skipping techniques [35]?. How can we\nextend the approach for queries q [tb, te]\nspecifying a time\ninterval instead of a time point? How can the described\ntime-travel text search functionality enable or speed up text\nmining along the time axis (e.g., tracking sentiment changes\nin customer opinions)?\n9. ACKNOWLEDGMENTS\nWe are grateful to the anonymous reviewers for their\nvaluable comments - in particular to the reviewer who pointed\nout the opportunity for algorithmic improvements in\nSection 5 and Section 6.2.\n10. REFERENCES\n[1] V. N. Anh and A. Moffat. Pruned Query Evaluation\nUsing Pre-Computed Impacts. In SIGIR, 2006.\n[2] V. N. Anh and A. Moffat. Pruning Strategies for\nMixed-Mode Querying. In CIKM, 2006.\nWIKI UKGOV\nS(M) EPC S(M) EPC\n5% Mean 95% 5% Mean 95%\nPopt 54,821,634,137 11.22 3,132.29 15,658.42 21,372,607,052 39.93 15,593.60 66,938.86\nSopt 379,962,802 114.05 30,186.52 149,820.1 187,387,342 63.15 22,852.67 102,923.85\nPG \u03b3 = 1.10 3,814,444,654 11.30 3,306.71 16,512.88 1,155,833,516 40.66 16,105.61 71,134.99\nPG \u03b3 = 1.25 1,827,163,576 12.37 3,629.05 18,120.86 649,884,260 43.62 17,059.47 75,749.00\nPG \u03b3 = 1.50 1,121,661,751 13.96 4,128.03 20,558.60 436,578,665 46.68 18,379.69 78,115.89\nPG \u03b3 = 1.75 878,959,582 15.48 4,560.99 22,476.77 345,422,898 51.26 19,150.06 82,028.48\nPG \u03b3 = 2.00 744,381,287 16.79 4,992.53 24,637.62 306,944,062 51.48 19,499.78 87,136.31\nPG \u03b3 = 2.50 614,258,576 18.28 5,801.66 28,849.02 269,178,107 53.36 20,279.62 87,897.95\nPG \u03b3 = 3.00 552,796,130 21.04 6,485.44 32,361.93 247,666,812 55.95 20,800.35 89,591.94\nSB \u03ba = 1.10 412,383,387 38.97 12,723.68 60,350.60 194,287,671 63.09 22,574.54 102,208.58\nSB \u03ba = 1.25 467,537,173 26.87 9,011.81 45,119.08 204,454,800 57.42 22,036.39 95,337.33\nSB \u03ba = 1.50 557,341,140 19.84 6,699.36 32,810.85 246,323,383 53.24 20,566.68 91,691.38\nSB \u03ba = 1.75 647,187,522 16.59 5,769.40 28,272.89 296,345,976 49.56 19,065.99 84,377.44\nSB \u03ba = 2.00 737,819,354 15.86 5,358.99 27,112.01 336,445,773 47.58 18,569.08 81,386.02\nSB \u03ba = 2.50 916,308,766 13.99 4,639.77 23,037.59 427,122,038 44.89 17,153.94 74,449.28\nSB \u03ba = 3.00 1,094,973,140 13.01 4,343.72 22,708.37 511,470,192 42.15 16,772.65 72,307.43\nTable 2: Required space and expected processing cost (in # postings) observed on coalesced indexes ( = 0.10)\n[3] P. G. Anick and R. A. Flynn. Versioning a Full-Text\nInformation Retrieval System. In SIGIR, 1992.\n[4] R. A. Baeza-Yates and B. Ribeiro-Neto. Modern\nInformation Retrieval. Addison-Wesley, 1999.\n[5] K. Berberich, S. Bedathur, T. Neumann, and\nG. Weikum. A Time Machine for Text search.\nTechnical Report MPI-I-2007-5-002, Max-Planck\nInstitute for Informatics, 2007.\n[6] M. H. B\u00a8ohlen, R. T. Snodgrass, and M. D. Soo.\nCoalescing in Temporal Databases. In VLDB, 1996.\n[7] P. Boldi, M. Santini, and S. Vigna. Do Your Worst to\nMake the Best: Paradoxical Effects in PageRank\nIncremental Computations. In WAW, 2004.\n[8] A. Z. Broder, N. Eiron, M. Fontoura, M. Herscovici,\nR. Lempel, J. McPherson, R. Qi, and E. J. Shekita.\nIndexing Shared Content in Information Retrieval\nSystems. In EDBT, 2006.\n[9] C. Buckley and A. F. Lewit. Optimization of Inverted\nVector Searches. In SIGIR, 1985.\n[10] M. Burrows and A. L. Hisgen. Method and Apparatus\nfor Generating and Searching Range-Based Index of\nWord Locations. U.S. Patent 5,915,251, 1999.\n[11] S. B\u00a8uttcher and C. L. A. Clarke. A Document-Centric\nApproach to Static Index Pruning in Text Retrieval\nSystems. In CIKM, 2006.\n[12] D. Carmel, D. Cohen, R. Fagin, E. Farchi,\nM. Herscovici, Y. S. Maarek, and A. Soffer. Static\nIndex Pruning for Information Retrieval Systems. In\nSIGIR, 2001.\n[13] http://www.europarchive.org.\n[14] R. Fagin, R. Kumar, and D. Sivakumar. Comparing\nTop k Lists. SIAM J. Discrete Math., 17(1):134-160,\n2003.\n[15] R. Fagin, A. Lotem, and M. Naor. Optimal\nAggregation Algorithms for Middleware. J. Comput.\nSyst. Sci., 66(4):614-656, 2003.\n[16] S. Guha, K. Shim, and J. Woo. REHIST: Relative\nError Histogram Construction Algorithms. In VLDB,\n2004.\n[17] M. Hersovici, R. Lempel, and S. Yogev. Efficient\nIndexing of Versioned Document Sequences. In ECIR,\n2007.\n[18] http://www.archive.org.\n[19] Y. E. Ioannidis and V. Poosala. Balancing Histogram\nOptimality and Practicality for Query Result Size\nEstimation. In SIGMOD, 1995.\n[20] H. V. Jagadish, N. Koudas, S. Muthukrishnan,\nV. Poosala, K. C. Sevcik, and T. Suel. Optimal\nHistograms with Quality Guarantees. In VLDB, 1998.\n[21] E. J. Keogh, S. Chu, D. Hart, and M. J. Pazzani. An\nOnline Algorithm for Segmenting Time Series. In\nICDM, 2001.\n[22] S. Kirkpatrick, D. G. Jr., and M. P. Vecchi.\nOptimization by Simulated Annealing. Science,\n220(4598):671-680, 1983.\n[23] J. Kleinberg and E. Tardos. Algorithm Design.\nAddison-Wesley, 2005.\n[24] U. Manber. Introduction to Algorithms: A Creative\nApproach. Addison-Wesley, 1989.\n[25] K. N\u00f8rv\u02daag and A. O. N. Nyb\u00f8. DyST: Dynamic and\nScalable Temporal Text Indexing. In TIME, 2006.\n[26] J. M. Ponte and W. B. Croft. A Language Modeling\nApproach to Information Retrieval. In SIGIR, 1998.\n[27] S. E. Robertson and S. Walker. Okapi/Keenbow at\nTREC-8. In TREC, 1999.\n[28] B. Salzberg and V. J. Tsotras. Comparison of Access\nMethods for Time-Evolving Data. ACM Comput.\nSurv., 31(2):158-221, 1999.\n[29] M. Stack. Full Text Search of Web Archive\nCollections. In IWAW, 2006.\n[30] E. Terzi and P. Tsaparas. Efficient Algorithms for\nSequence Segmentation. In SIAM-DM, 2006.\n[31] M. Theobald, G. Weikum, and R. Schenkel. Top-k\nQuery Evaluation with Probabilistic Guarantees. In\nVLDB, 2004.\n[32] http://www.wikipedia.org.\n[33] I. H. Witten, A. Moffat, and T. C. Bell. Managing\nGigabytes: Compressing and Indexing Documents and\nImages. Morgan Kaufmann publishers Inc., 1999.\n[34] J. Zhang and T. Suel. Efficient Search in Large\nTextual Collections with Redundancy. In WWW,\n2007.\n[35] J. Zobel and A. Moffat. Inverted Files for Text Search\nEngines. ACM Comput. Surv., 38(2):6, 2006.", "keywords": "text search;inverted file index;sublist materialization;temporal text index;time-travel text search;timestamped information feed;open source search-engine nutch;collaborative authoring environment;validity time-interval;web archive;approximate temporal coalescing;temporal search;versioned document collection;indexing range-based value;document-content overlap;time machine;static indexpruning technique"}
{"name": "train_H-45", "title": "Query Performance Prediction in Web Search Environments", "abstract": "Current prediction techniques, which are generally designed for content-based queries and are typically evaluated on relatively homogenous test collections of small sizes, face serious challenges in web search environments where collections are significantly more heterogeneous and different types of retrieval tasks exist. In this paper, we present three techniques to address these challenges. We focus on performance prediction for two types of queries in web search environments: content-based and Named-Page finding. Our evaluation is mainly performed on the GOV2 collection. In addition to evaluating our models for the two types of queries separately, we consider a more challenging and realistic situation that the two types of queries are mixed together without prior information on query types. To assist prediction under the mixed-query situation, a novel query classifier is adopted. Results show that our prediction of web query performance is substantially more accurate than the current stateof-the-art prediction techniques. Consequently, our paper provides a practical approach to performance prediction in realworld web settings.", "fulltext": "1. INTRODUCTION\nQuery performance prediction has many applications in a variety\nof information retrieval (IR) areas such as improving retrieval\nconsistency, query refinement, and distributed IR. The importance\nof this problem has been recognized by IR researchers and a\nnumber of new methods have been proposed for prediction\nrecently [1, 2, 17].\nMost work on prediction has focused on the traditional ad-hoc\nretrieval task where query performance is measured according to\ntopical relevance. These prediction models are evaluated on\nTREC document collections which typically consist of no more\nthan one million relatively homogenous newswire articles. With\nthe popularity and influence of the Web, prediction techniques\nthat will work well for web-style queries are highly preferable.\nHowever, web search environments pose significant challenges to\ncurrent prediction models that are mainly designed for traditional\nTREC settings. Here we outline some of these challenges.\nFirst, web collections, which are much larger than conventional\nTREC collections, include a variety of documents that are\ndifferent in many aspects such as quality and style. Current\nprediction techniques can be vulnerable to these characteristics of\nweb collections. For example, the reported prediction accuracy of\nthe ranking robustness technique and the clarity technique on the\nGOV2 collection (a large web collection) is significantly worse\ncompared to the other TREC collections [1]. Similar prediction\naccuracy on the GOV2 collection using another technique is\nreported in [2], confirming the difficult of predicting query\nperformance on a large web collection.\nFurthermore, web search goes beyond the scope of the ad-hoc\nretrieval task based on topical relevance. For example, the\nNamed-Page (NP) finding task, which is a navigational task, is\nalso popular in web retrieval. Query performance prediction for\nthe NP task is still necessary since NP retrieval performance is far\nfrom perfect. In fact, according to the report on the NP task of the\n2005 Terabyte Track [3], about 40% of the test queries perform\npoorly (no correct answer in the first 10 search results) even in the\nbest run from the top group. To our knowledge, little research has\nexplicitly addressed the problem of NP-query performance\nprediction. Current prediction models devised for content-based\nqueries will be less effective for NP queries considering the\nfundamental differences between the two.\nThird, in real-world web search environments, user queries are\nusually a mixture of different types and prior knowledge about the\ntype of each query is generally unavailable. The mixed-query\nsituation raises new problems for query performance prediction.\nFor instance, we may need to incorporate a query classifier into\nprediction models. Despite these problems, the ability to handle\nthis situation is a crucial step towards turning query performance\nprediction from an interesting research topic into a practical tool\nfor web retrieval.\nIn this paper, we present three techniques to address the above\nchallenges that current prediction models face in Web search\nenvironments. Our work focuses on query performance prediction\nfor the content-based (ad-hoc) retrieval task and the name-page\nfinding task in the context of web retrieval. Our first technique,\ncalled weighted information gain (WIG), makes use of both single\nterm and term proximity features to estimate the quality of top\nretrieved documents for prediction. We find that WIG offers\nconsistent prediction accuracy across various test collections and\nquery types. Moreover, we demonstrate that good prediction\naccuracy can be achieved for the mixed-query situation by using\nWIG with the help of a query type classifier. Query feedback and\nfirst rank change, which are our second and third prediction\ntechniques, perform well for content-based queries and NP\nqueries respectively.\nOur main contributions include: (1) considerably improved\nprediction accuracy for web content-based queries over several\nstate-of-the-art techniques. (2) new techniques for successfully\npredicting NP-query performance. (3) a practical and fully\nautomatic solution to predicting mixed-query performance. In\naddition, one minor contribution is that we find that the\nrobustness score [1], which was originally proposed for\nperformance prediction, is helpful for query classification.\n2. RELATED WORK\nAs we mentioned in the introduction, a number of prediction\ntechniques have been proposed recently that focus on\ncontentbased queries in the topical relevance (ad-hoc) task. We know of\nno published work that addresses other types of queries such as\nNP queries, let alone a mixture of query types. Next we review\nsome representative models.\nThe major difficulty of performance prediction comes from the\nfact that many factors have an impact on retrieval performance.\nEach factor affects performance to a different degree and the\noverall effect is hard to predict accurately. Therefore, it is not\nsurprising to notice that simple features, such as the frequency of\nquery terms in the collection [4] and the average IDF of query\nterms [5], do not predict well. In fact, most of the successful\ntechniques are based on measuring some characteristics of the\nretrieved document set to estimate topic difficulty. For example,\nthe clarity score [6] measures the coherence of a list of documents\nby the KL-divergence between the query model and the collection\nmodel. The robustness score [1] quantifies another property of a\nranked list: the robustness of the ranking in the presence of\nuncertainty. Carmel et al. [2] found that the distance measured by\nthe Jensen-Shannon divergence between the retrieved document\nset and the collection is significantly correlated to average\nprecision. Vinay et al.[7] proposed four measures to capture the\ngeometry of the top retrieved documents for prediction. The most\neffective measure is the sensitivity to document perturbation, an\nidea somewhat similar to the robustness score. Unfortunately,\ntheir way of measuring the sensitivity does not perform equally\nwell for short queries and prediction accuracy drops considerably\nwhen a state-of-the-art retrieval technique (like Okapi or a\nlanguage modeling approach) is adopted for retrieval instead of\nthe tf-idf weighting used in their paper [16].\nThe difficulties of applying these models in web search\nenvironments have already been mentioned. In this paper, we\nmainly adopt the clarity score and the robustness score as our\nbaselines. We experimentally show that the baselines, even after\nbeing carefully tuned, are inadequate for the web environment.\nOne of our prediction models, WIG, is related to the Markov\nrandom field (MRF) model for information retrieval [8]. The\nMRF model directly models term dependence and is found be to\nhighly effective across a variety of test collections (particularly\nweb collections) and retrieval tasks. This model is used to\nestimate the joint probability distribution over documents and\nqueries, an important part of WIG. The superiority of WIG over\nother prediction techniques based on unigram features, which will\nbe demonstrated later in our paper, coincides with that of MRF\nfor retrieval. In other word, it is interesting to note that term\ndependence, when being modeled appropriately, can be helpful\nfor both improving and predicting retrieval performance.\n3. PREDICTION MODELS\n3.1 Weighted Information Gain (WIG)\nThis section introduces a weighted information gain approach that\nincorporates both single term and proximity features for\npredicting performance for both content-based and Named-Page\n(NP) finding queries.\nGiven a set of queries Q={Qs} (s=1,2,..N) which includes all\npossible user queries and a set of documents D={Dt} (t=1,2\u2026M),\nwe assume that each query-document pair (Qs,Dt) is manually\njudged and will be put in a relevance list if Qs is found to be\nrelevant to Dt. The joint probability P(Qs,Dt) over queries Q and\ndocuments D denotes the probability that pair (Qs,Dt) will be in\nthe relevance list. Such assumptions are similar to those used in\n[8]. Assuming that the user issues query Qi \u2208Q and the retrieval\nresults in response to Qi is a ranked list L of documents, we\ncalculate the amount of information contained in P(Qs,Dt) with\nrespect to Qi and L by Eq.1 which is a variant of entropy called\nthe weighted entropy[13]. The weights in Eq.1 are solely\ndetermined by Qi and L.\n)1(),(log),(),(\n,\n, \u2211\u2212=\nts\ntststsLQ DQPDQweightDQH i\nIn this paper, we choose the weights as follows:\nLindocumentsKtopthecontainsLTwhere\notherwise\nLTDandisifK\nDQweight\nK\nKt\nts\n)(\n)2(\n,0\n)(,/1\n),(\n\u23a9\n\u23a8\n\u23a7 \u2208=\n=\nThe cutoff rank K is a parameter in our model that will be\ndiscussed later. Accordingly, Eq.1 can be simplified as follows:\n)3(),(log\n1\n),(\n)(\n, \u2211\u2208\n\u2212=\nLTD\ntitsLQ\nKt\ni\nDQP\nK\nDQH\nUnfortunately, weighted entropy ),(, tsLQ DQH i\ncomputed by Eq.3,\nwhich represents the amount of information about how likely the\ntop ranked documents in L would be relevant to query Qi on\naverage, cannot be compared across different queries, making it\ninappropriate for directly predicting query performance. To\nmitigate this problem, we come up with a background distribution\nP(Qs,C) over Q and D by imagining that every document in D is\nreplaced by the same special document C which represents\naverage language usage. In this paper, C is created by\nconcatenating every document in D. Roughly speaking, C is the\ncollection (the document set) {Dt} without document boundaries.\nSimilarly, weighted entropy ),(, CQH sLQi\ncalculated by Eq.3\nrepresents the amount of information about how likely an average\ndocument (represented by the whole collection) would be relevant\nto query Qi.\nNow we introduce our performance predictor WIG which is the\nweighted information gain [13] computed as the difference\nbetween ),(, tsLQ DQH i\nand ),(, CQH sLQi\n.Specifically, given query\nQi, collection C and ranked list L of documents, WIG is\ncalculated as follows:\n)4(\n),(\n),(\nlog\n1\n),(\n),(\nlog),(\n),(),(),,(\n)(,\n,,\n\u2211\u2211 \u2208\n==\n\u2212=\nLTD i\nti\nts s\nts\nts\ntsLQsLQi\nKt\nii\nCQP\nDQP\nKCQP\nDQP\nDQweight\nDQHCQHLCQWIG\nWIG computed by Eq.4 measures the change in information about\nthe quality of retrieval (in response to query Qi) from an\nimaginary state that only an average document is retrieved to a\nposterior state that the actual search results are observed. We\nhypothesize that WIG is positively correlated with retrieval\neffectiveness because high quality retrieval should be much more\neffective than just returning the average document.\nThe heart of this technique is how to estimate the joint\ndistribution P(Qs,Dt). In the language modeling approach to IR, a\nvariety of models can be applied readily to estimate this\ndistribution. Although most of these models are based on the\nbagof-words assumption, recent work on modeling term dependence\nunder the language modeling framework have shown consistent\nand significant improvements in retrieval effectiveness over\nbagof-words models. Inspired by the success of incorporating term\nproximity features into language models, we decide to adopt a\ngood dependence model to estimate the probability P(Qs,Dt). The\nmodel we chose for this paper is Metzler and Croft\"s Markov\nRandom Field (MRF) model, which has already demonstrated\nsuperiority over a number of collections and different retrieval\ntasks [8,9].\nAccording to the MRF model, log P(Qi, Dt) can be written as\n)5()|(loglog),(log\n)(\n1 \u2211\u2208\n+\u2212=\niQF\ntti DPZDQP\n\u03be\n\u03be \u03be\u03bb\nwhere Z1 is a constant that ensures that P(Qi, Dt) sums up to 1.\nF(Qi) consists of a set of features expanded from the original\nquery Qi . For example, assuming that query Qi is talented\nstudent program, F(Qi) includes features like program and\ntalented student. We consider two kinds of features: single\nterm features T and proximity features P. Proximity features\ninclude exact phrase (#1) and unordered window (#uwN) features\nas described in [8]. Note that F(Qi) is the union of T(Qi) and\nP(Qi). For more details on F(Qi) such as how to expand the\noriginal query Qi to F(Qi), we refer the reader to [8] and [9].\nP(\u03be|Dt) denotes the probability that feature \u03be will occur in Dt.\nMore details on P(\u03be|Dt) will be provided later in this section. The\nchoice of \u03bb\u03be is somewhat different from that used in [8] since \u03bb\u03be\nplays a dual role in our model. The first role, which is the same as\nin [8], is to weight between single term and proximity features.\nThe other role, which is specific to our prediction task, is to\nnormalize the size of F(Qi).We found that the following weight\nstrategy for \u03bb\u03be satisfies the above two roles and generalizes well\non a variety of collections and query types.\n)6(\n)(,\n|)(|\n1\n)(,\n|)(|\n\u23aa\n\u23aa\n\u23a9\n\u23aa\n\u23aa\n\u23a8\n\u23a7\n\u2208\n\u2212\n\u2208\n=\ni\ni\nT\ni\ni\nT\nQP\nQP\nQT\nQT\n\u03be\n\u03bb\n\u03be\n\u03bb\n\u03bb\u03be\nwhere |T(Qi)| and |P(Qi)| denote the number of single term and\nproximity features in F(Qi) respectively. The reason for choosing\nthe square root function in the denominator of \u03bb\u03be is to penalize a\nfeature set of large size appropriately, making WIG more\ncomparable across queries of various lengths. \u03bbT is a fixed\nparameter and set to 0.8 according to [8] throughout this paper.\nSimilarly, log P(Qi,C) can be written as:\n)7()|(loglog),(log\n)(\n2 \u2211\u2208\n+\u2212=\niQF\ni CPZCQP\n\u03be\n\u03be \u03be\u03bb\nWhen constant Z1 and Z2 are dropped, WIG computed in Eq.4 can\nbe rewritten as follows by plugging in Eq.5 and Eq.7 :\n)8(\n)|(\n)|(\nlog\n1\n),,(\n)( )(\n\u2211 \u2211\u2208 \u2208\n=\nLTD QF\nt\ni\nKt i\nCP\nDP\nK\nLCQWIG\n\u03be\n\u03be\n\u03be\n\u03be\n\u03bb\nOne of the advantages of WIG over other techniques is that it can\nhandle well both content-based and NP queries. Based on the type\n(or the predicted type) of Qi, the calculation of WIG in Eq. 8\ndiffers in two aspects: (1) how to estimate P(\u03be|Dt) and P(\u03be|C), and\n(2) how to choose K.\nFor content-based queries, P(\u03be|C) is estimated by the relative\nfrequency of feature \u03be in collection C as a whole. The estimation\nof P(\u03be|Dt) is the same as in [8]. Namely, we estimate P(\u03be|Dt) by\nthe relative frequency of feature \u03be in Dt linearly smoothed with\ncollection frequency P(\u03be|C). K in Eq.8 is treated as a free\nparameter. Note that K is the only free parameter in the\ncomputation of WIG for content-based queries because all\nparameters involved in P(\u03be|Dt) are assumed to be fixed by taking\nthe suggested values in [8].\nRegarding NP queries, we make use of document structure to\nestimate P(\u03be|Dt) and P(\u03be|C) by the so-called mixture of language\nmodels proposed in [10] and incorporated into the MRF model for\nNamed-Page finding retrieval in [9]. The basic idea is that a\ndocument (collection) is divided into several fields such as the\ntitle field, the main-body field and the heading field. P(\u03be|Dt) and\nP(\u03be|C) are estimated by a linear combination of the language\nmodels from each field. Due to space constraints, we refer the\nreader to [9] for details. We adopt the exact same set of\nparameters as used in [9] for estimation. With regard to K in Eq.8,\nwe set K to 1 because the Named-Page finding task heavily\nfocuses on the first ranked document. Consequently, there are no\nfree parameters in the computation of WIG for NP queries.\n3.2 Query Feedback\nIn this section, we introduce another technique called query\nfeedback (QF) for prediction. Suppose that a user issues query Q\nto a retrieval system and a ranked list L of documents is returned.\nWe view the retrieval system as a noisy channel. Specifically, we\nassume that the output of the channel is L and the input is Q.\nAfter going through the channel, Q becomes corrupted and is\ntransformed to ranked list L.\nBy thinking about the retrieval process this way, the problem of\npredicting retrieval effectiveness turns to the task of evaluating\nthe quality of the channel. In other words, prediction becomes\nfinding a way to measure the degree of corruption that arises\nwhen Q is transformed to L. As directly computing the degree of\nthe corruption is difficult, we tackle this problem by\napproximation. Our main idea is that we measure to what extent\ninformation on Q can be recovered from L on the assumption that\nonly L is observed. Specifically, we design a decoder that can\naccurately translate L back into new query Q\" and the similarity S\nbetween the original query Q and the new query Q\" is adopted as\na performance predictor. This is a sketch of how the QF technique\npredicts query performance. Before filling in more details, we\nbriefly discuss why this method would work.\nThere is a relation between the similarity S defined above and\nretrieval performance. On the one hand, if the retrieval has\nstrayed from the original sense of the query Q, the new query Q\"\nextracted from ranked list L in response to Q would be very\ndifferent from the original query Q. On the other hand, a query\ndistilled from a ranked list containing many relevant documents is\nlikely to be similar to the original query. Further examples in\nsupport of the relation will be provided later.\nNext we detail how to build the decoder and how to measure the\nsimilarity S.\nIn essence, the goal of the decoder is to compress ranked list L\ninto a few informative terms that should represent the content of\nthe top ranked documents in L. Our approach to this goal is to\nrepresent ranked list L by a language model (distribution over\nterms). Then terms are ranked by their contribution to the\nlanguage model\"s KL (Kullback-Leibler) divergence from the\nbackground collection model. Top ranked terms will be chosen to\nform the new query Q\". This approach is similar to that used in\nSection 4.1 of [11].\nSpecifically, we take three steps to compress ranked list L into\nquery Q\" without referring to the original query.\n1. We adopt the ranked list language model [14], to estimate a\nlanguage model based on ranked list L. The model can be written\nas:\n)9()|()|()|( \u2211\u2208\n=\nLD\nLDPDwPLwP\nwhere w is any term, D is a document. P(D|L) is estimated by a\nlinearly decreasing function of the rank of document D.\n2. Each term in P(w|L) is ranked by the following KL-divergence\ncontribution:\n)10(\n)|(\n)|(\nlog)|(\nCwP\nLwP\nLwP\nwhere P(w|C) is the collection model estimated by the relative\nfrequency of term w in collection C as a whole.\n3. The top N ranked terms by Eq.10 form a weighted query\nQ\"={(wi,ti)} i=1,N. where wi denotes the i-th ranked term and\nweight ti is the KL-divergence contribution of wi in Eq. 10.\nTerm cruise ship vessel sea passenger\nKL\ncontribution\n0.050 0.040 0.012 0.010 0.009\nTable 1: top 5 terms compressed from the ranked list in\nresponse to query Cruise ship damage sea life\nTwo representative examples, one for a poorly performing query\nCruise ship damage sea life (TREC topic 719; average\nprecision: 0.08) and the other for a high performing query\nprostate cancer treatments( TREC topic 710; average precision:\n0.49), are shown in Table 1 and 2 respectively. These examples\nindicate how the similarity between the original and the new\nquery correlates with retrieval performance. The parameter N in\nstep 3 is set to 20 empirically and choosing a larger value of N is\nunnecessary since the weights after the top 20 are usually too\nsmall to make any difference.\nTerm prostate cancer treatment men therapy\nKL\ncontribution\n0.177 0.140 0.028 0.025 0.020\nTable 2: top 5 terms compressed from the ranked list in\nresponse to query prostate cancer treatments\nTo measure the similarity between original query Q and new\nquery Q\", we first use Q\" to do retrieval on the same collection. A\nvariant of the query likelihood model [15] is adopted for retrieval.\nNamely, documents are ranked by:\n)11()|()|'(\n'),(\n\u2211\u2208\n=\nQtw\nt\ni\nii\ni\nDwPDQP\nwhere wi is a term in Q\" and ti is the associated weight. D is a\ndocument.\nLet L\" denote the new ranked list returned from the above\nretrieval. The similarity is measured by the overlap of documents\nin L and L\". Specifically, the percentage of documents in the top\nK documents of L that are also present in the top K documents in\nL\". the cutoff K is treated as a free parameter.\nWe summarize here how the QF technique predicts performance\ngiven a query Q and the associated ranked list L. We first obtain a\nweighted query Q\" compressed from L by the above three steps.\nThen we use Q\" to perform retrieval and the new ranked list is L\".\nThe overlap of documents in L and L\" is used for prediction.\n3.3 First Rank Change (FRC)\nIn this section, we propose a method called the first rank change\n(FRC) for performance prediction for NP queries. This method is\nderived from the ranking robustness technique [1] that is mainly\ndesigned for content-based queries. When directly applied to NP\nqueries, the robustness technique will be less effective because it\ntakes the top ranked documents as a whole into account while NP\nqueries usually have only one single relevant document. Instead,\nour technique focuses on the first rank document while the main\nidea of the robustness method remains. Specifically, the\npseudocode for computing FRC is shown in figure 1.\nInput: (1) ranked list L={Di} where i=1,100. Di denotes the i-th\nranked document. (2) query Q\n1 initialize: (1) set the number of trials J=100000 (2) counter c=0;\n2 for i=1 to J\n3 Perturb every document in L, let the outcome be a set F={Di\"}\nwhere Di\" denotes the perturbed version of Di.\n4 Do retrieval with query Q on set F\n5 c=c+1 if and only if D1\" is ranked first in step 4\n6 end of for\n7 return the ratio c/J\nFigure 1: pseudo-code for computing FRC\nFRC approximates the probability that the first ranked document\nin the original list L will remain ranked first even after the\ndocuments are perturbed. The higher the probability is, the more\nconfidence we have in the first ranked document. On the other\nhand, in the extreme case of a random ranking, the probability\nwould be as low as 0.5. We expect that FRC has a positive\nassociation with NP query performance. We adopt [1] to\nimplement the document perturbation step (step 4 in Fig.1) using\nPoisson distributions. For more details, we refer the reader to [1].\n4. EVALUATION\nWe now present the results of predicting query performance by\nour models. Three state-of-the-art techniques are adopted as our\nbaselines. We evaluate our techniques across a variety of Web\nretrieval settings. As mentioned before, we consider two types of\nqueries, that is, content-based (CB) queries and Named-Page(NP)\nfinding queries.\nFirst, suppose that the query types are known. We investigate the\ncorrelation between the predicted retrieval performance and the\nactual performance for both types of queries separately. Results\nshow that our methods yield considerable improvements over the\nbaselines.\nWe then consider a more challenging scenario where no prior\ninformation on query types is available. Two sub-cases are\nconsidered. In the first one, there exists only one type of query but\nthe actual type is unknown. We assume a mixture of the two\nquery types in the second case. We demonstrate that our models\nachieve good accuracy under this demanding scenario, making\nprediction practical in a real-world Web search environment.\n4.1 Experimental Setup\nOur evaluation focuses on the GOV2 collection which contains\nabout 25 million documents crawled from web sites in the .gov\ndomain during 2004 [3]. We create two kinds of data set for CB\nqueries and NP queries respectively. For the CB type, we use the\nad-hoc topics of the Terabyte Tracks of 2004, 2005 and 2006 and\nname them TB04-adhoc, TB05-adhoc and TB06-adhoc\nrespectively. In addition, we also use the ad-hoc topics of the\n2004 Robust Track (RT04) to test the adaptability of our\ntechniques to a non-Web environment. For NP queries, we use the\nNamed-Page finding topics of the Terabyte Tracks of 2005 and\n2006 and we name them TB05-NP and TB06-NP respectively. All\nqueries used in our experiments are titles of TREC topics as we\ncenter on web retrieval. Table 3 summarizes the above data sets.\nName Collection Topic Number Query Type\nTB04-adhoc GOV2 701-750 CB\nTB05-adhoc GOV2 751-800 CB\nTB06-adhoc GOV2 801-850 CB\nRT04 Disk 4+5\n(minus CR)\n\n301-450;601700\nCB\nTB05-NP GOV2 NP601-NP872 NP\nTB06-NP GOV2 NP901-NP1081 NP\nTable 3: Summary of test collections and topics\nRetrieval performance of individual content-based and NP queries\nis measured by the average precision and reciprocal rank of the\nfirst correct answer respectively. We make use of the Markov\nRandom field model for both ad-hoc and Named-Page finding\nretrieval. We adopt the same setting of retrieval parameters used\nin [8,9]. The Indri search engine [12] is used for all of our\nexperiments. Though not reported here, we also tried the query\nlikelihood model for ad-hoc retrieval and found that the results\nchange little because of the very high correlation between the\nquery performances obtained by the two retrieval models (0.96\nmeasured by Pearson\"s coefficient).\n4.2 Known Query Types\nSuppose that query types are known. We treat each type of query\nseparately and measure the correlation with average precision (or\nthe reciprocal rank in the case of NP queries). We adopt the\nPearson\"s correlation test which reflects the degree of linear\nrelationship between the predicted and the actual retrieval\nperformance.\n4.2.1 Content-based Queries\nMethods Clarity Robust JSD WIG QF WIG\n+QF\nTB04+0\n5 adhoc\n0.333 0.317 0.362 0.574 0.480 0.637\nTB06\nadhoc\n0.076 0.294 N/A 0.464 0.422 0.511\nTable 4: Pearson\"s correlation coefficients for correlation with\naverage precision on the Terabyte Tracks (ad-hoc) for clarity\nscore, robustness score, the JSD-based method(we directly\ncites the score reported in [2]), WIG, query feedback(QF) and\na linear combination of WIG and QF. Bold cases mean the\nresults are statistically significant at the 0.01 level.\nTable 4 shows the correlation with average precision on two data\nsets: one is a combination of TB04-adhoc and TB05-adhoc(100\ntopics in total) and the other is TB06-adhoc (50 topics). The\nreason that we put TB04-adhoc and TB05-adhoc together is to\nmake our results comparable to [2]. Our baselines are the clarity\nscore (clarity) [6],the robustness score (robust)[1] and the\nJSDbased method (JSD) [2]. For the clarity and robustness score, we\nhave tried different parameter settings and report the highest\ncorrelation coefficients we have found. We directly cite the result\nof the JSD-based method reported in [2]. The table also shows the\nresults for the Weighted Information Gain (WIG) method and the\nQuery Feedback (QF) method for predicting content-based\nqueries. As we described in the previous section, both WIG and\nQF have one free parameter to set, that is, the cutoff rank K. We\ntrain the parameter on one dataset and test on the other. When\ncombining WIG and QF, a simple linear combination is used and\nthe combination weight is learned from the training data set.\nFrom these results, we can see that our methods are considerably\nmore accurate compared to the baselines. We also observe that\nfurther improvements are obtained from the combination of WIG\nand QF, suggesting that they measure different properties of the\nretrieval process that relate to performance.\nWe discover that our methods generalize well on TB06-adhoc\nwhile the correlation for the clarity score with retrieval\nperformance on this data set is considerably worse. Further\ninvestigation shows that the mean average precision of\nTB06-adhoc is 0.342 and is about 10% better than that of the first data set.\nWhile the other three methods typically consider the top 100 or\nless documents given a ranked list, the clarity method usually\nneeds the top 500 or more documents to adequately measure the\ncoherence of a ranked list. Higher mean average precision makes\nranked lists retrieved by different queries more similar in terms of\ncoherence at the level of top 500 documents. We believe that this\nis the main reason for the low accuracy of the clarity score on the\nsecond data set.\nThough this paper focuses on a Web search environment, it is\ndesirable that our techniques will work consistently well in other\nsituations. To this end, we examine the effectiveness of our\ntechniques on the Robust 2004 Track. For our methods, we\nevenly divide all of the test queries into five groups and perform\nfive-fold cross validation. Each time we use one group for\ntraining and the remaining four groups for testing. We make use\nof all of the queries for our two baselines, that is, the clarity score\nand the robustness score. The parameters for our baselines are the\nsame as those used in [1].The results shown in Table 5\ndemonstrate that the prediction accuracy of our methods is on a\npar with that of the two strong baselines.\nClarity Robust WIG QF\n0.464 0.539 0.468 0.464\nTable 5: Comparison of Pearson\"s correlation coefficients on\nthe 2004 Robust Track for clarity score, robustness score,\nWIG and query feedback (QF). Bold cases mean the results\nare statistically significant at the 0.01 level.\nFurthermore, we examine the prediction sensitivity of our\nmethods to the cutoff rank K. With respect to WIG, it is quite\nrobust to K on the Terabyte Tracks (2004-2006) while it prefers a\nsmall value of K like 5 on the 2004 Robust Track. In other words,\na small value of K is a nearly-optimal choice for both kinds of\ntracks. Considering the fact that all other parameters involved in\nWIG are fixed and consequently the same for the two cases, this\nmeans WIG can achieve nearly-optimal prediction accuracy in\ntwo considerably different situations with exactly the same\nparameter setting. Regarding QF, it prefers a larger value of K\nsuch as 100 on the Terabyte Tracks and a smaller value of K such\nas 25 on the 2004 Robust Track.\n4.2.2 NP Queries\nWe adopt WIG and first rank change (FRC) for predicting\nNPquery performance. We also try a linear combination of the two as\nin the previous section. The combination weight is obtained from\nthe other data set. We use the correlation with the reciprocal ranks\nmeasured by the Pearson\"s correlation test to evaluate prediction\nquality. The results are presented in Table 6. Again, our baselines\nare the clarity score and the robustness score.\nTo make a fair comparison, we tune the clarity score in different\nways. We found that using the first ranked document to build the\nquery model yields the best prediction accuracy. We also\nattempted to utilize document structure by using the mixture of\nlanguage models mentioned in section 3.1. Little improvement\nwas obtained. The correlation coefficients for the clarity score\nreported in Table 6 are the best we have found. As we can see,\nour methods considerably outperform the clarity score technique\non both of the runs. This confirms our intuition that the use of a\ncoherence-based measure like the clarity score is inappropriate for\nNP queries.\nMethods Clarity Robust. WIG FRC WIG+FRC\nTB05-NP 0.150 -0.370 0.458 0.440 0.525\nTB06-NP 0.112 -0.160 0.478 0.386 0.515\nTable 6: Pearson\"s correlation coefficients for correlation with\nreciprocal ranks on the Terabyte Tracks (NP) for clarity\nscore, robustness score, WIG, the first rank change (FRC)\nand a linear combination of WIG and FRC. Bold cases mean\nthe results are statistically significant at the 0.01 level.\nRegarding the robustness score, we also tune the parameters and\nreport the best we have found. We observe an interesting and\nsurprising negative correlation with reciprocal ranks. We explain\nthis finding briefly. A high robustness score means that a number\nof top ranked documents in the original ranked list are still highly\nranked after perturbing the documents. The existence of such\ndocuments is a good sign of high performance for content-based\nqueries as these queries usually contain a number of relevant\ndocuments [1]. However, with regard to NP queries, one\nfundamental difference is that there is only one relevant document\nfor each query. The existence of such documents can confuse the\nranking function and lead to low retrieval performance. Although\nthe negative correlation with retrieval performance exists, the\nstrength of the correlation is weaker and less consistent compared\nto our methods as shown in Table 6.\nBased on the above analysis, we can see that current prediction\ntechniques like clarity score and robustness score that are mainly\ndesigned for content-based queries face significant challenges and\nare inadequate to deal with NP queries. Our two techniques\nproposed for NP queries consistently demonstrate good prediction\naccuracy, displaying initial success in solving the problem of\npredicting performance for NP queries. Another point we want to\nstress is that the WIG method works well for both types of\nqueries, a desirable property that most prediction techniques lack.\n4.3 Unknown Query Types\nIn this section, we run two kinds of experiments without access to\nquery type labels. First, we assume that only one type of query\nexists but the type is unknown. Second, we experiment on a\nmixture of content-based and NP queries. The following two\nsubsections will report results for the two conditions respectively.\n4.3.1 Only One Type exists\nWe assume that all queries are of the same type, that is, they are\neither NP queries or content-based queries. We choose WIG to\ndeal with this case because it shows good prediction accuracy for\nboth types of queries in the previous section. We consider two\ncases: (1) CB: all 150 title queries from the ad-hoc task of the\nTerabyte Tracks 2004-2006 (2)NP: all 433 NP queries from the\nnamed page finding task of the Terabyte Tracks 2005 and 2006.\nWe take a simple strategy by labeling all of the queries in each\ncase as the same type (either NP or CB) regardless of their actual\ntype. The computation of WIG will be based on the labeled query\ntype instead of the actual type. There are four possibilities with\nrespect to the relation between the actual type and the labeled\ntype. The correlation with retrieval performance under the four\npossibilities is presented in Table 7. For example, the value 0.445\nat the intersection between the second row and the third column\nshows the Pearson\"s correlation coefficient for correlation with\naverage precision when the content-based queries are incorrectly\nlabeled as the NP type.\nBased on these results, we recommend treating all queries as the\nNP type when only one query type exists and accurate query\nclassification is not feasible, considering the risk that a large loss\nof accuracy will occur if NP queries are incorrectly labeled as\ncontent-based queries. These results also demonstrate the strong\nadaptability of WIG to different query types.\nCB (labeled) NP (labeled)\nCB (actual) 0.536 0.445\nNP (actual) 0.174 0.467\nTable 7: Comparison of Pearson\"s correlation coefficients for\ncorrelation with retrieval performance under four possibilities\non the Terabyte Tracks (NP). Bold cases mean the results are\nstatistically significant at the 0.01 level.\n4.3.2 A mixture of contented-based and NP queries\nA mixture of the two types of queries is a more realistic situation\nthat a Web search engine will meet. We evaluate prediction\naccuracy by how accurately poorly-performing queries can be\nidentified by the prediction method assuming that actual query\ntypes are unknown (but we can predict query types). This is a\nchallenging task because both the predicted and actual\nperformance for one type of query can be incomparable to that for\nthe other type.\nNext we discuss how to implement our evaluation. We create a\nquery pool which consists of all of the 150 ad-hoc title queries\nfrom Terabyte Track 2004-2006 and all of the 433 NP queries\nfrom Terabyte Track 2005&2006. We divide the queries in the\npool into classes: good (better than 50% of the queries of the\nsame type in terms of retrieval performance) and bad\n(otherwise). According to these standards, a NP query with the\nreciprocal rank above 0.2 or a content-based query with the\naverage precision above 0.315 will be considered as good.\nThen, each time we randomly select one query Q from the pool\nwith probability p that Q is contented-based. The remaining\nqueries are used as training data. We first decide the type of query\nQ according to a query classifier. Namely, the query classifier\ntells us whether query Q is NP or content-based. Based on the\npredicted query type and the score computed for query Q by a\nprediction technique, a binary decision is made about whether\nquery Q is good or bad by comparing to the score threshold of the\npredicted query type obtained from the training data. Prediction\naccuracy is measured by the accuracy of the binary decision. In\nour implementation, we repeatedly take a test query from the\nquery pool and prediction accuracy is computed as the\npercentage of correct decisions, that is, a good(bad) query is\npredicted to be good (bad). It is obvious that random guessing will\nlead to 50% accuracy.\nLet us take the WIG method for example to illustrate the process.\nTwo WIG thresholds (one for NP queries and the other for\ncontent-based queries) are trained by maximizing the prediction\naccuracy on the training data. When a test query is labeled as the\nNP (CB) type by the query type classifier, it will be predicted to\nbe good if and only if the WIG score for this query is above the\nNP (CB) threshold. Similar procedures will be taken for other\nprediction techniques.\nNow we briefly introduce the automatic query type classifier used\nin this paper. We find that the robustness score, though originally\nproposed for performance prediction, is a good indicator of query\ntypes. We find that on average content-based queries have a\nmuch higher robustness score than NP queries. For example,\nFigure 2 shows the distributions of robustness scores for NP and\ncontent-based queries. According to this finding, the robustness\nscore classifier will attach a NP (CB) label to the query if the\nrobustness score for the query is below (above) a threshold\ntrained from the training data.\n0\n0.5\n1\n1.5\n2\n2.5\n-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1\nNP Content-based\nFigure 2: Distribution of robustness scores for NP and CB\nqueries. The NP queries are the 252 NP topics from the 2005\nTerabyte Track. The content-based queries are the 150 ad-hoc\ntitle from the Terabyte Tracks 2004-2006. The probability\ndistributions are estimated by the Kernel density estimation\nmethod.\nStrategies Robust WIG-1 WIG-2 WIG-3 Optimal\np=0.6 0.565 0.624 0.665 0.684 0.701\nP=0.4 0.567 0.633 0.654 0.673 0.696\nTable 8: Comparison of prediction accuracy for five strategies\nin the mixed-query situation. Two ways to sample a query\nfrom the pool: (1) the sampled query is content-based with the\nprobability p=0.6. (that is, the query is NP with probability\n0.4 ) (2) set the probability p=0.4.\nWe consider five strategies in our experiments. In the first\nstrategy (denoted by robust), we use the robustness score for\nquery performance prediction with the help of a perfect query\nclassifier that always correctly map a query into one of the two\ncategories (that is, NP or CB). This strategy represents the level of\nprediction accuracy that current prediction techniques can achieve\nin an ideal condition that query types are known. In the next\nfollowing three strategies, the WIG method is adopted for\nperformance prediction. The difference among the three is that\nthree different query classifiers are used for each strategy: (1) the\nclassifier always classifies a query into the NP type. (2) the\nRobustness Score\nProbabilityDensity\nclassifier is the robust score classifier mentioned above. (3) the\nclassifier is a perfect one. These three strategies are denoted by\nWIG-1, WIG-2 and WIG-3 respectively. The reason we are\ninterested in WIG-1 is based on the results from section 4.3.1. In\nthe last strategy (denoted by Optimal) which serves as an upper\nbound on how well we can do so far, we fully make use of our\nprediction techniques for each query type assuming a perfect\nquery classifier is available. Specifically, we linearly combine\nWIG and QF for content-based queries and WIG and FRC for NP\nqueries.\nThe results for the five strategies are shown in Table 8. For each\nstrategy, we try two ways to sample a query from the pool: (1) the\nsampled query is CB with probability p=0.6. (the query is NP\nwith probability 0.4) (2) set the probability p=0.4. From Table 8\nWe can see that in terms of prediction accuracy WIG-2 (the WIG\nmethod with the automatic query classifier) is not only better than\nthe first two cases, but also is close to WIG-3 where a perfect\nclassifier is assumed. Some further improvements over WIG-3 are\nobserved when combined with other prediction techniques. The\nmerit of WIG-2 is that it provides a practical solution to\nautomatically identifying poorly performing queries in a Web\nsearch environment with mixed query types, which poses\nconsiderable obstacles to traditional prediction techniques.\n5. CONCLUSIONS AND FUTURE WORK\nTo our knowledge, our paper is the first to thoroughly explore\nprediction of query performance in web search environments. We\ndemonstrated that our models resulted in higher prediction\naccuracy than previously published techniques not specially\ndevised for web search scenarios. In this paper, we focus on two\ntypes of queries in web search: content-based and Named-Page\n(NP) finding queries, corresponding to the ad-hoc retrieval task\nand the Named-Page finding task respectively. For both types of\nweb queries, our prediction models were shown to be\nsubstantially more accurate than the current state-of-the-art\ntechniques. Furthermore, we considered a more realistic case that\nno prior information on query types is available. We\ndemonstrated that the WIG method is particularly suitable for this\nsituation. Considering the adaptability of WIG to a range of\ncollections and query types, one of our future plans is to apply\nthis method to predict user preference of search results on realistic\ndata collected from a commercial search engine.\nOther than accuracy, another major issue that prediction\ntechniques have to deal with in a Web environment is efficiency.\nFortunately, since the WIG score is computed just over the terms\nand the phrases that appear in the query, this calculation can be\nmade very efficient with the support of index. On the other hand,\nthe computation of QF and FRC is relatively less efficient since\nQF needs to retrieve the whole collection twice and FRC needs to\nrepeatedly rank the perturbed documents. How to improve the\nefficiency of QF and FRC is our future work.\nIn addition, the prediction techniques proposed in this paper have\nthe potential of improving retrieval performance by combining\nwith other IR techniques. For example, our techniques can be\nincorporated to popular query modification techniques such as\nquery expansion and query relaxation. Guided by performance\nprediction, we can make a better decision on when to or how to\nmodify queries to enhance retrieval effectiveness. We would like\nto carry out research in this direction in the future.\n6. ACKNOWLEGMENTS\nThis work was supported in part by the Center for Intelligent\nInformation Retrieval, in part by the Defense Advanced Research\nProjects Agency (DARPA) under contract number\nHR0011-06-C0023, and in part by an award from Google. Any opinions,\nfindings and conclusions or recommendations expressed in this\nmaterial are those of the author and do not necessarily reflect\nthose of the sponsor. In addition, we thank Donald Metzler for his\nvaluable comments on this work.\n7. REFERENCES\n[1] Y. Zhou ,W. B. Croft ,Ranking Robustness: A Novel\nFramework to Predict Query Performance, in Proceedings of\nCIKM 2006.\n[2] D.Carmel, E.Yom-Tov, A.Darlow,D.Pelleg, What Makes a\nQuery Difficult?, in Proceedings of SIGIR 2006.\n[3] C.L.A. Clarke, F. Scholer, I.Soboroff, The TREC 2005\nTerabyte Track, In the Online Proceedings of 2005 TREC.\n[4] B. He and I.Ounis. Inferring query performance using\npreretrieval predictors. In proceedings of the SPIRE 2004.\n[5] S. Tomlinson. Robust, Web and Terabyte Retrieval with\nHummingbird SearchServer at TREC 2004. In the Online\nProceedings of 2004 TREC.\n[6] S. Cronen-Townsend, Y. Zhou, W. B. Croft, Predicting\nQuery Performance, in Proceedings of SIGIR 2002.\n[7] V.Vinay, I.J.Cox, N.Mill-Frayling,K.Wood, On Ranking the\nEffectiveness of Searcher, in Proceedings of SIGIR 2006.\n[8] D.Metzler, W.B.Croft, A Markov Random Filed Model for\nTerm Dependencies, in Proceedings of SIGIR 2005.\n[9] D.Metzler, T.Strohman,Y.Zhou,W.B.Croft, Indri at TREC\n2005: Terabyte Track, In the Online Proceedings of 2004\nTREC.\n[10] P. Ogilvie and J. Callan, Combining document\nrepresentations for known-item search, in Proceedings of\nSIGIR 2003.\n[11] A.Berger, J.Lafferty, Information retrieval as statistical\ntranslation, in Proceedings of SIGIR 1999.\n[12] Indri search engine : http://www.lemurproject.org/indri/\n[13] I.J. Taneja: On Generalized Information Measures and Their\nApplications, Advances in Electronics and Electron Physics,\nAcademic Press (USA), 76, 1989, 327-413.\n[14] S.Cronen-Townsend, Y. Zhou and Croft, W. B. , \"A\nFramework for Selective Query Expansion,\" in Proceedings\nof CIKM 2004.\n[15] F.Song, W.B.Croft, A general language model for\ninformation retrieval, in Proceedings of SIGIR 1999.\n[16] Personal email contact with Vishwa Vinay and our own\nexperiments\n[17] E.Yom-Tov, S.Fine, D.Carmel, A.Darlow, Learning to\nEstimate Query Difficulty Including Applications to Missing\nContent Detection and Distributed Information retrieval, in\nProceedings of SIGIR 2005", "keywords": "homogenous test collection;web search environment;kl-divergence;content-based and named-page finding;jensen-shannon divergence;weighted information gain;trec document collection;query performance prediction;content-based query;robustness score probabilitydensity classifier;web search;gov2 collection;wig;ranking robustness technique;query classification;mixed-query situation;named-page finding task"}
{"name": "train_H-46", "title": "Broad Expertise Retrieval in Sparse Data Environments", "abstract": "Expertise retrieval has been largely unexplored on data other than the W3C collection. At the same time, many intranets of universities and other knowledge-intensive organisations offer examples of relatively small but clean multilingual expertise data, covering broad ranges of expertise areas. We first present two main expertise retrieval tasks, along with a set of baseline approaches based on generative language modeling, aimed at finding expertise relations between topics and people. For our experimental evaluation, we introduce (and release) a new test set based on a crawl of a university site. Using this test set, we conduct two series of experiments. The first is aimed at determining the effectiveness of baseline expertise retrieval methods applied to the new test set. The second is aimed at assessing refined models that exploit characteristic features of the new test set, such as the organizational structure of the university, and the hierarchical structure of the topics in the test set. Expertise retrieval models are shown to be robust with respect to environments smaller than the W3C collection, and current techniques appear to be generalizable to other settings.", "fulltext": "1. INTRODUCTION\nAn organization\"s intranet provides a means for exchanging\ninformation between employees and for facilitating employee\ncollaborations. To efficiently and effectively achieve this, it is necessary\nto provide search facilities that enable employees not only to access\ndocuments, but also to identify expert colleagues.\nAt the TREC Enterprise Track [22] the need to study and\nunderstand expertise retrieval has been recognized through the\nintroduction of Expert Finding tasks. The goal of expert finding is to\nidentify a list of people who are knowledgeable about a given topic.\nThis task is usually addressed by uncovering associations between\npeople and topics [10]; commonly, a co-occurrence of the name\nof a person with topics in the same context is assumed to be\nevidence of expertise. An alternative task, which using the same idea\nof people-topic associations, is expert profiling, where the task is to\nreturn a list of topics that a person is knowledgeable about [3].\nThe launch of the Expert Finding task at TREC has generated a\nlot of interest in expertise retrieval, with rapid progress being made\nin terms of modeling, algorithms, and evaluation aspects. However,\nnearly all of the expert finding or profiling work performed has\nbeen validated experimentally using the W3C collection [24] from\nthe Enterprise Track. While this collection is currently the only\npublicly available test collection for expertise retrieval tasks, it only\nrepresents one type of intranet. With only one test collection it is\nnot possible to generalize conclusions to other realistic settings.\nIn this paper we focus on expertise retrieval in a realistic setting\nthat differs from the W3C setting-one in which relatively small\namounts of clean, multilingual data are available, that cover a broad\nrange of expertise areas, as can be found on the intranets of\nuniversities and other knowledge-intensive organizations. Typically, this\nsetting features several additional types of structure: topical\nstructure (e.g., topic hierarchies as employed by the organization),\norganizational structure (faculty, department, ...), as well as multiple\ntypes of documents (research and course descriptions, publications,\nand academic homepages). This setting is quite different from the\nW3C setting in ways that might impact upon the performance of\nexpertise retrieval tasks.\nWe focus on a number of research questions in this paper: Does\nthe relatively small amount of data available on an intranet affect\nthe quality of the topic-person associations that lie at the heart of\nexpertise retrieval algorithms? How do state-of-the-art algorithms\ndeveloped on the W3C data set perform in the alternative scenario\nof the type described above? More generally, do the lessons from\nthe Expert Finding task at TREC carry over to this setting? How\ndoes the inclusion or exclusion of different documents affect\nexpertise retrieval tasks? In addition to, how can the topical and\norganizational structure be used for retrieval purposes?\nTo answer our research questions, we first present a set of\nbaseline approaches, based on generative language modeling, aimed at\nfinding associations between topics and people. This allows us to\nformulate the expert finding and expert profiling tasks in a uniform\nway, and has the added benefit of allowing us to understand the\nrelations between the two tasks. For our experimental evaluation, we\nintroduce a new data set (the UvT Expert Collection) which is\nrepresentative of the type of intranet that we described above. Our\ncollection is based on publicly available data, crawled from the\nwebsite of Tilburg University (UvT). This type of data is particularly\ninteresting, since (1) it is clean, heterogeneous, structured, and\nfocused, but comprises a limited number of documents; (2) contains\ninformation on the organizational hierarchy; (3) it is bilingual\n(English and Dutch); and (4) the list of expertise areas of an individual\nare provided by the employees themselves. Using the UvT Expert\ncollection, we conduct two sets of experiments. The first is aimed\nat determining the effectiveness of baseline expertise finding and\nprofiling methods in this new setting. A second group of\nexperiments is aimed at extensions of the baseline methods that exploit\ncharacteristic features of the UvT Expert Collection; specifically,\nwe propose and evaluate refined expert finding and profiling\nmethods that incorporate topicality and organizational structure.\nApart from the research questions and data set that we contribute,\nour main contributions are as follows. The baseline models\ndeveloped for expertise finding perform well on the new data set. While\non the W3C setting the expert finding task appears to be more\ndifficult than profiling, for the UvT data the opposite is the case. We\nfind that profiling on the UvT data set is considerably more\ndifficult than on the W3C set, which we believe is due to the large\n(but realistic) number of topical areas that we used for profiling:\nabout 1,500 for the UvT set, versus 50 in the W3C case.\nTaking the similarity between topics into account can significantly\nimprove retrieval performance. The best performing similarity\nmeasures are content-based, therefore they can be applied on the W3C\n(and other) settings as well. Finally, we demonstrate that the\norganizational structure can be exploited in the form of a context model,\nimproving MAP scores for certain models by up to 70%.\nThe remainder of this paper is organized as follows. In the next\nsection we review related work. Then, in Section 3 we provide\ndetailed descriptions of the expertise retrieval tasks that we address\nin this paper: expert finding and expert profiling. In Section 4 we\npresent our baseline models, of which the performance is then\nassessed in Section 6 using the UvT data set that we introduce in\nSection 5. Advanced models exploiting specific features of our data are\npresented in Section 7 and evaluated in Section 8. We formulate our\nconclusions in Section 9.\n2. RELATED WORK\nInitial approaches to expertise finding often employed databases\ncontaining information on the skills and knowledge of each\nindividual in the organization [11]. Most of these tools (usually called\nyellow pages or people-finding systems) rely on people to self-assess\ntheir skills against a predefined set of keywords. For updating\nprofiles in these systems in an automatic fashion there is a need for\nintelligent technologies [5]. More recent approaches use specific\ndocument sets (such as email [6] or software [18]) to find expertise.\nIn contrast with focusing on particular document types, there is also\nan increased interest in the development of systems that index and\nmine published intranet documents as sources of evidence for\nexpertise. One such published approach is the P@noptic system [9],\nwhich builds a representation of each person by concatenating all\ndocuments associated with that person-this is similar to Model 1\nof Balog et al. [4], who formalize and compare two methods. Balog\net al.\"s Model 1 directly models the knowledge of an expert from\nassociated documents, while their Model 2 first locates documents\non the topic and then finds the associated experts. In the reported\nexperiments the second method performs significantly better when\nthere are sufficiently many associated documents per candidate.\nMost systems that took part in the 2005 and 2006 editions of the\nExpert Finding task at TREC implemented (variations on) one of\nthese two models; see [10, 20]. Macdonald and Ounis [16] propose\na different approach for ranking candidate expertise with respect to\na topic based on data fusion techniques, without using\ncollectionspecific heuristics; they find that applying field-based weighting\nmodels improves the ranking of candidates. Petkova and Croft [19]\npropose yet another approach, based on a combination of the above\nModel 1 and 2, explicitly modeling topics.\nTurning to other expert retrieval tasks that can also be addressed\nusing topic-people associations, Balog and de Rijke [3] addressed\nthe task of determining topical expert profiles. While their methods\nproved to be efficient on the W3C corpus, they require an amount\nof data that may not be available in the typical knowledge-intensive\norganization. Balog and de Rijke [2] study the related task of\nfinding experts that are similar to a small set of experts given as input.\nAs an aside, creating a textual summary of a person shows\nsome similarities to biography finding, which has received a\nconsiderable amount of attention recently; see e.g., [13].\nWe use generative language modeling to find associations\nbetween topics and people. In our modeling of expert finding and\nprofiling we collect evidence for expertise from multiple sources, in\na heterogeneous collection, and integrate it with the co-occurrence\nof candidates\" names and query terms-the language modeling\nsetting allows us to do this in a transparent manner. Our modeling\nproceeds in two steps. In the first step, we consider three baseline\nmodels, two taken from [4] (the Models 1 and 2 mentioned above),\nand one a refined version of a model introduced in [3] (which we\nrefer to as Model 3 below); this third model is also similar to the\nmodel described by Petkova and Croft [19]. The models we\nconsider in our second round of experiments are mixture models\nsimilar to contextual language models [1] and to the expanded\ndocuments of Tao et al. [21]; however, the features that we use for\ndefinining our expansions-including topical structure and\norganizational structure-have not been used in this way before.\n3. TASKS\nIn the expertise retrieval scenario that we envisage, users seeking\nexpertise within an organization have access to an interface that\ncombines a search box (where they can search for experts or topics)\nwith navigational structures (of experts and of topics) that allows\nthem to click their way to an expert page (providing the profile of a\nperson) or a topic page (providing a list of experts on the topic).\nTo feed the above interface, we face two expertise retrieval\ntasks, expert finding and expert profiling, that we first define and\nthen formalize using generative language models. In order to model\neither task, the probability of the query topic being associated to a\ncandidate expert plays a key role in the final estimates for searching\nand profiling. By using language models, both the candidates and\nthe query are characterized by distributions of terms in the\nvocabulary (used in the documents made available by the organization\nwhose expertise retrieval needs we are addressing).\n3.1 Expert finding\nExpert finding involves the task of finding the right person with\nthe appropriate skills and knowledge: Who are the experts on topic\nX?. E.g., an employee wants to ascertain who worked on a\nparticular project to find out why particular decisions were made without\nhaving to trawl through documentation (if there is any). Or, they\nmay be in need a trained specialist for consultancy on a specific\nproblem.\nWithin an organization there are usually many possible\ncandidates who could be experts for given topic. We can state this\nproblem as follows:\nWhat is the probability of a candidate ca being an\nexpert given the query topic q?\nThat is, we determine p(ca|q), and rank candidates ca according to\nthis probability. The candidates with the highest probability given\nthe query are deemed the most likely experts for that topic. The\nchallenge is how to estimate this probability accurately. Since the\nquery is likely to consist of only a few terms to describe the\nexpertise required, we should be able to obtain a more accurate estimate\nby invoking Bayes\" Theorem, and estimating:\np(ca|q) =\np(q|ca)p(ca)\np(q)\n, (1)\nwhere p(ca) is the probability of a candidate and p(q) is the\nprobability of a query. Since p(q) is a constant, it can be ignored for\nranking purposes. Thus, the probability of a candidate ca being an\nexpert given the query q is proportional to the probability of a query\ngiven the candidate p(q|ca), weighted by the a priori belief p(ca)\nthat candidate ca is an expert.\np(ca|q) \u221d p(q|ca)p(ca) (2)\nIn this paper our main focus is on estimating the probability of\na query given the candidate p(q|ca), because this probability\ncaptures the extent to which the candidate knows about the query topic.\nWhereas the candidate priors are generally assumed to be\nuniformand thus will not influence the ranking-it has been demonstrated\nthat a sensible choice of priors may improve the performance [20].\n3.2 Expert profiling\nWhile the task of expert searching was concerned with\nfinding experts given a particular topic, the task of expert profiling\nseeks to answer a related question: What topics does a candidate\nknow about? Essentially, this turns the questions of expert finding\naround. The profiling of an individual candidate involves the\nidentification of areas of skills and knowledge that they have expertise\nabout and an evaluation of the level of proficiency in each of these\nareas. This is the candidate\"s topical profile.\nGenerally, topical profiles within organizations consist of\ntabular structures which explicitly catalogue the skills and knowledge\nof each individual in the organization. However, such practice is\nlimited by the resources available for defining, creating,\nmaintaining, and updating these profiles over time. By focusing on\nautomatic methods which draw upon the available evidence within the\ndocument repositories of an organization, our aim is to reduce the\nhuman effort associated with the maintenance of topical profiles1\n.\nA topical profile of a candidate, then, is defined as a vector where\neach element i of the vector corresponds to the candidate ca\"s\nexpertise on a given topic ki, (i.e., s(ca, ki)). Each topic ki defines a\nparticular knowledge area or skill that the organization uses to\ndefine the candidate\"s topical profile. Thus, it is assumed that a list of\ntopics, {k1, . . . , kn}, where n is the number of pre-defined topics,\nis given:\nprofile(ca) = s(ca, k1), s(ca, k2), . . . , s(ca, kn) . (3)\n1\nContext and evidence are needed to help users of expertise\nfinding systems to decide whom to contact when seeking expertise in a\nparticular area. Examples of such context are: Who does she work\nwith? What are her contact details? Is she well-connected, just\nin case she is not able to help us herself? What is her role in the\norganization? Who is her superior? Collaborators, and affiliations,\netc. are all part of the candidate\"s social profile, and can serve as\na background against which the system\"s recommendations should\nbe interpreted. In this paper we only address the problem of\ndetermining topical profiles, and leave social profiling to further work.\nWe state the problem of quantifying the competence of a person on\na certain knowledge area as follows:\nWhat is the probability of a knowledge area (ki) being\npart of the candidate\"s (expertise) profile?\nwhere s(ca, ki) is defined by p(ki|ca). Our task, then, is to\nestimate p(ki|ca), which is equivalent to the problem of obtaining\np(q|ca), where the topic ki is represented as a query topic q, i.e., a\nsequence of keywords representing the expertise required.\nBoth the expert finding and profiling tasks rely on the accurate\nestimation of p(q|ca). The only difference derives from the prior\nprobability that a person is an expert (p(ca)), which can be\nincorporated into the expert finding task. This prior does not apply to\nthe profiling task since the candidate (individual) is fixed.\n4. BASELINE MODELS\nIn this section we describe our baseline models for estimating\np(q|ca), i.e., associations between topics and people. Both expert\nfinding and expert profiling boil down to this estimation. We\nemploy three models for calculating this probability.\n4.1 From topics to candidates\nUsing Candidate Models: Model 1 Model 1 [4] defines the\nprobability of a query given a candidate (p(q|ca)) using standard\nlanguage modeling techniques, based on a multinomial unigram\nlanguage model. For each candidate ca, a candidate language model\n\u03b8ca is inferred such that the probability of a term given \u03b8ca is\nnonzero for all terms, i.e., p(t|\u03b8ca) > 0. From the candidate model the\nquery is generated with the following probability:\np(q|\u03b8ca) =\nY\nt\u2208q\np(t|\u03b8ca)n(t,q)\n,\nwhere each term t in the query q is sampled identically and\nindependently, and n(t, q) is the number of times t occurs in q. The\ncandidate language model is inferred as follows: (1) an empirical\nmodel p(t|ca) is computed; (2) it is smoothed with background\nprobabilities. Using the associations between a candidate and a\ndocument, the probability p(t|ca) can be approximated by:\np(t|ca) =\nX\nd\np(t|d)p(d|ca),\nwhere p(d|ca) is the probability that candidate ca generates a\nsupporting document d, and p(t|d) is the probability of a term t\noccurring in the document d. We use the maximum-likelihood estimate\nof a term, that is, the normalised frequency of the term t in\ndocument d. The strength of the association between document d and\ncandidate ca expressed by p(d|ca) reflects the degree to which the\ncandidates expertise is described using this document. The\nestimation of this probability is presented later, in Section 4.2.\nThe candidate model is then constructed as a linear interpolation\nof p(t|ca) and the background model p(t) to ensure there are no\nzero probabilities, which results in the final estimation:\np(q|\u03b8ca) = (4)\nY\nt\u2208q\n(\n(1 \u2212 \u03bb)\nX\nd\np(t|d)p(d|ca)\n!\n+ \u03bbp(t)\n)n(t,q)\n.\nModel 1 amasses all the term information from all the documents\nassociated with the candidate, and uses this to represent that\ncandidate. This model is used to predict how likely a candidate would\nproduce a query q. This can can be intuitively interpreted as the\nprobability of this candidate talking about the query topic, where\nwe assume that this is indicative of their expertise.\nUsing Document Models: Model 2 Model 2 [4] takes a\ndifferent approach. Here, the process is broken into two parts. Given\na candidate ca, (1) a document that is associated with a candidate\nis selected with probability p(d|ca), and (2) from this document a\nquery q is generated with probability p(q|d). Then the sum over all\ndocuments is taken to obtain p(q|ca), such that:\np(q|ca) =\nX\nd\np(q|d)p(d|ca). (5)\nThe probability of a query given a document is estimated by\ninferring a document language model \u03b8d for each document d in a\nsimilar manner as the candidate model was inferred:\np(t|\u03b8d) = (1 \u2212 \u03bb)p(t|d) + \u03bbp(t), (6)\nwhere p(t|d) is the probability of the term in the document. The\nprobability of a query given the document model is:\np(q|\u03b8d) =\nY\nt\u2208q\np(t|\u03b8d)n(t,q)\n.\nThe final estimate of p(q|ca) is obtained by substituting p(q|d) for\np(q|\u03b8d) into Eq. 5 (see [4] for full details). Conceptually, Model 2\ndiffers from Model 1 because the candidate is not directly modeled.\nInstead, the document acts like a hidden variable in the process\nwhich separates the query from the candidate. This process is akin\nto how a user may search for candidates with a standard search\nengine: initially by finding the documents which are relevant, and\nthen seeing who is associated with that document. By examining a\nnumber of documents the user can obtain an idea of which\ncandidates are more likely to discuss the topic q.\nUsing Topic Models: Model 3 We introduce a third model, Model 3.\nInstead of attempting to model the query generation process via\ncandidate or document models, we represent the query as a topic\nlanguage model and directly estimate the probability of the\ncandidate p(ca|q). This approach is similar to the model presented\nin [3, 19]. As with the previous models, a language model is\ninferred, but this time for the query. We adapt the work of Lavrenko\nand Croft [14] to estimate a topic model from the query.\nThe procedure is as follows. Given a collection of documents\nand a query topic q, it is assumed that there exists an unknown\ntopic model \u03b8k that assigns probabilities p(t|\u03b8k) to the term\noccurrences in the topic documents. Both the query and the documents\nare samples from \u03b8k (as opposed to the previous approaches, where\na query is assumed to be sampled from a specific document or\ncandidate model). The main task is to estimate p(t|\u03b8k), the probability\nof a term given the topic model. Since the query q is very sparse,\nand as there are no examples of documents on the topic, this\ndistribution needs to be approximated. Lavrenko and Croft [14] suggest\na reasonable way of obtaining such an approximation, by assuming\nthat p(t|\u03b8k) can be approximated by the probability of term t given\nthe query q. We can then estimate p(t|q) using the joint probability\nof observing the term t together with the query terms, q1, . . . , qm,\nand dividing by the joint probability of the query terms:\np(t|\u03b8k) \u2248 p(t|q) =\np(t, q1, . . . , qm)\np(q1, . . . , qm)\n=\np(t, q1, . . . , qm)\nP\nt \u2208T p(t , q1, . . . , qm)\n,\nwhere p(q1, . . . , qm) =\nP\nt \u2208T p(t , q1, . . . , qm), and T is the\nentire vocabulary of terms. In order to estimate the joint probability\np(t, q1, . . . , qm), we follow [14, 15] and assume t and q1, . . . , qm\nare mutually independent, once we pick a source distribution from\nthe set of underlying source distributions U. If we choose U to be\na set of document models. then to construct this set, the query q\nwould be issued against the collection, and the top n returned are\nassumed to be relevant to the topic, and thus treated as samples\nfrom the topic model. (Note that candidate models could be used\ninstead.) With the document models forming U, the joint\nprobability of term and query becomes:\np(t, q1, . . . , qm) =\nX\nd\u2208U\np(d)\n\u02d8\np(t|\u03b8d)\nmY\ni=1\np(qi|\u03b8d)\n\u00af\n. (7)\nHere, p(d) denotes the prior distribution over the set U, which\nreflects the relevance of the document to the topic. We assume that\np(d) is uniform across U. In order to rank candidates according\nto the topic model defined, we use the Kullback-Leibler divergence\nmetric (KL, [8]) to measure the difference between the candidate\nmodels and the topic model:\nKL(\u03b8k||\u03b8ca) =\nX\nt\np(t|\u03b8k) log\np(t|\u03b8k)\np(t|\u03b8ca)\n. (8)\nCandidates with a smaller divergence from the topic model are\nconsidered to be more likely experts on that topic. The candidate model\n\u03b8ca is defined in Eq. 4. By using KL divergence instead of the\nprobability of a candidate given the topic model p(ca|\u03b8k), we avoid\nnormalization problems.\n4.2 Document-candidate associations\nFor our models we need to be able to estimate the probability\np(d|ca), which expresses the extent to which a document d\ncharacterizes the candidate ca. In [4], two methods are presented for\nestimating this probability, based on the number of person names\nrecognized in a document. However, in our (intranet) setting it is\nreasonable to assume that authors of documents can unambiguously be\nidentified (e.g., as the author of an article, the teacher assigned to a\ncourse, the owner of a web page, etc.) Hence, we set p(d|ca) to be\n1 if candidate ca is author of document d, otherwise the probability\nis 0. In Section 6 we describe how authorship can be determined\non different types of documents within the collection.\n5. THE UVT EXPERT COLLECTION\nThe UvT Expert collection used in the experiments in this paper\nfits the scenario outlined in Section 3. The collection is based on\nthe Webwijs (Webwise) system developed at Tilburg University\n(UvT) in the Netherlands. Webwijs (http://www.uvt.nl/\nwebwijs/) is a publicly accessible database of UvT employees\nwho are involved in research or teaching; currently, Webwijs\ncontains information about 1168 experts, each of whom has a page with\ncontact information and, if made available by the expert, a research\ndescription and publications list. In addition, each expert can\nselect expertise areas from a list of 1491 topics and is encouraged to\nsuggest new topics that need to be approved by the Webwijs editor.\nEach topic has a separate page that shows all experts associated\nwith that topic and, if available, a list of related topics.\nWebwijs is available in Dutch and English, and this bilinguality\nhas been preserved in the collection. Every Dutch Webwijs page\nhas an English translation. Not all Dutch topics have an English\ntranslation, but the reverse is true: the 981 English topics all have a\nDutch equivalent.\nAbout 42% of the experts teach courses at Tilburg University;\nthese courses were also crawled and included in the profile. In\naddition, about 27% of the experts link to their academic homepage\nfrom their Webwijs page. These home pages were crawled and\nadded to the collection. (This means that if experts put the full-text\nversions of their publications on their academic homepage, these\nwere also available for indexing.) We also obtained 1880 full-text\nversions of publications from the UvT institutional repository and\nDutch English\nno. of experts 1168 1168\nno. of experts with \u2265 1 topic 743 727\nno. of topics 1491 981\nno. of expert-topic pairs 4318 3251\navg. no. of topics/expert 5.8 5.9\nmax. no. of topics/expert (no. of experts) 60 (1) 35 (1)\nmin. no. of topics/expert (no. of experts) 1 (74) 1 (106)\navg. no. of experts/topic 2.9 3.3\nmax. no. of experts/topic (no. of topics) 30 (1) 30 (1)\nmin. no. of experts/topic (no. of topics) 1 (615) 1 (346)\nno. of experts with HP 318 318\nno. of experts with CD 318 318\navg. no. of CDs per teaching expert 3.5 3.5\nno. of experts with RD 329 313\nno. of experts with PUB 734 734\navg. no. of PUBs per expert 27.0 27.0\navg. no. of PUB citations per expert 25.2 25.2\navg. no. of full-text PUBs per expert 1.8 1.8\nTable 2: Descriptive statistics of the Dutch and English versions\nof the UvT Expert collection.\nconverted them to plain text. We ran the TextCat [23] language\nidentifier to classify the language of the home pages and the\nfulltext publications. We restricted ourselves to pages where the\nclassifier was confident about the language used on the page.\nThis resulted in four document types: research descriptions (RD),\ncourse descriptions (CD), publications (PUB; full-text and\ncitationonly versions), and academic homepages (HP). Everything was\nbundled into the UvT Expert collection which is available at http:\n//ilk.uvt.nl/uvt-expert-collection/.\nThe UvT Expert collection was extracted from a different\norganizational setting than the W3C collection and differs from it in\na number of ways. The UvT setting is one with relatively small\namounts of multilingual data. Document-author associations are\nclear and the data is structured and clean. The collection covers a\nbroad range of expertise areas, as one can typically find on intranets\nof universities and other knowledge-intensive institutes.\nAdditionally, our university setting features several types of structure\n(topical and organizational), as well as multiple document types.\nAnother important difference between the two data sets is that the\nexpertise areas in the UvT Expert collection are self-selected instead\nof being based on group membership or assignments by others.\nSize is another dimension along which the W3C and UvT Expert\ncollections differ: the latter is the smaller of the two. Also realistic\nare the large differences in the amount of information available for\neach expert. Utilizing Webwijs is voluntary; 425 Dutch experts\ndid not select any topics at all. This leaves us with 743 Dutch and\n727 English usable expert profiles. Table 2 provides descriptive\nstatistics for the UvT Expert collection.\nUniversities tend to have a hierarchical structure that goes from\nthe faculty level, to departments, research groups, down to the\nindividual researchers. In the UvT Expert collection we have\ninformation about the affiliations of researchers with faculties and\ninstitutes, providing us with a two-level organizational hierarchy.\nTilburg University has 22 organizational units at the faculty level\n(including the university office and several research institutes) and\n71 departments, which amounts to 3.2 departments per faculty.\nAs to the topical hierarchy used by Webwijs, 131 of the 1491\ntopics are top nodes in the hierarchy. This hierarchy has an average\ntopic chain length of 2.65 and a maximum length of 7 topics.\n6. EVALUATION\nBelow, we evaluate Section 4\"s models for expert finding and\nprofiling onthe UvT Expert collection. We detail our research\nquestions and experimental setup, and then present our results.\n6.1 Research Questions\nWe address the following research questions. Both expert finding\nand profiling rely on the estimations of p(q|ca). The question is\nhow the models compare on the different tasks, and in the setting of\nthe UvT Expert collection. In [4], Model 2 outperformed Model 1\non the W3C collection. How do they compare on our data set? And\nhow does Model 3 compare to Model 1? What about performance\ndifferences between the two languages in our test collection?\n6.2 Experimental Setup\nThe output of our models was evaluated against the self-assigned\ntopic labels, which were treated as relevance judgements. Results\nwere evaluated separately for English and Dutch. For English we\nonly used topics for which the Dutch translation was available; for\nDutch all topics were considered. The results were averaged for\nthe queries in the intersection of relevance judgements and results;\nmissing queries do not contribute a value of 0 to the scores.\nWe use standard information retrieval measures, such as Mean\nAverage Precision (MAP) and Mean Reciprocal Rank (MRR). We\nalso report the percentage of topics (%q) and candidates (%ca)\ncovered, for the expert finding and profiling tasks, respectively.\n6.3 Results\nTable 1 shows the performance of Model 1, 2, and 3 on the\nexpert finding and profiling tasks. The rows of the table correspond\nto the various document types (RD, CD, PUB, and HP) and to their\ncombinations. RD+CD+PUB+HP is equivalent to the full\ncollection and will be referred as the BASELINE of our experiments.\nLooking at Table 1 we see that Model 2 performs the best across\nthe board. However, when the data is clean and very focused (RD),\nModel 3 outperforms it in a number of cases. Model 1 has the\nbest coverage of candidates (%ca) and topics (%q). The various\ndocument types differ in their characteristics and how they improve\nthe finding and profiling tasks. Expert profiling benefits much from\nthe clean data present in the RD and CD document types, while the\npublications contribute the most to the expert finding task. Adding\nthe homepages does not prove to be particularly useful.\nWhen we compare the results across languages, we find that the\ncoverage of English topics (%q) is higher than of the Dutch ones\nfor expert finding. Apart from that, the scores fall in the same range\nfor both languages. For the profiling task the coverage of the\ncandidates (%ca) is very similar for both languages. However, the\nperformance is substantially better for the English topics.\nWhile it is hard to compare scores across collections, we\nconclude with a brief comparison of the absolute scores in Table 1 to\nthose reported in [3, 4] on the W3C test set (2005 edition). For\nexpert finding the MAP scores for Model 2 reported here are about\n50% higher than the corresponding figures in [4], while our MRR\nscores are slightly below those in [4]. For expert profiling, the\ndifferences are far more dramatic: the MAP scores for Model 2\nreported here are around 50% below the scores in [3], while the (best)\nMRR scores are about the same as those in [3]. The cause for the\nlatter differences seems to reside in the number of knowledge areas\nconsidered here-approx. 30 times more than in the W3C setting.\n7. ADVANCED MODELS\nNow that we have developed and assessed basic language\nmodeling techniques for expertise retrieval, we turn to refined models\nthat exploit special features of our test collection.\n7.1 Exploiting knowledge area similarity\nOne way to improve the scoring of a query given a candidate is\nto consider what other requests the candidate would satisfy and use\nthem as further evidence to support the original query, proportional\nExpert finding Expert profiling\nDocument types Model 1 Model 2 Model 3 Model 1 Model 2 Model 3\n%q MAP MRR %q MAP MRR %q MAP MRR %ca MAP MRR %ca MAP MRR %ca MAP MRR\nEnglish\nRD 97.8 0.126 0.269 83.5 0.144 0.311 83.3 0.129 0.271 100 0.089 0.189 39.3 0.232 0.465 41.1 0.166 0.337\nCD 97.8 0.118 0.227 91.7 0.123 0.248 91.7 0.118 0.226 32.8 0.188 0.381 32.4 0.195 0.385 32.7 0.203 0.370\nPUB 97.8 0.200 0.330 98.0 0.216 0.372 98.0 0.145 0.257 78.9 0.167 0.364 74.5 0.212 0.442 78.9 0.135 0.299\nHP 97.8 0.081 0.186 97.4 0.071 0.168 97.2 0.062 0.149 31.2 0.150 0.299 28.8 0.185 0.335 30.1 0.136 0.287\nRD+CD 97.8 0.188 0.352 92.9 0.193 0.360 92.9 0.150 0.273 100 0.145 0.286 61.3 0.251 0.477 63.2 0.217 0.416\nRD+CD+PUB 97.8 0.235 0.373 98.1 0.277 0.439 98.1 0.178 0.305 100 0.196 0.380 87.2 0.280 0.533 89.5 0.170 0.344\nRD+CD+PUB+HP 97.8 0.237 0.372 98.6 0.280 0.441 98.5 0.166 0.293 100 0.199 0.387 88.7 0.281 0.525 90.9 0.169 0.329\nDutch\nRD 61.3 0.094 0.229 38.4 0.137 0.336 38.3 0.127 0.295 38.0 0.127 0.386 34.1 0.138 0.420 38.0 0.105 0.327\nCD 61.3 0.107 0.212 49.7 0.128 0.256 49.7 0.136 0.261 32.5 0.151 0.389 31.8 0.158 0.396 32.5 0.170 0.380\nPUB 61.3 0.193 0.319 59.5 0.218 0.368 59.4 0.173 0.291 78.8 0.126 0.364 76.0 0.150 0.424 78.8 0.103 0.294\nHP 61.3 0.063 0.169 56.6 0.064 0.175 56.4 0.062 0.163 29.8 0.108 0.308 27.8 0.125 0.338 29.8 0.098 0.255\nRD+CD 61.3 0.159 0.314 51.9 0.184 0.360 51.9 0.169 0.324 60.5 0.151 0.410 57.2 0.166 0.431 60.4 0.159 0.384\nRD+CD+PUB 61.3 0.244 0.398 61.5 0.260 0.424 61.4 0.210 0.350 90.3 0.165 0.445 88.2 0.189 0.479 90.3 0.126 0.339\nRD+CD+PUB+HP 61.3 0.249 0.401 62.6 0.265 0.436 62.6 0.195 0.344 91.9 0.164 0.426 90.1 0.195 0.488 91.9 0.125 0.328\nTable 1: Performance of the models on the expert finding and profiling tasks, using different document types and their combinations.\n%q is the number of topics covered (applies to the expert finding task), %ca is the number of candidates covered (applies to the\nexpert profiling task). The top and bottom blocks correspond to English and Dutch respectively. The best scores are in boldface.\nto how related the other requests are to the original query. This can\nbe modeled by interpolating between the p(q|ca) and the further\nsupporting evidence from all similar requests q , as follows:\np (q|ca) = \u03bbp(q|ca) + (1 \u2212 \u03bb)\nX\nq\np(q|q )p(q |ca), (9)\nwhere p(q|q ) represents the similarity between the two topics q\nand q . To be able to work with similarity methods that are not\nnecessarily probabilities, we set p(q|q ) = w(q,q )\n\u03b3\n, where \u03b3 is\na normalizing constant, such that \u03b3 =\nP\nq w(q , q ). We\nconsider four methods for calculating the similarity score between two\ntopics. Three approaches are strictly content-based, and establish\nsimilarity by examining co-occurrence patterns of topics within the\ncollection, while the last approach exploits the hierarchical\nstructure of topical areas that may be present within an organization (see\n[7] for further examples of integrating word relationships into\nlanguage models).\nThe Kullback-Leibler (KL) divergence metric defined in Eq. 8\nprovides a measure of how different or similar two probability\ndistributions are. A topic model is inferred for q and q using the\nmethod presented in Section 4.1 to describe the query across the\nentire vocabulary. Since a lower KL score means the queries are\nmore similar, we let w(q, q ) = max(KL(\u03b8q||\u00b7) \u2212 KL(\u03b8q||\u03b8q )).\nPointwise Mutual Information (PMI, [17]) is a measure of\nassociation used in information theory to determine the extent of\nindependence between variables. The dependence between two queries\nis reflected by the SI(q, q ) score, where scores greater than zero\nindicate that it is likely that there is a dependence, which we take\nto mean that the queries are likely to be similar:\nSI(q, q ) = log\np(q, q )\np(q)p(q )\n(10)\nWe estimate the probability of a topic p(q) using the number of\ndocuments relevant to query q within the collection. The joint\nprobability p(q, q ) is estimated similarly, by using the\nconcatenation of q and q as a query. To obtain p(q|q ), we then set\nw(q, q ) = SI(q, q ) when SI(q, q ) > 0 otherwise w(q, q ) = 0,\nbecause we are only interested in including queries that are similar.\nThe log-likelihood statistic provides another measure of\ndependence, which is more reliable than the pointwise mutual\ninformation measure [17]. Let k1 be the number of co-occurrences of q\nand q , k2 the number of occurrences of q not co-occurring with q ,\nn1 the total number of occurrences of q , and n2 the total number\nof topic tokens minus the number of occurrences of q . Then, let\np1 = k1/n1, p2 = k2/n2, and p = (k1 + k2)/(n1 + n2),\n(q, q ) = 2( (p1, k1, n1) + (p2, k2, n2)\n\u2212 (p, k1, n1) \u2212 (p, k2, n2)),\nwhere (p, n, k) = k log p + (n \u2212 k) log(1 \u2212 p). The higher\nscore indicate that queries are also likely to be similar, thus we set\nw(q, q ) = (q, q ).\nFinally, we also estimate the similarity of two topics based on\ntheir distance within the topic hierarchy. The topic hierarchy is\nviewed as a directed graph, and for all topic-pairs the shortest path\nSP(q, q ) is calculated. We set the similarity score to be the\nreciprocal of the shortest path: w(q, q ) = 1/SP(q, q ).\n7.2 Contextual information\nGiven the hierarchy of an organization, the units to which a\nperson belong are regarded as a context so as to compensate for data\nsparseness. We model it as follows:\np (q|ca) =\n\n1 \u2212\nP\nou\u2208OU(ca) \u03bbou\n\n\u00b7 p(q|ca)\n+\nP\nou\u2208OU(ca) \u03bbou \u00b7 p(q|ou),\nwhere OU(ca) is the set of organizational units of which\ncandidate ca is a member of, and p(q|o) expresses the strength of the\nassociation between query q and the unit ou. The latter probability\ncan be estimated using either of the three basic models, by simply\nreplacing ca with ou in the corresponding equations. An\norganizational unit is associated with all the documents that its members\nhave authored. That is, p(d|ou) = maxca\u2208ou p(d|ca).\n7.3 A simple multilingual model\nFor knowledge institutes in Europe, academic or otherwise, a\nmultilingual (or at least bilingual) setting is typical. The following\nmodel builds on a kind of independence assumption: there is no\nspill-over of expertise/profiles across language boundaries. While a\nsimplification, this is a sensible first approach. That is: p (q|ca) =P\nl\u2208L \u03bbl \u00b7 p(ql|ca), where L is the set of languages used in the\ncollection, ql is the translation of the query q to language l, and \u03bbl is\na language specific smoothing parameter, such that\nP\nl\u2208L \u03bbl = 1.\n8. ADVANCED MODELS: EVALUATION\nIn this section we present an experimental evaluation of our\nadvanced models.\nExpert finding Expert profiling\nLanguage Model 1 Model 2 Model 3 Model 1 Model 2 Model 3\n%q MAP MRR %q MAP MRR %q MAP MRR %ca MAP MRR %ca MAP MRR %ca MAP MRR\nEnglish only 97.8 0.237 0.372 98.6 0.280 0.441 98.5 0.166 0.293 100 0.199 0.387 88.7 0.281 0.525 90.9 0.169 0.329\nDutch only 61.3 0.249 0.401 62.6 0.265 0.436 62.6 0.195 0.344 91.9 0.164 0.426 90.1 0.195 0.488 91.9 0.125 0.328\nCombination 99.4 0.297 0.444 99.7 0.324 0.491 99.7 0.223 0.388 100 0.241 0.445 92.1 0.313 0.564 93.2 0.224 0.411\nTable 3: Performance of the combination of languages on the expert finding and profiling tasks (on candidates). Best scores for each\nmodel are in italic, absolute best scores for the expert finding and profiling tasks are in boldface.\nMethod Model 1 Model 2 Model 3\nMAP MRR MAP MRR MAP MRR\nEnglish\nBASELINE 0.296 0.454 0.339 0.509 0.221 0.333\nKLDIV 0.291 0.453 0.327 0.503 0.219 0.330\nPMI 0.291 0.453 0.337 0.509 0.219 0.331\nLL 0.319 0.490 0.360 0.524 0.233 0.368\nHDIST 0.299 0.465 0.346 0.537 0.219 0.332\nDutch\nBASELINE 0.240 0.350 0.271 0.403 0.227 0.389\nKLDIV 0.239 0.347 0.253 0.386 0.224 0.385\nPMI 0.239 0.350 0.260 0.392 0.227 0.389\nLL 0.255 0.372 0.281 0.425 0.231 0.389\nHDIST 0.253 0.365 0.271 0.407 0.236 0.402\nMethod Model 1 Model 2 Model 3\nMAP MRR MAP MRR MAP MRR\nEnglish\nBASELINE 0.485 0.546 0.499 0.548 0.381 0.416\nKLDIV 0.510 0.564 0.513 0.558 0.381 0.416\nPMI 0.486 0.546 0.495 0.542 0.407 0.451\nLL 0.558 0.589 0.586 0.617 0.408 0.453\nHDIST 0.507 0.567 0.512 0.563 0.386 0.420\nDutch\nBASELINE 0.263 0.313 0.294 0.358 0.262 0.315\nKLDIV 0.284 0.336 0.271 0.321 0.261 0.314\nPMI 0.265 0.317 0.265 0.316 0.273 0.330\nLL 0.312 0.351 0.330 0.377 0.284 0.331\nHDIST 0.280 0.327 0.288 0.341 0.266 0.321\nTable 4: Performance on the expert finding (top) and profiling\n(bottom) tasks, using knowledge area similarities. Runs were\nevaluated on the main topics set. Best scores are in boldface.\n8.1 Research Questions\nOur questions follow the refinements presented in the preceding\nsection: Does exploiting the knowledge area similarity improve\neffectiveness? Which of the various methods for capturing word\nrelationships is most effective? Furthermore, is our way of bringing\nin contextual information useful? For which tasks? And finally, is\nour simple way of combining the monolingual scores sufficient for\nobtaining significant improvements?\n8.2 Experimental setup\nGiven that the self-assessments are also sparse in our collection,\nin order to be able to measure differences between the various\nmodels, we selected a subset of topics, and evaluated (some of the) runs\nonly on this subset. This set is referred as main topics, and consists\nof topics that are located at the top level of the topical hierarchy. (A\nmain topic has subtopics, but is not a subtopic of any other topic.)\nThis main set consists of 132 Dutch and 119 English topics. The\nrelevance judgements were restricted to the main topic set, but were\nnot expanded with subtopics.\n8.3 Exploiting knowledge area similarity\nTable 4 presents the results. The four methods used for\nestimating knowledge-area similarity are KL divergence (KLDIV),\nPointLang. Topics Model 1 Model 2 Model 3\nMAP MRR MAP MRR MAP MRR\nExpert finding\nUK ALL 0.423 0.545 0.654 0.799 0.494 0.629\nUK MAIN 0.500 0.621 0.704 0.834 0.587 0.699\nNL ALL 0.439 0.560 0.672 0.826 0.480 0.630\nNL MAIN 0.440 0.584 0.645 0.816 0.515 0.655\nExpert profiling\nUK ALL 0.240 0.640 0.306 0.778 0.223 0.616\nUK MAIN 0.523 0.677 0.519 0.648 0.461 0.587\nNL ALL 0.203 0.716 0.254 0.770 0.183 0.627\nNL MAIN 0.332 0.576 0.380 0.624 0.332 0.549\nTable 5: Evaluating the context models on organizational units.\nwise mutual information (PMI), log-likelihood (LL), and distance\nwithin topic hierarchy (HDIST). We managed to improve upon the\nbaseline in all cases, but the improvement is more noticeable for\nthe profiling task. For both tasks, the LL method performed best.\nThe content-based approaches performed consistently better than\nHDIST.\n8.4 Contextual information\nA two level hierarchy of organizational units (faculties and\ninstitutes) is available in the UvT Expert collection. The unit a person\nbelongs to is used as a context for that person. First, we evaluated\nthe models of the organizational units, using all topics (ALL) and\nonly the main topics (MAIN). An organizational unit is considered\nto be relevant for a given topic (or vice versa) if at least one member\nof the unit selected the given topic as an expertise area.\nTable 5 reports on the results. As far as expert finding goes, given\na topic, the corresponding organizational unit can be identified with\nhigh precision. However, the expert profiling task shows a different\npicture: the scores are low, and the task seems hard. The\nexplanation may be that general concepts (i.e., our main topics) may belong\nto several organizational units.\nSecond, we performed another evaluation, where we combined\nthe contextual models with the candidate models (to score\ncandidates again). Table 6 reports on the results. We find a positive\nimpact of the context models only for expert finding. Noticably,\nfor expert finding (and Model 1), it improves over 50% (for\nEnglish) and over 70% (for Dutch) on MAP. The poor performance\non expert profiling may be due to the fact that context models alone\ndid not perform very well on the profiling task to begin with.\n8.5 Multilingual models\nIn this subsection we evaluate the method for combining\nresults across multiple languages that we described in Section 7.3.\nIn our setting the set of languages consists of English and Dutch:\nL = {UK, NL}. The weights on these languages were set to be\nidentical (\u03bbUK = \u03bbNL = 0.5). We performed experiments with\nvarious \u03bb settings, but did not observe significant differences in\nperformance.\nTable 3 reports on the multilingual results, where performance is\nevaluated on the full topic set. All three models significantly\nimLang. Method Model 1 Model 2 Model 3\nMAP MRR MAP MRR MAP MRR\nExpert finding\nUK BL 0.296 0.454 0.339 0.509 0.221 0.333\nUK CT 0.330 0.491 0.342 0.500 0.228 0.342\nNL BL 0.240 0.350 0.271 0.403 0.227 0.389\nNL CT 0.251 0.382 0.267 0.410 0.246 0.404\nExpert profiling\nUK BL 0.485 0.546 0.499 0.548 0.381 0.416\nUK CT 0.562 0.620 0.508 0.558 0.440 0.486\nNL BL 0.263 0.313 0.294 0.358 0.262 0.315\nNL CT 0.330 0.384 0.317 0.387 0.294 0.345\nTable 6: Performance of the context models (CT) compared to\nthe baseline (BL). Best scores are in boldface.\nproved over all measures for both tasks. The coverage of topics\nand candidates for the expert finding and profiling tasks,\nrespectively, is close to 100% in all cases. The relative improvement\nof the precision scores ranges from 10% to 80%. These scores\ndemonstrate that despite its simplicity, our method for combining\nresults over multiple languages achieves substantial improvements\nover the baseline.\n9. CONCLUSIONS\nIn this paper we focused on expertise retrieval (expert finding\nand profiling) in a new setting of a typical knowledge-intensive\norganization in which the available data is of high quality,\nmultilingual, and covering a broad range of expertise area. Typically, the\namount of available data in such an organization (e.g., a university,\na research institute, or a research lab) is limited when compared to\nthe W3C collection that has mostly been used for the experimental\nevaluation of expertise retrieval so far.\nTo examine expertise retrieval in this setting, we introduced (and\nreleased) the UvT Expert collection as a representative case of such\nknowledge intensive organizations. The new collection reflects the\ntypical properties of knowledge-intensive institutes noted above and\nalso includes several features which may are potentially useful for\nexpertise retrieval, such as topical and organizational structure.\nWe evaluated how current state-of-the-art models for expert\nfinding and profiling performed in this new setting and then refined\nthese models in order to try and exploit the different\ncharacteristics within the data environment (language, topicality, and\norganizational structure). We found that current models of expertise\nretrieval generalize well to this new environment; in addition we\nfound that refining the models to account for the differences results\nin significant improvements, thus making up for problems caused\nby data sparseness issues.\nFuture work includes setting up manual assessments of\nautomatically generated profiles by the employees themselves, especially in\ncases where the employees have not provided a profile themselves.\n10. ACKNOWLEDGMENTS\nKrisztian Balog was supported by the Netherlands Organisation\nfor Scientific Research (NWO) under project number 220-80-001.\nMaarten de Rijke was also supported by NWO under project\nnumbers 017.001.190, 220-80-001, 264-70-050, 354-20-005,\n600.065.120, 612-13-001, 612.000.106, 612.066.302, 612.069.006,\n640.001.501, 640.002.501, and by the E.U. IST programme of the 6th\nFP for RTD under project MultiMATCH contract IST-033104.\nThe work of Toine Bogers and Antal van den Bosch was funded\nby the IOP-MMI-program of SenterNovem / The Dutch Ministry\nof Economic Affairs, as part of the `A Propos project.\n11. REFERENCES\n[1] L. Azzopardi. Incorporating Context in the Language Modeling\nFramework for ad-hoc Information Retrieval. PhD thesis, University\nof Paisley, 2005.\n[2] K. Balog and M. de Rijke. Finding similar experts. In This volume,\n2007.\n[3] K. Balog and M. de Rijke. Determining expert profiles (with an\napplication to expert finding). In IJCAI \"07: Proc. 20th Intern. Joint Conf.\non Artificial Intelligence, pages 2657-2662, 2007.\n[4] K. Balog, L. Azzopardi, and M. de Rijke. Formal models for expert\nfinding in enterprise corpora. In SIGIR \"06: Proc. 29th annual\nintern. ACM SIGIR conf. on Research and development in information\nretrieval, pages 43-50, 2006.\n[5] I. Becerra-Fernandez. 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Voting for candidates: adapting data\nfusion techniques for an expert search task. In CIKM \"06: Proc. 15th\nACM intern. conf. on Information and knowledge management, pages\n387-396, 2006.\n[17] C. Manning and H. Sch\u00a8utze. Foundations of Statistical Natural\nLanguage Processing. The MIT Press, 1999.\n[18] A. Mockus and J. D. Herbsleb. Expertise browser: a quantitative\napproach to identifying expertise. In ICSE \"02: Proc. 24th Intern. Conf.\non Software Engineering, pages 503-512, 2002.\n[19] D. Petkova and W. B. Croft. Hierarchical language models for expert\nfinding in enterprise corpora. In Proc. ICTAI 2006, pages 599-608,\n2006.\n[20] I. Soboroff, A. de Vries, and N. Craswell. Overview of the TREC\n2006 Enterprise Track. In TREC 2006 Working Notes, 2006.\n[21] T. Tao, X. Wang, Q. Mei, and C. Zhai. Language model information\nretrieval with document expansion. In HLT-NAACL 2006, 2006.\n[22] TREC. Enterprise track, 2005. 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{"name": "train_H-47", "title": "A Semantic Approach to Contextual Advertising", "abstract": "Contextual advertising or Context Match (CM) refers to the placement of commercial textual advertisements within the content of a generic web page, while Sponsored Search (SS) advertising consists in placing ads on result pages from a web search engine, with ads driven by the originating query. In CM there is usually an intermediary commercial ad-network entity in charge of optimizing the ad selection with the twin goal of increasing revenue (shared between the publisher and the ad-network) and improving the user experience. With these goals in mind it is preferable to have ads relevant to the page content, rather than generic ads. The SS market developed quicker than the CM market, and most textual ads are still characterized by bid phrases representing those queries where the advertisers would like to have their ad displayed. Hence, the first technologies for CM have relied on previous solutions for SS, by simply extracting one or more phrases from the given page content, and displaying ads corresponding to searches on these phrases, in a purely syntactic approach. However, due to the vagaries of phrase extraction, and the lack of context, this approach leads to many irrelevant ads. To overcome this problem, we propose a system for contextual ad matching based on a combination of semantic and syntactic features.", "fulltext": "1. INTRODUCTION\nWeb advertising supports a large swath of today\"s Internet\necosystem. The total internet advertiser spend in US alone\nin 2006 is estimated at over 17 billion dollars with a growth\nrate of almost 20% year over year. A large part of this\nmarket consists of textual ads, that is, short text messages\nusually marked as sponsored links or similar. The main\nadvertising channels used to distribute textual ads are:\n1. Sponsored Search or Paid Search advertising which\nconsists in placing ads on the result pages from a web\nsearch engine, with ads driven by the originating query.\nAll major current web search engines (Google, Yahoo!,\nand Microsoft) support such ads and act\nsimultaneously as a search engine and an ad agency.\n2. Contextual advertising or Context Match which refers\nto the placement of commercial ads within the\ncontent of a generic web page. In contextual advertising\nusually there is a commercial intermediary, called an\nad-network, in charge of optimizing the ad selection\nwith the twin goal of increasing revenue (shared\nbetween publisher and ad-network) and improving user\nexperience. Again, all major current web search\nengines (Google, Yahoo!, and Microsoft) provide such\nad-networking services but there are also many smaller\nplayers.\nThe SS market developed quicker than the CM market,\nand most textual ads are still characterized by bid phrases\nrepresenting those queries where the advertisers would like\nto have their ad displayed. (See [5] for a brief history).\nHowever, today, almost all of the for-profit non-transactional\nweb sites (that is, sites that do not sell anything directly)\nrely at least in part on revenue from context match. CM\nsupports sites that range from individual bloggers and small\nniche communities to large publishers such as major\nnewspapers. Without this model, the web would be a lot smaller!\nThe prevalent pricing model for textual ads is that the\nadvertisers pay a certain amount for every click on the\nadvertisement (pay-per-click or PPC). There are also other\nmodels used: pay-per-impression, where the advertisers pay\nfor the number of exposures of an ad and pay-per-action\nwhere the advertiser pays only if the ad leads to a sale or\nsimilar transaction. For simplicity, we only deal with the\nPPC model in this paper.\nGiven a page, rather than placing generic ads, it seems\npreferable to have ads related to the content to provide a\nbetter user experience and thus to increase the probability\nof clicks. This intuition is supported by the analogy to\nconventional publishing where there are very successful\nmagazines (e.g. Vogue) where a majority of the content is topical\nadvertising (fashion in the case of Vogue) and by user\nstudies that have confirmed that increased relevance increases\nthe number of ad-clicks [4, 13].\nPrevious published approaches estimated the ad relevance\nbased on co-occurrence of the same words or phrases within\nthe ad and within the page (see [7, 8] and Section 3 for\nmore details). However targeting mechanisms based solely\non phrases found within the text of the page can lead to\nproblems: For example, a page about a famous golfer named\nJohn Maytag might trigger an ad for Maytag\ndishwashers since Maytag is a popular brand. Another example\ncould be a page describing the Chevy Tahoe truck (a\npopular vehicle in US) triggering an ad about Lake Tahoe\nvacations. Polysemy is not the only culprit: there is a (maybe\napocryphal) story about a lurid news item about a headless\nbody found in a suitcase triggering an ad for Samsonite\nluggage! In all these examples the mismatch arises from the\nfact that the ads are not appropriate for the context.\nIn order to solve this problem we propose a matching\nmechanism that combines a semantic phase with the\ntraditional keyword matching, that is, a syntactic phase. The\nsemantic phase classifies the page and the ads into a\ntaxonomy of topics and uses the proximity of the ad and page\nclasses as a factor in the ad ranking formula. Hence we\nfavor ads that are topically related to the page and thus avoid\nthe pitfalls of the purely syntactic approach. Furthermore,\nby using a hierarchical taxonomy we allow for the gradual\ngeneralization of the ad search space in the case when there\nare no ads matching the precise topic of the page. For\nexample if the page is about an event in curling, a rare winter\nsport, and contains the words Alpine Meadows, the\nsystem would still rank highly ads for skiing in Alpine Meadows\nas these ads belong to the class skiing which is a sibling\nof the class curling and both of these classes share the\nparent winter sports.\nIn some sense, the taxonomy classes are used to select the\nset of applicable ads and the keywords are used to narrow\ndown the search to concepts that are of too small\ngranularity to be in the taxonomy. The taxonomy contains nodes for\ntopics that do not change fast, for example, brands of digital\ncameras, say Canon. The keywords capture the specificity\nto a level that is more dynamic and granular. In the\ndigital camera example this would correspond to the level of a\nparticular model, say Canon SD450 whose advertising life\nmight be just a few months. Updating the taxonomy with\nnew nodes or even new vocabulary each time a new model\ncomes to the market is prohibitively expensive when we are\ndealing with millions of manufacturers.\nIn addition to increased click through rate (CTR) due to\nincreased relevance, a significant but harder to quantify\nbenefit of the semantic-syntactic matching is that the resulting\npage has a unified feel and improves the user experience. In\nthe Chevy Tahoe example above, the classifier would\nestablish that the page is about cars/automotive and only those\nads will be considered. Even if there are no ads for this\nparticular Chevy model, the chosen ads will still be within the\nautomotive domain.\nTo implement our approach we need to solve a challenging\nproblem: classify both pages and ads within a large\ntaxonomy (so that the topic granularity would be small enough)\nwith high precision (to reduce the probability of mis-match).\nWe evaluated several classifiers and taxonomies and in this\npaper we present results using a taxonomy with close to\n6000 nodes using a variation of the Rocchio\"s classifier [9].\nThis classifier gave the best results in both page and ad\nclassification, and ultimately in ad relevance.\nThe paper proceeds as follows. In the next section we\nreview the basic principles of the contextual advertising.\nSection 3 overviews the related work. Section 4 describes\nthe taxonomy and document classifier that were used for\npage and ad classification. Section 5 describes the\nsemanticsyntactic method. In Section 6 we briefly discuss how to\nsearch efficiently the ad space in order to return the top-k\nranked ads. Experimental evaluation is presented in\nSection 7. Finally, Section 8 presents the concluding remarks.\n2. OVERVIEW OF CONTEXTUAL\nADVERTISING\nContextual advertising is an interplay of four players:\n\u2022 The publisher is the owner of the web pages on which\nthe advertising is displayed. The publisher typically\naims to maximize advertising revenue while providing\na good user experience.\n\u2022 The advertiser provides the supply of ads. Usually\nthe activity of the advertisers are organized around\ncampaigns which are defined by a set of ads with a\nparticular temporal and thematic goal (e.g. sale of digital\ncameras during the holiday season). As in traditional\nadvertising, the goal of the advertisers can be broadly\ndefined as the promotion of products or services.\n\u2022 The ad network is a mediator between the advertiser\nand the publisher and selects the ads that are put on\nthe pages. The ad-network shares the advertisement\nrevenue with the publisher.\n\u2022 Users visit the web pages of the publisher and interact\nwith the ads.\nContextual advertising usually falls into the category of\ndirect marketing (as opposed to brand advertising), that is\nadvertising whose aim is a direct response where the\neffect of an campaign is measured by the user reaction. One\nof the advantages of online advertising in general and\ncontextual advertising in particular is that, compared to the\ntraditional media, it is relatively easy to measure the user\nresponse. Usually the desired immediate reaction is for the\nuser to follow the link in the ad and visit the advertiser\"s\nweb site and, as noted, the prevalent financial model is that\nthe advertiser pays a certain amount for every click on the\nadvertisement (PPC). The revenue is shared between the\npublisher and the network.\nContext match advertising has grown from Sponsored Search\nadvertising, which consists in placing ads on the result pages\nfrom a web search engine, with ads driven by the originating\nquery. In most networks, the amount paid by the advertiser\nfor each SS click is determined by an auction process where\nthe advertisers place bids on a search phrase, and their\nposition in the tower of ads displayed in conjunction with the\nresult is determined by their bid. Thus each ad is\nannotated with one or more bid phrases. The bid phrase has no\ndirect bearing on the ad placement in CM. However, it is a\nconcise description of target ad audience as determined by\nthe advertiser and it has been shown to be an important\nfeature for successful CM ad placement [8]. In addition to\nthe bid phrase, an ad is also characterized by a title usually\ndisplayed in a bold font, and an abstract or creative, which\nis the few lines of text, usually less than 120 characters,\ndisplayed on the page.\nThe ad-network model aligns the interests of the\npublishers, advertisers and the network. In general, clicks bring\nbenefits to both the publisher and the ad network by\nproviding revenue, and to the advertiser by bringing traffic to\nthe target web site. The revenue of the network, given a\npage p, can be estimated as:\nR =\nX\ni=1..k\nP(click|p, ai)price(ai, i)\nwhere k is the number of ads displayed on page p and price(ai, i)\nis the click-price of the current ad ai at position i. The\nprice in this model depends on the set of ads presented on\nthe page. Several models have been proposed to determine\nthe price, most of them based on generalizations of second\nprice auctions. However, for simplicity we ignore the pricing\nmodel and concentrate on finding ads that will maximize the\nfirst term of the product, that is we search for\narg max\ni\nP(click|p, ai)\nFurthermore we assume that the probability of click for a\ngiven ad and page is determined by its relevance score with\nrespect to the page, thus ignoring the positional effect of\nthe ad placement on the page. We assume that this is an\northogonal factor to the relevance component and could be\neasily incorporated in the model.\n3. RELATED WORK\nOnline advertising in general and contextual advertising\nin particular are emerging areas of research. The published\nliterature is very sparse. A study presented in [13] confirms\nthe intuition that ads need to be relevant to the user\"s\ninterest to avoid degrading the user\"s experience and increase\nthe probability of reaction.\nA recent work by Ribeiro-Neto et. al. [8] examines a\nnumber of strategies to match pages to ads based on extracted\nkeywords. The ads and pages are represented as vectors in\na vector space. The first five strategies proposed in that\nwork match the pages and the ads based on the cosine of\nthe angle between the ad vector and the page vector. To\nfind out the important part of the ad, the authors explore\nusing different ad sections (bid phrase, title, body) as a\nbasis for the ad vector. The winning strategy out of the first\nfive requires the bid phrase to appear on the page and then\nranks all such ads by the cosine of the union of all the ad\nsections and the page vectors.\nWhile both pages and ads are mapped to the same space,\nthere is a discrepancy (impendence mismatch) between the\nvocabulary used in the ads and in the pages. Furthermore,\nsince in the vector model the dimensions are determined\nby the number of unique words, plain cosine similarity will\nnot take into account synonyms. To solve this problem,\nRibeiro-Neto et al expand the page vocabulary with terms\nfrom other similar pages weighted based on the overall\nsimilarity of the origin page to the matched page, and show\nimproved matching precision.\nIn a follow-up work [7] the authors propose a method to\nlearn impact of individual features using genetic\nprogramming to produce a matching function. The function is\nrepresented as a tree composed of arithmetic operators and the log\nfunction as internal nodes, and different numerical features\nof the query and ad terms as leafs. The results show that\ngenetic programming finds matching functions that\nsignificantly improve the matching compared to the best method\n(without page side expansion) reported in [8].\nAnother approach to contextual advertising is to reduce it\nto the problem of sponsored search advertising by\nextracting phrases from the page and matching them with the bid\nphrase of the ads. In [14] a system for phrase extraction is\ndescribed that used a variety of features to determine the\nimportance of page phrases for advertising purposes. The\nsystem is trained with pages that have been hand\nannotated with important phrases. The learning algorithm takes\ninto account features based on tf-idf, html meta data and\nquery logs to detect the most important phrases. During\nevaluation, each page phrase up to length 5 is considered\nas potential result and evaluated against a trained classifier.\nIn our work we also experimented with a phrase extractor\nbased on the work reported in [12]. While increasing slightly\nthe precision, it did not change the relative performance of\nthe explored algorithms.\n4. PAGE AND AD CLASSIFICATION\n4.1 Taxonomy Choice\nThe semantic match of the pages and the ads is performed\nby classifying both into a common taxonomy. The\nmatching process requires that the taxonomy provides sufficient\ndifferentiation between the common commercial topics. For\nexample, classifying all medical related pages into one node\nwill not result into a good classification since both sore\nfoot and flu pages will end up in the same node. The\nads suitable for these two concepts are, however, very\ndifferent. To obtain sufficient resolution, we used a taxonomy of\naround 6000 nodes primarily built for classifying commercial\ninterest queries, rather than pages or ads. This taxonomy\nhas been commercially built by Yahoo! US. We will explain\nbelow how we can use the same taxonomy to classify pages\nand ads as well.\nEach node in our source taxonomy is represented as a\ncollection of exemplary bid phrases or queries that correspond\nto that node concept. Each node has on average around 100\nqueries. The queries placed in the taxonomy are high\nvolume queries and queries of high interest to advertisers, as\nindicated by an unusually high cost-per-click (CPC) price.\nThe taxonomy has been populated by human editors\nusing keyword suggestions tools similar to the ones used by\nad networks to suggest keywords to advertisers. After\ninitial seeding with a few queries, using the provided tools a\nhuman editor can add several hundreds queries to a given\nnode. Nevertheless, it has been a significant effort to\ndevelop this 6000-nodes taxonomy and it has required several\nperson-years of work. A similar-in-spirit process for\nbuilding enterprise taxonomies via queries has been presented in\n[6]. However, the details and tools are completely different.\nFigure 1 provides some statistics about the taxonomy used\nin this work.\n4.2 Classification Method\nAs explained, the semantic phase of the matching relies\non ads and pages being topically close. Thus we need to\nclassify pages into the same taxonomy used to classify ads.\nIn this section we overview the methods we used to build a\npage and an ad classifier pair. The detailed description and\nevaluation of this process is outside the scope of this paper.\nGiven the taxonomy of queries (or bid-phrases - we use\nthese terms interchangeably) described in the previous\nsection, we tried three methods to build corresponding page\nand ad classifiers. For the first two methods we tried to\nfind exemplary pages and ads for each concept as follows:\nNumber of Categories By Level\n0\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n1800\n2000\n1 2 3 4 5 6 7 8 9\nLevel\nNumberofCategories\nNumber of Children per Nodes\n0\n50\n100\n150\n200\n250\n300\n350\n400\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\n20\n22\n24\n29\n31\n33\n35\n52\nNumber of Children\nNumberofNodes\nQueries per Node\n0\n500\n1000\n1500\n2000\n2500\n3000\n1\n50\n80\n120\n160\n200\n240\n280\n320\n360\n400\n440\n480\nNumber Queries (up to 500+)\nNumberofNodes\nFigure 1: Taxonomy statistics: categories per level; fanout for non-leaf nodes; and queries per node\nWe generated a page training set by running the queries in\nthe taxonomy over a Web search index and using the top\n10 results after some filtering as documents labeled with the\nquery\"s label. On the ad side we generated a training set\nfor each class by selecting the ads that have a bid phrase\nassigned to this class. Using this training sets we then trained\na hierarchical SVM [2] (one against all between every group\nof siblings) and a log-regression [11] classifier. (The\nsecond method differs from the first in the type of secondary\nfiltering used. This filtering eliminates low content pages,\npages deemed unsuitable for advertising, pages that lead to\nexcessive class confusion, etc.)\nHowever, we obtained the best performance by using the\nthird document classifier, based on the information in the\nsource taxonomy queries only. For each taxonomy node we\nconcatenated all the exemplary queries into a single\nmetadocument. We then used the meta document as a centroid\nfor a nearest-neighbor classifier based on Rocchio\"s\nframework [9] with only positive examples and no relevance\nfeedback. Each centroid is defined as a sum of the tf-idf values\nof each term, normalized by the number of queries in the\nclass\ncj =\n1\n|Cj|\nX\nq\u2208Cj\nq\nq\nwhere cj is the centroid for class Cj; q iterates over the\nqueries in a particular class.\nThe classification is based on the cosine of the angle\nbetween the document d and the centroid meta-documents:\nCmax = arg max\nCj \u2208C\ncj\ncj\n\u00b7\nd\nd\n= arg max\nCj \u2208C\nP\ni\u2208|F | ci\nj\u00b7 di\nqP\ni\u2208|F |(ci\nj)2\nqP\ni\u2208|F |(di)2\nwhere F is the set of features. The score is normalized by\nthe document and class length to produce comparable score.\nThe terms ci\nand di\nrepresent the weight of the ith feature\nin the class centroid and the document respectively. These\nweights are based on the standard tf-idf formula. As the\nscore of the max class is normalized with regard to document\nlength, the scores for different documents are comparable.\nWe conducted tests using professional editors to judge the\nquality of page and ad class assignments. The tests showed\nthat for both ads and pages the Rocchio classifier returned\nthe best results, especially on the page side. This is\nprobably a result of the noise induced by using a search engine\nto machine generate training pages for the SVM and\nlogregression classifiers. It is an area of current investigation\nhow to improve the classification using a noisy training set.\nBased on the test results we decided to use the Rocchio\"s\nclassifier on both the ad and the page side.\n5. SEMANTIC-SYNTACTIC MATCHING\nContextual advertising systems process the content of the\npage, extract features, and then search the ad space to find\nthe best matching ads. Given a page p and a set of ads\nA = {a1 . . . as} we estimate the relative probability of click\nP(click|p, a) with a score that captures the quality of the\nmatch between the page and the ad. To find the best ads\nfor a page we rank the ads in A and select the top few for\ndisplay. The problem can be formally defined as matching\nevery page in the set of all pages P = {p1, . . . ppc} to one or\nmore ads in the set of ads. Each page is represented as a\nset of page sections pi = {pi,1, pi,2 . . . pi,m}. The sections of\nthe page represent different structural parts, such as title,\nmetadata, body, headings, etc. In turn, each section is an\nunordered bag of terms (keywords). A page is represented\nby the union of the terms in each section:\npi = {pws1\n1 , pws1\n2 . . . pwsi\nm}\nwhere pw stands for a page word and the superscript\nindicates the section of each term. A term can be a unigram or\na phrase extracted by a phrase extractor [12].\nSimilarly, we represent each ad as a set of sections a =\n{a1, a2, . . . al}, each section in turn being an unordered set\nof terms:\nai = {aws1\n1 , aws1\n2 . . . awsj\nl }\nwhere aw is an ad word. The ads in our experiments have\n3 sections: title, body, and bid phrase. In this work, to\nproduce the match score we use only the ad/page textual\ninformation, leaving user information and other data for\nfuture work.\nNext, each page and ad term is associated with a weight\nbased on the tf-idf values. The tf value is determined based\non the individual ad sections. There are several choices for\nthe value of idf, based on different scopes. On the ad side,\nit has been shown in previous work that the set of ads of\none campaign provide good scope for the estimation of idf\nthat leads to improved matching results [8]. However, in this\nwork for simplicity we do not take into account campaigns.\nTo combine the impact of the term\"s section and its tf-idf\nscore, the ad/page term weight is defined as:\ntWeight(kwsi\n) = weightSection(Si) \u00b7 tf idf(kw)\nwhere tWeight stands for term weight and weightSection(Si)\nis the weight assigned to a page or ad section. This weight\nis a fixed parameter determined by experimentation.\nEach ad and page is classified into the topical taxonomy.\nWe define these two mappings:\nTax(pi) = {pci1, . . . pciu}\nTax(aj) = {acj1 . . . acjv}\nwhere pc and ac are page and ad classes correspondingly.\nEach assignment is associated with a weight given by the\nclassifier. The weights are normalized to sum to 1:\nX\nc\u2208T ax(xi)\ncWeight(c) = 1\nwhere xi is either a page or an ad, and cWeights(c) is the\nclass weight - normalized confidence assigned by the\nclassifier. The number of classes can vary between different pages\nand ads. This corresponds to the number of topics a page/ad\ncan be associated with and is almost always in the range 1-4.\nNow we define the relevance score of an ad ai and page\npi as a convex combination of the keyword (syntactic) and\nclassification (semantic) score:\nScore(pi, ai) = \u03b1 \u00b7 TaxScore(Tax(pi), Tax(ai))\n+(1 \u2212 \u03b1) \u00b7 KeywordScore(pi, ai)\nThe parameter \u03b1 determines the relative weight of the\ntaxonomy score and the keyword score.\nTo calculate the keyword score we use the vector space\nmodel [1] where both the pages and ads are represented\nin n-dimensional space - one dimension for each distinct\nterm. The magnitude of each dimension is determined by\nthe tWeight() formula. The keyword score is then defined as\nthe cosine of the angle between the page and the ad vectors:\nKeywordScore(pi, ai)\n=\nP\ni\u2208|K| tWeight(pwi)\u00b7 tWeight(awi)\nqP\ni\u2208|K|(tWeight(pwi))2\nqP\ni\u2208|K|(tWeight(awi))2\nwhere K is the set of all the keywords. The formula\nassumes independence between the words in the pages and\nads. Furthermore, it ignores the order and the proximity of\nthe terms in the scoring. We experimented with the impact\nof phrases and proximity on the keyword score and did not\nsee a substantial impact of these two factors.\nWe now turn to the definition of the TaxScore. This\nfunction indicates the topical match between a given ad and\na page. As opposed to the keywords that are treated as\nindependent dimensions, here the classes (topics) are\norganized into a hierarchy. One of the goals in the design of\nthe TaxScore function is to be able to generalize within the\ntaxonomy, that is accept topically related ads.\nGeneralization can help to place ads in cases when there is no ad that\nmatches both the category and the keywords of the page.\nThe example in Figure 2 illustrates this situation. In this\nexample, in the absence of ski ads, a page about skiing\ncontaining the word Atomic could be matched to the available\nsnowboarding ad for the same brand.\nIn general we would like the match to be stronger when\nboth the ad and the page are classified into the same node\nFigure 2: Two generalization paths\nand weaker when the distance between the nodes in the\ntaxonomy gets larger. There are multiple ways to specify the\ndistance between two taxonomy nodes. Besides the above\nrequirement, this function should lend itself to an efficient\nsearch of the ad space. Given a page we have to find the\nad in a few milliseconds, as this impacts the presentation to\na waiting user. This will be further discussed in the next\nsection.\nTo capture both the generalization and efficiency\nrequirements we define the TaxScore function as follows:\nTaxScore(PC, AC) =\nX\npc\u2208P C\nX\nac\u2208AC\nidist(LCA(pc, ac), ac)\u00b7cWeight(pc)\u00b7cWeight(ac)\nIn this function we consider every combination of page class\nand ad class. For each combination we multiply the product\nof the class weights with the inverse distance function\nbetween the least common ancestor of the two classes (LCA)\nand the ad class. The inverse distance function idist(c1, c2)\ntakes two nodes on the same path in the class taxonomy\nand returns a number in the interval [0, 1] depending on the\ndistance of the two class nodes. It returns 1 if the two nodes\nare the same, and declines toward 0 when LCA(pc, ac) or ac\nis the root of the taxonomy. The rate of decline determines\nthe weight of the generalization versus the other terms in\nthe scoring formula.\nTo determine the rate of decline we consider the impact\non the specificity of the match when we substitute a class\nwith one of its ancestors. In general the impact is topic\ndependent. For example the node Hobby in our taxonomy\nhas tens of children, each representing a different hobby, two\nexamples being Sailing and Knitting. Placing an ad\nabout Knitting on a page about Sailing does not make\nlots of sense. However, in the Winter Sports example\nabove, in the absence of better alternative, skiing ads could\nbe put on snowboarding pages as they might promote the\nsame venues, equipment vendors etc. Such detailed analysis\non a case by case basis is prohibitively expensive due to the\nsize of the taxonomy.\nOne option is to use the confidences of the ancestor classes\nas given by the classifier. However we found these\nnumbers not suitable for this purpose as the magnitude of the\nconfidences does not necessarily decrease when going up the\ntree. Another option is to use explore-exploit methods based\non machine-learning from the click feedback as described\nin [10]. However for simplicity, in this work we chose a\nsimple heuristic to determine the cost of generalization from a\nchild to a parent. In this heuristic we look at the\nbroadening of the scope when moving from a child to a parent. We\nestimate the broadening by the density of ads classified in\nthe parent nodes vs the child node. The density is obtained\nby classifying a large set of ads in the taxonomy using the\ndocument classifier described above. Based on this, let nc\nbe the number of document classified into the subtree rooted\nat c. Then we define:\nidist(c, p) =\nnc\nnp\nwhere c represents the child node and p is the parent node.\nThis fraction can be viewed as a probability of an ad\nbelonging to the parent topic being suitable for the child topic.\n6. SEARCHING THE AD SPACE\nIn the previous section we discussed the choice of scoring\nfunction to estimate the match between an ad and a page.\nThe top-k ads with the highest score are offered by the\nsystem for placement on the publisher\"s page. The process of\nscore calculation and ad selection is to be done in real time\nand therefore must be very efficient. As the ad collections\nare in the range of hundreds of millions of entries, there is a\nneed for indexed access to the ads.\nInverted indexes provide scalable and low latency\nsolutions for searching documents. However, these have been\ntraditionally used to search based on keywords. To be able\nto search the ads on a combination of keywords and classes\nwe have mapped the classification match to term match and\nadapted the scoring function to be suitable for fast\nevaluation over inverted indexes. In this section we overview the\nad indexing and the ranking function of our prototype ad\nsearch system for matching ads and pages.\nWe used a standard inverted index framework where there\nis one posting list for each distinct term. The ads are parsed\ninto terms and each term is associated with a weight based\non the section in which it appears. Weights from distinct\noccurrences of a term in an ad are added together, so that\nthe posting lists contain one entry per term/ad combination.\nThe next challenge is how to index the ads so that the class\ninformation is preserved in the index? A simple method is to\ncreate unique meta-terms for the classes and annotate each\nad with one meta-term for each assigned class. However\nthis method does not allow for generalization, since only the\nads matching an exact label of the page would be selected.\nTherefore we annotated each ad with one meta-term for each\nancestor of the assigned class. The weights of meta-terms\nare assigned according to the value of the idist() function\ndefined in the previous section. On the query side, given the\nkeywords and the class of a page, we compose a keyword only\nquery by inserting one class term for each ancestor of the\nclasses assigned to the page.\nThe scoring function is adapted to the two part\nscoreone for the class meta-terms and another for the text term.\nDuring the class score calculation, for each class path we use\nonly the lowest class meta-term, ignoring the others. For\nexample, if an ad belongs to the Skiing class and is\nannotated with both Skiing and its parent Winter Sports,\nthe index will contain the special class meta-terms for both\nSkiing and Winter Sports (and all their ancestors) with\nthe weights according to the product of the classifier\nconfidence and the idist function. When matching with a page\nclassified into Skiing, the query will contain terms for class\nSkiing and for each of its ancestors. However when scoring\nan ad classified into Skiing we will use the weight for the\nSkiing class meta-term. Ads classified into\nSnowboarding will be scored using the weight of the Winter Sports\nmeta-term. To make this check efficiently we keep a sorted\nlist of all the class paths and, at scoring time, we search the\npaths bottom up for a meta-term appearing in the ad. The\nfirst meta-term is used for scoring, the rest are ignored.\nAt runtime, we evaluate the query using a variant of the\nWAND algorithm [3]. This is a document-at-a-time\nalgorithm [1] that uses a branch-and-bound approach to derive\nefficient moves for the cursors associated to the postings\nlists. It finds the next cursor to be moved based on an\nupper bound of the score for the documents at which the\ncursors are currently positioned. The algorithm keeps a heap of\ncurrent best candidates. Documents with an upper bound\nsmaller than the current minimum score among the\ncandidate documents can be eliminated from further\nconsiderations, and thus the cursors can skip over them. To find the\nupper bound for a document, the algorithm assumes that all\ncursors that are before it will hit this document (i.e. the\ndocument contains all those terms represented by cursors before\nor at that document). It has been shown that WAND can\nbe used with any function that is monotonic with respect to\nthe number of matching terms in the document.\nOur scoring function is monotonic since the score can\nnever decrease when more terms are found in the document.\nIn the special case when we add a cursor representing an\nancestor of a class term already factored in the score, the\nscore simply does not change (we add 0). Given these\nproperties, we use an adaptation of the WAND algorithm where\nwe change the calculation of the scoring function and the\nupper bound score calculation to reflect our scoring function.\nThe rest of the algorithm remains unchanged.\n7. EXPERIMENTAL EVALUATION\n7.1 Data and Methodology\nWe quantify the effect of the semantic-syntactic matching\nusing a set of 105 pages. This set of pages was selected\nby a random sample of a larger set of around 20 million\npages with contextual advertising. Ads for each of these\npages have been selected from a larger pool of ads (tens of\nmillions) by previous experiments conducted by Yahoo! US\nfor other purposes. Each page-ad pair has been judged by\nthree or more human judges on a 1 to 3 scale:\n1. Relevant The ad is semantically directly related to\nthe main subject of the page. For example if the page\nis about the National Football League and the ad is\nabout tickets for NFL games, it would be scored as 1.\n2. Somewhat relevant The ad is related to the\nsecondary subject of the page, or is related to the main\ntopic of the page in a general way. In the NFL page\nexample, an ad about NFL branded products would\nbe judged as 2.\n3. Irrelevant The ad is unrelated to the page. For\nexample a mention of the NFL player John Maytag triggers\nwashing machine ads on a NFL page.\npages 105\nwords per page 868\njudgments 2946\njudg. inter-editor agreement 84%\nunique ads 2680\nunique ads per page 25.5\npage classification precision 70%\nad classification precision 86%\nTable 1: Dataset statistics\nTo obtain a score for a page-ad pair we average all the scores\nand then round to the closest integer. We then used these\njudgments to evaluate how well our methods distinguish the\npositive and the negative ad assignments for each page. The\nstatistics of the page dataset is given in Table 1.\nThe original experiments that paired the pages and the\nads are loosely related to the syntactic keyword based\nmatching and classification based assignment but used different\ntaxonomies and keyword extraction techniques. Therefore\nwe could not use standard pooling as an evaluation method\nsince we did not control the way the pairs were selected and\ncould not precisely establish the set of ads from which the\nplaced ads were selected.\nInstead, in our evaluation for each page we consider only\nthose ads for which we have judgment. Each different method\nwas applied to this set and the ads were ranked by the score.\nThe relative effectiveness of the algorithms were judged by\ncomparing how well the methods separated the ads with\npositive judgment from the ads with negative judgment. We\npresent precision on various levels of recall within this set.\nAs the set of ads per page is relatively small, the evaluation\nreports precision that is higher than it would be with a larger\nset of negative ads. However, these numbers still establish\nthe relative performance of the algorithms and we can use\nit to evaluate performance at different score thresholds.\nIn addition to the precision-recall over the judged ads,\nwe also present Kendall\"s \u03c4 rank correlation coefficient to\nestablish how far from the perfect ordering are the orderings\nproduced by our ranking algorithms. For this test we ranked\nthe judged ads by the scores assigned by the judges and then\ncompared this order to the order assigned by our algorithms.\nFinally we also examined the precision at position 1, 3 and\n5.\n7.2 Results\nFigure 3 shows the precision recall curves for the\nsyntactic matching (keywords only used) vs. a syntactic-semantic\nmatching with the optimal value of \u03b1 = 0.8 (judged by the\n11-point score [1]). In this figure, we assume that the\nadpage pairs judged with 1 or 2 are positive examples and the\n3s are negative examples. We also examined counting only\nthe pairs judged with 1 as positive examples and did not\nfind a significant change in the relative performance of the\ntested methods. Overlaid are also results using phrases in\nthe keyword match. We see that these additional features\ndo not change the relative performance of the algorithm.\nThe graphs show significant impact of the class\ninformation, especially in the mid range of recall values. In the\nlow recall part of the chart the curves meet. This indicates\nthat when the keyword match is really strong (i.e. when\nthe ad is almost contained within the page) the precision\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n0 0.2 0.4 0.6 0.8 1\nRecall\nPrecision\nAlpha=.9, no phrase Alpha=0, no phrase\nAlpha=0, phrase Alpha=.9, phrase\nFigure 3: Data Set 2: Precision vs. Recall of\nsyntactic match (\u03b1 = 0) vs. syntactic-semantic match\n(\u03b1 = 0.8)\n\u03b1 Kendall\"s \u03c4\n\u03b1 = 0 0.086\n\u03b1 = 0.25 0.155\n\u03b1 = 0.50 0.166\n\u03b1 = 0.75 0.158\n\u03b1 = 1 0.136\nTable 2: Kendall\"s \u03c4 for different \u03b1 values\nof the syntactic keyword match is comparable with that of\nthe semantic-syntactic match. Note however that the two\nmethods might produce different ads and could be used as\na complement at level of recall.\nThe semantic components provides largest lift in\nprecision at the mid range of recall where 25% improvement is\nachieved by using the class information for ad placement.\nThis means that when there is somewhat of a match\nbetween the ad and the page, the restriction to the right classes\nprovides a better scope for selecting the ads.\nTable 2 shows the Kendall\"s \u03c4 values for different values of\n\u03b1. We calculated the values by ranking all the judged ads for\neach page and averaging the values over all the pages. The\nads with tied judgment were given the rank of the middle\nposition. The results show that when we take into account\nall the ad-page pairs, the optimal value of \u03b1 is around 0.5.\nNote that purely syntactic match (\u03b1 = 0) is by far the\nweakest method.\nFigure 4 shows the effect of the parameter \u03b1 in the scoring.\nWe see that in most cases precision grows or is flat when we\nincrease \u03b1, except at the low level of recall where due to\nsmall number of data points there is a bit of jitter in the\nresults.\nTable 3 shows the precision at positions 1, 3 and 5. Again,\nthe purely syntactic method has clearly the lowest score by\nindividual positions and the total number of correctly placed\nads. The numbers are close due to the small number of the\nads considered, but there are still some noticeable trends.\nFor position 1 the optimal \u03b1 is in the range of 0.25 to 0.75.\nFor positions 3 and 5 the optimum is at \u03b1 = 1. This also\nindicates that for those ads that have a very high keyword\nscore, the semantic information is somewhat less important.\nIf almost all the words in an ad appear in the page, this ad is\nPrecision Vs Alpha for Different Levels of Recall\n(Data Set 2)\n0.45\n0.55\n0.65\n0.75\n0.85\n0.95\n0 0.2 0.4 0.6 0.8 1\nAlpha\nPrecision\n80% Recall 60% Recall 40% Recall 20% Recall\nFigure 4: Impact of \u03b1 on precision for different levels\nof recall\n\u03b1 #1 #3 #5 sum\n\u03b1 = 0 80 70 68 218\n\u03b1 = 0.25 89 76 73 238\n\u03b1 = 0.5 89 74 73 236\n\u03b1 = 0.75 89 78 73 240\n\u03b1 = 1 86 79 74 239\nTable 3: Precision at position 1, 3 and 5\nlikely to be relevant for this page. However when there is no\nsuch clear affinity, the class information becomes a dominant\nfactor.\n8. CONCLUSION\nContextual advertising is the economic engine behind a\nlarge number of non-transactional sites on the Web. Studies\nhave shown that one of the main success factors for\ncontextual ads is their relevance to the surrounding content. All\nexisting commercial contextual match solutions known to us\nevolved from search advertising solutions whereby a search\nquery is matched to the bid phrase of the ads. A natural\nextension of search advertising is to extract phrases from the\npage and match them to the bid phrase of the ads. However,\nindividual phrases and words might have multiple meanings\nand/or be unrelated to the overall topic of the page leading\nto miss-matched ads.\nIn this paper we proposed a novel way of matching\nadvertisements to web pages that rely on a topical (semantic)\nmatch as a major component of the relevance score. The\nsemantic match relies on the classification of pages and ads\ninto a 6000 nodes commercial advertising taxonomy to\ndetermine their topical distance. As the classification relies\non the full content of the page, it is more robust than\nindividual page phrases. The semantic match is complemented\nwith a syntactic match and the final score is a convex\ncombination of the two sub-scores with the relative weight of\neach determined by a parameter \u03b1.\nWe evaluated the semantic-syntactic approach against a\nsyntactic approach over a set of pages with different\ncontextual advertising. As shown in our experimental evaluation,\nthe optimal value of the parameter \u03b1 depends on the precise\nobjective of optimization (precision at particular position,\nprecision at given recall). However in all cases the optimal\nvalue of \u03b1 is between 0.25 and 0.9 indicating significant effect\nof the semantic score component. The effectiveness of the\nsyntactic match depends on the quality of the pages used. In\nlower quality pages we are more likely to make classification\nerrors that will then negatively impact the matching. We\ndemonstrated that it is feasible to build a large scale\nclassifier that has sufficient good precision for this application.\nWe are currently examining how to employ machine\nlearning algorithms to learn the optimal value of \u03b1 based on a\ncollection of features of the input pages.\n9. REFERENCES\n[1] R. Baeza-Yates and B. Ribeiro-Neto. Modern Information\nRetrieval. ACM, 1999.\n[2] Bernhard E. Boser, Isabelle Guyon, and Vladimir Vapnik.\nA training algorithm for optimal margin classifiers. In\nComputational Learning Theory, pages 144-152, 1992.\n[3] A. Z. Broder, D. Carmel, M. Herscovici, A. Soffer, and\nJ. Zien. Efficient query evaluation using a two-level\nretrieval process. In CIKM \"03: Proc. of the twelfth intl.\nconf. on Information and knowledge management, pages\n426-434, New York, NY, 2003. ACM.\n[4] P. Chatterjee, D. L. Hoffman, and T. P. Novak. Modeling\nthe clickstream: Implications for web-based advertising\nefforts. Marketing Science, 22(4):520-541, 2003.\n[5] D. Fain and J. Pedersen. Sponsored search: A brief history.\nIn In Proc. of the Second Workshop on Sponsored Search\nAuctions, 2006. Web publication, 2006.\n[6] S. C. Gates, W. Teiken, and K.-Shin F. Cheng. Taxonomies\nby the numbers: building high-performance taxonomies. In\nCIKM \"05: Proc. of the 14th ACM intl. conf. on\nInformation and knowledge management, pages 568-577,\nNew York, NY, 2005. ACM.\n[7] A. Lacerda, M. Cristo, M. Andre; G., W. Fan, N. Ziviani,\nand B. Ribeiro-Neto. Learning to advertise. In SIGIR \"06:\nProc. of the 29th annual intl. ACM SIGIR conf., pages\n549-556, New York, NY, 2006. ACM.\n[8] B. Ribeiro-Neto, M. Cristo, P. B. Golgher, and E. S.\nde Moura. Impedance coupling in content-targeted\nadvertising. In SIGIR \"05: Proc. of the 28th annual intl.\nACM SIGIR conf., pages 496-503, New York, NY, 2005.\nACM.\n[9] J. Rocchio. Relevance feedback in information retrieval. In\nThe SMART Retrieval System: Experiments in Automatic\nDocument Processing, pages 313-323. PrenticeHall, 1971.\n[10] P. Sandeep, D. Agarwal, D. Chakrabarti, and V. Josifovski.\nBandits for taxonomies: A model-based approach. In In\nProc. of the SIAM intl. conf. on Data Mining, 2007.\n[11] T. Santner and D. Duffy. The Statistical Analysis of\nDiscrete Data. Springer-Verlag, 1989.\n[12] R. Stata, K. Bharat, and F. Maghoul. The term vector\ndatabase: fast access to indexing terms for web pages.\nComputer Networks, 33(1-6):247-255, 2000.\n[13] C. Wang, P. Zhang, R. Choi, and M. D. Eredita.\nUnderstanding consumers attitude toward advertising. In\nEighth Americas conf. on Information System, pages\n1143-1148, 2002.\n[14] W. Yih, J. Goodman, and V. R. Carvalho. Finding\nadvertising keywords on web pages. In WWW \"06: Proc. of\nthe 15th intl. conf. on World Wide Web, pages 213-222,\nNew York, NY, 2006. ACM.", "keywords": "pay-per-click;semantics;contextual advertising;matching mechanism;semantic-syntactic matching;match;keyword matching;document classifier;ad relevance;contextual advertise;topical distance;top-k ad;hierarchical taxonomy class"}
{"name": "train_H-48", "title": "A New Approach for Evaluating Query Expansion: Query-Document Term Mismatch", "abstract": "The effectiveness of information retrieval (IR) systems is influenced by the degree of term overlap between user queries and relevant documents. Query-document term mismatch, whether partial or total, is a fact that must be dealt with by IR systems. Query Expansion (QE) is one method for dealing with term mismatch. IR systems implementing query expansion are typically evaluated by executing each query twice, with and without query expansion, and then comparing the two result sets. While this measures an overall change in performance, it does not directly measure the effectiveness of IR systems in overcoming the inherent issue of term mismatch between the query and relevant documents, nor does it provide any insight into how such systems would behave in the presence of query-document term mismatch. In this paper, we propose a new approach for evaluating query expansion techniques. The proposed approach is attractive because it provides an estimate of system performance under varying degrees of query-document term mismatch, it makes use of readily available test collections, and it does not require any additional relevance judgments or any form of manual processing.", "fulltext": "1. INTRODUCTION\nIn our domain,1\nand unlike web search, it is very\nimportant for attorneys to find all documents (e.g., cases) that\nare relevant to an issue. Missing relevant documents may\nhave non-trivial consequences on the outcome of a court\nproceeding. Attorneys are especially concerned about missing\nrelevant documents when researching a legal topic that is\nnew to them, as they may not be aware of all language\nvariations in such topics. Therefore, it is important to develop\ninformation retrieval systems that are robust with respect to\nlanguage variations or term mismatch between queries and\nrelevant documents. During our work on developing such\nsystems, we concluded that current evaluation methods are\nnot sufficient for this purpose.\n{Whooping cough, pertussis}, {heart attack, myocardial\ninfarction}, {car wash, automobile cleaning}, {attorney,\nlegal counsel, lawyer} are all examples of things that share\nthe same meaning. Often, the terms chosen by users in their\nqueries are different than those appearing in the documents\nrelevant to their information needs. This query-document\nterm mismatch arises from two sources: (1) the synonymy\nfound in natural language, both at the term and the phrasal\nlevel, and (2) the degree to which the user is an expert at\nsearching and/or has expert knowledge in the domain of the\ncollection being searched.\nIR evaluations are comparative in nature (cf. TREC).\nGenerally, IR evaluations show how System A did in\nrelation to System B on the same test collection based on various\nprecision- and recall-based metrics. Similarly, IR systems\nwith QE capabilities are typically evaluated by executing\neach search twice, once with and once without query\nexpansion, and then comparing the two result sets. While this\napproach shows which system may have performed better\noverall with respect to a particular test collection, it does\nnot directly or systematically measure the effectiveness of\nIR systems in overcoming query-document term mismatch.\nIf the goal of QE is to increase search performance by\nmitigating the effects of query-document term mismatch, then\nthe degree to which a system does so should be measurable\nin evaluation. An effective evaluation method should\nmeasure the performance of IR systems under varying degrees of\nquery-document term mismatch, not just in terms of overall\nperformance on a collection relative to another system.\n1\nThomson Corporation builds information based solutions\nto the professional markets including legal, financial, health\ncare, scientific, and tax and accounting.\nIn order to measure that a particular IR system is able\nto overcome query-document term mismatch by retrieving\ndocuments that are relevant to a user\"s query, but that do\nnot necessarily contain the query terms themselves, we\nsystematically introduce term mismatch into the test collection\nby removing query terms from known relevant documents.\nBecause we are purposely inducing term mismatch between\nthe queries and known relevant documents in our test\ncollections, the proposed evaluation framework is able to measure\nthe effectiveness of QE in a way that testing on the whole\ncollection is not. If a QE search method finds a document\nthat is known to be relevant but that is nonetheless missing\nquery terms, it shows that QE technique is indeed robust\nwith respect to query-document term mismatch.\n2. RELATED WORK\nAccounting for term mismatch between the terms in user\nqueries and the documents relevant to users\" information\nneeds has been a fundamental issue in IR research for\nalmost 40 years [38, 37, 47]. Query expansion (QE) is one\ntechnique used in IR to improve search performance by\nincreasing the likelihood of term overlap (either explicitly or\nimplicitly) between queries and documents that are relevant\nto users\" information needs. Explicit query expansion\noccurs at run-time, based on the initial search results, as is\nthe case with relevance feedback and pseudo relevance\nfeedback [34, 37]. Implicit query expansion can be based on\nstatistical properties of the document collection, or it may\nrely on external knowledge sources such as a thesaurus or an\nontology [32, 17, 26, 50, 51, 2]. Regardless of method, QE\nalgorithms that are capable of retrieving relevant documents\ndespite partial or total term mismatch between queries and\nrelevant documents should increase the recall of IR systems\n(by retrieving documents that would have previously been\nmissed) as well as their precision (by retrieving more\nrelevant documents).\nIn practice, QE tends to improve the average overall\nretrieval performance, doing so by improving performance on\nsome queries while making it worse on others. QE\ntechniques are judged as effective in the case that they help\nmore than they hurt overall on a particular collection [47,\n45, 41, 27]. Often, the expansion terms added to a query\nin the query expansion phase end up hurting the overall\nretrieval performance because they introduce semantic noise,\ncausing the meaning of the query to drift. As such, much\nwork has been done with respect to different strategies for\nchoosing semantically relevant QE terms to include in order\nto avoid query drift [34, 50, 51, 18, 24, 29, 30, 32, 3, 4, 5].\nThe evaluation of IR systems has received much attention\nin the research community, both in terms of developing test\ncollections for the evaluation of different systems [11, 12, 13,\n43] and in terms of the utility of evaluation metrics such as\nrecall, precision, mean average precision, precision at rank,\nBpref, etc. [7, 8, 44, 14]. In addition, there have been\ncomparative evaluations of different QE techniques on various\ntest collections [47, 45, 41].\nIn addition, the IR research community has given\nattention to differences between the performance of individual\nqueries. Research efforts have been made to predict which\nqueries will be improved by QE and then selectively\napplying it only to those queries [1, 5, 27, 29, 15, 48], to achieve\noptimal overall performance. In addition, related work on\npredicting query difficulty, or which queries are likely to\nperform poorly, has been done [1, 4, 5, 9]. There is general\ninterest in the research community to improve the\nrobustness of IR systems by improving retrieval performance on\ndifficult queries, as is evidenced by the Robust track in the\nTREC competitions and new evaluation measures such as\nGMAP. GMAP (geometric mean average precision) gives\nmore weight to the lower end of the average precision (as\nopposed to MAP), thereby emphasizing the degree to which\ndifficult or poorly performing queries contribute to the score\n[33].\nHowever, no attention is given to evaluating the\nrobustness of IR systems implementing QE with respect to\nquerydocument term mismatch in quantifiable terms. By\npurposely inducing mismatch between the terms in queries and\nrelevant documents, our evaluation framework allows us a\ncontrolled manner in which to degrade the quality of the\nqueries with respect to their relevant documents, and then\nto measure the both the degree of (induced) difficulty of the\nquery and the degree to which QE improves the retrieval\nperformance of the degraded query.\nThe work most similar to our own in the literature consists\nof work in which document collections or queries are altered\nin a systematic way to measure differences query\nperformance. [42] introduces into the document collection\npseudowords that are ambiguous with respect to word sense, in\norder to measure the degree to which word sense\ndisambiguation is useful in IR. [6] experiments with altering the\ndocument collection by adding semantically related expansion\nterms to documents at indexing time. In cross-language IR,\n[28] explores different query expansion techniques while\npurposely degrading their translation resources, in what amounts\nto expanding a query with only a controlled percentage of\nits translation terms. Although similar in introducing a\ncontrolled amount of variance into their test collections, these\nworks differ from the work being presented in this paper\nin that the work being presented here explicitly and\nsystematically measures query effectiveness in the presence of\nquery-document term mismatch.\n3. METHODOLOGY\nIn order to accurately measure IR system performance in\nthe presence of query-term mismatch, we need to be able\nto adjust the degree of term mismatch in a test corpus in\na principled manner. Our approach is to introduce\nquerydocument term mismatch into a corpus in a controlled\nmanner and then measure the performance of IR systems as\nthe degree of term mismatch changes. We systematically\nremove query terms from known relevant documents,\ncreating alternate versions of a test collection that differ only in\nhow many or which query terms have been removed from\nthe documents relevant to a particular query. Introducing\nquery-document term mismatch into the test collection in\nthis manner allows us to manipulate the degree of term\nmismatch between relevant documents and queries in a\ncontrolled manner.\nThis removal process affects only the relevant documents\nin the search collection. The queries themselves remain\nunaltered. Query terms are removed from documents one by\none, so the differences in IR system performance can be\nmeasured with respect to missing terms. In the most extreme\ncase (i.e., when the length of the query is less than or equal\nto the number of query terms removed from the relevant\ndocuments), there will be no term overlap between a query\nand its relevant documents. Notice that, for a given query,\nonly relevant documents are modified. Non-relevant\ndocuments are left unchanged, even in the case that they contain\nquery terms.\nAlthough, on the surface, we are changing the\ndistribution of terms between the relevant and non-relevant\ndocuments sets by removing query terms from the relevant\ndocuments, doing so does not change the conceptual relevancy\nof these documents. Systematically removing query terms\nfrom known relevant documents introduces a controlled amount\nof query-document term mismatch by which we can\nevaluate the degree to which particular QE techniques are able\nto retrieve conceptually relevant documents, despite a lack\nof actual term overlap. Removing a query term from\nrelevant documents simply masks the presence of that query\nterm in those documents. It does not in any way change the\nconceptual relevancy of the documents.\nThe evaluation framework presented in this paper consists\nof three elements: a test collection, C; a strategy for selecting\nwhich query terms to remove from the relevant documents in\nthat collection, S; and a metric by which to compare\nperformance of the IR systems, m. The test collection, C, consists\nof a document collection, queries, and relevance judgments.\nThe strategy, S, determines the order and manner in which\nquery terms are removed from the relevant documents in C.\nThis evaluation framework is not metric-specific; any metric\n(MAP, P@10, recall, etc.) can be used to measure IR system\nperformance.\nAlthough test collections are difficult to come by, it should\nbe noted that this evaluation framework can be used on\nany available test collection. In fact, using this framework\nstretches the value of existing test collections in that one\ncollection becomes several when query terms are removed from\nrelevant documents, thereby increasing the amount of\ninformation that can be gained from evaluating on a particular\ncollection.\nIn other evaluations of QE effectiveness, the controlled\nvariable is simply whether or not queries have been\nexpanded or not, compared in terms of some metric. In\ncontrast, the controlled variable in this framework is the query\nterm that has been removed from the documents relevant to\nthat query, as determined by the removal strategy, S. Query\nterms are removed one by one, in a manner and order\ndetermined by S, so that collections differ only with respect\nto the one term that has been removed (or masked) in the\ndocuments relevant to that query. It is in this way that we\ncan explicitly measure the degree to which an IR system\novercomes query-document term mismatch.\nThe choice of a query term removal strategy is relatively\nflexible; the only restriction in choosing a strategy S is that\nquery terms must be removed one at a time. Two\ndecisions must be made when choosing a removal strategy S.\nThe first is the order in which S removes terms from the\nrelevant documents. Possible orders for removal could be\nbased on metrics such as IDF or the global probability of a\nterm in a document collection. Based on the purpose of the\nevaluation and the retrieval algorithm being used, it might\nmake more sense to choose a removal order for S based on\nquery term IDF or perhaps based on a measure of query\nterm probability in the document collection.\nOnce an order for removal has been decided, a manner for\nterm removal/masking must be decided. It must be\ndetermined if S will remove the terms individually (i.e., remove\njust one different term each time) or additively (i.e., remove\none term first, then that term in addition to another, and so\non). The incremental additive removal of query terms from\nrelevant documents allows the evaluation to show the\ndegree to which IR system performance degrades as more and\nmore query terms are missing, thereby increasing the degree\nof query-document term mismatch. Removing terms\nindividually allows for a clear comparison of the contribution of\nQE in the absence of each individual query term.\n4. EXPERIMENTAL SET-UP\n4.1 IR Systems\nWe used the proposed evaluation framework to evaluate\nfour IR systems on two test collections. Of the four\nsystems used in the evaluation, two implement query\nexpansion techniques: Okapi (with pseudo-feedback for QE), and\na proprietary concept search engine (we\"ll call it TCS, for\nThomson Concept Search). TCS is a language modeling\nbased retrieval engine that utilizes a subject-appropriate\nexternal corpus (i.e., legal or news) as a knowledge source.\nThis external knowledge source is a corpus separate from,\nbut thematically related to, the document collection to be\nsearched. Translation probabilities for QE [2] are calculated\nfrom these large external corpora.\nOkapi (without feedback) and a language model query\nlikelihood (QL) model (implemented using Indri) are\nincluded as keyword-only baselines. Okapi without feedback\nis intended as an analogous baseline for Okapi with\nfeedback, and the QL model is intended as an appropriate\nbaseline for TCS, as they both implement language-modeling\nbased retrieval algorithms. We choose these as baselines\nbecause they are dependent only on the words appearing in\nthe queries and have no QE capabilities. As a result, we\nexpect that when query terms are removed from relevant\ndocuments, the performance of these systems should degrade\nmore dramatically than their counterparts that implement\nQE.\nThe Okapi and QL model results were obtained using the\nLemur Toolkit.2\nOkapi was run with the parameters k1=1.2,\nb=0.75, and k3=7. When run with feedback, the feedback\nparameters used in Okapi were set at 10 documents and 25\nterms. The QL model used Jelinek-Mercer smoothing, with\n\u03bb = 0.6.\n4.2 Test Collections\nWe evaluated the performance of the four IR systems\noutlined above on two different test collections. The two test\ncollections used were the TREC AP89 collection (TIPSTER\ndisk 1) and the FSupp Collection.\nThe FSupp Collection is a proprietary collection of 11,953\ncase law documents for which we have 44 queries (ranging\nfrom four to twenty-two words after stop word removal) with\nfull relevance judgments.3\nThe average length of documents\nin the FSupp Collection is 3444 words.\n2\nwww.lemurproject.org\n3\nEach of the 11,953 documents was evaluated by domain\nexperts with respect to each of the 44 queries.\nThe TREC AP89 test collection contains 84,678\ndocuments, averaging 252 words in length. In our evaluation, we\nused both the title and the description fields of topics\n151200 as queries, so we have two sets of results for the AP89\nCollection. After stop word removal, the title queries range\nfrom two to eleven words and the description queries range\nfrom four to twenty-six terms.\n4.3 Query Term Removal Strategy\nIn our experiments, we chose to sequentially and\nadditively remove query terms from highest-to-lowest inverse\ndocument frequency (IDF) with respect to the entire\ndocument collection. Terms with high IDF values tend to\ninfluence document ranking more than those with lower IDF\nvalues. Additionally, high IDF terms tend to be\ndomainspecific terms that are less likely to be known to non-expert\nuser, hence we start by removing these first.\nFor the FSupp Collection, queries were evaluated\nincrementally with one, two, three, five, and seven terms\nremoved from their corresponding relevant documents. The\nlonger description queries from TREC topics 151-200 were\nlikewise evaluated on the AP89 Collection with one, two,\nthree, five, and seven query terms removed from their\nrelevant documents. For the shorter TREC title queries, we\nremoved one, two, three, and five terms from the relevant\ndocuments.\n4.4 Metrics\nIn this implementation of the evaluation framework, we\nchose three metrics by which to compare IR system\nperformance: mean average precision (MAP), precision at 10\ndocuments (P10), and recall at 1000 documents. Although\nthese are the metrics we chose to demonstrate this\nframework, any appropriate IR metrics could be used within the\nframework.\n5. RESULTS\n5.1 FSupp Collection\nFigures 1, 2, and 3 show the performance (in terms of\nMAP, P10 and Recall, respectively) for the four search\nengines on the FSupp Collection. As expected, the\nperformance of the keyword-only IR systems, QL and Okapi, drops\nquickly as query terms are removed from the relevant\ndocuments in the collection. The performance of Okapi with\nfeedback (Okapi FB) is somewhat surprising in that on the\noriginal collection (i.e., prior to query term removal), its\nperformance is worse than that of Okapi without feedback on\nall three measures.\nTCS outperforms the QL keyword baseline on every\nmeasure except for MAP on the original collection (i.e., prior\nto removing any query terms). Because TCS employs\nimplicit query expansion using an external domain specific\nknowledge base, it is less sensitive to term removal (i.e.,\nmismatch) than the Okapi FB, which relies on terms from\nthe top-ranked documents retrieved by an initial\nkeywordonly search. Because overall search engine performance is\nfrequently measured in terms of MAP, and because other\nevaluations of QE often only consider performance on the\nentire collection (i.e., they do not consider term mismatch),\nthe QE implemented in TCS would be considered (in\nan0 1 2 3 4 5 6 7\nNumber of Query Terms Removed from Relevant Documents\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\n0.45\nMeanAveragePrecision(MAP)\nOkapi FB\nOkapi\nTCS\nQL\nFSupp: Mean Average Precision with Query Terms Removed\nFigure 1: The performance of the four retrieval\nsystems on the FSupp collection in terms of Mean\nAverage Precision (MAP) and as a function of the\nnumber of query terms removed (the horizontal axis).\n0 1 2 3 4 5 6 7\nNumber of Query Terms Removed from Relevant Documents\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\n0.45\n0.5\n0.55\n0.6\nPrecisionat10Documents(P10)\nOkapi FB\nOkapi\nTCS\nQL\nFSupp: P10 with Query Terms Removed\nFigure 2: The performance of the four retrieval\nsystems on the FSupp collection in terms of Precision\nat 10 and as a function of the number of query terms\nremoved (the horizontal axis).\nother evaluation) to hurt performance on the FSupp\nCollection. However, when we look at the comparison of TCS to\nQL when query terms are removed from the relevant\ndocuments, we can see that the QE in TCS is indeed contributing\npositively to the search.\n5.2 The AP89 Collection: using the\ndescription queries\nFigures 4, 5, and 6 show the performance of the four IR\nsystems on the AP89 Collection, using the TREC topic\ndescriptions as queries. The most interesting difference\nbetween the performance on the FSupp Collection and the\nAP89 collection is the reversal of Okapi FB and TCS. On\nFSupp, TCS outperformed the other engines consistently\n(see Figures 1, 2, and 3); on the AP89 Collection, Okapi\nFB is clearly the best performer (see Figures 4, 5, and 6).\nThis is all the more interesting, based on the fact that QE in\nOkapi FB takes place after the first search iteration, which\n0 1 2 3 4 5 6 7\nNumber of Query Terms Removed from Relevant Documents\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nRecall\nOkapi FB\nOkapi\nTCS\nIndri\nFSupp: Recall at 1000 documents with Query Terms Removed\nFigure 3: The Recall (at 1000) of the four retrieval\nsystems on the FSupp collection as a function of\nthe number of query terms removed (the horizontal\naxis).\n0 1 2 3 4 5 6 7\nNumber of Query Terms Removed from Relevant Documents\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\nMeanAveragePrecision(MAP)\nOkapi FB\nOkapi\nTCS\nQL\nAP89: Mean Average Precision with Query Terms Removed (description queries)\nFigure 4: MAP of the four IR systems on the AP89\nCollection, using TREC description queries. MAP\nis measured as a function of the number of query\nterms removed.\n0 1 2 3 4 5 6 7\nNumber of Query Terms Removed from Relevant Documents\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\n0.45\nPrecisionat10Documents(P10)\nOkapi FB\nOkapi\nTCS\nQL\nAP89: P10 with Query Terms Removed (description queries)\nFigure 5: Precision at 10 of the four IR systems\non the AP89 Collection, using TREC description\nqueries. P at 10 is measured as a function of the\nnumber of query terms removed.\n0 1 2 3 4 5 6 7\nNumber of Query Terms Removed from Relevant Documents\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\nRecall\nOkapi FB\nOkapi\nTCS\nQL\nAP89: Recall at 1000 documents with Query Terms Removed (description queries)\nFigure 6: Recall (at 1000) of the four IR systems\non the AP89 Collection, using TREC description\nqueries, and as a function of the number of query\nterms removed.\nwe would expect to be handicapped when query terms are\nremoved.\nLooking at P10 in Figure 5, we can see that TCS and\nOkapi FB score similarly on P10, starting at the point where\none query term is removed from relevant documents. At two\nquery terms removed, TCS starts outperforming Okapi FB.\nIf modeling this in terms of expert versus non-expert users,\nwe could conclude that TCS might be a better search engine\nfor non-experts to use on the AP89 Collection, while Okapi\nFB would be best for an expert searcher.\nIt is interesting to note that on each metric for the AP89\ndescription queries, TCS performs more poorly than all the\nother systems on the original collection, but quickly\nsurpasses the baseline systems and approaches Okapi FB\"s\nperformance as terms are removed. This is again a case where\nthe performance of a system on the entire collection is not\nnecessarily indicative of how it handles query-document term\nmismatch.\n5.3 The AP89 Collection: using the title queries\nFigures 7, 8, and 9 show the performance of the four IR\nsystems on the AP89 Collection, using the TREC topic titles\nas queries. As with the AP89 description queries, Okapi\nFB is again the best performer of the four systems in the\nevaluation. As before, the performance of the Okapi and\nQL systems, the non-QE baseline systems, sharply degrades\nas query terms are removed. On the shorter queries, TCS\nseems to have a harder time catching up to the performance\nof Okapi FB as terms are removed.\nPerhaps the most interesting result from our evaluation\nis that although the keyword-only baselines performed\nconsistently and as expected on both collections with respect\nto query term removal from relevant documents, the\nperformances of the engines implementing QE techniques differed\ndramatically between collections.\n0 1 2 3 4 5\nNumber of Query Terms Removed from Relevant Documents\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\nMeanAveragePrecision(MAP)\nOkapi FB\nOkapi\nTCS\nQL\nAP89: Mean Average Precision with Query Terms Removed (title queries)\nFigure 7: MAP of the four IR systems on the AP89\nCollection, using TREC title queries and as a\nfunction of the number of query terms removed.\n0 1 2 3 4 5\nNumber of Query Terms Removed from Relevant Documents\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\n0.45\n0.5\nPrecisionat10Documents(P10)\nOkapi FB\nOkapi\nTCS\nQL\nAP89: P10 with Query Terms Removed (title queries)\nFigure 8: Precision at 10 of the four IR systems on\nthe AP89 Collection, using TREC title queries, and\nas a function of the number of query terms removed.\n0 1 2 3 4 5\nNumber of Query Terms Removed from Relevant Documents\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\nRecall\nOkapi FB\nOkapi\nTCS\nQL\nAP89: Recall at 1000 documents with Query Terms Removed (title queries)\nFigure 9: Recall (at 1000) of the four IR systems on\nthe AP89 Collection, using TREC title queries and\nas a function of the number of query terms removed.\n6. DISCUSSION\nThe intuition behind this evaluation framework is to\nmeasure the degree to which various QE techniques overcome\nterm mismatch between queries and relevant documents. In\ngeneral, it is easy to evaluate the overall performance of\ndifferent techniques for QE in comparison to each other or\nagainst a non-QE variant on any complete test collection.\nSuch an approach does tell us which systems perform better\non a complete test collection, but it does not measure the\nability of a particular QE technique to retrieve relevant\ndocuments despite partial or complete term mismatch between\nqueries and relevant documents.\nA systematic evaluation of IR systems as outlined in this\npaper is useful not only with respect to measuring the\ngeneral success or failure of particular QE techniques in the\npresence of query-document term mismatch, but it also\nprovides insight into how a particular IR system will perform\nwhen used by expert versus non-expert users on a\nparticular collection. The less a user knows about the domain of\nthe document collection on which they are searching, the\nmore prevalent query-document term mismatch is likely to\nbe. This distinction is especially relevant in the case that\nthe test collection is domain-specific (i.e., medical or legal, as\nopposed to a more general domain, such as news), where the\ndistinction between experts and non-experts may be more\nmarked. For example, a non-expert in the medical domain\nmight search for whooping cough, but relevant documents\nmight instead contain the medical term pertussis.\nSince query terms are masked only the in relevant\ndocuments, this evaluation framework is actually biased against\nretrieving relevant documents. This is because non-relevant\ndocuments may also contain query terms, which can cause\na retrieval system to rank such documents higher than it\nwould have before terms were masked in relevant documents.\nStill, we think this is a more realistic scenario than removing\nterms from all documents regardless of relevance.\nThe degree to which a QE technique is well-suited to a\nparticular collection can be evaluated in terms of its ability\nto still find the relevant documents, even when they are\nmissing query terms, despite the bias of this approach against\nrelevant documents. However, given that Okapi FB and TCS\noutperformed each other on two different collection sets,\nfurther investigation into the degree of compatibility between\nQE expansion approach and target collection is probably\nwarranted. Furthermore, the investigation of other term\nremoval strategies could provide insight into the behavior of\ndifferent QE techniques and their overall impact on the user\nexperience.\nAs mentioned earlier, our choice of the term removal\nstrategy was motivated by (1) our desire to see the highest\nimpact on system performance as terms are removed and (2)\nbecause high IDF terms, in our domain context, are more\nlikely to be domain specific, which allows us to better\nunderstand the performance of an IR system as experienced\nby expert and non-expert users.\nAlthough not attempted in our experiments, another\napplication of this evaluation framework would be to remove\nquery terms individually, rather than incrementally, to\nanalyze which terms (or possibly which types of terms) are\nbeing helped most by a QE technique on a particular test\ncollection. This could lead to insight as to when QE should\nand should not be applied.\nThis evaluation framework allows us to see how IR\nsystems perform in the presence of query-document term\nmismatch. In other evaluations, the performance of a system is\nmeasured only on the entire collection, in which the degree\nof query-term document mismatch is not known. By\nsystematically introducing this mismatch, we can see that even\nif an IR system is not the best performer on the entire\ncollection, its performance may nonetheless be more robust to\nquery-document term mismatch than other systems. Such\nrobustness makes a system more user-friendly, especially to\nnon-expert users.\nThis paper presents a novel framework for IR system\nevaluation, the applications of which are numerous. The results\npresented in this paper are not by any means meant to be\nexhaustive or entirely representative of the ways in which\nthis evaluation could be applied. To be sure, there is much\nfuture work that could be done using this framework.\nIn addition to looking at average performance of IR\nsystems, the results of individual queries could be examined and\ncompared more closely, perhaps giving more insight into the\nclassification and prediction of difficult queries, or perhaps\nshowing which QE techniques improve (or degrade)\nindividual query performance under differing degrees of\nquerydocument term mismatch. Indeed, this framework would\nalso benefit from further testing on a larger collection.\n7. CONCLUSION\nThe proposed evaluation framework allows us to measure\nthe degree to which different IR systems overcome (or don\"t\novercome) term mismatch between queries and relevant\ndocuments. Evaluations of IR systems employing QE performed\nonly on the entire collection do not take into account that\nthe purpose of QE is to mitigate the effects of term mismatch\nin retrieval. By systematically removing query terms from\nrelevant documents, we can measure the degree to which\nQE contributes to a search by showing the difference\nbetween the performances of a QE system and its\nkeywordonly baseline when query terms have been removed from\nknown relevant documents. Further, we can model the\nbehavior of expert versus non-expert users by manipulating\nthe amount of query-document term mismatch introduced\ninto the collection.\nThe evaluation framework proposed in this paper is\nattractive for several reasons. Most importantly, it provides\na controlled manner in which to measure the performance\nof QE with respect to query-document term mismatch. In\naddition, this framework takes advantage and stretches the\namount of information we can get from existing test\ncollections. Further, this evaluation framework is not\nmetricspecific: information in terms of any metric (MAP, P@10,\netc.) can be gained from evaluating an IR system this way.\nIt should also be noted that this framework is\ngeneralizable to any IR system, in that it evaluates how well IR\nsystems evaluate users\" information needs as represented by\ntheir queries. An IR system that is easy to use should be\ngood at retrieving documents that are relevant to users\"\ninformation needs, even if the queries provided by the users do\nnot contain the same keywords as the relevant documents.\n8. REFERENCES\n[1] Amati, G., C. Carpineto, and G. Romano. Query\ndifficulty, robustness and selective application of query\nexpansion. In Proceedings of the 25th European\nConference on Information Retrieval (ECIR 2004),\npp. 127-137.\n[2] Berger, A. and J.D. Lafferty. 1999. Information\nretrieval as statistical translation. 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{"name": "train_H-49", "title": "Performance Prediction Using Spatial Autocorrelation", "abstract": "Evaluation of information retrieval systems is one of the core tasks in information retrieval. Problems include the inability to exhaustively label all documents for a topic, nongeneralizability from a small number of topics, and incorporating the variability of retrieval systems. Previous work addresses the evaluation of systems, the ranking of queries by difficulty, and the ranking of individual retrievals by performance. Approaches exist for the case of few and even no relevance judgments. Our focus is on zero-judgment performance prediction of individual retrievals. One common shortcoming of previous techniques is the assumption of uncorrelated document scores and judgments. If documents are embedded in a high-dimensional space (as they often are), we can apply techniques from spatial data analysis to detect correlations between document scores. We find that the low correlation between scores of topically close documents often implies a poor retrieval performance. When compared to a state of the art baseline, we demonstrate that the spatial analysis of retrieval scores provides significantly better prediction performance. These new predictors can also be incorporated with classic predictors to improve performance further. We also describe the first large-scale experiment to evaluate zero-judgment performance prediction for a massive number of retrieval systems over a variety of collections in several languages.", "fulltext": "1. INTRODUCTION\nIn information retrieval, a user poses a query to a system.\nThe system retrieves n documents each receiving a\nrealvalued score indicating the predicted degree of relevance.\nIf we randomly select pairs of documents from this set, we\nexpect some pairs to share the same topic and other pairs to\nnot share the same topic. Take two topically-related\ndocuments from the set and call them a and b. If the scores of a\nand b are very different, we may be concerned about the\nperformance of our system. That is, if a and b are both on the\ntopic of the query, we would like them both to receive a high\nscore; if a and b are not on the topic of the query, we would\nlike them both to receive a low score. We might become more\nworried as we find more differences between scores of related\ndocuments. We would be more comfortable with a retrieval\nwhere scores are consistent between related documents.\nOur paper studies the quantification of this inconsistency\nin a retrieval from a spatial perspective. Spatial analysis is\nappropriate since many retrieval models embed documents\nin some vector space. If documents are embedded in a space,\nproximity correlates with topical relationships. Score\nconsistency can be measured by the spatial version of\nautocorrelation known as the Moran coefficient or IM [5, 10]. In\nthis paper, we demonstrate a strong correlation between IM\nand retrieval performance.\nThe discussion up to this point is reminiscent of the\ncluster hypothesis. The cluster hypothesis states: closely-related\ndocuments tend to be relevant to the same request [12]. As we\nshall see, a retrieval function\"s spatial autocorrelation\nmeasures the degree to which closely-related documents receive\nsimilar scores. Because of this, we interpret\nautocorrelation as measuring the degree to which a retrieval function\nsatisfies the clustering hypothesis. If this connection is\nreasonable, in Section 6, we present evidence that failure to\nsatisfy the cluster hypothesis correlates strongly with poor\nperformance.\nIn this work, we provide the following contributions,\n1. A general, robust method for predicting the\nperformance of retrievals with zero relevance judgments\n(Section 3).\n2. A theoretical treatment of the similarities and\nmotivations behind several state-of-the-art performance\nprediction techniques (Section 4).\n3. The first large-scale experiments of zero-judgment,\nsingle run performance prediction (Sections 5 and 6).\n2. PROBLEM DEFINITION\nGiven a query, an information retrieval system produces\na ranking of documents in the collection encoded as a set\nof scores associated with documents. We refer to the set\nof scores for a particular query-system combination as a\nretrieval. We would like to predict the performance of this\nretrieval with respect to some evaluation measure (eg, mean\naverage precision). In this paper, we present results for\nranking retrievals from arbitrary systems. We would like\nthis ranking to approximate the ranking of retrievals by the\nevaluation measure. This is different from ranking queries\nby the average performance on each query. It is also\ndifferent from ranking systems by the average performance on a\nset of queries.\nScores are often only computed for the top n documents\nfrom the collection. We place these scores in the length\nn vector, y, where yi refers to the score of the ith-ranked\ndocument. We adjust scores to have zero mean and unit\nvariance. We use this method because of its simplicity and\nits success in previous work [15].\n3. SPATIAL CORRELATION\nIn information retrieval, we often assume that the\nrepresentations of documents exist in some high-dimensional\nvector space. For example, given a vocabulary, V, this vector\nspace may be an arbitrary |V|-dimensional space with cosine\ninner-product or a multinomial simplex with a\ndistributionbased distance measure. An embedding space is often\nselected to respect topical proximity; if two documents are\nnear, they are more likely to share a topic.\nBecause of the prevalence and success of spatial models\nof information retrieval, we believe that the application of\nspatial data analysis techniques are appropriate. Whereas\nin information retrieval, we are concerned with the score at\na point in a space, in spatial data analysis, we are concerned\nwith the value of a function at a point or location in a space.\nWe use the term function here to mean a mapping from a\nlocation to a real value. For example, we might be interested\nin the prevalence of a disease in the neighborhood of some\ncity. The function would map the location of a neighborhood\nto an infection rate.\nIf we want to quantify the spatial dependencies of a\nfunction, we would employ a measure referred to as the spatial\nautocorrelation [5, 10]. High spatial autocorrelation suggests\nthat knowing the value of a function at location a will tell\nus a great deal about the value at a neighboring location\nb. There is a high spatial autocorrelation for a function\nrepresenting the temperature of a location since knowing\nthe temperature at a location a will tell us a lot about the\ntemperature at a neighboring location b. Low spatial\nautocorrelation suggests that knowing the value of a function\nat location a tells us little about the value at a neighboring\nlocation b. There is low spatial autocorrelation in a function\nmeasuring the outcome of a coin toss at a and b.\nIn this section, we will begin by describing what we mean\nby spatial proximity for documents and then define a\nmeasure of spatial autocorrelation. We conclude by extending\nthis model to include information from multiple retrievals\nfrom multiple systems for a single query.\n3.1 Spatial Representation of Documents\nOur work does not focus on improving a specific similarity\nmeasure or defining a novel vector space. Instead, we choose\nan inner product known to be effective at detecting\ninterdocument topical relationships. Specifically, we adopt tf.idf\ndocument vectors,\n\u02dcdi = di log\n\u201e\n(n + 0.5) \u2212 ci\n0.5 + ci\n\u00ab\n(1)\nwhere d is a vector of term frequencies, c is the length-|V|\ndocument frequency vector. We use this weighting scheme\ndue to its success for topical link detection in the context\nof Topic Detection and Tracking (TDT) evaluations [6].\nAssuming vectors are scaled by their L2 norm, we use the inner\nproduct, \u02dcdi, \u02dcdj , to define similarity.\nGiven documents and some similarity measure, we can\nconstruct a matrix which encodes the similarity between\npairs of documents. Recall that we are given the top n\ndocuments retrieved in y. We can compute an n \u00d7 n\nsimilarity matrix, W. An element of this matrix, Wij represents\nthe similarity between documents ranked i and j. In\npractice, we only include the affinities for a document\"s k-nearest\nneighbors. In all of our experiments, we have fixed k to 5.\nWe leave exploration of parameter sensitivity to future work.\nWe also row normalize the matrix so that\nPn\nj=1 Wij = 1 for\nall i.\n3.2 Spatial Autocorrelation of a Retrieval\nRecall that we are interested in measuring the similarity\nbetween the scores of spatially-close documents. One such\nsuitable measure is the Moran coefficient of spatial\nautocorrelation. Assuming the function y over n locations, this is\ndefined as\n\u02dcIM =\nn\neTWe\nP\ni,j Wijyiyj\nP\ni y2\ni\n=\nn\neTWe\nyT\nWy\nyTy\n(2)\nwhere eT\nWe =\nP\nij Wij.\nWe would like to compare autocorrelation values for\ndifferent retrievals. Unfortunately, the bound for Equation 2\nis not consistent for different W and y. Therefore, we use\nthe Cauchy-Schwartz inequality to establish a bound,\n\u02dcIM \u2264\nn\neTWe\ns\nyTWTWy\nyTy\nAnd we define the normalized spatial autocorrelation as\nIM =\nyT\nWy\np\nyTy \u00d7 yTWTWy\nNotice that if we let \u02dcy = Wy, then we can write this formula\nas,\nIM =\nyT\n\u02dcy\ny 2 \u02dcy 2\n(3)\nwhich can be interpreted as the correlation between the\noriginal retrieval scores and a set of retrieval scores diffused\nin the space.\nWe present some examples of autocorrelations of functions\non a grid in Figure 1.\n3.3 Correlation with Other Retrievals\nSometimes we are interested in the performance of a single\nretrieval but have access to scores from multiple systems for\n(a) IM = 0.006 (b) IM = 0.241 (c) IM = 0.487\nFigure 1: The Moran coefficient, IM for a several\nbinary functions on a grid. The Moran coefficient\nis a local measure of function consistency. From the\nperspective of information retrieval, each of these\ngrid spaces would represent a document and\ndocuments would be organized so that they lay next to\ntopically-related documents. Binary retrieval scores\nwould define a pattern on this grid. Notice that,\nas the Moran coefficient increases, neighboring cells\ntend to have similar values.\nthe same query. In this situation, we can use combined\ninformation from these scores to construct a surrogate for\na high-quality ranking [17]. We can treat the correlation\nbetween the retrieval we are interested in and the combined\nscores as a predictor of performance.\nAssume that we are given m score functions, yi, for the\nsame n documents. We will represent the mean of these\nvectors as y\u00b5 =\nPm\ni=1 yi. We use the mean vector as an\napproximation to relevance. Since we use zero mean and unit\nvariance normalization, work in metasearch suggests that\nthis assumption is justified [15]. Because y\u00b5 represents a\nvery good retrieval, we hypothesize that a strong similarity\nbetween y\u00b5 and y will correlate positively with system\nperformance. We use Pearson\"s product-moment correlation to\nmeasure the similarity between these vectors,\n\u03c1(y, y\u00b5) =\nyT\ny\u00b5\ny 2 y\u00b5 2\n(4)\nWe will comment on the similarity between Equation 3 and\n4 in Section 7.\nOf course, we can combine \u03c1(y, \u02dcy) and \u03c1(y, y\u00b5) if we\nassume that they capture different factors in the prediction.\nOne way to accomplish this is to combine these predictors\nas independent variables in a linear regression. An\nalternative means of combination is suggested by the mathematical\nform of our predictors. Since \u02dcy encodes the spatial\ndependencies in y and y\u00b5 encodes the spatial properties of the\nmultiple runs, we can compute a third correlation between\nthese two vectors,\n\u03c1(\u02dcy, y\u00b5) =\n\u02dcyT\ny\u00b5\n\u02dcy 2 y\u00b5 2\n(5)\nWe can interpret Equation 5 as measuring the correlation\nbetween a high quality ranking (y\u00b5) and a spatially smoothed\nversion of the retrieval (\u02dcy).\n4. RELATIONSHIP WITH OTHER\nPREDICTORS\nOne way to predict the effectiveness of a retrieval is to\nlook at the shared vocabulary of the top n retrieved\ndocuments. If we computed the most frequent content words\nin this set, we would hope that they would be consistent\nwith our topic. In fact, we might believe that a bad\nretrieval would include documents on many disparate topics,\nresulting in an overlap of terminological noise. The Clarity\nof a query attempts to quantify exactly this [7]. Specifically,\nClarity measures the similarity of the words most frequently\nused in retrieved documents to those most frequently used\nin the whole corpus. The conjecture is that a good retrieval\nwill use language distinct from general text; the overlapping\nlanguage in a bad retrieval will tend to be more similar to\ngeneral text. Mathematically, we can compute a\nrepresentation of the language used in the initial retrieval as a weighted\ncombination of document language models,\nP(w|\u03b8Q) =\nnX\ni=1\nP(w|\u03b8i)\nP(Q|\u03b8i)\nZ\n(6)\nwhere \u03b8i is the language model of the ith-ranked\ndocument, P(Q|\u03b8i) is the query likelihood score of the ith-ranked\ndocument and Z =\nPn\ni=1 P(Q|\u03b8i) is a normalization\nconstant. The similarity between the multinomial P(w|\u03b8Q)\nand a model of general text can be computed using the\nKullback-Leibler divergence, DV\nKL(\u03b8Q \u03b8C ). Here, the\ndistribution P(w|\u03b8C ) is our model of general text which can be\ncomputed using term frequencies in the corpus. In Figure\n2a, we present Clarity as measuring the distance between the\nweighted center of mass of the retrieval (labeled y) and the\nunweighted center of mass of the collection (labeled O).\nClarity reaches a minimum when a retrieval assigns every\ndocument the same score.\nLet\"s again assume we have a set of n documents retrieved\nfor our query. Another way to quantify the dispersion of a\nset of documents is to look at how clustered they are. We\nmay hypothesize that a good retrieval will return a single,\ntight cluster. A poorly performing retrieval will return a\nloosely related set of documents covering many topics. One\nproposed method of quantifying this dispersion is to\nmeasure the distance from a random document a to it\"s nearest\nneighbor, b. A retrieval which is tightly clustered will, on\naverage, have a low distance between a and b; a retrieval\nwhich is less tightly-closed will, on average have high\ndistances between a and b. This average corresponds to using\nthe Cox-Lewis statistic to measure the randomness of the\ntop n documents retrieved from a system [18]. In Figure\n2a, this is roughly equivalent to measuring the area of the\nset n. Notice that we are throwing away information about\nthe retrieval function y. Therefore the Cox-Lewis statistic\nis highly dependent on selecting the top n documents.1\nRemember that we have n documents and a set of scores.\nLet\"s assume that we have access to the system which\nprovided the original scores and that we can also request scores\nfor new documents. This suggests a third method for\npredicting performance. Take some document, a, from the\nretrieved set and arbitrarily add or remove words at random\nto create a new document \u02dca. Now, we can ask our system\nto score \u02dca with respect to our query. If, on average over\nthe n documents, the scores of a and \u02dca tend to be very\ndifferent, we might suspect that the system is failing on this\nquery. So, an alternative approach is to measure the\nsimi1\nThe authors have suggested coupling the query with the\ndistance measure [18]. The information introduced by the\nquery, though, is retrieval-independent so that, if two\nretrievals return the same set of documents, the approximate\nCox-Lewis statistic will be the same regardless of the\nretrieval scores.\nyOy\n(a) Global Divergence\n\u00b5(y)\u02dcy\ny\n(b) Score Perturbation\n\u00b5(y)\ny\n(c) Multirun Averaging\nFigure 2: Representation of several performance predictors on a grid. In Figure 2a, we depict predictors\nwhich measure the divergence between the center of mass of a retrieval and the center of the embedding\nspace. In Figure 2b, we depict predictors which compare the original retrieval, y, to a perturbed version of\nthe retrieval, \u02dcy. Our approach uses a particular type of perturbation based on score diffusion. Finally, in\nFigure 2c, we depict prediction when given retrievals from several other systems on the same query. Here,\nwe can consider the fusion of these retrieval as a surrogate for relevance.\nlarity between the retrieval and a perturbed version of that\nretrieval [18, 19]. This can be accomplished by either\nperturbing the documents or queries. The similarity between\nthe two retrievals can be measured using some correlation\nmeasure. This is depicted in Figure 2b. The upper grid\nrepresents the original retrieval, y, while the lower grid\nrepresents the function after having been perturbed, \u02dcy. The\nnature of the perturbation process requires additional\nscorings or retrievals. Our predictor does not require access to\nthe original scoring function or additional retrievals. So,\nalthough our method is similar to other perturbation methods\nin spirit, it can be applied in situations when the retrieval\nsystem is inaccessible or costly to access.\nFinally, assume that we have, in addition to the retrieval\nwe want to evaluate, m retrievals from a variety of\ndifferent systems. In this case, we might take a document a,\ncompare its rank in the retrieval to its average rank in the\nm retrievals. If we believe that the m retrievals provide a\nsatisfactory approximation to relevance, then a very large\ndifference in rank would suggest that our retrieval is\nmisranking a. If this difference is large on average over all\nn documents, then we might predict that the retrieval is\nbad. If, on the other hand, the retrieval is very consistent\nwith the m retrievals, then we might predict that the\nretrieval is good. The similarity between the retrieval and\nthe combined retrieval may be computed using some\ncorrelation measure. This is depicted in Figure 2c. In previous\nwork, the Kullback-Leibler divergence between the\nnormalized scores of the retrieval and the normalized scores of the\ncombined retrieval provides the similarity [1].\n5. EXPERIMENTS\nOur experiments focus on testing the predictive power of\neach of our predictors: \u03c1(y, \u02dcy), \u03c1(y, y\u00b5), and \u03c1(\u02dcy, y\u00b5). As\nstated in Section 2, we are interested in predicting the\nperformance of the retrieval generated by an arbitrary system.\nOur methodology is consistent with previous research in that\nwe predict the relative performance of a retrieval by\ncomparing a ranking based on our predictor to a ranking based on\naverage precision.\nWe present results for two sets of experiments. The first\nset of experiments presents detailed comparisons of our\npredictors to previously-proposed predictors using identical data\nsets. Our second set of experiments demonstrates the\ngeneralizability of our approach to arbitrary retrieval methods,\ncorpus types, and corpus languages.\n5.1 Detailed Experiments\nIn these experiments, we will predict the performance of\nlanguage modeling scores using our autocorrelation\npredictor, \u03c1(y, \u02dcy); we do not consider \u03c1(y, y\u00b5) or \u03c1(\u02dcy, y\u00b5)\nbecause, in these detailed experiments, we focus on ranking\nthe retrievals from a single system. We use retrievals, values\nfor baseline predictors, and evaluation measures reported in\nprevious work [19].\n5.1.1 Topics and Collections\nThese performance prediction experiments use language\nmodel retrievals performed for queries associated with\ncollections in the TREC corpora. Using TREC collections\nallows us to confidently associate an average precision with a\nretrieval. In these experiments, we use the following topic\ncollections: TREC 4 ad-hoc, TREC 5 ad-hoc, Robust 2004,\nTerabyte 2004, and Terabyte 2005.\n5.1.2 Baselines\nWe provide two baselines. Our first baseline is the\nclassic Clarity predictor presented in Equation 6. Clarity is\ndesigned to be used with language modeling systems. Our\nsecond baseline is Zhou and Croft\"s ranking robustness\npredictor. This predictor corrupts the top k documents\nfrom retrieval and re-computes the language model scores\nfor these corrupted documents. The value of the predictor\nis the Spearman rank correlation between the original\nranking and the corrupted ranking. In our tables, we will label\nresults for Clarity using DV\nKL and the ranking robustness\npredictor using P.\n5.2 Generalizability Experiments\nOur predictors do not require a particular baseline\nretrieval system; the predictors can be computed for an\narbitrary retrieval, regardless of how scores were generated. We\nbelieve that that is one of the most attractive aspects of our\nalgorithm. Therefore, in a second set of experiments, we\ndemonstrate the ability of our techniques to generalize to a\nvariety of collections, topics, and retrieval systems.\n5.2.1 Topics and Collections\nWe gathered a diverse set of collections from all possible\nTREC corpora. We cast a wide net in order to locate\ncollections where our predictors might fail. Our hypothesis is that\ndocuments with high topical similarity should have\ncorrelated scores. Therefore, we avoided collections where scores\nwere unlikely to be correlated (eg, question-answering) or\nwere likely to be negatively correlated (eg, novelty).\nNevertheless, our collections include corpora where correlations\nare weakly justified (eg, non-English corpora) or not\njustified at all (eg, expert search). We use the ad-hoc tracks from\nTREC3-8, TREC Robust 2003-2005, TREC Terabyte\n20042005, TREC4-5 Spanish, TREC5-6 Chinese, and TREC\nEnterprise Expert Search 2005. In all cases, we use only the\nautomatic runs for ad-hoc tracks submitted to NIST.\nFor all English and Spanish corpora, we construct the\nmatrix W according to the process described in Section 3.1. For\nChinese corpora, we use na\u00a8\u0131ve character-based tf.idf vectors.\nFor entities, entries in W are proportional to the number of\ndocuments in which two entities cooccur.\n5.2.2 Baselines\nIn our detailed experiments, we used the Clarity measure\nas a baseline. Since we are predicting the performance of\nretrievals which are not based on language modeling, we\nuse a version of Clarity referred to as ranked-list Clarity\n[7]. Ranked-list clarity converts document ranks to P(Q|\u03b8i)\nvalues. This conversion begins by replacing all of the scores\nin y with the respective ranks. Our estimation of P(Q|\u03b8i)\nfrom the ranks, then is,\nP(Q|\u03b8i) =\n(\n2(c+1\u2212yi)\nc(c+1)\nif yi \u2264 c\n0 otherwise\n(7)\nwhere c is a cutoff parameter. As suggested by the authors,\nwe fix the algorithm parameters c and \u03bb2 so that c = 60\nand \u03bb2 = 0.10. We use Equation 6 to estimate P(w|\u03b8Q) and\nDV\nKL(\u03b8Q \u03b8C ) to compute the value of the predictor. We\nwill refer to this predictor as DV\nKL, superscripted by V to\nindicate that the Kullback-Leibler divergence is with respect\nto the term embedding space.\nWhen information from multiple runs on the same query is\navailable, we use Aslam and Pavlu\"s document-space\nmultinomial divergence as a baseline [1]. This rank-based method\nfirst normalizes the scores in a retrieval as an n-dimensional\nmultinomial. As with ranked-list Clarity, we begin by\nreplacing all of the scores in y with their respective ranks.\nThen, we adjust the elements of y in the following way,\n\u02c6yi =\n1\n2n\n0\n@1 +\nnX\nk=yi\n1\nk\n1\nA (8)\nIn our multirun experiments, we only use the top 75\ndocuments from each retrieval (n = 75); this is within the range\nof parameter values suggested by the authors. However, we\nadmit not tuning this parameter for either our system or the\nbaseline. The predictor is the divergence between the\ncandidate distribution, y, and the mean distribution, y\u00b5 . With\nthe uniform linear combination of these m retrievals\nrepresented as y\u00b5, we can compute the divergence as Dn\nKL(\u02c6y \u02c6y\u00b5)\nwhere we use the superscript n to indicate that the\nsummation is over the set of n documents. This baseline was\ndeveloped in the context of predicting query difficulty but\nwe adopt it as a reasonable baseline for predicting retrieval\nperformance.\n5.2.3 Parameter Settings\nWhen given multiple retrievals, we use documents in the\nunion of the top k = 75 documents from each of the m\nretrievals for that query. If the size of this union is \u02dcn, then\ny\u00b5 and each yi is of length \u02dcn. In some cases, a system\ndid not score a document in the union. Since we are\nmaking a Gaussian assumption about our scores, we can sample\nscores for these unseen documents from the negative tail\nof the distribution. Specifically, we sample from the part\nof the distribution lower than the minimum value of in the\nnormalized retrieval. This introduces randomness into our\nalgorithm but we believe it is more appropriate than\nassigning an arbitrary fixed value.\nWe optimized the linear regression using the square root\nof each predictor. We found that this substantially improved\nfits for all predictors, including the baselines. We considered\nlinear combinations of pairs of predictors (labeled by the\ncomponents) and all predictors (labeled as \u03b2).\n5.3 Evaluation\nGiven a set of retrievals, potentially from a combination\nof queries and systems, we measure the correlation of the\nrank ordering of this set by the predictor and by the\nperformance metric. In order to ensure comparability with\nprevious results, we present Kendall\"s \u03c4 correlation between the\npredictor\"s ranking and ranking based on average precision\nof the retrieval. Unless explicitly noted, all correlations are\nsignificant with p < 0.05.\nPredictors can sometimes perform better when linearly\ncombined [9, 11]. Although previous work has presented\nthe coefficient of determination (R2\n) to measure the quality\nof the regression, this measure cannot be reliably used when\ncomparing slight improvements from combining predictors.\nTherefore, we adopt the adjusted coefficient of\ndetermination which penalizes models with more variables. The\nadjusted R2\nallows us to evaluate the improvement in\nprediction achieved by adding a parameter but loses the statistical\ninterpretation of R2\n. We will use Kendall\"s \u03c4 to evaluate the\nmagnitude of the correlation and the adjusted R2\nto\nevaluate the combination of variables.\n6. RESULTS\nWe present results for our detailed experiments comparing\nthe prediction of language model scores in Table 1. Although\nthe Clarity measure is theoretically designed for language\nmodel scores, it consistently underperforms our system-agnostic\npredictor. Ranking robustness was presented as an\nimprovement to Clarity for web collections (represented in our\nexperiments by the terabyte04 and terabyte05 collections),\nshifting the \u03c4 correlation from 0.139 to 0.150 for terabyte04 and\n0.171 to 0.208 for terabyte05. However, these improvements\nare slight compared to the performance of autocorrelation\non these collections. Our predictor achieves a \u03c4 correlation\nof 0.454 for terabyte04 and 0.383 for terabyte05. Though\nnot always the strongest, autocorrelation achieves\ncorrelations competitive with baseline predictors. When\nexamining the performance of linear combinations of predictors, we\nnote that in every case, autocorrelation factors as a\nnecessary component of a strong predictor. We also note that the\nadjusted R2\nfor individual baselines are always significantly\nimproved by incorporating autocorrelation.\nWe present our generalizability results in Table 2. We\nbegin by examining the situation in column (a) where we\nare presented with a single retrieval and no information\nfrom additional retrievals. For every collection except one,\nwe achieve significantly better correlations than ranked-list\nClarity. Surprisingly, we achieve relatively strong\ncorrelations for Spanish and Chinese collections despite our na\u00a8\u0131ve\nprocessing. We do not have a ranked-list clarity correlation\nfor ent05 because entity modeling is itself an open research\nquestion. However, our autocorrelation measure does not\nachieve high correlations perhaps because relevance for\nentity retrieval does not propagate according to the\ncooccurrence links we use.\nAs noted above, the poor Clarity performance on web\ndata is consistent with our findings in the detailed\nexperiments. Clarity also notably underperforms for several news\ncorpora (trec5, trec7, and robust04). On the other hand,\nautocorrelation seems robust to the changes between different\ncorpora.\nNext, we turn to the introduction of information from\nmultiple retrievals. We compare the correlations between\nthose predictors which do not use this information in column\n(a) and those which do in column (b). For every collection,\nthe predictors in column (b) outperform the predictors in\ncolumn (a), indicating that the information from additional\nruns can be critical to making good predictions.\nInspecting the predictors in column (b), we only draw\nweak conclusions. Our new predictors tend to perform\nbetter on news corpora. And between our new predictors, the\nhybrid \u03c1(\u02dcy, y\u00b5) predictor tends to perform better. Recall\nthat our \u03c1(\u02dcy, y\u00b5) measure incorporates both spatial and\nmultiple retrieval information. Therefore, we believe that\nthe improvement in correlation is the result of\nincorporating information from spatial behavior.\nIn column (c), we can investigate the utility of\nincorporating spatial information with information from\nmultiple retrievals. Notice that in the cases where\nautocorrelation, \u03c1(y, \u02dcy), alone performs well (trec3, trec5-spanish, and\ntrec6-chinese), it is substantially improved by\nincorporating multiple-retrieval information from \u03c1(y, y\u00b5) in the\nlinear regression, \u03b2. In the cases where \u03c1(y, y\u00b5) performs well,\nincorporating autocorrelation rarely results in a significant\nimprovement in performance. In fact, in every case where\nour predictor outperforms the baseline, it includes\ninformation from multiple runs.\n7. DISCUSSION\nThe most important result from our experiments involves\nprediction when no information is available from multiple\nruns (Tables 1 and 2a). This situation arises often in system\ndesign. For example, a system may need to, at retrieval\ntime, assess its performance before deciding to conduct more\nintensive processing such as pseudo-relevance feedback or\ninteraction. Assuming the presence of multiple retrievals is\nunrealistic in this case.\nWe believe that autocorrelation is, like multiple-retrieval\nalgorithms, approximating a good ranking; in this case by\ndiffusing scores. Why is \u02dcy a reasonable surrogate? We know\nthat diffusion of scores on the web graph and language model\ngraphs improves performance [14, 16]. Therefore, if score\ndiffusion tends to, in general, improve performance, then\ndiffused scores will, in general, provide a good surrogate for\nrelevance. Our results demonstrate that this approximation\nis not as powerful as information from multiple retrievals.\nNevertheless, in situations where this information is lacking,\nautocorrelation provides substantial information.\nThe success of autocorrelation as a predictor may also\nhave roots in the clustering hypothesis. Recall that we\nregard autocorrelation as the degree to which a retrieval\nsatisfies the clustering hypothesis. Our experiments, then,\ndemonstrate that a failure to respect the clustering\nhypothesis correlates with poor performance. Why might systems\nfail to conform to the cluster hypothesis? Query-based\ninformation retrieval systems often score documents\nindependently. The score of document a may be computed by\nexamining query term or phrase matches, the document length,\nand perhaps global collection statistics. Once computed,\na system rarely compares the score of a to the score of a\ntopically-related document b. With some exceptions, the\ncorrelation of document scores has largely been ignored.\nWe should make it clear that we have selected tasks where\ntopical autocorrelation is appropriate. There are certainly\ncases where there is no reason to believe that retrieval scores\nwill have topical autocorrelation. For example, ranked lists\nwhich incorporate document novelty should not exhibit\nspatial autocorrelation; if anything autocorrelation should be\nnegative for this task. Similarly, answer candidates in a\nquestion-answering task may or may not exhibit\nautocorrelation; in this case, the semantics of links is questionable\ntoo. It is important before applying this measure to confirm\nthat, given the semantics for some link between two retrieved\nitems, we should expect a correlation between scores.\n8. RELATED WORK\nIn this section we draw more general comparisons to other\nwork in performance prediction and spatial data analysis.\nThere is a growing body of work which attempts to predict\nthe performance of individual retrievals [7, 3, 11, 9, 19]. We\nhave attempted to place our work in the context of much of\nthis work in Section 4. However, a complete comparison is\nbeyond the scope of this paper. We note, though, that our\nexperiments cover a larger and more diverse set of retrievals,\ncollections, and topics than previously examined.\nMuch previous work-particularly in the context of\nTRECfocuses on predicting the performance of systems. Here,\neach system generates k retrievals. The task is, given these\nretrievals, to predict the ranking of systems according to\nsome performance measure. Several papers attempt to\naddress this task under the constraint of few judgments [2, 4].\nSome work even attempts to use zero judgments by\nleveraging multiple retrievals for the same query [17]. Our task\ndiffers because we focus on ranking retrievals independent\nof the generating system. The task here is not to test the\nhypothesis system A is superior to system B but to test\nthe hypothesis retrieval A is superior to retrieval B.\nAutocorrelation manifests itself in many classification tasks.\nNeville and Jensen define relational autocorrelation for\nrelational learning problems and demonstrate that many\nclassification tasks manifest autocorrelation [13]. Temporal\nautocorrelation of initial retrievals has also been used to predict\nperformance [9]. However, temporal autocorrelation is\nperformed by projecting the retrieval function into the temporal\nembedding space. In our work, we focus on the behavior of\nthe function over the relationships between documents.\n\u03c4 adjusted R2\nDV\nKL P \u03c1(y, \u02dcy) DV\nKL P \u03c1(y, \u02dcy) DV\nKL, P DV\nKL, \u03c1(y, \u02dcy) P\u03c1(y, \u02dcy) \u03b2\ntrec4 0.353 0.548 0.513 0.168 0.363 0.422 0.466 0.420 0.557 0.553\ntrec5 0.311 0.329 0.357 0.116 0.190 0.236 0.238 0.244 0.266 0.269\nrobust04 0.418 0.398 0.373 0.256 0.304 0.278 0.403 0.373 0.402 0.442\nterabyte04 0.139 0.150 0.454 0.059 0.045 0.292 0.076 0.293 0.289 0.284\nterabyte05 0.171 0.208 0.383 0.022 0.072 0.193 0.120 0.225 0.218 0.257\nTable 1: Comparison to Robustness and Clarity measures for language model scores. Evaluation replicates\nexperiments from [19]. We present correlations between the classic Clarity measure (DV\nKL), the ranking\nrobustness measure (P), and autocorrelation (\u03c1(y, \u02dcy)) each with mean average precision in terms of Kendall\"s\n\u03c4. The adjusted coefficient of determination is presented to measure the effectiveness of combining predictors.\nMeasures in bold represent the strongest correlation for that test/collection pair.\nmultiple run\n(a) (b) (c)\n\u03c4 \u03c4 adjusted R2\nDKL \u03c1(y, \u02dcy) Dn\nKL \u03c1(y, y\u00b5) \u03c1(\u02dcy, y\u00b5) Dn\nKL \u03c1(y, \u02dcy) \u03c1(y, y\u00b5) \u03c1(\u02dcy, y\u00b5) \u03b2\ntrec3 0.201 0.461 0.461 0.439 0.456 0.444 0.395 0.394 0.386 0.498\ntrec4 0.252 0.396 0.455 0.482 0.489 0.379 0.263 0.429 0.482 0.483\ntrec5 0.016 0.277 0.433 0.459 0.393 0.280 0.157 0.375 0.323 0.386\ntrec6 0.230 0.227 0.352 0.428 0.418 0.203 0.089 0.323 0.325 0.325\ntrec7 0.083 0.326 0.341 0.430 0.483 0.264 0.182 0.363 0.442 0.400\ntrec8 0.235 0.396 0.454 0.508 0.567 0.402 0.272 0.490 0.580 0.523\nrobust03 0.302 0.354 0.377 0.385 0.447 0.269 0.206 0.274 0.392 0.303\nrobust04 0.183 0.308 0.301 0.384 0.453 0.200 0.182 0.301 0.393 0.335\nrobust05 0.224 0.249 0.371 0.377 0.404 0.341 0.108 0.313 0.328 0.336\nterabyte04 0.043 0.245 0.544 0.420 0.392 0.516 0.105 0.357 0.343 0.365\nterabyte05 0.068 0.306 0.480 0.434 0.390 0.491 0.168 0.384 0.309 0.403\ntrec4-spanish 0.307 0.388 0.488 0.398 0.395 0.423 0.299 0.282 0.299 0.388\ntrec5-spanish 0.220 0.458 0.446 0.484 0.475 0.411 0.398 0.428 0.437 0.529\ntrec5-chinese 0.092 0.199 0.367 0.379 0.384 0.379 0.199 0.273 0.276 0.310\ntrec6-chinese 0.144 0.276 0.265 0.353 0.376 0.115 0.128 0.188 0.223 0.199\nent05 - 0.181 0.324 0.305 0.282 0.211 0.043 0.158 0.155 0.179\nTable 2: Large scale prediction experiments. We predict the ranking of large sets of retrievals for various\ncollections and retrieval systems. Kendall\"s \u03c4 correlations are computed between the predicted ranking and\na ranking based on the retrieval\"s average precision. In column (a), we have predictors which do not use\ninformation from other retrievals for the same query. In columns (b) and (c) we present performance for\npredictors which incorporate information from multiple retrievals. The adjusted coefficient of determination\nis computed to determine effectiveness of combining predictors. Measures in bold represent the strongest\ncorrelation for that test/collection pair.\nFinally, regularization-based re-ranking processes are also\nclosely-related to our work [8]. These techniques seek to\nmaximize the agreement between scores of related\ndocuments by solving a constrained optimization problem. The\nmaximization of consistency is equivalent to maximizing the\nMoran autocorrelation. Therefore, we believe that our work\nprovides explanation for why regularization-based re-ranking\nworks.\n9. CONCLUSION\nWe have presented a new method for predicting the\nperformance of a retrieval ranking without any relevance\njudgments. We consider two cases. First, when making\npredictions in the absence of retrievals from other systems, our\npredictors demonstrate robust, strong correlations with\naverage precision. This performance, combined with a simple\nimplementation, makes our predictors, in particular, very\nattractive. We have demonstrated this improvement for many,\ndiverse settings. To our knowledge, this is the first large\nscale examination of zero-judgment, single-retrieval\nperformance prediction. Second, when provided retrievals from\nother systems, our extended methods demonstrate\ncompetitive performance with state of the art baselines. Our\nexperiments also demonstrate the limits of the usefulness of our\npredictors when information from multiple runs is provided.\nOur results suggest two conclusions. First, our results\ncould affect retrieval algorithm design. Retrieval algorithms\ndesigned to consider spatial autocorrelation will conform to\nthe cluster hypothesis and improve performance. Second,\nour results could affect the design of minimal test collection\nalgorithms. Much of the recent work in ranking systems\nsometimes ignores correlations between document labels and\nscores. We believe that these two directions could be\nrewarding given the theoretical and experimental evidence in this\npaper.\n10. ACKNOWLEDGMENTS\nThis work was supported in part by the Center for\nIntelligent Information Retrieval and in part by the Defense\nAdvanced Research Projects Agency (DARPA) under\ncontract number HR0011-06-C-0023. Any opinions, findings\nand conclusions or recommendations expressed in this\nmaterial are the author\"s and do not necessarily reflect those\nof the sponsor. We thank Yun Zhou and Desislava Petkova\nfor providing data and Andre Gauthier for technical\nassistance.\n11. REFERENCES\n[1] J. Aslam and V. Pavlu. Query hardness estimation using\njensen-shannon divergence among multiple scoring\nfunctions. In ECIR 2007: Proceedings of the 29th European\nConference on Information Retrieval, 2007.\n[2] J. A. Aslam, V. Pavlu, and E. Yilmaz. A statistical method\nfor system evaluation using incomplete judgments. In\nS. Dumais, E. N. Efthimiadis, D. Hawking, and K. Jarvelin,\neditors, Proceedings of the 29th Annual International ACM\nSIGIR Conference on Research and Development in\nInformation Retrieval, pages 541-548. ACM Press, August\n2006.\n[3] D. Carmel, E. Yom-Tov, A. Darlow, and D. Pelleg. What\nmakes a query difficult? In SIGIR \"06: Proceedings of the\n29th annual international ACM SIGIR conference on\nResearch and development in information retrieval, pages\n390-397, New York, NY, USA, 2006. ACM Press.\n[4] B. Carterette, J. Allan, and R. Sitaraman. Minimal test\ncollections for retrieval evaluation. In SIGIR \"06:\nProceedings of the 29th annual international ACM SIGIR\nconference on Research and development in information\nretrieval, pages 268-275, New York, NY, USA, 2006. ACM\nPress.\n[5] A. D. Cliff and J. K. Ord. Spatial Autocorrelation. Pion\nLtd., 1973.\n[6] M. Connell, A. Feng, G. Kumaran, H. Raghavan, C. Shah,\nand J. Allan. Umass at tdt 2004. Technical Report CIIR\nTechnical Report IR - 357, Department of Computer\nScience, University of Massachusetts, 2004.\n[7] S. Cronen-Townsend, Y. Zhou, and W. B. Croft. Precision\nprediction based on ranked list coherence. Inf. Retr.,\n9(6):723-755, 2006.\n[8] F. Diaz. Regularizing ad-hoc retrieval scores. In CIKM \"05:\nProceedings of the 14th ACM international conference on\nInformation and knowledge management, pages 672-679,\nNew York, NY, USA, 2005. ACM Press.\n[9] F. Diaz and R. Jones. Using temporal profiles of queries for\nprecision prediction. In SIGIR \"04: Proceedings of the 27th\nannual international ACM SIGIR conference on Research\nand development in information retrieval, pages 18-24,\nNew York, NY, USA, 2004. ACM Press.\n[10] D. A. Griffith. Spatial Autocorrelation and Spatial\nFiltering. Springer Verlag, 2003.\n[11] B. He and I. Ounis. Inferring Query Performance Using\nPre-retrieval Predictors. In The Eleventh Symposium on\nString Processing and Information Retrieval (SPIRE),\n2004.\n[12] N. Jardine and C. J. V. Rijsbergen. The use of hierarchic\nclustering in information retrieval. Information Storage and\nRetrieval, 7:217-240, 1971.\n[13] D. Jensen and J. Neville. Linkage and autocorrelation cause\nfeature selection bias in relational learning. In ICML \"02:\nProceedings of the Nineteenth International Conference on\nMachine Learning, pages 259-266, San Francisco, CA,\nUSA, 2002. Morgan Kaufmann Publishers Inc.\n[14] O. Kurland and L. Lee. Corpus structure, language models,\nand ad-hoc information retrieval. In SIGIR \"04:\nProceedings of the 27th annual international conference on\nResearch and development in information retrieval, pages\n194-201, New York, NY, USA, 2004. ACM Press.\n[15] M. Montague and J. A. Aslam. Relevance score\nnormalization for metasearch. In CIKM \"01: Proceedings of\nthe tenth international conference on Information and\nknowledge management, pages 427-433, New York, NY,\nUSA, 2001. ACM Press.\n[16] T. Qin, T.-Y. Liu, X.-D. Zhang, Z. Chen, and W.-Y. Ma. A\nstudy of relevance propagation for web search. In SIGIR\n\"05: Proceedings of the 28th annual international ACM\nSIGIR conference on Research and development in\ninformation retrieval, pages 408-415, New York, NY, USA,\n2005. ACM Press.\n[17] I. Soboroff, C. Nicholas, and P. Cahan. Ranking retrieval\nsystems without relevance judgments. In SIGIR \"01:\nProceedings of the 24th annual international ACM SIGIR\nconference on Research and development in information\nretrieval, pages 66-73, New York, NY, USA, 2001. ACM\nPress.\n[18] V. Vinay, I. J. Cox, N. Milic-Frayling, and K. Wood. On\nranking the effectiveness of searches. In SIGIR \"06:\nProceedings of the 29th annual international ACM SIGIR\nconference on Research and development in information\nretrieval, pages 398-404, New York, NY, USA, 2006. ACM\nPress.\n[19] Y. Zhou and W. B. Croft. Ranking robustness: a novel\nframework to predict query performance. In CIKM \"06:\nProceedings of the 15th ACM international conference on\nInformation and knowledge management, pages 567-574,\nNew York, NY, USA, 2006. ACM Press.", "keywords": "query ranking;spatial autocorrelation;predictor predictive power;predictor relationship;language model score;ranking of query;regularization;autocorrelation;performance prediction;information retrieval;zero relevance judgment;cluster hypothesis;predictive power of predictor;relationship of predictor"}
{"name": "train_H-50", "title": "An Outranking Approach for Rank Aggregation in Information Retrieval", "abstract": "Research in Information Retrieval usually shows performance improvement when many sources of evidence are combined to produce a ranking of documents (e.g., texts, pictures, sounds, etc.). In this paper, we focus on the rank aggregation problem, also called data fusion problem, where rankings of documents, searched into the same collection and provided by multiple methods, are combined in order to produce a new ranking. In this context, we propose a rank aggregation method within a multiple criteria framework using aggregation mechanisms based on decision rules identifying positive and negative reasons for judging whether a document should get a better rank than another. We show that the proposed method deals well with the Information Retrieval distinctive features. Experimental results are reported showing that the suggested method performs better than the well-known CombSUM and CombMNZ operators.", "fulltext": "1. INTRODUCTION\nA wide range of current Information Retrieval (IR)\napproaches are based on various search models (Boolean,\nVector Space, Probabilistic, Language, etc. [2]) in order to\nretrieve relevant documents in response to a user request. The\nresult lists produced by these approaches depend on the\nexact definition of the relevance concept.\nRank aggregation approaches, also called data fusion\napproaches, consist in combining these result lists in order\nto produce a new and hopefully better ranking. Such\napproaches give rise to metasearch engines in the Web context.\nWe consider, in the following, cases where only ranks are\navailable and no other additional information is provided\nsuch as the relevance scores. This corresponds indeed to the\nreality, where only ordinal information is available.\nData fusion is also relevant in other contexts, such as when\nthe user writes several queries of his/her information need\n(e.g., a boolean query and a natural language query) [4], or\nwhen many document surrogates are available [16].\nSeveral studies argued that rank aggregation has the\npotential of combining effectively all the various sources of\nevidence considered in various input methods. For instance,\nexperiments carried out in [16], [30], [4] and [19] showed that\ndocuments which appear in the lists of the majority of the\ninput methods are more likely to be relevant. Moreover, Lee\n[19] and Vogt and Cottrell [31] found that various retrieval\napproaches often return very different irrelevant documents,\nbut many of the same relevant documents. Bartell et al.\n[3] also found that rank aggregation methods improve the\nperformances w.r.t. those of the input methods, even when\nsome of them have weak individual performances. These\nmethods also tend to smooth out biases of the input\nmethods according to Montague and Aslam [22]. Data fusion has\nrecently been proved to improve performances for both the\nad-hoc retrieval and categorization tasks within the TREC\ngenomics track in 2005 [1].\nThe rank aggregation problem was addressed in various\nfields such as i) in social choice theory which studies\nvoting algorithms which specify winners of elections or winners\nof competitions in tournaments [29], ii) in statistics when\nstudying correlation between rankings, iii) in distributed\ndatabases when results from different databases must be\ncombined [12], and iv) in collaborative filtering [23].\nMost current rank aggregation methods consider each\ninput ranking as a permutation over the same set of items.\nThey also give rigid interpretation to the exact ranking of\nthe items. Both of these assumptions are rather not valid in\nthe IR context, as will be shown in the following sections.\nThe remaining of the paper is organized as follows. We\nfirst review current rank aggregation methods in Section 2.\nThen we outline the specificities of the data fusion problem\nin the IR context (Section 3). In Section 4, we present a\nnew aggregation method which is proven to best fit the IR\ncontext. Experimental results are presented in Section 5 and\nconclusions are provided in a final section.\n2. RELATED WORK\nAs pointed out by Riker [25], we can distinguish two\nfamilies of rank aggregation methods: positional methods which\nassign scores to items to be ranked according to the ranks\nthey receive and majoritarian methods which are based on\npairwise comparisons of items to be ranked. These two\nfamilies of methods find their roots in the pioneering works of\nBorda [5] and Condorcet [7], respectively, in the social choice\nliterature.\n2.1 Preliminaries\nWe first introduce some basic notations to present the\nrank aggregation methods in a uniform way. Let D =\n{d1, d2, . . . , dnd } be a set of nd documents. A list or a\nranking j is an ordering defined on Dj \u2286 D (j = 1, . . . , n).\nThus, di j di means di \u2018is ranked better than\" di in j.\nWhen Dj = D, j is said to be a full list. Otherwise, it\nis a partial list. If di belongs to Dj, rj\ni denotes the rank\nor position of di in j. We assume that the best answer\n(document) is assigned the position 1 and the worst one is\nassigned the position |Dj|. Let D be the set of all\npermutations on D or all subsets of D. A profile is a n-tuple\nof rankings PR = ( 1, 2, . . . , n). Restricting PR to the\nrankings containing document di defines PRi. We also call\nthe number of rankings which contain document di the rank\nhits of di [19].\nThe rank aggregation or data fusion problem consists of\nfinding a ranking function or mechanism \u03a8 (also called a\nsocial welfare function in the social choice theory terminology)\ndefined by:\n\u03a8 :\nn\nD \u2192 D\nPR = ( 1, 2, . . . , n) \u2192 \u03c3 = \u03a8(PR)\nwhere \u03c3 is called a consensus ranking.\n2.2 Positional Methods\n2.2.1 Borda Count\nThis method [5] first assigns a score n\nj=1 rj\ni to each\ndocument di. Documents are then ranked by increasing order\nof this score, breaking ties, if any, arbitrarily.\n2.2.2 Linear Combination Methods\nThis family of methods basically combine scores of\ndocuments. When used for the rank aggregation problem, ranks\nare assumed to be scores or performances to be combined\nusing aggregation operators such as the weighted sum or\nsome variation of it [3, 31, 17, 28].\nFor instance, Callan et al. [6] used the inference\nnetworks model [30] to combine rankings. Fox and Shaw [15]\nproposed several combination strategies which are\nCombSUM, CombMIN, CombMAX, CombANZ and CombMNZ.\nThe first three operators correspond to the sum, min and\nmax operators, respectively. CombANZ and CombMNZ\nrespectively divides and multiplies the CombSUM score by\nthe rank hits. It is shown in [19] that the CombSUM and\nCombMNZ operators perform better than the others.\nMetasearch engines such as SavvySearch and MetaCrawler use\nthe CombSUM strategy to fuse rankings.\n2.2.3 Footrule Optimal Aggregation\nIn this method, a consensus ranking minimizes the\nSpearman footrule distance from the input rankings [21].\nFormally, given two full lists j and j , this distance is given\nby F( j, j ) = nd\ni=1 |rj\ni \u2212 rj\ni |. It extends to several lists\nas follows. Given a profile PR and a consensus ranking\n\u03c3, the Spearman footrule distance of \u03c3 to PR is given by\nF(\u03c3, PR) = n\nj=1 F(\u03c3, j).\nCook and Kress [8] proposed a similar method which\nconsists in optimizing the distance D( j, j ) = 1\n2\nnd\ni,i =1 |rj\ni,i \u2212\nrj\ni,i |, where rj\ni,i = rj\ni \u2212rj\ni . This formulation has the\nadvantage that it considers the intensity of preferences.\n2.2.4 Probabilistic Methods\nThis kind of methods assume that the performance of the\ninput methods on a number of training queries is indicative\nof their future performance. During the training process,\nprobabilities of relevance are calculated. For subsequent\nqueries, documents are ranked based on these probabilities.\nFor instance, in [20], each input ranking j is divided into a\nnumber of segments, and the conditional probability of\nrelevance (R) of each document di depending on the segment\nk it occurs in, is computed, i.e. prob(R|di, k, j). For\nsubsequent queries, the score of each document di is given by\nn\nj=1\nprob(R|di,k, j )\nk\n. Le Calve and Savoy [18] suggest using\na logistic regression approach for combining scores. Training\ndata is needed to infer the model parameters.\n2.3 Majoritarian Methods\n2.3.1 Condorcet Procedure\nThe original Condorcet rule [7] specifies that a winner of\nthe election is any item that beats or ties with every other\nitem in a pairwise contest. Formally, let C(di\u03c3di ) = { j\u2208\nPR : di j di } be the coalition of rankings that are\nconcordant with establishing di\u03c3di , i.e. with the proposition\ndi \u2018should be ranked better than\" di in the final ranking \u03c3.\ndi beats or ties with di iff |C(di\u03c3di )| \u2265 |C(di \u03c3di)|.\nThe repetitive application of the Condorcet algorithm can\nproduce a ranking of items in a natural way: select the\nCondorcet winner, remove it from the lists, and repeat the\nprevious two steps until there are no more documents to rank.\nSince there is not always Condorcet winners, variations of\nthe Condorcet procedure have been developed within the\nmultiple criteria decision aid theory, with methods such as\nELECTRE [26].\n2.3.2 Kemeny Optimal Aggregation\nAs in section 2.2.3, a consensus ranking minimizes a\ngeometric distance from the input rankings, where the Kendall\ntau distance is used instead of the Spearman footrule\ndistance. Formally, given two full lists j and j , the Kendall\ntau distance is given by K( j, j ) = |{(di, di ) : i < i , rj\ni <\nrj\ni , rj\ni > rj\ni }|, i.e. the number of pairwise disagreements\nbetween the two lists. It is easy to show that the consensus\nranking corresponds to the geometric median of the input\nrankings and that the Kemeny optimal aggregation problem\ncorresponds to the minimum feedback edge set problem.\n2.3.3 Markov Chain Methods\nMarkov chains (MCs) have been used by Dwork et al. [11]\nas a \u2018natural\" method to obtain a consensus ranking where\nstates correspond to the documents to be ranked and the\ntransition probabilities vary depending on the interpretation\nof the transition event. In the same reference, the authors\nproposed four specific MCs and experimental testing had\nshown that the following MC is the best performing one\n(see also [24]):\n\u2022 MC4: move from the current state di to the next state\ndi by first choosing a document di uniformly from D.\nIf for the majority of the rankings, we have rj\ni \u2264 rj\ni ,\nthen move to di , else stay in di.\nThe consensus ranking corresponds to the stationary\ndistribution of MC4.\n3. SPECIFICITIES OF THE RANK\nAGGREGATION PROBLEM IN THE IR CONTEXT\n3.1 Limited Significance of the Rankings\nThe exact positions of documents in one input ranking\nhave limited significance and should not be overemphasized.\nFor instance, having three relevant documents in the first\nthree positions, any perturbation of these three items will\nhave the same value. Indeed, in the IR context, the complete\norder provided by an input method may hide ties. In this\ncase, we call such rankings semi orders. This was outlined in\n[13] as the problem of aggregation with ties. It is therefore\nimportant to build the consensus ranking based on robust\ninformation:\n\u2022 Documents with near positions in j are more likely\nto have similar interest or relevance. Thus a slight\nperturbation of the initial ranking is meaningless.\n\u2022 Assuming that document di is better ranked than\ndocument di in a ranking j, di is more likely to be\ndefinitively more relevant than di in j when the number\nof intermediate positions between di and di increases.\n3.2 Partial Lists\nIn real world applications, such as metasearch engines,\nrankings provided by the input methods are often partial\nlists. This was outlined in [14] as the problem of having to\nmerge top-k results from various input lists. For instance,\nin the experiments carried out by Dwork et al. [11], authors\nfound that among the top 100 best documents of 7 input\nsearch engines, 67% of the documents were present in only\none search engine, whereas less than two documents were\npresent in all the search engines.\nRank aggregation of partial lists raises four major\ndifficulties which we state hereafter, proposing for each of them\nvarious working assumptions:\n1. Partial lists can have various lengths, which can favour\nlong lists. We thus consider the following two working\nhypotheses:\nH1\nk : We only consider the top k best documents from\neach input ranking.\nH1\nall: We consider all the documents from each input\nranking.\n2. Since there are different documents in the input\nrankings, we must decide which documents should be kept\nin the consensus ranking. Two working hypotheses are\ntherefore considered:\nH2\nk : We only consider documents which are present in\nat least k input rankings (k > 1).\nH2\nall: We consider all the documents which are ranked\nin at least one input ranking.\nHereafter, we call documents which will be retained\nin the consensus ranking, candidate documents, and\ndocuments that will be excluded from the consensus\nranking, excluded documents. We also call a candidate\ndocument which is missing in one or more rankings, a\nmissing document.\n3. Some candidate documents are missing documents in\nsome input rankings. Main reasons for a missing\ndocument are that it was not indexed or it was indexed\nbut deemed irrelevant ; usually this information is not\navailable. We consider the following two working\nhypotheses:\nH3\nyes: Each missing document in each j is assigned\na position.\nH3\nno: No assumption is made, that is each missing\ndocument is considered neither better nor worse than any\nother document.\n4. When assumption H2\nk holds, each input ranking may\ncontain documents which will not be considered in the\nconsensus ranking. Regarding the positions of the\ncandidate documents, we can consider the following\nworking hypotheses:\nH4\ninit: The initial positions of candidate documents\nare kept in each input ranking.\nH4\nnew: Candidate documents receive new positions in\neach input ranking, after discarding excluded ones.\nIn the IR context, rank aggregation methods need to\ndecide more or less explicitly which assumptions to retain\nw.r.t. the above-mentioned difficulties.\n4. OUTRANKING APPROACH FOR RANK\nAGGREGATION\n4.1 Presentation\nPositional methods consider implicitly that the positions\nof the documents in the input rankings are scores giving thus\na cardinal meaning to an ordinal information. This\nconstitutes a strong assumption that is questionable, especially\nwhen the input rankings have different lengths. Moreover,\nfor positional methods, assumptions H3\nand H4\n, which are\noften arbitrary, have a strong impact on the results. For\ninstance, let us consider an input ranking of 500 documents\nout of 1000 candidate documents. Whether we assign to\neach of the missing documents the position 1, 501, 750 or\n1000 -corresponding to variations of H3\nyes- will give rise to\nvery contrasted results, especially regarding the top of the\nconsensus ranking.\nMajoritarian methods do not suffer from the\nabove-mentioned drawbacks of the positional methods since they build\nconsensus rankings exploiting only ordinal information\ncontained in the input rankings. Nevertheless, they suppose\nthat such rankings are complete orders, ignoring that they\nmay hide ties. Therefore, majoritarian methods base\nconsensus rankings on illusory discriminant information rather\nthan less discriminant but more robust information.\nTrying to overcome the limits of current rank aggregation\nmethods, we found that outranking approaches, which were\ninitially used for multiple criteria aggregation problems [26],\ncan also be used for the rank aggregation purpose, where\neach ranking plays the role of a criterion. Therefore, in\norder to decide whether a document di should be ranked\nbetter than di in the consensus ranking \u03c3, the two following\nconditions should be met:\n\u2022 a concordance condition which ensures that a\nmajority of the input rankings are concordant with di\u03c3di\n(majority principle).\n\u2022 a discordance condition which ensures that none of the\ndiscordant input rankings strongly refutes d\u03c3d\n(respect of minorities principle).\nFormally, the concordance coalition with di\u03c3di is\nCsp (di\u03c3di ) = { j\u2208 PR : rj\ni \u2264 rj\ni \u2212 sp}\nwhere sp is a preference threshold which is the variation\nof document positions -whether it is absolute or relative to\nthe ranking length- which draws the boundaries between an\nindifference and a preference situation between documents.\nThe discordance coalition with di\u03c3di is\nDsv (di\u03c3di ) = { j\u2208 PR : rj\ni \u2265 rj\ni + sv}\nwhere sv is a veto threshold which is the variation of\ndocument positions -whether it is absolute or relative to the\nranking length- which draws the boundaries between a weak\nand a strong opposition to di\u03c3di .\nDepending on the exact definition of the preceding\nconcordance and discordance coalitions leading to the definition\nof some decision rules, several outranking relations can be\ndefined. They can be more or less demanding depending on\ni) the values of the thresholds sp and sv, ii) the importance\nor minimal size cmin required for the concordance coalition,\nand iii) the importance or maximum size dmax of the\ndiscordance coalition.\nA generic outranking relation can thus be defined as\nfollows:\ndiS(sp,sv,cmin,dmax)di \u21d4 |Csp (di\u03c3di )| \u2265 cmin\nAND |Dsv (di\u03c3di )| \u2264 dmax\nThis expression defines a family of nested outranking\nrelations since S(sp,sv,cmin,dmax) \u2286 S(sp,sv,cmin,dmax) when\ncmin \u2265 cmin and/or dmax \u2264 dmax and/or sp \u2265 sp and/or\nsv \u2264 sv. This expression also generalizes the majority rule\nwhich corresponds to the particular relation S(0,\u221e, n\n2\n,n). It\nalso satisfies important properties of rank aggregation\nmethods, called neutrality, Pareto-optimality, Condorcet\nproperty and Extended Condorcet property, in the social choice\nliterature [29].\nOutranking relations are not necessarily transitive and do\nnot necessarily correspond to rankings since directed cycles\nmay exist. Therefore, we need specific procedures in order to\nderive a consensus ranking. We propose the following\nprocedure which finds its roots in [27]. It consists in partitioning\nthe set of documents into r ranked classes.\nEach class Ch contains documents with the same relevance\nand results from the application of all relations (if possible)\nto the set of documents remaining after previous classes are\ncomputed. Documents within the same equivalence class are\nranked arbitrarily.\nFormally, let\n\u2022 R be the set of candidate documents for a query,\n\u2022 S1\n, S2\n, . . . be a family of nested outranking relations,\n\u2022 Fk(di, E) = |{di \u2208 E : diSk\ndi }| be the number of\ndocuments in E(E \u2286 R) that could be considered\n\u2018worse\" than di according to relation Sk\n,\n\u2022 fk(di, E) = |{di \u2208 E : di Sk\ndi}| be the number of\ndocuments in E that could be considered \u2018better\" than\ndi according to Sk\n,\n\u2022 sk(di, E) = Fk(di, E) \u2212 fk(di, E) be the qualification\nof di in E according to Sk\n.\nEach class Ch results from a distillation process. It\ncorresponds to the last distillate of a series of sets E0 \u2287 E1 \u2287 . . .\nwhere E0 = R \\ (C1 \u222a . . . \u222a Ch\u22121) and Ek is a reduced\nsubset of Ek\u22121 resulting from the application of the following\nprocedure:\n1. compute for each di \u2208 Ek\u22121 its qualification according\nto Sk\n, i.e. sk(di, Ek\u22121),\n2. define smax = maxdi\u2208Ek\u22121 {sk(di, Ek\u22121)}, then\n3. Ek = {di \u2208 Ek\u22121 : sk(di, Ek\u22121) = smax}\nWhen one outranking relation is used, the distillation\nprocess stops after the first application of the previous\nprocedure, i.e., Ch corresponds to distillate E1. When different\noutranking relations are used, the distillation process stops\nwhen all the pre-defined outranking relations have been used\nor when |Ek| = 1.\n4.2 Illustrative Example\nThis section illustrates the concepts and procedures of\nsection 4.1. Let us consider a set of candidate documents\nR = {d1, d2, d3, d4, d5}. The following table gives a profile\nPR of different rankings of the documents of R: PR = ( 1\n, 2, 3, 4).\nTable 1: Rankings of documents\nrj\ni 1 2 3 4\nd1 1 3 1 5\nd2 2 1 3 3\nd3 3 2 2 1\nd4 4 4 5 2\nd5 5 5 4 4\nLet us suppose that the preference and veto thresholds\nare set to values 1 and 4 respectively, and that the\nconcordance and discordance thresholds are set to values 2 and 1\nrespectively. The following tables give the concordance,\ndiscordance and outranking matrices. Each entry csp (di, di )\n(dsv (di, di )) in the concordance (discordance) matrix gives\nthe number of rankings that are concordant (discordant)\nwith di\u03c3di , i.e. csp (di, di ) = |Csp (di\u03c3di )| and dsv (di, di ) =\n|Dsv (di\u03c3di )|.\nTable 2: Computation of the outranking relation\nd1 d2 d3 d4 d5\nd1 - 2 2 3 3\nd2 2 - 2 3 4\nd3 2 2 - 4 4\nd4 1 1 0 - 3\nd5 1 0 0\n1Concordance Matrix\nd1 d2 d3 d4 d5\nd1 - 0 1 0 0\nd2 0 - 0 0 0\nd3 0 0 - 0 0\nd4 1 0 0 - 0\nd5 1 1 0\n0Discordance Matrix\nd1 d2 d3 d4 d5\nd1 - 1 1 1 1\nd2 1 - 1 1 1\nd3 1 1 - 1 1\nd4 0 0 0 - 1\nd5 0 0 0\n0Outranking Matrix (S1)\nFor instance, the concordance coalition for the assertion\nd1\u03c3d4 is C1(d1\u03c3d4) = { 1, 2, 3} and the discordance\ncoalition for the same assertion is D4(d1\u03c3d4) = \u2205.\nTherefore, c1(d1, d4) = 3, d4(d1, d4) = 0 and d1S1\nd4 holds.\nNotice that Fk(di, R) (fk(di, R)) is given by summing the\nvalues of the ith\nrow (column) of the outranking matrix. The\nconsensus ranking is obtained as follows: to get the first class\nC1, we compute the qualifications of all the documents of\nE0 = R with respect to S1\n. They are respectively 2, 2, 2, -2\nand -4. Therefore smax equals 2 and C1 = E1 = {d1, d2, d3}.\nObserve that, if we had used a second outranking relation\nS2(\u2287 S1), these three documents could have been\npossibly discriminated. At this stage, we remove documents of\nC1 from the outranking matrix and compute the next class\nC2: we compute the new qualifications of the documents of\nE0 = R \\ C1 = {d4, d5}. They are respectively 1 and -1. So\nC3 = E1 = {d4}. The last document d5 is the only\ndocument of the last class C3. Thus, the consensus ranking is\n{d1, d2, d3} \u2192 {d4} \u2192 {d5}.\n5. EXPERIMENTS AND RESULTS\n5.1 Test Setting\nTo facilitate empirical investigation of the proposed\nmethodology, we developed a prototype metasearch engine that\nimplements a version of our outranking approach for rank\naggregation. In this paper, we apply our approach to the\nTopic Distillation (TD) task of TREC-2004 Web track [10].\nIn this task, there are 75 topics where only a short\ndescription of each is given. For each query, we retained the\nrankings of the 10 best runs of the TD task which are provided\nby TREC-2004 participating teams. The performances of\nthese runs are reported in table 3.\nTable 3: Performances of the 10 best runs of the TD\ntask of TREC-2004\nRun Id MAP P@10 S@1 S@5 S@10\nuogWebCAU150 17.9% 24.9% 50.7% 77.3% 89.3%\nMSRAmixed1 17.8% 25.1% 38.7% 72.0% 88.0%\nMSRC04C12 16.5% 23.1% 38.7% 74.7% 80.0%\nhumW04rdpl 16.3% 23.1% 37.3% 78.7% 90.7%\nTHUIRmix042 14.7% 20.5% 21.3% 58.7% 74.7%\nUAmsT04MWScb 14.6% 20.9% 36.0% 66.7% 76.0%\nICT04CIIS1AT 14.1% 20.8% 33.3% 64.0% 78.7%\nSJTUINCMIX5 12.9% 18.9% 29.3% 57.3% 72.0%\nMU04web1 11.5% 19.9% 33.3% 64.0% 76.0%\nMeijiHILw3 11.5% 15.3% 30.7% 54.7% 64.0%\nAverage 14.7% 21.2% 34.9% 66.8% 78.94%\nFor each query, each run provides a ranking of about 1000\ndocuments. The number of documents retrieved by all these\nruns ranges from 543 to 5769. Their average (median)\nnumber is 3340 (3386). It is worth noting that we found similar\ndistributions of the documents among the rankings as in\n[11].\nFor evaluation, we used the \u2018trec eval\" standard tool which\nis used by the TREC community to calculate the standard\nmeasures of system effectiveness which are Mean Average\nPrecision (MAP) and Success@n (S@n) for n=1, 5 and 10.\nOur approach effectiveness is compared against some high\nperforming official results from TREC-2004 as well as against\nsome standard rank aggregation algorithms. In the\nexperiments, significance testing is mainly based on the t-student\nstatistic which is computed on the basis of the MAP values of\nthe compared runs. In the tables of the following section,\nstatistically significant differences are marked with an\nasterisk. Values between brackets of the first column of each\ntable, indicate the parameter value of the corresponding run.\n5.2 Results\nWe carried out several series of runs in order to i) study\nperformance variations of the outranking approach when\ntuning the parameters and working assumptions, ii)\ncompare performances of the outranking approach vs standard\nrank aggregation strategies , and iii) check whether rank\naggregation performs better than the best input rankings.\nWe set our basic run mcm with the following parameters.\nWe considered that each input ranking is a complete\norder (sp = 0) and that an input ranking strongly refutes\ndi\u03c3di when the difference of both document positions is\nlarge enough (sv = 75%). Preference and veto thresholds\nare computed proportionally to the number of documents\nretained in each input ranking. They consequently may vary\nfrom one ranking to another. In addition, to accept the\nassertion di\u03c3di , we supposed that the majority of the\nrankings must be concordant (cmin = 50%) and that every input\nranking can impose its veto (dmax = 0). Concordance and\ndiscordance thresholds are computed for each tuple (di, di )\nas the percentage of the input rankings of PRi \u2229PRi . Thus,\nour choice of parameters leads to the definition of the\noutranking relation S(0,75%,50%,0).\nTo test the run mcm, we had chosen the following\nassumptions. We retained the top 100 best documents from each\ninput ranking (H1\n100), only considered documents which are\npresent in at least half of the input rankings (H2\n5 ) and\nassumed H3\nno and H4\nnew. In these conditions, the number of\nsuccessful documents was about 100 on average, and the\ncomputation time per query was less than one second.\nObviously, modifying the working assumptions should have\ndeeper impact on the performances than tuning our model\nparameters. This was validated by preliminary experiments.\nThus, we hereafter begin by studying performance variation\nwhen different sets of assumptions are considered.\nAfterwards, we study the impact of tuning parameters. Finally,\nwe compare our model performances w.r.t. the input\nrankings as well as some standard data fusion algorithms.\n5.2.1 Impact of the Working Assumptions\nTable 4 summarizes the performance variation of the\noutranking approach under different working hypotheses. In\nTable 4: Impact of the working assumptions\nRun Id MAP S@1 S@5 S@10\nmcm 18.47% 41.33% 81.33% 86.67%\nmcm22 (H3\nyes) 17.72% (-4.06%) 34.67% 81.33% 86.67%\nmcm23 (H4\ninit) 18.26% (-1.14%) 41.33% 81.33% 86.67%\nmcm24 (H1\nall) 20.67% (+11.91%*) 38.66% 80.00% 86.66%\nmcm25 (H2\nall) 21.68% (+17.38%*) 40.00% 78.66% 89.33%\nthis table, we first show that run mcm22, in which missing\ndocuments are all put in the same last position of each input\nranking, leads to performance drop w.r.t. run mcm.\nMoreover, S@1 moves from 41.33% to 34.67% (-16.11%). This\nshows that several relevant documents which were initially\nput at the first position of the consensus ranking in mcm, lose\nthis first position but remain ranked in the top 5 documents\nsince S@5 did not change. We also conclude that documents\nwhich have rather good positions in some input rankings are\nmore likely to be relevant, even though they are missing in\nsome other rankings. Consequently, when they are missing\nin some rankings, assigning worse ranks to these documents\nis harmful for performance.\nAlso, from Table 4, we found that the performances of\nruns mcm and mcm23 are similar. Therefore, the outranking\napproach is not sensitive to keeping the initial positions of\ncandidate documents or recomputing them by discarding\nexcluded ones.\nFrom the same Table 4, performance of the outranking\napproach increases significantly for runs mcm24 and mcm25.\nTherefore, whether we consider all the documents which are\npresent in half of the rankings (mcm24) or we consider all\nthe documents which are ranked in the first 100 positions in\none or more rankings (mcm25), increases performances. This\nresult was predictable since in both cases we have more\ndetailed information on the relative importance of documents.\nTables 5 and 6 confirm this evidence. Table 5, where\nvalues between brackets of the first column give the number\nof documents which are retained from each input ranking,\nshows that selecting more documents from each input\nranking leads to performance increase. It is worth mentioning\nthat selecting more than 600 documents from each input\nranking does not improve performance.\nTable 5: Impact of the number of retained\ndocuments\nRun Id MAP S@1 S@5 S@10\nmcm (100) 18.47% 41.33% 81.33% 86.67%\nmcm24-1 (200) 19.32% (+4.60%) 42.67% 78.67% 88.00%\nmcm24-2 (400) 19.88% (+7.63%*) 37.33% 80.00% 88.00%\nmcm24-3 (600) 20.80% (+12.62%*) 40.00% 80.00% 88.00%\nmcm24-4 (800) 20.66% (+11.86%*) 40.00% 78.67% 86.67%\nmcm24 (1000) 20.67% (+11.91%*) 38.66% 80.00% 86.66%\nTable 6 reports runs corresponding to variations of H2\nk .\nValues between brackets are rank hits. For instance, in\nthe run mcm32, only documents which are present in 3 or\nmore input rankings, were considered successful. This\ntable shows that performance is significantly better when rare\ndocuments are considered, whereas it decreases significantly\nwhen these documents are discarded. Therefore, we\nconclude that many of the relevant documents are retrieved by\na rather small set of IR models.\nTable 6: Performance considering different rank hits\nRun Id MAP S@1 S@5 S@10\nmcm25 (1) 21.68% (+17.38%*) 40.00% 78.67% 89.33%\nmcm32 (3) 18.98% (+2.76%) 38.67% 80.00% 85.33%\nmcm (5) 18.47% 41.33% 81.33% 86.67%\nmcm33 (7) 15.83% (-14.29%*) 37.33% 78.67% 85.33%\nmcm34 (9) 10.96% (-40.66%*) 36.11% 66.67% 70.83%\nmcm35 (10) 7.42% (-59.83%*) 39.22% 62.75% 64.70%\nFor both runs mcm24 and mcm25, the number of successful\ndocuments was about 1000 and therefore, the computation\ntime per query increased and became around 5 seconds.\n5.2.2 Impact of the Variation of the Parameters\nTable 7 shows performance variation of the outranking\napproach when different preference thresholds are considered.\nWe found performance improvement up to threshold values\nof about 5%, then there is a decrease in the performance\nwhich becomes significant for threshold values greater than\n10%. Moreover, S@1 improves from 41.33% to 46.67% when\npreference threshold changes from 0 to 5%. We can thus\nconclude that the input rankings are semi orders rather than\ncomplete orders.\nTable 8 shows the evolution of the performance measures\nw.r.t. the concordance threshold. We can conclude that in\norder to put document di before di in the consensus ranking,\nTable 7: Impact of the variation of the preference\nthreshold from 0 to 12.5%\nRun Id MAP S@1 S@5 S@10\nmcm (0%) 18.47% 41.33% 81.33% 86.67%\nmcm1 (1%) 18.57% (+0.54%) 41.33% 81.33% 86.67%\nmcm2 (2.5%) 18.63% (+0.87%) 42.67% 78.67% 86.67%\nmcm3 (5%) 18.69% (+1.19%) 46.67% 81.33% 86.67%\nmcm4 (7.5%) 18.24% (-1.25%) 46.67% 81.33% 86.67%\nmcm5 (10%) 17.93% (-2.92%) 40.00% 82.67% 86.67%\nmcm5b (12.5%) 17.51% (-5.20%*) 41.33% 80.00% 86.67%\nat least half of the input rankings of PRi \u2229 PRi should be\nconcordant. Performance drops significantly for very low\nand very high values of the concordance threshold. In fact,\nfor such values, the concordance condition is either fulfilled\nrather always by too many document pairs or not fulfilled at\nall, respectively. Therefore, the outranking relation becomes\neither too weak or too strong respectively.\nTable 8: Impact of the variation of cmin\nRun Id MAP S@1 S@5 S@10\nmcm11 (20%) 17.63% (-4.55%*) 41.33% 76.00% 85.33%\nmcm12 (40%) 18.37% (-0.54%) 42.67% 76.00% 86.67%\nmcm (50%) 18.47% 41.33% 81.33% 86.67%\nmcm13 (60%) 18.42% (-0.27%) 40.00% 78.67% 86.67%\nmcm14 (80%) 17.43% (-5.63%*) 40.00% 78.67% 86.67%\nmcm15 (100%) 16.12% (-12.72%*) 41.33% 70.67% 85.33%\nIn the experiments, varying the veto threshold as well as\nthe discordance threshold within reasonable intervals does\nnot have significant impact on performance measures. In\nfact, runs with different veto thresholds (sv \u2208 [50%; 100%])\nhad similar performances even though there is a slight\nadvantage for runs with high threshold values which means\nthat it is better not to allow the input rankings to put their\nveto easily. Also, tuning the discordance threshold was\ncarried out for values 50% and 75% of the veto threshold. For\nthese runs we did not get any noticeable performance\nvariation, although for low discordance thresholds (dmax < 20%),\nperformance slightly decreased.\n5.2.3 Impact of the Variation of the Number of Input\nRankings\nTo study performance evolution when different sets of\ninput rankings are considered, we carried three more runs\nwhere 2, 4, and 6 of the best performing sets of the\ninput rankings are considered. Results reported in Table 9\nare seemingly counter-intuitive and also do not support\nprevious findings regarding rank aggregation research [3].\nNevertheless, this result shows that low performing rankings\nbring more noise than information to the establishment of\nthe consensus ranking. Therefore, when they are considered,\nperformance decreases.\nTable 9: Performance considering different best\nperforming sets of input rankings\nRun Id MAP S@1 S@5 S@10\nmcm (10) 18.47% 41.33% 81.33% 86.67%\nmcm27 (6) 18.60% (+0.70%) 41.33% 80.00% 85.33%\nmcm28 (4) 19.02% (+2.98%) 40.00% 86.67% 88.00%\nmcm29 (2) 18.33% (-0.76%) 44.00% 76.00% 88.00%\n5.2.4 Comparison of the Performance of Different\nRank Aggregation Methods\nIn this set of runs, we compare the outranking approach\nwith some standard rank aggregation methods which were\nproven to have acceptable performance in previous studies:\nwe considered two positional methods which are the\nCombSUM and the CombMNZ strategies. We also examined\nthe performance of one majoritarian method which is the\nMarkov chain method (MC4). For the comparisons, we\nconsidered a specific outranking relation S\u2217\n= S(5%,50%,50%,30%)\nwhich results in good overall performances when tuning all\nthe parameters.\nThe first row of Table 10 gives performances of the rank\naggregation methods w.r.t. a basic assumption set A1 =\n(H1\n100, H2\n5 , H4\nnew): we only consider the 100 first documents\nfrom each ranking, then retain documents present in 5 or\nmore rankings and update ranks of successful documents.\nFor positional methods, we place missing documents at the\nqueue of the ranking (H3\nyes) whereas for our method as well\nas for MC4, we retained hypothesis H3\nno. The three\nfollowing rows of Table 10 report performances when changing\none element from the basic assumption set: the second row\ncorresponds to the assumption set A2 = (H1\n1000, H2\n5 , H4\nnew),\ni.e. changing the number of retained documents from 100\nto 1000. The third row corresponds to the assumption set\nA3 = (H1\n100, H2\nall, H4\nnew), i.e. considering the documents\npresent in at least one ranking. The fourth row corresponds\nto the assumption set A4 = (H1\n100, H2\n5 , H4\ninit), i.e. keeping\nthe original ranks of successful documents.\nThe fifth row of Table 10, labeled A5, gives performance\nwhen all the 225 queries of the Web track of TREC-2004 are\nconsidered. Obviously, performance level cannot be\ncompared with previous lines since the additional queries are\ndifferent from the TD queries and correspond to other tasks\n(Home Page and Named Page tasks [10]) of TREC-2004\nWeb track. This set of runs aims to show whether relative\nperformance of the various methods is task-dependent.\nThe last row of Table 10, labeled A6, reports performance\nof the various methods considering the TD task of\nTREC2002 instead of TREC-2004: we fused the results of input\nrankings of the 10 best official runs for each of the 50 TD\nqueries [9] considering the set of assumptions A1 of the first\nrow. This aims to show whether relative performance of the\nvarious methods changes from year to year.\nValues between brackets of Table 10 are variations of\nperformance of each rank aggregation method w.r.t.\nperformance of the outranking approach.\nTable 10: Performance (MAP) of different rank\naggregation methods under 3 different test collections\nmcm combSUM combMNZ markov\nA1 18.79% 17.54% (-6.65%*) 17.08% (-9.10%*) 18.63% (-0.85%)\nA2 21.36% 19.18% (-10.21%*) 18.61% (-12.87%*) 21.33% (-0.14%)\nA3 21.92% 21.38% (-2.46%) 20.88% (-4.74%) 19.35% (-11.72%*)\nA4 18.64% 17.58% (-5.69%*) 17.18% (-7.83%*) 18.63% (-0.05%)\nA5 55.39% 52.16% (-5.83%*) 49.70% (-10.27%*) 53.30% (-3.77%)\nA6 16.95% 15.65% (-7.67%*) 14.57% (-14.04%*) 16.39% (-3.30%)\nFrom the analysis of table 10 the following can be\nestablished:\n\u2022 for all the runs, considering all the documents in each\ninput ranking (A2) significantly improves performance\n(MAP increases by 11.62% on average). This is\npredictable since some initially unreported relevant\ndocuments would receive better positions in the consensus\nranking.\n\u2022 for all the runs, considering documents even those\npresent in only one input ranking (A3) significantly\nimproves performance. For mcm, combSUM and combMNZ,\nperformance improvement is more important (MAP\nincreases by 20.27% on average) than for the markov run\n(MAP increases by 3.86%).\n\u2022 preserving the initial positions of documents (A4) or\nrecomputing them (A1) does not have a noticeable\ninfluence on performance for both positional and\nmajoritarian methods.\n\u2022 considering all the queries of the Web track of\nTREC2004 (A5) as well as the TD queries of the Web track\nof TREC-2002 (A6) does not alter the relative\nperformance of the different data fusion methods.\n\u2022 considering the TD queries of the Web track of\nTREC2002, performances of all the data fusion methods are\nlower than that of the best performing input ranking\nfor which the MAP value equals 18.58%. This is because\nmost of the fused input rankings have very low\nperformances compared to the best one, which brings more\nnoise to the consensus ranking.\n\u2022 performances of the data fusion methods mcm and markov\nare significantly better than that of the best input\nranking uogWebCAU150. This remains true for runs\ncombSUM and combMNZ only under assumptions H1\nall or\nH2\nall. This shows that majoritarian methods are less\nsensitive to assumptions than positional methods.\n\u2022 outranking approach always performs significantly\nbetter than positional methods combSUM and combMNZ. It\nhas also better performances than the Markov chain\nmethod, especially under assumption H2\nall where\ndifference of performances becomes significant.\n6. CONCLUSIONS\nIn this paper, we address the rank aggregation problem\nwhere different, but not disjoint, lists of documents are to\nbe fused. We noticed that the input rankings can hide ties,\nso they should not be considered as complete orders. Only\nrobust information should be used from each input ranking.\nCurrent rank aggregation methods, and especially\npositional methods (e.g. combSUM [15]), are not initially\ndesigned to work with such rankings. They should be adapted\nby considering specific working assumptions.\nWe propose a new outranking method for rank\naggregation which is well adapted to the IR context. Indeed, it\nranks two documents w.r.t. the intensity of their positions\ndifference in each input ranking and also considering the\nnumber of the input rankings that are concordant and\ndiscordant in favor of a specific document. There is also no\nneed to make specific assumptions on the positions of the\nmissing documents. This is an important feature since the\nabsence of a document from a ranking should not be\nnecessarily interpreted negatively.\nExperimental results show that the outranking method\nsignificantly out-performs popular classical positional data\nfusion methods like combSUM and combMNZ strategies. It\nalso out-performs a good performing majoritarian methods\nwhich is the Markov chain method. These results are tested\nagainst different test collections and queries. From the\nexperiments, we can also conclude that in order to improve the\nperformances, we should fuse result lists of well performing\nIR models, and that majoritarian data fusion methods\nperform better than positional methods.\nThe proposed method can have a real impact on Web\nmetasearch performances since only ranks are available from\nmost primary search engines, whereas most of the current\napproaches need scores to merge result lists into one single\nlist.\nFurther work involves investigating whether the\noutranking approach performs well in various other contexts, e.g.\nusing the document scores or some combination of\ndocument ranks and scores.\nAcknowledgments\nThe authors would like to thank Jacques Savoy for his\nvaluable comments on a preliminary version of this paper.\n7. REFERENCES\n[1] A. Aronson, D. Demner-Fushman, S. Humphrey,\nJ. Lin, H. Liu, P. Ruch, M. Ruiz, L. Smith, L. Tanabe,\nand W. Wilbur. 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Marden. Analyzing and Modeling Rank Data.\nNumber 64 in Monographs on Statistics and Applied\nProbability. Chapman & Hall, 1995.\n[22] M. Montague and J. A. Aslam. Metasearch\nconsistency. In Proceedings ACM-SIGIR\"2001, pages\n386-387. ACM Press, 2001.\n[23] D. M. Pennock and E. Horvitz. Analysis of the\naxiomatic foundations of collaborative filtering. In\nWorkshop on AI for Electronic Commerce at the 16th\nNational Conference on Artificial Intelligence, 1999.\n[24] M. E. Renda and U. Straccia. Web metasearch: rank\nvs. score based rank aggregation methods. In\nProceedings ACM-SAC\"2003, pages 841-846. ACM\nPress, 2003.\n[25] W. H. Riker. Liberalism against populism. Waveland\nPress, 1982.\n[26] B. Roy. The outranking approach and the foundations\nof ELECTRE methods. Theory and Decision,\n31:49-73, 1991.\n[27] B. Roy and J. Hugonnard. Ranking of suburban line\nextension projects on the Paris metro system by a\nmulticriteria method. Transportation Research,\n16A(4):301-312, 1982.\n[28] L. Si and J. Callan. Using sampled data and regression\nto merge search engine results. In Proceedings\nACM-SIGIR\"2002, pages 19-26. ACM Press, 2002.\n[29] M. Truchon. An extension of the Condorcet criterion\nand Kemeny orders. Cahier 9813, Centre de Recherche\nen Economie et Finance Appliqu\u00b4ees, Oct. 1998.\n[30] H. Turtle and W. B. Croft. Inference networks for\ndocument retrieval. In Proceedings of ACM-SIGIR\"90,\npages 1-24. ACM Press, 1990.\n[31] C. C. Vogt and G. W. Cottrell. Fusion via a linear\ncombination of scores. Information Retrieval,\n1(3):151-173, 1999.", "keywords": "rank aggregation;multiple criterion framework;metasearch engine;combsum and combmnz strategy;ir model;datum fusion;decision rule;multiple criterium approach;outrank method;information retrieval;datum fusion problem;outranking approach;majoritarian method"}
{"name": "train_H-52", "title": "Vocabulary Independent Spoken Term Detection", "abstract": "We are interested in retrieving information from speech data like broadcast news, telephone conversations and roundtable meetings. Today, most systems use large vocabulary continuous speech recognition tools to produce word transcripts; the transcripts are indexed and query terms are retrieved from the index. However, query terms that are not part of the recognizer\"s vocabulary cannot be retrieved, and the recall of the search is affected. In addition to the output word transcript, advanced systems provide also phonetic transcripts, against which query terms can be matched phonetically. Such phonetic transcripts suffer from lower accuracy and cannot be an alternative to word transcripts. We present a vocabulary independent system that can handle arbitrary queries, exploiting the information provided by having both word transcripts and phonetic transcripts. A speech recognizer generates word confusion networks and phonetic lattices. The transcripts are indexed for query processing and ranking purpose. The value of the proposed method is demonstrated by the relative high performance of our system, which received the highest overall ranking for US English speech data in the recent NIST Spoken Term Detection evaluation [1].", "fulltext": "1. INTRODUCTION\nThe rapidly increasing amount of spoken data calls for\nsolutions to index and search this data.\nThe classical approach consists of converting the speech to\nword transcripts using a large vocabulary continuous speech\nrecognition (LVCSR) tool. In the past decade, most of the\nresearch efforts on spoken data retrieval have focused on\nextending classical IR techniques to word transcripts. Some of\nthese works have been done in the framework of the NIST\nTREC Spoken Document Retrieval tracks and are described\nby Garofolo et al. [12]. These tracks focused on retrieval\nfrom a corpus of broadcast news stories spoken by\nprofessionals. One of the conclusions of those tracks was that\nthe effectiveness of retrieval mostly depends on the\naccuracy of the transcripts. While the accuracy of automatic\nspeech recognition (ASR) systems depends on the scenario\nand environment, state-of-the-art systems achieved better\nthan 90% accuracy in transcription of such data. In 2000,\nGarofolo et al. concluded that Spoken document retrieval\nis a solved problem [12].\nHowever, a significant drawback of such approaches is that\nsearch on queries containing out-of-vocabulary (OOV) terms\nwill not return any results. OOV terms are missing words\nfrom the ASR system vocabulary and are replaced in the\noutput transcript by alternatives that are probable, given\nthe recognition acoustic model and the language model. It\nhas been experimentally observed that over 10% of user\nqueries can contain OOV terms [16], as queries often\nrelate to named entities that typically have a poor coverage\nin the ASR vocabulary. The effects of OOV query terms in\nspoken data retrieval are discussed by Woodland et al. [28].\nIn many applications the OOV rate may get worse over time\nunless the recognizer\"s vocabulary is periodically updated.\nAnother approach consists of converting the speech to\nphonetic transcripts and representing the query as a\nsequence of phones. The retrieval is based on searching the\nsequence of phones representing the query in the phonetic\ntranscripts. The main drawback of this approach is the\ninherent high error rate of the transcripts. Therefore, such\napproach cannot be an alternative to word transcripts,\nespecially for in-vocabulary (IV) query terms that are part of\nthe vocabulary of the ASR system.\nA solution would be to combine the two different\napproaches presented above: we index both word transcripts\nand phonetic transcripts; during query processing, the\ninformation is retrieved from the word index for IV terms and\nfrom the phonetic index for OOV terms. We would like to\nbe able to process also hybrid queries, i.e, queries that\ninclude both IV and OOV terms. Consequently, we need to\nmerge pieces of information retrieved from word index and\nphonetic index. Proximity information on the occurrences\nof the query terms is required for phrase search and for\nproximity-based ranking. In classical IR, the index stores for\neach occurrence of a term, its offset. Therefore, we cannot\nmerge posting lists retrieved by phonetic index with those\nretrieved by word index since the offset of the occurrences\nretrieved from the two different indices are not comparable.\nThe only element of comparison between phonetic and word\ntranscripts are the timestamps. No previous work\ncombining word and phonetic approach has been done on phrase\nsearch. We present a novel scheme for information retrieval\nthat consists of storing, during the indexing process, for each\nunit of indexing (phone or word) its timestamp. We search\nqueries by merging the information retrieved from the two\ndifferent indices, word index and phonetic index, according\nto the timestamps of the query terms. We analyze the\nretrieval effectiveness of this approach on the NIST Spoken\nTerm Detection 2006 evaluation data [1].\nThe paper is organized as follows. We describe the audio\nprocessing in Section 2. The indexing and retrieval methods\nare presented in section 3. Experimental setup and results\nare given in Section 4. In Section 5, we give an overview of\nrelated work. Finally, we conclude in Section 6.\n2. AUTOMATIC SPEECH RECOGNITION\nSYSTEM\nWe use an ASR system for transcribing speech data. It\nworks in speaker-independent mode. For best recognition\nresults, a speaker-independent acoustic model and a\nlanguage model are trained in advance on data with similar\ncharacteristics.\nTypically, ASR generates lattices that can be considered\nas directed acyclic graphs. Each vertex in a lattice is\nassociated with a timestamp and each edge (u, v) is labeled with\na word or phone hypothesis and its prior probability, which\nis the probability of the signal delimited by the timestamps\nof the vertices u and v, given the hypothesis. The 1-best\npath transcript is obtained from the lattice using dynamic\nprogramming techniques.\nMangu et al. [18] and Hakkani-Tur et al. [13] propose a\ncompact representation of a word lattice called word\nconfusion network (WCN). Each edge (u, v) is labeled with a word\nhypothesis and its posterior probability, i.e., the probability\nof the word given the signal. One of the main advantages\nof WCN is that it also provides an alignment for all of the\nwords in the lattice. As explained in [13], the three main\nsteps for building a WCN from a word lattice are as follows:\n1. Compute the posterior probabilities for all edges in the\nword lattice.\n2. Extract a path from the word lattice (which can be\nthe 1-best, the longest or any random path), and call\nit the pivot path of the alignment.\n3. Traverse the word lattice, and align all the transitions\nwith the pivot, merging the transitions that\ncorrespond to the same word (or label) and occur in the\nsame time interval by summing their posterior\nprobabilities.\nThe 1-best path of a WCN is obtained from the path\ncontaining the best hypotheses. As stated in [18], although\nWCNs are more compact than word lattices, in general the\n1-best path obtained from WCN has a better word accuracy\nthan the 1-best path obtained from the corresponding word\nlattice.\nTypical structures of a lattice and a WCN are given in\nFigure 1.\nFigure 1: Typical structures of a lattice and a WCN.\n3. RETRIEVAL MODEL\nThe main problem with retrieving information from\nspoken data is the low accuracy of the transcription\nparticularly on terms of interest such as named entities and\ncontent words. Generally, the accuracy of a word transcript\nis characterized by its word error rate (WER). There are\nthree kinds of errors that can occur in a transcript:\nsubstitution of a term that is part of the speech by another\nterm, deletion of a spoken term that is part of the speech\nand insertion of a term that is not part of the speech.\nSubstitutions and deletions reflect the fact that an\noccurrence of a term in the speech signal is not recognized. These\nmisses reduce the recall of the search. Substitutions and\ninsertions reflect the fact that a term which is not part of the\nspeech signal appears in the transcript. These misses reduce\nthe precision of the search.\nSearch recall can be enhanced by expanding the transcript\nwith extra words. These words can be taken from the other\nalternatives provided by the WCN; these alternatives may\nhave been spoken but were not the top choice of the ASR.\nSuch an expansion tends to correct the substitutions and\nthe deletions and consequently, might improve recall but\nwill probably reduce precision. Using an appropriate\nranking model, we can avoid the decrease in precision. Mamou et\nal. have presented in [17] the enhancement in the recall and\nthe MAP by searching on WCN instead of considering only\nthe 1-best path word transcript in the context of spoken\ndocument retrieval. We have adapted this model of IV search to\nterm detection. In word transcripts, OOV terms are deleted\nor substituted. Therefore, the usage of phonetic transcripts\nis more desirable. However, due to their low accuracy, we\nhave preferred to use only the 1-best path extracted from the\nphonetic lattices. We will show that the usage of phonetic\ntranscripts tends to improve the recall without affecting the\nprecision too much, using an appropriate ranking.\n3.1 Spoken document detection task\nAs stated in the STD 2006 evaluation plan [2], the task\nconsists in finding all the exact matches of a specific query\nin a given corpus of speech data. A query is a phrase\ncontaining several words. The queries are text and not speech.\nNote that this task is different from the more classical task of\nspoken document retrieval. Manual transcripts of the speech\nare not provided but are used by the evaluators to find true\noccurrences. By definition, true occurrences of a query are\nfound automatically by searching the manual transcripts\nusing the following rule: the gap between adjacent words in\na query must be less than 0.5 seconds in the corresponding\nspeech. For evaluating the results, each system output\noccurrence is judged as correct or not according to whether it\nis close in time to a true occurrence of the query retrieved\nfrom manual transcripts; it is judged as correct if the\nmidpoint of the system output occurrence is less than or equal\nto 0.5 seconds from the time span of a true occurrence of\nthe query.\n3.2 Indexing\nWe have used the same indexing process for WCN and\nphonetic transcripts. Each occurrence of a unit of indexing\n(word or phone) u in a transcript D is indexed with the\nfollowing information:\n\u2022 the begin time t of the occurrence of u,\n\u2022 the duration d of the occurrence of u.\nIn addition, for WCN indexing, we store\n\u2022 the confidence level of the occurrence of u at the\ntime t that is evaluated by its posterior probability\nPr(u|t, D),\n\u2022 the rank of the occurrence of u among the other\nhypotheses beginning at the same time t, rank(u|t, D).\nNote that since the task is to find exact matches of the\nphrase queries, we have not filtered stopwords and the\ncorpus is not stemmed before indexing.\n3.3 Search\nIn the following, we present our approach for\naccomplishing the STD task using the indices described above. The\nterms are extracted from the query. The vocabulary of the\nASR system building word transcripts is given. Terms that\nare part of this vocabulary are IV terms; the other terms\nare OOV. For an IV query term, the posting list is extracted\nfrom the word index. For an OOV query term, the term is\nconverted to a sequence of phones using a joint maximum\nentropy N-gram model [10]. For example, the term prosody\nis converted to the sequence of phones (p, r, aa, z, ih,\nd, iy). The posting list of each phone is extracted from the\nphonetic index.\nThe next step consists of merging the different posting\nlists according to the timestamp of the occurrences in order\nto create results matching the query. First, we check that\nthe words and phones appear in the right order according to\ntheir begin times. Second, we check that the gap in time\nbetween adjacent words and phones is reasonable.\nConforming to the requirements of the STD evaluation, the distance\nin time between two adjacent query terms must be less than\n0.5 seconds. For OOV search, we check that the distance\nin time between two adjacent phones of a query term is less\nthat 0.2 seconds; this value has been determined empirically.\nIn such a way, we can reduce the effect of insertion errors\nsince we allow insertions between the adjacent words and\nphones. Our query processing does not allow substitutions\nand deletions.\nExample: Let us consider the phrase query prosody\nresearch. The term prosody is OOV and the term research\nis IV. The term prosody is converted to the sequence of\nphones (p, r, aa, z, ih, d, iy). The posting list of each\nphone is extracted from the phonetic index. We merge the\nposting lists of the phones such that the sequence of phones\nappears in the right order and the gap in time between the\npairs of phones (p, r), (r, aa), (aa, z), (z, ih), (ih, d), (d, iy) is\nless than 0.2 seconds. We obtain occurrences of the term\nprosody. The posting list of research is extracted from the\nword index and we merge it with the occurrences found for\nprosody such that they appear in the right order and the\ndistance in time between prosody and research is less than\n0.5 seconds.\nNote that our indexing model allows to search for different\ntypes of queries:\n1. queries containing only IV terms using the word index.\n2. queries containing only OOV terms using the phonetic\nindex.\n3. keyword queries containing both IV and OOV terms\nusing the word index for IV terms and the phonetic\nindex for OOV terms; for query processing, the\ndifferent sets of matches are unified if the query terms have\nOR semantics and intersected if the query terms have\nAND semantics.\n4. phrase queries containing both IV and OOV terms; for\nquery processing, the posting lists of the IV terms\nretrieved from the word index are merged with the\nposting lists of the OOV terms retrieved from the phonetic\nindex. The merging is possible since we have stored\nthe timestamps for each unit of indexing (word and\nphone) in both indices.\nThe STD evaluation has focused on the fourth query type.\nIt is the hardest task since we need to combine posting lists\nretrieved from phonetic and word indices.\n3.4 Ranking\nSince IV terms and OOV terms are retrieved from two\ndifferent indices, we propose two different functions for scoring\nan occurrence of a term; afterward, an aggregate score is\nassigned to the query based on the scores of the query terms.\nBecause the task is term detection, we do not use a\ndocument frequency criterion for ranking the occurrences.\nLet us consider a query Q = (k0, ..., kn), associated with\na boosting vector B = (B1, ..., Bj). This vector associates\na boosting factor to each rank of the different hypotheses;\nthe boosting factors are normalized between 0 and 1. If the\nrank r is larger than j, we assume Br = 0.\n3.4.1 In vocabulary term ranking\nFor IV term ranking, we extend the work of Mamou et\nal. [17] on spoken document retrieval to term detection. We\nuse the information provided by the word index. We define\nthe score score(k, t, D) of a keyword k occurring at a time t\nin the transcript D, by the following formula:\nscore(k, t, D) = Brank(k|t,D) \u00d7 Pr(k|t, D)\nNote that 0 \u2264 score(k, t, D) \u2264 1.\n3.4.2 Out of vocabulary term ranking\nFor OOV term ranking, we use the information provided\nby the phonetic index. We give a higher rank to occurrences\nof OOV terms that contain phones close (in time) to each\nother. We define a scoring function that is related to the\naverage gap in time between the different phones. Let us\nconsider a keyword k converted to the sequence of phones\n(pk\n0 , ..., pk\nl ). We define the normalized score score(k, tk\n0 , D)\nof a keyword k = (pk\n0 , ..., pk\nl ), where each pk\ni occurs at time\ntk\ni with a duration of dk\ni in the transcript D, by the following\nformula:\nscore(k, tk\n0 , D) = 1 \u2212\nl\ni=1 5 \u00d7 (tk\ni \u2212 (tk\ni\u22121 + dk\ni\u22121))\nl\nNote that according to what we have ex-plained in\nSection 3.3, we have \u22001 \u2264 i \u2264 l, 0 < tk\ni \u2212 (tk\ni\u22121 + dk\ni\u22121) <\n0.2 sec, 0 < 5 \u00d7 (tk\ni \u2212 (tk\ni\u22121 + dk\ni\u22121)) < 1, and consequently,\n0 < score(k, tk\n0 , D) \u2264 1. The duration of the keyword\noccurrence is tk\nl \u2212 tk\n0 + dk\nl .\nExample: let us consider the sequence (p, r, aa, z,\nih, d, iy) and two different occurrences of the sequence.\nFor each phone, we give the begin time and the duration in\nsecond.\nOccurrence 1: (p, 0.25, 0.01), (r, 0.36, 0.01), (aa, 0.37, 0.01),\n(z, 0.38, 0.01), (ih, 0.39, 0.01), (d, 0.4, 0.01), (iy, 0.52, 0.01).\nOccurrence 2: (p, 0.45, 0.01), (r, 0.46, 0.01), (aa, 0.47, 0.01),\n(z, 0.48, 0.01), (ih, 0.49, 0.01), (d, 0.5, 0.01), (iy, 0.51, 0.01).\nAccording to our formula, the score of the first occurrence\nis 0.83 and the score of the second occurrence is 1. In the\nfirst occurrence, there are probably some insertion or silence\nbetween the phone p and r, and between the phone d and iy.\nThe silence can be due to the fact that the phones belongs\nto two different words ans therefore, it is not an occurrence\nof the term prosody.\n3.4.3 Combination\nThe score of an occurrence of a query Q at time t0 in the\ndocument D is determined by the multiplication of the score\nof each keyword ki, where each ki occurs at time ti with a\nduration di in the transcript D:\nscore(Q, t0, D) =\nn\ni=0\nscore(ki, ti, D)\u03b3n\nNote that according to what we have ex-plained in\nSection 3.3, we have \u22001 \u2264 i \u2264 n, 0 < ti \u2212(ti\u22121 +di\u22121) < 0.5 sec.\nOur goal is to estimate for each found occurrence how\nlikely the query appears. It is different from classical IR\nthat aims to rank the results and not to score them. Since\nthe probability to have a false alarm is inversely proportional\nto the length of the phrase query, we have boosted the score\nof queries by a \u03b3n exponent, that is related to the number\nof keywords in the phrase. We have determined empirically\nthe value of \u03b3n = 1/n.\nThe begin time of the query occurrence is determined by\nthe begin time t0 of the first query term and the duration\nof the query occurrence by tn \u2212 t0 + dn.\n4. EXPERIMENTS\n4.1 Experimental setup\nOur corpus consists of the evaluation set provided by NIST\nfor the STD 2006 evaluation [1]. It includes three\ndifferent source types in US English: three hours of broadcast\nnews (BNEWS), three hours of conversational telephony\nspeech (CTS) and two hours of conference room meetings\n(CONFMTG). As shown in Section 4.2, these different\ncollections have different accuracies. CTS and CONFMTG are\nspontaneous speech. For the experiments, we have processed\nthe query set provided by NIST that includes 1100 queries.\nEach query is a phrase containing between one to five terms,\ncommon and rare terms, terms that are in the manual\ntranscripts and those that are not. Testing and determination\nof empirical values have been achieved on another set of\nspeech data and queries, the development set, also provided\nby NIST.\nWe have used the IBM research prototype ASR system,\ndescribed in [26], for transcribing speech data. We have\nproduced WCNs for the three different source types. 1-best\nphonetic transcripts were generated only for BNEWS and\nCTS, since CONFMTG phonetic transcripts have too low\naccuracy. We have adapted Juru [7], a full-text search\nlibrary written in Java, to index the transcripts and to store\nthe timestamps of the words and phones; search results have\nbeen retrieved as described in Section 3.\nFor each found occurrence of the given query, our system\noutputs: the location of the term in the audio recording\n(begin time and duration), the score indicating how likely\nis the occurrence of query, (as defined in Section 3.4) and a\nhard (binary) decision as to whether the detection is\ncorrect. We measure precision and recall by comparing the\nresults obtained over the automatic transcripts (only the\nresults having true hard decision) to the results obtained over\nthe reference manual transcripts. Our aim is to evaluate the\nability of the suggested retrieval approach to handle\ntranscribed speech data. Thus, the closer the automatic results\nto the manual results is, the better the search effectiveness\nover the automatic transcripts will be. The results returned\nfrom the manual transcription for a given query are\nconsidered relevant and are expected to be retrieved with highest\nscores. This approach for measuring search effectiveness\nusing manual data as a reference is very common in speech\nretrieval research [25, 22, 8, 9, 17].\nBeside the recall and the precision, we use the evaluation\nmeasures defined by NIST for the 2006 STD evaluation [2]:\nthe Actual Term-Weighted Value (ATWV) and the\nMaximum Term-Weighted Value (MTWV). The term-weighted\nvalue (TWV) is computed by first computing the miss and\nfalse alarm probabilities for each query separately, then\nusing these and an (arbitrarily chosen) prior probability to\ncompute query-specific values, and finally averaging these\nquery-specific values over all queries q to produce an overall\nsystem value:\nTWV (\u03b8) = 1 \u2212 averageq{Pmiss(q, \u03b8) + \u03b2 \u00d7 PF A(q, \u03b8)}\nwhere \u03b2 = C\nV\n(Pr\u22121\nq \u2212 1). \u03b8 is the detection threshold. For\nthe evaluation, the cost/value ratio, C/V , has been\ndetermined to 0.1 and the prior probability of a query Prq to\n10\u22124\n. Therefore, \u03b2 = 999.9.\nMiss and false alarm probabilities for a given query q are\nfunctions of \u03b8:\nPmiss(q, \u03b8) = 1 \u2212\nNcorrect(q, \u03b8)\nNtrue(q)\nPF A(q, \u03b8) =\nNspurious(q, \u03b8)\nNNT (q)\ncorpus WER(%) SUBR(%) DELR(%) INSR(%)\nBNEWS WCN 12.7 49 42 9\nCTS WCN 19.6 51 38 11\nCONFMTG WCN 47.4 47 49 3\nTable 1: WER and distribution of the error types over word 1-best path extracted from WCNs for the\ndifferent source types.\nwhere:\n\u2022 Ncorrect(q, \u03b8) is the number of correct detections\n(retrieved by the system) of the query q with a score\ngreater than or equal to \u03b8.\n\u2022 Nspurious(q, \u03b8) is the number of spurious detections of\nthe query q with a score greater than or equal to \u03b8.\n\u2022 Ntrue(q) is the number of true occurrences of the query\nq in the corpus.\n\u2022 NNT (q) is the number of opportunities for incorrect\ndetection of the query q in the corpus; it is the\nNonTarget query trials. It has been defined by the\nfollowing formula: NNT (q) = Tspeech \u2212 Ntrue(q). Tspeech\nis the total amount of speech in the collection (in\nseconds).\nATWV is the actual term-weighted value; it is the\ndetection value attained by the system as a result of the system\noutput and the binary decision output for each putative\noccurrence. It ranges from \u2212\u221e to +1. MTWV is the\nmaximum term-weighted value over the range of all possible\nvalues of \u03b8. It ranges from 0 to +1.\nWe have also provided the detection error tradeoff (DET)\ncurve [19] of miss probability (Pmiss) vs. false alarm\nprobability (PF A).\nWe have used the STDEval tool to extract the relevant\nresults from the manual transcripts and to compute ATWV,\nMTWV and the DET curve.\nWe have determined empirically the following values for\nthe boosting vector defined in Section 3.4: Bi = 1\ni\n.\n4.2 WER analysis\nWe use the word error rate (WER) in order to characterize\nthe accuracy of the transcripts. WER is defined as follows:\nS + D + I\nN\n\u00d7 100\nwhere N is the total number of words in the corpus, and\nS, I, and D are the total number of substitution, insertion,\nand deletion errors, respectively. The substitution error rate\n(SUBR) is defined by\nS\nS + D + I\n\u00d7 100.\nDeletion error rate (DELR) and insertion error rate (INSR)\nare defined in a similar manner.\nTable 1 gives the WER and the distribution of the error\ntypes over 1-best path transcripts extracted from WCNs.\nThe WER of the 1-best path phonetic transcripts is\napproximately two times worse than the WER of word transcripts.\nThat is the reason why we have not retrieved from phonetic\ntranscripts on CONFMTG speech data.\n4.3 Theta threshold\nWe have determined empirically a detection threshold \u03b8\nper source type and the hard decision of the occurrences\nhaving a score less than \u03b8 is set to false; false occurrences\nreturned by the system are not considered as retrieved and\ntherefore, are not used for computing ATWV, precision and\nrecall.\nThe value of the threshold \u03b8 per source type is reported in\nTable 2. It is correlated to the accuracy of the transcripts.\nBasically, setting a threshold aims to eliminate from the\nretrieved occurrences, false alarms without adding misses.\nThe higher the WER is, the higher the \u03b8 threshold should\nbe.\nBNEWS CTS CONFMTG\n0.4 0.61 0.91\nTable 2: Values of the \u03b8 threshold per source type.\n4.4 Processing resource profile\nWe report in Table 3 the processing resource profile.\nConcerning the index size, note that our index is compressed\nusing IR index compression techniques. The indexing time\nincludes both audio processing (generation of word and\nphonetic transcripts) and building of the searchable indices.\nIndex size 0.3267 MB/HS\nIndexing time 7.5627 HP/HS\nIndex Memory Usage 1653.4297 MB\nSearch speed 0.0041 sec.P/HS\nSearch Memory Usage 269.1250 MB\nTable 3: Processing resource profile. (HS: Hours of\nSpeech. HP: Processing Hours. sec.P: Processing\nseconds)\n4.5 Retrieval measures\nWe compare our approach (WCN phonetic) presented in\nSection 4.1 with another approach (1-best-WCN phonetic).\nThe only difference between these two approaches is that,\nin 1-best-WCN phonetic, we index only the 1-best path\nextracted from the WCN instead of indexing all the WCN.\nWCN phonetic was our primary system for the evaluation\nand 1-best-WCN phonetic was one of our contrastive\nsystems. Average precision and recall, MTWV and ATWV on\nthe 1100 queries are given in Table 4. We provide also the\nDET curve for WCN phonetic approach in Figure 2. The\npoint that maximizes the TWV, the MTWV, is specified on\neach curve. Note that retrieval performance has been\nevaluated separately for each source type since the accuracy of\nthe speech differs per source type as shown in Section 4.2.\nAs expected, we can see that MTWV and ATWV decrease\nin higher WER. The retrieval performance is improved when\nmeasure BNEWS CTS CONFMTG\nWCN phonetic ATWV 0.8485 0.7392 0.2365\nMTWV 0.8532 0.7408 0.2508\nprecision 0.94 0.90 0.65\nrecall 0.89 0.81 0.37\n1-best-WCN phonetic ATWV 0.8279 0.7102 0.2381\nMTWV 0.8319 0.7117 0.2512\nprecision 0.95 0.91 0.66\nrecall 0.84 0.75 0.37\nTable 4: ATWV, MTWV, precision and recall per source type.\nFigure 2: DET curve for WCN phonetic approach.\nusing WCNs relatively to 1-best path. It is due to the fact\nthat miss probability is improved by indexing all the\nhypotheses provided by the WCNs. This observation confirms\nthe results shown by Mamou et al. [17] in the context of\nspoken document retrieval. The ATWV that we have obtained\nis close to the MTWV; we have combined our ranking model\nwith appropriate threshold \u03b8 to eliminate results with lower\nscore. Therefore, the effect of false alarms added by WCNs\nis reduced.\nWCN phonetic approach was used in the recent NIST STD\nevaluation and received the highest overall ranking among\neleven participants. For comparison, the system that ranked\nat the third place, obtained an ATWV of 0.8238 for BNEWS,\n0.6652 for CTS and 0.1103 for CONFMTG.\n4.6 Influence of the duration of the query on\nthe retrieval performance\nWe have analysed the retrieval performance according to\nthe average duration of the occurrences in the manual\ntranscripts. The query set was divided into three different\nquantiles according to the duration; we have reported in Table 5\nATWV and MTWV according to the duration. We can see\nthat we performed better on longer queries. One of the\nreasons is the fact that the ASR system is more accurate on\nlong words. Hence, it was justified to boost the score of the\nresults with the exponent \u03b3n, as explained in Section 3.4.3,\naccording to the length of the query.\nquantile 0-33 33-66 66-100\nBNEWS ATWV 0.7655 0.8794 0.9088\nMTWV 0.7819 0.8914 0.9124\nCTS ATWV 0.6545 0.8308 0.8378\nMTWV 0.6551 0.8727 0.8479\nCONFMTG ATWV 0.1677 0.3493 0.3651\nMTWV 0.1955 0.4109 0.3880\nTable 5: ATWV, MTWV according to the duration\nof the query occurrences per source type.\n4.7 OOV vs. IV query processing\nWe have randomly chosen three sets of queries from the\nquery sets provided by NIST: 50 queries containing only IV\nterms; 50 queries containing only OOV terms; and 50 hybrid\nqueries containing both IV and OOV terms. The following\nexperiment has been achieved on the BNEWS collection and\nIV and OOV terms has been determined according to the\nvocabulary of BNEWS ASR system.\nWe would like to compare three different approaches of\nretrieval: using only word index; using only phonetic index;\ncombining word and phonetic indices. Table 6 summarizes\nthe retrieval performance according to each approach and\nto each type of queries. Using a word-based approach for\ndealing with OOV and hybrid queries affects drastically the\nperformance of the retrieval; precision and recall are null.\nUsing a phone-based approach for dealing with IV queries\naffects also the performance of the retrieval relatively to the\nword-based approach.\nAs expected, the approach combining word and phonetic\nindices presented in Section 3 leads to the same retrieval\nperformance as the word approach for IV queries and to\nthe same retrieval performance as the phonetic approach for\nOOV queries. This approach always outperforms the others\nand it justifies the fact that we need to combine word and\nphonetic search.\n5. RELATED WORK\nIn the past decade, the research efforts on spoken data\nretrieval have focused on extending classical IR techniques\nto spoken documents. Some of these works have been done\nin the context of the TREC Spoken Document Retrieval\nevaluations and are described by Garofolo et al. [12]. An\nLVCSR system is used to transcribe the speech into 1-best\npath word transcripts. The transcripts are indexed as clean\ntext: for each occurrence, its document, its word offset and\nadditional information are stored in the index. A generic IR\nsystem over the text is used for word spotting and search\nas described by Brown et al. [6] and James [14]. This\nstratindex word phonetic word and phonetic\nprecision recall precision recall precision recall\nIV queries 0.8 0.96 0.11 0.77 0.8 0.96\nOOV queries 0 0 0.13 0.79 0.13 0.79\nhybrid queries 0 0 0.15 0.71 0.89 0.83\nTable 6: Comparison of word and phonetic approach on IV and OOV queries\negy works well for transcripts like broadcast news collections\nthat have a low WER (in the range of 15%-30%) and are\nredundant by nature (the same piece of information is\nspoken several times in different manners). Moreover, the\nalgorithms have been mostly tested over long queries stated in\nplain English and retrieval for such queries is more robust\nagainst speech recognition errors.\nAn alternative approach consists of using word lattices in\norder to improve the effectiveness of SDR. Singhal et al. [24,\n25] propose to add some terms to the transcript in order\nto alleviate the retrieval failures due to ASR errors. From\nan IR perspective, a classical way to bring new terms is\ndocument expansion using a similar corpus. Their approach\nconsists in using word lattices in order to determine which\nwords returned by a document expansion algorithm should\nbe added to the original transcript. The necessity to use a\ndocument expansion algorithm was justified by the fact that\nthe word lattices they worked with, lack information about\nword probabilities.\nChelba and Acero in [8, 9] propose a more compact word\nlattice, the position specific posterior lattice (PSPL). This\ndata structure is similar to WCN and leads to a more\ncompact index. The offset of the terms in the speech documents\nis also stored in the index. However, the evaluation\nframework is carried out on lectures that are relatively planned,\nin contrast to conversational speech. Their ranking model\nis based on the term confidence level but does not take into\nconsideration the rank of the term among the other\nhypotheses. Mamou et al. [17] propose a model for spoken document\nretrieval using WCNs in order to improve the recall and the\nMAP of the search. However, in the above works, the\nproblem of queries containing OOV terms is not addressed.\nPopular approaches to deal with OOV queries are based\non sub-words transcripts, where the sub-words are typically\nphones, syllables or word fragments (sequences of phones)\n[11, 20, 23]. The classical approach consists of using\nphonetic transcripts. The transcripts are indexed in the same\nmanner as words in using classical text retrieval techniques;\nduring query processing, the query is represented as a\nsequence of phones. The retrieval is based on searching the\nstring of phones representing the query in the phonetic\ntranscript. To account for the high recognition error rates, some\nother systems use richer transcripts like phonetic lattices.\nThey are attractive as they accommodate high error rate\nconditions as well as allow for OOV queries to be used [15,\n3, 20, 23, 21, 27]. However, phonetic lattices contain many\nedges that overlap in time with the same phonetic label, and\nare difficult to index. Moreover, beside the improvement in\nthe recall of the search, the precision is affected since\nphonetic lattices are often inaccurate. Consequently, phonetic\napproaches should be used only for OOV search; for\nsearching queries containing also IV terms, this technique affects\nthe performance of the retrieval in comparison to the word\nbased approach.\nSaraclar and Sproat in [22] show improvement in word\nspotting accuracy for both IV and OOV queries, using\nphonetic and word lattices, where a confidence measure of a\nword or a phone can be derived. They propose three\ndifferent retrieval strategies: search both the word and the\nphonetic indices and unify the two different sets of results;\nsearch the word index for IV queries, search the phonetic\nindex for OOV queries; search the word index and if no result\nis returned, search the phonetic index. However, no strategy\nis proposed to deal with phrase queries containing both IV\nand OOV terms. Amir et al. in [5, 4] propose to merge a\nword approach with a phonetic approach in the context of\nvideo retrieval. However, the phonetic transcript is obtained\nfrom a text to phonetic conversion of the 1-best path of the\nword transcript and is not based on a phonetic decoding of\nthe speech data.\nAn important issue to be considered when looking at the\nstate-of-the-art in retrieval of spoken data, is the lack of a\ncommon test set and appropriate query terms. This paper\nuses such a task and the STD evaluation is a good summary\nof the performance of different approaches on the same test\nconditions.\n6. CONCLUSIONS\nThis work studies how vocabulary independent spoken\nterm detection can be performed efficiently over different\ndata sources. Previously, phonetic-based and word-based\napproaches have been used for IR on speech data. The\nformer suffers from low accuracy and the latter from limited\nvocabulary of the recognition system. In this paper, we have\npresented a vocabulary independent model of indexing and\nsearch that combines both the approaches. The system can\ndeal with all kinds of queries although the phrases that need\nto combine for the retrieval, information extracted from two\ndifferent indices, a word index and a phonetic index. The\nscoring of OOV terms is based on the proximity (in time)\nbetween the different phones. The scoring of IV terms is based\non information provided by the WCNs. We have shown an\nimprovement in the retrieval performance when using all the\nWCN and not only the 1-best path and when using phonetic\nindex for search of OOV query terms. This approach always\noutperforms the other approaches using only word index or\nphonetic index.\nAs a future work, we will compare our model for OOV\nsearch on phonetic transcripts with a retrieval model based\non the edit distance.\n7. ACKNOWLEDGEMENTS\nJonathan Mamou is grateful to David Carmel and Ron\nHoory for helpful and interesting discussions.\n8. REFERENCES\n[1] NIST Spoken Term Detection 2006 Evaluation\nWebsite, http://www.nist.gov/speech/tests/std/.\n[2] NIST Spoken Term Detection (STD) 2006 Evaluation\nPlan,\nhttp://www.nist.gov/speech/tests/std/docs/std06-evalplan-v10.pdf.\n[3] C. Allauzen, M. Mohri, and M. Saraclar. General\nindexation of weighted automata - application to\nspoken utterance retrieval. In Proceedings of the\nHLT-NAACL 2004 Workshop on Interdiciplinary\nApproaches to Speech Indexing and Retrieval, Boston,\nMA, USA, 2004.\n[4] A. Amir, M. Berg, and H. Permuter. Mutual relevance\nfeedback for multimodal query formulation in video\nretrieval. In MIR \"05: Proceedings of the 7th ACM\nSIGMM international workshop on Multimedia\ninformation retrieval, pages 17-24, New York, NY,\nUSA, 2005. ACM Press.\n[5] A. Amir, A. Efrat, and S. Srinivasan. Advances in\nphonetic word spotting. In CIKM \"01: Proceedings of\nthe tenth international conference on Information and\nknowledge management, pages 580-582, New York,\nNY, USA, 2001. ACM Press.\n[6] M. Brown, J. Foote, G. Jones, K. Jones, and S. Young.\nOpen-vocabulary speech indexing for voice and video\nmail retrieval. In Proceedings ACM Multimedia 96,\npages 307-316, Hong-Kong, November 1996.\n[7] D. Carmel, E. Amitay, M. Herscovici, Y. S. Maarek,\nY. Petruschka, and A. Soffer. Juru at TREC\n10Experiments with Index Pruning. In Proceedings of the\nTenth Text Retrieval Conference (TREC-10). National\nInstitute of Standards and Technology. NIST, 2001.\n[8] C. Chelba and A. Acero. Indexing uncertainty for\nspoken document search. In Interspeech 2005, pages\n61-64, Lisbon, Portugal, 2005.\n[9] C. Chelba and A. Acero. Position specific posterior\nlattices for indexing speech. In Proceedings of the 43rd\nAnnual Conference of the Association for\nComputational Linguistics (ACL), Ann Arbor, MI,\n2005.\n[10] S. Chen. Conditional and joint models for\ngrapheme-to-phoneme conversion. In Eurospeech 2003,\nGeneva, Switzerland, 2003.\n[11] M. Clements, S. Robertson, and M. Miller. Phonetic\nsearching applied to on-line distance learning modules.\nIn Digital Signal Processing Workshop, 2002 and the\n2nd Signal Processing Education Workshop.\nProceedings of 2002 IEEE 10th, pages 186-191, 2002.\n[12] J. Garofolo, G. Auzanne, and E. Voorhees. The TREC\nspoken document retrieval track: A success story. In\nProceedings of the Ninth Text Retrieval Conference\n(TREC-9). National Institute of Standards and\nTechnology. NIST, 2000.\n[13] D. Hakkani-Tur and G. Riccardi. A general algorithm\nfor word graph matrix decomposition. In Proceedings\nof the IEEE Internation Conference on Acoustics,\nSpeech and Signal Processing (ICASSP), pages\n596-599, Hong-Kong, 2003.\n[14] D. James. The application of classical information\nretrieval techniques to spoken documents. PhD thesis,\nUniversity of Cambridge, Downing College, 1995.\n[15] D. A. James. A system for unrestricted topic retrieval\nfrom radio news broadcasts. In Proc. ICASSP \"96,\npages 279-282, Atlanta, GA, 1996.\n[16] B. Logan, P. Moreno, J. V. Thong, and E. Whittaker.\nAn experimental study of an audio indexing system\nfor the web. In Proceedings of ICSLP, 1996.\n[17] J. Mamou, D. Carmel, and R. Hoory. Spoken\ndocument retrieval from call-center conversations. In\nSIGIR \"06: Proceedings of the 29th annual\ninternational ACM SIGIR conference on Research and\ndevelopment in information retrieval, pages 51-58,\nNew York, NY, USA, 2006. ACM Press.\n[18] L. Mangu, E. Brill, and A. Stolcke. Finding consensus\nin speech recognition: word error minimization and\nother applications of confusion networks. Computer\nSpeech and Language, 14(4):373-400, 2000.\n[19] A. Martin, G. Doddington, T. Kamm, M. Ordowski,\nand M. Przybocki. The DET curve in assessment of\ndetection task performance. In Proc. Eurospeech \"97,\npages 1895-1898, Rhodes, Greece, 1997.\n[20] K. Ng and V. W. Zue. Subword-based approaches for\nspoken document retrieval. Speech Commun.,\n32(3):157-186, 2000.\n[21] Y. Peng and F. Seide. Fast two-stage\nvocabulary-independent search in spontaneous speech.\nIn Acoustics, Speech, and Signal Processing.\nProceedings. (ICASSP). IEEE International\nConference, volume 1, pages 481-484, 2005.\n[22] M. Saraclar and R. Sproat. Lattice-based search for\nspoken utterance retrieval. In HLT-NAACL 2004:\nMain Proceedings, pages 129-136, Boston,\nMassachusetts, USA, 2004.\n[23] F. Seide, P. Yu, C. Ma, and E. Chang.\nVocabulary-independent search in spontaneous speech.\nIn ICASSP-2004, IEEE International Conference on\nAcoustics, Speech, and Signal Processing, 2004.\n[24] A. Singhal, J. Choi, D. Hindle, D. Lewis, and\nF. Pereira. AT&T at TREC-7. In Proceedings of the\nSeventh Text Retrieval Conference (TREC-7).\nNational Institute of Standards and Technology.\nNIST, 1999.\n[25] A. Singhal and F. Pereira. Document expansion for\nspeech retrieval. In SIGIR \"99: Proceedings of the\n22nd annual international ACM SIGIR conference on\nresearch and development in information retrieval,\npages 34-41, New York, NY, USA, 1999. ACM Press.\n[26] H. Soltau, B. Kingsbury, L. Mangu, D. Povey,\nG. Saon, and G. Zweig. The IBM 2004 conversational\ntelephony system for rich transcription. In Proceedings\nof the IEEE International Conference on Acoustics,\nSpeech and Signal Processing (ICASSP), March 2005.\n[27] K. Thambiratnam and S. Sridharan. Dynamic match\nphone-lattice searches for very fast and accurate\nunrestricted vocabulary keyword spotting. In\nAcoustics, Speech, and Signal Processing. Proceedings.\n(ICASSP). IEEE International Conference, 2005.\n[28] P. C. Woodland, S. E. Johnson, P. Jourlin, and K. S.\nJones. Effects of out of vocabulary words in spoken\ndocument retrieval (poster session). In SIGIR \"00:\nProceedings of the 23rd annual international ACM\nSIGIR conference on Research and development in\ninformation retrieval, pages 372-374, New York, NY,\nUSA, 2000. ACM Press.", "keywords": "vocabulary independent system;out-of-vocabulary;vocabulary;indexing timestamp;phonetic index;oov search;speech retrieval;speak term detection;speech datum retrieval;index merging;automatic speech recognition;speech recognizer;word index;phonetic transcript;spoken term detection"}
{"name": "train_H-53", "title": "Context Sensitive Stemming for Web Search", "abstract": "Traditionally, stemming has been applied to Information Retrieval tasks by transforming words in documents to the their root form before indexing, and applying a similar transformation to query terms. Although it increases recall, this naive strategy does not work well for Web Search since it lowers precision and requires a significant amount of additional computation. In this paper, we propose a context sensitive stemming method that addresses these two issues. Two unique properties make our approach feasible for Web Search. First, based on statistical language modeling, we perform context sensitive analysis on the query side. We accurately predict which of its morphological variants is useful to expand a query term with before submitting the query to the search engine. This dramatically reduces the number of bad expansions, which in turn reduces the cost of additional computation and improves the precision at the same time. Second, our approach performs a context sensitive document matching for those expanded variants. This conservative strategy serves as a safeguard against spurious stemming, and it turns out to be very important for improving precision. Using word pluralization handling as an example of our stemming approach, our experiments on a major Web search engine show that stemming only 29% of the query traffic, we can improve relevance as measured by average Discounted Cumulative Gain (DCG5) by 6.1% on these queries and 1.8% over all query traffic.", "fulltext": "1. INTRODUCTION\nWeb search has now become a major tool in our daily lives\nfor information seeking. One of the important issues in Web\nsearch is that user queries are often not best formulated to\nget optimal results. For example, running shoe is a query\nthat occurs frequently in query logs. However, the query\nrunning shoes is much more likely to give better search\nresults than the original query because documents matching\nthe intent of this query usually contain the words running\nshoes.\nCorrectly formulating a query requires the user to\naccurately predict which word form is used in the documents\nthat best satisfy his or her information needs. This is\ndifficult even for experienced users, and especially difficult for\nnon-native speakers. One traditional solution is to use\nstemming [16, 18], the process of transforming inflected or\nderived words to their root form so that a search term will\nmatch and retrieve documents containing all forms of the\nterm. Thus, the word run will match running, ran,\nruns, and shoe will match shoes and shoeing.\nStemming can be done either on the terms in a document\nduring indexing (and applying the same transformation to the\nquery terms during query processing) or by expanding the\nquery with the variants during query processing. Stemming\nduring indexing allows very little flexibility during query\nprocessing, while stemming by query expansion allows\nhandling each query differently, and hence is preferred.\nAlthough traditional stemming increases recall by\nmatching word variants [13], it can reduce precision by retrieving\ntoo many documents that have been incorrectly matched.\nWhen examining the results of applying stemming to a large\nnumber of queries, one usually finds that nearly equal\nnumbers of queries are helped and hurt by the technique [6]. In\naddition, it reduces system performance because the search\nengine has to match all the word variants. As we will show\nin the experiments, this is true even if we simplify stemming\nto pluralization handling, which is the process of converting\na word from its plural to singular form, or vice versa. Thus,\none needs to be very cautious when using stemming in Web\nsearch engines.\nOne problem of traditional stemming is its blind\ntransformation of all query terms, that is, it always performs\nthe same transformation for the same query word without\nconsidering the context of the word. For example, the word\nbook has four forms book, books, booking, booked, and\nstore has four forms store, stores, storing, stored. For\nthe query book store, expanding both words to all of their\nvariants significantly increases computation cost and hurts\nprecision, since not all of the variants are useful for this\nquery. Transforming book store to match book stores\nis fine, but matching book storing or booking store is\nnot. A weighting method that gives variant words smaller\nweights alleviates the problems to a certain extent if the\nweights accurately reflect the importance of the variant in\nthis particular query. However uniform weighting is not\ngoing to work and a query dependent weighting is still a\nchallenging unsolved problem [20].\nA second problem of traditional stemming is its blind\nmatching of all occurrences in documents. For the query\nbook store, a transformation that allows the variant stores\nto be matched will cause every occurrence of stores in the\ndocument to be treated equivalent to the query term store.\nThus, a document containing the fragment reading a book\nin coffee stores will be matched, causing many wrong\ndocuments to be selected. Although we hope the ranking\nfunction can correctly handle these, with many more candidates\nto rank, the risk of making mistakes increases.\nTo alleviate these two problems, we propose a context\nsensitive stemming approach for Web search. Our solution\nconsists of two context sensitive analysis, one on the query\nside and the other on the document side. On the query side,\nwe propose a statistical language modeling based approach\nto predict which word variants are better forms than the\noriginal word for search purpose and expanding the query\nwith only those forms. On the document side, we propose a\nconservative context sensitive matching for the transformed\nword variants, only matching document occurrences in the\ncontext of other terms in the query. Our model is simple yet\neffective and efficient, making it feasible to be used in real\ncommercial Web search engines.\nWe use pluralization handling as a running example for\nour stemming approach. The motivation for using\npluralization handling as an example is to show that even such\nsimple stemming, if handled correctly, can give significant\nbenefits to search relevance. As far as we know, no\nprevious research has systematically investigated the usage of\npluralization in Web search. As we have to point out, the\nmethod we propose is not limited to pluralization handling,\nit is a general stemming technique, and can also be applied\nto general query expansion. Experiments on general\nstemming yield additional significant improvements over\npluralization handling for long queries, although details will not\nbe reported in this paper.\nIn the rest of the paper, we first present the related work\nand distinguish our method from previous work in Section 2.\nWe describe the details of the context sensitive stemming\napproach in Section 3. We then perform extensive\nexperiments on a major Web search engine to support our claims\nin Section 4, followed by discussions in Section 5. Finally,\nwe conclude the paper in Section 6.\n2. RELATED WORK\nStemming is a long studied technology. Many stemmers\nhave been developed, such as the Lovins stemmer [16] and\nthe Porter stemmer [18]. The Porter stemmer is widely used\ndue to its simplicity and effectiveness in many applications.\nHowever, the Porter stemming makes many mistakes\nbecause its simple rules cannot fully describe English\nmorphology. Corpus analysis is used to improve Porter stemmer [26]\nby creating equivalence classes for words that are\nmorphologically similar and occur in similar context as measured by\nexpected mutual information [23]. We use a similar corpus\nbased approach for stemming by computing the similarity\nbetween two words based on their distributional context\nfeatures which can be more than just adjacent words [15], and\nthen only keep the morphologically similar words as\ncandidates.\nUsing stemming in information retrieval is also a well\nknown technique [8, 10]. However, the effectiveness of\nstemming for English query systems was previously reported to\nbe rather limited. Lennon et al. [17] compared the Lovins\nand Porter algorithms and found little improvement in\nretrieval performance. Later, Harman [9] compares three\ngeneral stemming techniques in text retrieval experiments\nincluding pluralization handing (called S stemmer in the\npaper). They also proposed selective stemming based on query\nlength and term importance, but no positive results were\nreported. On the other hand, Krovetz [14] performed\ncomparisons over small numbers of documents (from 400 to 12k)\nand showed dramatic precision improvement (up to 45%).\nHowever, due to the limited number of tested queries (less\nthan 100) and the small size of the collection, the results\nare hard to generalize to Web search. These mixed results,\nmostly failures, led early IR researchers to deem stemming\nirrelevant in general for English [4], although recent research\nhas shown stemming has greater benefits for retrieval in\nother languages [2]. We suspect the previous failures were\nmainly due to the two problems we mentioned in the\nintroduction. Blind stemming, or a simple query length based\nselective stemming as used in [9] is not enough. Stemming\nhas to be decided on case by case basis, not only at the query\nlevel but also at the document level. As we will show, if\nhandled correctly, significant improvement can be achieved.\nA more general problem related to stemming is query\nreformulation [3, 12] and query expansion which expands\nwords not only with word variants [7, 22, 24, 25]. To\ndecide which expanded words to use, people often use\npseudorelevance feedback techniquesthat send the original query to\na search engine and retrieve the top documents, extract\nrelevant words from these top documents as additional query\nwords, and resubmit the expanded query again [21]. This\nnormally requires sending a query multiple times to search\nengine and it is not cost effective for processing the huge\namount of queries involved in Web search. In addition,\nquery expansion, including query reformulation [3, 12], has\na high risk of changing the user intent (called query drift).\nSince the expanded words may have different meanings, adding\nthem to the query could potentially change the intent of\nthe original query. Thus query expansion based on\npseudorelevance and query reformulation can provide suggestions\nto users for interactive refinement but can hardly be directly\nused for Web search. On the other hand, stemming is much\nmore conservative since most of the time, stemming\npreserves the original search intent. While most work on query\nexpansion focuses on recall enhancement, our work focuses\non increasing both recall and precision. The increase on\nrecall is obvious. With quality stemming, good documents\nwhich were not selected before stemming will be pushed up\nand those low quality documents will be degraded.\nOn selective query expansion, Cronen-Townsend et al. [6]\nproposed a method for selective query expansion based on\ncomparing the Kullback-Leibler divergence of the results\nfrom the unexpanded query and the results from the\nexpanded query. This is similar to the relevance feedback in\nthe sense that it requires multiple passes retrieval. If a word\ncan be expanded into several words, it requires running this\nprocess multiple times to decide which expanded word is\nuseful. It is expensive to deploy this in production Web\nsearch engines. Our method predicts the quality of\nexpansion based on o\ufb04ine information without sending the query\nto a search engine.\nIn summary, we propose a novel approach to attack an old,\nyet still important and challenging problem for Web search\n- stemming. Our approach is unique in that it performs\npredictive stemming on a per query basis without relevance\nfeedback from the Web, using the context of the variants in\ndocuments to preserve precision. It\"s simple, yet very\nefficient and effective, making real time stemming feasible for\nWeb search. Our results will affirm researchers that\nstemming is indeed very important to large scale information\nretrieval.\n3. CONTEXT SENSITIVE STEMMING\n3.1 Overview\nOur system has four components as illustrated in\nFigure 1: candidate generation, query segmentation and head\nword detection, context sensitive query stemming and\ncontext sensitive document matching. Candidate generation\n(component 1) is performed o\ufb04ine and generated candidates\nare stored in a dictionary. For an input query, we first\nsegment query into concepts and detect the head word for each\nconcept (component 2). We then use statistical language\nmodeling to decide whether a particular variant is useful\n(component 3), and finally for the expanded variants, we\nperform context sensitive document matching (component\n4). Below we discuss each of the components in more detail.\nComponent 4: context sensitive document matching\nInput Query:\nand head word detection\nComponent 2: segment Component 1: candidate generation\ncomparisons \u2212> comparison\nComponent 3: selective word expansion\ndecision: comparisons \u2212> comparison\nexample: hotel price comparisons\noutput: \"hotel\" \"comparisons\"\nhotel \u2212> hotels\nFigure 1: System Components\n3.2 Expansion candidate generation\nOne of the ways to generate candidates is using the Porter\nstemmer [18]. The Porter stemmer simply uses\nmorphological rules to convert a word to its base form. It has no\nknowledge of the semantic meaning of the words and sometimes\nmakes serious mistakes, such as executive to execution,\nnews to new, and paste to past. A more\nconservative way is based on using corpus analysis to improve the\nPorter stemmer results [26]. The corpus analysis we do is\nbased on word distributional similarity [15]. The rationale\nof using distributional word similarity is that true variants\ntend to be used in similar contexts. In the distributional\nword similarity calculation, each word is represented with a\nvector of features derived from the context of the word. We\nuse the bigrams to the left and right of the word as its\ncontext features, by mining a huge Web corpus. The similarity\nbetween two words is the cosine similarity between the two\ncorresponding feature vectors. The top 20 similar words to\ndevelop is shown in the following table.\nrank candidate score rank candidate score\n0 develop 1 10 berts 0.119\n1 developing 0.339 11 wads 0.116\n2 developed 0.176 12 developer 0.107\n3 incubator 0.160 13 promoting 0.100\n4 develops 0.150 14 developmental 0.091\n5 development 0.148 15 reengineering 0.090\n6 tutoring 0.138 16 build 0.083\n7 analyzing 0.128 17 construct 0.081\n8 developement 0.128 18 educational 0.081\n9 automation 0.126 19 institute 0.077\nTable 1: Top 20 most similar candidates to word\ndevelop. Column score is the similarity score.\nTo determine the stemming candidates, we apply a few\nPorter stemmer [18] morphological rules to the similarity\nlist. After applying these rules, for the word develop,\nthe stemming candidates are developing, developed,\ndevelops, development, developement, developer,\ndevelopmental. For the pluralization handling purpose, only the\ncandidate develops is retained.\nOne thing we note from observing the distributionally\nsimilar words is that they are closely related semantically.\nThese words might serve as candidates for general query\nexpansion, a topic we will investigate in the future.\n3.3 Segmentation and headword identification\nFor long queries, it is quite important to detect the\nconcepts in the query and the most important words for those\nconcepts. We first break a query into segments, each\nsegment representing a concept which normally is a noun phrase.\nFor each of the noun phrases, we then detect the most\nimportant word which we call the head word. Segmentation\nis also used in document sensitive matching (section 3.5) to\nenforce proximity.\nTo break a query into segments, we have to define a\ncriteria to measure the strength of the relation between words.\nOne effective method is to use mutual information as an\nindicator on whether or not to split two words [19]. We use\na log of 25M queries and collect the bigram and unigram\nfrequencies from it. For every incoming query, we compute\nthe mutual information of two adjacent words; if it passes\na predefined threshold, we do not split the query between\nthose two words and move on to next word. We continue\nthis process until the mutual information between two words\nis below the threshold, then create a concept boundary here.\nTable 2 shows some examples of query segmentation.\nThe ideal way of finding the head word of a concept is to\ndo syntactic parsing to determine the dependency structure\nof the query. Query parsing is more difficult than sentence\n[running shoe]\n[best] [new york] [medical schools]\n[pictures] [of] [white house]\n[cookies] [in] [san francisco]\n[hotel] [price comparison]\nTable 2: Query segmentation: a segment is\nbracketed.\nparsing since many queries are not grammatical and are very\nshort. Applying a parser trained on sentences from\ndocuments to queries will have poor performance. In our\nsolution, we just use simple heuristics rules, and it works very\nwell in practice for English. For an English noun phrase,\nthe head word is typically the last nonstop word, unless the\nphrase is of a particular pattern, like XYZ of/in/at/from\nUVW. In such cases, the head word is typically the last\nnonstop word of XYZ.\n3.4 Context sensitive word expansion\nAfter detecting which words are the most important words\nto expand, we have to decide whether the expansions will\nbe useful.\nOur statistics show that about half of the queries can be\ntransformed by pluralization via naive stemming. Among\nthis half, about 25% of the queries improve relevance when\ntransformed, the majority (about 50%) do not change their\ntop 5 results, and the remaining 25% perform worse. Thus,\nit is extremely important to identify which queries should\nnot be stemmed for the purpose of maximizing relevance\nimprovement and minimizing stemming cost. In addition,\nfor a query with multiple words that can be transformed,\nor a word with multiple variants, not all of the expansions\nare useful. Taking query hotel price comparison as an\nexample, we decide that hotel and price comparison are two\nconcepts. Head words hotel and comparison can be\nexpanded to hotels and comparisons. Are both\ntransformations useful?\nTo test whether an expansion is useful, we have to know\nwhether the expanded query is likely to get more relevant\ndocuments from the Web, which can be quantified by the\nprobability of the query occurring as a string on the Web.\nThe more likely a query to occur on the Web, the more\nrelevant documents this query is able to return. Now the\nwhole problem becomes how to calculate the probability of\nquery to occur on the Web.\nCalculating the probability of string occurring in a\ncorpus is a well known language modeling problem. The goal\nof language modeling is to predict the probability of\nnaturally occurring word sequences, s = w1w2...wN ; or more\nsimply, to put high probability on word sequences that\nactually occur (and low probability on word sequences that\nnever occur). The simplest and most successful approach to\nlanguage modeling is still based on the n-gram model. By\nthe chain rule of probability one can write the probability\nof any word sequence as\nPr(w1w2...wN ) =\nNY\ni=1\nPr(wi|w1...wi\u22121) (1)\nAn n-gram model approximates this probability by\nassuming that the only words relevant to predicting Pr(wi|w1...wi\u22121)\nare the previous n \u2212 1 words; i.e.\nPr(wi|w1...wi\u22121) = Pr(wi|wi\u2212n+1...wi\u22121)\nA straightforward maximum likelihood estimate of n-gram\nprobabilities from a corpus is given by the observed\nfrequency of each of the patterns\nPr(wi|wi\u2212n+1...wi\u22121) =\n#(wi\u2212n+1...wi)\n#(wi\u2212n+1...wi\u22121)\n(2)\nwhere #(.) denotes the number of occurrences of a specified\ngram in the training corpus. Although one could attempt to\nuse simple n-gram models to capture long range\ndependencies in language, attempting to do so directly immediately\ncreates sparse data problems: Using grams of length up to\nn entails estimating the probability of Wn\nevents, where W\nis the size of the word vocabulary. This quickly overwhelms\nmodern computational and data resources for even modest\nchoices of n (beyond 3 to 6). Also, because of the heavy\ntailed nature of language (i.e. Zipf\"s law) one is likely to\nencounter novel n-grams that were never witnessed during\ntraining in any test corpus, and therefore some mechanism\nfor assigning non-zero probability to novel n-grams is a\ncentral and unavoidable issue in statistical language modeling.\nOne standard approach to smoothing probability estimates\nto cope with sparse data problems (and to cope with\npotentially missing n-grams) is to use some sort of back-off\nestimator.\nPr(wi|wi\u2212n+1...wi\u22121)\n=\n8\n>><\n>>:\n\u02c6Pr(wi|wi\u2212n+1...wi\u22121),\nif #(wi\u2212n+1...wi) > 0\n\u03b2(wi\u2212n+1...wi\u22121) \u00d7 Pr(wi|wi\u2212n+2...wi\u22121),\notherwise\n(3)\nwhere\n\u02c6Pr(wi|wi\u2212n+1...wi\u22121) =\ndiscount #(wi\u2212n+1...wi)\n#(wi\u2212n+1...wi\u22121)\n(4)\nis the discounted probability and \u03b2(wi\u2212n+1...wi\u22121) is a\nnormalization constant\n\u03b2(wi\u2212n+1...wi\u22121) =\n1 \u2212\nX\nx\u2208(wi\u2212n+1...wi\u22121x)\n\u02c6Pr(x|wi\u2212n+1...wi\u22121)\n1 \u2212\nX\nx\u2208(wi\u2212n+1...wi\u22121x)\n\u02c6Pr(x|wi\u2212n+2...wi\u22121)\n(5)\nThe discounted probability (4) can be computed with\ndifferent smoothing techniques, including absolute smoothing,\nGood-Turing smoothing, linear smoothing, and Witten-Bell\nsmoothing [5]. We used absolute smoothing in our\nexperiments.\nSince the likelihood of a string, Pr(w1w2...wN ), is a very\nsmall number and hard to interpret, we use entropy as\ndefined below to score the string.\nEntropy = \u2212\n1\nN\nlog2 Pr(w1w2...wN ) (6)\nNow getting back to the example of the query hotel price\ncomparisons, there are four variants of this query, and the\nentropy of these four candidates are shown in Table 3. We\ncan see that all alternatives are less likely than the input\nquery. It is therefore not useful to make an expansion for this\nquery. On the other hand, if the input query is hotel price\ncomparisons which is the second alternative in the table,\nthen there is a better alternative than the input query, and\nit should therefore be expanded. To tolerate the variations\nin probability estimation, we relax the selection criterion to\nthose query alternatives if their scores are within a certain\ndistance (10% in our experiments) to the best score.\nQuery variations Entropy\nhotel price comparison 6.177\nhotel price comparisons 6.597\nhotels price comparison 6.937\nhotels price comparisons 7.360\nTable 3: Variations of query hotel price\ncomparison ranked by entropy score, with the original\nquery in bold face.\n3.5 Context sensitive document matching\nEven after we know which word variants are likely to be\nuseful, we have to be conservative in document matching\nfor the expanded variants. For the query hotel price\ncomparisons, we decided that word comparisons is expanded\nto include comparison. However, not every occurrence of\ncomparison in the document is of interest. A page which\nis about comparing customer service can contain all of the\nwords hotel price comparisons comparison. This page is not\na good page for the query.\nIf we accept matches of every occurrence of comparison,\nit will hurt retrieval precision and this is one of the main\nreasons why most stemming approaches do not work well\nfor information retrieval. To address this problem, we have\na proximity constraint that considers the context around\nthe expanded variant in the document. A variant match\nis considered valid only if the variant occurs in the same\ncontext as the original word does. The context is the left or\nthe right non-stop segments 1\nof the original word. Taking\nthe same query as an example, the context of comparisons\nis price. The expanded word comparison is only valid if\nit is in the same context of comparisons, which is after the\nword price. Thus, we should only match those occurrences\nof comparison in the document if they occur after the word\nprice. Considering the fact that queries and documents\nmay not represent the intent in exactly the same way, we\nrelax this proximity constraint to allow variant occurrences\nwithin a window of some fixed size. If the expanded word\ncomparison occurs within the context of price within\na window, it is considered valid. The smaller the window\nsize is, the more restrictive the matching. We use a window\nsize of 4, which typically captures contexts that include the\ncontaining and adjacent noun phrases.\n4. EXPERIMENTAL EVALUATION\n4.1 Evaluation metrics\nWe will measure both relevance improvement and the\nstemming cost required to achieve the relevance.\n1\na context segment can not be a single stop word.\n4.1.1 Relevance measurement\nWe use a variant of the average Discounted Cumulative\nGain (DCG), a recently popularized scheme to measure search\nengine relevance [1, 11]. Given a query and a ranked list of K\ndocuments (K is set to 5 in our experiments), the DCG(K)\nscore for this query is calculated as follows:\nDCG(K) =\nKX\nk=1\ngk\nlog2(1 + k)\n. (7)\nwhere gk is the weight for the document at rank k. Higher\ndegree of relevance corresponds to a higher weight. A page is\ngraded into one of the five scales: Perfect, Excellent, Good,\nFair, Bad, with corresponding weights. We use dcg to\nrepresent the average DCG(5) over a set of test queries.\n4.1.2 Stemming cost\nAnother metric is to measure the additional cost incurred\nby stemming. Given the same level of relevance\nimprovement, we prefer a stemming method that has less additional\ncost. We measure this by the percentage of queries that are\nactually stemmed, over all the queries that could possibly\nbe stemmed.\n4.2 Data preparation\nWe randomly sample 870 queries from a three month\nquery log, with 290 from each month. Among all these 870\nqueries, we remove all misspelled queries since misspelled\nqueries are not of interest to stemming. We also remove all\none word queries since stemming one word queries without\ncontext has a high risk of changing query intent, especially\nfor short words. In the end, we have 529 correctly spelled\nqueries with at least 2 words.\n4.3 Naive stemming for Web search\nBefore explaining the experiments and results in detail,\nwe\"d like to describe the traditional way of using stemming\nfor Web search, referred as the naive model. This is to treat\nevery word variant equivalent for all possible words in the\nquery. The query book store will be transformed into\n(book OR books)(store OR stores) when limiting stemming\nto pluralization handling only, where OR is an operator that\ndenotes the equivalence of the left and right arguments.\n4.4 Experimental setup\nThe baseline model is the model without stemming. We\nfirst run the naive model to see how well it performs over\nthe baseline. Then we improve the naive stemming model\nby document sensitive matching, referred as document\nsensitive matching model. This model makes the same stemming\nas the naive model on the query side, but performs\nconservative matching on the document side using the strategy\ndescribed in section 3.5. The naive model and document\nsensitive matching model stem the most queries. Out of the\n529 queries, there are 408 queries that they stem,\ncorresponding to 46.7% query traffic (out of a total of 870). We\nthen further improve the document sensitive matching model\nfrom the query side with selective word stemming based on\nstatistical language modeling (section 3.4), referred as\nselective stemming model. Based on language modeling\nprediction, this model stems only a subset of the 408 queries\nstemmed by the document sensitive matching model. We\nexperiment with unigram language model and bigram\nlanguage model. Since we only care how much we can improve\nthe naive model, we will only use these 408 queries (all the\nqueries that are affected by the naive stemming model) in\nthe experiments.\nTo get a sense of how these models perform, we also have\nan oracle model that gives the upper-bound performance a\nstemmer can achieve on this data. The oracle model only\nexpands a word if the stemming will give better results.\nTo analyze the pluralization handling influence on\ndifferent query categories, we divide queries into short queries\nand long queries. Among the 408 queries stemmed by the\nnaive model, there are 272 short queries with 2 or 3 words,\nand 136 long queries with at least 4 words.\n4.5 Results\nWe summarize the overall results in Table 4, and present\nthe results on short queries and long queries separately in\nTable 5. Each row in Table 4 is a stemming strategy\ndescribed in section 4.4. The first column is the name of the\nstrategy. The second column is the number of queries\naffected by this strategy; this column measures the stemming\ncost, and the numbers should be low for the same level of\ndcg. The third column is the average dcg score over all\ntested queries in this category (including the ones that were\nnot stemmed by the strategy). The fourth column is the\nrelative improvement over the baseline, and the last column\nis the p-value of Wilcoxon significance test.\nThere are several observations about the results. We can\nsee the naively stemming only obtains a statistically\ninsignificant improvement of 1.5%. Looking at Table 5, it gives an\nimprovement of 2.7% on short queries. However, it also\nhurts long queries by -2.4%. Overall, the improvement is\ncanceled out. The reason that it improves short queries is\nthat most short queries only have one word that can be\nstemmed. Thus, blindly pluralizing short queries is\nrelatively safe. However for long queries, most queries can have\nmultiple words that can be pluralized. Expanding all of\nthem without selection will significantly hurt precision.\nDocument context sensitive stemming gives a significant\nlift to the performance, from 2.7% to 4.2% for short queries\nand from -2.4% to -1.6% for long queries, with an overall\nlift from 1.5% to 2.8%. The improvement comes from the\nconservative context sensitive document matching. An\nexpanded word is valid only if it occurs within the context of\noriginal query in the document. This reduces many spurious\nmatches. However, we still notice that for long queries,\ncontext sensitive stemming is not able to improve performance\nbecause it still selects too many documents and gives the\nranking function a hard problem. While the chosen window\nsize of 4 works the best amongst all the choices, it still\nallows spurious matches. It is possible that the window size\nneeds to be chosen on a per query basis to ensure tighter\nproximity constraints for different types of noun phrases.\nSelective word pluralization further helps resolving the\nproblem faced by document context sensitive stemming. It\ndoes not stem every word that places all the burden on the\nranking algorithm, but tries to eliminate unnecessary\nstemming in the first place. By predicting which word variants\nare going to be useful, we can dramatically reduce the\nnumber of stemmed words, thus improving both the recall and\nthe precision. With the unigram language model, we can\nreduce the stemming cost by 26.7% (from 408/408 to 300/408)\nand lift the overall dcg improvement from 2.8% to 3.4%. In\nparticular, it gives significant improvements on long queries.\nThe dcg gain is turned from negative to positive, from \u22121.6%\nto 1.1%. This confirms our hypothesis that reducing\nunnecessary word expansion leads to precision improvement. For\nshort queries too, we observe both dcg improvement and\nstemming cost reduction with the unigram language model.\nThe advantages of predictive word expansion with a\nlanguage model is further boosted with a better bigram\nlanguage model. The overall dcg gain is lifted from 3.4%\nto 3.9%, and stemming cost is dramatically reduced from\n408/408 to 250/408, corresponding to only 29% of query\ntraffic (250 out of 870) and an overall 1.8% dcg\nimprovement overall all query traffic. For short queries, bigram\nlanguage model improves the dcg gain from 4.4% to 4.7%,\nand reduces stemming cost from 272/272 to 150/272. For\nlong queries, bigram language model improves dcg gain from\n1.1% to 2.5%, and reduces stemming cost from 136/136 to\n100/136. We observe that the bigram language model gives\na larger lift for long queries. This is because the uncertainty\nin long queries is larger and a more powerful language model\nis needed. We hypothesize that a trigram language model\nwould give a further lift for long queries and leave this for\nfuture investigation.\nConsidering the tight upper-bound 2\non the improvement\nto be gained from pluralization handling (via the oracle\nmodel), the current performance on short queries is very\nsatisfying. For short queries, the dcg gain upper-bound is 6.3%\nfor perfect pluralization handling, our current gain is 4.7%\nwith a bigram language model. For long queries, the dcg\ngain upper-bound is 4.6% for perfect pluralization handling,\nour current gain is 2.5% with a bigram language model. We\nmay gain additional benefit with a more powerful language\nmodel for long queries. However, the difficulties of long\nqueries come from many other aspects including the\nproximity and the segmentation problem. These problems have\nto be addressed separately. Looking at the the upper-bound\nof overhead reduction for oracle stemming, 75% (308/408)\nof the naive stemmings are wasteful. We currently capture\nabout half of them. Further reduction of the overhead\nrequires sacrificing the dcg gain.\nNow we can compare the stemming strategies from a\ndifferent aspect. Instead of looking at the influence over all\nqueries as we described above, Table 6 summarizes the dcg\nimprovements over the affected queries only. We can see\nthat the number of affected queries decreases as the\nstemming strategy becomes more accurate (dcg improvement).\nFor the bigram language model, over the 250/408 stemmed\nqueries, the dcg improvement is 6.1%. An interesting\nobservation is the average dcg decreases with a better model,\nwhich indicates a better stemming strategy stems more\ndifficult queries (low dcg queries).\n5. DISCUSSIONS\n5.1 Language models from query vs. from Web\nAs we mentioned in Section 1, we are trying to predict\nthe probability of a string occurring on the Web. The\nlanguage model should describe the occurrence of the string on\nthe Web. However, the query log is also a good resource.\n2\nNote that this upperbound is for pluralization handling\nonly, not for general stemming. General stemming gives a\n8% upperbound, which is quite substantial in terms of our\nmetrics.\nAffected Queries dcg dcg Improvement p-value\nbaseline 0/408 7.102 N/A N/A\nnaive model 408/408 7.206 1.5% 0.22\ndocument context sensitive model 408/408 7.302 2.8% 0.014\nselective model: unigram LM 300/408 7.321 3.4% 0.001\nselective model: bigram LM 250/408 7.381 3.9% 0.001\noracle model 100/408 7.519 5.9% 0.001\nTable 4: Results comparison of different stemming strategies over all queries affected by naive stemming\nShort Query Results\nAffected Queries dcg Improvement p-value\nbaseline 0/272 N/A N/A\nnaive model 272/272 2.7% 0.48\ndocument context sensitive model 272/272 4.2% 0.002\nselective model: unigram LM 185/272 4.4% 0.001\nselective model: bigram LM 150/272 4.7% 0.001\noracle model 71/272 6.3% 0.001\nLong Query Results\nAffected Queries dcg Improvement p-value\nbaseline 0/136 N/A N/A\nnaive model 136/136 -2.4% 0.25\ndocument context sensitive model 136/136 -1.6% 0.27\nselective model: unigram LM 115/136 1.1% 0.001\nselective model: bigram LM 100/136 2.5% 0.001\noracle model 29/136 4.6% 0.001\nTable 5: Results comparison of different stemming strategies overall short queries and long queries\nUsers reformulate a query using many different variants to\nget good results.\nTo test the hypothesis that we can learn reliable\ntransformation probabilities from the query log, we trained a\nlanguage model from the same query top 25M queries as used\nto learn segmentation, and use that for prediction. We\nobserved a slight performance decrease compared to the model\ntrained on Web frequencies. In particular, the performance\nfor unigram LM was not affected, but the dcg gain for bigram\nLM changed from 4.7% to 4.5% for short queries. Thus, the\nquery log can serve as a good approximation of the Web\nfrequencies.\n5.2 How linguistics helps\nSome linguistic knowledge is useful in stemming. For the\npluralization handling case, pluralization and de-pluralization\nis not symmetric. A plural word used in a query indicates\na special intent. For example, the query new york hotels\nis looking for a list of hotels in new york, not the specific\nnew york hotel which might be a hotel located in\nCalifornia. A simple equivalence of hotel to hotels might boost\na particular page about new york hotel to top rank. To\ncapture this intent, we have to make sure the document is a\ngeneral page about hotels in new york. We do this by\nrequiring that the plural word hotels appears in the document.\nOn the other hand, converting a singular word to plural is\nsafer since a general purpose page normally contains\nspecific information. We observed a slight overall dcg decrease,\nalthough not statistically significant, for document context\nsensitive stemming if we do not consider this asymmetric\nproperty.\n5.3 Error analysis\nOne type of mistakes we noticed, though rare but\nseriously hurting relevance, is the search intent change after\nstemming. Generally speaking, pluralization or\ndepluralization keeps the original intent. However, the intent could\nchange in a few cases. For one example of such a query,\njob at apple, we pluralize job to jobs. This\nstemming makes the original query ambiguous. The query job\nOR jobs at apple has two intents. One is the employment\nopportunities at apple, and another is a person working at\nApple, Steve Jobs, who is the CEO and co-founder of the\ncompany. Thus, the results after query stemming returns\nSteve Jobs as one of the results in top 5. One solution is\nperforming results set based analysis to check if the intent is\nchanged. This is similar to relevance feedback and requires\nsecond phase ranking.\nA second type of mistakes is the entity/concept\nrecognition problem, These include two kinds. One is that the\nstemmed word variant now matches part of an entity or\nconcept. For example, query cookies in san francisco is\npluralized to cookies OR cookie in san francisco. The\nresults will match cookie jar in san francisco. Although\ncookie still means the same thing as cookies, cookie\njar is a different concept. Another kind is the unstemmed\nword matches an entity or concept because of the stemming\nof the other words. For example, quote ICE is\npluralized to quote OR quotes ICE. The original intent for this\nquery is searching for stock quote for ticker ICE. However,\nwe noticed that among the top results, one of the results\nis Food quotes: Ice cream. This is matched because of\nAffected Queries old dcg new dcg dcg Improvement\nnaive model 408/408 7.102 7.206 1.5%\ndocument context sensitive model 408/408 7.102 7.302 2.8%\nselective model: unigram LM 300/408 5.904 6.187 4.8%\nselective model: bigram LM 250/408 5.551 5.891 6.1%\nTable 6: Results comparison over the stemmed queries only: column old/new dcg is the dcg score over the\naffected queries before/after applying stemming\nthe pluralized word quotes. The unchanged word ICE\nmatches part of the noun phrase ice cream here. To solve\nthis kind of problem, we have to analyze the documents and\nrecognize cookie jar and ice cream as concepts instead\nof two independent words.\nA third type of mistakes occurs in long queries. For the\nquery bar code reader software, two words are pluralized.\ncode to codes and reader to readers. In fact, bar\ncode reader in the original query is a strong concept and\nthe internal words should not be changed. This is the\nsegmentation and entity and noun phrase detection problem in\nqueries, which we actively are attacking. For long queries,\nwe should correctly identify the concepts in the query, and\nboost the proximity for the words within a concept.\n6. CONCLUSIONS AND FUTURE WORK\nWe have presented a simple yet elegant way of stemming\nfor Web search. It improves naive stemming in two aspects:\nselective word expansion on the query side and\nconservative word occurrence matching on the document side. Using\npluralization handling as an example, experiments on a\nmajor Web search engine data show it significantly improves\nthe Web relevance and reduces the stemming cost. It also\nsignificantly improves Web click through rate (details not\nreported in the paper).\nFor the future work, we are investigating the problems\nwe identified in the error analysis section. These include:\nentity and noun phrase matching mistakes, and improved\nsegmentation.\n7. REFERENCES\n[1] E. Agichtein, E. Brill, and S. T. Dumais. Improving\nWeb Search Ranking by Incorporating User Behavior\nInformation. In SIGIR, 2006.\n[2] E. Airio. Word Normalization and Decompounding in\nMono- and Bilingual IR. Information Retrieval,\n9:249-271, 2006.\n[3] P. Anick. Using Terminological Feedback for Web\nSearch Refinement: a Log-based Study. In SIGIR,\n2003.\n[4] R. Baeza-Yates and B. Ribeiro-Neto. Modern\nInformation Retrieval. ACM Press/Addison Wesley,\n1999.\n[5] S. Chen and J. Goodman. An Empirical Study of\nSmoothing Techniques for Language Modeling.\nTechnical Report TR-10-98, Harvard University, 1998.\n[6] S. Cronen-Townsend, Y. Zhou, and B. Croft. A\nFramework for Selective Query Expansion. In CIKM,\n2004.\n[7] H. Fang and C. Zhai. Semantic Term Matching in\nAxiomatic Approaches to Information Retrieval. In\nSIGIR, 2006.\n[8] W. B. Frakes. Term Conflation for Information\nRetrieval. In C. J. Rijsbergen, editor, Research and\nDevelopment in Information Retrieval, pages 383-389.\nCambridge University Press, 1984.\n[9] D. Harman. How Effective is Suffixing? JASIS,\n42(1):7-15, 1991.\n[10] D. Hull. Stemming Algorithms - A Case Study for\nDetailed Evaluation. JASIS, 47(1):70-84, 1996.\n[11] K. Jarvelin and J. Kekalainen. Cumulated Gain-Based\nEvaluation Evaluation of IR Techniques. ACM TOIS,\n20:422-446, 2002.\n[12] R. Jones, B. Rey, O. Madani, and W. Greiner.\nGenerating Query Substitutions. In WWW, 2006.\n[13] W. Kraaij and R. Pohlmann. Viewing Stemming as\nRecall Enhancement. In SIGIR, 1996.\n[14] R. Krovetz. Viewing Morphology as an Inference\nProcess. In SIGIR, 1993.\n[15] D. Lin. Automatic Retrieval and Clustering of Similar\nWords. In COLING-ACL, 1998.\n[16] J. B. Lovins. Development of a Stemming Algorithm.\nMechanical Translation and Computational\nLinguistics, II:22-31, 1968.\n[17] M. Lennon and D. Peirce and B. Tarry and P. Willett.\nAn Evaluation of Some Conflation Algorithms for\nInformation Retrieval. Journal of Information Science,\n3:177-188, 1981.\n[18] M. Porter. An Algorithm for Suffix Stripping.\nProgram, 14(3):130-137, 1980.\n[19] K. M. Risvik, T. Mikolajewski, and P. Boros. Query\nSegmentation for Web Search. In WWW, 2003.\n[20] S. E. Robertson. On Term Selection for Query\nExpansion. Journal of Documentation, 46(4):359-364,\n1990.\n[21] G. Salton and C. Buckley. Improving Retrieval\nPerformance by Relevance Feedback. JASIS, 41(4):288\n- 297, 1999.\n[22] R. Sun, C.-H. Ong, and T.-S. Chua. Mining\nDependency Relations for Query Expansion in\nPassage Retrieval. In SIGIR, 2006.\n[23] C. Van Rijsbergen. Information Retrieval.\nButterworths, second version, 1979.\n[24] B. V\u00b4elez, R. Weiss, M. A. Sheldon, and D. K. Gifford.\nFast and Effective Query Refinement. In SIGIR, 1997.\n[25] J. Xu and B. Croft. Query Expansion using Local and\nGlobal Document Analysis. In SIGIR, 1996.\n[26] J. Xu and B. Croft. Corpus-based Stemming using\nCooccurrence of Word Variants. ACM TOIS, 16\n(1):61-81, 1998.", "keywords": "stem;language model;bigram language model;head word detection;context sensitive document matching;lovin stemmer;porter stemmer;web search;candidate generation;query segmentation;unigram language model;context sensitive query stemming;stemming"}
{"name": "train_H-54", "title": "Knowledge-intensive Conceptual Retrieval and Passage Extraction of Biomedical Literature", "abstract": "This paper presents a study of incorporating domain-specific knowledge (i.e., information about concepts and relationships between concepts in a certain domain) in an information retrieval (IR) system to improve its effectiveness in retrieving biomedical literature. The effects of different types of domain-specific knowledge in performance contribution are examined. Based on the TREC platform, we show that appropriate use of domainspecific knowledge in a proposed conceptual retrieval model yields about 23% improvement over the best reported result in passage retrieval in the Genomics Track of TREC 2006.", "fulltext": "1. INTRODUCTION\nBiologists search for literature on a daily basis. For most\nbiologists, PubMed, an online service of U.S. National Library of\nMedicine (NLM), is the most commonly used tool for searching\nthe biomedical literature. PubMed allows for keyword search by\nusing Boolean operators. For example, if one desires documents on\nthe use of the drug propanolol in the disease hypertension, a\ntypical PubMed query might be propanolol AND hypertension,\nwhich will return all the documents having the two keywords.\nKeyword search in PubMed is effective if the query is well-crafted\nby the users using their expertise. However, information needs of\nbiologists, in some cases, are expressed as complex questions\n[8][9], which PubMed is not designed to handle. While NLM does\nmaintain an experimental tool for free-text queries [6], it is still\nbased on PubMed keyword search.\nThe Genomics track of the 2006 Text REtrieval Conference\n(TREC) provides a common platform to assess the methods and\ntechniques proposed by various groups for biomedical information\nretrieval. The queries were collected from real biologists and they\nare expressed as complex questions, such as How do mutations in\nthe Huntingtin gene affect Huntington\"s disease?. The document\ncollection contains 162,259 Highwire full-text documents in\nHTML format. Systems from participating groups are expected to\nfind relevant passages within the full-text documents. A passage is\ndefined as any span of text that does not include the HTML\nparagraph tag (i.e., <P> or </P>).\nWe approached the problem by utilizing domain-specific\nknowledge in a conceptual retrieval model. Domain-specific\nknowledge, in this paper, refers to information about concepts and\nrelationships between concepts in a certain domain. We assume\nthat appropriate use of domain-specific knowledge might improve\nthe effectiveness of retrieval. For example, given a query What is\nthe role of gene PRNP in the Mad Cow Disease?, expanding the\ngene symbol PRNP with its synonyms Prp, PrPSc, and\nprion protein, more relevant documents might be retrieved.\nPubMed and many other biomedical systems [8][9][10][13] also\nmake use of domain-specific knowledge to improve retrieval\neffectiveness.\nIntuitively, retrieval on the level of concepts should outperform\nbag-of-words approaches, since the semantic relationships\namong words in a concept are utilized. In some recent studies\n[13][15], positive results have been reported for this hypothesis. In\nthis paper, concepts are entry terms of the ontology Medical\nSubject Headings (MeSH), a controlled vocabulary maintained by\nNLM for indexing biomedical literature, or gene symbols in the\nEntrez gene database also from NLM. A concept could be a word,\nsuch as the gene symbol PRNP, or a phrase, such as Mad cow\ndiseases. In the conceptual retrieval model presented in this\npaper, the similarity between a query and a document is measured\non both concept and word levels.\nThis paper makes two contributions:\n1. We propose a conceptual approach to utilize domain-specific\nknowledge in an IR system to improve its effectiveness in\nretrieving biomedical literature. Based on this approach, our\nsystem achieved significant improvement (23%) over the best\nreported result in passage retrieval in the Genomics track of\nTREC 2006.\n2. We examine the effects of utilizing concepts and of different\ntypes of domain-specific knowledge in performance\ncontribution.\nThis paper is organized as follows: problem statement is given in\nthe next section. The techniques are introduced in section 3. In\nsection 4, we present the experimental results. Related works are\ngiven in section 5 and finally, we conclude the paper in section 6.\n2. PROBLEM STATEMENT\nWe describe the queries, document collection and the system\noutput in this section.\nThe query set used in the Genomics track of TREC 2006 consists\nof 28 questions collected from real biologists. As described in [8],\nthese questions all have the following general format:\nBiological object (1..m)\nRelationship\n\u2190\u23af\u23af\u23af\u23af\u2192 Biological process (1..n) (1)\nwhere a biological object might be a gene, protein, or gene\nmutation and a biological process can be a physiological process\nor disease. A question might involve multiple biological objects\n(m) and multiple biological processes (n). These questions were\nderived from four templates (Table 2).\nTable 2 Query templates and examples in the Genomics track\nof TREC 2006\nTemplate Example\nWhat is the role of gene in\ndisease?\nWhat is the role of DRD4 in\nalcoholism?\nWhat effect does gene have\non biological process?\nWhat effect does the insulin\nreceptor gene have on\ntumorigenesis?\nHow do genes interact in\norgan function?\nHow do HMG and HMGB1\ninteract in hepatitis?\nHow does a mutation in\ngene influence biological\nprocess?\nHow does a mutation in Ret\ninfluence thyroid function?\nFeatures of the queries: 1) They are different from the typical\nWeb queries and the PubMed queries, both of which usually\nconsist of 1 to 3 keywords; 2) They are generated from structural\ntemplates which can be used by a system to identify the query\ncomponents, the biological object or process.\nThe document collection contains 162,259 Highwire full-text\ndocuments in HTML format.\nThe output of the system is a list of passages ranked according to\ntheir similarities with the query. A passage is defined as any span\nof text that does not include the HTML paragraph tag (i.e., <P> or\n</P>). A passage could be a part of a sentence, a sentence, a set of\nconsecutive sentences or a paragraph (i.e., the whole span of text\nthat are inside of <P> and </P> HTML tags).\nThis is a passage-level information retrieval problem with the\nattempt to put biologists in contexts where relevant information is\nprovided.\n3. TECHNIQUES AND METHODS\nWe approached the problem by first retrieving the top-k most\nrelevant paragraphs, then extracting passages from these\nparagraphs, and finally ranking the passages. In this process, we\nemployed several techniques and methods, which will be\nintroduced in this section. First, we give two definitions:\nDefinition 3.1 A concept is 1) a entry term in the MeSH\nontology, or 2) a gene symbol in the Entrez gene database. This\ndefinition of concept can be generalized to include other\nbiomedical dictionary terms.\nDefinition 3.2 A semantic type is a category defined in the\nSemantic Network of the Unified Medical Language System\n(UMLS) [14]. The current release of the UMLS Semantic Network\ncontains 135 semantic types such as Disease or Syndrome. Each\nentry term in the MeSH ontology is assigned one or more semantic\ntypes. Each gene symbol in the Entrez gene database maps to the\nsemantic type Gene or Genome. In addition, these semantic\ntypes are linked by 54 relationships. For example, Antibiotic\nprevents Disease or Syndrome. These relationships among\nsemantic types represent general biomedical knowledge. We\nutilized these semantic types and their relationships to identify\nrelated concepts.\nThe rest of this section is organized as follows: in section 3.1, we\nexplain how the concepts are identified within a query. In section\n3.2, we specify five different types of domain-specific knowledge\nand introduce how they are compiled. In section 3.3, we present\nour conceptual IR model. Finally, our strategy for passage\nextraction is described in section 3.4.\n3.1 Identifying concepts within a query\nA concept, defined in Definition 3.1, is a gene symbol or a MeSH\nterm. We make use of the query templates to identify gene\nsymbols. For example, the query How do HMG and HMGB1\ninteract in hepatitis? is derived from the template How do genes\ninteract in organ function?. In this case, HMG and HMGB1\nwill be identified as gene symbols. In cases where the query\ntemplates are not provided, programs for recognition of gene\nsymbols within texts are needed.\nWe use the query translation functionality of PubMed to extract\nMeSH terms in a query. This is done by submitting the whole\nquery to PubMed, which will then return a file in which the MeSH\nterms in the query are labeled. In Table 3.1, three MeSH terms\nwithin the query What is the role of gene PRNP in the Mad cow\ndisease? are found in the PubMed translation: \"encephalopathy,\nbovine spongiform\" for Mad cow disease, genes for gene,\nand role for role.\nTable 3.1 The PubMed translation of the query \"What is the\nrole of gene PRNP in the Mad cow disease?\".\nTerm PubMed translation\nMad cow\ndisease\n\"bovine spongiform encephalopathy\"[Text Word]\nOR \"encephalopathy, bovine spongiform\"[MeSH\nTerms] OR Mad cow disease[Text Word]\ngene\n(\"genes\"[TIAB] NOT Medline[SB]) OR\n\"genes\"[MeSH Terms] OR gene[Text Word]\nrole \"role\"[MeSH Terms] OR role[Text Word]\n3.2 Compiling domain-specific knowledge\nIn this paper, domain-specific knowledge refers to information\nabout concepts and their relationships in a certain domain. We\nused five types of domain-specific knowledge in the domain of\ngenomics:\nType 1. Synonyms (terms listed in the thesauruses that refer to\nthe same meaning)\nType 2. Hypernyms (more generic terms, one level only)\nType 3. Hyponyms (more specific terms, one level only)\nType 4. Lexical variants (different forms of the same concept,\nsuch as abbreviations. They are commonly used in the\nliterature, but might not be listed in the thesauruses)\nType 5. Implicitly related concepts (terms that are semantically\nrelated and also co-occur more frequently than being\nindependent in the biomedical texts)\nKnowledge of type 1-3 is retrieved from the following two\nthesauruses: 1) MeSH, a controlled vocabulary maintained by\nNLM for indexing biomedical literature. The 2007 version of\nMeSH contains information about 190,000 concepts. These\nconcepts are organized in a tree hierarchy; 2) Entrez Gene, one of\nthe most widely used searchable databases of genes. The current\nversion of Entrez Gene contains information about 1.7 million\ngenes. It does not have a hierarchy. Only synonyms are retrieved\nfrom Entrez Gene. The compiling of type 4-5 knowledge is\nintroduced in section 3.2.1 and 3.2.2, respectively.\n3.2.1 Lexical variants\nLexical variants of gene symbols\nNew gene symbols and their lexical variants are regularly\nintroduced into the biomedical literature [7]. However, many\nreference databases, such as UMLS and Entrez Gene, may not be\nable to keep track of all this kind of variants. For example, for the\ngene symbol \"NF-kappa B\", at least 5 different lexical variants can\nbe found in the biomedical literature: \"NF-kappaB\", \"NFkappaB\",\n\"NFkappa B\", \"NF-kB\", and \"NFkB\", three of which are not in the\ncurrent UMLS and two not in the Entrez Gene. [3][21] have shown\nthat expanding gene symbols with their lexical variants improved\nthe retrieval effectiveness of their biomedical IR systems. In our\nsystem, we employed the following two strategies to retrieve\nlexical variants of gene symbols.\nStrategy I: This strategy is to automatically generate lexical\nvariants according to a set of manually crafted heuristics [3][21].\nFor example, given a gene symbol PLA2, a variant PLAII is\ngenerated according to the heuristic that Roman numerals and\nArabic numerals are convertible when naming gene symbols.\nAnother variant, PLA 2, is also generated since a hyphen or a\nspace could be inserted at the transition between alphabetic and\nnumerical characters in a gene symbol.\nStrategy II: This strategy is to retrieve lexical variants from an\nabbreviation database. ADAM [22] is an abbreviation database\nwhich covers frequently used abbreviations and their definitions\n(or long-forms) within MEDLINE, the authoritative repository of\ncitations from the biomedical literature maintained by the NLM.\nGiven a query How does nucleoside diphosphate kinase (NM23)\ncontribute to tumor progression?, we first identify the\nabbreviation NM23 and its long-form nucleoside diphosphate\nkinase using the abbreviation identification program from [4].\nSearching the long-form nucleoside diphosphate kinase in\nADAM, other abbreviations, such as NDPK or NDK, are\nretrieved. These abbreviations are considered as the lexical\nvariants of NM23.\nLexical variants of MeSH concepts\nADAM is used to obtain the lexical variants of MeSH concepts as\nwell. All the abbreviations of a MeSH concept in ADAM are\nconsidered as lexical variants to each other. In addition, those\nlong-forms that share the same abbreviation with the MeSH\nconcept and are different by an edit distance of 1 or 2 are also\nconsidered as its lexical variants. As an example, \"human\npapilloma viruses\" and \"human papillomaviruses\" have the same\nabbreviation HPV in ADAM and their edit distance is 1. Thus\nthey are considered as lexical variants to each other. The edit\ndistance between two strings is measured by the minimum number\nof insertions, deletions, and substitutions of a single character\nrequired to transform one string into the other [12].\n3.2.2 Implicitly related concepts\nMotivation: In some cases, there are few documents in the\nliterature that directly answer a given query. In this situation, those\ndocuments that implicitly answer their questions or provide\nsupporting information would be very helpful. For example, there\nare few documents in PubMed that directly answer the query\n\"What is the role of the genes HNF4 and COUP-tf I in the\nsuppression in the function of the liver?\". However, there exist\nsome documents about the role of \"HNF4\" and \"COUP-tf I\" in\nregulating \"hepatitis B virus\" transcription. It is very likely that the\nbiologists would be interested in these documents because\n\"hepatitis B virus\" is known as a virus that could cause serious\ndamage to the function of liver. In the given example, \"hepatitis B\nvirus\" is not a synonym, hypernym, hyponym, nor a lexical variant\nof any of the query concepts, but it is semantically related to the\nquery concepts according to the UMLS Semantic Network. We\ncall this type of concepts implicitly related concepts of the\nquery. This notion is similar to the B-term used in [19] for\nrelating two disjoint literatures for biomedical hypothesis\ngeneration. The difference is that we utilize the semantic\nrelationships among query concepts to exclusively focus on\nconcepts of certain semantic types.\nA query q in format (1) of section 2 can be represented by\nq = (A, C)\nwhere A is the set of biological objects and C is the set of\nbiological processes. Those concepts that are semantically related\nto both A and C according to the UMLS Semantic Network are\nconsidered as the implicitly related concepts of the query. In the\nabove example, A = {HNF4, COUP-tf I}, C = {function of\nliver}, and \"hepatitis B virus\" is one of the implicitly related\nconcepts.\nWe make use of the MEDLINE database to extract the implicitly\nrelated concepts. The 2006 version of MEDLINE database\ncontains citations (i.e., abstracts, titles, and etc.) of over 15 million\nbiomedical articles. Each document in MEDLINE is manually\nindexed by a list of MeSH terms to describe the topics covered by\nthat document. Implicitly related concepts are extracted and\nranked in the following steps:\nStep 1. Let list_A be the set of MeSH terms that are 1) used for\nindexing those MEDLINE citations having A, and 2) semantically\nrelated to A according to the UMLS Semantic Network. Similarly,\nlist_C is created for C. Concepts in B = list_A \u2229 list_C are\nconsidered as implicitly related concepts of the query.\nStep 2. For each concept b\u2208B, compute the association between\nb and A using the mutual information measure [5]:\nP( , )\n( , ) log\nP( )P( )\nb A\nI b A\nb A\n=\nwhere P(x) = n/N, n is the number of MEDLINE citations having x\nand N is the size of MEDLINE. A large value for I(b, A) means\nthat b and A co-occur much more often than being independent.\nI(b, C) is computed similarly.\nStep 3. Let r(b) = (I(b, A), I(b, C)), for b\u2208 B. Given b1, b2 \u2208 B,\nwe say r(b1) \u2264 r(b2) if I(b1, A) \u2264 I(b2, A) and I(b1, C) \u2264 I(b2, C).\nThen the association between b and the query q is measured by:\n{ : and ( ) ( )}\n( , )\n{ : and ( ) ( )}\nx x B r x r b\nscore b q\nx x B r b r x\n\u2208 \u2264\n=\n\u2208 \u2264\n(2)\nThe numerator in Formula 2 is the number of the concepts in B\nthat are associated with both A and C equally with or less than b.\nThe denominator is the number of the concepts in B that are\nassociated with both A and C equally with or more than b. Figure\n3.2.2 shows the top 4 implicitly related concepts for the sample\nquery.\nFigure 3.2.2 Top 4 implicitly related concepts for the query\n\"How do interactions between HNF4 and COUP-TF1 suppress\nliver function?\".\nIn Figure 3.2.2, the top 4 implicitly related concepts are all highly\nassociated with liver: Hepatocytes are liver cells;\nHepatoblastoma is a malignant liver neoplasm occurring in\nyoung children; the vast majority of Gluconeogenesis takes\nplace in the liver; and Hepatitis B virus is a virus that could\ncause serious damage to the function of liver.\nThe top-k ranked concepts in B are used for query expansion: if\nI(b, A) \u2265 I(b, C), then b is considered as an implicit related\nconcept of A. A document having b but not A will receive a partial\nweight of A. The expansion is similar for C when I(b, A) < I(b, C).\n3.3 Conceptual IR model\nWe now discuss our conceptual IR model. We first give the basic\nconceptual IR model in section 3.3.1. Then we explain how the\ndomain-specific knowledge is incorporated in the model using\nquery expansion in section 3.3.2. A pseudo-feedback strategy is\nintroduced in section 3.3.3. In section 3.3.4, we give a strategy to\nimprove the ranking by avoiding incorrect match of abbreviations.\n3.3.1 Basic model\nGiven a query q and a document d, our model measures two\nsimilarities, concept similarity and word similarity:\n( , ) ( , )( , ) ( , )\nconcept word\nsim q d sim q d sim q d=\nConcept similarity\nTwo vectors are derived from a query q,\n1 2\n1 11 12 1\n2 21 22 2\n( , )\n( , ,..., )\n( , ,..., )\nm\nn\nq v v\nv c c c\nv c c c\n=\n=\n=\nwhere v1 is a vector of concepts describing the biological object(s)\nand v2 is a vector of concepts describing the biological process(es).\nGiven a vector of concepts v, let s(v) be the set of concepts in v.\nThe weight of vi is then measured by:\n( ) max{log : ( ) ( ) and 0}i i v\nv\nN\nw v s v s v n\nn\n= \u2286 >\nwhere v is a vector that contains a subset of concepts in vi and nv is\nthe number of documents having all the concepts in v.\nThe concept similarity between q and d is then computed by\n2\n1\n( )( , ) i i\nconcept i\nw vsim q d \u03b1\n=\n= \u00d7\u2211\nwhere \u03b1i is a parameter to indicate the completeness of vi that\ndocument d has covered. \u03b1i is measured by:\nand i\ni\ni\nc\nc d c v\nc\nc v\nidf\nidf\n\u03b1\n\u2208 \u2208\n\u2208\n=\n\u2211\n\u2211\n(3)\nwhere idfc is the inverse document frequency of concept c.\nAn example: suppose we have a query How does Nurr-77 delete\nT cells before they migrate to the spleen or lymph nodes and how\ndoes this impact autoimmunity?. After identifying the concepts in\nthe query, we have:\n1\n2\n('Nurr-77')\n('T cells', 'spleen', 'autoimmunity', 'lymph nodes')\nv\nv\n=\n=\nSuppose that some document frequencies of different\ncombinations of concepts are as follows:\n25 df('Nurr-77')\n0 df('T cells', 'spleen', 'autoimmunity', 'lymph nodes')\n326 df('T cells', 'spleen', 'autoimmunity')\n82 df('spleen', 'autoimmunity', 'lymph nodes')\n147 df('T cells', 'autoimmunity', 'lymph nodes')\n2332 df('T cells', 'spleen', 'lymph nodes')\nThe weight of vi is then computed by (note that there does not exist\na document having all the concepts in v2):\n1\n2\n( ) log( / 25)\n( ) log( /82)\nw v N\nw v N\n=\n=\n.\nNow suppose a document d contains concepts \u2018Nurr-77\", 'T cells',\n'spleen', and 'lymph nodes', but not \u2018autoimmunity\", then the value\nof parameter \u03b1i is computed as follows:\n1\n2\n1\n('T cells')+ ('spleen')+ ('lymph nodes')\n('T cells')+ ('spleen')+ ('lymph nodes')+ ('autoimmunity')\nidf idf idf\nidf idf idf idf\n\u03b1\n\u03b1\n=\n=\nWord similarity\nThe similarity between q and d on the word level is computed\nusing Okapi [17]:\n10.5 ( 1)\nlog( )( , )\n0.5word w q\nN n k tf\nsim q d\nn K tf\u2208\n\u2212 + +\n=\n+ +\n\u2211 (4)\nwhere N is the size of the document collection; n is the number of\ndocuments containing w; K=k1 \u00d7 ((1-b)+b \u00d7 dl/avdl) and k1=1.2,\nC\nFunction\nof Liver\nImplicitly related concepts (B)\nHepatocytes\nHepatoblastoma\nGluconeogenesis\nHepatitis B virus\nHNF4 and\nCOUP-tf I\nA\nb=0.75 are constants. dl is the document length of d and avdl is the\naverage document length; tf is the term frequency of w within d.\nThe model\nGiven two documents d1 and d2, we say 1 2( , ) ( , )sim q d sim q d> or\nd1 will be ranked higher than d2, with respect to the same query q,\nif either\n1) 1 2( , ) ( , )\nconcept concept\nsim q d sim q d> or\n2) 1 2 1 2and( , ) ( , ) ( , ) ( , )\nconcept concept word word\nsim q d sim q d sim q d sim q d= >\nThis conceptual IR model emphasizes the similarity on the concept\nlevel. A similar model but applied to non-biomedical domain has\nbeen given in [15].\n3.3.2 Incorporating domain-specific knowledge\nGiven a concept c, a vector u is derived by incorporating its\ndomain-specific knowledge:\n1 2 3( , , , )u c u u u=\nwhere u1 is a vector of its synonyms, hyponyms, and lexical\nvariants; u2 is a vector of its hypernyms; and u3 is a vector of its\nimplicitly related concepts. An occurrence of any term in u1 will\nbe counted as an occurrence of c. idfc in Formula 3 is updated as:\n1,\nlogc\nc u\nN\nD\nidf =\n1,c uD is the set of documents having c or any term in 1u . The\nweight that a document d receives from u is given by:\nmax{ : and }tw t u t d\u2208 \u2208\nwhere wt = \u03b2 .cidf\u00d7 The weighting factor \u03b2 is an empirical tuning\nparameter determined as:\n1. \u03b2 = 1 if t is the original concept, its synonym, its hyponym, or\nits lexical variant;\n2. \u03b2 = 0.95 if t is a hypernym;\n3. \u03b2 = 0.90\u00d7 (k-i+1)/k if t is an implicitly related concept. k is\nthe number of selected top ranked implicitly related concepts\n(see section 3.2.2); i is the position of t in the ranking of\nimplicitly related concepts.\n3.3.3 Pseudo-feedback\nPseudo-feedback is a technique commonly used to improve\nretrieval performance by adding new terms into the original query.\nWe used a modified pseudo-feedback strategy described in [2].\nStep 1. Let C be the set of concepts in the top 15 ranked\ndocuments. For each concept c in C, compute the similarity\nbetween c and the query q, the computation of sim(q,c) can be\nfound in [2].\nStep 2. The top-k ranked concepts by sim(q,c) are selected.\nStep 3. Associate each selected concept c' with the concept cq in\nq that 1) has the same semantic type as c', and 2) is most related to\nc' among all the concepts in q. The association between c' and cq\nis computed by:\nP( ', )\n( ', ) log\nP( ')P( )\nq\nq\nq\nc c\nI c c\nc c\n=\nwhere P(x) = n/N, n is the number of documents having x and N is\nthe size of the document collection. A document having c' but not\ncq receives a weight given by: (0.5\u00d7 (k-i+1)/k) ,qcidf\u00d7 where i is the\nposition of c' in the ranking of step 2.\n3.3.4 Avoid incorrect match of abbreviations\nSome gene symbols are very short and thus ambiguous. For\nexample, the gene symbol APC could be the abbreviation for\nmany non-gene long-forms, such as air pollution control,\naerobic plate count, or argon plasma coagulation. This step is\nto avoid incorrect match of abbreviations in the top ranked\ndocuments.\nGiven an abbreviation X with the long-form L in the query, we\nscan the top-k ranked (k=1000) documents and when a document\nis found with X, we compare L with all the long-forms of X in that\ndocument. If none of these long-forms is equal or close to L (i.e.,\nthe edit distance between L and the long-form of X in that\ndocument is 1 or 2), then the concept similarity of X is subtracted.\n3.4 Passage extraction\nThe goal of passage extraction is to highlight the most relevant\nfragments of text in paragraphs. A passage is defined as any span\nof text that does not include the HTML paragraph tag (i.e., <P> or\n</P>). A passage could be a part of a sentence, a sentence, a set of\nconsecutive sentences or a paragraph (i.e., the whole span of text\nthat are inside of <P> and </P> HTML tags). It is also possible to\nhave more than one relevant passage in a single paragraph. Our\nstrategy for passage extraction assumes that the optimal passage(s)\nin a paragraph should have all the query concepts that the whole\nparagraph has. Also they should have higher density of query\nconcepts than other fragments of text in the paragraph.\nSuppose we have a query q and a paragraph p represented by a\nsequence of sentences 1 2... .np s s s= Let C be the set of concepts in\nq that occur in p and S = \u03a6.\nStep 1. For each sequence of consecutive sentences 1... ,i i js s s+ 1 \u2264\ni \u2264 j \u2264 n, let S = S 1{ ... }i i js s s+\u222a if 1...i i js s s+ satisfies that:\n1) Every query concept in C occurs in 1...i i js s s+ and\n2) There does not exist k, such that i < k < j and every query\nconcept in C occurs in 1...i i ks s s+ or 1 2... .k k js s s+ +\nCondition 1 requires 1...i i js s s+ having all the query concepts in p\nand condition 2 requires 1...i i js s s+ be the minimal.\nStep 2. Let 1min{ 1: ... }i i jL j i s s s S+= \u2212 + \u2208 . For every\n1...i i js s s+ in S, let 1{ ... }i i jS S s s s+= \u2212 if (j - i + 1) > L. This step is to\nremove those sequences of sentences in S that have lower density\nof query concepts.\nStep 3. For every two sequences of consecutive\nsentences 1 1 1 2 2 21 1... , and ...i i j i i js s s S s s s S+ +\u2208 \u2208 , if\n1 2 1 2\n2 1\n, and\n1\ni i j j\ni j\n\u2264 \u2264\n\u2264 +\n(5)\nthen do\nRepeat this step until for every two sequences of consecutive\nsentences in S, condition (5) does not apply. This step is to merge\nthose sequences of sentences in S that are adjacent or overlapped.\nFinally the remaining sequences of sentences in S are returned as\nthe optimal passages in the paragraph p with respect to the query.\n1 1 2\n1 1\n2 2 2\n1\n1 1\n1\n{ ... }\n{ ... }\n{ ... }\ni i j\ni i j\ni i j\nS S s s s\nS S s s s\nS S s s s\n+\n+\n+\n= \u222a\n= \u2212\n= \u2212\n4. EXPERIMENTAL RESULTS\nThe evaluation of our techniques and the experimental results are\ngiven in this section. We first describe the datasets and evaluation\nmetrics used in our experiments and then present the results.\n4.1 Data sets and evaluation metrics\nOur experiments were performed on the platform of the Genomics\ntrack of TREC 2006. The document collection contains 162,259\nfull-text documents from 49 Highwire biomedical journals. The set\nof queries consists of 28 queries collected from real biologists.\nThe performance is measured on three different levels (passage,\naspect, and document) to provide better insight on how the\nquestion is answered from different perspectives. Passage MAP:\nAs described in [8], this is a character-based precision calculated\nas follows: At each relevant retrieved passage, precision will be\ncomputed as the fraction of characters overlapping with the gold\nstandard passages divided by the total number of characters\nincluded in all nominated passages from this system for the topic\nup until that point. Similar to regular MAP, relevant passages that\nwere not retrieved will be added into the calculation as well, with\nprecision set to 0 for relevant passages not retrieved. Then the\nmean of these average precisions over all topics will be calculated\nto compute the mean average passage precision. Aspect MAP: A\nquestion could be addressed from different aspects. For example,\nthe question what is the role of gene PRNP in the Mad cow\ndisease? could be answered from aspects like Diagnosis,\nNeurologic manifestations, or Prions/Genetics. This measure\nindicates how comprehensive the question is answered. Document\nMAP: This is the standard IR measure. The precision is measured\nat every point where a relevant document is obtained and then\naveraged over all relevant documents to obtain the average\nprecision for a given query. For a set of queries, the mean of the\naverage precision for all queries is the MAP of that IR system.\nThe output of the system is a list of passages ranked according to\ntheir similarities with the query. The performances on the three\nlevels are then calculated based on the ranking of the passages.\n4.2 Results\nThe Wilcoxon signed-rank test was employed to determine the\nstatistical significance of the results. In the tables of the following\nsections, statistically significant improvements (at the 5% level)\nare marked with an asterisk.\n4.2.1 Conceptual IR model vs. term-based model\nThe initial baseline was established using word similarity only\ncomputed by the Okapi (Formula 4). Another run based on our\nbasic conceptual IR model was performed without using query\nexpansion, pseudo-feedback, or abbreviation correction. The\nexperimental result is shown in Table 4.2.1. Our basic conceptual\nIR model significantly outperforms the Okapi on all three levels,\nwhich suggests that, although it requires additional efforts to\nidentify concepts, retrieval on the concept level can achieve\nsubstantial improvements over purely term-based retrieval model.\n4.2.2 Contribution of different types of knowledge\nA series of experiments were performed to examine how each type\nof domain-specific knowledge contributes to the retrieval\nperformance. A new baseline was established using the basic\nconceptual IR model without incorporating any type of\ndomainspecific knowledge. Then five runs were conducted by adding\neach individual type of domain-specific knowledge. We also\nconducted a run by adding all types of domain-specific knowledge.\nResults of these experiments are shown in Table 4.2.2.\nWe found that any available type of domain-specific\nknowledge improved the performance in passage retrieval. The\nbiggest improvement comes from the lexical variants, which is\nconsistent with the result reported in [3]. This result also indicates\nthat biologists are likely to use different variants of the same\nconcept according to their own writing preferences and these\nvariants might not be collected in the existing biomedical\nthesauruses. It also suggests that the biomedical IR systems can\nbenefit from the domain-specific knowledge extracted from the\nliterature by text mining systems.\nSynonyms provided the second biggest improvement.\nHypernyms, hyponyms, and implicitly related concepts provided\nsimilar degrees of improvement. The overall performance is an\naccumulative result of adding different types of domain-specific\nknowledge and it is better than any individual addition. It is clearly\nshown that the performance is significantly improved (107% on\npassage level, 63.1% on aspect level, and 49.6% on document\nlevel) when the domain-specific knowledge is appropriately\nincorporated. Although it is not explicitly shown in Table 4.2.3,\ndifferent types of domain-specific knowledge affect different\nsubsets of queries. More specifically, each of these types (with the\nexception of the lexical variants which affects a large number of\nqueries) affects only a few queries. But for those affected queries,\ntheir improvement is significant. As a consequence, the\naccumulative improvement is very significant.\n4.2.3 Pseudo-feedback and abbreviation correction\nUsing the Baseline+All in Table 4.2.2 as a new baseline, the\ncontribution of abbreviation correction and pseudo-feedback is\ngiven in Table 4.2.3. There is little improvement by avoiding\nincorrect matching of abbreviations. The pseudo-feedback\ncontributed about 4.6% improvement in passage retrieval.\n4.2.4 Performance compared with best-reported results\nWe compared our result with the results reported in the Genomics\ntrack of TREC 2006 [8] on the conditions that 1) systems are\nautomatic systems and 2) passages are extracted from paragraphs.\nThe performance of our system relative to the best reported results\nis shown in Table 4.2.4 (in TREC 2006, some systems returned the\nwhole paragraphs as passages. As a consequence, excellent\nretrieval results were obtained on document and aspect levels at\nthe expense of performance on the passage level. We do not\ninclude the results of such systems here).\nTable 4.2.4 Performance compared with best-reported results.\nPassage MAP Aspect MAP Document MAP\nBest reported results 0.1486 0.3492 0.5320\nOur results 0.1823 0.3811 0.5391\nImprovement 22.68% 9.14% 1.33%\nThe best reported results in the first row of Table 4.2.4 on three\nlevels (passage, aspect, and document) are from different systems.\nOur result is from a single run on passage retrieval in which it is\nbetter than the best reported result by 22.68% in passage retrieval\nand at the same time, 9.14% better in aspect retrieval, and 1.33%\nbetter in document retrieval (Since the average precision of each\nindividual query was not reported, we can not apply the Wilcoxon\nsigned-rank test to calculate the significance of difference between\nour performance and the best reported result.).\nTable 4.2.1 Basic conceptual IR model vs. term-based model\nRun Passage Aspect Document\nMAP Imprvd qs # (%) MAP Imprvd qs # (%) MAP Imprvd qs # (%)\nOkapi 0.064 N/A 0.175 N/A 0.285 N/A\nBasic conceptual IR model 0.084* (+31.3%) 17 (65.4%) 0.233* (+33.1%) 12 (46.2%) 0.359* (+26.0%) 15 (57.7%)\nTable 4.2.2 Contribution of different types of domain-specific knowledge\nRun Passage Aspect Document\nMAP Imprvd qs # (%) MAP Imprvd qs # (%) MAP Imprvd qs # (%)\nBaseline\n= Basic conceptual IR model\n0.084 N/A 0.233 N/A 0.359 N/A\nBaseline+Synonyms 0.105 (+25%) 11 (42.3%) 0.246 (+5.6%) 9 (34.6%) 0.420 (+17%) 13 (50%)\nBaseline+Hypernyms 0.088 (+4.8%) 11 (42.3%) 0.225 (-3.4%) 9 (34.6%) 0.390 (+8.6%) 16 (61.5%)\nBaseline+Hyponyms 0.087 (+3.6%) 10 (38.5%) 0.217 (-6.9%) 7 (26.9%) 0.389 (+8.4%) 10 (38.5%)\nBaseline+Variants 0.150* (+78.6%) 16 (61.5%) 0.348* (+49.4%) 13 (50%) 0.495* (+37.9%) 10 (38.5%)\nBaseline+Related 0.086 (+2.4%) 9 (34.6%) 0.220 (-5.6%) 9 (34.6%) 0.387 (+7.8%) 13 (50%)\nBaseline+All 0.174* (107%) 25 (96.2%) 0.380* (+63.1%) 19 (73.1%) 0.537* (+49.6%) 14 (53.8%)\nTable 4.2.3 Contribution of abbreviation correction and pseudo-feedback\nRun Passage Aspect Document\nMAP Imprvd qs # (%) MAP Imprvd qs # (%) MAP Imprvd qs # (%)\nBaseline+All 0.174 N/A 0.380 N/A 0.537 N/A\nBaseline+All+Abbr 0.175 (+0.6%) 5 (19.2%) 0.375 (-1.3%) 4 (15.4%) 0.535 (-0.4%) 4 (15.4%)\nBaseline+All+Abbr+PF 0.182 (+4.6%) 10 (38.5%) 0.381 (+0.3%) 6 (23.1%) 0.539 (+0.4%) 9 (34.6%)\nA separate experiment has been done using a second testbed, the\nad-hoc Task of TREC Genomics 2005, to evaluate our\nknowledge-intensive conceptual IR model for document retrieval\nof biomedical literature. The overall performance in terms of MAP\nis 35.50%, which is about 22.92% above the best reported result\n[9]. Notice that the performance was only measured on the\ndocument level for the ad-hoc Task of TREC Genomics 2005.\n5. RELATED WORKS\nMany studies used manually-crafted thesauruses or knowledge\ndatabases created by text mining systems to improve retrieval\neffectiveness based on either word-statistical retrieval systems or\nconceptual retrieval systems.\n[11][1] assessed query expansion using the UMLS\nMetathesaurus. Based on a word-statistical retrieval system, [11]\nused definitions and different types of thesaurus relationships for\nquery expansion and a deteriorated performance was reported. [1]\nexpanded queries with phrases and UMLS concepts determined by\nthe MetaMap, a program which maps biomedical text to UMLS\nconcepts, and no significant improvement was shown. We used\nMeSH, Entrez gene, and other non-thesaurus knowledge resources\nsuch as an abbreviation database for query expansion. A critical\ndifference between our work and those in [11][1] is that our\nretrieval model is based on concepts, not on individual words.\nThe Genomics track in TREC provides a common platform to\nevaluate methods and techniques proposed by various groups for\nbiomedical information retrieval. As summarized in [8][9][10],\nmany groups utilized domain-specific knowledge to improve\nretrieval effectiveness. Among these groups, [3] assessed both\nthesaurus-based knowledge, such as gene information, and non\nthesaurus-based knowledge, such as lexical variants of gene\nsymbols, for query expansion. They have shown that query\nexpansion with acronyms and lexical variants of gene symbols\nproduced the biggest improvement, whereas, the query expansion\nwith gene information from gene databases deteriorated the\nperformance. [21] used a similar approach for generating lexical\nvariants of gene symbols and reported significant improvements.\nOur system utilized more types of domain-specific knowledge,\nincluding hyponyms, hypernyms and implicitly related concepts.\nIn addition, under the conceptual retrieval framework, we\nexamined more comprehensively the effects of different types of\ndomain-specific knowledge in performance contribution.\n[20][15] utilized WordNet, a database of English words and\ntheir lexical relationships developed by Princeton University, for\nquery expansion in the non-biomedical domain. In their studies,\nqueries were expanded using the lexical semantic relations such as\nsynonyms, hypernyms, or hyponyms. Little benefit has been\nshown in [20]. This has been due to ambiguity of the query terms\nwhich have different meanings in different contexts. When these\nsynonyms having multiple meanings are added to the query,\nsubstantial irrelevant documents are retrieved. In the biomedical\ndomain, this kind of ambiguity of query terms is relatively less\nfrequent, because, although the abbreviations are highly\nambiguous, general biomedical concepts usually have only one\nmeaning in the thesaurus, such as UMLS, whereas a term in\nWordNet usually have multiple meanings (represented as synsets\nin WordNet). Besides, we have implemented a post-ranking step\nto reduce the number of incorrect matches of abbreviations, which\nwill hopefully decrease the negative impact caused by the\nabbreviation ambiguity. Besides, we have implemented a\npostranking step to reduce the number of incorrect matches of\nabbreviations, which will hopefully decrease the negative impact\ncaused by the abbreviation ambiguity. The retrieval model in [15]\nemphasized the similarity between a query and a document on the\nphrase level assuming that phrases are more important than\nindividual words when retrieving documents. Although the\nassumption is similar, our conceptual model is based on the\nbiomedical concepts, not phrases.\n[13] presented a good study of the role of knowledge in the\ndocument retrieval of clinical medicine. They have shown that\nappropriate use of semantic knowledge in a conceptual retrieval\nframework can yield substantial improvements. Although the\nretrieval model is similar, we made a study in the domain of\ngenomics, in which the problem structure and task knowledge is\nnot as well-defined as in the domain of clinical medicine [18].\nAlso, our similarity function is very different from that in [13].\nIn summary, our approach differs from previous works in four\nimportant ways: First, we present a case study of conceptual\nretrieval in the domain of genomics, where many knowledge\nresources can be used to improve the performance of biomedical\nIR systems. Second, we have studied more types of\ndomainspecific knowledge than previous researchers and carried out more\ncomprehensive experiments to look into the effects of different\ntypes of domain-specific knowledge in performance contribution.\nThird, although some of the techniques seem similar to previously\npublished ones, they are actually quite different in details. For\nexample, in our pseudo-feedback process, we require that the unit\nof feedback is a concept and the concept has to be of the same\nsemantic type as a query concept. This is to ensure that our\nconceptual model of retrieval can be applied. As another example,\nthe way in which implicitly related concepts are extracted in this\npaper is significantly different from that given in [19]. Finally, our\nconceptual IR model is actually based on complex concepts\nbecause some biomedical meanings, such as biological processes,\nare represented by multiple simple concepts.\n6. CONCLUSION\nThis paper proposed a conceptual approach to utilize\ndomainspecific knowledge in an IR system to improve its effectiveness in\nretrieving biomedical literature. We specified five different types\nof domain-specific knowledge (i.e., synonyms, hyponyms,\nhypernyms, lexical variants, and implicitly related concepts) and\nexamined their effects in performance contribution. We also\nevaluated other two techniques, pseudo-feedback and abbreviation\ncorrection. Experimental results have shown that appropriate use\nof domain-specific knowledge in a conceptual IR model yields\nsignificant improvements (23%) in passage retrieval over the best\nknown results. In our future work, we will explore the use of other\nexisting knowledge resources, such as UMLS and the Wikipedia,\nand evaluate techniques such as disambiguation of gene symbols\nfor improving retrieval effectiveness. The application of our\nconceptual IR model in other domains such as clinical medicine\nwill be investigated.\n7. ACKNOWLEDGMENTS\ninsightful discussion.\n8. REFERENCES\n[1] Aronson A.R., Rindflesch T.C. Query expansion using the\nUMLS Metathesaurus. Proc AMIA Annu Fall Symp. 1997.\n485-9.\n[2] Baeza-Yates R., Ribeiro-Neto B. Modern Information\nRetrieval. Addison-Wesley, 1999, 129-131.\n[3] Buttcher S., Clarke C.L.A., Cormack G.V. Domain-specific\nsynonym expansion and validation for biomedical\ninformation retrieval (MultiText experiments for TREC\n2004). TREC\"04.\n[4] Chang J.T., Schutze H., Altman R.B. Creating an online\ndictionary of abbreviations from MEDLINE. Journal of the\nAmerican Medical Informatics Association. 2002 9(6).\n[5] Church K.W., Hanks P. Word association norms, mutual\ninformation and lexicography. Computational Linguistics.\n1990;16:22, C29.\n[6] Fontelo P., Liu F., Ackerman M. askMEDLINE: a free-text,\nnatural language query tool for MEDLINE/PubMed. BMC\nMed Inform Decis Mak. 2005 Mar 10;5(1):5.\n[7] Fukuda K., Tamura A., Tsunoda T., Takagi T. Toward\ninformation extraction: identifying protein names from\nbiological papers. Pac Symp Biocomput. 1998;:707-18.\n[8] Hersh W.R., and etc. TREC 2006 Genomics Track Overview.\nTREC\"06.\n[9] Hersh W.R., and etc. TREC 2005 Genomics Track Overview.\nIn TREC\"05.\n[10] Hersh W.R., and etc. TREC 2004 Genomics Track Overview.\nIn TREC\"04.\n[11] Hersh W.R., Price S., Donohoe L. Assessing thesaurus-based\nquery expansion using the UMLS Metathesaurus. Proc AMIA\nSymp. 344-8. 2000.\n[12] Levenshtein, V. Binary codes capable of correcting deletions,\ninsertions, and reversals. Soviet Physics - Doklady 10, 10\n(1996), 707-710.\n[13] Lin J., Demner-Fushman D. The Role of Knowledge in\nConceptual Retrieval: A Study in the Domain of Clinical\nMedicine. SIGIR\"06. 99-06.\n[14] Lindberg D., Humphreys B., and McCray A. The Unified\nMedical Language System. Methods of Information in\nMedicine. 32(4):281-291, 1993.\n[15] Liu S., Liu F., Yu C., and Meng W.Y. An Effective\nApproach to Document Retrieval via Utilizing WordNet and\nRecognizing Phrases. SIGIR\"04. 266-272\n[16] Proux D., Rechenmann F., Julliard L., Pillet V.V., Jacq B.\nDetecting Gene Symbols and Names in Biological Texts: A\nFirst Step toward Pertinent Information Extraction. Genome\nInform Ser Workshop Genome Inform. 1998;9:72-80.\n[17] Robertson S.E., Walker S. Okapi/Keenbow at TREC-8. NIST\nSpecial Publication 500-246: TREC 8.\n[18] Sackett D.L., and etc. Evidence-Based Medicine: How to\nPractice and Teach EBM. Churchill Livingstone. Second\nedition, 2000.\n[19] Swanson,D.R., Smalheiser,N.R. An interactive system for\nfinding complemen-tary literatures: a stimulus to scientific\ndiscovery. Artificial Intelligence, 1997; 91,183-203.\n[20] Voorhees E. Query expansion using lexical-semantic\nrelations. SIGIR 1994. 61-9\n[21] Zhong M., Huang X.J. Concept-based biomedical text\nretrieval. SIGIR\"06. 723-4\n[22] Zhou W., Torvik V.I., Smalheiser N.R. ADAM: Another\nDatabase of Abbreviations in MEDLINE. Bioinformatics.\n2006; 22(22): 2813-2818.", "keywords": "keyword search;document collection;document map;domain-specific knowledge;retrieval model;biomedical document;document retrieval;query concept;conceptual ir model;passage-level information retrieval;passage map;passage extraction;aspect map"}
{"name": "train_H-60", "title": "A Frequency-based and a Poisson-based Definition of the Probability of Being Informative", "abstract": "This paper reports on theoretical investigations about the assumptions underlying the inverse document frequency (idf ). We show that an intuitive idf -based probability function for the probability of a term being informative assumes disjoint document events. By assuming documents to be independent rather than disjoint, we arrive at a Poisson-based probability of being informative. The framework is useful for understanding and deciding the parameter estimation and combination in probabilistic retrieval models.", "fulltext": "1. INTRODUCTION AND BACKGROUND\nThe inverse document frequency (idf ) is one of the most\nsuccessful parameters for a relevance-based ranking of\nretrieved objects. With N being the total number of\ndocuments, and n(t) being the number of documents in which\nterm t occurs, the idf is defined as follows:\nidf(t) := \u2212 log\nn(t)\nN\n, 0 <= idf(t) < \u221e\nRanking based on the sum of the idf -values of the query\nterms that occur in the retrieved documents works well, this\nhas been shown in numerous applications. Also, it is well\nknown that the combination of a document-specific term\nweight and idf works better than idf alone. This approach\nis known as tf-idf , where tf(t, d) (0 <= tf(t, d) <= 1) is\nthe so-called term frequency of term t in document d. The\nidf reflects the discriminating power (informativeness) of a\nterm, whereas the tf reflects the occurrence of a term.\nThe idf alone works better than the tf alone does. An\nexplanation might be the problem of tf with terms that occur\nin many documents; let us refer to those terms as noisy\nterms. We use the notion of noisy terms rather than\nfrequent terms since frequent terms leaves open whether we\nrefer to the document frequency of a term in a collection or\nto the so-called term frequency (also referred to as\nwithindocument frequency) of a term in a document. We\nassociate noise with the document frequency of a term in a\ncollection, and we associate occurrence with the\nwithindocument frequency of a term. The tf of a noisy term might\nbe high in a document, but noisy terms are not good\ncandidates for representing a document. Therefore, the removal\nof noisy terms (known as stopword removal) is essential\nwhen applying tf . In a tf-idf approach, the removal of\nstopwords is conceptually obsolete, if stopwords are just words\nwith a low idf .\nFrom a probabilistic point of view, tf is a value with a\nfrequency-based probabilistic interpretation whereas idf has\nan informative rather than a probabilistic interpretation.\nThe missing probabilistic interpretation of idf is a problem\nin probabilistic retrieval models where we combine uncertain\nknowledge of different dimensions (e.g.: informativeness of\nterms, structure of documents, quality of documents, age\nof documents, etc.) such that a good estimate of the\nprobability of relevance is achieved. An intuitive solution is a\nnormalisation of idf such that we obtain values in the\ninterval [0; 1]. For example, consider a normalisation based on\nthe maximal idf -value. Let T be the set of terms occurring\nin a collection.\nPfreq (t is informative) :=\nidf(t)\nmaxidf\nmaxidf := max({idf(t)|t \u2208 T}), maxidf <= \u2212 log(1/N)\nminidf := min({idf(t)|t \u2208 T}), minidf >= 0\nminidf\nmaxidf\n\u2264 Pfreq (t is informative) \u2264 1.0\nThis frequency-based probability function covers the interval\n[0; 1] if the minimal idf is equal to zero, which is the case\nif we have at least one term that occurs in all documents.\nCan we interpret Pfreq , the normalised idf , as the probability\nthat the term is informative?\nWhen investigating the probabilistic interpretation of the\n227\nnormalised idf , we made several observations related to\ndisjointness and independence of document events. These\nobservations are reported in section 3. We show in section 3.1\nthat the frequency-based noise probability n(t)\nN\nused in the\nclassic idf -definition can be explained by three assumptions:\nbinary term occurrence, constant document containment and\ndisjointness of document containment events. In section 3.2\nwe show that by assuming independence of documents, we\nobtain 1 \u2212 e\u22121\n\u2248 1 \u2212 0.37 as the upper bound of the noise\nprobability of a term. The value e\u22121\nis related to the\nlogarithm and we investigate in section 3.3 the link to\ninformation theory. In section 4, we link the results of the previous\nsections to probability theory. We show the steps from\npossible worlds to binomial distribution and Poisson distribution.\nIn section 5, we emphasise that the theoretical framework\nof this paper is applicable for both idf and tf . Finally, in\nsection 6, we base the definition of the probability of\nbeing informative on the results of the previous sections and\ncompare frequency-based and Poisson-based definitions.\n2. BACKGROUND\nThe relationship between frequencies, probabilities and\ninformation theory (entropy) has been the focus of many\nresearchers. In this background section, we focus on work\nthat investigates the application of the Poisson distribution\nin IR since a main part of the work presented in this paper\naddresses the underlying assumptions of Poisson.\n[4] proposes a 2-Poisson model that takes into account\nthe different nature of relevant and non-relevant documents,\nrare terms (content words) and frequent terms (noisy terms,\nfunction words, stopwords). [9] shows experimentally that\nmost of the terms (words) in a collection are distributed\naccording to a low dimension n-Poisson model. [10] uses a\n2-Poisson model for including term frequency-based\nprobabilities in the probabilistic retrieval model. The non-linear\nscaling of the Poisson function showed significant\nimprovement compared to a linear frequency-based probability. The\nPoisson model was here applied to the term frequency of a\nterm in a document. We will generalise the discussion by\npointing out that document frequency and term frequency\nare dual parameters in the collection space and the\ndocument space, respectively. Our discussion of the Poisson\ndistribution focuses on the document frequency in a collection\nrather than on the term frequency in a document.\n[7] and [6] address the deviation of idf and Poisson, and\napply Poisson mixtures to achieve better Poisson-based\nestimates. The results proved again experimentally that a\nonedimensional Poisson does not work for rare terms, therefore\nPoisson mixtures and additional parameters are proposed.\n[3], section 3.3, illustrates and summarises\ncomprehensively the relationships between frequencies, probabilities\nand Poisson. Different definitions of idf are put into\ncontext and a notion of noise is defined, where noise is viewed\nas the complement of idf . We use in our paper a different\nnotion of noise: we consider a frequency-based noise that\ncorresponds to the document frequency, and we consider a\nterm noise that is based on the independence of document\nevents.\n[11], [12], [8] and [1] link frequencies and probability\nestimation to information theory. [12] establishes a framework\nin which information retrieval models are formalised based\non probabilistic inference. A key component is the use of a\nspace of disjoint events, where the framework mainly uses\nterms as disjoint events. The probability of being\ninformative defined in our paper can be viewed as the probability\nof the disjoint terms in the term space of [12].\n[8] address entropy and bibliometric distributions.\nEntropy is maximal if all events are equiprobable and the\nfrequency-based Lotka law (N/i\u03bb\nis the number of scientists\nthat have written i publications, where N and \u03bb are\ndistribution parameters), Zipf and the Pareto distribution are\nrelated. The Pareto distribution is the continuous case of the\nLotka and Lotka and Zipf show equivalences. The Pareto\ndistribution is used by [2] for term frequency normalisation.\nThe Pareto distribution compares to the Poisson\ndistribution in the sense that Pareto is fat-tailed, i. e. Pareto\nassigns larger probabilities to large numbers of events than\nPoisson distributions do. This makes Pareto interesting\nsince Poisson is felt to be too radical on frequent events.\nWe restrict in this paper to the discussion of Poisson,\nhowever, our results show that indeed a smoother distribution\nthan Poisson promises to be a good candidate for improving\nthe estimation of probabilities in information retrieval.\n[1] establishes a theoretical link between tf-idf and\ninformation theory and the theoretical research on the meaning\nof tf-idf clarifies the statistical model on which the different\nmeasures are commonly based. This motivation matches\nthe motivation of our paper: We investigate theoretically\nthe assumptions of classical idf and Poisson for a better\nunderstanding of parameter estimation and combination.\n3. FROM DISJOINT TO INDEPENDENT\nWe define and discuss in this section three probabilities:\nThe frequency-based noise probability (definition 1), the\ntotal noise probability for disjoint documents (definition 2).\nand the noise probability for independent documents\n(definition 3).\n3.1 Binary occurrence, constant containment\nand disjointness of documents\nWe show in this section, that the frequency-based noise\nprobability n(t)\nN\nin the idf definition can be explained as\na total probability with binary term occurrence, constant\ndocument containment and disjointness of document\ncontainments.\nWe refer to a probability function as binary if for all events\nthe probability is either 1.0 or 0.0. The occurrence\nprobability P(t|d) is binary, if P(t|d) is equal to 1.0 if t \u2208 d, and\nP(t|d) is equal to 0.0, otherwise.\nP(t|d) is binary : \u21d0\u21d2 P(t|d) = 1.0 \u2228 P(t|d) = 0.0\nWe refer to a probability function as constant if for all\nevents the probability is equal. The document containment\nprobability reflect the chance that a document occurs in a\ncollection. This containment probability is constant if we\nhave no information about the document containment or\nwe ignore that documents differ in containment.\nContainment could be derived, for example, from the size, quality,\nage, links, etc. of a document. For a constant containment\nin a collection with N documents, 1\nN\nis often assumed as\nthe containment probability. We generalise this definition\nand introduce the constant \u03bb where 0 \u2264 \u03bb \u2264 N. The\ncontainment of a document d depends on the collection c, this\nis reflected by the notation P(d|c) used for the containment\n228\nof a document.\nP(d|c) is constant : \u21d0\u21d2 \u2200d : P(d|c) =\n\u03bb\nN\nFor disjoint documents that cover the whole event space,\nwe set \u03bb = 1 and obtain\n\u00c8d P(d|c) = 1.0. Next, we define\nthe frequency-based noise probability and the total noise\nprobability for disjoint documents. We introduce the event\nnotation t is noisy and t occurs for making the difference\nbetween the noise probability P(t is noisy|c) in a collection\nand the occurrence probability P(t occurs|d) in a document\nmore explicit, thereby keeping in mind that the noise\nprobability corresponds to the occurrence probability of a term\nin a collection.\nDefinition 1. The frequency-based term noise\nprobability:\nPfreq (t is noisy|c) :=\nn(t)\nN\nDefinition 2. The total term noise probability for\ndisjoint documents:\nPdis (t is noisy|c) :=\nd\nP(t occurs|d) \u00b7 P(d|c)\nNow, we can formulate a theorem that makes assumptions\nexplicit that explain the classical idf .\nTheorem 1. IDF assumptions: If the occurrence\nprobability P(t|d) of term t over documents d is binary, and\nthe containment probability P(d|c) of documents d is\nconstant, and document containments are disjoint events, then\nthe noise probability for disjoint documents is equal to the\nfrequency-based noise probability.\nPdis (t is noisy|c) = Pfreq (t is noisy|c)\nProof. The assumptions are:\n\u2200d : (P(t occurs|d) = 1 \u2228 P(t occurs|d) = 0) \u2227\nP(d|c) =\n\u03bb\nN\n\u2227\nd\nP(d|c) = 1.0\nWe obtain:\nPdis (t is noisy|c) =\nd|t\u2208d\n1\nN\n=\nn(t)\nN\n= Pfreq (t is noisy|c)\nThe above result is not a surprise but it is a\nmathematical formulation of assumptions that can be used to explain\nthe classical idf . The assumptions make explicit that the\ndifferent types of term occurrence in documents (frequency\nof a term, importance of a term, position of a term,\ndocument part where the term occurs, etc.) and the different\ntypes of document containment (size, quality, age, etc.) are\nignored, and document containments are considered as\ndisjoint events.\nFrom the assumptions, we can conclude that idf\n(frequencybased noise, respectively) is a relatively simple but strict\nestimate. Still, idf works well. This could be explained\nby a leverage effect that justifies the binary occurrence and\nconstant containment: The term occurrence for small\ndocuments tends to be larger than for large documents, whereas\nthe containment for small documents tends to be smaller\nthan for large documents. From that point of view, idf\nmeans that P(t \u2227 d|c) is constant for all d in which t occurs,\nand P(t \u2227 d|c) is zero otherwise. The occurrence and\ncontainment can be term specific. For example, set P(t\u2227d|c) =\n1/ND(c) if t occurs in d, where ND(c) is the number of\ndocuments in collection c (we used before just N). We choose a\ndocument-dependent occurrence P(t|d) := 1/NT (d), i. e. the\noccurrence probability is equal to the inverse of NT (d), which\nis the total number of terms in document d. Next, we choose\nthe containment P(d|c) := NT (d)/NT (c)\u00b7NT (c)/ND(c) where\nNT (d)/NT (c) is a document length normalisation (number\nof terms in document d divided by the number of terms in\ncollection c), and NT (c)/ND(c) is a constant factor of the\ncollection (number of terms in collection c divided by the\nnumber of documents in collection c). We obtain P(t\u2227d|c) =\n1/ND(c).\nIn a tf-idf -retrieval function, the tf -component reflects\nthe occurrence probability of a term in a document. This is\na further explanation why we can estimate the idf with a\nsimple P(t|d), since the combined tf-idf contains the\noccurrence probability. The containment probability corresponds\nto a document normalisation (document length\nnormalisation, pivoted document length) and is normally attached to\nthe tf -component or the tf-idf -product.\nThe disjointness assumption is typical for frequency-based\nprobabilities. From a probability theory point of view, we\ncan consider documents as disjoint events, in order to achieve\na sound theoretical model for explaining the classical idf .\nBut does disjointness reflect the real world where the\ncontainment of a document appears to be independent of the\ncontainment of another document? In the next section, we\nreplace the disjointness assumption by the independence\nassumption.\n3.2 The upper bound of the noise probability\nfor independent documents\nFor independent documents, we compute the probability\nof a disjunction as usual, namely as the complement of the\nprobability of the conjunction of the negated events:\nP(d1 \u2228 . . . \u2228 dN ) = 1 \u2212 P(\u00acd1 \u2227 . . . \u2227 \u00acdN )\n= 1 \u2212\nd\n(1 \u2212 P(d))\nThe noise probability can be considered as the conjunction\nof the term occurrence and the document containment.\nP(t is noisy|c) := P(t occurs \u2227 (d1 \u2228 . . . \u2228 dN )|c)\nFor disjoint documents, this view of the noise probability\nled to definition 2. For independent documents, we use now\nthe conjunction of negated events.\nDefinition 3. The term noise probability for\nindependent documents:\nPin (t is noisy|c) :=\nd\n(1 \u2212 P(t occurs|d) \u00b7 P(d|c))\nWith binary occurrence and a constant containment P(d|c) :=\n\u03bb/N, we obtain the term noise of a term t that occurs in n(t)\ndocuments:\nPin (t is noisy|c) = 1 \u2212 1 \u2212\n\u03bb\nN\nn(t)\n229\nFor binary occurrence and disjoint documents, the\ncontainment probability was 1/N. Now, with independent\ndocuments, we can use \u03bb as a collection parameter that controls\nthe average containment probability. We show through the\nnext theorem that the upper bound of the noise probability\ndepends on \u03bb.\nTheorem 2. The upper bound of being noisy: If the\noccurrence P(t|d) is binary, and the containment P(d|c)\nis constant, and document containments are independent\nevents, then 1 \u2212 e\u2212\u03bb\nis the upper bound of the noise\nprobability.\n\u2200t : Pin (t is noisy|c) < 1 \u2212 e\u2212\u03bb\nProof. The upper bound of the independent noise\nprobability follows from the limit limN\u2192\u221e(1 + x\nN\n)N\n= ex\n(see\nany comprehensive math book, for example, [5], for the\nconvergence equation of the Euler function). With x = \u2212\u03bb, we\nobtain:\nlim\nN\u2192\u221e\n1 \u2212\n\u03bb\nN\nN\n= e\u2212\u03bb\nFor the term noise, we have:\nPin (t is noisy|c) = 1 \u2212 1 \u2212\n\u03bb\nN\nn(t)\nPin (t is noisy|c) is strictly monotonous: The noise of a term\ntn is less than the noise of a term tn+1, where tn occurs in\nn documents and tn+1 occurs in n + 1 documents.\nTherefore, a term with n = N has the largest noise probability.\nFor a collection with infinite many documents, the upper\nbound of the noise probability for terms tN that occur in all\ndocuments becomes:\nlim\nN\u2192\u221e\nPin (tN is noisy) = lim\nN\u2192\u221e\n1 \u2212 1 \u2212\n\u03bb\nN\nN\n= 1 \u2212 e\u2212\u03bb\nBy applying an independence rather a disjointness\nassumption, we obtain the probability e\u22121\nthat a term is not noisy\neven if the term does occur in all documents. In the disjoint\ncase, the noise probability is one for a term that occurs in\nall documents.\nIf we view P(d|c) := \u03bb/N as the average containment,\nthen \u03bb is large for a term that occurs mostly in large\ndocuments, and \u03bb is small for a term that occurs mostly in small\ndocuments. Thus, the noise of a term t is large if t occurs in\nn(t) large documents and the noise is smaller if t occurs in\nsmall documents. Alternatively, we can assume a constant\ncontainment and a term-dependent occurrence. If we\nassume P(d|c) := 1, then P(t|d) := \u03bb/N can be interpreted as\nthe average probability that t represents a document. The\ncommon assumption is that the average containment or\noccurrence probability is proportional to n(t). However, here\nis additional potential: The statistical laws (see [3] on Luhn\nand Zipf) indicate that the average probability could follow\na normal distribution, i. e. small probabilities for small n(t)\nand large n(t), and larger probabilities for medium n(t).\nFor the monotonous case we investigate here, the noise of\na term with n(t) = 1 is equal to 1 \u2212 (1 \u2212 \u03bb/N) = \u03bb/N and\nthe noise of a term with n(t) = N is close to 1\u2212 e\u2212\u03bb\n. In the\nnext section, we relate the value e\u2212\u03bb\nto information theory.\n3.3 The probability of a maximal informative\nsignal\nThe probability e\u22121\nis special in the sense that a signal\nwith that probability is a signal with maximal information as\nderived from the entropy definition. Consider the definition\nof the entropy contribution H(t) of a signal t.\nH(t) := P(t) \u00b7 \u2212 ln P(t)\nWe form the first derivation for computing the optimum.\n\u2202H(t)\n\u2202P(t)\n= \u2212 ln P(t) +\n\u22121\nP(t)\n\u00b7 P(t)\n= \u2212(1 + ln P(t))\nFor obtaining optima, we use:\n0 = \u2212(1 + ln P(t))\nThe entropy contribution H(t) is maximal for P(t) = e\u22121\n.\nThis result does not depend on the base of the logarithm as\nwe see next:\n\u2202H(t)\n\u2202P(t)\n= \u2212 logb P(t) +\n\u22121\nP(t) \u00b7 ln b\n\u00b7 P(t)\n= \u2212\n1\nln b\n+ logb P(t) = \u2212\n1 + ln P(t)\nln b\nWe summarise this result in the following theorem:\nTheorem 3. The probability of a maximal\ninformative signal: The probability Pmax = e\u22121\n\u2248 0.37 is the\nprobability of a maximal informative signal. The entropy of a\nmaximal informative signal is Hmax = e\u22121\n.\nProof. The probability and entropy follow from the\nderivation above.\nThe complement of the maximal noise probability is e\u2212\u03bb\nand we are looking now for a generalisation of the entropy\ndefinition such that e\u2212\u03bb\nis the probability of a maximal\ninformative signal. We can generalise the entropy definition\nby computing the integral of \u03bb+ ln P(t), i. e. this derivation\nis zero for e\u2212\u03bb\n. We obtain a generalised entropy:\n\u2212(\u03bb + ln P(t)) d(P(t)) = P(t) \u00b7 (1 \u2212 \u03bb \u2212 ln P(t))\nThe generalised entropy corresponds for \u03bb = 1 to the\nclassical entropy. By moving from disjoint to independent\ndocuments, we have established a link between the complement\nof the noise probability of a term that occurs in all\ndocuments and information theory. Next, we link independent\ndocuments to probability theory.\n4. THE LINK TO PROBABILITY THEORY\nWe review for independent documents three concepts of\nprobability theory: possible worlds, binomial distribution\nand Poisson distribution.\n4.1 Possible Worlds\nEach conjunction of document events (for each document,\nwe consider two document events: the document can be\ntrue or false) is associated with a so-called possible world.\nFor example, consider the eight possible worlds for three\ndocuments (N = 3).\n230\nworld w conjunction\nw7 d1 \u2227 d2 \u2227 d3\nw6 d1 \u2227 d2 \u2227 \u00acd3\nw5 d1 \u2227 \u00acd2 \u2227 d3\nw4 d1 \u2227 \u00acd2 \u2227 \u00acd3\nw3 \u00acd1 \u2227 d2 \u2227 d3\nw2 \u00acd1 \u2227 d2 \u2227 \u00acd3\nw1 \u00acd1 \u2227 \u00acd2 \u2227 d3\nw0 \u00acd1 \u2227 \u00acd2 \u2227 \u00acd3\nWith each world w, we associate a probability \u00b5(w), which\nis equal to the product of the single probabilities of the\ndocument events.\nworld w probability \u00b5(w)\nw7\n\u03bb\nN\n\u00a13\n\u00b7\n1 \u2212 \u03bb\nN\n\u00a10\nw6\n\u03bb\nN\n\u00a12\n\u00b7\n1 \u2212 \u03bb\nN\n\u00a11\nw5\n\u03bb\nN\n\u00a12\n\u00b7\n1 \u2212 \u03bb\nN\n\u00a11\nw4\n\u03bb\nN\n\u00a11\n\u00b7\n1 \u2212 \u03bb\nN\n\u00a12\nw3\n\u03bb\nN\n\u00a12\n\u00b7\n1 \u2212 \u03bb\nN\n\u00a11\nw2\n\u03bb\nN\n\u00a11\n\u00b7\n1 \u2212 \u03bb\nN\n\u00a12\nw1\n\u03bb\nN\n\u00a11\n\u00b7\n1 \u2212 \u03bb\nN\n\u00a12\nw0\n\u03bb\nN\n\u00a10\n\u00b7\n1 \u2212 \u03bb\nN\n\u00a13\nThe sum over the possible worlds in which k documents are\ntrue and N \u2212k documents are false is equal to the\nprobability function of the binomial distribution, since the binomial\ncoefficient yields the number of possible worlds in which k\ndocuments are true.\n4.2 Binomial distribution\nThe binomial probability function yields the probability\nthat k of N events are true where each event is true with\nthe single event probability p.\nP(k) := binom(N, k, p) :=\nN\nk\npk\n(1 \u2212 p)N \u2212k\nThe single event probability is usually defined as p := \u03bb/N,\ni. e. p is inversely proportional to N, the total number of\nevents. With this definition of p, we obtain for an infinite\nnumber of documents the following limit for the product of\nthe binomial coefficient and pk\n:\nlim\nN\u2192\u221e\nN\nk\npk\n=\n= lim\nN\u2192\u221e\nN \u00b7 (N \u22121) \u00b7 . . . \u00b7 (N \u2212k +1)\nk!\n\u03bb\nN\nk\n=\n\u03bbk\nk!\nThe limit is close to the actual value for k << N. For large\nk, the actual value is smaller than the limit.\nThe limit of (1\u2212p)N \u2212k follows from the limit limN\u2192\u221e(1+\nx\nN\n)N\n= ex\n.\nlim\nN\u2192\u221e\n(1 \u2212 p)N\u2212k\n= lim\nN\u2192\u221e\n1 \u2212\n\u03bb\nN\nN \u2212k\n= lim\nN\u2192\u221e\ne\u2212\u03bb\n\u00b7 1 \u2212\n\u03bb\nN\n\u2212k\n= e\u2212\u03bb\nAgain, the limit is close to the actual value for k << N. For\nlarge k, the actual value is larger than the limit.\n4.3 Poisson distribution\nFor an infinite number of events, the Poisson probability\nfunction is the limit of the binomial probability function.\nlim\nN\u2192\u221e\nbinom(N, k, p) =\n\u03bbk\nk!\n\u00b7 e\u2212\u03bb\nP(k) = poisson(k, \u03bb) :=\n\u03bbk\nk!\n\u00b7 e\u2212\u03bb\nThe probability poisson(0, 1) is equal to e\u22121\n, which is the\nprobability of a maximal informative signal. This shows\nthe relationship of the Poisson distribution and information\ntheory.\nAfter seeing the convergence of the binomial distribution,\nwe can choose the Poisson distribution as an approximation\nof the independent term noise probability. First, we define\nthe Poisson noise probability:\nDefinition 4. The Poisson term noise probability:\nPpoi (t is noisy|c) := e\u2212\u03bb\n\u00b7\nn(t)\nk=1\n\u03bbk\nk!\nFor independent documents, the Poisson distribution\napproximates the probability of the disjunction for large n(t),\nsince the independent term noise probability is equal to the\nsum over the binomial probabilities where at least one of\nn(t) document containment events is true.\nPin (t is noisy|c) =\nn(t)\nk=1\nn(t)\nk\npk\n(1 \u2212 p)N \u2212k\nPin (t is noisy|c) \u2248 Ppoi (t is noisy|c)\nWe have defined a frequency-based and a Poisson-based\nprobability of being noisy, where the latter is the limit of the\nindependence-based probability of being noisy. Before we\npresent in the final section the usage of the noise\nprobability for defining the probability of being informative, we\nemphasise in the next section that the results apply to the\ncollection space as well as to the the document space.\n5. THE COLLECTION SPACE AND THE\nDOCUMENT SPACE\nConsider the dual definitions of retrieval parameters in\ntable 1. We associate a collection space D \u00d7 T with a\ncollection c where D is the set of documents and T is the set\nof terms in the collection. Let ND := |D| and NT := |T|\nbe the number of documents and terms, respectively. We\nconsider a document as a subset of T and a term as a subset\nof D. Let nT (d) := |{t|d \u2208 t}| be the number of terms that\noccur in the document d, and let nD(t) := |{d|t \u2208 d}| be the\nnumber of documents that contain the term t.\nIn a dual way, we associate a document space L \u00d7 T with\na document d where L is the set of locations (also referred\nto as positions, however, we use the letters L and l and not\nP and p for avoiding confusion with probabilities) and T is\nthe set of terms in the document. The document dimension\nin a collection space corresponds to the location (position)\ndimension in a document space.\nThe definition makes explicit that the classical notion of\nterm frequency of a term in a document (also referred to as\nthe within-document term frequency) actually corresponds\nto the location frequency of a term in a document. For the\n231\nspace collection document\ndimensions documents and terms locations and terms\ndocument/location\nfrequency\nnD(t, c): Number of documents in which term t\noccurs in collection c\nnL(t, d): Number of locations (positions) at which\nterm t occurs in document d\nND(c): Number of documents in collection c NL(d): Number of locations (positions) in\ndocument d\nterm frequency nT (d, c): Number of terms that document d\ncontains in collection c\nnT (l, d): Number of terms that location l contains\nin document d\nNT (c): Number of terms in collection c NT (d): Number of terms in document d\nnoise/occurrence P(t|c) (term noise) P(t|d) (term occurrence)\ncontainment P(d|c) (document) P(l|d) (location)\ninformativeness \u2212 ln P(t|c) \u2212 ln P(t|d)\nconciseness \u2212 ln P(d|c) \u2212 ln P(l|d)\nP(informative) ln(P(t|c))/ ln(P(tmin, c)) ln(P(t|d))/ ln(P(tmin, d))\nP(concise) ln(P(d|c))/ ln(P(dmin|c)) ln(P(l|d))/ ln(P(lmin|d))\nTable 1: Retrieval parameters\nactual term frequency value, it is common to use the\nmaximal occurrence (number of locations; let lf be the location\nfrequency).\ntf(t, d):=lf(t, d):=\nPfreq (t occurs|d)\nPfreq (tmax occurs|d)\n=\nnL(t, d)\nnL(tmax , d)\nA further duality is between informativeness and\nconciseness (shortness of documents or locations): informativeness\nis based on occurrence (noise), conciseness is based on\ncontainment.\nWe have highlighted in this section the duality between\nthe collection space and the document space. We\nconcentrate in this paper on the probability of a term to be noisy\nand informative. Those probabilities are defined in the\ncollection space. However, the results regarding the term noise\nand informativeness apply to their dual counterparts: term\noccurrence and informativeness in a document. Also, the\nresults can be applied to containment of documents and\nlocations.\n6. THE PROBABILITY OF BEING\nINFORMATIVE\nWe showed in the previous sections that the disjointness\nassumption leads to frequency-based probabilities and that\nthe independence assumption leads to Poisson probabilities.\nIn this section, we formulate a frequency-based definition\nand a Poisson-based definition of the probability of being\ninformative and then we compare the two definitions.\nDefinition 5. The frequency-based probability of\nbeing informative:\nPfreq (t is informative|c) :=\n\u2212 ln n(t)\nN\n\u2212 ln 1\nN\n= \u2212 logN\nn(t)\nN\n= 1 \u2212 logN n(t) = 1 \u2212\nln n(t)\nln N\nWe define the Poisson-based probability of being\ninformative analogously to the frequency-based probability of being\ninformative (see definition 5).\nDefinition 6. The Poisson-based probability of\nbeing informative:\nPpoi (t is informative|c) :=\n\u2212 ln e\u2212\u03bb\n\u00b7\n\u00c8n(t)\nk=1\n\u03bbk\nk!\n\u2212 ln(e\u2212\u03bb \u00b7 \u03bb)\n=\n\u03bb \u2212 ln\n\u00c8n(t)\nk=1\n\u03bbk\nk!\n\u03bb \u2212 ln \u03bb\nFor the sum expression, the following limit holds:\nlim\nn(t)\u2192\u221e\nn(t)\nk=1\n\u03bbk\nk!\n= e\u03bb\n\u2212 1\nFor \u03bb >> 1, we can alter the noise and informativeness\nPoisson by starting the sum from 0, since e\u03bb\n>> 1. Then, the\nminimal Poisson informativeness is poisson(0, \u03bb) = e\u2212\u03bb\n. We\nobtain a simplified Poisson probability of being informative:\nPpoi (t is informative|c) \u2248\n\u03bb \u2212 ln\n\u00c8n(t)\nk=0\n\u03bbk\nk!\n\u03bb\n= 1 \u2212\nln\n\u00c8n(t)\nk=0\n\u03bbk\nk!\n\u03bb\nThe computation of the Poisson sum requires an\noptimisation for large n(t). The implementation for this paper\nexploits the nature of the Poisson density: The Poisson\ndensity yields only values significantly greater than zero in an\ninterval around \u03bb.\nConsider the illustration of the noise and\ninformativeness definitions in figure 1. The probability functions\ndisplayed are summarised in figure 2 where the simplified\nPoisson is used in the noise and informativeness graphs. The\nfrequency-based noise corresponds to the linear solid curve\nin the noise figure. With an independence assumption, we\nobtain the curve in the lower triangle of the noise figure. By\nchanging the parameter p := \u03bb/N of the independence\nprobability, we can lift or lower the independence curve. The\nnoise figure shows the lifting for the value \u03bb := ln N \u2248\n9.2. The setting \u03bb = ln N is special in the sense that the\nfrequency-based and the Poisson-based informativeness have\nthe same denominator, namely ln N, and the Poisson sum\nconverges to \u03bb. Whether we can draw more conclusions from\nthis setting is an open question.\nWe can conclude, that the lifting is desirable if we know\nfor a collection that terms that occur in relatively few\ndoc232\n0\n0.2\n0.4\n0.6\n0.8\n1\n0 2000 4000 6000 8000 10000\nProbabilityofbeingnoisy\nn(t): Number of documents with term t\nfrequency\nindependence: 1/N\nindependence: ln(N)/N\npoisson: 1000\npoisson: 2000\npoisson: 1000,2000\n0\n0.2\n0.4\n0.6\n0.8\n1\n0 2000 4000 6000 8000 10000\nProbabilityofbeinginformative\nn(t): Number of documents with term t\nfrequency\nindependence: 1/N\nindependence: ln(N)/N\npoisson: 1000\npoisson: 2000\npoisson: 1000,2000\nFigure 1: Noise and Informativeness\nProbability function Noise Informativeness\nFrequency Pfreq Def n(t)/N ln(n(t)/N)/ ln(1/N)\nInterval 1/N \u2264 Pfreq \u2264 1.0 0.0 \u2264 Pfreq \u2264 1.0\nIndependence Pin Def 1 \u2212 (1 \u2212 p)n(t)\nln(1 \u2212 (1 \u2212 p)n(t)\n)/ ln(p)\nInterval p \u2264 Pin < 1 \u2212 e\u2212\u03bb\nln(p) \u2264 Pin \u2264 1.0\nPoisson Ppoi Def e\u2212\u03bb \u00c8n(t)\nk=1\n\u03bbk\nk!\n(\u03bb \u2212 ln\n\u00c8n(t)\nk=1\n\u03bbk\nk!\n)/(\u03bb \u2212 ln \u03bb)\nInterval e\u2212\u03bb\n\u00b7 \u03bb \u2264 Ppoi < 1 \u2212 e\u2212\u03bb\n(\u03bb \u2212 ln(e\u03bb\n\u2212 1))/(\u03bb \u2212 ln \u03bb) \u2264 Ppoi \u2264 1.0\nPoisson Ppoi simplified Def e\u2212\u03bb \u00c8n(t)\nk=0\n\u03bbk\nk!\n(\u03bb \u2212 ln\n\u00c8n(t)\nk=0\n\u03bbk\nk!\n)/\u03bb\nInterval e\u2212\u03bb\n\u2264 Ppoi < 1.0 0.0 < Ppoi \u2264 1.0\nFigure 2: Probability functions\numents are no guarantee for finding relevant documents,\ni. e. we assume that rare terms are still relatively noisy. On\nthe opposite, we could lower the curve when assuming that\nfrequent terms are not too noisy, i. e. they are considered as\nbeing still significantly discriminative.\nThe Poisson probabilities approximate the independence\nprobabilities for large n(t); the approximation is better for\nlarger \u03bb. For n(t) < \u03bb, the noise is zero whereas for n(t) > \u03bb\nthe noise is one. This radical behaviour can be smoothened\nby using a multi-dimensional Poisson distribution. Figure 1\nshows a Poisson noise based on a two-dimensional Poisson:\npoisson(k, \u03bb1, \u03bb2) := \u03c0 \u00b7 e\u2212\u03bb1\n\u00b7\n\u03bbk\n1\nk!\n+ (1 \u2212 \u03c0) \u00b7 e\u2212\u03bb2\n\u00b7\n\u03bbk\n2\nk!\nThe two dimensional Poisson shows a plateau between \u03bb1 =\n1000 and \u03bb2 = 2000, we used here \u03c0 = 0.5. The idea\nbehind this setting is that terms that occur in less than 1000\ndocuments are considered to be not noisy (i.e. they are\ninformative), that terms between 1000 and 2000 are half noisy,\nand that terms with more than 2000 are definitely noisy.\nFor the informativeness, we observe that the radical\nbehaviour of Poisson is preserved. The plateau here is\napproximately at 1/6, and it is important to realise that this\nplateau is not obtained with the multi-dimensional Poisson\nnoise using \u03c0 = 0.5. The logarithm of the noise is\nnormalised by the logarithm of a very small number, namely\n0.5 \u00b7 e\u22121000\n+ 0.5 \u00b7 e\u22122000\n. That is why the informativeness\nwill be only close to one for very little noise, whereas for a\nbit of noise, informativeness will drop to zero. This effect\ncan be controlled by using small values for \u03c0 such that the\nnoise in the interval [\u03bb1; \u03bb2] is still very little. The setting\n\u03c0 = e\u22122000/6\nleads to noise values of approximately e\u22122000/6\nin the interval [\u03bb1; \u03bb2], the logarithms lead then to 1/6 for\nthe informativeness.\nThe indepence-based and frequency-based informativeness\nfunctions do not differ as much as the noise functions do.\nHowever, for the indepence-based probability of being\ninformative, we can control the average informativeness by the\ndefinition p := \u03bb/N whereas the control on the\nfrequencybased is limited as we address next.\nFor the frequency-based idf , the gradient is monotonously\ndecreasing and we obtain for different collections the same\ndistances of idf -values, i. e. the parameter N does not affect\nthe distance. For an illustration, consider the distance\nbetween the value idf(tn+1) of a term tn+1 that occurs in n+1\ndocuments, and the value idf(tn) of a term tn that occurs in\nn documents.\nidf(tn+1) \u2212 idf(tn) = ln\nn\nn + 1\nThe first three values of the distance function are:\nidf(t2) \u2212 idf(t1) = ln(1/(1 + 1)) = 0.69\nidf(t3) \u2212 idf(t2) = ln(1/(2 + 1)) = 0.41\nidf(t4) \u2212 idf(t3) = ln(1/(3 + 1)) = 0.29\nFor the Poisson-based informativeness, the gradient decreases\nfirst slowly for small n(t), then rapidly near n(t) \u2248 \u03bb and\nthen it grows again slowly for large n(t).\nIn conclusion, we have seen that the Poisson-based\ndefinition provides more control and parameter possibilities than\n233\nthe frequency-based definition does. Whereas more control\nand parameter promises to be positive for the\npersonalisation of retrieval systems, it bears at the same time the\ndanger of just too many parameters. The framework presented\nin this paper raises the awareness about the probabilistic\nand information-theoretic meanings of the parameters. The\nparallel definitions of the frequency-based probability and\nthe Poisson-based probability of being informative made\nthe underlying assumptions explicit. The frequency-based\nprobability can be explained by binary occurrence, constant\ncontainment and disjointness of documents. Independence\nof documents leads to Poisson, where we have to be aware\nthat Poisson approximates the probability of a disjunction\nfor a large number of events, but not for a small number.\nThis theoretical result explains why experimental\ninvestigations on Poisson (see [7]) show that a Poisson estimation\ndoes work better for frequent (bad, noisy) terms than for\nrare (good, informative) terms.\nIn addition to the collection-wide parameter setting, the\nframework presented here allows for document-dependent\nsettings, as explained for the independence probability. This\nis in particular interesting for heterogeneous and structured\ncollections, since documents are different in nature (size,\nquality, root document, sub document), and therefore,\nbinary occurrence and constant containment are less\nappropriate than in relatively homogeneous collections.\n7. SUMMARY\nThe definition of the probability of being informative\ntransforms the informative interpretation of the idf into a\nprobabilistic interpretation, and we can use the idf -based\nprobability in probabilistic retrieval approaches. We showed that\nthe classical definition of the noise (document frequency) in\nthe inverse document frequency can be explained by three\nassumptions: the term within-document occurrence\nprobability is binary, the document containment probability is\nconstant, and the document containment events are disjoint.\nBy explicitly and mathematically formulating the\nassumptions, we showed that the classical definition of idf does not\ntake into account parameters such as the different nature\n(size, quality, structure, etc.) of documents in a collection,\nor the different nature of terms (coverage, importance,\nposition, etc.) in a document. We discussed that the absence\nof those parameters is compensated by a leverage effect of\nthe within-document term occurrence probability and the\ndocument containment probability.\nBy applying an independence rather a disjointness\nassumption for the document containment, we could\nestablish a link between the noise probability (term occurrence\nin a collection), information theory and Poisson. From the\nfrequency-based and the Poisson-based probabilities of\nbeing noisy, we derived the frequency-based and Poisson-based\nprobabilities of being informative. The frequency-based\nprobability is relatively smooth whereas the Poisson probability\nis radical in distinguishing between noisy or not noisy, and\ninformative or not informative, respectively. We showed how\nto smoothen the radical behaviour of Poisson with a\nmultidimensional Poisson.\nThe explicit and mathematical formulation of idf - and\nPoisson-assumptions is the main result of this paper. Also,\nthe paper emphasises the duality of idf and tf , collection\nspace and document space, respectively. Thus, the result\napplies to term occurrence and document containment in a\ncollection, and it applies to term occurrence and position\ncontainment in a document. This theoretical framework is\nuseful for understanding and deciding the parameter\nestimation and combination in probabilistic retrieval models. The\nlinks between indepence-based noise as document frequency,\nprobabilistic interpretation of idf , information theory and\nPoisson described in this paper may lead to variable\nprobabilistic idf and tf definitions and combinations as required\nin advanced and personalised information retrieval systems.\nAcknowledgment: I would like to thank Mounia Lalmas,\nGabriella Kazai and Theodora Tsikrika for their comments\non the as they said heavy pieces. My thanks also go to the\nmeta-reviewer who advised me to improve the presentation\nto make it less formidable and more accessible for those\nwithout a theoretic bent. This work was funded by a\nresearch fellowship from Queen Mary University of London.\n8. REFERENCES\n[1] A. Aizawa. An information-theoretic perspective of\ntf-idf measures. Information Processing and\nManagement, 39:45-65, January 2003.\n[2] G. Amati and C. J. Rijsbergen. Term frequency\nnormalization via Pareto distributions. In 24th\nBCS-IRSG European Colloquium on IR Research,\nGlasgow, Scotland, 2002.\n[3] R. K. Belew. Finding out about. Cambridge University\nPress, 2000.\n[4] A. Bookstein and D. Swanson. Probabilistic models\nfor automatic indexing. Journal of the American\nSociety for Information Science, 25:312-318, 1974.\n[5] I. N. Bronstein. Taschenbuch der Mathematik. Harri\nDeutsch, Thun, Frankfurt am Main, 1987.\n[6] K. Church and W. Gale. Poisson mixtures. Natural\nLanguage Engineering, 1(2):163-190, 1995.\n[7] K. W. Church and W. A. Gale. Inverse document\nfrequency: A measure of deviations from poisson. In\nThird Workshop on Very Large Corpora, ACL\nAnthology, 1995.\n[8] T. Lafouge and C. Michel. Links between information\nconstruction and information gain: Entropy and\nbibliometric distribution. Journal of Information\nScience, 27(1):39-49, 2001.\n[9] E. Margulis. N-poisson document modelling. In\nProceedings of the 15th Annual International ACM\nSIGIR Conference on Research and Development in\nInformation Retrieval, pages 177-189, 1992.\n[10] S. E. Robertson and S. Walker. Some simple effective\napproximations to the 2-poisson model for\nprobabilistic weighted retrieval. In Proceedings of the\n17th Annual International ACM SIGIR Conference on\nResearch and Development in Information Retrieval,\npages 232-241, London, et al., 1994. Springer-Verlag.\n[11] S. Wong and Y. Yao. An information-theoric measure\nof term specificity. Journal of the American Society\nfor Information Science, 43(1):54-61, 1992.\n[12] S. Wong and Y. Yao. On modeling information\nretrieval with probabilistic inference. ACM\nTransactions on Information Systems, 13(1):38-68,\n1995.\n234", "keywords": "idf;informativeness;document disjointness;poisson distribution;probability theory;probabilistic information retrieval;information theory;independence assumption;inverse document frequency;information retrieval;poisson-based probability;collection space;frequency-based probability;noise probability;probability function;disjointness of document"}
{"name": "train_H-61", "title": "Impedance Coupling in Content-targeted Advertising", "abstract": "The current boom of the Web is associated with the revenues originated from on-line advertising. While search-based advertising is dominant, the association of ads with a Web page (during user navigation) is becoming increasingly important. In this work, we study the problem of associating ads with a Web page, referred to as content-targeted advertising, from a computer science perspective. We assume that we have access to the text of the Web page, the keywords declared by an advertiser, and a text associated with the advertiser\"s business. Using no other information and operating in fully automatic fashion, we propose ten strategies for solving the problem and evaluate their effectiveness. Our methods indicate that a matching strategy that takes into account the semantics of the problem (referred to as AAK for ads and keywords) can yield gains in average precision figures of 60% compared to a trivial vector-based strategy. Further, a more sophisticated impedance coupling strategy, which expands the text of the Web page to reduce vocabulary impedance with regard to an advertisement, can yield extra gains in average precision of 50%. These are first results. They suggest that great accuracy in content-targeted advertising can be attained with appropriate algorithms.", "fulltext": "1. INTRODUCTION\nThe emergence of the Internet has opened up new\nmarketing opportunities. In fact, a company has now the possibility\nof showing its advertisements (ads) to millions of people at a\nlow cost. During the 90\"s, many companies invested heavily\non advertising in the Internet with apparently no concerns\nabout their investment return [16]. This situation radically\nchanged in the following decade when the failure of many\nWeb companies led to a dropping in supply of cheap venture\ncapital and a considerable reduction in on-line advertising\ninvestments [15,16].\nIt was clear then that more effective strategies for on-line\nadvertising were required. For that, it was necessary to take\ninto account short-term and long-term interests of the users\nrelated to their information needs [9,14]. As a consequence,\nmany companies intensified the adoption of intrusive\ntechniques for gathering information of users mostly without\ntheir consent [8]. This raised privacy issues which\nstimulated the research for less invasive measures [16].\nMore recently, Internet information gatekeepers as, for\nexample, search engines, recommender systems, and\ncomparison shopping services, have employed what is called paid\nplacement strategies [3]. In such methods, an advertiser\ncompany is given prominent positioning in advertisement\nlists in return for a placement fee. Amongst these methods,\nthe most popular one is a non-intrusive technique called\nkeyword targeted marketing [16]. In this technique, keywords\nextracted from the user\"s search query are matched against\nkeywords associated with ads provided by advertisers. A\nranking of the ads, which also takes into consideration the\namount that each advertiser is willing to pay, is computed.\nThe top ranked ads are displayed in the search result page\ntogether with the answers for the user query.\nThe success of keyword targeted marketing has motivated\ninformation gatekeepers to offer their advertisement services\nin different contexts. For example, as shown in Figure 1,\nrelevant ads could be shown to users directly in the pages of\ninformation portals. The motivation is to take advantage of\n496\nthe users immediate information interests at browsing time.\nThe problem of matching ads to a Web page that is browsed,\nwhich we also refer to as content-targeted advertising [1],\nis different from that of keyword marketing. In this case,\ninstead of dealing with users\" keywords, we have to use the\ncontents of a Web page to decide which ads to display.\nFigure 1: Example of content-based advertising in\nthe page of a newspaper. The middle slice of the\npage shows the beginning of an article about the\nlaunch of a DVD movie. At the bottom slice, we can\nsee advertisements picked for this page by Google\"s\ncontent-based advertising system, AdSense.\nIt is important to notice that paid placement\nadvertising strategies imply some risks to information gatekeepers.\nFor instance, there is the possibility of a negative impact\non their credibility which, at long term, can demise their\nmarket share [3]. This makes investments in the quality of\nad recommendation systems even more important to\nminimize the possibility of exhibiting ads unrelated to the user\"s\ninterests. By investing in their ad systems, information\ngatekeepers are investing in the maintenance of their credibility\nand in the reinforcement of a positive user attitude towards\nthe advertisers and their ads [14]. Further, that can\ntranslate into higher clickthrough rates that lead to an increase in\nrevenues for information gatekeepers and advertisers, with\ngains to all parts [3].\nIn this work, we focus on the problem of content-targeted\nadvertising. We propose new strategies for associating ads\nwith a Web page. Five of these strategies are referred to as\nmatching strategies. They are based on the idea of matching\nthe text of the Web page directly to the text of the ads and\nits associated keywords. Five other strategies, which we here\nintroduce, are referred to as impedance coupling strategies.\nThey are based on the idea of expanding the Web page with\nnew terms to facilitate the task of matching ads and Web\npages. This is motivated by the observation that there is\nfrequently a mismatch between the vocabulary of a Web page\nand the vocabulary of an advertisement. We say that there\nis a vocabulary impedance problem and that our technique\nprovides a positive effect of impedance coupling by reducing\nthe vocabulary impedance. Further, all our strategies rely\non information that is already available to information\ngatekeepers that operate keyword targeted advertising systems.\nThus, no other data from the advertiser is required.\nUsing a sample of a real case database with over 93,000\nads and 100 Web pages selected for testing, we evaluate our\nad recommendation strategies. First, we evaluate the five\nmatching strategies. They match ads to a Web page\nusing a standard vector model and provide what we may call\ntrivial solutions. Our results indicate that a strategy that\nmatches the ad plus its keywords to a Web page, requiring\nthe keywords to appear in the Web page, provides\nimprovements in average precision figures of roughly 60% relative\nto a strategy that simply matches the ads to the Web page.\nSuch strategy, which we call AAK (for ads and keywords),\nis then taken as our baseline.\nFollowing we evaluate the five impedance coupling\nstrategies. They are based on the idea of expanding the ad and\nthe Web page with new terms to reduce the vocabulary\nimpedance between their texts. Our results indicate that it\nis possible to generate extra improvements in average\nprecision figures of roughly 50% relative to the AAK strategy.\nThe paper is organized as follows. In section 2, we\nintroduce five matching strategies to solve content-targeted\nadvertising. In section 3, we present our impedance\ncoupling strategies. In section 4, we describe our experimental\nmethodology and datasets and discuss our results. In\nsection 5 we discuss related work. In section 6 we present our\nconclusions.\n2. MATCHING STRATEGIES\nKeyword advertising relies on matching search queries to\nads and its associated keywords. Context-based\nadvertising, which we address here, relies on matching ads and its\nassociated keywords to the text of a Web page.\nGiven a certain Web page p, which we call triggering page,\nour task is to select advertisements related to the contents\nof p. Without loss of generality, we consider that an\nadvertisement ai is composed of a title, a textual description,\nand a hyperlink. To illustrate, for the first ad by Google\nshown in Figure 1, the title is Star Wars Trilogy Full,\nthe description is Get this popular DVD free. Free w/ free\nshopping. Sign up now, and the hyperlink points to the site\nwww.freegiftworld.com. Advertisements can be grouped\nby advertisers in groups called campaigns, such that a\ncampaign can have one or more advertisements.\nGiven our triggering page p and a set A of ads, a simple\nway of ranking ai \u2208 A with regard to p is by matching the\ncontents of p to the contents of ai. For this, we use the vector\nspace model [2], as discussed in the immediately following.\nIn the vector space model, queries and documents are\nrepresented as weighted vectors in an n-dimensional space. Let\nwiq be the weight associated with term ti in the query q\nand wij be the weight associated with term ti in the\ndocument dj. Then, q = (w1q, w2q, ..., wiq, ..., wnq) and dj =\n(w1j, w2j, ..., wij, ..., wnj) are the weighted vectors used to\nrepresent the query q and the document dj. These weights\ncan be computed using classic tf-idf schemes. In such schemes,\nweights are taken as the product between factors that\nquantify the importance of a term in a document (given by the\nterm frequency, or tf, factor) and its rarity in the whole\ncollection (given by the inverse document factor, or idf, factor),\nsee [2] for details. The ranking of the query q with regard\nto the document dj is computed by the cosine similarity\n497\nformula, that is, the cosine of the angle between the two\ncorresponding vectors:\nsim(q, dj) =\nq \u2022 dj\n|q| \u00d7 |dj|\n=\nPn\ni=1 wiq \u00b7 wij\nqPn\ni=1 w2\niq\nqPn\ni=1 w2\nij\n(1)\nBy considering p as the query and ai as the document, we\ncan rank the ads with regard to the Web page p. This is our\nfirst matching strategy. It is represented by the function AD\ngiven by:\nAD(p, ai) = sim(p, ai)\nwhere AD stands for direct match of the ad, composed by\ntitle and description and sim(p, ai) is computed according\nto Eq. (1).\nIn our second method, we use other source of evidence\nprovided by the advertisers: the keywords. With each\nadvertisement ai an advertiser associates a keyword ki, which\nmay be composed of one or more terms. We denote the\nassociation between an advertisement ai and a keyword ki\nas the pair (ai, ki) \u2208 K, where K is the set of associations\nmade by the advertisers. In the case of keyword targeted\nadvertising, such keywords are used to match the ads to the\nuser queries. In here, we use them to match ads to the Web\npage p. This provides our second method for ad matching\ngiven by:\nKW(p, ai) = sim(p, ki)\nwhere (ai, ki) \u2208 K and KW stands for match the ad\nkeywords.\nWe notice that most of the keywords selected by\nadvertisers are also present in the ads associated with those\nkeywords. For instance, in our advertisement test collection,\nthis is true for 90% of the ads. Thus, instead of using the\nkeywords as matching devices, we can use them to emphasize\nthe main concepts in an ad, in an attempt to improve our\nAD strategy. This leads to our third method of ad matching\ngiven by:\nAD KW(p, ai) = sim(p, ai \u222a ki)\nwhere (ai, ki) \u2208 K and AD KW stands for match the ad and\nits keywords.\nFinally, it is important to notice that the keyword ki\nassociated with ai could not appear at all in the triggering page\np, even when ai is highly ranked. However, if we assume that\nki summarizes the main topic of ai according to an\nadvertiser viewpoint, it can be interesting to assure its presence\nin p. This reasoning suggests that requiring the occurrence\nof the keyword ki in the triggering page p as a condition\nto associate ai with p might lead to improved results. This\nleads to two extra matching strategies as follows:\nANDKW(p, ai) =\n\uf6be\nsim(p, ai) if ki p\n0 if otherwise\nAD ANDKW(p, ai) = AAK(p, ai) =\n\uf6be\nsim(p, ai \u222a ki) if ki p\n0 if otherwise\nwhere (ai, ki) \u2208 K, ANDKW stands for match the ad keywords\nand force their appearance, and AD ANDKW (or AAK for ads\nand keywords) stands for match the ad, its keywords, and\nforce their appearance.\nAs we will see in our results, the best among these simple\nmethods is AAK. Thus, it will be used as baseline for our\nimpedance coupling strategies which we now discuss.\n3. IMPEDANCE COUPLING STRATEGIES\nTwo key issues become clear as one plays with the\ncontenttargeted advertising problem. First, the triggering page\nnormally belongs to a broader contextual scope than that of the\nadvertisements. Second, the association between a good\nadvertisement and the triggering page might depend on a topic\nthat is not mentioned explicitly in the triggering page.\nThe first issue is due to the fact that Web pages can be\nabout any subject and that advertisements are concise in\nnature. That is, ads tend to be more topic restricted than\nWeb pages. The second issue is related to the fact that, as\nwe later discuss, most advertisers place a small number of\nadvertisements. As a result, we have few terms describing\ntheir interest areas. Consequently, these terms tend to be\nof a more general nature. For instance, a car shop probably\nwould prefer to use car instead of super sport to describe\nits core business topic. As a consequence, many specific\nterms that appear in the triggering page find no match in\nthe advertisements. To make matters worst, a page might\nrefer to an entity or subject of the world through a label\nthat is distinct from the label selected by an advertiser to\nrefer to the same entity.\nA consequence of these two issues is that vocabularies of\npages and ads have low intersection, even when an ad is\nrelated to a page. We cite this problem from now on as\nthe vocabulary impedance problem. In our experiments, we\nrealized that this problem limits the final quality of direct\nmatching strategies. Therefore, we studied alternatives to\nreduce the referred vocabulary impedance.\nFor this, we propose to expand the triggering pages with\nnew terms. Figure 2 illustrates our intuition. We already\nknow that the addition of keywords (selected by the\nadvertiser) to the ads leads to improved results. We say that a\nkeyword reduces the vocabulary impedance by providing an\nalternative matching path. Our idea is to add new terms\n(words) to the Web page p to also reduce the vocabulary\nimpedance by providing a second alternative matching path.\nWe refer to our expansion technique as impedance coupling.\nFor this, we proceed as follows.\nexpansion\nterms keyword\nvocabulary impedance\ntriggering\npage p ad\nFigure 2: Addition of new terms to a Web page to\nreduce the vocabulary impedance.\nAn advertiser trying to describe a certain topic in a concise\nway probably will choose general terms to characterize that\ntopic. To facilitate the matching between this ad and our\ntriggering page p, we need to associate new general terms\nwith p. For this, we assume that Web documents similar\nto the triggering page p share common topics. Therefore,\n498\nby inspecting the vocabulary of these similar documents we\nmight find good terms for better characterizing the main\ntopics in the page p. We now describe this idea using a\nBayesian network model [10,11,13] depicted in Figure 3.\nR\nD0 D1 Dj Dk\nT1 T2 T3 Ti Tm\n... ...\n... ...\nFigure 3: Bayesian network model for our\nimpedance coupling technique.\nIn our model, which is based on the belief network in [11],\nthe nodes represent pieces of information in the domain.\nWith each node is associated a binary random variable,\nwhich takes the value 1 to mean that the corresponding\nentity (a page or terms) is observed and, thus, relevant in our\ncomputations. In this case, we say that the information was\nobserved. Node R represents the page r, a new\nrepresentation for the triggering page p. Let N be the set of the k\nmost similar documents to the triggering page, including the\ntriggering page p itself, in a large enough Web collection C.\nRoot nodes D0 through Dk represent the documents in N,\nthat is, the triggering page D0 and its k nearest neighbors,\nD1 through Dk, among all pages in C. There is an edge\nfrom node Dj to node R if document dj is in N. Nodes\nT1 through Tm represent the terms in the vocabulary of C.\nThere is an edge from node Dj to a node Ti if term ti occurs\nin document dj. In our model, the observation of the pages\nin N leads to the observation of a new representation of the\ntriggering page p and to a set of terms describing the main\ntopics associated with p and its neighbors.\nGiven these definitions, we can now use the network to\ndetermine the probability that a term ti is a good term for\nrepresenting a topic of the triggering page p. In other words,\nwe are interested in the probability of observing the final\nevidence regarding a term ti, given that the new\nrepresentation of the page p has been observed, P(Ti = 1|R = 1).\nThis translates into the following equation1\n:\nP(Ti|R) =\n1\nP(R)\nX\nd\nP(Ti|d)P(R|d)P(d) (2)\nwhere d represents the set of states of the document nodes.\nSince we are interested just in the states in which only a\nsingle document dj is observed and P(d) can be regarded as\na constant, we can rewrite Eq. (2) as:\nP(Ti|R) =\n\u03bd\nP(R)\nkX\nj=0\nP(Ti|dj)P(R|dj) (3)\nwhere dj represents the state of the document nodes in\nwhich only document dj is observed and \u03bd is a constant\n1\nTo simplify our notation we represent the probabilities\nP(X = 1) as P(X) and P(X = 0) as P(X).\nassociated with P(dj). Eq. (3) is the general equation to\ncompute the probability that a term ti is related to the\ntriggering page. We now define the probabilities P(Ti|dj) and\nP(R|dj) as follows:\nP(Ti|dj) = \u03b7 wij (4)\nP(R|dj) =\n\uf6be\n(1 \u2212 \u03b1) j = 0\n\u03b1 sim(r, dj) 1 \u2264 j \u2264 k\n(5)\nwhere \u03b7 is a normalizing constant, wij is the weight\nassociated with term ti in the document dj, and sim(p, dj) is\ngiven by Eq. (1), i.e., is the cosine similarity between p and\ndj. The weight wij is computed using a classic tf-idf scheme\nand is zero if term ti does not occur in document dj. Notice\nthat P(Ti|dj) = 1 \u2212 P(Ti|dj) and P(R|dj) = 1 \u2212 P(R|dj).\nBy defining the constant \u03b1, it is possible to determine how\nimportant should be the influence of the triggering page p\nto its new representation r. By substituting Eq. (4) and\nEq. (5) into Eq. (3), we obtain:\nP(Ti|R) = \u03c1 ((1 \u2212 \u03b1) wi0 + \u03b1\nkX\nj=1\nwij sim(r, dj)) (6)\nwhere \u03c1 = \u03b7 \u03bd is a normalizing constant.\nWe use Eq. (6) to determine the set of terms that will\ncompose r, as illustrated in Figure 2. Let ttop be the top\nranked term according to Eq. (6). The set r is composed\nof the terms ti such that P (Ti|R)\nP (Ttop|R)\n\u2265 \u03b2, where \u03b2 is a given\nthreshold. In our experiments, we have used \u03b2 = 0.05.\nNotice that the set r might contain terms that already occur\nin p. That is, while we will refer to the set r as expansion\nterms, it should be clear that p \u2229 r = \u2205.\nBy using \u03b1 = 0, we simply consider the terms originally\nin page p. By increasing \u03b1, we relax the context of the page\np, adding terms from neighbor pages, turning page p into its\nnew representation r. This is important because, sometimes,\na topic apparently not important in the triggering page offers\na good opportunity for advertising. For example, consider\na triggering page that describes a congress in London about\ndigital photography. Although London is probably not an\nimportant topic in this page, advertisements about hotels\nin London would be appropriate. Thus, adding hotels to\npage p is important. This suggests using \u03b1 > 0, that is,\npreserving the contents of p and using the terms in r to\nexpand p.\nIn this paper, we examine both approaches. Thus, in our\nsixth method we match r, the set of new expansion terms,\ndirectly to the ads, as follows:\nAAK T(p, ai) = AAK(r, ai)\nwhere AAK T stands for match the ad and keywords to the\nset r of expansion terms.\nIn our seventh method, we match an expanded page p to\nthe ads as follows:\nAAK EXP(p, ai) = AAK(p \u222a r, ai)\nwhere AAK EXP stands for match the ad and keywords to\nthe expanded triggering page.\n499\nTo improve our ad placement methods, other external\nsource that we can use is the content of the page h pointed to\nby the advertisement\"s hyperlink, that is, its landing page.\nAfter all, this page comprises the real target of the ad and\nperhaps could present a more detailed description of the\nproduct or service being advertised. Given that the\nadvertisement ai points to the landing page hi, we denote this\nassociation as the pair (ai, hi) \u2208 H, where H is the set of\nassociations between the ads and the pages they point to.\nOur eighth method consists of matching the triggering page\np to the landing pages pointed to by the advertisements, as\nfollows:\nH(p, ai) = sim(p, hi)\nwhere (ai, hi) \u2208 H and H stands for match the hyperlink\npointed to by the ad.\nWe can also combine this information with the more\npromising methods previously described, AAK and AAK EXP as\nfollows. Given that (ai, hi) \u2208 H and (ai, ki) \u2208 K, we have our\nlast two methods:\nAAK H(p, ai) =\n\uf6be\nsim(p, ai \u222a hi \u222a ki) if ki p\n0 if otherwise\nAAK EXP H(p, ai) =\n\uf6be\nsim(p \u222a r, ai \u222a hi \u222a ki) if ki (p \u222a r)\n0 if otherwise\nwhere AAK H stands for match ads and keywords also\nconsidering the page pointed by the ad and AAH EXP H stands\nfor match ads and keywords with expanded triggering page,\nalso considering the page pointed by the ad.\nNotice that other combinations were not considered in this\nstudy due to space restrictions. These other combinations\nled to poor results in our experimentation and for this reason\nwere discarded.\n4. EXPERIMENTS\n4.1 Methodology\nTo evaluate our ad placement strategies, we performed\na series of experiments using a sample of a real case ad\ncollection with 93,972 advertisements, 1,744 advertisers, and\n68,238 keywords2\n. The advertisements are grouped in 2,029\ncampaigns with an average of 1.16 campaigns per advertiser.\nFor the strategies AAK T and AAK EXP, we had to\ngenerate a set of expansion terms. For that, we used a database\nof Web pages crawled by the TodoBR search engine [12]\n(http://www.todobr.com.br/). This database is composed\nof 5,939,061 pages of the Brazilian Web, under the domain\n.br. For the strategies H, AAK H, and AAK EXP H, we also\ncrawled the pages pointed to by the advertisers. No other\nfiltering method was applied to these pages besides the\nremoval of HTML tags.\nSince we are initially interested in the placement of\nadvertisements in the pages of information portals, our test\ncollection was composed of 100 pages extracted from a\nBrazilian newspaper. These are our triggering pages. They were\ncrawled in such a way that only the contents of their\narticles was preserved. As we have no preferences for particular\n2\nData in portuguese provided by an on-line advertisement\ncompany that operates in Brazil.\ntopics, the crawled pages cover topics as diverse as politics,\neconomy, sports, and culture.\nFor each of our 100 triggering pages, we selected the top\nthree ranked ads provided by each of our 10 ad placement\nstrategies. Thus, for each triggering page we select no more\nthan 30 ads. These top ads were then inserted in a pool\nfor that triggering page. Each pool contained an average of\n15.81 advertisements. All advertisements in each pool were\nsubmitted to a manual evaluation by a group of 15 users.\nThe average number of relevant advertisements per page\npool was 5.15. Notice that we adopted the same pooling\nmethod used to evaluate the TREC Web-based collection [6].\nTo quantify the precision of our results, we used 11-point\naverage figures [2]. Since we are not able to evaluate the\nentire ad collection, recall values are relative to the set of\nevaluated advertisements.\n4.2 Tuning Idf factors\nWe start by analyzing the impact of different idf factors\nin our advertisement collection. Idf factors are important\nbecause they quantify how discriminative is a term in the\ncollection. In our ad collection, idf factors can be computed\nby taking ads, advertisers or campaigns as documents. To\nexemplify, consider the computation of ad idf for a term\nti that occurs 9 times in a collection of 100 ads. Then, the\ninverse document frequency of ti is given by:\nidfi = log\n100\n9\nHence, we can compute ad, advertiser or campaign idf\nfactors. As we observe in Figure 4, for the AD strategy, the best\nranking is obtained by the use of campaign idf, that is, by\ncalculating our idf factor so that it discriminates campaigns.\nSimilar results were obtained for all the other methods.\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\n0 0.2 0.4 0.6 0.8 1\nprecision\nrecall\nCampaign idf\nAdvertiser idf\nAd idf\nFigure 4: Precision-recall curves obtained for the\nAD strategy using ad, advertiser, and campaign idf\nfactors.\nThis reflects the fact that terms might be better\ndiscriminators for a business topic than for an specific ad. This\neffect can be accomplished by calculating the factor relative\nto idf advertisers or campaigns instead of ads. In fact,\ncampaign idf factors yielded the best results. Thus, they will be\nused in all the experiments reported from now on.\n500\n4.3 Results\nMatching Strategies\nFigure 5 displays the results for the matching strategies\npresented in Section 2. As shown, directly matching the\ncontents of the ad to the triggering page (AD strategy) is not so\neffective. The reason is that the ad contents are very noisy.\nIt may contain messages that do not properly describe the\nad topics such as requisitions for user actions (e.g, visit our\nsite) and general sentences that could be applied to any\nproduct or service (e.g, we delivery for the whole\ncountry). On the other hand, an advertiser provided keyword\nsummarizes well the topic of the ad. As a consequence, the\nKW strategy is superior to the AD and AD KW strategies. This\nsituation changes when we require the keywords to appear\nin the target Web page. By filtering out ads whose keywords\ndo not occur in the triggering page, much noise is discarded.\nThis makes ANDKW a better alternative than KW. Further, in\nthis new situation, the contents of the ad becomes useful\nto rank the most relevant ads making AD ANDKW (or AAK for\nads and keywords) the best among all described methods.\nFor this reason, we adopt AAK as our baseline in the next set\nof experiments.\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0 0.2 0.4 0.6 0.8 1\nprecision\nrecall\nAAK\nANDKW\nKW\nAD_KW\nAD\nFigure 5: Comparison among our five matching\nstrategies. AAK (ads and keywords) is superior.\nTable 1 illustrates average precision figures for Figure 5.\nWe also present actual hits per advertisement slot. We call\nhit an assignment of an ad (to the triggering page) that\nwas considered relevant by the evaluators. We notice that\nour AAK strategy provides a gain in average precision of 60%\nrelative to the trivial AD strategy. This shows that careful\nconsideration of the evidence related to the problem does\npay off.\nImpedance Coupling Strategies\nTable 2 shows top ranked terms that occur in a page\ncovering Argentinean wines produced using grapes derived from\nthe Bordeaux region of France. The p column includes the\ntop terms for this page ranked according to our tf-idf\nweighting scheme. The r column includes the top ranked\nexpansion terms generated according to Eq. (6). Notice that the\nexpansion terms not only emphasize important terms of the\ntarget page (by increasing their weights) such as wines and\nMethods Hits 11-pt average\n#1 #2 #3 total score gain(%)\nAD 41 32 13 86 0.104\nAD KW 51 28 17 96 0.106 +1.9\nKW 46 34 28 108 0.125 +20.2\nANDKW 49 37 35 121 0.153 +47.1\nAD ANDKW (AAK) 51 48 39 138 0.168 +61.5\nTable 1: Average precision figures, corresponding to\nFigure 5, for our five matching strategies. Columns\nlabelled #1, #2, and #3 indicate total of hits in\nfirst, second, and third advertisement slots,\nrespectively. The AAK strategy provides improvements of\n60% relative to the AD strategy.\nRank p r\nterm score term score\n1 argentina 0.090 wines 0.251\n2 obtained* 0.047 wine* 0.140\n3 class* 0.036 whites 0.091\n4 whites 0.035 red* 0.057\n5 french* 0.031 grape 0.051\n6 origin* 0.029 bordeaux 0.045\n7 france* 0.029 acideness* 0.038\n8 grape 0.017 argentina 0.037\n9 sweet* 0.016 aroma* 0.037\n10 country* 0.013 blanc* 0.036\n...\n35 wines 0.010\n-...\nTable 2: Top ranked terms for the triggering page\np according to our tf-idf weighting scheme and top\nranked terms for r, the expansion terms for p,\ngenerated according to Eq. (6). Ranking scores were\nnormalized in order to sum up to 1. Terms marked\nwith \u2018*\" are not shared by the sets p and r.\nwhites, but also reveal new terms related to the main topic\nof the page such as aroma and red. Further, they avoid\nsome uninteresting terms such as obtained and country.\nFigure 6 illustrates our results when the set r of\nexpansion terms is used. They show that matching the ads to\nthe terms in the set r instead of to the triggering page p\n(AAK T strategy) leads to a considerable improvement over\nour baseline, AAK. The gain is even larger when we use the\nterms in r to expand the triggering page (AAK EXP method).\nThis confirms our hypothesis that the triggering page could\nhave some interesting terms that should not be completely\ndiscarded.\nFinally, we analyze the impact on the ranking of using the\ncontents of pages pointed by the ads. Figure 7 displays our\nresults. It is clear that using only the contents of the pages\npointed by the ads (H strategy) yields very poor results.\nHowever, combining evidence from the pages pointed by the\nads with our baseline yields improved results. Most\nimportant, combining our best strategy so far (AAK EXP) with\npages pointed by ads (AAK EXP H strategy) leads to superior\nresults. This happens because the two additional sources\nof evidence, expansion terms and pages pointed by the ads,\nare distinct and complementary, providing extra and\nvaluable information for matching ads to a Web page.\n501\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0 0.2 0.4 0.6 0.8 1\nprecision\nrecall\nAAK_EXP\nAAK_T\nAAK\nFigure 6: Impact of using a new representation for\nthe triggering page, one that includes expansion\nterms.\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0 0.2 0.4 0.6 0.8 1\nprecision\nrecall\nAAK_EXP_H\nAAK_H\nAAK\nH\nFigure 7: Impact of using the contents of the page\npointed by the ad (the hyperlink).\nFigure 8 and Table 3 summarize all results described in\nthis section. In Figure 8 we show precision-recall curves\nand in Table 3 we show 11-point average figures. We also\npresent actual hits per advertisement slot and gains in\naverage precision relative to our baseline, AAK. We notice that\nthe highest number of hits in the first slot was generated by\nthe method AAK EXP. However, the method with best\noverall retrieval performance was AAK EXP H, yielding a gain in\naverage precision figures of roughly 50% over the baseline\n(AAK).\n4.4 Performance Issues\nIn a keyword targeted advertising system, ads are assigned\nat query time, thus the performance of the system is a very\nimportant issue. In content-targeted advertising systems,\nwe can associate ads with a page at publishing (or\nupdating) time. Also, if a new ad comes in we might consider\nassigning this ad to already published pages in o\ufb04ine mode.\nThat is, we might design the system such that its\nperformance depends fundamentally on the rate that new pages\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0 0.2 0.4 0.6 0.8 1\nprecision\nrecall\nAAK_EXP_H\nAAK_EXP\nAAK_T\nAAK_H\nAAK\nH\nFigure 8: Comparison among our ad placement\nstrategies.\nMethods Hits 11-pt average\n#1 #2 #3 total score gain(%)\nH 28 5 6 39 0.026 -84.3\nAAK 51 48 39 138 0.168\nAAK H 52 50 46 148 0.191 +13.5\nAAK T 65 49 43 157 0.226 +34.6\nAAK EXP 70 52 53 175 0.242 +43.8\nAAK EXP H 64 61 51 176 0.253 +50.3\nTable 3: Results for our impedance coupling\nstrategies.\nare published and the rate that ads are added or modified.\nFurther, the data needed by our strategies (page crawling,\npage expansion, and ad link crawling) can be gathered and\nprocessed o\ufb04ine, not affecting the user experience. Thus,\nfrom this point of view, the performance is not critical and\nwill not be addressed in this work.\n5. RELATED WORK\nSeveral works have stressed the importance of relevance\nin advertising. For example, in [14] it was shown that\nadvertisements that are presented to users when they are not\ninterested on them are viewed just as annoyance. Thus,\nin order to be effective, the authors conclude that\nadvertisements should be relevant to consumer concerns at the\ntime of exposure. The results in [9] enforce this conclusion\nby pointing out that the more targeted the advertising, the\nmore effective it is.\nTherefore it is not surprising that other works have\naddressed the relevance issue. For instance, in [8] it is proposed\na system called ADWIZ that is able to adapt online\nadvertisement to a user\"s short-term interests in a non-intrusive\nway. Contrary to our work, ADWIZ does not directly use\nthe content of the page viewed by the user. It relies on search\nkeywords supplied by the user to search engines and on the\nURL of the page requested by the user. On the other hand,\nin [7] the authors presented an intrusive approach in which\nan agent sits between advertisers and the user\"s browser\nallowing a banner to be placed into the currently viewed page.\nIn spite of having the opportunity to use the page\"s content,\n502\nthe agent infers relevance based on category information and\nuser\"s private information collected along the time.\nIn [5] the authors provide a comparison between the\nranking strategies used by Google and Overture for their keyword\nadvertising systems. Both systems select advertisements by\nmatching them to the keywords provided by the user in a\nsearch query and rank the resulting advertisement list\naccording to the advertisers\" willingness to pay. In\nparticular, Google approach also considers the clickthrough rate\nof each advertisement as an additional evidence for its\nrelevance. The authors conclude that Google\"s strategy is better\nthan that used by Overture. As mentioned before, the\nranking problem in keyword advertising is different from that of\ncontent-targeted advertising. Instead of dealing with\nkeywords provided by users in search queries, we have to deal\nwith the contents of a page which can be very diffuse.\nFinally, the work in [4] focuses on improving search\nengine results in a TREC collection by means of an automatic\nquery expansion method based on kNN [17]. Such method\nresembles our expansion approach presented in section 3.\nOur method is different from that presented by [4]. They\nexpand user queries applied to a document collection with\nterms extracted from the top k documents returned as\nanswer to the query in the same collection. In our case, we\nuse two collections: an advertisement and a Web collection.\nWe expand triggering pages with terms extracted from the\nWeb collection and then we match these expanded pages to\nthe ads from the advertisement collection. By doing this, we\nemphasize the main topics of the triggering pages, increasing\nthe possibility of associating relevant ads with them.\n6. CONCLUSIONS\nIn this work we investigated ten distinct strategies for\nassociating ads with a Web page that is browsed\n(contenttargeted advertising). Five of our strategies attempt to\nmatch the ads directly to the Web page. Because of that,\nthey are called matching strategies. The other five\nstrategies recognize that there is a vocabulary impedance problem\namong ads and Web pages and attempt to solve the problem\nby expanding the Web pages and the ads with new terms.\nBecause of that they are called impedance coupling\nstrategies.\nUsing a sample of a real case database with over 93\nthousand ads, we evaluated our strategies. For the five matching\nstrategies, our results indicated that planned consideration\nof additional evidence (such as the keywords provided by the\nadvertisers) yielded gains in average precision figures (for\nour test collection) of 60%. This was obtained by a\nstrategy called AAK (for ads and keywords), which is taken as\nthe baseline for evaluating our more advanced impedance\ncoupling strategies.\nFor our five impedance coupling strategies, the results\nindicate that additional gains in average precision of 50% (now\nrelative to the AAK strategy) are possible. These were\ngenerated by expanding the Web page with new terms (obtained\nusing a sample Web collection containing over five million\npages) and the ads with the contents of the page they point\nto (a hyperlink provided by the advertisers).\nThese are first time results that indicate that high quality\ncontent-targeted advertising is feasible and practical.\n7. ACKNOWLEDGEMENTS\nThis work was supported in part by the GERINDO\nproject, grant MCT/CNPq/CT-INFO 552.087/02-5, by CNPq\ngrant 300.188/95-1 (Berthier Ribeiro-Neto), and by CNPq\ngrant 303.576/04-9 (Edleno Silva de Moura). Marco Cristo\nis supported by Fucapi, Manaus, AM, Brazil.\n8. REFERENCES\n[1] The Google adwords. Google content-targeted advertising.\nhttp://adwords.google.com/select/ct_faq.html, November\n2004.\n[2] R. Baeza-Yates and B. Ribeiro-Neto. Modern Information\nRetrieval. Addison-Wesley-Longman, 1st edition, 1999.\n[3] H. K. Bhargava and J. Feng. Paid placement strategies for\ninternet search engines. 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{"name": "train_H-62", "title": "Implicit User Modeling for Personalized Search", "abstract": "Information retrieval systems (e.g., web search engines) are critical for overcoming information overload. A major deficiency of existing retrieval systems is that they generally lack user modeling and are not adaptive to individual users, resulting in inherently non-optimal retrieval performance. For example, a tourist and a programmer may use the same word java to search for different information, but the current search systems would return the same results. In this paper, we study how to infer a user\"s interest from the user\"s search context and use the inferred implicit user model for personalized search . We present a decision theoretic framework and develop techniques for implicit user modeling in information retrieval. We develop an intelligent client-side web search agent (UCAIR) that can perform eager implicit feedback, e.g., query expansion based on previous queries and immediate result reranking based on clickthrough information. Experiments on web search show that our search agent can improve search accuracy over the popular Google search engine.", "fulltext": "1. INTRODUCTION\nAlthough many information retrieval systems (e.g., web search\nengines and digital library systems) have been successfully deployed,\nthe current retrieval systems are far from optimal. A major\ndeficiency of existing retrieval systems is that they generally lack user\nmodeling and are not adaptive to individual users [17]. This\ninherent non-optimality is seen clearly in the following two cases:\n(1) Different users may use exactly the same query (e.g., Java) to\nsearch for different information (e.g., the Java island in Indonesia or\nthe Java programming language), but existing IR systems return the\nsame results for these users. Without considering the actual user, it\nis impossible to know which sense Java refers to in a query. (2)\nA user\"s information needs may change over time. The same user\nmay use Java sometimes to mean the Java island in Indonesia\nand some other times to mean the programming language.\nWithout recognizing the search context, it would be again impossible to\nrecognize the correct sense.\nIn order to optimize retrieval accuracy, we clearly need to model\nthe user appropriately and personalize search according to each\nindividual user. The major goal of user modeling for information\nretrieval is to accurately model a user\"s information need, which is,\nunfortunately, a very difficult task. Indeed, it is even hard for a user\nto precisely describe what his/her information need is.\nWhat information is available for a system to infer a user\"s\ninformation need? Obviously, the user\"s query provides the most direct\nevidence. Indeed, most existing retrieval systems rely solely on\nthe query to model a user\"s information need. However, since a\nquery is often extremely short, the user model constructed based\non a keyword query is inevitably impoverished . An effective way\nto improve user modeling in information retrieval is to ask the user\nto explicitly specify which documents are relevant (i.e., useful for\nsatisfying his/her information need), and then to improve user\nmodeling based on such examples of relevant documents. This is called\nrelevance feedback, which has been proved to be quite effective for\nimproving retrieval accuracy [19, 20]. Unfortunately, in real world\napplications, users are usually reluctant to make the extra effort to\nprovide relevant examples for feedback [11].\nIt is thus very interesting to study how to infer a user\"s\ninformation need based on any implicit feedback information, which\nnaturally exists through user interactions and thus does not require\nany extra user effort. Indeed, several previous studies have shown\nthat implicit user modeling can improve retrieval accuracy. In [3],\na web browser (Curious Browser) is developed to record a user\"s\nexplicit relevance ratings of web pages (relevance feedback) and\nbrowsing behavior when viewing a page, such as dwelling time,\nmouse click, mouse movement and scrolling (implicit feedback).\nIt is shown that the dwelling time on a page, amount of scrolling\non a page and the combination of time and scrolling have a strong\ncorrelation with explicit relevance ratings, which suggests that\nimplicit feedback may be helpful for inferring user information need.\nIn [10], user clickthrough data is collected as training data to learn\na retrieval function, which is used to produce a customized ranking\nof search results that suits a group of users\" preferences. In [25],\nthe clickthrough data collected over a long time period is exploited\nthrough query expansion to improve retrieval accuracy.\n824\nWhile a user may have general long term interests and\npreferences for information, often he/she is searching for documents to\nsatisfy an ad-hoc information need, which only lasts for a short\nperiod of time; once the information need is satisfied, the user\nwould generally no longer be interested in such information. For\nexample, a user may be looking for information about used cars\nin order to buy one, but once the user has bought a car, he/she is\ngenerally no longer interested in such information. In such cases,\nimplicit feedback information collected over a long period of time\nis unlikely to be very useful, but the immediate search context and\nfeedback information, such as which of the search results for the\ncurrent information need are viewed, can be expected to be much\nmore useful. Consider the query Java again. Any of the\nfollowing immediate feedback information about the user could\npotentially help determine the intended meaning of Java in the query:\n(1) The previous query submitted by the user is hashtable (as\nopposed to, e.g., travel Indonesia). (2) In the search results, the user\nviewed a page where words such as programming, software,\nand applet occur many times.\nTo the best of our knowledge, how to exploit such immediate\nand short-term search context to improve search has so far not been\nwell addressed in the previous work. In this paper, we study how to\nconstruct and update a user model based on the immediate search\ncontext and implicit feedback information and use the model to\nimprove the accuracy of ad-hoc retrieval. In order to maximally\nbenefit the user of a retrieval system through implicit user modeling,\nwe propose to perform eager implicit feedback. That is, as soon\nas we observe any new piece of evidence from the user, we would\nupdate the system\"s belief about the user\"s information need and\nrespond with improved retrieval results based on the updated user\nmodel. We present a decision-theoretic framework for optimizing\ninteractive information retrieval based on eager user model\nupdating, in which the system responds to every action of the user by\nchoosing a system action to optimize a utility function. In a\ntraditional retrieval paradigm, the retrieval problem is to match a query\nwith documents and rank documents according to their relevance\nvalues. As a result, the retrieval process is a simple independent\ncycle of query and result display. In the proposed new retrieval\nparadigm, the user\"s search context plays an important role and the\ninferred implicit user model is exploited immediately to benefit the\nuser. The new retrieval paradigm is thus fundamentally different\nfrom the traditional paradigm, and is inherently more general.\nWe further propose specific techniques to capture and exploit two\ntypes of implicit feedback information: (1) identifying related\nimmediately preceding query and using the query and the\ncorresponding search results to select appropriate terms to expand the current\nquery, and (2) exploiting the viewed document summaries to\nimmediately rerank any documents that have not yet been seen by the\nuser. Using these techniques, we develop a client-side web search\nagent UCAIR (User-Centered Adaptive Information Retrieval) on\ntop of a popular search engine (Google). Experiments on web\nsearch show that our search agent can improve search accuracy over\nGoogle. Since the implicit information we exploit already naturally\nexists through user interactions, the user does not need to make any\nextra effort. Thus the developed search agent can improve existing\nweb search performance without additional effort from the user.\nThe remaining sections are organized as follows. In Section 2,\nwe discuss the related work. In Section 3, we present a\ndecisiontheoretic interactive retrieval framework for implicit user modeling.\nIn Section 4, we present the design and implementation of an\nintelligent client-side web search agent (UCAIR) that performs eager\nimplicit feedback. In Section 5, we report our experiment results\nusing the search agent. Section 6 concludes our work.\n2. RELATED WORK\nImplicit user modeling for personalized search has been\nstudied in previous work, but our work differs from all previous work\nin several aspects: (1) We emphasize the exploitation of\nimmediate search context such as the related immediately preceding query\nand the viewed documents in the same session, while most previous\nwork relies on long-term collection of implicit feedback\ninformation [25]. (2) We perform eager feedback and bring the benefit of\nimplicit user modeling as soon as any new implicit feedback\ninformation is available, while the previous work mostly exploits\nlongterm implicit feedback [10]. (3) We propose a retrieval framework\nto integrate implicit user modeling with the interactive retrieval\nprocess, while the previous work either studies implicit user modeling\nseparately from retrieval [3] or only studies specific retrieval\nmodels for exploiting implicit feedback to better match a query with\ndocuments [23, 27, 22]. (4) We develop and evaluate a\npersonalized Web search agent with online user studies, while most existing\nwork evaluates algorithms offline without real user interactions.\nCurrently some search engines provide rudimentary\npersonalization, such as Google Personalized web search [6], which allows\nusers to explicitly describe their interests by selecting from\npredefined topics, so that those results that match their interests are\nbrought to the top, and My Yahoo! search [16], which gives users\nthe option to save web sites they like and block those they\ndislike. In contrast, UCAIR personalizes web search through implicit\nuser modeling without any additional user efforts. Furthermore, the\npersonalization of UCAIR is provided on the client side. There are\ntwo remarkable advantages on this. First, the user does not need to\nworry about the privacy infringement, which is a big concern for\npersonalized search [26]. Second, both the computation of\npersonalization and the storage of the user profile are done at the client\nside so that the server load is reduced dramatically [9].\nThere have been many works studying user query logs [1] or\nquery dynamics [13]. UCAIR makes direct use of a user\"s query\nhistory to benefit the same user immediately in the same search\nsession. UCAIR first judges whether two neighboring queries\nbelong to the same information session and if so, it selects terms from\nthe previous query to perform query expansion.\nOur query expansion approach is similar to automatic query\nexpansion [28, 15, 5], but instead of using pseudo feedback to expand\nthe query, we use user\"s implicit feedback information to expand\nthe current query. These two techniques may be combined.\n3. OPTIMIZATION IN INTERACTIVE IR\nIn interactive IR, a user interacts with the retrieval system through\nan action dialogue, in which the system responds to each user\naction with some system action. For example, the user\"s action may\nbe submitting a query and the system\"s response may be returning\na list of 10 document summaries. In general, the space of user\nactions and system responses and their granularities would depend on\nthe interface of a particular retrieval system.\nIn principle, every action of the user can potentially provide new\nevidence to help the system better infer the user\"s information need.\nThus in order to respond optimally, the system should use all the\nevidence collected so far about the user when choosing a response.\nWhen viewed in this way, most existing search engines are clearly\nnon-optimal. For example, if a user has viewed some documents on\nthe first page of search results, when the user clicks on the Next\nlink to fetch more results, an existing retrieval system would still\nreturn the next page of results retrieved based on the original query\nwithout considering the new evidence that a particular result has\nbeen viewed by the user.\n825\nWe propose to optimize retrieval performance by adapting\nsystem responses based on every action that a user has taken, and cast\nthe optimization problem as a decision task. Specifically, at any\ntime, the system would attempt to do two tasks: (1) User model\nupdating: Monitor any useful evidence from the user regarding\nhis/her information need and update the user model as soon as such\nevidence is available; (2) Improving search results: Rerank\nimmediately all the documents that the user has not yet seen, as soon\nas the user model is updated. We emphasize eager updating and\nreranking, which makes our work quite different from any existing\nwork. Below we present a formal decision theoretic framework for\noptimizing retrieval performance through implicit user modeling in\ninteractive information retrieval.\n3.1 A decision-theoretic framework\nLet A be the set of all user actions and R(a) be the set of all\npossible system responses to a user action a \u2208 A. At any time, let\nAt = (a1, ..., at) be the observed sequence of user actions so far\n(up to time point t) and Rt\u22121 = (r1, ..., rt\u22121) be the responses that\nthe system has made responding to the user actions. The system\"s\ngoal is to choose an optimal response rt \u2208 R(at) for the current\nuser action at.\nLet M be the space of all possible user models. We further\ndefine a loss function L(a, r, m) \u2208 , where a \u2208 A is a user action,\nr \u2208 R(a) is a system response, and m \u2208 M is a user model.\nL(a, r, m) encodes our decision preferences and assesses the\noptimality of responding with r when the current user model is m\nand the current user action is a. According to Bayesian decision\ntheory, the optimal decision at time t is to choose a response that\nminimizes the Bayes risk, i.e.,\nr\u2217\nt = argmin\nr\u2208R(at) M\nL(at, r, mt)P(mt|U, D, At, Rt\u22121)dmt (1)\nwhere P(mt|U, D, At, Rt\u22121) is the posterior probability of the\nuser model mt given all the observations about the user U we have\nmade up to time t.\nTo simplify the computation of Equation 1, let us assume that the\nposterior probability mass P(mt|U, D, At, Rt\u22121) is mostly\nconcentrated on the mode m\u2217\nt = argmaxmt P(mt|U, D, At, Rt\u22121).\nWe can then approximate the integral with the value of the loss\nfunction at m\u2217\nt . That is,\nr\u2217\nt \u2248 argminr\u2208R(at)L(at, r, m\u2217\nt ) (2)\nwhere m\u2217\nt = argmaxmt P(mt|U, D, At, Rt\u22121).\nLeaving aside how to define and estimate these probabilistic\nmodels and the loss function, we can see that such a decision-theoretic\nformulation suggests that, in order to choose the optimal response\nto at, the system should perform two tasks: (1) compute the\ncurrent user model and obtain m\u2217\nt based on all the useful\ninformation. (2) choose a response rt to minimize the loss function value\nL(at, rt, m\u2217\nt ). When at does not affect our belief about m\u2217\nt , the\nfirst step can be omitted and we may reuse m\u2217\nt\u22121 for m\u2217\nt .\nNote that our framework is quite general since we can\npotentially model any kind of user actions and system responses. In most\ncases, as we may expect, the system\"s response is some ranking of\ndocuments, i.e., for most actions a, R(a) consists of all the\npossible rankings of the unseen documents, and the decision problem\nboils down to choosing the best ranking of unseen documents based\non the most current user model. When a is the action of submitting\na keyword query, such a response is exactly what a current retrieval\nsystem would do. However, we can easily imagine that a more\nintelligent web search engine would respond to a user\"s clicking of\nthe Next link (to fetch more unseen results) with a more\noptimized ranking of documents based on any viewed documents in\nthe current page of results. In fact, according to our eager updating\nstrategy, we may even allow a system to respond to a user\"s clicking\nof browser\"s Back button after viewing a document in the same\nway, so that the user can maximally benefit from implicit feedback.\nThese are precisely what our UCAIR system does.\n3.2 User models\nA user model m \u2208 M represents what we know about the user\nU, so in principle, it can contain any information about the user\nthat we wish to model. We now discuss two important components\nin a user model.\nThe first component is a component model of the user\"s\ninformation need. Presumably, the most important factor affecting the\noptimality of the system\"s response is how well the response addresses\nthe user\"s information need. Indeed, at any time, we may assume\nthat the system has some belief about what the user is interested\nin, which we model through a term vector x = (x1, ..., x|V |),\nwhere V = {w1, ..., w|V |} is the set of all terms (i.e., vocabulary)\nand xi is the weight of term wi. Such a term vector is commonly\nused in information retrieval to represent both queries and\ndocuments. For example, the vector-space model, assumes that both\nthe query and the documents are represented as term vectors and\nthe score of a document with respect to a query is computed based\non the similarity between the query vector and the document\nvector [21]. In a language modeling approach, we may also regard\nthe query unigram language model [12, 29] or the relevance model\n[14] as a term vector representation of the user\"s information need.\nIntuitively, x would assign high weights to terms that characterize\nthe topics which the user is interested in.\nThe second component we may include in our user model is the\ndocuments that the user has already viewed. Obviously, even if a\ndocument is relevant, if the user has already seen the document, it\nwould not be useful to present the same document again. We thus\nintroduce another variable S \u2282 D (D is the whole set of documents\nin the collection) to denote the subset of documents in the search\nresults that the user has already seen/viewed.\nIn general, at time t, we may represent a user model as mt =\n(S, x, At, Rt\u22121), where S is the seen documents, x is the system\"s\nunderstanding of the user\"s information need, and (At, Rt\u22121)\nrepresents the user\"s interaction history. Note that an even more\ngeneral user model may also include other factors such as the user\"s\nreading level and occupation.\nIf we assume that the uncertainty of a user model mt is solely\ndue to the uncertainty of x, the computation of our current estimate\nof user model m\u2217\nt will mainly involve computing our best estimate\nof x. That is, the system would choose a response according to\nr\u2217\nt = argminr\u2208R(at)L(at, r, S, x\u2217\n, At, Rt\u22121) (3)\nwhere x\u2217\n= argmaxx P(x|U, D, At, Rt\u22121). This is the\ndecision mechanism implemented in the UCAIR system to be described\nlater. In this system, we avoided specifying the probabilistic model\nP(x|U, D, At, Rt\u22121) by computing x\u2217\ndirectly with some existing\nfeedback method.\n3.3 Loss functions\nThe exact definition of loss function L depends on the responses,\nthus it is inevitably application-specific. We now briefly discuss\nsome possibilities when the response is to rank all the unseen\ndocuments and present the top k of them. Let r = (d1, ..., dk) be the\ntop k documents, S be the set of seen documents by the user, and\nx\u2217\nbe the system\"s best guess of the user\"s information need. We\n826\nmay simply define the loss associated with r as the negative sum\nof the probability that each of the di is relevant, i.e., L(a, r, m) =\n\u2212 k\ni=1 P(relevant|di, m). Clearly, in order to minimize this\nloss function, the optimal response r would contain the k\ndocuments with the highest probability of relevance, which is intuitively\nreasonable.\nOne deficiency of this top-k loss function is that it is not\nsensitive to the internal order of the selected top k documents, so\nswitching the ranking order of a non-relevant document and a relevant one\nwould not affect the loss, which is unreasonable. To model\nranking, we can introduce a factor of the user model - the probability\nof each of the k documents being viewed by the user, P(view|di),\nand define the following ranking loss function:\nL(a, r, m) = \u2212\nk\ni=1\nP(view|di)P(relevant|di, m)\nSince in general, if di is ranked above dj (i.e., i < j), P(view|di) >\nP(view|dj), this loss function would favor a decision to rank\nrelevant documents above non-relevant ones, as otherwise, we could\nalways switch di with dj to reduce the loss value. Thus the\nsystem should simply perform a regular retrieval and rank documents\naccording to the probability of relevance [18].\nDepending on the user\"s retrieval preferences, there can be many\nother possibilities. For example, if the user does not want to see\nredundant documents, the loss function should include some\nredundancy measure on r based on the already seen documents S.\nOf course, when the response is not to choose a ranked list of\ndocuments, we would need a different loss function. We discuss\none such example that is relevant to the search agent that we\nimplement. When a user enters a query qt (current action), our search\nagent relies on some existing search engine to actually carry out\nsearch. In such a case, even though the search agent does not have\ncontrol of the retrieval algorithm, it can still attempt to optimize the\nsearch results through refining the query sent to the search engine\nand/or reranking the results obtained from the search engine. The\nloss functions for reranking are already discussed above; we now\ntake a look at the loss functions for query refinement.\nLet f be the retrieval function of the search engine that our agent\nuses so that f(q) would give us the search results using query q.\nGiven that the current action of the user is entering a query qt (i.e.,\nat = qt), our response would be f(q) for some q. Since we have\nno choice of f, our decision is to choose a good q. Formally,\nr\u2217\nt = argminrt L(a, rt, m)\n= argminf(q)L(a, f(q), m)\n= f(argminqL(qt, f(q), m))\nwhich shows that our goal is to find q\u2217\n= argminqL(qt, f(q), m),\ni.e., an optimal query that would give us the best f(q). A different\nchoice of loss function L(qt, f(q), m) would lead to a different\nquery refinement strategy. In UCAIR, we heuristically compute q\u2217\nby expanding qt with terms extracted from rt\u22121 whenever qt\u22121 and\nqt have high similarity. Note that rt\u22121 and qt\u22121 are contained in\nm as part of the user\"s interaction history.\n3.4 Implicit user modeling\nImplicit user modeling is captured in our framework through\nthe computation of x\u2217\n= argmaxx P(x|U, D, At, Rt\u22121), i.e., the\nsystem\"s current belief of what the user\"s information need is. Here\nagain there may be many possibilities, leading to different\nalgorithms for implicit user modeling. We now discuss a few of them.\nFirst, when two consecutive queries are related, the previous\nquery can be exploited to enrich the current query and provide more\nsearch context to help disambiguation. For this purpose, instead of\nperforming query expansion as we did in the previous section, we\ncould also compute an updated x\u2217\nbased on the previous query and\nretrieval results. The computed new user model can then be used to\nrank the documents with a standard information retrieval model.\nSecond, we can also infer a user\"s interest based on the\nsummaries of the viewed documents. When a user is presented with a\nlist of summaries of top ranked documents, if the user chooses to\nskip the first n documents and to view the (n+1)-th document, we\nmay infer that the user is not interested in the displayed summaries\nfor the first n documents, but is attracted by the displayed summary\nof the (n + 1)-th document. We can thus use these summaries as\nnegative and positive examples to learn a more accurate user model\nx\u2217\n. Here many standard relevance feedback techniques can be\nexploited [19, 20]. Note that we should use the displayed summaries,\nas opposed to the actual contents of those documents, since it is\npossible that the displayed summary of the viewed document is\nrelevant, but the document content is actually not. Similarly, a\ndisplayed summary may mislead a user to skip a relevant document.\nInferring user models based on such displayed information, rather\nthan the actual content of a document is an important difference\nbetween UCAIR and some other similar systems.\nIn UCAIR, both of these strategies for inferring an implicit user\nmodel are implemented.\n4. UCAIR: A PERSONALIZED\nSEARCH AGENT\n4.1 Design\nIn this section, we present a client-side web search agent called\nUCAIR, in which we implement some of the methods discussed\nin the previous section for performing personalized search through\nimplicit user modeling. UCAIR is a web browser plug-in 1\nthat\nacts as a proxy for web search engines. Currently, it is only\nimplemented for Internet Explorer and Google, but it is a matter of\nengineering to make it run on other web browsers and interact with\nother search engines.\nThe issue of privacy is a primary obstacle for deploying any real\nworld applications involving serious user modeling, such as\npersonalized search. For this reason, UCAIR is strictly running as\na client-side search agent, as opposed to a server-side application.\nThis way, the captured user information always resides on the\ncomputer that the user is using, thus the user does not need to release\nany information to the outside. Client-side personalization also\nallows the system to easily observe a lot of user information that may\nnot be easily available to a server. Furthermore, performing\npersonalized search on the client-side is more scalable than on the\nserverside, since the overhead of computation and storage is distributed\namong clients.\nAs shown in Figure 1, the UCAIR toolbar has 3 major\ncomponents: (1) The (implicit) user modeling module captures a user\"s\nsearch context and history information, including the submitted\nqueries and any clicked search results and infers search session\nboundaries. (2) The query modification module selectively\nimproves the query formulation according to the current user model.\n(3) The result re-ranking module immediately re-ranks any unseen\nsearch results whenever the user model is updated.\nIn UCAIR, we consider four basic user actions: (1) submitting a\nkeyword query; (2) viewing a document; (3) clicking the Back\nbutton; (4) clicking the Next link on a result page. For each\nof these four actions, the system responds with, respectively, (1)\n1\nUCAIR is available at: http://sifaka.cs.uiuc.edu/ir/ucair/download.html\n827\nSearch\nEngine\n(e.g.,\nGoogle)\nSearch History Log\n(e.g.,past queries,\nclicked results)\nQuery\nModification\nResult\nRe-Ranking\nUser\nModeling\nResult Buffer\nUCAIR\nUserquery\nresults\nclickthrough\u2026\nFigure 1: UCAIR architecture\ngenerating a ranked list of results by sending a possibly expanded\nquery to a search engine; (2) updating the information need model\nx; (3) reranking the unseen results on the current result page based\non the current model x; and (4) reranking the unseen pages and\ngenerating the next page of results based on the current model x.\nBehind these responses, there are three basic tasks: (1) Decide\nwhether the previous query is related to the current query and if so\nexpand the current query with useful terms from the previous query\nor the results of the previous query. (2) Update the information\nneed model x based on a newly clicked document summary. (3)\nRerank a set of unseen documents based on the current model x.\nBelow we describe our algorithms for each of them.\n4.2 Session boundary detection and query\nexpansion\nTo effectively exploit previous queries and their corresponding\nclickthrough information, UCAIR needs to judge whether two\nadjacent queries belong to the same search session (i.e., detect\nsession boundaries). Existing work on session boundary detection is\nmostly in the context of web log analysis (e.g., [8]), and uses\nstatistical information rather than textual features. Since our\nclientside agent does not have access to server query logs, we make\nsession boundary decisions based on textual similarity between two\nqueries. Because related queries do not necessarily share the same\nwords (e.g., java island and travel Indonesia), it is insufficient\nto use only query text. Therefore we use the search results of the\ntwo queries to help decide whether they are topically related. For\nexample, for the above queries java island and travel\nIndonesia\", the words java, bali, island, indonesia and travel\nmay occur frequently in both queries\" search results, yielding a high\nsimilarity score.\nWe only use the titles and summaries of the search results to\ncalculate the similarity since they are available in the retrieved search\nresult page and fetching the full text of every result page would\nsignificantly slow down the process. To compensate for the terseness\nof titles and summaries, we retrieve more results than a user would\nnormally view for the purpose of detecting session boundaries\n(typically 50 results).\nThe similarity between the previous query q and the current\nquery q is computed as follows. Let {s1, s2, . . . , sn } and\n{s1, s2, . . . , sn} be the result sets for the two queries. We use\nthe pivoted normalization TF-IDF weighting formula [24] to\ncompute a term weight vector si for each result si. We define the\naverage result savg to be the centroid of all the result vectors, i.e.,\n(s1 + s2 + . . . + sn)/n. The cosine similarity between the two\naverage results is calculated as\ns avg \u00b7 savg/ s\n2\navg \u00b7 s2\navg\nIf the similarity value exceeds a predefined threshold, the two queries\nwill be considered to be in the same information session.\nIf the previous query and the current query are found to belong\nto the same search session, UCAIR would attempt to expand the\ncurrent query with terms from the previous query and its search\nresults. Specifically, for each term in the previous query or the\ncorresponding search results, if its frequency in the results of the\ncurrent query is greater than a preset threshold (e.g. 5 results out\nof 50), the term would be added to the current query to form an\nexpanded query. In this case, UCAIR would send this expanded\nquery rather than the original one to the search engine and return\nthe results corresponding to the expanded query. Currently, UCAIR\nonly uses the immediate preceding query for query expansion; in\nprinciple, we could exploit all related past queries.\n4.3 Information need model updating\nSuppose at time t, we have observed that the user has viewed\nk documents whose summaries are s1, ..., sk. We update our user\nmodel by computing a new information need vector with a standard\nfeedback method in information retrieval (i.e., Rocchio [19]).\nAccording to the vector space retrieval model, each clicked summary\nsi can be represented by a term weight vector si with each term\nweighted by a TF-IDF weighting formula [21]. Rocchio computes\nthe centroid vector of all the summaries and interpolates it with the\noriginal query vector to obtain an updated term vector. That is,\nx = \u03b1q + (1 \u2212 \u03b1)\n1\nk\nk\ni=1\nsi\nwhere q is the query vector, k is the number of summaries the user\nclicks immediately following the current query and \u03b1 is a parameter\nthat controls the influence of the clicked summaries on the inferred\ninformation need model. In our experiments, \u03b1 is set to 0.5. Note\nthat we update the information need model whenever the user views\na document.\n4.4 Result reranking\nIn general, we want to rerank all the unseen results as soon as the\nuser model is updated. Currently, UCAIR implements reranking in\ntwo cases, corresponding to the user clicking the Back button\nand Next link in the Internet Explorer. In both cases, the current\n(updated) user model would be used to rerank the unseen results so\nthat the user would see improved search results immediately.\nTo rerank any unseen document summaries, UCAIR uses the\nstandard vector space retrieval model and scores each summary\nbased on the similarity of the result and the current user information\nneed vector x [21]. Since implicit feedback is not completely\nreliable, we bring up only a small number (e.g. 5) of highest reranked\nresults to be followed by any originally high ranked results.\n828\nGoogle result (user query = java map) UCAIR result (user query =java map)\nprevious query = travel Indonesia previous query = hashtable\nexpanded user query = java map Indonesia expanded user query = java map class\n1 Java map projections of the world ... Lonely Planet - Indonesia Map Map (Java 2 Platform SE v1.4.2)\nwww.btinternet.com/ se16/js/mapproj.htm www.lonelyplanet.com/mapshells/... java.sun.com/j2se/1.4.2/docs/...\n2 Java map projections of the world ... INDONESIA TOURISM : CENTRAL JAVA - MAP Java 2 Platform SE v1.3.1: Interface Map\nwww.btinternet.com/ se16/js/oldmapproj.htm www.indonesia-tourism.com/... java.sun.com/j2se/1.3/docs/api/java/...\n3 Java Map INDONESIA TOURISM : WEST JAVA - MAP An Introduction to Java Map Collection Classes\njava.sun.com/developer/... www.indonesia-tourism.com/ ... www.oracle.com/technology/...\n4 Java Technology Concept Map IndoStreets - Java Map An Introduction to Java Map Collection Classes\njava.sun.com/developer/onlineTraining/... www.indostreets.com/maps/java/ www.theserverside.com/news/...\n5 Science@NASA Home Indonesia Regions and Islands Maps, Bali, Java, ... Koders - Mappings.java\nscience.nasa.gov/Realtime/... www.maps2anywhere.com/Maps/... www.koders.com/java/\n6 An Introduction to Java Map Collection Classes Indonesia City Street Map,... Hibernate simplifies inheritance mapping\nwww.oracle.com/technology/... www.maps2anywhere.com/Maps/... www.ibm.com/developerworks/java/...\n7 Lonely Planet - Java Map Maps Of Indonesia tmap 30.map Class Hierarchy\nwww.lonelyplanet.com/mapshells/ www.embassyworld.com/maps/... tmap.pmel.noaa.gov/...\n8 ONJava.com: Java API Map Maps of Indonesia by Peter Loud Class Scope\nwww.onjava.com/pub/a/onjava/api map/ users.powernet.co.uk/... jalbum.net/api/se/datadosen/util/Scope.html\n9 GTA San Andreas : Sam Maps of Indonesia by Peter Loud Class PrintSafeHashMap\nwww.gtasanandreas.net/sam/ users.powernet.co.uk/mkmarina/indonesia/ jalbum.net/api/se/datadosen/...\n10 INDONESIA TOURISM : WEST JAVA - MAP indonesiaphoto.com Java Pro - Union and Vertical Mapping of Classes\nwww.indonesia-tourism.com/... www.indonesiaphoto.com/... www.fawcette.com/javapro/...\nTable 1: Sample results of query expansion\n5. EVALUATION OF UCAIR\nWe now present some results on evaluating the two major UCAIR\nfunctions: selective query expansion and result reranking based on\nuser clickthrough data.\n5.1 Sample results\nThe query expansion strategy implemented in UCAIR is\nintentionally conservative to avoid misinterpretation of implicit user\nmodels. In practice, whenever it chooses to expand the query, the\nexpansion usually makes sense. In Table 1, we show how UCAIR can\nsuccessfully distinguish two different search contexts for the query\njava map, corresponding to two different previous queries (i.e.,\ntravel Indonesia vs. hashtable). Due to implicit user modeling,\nUCAIR intelligently figures out to add Indonesia and class,\nrespectively, to the user\"s query java map, which would\notherwise be ambiguous as shown in the original results from Google\non March 21, 2005. UCAIR\"s results are much more accurate than\nGoogle\"s results and reflect personalization in search.\nThe eager implicit feedback component is designed to\nimmediately respond to a user\"s activity such as viewing a document. In\nFigure 2, we show how UCAIR can successfully disambiguate an\nambiguous query jaguar by exploiting a viewed document\nsummary. In this case, the initial retrieval results using jaguar (shown\non the left side) contain two results about the Jaguar cars followed\nby two results about the Jaguar software. However, after the user\nviews the web page content of the second result (about Jaguar\ncar) and returns to the search result page by clicking Back\nbutton, UCAIR automatically nominates two new search results about\nJaguar cars (shown on the right side), while the original two results\nabout Jaguar software are pushed down on the list (unseen from the\npicture).\n5.2 Quantitative evaluation\nTo further evaluate UCAIR quantitatively, we conduct a user\nstudy on the effectiveness of the eager implicit feedback\ncomponent. It is a challenge to quantitatively evaluate the potential\nperformance improvement of our proposed model and UCAIR over\nGoogle in an unbiased way [7]. Here, we design a user study,\nin which participants would do normal web search and judge a\nrandomly and anonymously mixed set of results from Google and\nUCAIR at the end of the search session; participants do not know\nwhether a result comes from Google or UCAIR.\nWe recruited 6 graduate students for this user study, who have\ndifferent backgrounds (3 computer science, 2 biology, and 1\nchem<top>\n<num> Number: 716\n<title> Spammer arrest sue\n<desc> Description: Have any spammers\nbeen arrested or sued for sending unsolicited\ne-mail?\n<narr> Narrative: Instances of arrests,\nprosecutions, convictions, and punishments\nof spammers, and lawsuits against them are\nrelevant. Documents which describe laws to\nlimit spam without giving details of lawsuits\nor criminal trials are not relevant.\n</top>\nFigure 3: An example of TREC query topic, expressed in a\nform which might be given to a human assistant or librarian\nistry). We use query topics from TREC 2\n2004 Terabyte track [2]\nand TREC 2003 Web track [4] topic distillation task in the way to\nbe described below.\nAn example topic from TREC 2004 Terabyte track appears in\nFigure 3. The title is a short phrase and may be used as a query\nto the retrieval system. The description field provides a slightly\nlonger statement of the topic requirement, usually expressed as a\nsingle complete sentence or question. Finally the narrative supplies\nadditional information necessary to fully specify the requirement,\nexpressed in the form of a short paragraph.\nInitially, each participant would browse 50 topics either from\nTerabyte track or Web track and pick 5 or 7 most interesting topics.\nFor each picked topic, the participant would essentially do the\nnormal web search using UCAIR to find many relevant web pages by\nusing the title of the query topic as the initial keyword query.\nDuring this process, the participant may view the search results and\npossibly click on some interesting ones to view the web pages, just\nas in a normal web search. There is no requirement or restriction\non how many queries the participant must submit or when the\nparticipant should stop the search for one topic. When the participant\nplans to change the search topic, he/she will simply press a button\n2\nText REtrieval Conference: http://trec.nist.gov/\n829\nFigure 2: Screen shots for result reranking\nto evaluate the search results before actually switching to the next\ntopic.\nAt the time of evaluation, 30 top ranked results from Google and\nUCAIR (some are overlapping) are randomly mixed together so\nthat the participant would not know whether a result comes from\nGoogle or UCAIR. The participant would then judge the relevance\nof these results. We measure precision at top n (n = 5, 10, 20, 30)\ndocuments of Google and UCAIR. We also evaluate precisions at\ndifferent recall levels.\nAltogether, 368 documents judged as relevant from Google search\nresults and 429 documents judged as relevant from UCAIR by\nparticipants. Scatter plots of precision at top 10 and top 20 documents\nare shown in Figure 4 and Figure 5 respectively (The scatter plot\nof precision at top 30 documents is very similar to precision at top\n20 documents). Each point of the scatter plots represents the\nprecisions of Google and UCAIR on one query topic.\nTable 2 shows the average precision at top n documents among\n32 topics. From Figure 4, Figure 5 and Table 2, we see that the\nsearch results from UCAIR are consistently better than those from\nGoogle by all the measures. Moreover, the performance\nimprovement is more dramatic for precision at top 20 documents than that\nat precision at top 10 documents. One explanation for this is that\nthe more interaction the user has with the system, the more\nclickthrough data UCAIR can be expected to collect. Thus the retrieval\nsystem can build more precise implicit user models, which lead to\nbetter retrieval accuracy.\nRanking Method prec@5 prec@10 prec@20 prec@30\nGoogle 0.538 0.472 0.377 0.308\nUCAIR 0.581 0.556 0.453 0.375\nImprovement 8.0% 17.8% 20.2% 21.8%\nTable 2: Table of average precision at top n documents for 32\nquery topics\nThe plot in Figure 6 shows the precision-recall curves for UCAIR\nand Google, where it is clearly seen that the performance of UCAIR\n0 0.2 0.4 0.6 0.8 1\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nUCAIR prec@10\nGoogleprec@10\nScatterplot of Precision at Top 10 Documents\nFigure 4: Precision at top 10 documents of UCAIR and Google\nis consistently and considerably better than that of Google at all\nlevels of recall.\n6. CONCLUSIONS\nIn this paper, we studied how to exploit implicit user modeling to\nintelligently personalize information retrieval and improve search\naccuracy. Unlike most previous work, we emphasize the use of\nimmediate search context and implicit feedback information as well\nas eager updating of search results to maximally benefit a user. We\npresented a decision-theoretic framework for optimizing\ninteractive information retrieval based on eager user model updating, in\nwhich the system responds to every action of the user by\nchoosing a system action to optimize a utility function. We further\npropose specific techniques to capture and exploit two types of implicit\nfeedback information: (1) identifying related immediately\npreceding query and using the query and the corresponding search results\nto select appropriate terms to expand the current query, and (2)\nexploiting the viewed document summaries to immediately rerank\nany documents that have not yet been seen by the user. Using these\ntechniques, we develop a client-side web search agent (UCAIR)\non top of a popular search engine (Google). Experiments on web\nsearch show that our search agent can improve search accuracy over\n830\n0 0.2 0.4 0.6 0.8 1\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nUCAIR prec@20\nGoogleprec@20\nScatterplot of Precision at Top 20 documents\nFigure 5: Precision at top 20 documents of UCAIR and Google\n0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1\n0.4\n0.45\n0.5\n0.55\n0.6\n0.65\n0.7\n0.75\n0.8\n0.85\n0.9\nrecall\nprecision\nPrecision\u2212Recall curves\nGoogle Result\nUCAIR Result\nFigure 6: Precision at top 20 result of UCAIR and Google\nGoogle. Since the implicit information we exploit already naturally\nexists through user interactions, the user does not need to make any\nextra effort. The developed search agent thus can improve\nexisting web search performance without any additional effort from the\nuser.\n7. ACKNOWLEDGEMENT\nWe thank the six participants of our evaluation experiments. This\nwork was supported in part by the National Science Foundation\ngrants IIS-0347933 and IIS-0428472.\n8. REFERENCES\n[1] S. M. Beitzel, E. C. Jensen, A. Chowdhury, D. Grossman,\nand O. Frieder. Hourly analysis of a very large topically\ncategorized web query log. In Proceedings of SIGIR 2004,\npages 321-328, 2004.\n[2] C. Clarke, N. Craswell, and I. Soboroff. Overview of the\nTREC 2004 terabyte track. In Proceedings of TREC 2004,\n2004.\n[3] M. Claypool, P. Le, M. Waseda, and D. Brown. Implicit\ninterest indicators. In Proceedings of Intelligent User\nInterfaces 2001, pages 33-40, 2001.\n[4] N. Craswell, D. Hawking, R. Wilkinson, and M. Wu.\nOverview of the TREC 2003 web track. In Proceedings of\nTREC 2003, 2003.\n[5] W. B. Croft, S. Cronen-Townsend, and V. Larvrenko.\nRelevance feedback and personalization: A language\nmodeling perspective. In Proeedings of Second DELOS\nWorkshop: Personalisation and Recommender Systems in\nDigital Libraries, 2001.\n[6] Google Personalized. http://labs.google.com/personalized.\n[7] D. Hawking, N. Craswell, P. B. Thistlewaite, and D. Harman.\nResults and challenges in web search evaluation. Computer\nNetworks, 31(11-16):1321-1330, 1999.\n[8] X. Huang, F. Peng, A. An, and D. Schuurmans. Dynamic\nweb log session identification with statistical language\nmodels. Journal of the American Society for Information\nScience and Technology, 55(14):1290-1303, 2004.\n[9] G. Jeh and J. Widom. Scaling personalized web search. In\nProceedings of WWW 2003, pages 271-279, 2003.\n[10] T. Joachims. Optimizing search engines using clickthrough\ndata. In Proceedings of SIGKDD 2002, pages 133-142,\n2002.\n[11] D. Kelly and J. Teevan. Implicit feedback for inferring user\npreference: A bibliography. SIGIR Forum, 37(2):18-28,\n2003.\n[12] J. Lafferty and C. Zhai. 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Prentice-Hall Inc.,\n1971.\n[20] G. Salton and C. Buckley. Improving retrieval performance\nby retrieval feedback. Journal of the American Society for\nInformation Science, 41(4):288-297, 1990.\n[21] G. Salton and M. J. McGill. Introduction to Modern\nInformation Retrieval. McGraw-Hill, 1983.\n[22] X. Shen, B. Tan, and C. Zhai. Context-sensitive information\nretrieval using implicit feedback. In Proceedings of SIGIR\n2005, pages 43-50, 2005.\n[23] X. Shen and C. Zhai. Exploiting query history for document\nranking in interactive information retrieval (Poster). In\nProceedings of SIGIR 2003, pages 377-378, 2003.\n[24] A. Singhal. Modern information retrieval: A brief overview.\nBulletin of the IEEE Computer Society Technical Committee\non Data Engineering, 24(4):35-43, 2001.\n[25] K. Sugiyama, K. Hatano, and M. Yoshikawa. Adaptive web\nsearch based on user profile constructed without any effort\nfrom users. In Proceedings of WWW 2004, pages 675-684,\n2004.\n[26] E. Volokh. Personalization and privacy. Communications of\nthe ACM, 43(8):84-88, 2000.\n[27] R. W. White, J. M. Jose, C. J. van Rijsbergen, and\nI. Ruthven. A simulated study of implicit feedback models.\nIn Proceedings of ECIR 2004, pages 311-326, 2004.\n[28] J. Xu and W. B. Croft. Query expansion using local and\nglobal document analysis. In Proceedings of SIGIR 1996,\npages 4-11, 1996.\n[29] C. Zhai and J. Lafferty. Model-based feedback in KL\ndivergence retrieval model. In Proceedings of the CIKM\n2001, pages 403-410, 2001.\n831", "keywords": "interactive ir;personalize search;user model;interactive retrieval;query expansion;personalized web search;user-centered adaptive information retrieval;personalize information retrieval;implicit feedback;search accuracy;implicit user modeling;information retrieval system;retrieval performance;query refinement"}
{"name": "train_H-63", "title": "Location based Indexing Scheme for DAYS", "abstract": "Data dissemination through wireless channels for broadcasting information to consumers is becoming quite common. Many dissemination schemes have been proposed but most of them push data to wireless channels for general consumption. Push based broadcast [1] is essentially asymmetric, i.e., the volume of data being higher from the server to the users than from the users back to the server. Push based scheme requires some indexing which indicates when the data will be broadcast and its position in the broadcast. Access latency and tuning time are the two main parameters which may be used to evaluate an indexing scheme. Two of the important indexing schemes proposed earlier were tree based and the exponential indexing schemes. None of these schemes were able to address the requirements of location dependent data (LDD) which is highly desirable feature of data dissemination. In this paper, we discuss the broadcast of LDD in our project DAta in Your Space (DAYS), and propose a scheme for indexing LDD. We argue that this scheme, when applied to LDD, significantly improves performance in terms of tuning time over the above mentioned schemes. We prove our argument with the help of simulation results.", "fulltext": "1. INTRODUCTION\nWireless data dissemination is an economical and efficient\nway to make desired data available to a large number of mobile or\nstatic users. The mode of data transfer is essentially asymmetric,\nthat is, the capacity of the transfer of data (downstream\ncommunication) from the server to the client (mobile user) is\nsignificantly larger than the client or mobile user to the server\n(upstream communication). The effectiveness of a data\ndissemination system is judged by its ability to provide user the\nrequired data at anywhere and at anytime. One of the best ways to\naccomplish this is through the dissemination of highly\npersonalized Location Based Services (LBS) which allows users\nto access personalized location dependent data. An example\nwould be someone using their mobile device to search for a\nvegetarian restaurant. The LBS application would interact with\nother location technology components or use the mobile user's\ninput to determine the user's location and download the\ninformation about the restaurants in proximity to the user by\ntuning into the wireless channel which is disseminating LDD.\nWe see a limited deployment of LBS by some service\nproviders. But there are every indications that with time some of\nthe complex technical problems such as uniform location\nframework, calculating and tracking locations in all types of\nplaces, positioning in various environments, innovative location\napplications, etc., will be resolved and LBS will become a\ncommon facility and will help to improve market productivity and\ncustomer comfort. In our project called DAYS, we use wireless\ndata broadcast mechanism to push LDD to users and mobile users\nmonitor and tune the channel to find and download the required\ndata. A simple broadcast, however, is likely to cause significant\nperformance degradation in the energy constrained mobile devices\nand a common solution to this problem is the use of efficient air\nindexing. The indexing approach stores control information which\ntells the user about the data location in the broadcast and how and\nwhen he could access it. A mobile user, thus, has some free time\nto go into the doze mode which conserves valuable power. It also\nallows the user to personalize his own mobile device by\nselectively tuning to the information of his choice.\nAccess efficiency and energy conservation are the two issues\nwhich are significant for data broadcast systems. Access efficiency\nrefers to the latency experienced when a request is initiated till the\nresponse is received. Energy conservation [7, 10] refers to the\nefficient use of the limited energy of the mobile device in\naccessing broadcast data. Two parameters that affect these are the\ntuning time and the access latency. Tuning time refers to the time\nduring which the mobile unit (MU) remains in active state to tune\nthe channel and download its required data. It can also be defined\nas the number of buckets tuned by the mobile device in active\nstate to get its required data. Access latency may be defined as the\ntime elapsed since a request has been issued till the response has\nbeen received.\n1\nThis research was supported by a grant from NSF IIS-0209170.\nSeveral indexing schemes have been proposed in the past and\nthe prominent among them are the tree based and the exponential\nindexing schemes [17]. The main disadvantages of the tree based\nschemes are that they are based on centralized tree structures. To\nstart a search, the MU has to wait until it reaches the root of the\nnext broadcast tree. This significantly affects the tuning time of\nthe mobile unit. The exponential schemes facilitate index\nreplication by sharing links in different search trees. For\nbroadcasts with large number of pages, the exponential scheme\nhas been shown to perform similarly as the tree based schemes in\nterms of access latency. Also, the average length of broadcast\nincreases due to the index replication and this may cause\nsignificant increase in the access latency. None of the above\nindexing schemes is equally effective in broadcasting location\ndependent data. In addition to providing low latency, they lack\nproperties which are used to address LDD issues. We propose an\nindexing scheme in DAYS which takes care of some these\nproblems. We show with simulation results that our scheme\noutperforms some of the earlier indexing schemes for\nbroadcasting LDD in terms of tuning time.\nThe rest of the paper is presented as follows. In section 2, we\ndiscuss previous work related to indexing of broadcast data.\nSection 3 describes our DAYS architecture. Location dependent\ndata, its generation and subsequent broadcast is presented in\nsection 4. Section 5 discusses our indexing scheme in detail.\nSimulation of our scheme and its performance evaluation is\npresented in section 6. Section 7 concludes the paper and\nmentions future related work.\n2. PREVIOUS WORK\nSeveral disk-based indexing techniques have been used for air\nindexing. Imielinski et al. [5, 6] applied the B+ index tree, where\nthe leaf nodes store the arrival times of the data items. The\ndistributed indexing method was proposed to efficiently replicate\nand distribute the index tree in a broadcast. Specifically, the index\ntree is divided into a replicated part and a non replicated part.\nEach broadcast consists of the replicated part and the\nnonreplicated part that indexes the data items immediately following\nit. As such, each node in the non-replicated part appears only once\nin a broadcast and, hence, reduces the replication cost and access\nlatency while achieving a good tuning time. Chen et al. [2] and\nShivakumar et al. [8] considered unbalanced tree structures to\noptimize energy consumption for non-uniform data access. These\nstructures minimize the average index search cost by reducing the\nnumber of index searches for hot data at the expense of spending\nmore on cold data. Tan and Yu discussed data and index\norganization under skewed broadcast Hashing and signature\nmethods have also been suggested for wireless broadcast that\nsupports equality queries [9]. A flexible indexing method was\nproposed in [5]. The flexible index first sorts the data items in\nascending (or descending) order of the search key values and then\ndivides them into p segments. The first bucket in each data\nsegment contains a control index, which is a binary index\nmapping a given key value to the segment containing that key,\nand a local index, which is an m-entry index mapping a given key\nvalue to the buckets within the current segment. By tuning the\nparameters of p and m, mobile clients can achieve either a good\ntuning time or good access latency. Another indexing technique\nproposed is the exponential indexing scheme [17]. In this scheme,\na parameterized index, called the exponential index is used to\noptimize the access latency or the tuning time. It facilitates index\nreplication by linking different search trees. All of the above\nmentioned schemes have been applied to data which are non\nrelated to each other. These non related data may be clustered or\nnon clustered. However, none of them has specifically addressed\nthe requirements of LDD. Location dependent data are data which\nare associated with a location. Presently there are several\napplications that deal with LDD [13, 16]. Almost all of them\ndepict LDD with the help of hierarchical structures [3, 4]. This is\nbased on the containment property of location dependent data.\nThe Containment property helps determining relative position of\nan object by defining or identifying locations that contains those\nobjects. The subordinate locations are hierarchically related to\neach other. Thus, Containment property limits the range of\navailability or operation of a service. We use this containment\nproperty in our indexing scheme to index LDD.\n3. DAYS ARCHITECTURE\nDAYS has been conceptualized to disseminate topical and\nnontopical data to users in a local broadcast space and to accept\nqueries from individual users globally. Topical data, for example,\nweather information, traffic information, stock information, etc.,\nconstantly changes over time. Non topical data such as hotel,\nrestaurant, real estate prices, etc., do not change so often. Thus,\nwe envision the presence of two types of data distribution: In the\nfirst case, server pushes data to local users through wireless\nchannels. The other case deals with the server sending results of\nuser queries through downlink wireless channels. Technically, we\nsee the presence of two types of queues in the pull based data\naccess. One is a heavily loaded queue containing globally\nuploaded queries. The other is a comparatively lightly loaded\nqueue consisting of locally uploaded queries. The DAYS\narchitecture [12] as shown in figure 1 consists of a Data Server,\nBroadcast Scheduler, DAYS Coordinator, Network of LEO\nsatellites for global data delivery and a Local broadcast space.\nData is pushed into the local broadcast space so that users may\ntune into the wireless channels to access the data. The local\nbroadcast space consists of a broadcast tower, mobile units and a\nnetwork of data staging machines called the surrogates. Data\nstaging in surrogates has been earlier investigated as a successful\ntechnique [12, 15] to cache users' related data. We believe that\ndata staging can be used to drastically reduce the latency time for\nboth the local broadcast data as well as global responses. Query\nrequest in the surrogates may subsequently be used to generate the\npopularity patterns which ultimately decide the broadcast\nschedule [12].\n18\nPopularity\nFeedback from\nSurrogates for\nBroadcast\nScheduler\nLocal Broadcast Space\nBroadcast Tower\nSurrogateMU\nMU\nMU\nMU\nData ServerBroadcast schedulerDAYS Coordinator\nLocal downlink\nchannel\nGlobal downlink\nchannel\nPull request queue\nGlobal request queue\nLocal request queue Location based index\nStarbucks\nPlaza\nKansas\nCity\nFigure 1. DAYS Architecture Figure 2. Location Structure ofStarbucks, Plaza\n4. LOCATION DEPENDENT DATA (LDD)\nWe argue that incorporating location information in wireless data\nbroadcast can significantly decrease the access latency. This\nproperty becomes highly useful for mobile unit which has limited\nstorage and processing capability. There are a variety of\napplications to obtain information about traffic, restaurant and\nhotel booking, fast food, gas stations, post office, grocery stores,\netc. If these applications are coupled with location information,\nthen the search will be fast and highly cost effective. An important\nproperty of the locations is Containment which helps to determine\nthe relative location of an object with respect to its parent that\ncontains the object. Thus, Containment limits the range of\navailability of a data. We use this property in our indexing\nscheme. The database contains the broadcast contents which are\nconverted into LDD [14] by associating them with respective\nlocations so that it can be broadcasted in a clustered manner. The\nclustering of LDD helps the user to locate information efficiently\nand supports containment property. We present an example to\njustify our proposition.\nExample: Suppose a user issues query Starbucks Coffee in\nPlaza please. to access information about the Plaza branch of\nStarbucks Coffee in Kansas City. In the case of location\nindependent set up the system will list all Starbucks coffee shops\nin Kansas City area. It is obvious that such responses will\nincrease access latency and are not desirable. These can be\nmanaged efficiently if the server has location dependent data, i.e.,\na mapping between a Starbucks coffee shop data and its physical\nlocation. Also, for a query including range of locations of\nStarbucks, a single query requesting locations for the entire\nregion of Kansas City, as shown in Figure 2, will suffice. This\nwill save enormous amount of bandwidth by decreasing the\nnumber of messages and at the same time will be helpful in\npreventing the scalability bottleneck in highly populated area.\n4.1 Mapping Function for LDD\nThe example justifies the need for a mapping function to process\nlocation dependent queries. This will be especially important for\npull based queries across the globe for which the reply could be\ncomposed for different parts of the world. The mapping function\nis necessary to construct the broadcast schedule.\nWe define Global Property Set (GPS) [11], Information Content\n(IC) set, and Location Hierarchy (LH) set where IC \u2286 GPS and\nLH \u2286 GPS to develop a mapping function. LH = {l1, l2, l3\u2026,lk}\nwhere li represent locations in the location tree and IC = {ic1, ic2,\nic3,\u2026,icn} where ici represent information type. For example, if\nwe have traffic, weather, and stock information are in broadcast\nthen IC = {ictraffic, icweather, and icstock}. The mapping scheme must\nbe able to identify and select an IC member and a LH node for (a)\ncorrect association, (b) granularity match, (c) and termination\ncondition. For example, weather \u2208 IC could be associated with a\ncountry or a state or a city or a town of LH. The granularity match\nbetween the weather and a LH node is as per user requirement.\nThus, with a coarse granularity weather information is associated\nwith a country to get country\"s weather and with town in a finer\ngranularity. If a town is the finest granularity, then it defines the\nterminal condition for association between IC and LH for weather.\nThis means that a user cannot get weather information about\nsubdivision of a town. In reality weather of a subdivision does\nnot make any sense.\nWe develop a simple heuristic mapping approach scheme based\non user requirement. Let IC = {m1, m2,m3 .,..., mk}, where mi\nrepresent its element and let LH = {n1, n2, n3, ..., nl}, where ni\nrepresents LH\"s member. We define GPS for IC (GPSIC) \u2286 GPS\nand for LH (GPSLH) \u2286 GPS as GPSIC = {P1, P2,\u2026, Pn}, where\nP1, P2, P3,\u2026, Pn are properties of its members and GPSLH = {Q1,\nQ2,\u2026, Qm} where Q1, Q2,\u2026, Qm are properties of its members.\nThe properties of a particular member of IC are a subset of\nGPSIC. It is generally true that (property set (mi\u2208 IC) \u222a property\nset (mj\u2208 IC)) \u2260 \u2205, however, there may be cases where the\nintersection is not null. For example, stock \u2208 IC and movie \u2208 IC\nrating do not have any property in common. We assume that any\ntwo or more members of IC have at least one common\ngeographical property (i.e. location) because DAYS broadcasts\ninformation about those categories, which are closely tied with a\nlocation. For example, stock of a company is related to a country,\nweather is related to a city or state, etc.\nWe define the property subset of mi\u2208 IC as PSm\ni\n\u2200 mi \u2208 IC and\nPSm\ni\n= {P1, P2, ..., Pr} where r \u2264 n. \u2200 Pr {Pr \u2208 PSm\ni\n\u2192 Pr\u2208\nGPSIC} which implies that \u2200 i, PSm\ni\n\u2286 GPSIC. The geographical\nproperties of this set are indicative of whether mi \u2208 IC can be\nmapped to only a single granularity level (i.e. a single location) in\nLH or a multiple granularity levels (i.e. more than one nodes in\n19\nthe hierarchy) in LH. How many and which granularity levels\nshould a mi map to, depends upon the level at which the service\nprovider wants to provide information about the mi in question.\nSimilarly we define a property subset of LH members as PSn\nj\n\u2200 nj\n\u2208 LH which can be written as PSn\nj\n={Q1, Q2, Q3, \u2026, Qs} where s \u2264\nm. In addition, \u2200 Qs {Qs\u2208 PSn\nj\n\u2192 Qs\u2208 GPSLH} which implies that\n\u2200j, PSn\nj\n\u2286 GPSLH.\nThe process of mapping from IC to LH is then identifying for\nsome mx\u2208 IC one or more ny\u2208 LH such that PSmx \u2229 PSnv \u2260 \u03c6.\nThis means that when mx maps to ny and all children of ny if mx\ncan map to multiple granularity levels or mx maps only to ny if mx\ncan map to a single granularity level.\nWe assume that new members can join and old member can leave\nIC or LH any time. The deletion of members from the IC space is\nsimple but addition of members to the IC space is more restrictive.\nIf we want to add a new member to the IC space, then we first\ndefine a property set for the new member: PSmnew_m ={P1, P2, P3,\n\u2026, Pt} and add it to the IC only if the condition:\u2200 Pw {Pw\u2208\nPSpnew_m \u2192 Pw\u2208 GPSIC} is satisfied. This scheme has an\nadditional benefit of allowing the information service providers to\nhave a control over what kind of information they wish to provide\nto the users. We present the following example to illustrate the\nmapping concept.\nIC = {Traffic, Stock, Restaurant, Weather, Important history\ndates, Road conditions}\nLH = {Country, State, City, Zip-code, Major-roads}\nGPSIC = {Surface-mobility, Roads, High, Low, Italian-food,\nStateName, Temp, CityName, Seat-availability, Zip, Traffic-jams,\nStock-price, CountryName, MajorRoadName, Wars, Discoveries,\nWorld}\nGPSLH = {Country, CountrySize, StateName, CityName, Zip,\nMajorRoadName}\nPs(ICStock) = {Stock-price, CountryName, High, Low}\nPs(ICTraffic) = {Surface-mobility, Roads, High, Low, Traffic-jams,\nCityName}\nPs(ICImportant dates in history) = {World, Wars, Discoveries}\nPs(ICRoad conditions) = {Precipitation, StateName, CityName}\nPs(ICRestaurant) = {Italian-food, Zip code}\nPs(ICWeather) = {StateName, CityName, Precipitation,\nTemperature}\nPS(LHCountry) = {CountryName, CountrySize}\nPS(LHState = {StateName, State size},\nPS(LHCity) ={CityName, City size}\nPS(LHZipcode) = {ZipCodeNum }\nPS(LHMajor roads) = {MajorRoadName}\nNow, only PS(ICStock) \u2229 PSCountry \u2260\u03c6. In addition, PS(ICStock)\nindicated that Stock can map to only a single location Country.\nWhen we consider the member Traffic of IC space, only\nPS(ICTraffic) \u2229 PScity \u2260 \u03c6. As PS(ICTraffic) indicates that Traffic can\nmap to only a single location, it maps only to City and none of its\nchildren. Now unlike Stock, mapping of Traffic with Major roads,\nwhich is a child of City, is meaningful. However service providers\nhave right to control the granularity levels at which they want to\nprovide information about a member of IC space.\nPS(ICRoad conditions) \u2229 PSState \u2260\u03c6 and PS(ICRoad conditions) \u2229 PSCity\u2260\u03c6.\nSo Road conditions maps to State as well as City. As PS(ICRoad\nconditions) indicates that Road conditions can map to multiple\ngranularity levels, Road conditions will also map to Zip Code and\nMajor roads, which are the children of State and City. Similarly,\nRestaurant maps only to Zip code, and Weather maps to State,\nCity and their children, Major Roads and Zip Code.\n5. LOCATION BASED INDEXING SCHEME\nThis section discusses our location based indexing scheme\n(LBIS). The scheme is designed to conform to the LDD broadcast\nin our project DAYS. As discussed earlier, we use the\ncontainment property of LDD in the indexing scheme. This\nsignificantly limits the search of our required data to a particular\nportion of broadcast. Thus, we argue that the scheme provides\nbounded tuning time.\nWe describe the architecture of our indexing scheme. Our scheme\ncontains separate data buckets and index buckets. The index\nbuckets are of two types. The first type is called the Major index.\nThe Major index provides information about the types of data\nbroadcasted. For example, if we intend to broadcast information\nlike Entertainment, Weather, Traffic etc., then the major index\npoints to either these major types of information and/or their main\nsubtypes of information, the number of main subtypes varying\nfrom one information to another. This strictly limits number of\naccesses to a Major index. The Major index never points to the\noriginal data. It points to the sub indexes called the Minor index.\nThe minor indexes are the indexes which actually points to the\noriginal data. We called these minor index pointers as Location\nPointers as they points to the data which are associated with a\nlocation. Thus, our search for a data includes accessing of a major\nindex and some minor indexes, the number of minor index\nvarying depending on the type of information.\nThus, our indexing scheme takes into account the hierarchical\nnature of the LDD, the Containment property, and requires our\nbroadcast schedule to be clustered based on data type and\nlocation. The structure of the location hierarchy requires the use\nof different types of index at different levels. The structure and\npositions of index strictly depend on the location hierarchy as\ndescribed in our mapping scheme earlier. We illustrate the\nimplementation of our scheme with an example. The rules for\nframing the index are mentioned subsequently.\n20\nA1\nEntertainment\nResturant\nMovie\nA2\nA3\nA4\nR1\nR2\nR3\nR4\nR5\nR6\nR7\nR8\nWeather\nKC\nSL\nJC\nSF\nEntertainment\nR1 R2 R3 R4 R5 R6 R7 R8 KC SL JC SF\n(A, R, NEXT = 8)\n3, R5\n4, R7\nType (S, L)\nER\nW\nE\nEM\n(1, 4)\n(5, 4)\n(1, 4), (9, 4)\n(9, 4)\nType (S, L)\nW\nE\nEM\nER\n(1, 4)\n(5, 8)\n(5, 4)\n(9, 4)\nType (S, L)\nE\nEM\nER\nW\n(1, 8)\n(1, 4)\n(5, 4)\n(9, 4)\nA1 A2 A3 A4\nMovie Resturant Weather\n1 2 3 4 5 6 7 8 9 10 11 12\nMajor index Major index Major index\nMinor index\nMajor index Minor index\nFigure 3. Location Mapped Information for Broadcast Figure 4. Data coupled with Location based Index\nExample: Let us suppose that our broadcast content contains\nICentertainment and ICweather which is represented as shown in Fig. 3.\nAi represents Areas of City and Ri represents roads in a certain\narea. The leaves of Weather structure represent four cities. The\nindex structure is given in Fig. 4 which shows the position of\nmajor and minor index and data in the broadcast schedule.\nWe propose the following rules for the creation of the air indexed\nbroadcast schedule:\n\u2022 The major index and the minor index are created.\n\u2022 The major index contains the position and range of different\ntypes of data items (Weather and Entertainment, Figure 3)\nand their categories. The sub categories of Entertainment,\nMovie and Restaurant, are also in the index. Thus, the major\nindex contains Entertainment (E), Entertainment-Movie\n(EM), Entertainment-Restaurant (ER), and Weather (W). The\ntuple (S, L) represents the starting position (S) of the data\nitem and L represents the range of the item in terms of\nnumber of data buckets.\n\u2022 The minor index contains the variables A, R and a pointer\nNext. In our example (Figure 3), road R represents the first\nnode of area A. The minor index is used to point to actual\ndata buckets present at the lowest levels of the hierarchy. In\ncontrast, the major index points to a broader range of\nlocations and so it contains information about main and sub\ncategories of data.\n\u2022 Index information is not incorporated in the data buckets.\nIndex buckets are separate containing only the control\ninformation.\n\u2022 The number of major index buckets m=#(IC), IC = {ic1, ic2,\nic3,\u2026,icn} where ici represent information type and #\nrepresents the cardinality of the Information Content set IC.\nIn this example, IC= {icMovie, icWeather, icRestaurant} and so\n#(IC) =3. Hence, the number of major index buckets is 3.\n\u2022 Mechanism to resolve the query is present in the java based\ncoordinator in MU. For example, if a query Q is presented as\nQ (Entertainment, Movie, Road_1), then the resultant search\nwill be for the EM information in the major index. We say,\nQ EM.\nOur proposed index works as follows: Let us suppose that an MU\nissues a query which is represented by Java Coordinator present in\nthe MU as Restaurant information on Road 7. This is resolved\nby the coordinator as Q ER. This means one has to search for\nER unit of index in the major index. Let us suppose that the MU\nlogs into the channel at R2. The first index it receives is a minor\nindex after R2. In this index, value of Next variable = 4, which\nmeans that the next major index is present after bucket 4. The MU\nmay go into doze mode. It becomes active after bucket 4 and\nreceives the major index. It searches for ER information which is\nthe first entry in this index. It is now certain that the MU will get\nthe position of the data bucket in the adjoining minor index. The\nsecond unit in the minor index depicts the position of the required\ndata R7. It tells that the data bucket is the first bucket in Area 4.\nThe MU goes into doze mode again and becomes active after\nbucket 6. It gets the required data in the next bucket. We present\nthe algorithm for searching the location based Index.\nAlgorithm 1 Location based Index Search in DAYS\n1. Scan broadcast for the next index bucket, found=false\n2. While (not found) do\n3. if bucket is Major Index then\n4. Find the Type & Tuple (S, L)\n5. if S is greater than 1, go into doze mode for S seconds\n6. end if\n7. Wake up at the Sth\nbucket and observe the Minor Index\n8. end if\n9. if bucket is Minor Index then\n10. if TypeRequested not equal to Typefound and (A,R)Request not\nequal to (A,R)found then\n11. Go into doze mode till NEXT & repeat from step 3\n12. end if\n13. else find entry in Minor Index which points to data\n14. Compute time of arrival T of data bucket\n15. Go into doze mode till T\n16. Wake up at T and access data, found = true\n17. end else\n18. end if\n19. end While\n21\n6. PERFORMANCE EVALUATION\nConservation of energy is the main concern when we try to access\ndata from wireless broadcast. An efficient scheme should allow\nthe mobile device to access its required data by staying active for\na minimum amount of time. This would save considerable amount\nof energy. Since items are distributed based on types and are\nmapped to suitable locations, we argue that our broadcast deals\nwith clustered data types. The mobile unit has to access a larger\nmajor index and a relatively much smaller minor index to get\ninformation about the time of arrival of data. This is in contrast to\nthe exponential scheme where the indexes are of equal sizes. The\nexample discussed and Algorithm 1 reveals that to access any\ndata, we need to access the major index only once followed by\none or more accesses to the minor index. The number of minor\nindex access depends on the number of internal locations. As the\nnumber of internal locations vary for item to item (for example,\nWeather is generally associated with a City whereas traffic is\ngranulated up to major and minor roads of a city), we argue that\nthe structure of the location mapped information may be\nvisualized as a forest which is a collection of general trees, the\nnumber of general trees depending on the types of information\nbroadcasted and depth of a tree depending on the granularity of\nthe location information associated with the information.\nFor our experiments, we assume the forest as a collection of\nbalanced M-ary trees. We further assume the M-ary trees to be\nfull by assuming the presence of dummy nodes in different levels\nof a tree.\nThus, if the number of data items is d and the height of the tree is\nm, then\nn= (m*d-1)/(m-1) where n is the number of vertices in the tree and\ni= (d-1)/(m-1) where i is the number of internal vertices.\nTuning time for a data item involves 1 unit of time required to\naccess the major index plus time required to access the data items\npresent in the leaves of the tree.\nThus, tuning time with d data items is t = logmd+1\nWe can say that tuning time is bounded by O(logmd).\nWe compare our scheme with the distributed indexing and\nexponential scheme. We assume a flat broadcast and number of\npages varying from 5000 to 25000. The various simulation\nparameters are shown in Table 1.\nFigure 5-8 shows the relative tuning times of three indexing\nalgorithms, ie, the LBIS, exponential scheme and the distributed\ntree scheme. Figure 5 shows the result for number of internal\nlocation nodes = 3. We can see that LBIS significantly\noutperforms both the other schemes. The tuning time in LBIS\nranges from approx 6.8 to 8. This large tuning time is due to the\nfact that after reaching the lowest minor index, the MU may have\nto access few buckets sequentially to get the required data bucket.\nWe can see that the tuning time tends to become stable as the\nlength of broadcast increases. In figure 6 we consider m= 4. Here\nwe can see that the exponential and the distributed perform almost\nsimilarly, though the former seems to perform slightly better as\nthe broadcast length increases. A very interesting pattern is visible\nin figure 7. For smaller broadcast size, the LBIS seems to have\nlarger tuning time than the other two schemes. But as the length of\nbroadcast increases, it is clearly visible the LBIS outperforms the\nother two schemes. The Distributed tree indexing shows similar\nbehavior like the LBIS. The tuning time in LBIS remains low\nbecause the algorithm allows the MU to skip some intermediate\nMinor Indexes. This allows the MU to move into lower levels\ndirectly after coming into active mode, thus saving valuable\nenergy. This action is not possible in the distributed tree indexing\nand hence we can observe that its tuning time is more than the\nLBIS scheme, although it performs better than the exponential\nscheme. Figure 8, in contrast, shows us that the tuning time in\nLBIS, though less than the other two schemes, tends to increase\nsharply as the broadcast length becomes greater than the 15000\npages. This may be attributed both due to increase in time\nrequired to scan the intermediate Minor Indexes and the length of\nthe broadcast. But we can observe that the slope of the LBIS\ncurve is significantly less than the other two curves.\nTable 1 Simulation Parameters\nP Definition Values\nN Number of data Items 5000 - 25000\nm Number of internal location nodes 3, 4, 5, 6\nB Capacity of bucket without index (for\nexponential index)\n10,64,128,256\ni Index base for exponential index 2,4,6,8\nk Index size for distributed tree 8 bytes\nThe simulation results establish some facts about our\nlocation based indexing scheme. The scheme performs\nbetter than the other two schemes in terms of tuning time in\nmost of the cases. As the length of the broadcast increases, after a\ncertain point, though the tuning time increases as a result of\nfactors which we have described before, the scheme always\nperforms better than the other two schemes. Due to the prescribed\nlimit of the number of pages in the paper, we are unable to show\nmore results. But these omitted results show similar trend as the\nresults depicted in figure 5-8.\n7. CONCLUSION AND FUTURE WORK\nIn this paper we have presented a scheme for mapping of wireless\nbroadcast data with their locations. We have presented an example\nto show how the hierarchical structure of the location tree maps\nwith the data to create LDD. We have presented a scheme called\nLBIS to index this LDD. We have used the containment property\nof LDD in the scheme that limits the search to a narrow range of\ndata in the broadcast, thus saving valuable energy in the device.\nThe mapping of data with locations and the indexing scheme will\nbe used in our DAYS project to create the push based\narchitecture. The LBIS has been compared with two other\nprominent indexing schemes, i.e., the distributed tree indexing\nscheme and the exponential indexing scheme. We showed in our\nsimulations that the LBIS scheme has the lowest tuning time for\nbroadcasts having large number of pages, thus saving valuable\nbattery power in the MU.\n22\nIn the future work we try to incorporate pull based architecture in\nour DAYS project. Data from the server is available for access by\nthe global users. This may be done by putting a request to the\nsource server. The query in this case is a global query. It is\ntransferred from the user\"s source server to the destination server\nthrough the use of LEO satellites. We intend to use our LDD\nscheme and data staging architecture in the pull based architecture.\nWe will show that the LDD scheme together with the data staging\narchitecture significantly improves the latency for global as well as\nlocal query.\n8. REFERENCES\n[1] Acharya, S., Alonso, R. Franklin, M and Zdonik S. Broadcast\ndisk: Data management for asymmetric communications\nenvironments. In Proceedings of ACM SIGMOD Conference\non Management of Data, pages 199-210, San Jose, CA, May\n1995.\n[2] Chen, M.S.,Wu, K.L. and Yu, P. S. Optimizing index\nallocation for sequential data broadcasting in wireless mobile\ncomputing. IEEE Transactions on Knowledge and Data\nEngineering (TKDE), 15(1):161-173, January/February 2003.\nFigure 5. Broadcast Size (# buckets)\nDist tree\nExpo\nLBIS\nFigure 6. Broadcast Size (# buckets)\nDist tree\nExpo\nLBIS\nFigure 7. Broadcast Size (# buckets)\nDist tree\nExpo\nLBIS\nFigure 8. Broadcast Size (# buckets)\nDist tree\nExpo\nLBIS\nAveragetuningtime\nAveragetuningtime\nAveragetuningtime\nAveragetuningtime\n23\n[3] Hu, Q. L., Lee, D. L. and Lee, W.C. Performance evaluation\nof a wireless hierarchical data dissemination system. In\nProceedings of the 5th\nAnnual ACM International Conference\non Mobile Computing and Networking (MobiCom\"99), pages\n163-173, Seattle, WA, August 1999.\n[4] Hu, Q. L. Lee, W.C. and Lee, D. L. Power conservative\nmulti-attribute queries on data broadcast. In Proceedings of\nthe 16th International Conference on Data Engineering\n(ICDE\"00), pages 157-166, San Diego, CA, February 2000.\n[5] Imielinski, T., Viswanathan, S. and Badrinath. B. R. Power\nefficient filtering of data on air. In Proceedings of the 4th\nInternational Conference on Extending Database Technology\n(EDBT\"94), pages 245-258, Cambridge, UK, March 1994.\n[6] Imielinski, T., Viswanathan, S. and Badrinath. B. R. Data on\nair - Organization and access. IEEE Transactions on\nKnowledge and Data Engineering (TKDE), 9(3):353-372,\nMay/June 1997.\n[7] Shih, E., Bahl, P. and Sinclair, M. J. Wake on wireless: An\nevent driven energy saving strategy for battery operated\ndevices. In Proceedings of the 8th Annual ACM International\nConference on Mobile Computing and Networking\n(MobiCom\"02), pages 160-171, Atlanta, GA, September\n2002.\n[8] Shivakumar N. and Venkatasubramanian, S. Energy-efficient\nindexing for information dissemination in wireless systems.\nACM/Baltzer Journal of Mobile Networks and Applications\n(MONET), 1(4):433-446, December 1996.\n[9] Tan K. L. and Yu, J. X. Energy efficient filtering of non\nuniform broadcast. In Proceedings of the 16th International\nConference on Distributed Computing Systems (ICDCS\"96),\npages 520-527, Hong Kong, May 1996.\n[10] Viredaz, M. A., Brakmo, L. S. and Hamburgen, W. R. Energy\nmanagement on handheld devices. ACM Queue, 1(7):44-52,\nOctober 2003.\n[11] Garg, N. Kumar, V., & Dunham, M.H. Information Mapping\nand Indexing in DAYS, 6th International Workshop on\nMobility in Databases and Distributed Systems, in\nconjunction with the 14th International Conference on\nDatabase and Expert Systems Applications September 1-5,\nPrague, Czech Republic, 2003.\n[12] Acharya D., Kumar, V., & Dunham, M.H. InfoSpace: Hybrid\nand Adaptive Public Data Dissemination System for\nUbiquitous Computing. Accepted for publication in the\nspecial issue of Pervasive Computing. Wiley Journal for\nWireless Communications and Mobile Computing, 2004.\n[13] Acharya D., Kumar, V., & Prabhu, N. Discovering and using\nWeb Services in M-Commerce, Proceedings for 5th VLDB\nWorkshop on Technologies for E-Services, Toronto,\nCanada,2004.\n[14] Acharya D., Kumar, V. Indexing Location Dependent Data in\nbroadcast environment. Accepted for publication, JDIM\nspecial issue on Distributed Data Management, 2005.\n[15] Flinn, J., Sinnamohideen, S., & Satyanarayan, M. Data\nStaging on Untrusted Surrogates, Intel Research, Pittsburg,\nUnpublished Report, 2003.\n[16] Seydim, A.Y., Dunham, M.H. & Kumar, V. Location\ndependent query processing, Proceedings of the 2nd ACM\ninternational workshop on Data engineering for wireless and\nmobile access, p.47-53, Santa Barbara, California, USA,\n2001.\n[17] Xu, J., Lee, W.C., Tang., X. Exponential Index: A\nParameterized Distributed Indexing Scheme for Data on Air.\nIn Proceedings of the 2nd ACM/USENIX International\nConference on Mobile Systems, Applications, and Services\n(MobiSys'04), Boston, MA, June 2004.\n24", "keywords": "wireless broadcast datum mapping;location base service;datum stage;indexing scheme;pull based datum access;wireless datum dissemination;tree structure;day;wireless datum broadcast;datum broadcast system;location dependent datum;ldd;location based service;index;wireless channel;mapping of wireless broadcast datum;mobile user"}
{"name": "train_H-64", "title": "Machine Learning for Information Architecture in a Large Governmental Website", "abstract": "This paper describes ongoing research into the application of machine learning techniques for improving access to governmental information in complex digital libraries. Under the auspices of the GovStat Project, our goal is to identify a small number of semantically valid concepts that adequately spans the intellectual domain of a collection. The goal of this discovery is twofold. First we desire a practical aid for information architects. Second, automatically derived documentconcept relationships are a necessary precondition for realworld deployment of many dynamic interfaces. The current study compares concept learning strategies based on three document representations: keywords, titles, and full-text. In statistical and user-based studies, human-created keywords provide significant improvements in concept learning over both title-only and full-text representations.", "fulltext": "1. INTRODUCTION\nThe GovStat Project is a joint effort of the University\nof North Carolina Interaction Design Lab and the\nUniversity of Maryland Human-Computer Interaction Lab1\n.\nCiting end-user difficulty in finding governmental information\n(especially statistical data) online, the project seeks to\ncreate an integrated model of user access to US government\nstatistical information that is rooted in realistic data\nmodels and innovative user interfaces. To enable such models\nand interfaces, we propose a data-driven approach, based\non data mining and machine learning techniques. In\nparticular, our work analyzes a particular digital library-the\nwebsite of the Bureau of Labor Statistics2\n(BLS)-in efforts\nto discover a small number of linguistically meaningful\nconcepts, or bins, that collectively summarize the semantic\ndomain of the site.\nThe project goal is to classify the site\"s web content\naccording to these inferred concepts as an initial step towards\ndata filtering via active user interfaces (cf. [13]). Many\ndigital libraries already make use of content classification,\nboth explicitly and implicitly; they divide their resources\nmanually by topical relation; they organize content into\nhierarchically oriented file systems. The goal of the present\n1\nhttp://www.ils.unc.edu/govstat\n2\nhttp://www.bls.gov\n151\nresearch is to develop another means of browsing the content\nof these collections. By analyzing the distribution of terms\nacross documents, our goal is to supplement the agency\"s\npre-existing information structures. Statistical learning\ntechnologies are appealing in this context insofar as they stand\nto define a data-driven-as opposed to an\nagency-drivennavigational structure for a site.\nOur approach combines supervised and unsupervised\nlearning techniques. A pure document clustering [12] approach\nto such a large, diverse collection as BLS led to poor results\nin early tests [6]. But strictly supervised techniques [5] are\ninappropriate, too. Although BLS designers have defined\nhigh-level subject headings for their collections, as we\ndiscuss in Section 2, this scheme is less than optimal. Thus we\nhope to learn an additional set of concepts by letting the\ndata speak for themselves.\nThe remainder of this paper describes the details of our\nconcept discovery efforts and subsequent evaluation. In\nSection 2 we describe the previously existing, human-created\nconceptual structure of the BLS website. This section also\ndescribes evidence that this structure leaves room for\nimprovement. Next (Sections 3-5), we turn to a description\nof the concepts derived via content clustering under three\ndocument representations: keyword, title only, and full-text.\nSection 6 describes a two-part evaluation of the derived\nconceptual structures. Finally, we conclude in Section 7 by\noutlining upcoming work on the project.\n2. STRUCTURING ACCESS TO THE BLS\nWEBSITE\nThe Bureau of Labor Statistics is a federal government\nagency charged with compiling and publishing statistics\npertaining to labor and production in the US and abroad. Given\nthis broad mandate, the BLS publishes a wide array of\ninformation, intended for diverse audiences. The agency\"s\nwebsite acts as a clearinghouse for this process. With over\n15,000 text/html documents (and many more documents if\nspreadsheets and typeset reports are included), providing\naccess to the collection provides a steep challenge to\ninformation architects.\n2.1 The Relation Browser\nThe starting point of this work is the notion that access\nto information in the BLS website could be improved by\nthe addition of a dynamic interface such as the relation\nbrowser described by Marchionini and Brunk [13]. The\nrelation browser allows users to traverse complex data sets by\niteratively slicing the data along several topics. In Figure\n1 we see a prototype instantiation of the relation browser,\napplied to the FedStats website3\n.\nThe relation browser supports information seeking by\nallowing users to form queries in a stepwise fashion, slicing and\nre-slicing the data as their interests dictate. Its motivation\nis in keeping with Shneiderman\"s suggestion that queries\nand their results should be tightly coupled [2]. Thus in\nFig3\nhttp://www.fedstats.gov\nFigure 1: Relation Browser Prototype\nure 1, users might limit their search set to those documents\nabout energy. Within this subset of the collection, they\nmight further eliminate documents published more than a\nyear ago. Finally, they might request to see only documents\npublished in PDF format.\nAs Marchionini and Brunk discuss, capturing the\npublication date and format of documents is trivial. But successful\nimplementations of the relation browser also rely on topical\nclassification. This presents two stumbling blocks for system\ndesigners:\n\u2022 Information architects must define the appropriate set\nof topics for their collection\n\u2022 Site maintainers must classify each document into its\nappropriate categories\nThese tasks parallel common problems in the metadata\ncommunity: defining appropriate elements and marking up\ndocuments to support metadata-aware information access.\nGiven a collection of over 15,000 documents, these\nhurdles are especially daunting, and automatic methods of\napproaching them are highly desirable.\n2.2 A Pre-Existing Structure\nPrior to our involvement with the project, designers at\nBLS created a shallow classificatory structure for the most\nimportant documents in their website. As seen in Figure 2,\nthe BLS home page organizes 65 top-level documents into\n15 categories. These include topics such as Employment and\nUnemployment, Productivity, and Inflation and Spending.\n152\nFigure 2: The BLS Home Page\nWe hoped initially that these pre-defined categories could\nbe used to train a 15-way document classifier, thus\nautomating the process of populating the relation browser altogether.\nHowever, this approach proved unsatisfactory. In personal\nmeetings, BLS officials voiced dissatisfaction with the\nexisting topics. Their form, it was argued, owed as much to\nthe institutional structure of BLS as it did to the inherent\ntopology of the website\"s information space. In other words,\nthe topics reflected official divisions rather than semantic\nclusters. The BLS agents suggested that re-designing this\nclassification structure would be desirable.\nThe agents\" misgivings were borne out in subsequent\nanalysis. The BLS topics comprise a shallow classificatory\nstructure; each of the 15 top-level categories is linked to a small\nnumber of related pages. Thus there are 7 pages associated\nwith Inflation. Altogether, the link structure of this\nclassificatory system contains 65 documents; that is, excluding\nnavigational links, there are 65 documents linked from the\nBLS home page, where each hyperlink connects a document\nto a topic (pages can be linked to multiple topics). Based on\nthis hyperlink structure, we defined M, a symmetric 65\u00d765\nmatrix, where mij counts the number of topics in which\ndocuments i and j are both classified on the BLS home page. To\nanalyze the redundancy inherent in the pre-existing\nstructure, we derived the principal components of M (cf. [11]).\nFigure 3 shows the resultant scree plot4\n.\nBecause all 65 documents belong to at least one BLS topic,\n4\nA scree plot shows the magnitude of the kth\neigenvalue\nversus its rank. During principal component analysis scree\nplots visualize the amount of variance captured by each\ncomponent.\nm00M0M\n0\n1010M10M\n10\n2020M20M\n20\n3030M30M\n30\n4040M40M\n40\n5050M50M\n50\n6060M60M\n60\nm00M0M\n0\n22M2M\n2\n44M4M\n4\n66M6M\n6\n88M8M\n8\n1010M10M\n10\n1212M12M\n12\n1414M14M\n14\nEigenvalue RankMEigenvalue RankM\nEigenvalue Rank\nEigenvlue MagnitudeMEigenvlue MagnitudeM\nEigenvlueMagnitude\nFigure 3: Scree Plot of BLS Categories\nthe rank of M is guaranteed to be less than or equal to\n15 (hence, eigenvalues 16 . . . 65 = 0). What is surprising\nabout Figure 3, however, is the precipitous decline in\nmagnitude among the first four eigenvalues. The four largest\neigenvlaues account for 62.2% of the total variance in the\ndata. This fact suggests a high degree of redundancy among\nthe topics. Topical redundancy is not in itself problematic.\nHowever, the documents in this very shallow classificatory\nstructure are almost all gateways to more specific\ninformation. Thus the listing of the Producer Price Index under\nthree categories could be confusing to the site\"s users. In\nlight of this potential for confusion and the agency\"s own\nrequest for redesign, we undertook the task of topic discovery\ndescribed in the following sections.\n3. A HYBRID APPROACH TO TOPIC\nDISCOVERY\nTo aid in the discovery of a new set of high-level topics for\nthe BLS website, we turned to unsupervised machine\nlearning methods. In efforts to let the data speak for themselves,\nwe desired a means of concept discovery that would be based\nnot on the structure of the agency, but on the content of the\nmaterial. To begin this process, we crawled the BLS\nwebsite, downloading all documents of MIME type text/html.\nThis led to a corpus of 15,165 documents. Based on this\ncorpus, we hoped to derive k \u2248 10 topical categories, such\nthat each document di is assigned to one or more classes.\n153\nDocument clustering (cf. [16]) provided an obvious, but\nonly partial solution to the problem of automating this type\nof high-level information architecture discovery. The\nproblems with standard clustering are threefold.\n1. Mutually exclusive clusters are inappropriate for\nidentifying the topical content of documents, since\ndocuments may be about many subjects.\n2. Due to the heterogeneity of the data housed in the\nBLS collection (tables, lists, surveys, etc.), many\ndocuments\" terms provide noisy topical information.\n3. For application to the relation browser, we require a\nsmall number (k \u2248 10) of topics. Without significant\ndata reduction, term-based clustering tends to deliver\nclusters at too fine a level of granularity.\nIn light of these problems, we take a hybrid approach to\ntopic discovery. First, we limit the clustering process to\na sample of the entire collection, described in Section 4.\nWorking on a focused subset of the data helps to overcome\nproblems two and three, listed above. To address the\nproblem of mutual exclusivity, we combine unsupervised with\nsupervised learning methods, as described in Section 5.\n4. FOCUSING ON CONTENT-RICH\nDOCUMENTS\nTo derive empirically evidenced topics we initially turned\nto cluster analysis. Let A be the n\u00d7p data matrix with n\nobservations in p variables. Thus aij shows the measurement\nfor the ith\nobservation on the jth\nvariable. As described\nin [12], the goal of cluster analysis is to assign each of the\nn observations to one of a small number k groups, each of\nwhich is characterized by high intra-cluster correlation and\nlow inter-cluster correlation. Though the algorithms for\naccomplishing such an arrangement are legion, our analysis\nfocuses on k-means clustering5\n, during which, each\nobservation oi is assigned to the cluster Ck whose centroid is closest\nto it, in terms of Euclidean distance. Readers interested in\nthe details of the algorithm are referred to [12] for a\nthorough treatment of the subject.\nClustering by k-means is well-studied in the statistical\nliterature, and has shown good results for text analysis (cf.\n[8, 16]). However, k-means clustering requires that the\nresearcher specify k, the number of clusters to define. When\napplying k-means to our 15,000 document collection,\nindicators such as the gap statistic [17] and an analysis of\nthe mean-squared distance across values of k suggested that\nk \u2248 80 was optimal. This paramterization led to\nsemantically intelligible clusters. However, 80 clusters are far too\nmany for application to an interface such as the relation\n5\nWe have focused on k-means as opposed to other clustering\nalgorithms for several reasons. Chief among these is the\ncomputational efficiency enjoyed by the k-means approach.\nBecause we need only a flat clustering there is little to be\ngained by the more expensive hierarchical algorithms. In\nfuture work we will turn to model-based clustering [7] as a\nmore principled method of selecting the number of clusters\nand of representing clusters.\nbrowser. Moreover, the granularity of these clusters was\nunsuitably fine. For instance, the 80-cluster solution derived\na cluster whose most highly associated words (in terms of\nlog-odds ratio [1]) were drug, pharmacy, and chemist. These\nwords are certainly related, but they are related at a level\nof specificity far below what we sought.\nTo remedy the high dimensionality of the data, we\nresolved to limit the algorithm to a subset of the collection.\nIn consultation with employees of the BLS, we continued\nour analysis on documents that form a series titled From\nthe Editor\"s Desk6\n. These are brief articles, written by BLS\nemployees. BLS agents suggested that we focus on the\nEditor\"s Desk because it is intended to span the intellectual\ndomain of the agency. The column is published daily, and\neach entry describes an important current issue in the BLS\ndomain. The Editor\"s Desk column has been written daily\n(five times per week) since 1998. As such, we operated on a\nset of N = 1279 documents.\nLimiting attention to these 1279 documents not only\nreduced the dimensionality of the problem. It also allowed\nthe clustering process to learn on a relatively clean data set.\nWhile the entire BLS collection contains a great deal of\nnonprose text (i.e. tables, lists, etc.), the Editor\"s Desk\ndocuments are all written in clear, journalistic prose. Each\ndocument is highly topical, further aiding the discovery of\ntermtopic relations. Finally, the Editor\"s Desk column provided\nan ideal learning environment because it is well-supplied\nwith topical metadata. Each of the 1279 documents\ncontains a list of one or more keywords. Additionally, a subset\nof the documents (1112) contained a subject heading. This\nmetadata informed our learning and evaluation, as described\nin Section 6.1.\n5. COMBINING SUPERVISED AND\nUNSUPERVISED LEARNING FORTOPIC\nDISCOVERY\nTo derive suitably general topics for the application of a\ndynamic interface to the BLS collection, we combined\ndocument clustering with text classification techniques.\nSpecifically, using k-means, we clustered each of the 1279\ndocuments into one of k clusters, with the number of clusters\nchosen by analyzing the within-cluster mean squared\ndistance at different values of k (see Section 6.1).\nConstructing mutually exclusive clusters violates our assumption that\ndocuments may belong to multiple classes. However, these\nclusters mark only the first step in a two-phase process of\ntopic identification. At the end of the process,\ndocumentcluster affinity is measured by a real-valued number.\nOnce the Editor\"s Desk documents were assigned to\nclusters, we constructed a k-way classifier that estimates the\nstrength of evidence that a new document di is a member\nof class Ck. We tested three statistical classification\ntechniques: probabilistic Rocchio (prind), naive Bayes, and\nsupport vector machines (SVMs). All were implemented using\nMcCallum\"s BOW text classification library [14]. Prind is a\nprobabilistic version of the Rocchio classification algorithm\n[9]. Interested readers are referred to Joachims\" article for\n6\nhttp://www.bls.gov/opub/ted\n154\nfurther details of the classification method. Like prind, naive\nBayes attempts to classify documents into the most\nprobable class. It is described in detail in [15]. Finally, support\nvector machines were thoroughly explicated by Vapnik [18],\nand applied specifically to text in [10]. They define a\ndecision boundary by finding the maximally separating\nhyperplane in a high-dimensional vector space in which document\nclasses become linearly separable.\nHaving clustered the documents and trained a suitable\nclassifier, the remaining 14,000 documents in the collection\nare labeled by means of automatic classification. That is, for\neach document di we derive a k-dimensional vector,\nquantifying the association between di and each class C1 . . . Ck.\nDeriving topic scores via naive Bayes for the entire\n15,000document collection required less than two hours of CPU\ntime. The output of this process is a score for every\ndocument in the collection on each of the automatically\ndiscovered topics. These scores may then be used to populate a\nrelation browser interface, or they may be added to a\ntraditional information retrieval system. To use these weights in\nthe relation browser we currently assign to each document\nthe two topics on which it scored highest. In future work we\nwill adopt a more rigorous method of deriving\ndocumenttopic weight thresholds. Also, evaluation of the utility of\nthe learned topics for users will be undertaken.\n6. EVALUATION OF CONCEPT\nDISCOVERY\nPrior to implementing a relation browser interface and\nundertaking the attendant user studies, it is of course\nimportant to evaluate the quality of the inferred concepts, and\nthe ability of the automatic classifier to assign documents\nto the appropriate subjects. To evaluate the success of the\ntwo-stage approach described in Section 5, we undertook\ntwo experiments. During the first experiment we compared\nthree methods of document representation for the\nclustering task. The goal here was to compare the quality of\ndocument clusters derived by analysis of full-text documents,\ndocuments represented only by their titles, and documents\nrepresented by human-created keyword metadata. During\nthe second experiment, we analyzed the ability of the\nstatistical classifiers to discern the subject matter of documents\nfrom portions of the database in addition to the Editor\"s\nDesk.\n6.1 Comparing Document Representations\nDocuments from The Editor\"s Desk column came\nsupplied with human-generated keyword metadata.\nAdditionally, The titles of the Editor\"s Desk documents tend to be\ngermane to the topic of their respective articles. With such\nan array of distilled evidence of each document\"s subject\nmatter, we undertook a comparison of document\nrepresentations for topic discovery by clustering. We hypothesized\nthat keyword-based clustering would provide a useful model.\nBut we hoped to see whether comparable performance could\nbe attained by methods that did not require extensive\nhuman indexing, such as the title-only or full-text\nrepresentations. To test this hypothesis, we defined three modes of\ndocument representation-full-text, title-only, and keyword\nonly-we generated three sets of topics, Tfull, Ttitle, and\nTkw, respectively.\nTopics based on full-text documents were derived by\napplication of k-means clustering to the 1279 Editor\"s Desk\ndocuments, where each document was represented by a\n1908dimensional vector. These 1908 dimensions captured the\nTF.IDF weights [3] of each term ti in document dj, for all\nterms that occurred at least three times in the data. To\narrive at the appropriate number of clusters for these data, we\ninspected the within-cluster mean-squared distance for each\nvalue of k = 1 . . . 20. As k approached 10 the reduction in\nerror with the addition of more clusters declined notably,\nsuggesting that k \u2248 10 would yield good divisions. To\nselect a single integer value, we calculated which value of k led\nto the least variation in cluster size. This metric stemmed\nfrom a desire to suppress the common result where one large\ncluster emerges from the k-means algorithm, accompanied\nby several accordingly small clusters. Without reason to\nbelieve that any single topic should have dramatically high\nprior odds of document membership, this heuristic led to\nkfull = 10.\nClusters based on document titles were constructed\nsimilarly. However, in this case, each document was represented\nin the vector space spanned by the 397 terms that occur\nat least twice in document titles. Using the same method\nof minimizing the variance in cluster membership ktitle-the\nnumber of clusters in the title-based representation-was also\nset to 10.\nThe dimensionality of the keyword-based clustering was\nvery similar to that of the title-based approach. There were\n299 keywords in the data, all of which were retained. The\nmedian number of keywords per document was 7, where a\nkeyword is understood to be either a single word, or a\nmultiword term such as consumer price index. It is worth noting\nthat the keywords were not drawn from any controlled\nvocabulary; they were assigned to documents by publishers at\nthe BLS. Using the keywords, the documents were clustered\ninto 10 classes.\nTo evaluate the clusters derived by each method of\ndocument representation, we used the subject headings that were\nincluded with 1112 of the Editor\"s Desk documents. Each\nof these 1112 documents was assigned one or more subject\nheadings, which were withheld from all of the cluster\napplications. Like the keywords, subject headings were assigned\nto documents by BLS publishers. Unlike the keywords,\nhowever, subject headings were drawn from a controlled\nvocabulary. Our analysis began with the assumption that\ndocuments with the same subject headings should cluster\ntogether. To facilitate this analysis, we took a conservative\napproach; we considered multi-subject classifications to be\nunique. Thus if document di was assigned to a single\nsubject prices, while document dj was assigned to two subjects,\ninternational comparisons, prices, documents di and dj are\nnot considered to come from the same class.\nTable 1 shows all Editor\"s Desk subject headings that were\nassigned to at least 10 documents. As noted in the table,\n155\nTable 1: Top Editor\"s Desk Subject Headings\nSubject Count\nprices 92\nunemployment 55\noccupational safety & health 53\ninternational comparisons, prices 48\nmanufacturing, prices 45\nemployment 44\nproductivity 40\nconsumer expenditures 36\nearnings & wages 27\nemployment & unemployment 27\ncompensation costs 25\nearnings & wages, metro. areas 18\nbenefits, compensation costs 18\nearnings & wages, occupations 17\nemployment, occupations 14\nbenefits 14\nearnings & wage, regions 13\nwork stoppages 12\nearnings & wages, industries 11\nTotal 609\nTable 2: Contingecy Table for Three Document\nRepresentations\nRepresentation Right Wrong Accuracy\nFull-text 392 217 0.64\nTitle 441 168 0.72\nKeyword 601 8 0.98\nthere were 19 such subject headings, which altogether\ncovered 609 (54%) of the documents with subjects assigned.\nThese document-subject pairings formed the basis of our\nanalysis. Limiting analysis to subjects with N > 10 kept\nthe resultant \u03c72\ntests suitably robust.\nThe clustering derived by each document representation\nwas tested by its ability to collocate documents with the\nsame subjects. Thus for each of the 19 subject headings\nin Table 1, Si, we calculated the proportion of documents\nassigned to Si that each clustering co-classified. Further,\nwe assumed that whichever cluster captured the majority of\ndocuments for a given class constituted the right answer\nfor that class. For instance, There were 92 documents whose\nsubject heading was prices. Taking the BLS editors\"\nclassifications as ground truth, all 92 of these documents should\nhave ended up in the same cluster. Under the full-text\nrepresentation 52 of these documents were clustered into category\n5, while 35 were in category 3, and 5 documents were in\ncategory 6. Taking the majority cluster as the putative right\nhome for these documents, we consider the accuracy of this\nclustering on this subject to be 52/92 = 0.56. Repeating\nthis process for each topic across all three representations\nled to the contingency table shown in Table 2.\nThe obvious superiority of the keyword-based clustering\nevidenced by Table 2 was borne out by a \u03c72\ntest on the\naccuracy proportions. Comparing the proportion right and\nTable 3: Keyword-Based Clusters\nbenefits costs international jobs\nplans compensation import employment\nbenefits costs prices jobs\nemployees benefits petroleum youth\noccupations prices productivity safety\nworkers prices productivity safety\nearnings index output health\noperators inflation nonfarm occupational\nspending unemployment\nexpenditures unemployment\nconsumer mass\nspending jobless\nwrong achieved by keyword and title-based clustering led to\np 0.001. Due to this result, in the remainder of this paper,\nwe focus our attention on the clusters derived by analysis of\nthe Editor\"s Desk keywords. The ten keyword-based clusters\nare shown in Table 3, represented by the three terms most\nhighly associated with each cluster, in terms of the log-odds\nratio. Additionally, each cluster has been given a label by\nthe researchers.\nEvaluating the results of clustering is notoriously difficult.\nIn order to lend our analysis suitable rigor and utility, we\nmade several simplifying assumptions. Most problematic is\nthe fact that we have assumed that each document belongs\nin only a single category. This assumption is certainly false.\nHowever, by taking an extremely rigid view of what\nconstitutes a subject-that is, by taking a fully qualified and\noften multipart subject heading as our unit of analysis-we\nmitigate this problem. Analogically, this is akin to\nconsidering the location of books on a library shelf. Although a\ngiven book may cover many subjects, a classification system\nshould be able to collocate books that are extremely similar,\nsay books about occupational safety and health. The most\nserious liability with this evaluation, then, is the fact that\nwe have compressed multiple subject headings, say prices :\ninternational into single subjects. This flattening obscures\nthe multivalence of documents. We turn to a more realistic\nassessment of document-class relations in Section 6.2.\n6.2 Accuracy of the Document Classifiers\nAlthough the keyword-based clusters appear to classify\nthe Editor\"s Desk documents very well, their discovery only\nsolved half of the problem required for the successful\nimplementation of a dynamic user interface such as the\nrelation browser. The matter of roughly fourteen thousand\nunclassified documents remained to be addressed. To solve\nthis problem, we trained the statistical classifiers described\nabove in Section 5. For each document in the collection\ndi, these classifiers give pi, a k-vector of probabilities or\ndistances (depending on the classification method used), where\npik quantifies the strength of association between the ith\ndocument and the kth\nclass. All classifiers were trained on\nthe full text of each document, regardless of the\nrepresentation used to discover the initial clusters. The different\ntraining sets were thus constructed simply by changing the\n156\nTable 4: Cross Validation Results for 3 Classifiers\nMethod Av. Percent Accuracy SE\nPrind 59.07 1.07\nNaive Bayes 75.57 0.4\nSVM 75.08 0.68\nclass variable for each instance (document) to reflect its\nassigned cluster under a given model.\nTo test the ability of each classifier to locate documents\ncorrectly, we first performed a 10-fold cross validation on\nthe Editor\"s Desk documents. During cross-validation the\ndata are split randomly into n subsets (in this case n = 10).\nThe process proceeds by iteratively holding out each of the\nn subsets as a test collection for a model trained on the\nremaining n \u2212 1 subsets. Cross validation is described in\n[15]. Using this methodology, we compared the performance\nof the three classification models described above. Table 4\ngives the results from cross validation.\nAlthough naive Bayes is not significantly more accurate\nfor these data than the SVM classifier, we limit the\nremainder of our attention to analysis of its performance. Our\nselection of naive Bayes is due to the fact that it appears to\nwork comparably to the SVM approach for these data, while\nbeing much simpler, both in theory and implementation.\nBecause we have only 1279 documents and 10 classes, the\nnumber of training documents per class is relatively small.\nIn addition to models fitted to the Editor\"s Desk data, then,\nwe constructed a fourth model, supplementing the training\nsets of each class by querying the Google search engine7\nand\napplying naive Bayes to the augmented test set. For each\nclass, we created a query by submitting the three terms\nwith the highest log-odds ratio with that class. Further,\neach query was limited to the domain www.bls.gov. For\neach class we retrieved up to 400 documents from Google\n(the actual number varied depending on the size of the\nresult set returned by Google). This led to a training set\nof 4113 documents in the augmented model, as we call\nit below8\n. Cross validation suggested that the augmented\nmodel decreased classification accuracy (accuracy= 58.16%,\nwith standard error= 0.32). As we discuss below, however,\naugmenting the training set appeared to help generalization\nduring our second experiment.\nThe results of our cross validation experiment are\nencouraging. However, the success of our classifiers on the Editor\"s\nDesk documents that informed the cross validation study\nmay not be good predictors of the models\" performance on\nthe remainder to the BLS website. To test the generality\nof the naive Bayes classifier, we solicited input from 11\nhuman judges who were familiar with the BLS website. The\nsample was chosen by convenience, and consisted of faculty\nand graduate students who work on the GovStat project.\nHowever, none of the reviewers had prior knowledge of the\noutcome of the classification before their participation. For\nthe experiment, a random sample of 100 documents was\ndrawn from the entire BLS collection. On average each\nre7\nhttp://www.google.com\n8\nA more formal treatment of the combination of labeled and\nunlabeled data is available in [4].\nTable 5: Human-Model Agreement on 100 Sample\nDocs.\nHuman Judge 1st\nChoice\nModel Model 1st\nChoice Model 2nd\nChoice\nN. Bayes (aug.) 14 24\nN. Bayes 24 1\nHuman Judge 2nd\nChoice\nModel Model 1st\nChoice Model 2nd\nChoice\nN. Bayes (aug.) 14 21\nN. Bayes 21 4\nviewer classified 83 documents, placing each document into\nas many of the categories shown in Table 3 as he or she saw\nfit.\nResults from this experiment suggest that room for\nimprovement remains with respect to generalizing to the whole\ncollection from the class models fitted to the Editor\"s Desk\ndocuments. In Table 5, we see, for each classifier, the\nnumber of documents for which it\"s first or second most probable\nclass was voted best or second best by the 11 human judges.\nIn the context of this experiment, we consider a first- or\nsecond-place classification by the machine to be accurate\nbecause the relation browser interface operates on a\nmultiway classification, where each document is classified into\nmultiple categories. Thus a document with the correct\nclass as its second choice would still be easily available to\na user. Likewise, a correct classification on either the most\npopular or second most popular category among the human\njudges is considered correct in cases where a given document\nwas classified into multiple classes. There were 72\nmulticlass documents in our sample, as seen in Figure 4. The\nremaining 28 documents were assigned to 1 or 0 classes.\nUnder this rationale, The augmented naive Bayes\nclassifier correctly grouped 73 documents, while the smaller model\n(not augmented by a Google search) correctly classified 50.\nThe resultant \u03c72\ntest gave p = 0.001, suggesting that\nincreasing the training set improved the ability of the naive\nBayes model to generalize from the Editor\"s Desk documents\nto the collection as a whole. However, the improvement\nafforded by the augmented model comes at some cost. In\nparticular, the augmented model is significantly inferior to the\nmodel trained solely on Editor\"s Desk documents if we\nconcern ourselves only with documents selected by the majority\nof human reviewers-i.e. only first-choice classes. Limiting\nthe right answers to the left column of Table 5 gives p = 0.02\nin favor of the non-augmented model. For the purposes of\napplying the relation browser to complex digital library\ncontent (where documents will be classified along multiple\ncategories), the augmented model is preferable. But this is not\nnecessarily the case in general.\nIt must also be said that 73% accuracy under a fairly\nliberal test condition leaves room for improvement in our\nassignment of topics to categories. We may begin to\nunderstand the shortcomings of the described techniques by\nconsulting Figure 5, which shows the distribution of\ncategories across documents given by humans and by the\naugmented naive Bayes model. The majority of reviewers put\n157\nNumber of Human-Assigned ClassesMNumber of Human-Assigned ClassesM\nNumber of Human-Assigned Classes\nFrequencyMFrequencyM\nFrequency\nm00M0M\n0\n11M1M\n1\n22M2M\n2\n33M3M\n3\n44M4M\n4\n55M5M\n5\n66M6M\n6\n77M7M\n7\nm00M0M 055M5M 51010M10M 101515M15M 152020M20M 202525M25M 253030M30M 303535M35M 35\nFigure 4: Number of Classes Assigned to\nDocuments by Judges\ndocuments into only three categories, jobs, benefits, and\noccupations. On the other hand, the naive Bayes classifier\ndistributed classes more evenly across the topics. This behavior\nsuggests areas for future improvement. Most importantly,\nwe observed a strong correlation among the three most\nfrequent classes among the human judges (for instance, there\nwas 68% correlation between benefits and occupations). This\nsuggests that improving the clustering to produce topics\nthat were more nearly orthogonal might improve\nperformance.\n7. CONCLUSIONS AND FUTURE WORK\nMany developers and maintainers of digital libraries share\nthe basic problem pursued here. Given increasingly large,\ncomplex bodies of data, how may we improve access to\ncollections without incurring extraordinary cost, and while also\nkeeping systems receptive to changes in content over time?\nData mining and machine learning methods hold a great deal\nof promise with respect to this problem. Empirical\nmethods of knowledge discovery can aid in the organization and\nretrieval of information. As we have argued in this paper,\nthese methods may also be brought to bear on the design\nand implementation of advanced user interfaces.\nThis study explored a hybrid technique for aiding\ninformation architects as they implement dynamic interfaces such\nas the relation browser. Our approach combines\nunsupervised learning techniques, applied to a focused subset of the\nBLS website. The goal of this initial stage is to discover the\nmost basic and far-reaching topics in the collection. Based\nmjobsjobsMjobsM\njobs\nbenefitsunemploymentpricespricesMpricesM\nprices\nsafetyinternationalspendingspendingMspendingM\nspending\noccupationscostscostsMcostsM\ncosts\nproductivityHuman ClassificationsMHuman ClassificationsM\nHuman Classifications\nm0.000.00M0.00M\n0.00\n0.050.100.150.15M0.15M\n0.15\n0.200.25mjobsjobsMjobsM\njobs\nbenefitsunemploymentpricespricesMpricesM\nprices\nsafetyinternationalspendingspendingMspendingM\nspending\noccupationscostscostsMcostsM\ncosts\nproductivityMachine ClassificationsMMachine ClassificationsM\nMachine Classifications\nm0.000.00M0.00M\n0.00\n0.050.100.10M0.10M\n0.10\n0.15\nFigure 5: Distribution of Classes Across Documents\non a statistical model of these topics, the second phase of\nour approach uses supervised learning (in particular, a naive\nBayes classifier, trained on individual words), to assign\ntopical relations to the remaining documents in the collection.\nIn the study reported here, this approach has\ndemonstrated promise. In its favor, our approach is highly scalable.\nIt also appears to give fairly good results. Comparing three\nmodes of document representation-full-text, title only, and\nkeyword-we found 98% accuracy as measured by\ncollocation of documents with identical subject headings. While it\nis not surprising that editor-generated keywords should give\nstrong evidence for such learning, their superiority over\nfulltext and titles was dramatic, suggesting that even a small\namount of metadata can be very useful for data mining.\nHowever, we also found evidence that learning topics from\na subset of the collection may lead to overfitted models.\nAfter clustering 1279 Editor\"s Desk documents into 10\ncategories, we fitted a 10-way naive Bayes classifier to categorize\nthe remaining 14,000 documents in the collection. While we\nsaw fairly good results (classification accuracy of 75% with\nrespect to a small sample of human judges), this experiment\nforced us to reconsider the quality of the topics learned by\nclustering. The high correlation among human judgments\nin our sample suggests that the topics discovered by\nanalysis of the Editor\"s Desk were not independent. While we do\nnot desire mutually exclusive categories in our setting, we\ndo desire independence among the topics we model.\nOverall, then, the techniques described here provide an\nencouraging start to our work on acquiring subject\nmetadata for dynamic interfaces automatically. It also suggests\nthat a more sophisticated modeling approach might yield\n158\nbetter results in the future. In upcoming work we will\nexperiment with streamlining the two-phase technique described\nhere. Instead of clustering documents to find topics and\nthen fitting a model to the learned clusters, our goal is to\nexpand the unsupervised portion of our analysis beyond a\nnarrow subset of the collection, such as The Editor\"s Desk.\nIn current work we have defined algorithms to identify\ndocuments likely to help the topic discovery task. Supplied with\na more comprehensive training set, we hope to experiment\nwith model-based clustering, which combines the clustering\nand classification processes into a single modeling procedure.\nTopic discovery and document classification have long been\nrecognized as fundamental problems in information retrieval\nand other forms of text mining. What is increasingly clear,\nhowever, as digital libraries grow in scope and complexity,\nis the applicability of these techniques to problems at the\nfront-end of systems such as information architecture and\ninterface design. Finally, then, in future work we will build\non the user studies undertaken by Marchionini and Brunk\nin efforts to evaluate the utility of automatically populated\ndynamic interfaces for the users of digital libraries.\n8. REFERENCES\n[1] A. Agresti. An Introduction to Categorical Data\nAnalysis. Wiley, New York, 1996.\n[2] C. Ahlberg, C. Williamson, and B. Shneiderman.\nDynamic queries for information exploration: an\nimplementation and evaluation. In Proceedings of the\nSIGCHI conference on Human factors in computing\nsystems, pages 619-626, 1992.\n[3] R. Baeza-Yates and B. Ribeiro-Neto. Modern\nInformation Retrieval. ACM Press, 1999.\n[4] A. Blum and T. Mitchell. Combining labeled and\nunlabeled data with co-training. In Proceedings of the\neleventh annual conference on Computational learning\ntheory, pages 92-100. ACM Press, 1998.\n[5] H. Chen and S. Dumais. Hierarchical classification of\nweb content. In Proceedings of the 23rd annual\ninternational ACM SIGIR conference on Research and\ndevelopment in information retrieval, pages 256-263,\n2000.\n[6] M. Efron, G. Marchionini, and J. Zhang. Implications\nof the recursive representation problem for automatic\nconcept identification in on-line governmental\ninformation. In Proceedings of the ASIST Special\nInterest Group on Classification Research (ASIST\nSIG-CR), 2003.\n[7] C. Fraley and A. E. Raftery. How many clusters?\nwhich clustering method? answers via model-based\ncluster analysis. The Computer Journal,\n41(8):578-588, 1998.\n[8] A. K. Jain, M. N. Murty, and P. J. Flynn. Data\nclustering: a review. ACM Computing Surveys,\n31(3):264-323, September 1999.\n[9] T. Joachims. A probabilistic analysis of the Rocchio\nalgorithm with TFIDF for text categorization. In\nD. H. Fisher, editor, Proceedings of ICML-97, 14th\nInternational Conference on Machine Learning, pages\n143-151, Nashville, US, 1997. Morgan Kaufmann\nPublishers, San Francisco, US.\n[10] T. Joachims. Text categorization with support vector\nmachines: learning with many relevant features. In\nC. N\u00b4edellec and C. Rouveirol, editors, Proceedings of\nECML-98, 10th European Conference on Machine\nLearning, pages 137-142, Chemnitz, DE, 1998.\nSpringer Verlag, Heidelberg, DE.\n[11] I. T. Jolliffe. Principal Component Analysis. Springer,\n2nd edition, 2002.\n[12] L. Kaufman and P. J. Rosseeuw. Finding Groups in\nData: an Introduction to Cluster Analysis. Wiley,\n1990.\n[13] G. Marchionini and B. Brunk. Toward a general\nrelation browser: a GUI for information architects.\nJournal of Digital Information, 4(1), 2003.\nhttp://jodi.ecs.soton.ac.uk/Articles/v04/i01/Marchionini/.\n[14] A. K. McCallum. Bow: A toolkit for statistical\nlanguage modeling, text retrieval, classification and\nclustering. http://www.cs.cmu.edu/\u02dcmccallum/bow,\n1996.\n[15] T. Mitchell. Machine Learning. McGraw Hill, 1997.\n[16] E. Rasmussen. Clustering algorithms. In W. B. Frakes\nand R. Baeza-Yates, editors, Information Retrieval:\nData Structures and Algorithms, pages 419-442.\nPrentice Hall, 1992.\n[17] R. Tibshirani, G. Walther, and T. Hastie. Estimating\nthe number of clusters in a dataset via the gap\nstatistic, 2000.\nhttp://citeseer.nj.nec.com/tibshirani00estimating.html.\n[18] V. N. Vapnik. The Nature of Statistical Learning\nTheory. Springer, 2000.\n159", "keywords": "machine learn;information architecture;interface design;multiway classification;access;bureau of labor statistics;bls collection;data-driven approach;digital library;k-means clustering;machine learning technique;eigenvalue;complex digital library;supervised and unsupervised learning technique"}
{"name": "train_H-69", "title": "Ranking Web Objects from Multiple Communities", "abstract": "Vertical search is a promising direction as it leverages domainspecific knowledge and can provide more precise information for users. In this paper, we study the Web object-ranking problem, one of the key issues in building a vertical search engine. More specifically, we focus on this problem in cases when objects lack relationships between different Web communities, and take high-quality photo search as the test bed for this investigation. We proposed two score fusion methods that can automatically integrate as many Web communities (Web forums) with rating information as possible. The proposed fusion methods leverage the hidden links discovered by a duplicate photo detection algorithm, and aims at minimizing score differences of duplicate photos in different forums. Both intermediate results and user studies show the proposed fusion methods are practical and efficient solutions to Web object ranking in cases we have described. Though the experiments were conducted on high-quality photo ranking, the proposed algorithms are also applicable to other ranking problems, such as movie ranking and music ranking.", "fulltext": "1. INTRODUCTION\nDespite numerous refinements and optimizations, general\npurpose search engines still fail to find relevant results for\nmany queries. As a new trend, vertical search has shown\npromise because it can leverage domain-specific knowledge\nand is more effective in connecting users with the\ninformation they want. There are many vertical search engines,\nincluding some for paper search (e.g. Libra [21], Citeseer\n[7] and Google Scholar [4]), product search (e.g. Froogle\n[5]), movie search [6], image search [1, 8], video search [6],\nlocal search [2], as well as news search [3]. We believe the\nvertical search engine trend will continue to grow.\nEssentially, building vertical search engines includes data\ncrawling, information extraction, object identification and\nintegration, and object-level Web information retrieval (or\nWeb object ranking) [20], among which ranking is one of the\nmost important factors. This is because it deals with the\ncore problem of how to combine and rank objects coming\nfrom multiple communities.\nAlthough object-level ranking has been well studied in\nbuilding vertical search engines, there are still some kinds\nof vertical domains in which objects cannot be effectively\nranked. For example, algorithms that evolved from\nPageRank [22], PopRank [21] and LinkFusion [27] were proposed\nto rank objects coming from multiple communities, but can\nonly work on well-defined graphs of heterogeneous data.\nWell-defined means that like objects (e.g. authors in\npaper search) can be identified in multiple communities (e.g.\nconferences). This allows heterogeneous objects to be well\nlinked to form a graph through leveraging all the\nrelationships (e.g. cited-by, authored-by and published-by) among\nthe multiple communities.\nHowever, this assumption does not always stand for some\ndomains. High-quality photo search, movie search and news\nsearch are exceptions. For example, a photograph forum\n377\nwebsite usually includes three kinds of objects: photos,\nauthors and reviewers. Yet different photo forums seem to\nlack any relationships, as there are no cited-by relationships.\nThis makes it difficult to judge whether two authors cited\nare the same author, or two photos are indeed identical\nphotos. Consequently, although each photo has a rating score\nin a forum, it is non-trivial to rank photos coming from\ndifferent photo forums. Similar problems also exist in movie\nsearch and news search. Although two movie titles can be\nidentified as the same one by title and director in different\nmovie discussion groups, it is non-trivial to combine\nrating scores from different discussion groups and rank movies\neffectively. We call such non-trivial object relationship in\nwhich identification is difficult, incomplete relationships.\nOther related work includes rank aggregation for the Web\n[13, 14], and learning algorithm for rank, such as RankBoost\n[15], RankSVM [17, 19], and RankNet [12]. We will contrast\ndifferences of these methods with the proposed methods\nafter we have described the problem and our methods.\nWe will specifically focus on Web object-ranking\nproblem in cases that lack object relationships or have with\nincomplete object relationships, and take high-quality photo\nsearch as the test bed for this investigation. In the following,\nwe will introduce rationale for building high-quality photo\nsearch.\n1.1 High-Quality Photo Search\nIn the past ten years, the Internet has grown to become\nan incredible resource, allowing users to easily access a huge\nnumber of images. However, compared to the more than 1\nbillion images indexed by commercial search engines, actual\nqueries submitted to image search engines are relatively\nminor, and occupy only 8-10 percent of total image and text\nqueries submitted to commercial search engines [24]. This\nis partially because user requirements for image search are\nfar less than those for general text search. On the other\nhand, current commercial search engines still cannot well\nmeet various user requirements, because there is no\neffective and practical solution to understand image content.\nTo better understand user needs in image search, we\nconducted a query log analysis based on a commercial search\nengine. The result shows that more than 20% of image\nsearch queries are related to nature and places and daily\nlife categories. Users apparently are interested in enjoying\nhigh-quality photos or searching for beautiful images of\nlocations or other kinds. However, such user needs are not\nwell supported by current image search engines because of\nthe difficulty of the quality assessment problem.\nIdeally, the most critical part of a search engine - the\nranking function - can be simplified as consisting of two\nkey factors: relevance and quality. For the relevance\nfactor, search in current commercial image search engines\nprovide most returned images that are quite relevant to queries,\nexcept for some ambiguity. However, as to quality factor,\nthere is still no way to give an optimal rank to an image.\nThough content-based image quality assessment has been\ninvestigated over many years [23, 25, 26], it is still far from\nready to provide a realistic quality measure in the immediate\nfuture.\nSeemingly, it really looks pessimistic to build an image\nsearch engine that can fulfill the potentially large\nrequirement of enjoying high-quality photos. Various proliferating\nWeb communities, however, notices us that people today\nhave created and shared a lot of high-quality photos on the\nWeb on virtually any topics, which provide a rich source for\nbuilding a better image search engine.\nIn general, photos from various photo forums are of higher\nquality than personal photos, and are also much more\nappealing to public users than personal photos. In addition,\nphotos uploaded to photo forums generally require rich\nmetadata about title, camera setting, category and description to\nbe provide by photographers. These metadata are actually\nthe most precise descriptions for photos and undoubtedly\ncan be indexed to help search engines find relevant results.\nMore important, there are volunteer users in Web\ncommunities actively providing valuable ratings for these photos.\nThe rating information is generally of great value in solving\nthe photo quality ranking problem.\nMotivated by such observations, we have been attempting\nto build a vertical photo search engine by extracting rich\nmetadata and integrating information form various photo\nWeb forums. In this paper, we specifically focus on how to\nrank photos from multiple Web forums.\nIntuitively, the rating scores from different photo forums\ncan be empirically normalized based on the number of\nphotos and the number of users in each forum. However, such\na straightforward approach usually requires large manual\neffort in both tedious parameter tuning and subjective\nresults evaluation, which makes it impractical when there are\ntens or hundreds of photo forums to combine. To address\nthis problem, we seek to build relationships/links between\ndifferent photo forums. That is, we first adopt an efficient\nalgorithm to find duplicate photos which can be considered\nas hidden links connecting multiple forums. We then\nformulate the ranking challenge as an optimization problem,\nwhich eventually results in an optimal ranking function.\n1.2 Main Contributions and Organization.\nThe main contributions of this paper are:\n1. We have proposed and built a vertical image search\nengine by leveraging rich metadata from various photo\nforum Web sites to meet user requirements of searching\nfor and enjoying high-quality photos, which is\nimpossible in traditional image search engines.\n2. We have proposed two kinds of Web object-ranking\nalgorithms for photos with incomplete relationships,\nwhich can automatically and efficiently integrate as\nmany as possible Web communities with rating\ninformation and achieves an equal qualitative result\ncompared with the manually tuned fusion scheme.\nThe rest of this paper is organized as follows. In Section\n2, we present in detail the proposed solutions to the\nranking problem, including how to find hidden links between\ndifferent forums, normalize rating scores, obtain the\noptimal ranking function, and contrast our methods with some\nother related research. In Section 3, we describe the\nexperimental setting and experiments and user studies conducted\nto evaluate our algorithm. Our conclusion and a discussion\nof future work is in Section 4.\nIt is worth noting that although we treat vertical photo\nsearch as the test bed in this paper, the proposed ranking\nalgorithm can also be applied to rank other content that\nincludes video clips, poems, short stories, drawings,\nsculptures, music, and so on.\n378\n2. ALGORITHM\n2.1 Overview\nThe difficulty of integrating multiple Web forums is in\ntheir different rating systems, where there are generally two\nkinds of freedom. The first kind of freedom is the rating\ninterval or rating scale including the minimal and maximal\nratings for each Web object. For example, some forums use\na 5-point rating scale whereas other forums use 3-point or\n10-point rating scales. It seems easy to fix this freedom, but\ndetailed analysis of the data and experiments show that it\nis a non-trivial problem.\nThe second kind of freedom is the varying rating criteria\nfound in different Web forums. That is, the same score does\nnot mean the same quality in different forums. Intuitively, if\nwe can detect same photographers or same photographs, we\ncan build relationships between any two photo forums and\ntherefore can standardize the rating criterion by score\nnormalization and transformation. Fortunately, we find that\nquite a number of duplicate photographs exist in various\nWeb photo forums. This fact is reasonable when\nconsidering that photographers sometimes submit a photo to more\nthan one forum to obtain critiques or in hopes of widespread\npublicity. In this work, we adopt an efficient duplicate photo\ndetection algorithm [10] to find these photos.\nThe proposed methods below are based on the following\nconsiderations. Faced with the need to overcome a ranking\nproblem, a standardized rating criterion rather than a\nreasonable rating criterion is needed. Therefore, we can take\na large scale forum as the reference forum, and align other\nforums by taking into account duplicate Web objects\n(duplicate photos in this work). Ideally, the scores of duplicate\nphotos should be equal even though they are in different\nforums. Yet we can deem that scores in different\nforumsexcept for the reference forum - can vary in a parametric\nspace. This can be determined by minimizing the objective\nfunction defined by the sum of squares of the score\ndifferences. By formulating the ranking problem as an\noptimization problem that attempts to make the scores of duplicate\nphotos in non-reference forums as close as possible to those\nin the reference forum, we can effectively solve the ranking\nproblem.\nFor convenience, the following notations are employed.\nSki and \u00afSki denote the total score and mean score of ith Web\nobject (photo) in the kth Web site, respectively. The total\nscore refers to the sum of the various rating scores (e.g.,\nnovelty rating and aesthetic rating), and the mean score refers\nto the mean of the various rating scores. Suppose there are\na total of K Web sites. We further use\n{Skl\ni |i = 1, ..., Ikl; k, l = 1, ..., K; k = l}\nto denote the set of scores for Web objects (photos) in kth\nWeb forums that are duplicate with the lth Web forums,\nwhere Ikl is the total number of duplicate Web objects\nbetween these two Web sites. In general, score fusion can be\nseen as the procedure of finding K transforms\n\u03c8k(Ski) = eSki, k = 1, ..., K\nsuch that eSki can be used to rank Web objects from different\nWeb sites. The objective function described in the above\nFigure 1: Web community integration. Each Web\ncommunity forms a subgraph, and all communities\nare linked together by some hidden links (dashed\nlines).\nparagraph can then be formulated as\nmin\n{\u03c8k|k=2,...,K}\nKX\nk=2\nIk1X\ni=1\n\u00afwk\ni\n\nS1k\ni \u2212 \u03c8k(Sk1\ni )\n2\n(1)\nwhere we use k = 1 as the reference forum and thus \u03c81(S1i) =\nS1i. \u00afwk\ni (\u2265 0) is the weight coefficient that can be set\nheuristically according to the numbers of voters (reviewers or\ncommenters) in both the reference forum and the non-reference\nforum. The more reviewers, the more popular the photo is\nand the larger the corresponding weight \u00afwk\ni should be. In\nthis work, we do not inspect the problem of how to choose \u00afwk\ni\nand simply set them to one. But we believe the proper use\nof \u00afwk\ni , which leverages more information, can significantly\nimprove the results.\nFigure 1 illustrates the aforementioned idea. The Web\nCommunity 1 is the reference community. The dashed lines\nare links indicating that the two linked Web objects are\nactually the same. The proposed algorithm will try to find the\nbest \u03c8k(k = 2, ..., K), which has certain parametric forms\naccording to certain models. So as to minimize the cost\nfunction defined in Eq. 1, the summation is taken on all the\nred dashed lines.\nWe will first discuss the score normalization methods in\nSection 2.2, which serves as the basis for the following work.\nBefore we describe the proposed ranking algorithms, we first\nintroduce a manually tuned method in Section 2.3, which is\nlaborious and even impractical when the number of\ncommunities become large. In Section 2.4, we will briefly explain\nhow to precisely find duplicate photos between Web forums.\nThen we will describe the two proposed methods: Linear\nfusion and Non-linear fusion, and a performance measure for\nresult evaluation in Section 2.5. Finally, in Section 2.6 we\nwill discuss the relationship of the proposed methods with\nsome other related work.\n2.2 Score Normalization\nSince different Web (photo) forums on the Web usually\nhave different rating criteria, it is necessary to normalize\nthem before applying different kinds of fusion methods. In\naddition, as there are many kinds of ratings, such as\nratings for novelty, ratings for aesthetics etc, it is reasonable\nto choose a common one - total score or average\nscorethat can always be extracted in any Web forum or\ncalculated by corresponding ratings. This allows the\nnormaliza379\ntion method on the total score or average score to be viewed\nas an impartial rating method between different Web\nforums.\nIt is straightforward to normalize average scores by\nlinearly transforming them to a fixed interval. We call this\nkind of score as Scaled Mean Score. The difficulty, however,\nof using this normalization method is that, if there are only\na few users rating an object, say a photo in a photo forum,\nthe average score for the object is likely to be spammed or\nskewed.\nTotal score can avoid such drawbacks that contain more\ninformation such as a Web object\"s quality and popularity.\nThe problem is thus how to normalize total scores in\ndifferent Web forums. The simplest way may be normalization\nby the maximal and minimal scores. The drawback of this\nnormalization method is it is non robust, or in other words,\nit is sensitive to outliers.\nTo make the normalization insensitive to unusual data,\nwe propose the Mode-90% Percentile normalization method.\nHere, the mode score represents the total score that has been\nassigned to more photos than any other total score. And The\nhigh percentile score (e.g.,90%) represents the total score for\nwhich the high percentile of images have a lower total score.\nThis normalization method utilizes the mode and 90%\npercentile as two reference points to align two rating systems,\nwhich makes the distributions of total scores in different\nforums more consistent. The underlying assumption, for\nexample in different photo forums, is that even the qualities of\ntop photos in different forums may vary greatly and be less\ndependent on the forum quality, the distribution of photos\nof middle-level quality (from mode to 90% percentile) should\nbe almost of the same quality up to the freedom which\nreflects the rating criterion (strictness) of Web forums.\nPhotos of this middle-level in a Web forum usually occupy more\nthan 70 % of total photos in that forum.\nWe will give more detailed analysis of the scores in Section\n3.2.\n2.3 Manual Fusion\nThe Web movie forum, IMDB [16], proposed to use a\nBayesian-ranking function to normalize rating scores within\none community. Motivated by this ranking function, we\npropose this manual fusion method: For the kth Web site, we\nuse the following formula\neSki = \u03b1k \u00b7\n\u201e\nnk \u00b7 \u00afSki\nnk + n\u2217\nk\n+\nn\u2217\nk \u00b7 S\u2217\nk\nnk + n\u2217\nk\n\u00ab\n(2)\nto rank photos, where nk is the number of votes and n\u2217\nk,\nS\u2217\nk and \u03b1k are three parameters. This ranking function first\ntakes a balance between the original mean score \u00afSki and a\nreference score S\u2217\nk to get a weighted mean score which may\nbe more reliable than \u00afSki. Then the weighted mean score is\nscaled by \u03b1k to get the final score fSki.\nFor n Web communities, there are then about 3n\nparameters in {(\u03b1k, n\u2217\nk, S\u2217\nk)|k = 1, ..., n} to tune. Though this\nmethod can achieves pretty good results after careful and\nthorough manual tuning on these parameters, when n\nbecomes increasingly large, say there are tens or hundreds of\nWeb communities crawled and indexed, this method will\nbecome more and more laborious and will eventually become\nimpractical. It is therefore desirable to find an effective\nfusion method whose parameters can be automatically\ndetermined.\n2.4 Duplicate Photo Detection\nWe use Dedup [10], an efficient and effective duplicate\nimage detection algorithm, to find duplicate photos between\nany two photo forums. This algorithm uses hash function\nto map a high dimensional feature to a 32 bits hash code\n(see below for how to construct the hash code). Its\ncomputational complexity to find all the duplicate images among\nn images is about O(n log n). The low-level visual feature\nfor each photo is extracted on k \u00d7 k regular grids. Based\non all features extracted from the image database, a PCA\nmodel is built. The visual features are then transformed to\na relatively low-dimensional and zero mean PCA space, or\n29 dimensions in our system. Then the hash code for each\nphoto is built as follows: each dimension is transformed to\none, if the value in this dimension is greater than 0, and 0\notherwise. Photos in the same bucket are deemed potential\nduplicates and are further filtered by a threshold in terms\nof Euclidean similarity in the visual feature space.\nFigure 2 illustrates the hashing procedure, where visual\nfeatures - mean gray values - are extracted on both 6 \u00d7 6\nand 7\u00d77 grids. The 85-dimensional features are transformed\nto a 32-dimensional vector, and the hash code is generated\naccording to the signs.\nFigure 2: Hashing procedure for duplicate photo\ndectection\n2.5 Score Fusion\nIn this section, we will present two solutions on score\nfusion based on different parametric form assumptions of \u03c8k\nin Eq. 1.\n2.5.1 Linear Fusion by Duplicate Photos\nIntuitively, the most straightforward way to factor out the\nuncertainties caused by the different criterion is to scale,\nrel380\native to a given center, the total scores of each unreferenced\nWeb photo forum with respect to the reference forum. More\nstrictly, we assume \u03c8k has the following form\n\u03c8k(Ski) = \u03b1kSki + tk, k = 2, ..., K (3)\n\u03c81(S1i) = S1i (4)\nwhich means that the scores of k(= 1)th forum should be\nscaled by \u03b1k relative to the center tk\n1\u2212\u03b1k\nas shown in Figure\n3.\nThen, if we substitute above \u03c8k to Eq. 1, we get the\nfollowing objective function,\nmin\n{\u03b1k,tk|k=2,...,K}\nKX\nk=2\nIk1X\ni=1\n\u00afwk\ni\nh\nS1k\ni \u2212 \u03b1kSk1\ni \u2212 tk\ni2\n. (5)\nBy solving the following set of functions,\n(\n\u2202f\n\u2202\u03b1k\n= = 0\n\u2202f\n\u2202tk\n= 0\n, k = 1, ..., K\nwhere f is the objective function defined in Eq. 5, we get\nthe closed form solution as:\n\u201e\n\u03b1k\ntk\n\u00ab\n= A\u22121\nk Lk (6)\nwhere\nAk =\n\u201e P\ni \u00afwi(Sk1\ni )2 P\ni \u00afwiSk1\niP\ni \u00afwiSk1\ni\nP\ni \u00afwi\n\u00ab\n(7)\nLk =\n\u201e P\ni \u00afwiS1k\ni Sk1\niP\ni \u00afwiS1k\ni\n\u00ab\n(8)\nand k = 2, ..., K.\nThis is a linear fusion method. It enjoys simplicity and\nexcellent performance in the following experiments.\nFigure 3: Linear Fusion method\n2.5.2 Nonlinear Fusion by Duplicate Photos\nSometimes we want a method which can adjust scores on\nintervals with two endpoints unchanged. As illustrated in\nFigure 4, the method can tune scores between [C0, C1] while\nleaving scores C0 and C1 unchanged. This kind of fusion\nmethod is then much finer than the linear ones and\ncontains many more parameters to tune and expect to further\nimprove the results.\nHere, we propose a nonlinear fusion solution to satisfy\nsuch constraints. First, we introduce a transform:\n\u03b7c0,c1,\u03b1(x) =\n(\nx\u2212c0\nc1\u2212c0\n\u03b1\n(c1 \u2212 c0) + c0, if x \u2208 (c0, c1]\nx otherwise\nwhere \u03b1 > 0. This transform satisfies that for x \u2208 [c0, c1],\n\u03b7c0,c1,\u03b1(x) \u2208 [c0, c1] with \u03b7c0,c1,\u03b1(c0) = c0 and \u03b7c0,c1,\u03b1(c1) =\nc1. Then we can utilize this nonlinear transform to adjust\nthe scores in certain interval, say (M, T],\n\u03c8k(Ski) = \u03b7M,T,\u03b1(Ski) . (9)\nFigure 4: Nonlinear Fusion method. We intent to\nfinely adjust the shape of the curves in each segment.\nEven there is no closed-form solution for the following\noptimization problem,\nmin\n{\u03b1k|k\u2208[2,K]}\nKX\nk=2\nIk1X\ni=1\n\u00afwk\ni\nh\nS1k\ni \u2212 \u03b7M,T,\u03b1(Ski)\ni2\nit is not hard to get the numeric one. Under the same\nassumptions made in Section 2.2, we can use this method to\nadjust scores of the middle-level (from the mode point to\nthe 90 % percentile).\nThis more complicated non-linear fusion method is\nexpected to achieve better results than the linear one.\nHowever, difficulties in evaluating the rank results block us from\ntuning these parameters extensively. The current\nexperiments in Section 3.5 do not reveal any advantages over the\nsimple linear model.\n2.5.3 Performance Measure of the Fusion Results\nSince our objective function is to make the scores of the\nsame Web objects (e.g. duplicate photos) between a\nnonreference forum and the reference forum as close as possible,\nit is natural to investigate how close they become to each\nother and how the scores of the same Web objects change\nbetween the two non-reference forums before and after score\nfusion.\nTaken Figure 1 as an example, the proposed algorithms\nminimize the score differences of the same Web objects in\ntwo Web forums: the reference forum (the Web Community\n1) and a non-reference forum, which corresponds to\nminimizing the objective function on the red dashed (hidden)\nlinks. After the optimization, we must ask what happens to\nthe score differences of the same Web objects in two\nnonreference forums? Or, in other words, whether the scores\nof two objects linked by the green dashed (hidden) links\nbecome more consistent?\nWe therefore define the following performance\nmeasure\u03b4 measure - to quantify the changes for scores of the same\nWeb objects in different Web forums as\n\u03b4kl = Sim(Slk\n, Skl\n) \u2212 Sim(Slk\n\u2217 , Skl\n\u2217 ) (10)\n381\nwhere Skl\n= (Skl\n1 , ..., Skl\nIkl\n)T\n, Skl\n\u2217 = (eSkl\n1 , ..., eSkl\nIkl\n)T\nand\nSim(a, b) =\na \u00b7 b\n||a||||b||\n.\n\u03b4kl > 0 means after score fusion, scores on the same Web\nobjects between kth and lth Web forum become more\nconsistent, which is what we expect. On the contrary, if \u03b4kl < 0,\nthose scores become more inconsistent.\nAlthough we cannot rely on this measure to evaluate our\nfinal fusion results as ranking photos by their popularity and\nqualities is such a subjective process that every person can\nhave its own results, it can help us understand the\nintermediate ranking results and provide insights into the final\nperformances of different ranking methods.\n2.6 Contrasts with Other Related Work\nWe have already mentioned the differences of the proposed\nmethods with the traditional methods, such as PageRank\n[22], PopRank [21], and LinkFusion [27] algorithms in\nSection 1. Here, we discuss some other related works.\nThe current problem can also be viewed as a rank\naggregation one [13, 14] as we deal with the problem of how to\ncombine several rank lists. However, there are\nfundamental differences between them. First of all, unlike the Web\npages, which can be easily and accurately detected as the\nsame pages, detecting the same photos in different Web\nforums is a non-trivial work, and can only be implemented by\nsome delicate algorithms while with certain precision and\nrecall. Second, the numbers of the duplicate photos from\ndifferent Web forums are small relative to the whole photo\nsets (see Table 1). In another words, the top K rank lists\nof different Web forums are almost disjointed for a given\nquery. Under this condition, both the algorithms proposed\nin [13] and their measurements - Kendall tau distance or\nSpearman footrule distance - will degenerate to some\ntrivial cases.\nAnother category of rank fusion (aggregation) methods is\nbased on machine learning algorithms, such as RankSVM\n[17, 19], RankBoost [15], and RankNet [12]. All of these\nmethods entail some labelled datasets to train a model. In\ncurrent settings, it is difficult or even impossible to get these\ndatasets labelled as to their level of professionalism or\npopularity, since the photos are too vague and subjective to rank.\nInstead, the problem here is how to combine several ordered\nsub lists to form a total order list.\n3. EXPERIMENTS\nIn this section, we carry out our research on high-quality\nphoto search. We first briefly introduce the newly proposed\nvertical image search engine - EnjoyPhoto in section 3.1.\nThen we focus on how to rank photos from different Web\nforums. In order to do so, we first normalize the scores\n(ratings) for photos from different multiple Web forums in\nsection 3.2. Then we try to find duplicate photos in section\n3.3. Some intermediate results are discussed using \u03b4 measure\nin section 3.4. Finally a set of user studies is carried out\ncarefully to justify our proposed method in section 3.5.\n3.1 EnjoyPhoto: high-quality Photo Search\nEngine\nIn order to meet user requirement of enjoying high-quality\nphotos, we propose and build a high-quality photo search\nengine - EnjoyPhoto, which accounts for the following three\nkey issues: 1. how to crawl and index photos, 2. how to\ndetermine the qualities of each photo and 3. how to\ndisplay the search results in order to make the search process\nenjoyable. For a given text based query, this system ranks\nthe photos based on certain combination of relevance of the\nphoto to this query (Issue 1) and the quality of the photo\n(Issue 2), and finally displays them in an enjoyable manner\n(Issue 3).\nAs for Issue 3, we devise the interface of the system\ndeliberately in order to smooth the users\" process of enjoying\nhigh-quality photos. Techniques, such as Fisheye and slides\nshow, are utilized in current system. Figure 5 shows the\ninterface. We will not talk more about this issue as it is not\nan emphasis of this paper.\nFigure 5: EnjoyPhoto: an enjoyable high-quality\nphoto search engine, where 26,477 records are\nreturned for the query fall in about 0.421 seconds\nAs for Issue 1, we extracted from a commercial search\nengine a subset of photos coming from various photo forums\nall over the world, and explicitly parsed the Web pages\ncontaining these photos. The number of photos in the data\ncollection is about 2.5 million. After the parsing, each photo\nwas associated with its title, category, description, camera\nsetting, EXIF data 1\n(when available for digital images),\nlocation (when available in some photo forums), and many\nkinds of ratings. All these metadata are generally precise\ndescriptions or annotations for the image content, which are\nthen indexed by general text-based search technologies [9,\n18, 11]. In current system, the ranking function was\nspecifically tuned to emphasize title, categorization, and rating\ninformation.\nIssue 2 is essentially dealt with in the following sections\nwhich derive the quality of photos by analyzing ratings\nprovided by various Web photo forums. Here we chose six photo\nforums to study the ranking problem and denote them as\nWeb-A, Web-B, Web-C, Web-D, Web-E and Web-F.\n3.2 Photo Score Normalization\nDetailed analysis of different score normalization\nmethods are analyzed in this section. In this analysis, the zero\n1\nDigital cameras save JPEG (.jpg) files with EXIF\n(Exchangeable Image File) data. Camera settings and scene\ninformation are recorded by the camera into the image file.\nwww.digicamhelp.com/what-is-exif/\n382\n0 2 4 6 8 10\n0\n1000\n2000\n3000\n4000\nNormalized Score\nTotalNumber\n(a) Web-A\n0 2 4 6 8 10\n0\n0.5\n1\n1.5\n2\n2.5\n3\nx 10\n4\nNormalized Score\nTotalNumber\n(b) Web-B\n0 2 4 6 8 10\n0\n0.5\n1\n1.5\n2\nx 10\n5\nNormalized Score\nTotalNumber\n(c) Web-C\n0 2 4 6 8 10\n0\n2\n4\n6\n8\n10\nx 10\n4\nNormalized Score\nTotalNumber\n(d) Web-D\n0 2 4 6 8 10\n0\n2000\n4000\n6000\n8000\n10000\n12000\n14000\nNormalized Score\nTotalNumber\n(e) Web-E\n0 2 4 6 8 10\n0\n1\n2\n3\n4\n5\n6\nx 10\n4\nNormalized Score\nTotalNumber\n(f) Web-F\nFigure 6: Distributions of mean scores normalized\nto [0, 10]\nscores that usually occupy about than 30% of the total\nnumber of photos for some Web forums are not currently taken\ninto account. How to utilize these photos is left for future\nexplorations.\nIn Figure 6, we list the distributions of the mean score,\nwhich is transformed to a fixed interval [0, 10]. The\ndistributions of the average scores of these Web forums look quite\ndifferent. Distributions in Figure 6(a), 6(b), and 6(e) looks\nlike Gaussian distributions, while those in Figure 6(d) and\n6(f) are dominated by the top score. The reason of these\neccentric distributions for Web-D and Web-F lies in their\ncoarse rating systems. In fact, Web-D and Web-F use 2 or\n3 point rating scales whereas other Web forums use 7 or 14\npoint rating scales. Therefore, it will be problematic if we\ndirectly use these averaged scores. Furthermore the average\nscore is very likely to be spammed, if there are only a few\nusers rating a photo.\nFigure 7 shows the total score normalization method by\nmaximal and minimal scores, which is one of our base line\nsystem. All the total scores of a given Web forum are\nnormalized to [0, 100] according to the maximal score and\nminimal score of corresponding Web forum. We notice that total\nscore distribution of Web-A in Figure 7(a) has two larger\ntails than all the others. To show the shape of the\ndistributions more clearly, we only show the distributions on [0, 25]\nin Figure 7(b),7(c),7(d),7(e), and 7(f).\nFigure 8 shows the Mode-90% Percentile normalization\nmethod, where the modes of the six distributions are\nnormalized to 5 and the 90% percentile to 8. We can see that\nthis normalization method makes the distributions of total\nscores in different forums more consistent. The two proposed\nalgorithms are all based on these normalization methods.\n3.3 Duplicate photo detection\nTargeting at computational efficiency, the Dedup\nalgorithm may lose some recall rate, but can achieve a high\nprecision rate. We also focus on finding precise hidden links\nrather than all hidden links. Figure 9 shows some duplicate\ndetection examples. The results are shown in Table 1 and\nverify that large numbers of duplicate photos exist in any\ntwo Web forums even with the strict condition for Dedup\nwhere we chose first 29 bits as the hash code. Since there\nare only a few parameters to estimate in the proposed fusion\nmethods, the numbers of duplicate photos shown Table 1 are\n0 20 40 60 80 100\n0\n100\n200\n300\n400\n500\n600\nNormalized Score\nTotalNumber\n(a) Web-A\n0 5 10 15 20 25\n0\n1\n2\n3\n4\n5\nx 10\n4\nNormalized Score\nTotalNumber\n(b) Web-B\n0 5 10 15 20 25\n0\n1\n2\n3\n4\n5\nx 10\n5\nNormalized Score\nTotalNumber\n(c) Web-C\n0 5 10 15 20 25\n0\n0.5\n1\n1.5\n2\n2.5\nx 10\n4\nNormalized Score\nTotalNumber\n(d) Web-D\n0 5 10 15 20 25\n0\n2000\n4000\n6000\n8000\n10000\nNormalized Score\nTotalNumber\n(e) Web-E\n0 5 10 15 20 25\n0\n0.5\n1\n1.5\n2\n2.5\n3\nx 10\n4\nNormalized Score\nTotalNumber\n(f) Web-F\nFigure 7: Maxmin Normalization\n0 5 10 15\n0\n200\n400\n600\n800\n1000\n1200\n1400\nNormalized Score\nTotalNumber\n(a) Web-A\n0 5 10 15\n0\n1\n2\n3\n4\n5\nx 10\n4\nNormalized Score\nTotalNumber\n(b) Web-B\n0 5 10 15\n0\n2\n4\n6\n8\n10\n12\n14\nx 10\n4\nNormalized Score\nTotalNumber\n(c) Web-C\n0 5 10 15\n0\n0.5\n1\n1.5\n2\n2.5\nx 10\n4\nNormalized Score\nTotalNumber\n(d) Web-D\n0 5 10 15\n0\n2000\n4000\n6000\n8000\n10000\n12000\nNormalized Score\nTotalNumber\n(e) Web-E\n0 5 10 15\n0\n2000\n4000\n6000\n8000\n10000\nNormalized Score\nTotalNumber\n(f) Web-F\nFigure 8: Mode-90% Percentile Normalization\nsufficient to determine these parameters. The last table\ncolumn lists the total number of photos in the corresponding\nWeb forums.\n3.4 \u03b4 Measure\nThe parameters of the proposed linear and nonlinear\nalgorithms are calculated using the duplicate data shown in\nTable 1, where the Web-C is chosen as the reference Web\nforum since it shares the most duplicate photos with other\nforums.\nTable 2 and 3 show the \u03b4 measure on the linear model and\nnonlinear model. As \u03b4kl is symmetric and \u03b4kk = 0, we only\nshow the upper triangular part. The NaN values in both\ntables lie in that no duplicate photos have been detected by\nthe Dedup algorithm as reported in Table 1.\nThe linear model guarantees that the \u03b4 measures related\nTable 1: Number of duplicate photos between each\npair of Web forums\nA B C D E F Scale\nA 0 316 1,386 178 302 0 130k\nB 316 0 14,708 909 8,023 348 675k\nC 1,386 14,708 0 1,508 19,271 1,083 1,003k\nD 178 909 1,508 0 1,084 21 155k\nE 302 8,023 19,271 1,084 0 98 448k\nF 0 348 1,083 21 98 0 122k\n383\nFigure 9: Some results of duplicate photo detection\nTable 2: \u03b4 measure on the linear model.\nWeb-B Web-C Web-D Web-E Web-F\nWeb-A 0.0659 0.0911 0.0956 0.0928 NaN\nWeb-B - 0.0672 0.0578 0.0791 0.4618\nWeb-C - - 0.0105 0.0070 0.2220\nWeb-D - - - 0.0566 0.0232\nWeb-E - - - - 0.6525\nto the reference community should be no less than 0\ntheoretically. It is indeed the case (see the underlined numbers\nin Table 2). But this model can not guarantee that the \u03b4\nmeasures on the non-reference communities can also be no\nless than 0, as the normalization steps are based on\nduplicate photos between the reference community and a\nnonreference community. Results shows that all the numbers in\nthe \u03b4 measure are greater than 0 (see all the non-underlined\nnumbers in Table 2), which indicates that it is probable that\nthis model will give optimal results.\nOn the contrary, the nonlinear model does not guarantee\nthat \u03b4 measures related to the reference community should\nbe no less than 0, as not all duplicate photos between the\ntwo Web forums can be used when optimizing this model.\nIn fact, the duplicate photos that lie in different intervals\nwill not be used in this model. It is these specific duplicate\nphotos that make the \u03b4 measure negative. As a result, there\nare both negative and positive items in Table 3, but overall\nthe number of positive ones are greater than negative ones\n(9:5), that indicates the model may be better than the\nnormalization only method (see next subsection) which has an\nall-zero \u03b4 measure, and worse than the linear model.\n3.5 User Study\nBecause it is hard to find an objective criterion to evaluate\nTable 3: \u03b4 measure on the nonlinear model.\nWeb-B Web-C Web-D Web-E Web-F\nWeb-A 0.0559 0.0054 -0.0185 -0.0054 NaN\nWeb-B - -0.0162 -0.0345 -0.0301 0.0466\nWeb-C - - 0.0136 0.0071 0.1264\nWeb-D - - - 0.0032 0.0143\nWeb-E - - - - 0.214\nwhich ranking function is better, we chose to employ user\nstudies for subjective evaluations. Ten subjects were invited\nto participate in the user study. They were recruited from\nnearby universities. As search engines of both text search\nand image search are familiar to university students, there\nwas no prerequisite criterion for choosing students.\nWe conducted user studies using Internet Explorer 6.0 on\nWindows XP with 17-inch LCD monitors set at 1,280 pixels\nby 1,024 pixels in 32-bit color. Data was recorded with\nserver logs and paper-based surveys after each task.\nFigure 10: User study interface\nWe specifically device an interface for user study as shown\nin Figure 10. For each pair of fusion methods, participants\nwere encouraged to try any query they wished. For those\nwithout specific ideas, two combo boxes (category list and\nquery list) were listed on the bottom panel, where the top\n1,000 image search queries from a commercial search engine\nwere provided. After a participant submitted a query, the\nsystem randomly selected the left or right frame to display\neach of the two ranking results. The participant were then\nrequired to judge which ranking result was better of the two\nranking results, or whether the two ranking results were of\nequal quality, and submit the judgment by choosing the\ncorresponding radio button and clicking the Submit button.\nFor example, in Figure 10, query sunset is submitted to\nthe system. Then, 79,092 photos were returned and ranked\nby the Minmax fusion method in the left frame and linear\nfusion method in the right frame. A participant then\ncompares the two ranking results (without knowing the ranking\nmethods) and submits his/her feedback by choosing answers\nin the Your option.\nTable 4: Results of user study\nNorm.Only Manually Linear\nLinear 29:13:10\n14:22:15Nonlinear 29:15:9 12:27:12 6:4:45\nTable 4 shows the experimental results, where Linear\ndenotes the linear fusion method, Nonlinear denotes the\nnon linear fusion method, Norm. Only means Maxmin\nnormalization method, Manually means the manually tuned\nmethod. The three numbers in each item, say 29:13:10,\nmean that 29 judgments prefer the linear fusion results, 10\n384\njudgments prefer the normalization only method, and 13\njudgments consider these two methods as equivalent.\nWe conduct the ANOVA analysis, and obtain the\nfollowing conclusions:\n1. Both the linear and nonlinear methods are significantly\nbetter than the Norm. Only method with respective\nP-values 0.00165(< 0.05) and 0.00073(<< 0.05). This\nresult is consistent with the \u03b4-measure evaluation\nresult. The Norm. Only method assumes that the top\n10% photos in different forums are of the same\nquality. However, this assumption does not stand in\ngeneral. For example, a top 10% photo in a top tier photo\nforum is generally of higher quality than a top 10%\nphoto in a second-tier photo forum. This is similar\nto that, those top 10% students in a top-tier\nuniversity and those in a second-tier university are generally\nof different quality. Both linear and nonlinear fusion\nmethods acknowledge the existence of such differences\nand aim at quantizing the differences. Therefore, they\nperform better than the Norm. Only method.\n2. The linear fusion method is significantly better than\nthe nonlinear one with P-value 1.195 \u00d7 10\u221210\n. This\nresult is rather surprising as this more complicated\nranking method is expected to tune the ranking more\nfinely than the linear one. The main reason for this\nresult may be that it is difficult to find the best\nintervals where the nonlinear tuning should be carried out\nand yet simply the middle part of the Mode-90%\nPercentile Normalization method was chosen. The\ntimeconsuming and subjective evaluation methods - user\nstudies - blocked us extensively tuning these\nparameters.\n3. The proposed linear and nonlinear methods perform\nalmost the same with or slightly better than the\nmanually tuned method. Given that the linear/nonlinear\nfusion methods are fully automatic approaches, they\nare considered practical and efficient solutions when\nmore communities (e.g. dozens of communities) need\nto be integrated.\n4. CONCLUSIONS AND FUTURE WORK\nIn this paper, we studied the Web object-ranking\nproblem in the cases of lacking object relationships where\ntraditional ranking algorithms are no longer valid, and took\nhigh-quality photo search as the test bed for this\ninvestigation. We have built a vertical high-quality photo search\nengine, and proposed score fusion methods which can\nautomatically integrate as many data sources (Web forums) as\npossible. The proposed fusion methods leverage the hidden\nlinks discovered by duplicate photo detection algorithm, and\nminimize score differences of duplicate photos in different\nforums. Both the intermediate results and the user\nstudies show that the proposed fusion methods are a practical\nand efficient solution to Web object ranking in the\naforesaid relationships. Though the experiments were conducted\non high-quality photo ranking, the proposed algorithms are\nalso applicable to other kinds of Web objects including video\nclips, poems, short stories, music, drawings, sculptures, and\nso on.\nCurrent system is far from being perfect. In order to make\nthis system more effective, more delicate analysis for the\nvertical domain (e.g., Web photo forums) are needed. The\nfollowing points, for example, may improve the searching\nresults and will be our future work: 1. more subtle\nanalysis and then utilization of different kinds of ratings (e.g.,\nnovelty ratings, aesthetic ratings); 2. differentiating various\ncommunities who may have different interests and\npreferences or even distinct culture understandings; 3.\nincorporating more useful information, including photographers\" and\nreviewers\" information, to model the photos in a\nheterogeneous data space instead of the current homogeneous one.\nWe will further utilize collaborative filtering to recommend\nrelevant high-quality photos to browsers.\nOne open problem is whether we can find an objective and\nefficient criterion for evaluating the ranking results, instead\nof employing subjective and inefficient user studies, which\nblocked us from trying more ranking algorithms and tuning\nparameters in one algorithm.\n5. ACKNOWLEDGMENTS\nWe thank Bin Wang and Zhi Wei Li for providing Dedup\ncodes to detect duplicate photos; Zhen Li for helping us\ndesign the interface of EnjoyPhoto; Ming Jing Li, Longbin\nChen, Changhu Wang, Yuanhao Chen, and Li Zhuang etc.\nfor useful discussions. Special thanks go to Dwight Daniels\nfor helping us revise the language of this paper.\n6. REFERENCES\n[1] Google image search. http://images.google.com.\n[2] Google local search. http://local.google.com/.\n[3] Google news search. http://news.google.com.\n[4] Google paper search. http://Scholar.google.com.\n[5] Google product search. http://froogle.google.com.\n[6] Google video search. http://video.google.com.\n[7] Scientific literature digital library.\nhttp://citeseer.ist.psu.edu.\n[8] Yahoo image search. http://images.yahoo.com.\n[9] R. Baeza-Yates and B. Ribeiro-Neto. Modern\nInformation Retrieval. New York: ACM Press;\nHarlow, England: Addison-Wesley, 1999.\n[10] W. Bin, L. Zhiwei, L. Ming Jing, and M. 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{"name": "train_H-73", "title": "Unified Utility Maximization Framework for Resource Selection", "abstract": "This paper presents a unified utility framework for resource selection of distributed text information retrieval. This new framework shows an efficient and effective way to infer the probabilities of relevance of all the documents across the text databases. With the estimated relevance information, resource selection can be made by explicitly optimizing the goals of different applications. Specifically, when used for database recommendation, the selection is optimized for the goal of highrecall (include as many relevant documents as possible in the selected databases); when used for distributed document retrieval, the selection targets the high-precision goal (high precision in the final merged list of documents). This new model provides a more solid framework for distributed information retrieval. Empirical studies show that it is at least as effective as other state-of-the-art algorithms.", "fulltext": "1. INTRODUCTION\nConventional search engines such as Google or AltaVista use\nad-hoc information retrieval solution by assuming all the\nsearchable documents can be copied into a single centralized\ndatabase for the purpose of indexing. Distributed information\nretrieval, also known as federated search [1,4,7,11,14,22] is\ndifferent from ad-hoc information retrieval as it addresses the\ncases when documents cannot be acquired and stored in a single\ndatabase. For example, Hidden Web contents (also called\ninvisible or deep Web contents) are information on the Web\nthat cannot be accessed by the conventional search engines.\nHidden web contents have been estimated to be 2-50 [19] times\nlarger than the contents that can be searched by conventional\nsearch engines. Therefore, it is very important to search this type\nof valuable information.\nThe architecture of distributed search solution is highly\ninfluenced by different environmental characteristics. In a small\nlocal area network such as small company environments, the\ninformation providers may cooperate to provide corpus statistics\nor use the same type of search engines. Early distributed\ninformation retrieval research focused on this type of\ncooperative environments [1,8]. On the other side, in a wide\narea network such as very large corporate environments or on\nthe Web there are many types of search engines and it is difficult\nto assume that all the information providers can cooperate as\nthey are required. Even if they are willing to cooperate in these\nenvironments, it may be hard to enforce a single solution for all\nthe information providers or to detect whether information\nsources provide the correct information as they are required.\nMany applications fall into the latter type of uncooperative\nenvironments such as the Mind project [16] which integrates\nnon-cooperating digital libraries or the QProber system [9]\nwhich supports browsing and searching of uncooperative hidden\nWeb databases. In this paper, we focus mainly on uncooperative\nenvironments that contain multiple types of independent search\nengines.\nThere are three important sub-problems in distributed\ninformation retrieval. First, information about the contents of\neach individual database must be acquired (resource\nrepresentation) [1,8,21]. Second, given a query, a set of\nresources must be selected to do the search (resource selection)\n[5,7,21]. Third, the results retrieved from all the selected\nresources have to be merged into a single final list before it can\nbe presented to the end user (retrieval and results merging)\n[1,5,20,22].\nMany types of solutions exist for distributed information\nretrieval. Invisible-web.net1\nprovides guided browsing of hidden\nWeb databases by collecting the resource descriptions of these\ndatabases and building hierarchies of classes that group them by\nsimilar topics. A database recommendation system goes a step\nfurther than a browsing system like Invisible-web.net by\nrecommending most relevant information sources to users\"\nqueries. It is composed of the resource description and the\nresource selection components. This solution is useful when the\nusers want to browse the selected databases by themselves\ninstead of asking the system to retrieve relevant documents\nautomatically. Distributed document retrieval is a more\nsophisticated task. It selects relevant information sources for\nusers\" queries as the database recommendation system does.\nFurthermore, users\" queries are forwarded to the corresponding\nselected databases and the returned individual ranked lists are\nmerged into a single list to present to the users.\nThe goal of a database recommendation system is to select a\nsmall set of resources that contain as many relevant documents\nas possible, which we call a high-recall goal. On the other side,\nthe effectiveness of distributed document retrieval is often\nmeasured by the Precision of the final merged document result\nlist, which we call a high-precision goal. Prior research\nindicated that these two goals are related but not identical [4,21].\nHowever, most previous solutions simply use effective resource\nselection algorithm of database recommendation system for\ndistributed document retrieval system or solve the inconsistency\nwith heuristic methods [1,4,21].\nThis paper presents a unified utility maximization framework to\nintegrate the resource selection problem of both database\nrecommendation and distributed document retrieval together by\ntreating them as different optimization goals.\nFirst, a centralized sample database is built by randomly\nsampling a small amount of documents from each database with\nquery-based sampling [1]; database size statistics are also\nestimated [21]. A logistic transformation model is learned off\nline with a small amount of training queries to map the\ncentralized document scores in the centralized sample database\nto the corresponding probabilities of relevance.\nSecond, after a new query is submitted, the query can be used to\nsearch the centralized sample database which produces a score\nfor each sampled document. The probability of relevance for\neach document in the centralized sample database can be\nestimated by applying the logistic model to each document\"s\nscore. Then, the probabilities of relevance of all the (mostly\nunseen) documents among the available databases can be\nestimated using the probabilities of relevance of the documents\nin the centralized sample database and the database size\nestimates.\nFor the task of resource selection for a database\nrecommendation system, the databases can be ranked by the\nexpected number of relevant documents to meet the high-recall\ngoal. For resource selection for a distributed document retrieval\nsystem, databases containing a small number of documents with\nlarge probabilities of relevance are favored over databases\ncontaining many documents with small probabilities of\nrelevance. This selection criterion meets the high-precision goal\nof distributed document retrieval application. Furthermore, the\nSemi-supervised learning (SSL) [20,22] algorithm is applied to\nmerge the returned documents into a final ranked list.\nThe unified utility framework makes very few assumptions and\nworks in uncooperative environments. Two key features make it\na more solid model for distributed information retrieval: i) It\nformalizes the resource selection problems of different\napplications as various utility functions, and optimizes the utility\nfunctions to achieve the optimal results accordingly; and ii) It\nshows an effective and efficient way to estimate the probabilities\nof relevance of all documents across databases. Specifically, the\nframework builds logistic models on the centralized sample\ndatabase to transform centralized retrieval scores to the\ncorresponding probabilities of relevance and uses the centralized\nsample database as the bridge between individual databases and\nthe logistic model. The human effort (relevance judgment)\nrequired to train the single centralized logistic model does not\nscale with the number of databases. This is a large advantage\nover previous research, which required the amount of human\neffort to be linear with the number of databases [7,15].\nThe unified utility framework is not only more theoretically\nsolid but also very effective. Empirical studies show the new\nmodel to be at least as accurate as the state-of-the-art algorithms\nin a variety of configurations.\nThe next section discusses related work. Section 3 describes the\nnew unified utility maximization model. Section 4 explains our\nexperimental methodology. Sections 5 and 6 present our\nexperimental results for resource selection and document\nretrieval. Section 7 concludes.\n2. PRIOR RESEARCH\nThere has been considerable research on all the sub-problems of\ndistributed information retrieval. We survey the most related\nwork in this section.\nThe first problem of distributed information retrieval is resource\nrepresentation. The STARTS protocol is one solution for\nacquiring resource descriptions in cooperative environments [8].\nHowever, in uncooperative environments, even the databases are\nwilling to share their information, it is not easy to judge whether\nthe information they provide is accurate or not. Furthermore, it\nis not easy to coordinate the databases to provide resource\nrepresentations that are compatible with each other. Thus, in\nuncooperative environments, one common choice is query-based\nsampling, which randomly generates and sends queries to\nindividual search engines and retrieves some documents to build\nthe descriptions. As the sampled documents are selected by\nrandom queries, query-based sampling is not easily fooled by\nany adversarial spammer that is interested to attract more traffic.\nExperiments have shown that rather accurate resource\ndescriptions can be built by sending about 80 queries and\ndownloading about 300 documents [1].\nMany resource selection algorithms such as gGlOSS/vGlOSS\n[8] and CORI [1] have been proposed in the last decade. The\nCORI algorithm represents each database by its terms, the\ndocument frequencies and a small number of corpus statistics\n(details in [1]). As prior research on different datasets has shown\nthe CORI algorithm to be the most stable and effective of the\nthree algorithms [1,17,18], we use it as a baseline algorithm in\nthis work. The relevant document distribution estimation\n(ReDDE [21]) resource selection algorithm is a recent algorithm\nthat tries to estimate the distribution of relevant documents\nacross the available databases and ranks the databases\naccordingly. Although the ReDDE algorithm has been shown to\nbe effective, it relies on heuristic constants that are set\nempirically [21].\nThe last step of the document retrieval sub-problem is results\nmerging, which is the process of transforming database-specific\n33\ndocument scores into comparable database-independent\ndocument scores. The semi supervised learning (SSL) [20,22]\nresult merging algorithm uses the documents acquired by\nquerybased sampling as training data and linear regression to learn the\ndatabase-specific, query-specific merging models. These linear\nmodels are used to convert the database-specific document\nscores into the approximated centralized document scores. The\nSSL algorithm has been shown to be effective [22]. It serves as\nan important component of our unified utility maximization\nframework (Section 3).\nIn order to achieve accurate document retrieval results, many\nprevious methods simply use resource selection algorithms that\nare effective of database recommendation system. But as\npointed out above, a good resource selection algorithm\noptimized for high-recall may not work well for document\nretrieval, which targets the high-precision goal. This type of\ninconsistency has been observed in previous research [4,21].\nThe research in [21] tried to solve the problem with a heuristic\nmethod.\nThe research most similar to what we propose here is the\ndecision-theoretic framework (DTF) [7,15]. This framework\ncomputes a selection that minimizes the overall costs (e.g.,\nretrieval quality, time) of document retrieval system and several\nmethods [15] have been proposed to estimate the retrieval\nquality. However, two points distinguish our research from the\nDTF model. First, the DTF is a framework designed specifically\nfor document retrieval, but our new model integrates two\ndistinct applications with different requirements (database\nrecommendation and distributed document retrieval) into the\nsame unified framework. Second, the DTF builds a model for\neach database to calculate the probabilities of relevance. This\nrequires human relevance judgments for the results retrieved\nfrom each database. In contrast, our approach only builds one\nlogistic model for the centralized sample database. The\ncentralized sample database can serve as a bridge to connect the\nindividual databases with the centralized logistic model, thus the\nprobabilities of relevance of documents in different databases\ncan be estimated. This strategy can save large amount of human\njudgment effort and is a big advantage of the unified utility\nmaximization framework over the DTF especially when there\nare a large number of databases.\n3. UNIFIED UTILITY MAXIMIZATION\nFRAMEWORK\nThe Unified Utility Maximization (UUM) framework is based\non estimating the probabilities of relevance of the (mostly\nunseen) documents available in the distributed search\nenvironment. In this section we describe how the probabilities of\nrelevance are estimated and how they are used by the Unified\nUtility Maximization model. We also describe how the model\ncan be optimized for the high-recall goal of a database\nrecommendation system and the high-precision goal of a\ndistributed document retrieval system.\n3.1 Estimating Probabilities of Relevance\nAs pointed out above, the purpose of resource selection is\nhighrecall and the purpose of document retrieval is high-precision. In\norder to meet these diverse goals, the key issue is to estimate the\nprobabilities of relevance of the documents in various databases.\nThis is a difficult problem because we can only observe a\nsample of the contents of each database using query-based\nsampling. Our strategy is to make full use of all the available\ninformation to calculate the probability estimates.\n3.1.1 Learning Probabilities of Relevance\nIn the resource description step, the centralized sample database\nis built by query-based sampling and the database sizes are\nestimated using the sample-resample method [21]. At the same\ntime, an effective retrieval algorithm (Inquery [2]) is applied on\nthe centralized sample database with a small number (e.g., 50)\nof training queries. For each training query, the CORI resource\nselection algorithm [1] is applied to select some number\n(e.g., 10) of databases and retrieve 50 document ids from each\ndatabase. The SSL results merging algorithm [20,22] is used to\nmerge the results. Then, we can download the top 50 documents\nin the final merged list and calculate their corresponding\ncentralized scores using Inquery and the corpus statistics of the\ncentralized sample database. The centralized scores are further\nnormalized (divided by the maximum centralized score for each\nquery), as this method has been suggested to improve estimation\naccuracy in previous research [15]. Human judgment is acquired\nfor those documents and a logistic model is built to transform\nthe normalized centralized document scores to probabilities of\nrelevance as follows:\n( )\n))(exp(1\n))(exp(\n|)( _\n_\ndSba\ndSba\ndrelPdR\nccc\nccc\n++\n+\n== (1)\nwhere )(\n_\ndSc\nis the normalized centralized document score and\nac and bc are the two parameters of the logistic model. These two\nparameters are estimated by maximizing the probabilities of\nrelevance of the training queries. The logistic model provides us\nthe tool to calculate the probabilities of relevance from\ncentralized document scores.\n3.1.2 Estimating Centralized Document Scores\nWhen the user submits a new query, the centralized document\nscores of the documents in the centralized sample database are\ncalculated. However, in order to calculate the probabilities of\nrelevance, we need to estimate centralized document scores for\nall documents across the databases instead of only the sampled\ndocuments. This goal is accomplished using: the centralized\nscores of the documents in the centralized sample database, and\nthe database size statistics.\nWe define the database scale factor for the ith\ndatabase as the\nratio of the estimated database size and the number of\ndocuments sampled from this database as follows:\n^\n_\ni\ni\ni\ndb\ndb\ndb samp\nN\nSF\nN\n= (2)\nwhere\n^\nidbN is the estimated database size and _idb sampN is the\nnumber of documents from the ith\ndatabase in the centralized\nsample database. The intuition behind the database scale factor\nis that, for a database whose scale factor is 50, if one document\nfrom this database in the centralized sample database has a\ncentralized document score of 0.5, we may guess that there are\nabout 50 documents in that database which have scores of about\n0.5. Actually, we can apply a finer non-parametric linear\ninterpolation method to estimate the centralized document score\ncurve for each database. Formally, we rank all the sampled\ndocuments from the ith\ndatabase by their centralized document\n34\nscores to get the sampled centralized document score list\n{Sc(dsi1), Sc(dsi2), Sc(dsi3),\u2026..} for the ith\ndatabase; we assume\nthat if we could calculate the centralized document scores for all\nthe documents in this database and get the complete centralized\ndocument score list, the top document in the sampled list would\nhave rank SFdbi/2, the second document in the sampled list\nwould rank SFdbi3/2, and so on. Therefore, the data points of\nsampled documents in the complete list are: {(SFdbi/2, Sc(dsi1)),\n(SFdbi3/2, Sc(dsi2)), (SFdbi5/2, Sc(dsi3)),\u2026..}. Piecewise linear\ninterpolation is applied to estimate the centralized document\nscore curve, as illustrated in Figure 1. The complete centralized\ndocument score list can be estimated by calculating the values of\ndifferent ranks on the centralized document curve as:\n],1[,)(S\n^^\nc idbij Njd \u2208 .\nIt can be seen from Figure 1 that more sample data points\nproduce more accurate estimates of the centralized document\nscore curves. However, for databases with large database scale\nratios, this kind of linear interpolation may be rather inaccurate,\nespecially for the top ranked (e.g., [1, SFdbi/2]) documents.\nTherefore, an alternative solution is proposed to estimate the\ncentralized document scores of the top ranked documents for\ndatabases with large scale ratios (e.g., larger than 100).\nSpecifically, a logistic model is built for each of these databases.\nThe logistic model is used to estimate the centralized document\nscore of the top 1 document in the corresponding database by\nusing the two sampled documents from that database with\nhighest centralized scores.\n))()(exp(1\n))()(exp(\n)(\n22110\n22110\n^\n1\niciicii\niciicii\nic\ndsSdsS\ndsSdsS\ndS\n\u03b1\u03b1\u03b1\n\u03b1\u03b1\u03b1\n+++\n++\n= (3)\n0i\u03b1 , 1i\u03b1 and 2i\u03b1 are the parameters of the logistic model. For\neach training query, the top retrieved document of each database\nis downloaded and the corresponding centralized document\nscore is calculated. Together with the scores of the top two\nsampled documents, these parameters can be estimated.\nAfter the centralized score of the top document is estimated, an\nexponential function is fitted for the top part ([1, SFdbi/2]) of the\ncentralized document score curve as:\n]2/,1[)*exp()( 10\n^\nidbiiijc SFjjdS \u2208+= \u03b2\u03b2 (4)\n^\n0 1 1log( ( ))i c i iS d\u03b2 \u03b2= \u2212 (5)\n)12/(\n))(log()((log(\n^\n11\n1\n\u2212\n\u2212\n=\nidb\nicic\ni\nSF\ndSdsS\n\u03b2 (6)\nThe two parameters 0i\u03b2 and 1i\u03b2 are fitted to make sure the\nexponential function passes through the two points (1,\n^\n1)( ic dS )\nand (SFdbi/2, Sc(dsi1)). The exponential function is only used to\nadjust the top part of the centralized document score curve and\nthe lower part of the curve is still fitted with the linear\ninterpolation method described above. The adjustment by fitting\nexponential function of the top ranked documents has been\nshown empirically to produce more accurate results.\nFrom the centralized document score curves, we can estimate\nthe complete centralized document score lists accordingly for all\nthe available databases. After the estimated centralized\ndocument scores are normalized, the complete lists of\nprobabilities of relevance can be constructed out of the complete\ncentralized document score lists by Equation 1. Formally for the\nith\ndatabase, the complete list of probabilities of relevance is:\n],1[,)(R\n^^\nidbij Njd \u2208 .\n3.2 The Unified Utility Maximization Model\nIn this section, we formally define the new unified utility\nmaximization model, which optimizes the resource selection\nproblems for two goals of high-recall (database\nrecommendation) and high-precision (distributed document\nretrieval) in the same framework.\nIn the task of database recommendation, the system needs to\ndecide how to rank databases. In the task of document retrieval,\nthe system not only needs to select the databases but also needs\nto decide how many documents to retrieve from each selected\ndatabase. We generalize the database recommendation selection\nprocess, which implicitly recommends all documents in every\nselected database, as a special case of the selection decision for\nthe document retrieval task. Formally, we denote di as the\nnumber of documents we would like to retrieve from the ith\ndatabase and ,.....},{ 21 ddd = as a selection action for all the\ndatabases.\nThe database selection decision is made based on the complete\nlists of probabilities of relevance for all the databases. The\ncomplete lists of probabilities of relevance are inferred from all\nthe available information specifically sR , which stands for the\nresource descriptions acquired by query-based sampling and the\ndatabase size estimates acquired by sample-resample; cS stands\nfor the centralized document scores of the documents in the\ncentralized sample database.\nIf the method of estimating centralized document scores and\nprobabilities of relevance in Section 3.1 is acceptable, then the\nmost probable complete lists of probabilities of relevance can be\nderived and we denote them as 1\n^ ^\n*\n1{(R( ), [1, ]),dbjd j N\u03b8 = \u2208\n2\n^ ^\n2(R( ), [1, ]),.......}dbjd j N\u2208 . Random vector\n\ndenotes an\narbitrary set of complete lists of probabilities of relevance and\n),|( cs SRP \u03b8 as the probability of generating this set of lists.\nFinally, to each selection action d and a set of complete lists of\nFigure 1. Linear interpolation construction of the complete\ncentralized document score list (database scale factor is 50).\n35\nprobabilities of relevance \u03b8 , we associate a utility function\n),( dU \u03b8 which indicates the benefit from making the d\nselection when the true complete lists of probabilities of\nrelevance are \u03b8 .\nTherefore, the selection decision defined by the Bayesian\nframework is:\n\u03b8\u03b8\u03b8\n\u03b8\ndSRPdUd cs\nd\n).|(),(maxarg\n*\n= (7)\nOne common approach to simplify the computation in the\nBayesian framework is to only calculate the utility function at\nthe most probable parameter values instead of calculating the\nwhole expectation. In other words, we only need to calculate\n),( *\ndU \u03b8 and Equation 7 is simplified as follows:\n),(maxarg *\n*\n\u03b8dUd\nd\n= (8)\nThis equation serves as the basic model for both the database\nrecommendation system and the document retrieval system.\n3.3 Resource Selection for High-Recall\nHigh-recall is the goal of the resource selection algorithm in\nfederated search tasks such as database recommendation. The\ngoal is to select a small set of resources (e.g., less than Nsdb\ndatabases) that contain as many relevant documents as possible,\nwhich can be formally defined as:\n=\n=\ni\nN\nj\niji\nidb\nddIdU\n^\n1\n^\n*\n)(R)(),( \u03b8 (9)\nI(di) is the indicator function, which is 1 when the ith\ndatabase is\nselected and 0 otherwise. Plug this equation into the basic model\nin Equation 8 and associate the selected database number\nconstraint to obtain the following:\nsdb\ni\ni\ni\nN\nj\niji\nd\nNdItoSubject\nddId\nidb\n=\n=\n=\n)(:\n)(R)(maxarg\n^\n1\n^*\n(10)\nThe solution of this optimization problem is very simple. We\ncan calculate the expected number of relevant documents for\neach database as follows:\n=\n=\nidb\ni\nN\nj\nijRd dN\n^\n1\n^^\n)(R (11)\nThe Nsdb databases with the largest expected number of relevant\ndocuments can be selected to meet the high-recall goal. We call\nthis the UUM/HR algorithm (Unified Utility Maximization for\nHigh-Recall).\n3.4 Resource Selection for High-Precision\nHigh-Precision is the goal of resource selection algorithm in\nfederated search tasks such as distributed document retrieval. It\nis measured by the Precision at the top part of the final merged\ndocument list. This high-precision criterion is realized by the\nfollowing utility function, which measures the Precision of\nretrieved documents from the selected databases.\n=\n=\ni\nd\nj\niji\ni\nddIdU\n1\n^\n*\n)(R)(),( \u03b8 (12)\nNote that the key difference between Equation 12 and Equation\n9 is that Equation 9 sums up the probabilities of relevance of all\nthe documents in a database, while Equation 12 only considers a\nmuch smaller part of the ranking. Specifically, we can calculate\nthe optimal selection decision by:\n=\n=\ni\nd\nj\niji\nd\ni\nddId\n1\n^*\n)(R)(maxarg (13)\nDifferent kinds of constraints caused by different characteristics\nof the document retrieval tasks can be associated with the above\noptimization problem. The most common one is to select a fixed\nnumber (Nsdb) of databases and retrieve a fixed number (Nrdoc) of\ndocuments from each selected database, formally defined as:\n0,\n)(:\n)(R)(maxarg\n1\n^*\n\u2260=\n=\n=\n=\nirdoci\nsdb\ni\ni\ni\nd\nj\niji\nd\ndifNd\nNdItoSubject\nddId\ni\n(14)\nThis optimization problem can be solved easily by calculating\nthe number of expected relevant documents in the top part of the\neach database\"s complete list of probabilities of relevance:\n=\n=\nrdoc\ni\nN\nj\nijRdTop dN\n1\n^^\n_ )(R (15)\nThen the databases can be ranked by these values and selected.\nWe call this the UUM/HP-FL algorithm (Unified Utility\nMaximization for High-Precision with Fixed Length document\nrankings from each selected database).\nA more complex situation is to vary the number of retrieved\ndocuments from each selected database. More specifically, we\nallow different selected databases to return different numbers of\ndocuments. For simplification, the result list lengths are required\nto be multiples of a baseline number 10. (This value can also be\nvaried, but for simplification it is set to 10 in this paper.) This\nrestriction is set to simulate the behavior of commercial search\nengines on the Web. (Search engines such as Google and\nAltaVista return only 10 or 20 document ids for every result\npage.) This procedure saves the computation time of calculating\noptimal database selection by allowing the step of dynamic\nprogramming to be 10 instead of 1 (more detail is discussed\nlatterly). For further simplification, we restrict to select at most\n100 documents from each database (di<=100) Then, the\nselection optimization problem is formalized as follows:\n]10..,,2,1,0[,*10\n)(:\n)(R)(maxarg\n_\n1\n^*\n\u2208=\n=\n=\n=\n=\nkkd\nNd\nNdItoSubject\nddId\ni\nrdocTotal\ni\ni\nsdb\ni\ni\ni\nd\nj\niji\nd\ni\n(16)\nNTotal_rdoc is the total number of documents to be retrieved.\nUnfortunately, there is no simple solution for this optimization\nproblem as there are for Equations 10 and 14. However, a\n36\ndynamic programming algorithm can be applied to calculate the\noptimal solution. The basic steps of this dynamic programming\nmethod are described in Figure 2. As this algorithm allows\nretrieving result lists of varying lengths from each selected\ndatabase, it is called UUM/HP-VL algorithm.\nAfter the selection decisions are made, the selected databases are\nsearched and the corresponding document ids are retrieved from\neach database. The final step of document retrieval is to merge\nthe returned results into a single ranked list with the\nsemisupervised learning algorithm. It was pointed out before that the\nSSL algorithm maps the database-specific scores into the\ncentralized document scores and builds the final ranked list\naccordingly, which is consistent with all our selection\nprocedures where documents with higher probabilities of\nrelevance (thus higher centralized document scores) are selected.\n4. EXPERIMENTAL METHODOLOGY\n4.1 Testbeds\nIt is desirable to evaluate distributed information retrieval\nalgorithms with testbeds that closely simulate the real world\napplications.\nThe TREC Web collections WT2g or WT10g [4,13] provide a\nway to partition documents by different Web servers. In this\nway, a large number (O(1000)) of databases with rather diverse\ncontents could be created, which may make this testbed a good\ncandidate to simulate the operational environments such as open\ndomain hidden Web. However, two weakness of this testbed are:\ni) Each database contains only a small amount of document (259\ndocuments by average for WT2g) [4]; and ii) The contents of\nWT2g or WT10g are arbitrarily crawled from the Web. It is not\nlikely for a hidden Web database to provide personal homepages\nor web pages indicating that the pages are under construction\nand there is no useful information at all. These types of web\npages are contained in the WT2g/WT10g datasets. Therefore,\nthe noisy Web data is not similar with that of high-quality\nhidden Web database contents, which are usually organized by\ndomain experts.\nAnother choice is the TREC news/government data [1,15,17,\n18,21]. TREC news/government data is concentrated on\nrelatively narrow topics. Compared with TREC Web data: i) The\nnews/government documents are much more similar to the\ncontents provided by a topic-oriented database than an arbitrary\nweb page, ii) A database in this testbed is larger than that of\nTREC Web data. By average a database contains thousands of\ndocuments, which is more realistic than a database of TREC\nWeb data with about 250 documents. As the contents and sizes\nof the databases in the TREC news/government testbed are more\nsimilar with that of a topic-oriented database, it is a good\ncandidate to simulate the distributed information retrieval\nenvironments of large organizations (companies) or\ndomainspecific hidden Web sites, such as West that provides access to\nlegal, financial and news text databases [3]. As most current\ndistributed information retrieval systems are developed for the\nenvironments of large organizations (companies) or\ndomainspecific hidden Web other than open domain hidden Web,\nTREC news/government testbed was chosen in this work.\nTrec123-100col-bysource testbed is one of the most used TREC\nnews/government testbed [1,15,17,21]. It was chosen in this\nwork. Three testbeds in [21] with skewed database size\ndistributions and different types of relevant document\ndistributions were also used to give more thorough simulation\nfor real environments.\nTrec123-100col-bysource: 100 databases were created from\nTREC CDs 1, 2 and 3. They were organized by source and\npublication date [1]. The sizes of the databases are not skewed.\nDetails are in Table 1.\nThree testbeds built in [21] were based on the\ntrec123-100colbysource testbed. Each testbed contains many small databases\nand two large databases created by merging about 10-20 small\ndatabases together.\nInput: Complete lists of probabilities of relevance for all\nthe |DB| databases.\nOutput: Optimal selection solution for Equation 16.\ni) Create the three-dimensional array:\nSel (1..|DB|, 1..NTotal_rdoc/10, 1..Nsdb)\nEach Sel (x, y, z) is associated with a selection\ndecision xyzd , which represents the best selection\ndecision in the condition: only databases from number 1\nto number x are considered for selection; totally y*10\ndocuments will be retrieved; only z databases are\nselected out of the x database candidates. And\nSel (x, y, z) is the corresponding utility value by\nchoosing the best selection.\nii) Initialize Sel (1, 1..NTotal_rdoc/10, 1..Nsdb) with only the\nestimated relevance information of the 1st\ndatabase.\niii) Iterate the current database candidate i from 2 to |DB|\nFor each entry Sel (i, y, z):\nFind k such that:\n)10,min(1:\n))()1,,1((maxarg\n*10\n^\n*\nyktosubject\ndRzkyiSelk\nkj\nij\nk\n\u2264\u2264\n+\u2212\u2212\u2212=\n\u2264\n),,1())()1,,1((\n*\n*10\n^\n*\nzyiSeldRzkyiSelIf\nkj\nij \u2212>+\u2212\u2212\u2212\n\u2264\nThis means that we should retrieve *\n10 k\u2217 documents\nfrom the ith\ndatabase, otherwise we should not select this\ndatabase and the previous best solution Sel (i-1, y, z)\nshould be kept.\nThen set the value of iyzd and Sel (i, y, z) accordingly.\niv) The best selection solution is given by _ /10| | Toral rdoc sdbDB N Nd\nand the corresponding utility value is Sel (|DB|,\nNTotal_rdoc/10, Nsdb).\nFigure 2. The dynamic programming optimization\nprocedure for Equation 16.\nTable1: Testbed statistics.\nNumber of documents Size (MB)\nTestbed\nSize\n(GB) Min Avg Max Min Avg Max\nTrec123 3.2 752 10782 39713 28 32 42\nTable2: Query set statistics.\nName\nTREC\nTopic Set\nTREC\nTopic Field\nAverage Length\n(Words)\nTrec123 51-150 Title 3.1\n37\nTrec123-2ldb-60col (representative): The databases in the\ntrec123-100col-bysource were sorted with alphabetical order.\nTwo large databases were created by merging 20 small\ndatabases with the round-robin method. Thus, the two large\ndatabases have more relevant documents due to their large sizes,\neven though the densities of relevant documents are roughly the\nsame as the small databases.\nTrec123-AP-WSJ-60col (relevant): The 24 Associated Press\ncollections and the 16 Wall Street Journal collections in the\ntrec123-100col-bysource testbed were collapsed into two large\ndatabases APall and WSJall. The other 60 collections were left\nunchanged. The APall and WSJall databases have higher\ndensities of documents relevant to TREC queries than the small\ndatabases. Thus, the two large databases have many more\nrelevant documents than the small databases.\nTrec123-FR-DOE-81col (nonrelevant): The 13 Federal\nRegister collections and the 6 Department of Energy collections\nin the trec123-100col-bysource testbed were collapsed into two\nlarge databases FRall and DOEall. The other 80 collections were\nleft unchanged. The FRall and DOEall databases have lower\ndensities of documents relevant to TREC queries than the small\ndatabases, even though they are much larger.\n100 queries were created from the title fields of TREC topics\n51-150. The queries 101-150 were used as training queries and\nthe queries 51-100 were used as test queries (details in Table 2).\n4.2 Search Engines\nIn the uncooperative distributed information retrieval\nenvironments of large organizations (companies) or\ndomainspecific hidden Web, different databases may use different types\nof search engine. To simulate the multiple type-engine\nenvironment, three different types of search engines were used\nin the experiments: INQUERY [2], a unigram statistical\nlanguage model with linear smoothing [12,20] and a TFIDF\nretrieval algorithm with ltc weight [12,20]. All these\nalgorithms were implemented with the Lemur toolkit [12].\nThese three kinds of search engines were assigned to the\ndatabases among the four testbeds in a round-robin manner.\n5. RESULTS: RESOURCE SELECTION OF\nDATABASE RECOMMENDATION\nAll four testbeds described in Section 4 were used in the\nexperiments to evaluate the resource selection effectiveness of\nthe database recommendation system.\nThe resource descriptions were created using query-based\nsampling. About 80 queries were sent to each database to\ndownload 300 unique documents. The database size statistics\nwere estimated by the sample-resample method [21]. Fifty\nqueries (101-150) were used as training queries to build the\nrelevant logistic model and to fit the exponential functions of the\ncentralized document score curves for large ratio databases\n(details in Section 3.1). Another 50 queries (51-100) were used\nas test data.\nResource selection algorithms of database recommendation\nsystems are typically compared using the recall metric nR\n[1,17,18,21]. Let B denote a baseline ranking, which is often the\nRBR (relevance based ranking), and E as a ranking provided by\na resource selection algorithm. And let Bi and Ei denote the\nnumber of relevant documents in the ith\nranked database of B or\nE. Then Rn is defined as follows:\n=\n=\n= k\ni i\nk\ni i\nk\nB\nE\nR\n1\n1\n(17)\nUsually the goal is to search only a few databases, so our figures\nonly show results for selecting up to 20 databases.\nThe experiments summarized in Figure 3 compared the\neffectiveness of the three resource selection algorithms, namely\nthe CORI, ReDDE and UUM/HR. The UUM/HR algorithm is\ndescribed in Section 3.3. It can be seen from Figure 3 that the\nReDDE and UUM/HR algorithms are more effective (on the\nrepresentative, relevant and nonrelevant testbeds) or as good as\n(on the Trec123-100Col testbed) the CORI resource selection\nalgorithm. The UUM/HR algorithm is more effective than the\nReDDE algorithm on the representative and relevant testbeds\nand is about the same as the ReDDE algorithm on the\nTrec123100Col and the nonrelevant testbeds. This suggests that the\nUUM/HR algorithm is more robust than the ReDDE algorithm.\nIt can be noted that when selecting only a few databases on the\nTrec123-100Col or the nonrelevant testbeds, the ReDEE\nalgorithm has a small advantage over the UUM/HR algorithm.\nWe attribute this to two causes: i) The ReDDE algorithm was\ntuned on the Trec123-100Col testbed; and ii) Although the\ndifference is small, this may suggest that our logistic model of\nestimating probabilities of relevance is not accurate enough.\nMore training data or a more sophisticated model may help to\nsolve this minor puzzle.\nCollections Selected. Collections Selected.\nTrec123-100Col Testbed. Representative Testbed.\nCollection Selected. Collection Selected.\nRelevant Testbed. Nonrelevant Testbed.\nFigure 3. Resource selection experiments on the four testbeds.\n38\n6. RESULTS: DOCUMENT RETRIEVAL\nEFFECTIVENESS\nFor document retrieval, the selected databases are searched and\nthe returned results are merged into a single final list. In all of\nthe experiments discussed in this section the results retrieved\nfrom individual databases were combined by the\nsemisupervised learning results merging algorithm. This version of\nthe SSL algorithm [22] is allowed to download a small number\nof returned document texts on the fly to create additional\ntraining data in the process of learning the linear models which\nmap database-specific document scores into estimated\ncentralized document scores. It has been shown to be very\neffective in environments where only short result-lists are\nretrieved from each selected database [22]. This is a common\nscenario in operational environments and was the case for our\nexperiments.\nDocument retrieval effectiveness was measured by Precision at\nthe top part of the final document list. The experiments in this\nsection were conducted to study the document retrieval\neffectiveness of five selection algorithms, namely the CORI,\nReDDE, UUM/HR, UUM/HP-FL and UUM/HP-VL algorithms.\nThe last three algorithms were proposed in Section 3. All the\nfirst four algorithms selected 3 or 5 databases, and 50 documents\nwere retrieved from each selected database. The UUM/HP-FL\nalgorithm also selected 3 or 5 databases, but it was allowed to\nadjust the number of documents to retrieve from each selected\ndatabase; the number retrieved was constrained to be from 10 to\n100, and a multiple of 10.\nThe Trec123-100Col and representative testbeds were selected\nfor document retrieval as they represent two extreme cases of\nresource selection effectiveness; in one case the CORI algorithm\nis as good as the other algorithms and in the other case it is quite\nTable 5. Precision on the representative testbed when 3 databases were selected. (The first baseline is CORI; the second baseline for\nUUM/HP methods is UUM/HR.)\nPrecision at\nDoc Rank\nCORI ReDDE UUM/HR UUM/HP-FL UUM/HP-VL\n5 docs 0.3720 0.4080 (+9.7%) 0.4640 (+24.7%) 0.4600 (+23.7%)(-0.9%) 0.5000 (+34.4%)(+7.8%)\n10 docs 0.3400 0.4060 (+19.4%) 0.4600 (+35.3%) 0.4540 (+33.5%)(-1.3%) 0.4640 (+36.5%)(+0.9%)\n15 docs 0.3120 0.3880 (+24.4%) 0.4320 (+38.5%) 0.4240 (+35.9%)(-1.9%) 0.4413 (+41.4%)(+2.2)\n20 docs 0.3000 0.3750 (+25.0%) 0.4080 (+36.0%) 0.4040 (+34.7%)(-1.0%) 0.4240 (+41.3%)(+4.0%)\n30 docs 0.2533 0.3440 (+35.8%) 0.3847 (+51.9%) 0.3747 (+47.9%)(-2.6%) 0.3887 (+53.5%)(+1.0%)\nTable 6. Precision on the representative testbed when 5 databases were selected. (The first baseline is CORI; the second baseline for\nUUM/HP methods is UUM/HR.)\nPrecision at\nDoc Rank\nCORI ReDDE UUM/HR UUM/HP-FL UUM/HP-VL\n5 docs 0.3960 0.4080 (+3.0%) 0.4560 (+15.2%) 0.4280 (+8.1%)(-6.1%) 0.4520 (+14.1%)(-0.9%)\n10 docs 0.3880 0.4060 (+4.6%) 0.4280 (+10.3%) 0.4460 (+15.0%)(+4.2%) 0.4560 (+17.5%)(+6.5%)\n15 docs 0.3533 0.3987 (+12.9%) 0.4227 (+19.6%) 0.4440 (+25.7%)(+5.0%) 0.4453 (+26.0%)(+5.4%)\n20 docs 0.3330 0.3960 (+18.9%) 0.4140 (+24.3%) 0.4290 (+28.8%)(+3.6%) 0.4350 (+30.6%)(+5.1%)\n30 docs 0.2967 0.3740 (+26.1%) 0.4013 (+35.3%) 0.3987 (+34.4%)(-0.7%) 0.4060 (+36.8%)(+1.2%)\nTable 3. Precision on the trec123-100col-bysource testbed when 3 databases were selected. (The first baseline is CORI; the second\nbaseline for UUM/HP methods is UUM/HR.)\nPrecision at\nDoc Rank\nCORI ReDDE UUM/HR UUM/HP-FL UUM/HP-VL\n5 docs 0.3640 0.3480 (-4.4%) 0.3960 (+8.8%) 0.4680 (+28.6%)(+18.1%) 0.4640 (+27.5%)(+17.2%)\n10 docs 0.3360 0.3200 (-4.8%) 0.3520 (+4.8%) 0.4240 (+26.2%)(+20.5%) 0.4220 (+25.6%)(+19.9%)\n15 docs 0.3253 0.3187 (-2.0%) 0.3347 (+2.9%) 0.3973 (+22.2%)(+15.7%) 0.3920 (+20.5%)(+17.1%)\n20 docs 0.3140 0.2980 (-5.1%) 0.3270 (+4.1%) 0.3720 (+18.5%)(+13.8%) 0.3700 (+17.8%)(+13.2%)\n30 docs 0.2780 0.2660 (-4.3%) 0.2973 (+6.9%) 0.3413 (+22.8%)(+14.8%) 0.3400 (+22.3%)(+14.4%)\nTable 4. Precision on the trec123-100col-bysource testbed when 5 databases were selected. (The first baseline is CORI; the second\nbaseline for UUM/HP methods is UUM/HR.)\nPrecision at\nDoc Rank\nCORI ReDDE UUM/HR UUM/HP-FL UUM/HP-VL\n5 docs 0.4000 0.3920 (-2.0%) 0.4280 (+7.0%) 0.4680 (+17.0%)(+9.4%) 0.4600 (+15.0%)(+7.5%)\n10 docs 0.3800 0.3760 (-1.1%) 0.3800 (+0.0%) 0.4180 (+10.0%)(+10.0%) 0.4320 (+13.7%)(+13.7%)\n15 docs 0.3560 0.3560 (+0.0%) 0.3720 (+4.5%) 0.3920 (+10.1%)(+5.4%) 0.4080 (+14.6%)(+9.7%)\n20 docs 0.3430 0.3390 (-1.2%) 0.3550 (+3.5%) 0.3710 (+8.2%)(+4.5%) 0.3830 (+11.7%)(+7.9%)\n30 docs 0.3240 0.3140 (-3.1%) 0.3313 (+2.3%) 0.3500 (+8.0%)(+5.6%) 0.3487 (+7.6%)(+5.3%)\n39\na lot worse than the other algorithms. Tables 3 and 4 show the\nresults on the Trec123-100Col testbed, and Tables 5 and 6 show\nthe results on the representative testbed.\nOn the Trec123-100Col testbed, the document retrieval\neffectiveness of the CORI selection algorithm is roughly the\nsame or a little bit better than the ReDDE algorithm but both of\nthem are worse than the other three algorithms (Tables 3 and 4).\nThe UUM/HR algorithm has a small advantage over the CORI\nand ReDDE algorithms. One main difference between the\nUUM/HR algorithm and the ReDDE algorithm was pointed out\nbefore: The UUM/HR uses training data and linear interpolation\nto estimate the centralized document score curves, while the\nReDDE algorithm [21] uses a heuristic method, assumes the\ncentralized document score curves are step functions and makes\nno distinction among the top part of the curves. This difference\nmakes UUM/HR better than the ReDDE algorithm at\ndistinguishing documents with high probabilities of relevance\nfrom low probabilities of relevance. Therefore, the UUM/HR\nreflects the high-precision retrieval goal better than the ReDDE\nalgorithm and thus is more effective for document retrieval.\nThe UUM/HR algorithm does not explicitly optimize the\nselection decision with respect to the high-precision goal as the\nUUM/HP-FL and UUM/HP-VL algorithms are designed to do.\nIt can be seen that on this testbed, the UUM/HP-FL and\nUUM/HP-VL algorithms are much more effective than all the\nother algorithms. This indicates that their power comes from\nexplicitly optimizing the high-precision goal of document\nretrieval in Equations 14 and 16.\nOn the representative testbed, CORI is much less effective than\nother algorithms for distributed document retrieval (Tables 5 and\n6). The document retrieval results of the ReDDE algorithm are\nbetter than that of the CORI algorithm but still worse than the\nresults of the UUM/HR algorithm. On this testbed the three\nUUM algorithms are about equally effective. Detailed analysis\nshows that the overlap of the selected databases between the\nUUM/HR, UUM/HP-FL and UUM/HP-VL algorithms is much\nlarger than the experiments on the Trec123-100Col testbed,\nsince all of them tend to select the two large databases. This\nexplains why they are about equally effective for document\nretrieval.\nIn real operational environments, databases may return no\ndocument scores and report only ranked lists of results. As the\nunified utility maximization model only utilizes retrieval scores\nof sampled documents with a centralized retrieval algorithm to\ncalculate the probabilities of relevance, it makes database\nselection decisions without referring to the document scores\nfrom individual databases and can be easily generalized to this\ncase of rank lists without document scores. The only adjustment\nis that the SSL algorithm merges ranked lists without document\nscores by assigning the documents with pseudo-document scores\nnormalized for their ranks (In a ranked list of 50 documents, the\nfirst one has a score of 1, the second has a score of 0.98 etc)\n,which has been studied in [22]. The experiment results on\ntrec123-100Col-bysource testbed with 3 selected databases are\nshown in Table 7. The experiment setting was the same as\nbefore except that the document scores were eliminated\nintentionally and the selected databases only return ranked lists\nof document ids. It can be seen from the results that the\nUUM/HP-FL and UUM/HP-VL work well with databases\nreturning no document scores and are still more effective than\nother alternatives. Other experiments with databases that return\nno document scores are not reported but they show similar\nresults to prove the effectiveness of UUM/HP-FL and\nUUM/HPVL algorithms.\nThe above experiments suggest that it is very important to\noptimize the high-precision goal explicitly in document\nretrieval. The new algorithms based on this principle achieve\nbetter or at least as good results as the prior state-of-the-art\nalgorithms in several environments.\n7. CONCLUSION\nDistributed information retrieval solves the problem of finding\ninformation that is scattered among many text databases on local\narea networks and Internets. Most previous research use\neffective resource selection algorithm of database\nrecommendation system for distributed document retrieval\napplication. We argue that the high-recall resource selection\ngoal of database recommendation and high-precision goal of\ndocument retrieval are related but not identical. This kind of\ninconsistency has also been observed in previous work, but the\nprior solutions either used heuristic methods or assumed\ncooperation by individual databases (e.g., all the databases used\nthe same kind of search engines), which is frequently not true in\nthe uncooperative environment.\nIn this work we propose a unified utility maximization model to\nintegrate the resource selection of database recommendation and\ndocument retrieval tasks into a single unified framework. In this\nframework, the selection decisions are obtained by optimizing\ndifferent objective functions. As far as we know, this is the first\nwork that tries to view and theoretically model the distributed\ninformation retrieval task in an integrated manner.\nThe new framework continues a recent research trend studying\nthe use of query-based sampling and a centralized sample\ndatabase. A single logistic model was trained on the centralized\nTable 7. Precision on the trec123-100col-bysource testbed when 3 databases were selected (The first baseline is CORI; the second\nbaseline for UUM/HP methods is UUM/HR.) (Search engines do not return document scores)\nPrecision at\nDoc Rank\nCORI ReDDE UUM/HR UUM/HP-FL UUM/HP-VL\n5 docs 0.3520 0.3240 (-8.0%) 0.3680 (+4.6%) 0.4520 (+28.4%)(+22.8%) 0.4520 (+28.4%)(+22.8)\n10 docs 0.3320 0.3140 (-5.4%) 0.3340 (+0.6%) 0.4120 (+24.1%)(+23.4%) 0.4020 (+21.1%)(+20.4%)\n15 docs 0.3227 0.2987 (-7.4%) 0.3280 (+1.6%) 0.3920 (+21.5%)(+19.5%) 0.3733 (+15.7%)(+13.8%)\n20 docs 0.3030 0.2860 (-5.6%) 0.3130 (+3.3%) 0.3670 (+21.2%)(+17.3%) 0.3590 (+18.5%)(+14.7%)\n30 docs 0.2727 0.2640 (-3.2%) 0.2900 (+6.3%) 0.3273 (+20.0%)(+12.9%) 0.3273 (+20.0%)(+12.9%)\n40\nsample database to estimate the probabilities of relevance of\ndocuments by their centralized retrieval scores, while the\ncentralized sample database serves as a bridge to connect the\nindividual databases with the centralized logistic model.\nTherefore, the probabilities of relevance for all the documents\nacross the databases can be estimated with very small amount of\nhuman relevance judgment, which is much more efficient than\nprevious methods that build a separate model for each database.\nThis framework is not only more theoretically solid but also\nvery effective. One algorithm for resource selection (UUM/HR)\nand two algorithms for document retrieval (UUM/HP-FL and\nUUM/HP-VL) are derived from this framework. Empirical\nstudies have been conducted on testbeds to simulate the\ndistributed search solutions of large organizations (companies)\nor domain-specific hidden Web. Furthermore, the UUM/HP-FL\nand UUM/HP-VL resource selection algorithms are extended\nwith a variant of SSL results merging algorithm to address the\ndistributed document retrieval task when selected databases do\nnot return document scores. Experiments have shown that these\nalgorithms achieve results that are at least as good as the prior\nstate-of-the-art, and sometimes considerably better. Detailed\nanalysis indicates that the advantage of these algorithms comes\nfrom explicitly optimizing the goals of the specific tasks.\nThe unified utility maximization framework is open for different\nextensions. When cost is associated with searching the online\ndatabases, the utility framework can be adjusted to automatically\nestimate the best number of databases to search so that a large\namount of relevant documents can be retrieved with relatively\nsmall costs. Another extension of the framework is to consider\nthe retrieval effectiveness of the online databases, which is an\nimportant issue in the operational environments. All of these are\nthe directions of future research.\nACKNOWLEDGEMENT\nThis research was supported by NSF grants EIA-9983253 and\nIIS-0118767. Any opinions, findings, conclusions, or\nrecommendations expressed in this paper are the authors\", and\ndo not necessarily reflect those of the sponsor.\nREFERENCES\n[1] J. Callan. (2000). Distributed information retrieval. In W.B.\nCroft, editor, Advances in Information Retrieval. Kluwer\nAcademic Publishers. (pp. 127-150).\n[2] J. Callan, W.B. Croft, and J. Broglio. (1995). TREC and\nTIPSTER experiments with INQUERY. 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(pp. 457-491).\n41", "keywords": "distributed document retrieval;resource selection;retrieval and result merging;unified utility maximization model;distributed text information retrieval resource selection;semi-supervised learning;resource representation;logistic transformation model;distribute information retrieval;hidden web content;resource selection of distributed text information retrieval;federated search;database recommendation"}
{"name": "train_H-77", "title": "Automatic Extraction of Titles from General Documents using Machine Learning", "abstract": "In this paper, we propose a machine learning approach to title extraction from general documents. By general documents, we mean documents that can belong to any one of a number of specific genres, including presentations, book chapters, technical papers, brochures, reports, and letters. Previously, methods have been proposed mainly for title extraction from research papers. It has not been clear whether it could be possible to conduct automatic title extraction from general documents. As a case study, we consider extraction from Office including Word and PowerPoint. In our approach, we annotate titles in sample documents (for Word and PowerPoint respectively) and take them as training data, train machine learning models, and perform title extraction using the trained models. Our method is unique in that we mainly utilize formatting information such as font size as features in the models. It turns out that the use of formatting information can lead to quite accurate extraction from general documents. Precision and recall for title extraction from Word is 0.810 and 0.837 respectively, and precision and recall for title extraction from PowerPoint is 0.875 and 0.895 respectively in an experiment on intranet data. Other important new findings in this work include that we can train models in one domain and apply them to another domain, and more surprisingly we can even train models in one language and apply them to another language. Moreover, we can significantly improve search ranking results in document retrieval by using the extracted titles.", "fulltext": "1. INTRODUCTION\nMetadata of documents is useful for many kinds of document\nprocessing such as search, browsing, and filtering. Ideally,\nmetadata is defined by the authors of documents and is then used\nby various systems. However, people seldom define document\nmetadata by themselves, even when they have convenient\nmetadata definition tools [26]. Thus, how to automatically extract\nmetadata from the bodies of documents turns out to be an\nimportant research issue.\nMethods for performing the task have been proposed. However,\nthe focus was mainly on extraction from research papers. For\ninstance, Han et al. [10] proposed a machine learning based\nmethod to conduct extraction from research papers. They\nformalized the problem as that of classification and employed\nSupport Vector Machines as the classifier. They mainly used\nlinguistic features in the model.1\nIn this paper, we consider metadata extraction from general\ndocuments. By general documents, we mean documents that may\nbelong to any one of a number of specific genres. General\ndocuments are more widely available in digital libraries, intranets\nand the internet, and thus investigation on extraction from them is\nsorely needed. Research papers usually have well-formed styles\nand noticeable characteristics. In contrast, the styles of general\ndocuments can vary greatly. It has not been clarified whether a\nmachine learning based approach can work well for this task.\nThere are many types of metadata: title, author, date of creation,\netc. As a case study, we consider title extraction in this paper.\nGeneral documents can be in many different file formats:\nMicrosoft Office, PDF (PS), etc. As a case study, we consider\nextraction from Office including Word and PowerPoint.\nWe take a machine learning approach. We annotate titles in\nsample documents (for Word and PowerPoint respectively) and\ntake them as training data to train several types of models, and\nperform title extraction using any one type of the trained models.\nIn the models, we mainly utilize formatting information such as\nfont size as features. We employ the following models: Maximum\nEntropy Model, Perceptron with Uneven Margins, Maximum\nEntropy Markov Model, and Voted Perceptron.\nIn this paper, we also investigate the following three problems,\nwhich did not seem to have been examined previously.\n(1) Comparison between models: among the models above, which\nmodel performs best for title extraction;\n(2) Generality of model: whether it is possible to train a model on\none domain and apply it to another domain, and whether it is\npossible to train a model in one language and apply it to another\nlanguage;\n(3) Usefulness of extracted titles: whether extracted titles can\nimprove document processing such as search.\nExperimental results indicate that our approach works well for\ntitle extraction from general documents. Our method can\nsignificantly outperform the baselines: one that always uses the\nfirst lines as titles and the other that always uses the lines in the\nlargest font sizes as titles. Precision and recall for title extraction\nfrom Word are 0.810 and 0.837 respectively, and precision and\nrecall for title extraction from PowerPoint are 0.875 and 0.895\nrespectively. It turns out that the use of format features is the key\nto successful title extraction.\n(1) We have observed that Perceptron based models perform\nbetter in terms of extraction accuracies. (2) We have empirically\nverified that the models trained with our approach are generic in\nthe sense that they can be trained on one domain and applied to\nanother, and they can be trained in one language and applied to\nanother. (3) We have found that using the extracted titles we can\nsignificantly improve precision of document retrieval (by 10%).\nWe conclude that we can indeed conduct reliable title extraction\nfrom general documents and use the extracted results to improve\nreal applications.\nThe rest of the paper is organized as follows. In section 2, we\nintroduce related work, and in section 3, we explain the\nmotivation and problem setting of our work. In section 4, we\ndescribe our method of title extraction, and in section 5, we\ndescribe our method of document retrieval using extracted titles.\nSection 6 gives our experimental results. We make concluding\nremarks in section 7.\n2. RELATED WORK\n2.1 Document Metadata Extraction\nMethods have been proposed for performing automatic metadata\nextraction from documents; however, the main focus was on\nextraction from research papers.\nThe proposed methods fall into two categories: the rule based\napproach and the machine learning based approach.\nGiuffrida et al. [9], for instance, developed a rule-based system for\nautomatically extracting metadata from research papers in\nPostscript. They used rules like titles are usually located on the\nupper portions of the first pages and they are usually in the largest\nfont sizes. Liddy et al. [14] and Yilmazel el al. [23] performed\nmetadata extraction from educational materials using rule-based\nnatural language processing technologies. Mao et al. [16] also\nconducted automatic metadata extraction from research papers\nusing rules on formatting information.\nThe rule-based approach can achieve high performance. However,\nit also has disadvantages. It is less adaptive and robust when\ncompared with the machine learning approach.\nHan et al. [10], for instance, conducted metadata extraction with\nthe machine learning approach. They viewed the problem as that\nof classifying the lines in a document into the categories of\nmetadata and proposed using Support Vector Machines as the\nclassifier. They mainly used linguistic information as features.\nThey reported high extraction accuracy from research papers in\nterms of precision and recall.\n2.2 Information Extraction\nMetadata extraction can be viewed as an application of\ninformation extraction, in which given a sequence of instances, we\nidentify a subsequence that represents information in which we\nare interested. Hidden Markov Model [6], Maximum Entropy\nModel [1, 4], Maximum Entropy Markov Model [17], Support\nVector Machines [3], Conditional Random Field [12], and Voted\nPerceptron [2] are widely used information extraction models.\nInformation extraction has been applied, for instance, to\npart-ofspeech tagging [20], named entity recognition [25] and table\nextraction [19].\n2.3 Search Using Title Information\nTitle information is useful for document retrieval.\nIn the system Citeseer, for instance, Giles et al. managed to\nextract titles from research papers and make use of the extracted\ntitles in metadata search of papers [8].\nIn web search, the title fields (i.e., file properties) and anchor texts\nof web pages (HTML documents) can be viewed as \u2018titles\" of the\npages [5]. Many search engines seem to utilize them for web page\nretrieval [7, 11, 18, 22]. Zhang et al., found that web pages with\nwell-defined metadata are more easily retrieved than those without\nwell-defined metadata [24].\nTo the best of our knowledge, no research has been conducted on\nusing extracted titles from general documents (e.g., Office\ndocuments) for search of the documents.\n146\n3. MOTIVATION AND PROBLEM\nSETTING\nWe consider the issue of automatically extracting titles from\ngeneral documents.\nBy general documents, we mean documents that belong to one of\nany number of specific genres. The documents can be\npresentations, books, book chapters, technical papers, brochures,\nreports, memos, specifications, letters, announcements, or resumes.\nGeneral documents are more widely available in digital libraries,\nintranets, and internet, and thus investigation on title extraction\nfrom them is sorely needed.\nFigure 1 shows an estimate on distributions of file formats on\nintranet and internet [15]. Office and PDF are the main file\nformats on the intranet. Even on the internet, the documents in the\nformats are still not negligible, given its extremely large size. In\nthis paper, without loss of generality, we take Office documents as\nan example.\nFigure 1. Distributions of file formats in internet and intranet.\nFor Office documents, users can define titles as file properties\nusing a feature provided by Office. We found in an experiment,\nhowever, that users seldom use the feature and thus titles in file\nproperties are usually very inaccurate. That is to say, titles in file\nproperties are usually inconsistent with the \u2018true\" titles in the file\nbodies that are created by the authors and are visible to readers.\nWe collected 6,000 Word and 6,000 PowerPoint documents from\nan intranet and the internet and examined how many titles in the\nfile properties are correct. We found that surprisingly the accuracy\nwas only 0.265 (cf., Section 6.3 for details). A number of reasons\ncan be considered. For example, if one creates a new file by\ncopying an old file, then the file property of the new file will also\nbe copied from the old file.\nIn another experiment, we found that Google uses the titles in file\nproperties of Office documents in search and browsing, but the\ntitles are not very accurate. We created 50 queries to search Word\nand PowerPoint documents and examined the top 15 results of\neach query returned by Google. We found that nearly all the titles\npresented in the search results were from the file properties of the\ndocuments. However, only 0.272 of them were correct.\nActually, \u2018true\" titles usually exist at the beginnings of the bodies\nof documents. If we can accurately extract the titles from the\nbodies of documents, then we can exploit reliable title information\nin document processing. This is exactly the problem we address in\nthis paper.\nMore specifically, given a Word document, we are to extract the\ntitle from the top region of the first page. Given a PowerPoint\ndocument, we are to extract the title from the first slide. A title\nsometimes consists of a main title and one or two subtitles. We\nonly consider extraction of the main title.\nAs baselines for title extraction, we use that of always using the\nfirst lines as titles and that of always using the lines with largest\nfont sizes as titles.\nFigure 2. Title extraction from Word document.\nFigure 3. Title extraction from PowerPoint document.\nNext, we define a \u2018specification\" for human judgments in title data\nannotation. The annotated data will be used in training and testing\nof the title extraction methods.\nSummary of the specification: The title of a document should be\nidentified on the basis of common sense, if there is no difficulty in\nthe identification. However, there are many cases in which the\nidentification is not easy. There are some rules defined in the\nspecification that guide identification for such cases. The rules\ninclude a title is usually in consecutive lines in the same format,\na document can have no title, titles in images are not\nconsidered, a title should not contain words like \u2018draft\",\n147\n\u2018whitepaper\", etc, if it is difficult to determine which is the title,\nselect the one in the largest font size, and if it is still difficult to\ndetermine which is the title, select the first candidate. (The\nspecification covers all the cases we have encountered in data\nannotation.)\nFigures 2 and 3 show examples of Office documents from which\nwe conduct title extraction. In Figure 2, \u2018Differences in Win32\nAPI Implementations among Windows Operating Systems\" is the\ntitle of the Word document. \u2018Microsoft Windows\" on the top of\nthis page is a picture and thus is ignored. In Figure 3, \u2018Building\nCompetitive Advantages through an Agile Infrastructure\" is the\ntitle of the PowerPoint document.\nWe have developed a tool for annotation of titles by human\nannotators. Figure 4 shows a snapshot of the tool.\nFigure 4. Title annotation tool.\n4. TITLE EXTRACTION METHOD\n4.1 Outline\nTitle extraction based on machine learning consists of training and\nextraction. The same pre-processing step occurs before training\nand extraction.\nDuring pre-processing, from the top region of the first page of a\nWord document or the first slide of a PowerPoint document a\nnumber of units for processing are extracted. If a line (lines are\nseparated by \u2018return\" symbols) only has a single format, then the\nline will become a unit. If a line has several parts and each of\nthem has its own format, then each part will become a unit. Each\nunit will be treated as an instance in learning. A unit contains not\nonly content information (linguistic information) but also\nformatting information. The input to pre-processing is a document\nand the output of pre-processing is a sequence of units (instances).\nFigure 5 shows the units obtained from the document in Figure 2.\nFigure 5. Example of units.\nIn learning, the input is sequences of units where each sequence\ncorresponds to a document. We take labeled units (labeled as\ntitle_begin, title_end, or other) in the sequences as training data\nand construct models for identifying whether a unit is title_begin\ntitle_end, or other. We employ four types of models: Perceptron,\nMaximum Entropy (ME), Perceptron Markov Model (PMM), and\nMaximum Entropy Markov Model (MEMM).\nIn extraction, the input is a sequence of units from one document.\nWe employ one type of model to identify whether a unit is\ntitle_begin, title_end, or other. We then extract units from the unit\nlabeled with \u2018title_begin\" to the unit labeled with \u2018title_end\". The\nresult is the extracted title of the document.\nThe unique characteristic of our approach is that we mainly utilize\nformatting information for title extraction. Our assumption is that\nalthough general documents vary in styles, their formats have\ncertain patterns and we can learn and utilize the patterns for title\nextraction. This is in contrast to the work by Han et al., in which\nonly linguistic features are used for extraction from research\npapers.\n4.2 Models\nThe four models actually can be considered in the same metadata\nextraction framework. That is why we apply them together to our\ncurrent problem.\nEach input is a sequence of instances kxxx L21 together with a\nsequence of labels kyyy L21 . ix and iy represents an instance\nand its label, respectively ( ki ,,2,1 L= ). Recall that an instance\nhere represents a unit. A label represents title_begin, title_end, or\nother. Here, k is the number of units in a document.\nIn learning, we train a model which can be generally denoted as a\nconditional probability distribution )|( 11 kk XXYYP LL where\niX and iY denote random variables taking instance ix and label\niy as values, respectively ( ki ,,2,1 L= ).\nLearning Tool\nExtraction Tool\n21121\n2222122221\n1121111211\nnknnknn\nkk\nkk\nyyyxxx\nyyyxxx\nyyyxxx\nLL\nLL\nLL\nLL\n\u2192\n\u2192\n\u2192\n)|(maxarg 11 mkmmkm xxyyP LL\n)|( 11 kk XXYYP LL\nConditional\nDistribution\nmkmm xxx L21\nFigure 6. Metadata extraction model.\nWe can make assumptions about the general model in order to\nmake it simple enough for training.\n148\nFor example, we can assume that kYY ,,1 L are independent of\neach other given kXX ,,1 L . Thus, we have\n)|()|(\n)|(\n11\n11\nkk\nkk\nXYPXYP\nXXYYP\nL\nLL\n=\nIn this way, we decompose the model into a number of classifiers.\nWe train the classifiers locally using the labeled data. As the\nclassifier, we employ the Perceptron or Maximum Entropy model.\nWe can also assume that the first order Markov property holds for\nkYY ,,1 L given kXX ,,1 L . Thus, we have\n)|()|(\n)|(\n111\n11\nkkk\nkk\nXYYPXYP\nXXYYP\n\u2212= L\nLL\nAgain, we obtain a number of classifiers. However, the classifiers\nare conditioned on the previous label. When we employ the\nPercepton or Maximum Entropy model as a classifier, the models\nbecome a Percepton Markov Model or Maximum Entropy Markov\nModel, respectively. That is to say, the two models are more\nprecise.\nIn extraction, given a new sequence of instances, we resort to one\nof the constructed models to assign a sequence of labels to the\nsequence of instances, i.e., perform extraction.\nFor Perceptron and ME, we assign labels locally and combine the\nresults globally later using heuristics. Specifically, we first\nidentify the most likely title_begin. Then we find the most likely\ntitle_end within three units after the title_begin. Finally, we\nextract as a title the units between the title_begin and the title_end.\nFor PMM and MEMM, we employ the Viterbi algorithm to find\nthe globally optimal label sequence.\nIn this paper, for Perceptron, we actually employ an improved\nvariant of it, called Perceptron with Uneven Margin [13]. This\nversion of Perceptron can work well especially when the number\nof positive instances and the number of negative instances differ\ngreatly, which is exactly the case in our problem.\nWe also employ an improved version of Perceptron Markov\nModel in which the Perceptron model is the so-called Voted\nPerceptron [2]. In addition, in training, the parameters of the\nmodel are updated globally rather than locally.\n4.3 Features\nThere are two types of features: format features and linguistic\nfeatures. We mainly use the former. The features are used for both\nthe title-begin and the title-end classifiers.\n4.3.1 Format Features\nFont Size: There are four binary features that represent the\nnormalized font size of the unit (recall that a unit has only one\ntype of font).\nIf the font size of the unit is the largest in the document, then the\nfirst feature will be 1, otherwise 0. If the font size is the smallest\nin the document, then the fourth feature will be 1, otherwise 0. If\nthe font size is above the average font size and not the largest in\nthe document, then the second feature will be 1, otherwise 0. If the\nfont size is below the average font size and not the smallest, the\nthird feature will be 1, otherwise 0.\nIt is necessary to conduct normalization on font sizes. For\nexample, in one document the largest font size might be \u201812pt\",\nwhile in another the smallest one might be \u201818pt\".\nBoldface: This binary feature represents whether or not the\ncurrent unit is in boldface.\nAlignment: There are four binary features that respectively\nrepresent the location of the current unit: \u2018left\", \u2018center\", \u2018right\",\nand \u2018unknown alignment\".\nThe following format features with respect to \u2018context\" play an\nimportant role in title extraction.\nEmpty Neighboring Unit: There are two binary features that\nrepresent, respectively, whether or not the previous unit and the\ncurrent unit are blank lines.\nFont Size Change: There are two binary features that represent,\nrespectively, whether or not the font size of the previous unit and\nthe font size of the next unit differ from that of the current unit.\nAlignment Change: There are two binary features that represent,\nrespectively, whether or not the alignment of the previous unit and\nthe alignment of the next unit differ from that of the current one.\nSame Paragraph: There are two binary features that represent,\nrespectively, whether or not the previous unit and the next unit are\nin the same paragraph as the current unit.\n4.3.2 Linguistic Features\nThe linguistic features are based on key words.\nPositive Word: This binary feature represents whether or not the\ncurrent unit begins with one of the positive words. The positive\nwords include \u2018title:\", \u2018subject:\", \u2018subject line:\" For example, in\nsome documents the lines of titles and authors have the same\nformats. However, if lines begin with one of the positive words,\nthen it is likely that they are title lines.\nNegative Word: This binary feature represents whether or not the\ncurrent unit begins with one of the negative words. The negative\nwords include \u2018To\", \u2018By\", \u2018created by\", \u2018updated by\", etc.\nThere are more negative words than positive words. The above\nlinguistic features are language dependent.\nWord Count: A title should not be too long. We heuristically\ncreate four intervals: [1, 2], [3, 6], [7, 9] and [9, \u221e) and define one\nfeature for each interval. If the number of words in a title falls into\nan interval, then the corresponding feature will be 1; otherwise 0.\nEnding Character: This feature represents whether the unit ends\nwith \u2018:\", \u2018-\", or other special characters. A title usually does not\nend with such a character.\n5. DOCUMENT RETRIEVAL METHOD\nWe describe our method of document retrieval using extracted\ntitles.\nTypically, in information retrieval a document is split into a\nnumber of fields including body, title, and anchor text. A ranking\nfunction in search can use different weights for different fields of\n149\nthe document. Also, titles are typically assigned high weights,\nindicating that they are important for document retrieval. As\nexplained previously, our experiment has shown that a significant\nnumber of documents actually have incorrect titles in the file\nproperties, and thus in addition of using them we use the extracted\ntitles as one more field of the document. By doing this, we attempt\nto improve the overall precision.\nIn this paper, we employ a modification of BM25 that allows field\nweighting [21]. As fields, we make use of body, title, extracted\ntitle and anchor. First, for each term in the query we count the\nterm frequency in each field of the document; each field\nfrequency is then weighted according to the corresponding weight\nparameter:\n\u2211=\nf\ntfft tfwwtf\nSimilarly, we compute the document length as a weighted sum of\nlengths of each field. Average document length in the corpus\nbecomes the average of all weighted document lengths.\n\u2211=\nf\nff dlwwdl\nIn our experiments we used 75.0,8.11 == bk . Weight for content\nwas 1.0, title was 10.0, anchor was 10.0, and extracted title was\n5.0.\n6. EXPERIMENTAL RESULTS\n6.1 Data Sets and Evaluation Measures\nWe used two data sets in our experiments.\nFirst, we downloaded and randomly selected 5,000 Word\ndocuments and 5,000 PowerPoint documents from an intranet of\nMicrosoft. We call it MS hereafter.\nSecond, we downloaded and randomly selected 500 Word and 500\nPowerPoint documents from the DotGov and DotCom domains on\nthe internet, respectively.\nFigure 7 shows the distributions of the genres of the documents.\nWe see that the documents are indeed \u2018general documents\" as we\ndefine them.\nFigure 7. Distributions of document genres.\nThird, a data set in Chinese was also downloaded from the internet.\nIt includes 500 Word documents and 500 PowerPoint documents\nin Chinese.\nWe manually labeled the titles of all the documents, on the basis\nof our specification.\nNot all the documents in the two data sets have titles. Table 1\nshows the percentages of the documents having titles. We see that\nDotCom and DotGov have more PowerPoint documents with titles\nthan MS. This might be because PowerPoint documents published\non the internet are more formal than those on the intranet.\nTable 1. The portion of documents with titles\nDomain\nType\nMS DotCom DotGov\nWord 75.7% 77.8% 75.6%\nPowerPoint 82.1% 93.4% 96.4%\nIn our experiments, we conducted evaluations on title extraction in\nterms of precision, recall, and F-measure. The evaluation\nmeasures are defined as follows:\nPrecision: P = A / ( A + B )\nRecall: R = A / ( A + C )\nF-measure: F1 = 2PR / ( P + R )\nHere, A, B, C, and D are numbers of documents as those defined\nin Table 2.\nTable 2. Contingence table with regard to title extraction\nIs title Is not title\nExtracted A B\nNot extracted C D\n6.2 Baselines\nWe test the accuracies of the two baselines described in section\n4.2. They are denoted as \u2018largest font size\" and \u2018first line\"\nrespectively.\n6.3 Accuracy of Titles in File Properties\nWe investigate how many titles in the file properties of the\ndocuments are reliable. We view the titles annotated by humans as\ntrue titles and test how many titles in the file properties can\napproximately match with the true titles. We use Edit Distance to\nconduct the approximate match. (Approximate match is only used\nin this evaluation). This is because sometimes human annotated\ntitles can be slightly different from the titles in file properties on\nthe surface, e.g., contain extra spaces).\nGiven string A and string B:\nif ( (D == 0) or ( D / ( La + Lb ) < \u03b8 ) ) then string A = string B\nD: Edit Distance between string A and string B\nLa: length of string A\nLb: length of string B\n\u03b8: 0.1\n\u2211 \u00d7\n++\u2212\n+\n=\nt\nt\nn\nN\nwtf\navwdl\nwdl\nbbk\nkwtf\nFBM )log(\n))1((\n)1(\n25\n1\n1\n150\nTable 3. Accuracies of titles in file properties\nFile Type Domain Precision Recall F1\nMS 0.299 0.311 0.305\nDotCom 0.210 0.214 0.212Word\nDotGov 0.182 0.177 0.180\nMS 0.229 0.245 0.237\nDotCom 0.185 0.186 0.186PowerPoint\nDotGov 0.180 0.182 0.181\n6.4 Comparison with Baselines\nWe conducted title extraction from the first data set (Word and\nPowerPoint in MS). As the model, we used Perceptron.\nWe conduct 4-fold cross validation. Thus, all the results reported\nhere are those averaged over 4 trials. Tables 4 and 5 show the\nresults. We see that Perceptron significantly outperforms the\nbaselines. In the evaluation, we use exact matching between the\ntrue titles annotated by humans and the extracted titles.\nTable 4. Accuracies of title extraction with Word\nPrecision Recall F1\nModel Perceptron 0.810 0.837 0.823\nLargest font size 0.700 0.758 0.727\nBaselines\nFirst line 0.707 0.767 0.736\nTable 5. Accuracies of title extraction with PowerPoint\nPrecision Recall F1\nModel Perceptron 0.875 0. 895 0.885\nLargest font size 0.844 0.887 0.865\nBaselines\nFirst line 0.639 0.671 0.655\nWe see that the machine learning approach can achieve good\nperformance in title extraction. For Word documents both\nprecision and recall of the approach are 8 percent higher than\nthose of the baselines. For PowerPoint both precision and recall of\nthe approach are 2 percent higher than those of the baselines.\nWe conduct significance tests. The results are shown in Table 6.\nHere, \u2018Largest\" denotes the baseline of using the largest font size,\n\u2018First\" denotes the baseline of using the first line. The results\nindicate that the improvements of machine learning over baselines\nare statistically significant (in the sense p-value < 0.05)\nTable 6. Sign test results\nDocuments Type Sign test between p-value\nPerceptron vs. Largest 3.59e-26\nWord\nPerceptron vs. First 7.12e-10\nPerceptron vs. Largest 0.010\nPowerPoint\nPerceptron vs. First 5.13e-40\nWe see, from the results, that the two baselines can work well for\ntitle extraction, suggesting that font size and position information\nare most useful features for title extraction. However, it is also\nobvious that using only these two features is not enough. There\nare cases in which all the lines have the same font size (i.e., the\nlargest font size), or cases in which the lines with the largest font\nsize only contain general descriptions like \u2018Confidential\", \u2018White\npaper\", etc. For those cases, the \u2018largest font size\" method cannot\nwork well. For similar reasons, the \u2018first line\" method alone\ncannot work well, either. With the combination of different\nfeatures (evidence in title judgment), Perceptron can outperform\nLargest and First.\nWe investigate the performance of solely using linguistic features.\nWe found that it does not work well. It seems that the format\nfeatures play important roles and the linguistic features are\nsupplements..\nFigure 8. An example Word document.\nFigure 9. An example PowerPoint document.\nWe conducted an error analysis on the results of Perceptron. We\nfound that the errors fell into three categories. (1) About one third\nof the errors were related to \u2018hard cases\". In these documents, the\nlayouts of the first pages were difficult to understand, even for\nhumans. Figure 8 and 9 shows examples. (2) Nearly one fourth of\nthe errors were from the documents which do not have true titles\nbut only contain bullets. Since we conduct extraction from the top\nregions, it is difficult to get rid of these errors with the current\napproach. (3). Confusions between main titles and subtitles were\nanother type of error. Since we only labeled the main titles as\ntitles, the extractions of both titles were considered incorrect. This\ntype of error does little harm to document processing like search,\nhowever.\n6.5 Comparison between Models\nTo compare the performance of different machine learning models,\nwe conducted another experiment. Again, we perform 4-fold cross\n151\nvalidation on the first data set (MS). Table 7, 8 shows the results\nof all the four models.\nIt turns out that Perceptron and PMM perform the best, followed\nby MEMM, and ME performs the worst. In general, the\nMarkovian models perform better than or as well as their classifier\ncounterparts. This seems to be because the Markovian models are\ntrained globally, while the classifiers are trained locally. The\nPerceptron based models perform better than the ME based\ncounterparts. This seems to be because the Perceptron based\nmodels are created to make better classifications, while ME\nmodels are constructed for better prediction.\nTable 7. Comparison between different learning models for\ntitle extraction with Word\nModel Precision Recall F1\nPerceptron 0.810 0.837 0.823\nMEMM 0.797 0.824 0.810\nPMM 0.827 0.823 0.825\nME 0.801 0.621 0.699\nTable 8. Comparison between different learning models for\ntitle extraction with PowerPoint\nModel Precision Recall F1\nPerceptron 0.875 0. 895 0. 885\nMEMM 0.841 0.861 0.851\nPMM 0.873 0.896 0.885\nME 0.753 0.766 0.759\n6.6 Domain Adaptation\nWe apply the model trained with the first data set (MS) to the\nsecond data set (DotCom and DotGov). Tables 9-12 show the\nresults.\nTable 9. Accuracies of title extraction with Word in DotGov\nPrecision Recall F1\nModel Perceptron 0.716 0.759 0.737\nLargest font size 0.549 0.619 0.582Baselines\nFirst line 0.462 0.521 0.490\nTable 10. Accuracies of title extraction with PowerPoint in\nDotGov\nPrecision Recall F1\nModel Perceptron 0.900 0.906 0.903\nLargest font size 0.871 0.888 0.879Baselines\nFirst line 0.554 0.564 0.559\nTable 11. Accuracies of title extraction with Word in DotCom\nPrecisio\nn\nRecall F1\nModel Perceptron 0.832 0.880 0.855\nLargest font size 0.676 0.753 0.712Baselines\nFirst line 0.577 0.643 0.608\nTable 12. Performance of PowerPoint document title\nextraction in DotCom\nPrecisio\nn\nRecall F1\nModel Perceptron 0.910 0.903 0.907\nLargest font size 0.864 0.886 0.875Baselines\nFirst line 0.570 0.585 0.577\nFrom the results, we see that the models can be adapted to\ndifferent domains well. There is almost no drop in accuracy. The\nresults indicate that the patterns of title formats exist across\ndifferent domains, and it is possible to construct a domain\nindependent model by mainly using formatting information.\n6.7 Language Adaptation\nWe apply the model trained with the data in English (MS) to the\ndata set in Chinese.\nTables 13-14 show the results.\nTable 13. Accuracies of title extraction with Word in Chinese\nPrecision Recall F1\nModel Perceptron 0.817 0.805 0.811\nLargest font size 0.722 0.755 0.738Baselines\nFirst line 0.743 0.777 0.760\nTable 14. Accuracies of title extraction with PowerPoint in\nChinese\nPrecision Recall F1\nModel Perceptron 0.766 0.812 0.789\nLargest font size 0.753 0.813 0.782Baselines\nFirst line 0.627 0.676 0.650\nWe see that the models can be adapted to a different language.\nThere are only small drops in accuracy. Obviously, the linguistic\nfeatures do not work for Chinese, but the effect of not using them\nis negligible. The results indicate that the patterns of title formats\nexist across different languages.\nFrom the domain adaptation and language adaptation results, we\nconclude that the use of formatting information is the key to a\nsuccessful extraction from general documents.\n6.8 Search with Extracted Titles\nWe performed experiments on using title extraction for document\nretrieval. As a baseline, we employed BM25 without using\nextracted titles. The ranking mechanism was as described in\nSection 5. The weights were heuristically set. We did not conduct\noptimization on the weights.\nThe evaluation was conducted on a corpus of 1.3 M documents\ncrawled from the intranet of Microsoft using 100 evaluation\nqueries obtained from this intranet\"s search engine query logs. 50\nqueries were from the most popular set, while 50 queries other\nwere chosen randomly. Users were asked to provide judgments of\nthe degree of document relevance from a scale of 1to 5 (1\nmeaning detrimental, 2 - bad, 3 - fair, 4 - good and 5 - excellent).\n152\nFigure 10 shows the results. In the chart two sets of precision\nresults were obtained by either considering good or excellent\ndocuments as relevant (left 3 bars with relevance threshold 0.5), or\nby considering only excellent documents as relevant (right 3 bars\nwith relevance threshold 1.0)\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\n0.45\nP@10 P@5 Reciprocal P@10 P@5 Reciprocal\n0.5 1\nBM25 Anchor, Title, Body\nBM25 Anchor, Title, Body, ExtractedTitle\nName All\nRelevanceThreshold Data\nDescription\nFigure 10. Search ranking results.\nFigure 10 shows different document retrieval results with different\nranking functions in terms of precision @10, precision @5 and\nreciprocal rank:\n\u2022 Blue bar - BM25 including the fields body, title (file\nproperty), and anchor text.\n\u2022 Purple bar - BM25 including the fields body, title (file\nproperty), anchor text, and extracted title.\nWith the additional field of extracted title included in BM25 the\nprecision @10 increased from 0.132 to 0.145, or by ~10%. Thus,\nit is safe to say that the use of extracted title can indeed improve\nthe precision of document retrieval.\n7. CONCLUSION\nIn this paper, we have investigated the problem of automatically\nextracting titles from general documents. We have tried using a\nmachine learning approach to address the problem.\nPrevious work showed that the machine learning approach can\nwork well for metadata extraction from research papers. In this\npaper, we showed that the approach can work for extraction from\ngeneral documents as well. Our experimental results indicated that\nthe machine learning approach can work significantly better than\nthe baselines in title extraction from Office documents. Previous\nwork on metadata extraction mainly used linguistic features in\ndocuments, while we mainly used formatting information. It\nappeared that using formatting information is a key for\nsuccessfully conducting title extraction from general documents.\nWe tried different machine learning models including Perceptron,\nMaximum Entropy, Maximum Entropy Markov Model, and Voted\nPerceptron. We found that the performance of the Perceptorn\nmodels was the best. We applied models constructed in one\ndomain to another domain and applied models trained in one\nlanguage to another language. We found that the accuracies did\nnot drop substantially across different domains and across\ndifferent languages, indicating that the models were generic. We\nalso attempted to use the extracted titles in document retrieval. We\nobserved a significant improvement in document ranking\nperformance for search when using extracted title information. All\nthe above investigations were not conducted in previous work, and\nthrough our investigations we verified the generality and the\nsignificance of the title extraction approach.\n8. ACKNOWLEDGEMENTS\nWe thank Chunyu Wei and Bojuan Zhao for their work on data\nannotation. We acknowledge Jinzhu Li for his assistance in\nconducting the experiments. We thank Ming Zhou, John Chen,\nJun Xu, and the anonymous reviewers of JCDL\"05 for their\nvaluable comments on this paper.\n9. REFERENCES\n[1] Berger, A. L., Della Pietra, S. A., and Della Pietra, V. J. 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In Proceedings of\nthe 26th Annual International ACM SIGIR Conference on\nResearch and Development in Information Retrieval,\n235242, 2003.\n[20] Ratnaparkhi, A. Unsupervised statistical models for\nprepositional phrase attachment. In Proceedings of the\nSeventeenth International Conference on Computational\nLinguistics. 1079-1085, 1998.\n[21] Robertson, S., Zaragoza, H., and Taylor, M. Simple BM25\nextension to multiple weighted fields, In Proceedings of\nACM Thirteenth Conference on Information and Knowledge\nManagement, 42-49, 2004.\n[22] Yi, J. and Sundaresan, N. Metadata based Web mining for\nrelevance, In Proceedings of the 2000 International\nSymposium on Database Engineering & Applications,\n113121, 2000.\n[23] Yilmazel, O., Finneran, C. M., and Liddy, E. D. MetaExtract:\nAn NLP system to automatically assign metadata. In\nProceedings of the 2004 Joint ACM/IEEE Conference on\nDigital Libraries, 241-242, 2004.\n[24] Zhang, J. and Dimitroff, A. Internet search engines' response\nto metadata Dublin Core implementation. Journal of\nInformation Science, 30:310-320, 2004.\n[25] Zhang, L., Pan, Y., and Zhang, T. Recognising and using\nnamed entities: focused named entity recognition using\nmachine learning. In Proceedings of the 27th Annual\nInternational ACM SIGIR Conference on Research and\nDevelopment in Information Retrieval, 281-288, 2004.\n[26] http://dublincore.org/groups/corporate/Seattle/\n154", "keywords": "machine learn;formatting information;metada of document;title extraction;language independence;linguistic feature;usefulness of extracted title;extracted title usefulness;genre;classifier;automatic title extraction;information extraction;model generality;metada extraction;search;document retrieval;comparison between model;generality of model"}
{"name": "train_H-79", "title": "Beyond PageRank: Machine Learning for Static Ranking", "abstract": "Since the publication of Brin and Page\"s paper on PageRank, many in the Web community have depended on PageRank for the static (query-independent) ordering of Web pages. We show that we can significantly outperform PageRank using features that are independent of the link structure of the Web. We gain a further boost in accuracy by using data on the frequency at which users visit Web pages. We use RankNet, a ranking machine learning algorithm, to combine these and other static features based on anchor text and domain characteristics. The resulting model achieves a static ranking pairwise accuracy of 67.3% (vs. 56.7% for PageRank or 50% for random).", "fulltext": "1. INTRODUCTION\nOver the past decade, the Web has grown exponentially in size.\nUnfortunately, this growth has not been isolated to good-quality\npages. The number of incorrect, spamming, and malicious (e.g.,\nphishing) sites has also grown rapidly. The sheer number of both\ngood and bad pages on the Web has led to an increasing reliance\non search engines for the discovery of useful information. Users\nrely on search engines not only to return pages related to their\nsearch query, but also to separate the good from the bad, and\norder results so that the best pages are suggested first.\nTo date, most work on Web page ranking has focused on\nimproving the ordering of the results returned to the user\n(querydependent ranking, or dynamic ranking). However, having a good\nquery-independent ranking (static ranking) is also crucially\nimportant for a search engine. A good static ranking algorithm\nprovides numerous benefits:\n\u2022 Relevance: The static rank of a page provides a general\nindicator to the overall quality of the page. This is a\nuseful input to the dynamic ranking algorithm.\n\u2022 Efficiency: Typically, the search engine\"s index is\nordered by static rank. By traversing the index from\nhighquality to low-quality pages, the dynamic ranker may\nabort the search when it determines that no later page\nwill have as high of a dynamic rank as those already\nfound. The more accurate the static rank, the better this\nearly-stopping ability, and hence the quicker the search\nengine may respond to queries.\n\u2022 Crawl Priority: The Web grows and changes as quickly\nas search engines can crawl it. Search engines need a way\nto prioritize their crawl-to determine which pages to\nrecrawl, how frequently, and how often to seek out new\npages. Among other factors, the static rank of a page is\nused to determine this prioritization. A better static rank\nthus provides the engine with a higher quality, more\nupto-date index.\nGoogle is often regarded as the first commercially successful\nsearch engine. Their ranking was originally based on the\nPageRank algorithm [5][27]. Due to this (and possibly due to\nGoogle\"s promotion of PageRank to the public), PageRank is\nwidely regarded as the best method for the static ranking of Web\npages.\nThough PageRank has historically been thought to perform quite\nwell, there has yet been little academic evidence to support this\nclaim. Even worse, there has recently been work showing that\nPageRank may not perform any better than other simple measures\non certain tasks. Upstill et al. have found that for the task of\nfinding home pages, the number of pages linking to a page and the\ntype of URL were as, or more, effective than PageRank [32]. They\nfound similar results for the task of finding high quality\ncompanies [31]. PageRank has also been used in systems for\nTREC\"s very large collection and Web track competitions,\nbut with much less success than had been expected [17]. Finally,\nAmento et al. [1] found that simple features, such as the number\nof pages on a site, performed as well as PageRank.\nDespite these, the general belief remains among many, both\nacademic and in the public, that PageRank is an essential factor\nfor a good static rank. Failing this, it is still assumed that using the\nlink structure is crucial, in the form of the number of inlinks or the\namount of anchor text.\nIn this paper, we show there are a number of simple url- or\npagebased features that significantly outperform PageRank (for the\npurposes of statically ranking Web pages) despite ignoring the\nstructure of the Web. We combine these and other static features\nusing machine learning to achieve a ranking system that is\nsignificantly better than PageRank (in pairwise agreement with\nhuman labels).\nA machine learning approach for static ranking has other\nadvantages besides the quality of the ranking. Because the\nmeasure consists of many features, it is harder for malicious users\nto manipulate it (i.e., to raise their page\"s static rank to an\nundeserved level through questionable techniques, also known as\nWeb spamming). This is particularly true if the feature set is not\nknown. In contrast, a single measure like PageRank can be easier\nto manipulate because spammers need only concentrate on one\ngoal: how to cause more pages to point to their page. With an\nalgorithm that learns, a feature that becomes unusable due to\nspammer manipulation will simply be reduced or removed from\nthe final computation of rank. This flexibility allows a ranking\nsystem to rapidly react to new spamming techniques.\nA machine learning approach to static ranking is also able to take\nadvantage of any advances in the machine learning field. For\nexample, recent work on adversarial classification [12] suggests\nthat it may be possible to explicitly model the Web page\nspammer\"s (the adversary) actions, adjusting the ranking model in\nadvance of the spammer\"s attempts to circumvent it. Another\nexample is the elimination of outliers in constructing the model,\nwhich helps reduce the effect that unique sites may have on the\noverall quality of the static rank. By moving static ranking to a\nmachine learning framework, we not only gain in accuracy, but\nalso gain in the ability to react to spammer\"s actions, to rapidly\nadd new features to the ranking algorithm, and to leverage\nadvances in the rapidly growing field of machine learning.\nFinally, we believe there will be significant advantages to using\nthis technique for other domains, such as searching a local hard\ndrive or a corporation\"s intranet. These are domains where the\nlink structure is particularly weak (or non-existent), but there are\nother domain-specific features that could be just as powerful. For\nexample, the author of an intranet page and his/her position in the\norganization (e.g., CEO, manager, or developer) could provide\nsignificant clues as to the importance of that page. A machine\nlearning approach thus allows rapid development of a good static\nalgorithm in new domains.\nThis paper\"s contribution is a systematic study of static features,\nincluding PageRank, for the purposes of (statically) ranking Web\npages. Previous studies on PageRank typically used subsets of the\nWeb that are significantly smaller (e.g., the TREC VLC2 corpus,\nused by many, contains only 19 million pages). Also, the\nperformance of PageRank and other static features has typically\nbeen evaluated in the context of a complete system for dynamic\nranking, or for other tasks such as question answering. In contrast,\nwe explore the use of PageRank and other features for the direct\ntask of statically ranking Web pages.\nWe first briefly describe the PageRank algorithm. In Section 3 we\nintroduce RankNet, the machine learning technique used to\ncombine static features into a final ranking. Section 4 describes\nthe static features. The heart of the paper is in Section 5, which\npresents our experiments and results. We conclude with a\ndiscussion of related and future work.\n2. PAGERANK\nThe basic idea behind PageRank is simple: a link from a Web\npage to another can be seen as an endorsement of that page. In\ngeneral, links are made by people. As such, they are indicative of\nthe quality of the pages to which they point - when creating a\npage, an author presumably chooses to link to pages deemed to be\nof good quality. We can take advantage of this linkage\ninformation to order Web pages according to their perceived\nquality.\nImagine a Web surfer who jumps from Web page to Web page,\nchoosing with uniform probability which link to follow at each\nstep. In order to reduce the effect of dead-ends or endless cycles\nthe surfer will occasionally jump to a random page with some\nsmall probability \u03b1, or when on a page with no out-links. If\naveraged over a sufficient number of steps, the probability the\nsurfer is on page j at some point in time is given by the formula:\n\u2211\u2208\n+\n\u2212\n=\nji i\niP\nN\njP\nB F\n)()1(\n)( \u03b1\n\u03b1 (1)\nWhere Fi is the set of pages that page i links to, and Bj is the set of\npages that link to page j. The PageRank score for node j is defined\nas this probability: PR(j)=P(j). Because equation (1) is recursive,\nit must be iteratively evaluated until P(j) converges (typically, the\ninitial distribution for P(j) is uniform). The intuition is, because a\nrandom surfer would end up at the page more frequently, it is\nlikely a better page. An alternative view for equation (1) is that\neach page is assigned a quality, P(j). A page gives an equal\nshare of its quality to each page it points to.\nPageRank is computationally expensive. Our collection of 5\nbillion pages contains approximately 370 billion links. Computing\nPageRank requires iterating over these billions of links multiple\ntimes (until convergence). It requires large amounts of memory\n(or very smart caching schemes that slow the computation down\neven further), and if spread across multiple machines, requires\nsignificant communication between them. Though much work has\nbeen done on optimizing the PageRank computation (see e.g.,\n[25] and [6]), it remains a relatively slow, computationally\nexpensive property to compute.\n3. RANKNET\nMuch work in machine learning has been done on the problems of\nclassification and regression. Let X={xi} be a collection of feature\nvectors (typically, a feature is any real valued number), and\nY={yi} be a collection of associated classes, where yi is the class\nof the object described by feature vector xi. The classification\nproblem is to learn a function f that maps yi=f(xi), for all i. When\nyi is real-valued as well, this is called regression.\nStatic ranking can be seen as a regression problem. If we let xi\nrepresent features of page i, and yi be a value (say, the rank) for\neach page, we could learn a regression function that mapped each\npage\"s features to their rank. However, this over-constrains the\nproblem we wish to solve. All we really care about is the order of\nthe pages, not the actual value assigned to them.\nRecent work on this ranking problem [7][13][18] directly\nattempts to optimize the ordering of the objects, rather than the\nvalue assigned to them. For these, let Z={<i,j>} be a collection of\npairs of items, where item i should be assigned a higher value than\nitem j. The goal of the ranking problem, then, is to learn a\nfunction f such that,\n)()(,, ji ffji xxZ >\u2208\u2200\n708\nNote that, as with learning a regression function, the result of this\nprocess is a function (f) that maps feature vectors to real values.\nThis function can still be applied anywhere that a\nregressionlearned function could be applied. The only difference is the\ntechnique used to learn the function. By directly optimizing the\nordering of objects, these methods are able to learn a function that\ndoes a better job of ranking than do regression techniques.\nWe used RankNet [7], one of the aforementioned techniques for\nlearning ranking functions, to learn our static rank function.\nRankNet is a straightforward modification to the standard neural\nnetwork back-prop algorithm. As with back-prop, RankNet\nattempts to minimize the value of a cost function by adjusting\neach weight in the network according to the gradient of the cost\nfunction with respect to that weight. The difference is that, while a\ntypical neural network cost function is based on the difference\nbetween the network output and the desired output, the RankNet\ncost function is based on the difference between a pair of network\noutputs. That is, for each pair of feature vectors <i,j> in the\ntraining set, RankNet computes the network outputs oi and oj.\nSince vector i is supposed to be ranked higher than vector j, the\nlarger is oj-oi, the larger the cost.\nRankNet also allows the pairs in Z to be weighted with a\nconfidence (posed as the probability that the pair satisfies the\nordering induced by the ranking function). In this paper, we used\na probability of one for all pairs. In the next section, we will\ndiscuss the features used in our feature vectors, xi.\n4. FEATURES\nTo apply RankNet (or other machine learning techniques) to the\nranking problem, we needed to extract a set of features from each\npage. We divided our feature set into four, mutually exclusive,\ncategories: page-level (Page), domain-level (Domain), anchor text\nand inlinks (Anchor), and popularity (Popularity). We also\noptionally used the PageRank of a page as a feature. Below, we\ndescribe each of these feature categories in more detail.\nPageRank\nWe computed PageRank on a Web graph of 5 billion crawled\npages (and 20 billion known URLs linked to by these pages).\nThis represents a significant portion of the Web, and is\napproximately the same number of pages as are used by\nGoogle, Yahoo, and MSN for their search engines.\nBecause PageRank is a graph-based algorithm, it is important\nthat it be run on as large a subset of the Web as possible. Most\nprevious studies on PageRank used subsets of the Web that are\nsignificantly smaller (e.g. the TREC VLC2 corpus, used by\nmany, contains only 19 million pages)\nWe computed PageRank using the standard value of 0.85 for \u03b1.\nPopularity\nAnother feature we used is the actual popularity of a Web page,\nmeasured as the number of times that it has been visited by\nusers over some period of time. We have access to such data\nfrom users who have installed the MSN toolbar and have opted\nto provide it to MSN. The data is aggregated into a count, for\neach Web page, of the number of users who viewed that page.\nThough popularity data is generally unavailable, there are two\nother sources for it. The first is from proxy logs. For example, a\nuniversity that requires its students to use a proxy has a record\nof all the pages they have visited while on campus.\nUnfortunately, proxy data is quite biased and relatively small.\nAnother source, internal to search engines, are records of which\nresults their users clicked on. Such data was used by the search\nengine Direct Hit, and has recently been explored for\ndynamic ranking purposes [20]. An advantage of the toolbar\ndata over this is that it contains information about URL visits\nthat are not just the result of a search.\nThe raw popularity is processed into a number of features such\nas the number of times a page was viewed and the number of\ntimes any page in the domain was viewed. More details are\nprovided in section 5.5.\nAnchor text and inlinks\nThese features are based on the information associated with\nlinks to the page in question. It includes features such as the\ntotal amount of text in links pointing to the page (anchor\ntext), the number of unique words in that text, etc.\nPage\nThis category consists of features which may be determined by\nlooking at the page (and its URL) alone. We used only eight,\nsimple features such as the number of words in the body, the\nfrequency of the most common term, etc.\nDomain\nThis category contains features that are computed as averages\nacross all pages in the domain. For example, the average\nnumber of outlinks on any page and the average PageRank.\nMany of these features have been used by others for ranking Web\npages, particularly the anchor and page features. As mentioned,\nthe evaluation is typically for dynamic ranking, and we wish to\nevaluate the use of them for static ranking. Also, to our\nknowledge, this is the first study on the use of actual page\nvisitation popularity for static ranking. The closest similar work is\non using click-through behavior (that is, which search engine\nresults the users click on) to affect dynamic ranking (see e.g.,\n[20]).\nBecause we use a wide variety of features to come up with a static\nranking, we refer to this as fRank (for feature-based ranking).\nfRank uses RankNet and the set of features described in this\nsection to learn a ranking function for Web pages. Unless\notherwise specified, fRank was trained with all of the features.\n5. EXPERIMENTS\nIn this section, we will demonstrate that we can out perform\nPageRank by applying machine learning to a straightforward set\nof features. Before the results, we first discuss the data, the\nperformance metric, and the training method.\n5.1 Data\nIn order to evaluate the quality of a static ranking, we needed a\ngold standard defining the correct ordering for a set of pages.\nFor this, we employed a dataset which contains human judgments\nfor 28000 queries. For each query, a number of results are\nmanually assigned a rating, from 0 to 4, by human judges. The\nrating is meant to be a measure of how relevant the result is for\nthe query, where 0 means poor and 4 means excellent. There\nare approximately 500k judgments in all, or an average of 18\nratings per query.\nThe queries are selected by randomly choosing queries from\namong those issued to the MSN search engine. The probability\nthat a query is selected is proportional to its frequency among all\n709\nof the queries. As a result, common queries are more likely to be\njudged than uncommon queries. As an example of how diverse\nthe queries are, the first four queries in the training set are chef\nschools, chicagoland speedway, eagles fan club, and\nTurkish culture. The documents selected for judging are those\nthat we expected would, on average, be reasonably relevant (for\nexample, the top ten documents returned by MSN\"s search\nengine). This provides significantly more information than\nrandomly selecting documents on the Web, the vast majority of\nwhich would be irrelevant to a given query.\nBecause of this process, the judged pages tend to be of higher\nquality than the average page on the Web, and tend to be pages\nthat will be returned for common search queries. This bias is good\nwhen evaluating the quality of static ranking for the purposes of\nindex ordering and returning relevant documents. This is because\nthe most important portion of the index to be well-ordered and\nrelevant is the portion that is frequently returned for search\nqueries. Because of this bias, however, the results in this paper are\nnot applicable to crawl prioritization. In order to obtain\nexperimental results on crawl prioritization, we would need\nratings on a random sample of Web pages.\nTo convert the data from query-dependent to query-independent,\nwe simply removed the query, taking the maximum over\njudgments for a URL that appears in more than one query. The\nreasoning behind this is that a page that is relevant for some query\nand irrelevant for another is probably a decent page and should\nhave a high static rank. Because we evaluated the pages on\nqueries that occur frequently, our data indicates the correct index\nordering, and assigns high value to pages that are likely to be\nrelevant to a common query.\nWe randomly assigned queries to a training, validation, or test set,\nsuch that they contained 84%, 8%, and 8% of the queries,\nrespectively. Each set contains all of the ratings for a given query,\nand no query appears in more than one set. The training set was\nused to train fRank. The validation set was used to select the\nmodel that had the highest performance. The test set was used for\nthe final results.\nThis data gives us a query-independent ordering of pages. The\ngoal for a static ranking algorithm will be to reproduce this\nordering as closely as possible. In the next section, we describe\nthe measure we used to evaluate this.\n5.2 Measure\nWe chose to use pairwise accuracy to evaluate the quality of a\nstatic ranking. The pairwise accuracy is the fraction of time that\nthe ranking algorithm and human judges agree on the ordering of\na pair of Web pages.\nIf S(x) is the static ranking assigned to page x, and H(x) is the\nhuman judgment of relevance for x, then consider the following\nsets:\n)}()(:,{ yHxHyx >=pH and )}()(:,{ ySxSyx >=pS\nThe pairwise accuracy is the portion of Hp that is also contained\nin Sp:\np\npp\nH\nSH \u2229\n=accuracypairwise\nThis measure was chosen for two reasons. First, the discrete\nhuman judgments provide only a partial ordering over Web pages,\nmaking it difficult to apply a measure such as the Spearman rank\norder correlation coefficient (in the pairwise accuracy measure, a\npair of documents with the same human judgment does not affect\nthe score). Second, the pairwise accuracy has an intuitive\nmeaning: it is the fraction of pairs of documents that, when the\nhumans claim one is better than the other, the static rank\nalgorithm orders them correctly.\n5.3 Method\nWe trained fRank (a RankNet based neural network) using the\nfollowing parameters. We used a fully connected 2 layer network.\nThe hidden layer had 10 hidden nodes. The input weights to this\nlayer were all initialized to be zero. The output layer (just a\nsingle node) weights were initialized using a uniform random\ndistribution in the range [-0.1, 0.1]. We used tanh as the transfer\nfunction from the inputs to the hidden layer, and a linear function\nfrom the hidden layer to the output. The cost function is the\npairwise cross entropy cost function as discussed in section 3.\nThe features in the training set were normalized to have zero mean\nand unit standard deviation. The same linear transformation was\nthen applied to the features in the validation and test sets.\nFor training, we presented the network with 5 million pairings of\npages, where one page had a higher rating than the other. The\npairings were chosen uniformly at random (with replacement)\nfrom all possible pairings. When forming the pairs, we ignored the\nmagnitude of the difference between the ratings (the rating spread)\nfor the two URLs. Hence, the weight for each pair was constant\n(one), and the probability of a pair being selected was\nindependent of its rating spread.\nWe trained the network for 30 epochs. On each epoch, the\ntraining pairs were randomly shuffled. The initial training rate was\n0.001. At each epoch, we checked the error on the training set. If\nthe error had increased, then we decreased the training rate, under\nthe hypothesis that the network had probably overshot. The\ntraining rate at each epoch was thus set to:\nTraining rate =\n1+\u03b5\n\u03ba\nWhere \u03ba is the initial rate (0.001), and \u03b5 is the number of times\nthe training set error has increased. After each epoch, we\nmeasured the performance of the neural network on the validation\nset, using 1 million pairs (chosen randomly with replacement).\nThe network with the highest pairwise accuracy on the validation\nset was selected, and then tested on the test set. We report the\npairwise accuracy on the test set, calculated using all possible\npairs.\nThese parameters were determined and fixed before the static rank\nexperiments in this paper. In particular, the choice of initial\ntraining rate, number of epochs, and training rate decay function\nwere taken directly from Burges et al [7].\nThough we had the option of preprocessing any of the features\nbefore they were input to the neural network, we refrained from\ndoing so on most of them. The only exception was the popularity\nfeatures. As with most Web phenomenon, we found that the\ndistribution of site popularity is Zipfian. To reduce the dynamic\nrange, and hopefully make the feature more useful, we presented\nthe network with both the unpreprocessed, as well as the\nlogarithm, of the popularity features (As with the others, the\nlogarithmic feature values were also normalized to have zero\nmean and unit standard deviation).\n710\nApplying fRank to a document is computationally efficient, taking\ntime that is only linear in the number of input features; it is thus\nwithin a constant factor of other simple machine learning methods\nsuch as na\u00efve Bayes. In our experiments, computing the fRank for\nall five billion Web pages was approximately 100 times faster\nthan computing the PageRank for the same set.\n5.4 Results\nAs Table 1 shows, fRank significantly outperforms PageRank for\nthe purposes of static ranking. With a pairwise accuracy of 67.4%,\nfRank more than doubles the accuracy of PageRank (relative to\nthe baseline of 50%, which is the accuracy that would be achieved\nby a random ordering of Web pages). Note that one of fRank\"s\ninput features is the PageRank of the page, so we would expect it\nto perform no worse than PageRank. The significant increase in\naccuracy implies that the other features (anchor, popularity, etc.)\ndo in fact contain useful information regarding the overall quality\nof a page.\nTable 1: Basic Results\nTechnique Accuracy (%)\nNone (Baseline) 50.00\nPageRank 56.70\nfRank 67.43\nThere are a number of decisions that go into the computation of\nPageRank, such as how to deal with pages that have no outlinks,\nthe choice of \u03b1, numeric precision, convergence threshold, etc.\nWe were able to obtain a computation of PageRank from a\ncompletely independent implementation (provided by Marc\nNajork) that varied somewhat in these parameters. It achieved a\npairwise accuracy of 56.52%, nearly identical to that obtained by\nour implementation. We thus concluded that the quality of the\nPageRank is not sensitive to these minor variations in algorithm,\nnor was PageRank\"s low accuracy due to problems with our\nimplementation of it.\nWe also wanted to find how well each feature set performed. To\nanswer this, for each feature set, we trained and tested fRank\nusing only that set of features. The results are shown in Table 2.\nAs can be seen, every single feature set individually outperformed\nPageRank on this test. Perhaps the most interesting result is that\nthe Page-level features had the highest performance out of all the\nfeature sets. This is surprising because these are features that do\nnot depend on the overall graph structure of the Web, nor even on\nwhat pages point to a given page. This is contrary to the common\nbelief that the Web graph structure is the key to finding a good\nstatic ranking of Web pages.\nTable 2: Results for individual feature sets.\nFeature Set Accuracy (%)\nPageRank 56.70\nPopularity 60.82\nAnchor 59.09\nPage 63.93\nDomain 59.03\nAll Features 67.43\nBecause we are using a two-layer neural network, the features in\nthe learned network can interact with each other in interesting,\nnonlinear ways. This means that a particular feature that appears\nto have little value in isolation could actually be very important\nwhen used in combination with other features. To measure the\nfinal contribution of a feature set, in the context of all the other\nfeatures, we performed an ablation study. That is, for each set of\nfeatures, we trained a network to contain all of the features except\nthat set. We then compared the performance of the resulting\nnetwork to the performance of the network with all of the features.\nTable 3 shows the results of this experiment, where the decrease\nin accuracy is the difference in pairwise accuracy between the\nnetwork trained with all of the features, and the network missing\nthe given feature set.\nTable 3: Ablation study. Shown is the decrease in accuracy\nwhen we train a network that has all but the given set of\nfeatures. The last line is shows the effect of removing the\nanchor, PageRank, and domain features, hence a model\ncontaining no network or link-based information whatsoever.\nFeature Set Decrease in\nAccuracy\nPageRank 0.18\nPopularity 0.78\nAnchor 0.47\nPage 5.42\nDomain\nAnchor, PageRank & Domain\n0.10\n0.60\nThe results of the ablation study are consistent with the individual\nfeature set study. Both show that the most important feature set is\nthe Page-level feature set, and the second most important is the\npopularity feature set.\nFinally, we wished to see how the performance of fRank\nimproved as we added features; we wanted to find at what point\nadding more feature sets became relatively useless. Beginning\nwith no features, we greedily added the feature set that improved\nperformance the most. The results are shown in Table 4. For\nexample, the fourth line of the table shows that fRank using the\npage, popularity, and anchor features outperformed any network\nthat used the page, popularity, and some other feature set, and that\nthe performance of this network was 67.25%.\nTable 4: fRank performance as feature sets are added. At each\nrow, the feature set that gave the greatest increase in accuracy\nwas added to the list of features (i.e., we conducted a greedy\nsearch over feature sets).\nFeature Set Accuracy (%)\nNone 50.00\n+Page 63.93\n+Popularity 66.83\n+Anchor 67.25\n+PageRank 67.31\n+Domain 67.43\n711\nFinally, we present a qualitative comparison of PageRank vs.\nfRank. In Table 5 are the top ten URLs returned for PageRank and\nfor fRank. PageRank\"s results are heavily weighted towards\ntechnology sites. It contains two QuickTime URLs (Apple\"s video\nplayback software), as well as Internet Explorer and FireFox\nURLs (both of which are Web browsers). fRank, on the other\nhand, contains more consumer-oriented sites such as American\nExpress, Target, Dell, etc. PageRank\"s bias toward technology can\nbe explained through two processes. First, there are many pages\nwith buttons at the bottom suggesting that the site is optimized\nfor Internet Explorer, or that the visitor needs QuickTime. These\ngenerally link back to, in these examples, the Internet Explorer\nand QuickTime download sites. Consequently, PageRank ranks\nthose pages highly. Though these pages are important, they are\nnot as important as it may seem by looking at the link structure\nalone. One fix for this is to add information about the link to the\nPageRank computation, such as the size of the text, whether it was\nat the bottom of the page, etc.\nThe other bias comes from the fact that the population of Web site\nauthors is different than the population of Web users. Web\nauthors tend to be technologically-oriented, and thus their linking\nbehavior reflects those interests. fRank, by knowing the actual\nvisitation popularity of a site (the popularity feature set), is able to\neliminate some of that bias. It has the ability to depend more on\nwhere actual Web users visit rather than where the Web site\nauthors have linked.\nThe results confirm that fRank outperforms PageRank in pairwise\naccuracy. The two most important feature sets are the page and\npopularity features. This is surprising, as the page features\nconsisted only of a few (8) simple features. Further experiments\nfound that, of the page features, those based on the text of the\npage (as opposed to the URL) performed the best. In the next\nsection, we explore the popularity feature in more detail.\n5.5 Popularity Data\nAs mentioned in section 4, our popularity data came from MSN\ntoolbar users. For privacy reasons, we had access only to an\naggregate count of, for each URL, how many times it was visited\nby any toolbar user. This limited the possible features we could\nderive from this data. For possible extensions, see section 6.3,\nfuture work.\nFor each URL in our train and test sets, we provided a feature to\nfRank which was how many times it had been visited by a toolbar\nuser. However, this feature was quite noisy and sparse,\nparticularly for URLs with query parameters (e.g.,\nhttp://search.msn.com/results.aspx?q=machine+learning&form=QBHP). One\nsolution was to provide an additional feature which was the\nnumber of times any URL at the given domain was visited by a\ntoolbar user. Adding this feature dramatically improved the\nperformance of fRank.\nWe took this one step further and used the built-in hierarchical\nstructure of URLs to construct many levels of backoff between the\nfull URL and the domain. We did this by using the set of features\nshown in Table 6.\nTable 6: URL functions used to compute the Popularity\nfeature set.\nFunction Example\nExact URL cnn.com/2005/tech/wikipedia.html?v=mobile\nNo Params cnn.com/2005/tech/wikipedia.html\nPage wikipedia.html\nURL-1 cnn.com/2005/tech\nURL-2 cnn.com/2005\n\u2026\nDomain cnn.com\nDomain+1 cnn.com/2005\n\u2026\nEach URL was assigned one feature for each function shown in\nthe table. The value of the feature was the count of the number of\ntimes a toolbar user visited a URL, where the function applied to\nthat URL matches the function applied to the URL in question.\nFor example, a user\"s visit to cnn.com/2005/sports.html would\nincrement the Domain and Domain+1 features for the URL\ncnn.com/2005/tech/wikipedia.html.\nAs seen in Table 7, adding the domain counts significantly\nimproved the quality of the popularity feature, and adding the\nnumerous backoff functions listed in Table 6 improved the\naccuracy even further.\nTable 7: Effect of adding backoff to the popularity feature set\nFeatures Accuracy (%)\nURL count 58.15\nURL and Domain counts 59.31\nAll backoff functions (Table 6) 60.82\nTable 5: Top ten URLs for PageRank vs. fRank\nPageRank fRank\ngoogle.com google.com\napple.com/quicktime/download yahoo.com\namazon.com americanexpress.com\nyahoo.com hp.com\nmicrosoft.com/windows/ie target.com\napple.com/quicktime bestbuy.com\nmapquest.com dell.com\nebay.com autotrader.com\nmozilla.org/products/firefox dogpile.com\nftc.gov bankofamerica.com\n712\nBacking off to subsets of the URL is one technique for dealing\nwith the sparsity of data. It is also informative to see how the\nperformance of fRank depends on the amount of popularity data\nthat we have collected. In Figure 1 we show the performance of\nfRank trained with only the popularity feature set vs. the amount\nof data we have for the popularity feature set. Each day, we\nreceive additional popularity data, and as can be seen in the plot,\nthis increases the performance of fRank. The relation is\nlogarithmic: doubling the amount of popularity data provides a\nconstant improvement in pairwise accuracy.\nIn summary, we have found that the popularity features provide a\nuseful boost to the overall fRank accuracy. Gathering more\npopularity data, as well as employing simple backoff strategies,\nimprove this boost even further.\n5.6 Summary of Results\nThe experiments provide a number of conclusions. First, fRank\nperforms significantly better than PageRank, even without any\ninformation about the Web graph. Second, the page level and\npopularity features were the most significant contributors to\npairwise accuracy. Third, by collecting more popularity data, we\ncan continue to improve fRank\"s performance.\nThe popularity data provides two benefits to fRank. First, we see\nthat qualitatively, fRank\"s ordering of Web pages has a more\nfavorable bias than PageRank\"s. fRank\"s ordering seems to\ncorrespond to what Web users, rather than Web page authors,\nprefer. Second, the popularity data is more timely than\nPageRank\"s link information. The toolbar provides information\nabout which Web pages people find interesting right now,\nwhereas links are added to pages more slowly, as authors find the\ntime and interest.\n6. RELATED AND FUTURE WORK\n6.1 Improvements to PageRank\nSince the original PageRank paper, there has been work on\nimproving it. Much of that work centers on speeding up and\nparallelizing the computation [15][25].\nOne recognized problem with PageRank is that of topic drift: A\npage about dogs will have high PageRank if it is linked to by\nmany pages that themselves have high rank, regardless of their\ntopic. In contrast, a search engine user looking for good pages\nabout dogs would likely prefer to find pages that are pointed to by\nmany pages that are themselves about dogs. Hence, a link that is\non topic should have higher weight than a link that is not.\nRichardson and Domingos\"s Query Dependent PageRank [29]\nand Haveliwala\"s Topic-Sensitive PageRank [16] are two\napproaches that tackle this problem.\nOther variations to PageRank include differently weighting links\nfor inter- vs. intra-domain links, adding a backwards step to the\nrandom surfer to simulate the back button on most browsers\n[24] and modifying the jump probability (\u03b1) [3]. See Langville\nand Meyer [23] for a good survey of these, and other\nmodifications to PageRank.\n6.2 Other related work\nPageRank is not the only link analysis algorithm used for ranking\nWeb pages. The most well-known other is HITS [22], which is\nused by the Teoma search engine [30]. HITS produces a list of\nhubs and authorities, where hubs are pages that point to many\nauthority pages, and authorities are pages that are pointed to by\nmany hubs. Previous work has shown HITS to perform\ncomparably to PageRank [1].\nOne field of interest is that of static index pruning (see e.g.,\nCarmel et al. [8]). Static index pruning methods reduce the size of\nthe search engine\"s index by removing documents that are\nunlikely to be returned by a search query. The pruning is typically\ndone based on the frequency of query terms. Similarly, Pandey\nand Olston [28] suggest crawling pages frequently if they are\nlikely to incorrectly appear (or not appear) as a result of a search.\nSimilar methods could be incorporated into the static rank (e.g.,\nhow many frequent queries contain words found on this page).\nOthers have investigated the effect that PageRank has on the Web\nat large [9]. They argue that pages with high PageRank are more\nlikely to be found by Web users, thus more likely to be linked to,\nand thus more likely to maintain a higher PageRank than other\npages. The same may occur for the popularity data. If we increase\nthe ranking for popular pages, they are more likely to be clicked\non, thus further increasing their popularity. Cho et al. [10] argue\nthat a more appropriate measure of Web page quality would\ndepend on not only the current link structure of the Web, but also\non the change in that link structure. The same technique may be\napplicable to popularity data: the change in popularity of a page\nmay be more informative than the absolute popularity.\nOne interesting related work is that of Ivory and Hearst [19].\nTheir goal was to build a model of Web sites that are considered\nhigh quality from the perspective of content, structure and\nnavigation, visual design, functionality, interactivity, and overall\nexperience. They used over 100 page level features, as well as\nfeatures encompassing the performance and structure of the site.\nThis let them qualitatively describe the qualities of a page that\nmake it appear attractive (e.g., rare use of italics, at least 9 point\nfont, \u2026), and (in later work) to build a system that assists novel\nWeb page authors in creating quality pages by evaluating it\naccording to these features. The primary differences between this\nwork and ours are the goal (discovering what constitutes a good\nWeb page vs. ordering Web pages for the purposes of Web\nsearch), the size of the study (they used a dataset of less than 6000\npages vs. our set of 468,000), and our comparison with PageRank.\ny = 0.577Ln(x) + 58.283\nR\n2\n= 0.9822\n58\n58.5\n59\n59.5\n60\n60.5\n61\n1 10 100\nDays of Toolbar Data\nPairwiseAccuracy\nFigure 1: Relation between the amount of popularity data and\nthe performance of the popularity feature set. Note the x-axis\nis a logarithmic scale.\n713\nNevertheless, their work provides insights to additional useful\nstatic features that we could incorporate into fRank in the future.\nRecent work on incorporating novel features into dynamic ranking\nincludes that by Joachims et al. [21], who investigate the use of\nimplicit feedback from users, in the form of which search engine\nresults are clicked on. Craswell et al. [11] present a method for\ndetermining the best transformation to apply to query independent\nfeatures (such as those used in this paper) for the purposes of\nimproving dynamic ranking. Other work, such as Boyan et al. [4]\nand Bartell et al. [2] apply machine learning for the purposes of\nimproving the overall relevance of a search engine (i.e., the\ndynamic ranking). They do not apply their techniques to the\nproblem of static ranking.\n6.3 Future work\nThere are many ways in which we would like to extend this work.\nFirst, fRank uses only a small number of features. We believe we\ncould achieve even more significant results with more features. In\nparticular the existence, or lack thereof, of certain words could\nprove very significant (for instance, under construction\nprobably signifies a low quality page). Other features could\ninclude the number of images on a page, size of those images,\nnumber of layout elements (tables, divs, and spans), use of style\nsheets, conforming to W3C standards (like XHTML 1.0 Strict),\nbackground color of a page, etc.\nMany pages are generated dynamically, the contents of which may\ndepend on parameters in the URL, the time of day, the user\nvisiting the site, or other variables. For such pages, it may be\nuseful to apply the techniques found in [26] to form a static\napproximation for the purposes of extracting features. The\nresulting grammar describing the page could itself be a source of\nadditional features describing the complexity of the page, such as\nhow many non-terminal nodes it has, the depth of the grammar\ntree, etc.\nfRank allows one to specify a confidence in each pairing of\ndocuments. In the future, we will experiment with probabilities\nthat depend on the difference in human judgments between the\ntwo items in the pair. For example, a pair of documents where one\nwas rated 4 and the other 0 should have a higher confidence than\na pair of documents rated 3 and 2.\nThe experiments in this paper are biased toward pages that have\nhigher than average quality. Also, fRank with all of the features\ncan only be applied to pages that have already been crawled.\nThus, fRank is primarily useful for index ordering and improving\nrelevance, not for directing the crawl. We would like to\ninvestigate a machine learning approach for crawl prioritization as\nwell. It may be that a combination of methods is best: for\nexample, using PageRank to select the best 5 billion of the 20\nbillion pages on the Web, then using fRank to order the index and\naffect search relevancy.\nAnother interesting direction for exploration is to incorporate\nfRank and page-level features directly into the PageRank\ncomputation itself. Work on biasing the PageRank jump vector\n[16], and transition matrix [29], have demonstrated the feasibility\nand advantages of such an approach. There is reason to believe\nthat a direct application of [29], using the fRank of a page for its\nrelevance, could lead to an improved overall static rank.\nFinally, the popularity data can be used in other interesting ways.\nThe general surfing and searching habits of Web users varies by\ntime of day. Activity in the morning, daytime, and evening are\noften quite different (e.g., reading the news, solving problems,\nand accessing entertainment, respectively). We can gain insight\ninto these differences by using the popularity data, divided into\nsegments of the day. When a query is issued, we would then use\nthe popularity data matching the time of query in order to do the\nranking of Web pages. We also plan to explore popularity features\nthat use more than just the counts of how often a page was visited.\nFor example, how long users tended to dwell on a page, did they\nleave the page by clicking a link or by hitting the back button, etc.\nFox et al. did a study that showed that features such as this can be\nvaluable for the purposes of dynamic ranking [14]. Finally, the\npopularity data could be used as the label rather than as a feature.\nUsing fRank in this way to predict the popularity of a page may\nuseful for the tasks of relevance, efficiency, and crawl priority.\nThere is also significantly more popularity data than human\nlabeled data, potentially enabling more complex machine learning\nmethods, and significantly more features.\n7. CONCLUSIONS\nA good static ranking is an important component for today\"s\nsearch engines and information retrieval systems. We have\ndemonstrated that PageRank does not provide a very good static\nranking; there are many simple features that individually out\nperform PageRank. By combining many static features, fRank\nachieves a ranking that has a significantly higher pairwise\naccuracy than PageRank alone. A qualitative evaluation of the top\ndocuments shows that fRank is less technology-biased than\nPageRank; by using popularity data, it is biased toward pages that\nWeb users, rather than Web authors, visit. The machine learning\ncomponent of fRank gives it the additional benefit of being more\nrobust against spammers, and allows it to leverage further\ndevelopments in the machine learning community in areas such as\nadversarial classification. We have only begun to explore the\noptions, and believe that significant strides can be made in the\narea of static ranking by further experimentation with additional\nfeatures, other machine learning techniques, and additional\nsources of data.\n8. ACKNOWLEDGMENTS\nThank you to Marc Najork for providing us with additional\nPageRank computations and to Timo Burkard for assistance with\nthe popularity data. Many thanks to Chris Burges for providing\ncode and significant support in using training RankNets. Also, we\nthank Susan Dumais and Nick Craswell for their edits and\nsuggestions.\n9. REFERENCES\n[1] B. Amento, L. Terveen, and W. Hill. Does authority mean\nquality? Predicting expert quality ratings of Web documents.\nIn Proceedings of the 23rd\nAnnual International ACM SIGIR\nConference on Research and Development in Information\nRetrieval, 2000.\n[2] B. Bartell, G. Cottrell, and R. Belew. Automatic combination\nof multiple ranked retrieval systems. In Proceedings of the\n17th Annual International ACM SIGIR Conference on\nResearch and Development in Information Retrieval, 1994.\n[3] P. Boldi, M. Santini, and S. Vigna. PageRank as a function\nof the damping factor. 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{"name": "train_H-81", "title": "Distance Measures for MPEG-7-based Retrieval", "abstract": "In visual information retrieval the careful choice of suitable proximity measures is a crucial success factor. The evaluation presented in this paper aims at showing that the distance measures suggested by the MPEG-7 group for the visual descriptors can be beaten by general-purpose measures. Eight visual MPEG-7 descriptors were selected and 38 distance measures implemented. Three media collections were created and assessed, performance indicators developed and more than 22500 tests performed. Additionally, a quantisation model was developed to be able to use predicate-based distance measures on continuous data as well. The evaluation shows that the distance measures recommended in the MPEG-7-standard are among the best but that other measures perform even better.", "fulltext": "1. INTRODUCTION\nThe MPEG-7 standard defines - among others - a set of\ndescriptors for visual media. Each descriptor consists of a feature\nextraction mechanism, a description (in binary and XML format)\nand guidelines that define how to apply the descriptor on different\nkinds of media (e.g. on temporal media). The MPEG-7 descriptors\nhave been carefully designed to meet - partially\ncomplementaryrequirements of different application domains: archival, browsing,\nretrieval, etc. [9]. In the following, we will exclusively deal with\nthe visual MPEG-7 descriptors in the context of media retrieval.\nThe visual MPEG-7 descriptors fall in five groups: colour,\ntexture, shape, motion and others (e.g. face description) and sum\nup to 16 basic descriptors. For retrieval applications, a rule for\neach descriptor is mandatory that defines how to measure the\nsimilarity of two descriptions. Common rules are distance\nfunctions, like the Euclidean distance and the Mahalanobis\ndistance. Unfortunately, the MPEG-7 standard does not include\ndistance measures in the normative part, because it was not\ndesigned to be (and should not exclusively understood to be)\nretrieval-specific. However, the MPEG-7 authors give\nrecommendations, which distance measure to use on a particular\ndescriptor. These recommendations are based on accurate\nknowledge of the descriptors' behaviour and the description\nstructures.\nIn the present study a large number of successful distance\nmeasures from different areas (statistics, psychology, medicine,\nsocial and economic sciences, etc.) were implemented and applied\non MPEG-7 data vectors to verify whether or not the\nrecommended MPEG-7 distance measures are really the best for\nany reasonable class of media objects. From the MPEG-7 tests\nand the recommendations it does not become clear, how many and\nwhich distance measures have been tested on the visual\ndescriptors and the MPEG-7 test datasets. The hypothesis is that\nanalytically derived distance measures may be good in general but\nonly a quantitative analysis is capable to identify the best distance\nmeasure for a specific feature extraction method.\nThe paper is organised as follows. Section 2 gives a minimum of\nbackground information on the MPEG-7 descriptors and distance\nmeasurement in visual information retrieval (VIR, see [3], [16]).\nSection 3 gives an overview over the implemented distance\nmeasures. Section 4 describes the test setup, including the test\ndata and the implemented evaluation methods. Finally, Section 5\npresents the results per descriptor and over all descriptors.\n2. BACKGROUND\n2.1 MPEG-7: visual descriptors\nThe visual part of the MPEG-7 standard defines several\ndescriptors. Not all of them are really descriptors in the sense that\nthey extract properties from visual media. Some of them are just\nstructures for descriptor aggregation or localisation. The basic\ndescriptors are Color Layout, Color Structure, Dominant Color,\nScalable Color, Edge Histogram, Homogeneous Texture, Texture\nBrowsing, Region-based Shape, Contour-based Shape, Camera\nMotion, Parametric Motion and Motion Activity.\nOther descriptors are based on low-level descriptors or semantic\ninformation: Group-of-Frames/Group-of-Pictures Color (based on\nScalable Color), Shape 3D (based on 3D mesh information),\nMotion Trajectory (based on object segmentation) and Face\nRecognition (based on face extraction).\nDescriptors for spatiotemporal aggregation and localisation are:\nSpatial 2D Coordinates, Grid Layout, Region Locator (spatial),\nTime Series, Temporal Interpolation (temporal) and\nSpatioTemporal Locator (combined). Finally, other structures\nexist for colour spaces, colour quantisation and multiple 2D views\nof 3D objects.\nThese additional structures allow combining the basic descriptors\nin multiple ways and on different levels. But they do not change\nthe characteristics of the extracted information. Consequently,\nstructures for aggregation and localisation were not considered in\nthe work described in this paper.\n2.2 Similarity measurement on visual data\nGenerally, similarity measurement on visual information aims at\nimitating human visual similarity perception. Unfortunately,\nhuman perception is much more complex than any of the existing\nsimilarity models (it includes perception, recognition and\nsubjectivity).\nThe common approach in visual information retrieval is\nmeasuring dis-similarity as distance. Both, query object and\ncandidate object are represented by their corresponding feature\nvectors. The distance between these objects is measured by\ncomputing the distance between the two vectors. Consequently,\nthe process is independent of the employed querying paradigm\n(e.g. query by example). The query object may be natural (e.g. a\nreal object) or artificial (e.g. properties of a group of objects).\nGoal of the measurement process is to express a relationship\nbetween the two objects by their distance. Iteration for multiple\ncandidates allows then to define a partial order over the\ncandidates and to address those in a (to be defined)\nneighbourhood being similar to the query object. At this point, it\nhas to be mentioned that in a multi-descriptor\nenvironmentespecially in MPEG-7 - we are only half way towards a statement\non similarity. If multiple descriptors are used (e.g. a descriptor\nscheme), a rule has to be defined how to combine all distances to\na global value for each object. Still, distance measurement is the\nmost important first step in similarity measurement.\nObviously, the main task of good distance measures is to\nreorganise descriptor space in a way that media objects with the\nhighest similarity are nearest to the query object. If distance is\ndefined minimal, the query object is always in the origin of\ndistance space and similar candidates should form clusters around\nthe origin that are as large as possible. Consequently, many well\nknown distance measures are based on geometric assumptions of\ndescriptor space (e.g. Euclidean distance is based on the metric\naxioms). Unfortunately, these measures do not fit ideally with\nhuman similarity perception (e.g. due to human subjectivity). To\novercome this shortage, researchers from different areas have\ndeveloped alternative models that are mostly predicate-based\n(descriptors are assumed to contain just binary elements, e.g.\nTversky's Feature Contrast Model [17]) and fit better with human\nperception. In the following distance measures of both groups of\napproaches will be considered.\n3. DISTANCE MEASURES\nThe distance measures used in this work have been collected from\nvarious areas (Subsection 3.1). Because they work on differently\nquantised data, Subsection 3.2 sketches a model for unification on\nthe basis of quantitative descriptions. Finally, Subsection 3.3\nintroduces the distance measures as well as their origin and the\nidea they implement.\n3.1 Sources\nDistance measurement is used in many research areas such as\npsychology, sociology (e.g. comparing test results), medicine (e.g.\ncomparing parameters of test persons), economics (e.g. comparing\nbalance sheet ratios), etc. Naturally, the character of data available\nin these areas differs significantly. Essentially, there are two\nextreme cases of data vectors (and distance measures):\npredicatebased (all vector elements are binary, e.g. {0, 1}) and quantitative\n(all vector elements are continuous, e.g. [0, 1]).\nPredicates express the existence of properties and represent\nhighlevel information while quantitative values can be used to measure\nand mostly represent low-level information. Predicates are often\nemployed in psychology, sociology and other human-related\nsciences and most predicate-based distance measures were\ntherefore developed in these areas. Descriptions in visual\ninformation retrieval are nearly ever (if they do not integrate\nsemantic information) quantitative. Consequently, mostly\nquantitative distance measures are used in visual information\nretrieval.\nThe goal of this work is to compare the MPEG-7 distance\nmeasures with the most powerful distance measures developed in\nother areas. Since MPEG-7 descriptions are purely quantitative\nbut some of the most sophisticated distance measures are defined\nexclusively on predicates, a model is mandatory that allows the\napplication of predicate-based distance measures on quantitative\ndata. The model developed for this purpose is presented in the\nnext section.\n3.2 Quantisation model\nThe goal of the quantisation model is to redefine the set operators\nthat are usually used in predicate-based distance measures on\ncontinuous data. The first in visual information retrieval to follow\nthis approach were Santini and Jain, who tried to apply Tversky's\nFeature Contrast Model [17] to content-based image retrieval\n[12], [13]. They interpreted continuous data as fuzzy predicates\nand used fuzzy set operators. Unfortunately, their model suffered\nfrom several shortcomings they described in [12], [13] (for\nexample, the quantitative model worked only for one specific\nversion of the original predicate-based measure).\nThe main idea of the presented quantisation model is that set\noperators are replaced by statistical functions. In [5] the authors\ncould show that this interpretation of set operators is reasonable.\nThe model offers a solution for the descriptors considered in the\nevaluation. It is not specific to one distance measure, but can be\napplied to any predicate-based measure. Below, it will be shown\nthat the model does not only work for predicate data but for\nquantitative data as well. Each measure implementing the model\ncan be used as a substitute for the original predicate-based measure.\nGenerally, binary properties of two objects (e.g. media objects)\ncan exist in both objects (denoted as a), in just one (b, c) or in\nnone of them (d). The operator needed for these relationships are\nUNION, MINUS and NOT. In the quantisation model they are\nreplaced as follows (see [5] for further details).\n131\n\u2211\n\uf8f4\uf8f3\n\uf8f4\n\uf8f2\n\uf8f1\n\u2264\n+\n\u2212\n+\n==\u2229=\nk\njkikjkik\nkkji\nelse\nxx\nMif\nxx\nssXXa\n0\n22, 1\u03b5\n( )\n( )\n\u2211\n\u2211\n\u2211\n\uf8f4\uf8f3\n\uf8f4\n\uf8f2\n\uf8f1\n\u2264\n++\n\u2212==\u00ac\u2229\u00ac=\n\uf8f3\n\uf8f2\n\uf8f1 \u2264\u2212\u2212\u2212\n==\u2212=\n\uf8f3\n\uf8f2\n\uf8f1 \u2264\u2212\u2212\u2212\n==\u2212=\nk\njkikjkik\nkkji\nk\nikjkikjk\nkkij\nk\njkikjkik\nkkji\nelse\nxx\nif\nxx\nMssXXd\nelse\nxxMifxx\nssXXc\nelse\nxxMifxx\nssXXb\n0\n22,\n0\n,\n0\n,\n1\n2\n2\n\u03b5\n\u03b5\n\u03b5\nwith:\n( ) [ ]\n( )\n{ }0\\\n.\n0\n1\n.\n0\n1\n,\n2\n2\n1\nminmax\nmaxmin\n+\n\u2208\n\u2212\n=\n\uf8f4\uf8f3\n\uf8f4\n\uf8f2\n\uf8f1\n\u2265\uf8f7\n\uf8f8\n\uf8f6\n\uf8ec\n\uf8ed\n\uf8eb\n\u2212\n=\n=\n\uf8f4\uf8f3\n\uf8f4\n\uf8f2\n\uf8f1\n\u2265\uf8f7\n\uf8f8\n\uf8f6\n\uf8ec\n\uf8ed\n\uf8eb\n\u2212\n=\n\u2212=\n\u2208=\n\u2211 \u2211\n\u2211 \u2211\nRp\nki\nx\nwhere\nelse\npif\np\nM\nki\nx\nwhere\nelse\npif\np\nM\nxxM\nxxxwithxX\ni k\nik\ni k\nik\nikiki\n\u00b5\n\u03c3\n\u03c3\n\u03c3\n\u03b5\n\u00b5\n\u00b5\n\u00b5\n\u03b5\na selects properties that are present in both data vectors (Xi, Xj\nrepresenting media objects), b and c select properties that are\npresent in just one of them and d selects properties that are present\nin neither of the two data vectors. Every property is selected by\nthe extent to which it is present (a and d: mean, b and c:\ndifference) and only if the amount to which it is present exceeds a\ncertain threshold (depending on the mean and standard deviation\nover all elements of descriptor space).\nThe implementation of these operators is based on one assumption.\nIt is assumed that vector elements measure on interval scale. That\nmeans, each element expresses that the measured property is\n\"more or less\" present (\"0\": not at all, \"M\": fully present). This is\ntrue for most visual descriptors and all MPEG-7 descriptors. A\nnatural origin as it is assumed here (\"0\") is not needed.\nIntroducing p (called discriminance-defining parameter) for the\nthresholds 21 ,\u03b5\u03b5 has the positive consequence that a, b, c, d can\nthen be controlled through a single parameter. p is an additional\ncriterion for the behaviour of a distance measure and determines\nthe thresholds used in the operators. It expresses how accurate\ndata items are present (quantisation) and consequently, how\naccurate they should be investigated. p can be set by the user or\nautomatically. Interesting are the limits:\n1. Mp \u2192\u21d2\u221e\u2192 21 ,\u03b5\u03b5\nIn this case, all elements (=properties) are assumed to be\ncontinuous (high quantisation). In consequence, all properties of a\ndescriptor are used by the operators. Then, the distance measure is\nnot discriminant for properties.\n2. 0,0 21 \u2192\u21d2\u2192 \u03b5\u03b5p\nIn this case, all properties are assumed to be predicates. In\nconsequence, only binary elements (=predicates) are used by the\noperators (1-bit quantisation). The distance measure is then highly\ndiscriminant for properties.\nBetween these limits, a distance measure that uses the\nquantisation model is - depending on p - more or less\ndiscriminant for properties. This means, it selects a subset of all\navailable description vector elements for distance measurement.\nFor both predicate data and quantitative data it can be shown that\nthe quantisation model is reasonable. If description vectors consist\nof binary elements only, p should be used as follows (for example,\np can easily be set automatically):\n( )\u03c3\u00b5\u03b5\u03b5 ,min..,0,0 21 ==\u21d2\u2192 pgep\nIn this case, a, b, c, d measure like the set operators they replace.\nFor example, Table 1 shows their behaviour for two\nonedimensional feature vectors Xi and Xj. As can be seen, the\nstatistical measures work like set operators. Actually, the\nquantisation model works accurate on predicate data for any p\u2260\u221e.\nTo show that the model is reasonable for quantitative data the\nfollowing fact is used. It is easy to show that for predicate data\nsome quantitative distance measures degenerate to\npredicatebased measures. For example, the L1\nmetric (Manhattan metric)\ndegenerates to the Hamming distance (from [9], without weights):\ndistanceHammingcbxxL\nk\njkik =+\u2261\u2212= \u22111\nIf it can be shown that the quantisation model is able to\nreconstruct the quantitative measure from the degenerated\npredicate-based measure, the model is obviously able to extend\npredicate-based measures to the quantitative domain. This is easy\nto illustrate. For purely quantitative feature vectors, p should be\nused as follows (again, p can easily be set automatically):\n1, 21 =\u21d2\u221e\u2192 \u03b5\u03b5p\nThen, a and d become continuous functions:\n\u2211\n\u2211\n+\n\u2212==\u21d2\u2261\u2264\n+\n+\n==\u21d2\u2261\u2264\n+\n\u2212\nk\njkik\nkk\njkik\nk\njkik\nkk\njkik\nxx\nMswheresdtrueM\nxx\nxx\nswheresatrueM\nxx\nM\n22\n22\nb and c can be made continuous for the following expressions:\n( )\n( )\n\u2211\n\u2211\n\u2211\n\u2212==+\u21d2\n\uf8f3\n\uf8f2\n\uf8f1 \u2265\u2212\u2212\n==\u21d2\n\u2265\u2212\u2261\u2264\u2212\u2212\n\uf8f3\n\uf8f2\n\uf8f1 \u2265\u2212\u2212\n==\u21d2\n\u2265\u2212\u2261\u2264\u2212\u2212\nk\njkikkk\nk\nikjkikjk\nkk\nikjkikjk\nk\njkikjkik\nkk\njkikjkik\nxxswherescb\nelse\nxxifxx\nswheresc\nxxMxxM\nelse\nxxifxx\nswheresb\nxxMxxM\n0\n0\n0\n0\n0\n0\nTable 1. Quantisation model on predicate vectors.\nXi Xj a b c d\n(1) (1) 1 0 0 0\n(1) (0) 0 1 0 0\n(0) (1) 0 0 1 0\n(0) (0) 0 0 0 1\n132\n\u2211\n\u2211\n\u2212==\u2212\n\u2212==\u2212\nk\nikjkkk\nk\njkikkk\nxxswheresbc\nxxswherescb\nThis means, for sufficiently high p every predicate-based distance\nmeasure that is either not using b and c or just as b+c, b-c or c-b,\ncan be transformed into a continuous quantitative distance\nmeasure. For example, the Hamming distance (again, without\nweights):\n1\nLxxxxswherescb\nk\njkik\nk\njkikkk =\u2212=\u2212==+ \u2211\u2211\nThe quantisation model successfully reconstructs the L1\nmetric\nand no distance measure-specific modification has to be made to\nthe model. This demonstrates that the model is reasonable. In the\nfollowing it will be used to extend successful predicate-based\ndistance measures on the quantitative domain.\nThe major advantages of the quantisation model are: (1) it is\napplication domain independent, (2) the implementation is\nstraightforward, (3) the model is easy to use and finally, (4) the\nnew parameter p allows to control the similarity measurement\nprocess in a new way (discriminance on property level).\n3.3 Implemented measures\nFor the evaluation described in this work next to predicate-based\n(based on the quantisation model) and quantitative measures, the\ndistance measures recommended in the MPEG-7 standard were\nimplemented (all together 38 different distance measures).\nTable 2 summarises those predicate-based measures that\nperformed best in the evaluation (in sum 20 predicate-based\nmeasures were investigated). For these measures, K is the number\nof predicates in the data vectors Xi and Xj. In P1, the sum is used\nfor Tversky's f() (as Tversky himself does in [17]) and \u03b1, \u03b2 are\nweights for element b and c. In [5] the author's investigated\nTversky's Feature Contrast Model and found \u03b1=1, \u03b2=0 to be the\noptimum parameters.\nSome of the predicate-based measures are very simple (e.g. P2,\nP4) but have been heavily exploited in psychological research.\nPattern difference (P6) - a very powerful measure - is used in the\nstatistics package SPSS for cluster analysis. P7 is a correlation\ncoefficient for predicates developed by Pearson.\nTable 3 shows the best quantitative distance measures that were\nused. Q1 and Q2 are metric-based and were implemented as\nrepresentatives for the entire group of Minkowski distances. The\nwi are weights. In Q5, ii \u03c3\u00b5 , are mean and standard deviation\nfor the elements of descriptor Xi. In Q6, m is\n2\nM\n(=0.5). Q3, the\nCanberra metric, is a normalised form of Q1. Similarly, Q4,\nClark's divergence coefficient is a normalised version of Q2. Q6 is\na further-developed correlation coefficient that is invariant against\nsign changes. This measure is used even though its particular\nproperties are of minor importance for this application domain.\nFinally, Q8 is a measure that takes the differences between\nadjacent vector elements into account. This makes it structurally\ndifferent from all other measures.\nObviously, one important distance measure is missing. The\nMahalanobis distance was not considered, because different\ndescriptors would require different covariance matrices and for\nsome descriptors it is simply impossible to define a covariance\nmatrix. If the identity matrix was used in this case, the\nMahalanobis distance would degenerate to a Minkowski distance.\nAdditionally, the recommended MPEG-7 distances were\nimplemented with the following parameters: In the distance\nmeasure of the Color Layout descriptor all weights were set to \"1\"\n(as in all other implemented measures). In the distance measure of\nthe Dominant Color descriptor the following parameters were\nused: 20,1,3.0,7.0 21 ==== dTww \u03b1 (as recommended). In the\nHomogeneous Texture descriptor's distance all ( )k\u03b1 were set to\n\"1\" and matching was done rotation- and scale-invariant.\nImportant! Some of the measures presented in this section are\ndistance measures while others are similarity measures. For the\ntests, it is important to notice, that all similarity measures were\ninverted to distance measures.\n4. TEST SETUP\nSubsection 4.1 describes the descriptors (including parameters)\nand the collections (including ground truth information) that were\nused in the evaluation. Subsection 4.2 discusses the evaluation\nmethod that was implemented and Subsection 4.3 sketches the test\nenvironment used for the evaluation process.\n4.1 Test data\nFor the evaluation eight MPEG-7 descriptors were used. All\ncolour descriptors: Color Layout, Color Structure, Dominant\nColor, Scalable Color, all texture descriptors: Edge Histogram,\nHomogeneous Texture, Texture Browsing and one shape\ndescriptor: Region-based Shape. Texture Browsing was used even\nthough the MPEG-7 standard suggests that it is not suitable for\nretrieval. The other basic shape descriptor, Contour-based Shape,\nwas not used, because it produces structurally different\ndescriptions that cannot be transformed to data vectors with\nelements measuring on interval-scales. The motion descriptors\nwere not used, because they integrate the temporal dimension of\nvisual media and would only be comparable, if the basic colour,\ntexture and shape descriptors would be aggregated over time. This\nwas not done. Finally, no high-level descriptors were used\n(Localisation, Face Recognition, etc., see Subsection 2.1),\nbecause - to the author's opinion - the behaviour of the basic\ndescriptors on elementary media objects should be evaluated\nbefore conclusions on aggregated structures can be drawn.\nTable 2. Predicate-based distance measures.\nNo. Measure Comment\nP1 cba .. \u03b2\u03b1 \u2212\u2212 Feature Contrast Model,\nTversky 1977 [17]\nP2 a No. of co-occurrences\nP3 cb + Hamming distance\nP4\nK\na Russel 1940 [14]\nP5\ncb\na\n+\nKulczvnski 1927 [14]\nP6\n2\nK\nbc Pattern difference [14]\nP7\n( )( )( )( )dcdbcaba\nbcad\n++++\n\u2212 Pearson 1926 [11]\n133\nThe Texture Browsing descriptions had to be transformed from\nfive bins to an eight bin representation in order that all elements\nof the descriptor measure on an interval scale. A Manhattan metric\nwas used to measure proximity (see [6] for details).\nDescriptor extraction was performed using the MPEG-7 reference\nimplementation. In the extraction process each descriptor was\napplied on the entire content of each media object and the\nfollowing extraction parameters were used. Colour in Color\nStructure was quantised to 32 bins. For Dominant Color colour\nspace was set to YCrCb, 5-bit default quantisation was used and\nthe default value for spatial coherency was used. Homogeneous\nTexture was quantised to 32 components. Scalable Color values\nwere quantised to sizeof(int)-3 bits and 64 bins were used. Finally,\nTexture Browsing was used with five components.\nThese descriptors were applied on three media collections with\nimage content: the Brodatz dataset (112 images, 512x512 pixel), a\nsubset of the Corel dataset (260 images, 460x300 pixel, portrait\nand landscape) and a dataset with coats-of-arms images (426\nimages, 200x200 pixel). Figure 1 shows examples from the three\ncollections.\nDesigning appropriate test sets for a visual evaluation is a highly\ndifficult task (for example, see the TREC video 2002 report [15]).\nOf course, for identifying the best distance measure for a\ndescriptor, it should be tested on an infinite number of media\nobjects. But this is not the aim of this study. It is just evaluated if\n- for likely image collections - better proximity measures than\nthose suggested by the MPEG-7 group can be found. Collections\nof this relatively small size were used in the evaluation, because\nthe applied evaluation methods are above a certain minimum size\ninvariant against collection size and for smaller collections it is\neasier to define a high-quality ground truth. Still, the average ratio\nof ground truth size to collection size is at least 1:7. Especially, no\ncollection from the MPEG-7 dataset was used in the evaluation\nbecause the evaluations should show, how well the descriptors\nand the recommended distance measures perform on \"unknown\"\nmaterial.\nWhen the descriptor extraction was finished, the resulting XML\ndescriptions were transformed into a data matrix with 798 lines\n(media objects) and 314 columns (descriptor elements). To be\nusable with distance measures that do not integrate domain\nknowledge, the elements of this data matrix were normalised to\n[0, 1].\nFor the distance evaluation - next to the normalised data\nmatrixhuman similarity judgement is needed. In this work, the ground\ntruth is built of twelve groups of similar images (four for each\ndataset). Group membership was rated by humans based on\nsemantic criterions. Table 4 summarises the twelve groups and the\nunderlying descriptions. It has to be noticed, that some of these\ngroups (especially 5, 7 and 10) are much harder to find with\nlowlevel descriptors than others.\n4.2 Evaluation method\nUsually, retrieval evaluation is performed based on a ground truth\nwith recall and precision (see, for example, [3], [16]). In\nmultidescriptor environments this leads to a problem, because the\nresulting recall and precision values are strongly influenced by the\nmethod used to merge the distance values for one media object.\nEven though it is nearly impossible to say, how big the influence\nof a single distance measure was on the resulting recall and\nprecision values, this problem has been almost ignored so far.\nIn Subsection 2.2 it was stated that the major task of a distance\nmeasure is to bring the relevant media objects as close to the\norigin (where the query object lies) as possible. Even in a\nmultidescriptor environment it is then simple to identify the similar\nobjects in a large distance space. Consequently, it was decided to\nTable 3. Quantitative distance measures.\nNo. Measure Comment No. Measure Comment\nQ1\n\u2211 \u2212\nk\njkiki xxw\nCity block\ndistance (L1\n)\nQ2\n( )\u2211 \u2212\nk\njkiki xxw\n2\nEuclidean\ndistance (L2\n)\nQ3\n\u2211 +\n\u2212\nk jkik\njkik\nxx\nxx Canberra metric,\nLance, Williams\n1967 [8]\nQ4 ( )\n\u2211 +\n\u2212\nk jkik\njkik\nxx\nxx\nK\n2\n1\nDivergence\ncoefficient,\nClark 1952 [1]\nQ5 ( )( )\n( ) ( )\u2211 \u2211\n\u2211\n\u2212\u2212\n\u2212\u2212\nk k\njjkiik\nk\njjkiik\nxx\nxx\n22\n\u00b5\u00b5\n\u00b5\u00b5 Correlation\ncoefficient\nQ6\n\uf8f7\n\uf8f8\n\uf8f6\n\uf8ec\n\uf8ed\n\uf8eb\n\u2212+\uf8f7\n\uf8f8\n\uf8f6\n\uf8ec\n\uf8ed\n\uf8eb\n\u2212\u2212\n\uf8f7\n\uf8f8\n\uf8f6\n\uf8ec\n\uf8ed\n\uf8eb\n+\u2212\u2212\n\u2211\u2211\u2211\n\u2211 \u2211\u2211\nk\nik\nk\njkik\nk\nik\nk k\njk\nk\nikjkik\nxmKmxxmKmx\nxxmKmxx\n2..2 2222\nCohen 1969 [2]\nQ7\n\u2211 \u2211\n\u2211\nk k\njkik\nk\njkik\nxx\nxx\n22\nAngular distance,\nGower 1967 [7]\nQ8\n( ) ( )( )\u2211\n\u2212\n++ \u2212\u2212\u2212\n1\n2\n11\nK\nk\njkjkikik xxxx\nMeehl Index\n[10]\nTable 4. Ground truth information.\nColl. No Images Description\n1 19 Regular, chequered patterns\n2 38 Dark white noise\n3 33 Moon-like surfaces\nBrodatz\n4 35 Water-like surfaces\n5 73 Humans in nature (difficult)\n6 17 Images with snow (mountains, skiing)\n7 76 Animals in nature (difficult)\nCorel\n8 27 Large coloured flowers\n9 12 Bavarian communal arms\n10 10 All Bavarian arms (difficult)\n11 18 Dark objects / light unsegmented shield\nArms\n12 14 Major charges on blue or red shield\n134\nuse indicators measuring the distribution in distance space of\ncandidates similar to the query object for this evaluation instead\nof recall and precision. Identifying clusters of similar objects\n(based on the given ground truth) is relatively easy, because the\nresulting distance space for one descriptor and any distance\nmeasure is always one-dimensional. Clusters are found by\nsearching from the origin of distance space to the first similar\nobject, grouping all following similar objects in the cluster,\nbreaking off the cluster with the first un-similar object and so\nforth.\nFor the evaluation two indicators were defined. The first measures\nthe average distance of all cluster means to the origin:\ndistanceavgclustersno\nsizecluster\ndistanceclustersno\ni i\nsizecluster\nj\nij\nd\ni\n_._\n_\n_\n_\n\u2211\n\u2211\n=\u00b5\nwhere distanceij is the distance value of the j-th element in the i-th\ncluster,\n\u2211\n\u2211 \u2211\n= CLUSTERS\ni\ni\nCLUSTERS\ni\nsizecluster\nj\nij\nsizecluster\ndistance\ndistanceavg\ni\n_\n_\n_\n, no_clusters is the\nnumber of found clusters and cluster_sizei is the size of the i-th\ncluster. The resulting indicator is normalised by the distribution\ncharacteristics of the distance measure (avg_distance).\nAdditionally, the standard deviation is used. In the evaluation\nprocess this measure turned out to produce valuable results and to\nbe relatively robust against parameter p of the quantisation model.\nIn Subsection 3.2 we noted that p affects the discriminance of a\npredicate-based distance measure: The smaller p is set the larger\nare the resulting clusters because the quantisation model is then\nmore discriminant against properties and less elements of the data\nmatrix are used. This causes a side-effect that is measured by the\nsecond indicator: more and more un-similar objects come out with\nexactly the same distance value as similar objects (a problem that\ndoes not exist for large p's) and become indiscernible from similar\nobjects. Consequently, they are (false) cluster members. This\nphenomenon (conceptually similar to the \"false negatives\"\nindicator) was named \"cluster pollution\" and the indicator\nmeasures the average cluster pollution over all clusters:\nclustersno\ndoublesno\ncp\nclustersno\ni\nsizecluster\nj\nij\ni\n_\n_\n_ _\n\u2211 \u2211\n=\nwhere no_doublesij is the number of indiscernible un-similar\nobjects associated with the j-th element of cluster i.\nRemark: Even though there is a certain influence, it could be\nproven in [5] that no significant correlation exists between\nparameter p of the quantisation model and cluster pollution.\n4.3 Test environment\nAs pointed out above, to generate the descriptors, the MPEG-7\nreference implementation in version 5.6 was used (provided by\nTU Munich). Image processing was done with Adobe Photoshop\nand normalisation and all evaluations were done with Perl. The\nquerying process was performed in the following steps: (1)\nrandom selection of a ground truth group, (2) random selection of\na query object from this group, (3) distance comparison for all\nother objects in the dataset, (4) clustering of the resulting distance\nspace based on the ground truth and finally, (5) evaluation.\nFor each combination of dataset and distance measure 250 queries\nwere issued and evaluations were aggregated over all datasets and\ndescriptors. The next section shows the - partially\nsurprisingresults.\n5. RESULTS\nIn the results presented below the first indicator from Subsection\n4.2 was used to evaluate distance measures. In a first step\nparameter p had to be set in a way that all measures are equally\ndiscriminant. Distance measurement is fair if the following\ncondition holds true for any predicate-based measure dP and any\ncontinuous measure dC:\n( ) ( )CP dcppdcp \u2248,\nThen, it is guaranteed that predicate-based measures do not create\nlarger clusters (with a higher number of similar objects) for the\nprice of higher cluster pollution. In more than 1000 test queries\nthe optimum value was found to be p=1.\nResults are organised as follows: Subsection 5.1 summarises the\nFigure 1. Test datasets. Left: Brodatz dataset, middle: Corel dataset, right: coats-of-arms dataset.\n135\nbest distance measures per descriptor, Section 5.2 shows the best\noverall distance measures and Section 5.3 points out other\ninteresting results (for example, distance measures that work\nparticularly good on specific ground truth groups).\n5.1 Best measure per descriptor\nFigure 2 shows the evaluation results for the first indicator. For\neach descriptor the best measure and the performance of the\nMPEG-7 recommendation are shown. The results are aggregated\nover the tested datasets.\nOn first sight, it becomes clear that the MPEG-7\nrecommendations are mostly relatively good but never the best.\nFor Color Layout the difference between MP7 and the best\nmeasure, the Meehl index (Q8), is just 4% and the MPEG-7\nmeasure has a smaller standard deviation. The reason why the\nMeehl index is better may be that this descriptors generates\ndescriptions with elements that have very similar variance.\nStatistical analysis confirmed that (see [6]).\nFor Color Structure, Edge Histogram, Homogeneous Texture,\nRegion-based Shape and Scalable Color by far the best measure is\npattern difference (P6). Psychological research on human visual\nperception has revealed that in many situation differences between\nthe query object and a candidate weigh much stronger than\ncommon properties. The pattern difference measure implements\nthis insight in the most consequent way. In the author's opinion,\nthe reason why pattern difference performs so extremely well on\nmany descriptors is due to this fact. Additional advantages of\npattern difference are that it usually has a very low variance\nandbecause it is a predicate-based measure - its discriminance (and\ncluster structure) can be tuned with parameter p.\nThe best measure for Dominant Color turned out to be Clark's\nDivergence coefficient (Q4). This is a similar measure to pattern\ndifference on the continuous domain. The Texture Browsing\ndescriptor is a special problem. In the MPEG-7 standard it is\nrecommended to use it exclusively for browsing. After testing it\nfor retrieval on various distance measures the author supports this\nopinion. It is very difficult to find a good distance measure for\nTexture Browsing. The proposed Manhattan metric, for example,\nperforms very bad. The best measure is predicate-based (P7). It\nworks on common properties (a, d) but produces clusters with\nvery high cluster pollution. For this descriptor the second\nindicator is up to eight times higher than for predicate-based\nmeasures on other descriptors.\n5.2 Best overall measures\nFigure 3 summarises the results over all descriptors and media\ncollections. The diagram should give an indication on the general\npotential of the investigated distance measures for visual\ninformation retrieval.\nIt can be seen that the best overall measure is a predicate-based\none. The top performance of pattern difference (P6) proves that\nthe quantisation model is a reasonable method to extend\npredicate-based distance measures on the continuous domain. The\nsecond best group of measures are the MPEG-7\nrecommendations, which have a slightly higher mean but a lower\nstandard deviation than pattern difference. The third best measure\nis the Meehl index (Q8), a measure developed for psychological\napplications but because of its characteristic properties\ntailormade for certain (homogeneous) descriptors.\nMinkowski metrics are also among the best measures: the average\nmean and variance of the Manhattan metric (Q1) and the\nEuclidean metric (Q2) are in the range of Q8. Of course, these\nmeasures do not perform particularly well for any of the\ndescriptors. Remarkably for a predicate-based measure, Tversky's\nFeature Contrast Model (P1) is also in the group of very good\nmeasures (even though it is not among the best) that ends with\nQ5, the correlation coefficient. The other measures either have a\nsignificantly higher mean or a very large standard deviation.\n5.3 Other interesting results\nDistance measures that perform in average worse than others may\nin certain situations (e.g. on specific content) still perform better.\nFor Color Layout, for example, Q7 is a very good measure on\ncolour photos. It performs as good as Q8 and has a lower standard\ndeviation. For artificial images the pattern difference and the\nHamming distance produce comparable results as well.\nIf colour information is available in media objects, pattern\ndifference performs well on Dominant Color (just 20% worse Q4)\nand in case of difficult ground truth (group 5, 7, 10) the Meehl\nindex is as strong as P6.\n0,000\n0,001\n0,002\n0,003\n0,004\n0,005\n0,006\n0,007\n0,008\nQ8\nMP7\nP6\nMP7\nQ4\nMP7\nP6\nMP7\nP6\nMP7\nP6\nMP7\nP6\nMP7\nP7\nQ2\nColor\nLayout\nColor\nStructure\nDominant\nColor\nEdge\nHistogram\nHomog.\nTexture\nRegion\nShape\nScalable\nColor\nTexture\nBrowsing\nFigure 2. Results per measure and descriptor. The horizontal axis shows the best measure and the performance of the MPEG-7\nrecommendation for each descriptor. The vertical axis shows the values for the first indicator (smaller value = better cluster structure).\nShades have the following meaning: black=\u00b5-\u03c3 (good cases), black + dark grey=\u00b5 (average) and black + dark grey + light grey=\u00b5+\u03c3 (bad).\n136\n6. CONCLUSION\nThe evaluation presented in this paper aims at testing the\nrecommended distance measures and finding better ones for the\nbasic visual MPEG-7 descriptors. Eight descriptors were selected,\n38 distance measures were implemented, media collections were\ncreated and assessed, performance indicators were defined and\nmore than 22500 tests were performed. To be able to use\npredicate-based distance measures next to quantitative measures a\nquantisation model was defined that allows the application of\npredicate-based measures on continuous data.\nIn the evaluation the best overall distance measures for visual\ncontent - as extracted by the visual MPEG-7 descriptors - turned\nout to be the pattern difference measure and the Meehl index (for\nhomogeneous descriptions). Since these two measures perform\nsignificantly better than the MPEG-7 recommendations they\nshould be further tested on large collections of image and video\ncontent (e.g. from [15]).\nThe choice of the right distance function for similarity\nmeasurement depends on the descriptor, the queried media\ncollection and the semantic level of the user's idea of similarity.\nThis work offers suitable distance measures for various situations.\nIn consequence, the distance measures identified as the best will\nbe implemented in the open MPEG-7 based visual information\nretrieval framework VizIR [4].\nACKNOWLEDGEMENTS\nThe author would like to thank Christian Breiteneder for his\nvaluable comments and suggestions for improvement. The work\npresented in this paper is part of the VizIR project funded by the\nAustrian Scientific Research Fund FWF under grant no. P16111.\nREFERENCES\n[1] Clark, P.S. An extension of the coefficient of divergence for\nuse with multiple characters. Copeia, 2 (1952), 61-64.\n[2] Cohen, J. A profile similarity coefficient invariant over\nvariable reflection. Psychological Bulletin, 71 (1969),\n281284.\n[3] Del Bimbo, A. Visual information retrieval. Morgan\nKaufmann Publishers, San Francisco CA, 1999.\n[4] Eidenberger, H., and Breiteneder, C. A framework for visual\ninformation retrieval. In Proceedings Visual Information\nSystems Conference (HSinChu Taiwan, March 2002), LNCS\n2314, Springer Verlag, 105-116.\n[5] Eidenberger, H., and Breiteneder, C. Visual similarity\nmeasurement with the Feature Contrast Model. In\nProceedings SPIE Storage and Retrieval for Media Databases\nConference (Santa Clara CA, January 2003), SPIE Vol.\n5021, 64-76.\n[6] Eidenberger, H., How good are the visual MPEG-7 features?\nIn Proceedings SPIE Visual Communications and Image\nProcessing Conference (Lugano Switzerland, July 2003),\nSPIE Vol. 5150, 476-488.\n[7] Gower, J.G. Multivariate analysis and multidimensional\ngeometry. The Statistician, 17 (1967),13-25.\n[8] Lance, G.N., and Williams, W.T. Mixed data classificatory\nprograms. Agglomerative Systems Australian Comp. Journal,\n9 (1967), 373-380.\n[9] Manjunath, B.S., Ohm, J.R., Vasudevan, V.V., and Yamada,\nA. Color and texture descriptors. In Special Issue on\nMPEG7. IEEE Transactions on Circuits and Systems for Video\nTechnology, 11/6 (June 2001), 703-715.\n[10] Meehl, P. E. The problem is epistemology, not statistics:\nReplace significance tests by confidence intervals and\nquantify accuracy of risky numerical predictions. In Harlow,\nL.L., Mulaik, S.A., and Steiger, J.H. (Eds.). What if there\nwere no significance tests? Erlbaum, Mahwah NJ, 393-425.\n[11] Pearson, K. On the coefficients of racial likeness. Biometrica,\n18 (1926), 105-117.\n[12] Santini, S., and Jain, R. Similarity is a geometer. Multimedia\nTools and Application, 5/3 (1997), 277-306.\n[13] Santini, S., and Jain, R. Similarity measures. IEEE\nTransactions on Pattern Analysis and Machine Intelligence,\n21/9 (September 1999), 871-883.\n[14] Sint, P.P. Similarity structures and similarity measures.\nAustrian Academy of Sciences Press, Vienna Austria, 1975\n(in German).\n[15] Smeaton, A.F., and Over, P. The TREC-2002 video track\nreport. NIST Special Publication SP 500-251 (March 2003),\navailable from: http://trec.nist.gov/pubs/trec11/papers/\nVIDEO.OVER.pdf (last visited: 2003-07-29)\n[16] Smeulders, A.W.M., Worring, M., Santini, S., Gupta, A., and\nJain, R. Content-based image retrieval at the end of the early\nyears. IEEE Transactions on Pattern Analysis and Machine\nIntelligence, 22/12 (December 2000), 1349-1380.\n[17] Tversky, A. Features of similarity. Psychological Review,\n84/4 (July 1977), 327-351.\n0,000\n0,002\n0,004\n0,006\n0,008\n0,010\n0,012\n0,014\n0,016\n0,018\n0,020\nP6\nMP7\nQ8\nQ1\nQ4\nQ2\nP2\nP4\nQ6\nQ3\nQ7\nP1\nQ5\nP3\nP5\nP7\nFigure 3. Overall results (ordered by the first indicator). The vertical axis shows the values for the first indicator (smaller value = better\ncluster structure). Shades have the following meaning: black=\u00b5-\u03c3, black + dark grey=\u00b5 and black + dark grey + light grey=\u00b5+\u03c3.\n137", "keywords": "similarity measurement;performance indicator;visual media;content-base video retrieval;media collection;distance measurement;distance measure;mpeg-7;visual descriptor;mpeg-7-based retrieval;meehl index;visual information retrieval;similarity perception;human similarity perception;content-base image retrieval;predicate-based model"}
{"name": "train_H-82", "title": "Downloading Textual Hidden Web Content Through Keyword Queries", "abstract": "An ever-increasing amount of information on the Web today is available only through search interfaces: the users have to type in a set of keywords in a search form in order to access the pages from certain Web sites. These pages are often referred to as the Hidden Web or the Deep Web. Since there are no static links to the Hidden Web pages, search engines cannot discover and index such pages and thus do not return them in the results. However, according to recent studies, the content provided by many Hidden Web sites is often of very high quality and can be extremely valuable to many users. In this paper, we study how we can build an effective Hidden Web crawler that can autonomously discover and download pages from the Hidden Web. Since the only entry point to a Hidden Web site is a query interface, the main challenge that a Hidden Web crawler has to face is how to automatically generate meaningful queries to issue to the site. Here, we provide a theoretical framework to investigate the query generation problem for the Hidden Web and we propose effective policies for generating queries automatically. Our policies proceed iteratively, issuing a different query in every iteration. We experimentally evaluate the effectiveness of these policies on 4 real Hidden Web sites and our results are very promising. For instance, in one experiment, one of our policies downloaded more than 90% of a Hidden Web site (that contains 14 million documents) after issuing fewer than 100 queries.", "fulltext": "1. INTRODUCTION\nRecent studies show that a significant fraction of Web content\ncannot be reached by following links [7, 12]. In particular, a large\npart of the Web is hidden behind search forms and is reachable\nonly when users type in a set of keywords, or queries, to the forms.\nThese pages are often referred to as the Hidden Web [17] or the\nDeep Web [7], because search engines typically cannot index the\npages and do not return them in their results (thus, the pages are\nessentially hidden from a typical Web user).\nAccording to many studies, the size of the Hidden Web increases\nrapidly as more organizations put their valuable content online\nthrough an easy-to-use Web interface [7]. In [12], Chang et al.\nestimate that well over 100,000 Hidden-Web sites currently exist\non the Web. Moreover, the content provided by many Hidden-Web\nsites is often of very high quality and can be extremely valuable\nto many users [7]. For example, PubMed hosts many high-quality\npapers on medical research that were selected from careful\npeerreview processes, while the site of the US Patent and Trademarks\nOffice1\nmakes existing patent documents available, helping\npotential inventors examine prior art.\nIn this paper, we study how we can build a Hidden-Web crawler2\nthat can automatically download pages from the Hidden Web, so\nthat search engines can index them. Conventional crawlers rely\non the hyperlinks on the Web to discover pages, so current search\nengines cannot index the Hidden-Web pages (due to the lack of\nlinks). We believe that an effective Hidden-Web crawler can have\na tremendous impact on how users search information on the Web:\n\u2022 Tapping into unexplored information: The Hidden-Web\ncrawler will allow an average Web user to easily explore the\nvast amount of information that is mostly hidden at present.\nSince a majority of Web users rely on search engines to discover\npages, when pages are not indexed by search engines, they are\nunlikely to be viewed by many Web users. Unless users go\ndirectly to Hidden-Web sites and issue queries there, they cannot\naccess the pages at the sites.\n\u2022 Improving user experience: Even if a user is aware of a\nnumber of Hidden-Web sites, the user still has to waste a significant\namount of time and effort, visiting all of the potentially relevant\nsites, querying each of them and exploring the result. By making\nthe Hidden-Web pages searchable at a central location, we can\nsignificantly reduce the user\"s wasted time and effort in\nsearching the Hidden Web.\n\u2022 Reducing potential bias: Due to the heavy reliance of many Web\nusers on search engines for locating information, search engines\ninfluence how the users perceive the Web [28]. Users do not\nnecessarily perceive what actually exists on the Web, but what\nis indexed by search engines [28]. According to a recent\narticle [5], several organizations have recognized the importance of\nbringing information of their Hidden Web sites onto the surface,\nand committed considerable resources towards this effort. Our\n1\nUS Patent Office: http://www.uspto.gov\n2\nCrawlers are the programs that traverse the Web automatically and\ndownload pages for search engines.\n100\nFigure 1: A single-attribute search interface\nHidden-Web crawler attempts to automate this process for\nHidden Web sites with textual content, thus minimizing the\nassociated costs and effort required.\nGiven that the only entry to Hidden Web pages is through\nquerying a search form, there are two core challenges to\nimplementing an effective Hidden Web crawler: (a) The crawler has to\nbe able to understand and model a query interface, and (b) The\ncrawler has to come up with meaningful queries to issue to the\nquery interface. The first challenge was addressed by Raghavan\nand Garcia-Molina in [29], where a method for learning search\ninterfaces was presented. Here, we present a solution to the second\nchallenge, i.e. how a crawler can automatically generate queries so\nthat it can discover and download the Hidden Web pages.\nClearly, when the search forms list all possible values for a query\n(e.g., through a drop-down list), the solution is straightforward. We\nexhaustively issue all possible queries, one query at a time. When\nthe query forms have a free text input, however, an infinite\nnumber of queries are possible, so we cannot exhaustively issue all\npossible queries. In this case, what queries should we pick? Can the\ncrawler automatically come up with meaningful queries without\nunderstanding the semantics of the search form?\nIn this paper, we provide a theoretical framework to investigate\nthe Hidden-Web crawling problem and propose effective ways of\ngenerating queries automatically. We also evaluate our proposed\nsolutions through experiments conducted on real Hidden-Web sites.\nIn summary, this paper makes the following contributions:\n\u2022 We present a formal framework to study the problem of\nHiddenWeb crawling. (Section 2).\n\u2022 We investigate a number of crawling policies for the Hidden\nWeb, including the optimal policy that can potentially download\nthe maximum number of pages through the minimum number of\ninteractions. Unfortunately, we show that the optimal policy is\nNP-hard and cannot be implemented in practice (Section 2.2).\n\u2022 We propose a new adaptive policy that approximates the optimal\npolicy. Our adaptive policy examines the pages returned from\nprevious queries and adapts its query-selection policy\nautomatically based on them (Section 3).\n\u2022 We evaluate various crawling policies through experiments on\nreal Web sites. Our experiments will show the relative\nadvantages of various crawling policies and demonstrate their\npotential. The results from our experiments are very promising. In\none experiment, for example, our adaptive policy downloaded\nmore than 90% of the pages within PubMed (that contains 14\nmillion documents) after it issued fewer than 100 queries.\n2. FRAMEWORK\nIn this section, we present a formal framework for the study of\nthe Hidden-Web crawling problem. In Section 2.1, we describe our\nassumptions on Hidden-Web sites and explain how users interact\nwith the sites. Based on this interaction model, we present a\nhighlevel algorithm for a Hidden-Web crawler in Section 2.2. Finally in\nSection 2.3, we formalize the Hidden-Web crawling problem.\n2.1 Hidden-Web database model\nThere exists a variety of Hidden Web sources that provide\ninformation on a multitude of topics. Depending on the type of\ninformation, we may categorize a Hidden-Web site either as a textual\ndatabase or a structured database. A textual database is a site that\nFigure 2: A multi-attribute search interface\nmainly contains plain-text documents, such as PubMed and\nLexisNexis (an online database of legal documents [1]). Since\nplaintext documents do not usually have well-defined structure, most\ntextual databases provide a simple search interface where users\ntype a list of keywords in a single search box (Figure 1). In\ncontrast, a structured database often contains multi-attribute relational\ndata (e.g., a book on the Amazon Web site may have the fields\ntitle=\u2018Harry Potter\", author=\u2018J.K. Rowling\" and\nisbn=\u20180590353403\") and supports multi-attribute search\ninterfaces (Figure 2). In this paper, we will mainly focus on\ntextual databases that support single-attribute keyword queries. We\ndiscuss how we can extend our ideas for the textual databases to\nmulti-attribute structured databases in Section 6.1.\nTypically, the users need to take the following steps in order to\naccess pages in a Hidden-Web database:\n1. Step 1. First, the user issues a query, say liver, through the\nsearch interface provided by the Web site (such as the one shown\nin Figure 1).\n2. Step 2. Shortly after the user issues the query, she is presented\nwith a result index page. That is, the Web site returns a list of\nlinks to potentially relevant Web pages, as shown in Figure 3(a).\n3. Step 3. From the list in the result index page, the user identifies\nthe pages that look interesting and follows the links. Clicking\non a link leads the user to the actual Web page, such as the one\nshown in Figure 3(b), that the user wants to look at.\n2.2 A generic Hidden Web crawling algorithm\nGiven that the only entry to the pages in a Hidden-Web site\nis its search from, a Hidden-Web crawler should follow the three\nsteps described in the previous section. That is, the crawler has\nto generate a query, issue it to the Web site, download the result\nindex page, and follow the links to download the actual pages. In\nmost cases, a crawler has limited time and network resources, so\nthe crawler repeats these steps until it uses up its resources.\nIn Figure 4 we show the generic algorithm for a Hidden-Web\ncrawler. For simplicity, we assume that the Hidden-Web crawler\nissues single-term queries only.3\nThe crawler first decides which\nquery term it is going to use (Step (2)), issues the query, and\nretrieves the result index page (Step (3)). Finally, based on the links\nfound on the result index page, it downloads the Hidden Web pages\nfrom the site (Step (4)). This same process is repeated until all the\navailable resources are used up (Step (1)).\nGiven this algorithm, we can see that the most critical decision\nthat a crawler has to make is what query to issue next. If the\ncrawler can issue successful queries that will return many matching\npages, the crawler can finish its crawling early on using minimum\nresources. In contrast, if the crawler issues completely irrelevant\nqueries that do not return any matching pages, it may waste all\nof its resources simply issuing queries without ever retrieving\nactual pages. Therefore, how the crawler selects the next query can\ngreatly affect its effectiveness. In the next section, we formalize\nthis query selection problem.\n3\nFor most Web sites that assume AND for multi-keyword\nqueries, single-term queries return the maximum number of results.\nExtending our work to multi-keyword queries is straightforward.\n101\n(a) List of matching pages for query liver. (b) The first matching page for liver.\nFigure 3: Pages from the PubMed Web site.\nALGORITHM 2.1. Crawling a Hidden Web site\nProcedure\n(1) while ( there are available resources ) do\n// select a term to send to the site\n(2) qi = SelectTerm()\n// send query and acquire result index page\n(3) R(qi) = QueryWebSite( qi )\n// download the pages of interest\n(4) Download( R(qi) )\n(5) done\nFigure 4: Algorithm for crawling a Hidden Web site.\nS\nq1\nq\nqq\n2\n34\nFigure 5: A set-formalization of the optimal query selection\nproblem.\n2.3 Problem formalization\nTheoretically, the problem of query selection can be formalized\nas follows: We assume that the crawler downloads pages from a\nWeb site that has a set of pages S (the rectangle in Figure 5). We\nrepresent each Web page in S as a point (dots in Figure 5). Every\npotential query qi that we may issue can be viewed as a subset of S,\ncontaining all the points (pages) that are returned when we issue qi\nto the site. Each subset is associated with a weight that represents\nthe cost of issuing the query. Under this formalization, our goal is to\nfind which subsets (queries) cover the maximum number of points\n(Web pages) with the minimum total weight (cost). This problem\nis equivalent to the set-covering problem in graph theory [16].\nThere are two main difficulties that we need to address in this\nformalization. First, in a practical situation, the crawler does not\nknow which Web pages will be returned by which queries, so the\nsubsets of S are not known in advance. Without knowing these\nsubsets the crawler cannot decide which queries to pick to\nmaximize the coverage. Second, the set-covering problem is known to\nbe NP-Hard [16], so an efficient algorithm to solve this problem\noptimally in polynomial time has yet to be found.\nIn this paper, we will present an approximation algorithm that\ncan find a near-optimal solution at a reasonable computational cost.\nOur algorithm leverages the observation that although we do not\nknow which pages will be returned by each query qi that we issue,\nwe can predict how many pages will be returned. Based on this\ninformation our query selection algorithm can then select the best\nqueries that cover the content of the Web site. We present our\nprediction method and our query selection algorithm in Section 3.\n2.3.1 Performance Metric\nBefore we present our ideas for the query selection problem, we\nbriefly discuss some of our notation and the cost/performance\nmetrics.\nGiven a query qi, we use P(qi) to denote the fraction of pages\nthat we will get back if we issue query qi to the site. For example, if\na Web site has 10,000 pages in total, and if 3,000 pages are returned\nfor the query qi = medicine, then P(qi) = 0.3. We use P(q1 \u2227\nq2) to represent the fraction of pages that are returned from both\nq1 and q2 (i.e., the intersection of P(q1) and P(q2)). Similarly, we\nuse P(q1 \u2228 q2) to represent the fraction of pages that are returned\nfrom either q1 or q2 (i.e., the union of P(q1) and P(q2)).\nWe also use Cost(qi) to represent the cost of issuing the query\nqi. Depending on the scenario, the cost can be measured either in\ntime, network bandwidth, the number of interactions with the site,\nor it can be a function of all of these. As we will see later, our\nproposed algorithms are independent of the exact cost function.\nIn the most common case, the query cost consists of a number\nof factors, including the cost for submitting the query to the site,\nretrieving the result index page (Figure 3(a)) and downloading the\nactual pages (Figure 3(b)). We assume that submitting a query\nincurs a fixed cost of cq. The cost for downloading the result index\npage is proportional to the number of matching documents to the\nquery, while the cost cd for downloading a matching document is\nalso fixed. Then the overall cost of query qi is\nCost(qi) = cq + crP(qi) + cdP(qi). (1)\nIn certain cases, some of the documents from qi may have already\nbeen downloaded from previous queries. In this case, the crawler\nmay skip downloading these documents and the cost of qi can be\nCost(qi) = cq + crP(qi) + cdPnew(qi). (2)\nHere, we use Pnew(qi) to represent the fraction of the new\ndocuments from qi that have not been retrieved from previous queries.\nLater in Section 3.1 we will study how we can estimate P(qi) and\nPnew(qi) to estimate the cost of qi.\nSince our algorithms are independent of the exact cost function,\nwe will assume a generic cost function Cost(qi) in this paper. When\nwe need a concrete cost function, however, we will use Equation 2.\nGiven the notation, we can formalize the goal of a Hidden-Web\ncrawler as follows:\n102\nPROBLEM 1. Find the set of queries q1, . . . , qn that maximizes\nP(q1 \u2228 \u00b7 \u00b7 \u00b7 \u2228 qn)\nunder the constraint\nn\ni=1\nCost(qi) \u2264 t.\nHere, t is the maximum download resource that the crawler has.\n3. KEYWORD SELECTION\nHow should a crawler select the queries to issue? Given that the\ngoal is to download the maximum number of unique documents\nfrom a textual database, we may consider one of the following\noptions:\n\u2022 Random: We select random keywords from, say, an English\ndictionary and issue them to the database. The hope is that a random\nquery will return a reasonable number of matching documents.\n\u2022 Generic-frequency: We analyze a generic document corpus\ncollected elsewhere (say, from the Web) and obtain the generic\nfrequency distribution of each keyword. Based on this generic\ndistribution, we start with the most frequent keyword, issue it to the\nHidden-Web database and retrieve the result. We then continue\nto the second-most frequent keyword and repeat this process\nuntil we exhaust all download resources. The hope is that the\nfrequent keywords in a generic corpus will also be frequent in the\nHidden-Web database, returning many matching documents.\n\u2022 Adaptive: We analyze the documents returned from the previous\nqueries issued to the Hidden-Web database and estimate which\nkeyword is most likely to return the most documents. Based on\nthis analysis, we issue the most promising query, and repeat\nthe process.\nAmong these three general policies, we may consider the\nrandom policy as the base comparison point since it is expected to\nperform the worst. Between the generic-frequency and the\nadaptive policies, both policies may show similar performance if the\ncrawled database has a generic document collection without a\nspecialized topic. The adaptive policy, however, may perform\nsignificantly better than the generic-frequency policy if the database has a\nvery specialized collection that is different from the generic corpus.\nWe will experimentally compare these three policies in Section 4.\nWhile the first two policies (random and generic-frequency\npolicies) are easy to implement, we need to understand how we can\nanalyze the downloaded pages to identify the most promising query\nin order to implement the adaptive policy. We address this issue in\nthe rest of this section.\n3.1 Estimating the number of matching pages\nIn order to identify the most promising query, we need to\nestimate how many new documents we will download if we issue the\nquery qi as the next query. That is, assuming that we have issued\nqueries q1, . . . , qi\u22121 we need to estimate P(q1\u2228\u00b7 \u00b7 \u00b7\u2228qi\u22121\u2228qi), for\nevery potential next query qi and compare this value. In estimating\nthis number, we note that we can rewrite P(q1 \u2228 \u00b7 \u00b7 \u00b7 \u2228 qi\u22121 \u2228 qi)\nas:\nP((q1 \u2228 \u00b7 \u00b7 \u00b7 \u2228 qi\u22121) \u2228 qi)\n= P(q1 \u2228 \u00b7 \u00b7 \u00b7 \u2228 qi\u22121) + P(qi) \u2212 P((q1 \u2228 \u00b7 \u00b7 \u00b7 \u2228 qi\u22121) \u2227 qi)\n= P(q1 \u2228 \u00b7 \u00b7 \u00b7 \u2228 qi\u22121) + P(qi)\n\u2212 P(q1 \u2228 \u00b7 \u00b7 \u00b7 \u2228 qi\u22121)P(qi|q1 \u2228 \u00b7 \u00b7 \u00b7 \u2228 qi\u22121) (3)\nIn the above formula, note that we can precisely measure P(q1 \u2228\n\u00b7 \u00b7 \u00b7 \u2228 qi\u22121) and P(qi | q1 \u2228 \u00b7 \u00b7 \u00b7 \u2228 qi\u22121) by analyzing\npreviouslydownloaded pages: We know P(q1 \u2228 \u00b7 \u00b7 \u00b7 \u2228 qi\u22121), the union of\nall pages downloaded from q1, . . . , qi\u22121, since we have already\nissued q1, . . . , qi\u22121 and downloaded the matching pages.4\nWe can\nalso measure P(qi | q1 \u2228 \u00b7 \u00b7 \u00b7 \u2228 qi\u22121), the probability that qi\nappears in the pages from q1, . . . , qi\u22121, by counting how many times\nqi appears in the pages from q1, . . . , qi\u22121. Therefore, we only need\nto estimate P(qi) to evaluate P(q1 \u2228 \u00b7 \u00b7 \u00b7 \u2228 qi). We may consider a\nnumber of different ways to estimate P(qi), including the\nfollowing:\n1. Independence estimator: We assume that the appearance of the\nterm qi is independent of the terms q1, . . . , qi\u22121. That is, we\nassume that P(qi) = P(qi|q1 \u2228 \u00b7 \u00b7 \u00b7 \u2228 qi\u22121).\n2. Zipf estimator: In [19], Ipeirotis et al. proposed a method to\nestimate how many times a particular term occurs in the entire\ncorpus based on a subset of documents from the corpus. Their\nmethod exploits the fact that the frequency of terms inside text\ncollections follows a power law distribution [30, 25]. That is,\nif we rank all terms based on their occurrence frequency (with\nthe most frequent term having a rank of 1, second most frequent\na rank of 2 etc.), then the frequency f of a term inside the text\ncollection is given by:\nf = \u03b1(r + \u03b2)\u2212\u03b3\n(4)\nwhere r is the rank of the term and \u03b1, \u03b2, and \u03b3 are constants that\ndepend on the text collection.\nTheir main idea is (1) to estimate the three parameters, \u03b1, \u03b2 and\n\u03b3, based on the subset of documents that we have downloaded\nfrom previous queries, and (2) use the estimated parameters to\npredict f given the ranking r of a term within the subset. For\na more detailed description on how we can use this method to\nestimate P(qi), we refer the reader to the extended version of\nthis paper [27].\nAfter we estimate P(qi) and P(qi|q1 \u2228 \u00b7 \u00b7 \u00b7 \u2228 qi\u22121) values, we\ncan calculate P(q1 \u2228 \u00b7 \u00b7 \u00b7 \u2228 qi). In Section 3.3, we explain how\nwe can efficiently compute P(qi|q1 \u2228 \u00b7 \u00b7 \u00b7 \u2228 qi\u22121) by maintaining a\nsuccinct summary table. In the next section, we first examine how\nwe can use this value to decide which query we should issue next\nto the Hidden Web site.\n3.2 Query selection algorithm\nThe goal of the Hidden-Web crawler is to download the\nmaximum number of unique documents from a database using its\nlimited download resources. Given this goal, the Hidden-Web crawler\nhas to take two factors into account. (1) the number of new\ndocuments that can be obtained from the query qi and (2) the cost of\nissuing the query qi. For example, if two queries, qi and qj, incur\nthe same cost, but qi returns more new pages than qj, qi is more\ndesirable than qj. Similarly, if qi and qj return the same number\nof new documents, but qi incurs less cost then qj, qi is more\ndesirable. Based on this observation, the Hidden-Web crawler may\nuse the following efficiency metric to quantify the desirability of\nthe query qi:\nEfficiency(qi) =\nPnew(qi)\nCost(qi)\nHere, Pnew(qi) represents the amount of new documents returned\nfor qi (the pages that have not been returned for previous queries).\nCost(qi) represents the cost of issuing the query qi.\nIntuitively, the efficiency of qi measures how many new\ndocuments are retrieved per unit cost, and can be used as an indicator of\n4\nFor exact estimation, we need to know the total number of pages in\nthe site. However, in order to compare only relative values among\nqueries, this information is not actually needed.\n103\nALGORITHM 3.1. Greedy SelectTerm()\nParameters:\nT: The list of potential query keywords\nProcedure\n(1) Foreach tk in T do\n(2) Estimate Efficiency(tk) = Pnew(tk)\nCost(tk)\n(3) done\n(4) return tk with maximum Efficiency(tk)\nFigure 6: Algorithm for selecting the next query term.\nhow well our resources are spent when issuing qi. Thus, the\nHidden Web crawler can estimate the efficiency of every candidate qi,\nand select the one with the highest value. By using its resources\nmore efficiently, the crawler may eventually download the\nmaximum number of unique documents. In Figure 6, we show the query\nselection function that uses the concept of efficiency. In principle,\nthis algorithm takes a greedy approach and tries to maximize the\npotential gain in every step.\nWe can estimate the efficiency of every query using the\nestimation method described in Section 3.1. That is, the size of the new\ndocuments from the query qi, Pnew(qi), is\nPnew(qi)\n= P(q1 \u2228 \u00b7 \u00b7 \u00b7 \u2228 qi\u22121 \u2228 qi) \u2212 P(q1 \u2228 \u00b7 \u00b7 \u00b7 \u2228 qi\u22121)\n= P(qi) \u2212 P(q1 \u2228 \u00b7 \u00b7 \u00b7 \u2228 qi\u22121)P(qi|q1 \u2228 \u00b7 \u00b7 \u00b7 \u2228 qi\u22121)\nfrom Equation 3, where P(qi) can be estimated using one of the\nmethods described in section 3. We can also estimate Cost(qi)\nsimilarly. For example, if Cost(qi) is\nCost(qi) = cq + crP(qi) + cdPnew(qi)\n(Equation 2), we can estimate Cost(qi) by estimating P(qi) and\nPnew(qi).\n3.3 Efficient calculation of query statistics\nIn estimating the efficiency of queries, we found that we need to\nmeasure P(qi|q1\u2228\u00b7 \u00b7 \u00b7\u2228qi\u22121) for every potential query qi. This\ncalculation can be very time-consuming if we repeat it from scratch for\nevery query qi in every iteration of our algorithm. In this section,\nwe explain how we can compute P(qi|q1 \u2228 \u00b7 \u00b7 \u00b7 \u2228 qi\u22121) efficiently\nby maintaining a small table that we call a query statistics table.\nThe main idea for the query statistics table is that P(qi|q1 \u2228\u00b7 \u00b7 \u00b7\u2228\nqi\u22121) can be measured by counting how many times the keyword\nqi appears within the documents downloaded from q1, . . . , qi\u22121.\nWe record these counts in a table, as shown in Figure 7(a). The\nleft column of the table contains all potential query terms and the\nright column contains the number of previously-downloaded\ndocuments containing the respective term. For example, the table in\nFigure 7(a) shows that we have downloaded 50 documents so far, and\nthe term model appears in 10 of these documents. Given this\nnumber, we can compute that P(model|q1 \u2228 \u00b7 \u00b7 \u00b7 \u2228 qi\u22121) = 10\n50\n= 0.2.\nWe note that the query statistics table needs to be updated\nwhenever we issue a new query qi and download more documents. This\nupdate can be done efficiently as we illustrate in the following\nexample.\nEXAMPLE 1. After examining the query statistics table of\nFigure 7(a), we have decided to use the term computer as our next\nquery qi. From the new query qi = computer, we downloaded\n20 more new pages. Out of these, 12 contain the keyword model\nTerm tk N(tk)\nmodel 10\ncomputer 38\ndigital 50\nTerm tk N(tk)\nmodel 12\ncomputer 20\ndisk 18\nTotal pages: 50 New pages: 20\n(a) After q1, . . . , qi\u22121 (b) New from qi = computer\nTerm tk N(tk)\nmodel 10+12 = 22\ncomputer 38+20 = 58\ndisk 0+18 = 18\ndigital 50+0 = 50\nTotal pages: 50 + 20 = 70\n(c) After q1, . . . , qi\nFigure 7: Updating the query statistics table.\nq\ni1 i\u22121\nq\\/ ... \\/q\nq\ni\n/\nS\nFigure 8: A Web site that does not return all the results.\nand 18 the keyword disk. The table in Figure 7(b) shows the\nfrequency of each term in the newly-downloaded pages.\nWe can update the old table (Figure 7(a)) to include this new\ninformation by simply adding corresponding entries in Figures 7(a)\nand (b). The result is shown on Figure 7(c). For example, keyword\nmodel exists in 10 + 12 = 22 pages within the pages retrieved\nfrom q1, . . . , qi. According to this new table, P(model|q1\u2228\u00b7 \u00b7 \u00b7\u2228qi)\nis now 22\n70\n= 0.3.\n3.4 Crawling sites that limit the number of\nresults\nIn certain cases, when a query matches a large number of pages,\nthe Hidden Web site returns only a portion of those pages. For\nexample, the Open Directory Project [2] allows the users to see only\nup to 10, 000 results after they issue a query. Obviously, this kind\nof limitation has an immediate effect on our Hidden Web crawler.\nFirst, since we can only retrieve up to a specific number of pages\nper query, our crawler will need to issue more queries (and\npotentially will use up more resources) in order to download all the\npages. Second, the query selection method that we presented in\nSection 3.2 assumes that for every potential query qi, we can find\nP(qi|q1 \u2228 \u00b7 \u00b7 \u00b7 \u2228 qi\u22121). That is, for every query qi we can find the\nfraction of documents in the whole text database that contains qi\nwith at least one of q1, . . . , qi\u22121. However, if the text database\nreturned only a portion of the results for any of the q1, . . . , qi\u22121 then\nthe value P(qi|q1 \u2228 \u00b7 \u00b7 \u00b7 \u2228 qi\u22121) is not accurate and may affect our\ndecision for the next query qi, and potentially the performance of\nour crawler. Since we cannot retrieve more results per query than\nthe maximum number the Web site allows, our crawler has no other\nchoice besides submitting more queries. However, there is a way\nto estimate the correct value for P(qi|q1 \u2228 \u00b7 \u00b7 \u00b7 \u2228 qi\u22121) in the case\nwhere the Web site returns only a portion of the results.\n104\nAgain, assume that the Hidden Web site we are currently\ncrawling is represented as the rectangle on Figure 8 and its pages as\npoints in the figure. Assume that we have already issued queries\nq1, . . . , qi\u22121 which returned a number of results less than the\nmaximum number than the site allows, and therefore we have\ndownloaded all the pages for these queries (big circle in Figure 8). That\nis, at this point, our estimation for P(qi|q1 \u2228\u00b7 \u00b7 \u00b7\u2228qi\u22121) is accurate.\nNow assume that we submit query qi to the Web site, but due to a\nlimitation in the number of results that we get back, we retrieve the\nset qi (small circle in Figure 8) instead of the set qi (dashed circle\nin Figure 8). Now we need to update our query statistics table so\nthat it has accurate information for the next step. That is, although\nwe got the set qi back, for every potential query qi+1 we need to\nfind P(qi+1|q1 \u2228 \u00b7 \u00b7 \u00b7 \u2228 qi):\nP(qi+1|q1 \u2228 \u00b7 \u00b7 \u00b7 \u2228 qi)\n=\n1\nP(q1 \u2228 \u00b7 \u00b7 \u00b7 \u2228 qi)\n\u00b7 [P(qi+1 \u2227 (q1 \u2228 \u00b7 \u00b7 \u00b7 \u2228 qi\u22121))+\nP(qi+1 \u2227 qi) \u2212 P(qi+1 \u2227 qi \u2227 (q1 \u2228 \u00b7 \u00b7 \u00b7 \u2228 qi\u22121))] (5)\nIn the previous equation, we can find P(q1 \u2228\u00b7 \u00b7 \u00b7\u2228qi) by\nestimating P(qi) with the method shown in Section 3. Additionally, we\ncan calculate P(qi+1 \u2227 (q1 \u2228 \u00b7 \u00b7 \u00b7 \u2228 qi\u22121)) and P(qi+1 \u2227 qi \u2227 (q1 \u2228\n\u00b7 \u00b7 \u00b7 \u2228 qi\u22121)) by directly examining the documents that we have\ndownloaded from queries q1, . . . , qi\u22121. The term P(qi+1 \u2227 qi)\nhowever is unknown and we need to estimate it. Assuming that qi\nis a random sample of qi, then:\nP(qi+1 \u2227 qi)\nP(qi+1 \u2227 qi)\n=\nP(qi)\nP(qi)\n(6)\nFrom Equation 6 we can calculate P(qi+1 \u2227 qi) and after we\nreplace this value to Equation 5 we can find P(qi+1|q1 \u2228 \u00b7 \u00b7 \u00b7 \u2228 qi).\n4. EXPERIMENTAL EVALUATION\nIn this section we experimentally evaluate the performance of\nthe various algorithms for Hidden Web crawling presented in this\npaper. Our goal is to validate our theoretical analysis through\nrealworld experiments, by crawling popular Hidden Web sites of\ntextual databases. Since the number of documents that are discovered\nand downloaded from a textual database depends on the selection\nof the words that will be issued as queries5\nto the search interface\nof each site, we compare the various selection policies that were\ndescribed in section 3, namely the random, generic-frequency, and\nadaptive algorithms.\nThe adaptive algorithm learns new keywords and terms from the\ndocuments that it downloads, and its selection process is driven by\na cost model as described in Section 3.2. To keep our experiment\nand its analysis simple at this point, we will assume that the cost for\nevery query is constant. That is, our goal is to maximize the number\nof downloaded pages by issuing the least number of queries. Later,\nin Section 4.4 we will present a comparison of our policies based\non a more elaborate cost model. In addition, we use the\nindependence estimator (Section 3.1) to estimate P(qi) from downloaded\npages. Although the independence estimator is a simple estimator,\nour experiments will show that it can work very well in practice.6\nFor the generic-frequency policy, we compute the frequency\ndistribution of words that appear in a 5.5-million-Web-page corpus\n5\nThroughout our experiments, once an algorithm has submitted a\nquery to a database, we exclude the query from subsequent\nsubmissions to the same database from the same algorithm.\n6\nWe defer the reporting of results based on the Zipf estimation to a\nfuture work.\ndownloaded from 154 Web sites of various topics [26]. Keywords\nare selected based on their decreasing frequency with which they\nappear in this document set, with the most frequent one being\nselected first, followed by the second-most frequent keyword, etc.7\nRegarding the random policy, we use the same set of words\ncollected from the Web corpus, but in this case, instead of selecting\nkeywords based on their relative frequency, we choose them\nrandomly (uniform distribution). In order to further investigate how\nthe quality of the potential query-term list affects the random-based\nalgorithm, we construct two sets: one with the 16, 000 most\nfrequent words of the term collection used in the generic-frequency\npolicy (hereafter, the random policy with the set of 16,000 words\nwill be referred to as random-16K), and another set with the 1\nmillion most frequent words of the same collection as above (hereafter,\nreferred to as random-1M). The former set has frequent words that\nappear in a large number of documents (at least 10, 000 in our\ncollection), and therefore can be considered of high-quality terms.\nThe latter set though contains a much larger collection of words,\namong which some might be bogus, and meaningless.\nThe experiments were conducted by employing each one of the\naforementioned algorithms (adaptive, generic-frequency,\nrandom16K, and random-1M) to crawl and download contents from three\nHidden Web sites: The PubMed Medical Library,8\nAmazon,9\nand\nthe Open Directory Project[2]. According to the information on\nPubMed\"s Web site, its collection contains approximately 14\nmillion abstracts of biomedical articles. We consider these abstracts\nas the documents in the site, and in each iteration of the adaptive\npolicy, we use these abstracts as input to the algorithm. Thus our\ngoal is to discover as many unique abstracts as possible by\nrepeatedly querying the Web query interface provided by PubMed. The\nHidden Web crawling on the PubMed Web site can be considered\nas topic-specific, due to the fact that all abstracts within PubMed\nare related to the fields of medicine and biology.\nIn the case of the Amazon Web site, we are interested in\ndownloading all the hidden pages that contain information on books.\nThe querying to Amazon is performed through the Software\nDeveloper\"s Kit that Amazon provides for interfacing to its Web site,\nand which returns results in XML form. The generic keyword\nfield is used for searching, and as input to the adaptive policy we\nextract the product description and the text of customer reviews\nwhen present in the XML reply. Since Amazon does not provide\nany information on how many books it has in its catalogue, we use\nrandom sampling on the 10-digit ISBN number of the books to\nestimate the size of the collection. Out of the 10, 000 random ISBN\nnumbers queried, 46 are found in the Amazon catalogue, therefore\nthe size of its book collection is estimated to be 46\n10000\n\u00b7 1010\n= 4.6\nmillion books. It\"s also worth noting here that Amazon poses an\nupper limit on the number of results (books in our case) returned\nby each query, which is set to 32, 000.\nAs for the third Hidden Web site, the Open Directory Project\n(hereafter also referred to as dmoz), the site maintains the links to\n3.8 million sites together with a brief summary of each listed site.\nThe links are searchable through a keyword-search interface. We\nconsider each indexed link together with its brief summary as the\ndocument of the dmoz site, and we provide the short summaries\nto the adaptive algorithm to drive the selection of new keywords\nfor querying. On the dmoz Web site, we perform two Hidden Web\ncrawls: the first is on its generic collection of 3.8-million indexed\n7\nWe did not manually exclude stop words (e.g., the, is, of, etc.)\nfrom the keyword list. As it turns out, all Web sites except PubMed\nreturn matching documents for the stop words, such as the.\n8\nPubMed Medical Library: http://www.pubmed.org\n9\nAmazon Inc.: http://www.amazon.com\n105\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n0 50 100 150 200\nfractionofdocuments\nquery number\nCumulative fraction of unique documents - PubMed website\nadaptive\ngeneric-frequency\nrandom-16K\nrandom-1M\nFigure 9: Coverage of policies for Pubmed\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n0 100 200 300 400 500 600 700\nfractionofdocuments\nquery number\nCumulative fraction of unique documents - Amazon website\nadaptive\ngeneric-frequency\nrandom-16K\nrandom-1M\nFigure 10: Coverage of policies for Amazon\nsites, regardless of the category that they fall into. The other crawl\nis performed specifically on the Arts section of dmoz (http://\ndmoz.org/Arts), which comprises of approximately 429, 000\nindexed sites that are relevant to Arts, making this crawl\ntopicspecific, as in PubMed. Like Amazon, dmoz also enforces an upper\nlimit on the number of returned results, which is 10, 000 links with\ntheir summaries.\n4.1 Comparison of policies\nThe first question that we seek to answer is the evolution of the\ncoverage metric as we submit queries to the sites. That is, what\nfraction of the collection of documents stored in the Hidden Web\nsite can we download as we continuously query for new words\nselected using the policies described above? More formally, we are\ninterested in the value of P(q1 \u2228 \u00b7 \u00b7 \u00b7 \u2228 qi\u22121 \u2228 qi), after we submit\nq1, . . . , qi queries, and as i increases.\nIn Figures 9, 10, 11, and 12 we present the coverage metric for\neach policy, as a function of the query number, for the Web sites\nof PubMed, Amazon, general dmoz and the art-specific dmoz,\nrespectively. On the y-axis the fraction of the total documents\ndownloaded from the website is plotted, while the x-axis represents the\nquery number. A first observation from these graphs is that in\ngeneral, the generic-frequency and the adaptive policies perform much\nbetter than the random-based algorithms. In all of the figures, the\ngraphs for the random-1M and the random-16K are significantly\nbelow those of other policies.\nBetween the generic-frequency and the adaptive policies, we can\nsee that the latter outperforms the former when the site is topic\nspe0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n0 100 200 300 400 500 600 700\nfractionofdocuments\nquery number\nCumulative fraction of unique documents - dmoz website\nadaptive\ngeneric-frequency\nrandom-16K\nrandom-1M\nFigure 11: Coverage of policies for general dmoz\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n0 50 100 150 200 250 300 350 400 450\nfractionofdocuments\nquery number\nCumulative fraction of unique documents - dmoz/Arts website\nadaptive\ngeneric-frequency\nrandom-16K\nrandom-1M\nFigure 12: Coverage of policies for the Arts section of dmoz\ncific. For example, for the PubMed site (Figure 9), the adaptive\nalgorithm issues only 83 queries to download almost 80% of the\ndocuments stored in PubMed, but the generic-frequency algorithm\nrequires 106 queries for the same coverage,. For the dmoz/Arts\ncrawl (Figure 12), the difference is even more substantial: the\nadaptive policy is able to download 99.98% of the total sites indexed in\nthe Directory by issuing 471 queries, while the frequency-based\nalgorithm is much less effective using the same number of queries,\nand discovers only 72% of the total number of indexed sites. The\nadaptive algorithm, by examining the contents of the pages that it\ndownloads at each iteration, is able to identify the topic of the site as\nexpressed by the words that appear most frequently in the result-set.\nConsequently, it is able to select words for subsequent queries that\nare more relevant to the site, than those preferred by the\ngenericfrequency policy, which are drawn from a large, generic collection.\nTable 1 shows a sample of 10 keywords out of 211 chosen and\nsubmitted to the PubMed Web site by the adaptive algorithm, but not\nby the other policies. For each keyword, we present the number of\nthe iteration, along with the number of results that it returned. As\none can see from the table, these keywords are highly relevant to\nthe topics of medicine and biology of the Public Medical Library,\nand match against numerous articles stored in its Web site.\nIn both cases examined in Figures 9, and 12, the random-based\npolicies perform much worse than the adaptive algorithm, and the\ngeneric-frequency. It is worthy noting however, that the\nrandombased policy with the small, carefully selected set of 16, 000\nquality words manages to download a considerable fraction of 42.5%\n106\nIteration Keyword Number of Results\n23 department 2, 719, 031\n34 patients 1, 934, 428\n53 clinical 1, 198, 322\n67 treatment 4, 034, 565\n69 medical 1, 368, 200\n70 hospital 503, 307\n146 disease 1, 520, 908\n172 protein 2, 620, 938\nTable 1: Sample of keywords queried to PubMed exclusively by\nthe adaptive policy\nfrom the PubMed Web site after 200 queries, while the coverage\nfor the Arts section of dmoz reaches 22.7%, after 471 queried\nkeywords. On the other hand, the random-based approach that makes\nuse of the vast collection of 1 million words, among which a large\nnumber is bogus keywords, fails to download even a mere 1% of the\ntotal collection, after submitting the same number of query words.\nFor the generic collections of Amazon and the dmoz sites, shown\nin Figures 10 and 11 respectively, we get mixed results: The\ngenericfrequency policy shows slightly better performance than the\nadaptive policy for the Amazon site (Figure 10), and the adaptive method\nclearly outperforms the generic-frequency for the general dmoz site\n(Figure 11). A closer look at the log files of the two Hidden Web\ncrawlers reveals the main reason: Amazon was functioning in a\nvery flaky way when the adaptive crawler visited it, resulting in\na large number of lost results. Thus, we suspect that the slightly\npoor performance of the adaptive policy is due to this\nexperimental variance. We are currently running another experiment to\nverify whether this is indeed the case. Aside from this experimental\nvariance, the Amazon result indicates that if the collection and the\nwords that a Hidden Web site contains are generic enough, then the\ngeneric-frequency approach may be a good candidate algorithm for\neffective crawling.\nAs in the case of topic-specific Hidden Web sites, the\nrandombased policies also exhibit poor performance compared to the other\ntwo algorithms when crawling generic sites: for the Amazon Web\nsite, random-16K succeeds in downloading almost 36.7% after\nissuing 775 queries, alas for the generic collection of dmoz, the\nfraction of the collection of links downloaded is 13.5% after the 770th\nquery. Finally, as expected, random-1M is even worse than\nrandom16K, downloading only 14.5% of Amazon and 0.3% of the generic\ndmoz.\nIn summary, the adaptive algorithm performs remarkably well in\nall cases: it is able to discover and download most of the documents\nstored in Hidden Web sites by issuing the least number of queries.\nWhen the collection refers to a specific topic, it is able to identify\nthe keywords most relevant to the topic of the site and consequently\nask for terms that is most likely that will return a large number of\nresults . On the other hand, the generic-frequency policy proves to\nbe quite effective too, though less than the adaptive: it is able to\nretrieve relatively fast a large portion of the collection, and when the\nsite is not topic-specific, its effectiveness can reach that of\nadaptive (e.g. Amazon). Finally, the random policy performs poorly in\ngeneral, and should not be preferred.\n4.2 Impact of the initial query\nAn interesting issue that deserves further examination is whether\nthe initial choice of the keyword used as the first query issued by\nthe adaptive algorithm affects its effectiveness in subsequent\niterations. The choice of this keyword is not done by the selection of the\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n0 10 20 30 40 50 60\nfractionofdocuments\nquery number\nConvergence of adaptive under different initial queries - PubMed website\npubmed\ndata\ninformation\nreturn\nFigure 13: Convergence of the adaptive algorithm using\ndifferent initial queries for crawling the PubMed Web site\nadaptive algorithm itself and has to be manually set, since its query\nstatistics tables have not been populated yet. Thus, the selection is\ngenerally arbitrary, so for purposes of fully automating the whole\nprocess, some additional investigation seems necessary.\nFor this reason, we initiated three adaptive Hidden Web crawlers\ntargeting the PubMed Web site with different seed-words: the word\ndata, which returns 1,344,999 results, the word information\nthat reports 308, 474 documents, and the word return that\nretrieves 29, 707 pages, out of 14 million. These keywords\nrepresent varying degrees of term popularity in PubMed, with the first\none being of high popularity, the second of medium, and the third\nof low. We also show results for the keyword pubmed, used in\nthe experiments for coverage of Section 4.1, and which returns 695\narticles. As we can see from Figure 13, after a small number of\nqueries, all four crawlers roughly download the same fraction of\nthe collection, regardless of their starting point: Their coverages\nare roughly equivalent from the 25th query. Eventually, all four\ncrawlers use the same set of terms for their queries, regardless of\nthe initial query. In the specific experiment, from the 36th query\nonward, all four crawlers use the same terms for their queries in each\niteration, or the same terms are used off by one or two query\nnumbers. Our result confirms the observation of [11] that the choice of\nthe initial query has minimal effect on the final performance. We\ncan explain this intuitively as follows: Our algorithm approximates\nthe optimal set of queries to use for a particular Web site. Once\nthe algorithm has issued a significant number of queries, it has an\naccurate estimation of the content of the Web site, regardless of\nthe initial query. Since this estimation is similar for all runs of the\nalgorithm, the crawlers will use roughly the same queries.\n4.3 Impact of the limit in the number of results\nWhile the Amazon and dmoz sites have the respective limit of\n32,000 and 10,000 in their result sizes, these limits may be larger\nthan those imposed by other Hidden Web sites. In order to\ninvestigate how a tighter limit in the result size affects the\nperformance of our algorithms, we performed two additional crawls to\nthe generic-dmoz site: we ran the generic-frequency and adaptive\npolicies but we retrieved only up to the top 1,000 results for\nevery query. In Figure 14 we plot the coverage for the two policies\nas a function of the number of queries. As one might expect, by\ncomparing the new result in Figure 14 to that of Figure 11 where\nthe result limit was 10,000, we conclude that the tighter limit\nrequires a higher number of queries to achieve the same coverage.\nFor example, when the result limit was 10,000, the adaptive\npol107\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n0 500 1000 1500 2000 2500 3000 3500\nFractionofUniquePages\nQuery Number\nCumulative fraction of unique pages downloaded per query - Dmoz Web site (cap limit 1000)\nadaptive\ngeneric-frequency\nFigure 14: Coverage of general dmoz after limiting the number\nof results to 1,000\nicy could download 70% of the site after issuing 630 queries, while\nit had to issue 2,600 queries to download 70% of the site when\nthe limit was 1,000. On the other hand, our new result shows that\neven with a tight result limit, it is still possible to download most\nof a Hidden Web site after issuing a reasonable number of queries.\nThe adaptive policy could download more than 85% of the site\nafter issuing 3,500 queries when the limit was 1,000. Finally, our\nresult shows that our adaptive policy consistently outperforms the\ngeneric-frequency policy regardless of the result limit. In both\nFigure 14 and Figure 11, our adaptive policy shows significantly larger\ncoverage than the generic-frequency policy for the same number of\nqueries.\n4.4 Incorporating the document download\ncost\nFor brevity of presentation, the performance evaluation results\nprovided so far assumed a simplified cost-model where every query\ninvolved a constant cost. In this section we present results regarding\nthe performance of the adaptive and generic-frequency algorithms\nusing Equation 2 to drive our query selection process. As we\ndiscussed in Section 2.3.1, this query cost model includes the cost for\nsubmitting the query to the site, retrieving the result index page,\nand also downloading the actual pages. For these costs, we\nexamined the size of every result in the index page and the sizes of the\ndocuments, and we chose cq = 100, cr = 100, and cd = 10000,\nas values for the parameters of Equation 2, and for the particular\nexperiment that we ran on the PubMed website. The values that\nwe selected imply that the cost for issuing one query and retrieving\none result from the result index page are roughly the same, while\nthe cost for downloading an actual page is 100 times larger. We\nbelieve that these values are reasonable for the PubMed Web site.\nFigure 15 shows the coverage of the adaptive and\ngenericfrequency algorithms as a function of the resource units used\nduring the download process. The horizontal axis is the amount of\nresources used, and the vertical axis is the coverage. As it is\nevident from the graph, the adaptive policy makes more efficient use of\nthe available resources, as it is able to download more articles than\nthe generic-frequency, using the same amount of resource units.\nHowever, the difference in coverage is less dramatic in this case,\ncompared to the graph of Figure 9. The smaller difference is due\nto the fact that under the current cost metric, the download cost of\ndocuments constitutes a significant portion of the cost. Therefore,\nwhen both policies downloaded the same number of documents,\nthe saving of the adaptive policy is not as dramatic as before. That\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n0 5000 10000 15000 20000 25000 30000\nFractionofUniquePages\nTotal Cost (cq=100, cr=100, cd=10000)\nCumulative fraction of unique pages downloaded per cost unit - PubMed Web site\nadaptive\nfrequency\nFigure 15: Coverage of PubMed after incorporating the\ndocument download cost\nis, the savings in the query cost and the result index download cost\nis only a relatively small portion of the overall cost. Still, we\nobserve noticeable savings from the adaptive policy. At the total cost\nof 8000, for example, the coverage of the adaptive policy is roughly\n0.5 while the coverage of the frequency policy is only 0.3.\n5. RELATED WORK\nIn a recent study, Raghavan and Garcia-Molina [29] present an\narchitectural model for a Hidden Web crawler. The main focus of\nthis work is to learn Hidden-Web query interfaces, not to\ngenerate queries automatically. The potential queries are either provided\nmanually by users or collected from the query interfaces. In\ncontrast, our main focus is to generate queries automatically without\nany human intervention.\nThe idea of automatically issuing queries to a database and\nexamining the results has been previously used in different contexts.\nFor example, in [10, 11], Callan and Connel try to acquire an\naccurate language model by collecting a uniform random sample from\nthe database. In [22] Lawrence and Giles issue random queries to\na number of Web Search Engines in order to estimate the fraction\nof the Web that has been indexed by each of them. In a similar\nfashion, Bharat and Broder [8] issue random queries to a set of\nSearch Engines in order to estimate the relative size and overlap of\ntheir indexes. In [6], Barbosa and Freire experimentally evaluate\nmethods for building multi-keyword queries that can return a large\nfraction of a document collection. Our work differs from the\nprevious studies in two ways. First, it provides a theoretical framework\nfor analyzing the process of generating queries for a database and\nexamining the results, which can help us better understand the\neffectiveness of the methods presented in the previous work. Second,\nwe apply our framework to the problem of Hidden Web crawling\nand demonstrate the efficiency of our algorithms.\nCope et al. [15] propose a method to automatically detect whether\na particular Web page contains a search form. This work is\ncomplementary to ours; once we detect search interfaces on the Web\nusing the method in [15], we may use our proposed algorithms to\ndownload pages automatically from those Web sites.\nReference [4] reports methods to estimate what fraction of a\ntext database can be eventually acquired by issuing queries to the\ndatabase. In [3] the authors study query-based techniques that can\nextract relational data from large text databases. Again, these works\nstudy orthogonal issues and are complementary to our work.\nIn order to make documents in multiple textual databases\nsearchable at a central place, a number of harvesting approaches have\n108\nbeen proposed (e.g., OAI [21], DP9 [24]). These approaches\nessentially assume cooperative document databases that willingly share\nsome of their metadata and/or documents to help a third-party search\nengine to index the documents. Our approach assumes\nuncooperative databases that do not share their data publicly and whose\ndocuments are accessible only through search interfaces.\nThere exists a large body of work studying how to identify the\nmost relevant database given a user query [20, 19, 14, 23, 18]. This\nbody of work is often referred to as meta-searching or database\nselection problem over the Hidden Web. For example, [19]\nsuggests the use of focused probing to classify databases into a topical\ncategory, so that given a query, a relevant database can be selected\nbased on its topical category. Our vision is different from this body\nof work in that we intend to download and index the Hidden pages\nat a central location in advance, so that users can access all the\ninformation at their convenience from one single location.\n6. CONCLUSION AND FUTURE WORK\nTraditional crawlers normally follow links on the Web to\ndiscover and download pages. Therefore they cannot get to the Hidden\nWeb pages which are only accessible through query interfaces. In\nthis paper, we studied how we can build a Hidden Web crawler that\ncan automatically query a Hidden Web site and download pages\nfrom it. We proposed three different query generation policies for\nthe Hidden Web: a policy that picks queries at random from a list\nof keywords, a policy that picks queries based on their frequency\nin a generic text collection, and a policy which adaptively picks a\ngood query based on the content of the pages downloaded from the\nHidden Web site. Experimental evaluation on 4 real Hidden Web\nsites shows that our policies have a great potential. In particular, in\ncertain cases the adaptive policy can download more than 90% of\na Hidden Web site after issuing approximately 100 queries. Given\nthese results, we believe that our work provides a potential\nmechanism to improve the search-engine coverage of the Web and the\nuser experience of Web search.\n6.1 Future Work\nWe briefly discuss some future-research avenues.\nMulti-attribute Databases We are currently investigating how\nto extend our ideas to structured multi-attribute databases. While\ngenerating queries for multi-attribute databases is clearly a more\ndifficult problem, we may exploit the following observation to\naddress this problem: When a site supports multi-attribute queries,\nthe site often returns pages that contain values for each of the query\nattributes. For example, when an online bookstore supports queries\non title, author and isbn, the pages returned from a query\ntypically contain the title, author and ISBN of corresponding books.\nThus, if we can analyze the returned pages and extract the values\nfor each field (e.g, title = \u2018Harry Potter\", author =\n\u2018J.K. Rowling\", etc), we can apply the same idea that we\nused for the textual database: estimate the frequency of each\nattribute value and pick the most promising one. The main challenge\nis to automatically segment the returned pages so that we can\nidentify the sections of the pages that present the values corresponding\nto each attribute. Since many Web sites follow limited formatting\nstyles in presenting multiple attributes - for example, most book\ntitles are preceded by the label Title: - we believe we may learn\npage-segmentation rules automatically from a small set of training\nexamples.\nOther Practical Issues In addition to the automatic query\ngeneration problem, there are many practical issues to be addressed\nto build a fully automatic Hidden-Web crawler. For example, in\nthis paper we assumed that the crawler already knows all query\ninterfaces for Hidden-Web sites. But how can the crawler discover\nthe query interfaces? The method proposed in [15] may be a good\nstarting point. In addition, some Hidden-Web sites return their\nresults in batches of, say, 20 pages, so the user has to click on a\nnext button in order to see more results. In this case, a fully\nautomatic Hidden-Web crawler should know that the first result index\npage contains only a partial result and press the next button\nautomatically. Finally, some Hidden Web sites may contain an infinite\nnumber of Hidden Web pages which do not contribute much\nsignificant content (e.g. a calendar with links for every day). In this\ncase the Hidden-Web crawler should be able to detect that the site\ndoes not have much more new content and stop downloading pages\nfrom the site. Page similarity detection algorithms may be useful\nfor this purpose [9, 13].\n7. REFERENCES\n[1] Lexisnexis http://www.lexisnexis.com.\n[2] The Open Directory Project, http://www.dmoz.org.\n[3] E. Agichtein and L. Gravano. Querying text databases for efficient information\nextraction. In ICDE, 2003.\n[4] E. Agichtein, P. Ipeirotis, and L. Gravano. Modeling query-based access to text\ndatabases. In WebDB, 2003.\n[5] Article on New York Times. Old Search Engine, the Library, Tries to Fit Into a\nGoogle World. Available at: http:\n//www.nytimes.com/2004/06/21/technology/21LIBR.html,\nJune 2004.\n[6] L. Barbosa and J. Freire. Siphoning hidden-web data through keyword-based\ninterfaces. In SBBD, 2004.\n[7] M. K. Bergman. The deep web: Surfacing hidden value,http:\n//www.press.umich.edu/jep/07-01/bergman.html.\n[8] K. Bharat and A. Broder. A technique for measuring the relative size and\noverlap of public web search engines. In WWW, 1998.\n[9] A. Z. Broder, S. C. Glassman, M. S. Manasse, and G. Zweig. Syntactic\nclustering of the web. In WWW, 1997.\n[10] J. Callan, M. Connell, and A. Du. Automatic discovery of language models for\ntext databases. In SIGMOD, 1999.\n[11] J. P. Callan and M. E. Connell. Query-based sampling of text databases.\nInformation Systems, 19(2):97-130, 2001.\n[12] K. C.-C. Chang, B. He, C. Li, and Z. Zhang. Structured databases on the web:\nObservations and implications. Technical report, UIUC.\n[13] J. Cho, N. Shivakumar, and H. Garcia-Molina. Finding replicated web\ncollections. In SIGMOD, 2000.\n[14] W. Cohen and Y. Singer. Learning to query the web. In AAAI Workshop on\nInternet-Based Information Systems, 1996.\n[15] J. Cope, N. Craswell, and D. Hawking. Automated discovery of search\ninterfaces on the web. In 14th Australasian conference on Database\ntechnologies, 2003.\n[16] T. H. Cormen, C. E. Leiserson, and R. L. Rivest. Introduction to Algorithms,\n2nd Edition. MIT Press/McGraw Hill, 2001.\n[17] D. Florescu, A. Y. Levy, and A. O. Mendelzon. Database techniques for the\nworld-wide web: A survey. SIGMOD Record, 27(3):59-74, 1998.\n[18] B. He and K. C.-C. Chang. Statistical schema matching across web query\ninterfaces. In SIGMOD Conference, 2003.\n[19] P. Ipeirotis and L. Gravano. Distributed search over the hidden web:\nHierarchical database sampling and selection. In VLDB, 2002.\n[20] P. G. Ipeirotis, L. Gravano, and M. Sahami. Probe, count, and classify:\nCategorizing hidden web databases. In SIGMOD, 2001.\n[21] C. Lagoze and H. V. Sompel. The Open Archives Initiative: Building a\nlow-barrier interoperability framework In JCDL, 2001.\n[22] S. Lawrence and C. L. Giles. Searching the World Wide Web. Science,\n280(5360):98-100, 1998.\n[23] V. Z. Liu, J. C. Richard C. Luo and, and W. W. Chu. Dpro: A probabilistic\napproach for hidden web database selection using dynamic probing. In ICDE,\n2004.\n[24] X. Liu, K. Maly, M. Zubair and M. L. Nelson. DP9-An OAI Gateway Service\nfor Web Crawlers. In JCDL, 2002.\n[25] B. B. Mandelbrot. Fractal Geometry of Nature. W. H. Freeman & Co.\n[26] A. Ntoulas, J. Cho, and C. Olston. What\"s new on the web? the evolution of the\nweb from a search engine perspective. In WWW, 2004.\n[27] A. Ntoulas, P. Zerfos, and J. Cho. Downloading hidden web content. Technical\nreport, UCLA, 2004.\n[28] S. Olsen. Does search engine\"s power threaten web\"s independence?\nhttp://news.com.com/2009-1023-963618.html.\n[29] S. Raghavan and H. Garcia-Molina. Crawling the hidden web. In VLDB, 2001.\n[30] G. K. Zipf. Human Behavior and the Principle of Least-Effort.\nAddison-Wesley, Cambridge, MA, 1949.\n109", "keywords": "textual database;independence estimator;hidden web;hide web crawl;generic-frequency policy;deep web crawler;query selection;query-selection policy;adaptive algorithm;crawling policy;adaptive policy;keyword query;deep web;hidden web crawler"}
{"name": "train_H-83", "title": "Estimating the Global PageRank of Web Communities", "abstract": "Localized search engines are small-scale systems that index a particular community on the web. They offer several benefits over their large-scale counterparts in that they are relatively inexpensive to build, and can provide more precise and complete search capability over their relevant domains. One disadvantage such systems have over large-scale search engines is the lack of global PageRank values. Such information is needed to assess the value of pages in the localized search domain within the context of the web as a whole. In this paper, we present well-motivated algorithms to estimate the global PageRank values of a local domain. The algorithms are all highly scalable in that, given a local domain of size n, they use O(n) resources that include computation time, bandwidth, and storage. We test our methods across a variety of localized domains, including site-specific domains and topic-specific domains. We demonstrate that by crawling as few as n or 2n additional pages, our methods can give excellent global PageRank estimates.", "fulltext": "1. INTRODUCTION\nLocalized search engines are small-scale search engines\nthat index only a single community of the web. Such\ncommunities can be site-specific domains, such as pages within\nthe cs.utexas.edu domain, or topic-related\ncommunitiesfor example, political websites. Compared to the web graph\ncrawled and indexed by large-scale search engines, the size\nof such local communities is typically orders of magnitude\nsmaller. Consequently, the computational resources needed\nto build such a search engine are also similarly lighter. By\nrestricting themselves to smaller, more manageable sections\nof the web, localized search engines can also provide more\nprecise and complete search capabilities over their respective\ndomains.\nOne drawback of localized indexes is the lack of global\ninformation needed to compute link-based rankings. The\nPageRank algorithm [3], has proven to be an effective such\nmeasure. In general, the PageRank of a given page is\ndependent on pages throughout the entire web graph. In the\ncontext of a localized search engine, if the PageRanks are\ncomputed using only the local subgraph, then we would\nexpect the resulting PageRanks to reflect the perceived\npopularity within the local community and not of the web as a\nwhole. For example, consider a localized search engine that\nindexes political pages with conservative views. A person\nwishing to research the opinions on global warming within\nthe conservative political community may encounter\nnumerous such opinions across various websites. If only local\nPageRank values are available, then the search results will reflect\nonly strongly held beliefs within the community. However, if\nglobal PageRanks are also available, then the results can\nadditionally reflect outsiders\" views of the conservative\ncommunity (those documents that liberals most often access within\nthe conservative community).\nThus, for many localized search engines, incorporating\nglobal PageRanks can improve the quality of search results.\nHowever, the number of pages a local search engine indexes\nis typically orders of magnitude smaller than the number of\npages indexed by their large-scale counterparts. Localized\nsearch engines do not have the bandwidth, storage capacity,\nor computational power to crawl, download, and compute\nthe global PageRanks of the entire web. In this work, we\npresent a method of approximating the global PageRanks of\na local domain while only using resources of the same\norder as those needed to compute the PageRanks of the local\nsubgraph.\nOur proposed method looks for a supergraph of our local\nsubgraph such that the local PageRanks within this\nsupergraph are close to the true global PageRanks. We construct\nthis supergraph by iteratively crawling global pages on the\ncurrent web frontier-i.e., global pages with inlinks from\npages that have already been crawled. In order to provide\n116\nResearch Track Paper\na good approximation to the global PageRanks, care must\nbe taken when choosing which pages to crawl next; in this\npaper, we present a well-motivated page selection algorithm\nthat also performs well empirically. This algorithm is\nderived from a well-defined problem objective and has a\nrunning time linear in the number of local nodes.\nWe experiment across several types of local subgraphs,\nincluding four topic related communities and several\nsitespecific domains. To evaluate performance, we measure the\ndifference between the current global PageRank estimate\nand the global PageRank, as a function of the number of\npages crawled. We compare our algorithm against several\nheuristics and also against a baseline algorithm that chooses\npages at random, and we show that our method outperforms\nthese other methods. Finally, we empirically demonstrate\nthat, given a local domain of size n, we can provide good\napproximations to the global PageRank values by crawling\nat most n or 2n additional pages.\nThe paper is organized as follows. Section 2 gives an\noverview of localized search engines and outlines their\nadvantages over global search. Section 3 provides background\non the PageRank algorithm. Section 4 formally defines our\nproblem, and section 5 presents our page selection criteria\nand derives our algorithms. Section 6 provides\nexperimental results, section 7 gives an overview of related work, and,\nfinally, conclusions are given in section 8.\n2. LOCALIZED SEARCH ENGINES\nLocalized search engines index a single community of the\nweb, typically either a site-specific community, or a\ntopicspecific community. Localized search engines enjoy three\nmajor advantages over their large-scale counterparts: they\nare relatively inexpensive to build, they can offer more\nprecise search capability over their local domain, and they can\nprovide a more complete index.\nThe resources needed to build a global search engine are\nenormous. A 2003 study by Lyman et al. [13] found that\nthe \u2018surface web\" (publicly available static sites) consists of\n8.9 billion pages, and that the average size of these pages is\napproximately 18.7 kilobytes. To download a crawl of this\nsize, approximately 167 terabytes of space is needed. For a\nresearcher who wishes to build a search engine with access\nto a couple of workstations or a small server, storage of this\nmagnitude is simply not available. However, building a\nlocalized search engine over a web community of a hundred\nthousand pages would only require a few gigabytes of\nstorage. The computational burden required to support search\nqueries over a database this size is more manageable as well.\nWe note that, for topic-specific search engines, the relevant\ncommunity can be efficiently identified and downloaded by\nusing a focused crawler [21, 4].\nFor site-specific domains, the local domain is readily\navailable on their own web server. This obviates the need for\ncrawling or spidering, and a complete and up-to-date\nindex of the domain can thus be guaranteed. This is in\ncontrast to their large-scale counterparts, which suffer from\nseveral shortcomings. First, crawling dynamically generated\npages-pages in the \u2018hidden web\"-has been the subject of\nresearch [20] and is a non-trivial task for an external crawler.\nSecond, site-specific domains can enable the robots\nexclusion policy. This prohibits external search engines\" crawlers\nfrom downloading content from the domain, and an external\nsearch engine must instead rely on outside links and anchor\ntext to index these restricted pages.\nBy restricting itself to only a specific domain of the\ninternet, a localized search engine can provide more precise\nsearch results. Consider the canonical ambiguous search\nquery, \u2018jaguar\", which can refer to either the car\nmanufacturer or the animal. A scientist trying to research the\nhabitat and evolutionary history of a jaguar may have better\nsuccess using a finely tuned zoology-specific search engine\nthan querying Google with multiple keyword searches and\nwading through irrelevant results. A method to learn\nbetter ranking functions for retrieval was recently proposed by\nRadlinski and Joachims [19] and has been applied to various\nlocal domains, including Cornell University\"s website [8].\n3. PAGERANK OVERVIEW\nThe PageRank algorithm defines the importance of web\npages by analyzing the underlying hyperlink structure of a\nweb graph. The algorithm works by building a Markov chain\nfrom the link structure of the web graph and computing its\nstationary distribution. One way to compute the\nstationary distribution of a Markov chain is to find the limiting\ndistribution of a random walk over the chain. Thus, the\nPageRank algorithm uses what is sometimes referred to as\nthe \u2018random surfer\" model. In each step of the random walk,\nthe \u2018surfer\" either follows an outlink from the current page\n(i.e. the current node in the chain), or jumps to a random\npage on the web.\nWe now precisely define the PageRank problem. Let U\nbe an m \u00d7 m adjacency matrix for a given web graph such\nthat Uji = 1 if page i links to page j and Uji = 0 otherwise.\nWe define the PageRank matrix PU to be:\nPU = \u03b1UD\u22121\nU + (1 \u2212 \u03b1)veT\n, (1)\nwhere DU is the (unique) diagonal matrix such that UD\u22121\nU\nis column stochastic, \u03b1 is a given scalar such that 0 \u2264 \u03b1 \u2264 1,\ne is the vector of all ones, and v is a non-negative,\nL1normalized vector, sometimes called the \u2018random surfer\"\nvector. Note that the matrix D\u22121\nU is well-defined only if each\ncolumn of U has at least one non-zero entry-i.e., each page\nin the webgraph has at least one outlink. In the presence of\nsuch \u2018dangling nodes\" that have no outlinks, one commonly\nused solution, proposed by Brin et al. [3], is to replace each\nzero column of U by a non-negative, L1-normalized vector.\nThe PageRank vector r is the dominant eigenvector of the\nPageRank matrix, r = PU r. We will assume, without loss of\ngenerality, that r has an L1-norm of one. Computationally,\nr can be computed using the power method. This method\nfirst chooses a random starting vector r(0)\n, and iteratively\nmultiplies the current vector by the PageRank matrix PU ;\nsee Algorithm 1. In general, each iteration of the power\nmethod can take O(m2\n) operations when PU is a dense\nmatrix. However, in practice, the number of links in a web\ngraph will be of the order of the number of pages. By\nexploiting the sparsity of the PageRank matrix, the work per\niteration can be reduced to O(km), where k is the average\nnumber of links per web page. It has also been shown that\nthe total number of iterations needed for convergence is\nproportional to \u03b1 and does not depend on the size of the web\ngraph [11, 7]. Finally, the total space needed is also O(km),\nmainly to store the matrix U.\n117\nResearch Track Paper\nAlgorithm 1: A linear time (per iteration) algorithm for\ncomputing PageRank.\nComputePR(U)\nInput: U: Adjacency matrix.\nOutput: r: PageRank vector.\nChoose (randomly) an initial non-negative vector r(0)\nsuch that r(0)\n1 = 1.\ni \u2190 0\nrepeat\ni \u2190 i + 1\n\u03bd \u2190 \u03b1UD\u22121\nU r(i\u22121)\n{\u03b1 is the random surfing\nprobability}\nr(i)\n\u2190 \u03bd + (1 \u2212 \u03b1)v {v is the random surfer vector.}\nuntil r(i)\n\u2212 r(i\u22121)\n< \u03b4 {\u03b4 is the convergence threshold.}\nr \u2190 r(i)\n4. PROBLEM DEFINITION\nGiven a local domain L, let G be an N \u00d7 N adjacency\nmatrix for the entire connected component of the web that\ncontains L, such that Gji = 1 if page i links to page j\nand Gji = 0 otherwise. Without loss of generality, we will\npartition G as:\nG =\nL Gout\nLout Gwithin\n, (2)\nwhere L is the n \u00d7 n local subgraph corresponding to links\ninside the local domain, Lout is the subgraph that\ncorresponds to links from the local domain pointing out to the\nglobal domain, Gout is the subgraph containing links from\nthe global domain into the local domain, and Gwithin\ncontains links within the global domain. We assume that when\nbuilding a localized search engine, only pages inside the\nlocal domain are crawled, and the links between these pages\nare represented by the subgraph L. The links in Lout are\nalso known, as these point from crawled pages in the local\ndomain to uncrawled pages in the global domain.\nAs defined in equation (1), PG is the PageRank matrix\nformed from the global graph G, and we define the global\nPageRank vector of this graph to be g. Let the n-length\nvector p\u2217\nbe the L1-normalized vector corresponding to the\nglobal PageRank of the pages in the local domain L:\np\u2217\n=\nEL g\nELg 1\n,\nwhere EL = [ I | 0 ] is the restriction matrix that selects\nthe components from g corresponding to nodes in L. Let p\ndenote the PageRank vector constructed from the local\ndomain subgraph L. In practice, the observed local PageRank\np and the global PageRank p\u2217\nwill be quite different. One\nwould expect that as the size of local matrix L approaches\nthe size of global matrix G, the global PageRank and the\nobserved local PageRank will become more similar. Thus, one\napproach to estimating the global PageRank is to crawl the\nentire global domain, compute its PageRank, and extract\nthe PageRanks of the local domain.\nTypically, however, n N , i.e., the number of global\npages is much larger than the number of local pages.\nTherefore, crawling all global pages will quickly exhaust all local\nresources (computational, storage, and bandwidth) available\nto create the local search engine. We instead seek a\nsupergraph \u02c6F of our local subgraph L with size O(n). Our goal\nAlgorithm 2: The FindGlobalPR algorithm.\nFindGlobalPR(L, Lout, T, k)\nInput: L: zero-one adjacency matrix for the local\ndomain, Lout: zero-one outlink matrix from L to global\nsubgraph as in (2), T: number of iterations, k: number of\npages to crawl per iteration.\nOutput: \u02c6p: an improved estimate of the global\nPageRank of L.\nF \u2190 L\nFout \u2190 Lout\nf \u2190 ComputePR(F )\nfor (i = 1 to T)\n{Determine which pages to crawl next}\npages \u2190 SelectNodes(F , Fout, f, k)\nCrawl pages, augment F and modify Fout\n{Update PageRanks for new local domain}\nf \u2190 ComputePR(F )\nend\n{Extract PageRanks of original local domain & normalize}\n\u02c6p \u2190 ELf\nELf 1\nis to find such a supergraph \u02c6F with PageRank \u02c6f, so that\n\u02c6f when restricted to L is close to p\u2217\n. Formally, we seek to\nminimize\nGlobalDiff( \u02c6f) =\nEL\n\u02c6f\nEL\n\u02c6f 1\n\u2212 p\u2217\n1\n. (3)\nWe choose the L1 norm for measuring the error as it does\nnot place excessive weight on outliers (as the L2 norm does,\nfor example), and also because it is the most commonly used\ndistance measure in the literature for comparing PageRank\nvectors, as well as for detecting convergence of the\nalgorithm [3].\nWe propose a greedy framework, given in Algorithm 2,\nfor constructing \u02c6F . Initially, F is set to the local subgraph\nL, and the PageRank f of this graph is computed. The\nalgorithm then proceeds as follows. First, the SelectNodes\nalgorithm (which we discuss in the next section) is called\nand it returns a set of k nodes to crawl next from the set\nof nodes in the current crawl frontier, Fout. These selected\nnodes are then crawled to expand the local subgraph, F , and\nthe PageRanks of this expanded graph are then recomputed.\nThese steps are repeated for each of T iterations. Finally,\nthe PageRank vector \u02c6p, which is restricted to pages within\nthe original local domain, is returned. Given our\ncomputation, bandwidth, and memory restrictions, we will assume\nthat the algorithm will crawl at most O(n) pages. Since the\nPageRanks are computed in each iteration of the algorithm,\nwhich is an O(n) operation, we will also assume that the\nnumber of iterations T is a constant. Of course, the main\nchallenge here is in selecting which set of k nodes to crawl\nnext. In the next section, we formally define the problem\nand give efficient algorithms.\n5. NODE SELECTION\nIn this section, we present node selection algorithms that\noperate within the greedy framework presented in the\nprevious section. We first give a well-defined criteria for the\npage selection problem and provide experimental evidence\nthat this criteria can effectively identify pages that optimize\nour problem objective (3). We then present our main\nal118\nResearch Track Paper\ngorithmic contribution of the paper, a method with linear\nrunning time that is derived from this page selection\ncriteria. Finally, we give an intuitive analysis of our algorithm in\nterms of \u2018leaks\" and \u2018flows\". We show that if only the \u2018flow\"\nis considered, then the resulting method is very similar to a\nwidely used page selection heuristic [6].\n5.1 Formulation\nFor a given page j in the global domain, we define the\nexpanded local graph Fj:\nFj =\nF s\nuT\nj 0\n, (4)\nwhere uj is the zero-one vector containing the outlinks from\nF into page j, and s contains the inlinks from page j into\nthe local domain. Note that we do not allow self-links in\nthis framework. In practice, self-links are often removed, as\nthey only serve to inflate a given page\"s PageRank.\nObserve that the inlinks into F from node j are not known\nuntil after node j is crawled. Therefore, we estimate this\ninlink vector as the expectation over inlink counts among\nthe set of already crawled pages,\ns =\nF T\ne\nF T e 1\n. (5)\nIn practice, for any given page, this estimate may not reflect\nthe true inlinks from that page. Furthermore, this\nexpectation is sampled from the set of links within the crawled\ndomain, whereas a better estimate would also use links from\nthe global domain. However, the latter distribution is not\nknown to a localized search engine, and we contend that the\nabove estimate will, on average, be a better estimate than\nthe uniform distribution, for example.\nLet the PageRank of F be f. We express the PageRank\nf+\nj of the expanded local graph Fj as\nf+\nj =\n(1 \u2212 xj)fj\nxj\n, (6)\nwhere xj is the PageRank of the candidate global node j,\nand fj is the L1-normalized PageRank vector restricted to\nthe pages in F .\nSince directly optimizing our problem goal requires\nknowing the global PageRank p\u2217\n, we instead propose to crawl\nthose nodes that will have the greatest influence on the\nPageRanks of pages in the original local domain L:\ninfluence(j) =\nk\u2208L\n|fj[k] \u2212 f[k]| (7)\n= EL (fj \u2212 f) 1.\nExperimentally, the influence score is a very good predictor\nof our problem objective (3). For each candidate global node\nj, figure 1(a) shows the objective function value Global Diff(fj)\nas a function of the influence of page j. The local domain\nused here is a crawl of conservative political pages (we will\nprovide more details about this dataset in section 6); we\nobserved similar results in other domains. The correlation\nis quite strong, implying that the influence criteria can\neffectively identify pages that improve the global PageRank\nestimate. As a baseline, figure 1(b) compares our\nobjective with an alternative criteria, outlink count. The outlink\ncount is defined as the number of outlinks from the local\ndomain to page j. The correlation here is much weaker.\n.00001 .0001 .001 .01\n0.26\n0.262\n0.264\n0.266\nInfluence\nObjective\n1 10 100 1000\n0.266\n0.264\n0.262\n0.26\nOutlink Count\nObjective\n(a) (b)\nFigure 1: (a) The correlation between our influence\npage selection criteria (7) and the actual objective\nfunction (3) value is quite strong. (b) This is in\ncontrast to other criteria, such as outlink count, which\nexhibit a much weaker correlation.\n5.2 Computation\nAs described, for each candidate global page j, the\ninfluence score (7) must be computed. If fj is computed\nexactly for each global page j, then the PageRank\nalgorithm would need to be run for each of the O(n) such global\npages j we consider, resulting in an O(n2\n) computational\ncost for the node selection method. Thus, computing the\nexact value of fj will lead to a quadratic algorithm, and we\nmust instead turn to methods of approximating this vector.\nThe algorithm we present works by performing one power\nmethod iteration used by the PageRank algorithm\n(Algorithm 1). The convergence rate for the PageRank algorithm\nhas been shown to equal the random surfer probability \u03b1 [7,\n11]. Given a starting vector x(0)\n, if k PageRank iterations\nare performed, the current PageRank solution x(k)\nsatisfies:\nx(k)\n\u2212 x\u2217\n1 = O(\u03b1k\nx(0)\n\u2212 x\u2217\n1), (8)\nwhere x\u2217\nis the desired PageRank vector. Therefore, if only\none iteration is performed, choosing a good starting vector\nis necessary to achieve an accurate approximation.\nWe partition the PageRank matrix PFj , corresponding to\nthe \u00d7 subgraph Fj as:\nPFj =\n\u02dcF \u02dcs\n\u02dcuT\nj w\n, (9)\nwhere \u02dcF = \u03b1F (DF + diag(uj))\u22121\n+ (1 \u2212 \u03b1)\ne\n+ 1\neT\n,\n\u02dcs = \u03b1s + (1 \u2212 \u03b1)\ne\n+ 1\n,\n\u02dcuj = \u03b1(DF + diag(uj))\u22121\nuj + (1 \u2212 \u03b1)\ne\n+ 1\n,\nw =\n1 \u2212 \u03b1\n+ 1\n,\nand diag(uj) is the diagonal matrix with the (i, i)th\nentry\nequal to one if the ith\nelement of uj equals one, and is zero\notherwise. We have assumed here that the random surfer\nvector is the uniform vector, and that L has no \u2018dangling\nlinks\". These assumptions are not necessary and serve only\nto simplify discussion and analysis.\nA simple approach for estimating fj is the following. First,\nestimate the PageRank f+\nj of Fj by computing one\nPageRank iteration over the matrix PFj , using the starting\nvector \u03bd =\nf\n0\n. Then, estimate fj by removing the last\n119\nResearch Track Paper\ncomponent from our estimate of f+\nj (i.e., the component\ncorresponding to the added node j), and renormalizing.\nThe problem with this approach is in the starting vector.\nRecall from (6) that xj is the PageRank of the added node\nj. The difference between the actual PageRank f+\nj of PFj\nand the starting vector \u03bd is\n\u03bd \u2212 f+\nj 1 = xj + f \u2212 (1 \u2212 xj)fj 1\n\u2265 xj + | f 1 \u2212 (1 \u2212 xj) fj 1|\n= xj + |xj|\n= 2xj.\nThus, by (8), after one PageRank iteration, we expect our\nestimate of f+\nj to still have an error of about 2\u03b1xj. In\nparticular, for candidate nodes j with relatively high PageRank\nxj, this method will yield more inaccurate results. We will\nnext present a method that eliminates this bias and runs in\nO(n) time.\n5.2.1 Stochastic Complementation\nSince f+\nj , as given in (6) is the PageRank of the matrix\nPFj , we have:\nfj(1 \u2212 xj)\nxj\n=\n\u02dcF \u02dcs\n\u02dcuT\nj w\nfj(1 \u2212 xj)\nxj\n=\n\u02dcF fj(1 \u2212 xj) + \u02dcsxj\n\u02dcuT\nj fj(1 \u2212 xj) + wxj\n.\nSolving the above system for fj can be shown to yield\nfj = ( \u02dcF + (1 \u2212 w)\u22121\n\u02dcs\u02dcuT\nj )fj. (10)\nThe matrix S = \u02dcF +(1\u2212w)\u22121\n\u02dcs\u02dcuT\nj is known as the stochastic\ncomplement of the column stochastic matrix PFj with\nrespect to the sub matrix \u02dcF . The theory of stochastic\ncomplementation is well studied, and it can be shown the stochastic\ncomplement of an irreducible matrix (such as the PageRank\nmatrix) is unique. Furthermore, the stochastic complement\nis also irreducible and therefore has a unique stationary\ndistribution as well. For an extensive study, see [15].\nIt can be easily shown that the sub-dominant eigenvalue\nof S is at most +1\n\u03b1, where is the size of F . For sufficiently\nlarge , this value will be very close to \u03b1. This is important,\nas other properties of the PageRank algorithm, notably the\nalgorithm\"s sensitivity, are dependent on this value [11].\nIn this method, we estimate the length vector fj by\ncomputing one PageRank iteration over the \u00d7 stochastic\ncomplement S, starting at the vector f:\nfj \u2248 Sf. (11)\nThis is in contrast to the simple method outlined in the\nprevious section, which first iterates over the ( + 1) \u00d7 ( + 1)\nmatrix PFj to estimate f+\nj , and then removes the last\ncomponent from the estimate and renormalizes to approximate\nfj. The problem with the latter method is in the choice\nof the ( + 1) length starting vector, \u03bd. Consequently, the\nPageRank estimate given by the simple method differs from\nthe true PageRank by at least 2\u03b1xj, where xj is the\nPageRank of page j. By using the stochastic complement, we\ncan establish a tight lower bound of zero for this difference.\nTo see this, consider the case in which a node k is added\nto F to form the augmented local subgraph Fk, and that\nthe PageRank of this new graph is\n(1 \u2212 xk)f\nxk\n.\nSpecifically, the addition of page k does not change the PageRanks\nof the pages in F , and thus fk = f. By construction of\nthe stochastic complement, fk = Sfk, so the approximation\ngiven in equation (11) will yield the exact solution.\nNext, we present the computational details needed to\nefficiently compute the quantity fj \u2212f 1 over all known global\npages j. We begin by expanding the difference fj \u2212f, where\nthe vector fj is estimated as in (11),\nfj \u2212 f \u2248 Sf \u2212 f\n= \u03b1F (DF + diag(uj))\u22121\nf + (1 \u2212 \u03b1)\ne\n+ 1\neT\nf\n+(1 \u2212 w)\u22121\n(\u02dcuT\nj f)\u02dcs \u2212 f. (12)\nNote that the matrix (DF +diag(uj))\u22121\nis diagonal. Letting\no[k] be the outlink count for page k in F , we can express\nthe kth\ndiagonal element as:\n(DF + diag(uj))\u22121\n[k, k] =\n1\no[k]+1\nif uj[k] = 1\n1\no[k]\nif uj[k] = 0\nNoting that (o[k] + 1)\u22121\n= o[k]\u22121\n\u2212 (o[k](o[k] + 1))\u22121\nand\nrewriting this in matrix form yields\n(DF +diag(uj))\u22121\n= D\u22121\nF \u2212D\u22121\nF (DF +diag(uj))\u22121\ndiag(uj).\n(13)\nWe use the same identity to express\ne\n+ 1\n=\ne\n\u2212\ne\n( + 1)\n. (14)\nRecall that, by definition, we have PF = \u03b1F D\u22121\nF +(1\u2212\u03b1)e\n.\nSubstituting (13) and (14) in (12) yields\nfj \u2212 f \u2248 (PF f \u2212 f)\n\u2212\u03b1F D\u22121\nF (DF + diag(uj))\u22121\ndiag(uj)f\n\u2212(1 \u2212 \u03b1)\ne\n( + 1)\n+ (1 \u2212 w)\u22121\n(\u02dcuT\nj f)\u02dcs\n= x + y + (\u02dcuT\nj f)z, (15)\nnoting that by definition, f = PF f, and defining the vectors\nx, y, and z to be\nx = \u2212\u03b1F D\u22121\nF (DF + diag(uj))\u22121\ndiag(uj)f (16)\ny = \u2212(1 \u2212 \u03b1)\ne\n( + 1)\n(17)\nz = (1 \u2212 w)\u22121\n\u02dcs. (18)\nThe first term x is a sparse vector, and takes non-zero values\nonly for local pages k that are siblings of the global page\nj. We define (i, j) \u2208 F if and only if F [j, i] = 1\n(equivalently, page i links to page j) and express the value of the\ncomponent x[k ] as:\nx[k ] = \u2212\u03b1\nk:(k,k )\u2208F ,uj [k]=1\nf[k]\no[k](o[k] + 1)\n, (19)\nwhere o[k], as before, is the number of outlinks from page k\nin the local domain. Note that the last two terms, y and z\nare not dependent on the current global node j. Given the\nfunction hj(f) = y + (\u02dcuT\nj f)z 1, the quantity fj \u2212 f 1\n120\nResearch Track Paper\ncan be expressed as\nfj \u2212 f 1 =\nk\nx[k] + y[k] + (\u02dcuT\nj f)z[k]\n=\nk:x[k]=0\ny[k] + (\u02dcuT\nj f)z[k]\n+\nk:x[k]=0\nx[k] + y[k] + (\u02dcuT\nj f)z[k]\n= hj(f) \u2212\nk:x[k]=0\ny[k] + (\u02dcuT\nj f)z[k]\n+\nk:x[k]=0\nx[k] + y[k] + (\u02dcuT\nj f)z[k] .(20)\nIf we can compute the function hj in linear time, then we\ncan compute each value of fj \u2212 f 1 using an additional\namount of time that is proportional to the number of\nnonzero components in x. These optimizations are carried out\nin Algorithm 3. Note that (20) computes the difference\nbetween all components of f and fj, whereas our node\nselection criteria, given in (7), is restricted to the components\ncorresponding to nodes in the original local domain L.\nLet us examine Algorithm 3 in more detail. First, the\nalgorithm computes the outlink counts for each page in the\nlocal domain. The algorithm then computes the quantity\n\u02dcuT\nj f for each known global page j. This inner product can\nbe written as\n(1 \u2212 \u03b1)\n1\n+ 1\n+ \u03b1\nk:(k,j)\u2208Fout\nf[k]\no[k] + 1\n,\nwhere the second term sums over the set of local pages that\nlink to page j. Since the total number of edges in Fout was\nassumed to have size O( ) (recall that is the number of\npages in F ), the running time of this step is also O( ).\nThe algorithm then computes the vectors y and z, as\ngiven in (17) and (18), respectively. The L1NormDiff\nmethod is called on the components of these vectors which\ncorrespond to the pages in L, and it estimates the value of\nEL(y + (\u02dcuT\nj f)z) 1 for each page j. The estimation works\nas follows. First, the values of \u02dcuT\nj f are discretized uniformly\ninto c values {a1, ..., ac}. The quantity EL(y + aiz) 1 is\nthen computed for each discretized value of ai and stored in\na table. To evaluate EL (y + az) 1 for some a \u2208 [a1, ac],\nthe closest discretized value ai is determined, and the\ncorresponding entry in the table is used. The total running time\nfor this method is linear in and the discretization\nparameter c (which we take to be a constant). We note that if exact\nvalues are desired, we have also developed an algorithm that\nruns in O( log ) time that is not described here.\nIn the main loop, we compute the vector x, as defined\nin equation (16). The nested loops iterate over the set of\npages in F that are siblings of page j. Typically, the size\nof this set is bounded by a constant. Finally, for each page\nj, the scores vector is updated over the set of non-zero\ncomponents k of the vector x with k \u2208 L. This set has\nsize equal to the number of local siblings of page j, and is\na subset of the total number of siblings of page j. Thus,\neach iteration of the main loop takes constant time, and the\ntotal running time of the main loop is O( ). Since we have\nassumed that the size of F will not grow larger than O(n),\nthe total running time for the algorithm is O(n).\nAlgorithm 3: Node Selection via Stochastic\nComplementation.\nSC-Select(F , Fout, f, k)\nInput: F : zero-one adjacency matrix of size\ncorresponding to the current local subgraph, Fout: zero-one\noutlink matrix from F to global subgraph, f:\nPageRank of F , k: number of pages to return\nOutput: pages: set of k pages to crawl next\n{Compute outlink sums for local subgraph}\nforeach (page j \u2208 F )\no[j] \u2190 k:(j,k)\u2208F F[j, k]\nend\n{Compute scalar \u02dcuT\nj f for each global node j }\nforeach (page j \u2208 Fout)\ng[j] \u2190 (1 \u2212 \u03b1) 1\n+1\nforeach (page k : (k, j) \u2208 Fout)\ng[j] \u2190 g[j] + \u03b1 f[k]\no[k]+1\nend\nend\n{Compute vectors y and z as in (17) and (18) }\ny \u2190 \u2212(1 \u2212 \u03b1) e\n( +1)\nz \u2190 (1 \u2212 w)\u22121\n\u02dcs\n{Approximate y + g[j] \u2217 z 1 for all values g[j]}\nnorm diffs \u2190L1NormDiffs(g, ELy, ELz)\nforeach (page j \u2208 Fout)\n{Compute sparse vector x as in (19)}\nx \u2190 0\nforeach (page k : (k, j) \u2208 Fout)\nforeach (page k : (k, k ) \u2208 F ))\nx[k ] \u2190 x[k ] \u2212 f[k]\no[k](o[k]+1)\nend\nend\nx \u2190 \u03b1x\nscores[j] \u2190 norm diffs[j]\nforeach (k : x[k] > 0 and page k \u2208 L)\nscores[j] \u2190 scores[j] \u2212 |y[k] + g[j] \u2217 z[k]|\n+|x[k]+y[k]+g[j]\u2217z[k])|\nend\nend\nReturn k pages with highest scores\n5.2.2 PageRank Flows\nWe now present an intuitive analysis of the stochastic\ncomplementation method by decomposing the change in\nPageRank in terms of \u2018leaks\" and \u2018flows\". This analysis is\nmotivated by the decomposition given in (15). PageRank \u2018flow\" is\nthe increase in the local PageRanks originating from global\npage j. The flows are represented by the non-negative vector\n(\u02dcuT\nj f)z (equations (15) and (18)). The scalar \u02dcuT\nj f can be\nthought of as the total amount of PageRank flow that page\nj has available to distribute. The vector z dictates how the\nflow is allocated to the local domain; the flow that local\npage k receives is proportional to (within a constant factor\ndue to the random surfer vector) the expected number of its\ninlinks.\nThe PageRank \u2018leaks\" represent the decrease in PageRank\nresulting from the addition of page j. The leakage can\nbe quantified in terms of the non-positive vectors x and\ny (equations (16) and (17)). For vector x, we can see from\nequation (19) that the amount of PageRank leaked by a\nlocal page is proportional to the weighted sum of the\nPage121\nResearch Track Paper\nRanks of its siblings. Thus, pages that have siblings with\nhigher PageRanks (and low outlink counts) will experience\nmore leakage. The leakage caused by y is an artifact of the\nrandom surfer vector.\nWe will next show that if only the \u2018flow\" term, (\u02dcuT\nj f)z,\nis considered, then the resulting method is very similar to\na heuristic proposed by Cho et al. [6] that has been widely\nused for the Crawling Through URL Ordering problem.\nThis heuristic is computationally cheaper, but as we will see\nlater, not as effective as the Stochastic Complementation\nmethod.\nOur node selection strategy chooses global nodes that\nhave the largest influence (equation (7)). If this influence is\napproximated using only \u2018flows\", the optimal node j\u2217\nis:\nj\u2217\n= argmaxj EL \u02dcuT\nj fz 1\n= argmaxj \u02dcuT\nj f EL z 1\n= argmaxj \u02dcuT\nj f\n= argmaxj \u03b1(DF + diag(uj))\u22121\nuj + (1 \u2212 \u03b1)\ne\n+ 1\n, f\n= argmaxjfT\n(DF + diag(uj))\u22121\nuj.\nThe resulting page selection score can be expressed as a sum\nof the PageRanks of each local page k that links to j, where\neach PageRank value is normalized by o[k]+1. Interestingly,\nthe normalization that arises in our method differs from the\nheuristic given in [6], which normalizes by o[k]. The\nalgorithm PF-Select, which is omitted due to lack of space,\nfirst computes the quantity fT\n(DF +diag(uj))\u22121\nuj for each\nglobal page j, and then returns the pages with the k largest\nscores. To see that the running time for this algorithm is\nO(n), note that the computation involved in this method is\na subset of that needed for the SC-Select method\n(Algorithm 3), which was shown to have a running time of O(n).\n6. EXPERIMENTS\nIn this section, we provide experimental evidence to\nverify the effectiveness of our algorithms. We first outline our\nexperimental methodology and then provide results across\na variety of local domains.\n6.1 Methodology\nGiven the limited resources available at an academic\ninstitution, crawling a section of the web that is of the same\nmagnitude as that indexed by Google or Yahoo! is clearly\ninfeasible. Thus, for a given local domain, we approximate\nthe global graph by crawling a local neighborhood around\nthe domain that is several orders of magnitude larger than\nthe local subgraph. Even though such a graph is still orders\nof magnitude smaller than the \u2018true\" global graph, we\ncontend that, even if there exist some highly influential pages\nthat are very far away from our local domain, it is\nunrealistic for any local node selection algorithm to find them. Such\npages also tend to be highly unrelated to pages within the\nlocal domain.\nWhen explaining our node selection strategies in section\n5, we made the simplifying assumption that our local graph\ncontained no dangling nodes. This assumption was only\nmade to ease our analysis. Our implementation efficiently\nhandles dangling links by replacing each zero column of our\nadjacency matrix with the uniform vector. We evaluate the\nalgorithm using the two node selection strategies given in\nSection 5.2, and also against the following baseline methods:\n\u2022 Random: Nodes are chosen uniformly at random among\nthe known global nodes.\n\u2022 OutlinkCount: Global nodes with the highest\nnumber of outlinks from the local domain are chosen.\nAt each iteration of the FindGlobalPR algorithm, we\nevaluate performance by computing the difference between the\ncurrent PageRank estimate of the local domain, ELf\nELf 1\n, and\nthe global PageRank of the local domain ELg\nELg 1\n. All\nPageRank calculations were performed using the uniform\nrandom surfer vector. Across all experiments, we set the\nrandom surfer parameter \u03b1, to be .85, and used a convergence\nthreshold of 10\u22126\n. We evaluate the difference between the\nlocal and global PageRank vectors using three different\nmetrics: the L1 and L\u221e norms, and Kendall\"s tau. The L1 norm\nmeasures the sum of the absolute value of the differences\nbetween the two vectors, and the L\u221e norm measures the\nabsolute value of the largest difference. Kendall\"s tau metric is\na popular rank correlation measure used to compare\nPageRanks [2, 11]. This metric can be computed by counting\nthe number of pairs of pairs that agree in ranking, and\nsubtracting from that the number of pairs of pairs that disagree\nin ranking. The final value is then normalized by the total\nnumber of n\n2\nsuch pairs, resulting in a [\u22121, 1] range, where\na negative score signifies anti-correlation among rankings,\nand values near one correspond to strong rank correlation.\n6.2 Results\nOur experiments are based on two large web crawls and\nwere downloaded using the web crawler that is part of the\nNutch open source search engine project [18]. All crawls\nwere restricted to only \u2018http\" pages, and to limit the\nnumber of dynamically generated pages that we crawl, we\nignored all pages with urls containing any of the characters\n\u2018?\", \u2018*\", \u2018@\", or \u2018=\". The first crawl, which we will refer to\nas the \u2018edu\" dataset, was seeded by homepages of the top\n100 graduate computer science departments in the USA, as\nrated by the US News and World Report [16], and also by\nthe home pages of their respective institutions. A crawl of\ndepth 5 was performed, restricted to pages within the \u2018.edu\"\ndomain, resulting in a graph with approximately 4.7 million\npages and 22.9 million links. The second crawl was seeded\nby the set of pages under the \u2018politics\" hierarchy in the dmoz\nopen directory project[17]. We crawled all pages up to four\nlinks away, which yielded a graph with 4.4 million pages and\n17.3 million links.\nWithin the \u2018edu\" crawl, we identified the five site-specific\ndomains corresponding to the websites of the top five\ngraduate computer science departments, as ranked by the US\nNews and World Report. This yielded local domains of\nvarious sizes, from 10,626 (UIUC) to 59,895 (Berkeley). For each\nof these site-specific domains with size n, we performed 50\niterations of the FindGlobalPR algorithm to crawl a total\nof 2n additional nodes. Figure 2(a) gives the (L1) difference\nfrom the PageRank estimate at each iteration to the global\nPageRank, for the Berkeley local domain.\nThe performance of this dataset was representative of the\ntypical performance across the five computer science\nsitespecific local domains. Initially, the L1 difference between\nthe global and local PageRanks ranged from .0469\n(Stanford) to .149 (MIT). For the first several iterations, the\n122\nResearch Track Paper\n0 5 10 15 20 25 30 35 40 45 50\n0.015\n0.02\n0.025\n0.03\n0.035\n0.04\n0.045\n0.05\n0.055\nNumber of Iterations\nGlobalandLocalPageRankDifference(L1)\nStochastic Complement\nPageRank Flow\nOutlink Count\nRandom\n0 10 20 30 40 50\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\nNumber of Iterations\nGlobalandLocalPageRankDifference(L1)\nStochastic Complement\nPageRank Flow\nOutlink Count\nRandom\n0 5 10 15 20 25\n0.16\n0.18\n0.2\n0.22\n0.24\n0.26\n0.28\n0.3\n0.32\n0.34\nNumber of Iterations\nGlobalandLocalPageRankDifference(L1)\nStochastic Complement\nPageRank Flow\nOutlink Count\nRandom\n(a) www.cs.berkeley.edu (b) www.enterstageright.com (c) Politics\nFigure 2: L1 difference between the estimated and true global PageRanks for (a) Berkeley\"s computer science\nwebsite, (b) the site-specific domain, www.enterstageright.com, and (c) the \u2018politics\" topic-specific domain. The\nstochastic complement method outperforms all other methods across various domains.\nthree link-based methods all outperform the random\nselection heuristic. After these initial iterations, the random\nheuristic tended to be more competitive with (or even\noutperform, as in the Berkeley local domain) the outlink count\nand PageRank flow heuristics. In all tests, the stochastic\ncomplementation method either outperformed, or was\ncompetitive with, the other methods. Table 1 gives the average\ndifference between the final estimated global PageRanks and\nthe true global PageRanks for various distance measures.\nAlgorithm L1 L\u221e Kendall\nStoch. Comp. .0384 .00154 .9257\nPR Flow .0470 .00272 .8946\nOutlink .0419 .00196 .9053\nRandom .0407 .00204 .9086\nTable 1: Average final performance of various node\nselection strategies for the five site-specific\ncomputer science local domains. Note that Kendall\"s\nTau measures similarity, while the other metrics are\ndissimilarity measures. Stochastic\nComplementation clearly outperforms the other methods in all\nmetrics.\nWithin the \u2018politics\" dataset, we also performed two\nsitespecific tests for the largest websites in the crawl:\nwww.adamsmith.org, the website for the London based Adam Smith\nInstitute, and www.enterstageright.com, an online\nconservative journal. As with the \u2018edu\" local domains, we ran our\nalgorithm for 50 iterations, crawling a total of 2n nodes.\nFigure 2 (b) plots the results for the www.enterstageright.com\ndomain. In contrast to the \u2018edu\" local domains, the Random\nand OutlinkCount methods were not competitive with\neither the SC-Select or the PF-Select methods. Among all\ndatasets and all node selection methods, the stochastic\ncomplementation method was most impressive in this dataset,\nrealizing a final estimate that differed only .0279 from the\nglobal PageRank, a ten-fold improvement over the initial\nlocal PageRank difference of .299. For the Adam Smith local\ndomain, the initial difference between the local and global\nPageRanks was .148, and the final estimates given by the\nSC-Select, PF-Select, OutlinkCount, and Random\nmethods were .0208, .0193, .0222, and .0356, respectively.\nWithin the \u2018politics\" dataset, we constructed four\ntopicspecific local domains. The first domain consisted of all\npages in the dmoz politics category, and also all pages within\neach of these sites up to two links away. This yielded a local\ndomain of 90,811 pages, and the results are given in figure 2\n(c). Because of the larger size of the topic-specific domains,\nwe ran our algorithm for only 25 iterations to crawl a total\nof n nodes.\nWe also created topic-specific domains from three\npolitical sub-topics: liberalism, conservatism, and socialism. The\npages in these domains were identified by their\ncorresponding dmoz categories. For each sub-topic, we set the local\ndomain to be all pages within three links from the\ncorresponding dmoz category pages. Table 2 summarizes the\nperformance of these three topic-specific domains, and also\nthe larger political domain.\nTo quantify a global page j\"s effect on the global\nPageRank values of pages in the local domain, we define page\nj\"s impact to be its PageRank value, g[j], normalized by the\nfraction of its outlinks pointing to the local domain:\nimpact(j) =\noL[j]\no[j]\n\u00b7 g[j],\nwhere, oL[j] is the number of outlinks from page j to pages\nin the local domain L, and o[j] is the total number of j\"s\noutlinks. In terms of the random surfer model, the impact\nof page j is the probability that the random surfer (1) is\ncurrently at global page j in her random walk and (2) takes\nan outlink to a local page, given that she has already decided\nnot to jump to a random page.\nFor the politics local domain, we found that many of the\npages with high impact were in fact political pages that\nshould have been included in the dmoz politics topic, but\nwere not. For example, the two most influential global pages\nwere the political search engine www.askhenry.com, and the\nhome page of the online political magazine,\nwww.policyreview.com. Among non-political pages, the home page of\nthe journal Education Next was most influential. The\njournal is freely available online and contains articles\nregarding various aspect of K-12 education in America. To provide\nsome anecdotal evidence for the effectiveness of our page\nselection methods, we note that the SC-Select method chose\n11 pages within the www.educationnext.org domain, the\nPF-Select method discovered 7 such pages, while the\nOutlinkCount and Random methods found only 6 pages each.\nFor the conservative political local domain, the socialist\nwebsite www.ornery.org had a very high impact score. This\n123\nResearch Track Paper\nAll Politics:\nAlgorithm L1 L2 Kendall\nStoch. Comp. .1253 .000700 .8671\nPR Flow .1446 .000710 .8518\nOutlink .1470 .00225 .8642\nRandom .2055 .00203 .8271\nConservativism:\nAlgorithm L1 L2 Kendall\nStoch. Comp. .0496 .000990 .9158\nPR Flow .0554 .000939 .9028\nOutlink .0602 .00527 .9144\nRandom .1197 .00102 .8843\nLiberalism:\nAlgorithm L1 L2 Kendall\nStoch. Comp. .0622 .001360 .8848\nPR Flow .0799 .001378 .8669\nOutlink .0763 .001379 .8844\nRandom .1127 .001899 .8372\nSocialism:\nAlgorithm L1 L\u221e Kendall\nStoch. Comp. .04318 .00439 .9604\nPR Flow .0450 .004251 .9559\nOutlink .04282 .00344 .9591\nRandom .0631 .005123 .9350\nTable 2: Final performance among node selection\nstrategies for the four political topic-specific crawls.\nNote that Kendall\"s Tau measures similarity, while\nthe other metrics are dissimilarity measures.\nwas largely due to a link from the front page of this site\nto an article regarding global warming published by the\nNational Center for Public Policy Research, a conservative\nresearch group in Washington, DC. Not surprisingly, the\nglobal PageRank of this article (which happens to be on the\nhome page of the NCCPR, www.nationalresearch.com),\nwas approximately .002, whereas the local PageRank of this\npage was only .00158. The SC-Select method yielded a\nglobal PageRank estimate of approximately .00182, the\nPFSelect method estimated a value of .00167, and the\nRandom and OutlinkCount methods yielded values of .01522\nand .00171, respectively.\n7. RELATED WORK\nThe node selection framework we have proposed is similar\nto the url ordering for crawling problem proposed by Cho\net al. in [6]. Whereas our framework seeks to minimize the\ndifference between the global and local PageRank, the\nobjective used in [6] is to crawl the most highly (globally) ranked\npages first. They propose several node selection algorithms,\nincluding the outlink count heuristic, as well as a variant of\nour PF-Select algorithm which they refer to as the\n\u2018PageRank ordering metric\". They found this method to be most\neffective in optimizing their objective, as did a recent survey\nof these methods by Baeza-Yates et al. [1]. Boldi et al. also\nexperiment within a similar crawling framework in [2], but\nquantify their results by comparing Kendall\"s rank\ncorrelation between the PageRanks of the current set of crawled\npages and those of the entire global graph. They found that\nnode selection strategies that crawled pages with the\nhighest global PageRank first actually performed worse (with\nrespect to Kendall\"s Tau correlation between the local and\nglobal PageRanks) than basic depth first or breadth first\nstrategies. However, their experiments differ from our work\nin that our node selection algorithms do not use (or have\naccess to) global PageRank values.\nMany algorithmic improvements for computing exact\nPageRank values have been proposed [9, 10, 14]. If such\nalgorithms are used to compute the global PageRanks of our\nlocal domain, they would all require O(N) computation,\nstorage, and bandwidth, where N is the size of the global\ndomain. This is in contrast to our method, which\napproximates the global PageRank and scales linearly with the size\nof the local domain.\nWang and Dewitt [22] propose a system where the set of\nweb servers that comprise the global domain communicate\nwith each other to compute their respective global\nPageRanks. For a given web server hosting n pages, the\ncomputational, bandwidth, and storage requirements are also\nlinear in n. One drawback of this system is that the\nnumber of distinct web servers that comprise the global domain\ncan be very large. For example, our \u2018edu\" dataset contains\nwebsites from over 3,200 different universities; coordinating\nsuch a system among a large number of sites can be very\ndifficult.\nGan, Chen, and Suel propose a method for estimating the\nPageRank of a single page [5] which uses only constant\nbandwidth, computation, and space. Their approach relies on the\navailability of a remote connectivity server that can supply\nthe set of inlinks to a given page, an assumption not used in\nour framework. They experimentally show that a reasonable\nestimate of the node\"s PageRank can be obtained by visiting\nat most a few hundred nodes. Using their algorithm for our\nproblem would require that either the entire global domain\nfirst be downloaded or a connectivity server be used, both\nof which would lead to very large web graphs.\n8. CONCLUSIONS AND FUTURE WORK\nThe internet is growing exponentially, and in order to\nnavigate such a large repository as the web, global search\nengines have established themselves as a necessity. Along with\nthe ubiquity of these large-scale search engines comes an\nincrease in search users\" expectations. By providing complete\nand isolated coverage of a particular web domain, localized\nsearch engines are an effective outlet to quickly locate\ncontent that could otherwise be difficult to find. In this work,\nwe contend that the use of global PageRank in a localized\nsearch engine can improve performance.\nTo estimate the global PageRank, we have proposed an\niterative node selection framework where we select which\npages from the global frontier to crawl next. Our primary\ncontribution is our stochastic complementation page\nselection algorithm. This method crawls nodes that will most\nsignificantly impact the local domain and has running time\nlinear in the number of nodes in the local domain.\nExperimentally, we validate these methods across a diverse set of\nlocal domains, including seven site-specific domains and four\ntopic-specific domains. We conclude that by crawling an\nadditional n or 2n pages, our methods find an estimate of the\nglobal PageRanks that is up to ten times better than just\nusing the local PageRanks. Furthermore, we demonstrate\nthat our algorithm consistently outperforms other existing\nheuristics.\n124\nResearch Track Paper\nOften times, topic-specific domains are discovered using\na focused web crawler which considers a page\"s content in\nconjunction with link anchor text to decide which pages to\ncrawl next [4]. Although such crawlers have proven to be\nquite effective in discovering topic-related content, many\nirrelevant pages are also crawled in the process. Typically,\nthese pages are deleted and not indexed by the localized\nsearch engine. These pages can of course provide valuable\ninformation regarding the global PageRank of the local\ndomain. One way to integrate these pages into our framework\nis to start the FindGlobalPR algorithm with the current\nsubgraph F equal to the set of pages that were crawled by\nthe focused crawler.\nThe global PageRank estimation framework, along with\nthe node selection algorithms presented, all require O(n)\ncomputation per iteration and bandwidth proportional to\nthe number of pages crawled, Tk. If the number of\niterations T is relatively small compared to the number of pages\ncrawled per iteration, k, then the bottleneck of the algorithm\nwill be the crawling phase. However, as the number of\niterations increases (relative to k), the bottleneck will reside in\nthe node selection computation. In this case, our algorithms\nwould benefit from constant factor optimizations. Recall\nthat the FindGlobalPR algorithm (Algorithm 2) requires\nthat the PageRanks of the current expanded local domain be\nrecomputed in each iteration. Recent work by Langville and\nMeyer [12] gives an algorithm to quickly recompute\nPageRanks of a given webgraph if a small number of nodes are\nadded. This algorithm was shown to give speedup of five to\nten times on some datasets. We plan to investigate this and\nother such optimizations as future work.\nIn this paper, we have objectively evaluated our methods\nby measuring how close our global PageRank estimates are\nto the actual global PageRanks. To determine the\nbenefit of using global PageRanks in a localized search engine,\nwe suggest a user study in which users are asked to rate\nthe quality of search results for various search queries. For\nsome queries, only the local PageRanks are used in\nranking, and for the remaining queries, local PageRanks and the\napproximate global PageRanks, as computed by our\nalgorithms, are used. The results of such a study can then be\nanalyzed to determine the added benefit of using the global\nPageRanks computed by our methods, over just using the\nlocal PageRanks.\nAcknowledgements. This research was supported by NSF\ngrant CCF-0431257, NSF Career Award ACI-0093404, and\na grant from Sabre, Inc.\n9. REFERENCES\n[1] R. Baeza-Yates, M. Marin, C. Castillo, and\nA. Rodriguez. Crawling a country: better strategies\nthan breadth-first for web page ordering. World-Wide\nWeb Conference, 2005.\n[2] P. Boldi, M. Santini, and S. Vigna. Do your worst to\nmake the best: paradoxical effects in pagerank\nincremental computations. Workshop on Web Graphs,\n3243:168-180, 2004.\n[3] S. Brin and L. Page. The anatomy of a large-scale\nhypertextual web search engine. Computer Networks\nand ISDN Systems, 33(1-7):107-117, 1998.\n[4] S. Chakrabarti, M. van den Berg, and B. Dom.\nFocused crawling: a new approach to topic-specific\nweb resource discovery. World-Wide Web Conference,\n1999.\n[5] Y. Chen, Q. Gan, and T. Suel. Local methods for\nestimating pagerank values. Conference on\nInformation and Knowledge Management, 2004.\n[6] J. Cho, H. Garcia-Molina, and L. Page. Efficient\ncrawling through url ordering. World-Wide Web\nConference, 1998.\n[7] T. H. Haveliwala and S. D. Kamvar. The second\neigenvalue of the Google matrix. Technical report,\nStanford University, 2003.\n[8] T. Joachims, F. Radlinski, L. Granka, A. Cheng,\nC. Tillekeratne, and A. Patel. Learning retrieval\nfunctions from implicit feedback.\nhttp://www.cs.cornell.edu/People/tj/career.\n[9] S. D. Kamvar, T. H. Haveliwala, C. D. Manning, and\nG. H. Golub. Exploiting the block structure of the\nweb for computing pagerank. World-Wide Web\nConference, 2003.\n[10] S. D. Kamvar, T. H. Haveliwala, C. D. Manning, and\nG. H. Golub. Extrapolation methods for accelerating\npagerank computation. World-Wide Web Conference,\n2003.\n[11] A. N. Langville and C. D. Meyer. Deeper inside\npagerank. Internet Mathematics, 2004.\n[12] A. N. Langville and C. D. Meyer. Updating the\nstationary vector of an irreducible markov chain with\nan eye on Google\"s pagerank. SIAM Journal on\nMatrix Analysis, 2005.\n[13] P. Lyman, H. R. Varian, K. Swearingen, P. Charles,\nN. Good, L. L. Jordan, and J. Pal. How much\ninformation 2003? School of Information Management\nand System, University of California at Berkely, 2003.\n[14] F. McSherry. A uniform approach to accelerated\npagerank computation. World-Wide Web Conference,\n2005.\n[15] C. D. Meyer. Stochastic complementation, uncoupling\nmarkov chains, and the theory of nearly reducible\nsystems. SIAM Review, 31:240-272, 1989.\n[16] US News and World Report. http://www.usnews.com.\n[17] Dmoz open directory project. http://www.dmoz.org.\n[18] Nutch open source search engine.\nhttp://www.nutch.org.\n[19] F. Radlinski and T. Joachims. Query chains: learning\nto rank from implicit feedback. ACM SIGKDD\nInternational Conference on Knowledge Discovery and\nData Mining, 2005.\n[20] S. Raghavan and H. Garcia-Molina. Crawling the\nhidden web. In Proceedings of the Twenty-seventh\nInternational Conference on Very Large Databases,\n2001.\n[21] T. Tin Tang, D. Hawking, N. Craswell, and\nK. Griffiths. Focused crawling for both topical\nrelevance and quality of medical information.\nConference on Information and Knowledge\nManagement, 2005.\n[22] Y. Wang and D. J. DeWitt. Computing pagerank in a\ndistributed internet search system. Proceedings of the\n30th VLDB Conference, 2004.\n125\nResearch Track Paper", "keywords": "algorithm;localized search engine;web community;experimentation;subgraph;link-based ranking;topic-specific domain;large-scale search engine;local domain;global pagerank;crawling problem;global graph"}
{"name": "train_H-84", "title": "Event Threading within News Topics", "abstract": "With the overwhelming volume of online news available today, there is an increasing need for automatic techniques to analyze and present news to the user in a meaningful and efficient manner. Previous research focused only on organizing news stories by their topics into a flat hierarchy. We believe viewing a news topic as a flat collection of stories is too restrictive and inefficient for a user to understand the topic quickly. In this work, we attempt to capture the rich structure of events and their dependencies in a news topic through our event models. We call the process of recognizing events and their dependencies event threading. We believe our perspective of modeling the structure of a topic is more effective in capturing its semantics than a flat list of on-topic stories. We formally define the novel problem, suggest evaluation metrics and present a few techniques for solving the problem. Besides the standard word based features, our approaches take into account novel features such as temporal locality of stories for event recognition and time-ordering for capturing dependencies. Our experiments on a manually labeled data sets show that our models effectively identify the events and capture dependencies among them.", "fulltext": "1. INTRODUCTION\nNews forms a major portion of information disseminated in the\nworld everyday. Common people and news analysts alike are very\ninterested in keeping abreast of new things that happen in the news,\nbut it is becoming very difficult to cope with the huge volumes\nof information that arrives each day. Hence there is an increasing\nneed for automatic techniques to organize news stories in a way that\nhelps users interpret and analyze them quickly. This problem is\naddressed by a research program called Topic Detection and Tracking\n(TDT) [3] that runs an open annual competition on standardized\ntasks of news organization.\nOne of the shortcomings of current TDT evaluation is its view of\nnews topics as flat collection of stories. For example, the detection\ntask of TDT is to arrange a collection of news stories into clusters\nof topics. However, a topic in news is more than a mere collection\nof stories: it is characterized by a definite structure of inter-related\nevents. This is indeed recognized by TDT which defines a topic as\n\u2018a set of news stories that are strongly related by some seminal\nrealworld event\" where an event is defined as \u2018something that happens\nat a specific time and location\" [3]. For example, when a bomb\nexplodes in a building, that is the seminal event that triggers the\ntopic. Other events in the topic may include the rescue attempts,\nthe search for perpetrators, arrests and trials and so on. We see\nthat there is a pattern of dependencies between pairs of events in\nthe topic. In the above example, the event of rescue attempts is\n\u2018influenced\" by the event of bombing and so is the event of search\nfor perpetrators.\nIn this work we investigate methods for modeling the structure\nof a topic in terms of its events. By structure, we mean not only\nidentifying the events that make up a topic, but also establishing\ndependencies-generally causal-among them. We call the\nprocess of recognizing events and identifying dependencies among\nthem event threading, an analogy to email threading that shows\nconnections between related email messages. We refer to the\nresulting interconnected structure of events as the event model of the\ntopic. Although this paper focuses on threading events within an\nexisting news topic, we expect that such event based dependency\nstructure more accurately reflects the structure of news than strictly\nbounded topics do. From a user\"s perspective, we believe that our\nview of a news topic as a set of interconnected events helps him/her\nget a quick overview of the topic and also allows him/her navigate\nthrough the topic faster.\nThe rest of the paper is organized as follows. In section 2, we\ndiscuss related work. In section 3, we define the problem and use\nan example to illustrate threading of events within a news topic. In\nsection 4, we describe how we built the corpus for our problem.\nSection 5 presents our evaluation techniques while section 6\ndescribes the techniques we use for modeling event structure. In\nsection 7 we present our experiments and results. Section 8 concludes\nthe paper with a few observations on our results and comments on\nfuture work.\n446\n2. RELATED WORK\nThe process of threading events together is related to threading\nof electronic mail only by name for the most part. Email usually\nincorporates a strong structure of referenced messages and\nconsistently formatted subject headings-though information retrieval\ntechniques are useful when the structure breaks down [7]. Email\nthreading captures reference dependencies between messages and\ndoes not attempt to reflect any underlying real-world structure of\nthe matter under discussion.\nAnother area of research that looks at the structure within a topic\nis hierarchical text classification of topics [9, 6]. The hierarchy\nwithin a topic does impose a structure on the topic, but we do not\nknow of an effort to explore the extent to which that structure\nreflects the underlying event relationships.\nBarzilay and Lee [5] proposed a content structure modeling\ntechnique where topics within text are learnt using unsupervised\nmethods, and a linear order of these topics is modeled using hidden\nMarkov models. Our work differs from theirs in that we do not\nconstrain the dependency to be linear. Also their algorithms are tuned\nto work on specific genres of topics such as earthquakes, accidents,\netc., while we expect our algorithms to generalize over any topic.\nIn TDT, researchers have traditionally considered topics as\nflatclusters [1]. However, in TDT-2003, a hierarchical structure of\ntopic detection has been proposed and [2] made useful attempts\nto adopt the new structure. However this structure still did not\nexplicitly model any dependencies between events.\nIn a work closest to ours, Makkonen [8] suggested modeling\nnews topics in terms of its evolving events. However, the paper\nstopped short of proposing any models to the problem. Other\nrelated work that dealt with analysis within a news topic includes\ntemporal summarization of news topics [4].\n3. PROBLEM DEFINITION AND NOTATION\nIn this work, we have adhered to the definition of event and topic\nas defined in TDT. We present some definitions (in italics) and our\ninterpretations (regular-faced) below for clarity.\n1. Story: A story is a news article delivering some information\nto users. In TDT, a story is assumed to refer to only a single\ntopic. In this work, we also assume that each story discusses\na single event. In other words, a story is the smallest atomic\nunit in the hierarchy (topic event story). Clearly, both\nthe assumptions are not necessarily true in reality, but we\naccept them for simplicity in modeling.\n2. Event: An event is something that happens at some specific\ntime and place [10]. In our work, we represent an event by\na set of stories that discuss it. Following the assumption of\natomicity of a story, this means that any set of distinct events\ncan be represented by a set of non-overlapping clusters of\nnews stories.\n3. Topic: A set of news stories strongly connected by a seminal\nevent. We expand on this definition and interpret a topic as\na series of related events. Thus a topic can be represented\nby clusters of stories each representing an event and a set of\n(directed or undirected) edges between pairs of these clusters\nrepresenting the dependencies between these events. We will\ndescribe this representation of a topic in more detail in the\nnext section.\n4. Topic detection and tracking (TDT) :Topic detection\ndetects clusters of stories that discuss the same topic; Topic\ntracking detects stories that discuss a previously known topic [3].\nThus TDT concerns itself mainly with clustering stories into\ntopics that discuss them.\n5. Event threading: Event threading detects events within in a\ntopic, and also captures the dependencies among the events.\nThus the main difference between event threading and TDT\nis that we focus our modeling effort on microscopic events\nrather than larger topics. Additionally event threading\nmodels the relatedness or dependencies between pairs of events\nin a topic while TDT models topics as unrelated clusters of\nstories.\nWe first define our problem and representation of our model\nformally and then illustrate with the help of an example. We are\ngiven a set of \u00d2 news stories \u00cb \u00d7\u00bd \u00a1 \u00a1 \u00a1 \u00d7\u00d2 on a given topic\n\u00cc and their time of publication. We define a set of events\n\u00bd \u00a1 \u00a1 \u00a1 \u00d1 with the following constraints:\n\u00be \u00be\n\u00cb (1)\n\u00d7 \u00d8 (2)\n\u00d7 \u00be \u00d7 \u00d8 \u00d7 \u00be (3)\nWhile the first constraint says that each event is an element in the\npower set of S, the second constraint ensures that each story can\nbelong to at most one event. The last constraint tells us that every\nstory belongs to one of the events in . In fact this allows us to\ndefine a mapping function from stories to events as follows:\n\u00b4\u00d7 \u00b5 iff \u00d7 \u00be (4)\nFurther, we also define a set of directed edges \u00b4 \u00b5\nwhich denote dependencies between events. It is important to\nexplain what we mean by this directional dependency: While the\nexistence of an edge itself represents relatedness of two events, the\ndirection could imply causality or temporal-ordering. By causal\ndependency we mean that the occurrence of event B is related to\nand is a consequence of the occurrence of event A. By temporal\nordering, we mean that event B happened after event A and is related\nto A but is not necessarily a consequence of A. For example,\nconsider the following two events: \u2018plane crash\" (event A) and\n\u2018subsequent investigations\" (event B) in a topic on a plane crash incident.\nClearly, the investigations are a result of the crash. Hence an\narrow from A to B falls under the category of causal dependency.\nNow consider the pair of events \u2018Pope arrives in Cuba\"(event A)\nand \u2018Pope meets Castro\"(event B) in a topic that discusses Pope\"s\nvisit to Cuba. Now events A and B are closely related through their\nassociation with the Pope and Cuba but event B is not necessarily\na consequence of the occurrence of event A. An arrow in such\nscenario captures what we call time ordering. In this work, we do not\nmake an attempt to distinguish between these two kinds of\ndependencies and our models treats them as identical. A simpler (and\nhence less controversial) choice would be to ignore direction in the\ndependencies altogether and consider only undirected edges. This\nchoice definitely makes sense as a first step but we chose the former\nsince we believe directional edges make more sense to the user as\nthey provide a more illustrative flow-chart perspective to the topic.\nTo make the idea of event threading more concrete, consider the\nexample of TDT3 topic 30005, titled \u2018Osama bin Laden\"s\nIndictment\" (in the 1998 news). This topic has 23 stories which form 5\nevents. An event model of this topic can be represented as in figure\n1. Each box in the figure indicates an event in the topic of Osama\"s\nindictment. The occurrence of event 2, namely \u2018Trial and\nIndictment of Osama\" is dependent on the event of \u2018evidence gathered\nby CIA\", i.e., event 1. Similarly, event 2 influences the occurrences\nof events 3, 4 and 5, namely \u2018Threats from Militants\", \u2018Reactions\n447\nfrom Muslim World\" and \u2018announcement of reward\". Thus all the\ndependencies in the example are causal.\nExtending our notation further, we call an event A a parent of B\nand B the child of A, if \u00b4 \u00b5 \u00be . We define an event model\n\u00c5 \u00b4 \u00b5 to be a tuple of the set of events and set of\ndependencies.\nTrial and\n(5)\n(3)\n(4)\nCIA announces reward\nMuslim world\nReactions from\nIslamic militants\nThreats from\n(2)\n(1)\nOsama\nIndictment of\nCIA\ngathered by\nEvidence\nFigure 1: An event model of TDT topic \u2018Osama bin Laden\"s\nindictment\".\nEvent threading is strongly related to topic detection and\ntracking, but also different from it significantly. It goes beyond topics,\nand models the relationships between events. Thus, event\nthreading can be considered as a further extension of topic detection and\ntracking and is more challenging due to at least the following\ndifficulties.\n1. The number of events is unknown.\n2. The granularity of events is hard to define.\n3. The dependencies among events are hard to model.\n4. Since it is a brand new research area, no standard evaluation\nmetrics and benchmark data is available.\nIn the next few sections, we will describe our attempts to tackle\nthese problems.\n4. LABELED DATA\nWe picked 28 topics from the TDT2 corpus and 25 topics from\nthe TDT3 corpus. The criterion we used for selecting a topic is that\nit should contain at least 15 on-topic stories from CNN headline\nnews. If the topic contained more than 30 CNN stories, we picked\nonly the first 30 stories to keep the topic short enough for\nannotators. The reason for choosing only CNN as the source is that the\nstories from this source tend to be short and precise and do not tend\nto digress or drift too far away from the central theme. We believe\nmodeling such stories would be a useful first step before dealing\nwith more complex data sets.\nWe hired an annotator to create truth data. Annotation includes\ndefining the event membership for each story and also the\ndependencies. We supervised the annotator on a set of three topics that\nwe did our own annotations on and then asked her to annotate the\n28 topics from TDT2 and 25 topics from TDT3.\nIn identifying events in a topic, the annotator was asked to broadly\nfollow the TDT definition of an event, i.e., \u2018something that happens\nat a specific time and location\". The annotator was encouraged to\nmerge two events A and B into a single event C if any of the\nstories discusses both A and B. This is to satisfy our assumption that\neach story corresponds to a unique event. The annotator was also\nencouraged to avoid singleton events, events that contain a single\nnews story, if possible. We realized from our own experience that\npeople differ in their perception of an event especially when the\nnumber of stories in that event is small. As part of the guidelines,\nwe instructed the annotator to assign titles to all the events in each\ntopic. We believe that this would help make her understanding of\nthe events more concrete. We however, do not use or model these\ntitles in our algorithms.\nIn defining dependencies between events, we imposed no\nrestrictions on the graph structure. Each event could have single,\nmultiple or no parents. Further, the graph could have cycles or\norphannodes. The annotator was however instructed to assign a\ndependency from event A to event B if and only if the occurrence of B\nis \u2018either causally influenced by A or is closely related to A and\nfollows A in time\".\nFrom the annotated topics, we created a training set of 26 topics\nand a test set of 27 topics by merging the 28 topics from TDT2 and\n25 from TDT3 and splitting them randomly. Table 1 shows that the\ntraining and test sets have fairly similar statistics.\nFeature Training set Test set\nNum. topics 26 27\nAvg. Num. Stories/Topic 28.69 26.74\nAvg. Doc. Len. 64.60 64.04\nAvg. Num. Stories/Event 5.65 6.22\nAvg. Num. Events/Topic 5.07 4.29\nAvg. Num. Dependencies/Topic 3.07 2.92\nAvg. Num. Dependencies/Event 0.61 0.68\nAvg. Num. Days/Topic 30.65 34.48\nTable 1: Statistics of annotated data\n5. EVALUATION\nA system can generate some event model \u00c5\u00bc \u00b4\n\u00bc \u00bc\u00b5 using\ncertain algorithms, which is usually different from the truth model\n\u00c5 \u00b4 \u00b5 (we assume the annotator did not make any\nmistake). Comparing a system event model \u00c5\u00bc with the true model\n\u00c5 requires comparing the entire event models including their\ndependency structure. And different event granularities may bring\nhuge discrepancy between \u00c5\u00bc and \u00c5. This is certainly non-trivial\nas even testing whether two graphs are isomorphic has no known\npolynomial time solution. Hence instead of comparing the actual\nstructure we examine a pair of stories at a time and verify if the\nsystem and true labels agree on their event-memberships and\ndependencies. Specifically, we compare two kinds of story pairs:\n\u00af Cluster pairs ( \u00b4\u00c5\u00b5): These are the complete set of\nunordered pairs \u00b4\u00d7 \u00d7 \u00b5 of stories \u00d7 and \u00d7 that fall within the\nsame event given a model \u00c5. Formally,\n\u00b4\u00c5\u00b5 \u00b4\u00d7 \u00d7 \u00b5 \u00d7 \u00d7 \u00be \u00cb \u00b4\u00d7 \u00b5 \u00b4\u00d7 \u00b5 (5)\nwhere is the function in \u00c5 that maps stories to events as\ndefined in equation 4.\n\u00af Dependency pairs ( \u00b4\u00c5\u00b5): These are the set of all ordered\npairs of stories \u00b4\u00d7 \u00d7 \u00b5 such that there is a dependency from\nthe event of \u00d7 to the event of \u00d7 in the model \u00c5.\n\u00b4\u00c5\u00b5 \u00b4\u00d7 \u00d7 \u00b5 \u00b4 \u00b4\u00d7 \u00b5 \u00b4\u00d7 \u00b5\u00b5 \u00be (6)\nNote the story pair is ordered here, so \u00b4\u00d7 \u00d7 \u00b5 is not\nequivalent to \u00b4\u00d7 \u00d7 \u00b5. In our evaluation, a correct pair with wrong\n448\n(B->D)\nCluster pairs\n(A,C)\nDependency pairs\n(A->B)\n(C->B)\n(B->D)\nD,E\nD,E\n(D,E)\n(D,E)\n(A->C) (A->E)\n(B->C) (B->E)\n(B->E)\nCluster precision: 1/2\nCluster Recall: 1/2\nDependency Recall: 2/6\nDependency Precision: 2/4\n(A->D)\nTrue event model System event model\nA,B\nC\nA,C B\nCluster pairs\n(A,B)\nDependency pairs\nFigure 2: Evaluation measures\ndirection will be considered a mistake. As we mentioned\nearlier in section 3, ignoring the direction may make the\nproblem simpler, but we will lose the expressiveness of our\nrepresentation.\nGiven these two sets of story pairs corresponding to the true\nevent model \u00c5 and the system event model \u00c5\u00bc, we define recall\nand precision for each category as follows.\n\u00af Cluster Precision (CP): It is the probability that two\nrandomly selected stories \u00d7 and \u00d7 are in the same true-event\ngiven that they are in the same system event.\n\u00c8 \u00c8\u00b4 \u00b4\u00d7 \u00b5 \u00b4\u00d7 \u00b5\n\u00bc\u00b4\u00d7 \u00b5\n\u00bc\u00b4\u00d7 \u00b5\u00b5\n\u00b4\u00c5\u00b5 \u00b4\u00c5\u00bc\u00b5\n\u00b4\u00c5\u00bc\u00b5\n(7)\nwhere \u00bc is the story-event mapping function corresponding\nto the model \u00c5\u00bc.\n\u00af Cluster Recall(CR): It is the probability that two randomly\nselected stories \u00d7 and \u00d7 are in the same system-event given\nthat they are in the same true event.\n\u00ca \u00c8\u00b4\n\u00bc\u00b4\u00d7 \u00b5\n\u00bc\u00b4\u00d7 \u00b5 \u00b4\u00d7 \u00b5 \u00b4\u00d7 \u00b5\u00b5\n\u00b4\u00c5\u00b5 \u00b4\u00c5\u00bc\u00b5\n\u00b4\u00c5\u00b5\n(8)\n\u00af Dependency Precision(DP): It is the probability that there is\na dependency between the events of two randomly selected\nstories \u00d7 and \u00d7 in the true model \u00c5 given that they have a\ndependency in the system model \u00c5\u00bc. Note that the direction\nof dependency is important in comparison.\n\u00c8 \u00c8\u00b4\u00b4 \u00b4\u00d7 \u00b5 \u00b4\u00d7 \u00b5\u00b5 \u00be \u00b4\n\u00bc\u00b4\u00d7 \u00b5\n\u00bc\u00b4\u00d7 \u00b5\u00b5 \u00be\n\u00bc\u00b5\n\u00b4\u00c5\u00b5 \u00b4\u00c5\u00bc\u00b5\n\u00b4\u00c5\u00bc\u00b5\n(9)\n\u00af Dependency Recall(DR): It is the probability that there is\na dependency between the events of two randomly selected\nstories \u00d7 and \u00d7 in the system model \u00c5\u00bc given that they have\na dependency in the true model \u00c5. Again, the direction of\ndependency is taken into consideration.\n\u00ca \u00c8\u00b4\u00b4\n\u00bc\u00b4\u00d7 \u00b5\n\u00bc\u00b4\u00d7 \u00b5\u00b5 \u00be\n\u00bc \u00b4 \u00b4\u00d7 \u00b5 \u00b4\u00d7 \u00b5\u00b5 \u00be \u00b5\n\u00b4\u00c5\u00b5 \u00b4\u00c5\u00bc\u00b5\n\u00b4\u00c5\u00b5\n(10)\nThe measures are illustrated by an example in figure 2. We also\ncombine these measures using the well known F1-measure\ncommonly used in text classification and other research areas as shown\nbelow.\n\u00be \u00a2 \u00c8 \u00a2 \u00ca\n\u00c8 \u00b7 \u00ca\n\u00be \u00a2 \u00c8 \u00a2 \u00ca\n\u00c8 \u00b7 \u00ca\n\u00c2 \u00be \u00a2 \u00a2\n\u00b7\n(11)\nwhere and are the cluster and dependency F1-measures\nrespectively and \u00c2 is the Joint F1-measure (\u00c2 ) that we use to\nmeasure the overall performance.\n6. TECHNIQUES\nThe task of event modeling can be split into two parts: clustering\nthe stories into unique events in the topic and constructing\ndependencies among them. In the following subsections, we describe\ntechniques we developed for each of these sub-tasks.\n6.1 Clustering\nEach topic is composed of multiple events, so stories must be\nclustered into events before we can model the dependencies among\nthem. For simplicity, all stories in the same topic are assumed to\nbe available at one time, rather than coming in a text stream. This\ntask is similar to traditional clustering but features other than word\ndistributions may also be critical in our application.\nIn many text clustering systems, the similarity between two\nstories is the inner product of their tf-idf vectors, hence we use it as\none of our features. Stories in the same event tend to follow\ntemporal locality, so the time stamp of each story can be a useful feature.\nAdditionally, named-entities such as person and location names are\nanother obvious feature when forming events. Stories in the same\nevent tend to be related to the same person(s) and locations(s).\nIn this subsection, we present an agglomerative clustering\nalgorithm that combines all these features. In our experiments,\nhowever, we study the effect of each feature on the performance\nseparately using modified versions of this algorithm.\n6.1.1 Agglomerative clustering with\ntime decay (ACDT)\nWe initialize our events to singleton events (clusters), i.e., each\ncluster contains exactly one story. So the similarity between two\nevents, to start with, is exactly the similarity between the\ncorresponding stories. The similarity \u00db\u00d7\u00d9\u00d1\u00b4\u00d7\u00bd \u00d7\u00be\u00b5 between two\nstories \u00d7\u00bd and \u00d7\u00be is given by the following formula:\n\u00db\u00d7\u00d9\u00d1\u00b4\u00d7\u00bd \u00d7\u00be\u00b5 \u00bd \u00d3\u00d7\u00b4\u00d7\u00bd \u00d7\u00be\u00b5 \u00b7 \u00be\u00c4\u00d3 \u00b4\u00d7\u00bd \u00d7\u00be\u00b5 \u00b7 \u00bf\u00c8 \u00d6\u00b4\u00d7\u00bd \u00d7\u00be\u00b5\n(12)\nHere \u00bd, \u00be, \u00bf are the weights on different features. In this work,\nwe determined them empirically, but in the future, one can\nconsider more sophisticated learning techniques to determine them.\n\u00d3\u00d7\u00b4\u00d7\u00bd \u00d7\u00be\u00b5 is the cosine similarity of the term vectors. \u00c4\u00d3 \u00b4\u00d7\u00bd \u00d7\u00be\u00b5\nis 1 if there is some location that appears in both stories, otherwise\nit is 0. \u00c8 \u00d6\u00b4\u00d7\u00bd \u00d7\u00be\u00b5 is similarly defined for person name.\nWe use time decay when calculating similarity of story pairs,\ni.e., the larger time difference between two stories, the smaller their\nsimilarities. The time period of each topic differs a lot, from a few\ndays to a few months. So we normalize the time difference using\nthe whole duration of that topic. The time decay adjusted similarity\n449\n\u00d7 \u00d1\u00b4\u00d7\u00bd \u00d7\u00be\u00b5 is given by\n\u00d7 \u00d1\u00b4\u00d7\u00bd \u00d7\u00be\u00b5 \u00db\u00d7\u00d9\u00d1\u00b4\u00d7\u00bd \u00d7\u00be\u00b5\n\u00ab \u00d8\u00bd\u00a0\u00d8\u00be\n\u00cc (13)\nwhere \u00d8\u00bd and \u00d8\u00be are the time stamps for story 1 and 2 respectively.\nT is the time difference between the earliest and the latest story in\nthe given topic. \u00ab is the time decay factor.\nIn each iteration, we find the most similar event pair and merge\nthem. We have three different ways to compute the similarity\nbetween two events \u00d9 and \u00da:\n\u00af Average link: In this case the similarity is the average of the\nsimilarities of all pairs of stories between \u00d9 and \u00da as shown\nbelow:\n\u00d7 \u00d1\u00b4 \u00d9 \u00da \u00b5\n\u00c8\u00d7\u00d9\u00be \u00d9\n\u00c8\u00d7\u00da\u00be \u00da \u00d7 \u00d1\u00b4\u00d7\u00d9 \u00d7\u00da \u00b5\n\u00d9 \u00da\n(14)\n\u00af Complete link: The similarity between two events is given\nby the smallest of the pair-wise similarities.\n\u00d7 \u00d1\u00b4 \u00d9 \u00da \u00b5 \u00d1 \u00d2\n\u00d7\u00d9\u00be \u00d9 \u00d7\u00da\u00be \u00da\n\u00d7 \u00d1\u00b4\u00d7\u00d9 \u00d7\u00da \u00b5 (15)\n\u00af Single link: Here the similarity is given by the best similarity\nbetween all pairs of stories.\n\u00d7 \u00d1\u00b4 \u00d9 \u00da \u00b5 \u00d1 \u00dc\n\u00d7\u00d9\u00be \u00d9 \u00d7\u00da\u00be \u00da\n\u00d7 \u00d1\u00b4\u00d7\u00d9 \u00d7\u00da \u00b5 (16)\nThis process continues until the maximum similarity falls below\nthe threshold or the number of clusters is smaller than a given\nnumber.\n6.2 Dependency modeling\nCapturing dependencies is an extremely hard problem because\nit may require a \u2018deeper understanding\" of the events in question.\nA human annotator decides on dependencies not just based on the\ninformation in the events but also based on his/her vast repertoire\nof domain-knowledge and general understanding of how things\noperate in the world. For example, in Figure 1 a human knows \u2018Trial\nand indictment of Osama\" is influenced by \u2018Evidence gathered by\nCIA\" because he/she understands the process of law in general.\nWe believe a robust model should incorporate such domain\nknowledge in capturing dependencies, but in this work, as a first step, we\nwill rely on surface-features such as time-ordering of news stories\nand word distributions to model them. Our experiments in later\nsections demonstrate that such features are indeed useful in capturing\ndependencies to a large extent.\nIn this subsection, we describe the models we considered for\ncapturing dependencies. In the rest of the discussion in this subsection,\nwe assume that we are already given the mapping \u00bc \u00cb and\nwe focus only on modeling the edges \u00bc. First we define a couple\nof features that the following models will employ.\nFirst we define a 1-1 time-ordering function \u00d8 \u00cb \u00bd \u00a1 \u00a1 \u00a1 \u00d2\nthat sorts stories in ascending order by their time of publication.\nNow, the event-time-ordering function \u00d8 is defined as follows.\n\u00d8 \u00bd \u00a1 \u00a1 \u00a1 \u00d1 \u00d7 \u00d8\n\u00d9 \u00da \u00be \u00d8 \u00b4 \u00d9\u00b5 \u00d8 \u00b4 \u00da\u00b5 \u00b4\u00b5 \u00d1 \u00d2\n\u00d7\u00d9\u00be \u00d9\n\u00d8\u00b4\u00d7\u00d9\u00b5 \u00d1 \u00d2\n\u00d7\u00da\u00be \u00da\n\u00d8\u00b4\u00d7\u00da\u00b5\n(17)\nIn other words, \u00d8 time-orders events based on the time-ordering of\ntheir respective first stories.\nWe will also use average cosine similarity between two events as\na feature and it is defined as follows.\n\u00da \u00cb \u00d1\u00b4 \u00d9 \u00da \u00b5\n\u00c8\u00d7\u00d9\u00be \u00d9\n\u00c8\u00d7\u00da\u00be \u00da \u00d3\u00d7\u00b4\u00d7\u00d9 \u00d7\u00da \u00b5\n\u00d9 \u00da\n(18)\n6.2.1 Complete-Link model\nIn this model, we assume that there are dependencies between all\npairs of events. The direction of dependency is determined by the\ntime-ordering of the first stories in the respective events. Formally,\nthe system edges are defined as follows.\n\u00bc \u00b4 \u00d9 \u00da \u00b5 \u00d8 \u00b4 \u00d9\u00b5 \u00d8 \u00b4 \u00da \u00b5 (19)\nwhere \u00d8 is the event-time-ordering function. In other words, the\ndependency edge is directed from event \u00d9 to event \u00da , if the first\nstory in event \u00d9 is earlier than the first story in event \u00da . We point\nout that this is not to be confused with the complete-link algorithm\nin clustering. Although we use the same names, it will be clear\nfrom the context which one we refer to.\n6.2.2 Simple Thresholding\nThis model is an extension of the complete link model with an\nadditional constraint that there is a dependency between any two\nevents \u00d9 and \u00da only if the average cosine similarity between\nevent \u00d9 and event \u00da is greater than a threshold \u00cc. Formally,\n\u00bc \u00b4 \u00d9 \u00da\u00b5 \u00da \u00cb \u00d1\u00b4 \u00d9 \u00da \u00b5 \u00cc\n\u00d8 \u00b4 \u00d9\u00b5 \u00d8 \u00b4 \u00da \u00b5 (20)\n6.2.3 Nearest Parent Model\nIn this model, we assume that each event can have at most one\nparent. We define the set of dependencies as follows.\n\u00bc \u00b4 \u00d9 \u00da\u00b5 \u00da \u00cb \u00d1\u00b4 \u00d9 \u00da \u00b5 \u00cc\n\u00d8 \u00b4 \u00da\u00b5 \u00d8 \u00b4 \u00d9\u00b5 \u00b7 \u00bd (21)\nThus, for each event \u00da , the nearest parent model considers only\nthe event preceding it as defined by \u00d8 as a potential candidate. The\ncandidate is assigned as the parent only if the average similarity\nexceeds a pre-defined threshold \u00cc.\n6.2.4 Best Similarity Model\nThis model also assumes that each event can have at most one\nparent. An event \u00da is assigned a parent \u00d9 if and only if \u00d9 is\nthe most similar earlier event to \u00da and the similarity exceeds a\nthreshold \u00cc. Mathematically, this can be expressed as:\n\u00bc \u00b4 \u00d9 \u00da \u00b5 \u00da \u00cb \u00d1\u00b4 \u00d9 \u00da\u00b5 \u00cc\n\u00d9 \u00d6 \u00d1 \u00dc\n\u00db \u00d8 \u00b4 \u00db\u00b5 \u00d8 \u00b4 \u00da\u00b5\n\u00da \u00cb \u00d1\u00b4 \u00db \u00da \u00b5\n(22)\n6.2.5 Maximum Spanning Tree model\nIn this model, we first build a maximum spanning tree (MST)\nusing a greedy algorithm on the following fully connected weighted,\nundirected graph whose vertices are the events and whose edges\nare defined as follows:\n\u00b4 \u00d9 \u00da \u00b5 \u00db\u00b4 \u00d9 \u00da \u00b5 \u00da \u00cb \u00d1\u00b4 \u00d9 \u00da\u00b5 (23)\nLet \u00c5\u00cb\u00cc\u00b4 \u00b5 be the set of edges in the maximum spanning tree of\n\u00bc. Now our directed dependency edges are defined as follows.\n\u00bc \u00b4 \u00d9 \u00da \u00b5 \u00b4 \u00d9 \u00da \u00b5 \u00be \u00c5\u00cb\u00cc\u00b4 \u00b5 \u00d8 \u00b4 \u00d9\u00b5 \u00d8 \u00b4 \u00da\u00b5\n\u00da \u00cb \u00d1\u00b4 \u00d9 \u00da \u00b5 \u00cc (24)\n450\nThus in this model, we assign dependencies between the most\nsimilar events in the topic.\n7. EXPERIMENTS\nOur experiments consists of three parts. First we modeled only\nthe event clustering part (defining the mapping function \u00bc) using\nclustering algorithms described in section 6.1. Then we modeled\nonly the dependencies by providing to the system the true clusters\nand running only the dependency algorithms of section 6.2. Finally,\nwe experimented with combinations of clustering and dependency\nalgorithms to produce the complete event model. This way of\nexperimentation allows us to compare the performance of our\nalgorithms in isolation and in association with other components. The\nfollowing subsections present the three parts of our\nexperimentation.\n7.1 Clustering\nWe have tried several variations of the \u00cc algorithm to study\nthe effects of various features on the clustering performance. All\nthe parameters are learned by tuning on the training set. We also\ntested the algorithms on the test set with parameters fixed at their\noptimal values learned from training. We used agglomerative\nclusModel best T CP CR CF P-value\ncos+1-lnk 0.15 0.41 0.56\n0.43cos+all-lnk 0.00 0.40 0.62\n0.45cos+Loc+avg-lnk 0.07 0.37 0.74\n0.45cos+Per+avg-lnk 0.07 0.39 0.70\n0.46cos+TD+avg-lnk 0.04 0.45 0.70 0.53 2.9e-4*\ncos+N(T)+avg-lnk - 0.41 0.62 0.48 7.5e-2\ncos+N(T)+T+avg-lnk 0.03 0.42 0.62 0.49 2.4e-2*\ncos+TD+N(T)+avg-lnk - 0.44 0.66 0.52 7.0e-3*\ncos+TD+N(T)+T+avg-lnk 0.03 0.47 0.64 0.53 1.1e-3*\nBaseline(cos+avg-lnk) 0.05 0.39 0.67\n0.46Table 2: Comparison of agglomerative clustering algorithms\n(training set)\ntering based on only cosine similarity as our clustering baseline.\nThe results on the training and test sets are in Table 2 and 3\nrespectively. We use the Cluster F1-measure (CF) averaged over all topics\nas our evaluation criterion.\nModel CP CR CF P-value\ncos+1-lnk 0.43 0.49\n0.39cos+all-lnk 0.43 0.62\n0.47cos+Loc+avg-lnk 0.37 0.73\n0.45cos+Per+avg-lnk 0.44 0.62\n0.45cos+TD+avg-lnk 0.48 0.70 0.54 0.014*\ncos+N(T)+avg-lnk 0.41 0.71 0.51 0.31\ncos+N(T)+T+avg-lnk 0.43 0.69* 0.52 0.14\ncos+TD+N(T)+avg-lnk 0.43 0.76 0.54 0.025*\ncos+TD+N(T)+T+avg-lnk 0.47 0.69 0.54 0.0095*\nBaseline(cos+avg-lnk) 0.44 0.67\n0.50Table 3: Comparison of agglomerative clustering algorithms\n(test set)\nP-value marked with a \u00a3 means that it is a statistically significant\nimprovement over the baseline (95% confidence level, one tailed\nT-test). The methods shown in table 2 and 3 are:\n\u00af Baseline: tf-idf vector weight, cosine similarity, average link\nin clustering. In equation 12, \u00bd \u00bd, \u00be \u00bf \u00bc. And\n\u00ab \u00bc in equation 13. This F-value is the maximum obtained\nby tuning the threshold.\n\u00af cos+1-lnk: Single link comparison (see equation 16) is used\nwhere similarity of two clusters is the maximum of all story\npairs, other configurations are the same as the baseline run.\n\u00af cos+all-lnk: Complete link algorithm of equation 15 is used.\nSimilar to single link but it takes the minimum similarity of\nall story pairs.\n\u00af cos+Loc+avg-lnk: Location names are used when\ncalculating similarity. \u00be \u00bc \u00bc in equation 12. All algorithms\nstarting from this one use average link (equation 14), since\nsingle link and complete link do not show any improvement\nof performance.\n\u00af cos+Per+avg-lnk: \u00bf \u00bc \u00bc in equation 12, i.e., we put\nsome weight on person names in the similarity.\n\u00af cos+TD+avg-lnk: Time Decay coefficient \u00ab \u00bd in equation\n13, which means the similarity between two stories will be\ndecayed to \u00bd if they are at different ends of the topic.\n\u00af cos+N(T)+avg-lnk: Use the number of true events to control\nthe agglomerative clustering algorithm. When the number\nof clusters is fewer than that of truth events, stop merging\nclusters.\n\u00af cos+N(T)+T+avg-lnk: similar to N(T) but also stop\nagglomeration if the maximal similarity is below the threshold \u00cc.\n\u00af cos+TD:+N(T)+avg-lnk: similar to N(T) but the similarities\nare decayed, \u00ab \u00bd in equation 13.\n\u00af cos+TD+N(T)+T+avg-lnk: similar to TD+N(Truth) but\ncalculation halts when the maximal similarity is smaller than\nthe threshold \u00cc.\nOur experiments demonstrate that single link and complete link\nsimilarities perform worse than average link, which is reasonable\nsince average link is less sensitive to one or two story pairs. We\nhad expected locations and person names to improve the result, but\nit is not the case. Analysis of topics shows that many on-topic\nstories share the same locations or persons irrespective of the event\nthey belong to, so these features may be more useful in identifying\ntopics rather than events. Time decay is successful because events\nare temporally localized, i.e., stories discussing the same event tend\nto be adjacent to each other in terms of time. Also we noticed\nthat providing the number of true events improves the performance\nsince it guides the clustering algorithm to get correct granularity.\nHowever, for most applications, it is not available. We used it only\nas a cheat experiment for comparison with other algorithms. On\nthe whole, time decay proved to the most powerful feature besides\ncosine similarity on both training and test sets.\n7.2 Dependencies\nIn this subsection, our goal is to model only dependencies. We\nuse the true mapping function and by implication the true events\n\u00ce . We build our dependency structure \u00bc using all the five\nmodels described in section 6.2. We first train our models on the 26\ntraining topics. Training involves learning the best threshold \u00cc\nfor each of the models. We then test the performances of all the\ntrained models on the 27 test topics. We evaluate our performance\n451\nusing the average values of Dependency Precision (DP),\nDependency Recall (DR) and Dependency F-measure (DF). We consider\nthe complete-link model to be our baseline since for each event, it\ntrivially considers all earlier events to be parents.\nTable 4 lists the results on the training set. We see that while all\nthe algorithms except MST outperform the baseline complete-link\nalgorithm , the nearest Parent algorithm is statistically significant\nfrom the baseline in terms of its DF-value using a one-tailed paired\nT-test at 95% confidence level.\nModel best \u00cc DP DR DF P-value\nNearest Parent 0.025 0.55 0.62 0.56 0.04*\nBest Similarity 0.02 0.51 0.62 0.53 0.24\nMST 0.0 0.46 0.58\n0.48Simple Thresh. 0.045 0.45 0.76 0.52 0.14\nComplete-link - 0.36 0.93\n0.48Table 4: Results on the training set: Best \u00cc is the optimal value\nof the threshold \u00cc. * indicates the corresponding model is\nstatistically significant compared to the baseline using a one-tailed,\npaired T-test at 95% confidence level.\nIn table 5 we present the comparison of the models on the test\nset. Here, we do not use any tuning but set the threshold to the\ncorresponding optimal values learned from the training set. The\nresults throw some surprises: The nearest parent model, which was\nsignificantly better than the baseline on training set, turns out to be\nworse than the baseline on the test set. However all the other\nmodels are better than the baseline including the best similarity which\nis statistically significant. Notice that all the models that perform\nbetter than the baseline in terms of DF, actually sacrifice their\nrecall performance compared to the baseline, but improve on their\nprecision substantially thereby improving their performance on the\nDF-measure.\nWe notice that both simple-thresholding and best similarity are\nbetter than the baseline on both training and test sets although the\nimprovement is not significant. On the whole, we observe that the\nsurface-level features we used capture the dependencies to a\nreasonable level achieving a best value of 0.72 DF on the test set.\nAlthough there is a lot of room for improvement, we believe this is\na good first step.\nModel DP DR DF P-value\nNearest Parent 0.61 0.60\n0.60Best Similarity 0.71 0.74 0.72 0.04*\nMST 0.70 0.68 0.69 0.22\nSimple Thresh. 0.57 0.75 0.64 0.24\nBaseline (Complete-link) 0.50 0.94\n0.63Table 5: Results on the test set\n7.3 Combining Clustering and Dependencies\nNow that we have studied the clustering and dependency\nalgorithms in isolation, we combine the best performing algorithms and\nbuild the entire event model. Since none of the dependency\nalgorithms has been shown to be consistently and significantly better\nthan the others, we use all of them in our experimentation. From\nthe clustering techniques, we choose the best performing Cos+TD.\nAs a baseline, we use a combination of the baselines in each\ncomponents, i.e., cos for clustering and complete-link for dependencies.\nNote that we need to retrain all the algorithms on the training\nset because our objective function to optimize is now JF, the joint\nF-measure. For each algorithm, we need to optimize both the\nclustering threshold and the dependency threshold. We did this\nempirically on the training set and the optimal values are listed in table\n6.\nThe results on the training set, also presented in table 6, indicate\nthat cos+TD+Simple-Thresholding is significantly better than the\nbaseline in terms of the joint F-value JF, using a one-tailed paired\nTtest at 95% confidence level. On the whole, we notice that while the\nclustering performance is comparable to the experiments in section\n7.1, the overall performance is undermined by the low dependency\nperformance. Unlike our experiments in section 7.2 where we had\nprovided the true clusters to the system, in this case, the system\nhas to deal with deterioration in the cluster quality. Hence the\nperformance of the dependency algorithms has suffered substantially\nthereby lowering the overall performance.\nThe results on the test set present a very similar story as shown\nin table 7. We also notice a fair amount of consistency in the\nperformance of the combination algorithms. cos+TD+Simple-Thresholding\noutperforms the baseline significantly. The test set results also point\nto the fact that the clustering component remains a bottleneck in\nachieving an overall good performance.\n8. DISCUSSION AND CONCLUSIONS\nIn this paper, we have presented a new perspective of modeling\nnews topics. Contrary to the TDT view of topics as flat\ncollection of news stories, we view a news topic as a relational structure\nof events interconnected by dependencies. In this paper, we also\nproposed a few approaches for both clustering stories into events\nand constructing dependencies among them. We developed a\ntimedecay based clustering approach that takes advantage of\ntemporallocalization of news stories on the same event and showed that it\nperforms significantly better than the baseline approach based on\ncosine similarity. Our experiments also show that we can do fairly\nwell on dependencies using only surface-features such as\ncosinesimilarity and time-stamps of news stories as long as true events\nare provided to the system. However, the performance deteriorates\nrapidly if the system has to discover the events by itself. Despite\nthat discouraging result, we have shown that our combined\nalgorithms perform significantly better than the baselines.\nOur results indicate modeling dependencies can be a very hard\nproblem especially when the clustering performance is below ideal\nlevel. Errors in clustering have a magnifying effect on errors in\ndependencies as we have seen in our experiments. Hence, we should\nfocus not only on improving dependencies but also on clustering at\nthe same time.\nAs part of our future work, we plan to investigate further into\nthe data and discover new features that influence clustering as well\nas dependencies. And for modeling dependencies, a probabilistic\nframework should be a better choice since there is no definite\nanswer of yes/no for the causal relations among some events. We also\nhope to devise an iterative algorithm which can improve clustering\nand dependency performance alternately as suggested by one of\nthe reviewers. We also hope to expand our labeled corpus further\nto include more diverse news sources and larger and more complex\nevent structures.\nAcknowledgments\nWe would like to thank the three anonymous reviewers for their\nvaluable comments. This work was supported in part by the Center\n452\nModel Cluster T Dep. T CP CR CF DP DR DF JF P-value\ncos+TD+Nearest-Parent 0.055 0.02 0.51 0.53 0.49 0.21 0.19 0.19\n0.27cos+TD+Best-Similarity 0.04 0.02 0.45 0.70 0.53 0.21 0.33 0.23\n0.32cos+TD+MST 0.04 0.00 0.45 0.70 0.53 0.22 0.35 0.25\n0.33cos+TD+Simple-Thresholding 0.065 0.02 0.56 0.47 0.48 0.23 0.61 0.32 0.38 0.0004*\nBaseline (cos+Complete-link) 0.10 - 0.58 0.31 0.38 0.20 0.67 0.30\n0.33Table 6: Combined results on the training set\nModel CP CR CF DP DR DF JF P-value\ncos+TD+Nearest Parent 0.57 0.50 0.50 0.27 0.19 0.21\n0.30cos+TD+Best Similarity 0.48 0.70 0.54 0.31 0.27 0.26\n0.35cos+TD+MST 0.48 0.70 0.54 0.31 0.30 0.28\n0.37cos+TD+Simple Thresholding 0.60 0.39 0.44 0.32 0.66 0.42 0.43 0.0081*\nBaseline (cos+Complete-link) 0.66 0.27 0.36 0.30 0.72 0.43\n0.39Table 7: Combined results on the test set\nfor Intelligent Information Retrieval and in part by\nSPAWARSYSCENSD grant number N66001-02-1-8903. Any opinions, findings and\nconclusions or recommendations expressed in this material are the\nauthors\" and do not necessarily reflect those of the sponsor.\n9. REFERENCES\n[1] J. Allan, J. Carbonell, G. Doddington, J. Yamron, and\nY. Yang. Topic detection and tracking pilot study: Final\nreport. In Proceedings of the DARPA Broadcast News\nTranscription and Understanding Workshop, pages 194-218,\n1998.\n[2] J. Allan, A. Feng, and A. Bolivar. Flexible intrinsic\nevaluation of hierarchical clustering for tdt. volume In the\nProc. of the ACM Twelfth International Conference on\nInformation and Knowledge Management, pages 263-270,\nNov 2003.\n[3] James Allan, editor. Topic Detection and Tracking:Event\nbased Information Organization. Kluwer Academic\nPublishers, 2000.\n[4] James Allan, Rahul Gupta, and Vikas Khandelwal. Temporal\nsummaries of new topics. In Proceedings of the 24th annual\ninternational ACM SIGIR conference on Research and\ndevelopment in information retrieval, pages 10-18. ACM\nPress, 2001.\n[5] Regina Barzilay and Lillian Lee. Catching the drift:\nProbabilistic content models, with applications to generation\nand summarization. In Proceedings of Human Language\nTechnology Conference and North American Chapter of the\nAssociation for Computational Linguistics(HLT-NAACL),\npages 113-120, 2004.\n[6] D. Lawrie and W. B. Croft. Discovering and comparing topic\nhierarchies. In Proceedings of RIAO 2000 Conference, pages\n314-330, 1999.\n[7] David D. Lewis and Kimberly A. Knowles. Threading\nelectronic mail: a preliminary study. Inf. Process. Manage.,\n33(2):209-217, 1997.\n[8] Juha Makkonen. Investigations on event evolution in tdt. In\nProceedings of HLT-NAACL 2003 Student Workshop, pages\n43-48, 2004.\n[9] Aixin Sun and Ee-Peng Lim. Hierarchical text classification\nand evaluation. 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{"name": "train_H-85", "title": "Learning User Interaction Models for Predicting Web Search Result Preferences", "abstract": "Evaluating user preferences of web search results is crucial for search engine development, deployment, and maintenance. We present a real-world study of modeling the behavior of web search users to predict web search result preferences. Accurate modeling and interpretation of user behavior has important applications to ranking, click spam detection, web search personalization, and other tasks. Our key insight to improving robustness of interpreting implicit feedback is to model query-dependent deviations from the expected noisy user behavior. We show that our model of clickthrough interpretation improves prediction accuracy over state-of-the-art clickthrough methods. We generalize our approach to model user behavior beyond clickthrough, which results in higher preference prediction accuracy than models based on clickthrough information alone. We report results of a large-scale experimental evaluation that show substantial improvements over published implicit feedback interpretation methods.", "fulltext": "1. INTRODUCTION\nRelevance measurement is crucial to web search and to\ninformation retrieval in general. Traditionally, search relevance is\nmeasured by using human assessors to judge the relevance of\nquery-document pairs. However, explicit human ratings are\nexpensive and difficult to obtain. At the same time, millions of\npeople interact daily with web search engines, providing valuable\nimplicit feedback through their interactions with the search\nresults. If we could turn these interactions into relevance\njudgments, we could obtain large amounts of data for evaluating,\nmaintaining, and improving information retrieval systems.\nRecently, automatic or implicit relevance feedback has\ndeveloped into an active area of research in the information\nretrieval community, at least in part due to an increase in\navailable resources and to the rising popularity of web search.\nHowever, most traditional IR work was performed over\ncontrolled test collections and carefully-selected query sets and\ntasks. Therefore, it is not clear whether these techniques will\nwork for general real-world web search. A significant distinction\nis that web search is not controlled. Individual users may behave\nirrationally or maliciously, or may not even be real users; all of\nthis affects the data that can be gathered. But the amount of the\nuser interaction data is orders of magnitude larger than anything\navailable in a non-web-search setting. By using the aggregated\nbehavior of large numbers of users (and not treating each user as\nan individual expert) we can correct for the noise inherent in\nindividual interactions, and generate relevance judgments that\nare more accurate than techniques not specifically designed for\nthe web search setting.\nFurthermore, observations and insights obtained in laboratory\nsettings do not necessarily translate to real world usage. Hence,\nit is preferable to automatically induce feedback interpretation\nstrategies from large amounts of user interactions. Automatically\nlearning to interpret user behavior would allow systems to adapt\nto changing conditions, changing user behavior patterns, and\ndifferent search settings. We present techniques to automatically\ninterpret the collective behavior of users interacting with a web\nsearch engine to predict user preferences for search results. Our\ncontributions include:\n\u2022 A distributional model of user behavior, robust to noise\nwithin individual user sessions, that can recover relevance\npreferences from user interactions (Section 3).\n\u2022 Extensions of existing clickthrough strategies to include\nricher browsing and interaction features (Section 4).\n\u2022 A thorough evaluation of our user behavior models, as well\nas of previously published state-of-the-art techniques, over\na large set of web search sessions (Sections 5 and 6).\nWe discuss our results and outline future directions and\nvarious applications of this work in Section 7, which concludes\nthe paper.\n2. BACKGROUND AND RELATED WORK\nRanking search results is a fundamental problem in\ninformation retrieval. The most common approaches in the\ncontext of the web use both the similarity of the query to the\npage content, and the overall quality of a page [3, 20]. A\nstate-ofthe-art search engine may use hundreds of features to describe a\ncandidate page, employing sophisticated algorithms to rank\npages based on these features. Current search engines are\ncommonly tuned on human relevance judgments. Human\nannotators rate a set of pages for a query according to perceived\nrelevance, creating the gold standard against which different\nranking algorithms can be evaluated. Reducing the dependence on\nexplicit human judgments by using implicit relevance feedback\nhas been an active topic of research.\nSeveral research groups have evaluated the relationship\nbetween implicit measures and user interest. In these studies,\nboth reading time and explicit ratings of interest are collected.\nMorita and Shinoda [14] studied the amount of time that users\nspent reading Usenet news articles and found that reading time\ncould predict a user\"s interest levels. Konstan et al. [13] showed\nthat reading time was a strong predictor of user interest in their\nGroupLens system. Oard and Kim [15] studied whether implicit\nfeedback could substitute for explicit ratings in recommender\nsystems. More recently, Oard and Kim [16] presented a\nframework for characterizing observable user behaviors using two\ndimensions-the underlying purpose of the observed behavior and\nthe scope of the item being acted upon.\nGoecks and Shavlik [8] approximated human labels by\ncollecting a set of page activity measures while users browsed the\nWorld Wide Web. The authors hypothesized correlations between\na high degree of page activity and a user\"s interest. While the\nresults were promising, the sample size was small and the\nimplicit measures were not tested against explicit judgments of\nuser interest. Claypool et al. [6] studied how several implicit\nmeasures related to the interests of the user. They developed a\ncustom browser called the Curious Browser to gather data, in a\ncomputer lab, about implicit interest indicators and to probe for\nexplicit judgments of Web pages visited. Claypool et al. found\nthat the time spent on a page, the amount of scrolling on a page,\nand the combination of time and scrolling have a strong positive\nrelationship with explicit interest, while individual scrolling\nmethods and mouse-clicks were not correlated with explicit\ninterest. Fox et al. [7] explored the relationship between implicit\nand explicit measures in Web search. They built an instrumented\nbrowser to collect data and then developed Bayesian models to\nrelate implicit measures and explicit relevance judgments for both\nindividual queries and search sessions. They found that\nclickthrough was the most important individual variable but that\npredictive accuracy could be improved by using additional\nvariables, notably dwell time on a page.\nJoachims [9] developed valuable insights into the collection of\nimplicit measures, introducing a technique based entirely on\nclickthrough data to learn ranking functions. More recently,\nJoachims et al. [10] presented an empirical evaluation of\ninterpreting clickthrough evidence. By performing eye tracking\nstudies and correlating predictions of their strategies with explicit\nratings, the authors showed that it is possible to accurately\ninterpret clickthrough events in a controlled, laboratory setting. A\nmore comprehensive overview of studies of implicit measures is\ndescribed in Kelly and Teevan [12].\nUnfortunately, the extent to which existing research applies to\nreal-world web search is unclear. In this paper, we build on\nprevious research to develop robust user behavior interpretation\nmodels for the real web search setting.\n3. LEARNING USER BEHAVIOR MODELS\nAs we noted earlier, real web search user behavior can be\nnoisy in the sense that user behaviors are only probabilistically\nrelated to explicit relevance judgments and preferences. Hence,\ninstead of treating each user as a reliable expert, we aggregate\ninformation from many unreliable user search session traces. Our\nmain approach is to model user web search behavior as if it were\ngenerated by two components: a relevance component -\nqueryspecific behavior influenced by the apparent result relevance, and\na background component - users clicking indiscriminately.\nOur general idea is to model the deviations from the expected\nuser behavior. Hence, in addition to basic features, which we\nwill describe in detail in Section 3.2, we compute derived\nfeatures that measure the deviation of the observed feature value\nfor a given search result from the expected values for a result,\nwith no query-dependent information. We motivate our\nintuitions with a particularly important behavior feature, result\nclickthrough, analyzed next, and then introduce our general\nmodel of user behavior that incorporates other user actions\n(Section 3.2).\n3.1 A Case Study in Click Distributions\nAs we discussed, we aggregate statistics across many user\nsessions. A click on a result may mean that some user found the\nresult summary promising; it could also be caused by people\nclicking indiscriminately. In general, individual user behavior,\nclickthrough and otherwise, is noisy, and cannot be relied upon\nfor accurate relevance judgments. The data set is described in\nmore detail in Section 5.2. For the present it suffices to note that\nwe focus on a random sample of 3,500 queries that were\nrandomly sampled from query logs. For these queries we\naggregate click data over more than 120,000 searches performed\nover a three week period. We also have explicit relevance\njudgments for the top 10 results for each query.\nFigure 3.1 shows the relative clickthrough frequency as a\nfunction of result position. The aggregated click frequency at\nresult position p is calculated by first computing the frequency of\na click at p for each query (i.e., approximating the probability\nthat a randomly chosen click for that query would land on\nposition p). These frequencies are then averaged across queries\nand normalized so that relative frequency of a click at the top\nposition is 1. The resulting distribution agrees with previous\nobservations that users click more often on top-ranked results.\nThis reflects the fact that search engines do a reasonable job of\nranking results as well as biases to click top results and\nnoisewe attempt to separate these components in the analysis that\nfollows.\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n1 3 5 7 9 11 13 15 17 19 21 23 25 27 29\nresult position\nRelativeClickFrequency\nFigure 3.1: Relative click frequency for top 30 result\npositions over 3,500 queries and 120,000 searches.\nFirst we consider the distribution of clicks for the relevant\ndocuments for these queries. Figure 3.2 reports the aggregated\nclick distribution for queries with varying Position of Top\nRelevant document (PTR). While there are many clicks above\nthe first relevant document for each distribution, there are\nclearly peaks in click frequency for the first relevant result.\nFor example, for queries with top relevant result in position 2,\nthe relative click frequency at that position (second bar) is higher\nthan the click frequency at other positions for these queries.\nNevertheless, many users still click on the non-relevant results\nin position 1 for such queries. This shows a stronger property of\nthe bias in the click distribution towards top results - users click\nmore often on results that are ranked higher, even when they are\nnot relevant.\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n1 2 3 5 10\nresult position\nrelativeclickfrequency\nPTR=1\nPTR=2\nPTR=3\nPTR=5\nPTR=10\nBackground\nFigure 3.2: Relative click frequency for queries with varying\nPTR (Position of Top Relevant document).\n-0.06\n-0.04\n-0.02\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n1 2 3 5 10\nresult position\ncorrectedrelativeclickfrequency\nPTR=1\nPTR=2\nPTR=3\nPTR=5\nPTR=10\nFigure 3.3: Relative corrected click frequency for relevant\ndocuments with varying PTR (Position of Top Relevant).\nIf we subtract the background distribution of Figure 3.1 from the\nmixed distribution of Figure 3.2, we obtain the distribution in\nFigure 3.3, where the remaining click frequency distribution can\nbe interpreted as the relevance component of the results. Note that\nthe corrected click distribution correlates closely with actual\nresult relevance as explicitly rated by human judges.\n3.2 Robust User Behavior Model\nClicks on search results comprise only a small fraction of the\npost-search activities typically performed by users. We now\nintroduce our techniques for going beyond the clickthrough\nstatistics and explicitly modeling post-search user behavior.\nAlthough clickthrough distributions are heavily biased towards\ntop results, we have just shown how the \u2018relevance-driven\" click\ndistribution can be recovered by correcting for the prior,\nbackground distribution. We conjecture that other aspects of user\nbehavior (e.g., page dwell time) are similarly distorted. Our\ngeneral model includes two feature types for describing user\nbehavior: direct and deviational where the former is the directly\nmeasured values, and latter is deviation from the expected values\nestimated from the overall (query-independent) distributions for\nthe corresponding directly observed features.\nMore formally, we postulate that the observed value o of a\nfeature f for a query q and result r can be expressed as a mixture\nof two components:\n),,()(),,( frqrelfCfrqo += (1)\nwhere )( fC is the prior background distribution for values of f\naggregated across all queries, and rel(q,r,f) is the component of\nthe behavior influenced by the relevance of the result r. As\nillustrated above with the clickthrough feature, if we subtract the\nbackground distribution (i.e., the expected clickthrough for a\nresult at a given position) from the observed clickthrough\nfrequency at a given position, we can approximate the relevance\ncomponent of the clickthrough value1\n. In order to reduce the\neffect of individual user variations in behavior, we average\nobserved feature values across all users and search sessions for\neach query-URL pair. This aggregation gives additional\nrobustness of not relying on individual noisy user interactions.\nIn summary, the user behavior for a query-URL pair is\nrepresented by a feature vector that includes both the directly\nobserved features and the derived, corrected feature values.\nWe now describe the actual features we use to represent user\nbehavior.\n3.3 Features for Representing User Behavior\nOur goal is to devise a sufficiently rich set of features that\nallow us to characterize when a user will be satisfied with a web\nsearch result. Once the user has submitted a query, they perform\nmany different actions (reading snippets, clicking results,\nnavigating, refining their query) which we capture and\nsummarize. This information was obtained via opt-in client-side\ninstrumentation from users of a major web search engine.\nThis rich representation of user behavior is similar in many\nrespects to the recent work by Fox et al. [7]. An important\ndifference is that many of our features are (by design) query\nspecific whereas theirs was (by design) a general,\nqueryindependent model of user behavior. Furthermore, we include\nderived, distributional features computed as described above.\nThe features we use to represent user search interactions are\nsummarized in Table 3.1. For clarity, we organize the features\ninto the groups Query-text, Clickthrough, and Browsing.\nQuery-text features: Users decide which results to examine in\nmore detail by looking at the result title, URL, and summary - in\nsome cases, looking at the original document is not even\nnecessary. To model this aspect of user experience we defined\nfeatures to characterize the nature of the query and its relation to\nthe snippet text. These include features such as overlap between\nthe words in title and in query (TitleOverlap), the fraction of\nwords shared by the query and the result summary\n(SummaryOverlap), etc.\nBrowsing features: Simple aspects of the user web page\ninteractions can be captured and quantified. These features are\nused to characterize interactions with pages beyond the results\npage. For example, we compute how long users dwell on a page\n(TimeOnPage) or domain (TimeOnDomain), and the deviation\nof dwell time from expected page dwell time for a query. These\nfeatures allows us to model intra-query diversity of page\nbrowsing behavior (e.g., navigational queries, on average, are\nlikely to have shorter page dwell time than transactional or\ninformational queries). We include both the direct features and\nthe derived features described above.\nClickthrough features: Clicks are a special case of user\ninteraction with the search engine. We include all the features\nnecessary to learn the clickthrough-based strategies described\nin Sections 4.1 and 4.4. For example, for a query-URL pair we\nprovide the number of clicks for the result (ClickFrequency), as\n1\nOf course, this is just a rough estimate, as the observed\nbackground distribution also includes the relevance\ncomponent.\nwell as whether there was a click on result below or above the\ncurrent URL (IsClickBelow, IsClickAbove). The derived feature\nvalues such as ClickRelativeFrequency and ClickDeviation are\ncomputed as described in Equation 1.\nQuery-text features\nTitleOverlap Fraction of shared words between query and title\nSummaryOverlap Fraction of shared words between query and summary\nQueryURLOverlap Fraction of shared words between query and URL\nQueryDomainOverlap Fraction of shared words between query and domain\nQueryLength Number of tokens in query\nQueryNextOverlap Average fraction of words shared with next query\nBrowsing features\nTimeOnPage Page dwell time\nCumulativeTimeOnPage Cumulative time for all subsequent pages after search\nTimeOnDomain Cumulative dwell time for this domain\nTimeOnShortUrl Cumulative time on URL prefix, dropping parameters\nIsFollowedLink 1 if followed link to result, 0 otherwise\nIsExactUrlMatch 0 if aggressive normalization used, 1 otherwise\nIsRedirected 1 if initial URL same as final URL, 0 otherwise\nIsPathFromSearch 1 if only followed links after query, 0 otherwise\nClicksFromSearch Number of hops to reach page from query\nAverageDwellTime Average time on page for this query\nDwellTimeDeviation Deviation from overall average dwell time on page\nCumulativeDeviation Deviation from average cumulative time on page\nDomainDeviation Deviation from average time on domain\nShortURLDeviation Deviation from average time on short URL\nClickthrough features\nPosition Position of the URL in Current ranking\nClickFrequency Number of clicks for this query, URL pair\nClickRelativeFrequency Relative frequency of a click for this query and URL\nClickDeviation Deviation from expected click frequency\nIsNextClicked 1 if there is a click on next position, 0 otherwise\nIsPreviousClicked 1 if there is a click on previous position, 0 otherwise\nIsClickAbove 1 if there is a click above, 0 otherwise\nIsClickBelow 1 if there is click below, 0 otherwise\nTable 3.1: Features used to represent post-search interactions\nfor a given query and search result URL\n3.4 Learning a Predictive Behavior Model\nHaving described our features, we now turn to the actual\nmethod of mapping the features to user preferences. We attempt\nto learn a general implicit feedback interpretation strategy\nautomatically instead of relying on heuristics or insights. We\nconsider this approach to be preferable to heuristic strategies,\nbecause we can always mine more data instead of relying (only)\non our intuition and limited laboratory evidence. Our general\napproach is to train a classifier to induce weights for the user\nbehavior features, and consequently derive a predictive model of\nuser preferences. The training is done by comparing a wide range\nof implicit behavior measures with explicit user judgments for a\nset of queries.\nFor this, we use a large random sample of queries in the search\nquery log of a popular web search engine, the sets of results\n(identified by URLs) returned for each of the queries, and any\nexplicit relevance judgments available for each query/result pair.\nWe can then analyze the user behavior for all the instances where\nthese queries were submitted to the search engine.\nTo learn the mapping from features to relevance preferences,\nwe use a scalable implementation of neural networks, RankNet\n[4], capable of learning to rank a set of given items. More\nspecifically, for each judged query we check if a result link has\nbeen judged. If so, the label is assigned to the query/URL pair and\nto the corresponding feature vector for that search result. These\nvectors of feature values corresponding to URLs judged relevant\nor non-relevant by human annotators become our training set.\nRankNet has demonstrated excellent performance in learning to\nrank objects in a supervised setting, hence we use RankNet for\nour experiments.\n4. PREDICTING USER PREFERENCES\nIn our experiments, we explore several models for predicting\nuser preferences. These models range from using no implicit\nuser feedback to using all available implicit user feedback.\nRanking search results to predict user preferences is a\nfundamental problem in information retrieval. Most traditional\nIR and web search approaches use a combination of page and\nlink features to rank search results, and a representative\nstate-ofthe-art ranking system will be used as our baseline ranker\n(Section 4.1). At the same time, user interactions with a search\nengine provide a wealth of information. A commonly considered\ntype of interaction is user clicks on search results. Previous work\n[9], as described above, also examined which results were\nskipped (e.g., \u2018skip above\" and \u2018skip next\") and other related\nstrategies to induce preference judgments from the users\"\nskipping over results and not clicking on following results. We\nhave also added refinements of these strategies to take into\naccount the variability observed in realistic web scenarios.. We\ndescribe these strategies in Section 4.2.\nAs clickthroughs are just one aspect of user interaction, we\nextend the relevance estimation by introducing a machine\nlearning model that incorporates clicks as well as other aspects\nof user behavior, such as follow-up queries and page dwell time\n(Section 4.3). We conclude this section by briefly describing our\nbaseline - a state-of-the-art ranking algorithm used by an\noperational web search engine.\n4.1 Baseline Model\nA key question is whether browsing behavior can provide\ninformation absent from existing explicit judgments used to train\nan existing ranker. For our baseline system we use a\nstate-of-theart page ranking system currently used by a major web search\nengine. Hence, we will call this system Current for the\nsubsequent discussion. While the specific algorithms used by the\nsearch engine are beyond the scope of this paper, the algorithm\nranks results based on hundreds of features such as query to\ndocument similarity, query to anchor text similarity, and\nintrinsic page quality. The Current web search engine rankings\nprovide a strong system for comparison and experiments of the\nnext two sections.\n4.2 Clickthrough Model\nIf we assume that every user click was motivated by a rational\nprocess that selected the most promising result summary, we can\nthen interpret each click as described in Joachims et al.[10]. By\nstudying eye tracking and comparing clicks with explicit\njudgments, they identified a few basic strategies. We discuss the\ntwo strategies that performed best in their experiments, Skip\nAbove and Skip Next.\nStrategy SA (Skip Above): For a set of results for a query\nand a clicked result at position p, all unclicked results\nranked above p are predicted to be less relevant than the\nresult at p.\nIn addition to information about results above the clicked\nresult, we also have information about the result immediately\nfollowing the clicked one. Eye tracking study performed by\nJoachims et al. [10] showed that users usually consider the result\nimmediately following the clicked result in current ranking. Their\nSkip Next strategy uses this observation to predict that a result\nfollowing the clicked result at p is less relevant than the clicked\nresult, with accuracy comparable to the SA strategy above. For\nbetter coverage, we combine the SA strategy with this extension to\nderive the Skip Above + Skip Next strategy:\nStrategy SA+N (Skip Above + Skip Next): This strategy\npredicts all un-clicked results immediately following a\nclicked result as less relevant than the clicked result, and\ncombines these predictions with those of the SA strategy\nabove.\nWe experimented with variations of these strategies, and found\nthat SA+N outperformed both SA and the original Skip Next\nstrategy, so we will consider the SA and SA+N strategies in the\nrest of the paper. These strategies are motivated and empirically\ntested for individual users in a laboratory setting. As we will\nshow, these strategies do not work as well in real web search\nsetting due to inherent inconsistency and noisiness of individual\nusers\" behavior.\nThe general approach for using our clickthrough models\ndirectly is to filter clicks to those that reflect higher-than-chance\nclick frequency. We then use the same SA and SA+N strategies,\nbut only for clicks that have higher-than-expected frequency\naccording to our model. For this, we estimate the relevance\ncomponent rel(q,r,f) of the observed clickthrough feature f as the\ndeviation from the expected (background) clickthrough\ndistribution )( fC .\nStrategy CD (deviation d): For a given query, compute the\nobserved click frequency distribution o(r, p) for all results r\nin positions p. The click deviation for a result r in position p,\ndev(r, p) is computed as:\n)(),(),( pCproprdev \u2212=\nwhere C(p) is the expected clickthrough at position p. If\ndev(r,p)>d, retain the click as input to the SA+N strategy\nabove, and apply SA+N strategy over the filtered set of click\nevents.\nThe choice of d selects the tradeoff between recall and\nprecision. While the above strategy extends SA and SA+N, it still\nassumes that a (filtered) clicked result is preferred over all\nunclicked results presented to the user above a clicked position.\nHowever, for informational queries, multiple results may be\nclicked, with varying frequency. Hence, it is preferable to\nindividually compare results for a query by considering the\ndifference between the estimated relevance components of the\nclick distribution of the corresponding query results. We now\ndefine a generalization of the previous clickthrough interpretation\nstrategy:\nStrategy CDiff (margin m): Compute deviation dev(r,p) for\neach result r1...rn in position p. For each pair of results ri and\nrj, predict preference of ri over rj iff dev(ri,pi)-dev(ri,pj)>m.\nAs in CD, the choice of m selects the tradeoff between recall\nand precision. The pairs may be preferred in the original order or\nin reverse of it. Given the margin, two results might be effectively\nindistinguishable, but only one can possibly be preferred over the\nother. Intuitively, CDiff generalizes the skip idea above to include\ncases where the user skipped (i.e., clicked less than expected)\non uj and preferred (i.e., clicked more than expected) on ui.\nFurthermore, this strategy allows for differentiation within the set\nof clicked results, making it more appropriate to noisy user\nbehavior.\nCDiff and CD are complimentary. CDiff is a generalization of\nthe clickthrough frequency model of CD, but it ignores the\npositional information used in CD. Hence, combining the two\nstrategies to improve coverage is a natural approach:\nStrategy CD+CDiff (deviation d, margin m): Union\nof CD and CDiff predictions.\nOther variations of the above strategies were considered, but\nthese five methods cover the range of observed performance.\n4.3 General User Behavior Model\nThe strategies described in the previous section generate\norderings based solely on observed clickthrough frequencies. As\nwe discussed, clickthrough is just one, albeit important, aspect\nof user interactions with web search engine results. We now\npresent our general strategy that relies on the automatically\nderived predictive user behavior models (Section 3).\nThe UserBehavior Strategy: For a given query, each\nresult is represented with the features in Table 3.1.\nRelative user preferences are then estimated using the\nlearned user behavior model described in Section 3.4.\nRecall that to learn a predictive behavior model we used the\nfeatures from Table 3.1 along with explicit relevance judgments\nas input to RankNet which learns an optimal weighting of\nfeatures to predict preferences.\nThis strategy models user interaction with the search engine,\nallowing it to benefit from the wisdom of crowds interacting\nwith the results and the pages beyond. As our experiments in the\nsubsequent sections demonstrate, modeling a richer set of user\ninteractions beyond clickthroughs results in more accurate\npredictions of user preferences.\n5. EXPERIMENTAL SETUP\nWe now describe our experimental setup. We first describe\nthe methodology used, including our evaluation metrics (Section\n5.1). Then we describe the datasets (Section 5.2) and the\nmethods we compared in this study (Section 5.3).\n5.1 Evaluation Methodology and Metrics\nOur evaluation focuses on the pairwise agreement between\npreferences for results. This allows us to compare to previous\nwork [9,10]. Furthermore, for many applications such as tuning\nranking functions, pairwise preference can be used directly for\ntraining [1,4,9]. The evaluation is based on comparing\npreferences predicted by various models to the correct\npreferences derived from the explicit user relevance judgments.\nWe discuss other applications of our models beyond web search\nranking in Section 7.\nTo create our set of test pairs we take each query and\ncompute the cross-product between all search results, returning\npreferences for pairs according to the order of the associated\nrelevance labels. To avoid ambiguity in evaluation, we discard\nall ties (i.e., pairs with equal label).\nIn order to compute the accuracy of our preference predictions\nwith respect to the correct preferences, we adapt the standard\nRecall and Precision measures [20]. While our task of computing\npairwise agreement is different from the absolute relevance\nranking task, the metrics are used in the similar way.\nSpecifically, we report the average query recall and precision.\nFor our task, Query Precision and Query Recall for a query q are\ndefined as:\n\u2022 Query Precision: Fraction of predicted preferences for results\nfor q that agree with preferences obtained from explicit\nhuman judgment.\n\u2022 Query Recall: Fraction of preferences obtained from explicit\nhuman judgment for q that were correctly predicted.\nThe overall Recall and Precision are computed as the average of\nQuery Recall and Query Precision, respectively. A drawback of\nthis evaluation measure is that some preferences may be more\nvaluable than others, which pairwise agreement does not capture.\nWe discuss this issue further when we consider extensions to the\ncurrent work in Section 7.\n5.2 Datasets\nFor evaluation we used 3,500 queries that were randomly\nsampled from query logs(for a major web search engine. For each\nquery the top 10 returned search results were manually rated on a\n6-point scale by trained judges as part of ongoing relevance\nimprovement effort. In addition for these queries we also had user\ninteraction data for more than 120,000 instances of these queries.\nThe user interactions were harvested from anonymous\nbrowsing traces that immediately followed a query submitted to\nthe web search engine. This data collection was part of voluntary\nopt-in feedback submitted by users from October 11 through\nOctober 31. These three weeks (21 days) of user interaction data\nwas filtered to include only the users in the English-U.S. market.\nIn order to better understand the effect of the amount of user\ninteraction data available for a query on accuracy, we created\nsubsets of our data (Q1, Q10, and Q20) that contain different\namounts of interaction data:\n\u2022 Q1: Human-rated queries with at least 1 click on results\nrecorded (3500 queries, 28,093 query-URL pairs)\n\u2022 Q10: Queries in Q1 with at least 10 clicks (1300 queries,\n18,728 query-URL pairs).\n\u2022 Q20: Queries in Q1 with at least 20 clicks (1000 queries total,\n12,922 query-URL pairs).\nThese datasets were collected as part of normal user experience\nand hence have different characteristics than previously reported\ndatasets collected in laboratory settings. Furthermore, the data\nsize is order of magnitude larger than any study reported in the\nliterature.\n5.3 Methods Compared\nWe considered a number of methods for comparison. We\ncompared our UserBehavior model (Section 4.3) to previously\npublished implicit feedback interpretation techniques and some\nvariants of these approaches (Section 4.2), and to the current\nsearch engine ranking based on query and page features alone\n(Section 4.1). Specifically, we compare the following strategies:\n\u2022 SA: The Skip Above clickthrough strategy (Section 4.2)\n\u2022 SA+N: A more comprehensive extension of SA that takes\nbetter advantage of current search engine ranking.\n\u2022 CD: Our refinement of SA+N that takes advantage of our\nmixture model of clickthrough distribution to select trusted\nclicks for interpretation (Section 4.2).\n\u2022 CDiff: Our generalization of the CD strategy that explicitly\nuses the relevance component of clickthrough probabilities to\ninduce preferences between search results (Section 4.2).\n\u2022 CD+CDiff: The strategy combining CD and CDiff as the\nunion of predicted preferences from both (Section 4.2).\n\u2022 UserBehavior: We order predictions based on decreasing\nhighest score of any page. In our preliminary experiments\nwe observed that higher ranker scores indicate higher\nconfidence in the predictions. This heuristic allows us to\ndo graceful recall-precision tradeoff using the score of the\nhighest ranked result to threshold the queries (Section 4.3)\n\u2022 Current: Current search engine ranking (section 4.1). Note\nthat the Current ranker implementation was trained over a\nsuperset of the rated query/URL pairs in our datasets, but\nusing the same truth labels as we do for our evaluation.\nTraining/Test Split: The only strategy for which splitting the\ndatasets into training and test was required was the\nUserBehavior method. To evaluate UserBehavior we train and\nvalidate on 75% of labeled queries, and test on the remaining\n25%. The sampling was done per query (i.e., all results for a\nchosen query were included in the respective dataset, and there\nwas no overlap in queries between training and test sets).\nIt is worth noting that both the ad-hoc SA and SA+N, as well\nas the distribution-based strategies (CD, CDiff, and CD+CDiff),\ndo not require a separate training and test set, since they are\nbased on heuristics for detecting anomalous click frequencies\nfor results. Hence, all strategies except for UserBehavior were\ntested on the full set of queries and associated relevance\npreferences, while UserBehavior was tested on a randomly\nchosen hold-out subset of the queries as described above. To\nmake sure we are not favoring UserBehavior, we also tested all\nother strategies on the same hold-out test sets, resulting in the\nsame accuracy results as testing over the complete datasets.\n6. RESULTS\nWe now turn to experimental evaluation of predicting\nrelevance preference of web search results. Figure 6.1 shows the\nrecall-precision results over the Q1 query set (Section 5.2). The\nresults indicate that previous click interpretation strategies, SA\nand SA+N perform suboptimally in this setting, exhibiting\nprecision 0.627 and 0.638 respectively. Furthermore, there is no\nmechanism to do recall-precision trade-off with SA and SA+N,\nas they do not provide prediction confidence. In contrast, our\nclickthrough distribution-based techniques CD and CD+CDiff\nexhibit somewhat higher precision than SA and SA+N (0.648\nand 0.717 at Recall of 0.08, maximum achieved by SA or\nSA+N).\nSA+N\nSA\n0.6\n0.62\n0.64\n0.66\n0.68\n0.7\n0.72\n0.74\n0.76\n0.78\n0.8\n0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45\nRecall\nPrecision\nSA SA+N\nCD CDiff\nCD+CDiff UserBehavior\nCurrent\nFigure 6.1: Precision vs. Recall of SA, SA+N, CD, CDiff,\nCD+CDiff, UserBehavior, and Current relevance prediction\nmethods over the Q1 dataset.\nInterestingly, CDiff alone exhibits precision equal to SA\n(0.627) at the same recall at 0.08. In contrast, by combining CD\nand CDiff strategies (CD+CDiff method) we achieve the best\nperformance of all clickthrough-based strategies, exhibiting\nprecision of above 0.66 for recall values up to 0.14, and higher at\nlower recall levels. Clearly, aggregating and intelligently\ninterpreting clickthroughs, results in significant gain for realistic\nweb search, than previously described strategies. However, even\nthe CD+CDiff clickthrough interpretation strategy can be\nimproved upon by automatically learning to interpret the\naggregated clickthrough evidence.\nBut first, we consider the best performing strategy,\nUserBehavior. Incorporating post-search navigation history in\naddition to clickthroughs (Browsing features) results in the\nhighest recall and precision among all methods compared. Browse\nexhibits precision of above 0.7 at recall of 0.16, significantly\noutperforming our Baseline and clickthrough-only strategies.\nFurthermore, Browse is able to achieve high recall (as high as\n0.43) while maintaining precision (0.67) significantly higher than\nthe baseline ranking.\nTo further analyze the value of different dimensions of implicit\nfeedback modeled by the UserBehavior strategy, we consider each\ngroup of features in isolation. Figure 6.2 reports Precision vs.\nRecall for each feature group. Interestingly, Query-text alone has\nlow accuracy (only marginally better than Random). Furthermore,\nBrowsing features alone have higher precision (with lower\nmaximum recall achieved) than considering all of the features in\nour UserBehavior model. Applying different machine learning\nmethods for combining classifier predictions may increase\nperformance of using all features for all recall values.\n0.5\n0.55\n0.6\n0.65\n0.7\n0.75\n0.8\n0.01 0.05 0.09 0.13 0.17 0.21 0.25 0.29 0.33 0.37 0.41 0.45\nRecall\nPrecision\nAll Features\nClickthrough\nQuery-text\nBrowsing\nFigure 6.2: Precision vs. recall for predicting relevance with\neach group of features individually.\n0.65\n0.67\n0.69\n0.71\n0.73\n0.75\n0.77\n0.79\n0.81\n0.83\n0.85\n0.01 0.05 0.09 0.13 0.17 0.21 0.25 0.29 0.33 0.37 0.41 0.45 0.49\nRecall\nPrecision\nCD+CDiff:Q1 UserBehavior:Q1\nCD+CDiff:Q10 UserBehavior:Q10\nCD+CDiff:Q20 UserBehavior:Q20\nFigure 6.3: Recall vs. Precision of CD+CDiff and\nUserBehavior for query sets Q1, Q10, and Q20 (queries with\nat least 1, at least 10, and at least 20 clicks respectively).\nInterestingly, the ranker trained over Clickthrough-only\nfeatures achieves substantially higher recall and precision than\nhuman-designed clickthrough-interpretation strategies described\nearlier. For example, the clickthrough-trained classifier achieves\n0.67 precision at 0.42 Recall vs. the maximum recall of 0.14\nachieved by the CD+CDiff strategy.\nOur clickthrough and user behavior interpretation strategies\nrely on extensive user interaction data. We consider the effects\nof having sufficient interaction data available for a query before\nproposing a re-ranking of results for that query. Figure 6.3\nreports recall-precision curves for the CD+CDiff and\nUserBehavior methods for different test query sets with at least\n1 click (Q1), 10 clicks (Q10) and 20 clicks (Q20) available per\nquery. Not surprisingly, CD+CDiff improves with more clicks.\nThis indicates that accuracy will improve as more user\ninteraction histories become available, and more queries from\nthe Q1 set will have comprehensive interaction histories.\nSimilarly, the UserBehavior strategy performs better for queries\nwith 10 and 20 clicks, although the improvement is less dramatic\nthan for CD+CDiff. For queries with sufficient clicks, CD+CDiff\nexhibits precision comparable with Browse at lower recall.\n0\n0.05\n0.1\n0.15\n0.2\n7 12 17 21\nDays of user interaction data harvested\nRecall\nCD+CDiff\nUserBehavior\nFigure 6.4: Recall of CD+CDiff and UserBehavior strategies\nat fixed minimum precision 0.7 for varying amounts of user\nactivity data (7, 12, 17, 21 days).\nOur techniques often do not make relevance predictions for\nsearch results (i.e., if no interaction data is available for the\nlower-ranked results), consequently maintaining higher precision\nat the expense of recall. In contrast, the current search engine\nalways makes a prediction for every result for a given query. As\na consequence, the recall of Current is high (0.627) at the\nexpense of lower precision As another dimension of acquiring\ntraining data we consider the learning curve with respect to\namount (days) of training data available. Figure 6.4 reports the\nRecall of CD+CDiff and UserBehavior strategies for varying\namounts of training data collected over time. We fixed minimum\nprecision for both strategies at 0.7 as a point substantially higher\nthan the baseline (0.625). As expected, Recall of both strategies\nimproves quickly with more days of interaction data examined.\nWe now briefly summarize our experimental results. We\nshowed that by intelligently aggregating user clickthroughs\nacross queries and users, we can achieve higher accuracy on\npredicting user preferences. Because of the skewed distribution\nof user clicks our clickthrough-only strategies have high\nprecision, but low recall (i.e., do not attempt to predict relevance\nof many search results). Nevertheless, our CD+CDiff\nclickthrough strategy outperforms most recent state-of-the-art\nresults by a large margin (0.72 precision for CD+CDiff vs. 0.64\nfor SA+N) at the highest recall level of SA+N.\nFurthermore, by considering the comprehensive UserBehavior\nfeatures that model user interactions after the search and beyond\nthe initial click, we can achieve substantially higher precision\nand recall than considering clickthrough alone. Our\nUserBehavior strategy achieves recall of over 0.43 with precision\nof over 0.67 (with much higher precision at lower recall levels),\nsubstantially outperforms the current search engine preference\nranking and all other implicit feedback interpretation methods.\n7. CONCLUSIONS AND FUTURE WORK\nOur paper is the first, to our knowledge, to interpret\npostsearch user behavior to estimate user preferences in a real web\nsearch setting. We showed that our robust models result in higher\nprediction accuracy than previously published techniques.\nWe introduced new, robust, probabilistic techniques for\ninterpreting clickthrough evidence by aggregating across users\nand queries. Our methods result in clickthrough interpretation\nsubstantially more accurate than previously published results not\nspecifically designed for web search scenarios. Our methods\"\npredictions of relevance preferences are substantially more\naccurate than the current state-of-the-art search result ranking that\ndoes not consider user interactions. We also presented a general\nmodel for interpreting post-search user behavior that incorporates\nclickthrough, browsing, and query features. By considering the\ncomplete search experience after the initial query and click, we\ndemonstrated prediction accuracy far exceeding that of\ninterpreting only the limited clickthrough information.\nFurthermore, we showed that automatically learning to\ninterpret user behavior results in substantially better performance\nthan the human-designed ad-hoc clickthrough interpretation\nstrategies. Another benefit of automatically learning to interpret\nuser behavior is that such methods can adapt to changing\nconditions and changing user profiles. For example, the user\nbehavior model on intranet search may be different from the web\nsearch behavior. Our general UserBehavior method would be able\nto adapt to these changes by automatically learning to map new\nbehavior patterns to explicit relevance ratings.\nA natural application of our preference prediction models is to\nimprove web search ranking [1]. In addition, our work has many\npotential applications including click spam detection, search\nabuse detection, personalization, and domain-specific ranking. For\nexample, our automatically derived behavior models could be\ntrained on examples of search abuse or click spam behavior\ninstead of relevance labels. Alternatively, our models could be\nused directly to detect anomalies in user behavior - either due to\nabuse or to operational problems with the search engine.\nWhile our techniques perform well on average, our\nassumptions about clickthrough distributions (and learning the\nuser behavior models) may not hold equally well for all queries.\nFor example, queries with divergent access patterns (e.g., for\nambiguous queries with multiple meanings) may result in\nbehavior inconsistent with the model learned for all queries.\nHence, clustering queries and learning different predictive models\nfor each query type is a promising research direction. Query\ndistributions also change over time, and it would be productive to\ninvestigate how that affects the predictive ability of these models.\nFurthermore, some predicted preferences may be more valuable\nthan others, and we plan to investigate different metrics to capture\nthe utility of the predicted preferences.\nAs we showed in this paper, using the wisdom of crowds can\ngive us accurate interpretation of user interactions even in the\ninherently noisy web search setting. Our techniques allow us to\nautomatically predict relevance preferences for web search results\nwith accuracy greater than the previously published methods. The\npredicted relevance preferences can be used for automatic\nrelevance evaluation and tuning, for deploying search in new\nsettings, and ultimately for improving the overall web search\nexperience.\n8. REFERENCES\n[1] E. Agichtein, E. Brill, and S. Dumais, Improving Web Search Ranking\nby Incorporating User Behavior, in Proceedings of the ACM\nConference on Research and Development on Information Retrieval\n(SIGIR), 2006\n[2] J. Allan. HARD Track Overview in TREC 2003: High Accuracy\nRetrieval from Documents. In Proceedings of TREC 2003, 24-37,\n2004.\n[3] S. Brin and L. Page, The Anatomy of a Large-scale Hypertextual Web\nSearch Engine,. In Proceedings of WWW7, 107-117, 1998.\n[4] C.J.C. Burges, T. Shaked, E. Renshaw, A. Lazier, M. Deeds, N.\nHamilton, and G. Hullender, Learning to Rank using Gradient\nDescent, in Proceedings of the International Conference on Machine\nLearning (ICML), 2005\n[5] D.M. Chickering, The WinMine Toolkit, Microsoft Technical Report\nMSR-TR-2002-103, 2002\n[6] M. Claypool, D. Brown, P. Lee and M. Waseda. Inferring user interest,\nin IEEE Internet Computing. 2001\n[7] S. Fox, K. Karnawat, M. Mydland, S. T. Dumais and T. White.\nEvaluating implicit measures to improve the search experience. In\nACM Transactions on Information Systems, 2005\n[8] J. Goecks and J. Shavlick. Learning users\" interests by unobtrusively\nobserving their normal behavior. In Proceedings of the IJCAI\nWorkshop on Machine Learning for Information Filtering. 1999.\n[9] T. Joachims, Optimizing Search Engines Using Clickthrough Data, in\nProceedings of the ACM Conference on Knowledge Discovery and\nDatamining (SIGKDD), 2002\n[10] T. Joachims, L. Granka, B. Pang, H. Hembrooke and G. Gay,\nAccurately Interpreting Clickthrough Data as Implicit Feedback, in\nProceedings of the ACM Conference on Research and Development\non Information Retrieval (SIGIR), 2005\n[11] T. Joachims, Making Large-Scale SVM Learning Practical. Advances\nin Kernel Methods, in Support Vector Learning, MIT Press, 1999\n[12] D. Kelly and J. Teevan, Implicit feedback for inferring user preference:\nA bibliography. In SIGIR Forum, 2003\n[13] J. Konstan, B. Miller, D. Maltz, J. Herlocker, L. Gordon and J. Riedl.\nGroupLens: Applying collaborative filtering to usenet news. In\nCommunications of ACM, 1997.\n[14] M. Morita, and Y. Shinoda, Information filtering based on user\nbehavior analysis and best match text retrieval. In Proceedings of the\nACM Conference on Research and Development on Information\nRetrieval (SIGIR), 1994\n[15] D. Oard and J. Kim. Implicit feedback for recommender systems. in\nProceedings of AAAI Workshop on Recommender Systems. 1998\n[16] D. Oard and J. Kim. Modeling information content using observable\nbehavior. In Proceedings of the 64th Annual Meeting of the\nAmerican Society for Information Science and Technology. 2001\n[17] P. Pirolli, The Use of Proximal Information Scent to Forage for Distal\nContent on the World Wide Web. In Working with Technology in\nMind: Brunswikian. Resources for Cognitive Science and\nEngineering, Oxford University Press, 2004\n[18] F. Radlinski and T. Joachims, Query Chains: Learning to Rank from\nImplicit Feedback, in Proceedings of the ACM Conference on\nKnowledge Discovery and Data Mining (KDD), ACM, 2005\n[19] F. Radlinski and T. Joachims, Evaluating the Robustness of Learning\nfrom Implicit Feedback, in the ICML Workshop on Learning in Web\nSearch, 2005\n[20] G. Salton and M. McGill. Introduction to modern information\nretrieval. McGraw-Hill, 1983\n[21] E.M. Voorhees, D. Harman, Overview of TREC, 2001", "keywords": "precision measure;relevance measurement;recall measure;predictive model;induce weight;clickthrough;top relevant document position;search abuse detection;predictive behavior model;low recall;information retrieval;predict relevance preference;position of top relevant document;explicit relevance judgment;user preference;interpret implicit relevance feedback;follow-up query;web search ranking;click spam detection;domain-specific ranking;page dwell time;implicit feedback;user behavior model;personalization"}
{"name": "train_H-87", "title": "Robustness of Adaptive Filtering Methods In a Cross-benchmark Evaluation", "abstract": "This paper reports a cross-benchmark evaluation of regularized logistic regression (LR) and incremental Rocchio for adaptive filtering. Using four corpora from the Topic Detection and Tracking (TDT) forum and the Text Retrieval Conferences (TREC) we evaluated these methods with non-stationary topics at various granularity levels, and measured performance with different utility settings. We found that LR performs strongly and robustly in optimizing T11SU (a TREC utility function) while Rocchio is better for optimizing Ctrk (the TDT tracking cost), a high-recall oriented objective function. Using systematic cross-corpus parameter optimization with both methods, we obtained the best results ever reported on TDT5, TREC10 and TREC11. Relevance feedback on a small portion (0.05~0.2%) of the TDT5 test documents yielded significant performance improvements, measuring up to a 54% reduction in Ctrk and a 20.9% increase in T11SU (with \u03b2=0.1), compared to the results of the top-performing system in TDT2004 without relevance feedback information.", "fulltext": "1. INTRODUCTION\nAdaptive filtering (AF) has been a challenging research topic in\ninformation retrieval. The task is for the system to make an\nonline topic membership decision (yes or no) for every\ndocument, as soon as it arrives, with respect to each pre-defined\ntopic of interest. Starting from 1997 in the Topic Detection and\nTracking (TDT) area and 1998 in the Text Retrieval\nConferences (TREC), benchmark evaluations have been\nconducted by NIST under the following\nconditions[6][7][8][3][4]:\n\u2022 A very small number (1 to 4) of positive training examples\nwas provided for each topic at the starting point.\n\u2022 Relevance feedback was available but only for the\nsystemaccepted documents (with a yes decision) in the TREC\nevaluations for AF.\n\u2022 Relevance feedback (RF) was not allowed in the TDT\nevaluations for AF (or topic tracking in the TDT\nterminology) until 2004.\n\u2022 TDT2004 was the first time that TREC and TDT metrics\nwere jointly used in evaluating AF methods on the same\nbenchmark (the TDT5 corpus) where non-stationary topics\ndominate.\nThe above conditions attempt to mimic realistic situations where\nan AF system would be used. That is, the user would be willing\nto provide a few positive examples for each topic of interest at\nthe start, and might or might not be able to provide additional\nlabeling on a small portion of incoming documents through\nrelevance feedback. Furthermore, topics of interest might\nchange over time, with new topics appearing and growing, and\nold topics shrinking and diminishing. These conditions make\nadaptive filtering a difficult task in statistical learning (online\nclassification), for the following reasons:\n1) it is difficult to learn accurate models for prediction based\non extremely sparse training data;\n2) it is not obvious how to correct the sampling bias (i.e.,\nrelevance feedback on system-accepted documents only)\nduring the adaptation process;\n3) it is not well understood how to effectively tune parameters\nin AF methods using cross-corpus validation where the\nvalidation and evaluation topics do not overlap, and the\ndocuments may be from different sources or different\nepochs.\nNone of these problems is addressed in the literature of\nstatistical learning for batch classification where all the training\ndata are given at once. The first two problems have been\nstudied in the adaptive filtering literature, including topic profile\nadaptation using incremental Rocchio, Gaussian-Exponential\ndensity models, logistic regression in a Bayesian framework,\netc., and threshold optimization strategies using probabilistic\ncalibration or local fitting techniques [1][2][9][10][11][12][13].\nAlthough these works provide valuable insights for\nunderstanding the problems and possible solutions, it is difficult\nto draw conclusions regarding the effectiveness and robustness\nof current methods because the third problem has not been\nthoroughly investigated. Addressing the third issue is the main\nfocus in this paper.\nWe argue that robustness is an important measure for evaluating\nand comparing AF methods. By robust we mean consistent\nand strong performance across benchmark corpora with a\nsystematic method for parameter tuning across multiple corpora.\nMost AF methods have pre-specified parameters that may\ninfluence the performance significantly and that must be\ndetermined before the test process starts. Available training\nexamples, on the other hand, are often insufficient for tuning the\nparameters. In TDT5, for example, there is only one labeled\ntraining example per topic at the start; parameter optimization\non such training data is doomed to be ineffective.\nThis leaves only one option (assuming tuning on the test set is\nnot an alternative), that is, choosing an external corpus as the\nvalidation set. Notice that the validation-set topics often do not\noverlap with the test-set topics, thus the parameter optimization\nis performed under the tough condition that the validation data\nand the test data may be quite different from each other. Now\nthe important question is: which methods (if any) are robust\nunder the condition of using cross-corpus validation to tune\nparameters? Current literature does not offer an answer because\nno thorough investigation on the robustness of AF methods has\nbeen reported.\nIn this paper we address the above question by conducting a\ncross-benchmark evaluation with two effective approaches in\nAF: incremental Rocchio and regularized logistic regression\n(LR). Rocchio-style classifiers have been popular in AF, with\ngood performance in benchmark evaluations (TREC and TDT)\nif appropriate parameters were used and if combined with an\neffective threshold calibration strategy [2][4][7][8][9][11][13].\nLogistic regression is a classical method in statistical learning,\nand one of the best in batch-mode text categorization [15][14]. It\nwas recently evaluated in adaptive filtering and was found to\nhave relatively strong performance (Section 5.1). Furthermore, a\nrecent paper [13] reported that the joint use of Rocchio and LR\nin a Bayesian framework outperformed the results of using each\nmethod alone on the TREC11 corpus. Stimulated by those\nfindings, we decided to include Rocchio and LR in our\ncrossbenchmark evaluation for robustness testing. Specifically, we\nfocus on how much the performance of these methods depends\non parameter tuning, what the most influential parameters are in\nthese methods, how difficult (or how easy) to optimize these\ninfluential parameters using cross-corpus validation, how strong\nthese methods perform on multiple benchmarks with the\nsystematic tuning of parameters on other corpora, and how\nefficient these methods are in running AF on large benchmark\ncorpora.\nThe organization of the paper is as follows: Section 2 introduces\nthe four benchmark corpora (TREC10 and TREC11, TDT3 and\nTDT5) used in this study. Section 3 analyzes the differences\namong the TREC and TDT metrics (utilities and tracking cost)\nand the potential implications of those differences. Section 4\noutlines the Rocchio and LR approaches to AF, respectively.\nSection 5 reports the experiments and results. Section 6\nconcludes the main findings in this study.\n2. BENCHMARK CORPORA\nWe used four benchmark corpora in our study. Table 1 shows\nthe statistics about these data sets.\nTREC10 was the evaluation benchmark for adaptive filtering in\nTREC 2001, consisting of roughly 806,791 Reuters news stories\nfrom August 1996 to August 1997 with 84 topic labels (subject\ncategories)[7]. The first two weeks (August 20th\nto 31st\n, 1996) of\ndocuments is the training set, and the remaining 11 & \u00bd months\n(from September 1st\n, 1996 to August 19th\n, 1997) is the test set.\nTREC11 was the evaluation benchmark for adaptive filtering in\nTREC 2002, consisting of the same set of documents as those in\nTREC10 but with a slightly different splitting point for the\ntraining and test sets. The TREC11 topics (50) are quite\ndifferent from those in TREC10; they are queries for retrieval\nwith relevance judgments by NIST assessors [8].\nTDT3 was the evaluation benchmark in the TDT2001 dry run1\n.\nThe tracking part of the corpus consists of 71,388 news stories\nfrom multiple sources in English and Mandarin (AP, NYT,\nCNN, ABC, NBC, MSNBC, Xinhua, Zaobao, Voice of America\nand PRI the World) in the period of October to December 1998.\nMachine-translated versions of the non-English stories (Xinhua,\nZaobao and VOA Mandarin) are provided as well. The splitting\npoint for training-test sets is different for each topic in TDT.\nTDT5 was the evaluation benchmark in TDT2004 [4]. The\ntracking part of the corpus consists of 407,459 news stories in\nthe period of April to September, 2003 from 15 news agents or\nbroadcast sources in English, Arabic and Mandarin, with\nmachine-translated versions of the non-English stories. We only\nused the English versions of those documents in our\nexperiments for this paper.\nThe TDT topics differ from TREC topics both conceptually\nand statistically. Instead of generic, ever-lasting subject\ncategories (as those in TREC), TDT topics are defined at a finer\nlevel of granularity, for events that happen at certain times and\nlocations, and that are born and die, typically associated\nwith a bursty distribution over chronologically ordered news\nstories. The average size of TDT topics (events) is two orders\nof magnitude smaller than that of the TREC10 topics. Figure 1\ncompares the document densities of a TREC topic (Civil\nWars) and two TDT topics (Gunshot and APEC Summit\nMeeting, respectively) over a 3-month time period, where the\narea under each curve is normalized to one.\nThe granularity differences among topics and the corresponding\nnon-stationary distributions make the cross-benchmark\nevaluation interesting. For example, algorithms favoring large\nand stable topics may not work well for short-lasting and\nnonstationary topics, and vice versa. Cross-benchmark evaluations\nallow us to test this hypothesis and possibly identify the\nweaknesses in current approaches to adaptive filtering in\ntracking the drifting trends of topics.\n1\nhttp://www.ldc.upenn.edu/Projects/TDT2001/topics.html\nTable 1: Statistics of benchmark corpora for adaptive filtering evaluations\nN(tr) is the number of the initial training documents; N(ts) is the number of the test documents;\nn+ is the number of positive examples of a predefined topic; * is an average over all the topics.\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n0 1 2 3 4 5 6 7 8 9 10 11 12 13 14\nWeek\nP(topic|week)\nGunshot (TDT5)\nAPEC Summit Meeting (TDT3)\nCivil War(TREC10)\nFigure 1: The temporal nature of topics\n3. METRICS\nTo make our results comparable to the literature, we decided to\nuse both TREC-conventional and TDT-conventional metrics in\nour evaluation.\n3.1 TREC11 metrics\nLet A, B, C and D be, respectively, the numbers of true\npositives, false alarms, misses and true negatives for a specific\ntopic, and DCBAN +++= be the total number of test\ndocuments. The TREC-conventional metrics are defined as:\nPrecision )/( BAA += , Recall )/( CAA +=\n)(2\n)21(\nCABA\nA\nF\n+++\n+\n=\n\u03b2\n\u03b2\n\u03b2\n( )\n\u03b7\n\u03b7\u03b7\u03b2\n\u03b7\u03b2\n\u2212\n\u2212+\u2212\n=\n1\n),/()(max\n11 ,\nCABA\nSUT\nwhere parameters \u03b2 and \u03b7 were set to 0.5 and -0.5 respectively\nin TREC10 (2001) and TREC11 (2002). For evaluating the\nperformance of a system, the performance scores are computed\nfor individual topics first and then averaged over topics\n(macroaveraging).\n3.2 TDT metrics\nThe TDT-conventional metric for topic tracking is defined as:\nfamisstrk PTPwPTPwTC ))(1()()( 21 \u2212+=\nwhere P(T) is the percentage of documents on topic T, missP is\nthe miss rate by the system on that topic, faP is the false alarm\nrate, and 1w and 2w are the costs (pre-specified constants) for a\nmiss and a false alarm, respectively. The TDT benchmark\nevaluations (since 1997) have used the settings\nof 11 =w , 1.02 =w and 02.0)( =TP for all topics. For evaluating\nthe performance of a system, Ctrk is computed for each topic\nfirst and then the resulting scores are averaged for a single\nmeasure (the topic-weighted Ctrk).\nTo make the intuition behind this measure transparent, we\nsubstitute the terms in the definition of Ctrk as follows:\nN\nCA\nTP\n+\n=)( ,\nN\nDB\nTP\n+\n=\u2212 )(1 ,\nCA\nC\nPmiss\n+\n= ,\nDB\nB\nPfa\n+\n= ,\n)(\n1\n)(\n21\n21\nBwCw\nN\nDB\nB\nN\nDB\nw\nCA\nC\nN\nCA\nwTCtrk\n+\u22c5=\n+\n\u22c5\n+\n\u22c5+\n+\n\u22c5\n+\n\u22c5=\nClearly, trkC is the average cost per error on topic T, with 1w\nand 2w controlling the penalty ratio for misses vs. false alarms.\nIn addition to trkC , TDT2004 also employed 1.011 =\u03b2SUT as a\nutility metric. To distinguish this from the 5.011 =\u03b2SUT in\nTREC11, we call former TDT5SU in the rest of this paper.\nCorpus #Topics N(tr) N(ts) Avg\nn+ (tr)\nAvg\nn+ (ts)\nMax\nn+ (ts)\nMin\nn+ (ts)\n#Topics per\ndoc (ts)\nTREC10 84 20,307 783,484 2 9795.3 39,448 38 1.57\nTREC11 50 80.664 726,419 3 378.0 597 198 1.12\nTDT3 53 18,738* 37,770* 4 79.3 520 1 1.06\nTDT5 111 199,419* 207,991* 1 71.3 710 1 1.01\n3.3 The correlations and the differences\nFrom an optimization point of view, TDT5SU and T11SU are\nboth utility functions while Ctrk is a cost function. Our objective\nis to maximize the former or to minimize the latter on test\ndocuments. The differences and correlations among these\nobjective functions can be analyzed through the shared counts\nof A, B, C and D in their definitions. For example, both\nTDT5SU and T11SU are positively correlated to the values of A\nand D, and negatively correlated to the values of B and C; the\nonly difference between them is in their penalty ratios for\nmisses vs. false alarms, i.e., 10:1 in TDT5SU and 2:1 in T11SU.\nThe Ctrk function, on the other hand, is positively correlated to\nthe values of C and B, and negatively correlated to the values of\nA and D; hence, it is negatively correlated to T11SU and\nTDT5SU.\nMore importantly, there is a subtle and major difference\nbetween Ctrk and the utility functions: T11SU and TDT5SU.\nThat is, Ctrk has a very different penalty ratio for misses vs.\nfalse alarms: it favors recall-oriented systems to an extreme. At\nfirst glance, one would think that the penalty ratio in Ctrk is\n10:1 since 11 =w and 1.02 =w . However, this is not true if\n02.0)( =TP is an inaccurate estimate of the on-topic documents\non average for the test corpus. Using TDT3 as an example, the\ntrue percentage is:\n002.0\n37770\n3.79\n)( \u2248=\n+\n=\nN\nn\nTP\nwhere N is the average size of the test sets in TDT3, and n+ is\nthe average number of positive examples per topic in the test\nsets. Using 02.0)(\u02c6 =TP as an (inaccurate) estimate of 0.002\nenlarges the intended penalty ratio of 10:1 to 100:1, roughly\nspeaking. To wit:\n)1.010(\n1\n1.010\n)3.7937770(37770\n3.79\n1011.0101\n1011.0101\n))(1(2)(1\n)02.01(202.01)(\nBC\nNN\nB\nN\nC\nB\nN\nC\nDB\nB\nN\nCA\nN\nC\nfaPTPwmissPTPw\nfaPwmissPwTtrkC\n\u00d7+\u00d7=\u00d7+\u00d7\u2248\n\u2212\n\u00d7\u2212\u00d7+\u00d7\u00d7=\n+\n+\n\u00d7\u2212\u00d7+\u00d7\u00d7=\n\u00d7\u2212\u22c5+\u00d7\u00d7=\n\u2212\u00d7+\u00d7\u00d7=\n\u239f\n\u23a0\n\u239e\n\u239c\n\u239d\n\u239b\n\u239f\n\u23a0\n\u239e\n\u239c\n\u239d\n\u239b\n\u03c1\u03c1\nwhere 10\n002.0\n02.0\n)(\n)(\u02c6\n===\nTP\nTP\n\u03c1 is the factor of enlargement in the\nestimation of P(T) compared to the truth. Comparing the above\nresult to formula 2, we can see the actual penalty ratio for\nmisses vs. false alarms was 100:1 in the evaluations on TDT3\nusing Ctrk. Similarly, we can compute the enlargement factor\nfor TDT5 using the statistics in Table 1 as follows:\n3.58\n991,207/3.71\n02.0\n)(\n)(\u02c6\n===\nTP\nTP\n\u03c1\nwhich means the actual penalty ratio for misses vs. false alarms\nin the evaluation on TDT5 using Ctrk was approximately 583:1.\nThe implications of the above analysis are rather significant:\n\u2022 Ctrk defined in the same formula does not necessarily\nmean the same objective function in evaluation; instead,\nthe optimization criterion depends on the test corpus.\n\u2022 Systems optimized for Ctrk would not optimize TDT5SU\n(and T11SU) because the former favors high-recall\noriented to an extreme while the latter does not.\n\u2022 Parameters tuned on one corpus (e.g., TDT3) might not\nwork for an evaluation on another corpus (say, TDT5)\nunless we account for the previously-unknown subtle\ndependency of Ctrk on data.\n\u2022 Results in Ctrk in the past years of TDT evaluations may\nnot be directly comparable to each other because the\nevaluation collections changed most years and hence the\npenalty ratio in Ctrk varied.\nAlthough these problems with Ctrk were not originally\nanticipated, it offered an opportunity to examine the ability of\nsystems in trading off precision for extreme recall. This was a\nchallenging part of the TDT2004 evaluation for AF.\nComparing the metrics in TDT and TREC from a utility or cost\noptimization point of view is important for understanding the\nevaluation results of adaptive filtering methods. This is the first\ntime this issue is explicitly analyzed, to our knowledge.\n4. METHODS\n4.1 Incremental Rocchio for AF\nWe employed a common version of Rocchio-style classifiers\nwhich computes a prototype vector per topic (T) as follows:\n|)(|\n'\n|)(|\n)()(\n)(')(\nTD\nd\nTD\nd\nTqTp\nTDdTDd\n\u2212\n\u2208\n+\n\u2208 \u2211\u2211 \u2212+\n\u2212+=\nrr\nrr\nrr\n\u03b3\u03b2\u03b1\nThe first term on the RHS is the weighted vector representation\nof topic description whose elements are terms weights. The\nsecond term is the weighted centroid of the set )(TD+ of\npositive training examples, each of which is a vector of\nwithindocument term weights. The third term is the weighted centroid\nof the set )(TD\u2212 of negative training examples which are the\nnearest neighbors of the positive centroid. The three terms are\ngiven pre-specified weights of \u03b2\u03b1, and \u03b3 , controlling the\nrelative influence of these components in the prototype.\nThe prototype of a topic is updated each time the system makes\na yes decision on a new document for that topic. If relevance\nfeedback is available (as is the case in TREC adaptive filtering),\nthe new document is added to the pool of\neither )(TD+ or )(TD\u2212 , and the prototype is recomputed\naccordingly; if relevance feedback is not available (as is the case\nin TDT event tracking), the system\"s prediction (yes) is\ntreated as the truth, and the new document is added to )(TD+ for\nupdating the prototype. Both cases are part of our experiments\nin this paper (and part of the TDT 2004 evaluations for AF). To\ndistinguish the two, we call the first case simply Rocchio and\nthe second case PRF Rocchio where PRF stands for\npseudorelevance feedback.\nThe predictions on a new document are made by computing the\ncosine similarity between each topic prototype and the\ndocument vector, and then comparing the resulting scores\nagainst a threshold:\n\u23a9\n\u23a8\n\u23a7\n\u2212\n+\n=\u2212\n)(\n)(\n))),((cos(\nno\nyes\ndTpsign new \u03b8\nrr\nThreshold calibration in incremental Rocchio is a challenging\nresearch topic. Multiple approaches have been developed. The\nsimplest is to use a universal threshold for all topics, tuned on a\nvalidation set and fixed during the testing phase. More elaborate\nmethods include probabilistic threshold calibration which\nconverts the non-probabilistic similarity scores to probabilities\n(i.e., )|( dTP\nr\n) for utility optimization [9][13], and margin-based\nlocal regression for risk reduction [11].\nIt is beyond the scope of this paper to compare all the different\nways to adapt Rocchio-style methods for AF. Instead, our focus\nhere is to investigate the robustness of Rocchio-style methods in\nterms of how much their performance depends on elaborate\nsystem tuning, and how difficult (or how easy) it is to get good\nperformance through cross-corpus parameter optimization.\nHence, we decided to use a relatively simple version of Rocchio\nas the baseline, i.e., with a universal threshold tuned on a\nvalidation corpus and fixed for all topics in the testing phase.\nThis simple version of Rocchio has been commonly used in the\npast TDT benchmark evaluations for topic tracking, and had\nstrong performance in the TDT2004 evaluations for adaptive\nfiltering with and without relevance feedback (Section 5.1).\nResults of more complex variants of Rocchio are also discussed\nwhen relevant.\n4.2 Logistic Regression for AF\nLogistic regression (LR) estimates the posterior probability of a\ntopic given a document using a sigmoid function\n)1/(1),|1( xw\newxyP\nrrrr \u22c5\u2212\n+==\nwhere x\nr\nis the document vector whose elements are term\nweights, w\nr\nis the vector of regression coefficients, and\n}1,1{ \u2212+\u2208y is the output variable corresponding to yes or\nno with respect to a particular topic. Given a training set of\nlabeled documents { }),(,),,( 11 nn yxyxD\nr\nL\nr\n= , the\nstandard regression problem is defined as to find the maximum\nlikelihood estimates of the regression coefficients (the model\nparameters):\n{ } { }\n{ }))exp(1(1logminarg\n)|(logmaxarg)|(maxarg\nii xwyn\ni\nw\nwDP\nw\nwDP\nw\nmlw\nrr\nr\nr\nr\nr\nr\nr\n\u22c5\u2212+\u2211 ==\n==\nThis is a convex optimization problem which can be solved\nusing a standard conjugate gradient algorithm in O(INF) time\nfor training per topic, where I is the average number of\niterations needed for convergence, and N and F are the number\nof training documents and number of features respectively [14].\nOnce the regression coefficients are optimized on the training\ndata, the filtering prediction on each incoming document is\nmade as:\n( )\n\u23a9\n\u23a8\n\u23a7\n\u2212\n+\n=\u2212\n)(\n)(\n),|(\nno\nyes\nwxyPsign optnew \u03b8\nrr\nNote that w\nr\nis constantly updated whenever a new relevance\njudgment is available in the testing phase of AF, while the\noptimal threshold opt\u03b8 is constant, depending only on the\npredefined utility (or cost) function for evaluation. If T11SU is the\nmetric, for example, with the penalty ratio of 2:1 for misses and\nfalse alarms (Section 3.1), the optimal threshold for LR\nis 33.0)12/(1 =+ for all topics.\nWe modified the standard (above) version of LR to allow more\nflexible optimization criteria as follows:\n\u23ad\n\u23ac\n\u23ab\n\u23a9\n\u23a8\n\u23a7\n\u2212++= \u2211=\n\u22c5\u2212 2\n1\n)1log()(minarg \u03bc\u03bb\nrrr rr\nr\nweysw\nn\ni\nxwy\ni\nw\nmap\nii\nwhere )( iys is taken to be \u03b1 , \u03b2 and \u03b3 for query, positive\nand negative documents respectively, which are similar to those\nin Rocchio, giving different weights to the three kinds of\ntraining examples: topic descriptions (queries), on-topic\ndocuments and off-topic documents. The second term in the\nobjective function is for regularization, equivalent to adding a\nGaussian prior to the regression coefficients with mean \u03bc\nr\nand\ncovariance variance matrix \u0399\u22c5\u03bb2/1 , where \u0399 is the identity\nmatrix. Tuning \u03bb (\u22650) is theoretically justified for reducing\nmodel complexity (the effective degree of freedom) and\navoiding over-fitting on training data [5]. How to find an\neffective \u03bc\nr\nis an open issue for research, depending on the\nuser\"s belief about the parameter space and the optimal range.\nThe solution of the modified objective function is called the\nMaximum A Posteriori (MAP) estimate, which reduces to the\nmaximum likelihood solution for standard LR if 0=\u03bb .\n5. EVALUATIONS\nWe report our empirical findings in four parts: the TDT2004\nofficial evaluation results, the cross-corpus parameter\noptimization results, and the results corresponding to the\namounts of relevance feedback.\n5.1 TDT2004 benchmark results\nThe TDT2004 evaluations for adaptive filtering were conducted\nby NIST in November 2004. Multiple research teams\nparticipated and multiple runs from each team were allowed.\nCtrk and TDT5SU were used as the metrics. Figure 2 and Figure\n3 show the results; the best run from each team was selected\nwith respect to Ctrk or TDT5SU, respectively. Our Rocchio\n(with adaptive profiles but fixed universal threshold for all\ntopics) had the best result in Ctrk, and our logistic regression\nhad the best result in TDT5SU. All the parameters of our runs\nwere tuned on the TDT3 corpus. Results for other sites are also\nlisted anonymously for comparison.\nCtrk\nOurs 0.0324\nSite2 0.0467\nSite3 0.1366\nSite4 0.2438\nMetric = Ctrk (the lower the better)\n0.0324 0.0467\n0.1366\n0.2438\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\nOurs Site2 Site3 Site4\nFigure 2: TDT2004 results in Ctrk of systems using true\nrelevance feedback. (Ours is the Rocchio method.) We\nalso put the 1st\nand 3rd\nquartiles as sticks for each site.2\nT11SU\nOurs 0.7328\nSite3 0.7281\nSite2 0.6672\nSite4 0.382\nMetric = TDT5SU (the higher the better)\n0.7328 0.7281\n0.6672\n0.382\n0\n0.2\n0.4\n0.6\n0.8\n1\nOurs Site3 Site2 Site4\nFigure 3:TDT2004 results in TDT5SU of systems using true\nrelevance feedback. (Ours is LR\nwith 0=\u03bc\nr\nand 005.0=\u03bb ).\nCTrk\nOurs 0.0707\nSite2 0.1545\nSite5 0.5669\nSite4 0.6507\nSite6 0.8973\nPrimary Topic Traking Results in TDT2004\n0.0707\n0.8973\n0.6507\n0.1545\n0.5669\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\nOurs Site2 Site5 Site4 Site6\nCtrk\nFigure 4:TDT2004 results in Ctrk of systems without using\ntrue relevance feedback. (Ours is PRF Rocchio.)\nAdaptive filtering without using true relevance feedback was\nalso a part of the evaluations. In this case, systems had only one\nlabeled training example per topic during the entire training and\ntesting processes, although unlabeled test documents could be\nused as soon as predictions on them were made. Such a setting\nhas been conventional for the Topic Tracking task in TDT until\n2004. Figure 4 shows the summarized official submissions from\neach team. Our PRF Rocchio (with a fixed threshold for all the\ntopics) had the best performance.\n2\nWe use quartiles rather than standard deviations since the\nformer is more resistant to outliers.\n5.2 Cross-corpus parameter optimization\nHow much the strong performance of our systems depends on\nparameter tuning is an important question.\nBoth Rocchio and LR have parameters that must be\nprespecified before the AF process. The shared parameters include\nthe sample weights\u03b1 , \u03b2 and \u03b3 , the sample size of the negative\ntraining documents (i.e., )(TD\u2212 ), the term-weighting scheme,\nand the maximal number of non-zero elements in each\ndocument vector. The method-specific parameters include the\ndecision threshold in Rocchio, and \u03bc\nr\n, \u03bb and MI (the maximum\nnumber of iterations in training) in LR. Given that we only have\none labeled example per topic in the TDT5 training sets, it is\nimpossible to effectively optimize these parameters on the\ntraining data, and we had to choose an external corpus for\nvalidation. Among the choices of TREC10, TREC11 and TDT3,\nwe chose TDT3 (c.f. Section 2) because it is most similar to\nTDT5 in terms of the nature of the topics (Section 2). We\noptimized the parameters of our systems on TDT3, and fixed\nthose parameters in the runs on TDT5 for our submissions to\nTDT2004. We also tested our methods on TREC10 and\nTREC11 for further analysis. Since exhaustive testing of all\npossible parameter settings is computationally intractable, we\nfollowed a step-wise forward chaining procedure instead: we\npre-specified an order of the parameters in a method (Rocchio\nor LR), and then tuned one parameter at the time while fixing\nthe settings of the remaining parameters. We repeated this\nprocedure for several passes as time allowed.\n0.05\n0.26\n0.67\n0.69\n0.00\n0.10\n0.20\n0.30\n0.40\n0.50\n0.60\n0.70\n0.80\n0.90\n0.02 0.03 0.04 0.06 0.08 0.1 0.15 0.2 0.25 0.3\nThreshold\nTDT5SU\nTDT3 TDT5 TREC10 TREC11\nFigure 5: Performance curves of adaptive Rocchio\nFigure 5 compares the performance curves in TDT5SU for\nRocchio on TDT3, TDT5, TREC10 and TREC11 when the\ndecision threshold varied. These curves peak at different\nlocations: the TDT3-optimal is closest to the TDT5-optimal\nwhile the TREC10-optimal and TREC1-optimal are quite far\naway from the TDT5-optimal. If we were using TREC10 or\nTREC11 instead of TDT3 as the validation corpus for TDT5, or\nif the TDT3 corpus were not available, we would have difficulty\nin obtaining strong performance for Rocchio in TDT2004. The\ndifficulty comes from the ad-hoc (non-probabilistic) scores\ngenerated by the Rocchio method: the distribution of the scores\ndepends on the corpus, making cross-corpus threshold\noptimization a tricky problem.\nLogistic regression has less difficulty with respect to threshold\ntuning because it produces probabilistic scores of )|1Pr( xy =\nupon which the optimal threshold can be directly computed if\nprobability estimation is accurate. Given the penalty ratio for\nmisses vs. false alarms as 2:1 in T11SU, 10:1 in TDT5SU and\n583:1 in Ctrk (Section 3.3), the corresponding optimal\nthresholds (t) are 0.33, 0.091 and 0.0017 respectively.\nAlthough the theoretical threshold could be inaccurate, it still\nsuggests the range of near-optimal settings. With these threshold\nsettings in our experiments for LR, we focused on the\ncrosscorpus validation of the Bayesian prior parameters, that is, \u03bc\nr\nand \u03bb. Table 2 summarizes the results 3\n. We measured the\nperformance of the runs on TREC10 and TREC11 using T11SU,\nand the performance of the runs on TDT3 and TDT5 using\nTDT5SU. For comparison we also include the best results of\nRocchio-based methods on these corpora, which are our own\nresults of Rocchio on TDT3 and TDT5, and the best results\nreported by NIST for TREC10 and TREC11. From this set of\nresults, we see that LR significantly outperformed Rocchio on\nall the corpora, even in the runs of standard LR without any\ntuning, i.e. \u03bb=0. This empirical finding is consistent with a\nprevious report [13] for LR on TREC11 although our results of\nLR (0.585~0.608 in T11SU) are stronger than the results (0.49\nfor standard LR and 0.54 for LR using Rocchio prototype as the\nprior) in that report. More importantly, our cross-benchmark\nevaluation gives strong evidence for the robustness of LR. The\nrobustness, we believe, comes from the probabilistic nature of\nthe system-generated scores. That is, compared to the ad-hoc\nscores in Rocchio, the normalized posterior probabilities make\nthe threshold optimization in LR a much easier problem.\nMoreover, logistic regression is known to converge towards the\nBayes classifier asymptotically while Rocchio classifiers\"\nparameters do not.\nAnother interesting observation in these results is that the\nperformance of LR did not improve when using a Rocchio\nprototype as the mean in the prior; instead, the performance\ndecreased in some cases. This observation does not support the\nprevious report by [13], but we are not surprised because we are\nnot convinced that Rocchio prototypes are more accurate than\nLR models for topics in the early stage of the AF process, and\nwe believe that using a Rocchio prototype as the mean in the\nGaussian prior would introduce undesirable bias to LR. We also\nbelieve that variance reduction (in the testing phase) should be\ncontrolled by the choice of \u03bb (but not \u03bc\nr\n), for which we\nconducted the experiments as shown in Figure 6.\nTable 2: Results of LR with different Bayesian priors\nCorpus TDT3 TDT5 TREC10 TREC11\nLR(\u03bc=0,\u03bb=0) 0.7562 0.7737 0.585 0.5715\nLR(\u03bc=0,\u03bb=0.01) 0.8384 0.7812 0.6077 0.5747\nLR(\u03bc=roc*,\u03bb=0.01) 0.8138 0.7811 0.5803 0.5698\nBest Rocchio 0.6628 0.6917 0.4964\n0.475\n3\nThe LR results (0.77~0.78) on TDT5 in this table are better\nthan our TDT2004 official result (0.73) because parameter\noptimization has been improved afterwards.\n4\nThe TREC10-best result (0.496 by Oracle) is only available in\nT10U which is not directly comparable to the scores in\nT11SU, just indicative.\n*: \u03bc\nr\nwas set to the Rocchio prototype\n0\n0.2\n0.4\n0.6\n0.8\n0.000 0.001 0.005 0.050 0.500\nLambda\nPerformance\nCtrk on TDT3 TDT5SU on TDT3\nTDT5SU on TDT5 T11SU on TREC11\nFigure 6: LR with varying lambda.\nThe performance of LR is summarized with respect to \u03bb tuning\non the corpora of TREC10, TREC11 and TDT3. The\nperformance on each corpus was measured using the\ncorresponding metrics, that is, T11SU for the runs on TREC10\nand TREC11, and TDT5SU and Ctrk for the runs on TDT3,. In\nthe case of maximizing the utilities, the safe interval for \u03bb is\nbetween 0 and 0.01, meaning that the performance of\nregularized LR is stable, the same as or improved slightly over\nthe performance of standard LR. In the case of minimizing Ctrk,\nthe safe range for \u03bb is between 0 and 0.1, and setting \u03bb between\n0.005 and 0.05 yielded relatively large improvements over the\nperformance of standard LR because training a model for\nextremely high recall is statistically more tricky, and hence\nmore regularization is needed. In either case, tuning \u03bb is\nrelatively safe, and easy to do successfully by cross-corpus\ntuning.\nAnother influential choice in our experiment settings is term\nweighting: we examined the choices of binary, TF and TF-IDF\n(the ltc version) schemes. We found TF-IDF most effective\nfor both Rocchio and LR, and used this setting in all our\nexperiments.\n5.3 Percentages of labeled data\nHow much relevance feedback (RF) would be needed during the\nAF process is a meaningful question in real-world applications.\nTo answer it, we evaluated Rocchio and LR on TDT with the\nfollowing settings:\n\u2022 Basic Rocchio, no adaptation at all\n\u2022 PRF Rocchio, updating topic profiles without using true\nrelevance feedback;\n\u2022 Adaptive Rocchio, updating topic profiles using relevance\nfeedback on system-accepted documents plus 10\ndocuments randomly sampled from the pool of\nsystemrejected documents;\n\u2022 LR with 0\nrr\n=\u03bc , 01.0=\u03bb and threshold = 0.004;\n\u2022 All the parameters in Rocchio tuned on TDT3.\nTable 3 summarizes the results in Ctrk: Adaptive Rocchio with\nrelevance feedback on 0.6% of the test documents reduced the\ntracking cost by 54% over the result of the PRF Rocchio, the\nbest system in the TDT2004 evaluation for topic tracking\nwithout relevance feedback information. Incremental LR, on the\nother hand, was weaker but still impressive. Recall that Ctrk is\nan extremely high-recall oriented metric, causing frequent\nupdating of profiles and hence an efficiency problem in LR. For\nthis reason we set a higher threshold (0.004) instead of the\ntheoretically optimal threshold (0.0017) in LR to avoid an\nuntolerable computation cost. The computation time in\nmachine-hours was 0.33 for the run of adaptive Rocchio and 14\nfor the run of LR on TDT5 when optimizing Ctrk. Table 4\nsummarizes the results in TDT5SU; adaptive LR was the winner\nin this case, with relevance feedback on 0.05% of the test\ndocuments improving the utility by 20.9% over the results of\nPRF Rocchio.\nTable 3: AF methods on TDT5 (Performance in Ctrk)\nBase Roc PRF Roc Adp Roc LR\n% of RF 0% 0% 0.6% 0.2%\nCtrk 0.076 0.0707 0.0324 0.0382\n\u00b1% +7% (baseline) -54% -46%\nTable 4: AF methods on TDT5 (Performance in TDT5SU)\nBase Roc PRF Roc Adp Roc LR(\u03bb=.01)\n% of RF 0% 0% 0.04% 0.05%\nTDT5SU 0.57 0.6452 0.69 0.78\n\u00b1% -11.7% (baseline) +6.9% +20.9%\nEvidently, both Rocchio and LR are highly effective in adaptive\nfiltering, in terms of using of a small amount of labeled data to\nsignificantly improve the model accuracy in statistical learning,\nwhich is the main goal of AF.\n5.4 Summary of Adaptation Process\nAfter we decided the parameter settings using validation, we\nperform the adaptive filtering in the following steps for each\ntopic: 1) Train the LR/Rocchio model using the provided\npositive training examples and 30 randomly sampled negative\nexamples; 2) For each document in the test corpus: we first\nmake a prediction about relevance, and then get relevance\nfeedback for those (predicted) positive documents. 3) Model and\nIDF statistics will be incrementally updated if we obtain its true\nrelevance feedback.\n6. CONCLUDING REMARKS\nWe presented a cross-benchmark evaluation of incremental\nRocchio and incremental LR in adaptive filtering, focusing on\ntheir robustness in terms of performance consistency with\nrespect to cross-corpus parameter optimization. Our main\nconclusions from this study are the following:\n\u2022 Parameter optimization in AF is an open challenge but has\nnot been thoroughly studied in the past.\n\u2022 Robustness in cross-corpus parameter tuning is important\nfor evaluation and method comparison.\n\u2022 We found LR more robust than Rocchio; it had the best\nresults (in T11SU) ever reported on TDT5, TREC10 and\nTREC11 without extensive tuning.\n\u2022 We found Rocchio performs strongly when a good\nvalidation corpus is available, and a preferred choice when\noptimizing Ctrk is the objective, favoring recall over\nprecision to an extreme.\nFor future research we want to study explicit modeling of the\ntemporal trends in topic distributions and content drifting.\nAcknowledgments\nThis material is based upon work supported in parts by the\nNational Science Foundation (NSF) under grant IIS-0434035,\nby the DoD under award 114008-N66001992891808 and by the\nDefense Advanced Research Project Agency (DARPA) under\nContract No. NBCHD030010. Any opinions, findings and\nconclusions or recommendations expressed in this material are\nthose of the author(s) and do not necessarily reflect the views of\nthe sponsors.\n7. REFERENCES\n[1] J. Allan. Incremental relevance feedback for information\nfiltering. In SIGIR-96, 1996.\n[2] J. Callan. Learning while filtering documents. In SIGIR-98,\n224-231, 1998.\n[3] J. Fiscus and G. Duddington. Topic detection and tracking\noverview. In Topic detection and tracking: event-based\ninformation organization, 17-31, 2002.\n[4] J. Fiscus and B. Wheatley. Overview of the TDT 2004\nEvaluation and Results. In TDT-04, 2004.\n[5] T. Hastie, R. Tibshirani and J. Friedman. Elements of\nStatistical Learning. Springer, 2001.\n[6] S. Robertson and D. Hull. The TREC-9 filtering track final\nreport. In TREC-9, 2000.\n[7] S. Robertson and I. Soboroff. The TREC-10 filtering track\nfinal report. In TREC-10, 2001.\n[8] S. Robertson and I. Soboroff. The TREC 2002 filtering\ntrack report. 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Retr. 4(1):\n5-31 (2001).", "keywords": "logistic regression;adaptive filter;gaussian;topic track;validation set;cost function;topic detection;statistical learning;posterior probability;sigmoid function;information retrieval;relevance feedback;optimization criterion;cross-benchmark evaluation;topic tracking;bias;systematic method for parameter tuning across multiple corpora;rocchio-style method;rocchio;cross-corpus parameter optimization;penalty ratio;robustness;granularity difference;adaptive filtering;external corpus;utility function;probabilistic threshold calibration;regularization;lr"}
{"name": "train_H-88", "title": "Controlling Overlap in Content-Oriented XML Retrieval", "abstract": "The direct application of standard ranking techniques to retrieve individual elements from a collection of XML documents often produces a result set in which the top ranks are dominated by a large number of elements taken from a small number of highly relevant documents. This paper presents and evaluates an algorithm that re-ranks this result set, with the aim of minimizing redundant content while preserving the benefits of element retrieval, including the benefit of identifying topic-focused components contained within relevant documents. The test collection developed by the INitiative for the Evaluation of XML Retrieval (INEX) forms the basis for the evaluation.", "fulltext": "1. INTRODUCTION\nThe representation of documents in XML provides an\nopportunity for information retrieval systems to take\nadvantage of document structure, returning individual document\ncomponents when appropriate, rather than complete\ndocuments in all circumstances. In response to a user query, an\nXML information retrieval system might return a mixture\nof paragraphs, sections, articles, bibliographic entries and\nother components. This facility is of particular benefit when\na collection contains very long documents, such as product\nmanuals or books, where the user should be directed to the\nmost relevant portions of these documents.\n<article>\n<fm>\n<atl>Text Compression for\nDynamic Document Databases</atl>\n<au>Alistair Moffat</au>\n<au>Justin Zobel</au>\n<au>Neil Sharman</au>\n<abs><p><b>Abstract</b> For ...</p></abs>\n</fm>\n<bdy>\n<sec><st>INTRODUCTION</st>\n<ip1>Modern document databases...</ip1>\n<p>There are good reasons to compress...</p>\n</sec>\n<sec><st>REDUCING MEMORY REQUIREMENTS</st>...\n<ss1><st>2.1 Method A</st>...\n</sec>\n...\n</bdy>\n</article>\nFigure 1: A journal article encoded in XML.\nFigure 1 provides an example of a journal article encoded\nin XML, illustrating many of the important characteristics\nof XML documents. Tags indicate the beginning and end of\neach element, with elements varying widely in size, from one\nword to thousands of words. Some elements, such as\nparagraphs and sections, may be reasonably presented to the user\nas retrieval results, but others are not appropriate. Elements\noverlap each other - articles contain sections, sections\ncontain subsections, and subsections contain paragraphs. Each\nof these characteristics affects the design of an XML IR\nsystem, and each leads to fundamental problems that must be\nsolved in an successful system. Most of these fundamental\nproblems can be solved through the careful adaptation of\nstandard IR techniques, but the problems caused by overlap\nare unique to this area [4,11] and form the primary focus of\nthis paper.\nThe article of figure 1 may be viewed as an XML tree,\nas illustrated in figure 2. Formally, a collection of XML\ndocuments may be represented as a forest of ordered, rooted\ntrees, consisting of a set of nodes N and a set of directed\nedges E connecting these nodes. For each node x \u2208 N , the\nnotation x.parent refers to the parent node of x, if one exists,\nand the notation x.children refers to the set of child nodes\nsec\nbdyfm\natl au au au\nabs\np\nb\nst ip1\nsec\nst\nss1\nst\narticle\np\nFigure 2: Example XML tree.\nof x. Since an element may be represented by the node at\nits root, the output of an XML IR system may be viewed as\na ranked list of the top-m nodes.\nThe direct application of a standard relevance ranking\ntechnique to a set of XML elements can produce a result\nin which the top ranks are dominated by many structurally\nrelated elements. A high scoring section is likely to contain\nseveral high scoring paragraphs and to be contained in an\nhigh scoring article. For example, many of the elements in\nfigure 2 would receive a high score on the keyword query\ntext index compression algorithms. If each of these\nelements are presented to a user as an individual and\nseparate result, she may waste considerable time reviewing and\nrejecting redundant content.\nOne possible solution is to report only the highest\nscoring element along a given path in the tree, and to remove\nfrom the lower ranks any element containing it, or contained\nwithin it. Unfortunately, this approach destroys some of the\npossible benefits of XML IR. For example, an outer element\nmay contain a substantial amount of information that does\nnot appear in an inner element, but the inner element may\nbe heavily focused on the query topic and provide a short\noverview of the key concepts. In such cases, it is reasonable\nto report elements which contain, or are contained in, higher\nranking elements. Even when an entire book is relevant, a\nuser may still wish to have the most important paragraphs\nhighlighted, to guide her reading and to save time [6].\nThis paper presents a method for controlling overlap.\nStarting with an initial element ranking, a re-ranking algorithm\nadjusts the scores of lower ranking elements that contain, or\nare contained within, higher ranking elements, reflecting the\nfact that this information may now be redundant. For\nexample, once an element representing a section appears in the\nranking, the scores for the paragraphs it contains and the\narticle that contains it are reduced. The inspiration for this\nstrategy comes partially from recent work on structured\ndocuments retrieval, where terms appearing in different fields,\nsuch as the title and body, are given different weights [20].\nExtending that approach, the re-ranking algorithm varies\nweights dynamically as elements are processed.\nThe remainder of the paper is organized as follows: After\na discussion of background work and evaluation\nmethodology, a baseline retrieval method is presented in section 4.\nThis baseline method represents a reasonable adaptation of\nstandard IR technology to XML. Section 5 then outlines a\nstrategy for controlling overlap, using the baseline method as\na starting point. A re-ranking algorithm implementing this\nstrategy is presented in section 6 and evaluated in section 7.\nSection 8 discusses an extended version of the algorithm.\n2. BACKGROUND\nThis section provides a general overview of XML\ninformation retrieval and discusses related work, with an emphasis\non the fundamental problems mentioned in the introduction.\nMuch research in the area of XML retrieval views it from a\ntraditional database perspective, being concerned with such\nproblems as the implementation of structured query\nlanguages [5] and the processing of joins [1]. Here, we take\na content oriented IR perceptive, focusing on XML\ndocuments that primarily contain natural language data and\nqueries that are primarily expressed in natural language.\nWe assume that these queries indicate only the nature of\ndesired content, not its structure, and that the role of the\nIR system is to determine which elements best satisfy the\nunderlying information need. Other IR research has\nconsidered mixed queries, in which both content and structural\nrequirements are specified [2,6,14,17,23].\n2.1 Term and Document Statistics\nIn traditional information retrieval applications the\nstandard unit of retrieval is taken to be the document.\nDepending on the application, this term might be interpreted\nto encompass many different objects, including web pages,\nnewspaper articles and email messages.\nWhen applying standard relevance ranking techniques in\nthe context of XML IR, a natural approach is to treat each\nelement as a separate document, with term statistics\navailable for each [16]. In addition, most ranking techniques\nrequire global statistics (e.g. inverse document frequency)\ncomputed over the collection as a whole. If we consider this\ncollection to include all elements that might be returned by\nthe system, a specific occurrence of a term may appear in\nseveral different documents, perhaps in elements\nrepresenting a paragraph, a subsection, a section and an article.\nIt is not appropriate to compute inverse document frequency\nunder the assumption that the term is contained in all of\nthese elements, since the number of elements that contain a\nterm depends entirely on the structural arrangement of the\ndocuments [13,23].\n2.2 Retrievable Elements\nWhile an XML IR system might potentially retrieve any\nelement, many elements may not be appropriate as retrieval\nresults. This is usually the case when elements contain very\nlittle text [10]. For example, a section title containing only\nthe query terms may receive a high score from a ranking\nalgorithm, but alone it would be of limited value to a user, who\nmight prefer the actual section itself. Other elements may\nreflect the document\"s physical, rather than logical,\nstructure, which may have little or no meaning to a user. An\neffective XML IR system must return only those elements\nthat have sufficient content to be usable and are able to\nstand alone as independent objects [15,18]. Standard\ndocument components such as paragraphs, sections, subsections,\nand abstracts usually meet these requirements; titles,\nitalicized phrases, and individual metadata fields often do not.\n2.3 Evaluation Methodology\nOver the past three years, the INitiative for the\nEvaluation of XML Retrieval (INEX) has encouraged research into\nXML information retrieval technology [7,8]. INEX is an\nexperimental conference series, similar to TREC, with groups\nfrom different institutions completing one or more\nexperimental tasks using their own tools and systems, and\ncomparing their results at the conference itself. Over 50 groups\nparticipated in INEX 2004, and the conference has become\nas influential in the area of XML IR as TREC is in other IR\nareas. The research described in this paper, as well as much\nof the related work it cites, depends on the test collections\ndeveloped by INEX.\nOverlap causes considerable problems with retrieval\nevaluation, and the INEX organizers and participants have\nwrestled with these problems since the beginning. While\nsubstantial progress has been made, these problem are still not\ncompletely solved. Kazai et al. [11] provide a detailed\nexposition of the overlap problem in the context of INEX\nretrieval evaluation and discuss both current and proposed\nevaluation metrics. Many of these metrics are applied to\nevaluate the experiments reported in this paper, and they\nare briefly outlined in the next section.\n3. INEX 2004\nSpace limitations prevent the inclusion of more than a\nbrief summary of INEX 2004 tasks and evaluation\nmethodology. For detailed information, the proceedings of the\nconference itself should be consulted [8].\n3.1 Tasks\nFor the main experimental tasks, INEX 2004 participants\nwere provided with a collection of 12,107 articles taken from\nthe IEEE Computer Societies magazines and journals\nbetween 1995 and 2002. Each document is encoded in XML\nusing a common DTD, with the document of figures 1 and 2\nproviding one example.\nAt INEX 2004, the two main experimental tasks were both\nadhoc retrieval tasks, investigating the performance of\nsystems searching a static collection using previously unseen\ntopics. The two tasks differed in the types of topics they\nused. For one task, the content-only or CO task, the\ntopics consist of short natural language statements with no\ndirect reference to the structure of the documents in the\ncollection. For this task, the IR system is required to select the\nelements to be returned. For the other task, the\ncontentand-structure or CAS task, the topics are written in an\nXML query language [22] and contain explicit references to\ndocument structure, which the IR system must attempt to\nsatisfy. Since the work described in this paper is directed\nat the content-only task, where the IR system receives no\nguidance regarding the elements to return, the CAS task is\nignored in the remainder of our description.\nIn 2004, 40 new CO topics were selected by the conference\norganizers from contributions provided by the conference\nparticipants. Each topic includes a short keyword query,\nwhich is executed over the collection by each participating\ngroup on their own XML IR system. Each group could\nsubmit up to three experimental runs consisting of the top\nm = 1500 elements for each topic.\n3.2 Relevance Assessment\nSince XML IR is concerned with locating those elements\nthat provide complete coverage of a topic while containing as\nlittle extraneous information as possible, simple relevant\nvs. not relevant judgments are not sufficient. Instead, the\nINEX organizers adopted two dimensions for relevance\nassessment: The exhaustivity dimension reflects the degree to\nwhich an element covers the topic, and the specificity\ndimension reflects the degree to which an element is focused on the\ntopic. A four-point scale is used in both dimensions. Thus,\na (3,3) element is highly exhaustive and highly specific, a\n(1,3) element is marginally exhaustive and highly specific,\nand a (0,0) element is not relevant. Additional information\non the assessment methodology may be found in Piwowarski\nand Lalmas [19], who provide a detailed rationale.\n3.3 Evaluation Metrics\nThe principle evaluation metric used at INEX 2004 is a\nversion of mean average precision (MAP), adjusted by\nvarious quantization functions to give different weights to\ndifferent elements, depending on their exhaustivity and specificity\nvalues. One variant, the strict quantization function gives a\nweight of 1 to (3,3) elements and a weight of 0 to all others.\nThis variant is essentially the familiar MAP value, with (3,3)\nelements treated as relevant and all other elements treated\nas not relevant. Other quantization functions are designed\nto give partial credit to elements which are near misses,\ndue to a lack or exhaustivity and/or specificity. Both the\ngeneralized quantization function and the specificity-oriented\ngeneralization (sog) function credit elements according to\ntheir degree of relevance [11], with the second function\nplacing greater emphasis on specificity. This paper reports\nresults of this metric using all three of these quantization\nfunctions. Since this metric was first introduced at INEX 2002,\nit is generally referred as the inex-2002 metric.\nThe inex-2002 metric does not penalize overlap. In\nparticular, both the generalized and sog quantization functions\ngive partial credit to a near miss even when a (3,3)\nelement overlapping it is reported at a higher rank. To address\nthis problem, Kazai et al. [11] propose an XML cumulated\ngain metric, which compares the cumulated gain [9] of a\nranked list to an ideal gain vector. This ideal gain vector\nis constructed from the relevance judgments by\neliminating overlap and retaining only best element along a given\npath. Thus, the XCG metric rewards retrieval runs that\navoid overlap. While XCG was not used officially at INEX\n2004, a version of it is likely to be used in the future.\nAt INEX 2003, yet another metric was introduced to\nameliorate the perceived limitations of the inex-2002 metric.\nThis inex-2003 metric extends the definitions of precision\nand recall to consider both the size of reported components\nand the overlap between them. Two versions were created,\none that considered only component size and another that\nconsidered both size and overlap. While the inex-2003\nmetric exhibits undesirable anomalies [11], and was not used in\n2004, values are reported in the evaluation section to provide\nan additional instrument for investigating overlap.\n4. BASELINE RETRIEVAL METHOD\nThis section provides an overview of baseline XML\ninformation retrieval method currently used in the MultiText\nIR system, developed by the Information Retrieval Group at\nthe University of Waterloo [3]. This retrieval method results\nfrom the adaptation and tuning of the Okapi BM25\nmeasure [21] to the XML information retrieval task. The\nMultiText system performed respectably at INEX 2004, placing\nin the top ten under all of the quantization functions, and\nplacing first when the quantization function emphasized\nexhaustivity.\nTo support retrieval from XML and other structured\ndocument types, the system provides generalized queries of the\nform:\nrank X by Y\nwhere X is a sub-query specifying a set of document elements\nto be ranked and Y is a vector of sub-queries specifying\nindividual retrieval terms.\nFor our INEX 2004 runs, the sub-query X specified a list\nof retrievable elements as those with tag names as follows:\nabs app article bb bdy bm fig fm ip1\nli p sec ss1 ss2 vt\nThis list includes bibliographic entries (bb) and figure\ncaptions (fig) as well as paragraphs, sections and subsections.\nPrior to INEX 2004, the INEX collection and the INEX 2003\nrelevance judgments were manually analyzed to select these\ntag names. Tag names were selected on the basis of their\nfrequency in the collection, the average size of their\nassociated elements, and the relative number of positive relevance\njudgments they received. Automating this selection process\nis planned as future work.\nFor INEX 2004, the term vector Y was derived from the\ntopic by splitting phrases into individual words, eliminating\nstopwords and negative terms (those starting with -), and\napplying a stemmer. For example, keyword field of topic\n166\n+\"tree edit distance\" + XML -image\nbecame the four-term query\n\"$tree\" \"$edit\" \"$distance\" \"$xml\"\nwhere the $ operator within a quoted string stems the\nterm that follows it.\nOur implementation of Okapi BM25 is derived from the\nformula of Robertson et al. [21] by setting parameters k2 = 0\nand k3 = \u221e. Given a term set Q, an element x is assigned\nthe score\n\nt\u2208Q\nw(1)\nqt\n(k1 + 1)xt\nK + xt\n(1)\nwhere\nw(1)\n= log \u00a1\nD \u2212 Dt + 0.5\nDt + 0.5 \u00a2\nD = number of documents in the corpus\nDt = number of documents containing t\nqt = frequency that t occurs in the topic\nxt = frequency that t occurs in x\nK = k1((1 \u2212 b) + b \u00b7 lx/lavg)\nlx = length of x\nlavg = average document length\n0.07\n0.08\n0.09\n0.10\n0.11\n0.12\n0.13\n0.14\n0.15\n0 2 4 6 8 10 12 14 16\nMeanAveragePrecision(inex-2002)\nk1\nstrict\ngeneralized\nsog\nFigure 3: Impact of k1 on inex-2002 mean average\nprecision with b = 0.75 (INEX 2003 CO topics).\nPrior to INEX 2004, the INEX 2003 topics and judgments\nwere used to tune the b and k1 parameters, and the impact\nof this tuning is discussed later in this section.\nFor the purposes of computing document-level statistics\n(D, Dt and lavg) a document is defined to be an article.\nThese statistics are used for ranking all element types.\nFollowing the suggestion of Kamps et al. [10], the retrieval\nresults are filtered to eliminate very short elements, those less\nthan 25 words in length.\nThe use of article statistics for all element types might\nbe questioned. This approach may be justified by\nviewing the collection as a set of articles to be searched using\nstandard document-oriented techniques, where only articles\nmay be returned. The score computed for an element is\nessentially the score it would receive if it were added to the\ncollection as a new document, ignoring the minor\nadjustments needed to the document-level statistics. Nonetheless,\nwe plan to examine this issue again in the future.\nIn our experience, the performance of BM25 typically\nbenefits from tuning the b and k1 parameters to the\ncollection, whenever training queries are available for this\npurpose. Prior to INEX 2004, we trained the MultiText system\nusing the INEX 2003 queries. As a starting point we used\nthe values b = 0.75 and k1 = 1.2, which perform well on\nTREC adhoc collections and are used as default values in\nour system. The results were surprising. Figure 3 shows the\nresult of varying k1 with b = 0.75 on the MAP values under\nthree quantization functions. In our experience, optimal\nvalues for k1 are typically in the range 0.0 to 2.0. In this case,\nlarge values are required for good performance. Between\nk1 = 1.0 and k1 = 6.0 MAP increases by over 15% under\nthe strict quantization. Similar improvements are seen\nunder the generalized and sog quantizations. In contrast, our\ndefault value of b = 0.75 works well under all quantization\nfunctions (figure 4). After tuning over a wide range of\nvalues under several quantization functions, we selected values\nof k = 10.0 and b = 0.80 for our INEX 2004 experiments,\nand these values are used for the experiments reported in\nsection 7.\n0.07\n0.08\n0.09\n0.10\n0.11\n0.12\n0.13\n0.14\n0.15\n0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0\nMeanAveragePrecision(inex-2002)\nb\nstrict\ngeneralized\nsog\nFigure 4: Impact of b on inex-2002 mean average\nprecision with k1 = 10 (INEX 2003 CO topics).\n5. CONTROLLING OVERLAP\nStarting with an element ranking generated by the\nbaseline method described in the previous section, elements are\nre-ranked to control overlap by iteratively adjusting the scores\nof those elements containing or contained in higher ranking\nelements. At a conceptual level, re-ranking proceeds as\nfollows:\n1. Report the highest ranking element.\n2. Adjust the scores of the unreported elements.\n3. Repeat steps 1 and 2 until m elements are reported.\nOne approach to adjusting the scores of unreported elements\nin step 2 might be based on the Okapi BM25 scores of the\ninvolved elements. For example, assume a paragraph with\nscore p is reported in step 1. In step 2, the section\ncontaining the paragraph might then have its score s lowered\nby an amount \u03b1 \u00b7 p to reflect the reduced contribution the\nparagraph should make to the section\"s score.\nIn a related context, Robertson et al. [20] argue strongly\nagainst the linear combination of Okapi scores in this\nfashion. That work considers the problem of assigning different\nweights to different document fields, such as the title and\nbody associated with Web pages. A common approach to\nthis problem scores the title and body separately and\ngenerates a final score as a linear combination of the two.\nRobertson et al. discuss the theoretical flaws in this approach and\ndemonstrate experimentally that it can actually harm\nretrieval effectiveness. Instead, they apply the weights at the\nterm frequency level, with an occurrence of a query term\nt in the title making a greater contribution to the score\nthan an occurrence in the body. In equation 1, xt becomes\n\u03b10 \u00b7 yt + \u03b11 \u00b7 zt, where yt is the number of times t occurs in\nthe title and zt is the number of times t occurs in the body.\nTranslating this approach to our context, the\ncontribution of terms appearing in elements is dynamically reduced\nas they are reported. The next section presents and\nanalysis a simple re-ranking algorithm that follows this strategy.\nThe algorithm is evaluated experimentally in section 7. One\nlimitation of the algorithm is that the contribution of terms\nappearing in reported elements is reduced by the same\nfactor regardless of the number of reported elements in which\nit appears. In section 8 the algorithm is extended to apply\nincreasing weights, lowering the score, when a term appears\nin more than one reported element.\n6. RE-RANKING ALGORITHM\nThe re-ranking algorithm operates over XML trees, such\nas the one appearing in figure 2. Input to the algorithm is\na list of n elements ranked according to their initial BM25\nscores. During the initial ranking the XML tree is\ndynamically re-constructed to include only those nodes with\nnonzero BM25 scores, so n may be considerably less than |N |.\nOutput from the algorithm is a list of the top m elements,\nranked according to their adjusted scores.\nAn element is represented by the node x \u2208 N at its root.\nAssociated with this node are fields storing the length of\nelement, term frequencies, and other information required\nby the re-ranking algorithm, as follows:\nx.f - term frequency vector\nx.g - term frequency adjustments\nx.l - element length\nx.score - current Okapi BM25 score\nx.reported - boolean flag, initially false\nx.children - set of child nodes\nx.parent - parent node, if one exists\nThese fields are populated during the initial ranking process,\nand updated as the algorithm progresses. The vector x.f\ncontains term frequency information corresponding to each\nterm in the query. The vector x.g is initially zero and is\nupdated by the algorithm as elements are reported.\nThe score field contains the current BM25 score for the\nelement, which will change as the values in x.g change. The\nscore is computed using equation 1, with the xt value for\neach term determined by a combination of the values in x.f\nand x.g. Given a term t \u2208 Q, let ft be the component of\nx.f corresponding to t, and let gt be the component of x.g\ncorresponding to t, then:\nxt = ft \u2212 \u03b1 \u00b7 gt (2)\nFor processing by the re-ranking algorithm, nodes are\nstored in priority queues, ordered by decreasing score. Each\npriority queue PQ supports three operations:\nPQ.front() - returns the node with greatest score\nPQ.add (x) - adds node x to the queue\nPQ.remove(x) - removes node x from the queue\nWhen implemented using standard data structures, the front\noperation requires O(1) time, and the other operations\nrequire O(log n) time, where n is the size of the queue.\nThe core of the re-ranking algorithm is presented in\nfigure 5. The algorithm takes as input the priority queue S\ncontaining the initial ranking, and produces the top-m\nreranked nodes in the priority queue F. After initializing F to\nbe empty on line 1, the algorithm loops m times over lines\n215, transferring at least one node from S to F during each\niteration. At the start of each iteration, the unreported node\nat the front of S has the greatest adjusted score, and it is\nremoved and added to F. The algorithm then traverses the\n1 F \u2190 \u2205\n2 for i \u2190 1 to m do\n3 x \u2190 S.front()\n4 S.remove(x)\n5 x.reported \u2190 true\n6 F.add(x)\n7\n8 foreach y \u2208 x.children do\n9 Down (y)\n10 end do\n11\n12 if x is not a root node then\n13 Up (x, x.parent)\n14 end if\n15 end do\nFigure 5: Re-Ranking Algorithm - As input, the\nalgorithm takes a priority queue S, containing XML\nnodes ranked by their initial scores, and returns\nits results in priority queue F, ranked by adjusted\nscores.\n1 Up(x, y) \u2261\n2 S.remove(y)\n3 y.g \u2190 y.g + x.f \u2212 x.g\n4 recompute y.score\n5 S.add(y)\n6 if y is not a root node then\n7 Up (x, y.parent)\n8 end if\n9\n10 Down(x) \u2261\n11 if not x.reported then\n12 S.remove(x)\n14 x.g \u2190 x.f\n15 recompute x.score\n16 if x.score > 0 then\n17 F.add(x)\n18 end if\n19 x.reported \u2190 true\n20 foreach y \u2208 x.children do\n21 Down (y)\n22 end do\n23 end if\nFigure 6: Tree traversal routines called by the\nreranking algorithm.\n0.0\n0.02\n0.04\n0.06\n0.08\n0.10\n0.12\n0.14\n0.16\n0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0\n0.25\n0.26\n0.27\n0.28\n0.29\n0.30\n0.31\n0.32\n0.33\n0.34\n0.35\n0.36\nMeanAveragePrecision(inex-2002)\nXMLCumulatedGain(XCG)\nalpha\nMAP (strict)\nMAP (generalized)\nMAP (sog)\nXCG (sog2)\nFigure 7: Impact of \u03b1 on XCG and inex-2002 MAP\n(INEX 2004 CO topics; assessment set I).\nnode\"s ancestors (lines 8-10) and descendants (lines 12-14)\nadjusting the scores of these nodes.\nThe tree traversal routines, Up and Down are given in\nfigure 6. The Up routine removes each ancestor node from S,\nadjusts its term frequency values, recomputes its score, and\nadds it back into S. The adjustment of the term frequency\nvalues (line 3) adds to y.g only the previously unreported\nterm occurrences in x. Re-computation of the score on line 4\nuses equations 1 and 2. The Down routine performs a similar\noperation on each descendant. However, since the contents\nof each descendant are entirely contained in a reported\nelement its final score may be computed, and it is removed\nfrom S and added to F.\nIn order to determine the time complexity of the\nalgorithm, first note that a node may be an argument to Down\nat most once. Thereafter, the reported flag of its parent is\ntrue. During each call to Down a node may be moved from\nS to F, requiring O(log n) time. Thus, the total time for all\ncalls to Down is O(n log n), and we may temporarily ignore\nlines 8-10 of figure 5 when considering the time complexity\nof the loop over lines 2-15. During each iteration of this loop,\na node and each of its ancestors are removed from a priority\nqueue and then added back into a priority queue. Since a\nnode may have at most h ancestors, where h is the maximum\nheight of any tree in the collection, each of the m iterations\nrequires O(h log n) time. Combining these observations\nproduces an overall time complexity of O((n + mh) log n).\nIn practice, re-ranking an INEX result set requires less\nthan 200ms on a three-year-old desktop PC.\n7. EVALUATION\nNone of the metrics described in section 3.3 is a close fit\nwith the view of overlap advocated by this paper.\nNonetheless, when taken together they provide insight into the\nbehaviour of the re-ranking algorithm. The INEX evaluation\npackages (inex_eval and inex_eval_ng) were used to\ncompute values for the inex-2002 and inex-2003 metrics. Values\nfor the XCG metrics were computed using software supplied\nby its inventors [11].\nFigure 7 plots the three variants of inex-2002 MAP metric\ntogether with the XCG metric. Values for these metrics\n0.0\n0.02\n0.04\n0.06\n0.08\n0.10\n0.12\n0.14\n0.16\n0.18\n0.20\n0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0\nMeanAveragePrecision(inex-2003)\nalpha\nstrict, overlap not considered\nstrict, overlap considered\ngeneralized, overlap not considered\ngeneralized, overlap considered\nFigure 8: Impact of \u03b1 on inex-2003 MAP (INEX\n2004 CO topics; assessment set I).\nare plotted for values of \u03b1 between 0.0 and 1.0. Recalling\nthat the XCG metric is designed to penalize overlap, while\nthe inex-2002 metric ignores overlap, the conflict between\nthe metrics is obvious. The MAP values at one extreme\n(\u03b1 = 0.0) and the XCG value at the other extreme (\u03b1 =\n1.0) represent retrieval performance comparable to the best\nsystems at INEX 2004 [8,12].\nFigure 8 plots values of the inex-2003 MAP metric for two\nquantizations, with and without consideration of overlap.\nOnce again, conflict is apparent, with the influence of \u03b1\nsubstantially lessened when overlap is considered.\n8. EXTENDED ALGORITHM\nOne limitation of the re-ranking algorithm is that a single\nweight \u03b1 is used to adjust the scores of both the ancestors\nand descendants of reported elements. An obvious extension\nis to use different weights in these two cases. Furthermore,\nthe same weight is used regardless of the number of times\nan element is contained in a reported element. For example,\na paragraph may form part of a reported section and then\nform part of a reported article. Since the user may now\nhave seen this paragraph twice, its score should be further\nlowered by increasing the value of the weight.\nMotivated by these observations, the re-ranking algorithm\nmay be extended with a series of weights\n1 = \u03b20 \u2265 \u03b21 \u2265 \u03b22 \u2265 ... \u2265 \u03b2M \u2265 0.\nwhere \u03b2j is the weight applied to a node that has been a\ndescendant of a reported node j times. Note that an upper\nbound on M is h, the maximum height of any XML tree\nin the collection. However, in practice M is likely to be\nrelatively small (perhaps 3 or 4).\nFigure 9 presents replacements for the Up and Down\nroutines of figure 6, incorporating this series of weights. One\nextra field is required in each node, as follows:\nx.j - down count\nThe value of x.j is initially set to zero in all nodes and is\nincremented each time Down is called with x as its argument.\nWhen computing the score of node, the value of x.j selects\n1 Up(x, y) \u2261\n2 if not y.reported then\n3 S.remove(y)\n4 y.g \u2190 y.g + x.f \u2212 x.g\n5 recompute y.score\n6 S.add(y)\n8 if y is not a root node then\n9 Up (x, y.parent)\n10 end if\n11 end if\n12\n13 Down(x) \u2261\n14 if x.j < M then\n15 x.j \u2190 x.j + 1\n16 if not x.reported then\n17 S.remove(x)\n18 recompute x.score\n19 S.add(x)\n20 end if\n21 foreach y \u2208 x.children do\n22 Down (y)\n23 end do\n24 end if\nFigure 9: Extended tree traversal routines.\nthe weight to be applied to the node by adjusting the value\nof xt in equation 1, as follows:\nxt = \u03b2x.j \u00b7 (ft \u2212 \u03b1 \u00b7 gt) (3)\nwhere ft and gt are the components of x.f and x.g\ncorresponding to term t.\nA few additional changes are required to extend Up and\nDown. The Up routine returns immediately (line 2) if its\nargument has already been reported, since term frequencies\nhave already been adjusted in its ancestors. The Down\nroutine does not report its argument, but instead recomputes\nits score and adds it back into S.\nA node cannot be an argument to Down more than M +1\ntimes, which in turn implies an overall time complexity of\nO((nM + mh) log n). Since M \u2264 h and m \u2264 n, the time\ncomplexity is also O(nh log n).\n9. CONCLUDING DISCUSSION\nWhen generating retrieval results over an XML collection,\nsome overlap in the results should be tolerated, and may be\nbeneficial. For example, when a highly exhaustive and fairly\nspecific (3,2) element contains a much smaller (2,3) element,\nboth should be reported to the user, and retrieval algorithms\nand evaluation metrics should respect this relationship. The\nalgorithm presented in this paper controls overlap by\nweighting the terms occurring in reported elements to reflect their\nreduced importance.\nOther approaches may also help to control overlap. For\nexample, when XML retrieval results are presented to users\nit may be desirable to cluster structurally related elements\ntogether, visually illustrating the relationships between them.\nWhile this style of user interface may help a user cope with\noverlap, the strategy presented in this paper continues to be\napplicable, by determining the best elements to include in\neach cluster.\nAt Waterloo, we continue to develop and test our ideas\nfor INEX 2005. In particular, we are investigating methods\nfor learning the \u03b1 and \u03b2j weights. We are also re-evaluating\nour approach to document statistics and examining\nappropriate adjustments to the k1 parameter as term weights\nchange [20].\n10. ACKNOWLEDGMENTS\nThanks to Gabriella Kazai and Arjen de Vries for\nproviding an early version of their software for computing the XCG\nmetric, and thanks to Phil Tilker and Stefan B\u00a8uttcher for\ntheir help with the experimental evaluation. In part,\nfunding for this project was provided by IBM Canada through\nthe National Institute for Software Research.\n11. REFERENCES\n[1] N. Bruno, N. Koudas, and D. Srivastava. Holistic twig\njoins: Optimal XML pattern matching. In Proceedings\nof the 2002 ACM SIGMOD International Conference\non the Management of Data, pages 310-321, Madison,\nWisconsin, June 2002.\n[2] D. Carmel, Y. S. Maarek, M. Mandelbrod, Y. Mass,\nand A. Soffer. Searching XML documents via XML\nfragments. In Proceedings of the 26th Annual\nInternational ACM SIGIR Conference on Research\nand Development in Information Retrieval, pages\n151-158, Toronto, Canada, 2003.\n[3] C. L. A. Clarke and P. L. Tilker. MultiText\nexperiments for INEX 2004. In INEX 2004 Workshop\nProceedings, 2004. Published in LNCS 3493 [8].\n[4] A. P. de Vries, G. Kazai, and M. Lalmas. Tolerance to\nirrelevance: A user-effort oriented evaluation of\nretrieval systems without predefined retrieval unit. In\nRIAO 2004 Conference Proceedings, pages 463-473,\nAvignon, France, April 2004.\n[5] D. DeHaan, D. Toman, M. P. Consens, and M. T.\n\u00a8Ozsu. A comprehensive XQuery to SQL translation\nusing dynamic interval encoding. In Proceedings of the\n2003 ACM SIGMOD International Conference on the\nManagement of Data, San Diego, June 2003.\n[6] N. Fuhr and K. Gro\u00dfjohann. XIRQL: A query\nlanguage for information retrieval in XML documents.\nIn Proceedings of the 24th Annual International ACM\nSIGIR Conference on Research and Development in\nInformation Retrieval, pages 172-180, New Orleans,\nSeptember 2001.\n[7] N. Fuhr, M. Lalmas, and S. Malik, editors. Initiative\nfor the Evaluation of XML Retrieval. Proceedings of\nthe Second Workshop (INEX 2003), Dagstuhl,\nGermany, December 2003.\n[8] N. Fuhr, M. Lalmas, S. Malik, and Zolt\u00b4an Szl\u00b4avik,\neditors. Initiative for the Evaluation of XML\nRetrieval. Proceedings of the Third Workshop (INEX\n2004), Dagstuhl, Germany, December 2004. Published\nas Advances in XML Information Retrieval, Lecture\nNotes in Computer Science, volume 3493, Springer,\n2005.\n[9] K. J\u00a8avelin and J. Kek\u00a8al\u00a8ainen. Cumulated gain-based\nevaluation of IR techniques. ACM Transactions on\nInformation Systems, 20(4):422-446, 2002.\n[10] J. Kamps, M. de Rijke, and B. Sigurbj\u00a8ornsson. Length\nnormalization in XML retrieval. In Proceedings of the\n27th Annual International ACM SIGIR Conference on\nResearch and Development in Information Retrieval,\npages 80-87, Sheffield, UK, July 2004.\n[11] G. Kazai, M. Lalmas, and A. P. de Vries. The overlap\nproblem in content-oriented XML retrieval evaluation.\nIn Proceedings of the 27th Annual International ACM\nSIGIR Conference on Research and Development in\nInformation Retrieval, pages 72-79, Sheffield, UK,\nJuly 2004.\n[12] G. Kazai, M. Lalmas, and A. P. de Vries. Reliability\ntests for the XCG and inex-2002 metrics. In INEX\n2004 Workshop Proceedings, 2004. Published in LNCS\n3493 [8].\n[13] J. Kek\u00a8al\u00a8ainen, M. Junkkari, P. Arvola, and T. Aalto.\nTRIX 2004 - Struggling with the overlap. In INEX\n2004 Workshop Proceedings, 2004. Published in LNCS\n3493 [8].\n[14] S. Liu, Q. Zou, and W. W. Chu. Configurable\nindexing and ranking for XML information retrieval.\nIn Proceedings of the 27th Annual International ACM\nSIGIR Conference on Research and Development in\nInformation Retrieval, pages 88-95, Sheffield, UK,\nJuly 2004.\n[15] Y. Mass and M. Mandelbrod. Retrieving the most\nrelevant XML components. In INEX 2003 Workshop\nProceedings, Dagstuhl, Germany, December 2003.\n[16] Y. Mass and M. Mandelbrod. Component ranking and\nautomatic query refinement for XML retrieval. In\nINEX 2004 Workshop Proceedings, 2004. Published in\nLNCS 3493 [8].\n[17] P. Ogilvie and J. Callan. Hierarchical language models\nfor XML component retrieval. In INEX 2004\nWorkshop Proceedings, 2004. Published in LNCS\n3493 [8].\n[18] J. Pehcevski, J. A. Thom, and A. Vercoustre. Hybrid\nXML retrieval re-visited. In INEX 2004 Workshop\nProceedings, 2004. Published in LNCS 3493 [8].\n[19] B. Piwowarski and M. Lalmas. Providing consistent\nand exhaustive relevance assessments for XML\nretrieval evaluation. In Proceedings of the 13th ACM\nConference on Information and Knowledge\nManagement, pages 361-370, Washington, DC,\nNovember 2004.\n[20] S. Robertson, H. Zaragoza, and M. Taylor. Simple\nBM25 extension to multiple weighted fields. In\nProceedings of the 13th ACM Conference on\nInformation and Knowledge Management, pages\n42-50, Washington, DC, November 2004.\n[21] S. E. Robertson, S. Walker, and M. Beaulieu. Okapi at\nTREC-7: Automatic ad-hoc, filtering, VLC and\ninteractive track. In Proceedings of the Seventh Text\nREtrieval Conference, Gaithersburg, MD, November\n1998.\n[22] A. Trotman and B. Sigurbj\u00a8ornsson. NEXI, now and\nnext. In INEX 2004 Workshop Proceedings, 2004.\nPublished in LNCS 3493 [8].\n[23] J. Vittaut, B. Piwowarski, and P. Gallinari. An\nalgebra for structured queries in bayesian networks. In\nINEX 2004 Workshop Proceedings, 2004. Published in\nLNCS 3493 [8].", "keywords": "baseline retrieval;inex;extended tree traversal routine;ideal gain vector;xml ir;xml cumulated gain metric;priority queue;cumulated gain;multitext system;term frequency vector;rank;sog quantization;xml;information retrieval;time complexity;xcg metric reward retrieval;re-ranking algorithm"}
{"name": "train_H-90", "title": "Context-Sensitive Information Retrieval Using Implicit Feedback", "abstract": "A major limitation of most existing retrieval models and systems is that the retrieval decision is made based solely on the query and document collection; information about the actual user and search context is largely ignored. In this paper, we study how to exploit implicit feedback information, including previous queries and clickthrough information, to improve retrieval accuracy in an interactive information retrieval setting. We propose several contextsensitive retrieval algorithms based on statistical language models to combine the preceding queries and clicked document summaries with the current query for better ranking of documents. We use the TREC AP data to create a test collection with search context information, and quantitatively evaluate our models using this test set. Experiment results show that using implicit feedback, especially the clicked document summaries, can improve retrieval performance substantially.", "fulltext": "1. INTRODUCTION\nIn most existing information retrieval models, the retrieval\nproblem is treated as involving one single query and a set of documents.\nFrom a single query, however, the retrieval system can only have\nvery limited clue about the user\"s information need. An optimal\nretrieval system thus should try to exploit as much additional context\ninformation as possible to improve retrieval accuracy, whenever it\nis available. Indeed, context-sensitive retrieval has been identified\nas a major challenge in information retrieval research[2].\nThere are many kinds of context that we can exploit. Relevance\nfeedback [14] can be considered as a way for a user to provide\nmore context of search and is known to be effective for\nimproving retrieval accuracy. However, relevance feedback requires that\na user explicitly provides feedback information, such as specifying\nthe category of the information need or marking a subset of\nretrieved documents as relevant documents. Since it forces the user\nto engage additional activities while the benefits are not always\nobvious to the user, a user is often reluctant to provide such feedback\ninformation. Thus the effectiveness of relevance feedback may be\nlimited in real applications.\nFor this reason, implicit feedback has attracted much attention\nrecently [11, 13, 18, 17, 12]. In general, the retrieval results using the\nuser\"s initial query may not be satisfactory; often, the user would\nneed to revise the query to improve the retrieval/ranking accuracy\n[8]. For a complex or difficult information need, the user may need\nto modify his/her query and view ranked documents with many\niterations before the information need is completely satisfied. In such\nan interactive retrieval scenario, the information naturally available\nto the retrieval system is more than just the current user query and\nthe document collection - in general, all the interaction history can\nbe available to the retrieval system, including past queries,\ninformation about which documents the user has chosen to view, and even\nhow a user has read a document (e.g., which part of a document the\nuser spends a lot of time in reading). We define implicit feedback\nbroadly as exploiting all such naturally available interaction history\nto improve retrieval results.\nA major advantage of implicit feedback is that we can improve\nthe retrieval accuracy without requiring any user effort. For\nexample, if the current query is java, without knowing any extra\ninformation, it would be impossible to know whether it is intended\nto mean the Java programming language or the Java island in\nIndonesia. As a result, the retrieved documents will likely have both\nkinds of documents - some may be about the programming\nlanguage and some may be about the island. However, any particular\nuser is unlikely searching for both types of documents. Such an\nambiguity can be resolved by exploiting history information. For\nexample, if we know that the previous query from the user is cgi\nprogramming, it would strongly suggest that it is the programming\nlanguage that the user is searching for.\nImplicit feedback was studied in several previous works. In [11],\nJoachims explored how to capture and exploit the clickthrough\ninformation and demonstrated that such implicit feedback\ninformation can indeed improve the search accuracy for a group of\npeople. In [18], a simulation study of the effectiveness of different\nimplicit feedback algorithms was conducted, and several retrieval\nmodels designed for exploiting clickthrough information were\nproposed and evaluated. In [17], some existing retrieval algorithms are\nadapted to improve search results based on the browsing history of\na user. Other related work on using context includes personalized\nsearch [1, 3, 4, 7, 10], query log analysis [5], context factors [12],\nand implicit queries [6].\nWhile the previous work has mostly focused on using\nclickthrough information, in this paper, we use both clickthrough\ninformation and preceding queries, and focus on developing new\ncontext-sensitive language models for retrieval. Specifically, we\ndevelop models for using implicit feedback information such as\nquery and clickthrough history of the current search session to\nimprove retrieval accuracy. We use the KL-divergence retrieval model\n[19] as the basis and propose to treat context-sensitive retrieval as\nestimating a query language model based on the current query and\nany search context information. We propose several statistical\nlanguage models to incorporate query and clickthrough history into\nthe KL-divergence model.\nOne challenge in studying implicit feedback models is that there\ndoes not exist any suitable test collection for evaluation. We thus\nuse the TREC AP data to create a test collection with implicit\nfeedback information, which can be used to quantitatively evaluate\nimplicit feedback models. To the best of our knowledge, this is the\nfirst test set for implicit feedback. We evaluate the proposed\nmodels using this data set. The experimental results show that using\nimplicit feedback information, especially the clickthrough data, can\nsubstantially improve retrieval performance without requiring\nadditional effort from the user.\nThe remaining sections are organized as follows. In Section 2,\nwe attempt to define the problem of implicit feedback and introduce\nsome terms that we will use later. In Section 3, we propose several\nimplicit feedback models based on statistical language models. In\nSection 4, we describe how we create the data set for implicit\nfeedback experiments. In Section 5, we evaluate different implicit\nfeedback models on the created data set. Section 6 is our conclusions\nand future work.\n2. PROBLEM DEFINITION\nThere are two kinds of context information we can use for\nimplicit feedback. One is short-term context, which is the immediate\nsurrounding information which throws light on a user\"s current\ninformation need in a single session. A session can be considered as a\nperiod consisting of all interactions for the same information need.\nThe category of a user\"s information need (e.g., kids or sports),\nprevious queries, and recently viewed documents are all examples of\nshort-term context. Such information is most directly related to the\ncurrent information need of the user and thus can be expected to be\nmost useful for improving the current search. In general, short-term\ncontext is most useful for improving search in the current session,\nbut may not be so helpful for search activities in a different\nsession. The other kind of context is long-term context, which refers\nto information such as a user\"s education level and general interest,\naccumulated user query history and past user clickthrough\ninformation; such information is generally stable for a long time and is\noften accumulated over time. Long-term context can be applicable\nto all sessions, but may not be as effective as the short-term context\nin improving search accuracy for a particular session. In this paper,\nwe focus on the short-term context, though some of our methods\ncan also be used to naturally incorporate some long-term context.\nIn a single search session, a user may interact with the search\nsystem several times. During interactions, the user would\ncontinuously modify the query. Therefore for the current query Qk\n(except for the first query of a search session) , there is a query history,\nHQ = (Q1, ..., Qk\u22121) associated with it, which consists of the\npreceding queries given by the same user in the current session. Note\nthat we assume that the session boundaries are known in this paper.\nIn practice, we need techniques to automatically discover session\nboundaries, which have been studied in [9, 16]. Traditionally, the\nretrieval system only uses the current query Qk to do retrieval. But\nthe short-term query history clearly may provide useful clues about\nthe user\"s current information need as seen in the java example\ngiven in the previous section. Indeed, our previous work [15] has\nshown that the short-term query history is useful for improving\nretrieval accuracy.\nIn addition to the query history, there may be other short-term\ncontext information available. For example, a user would\npresumably frequently click some documents to view. We refer to data\nassociated with these actions as clickthrough history. The\nclickthrough data may include the title, summary, and perhaps also the\ncontent and location (e.g., the URL) of the clicked document.\nAlthough it is not clear whether a viewed document is actually\nrelevant to the user\"s information need, we may safely assume that\nthe displayed summary/title information about the document is\nattractive to the user, thus conveys information about the user\"s\ninformation need. Suppose we concatenate all the displayed text\ninformation about a document (usually title and summary) together, we\nwill also have a clicked summary Ci in each round of retrieval. In\ngeneral, we may have a history of clicked summaries C1, ..., Ck\u22121.\nWe will also exploit such clickthrough history HC = (C1, ..., Ck\u22121)\nto improve our search accuracy for the current query Qk. Previous\nwork has also shown positive results using similar clickthrough\ninformation [11, 17].\nBoth query history and clickthrough history are implicit\nfeedback information, which naturally exists in interactive information\nretrieval, thus no additional user effort is needed to collect them. In\nthis paper, we study how to exploit such information (HQ and HC ),\ndevelop models to incorporate the query history and clickthrough\nhistory into a retrieval ranking function, and quantitatively evaluate\nthese models.\n3. LANGUAGE MODELS FOR\nCONTEXTSENSITIVEINFORMATIONRETRIEVAL\nIntuitively, the query history HQ and clickthrough history HC\nare both useful for improving search accuracy for the current query\nQk. An important research question is how we can exploit such\ninformation effectively. We propose to use statistical language\nmodels to model a user\"s information need and develop four specific\ncontext-sensitive language models to incorporate context\ninformation into a basic retrieval model.\n3.1 Basic retrieval model\nWe use the Kullback-Leibler (KL) divergence method [19] as\nour basic retrieval method. According to this model, the retrieval\ntask involves computing a query language model \u03b8Q for a given\nquery and a document language model \u03b8D for a document and then\ncomputing their KL divergence D(\u03b8Q||\u03b8D), which serves as the\nscore of the document.\nOne advantage of this approach is that we can naturally\nincorporate the search context as additional evidence to improve our\nestimate of the query language model.\nFormally, let HQ = (Q1, ..., Qk\u22121) be the query history and\nthe current query be Qk. Let HC = (C1, ..., Ck\u22121) be the\nclickthrough history. Note that Ci is the concatenation of all clicked\ndocuments\" summaries in the i-th round of retrieval since we may\nreasonably treat all these summaries equally. Our task is to estimate\na context query model, which we denote by p(w|\u03b8k), based on the\ncurrent query Qk, as well as the query history HQ and clickthrough\nhistory HC . We now describe several different language models for\nexploiting HQ and HC to estimate p(w|\u03b8k). We will use c(w, X)\nto denote the count of word w in text X, which could be either a\nquery or a clicked document\"s summary or any other text. We will\nuse |X| to denote the length of text X or the total number of words\nin X.\n3.2 Fixed Coefficient Interpolation (FixInt)\nOur first idea is to summarize the query history HQ with a\nunigram language model p(w|HQ) and the clickthrough history HC\nwith another unigram language model p(w|HC ). Then we linearly\ninterpolate these two history models to obtain the history model\np(w|H). Finally, we interpolate the history model p(w|H) with\nthe current query model p(w|Qk). These models are defined as\nfollows.\np(w|Qi) =\nc(w, Qi)\n|Qi|\np(w|HQ) =\n1\nk \u2212 1\ni=k\u22121\ni=1\np(w|Qi)\np(w|Ci) =\nc(w, Ci)\n|Ci|\np(w|HC ) =\n1\nk \u2212 1\ni=k\u22121\ni=1\np(w|Ci)\np(w|H) = \u03b2p(w|HC ) + (1 \u2212 \u03b2)p(w|HQ)\np(w|\u03b8k) = \u03b1p(w|Qk) + (1 \u2212 \u03b1)p(w|H)\nwhere \u03b2 \u2208 [0, 1] is a parameter to control the weight on each\nhistory model, and where \u03b1 \u2208 [0, 1] is a parameter to control the\nweight on the current query and the history information.\nIf we combine these equations, we see that\np(w|\u03b8k) = \u03b1p(w|Qk) + (1 \u2212 \u03b1)[\u03b2p(w|HC ) + (1 \u2212 \u03b2)p(w|HQ)]\nThat is, the estimated context query model is just a fixed coefficient\ninterpolation of three models p(w|Qk), p(w|HQ), and p(w|HC ).\n3.3 Bayesian Interpolation (BayesInt)\nOne possible problem with the FixInt approach is that the\ncoefficients, especially \u03b1, are fixed across all the queries. But intuitively,\nif our current query Qk is very long, we should trust the current\nquery more, whereas if Qk has just one word, it may be beneficial\nto put more weight on the history. To capture this intuition, we treat\np(w|HQ) and p(w|HC ) as Dirichlet priors and Qk as the observed\ndata to estimate a context query model using Bayesian estimator.\nThe estimated model is given by\np(w|\u03b8k) =\nc(w, Qk) + \u00b5p(w|HQ) + \u03bdp(w|HC )\n|Qk| + \u00b5 + \u03bd\n=\n|Qk|\n|Qk| + \u00b5 + \u03bd\np(w|Qk)+\n\u00b5 + \u03bd\n|Qk| + \u00b5 + \u03bd\n[\n\u00b5\n\u00b5 + \u03bd\np(w|HQ)+\n\u03bd\n\u00b5 + \u03bd\np(w|HC )]\nwhere \u00b5 is the prior sample size for p(w|HQ) and \u03bd is the prior\nsample size for p(w|HC ). We see that the only difference between\nBayesInt and FixInt is the interpolation coefficients are now\nadaptive to the query length. Indeed, when viewing BayesInt as FixInt,\nwe see that \u03b1 = |Qk|\n|Qk|+\u00b5+\u03bd\n, \u03b2 = \u03bd\n\u03bd+\u00b5\n, thus with fixed \u00b5 and \u03bd,\nwe will have a query-dependent \u03b1. Later we will show that such an\nadaptive \u03b1 empirically performs better than a fixed \u03b1.\n3.4 Online Bayesian Updating (OnlineUp)\nBoth FixInt and BayesInt summarize the history information by\naveraging the unigram language models estimated based on\nprevious queries or clicked summaries. This means that all previous\nqueries are treated equally and so are all clicked summaries.\nHowever, as the user interacts with the system and acquires more\nknowledge about the information in the collection, presumably, the\nreformulated queries will become better and better. Thus assigning\ndecaying weights to the previous queries so as to trust a recent query\nmore than an earlier query appears to be reasonable. Interestingly,\nif we incrementally update our belief about the user\"s information\nneed after seeing each query, we could naturally obtain decaying\nweights on the previous queries. Since such an incremental online\nupdating strategy can be used to exploit any evidence in an\ninteractive retrieval system, we present it in a more general way.\nIn a typical retrieval system, the retrieval system responds to\nevery new query entered by the user by presenting a ranked list\nof documents. In order to rank documents, the system must have\nsome model for the user\"s information need. In the KL divergence\nretrieval model, this means that the system must compute a query\nmodel whenever a user enters a (new) query. A principled way of\nupdating the query model is to use Bayesian estimation, which we\ndiscuss below.\n3.4.1 Bayesian updating\nWe first discuss how we apply Bayesian estimation to update a\nquery model in general. Let p(w|\u03c6) be our current query model\nand T be a new piece of text evidence observed (e.g., T can be a\nquery or a clicked summary). To update the query model based on\nT, we use \u03c6 to define a Dirichlet prior parameterized as\nDir(\u00b5T p(w1|\u03c6), ..., \u00b5T p(wN |\u03c6))\nwhere \u00b5T is the equivalent sample size of the prior. We use\nDirichlet prior because it is a conjugate prior for multinomial\ndistributions. With such a conjugate prior, the predictive distribution of \u03c6\n(or equivalently, the mean of the posterior distribution of \u03c6 is given\nby\np(w|\u03c6) =\nc(w, T) + \u00b5T p(w|\u03c6)\n|T| + \u00b5T\n(1)\nwhere c(w, T) is the count of w in T and |T| is the length of T.\nParameter \u00b5T indicates our confidence in the prior expressed in\nterms of an equivalent text sample comparable with T. For\nexample, \u00b5T = 1 indicates that the influence of the prior is equivalent to\nadding one extra word to T.\n3.4.2 Sequential query model updating\nWe now discuss how we can update our query model over time\nduring an interactive retrieval process using Bayesian estimation.\nIn general, we assume that the retrieval system maintains a current\nquery model \u03c6i at any moment. As soon as we obtain some implicit\nfeedback evidence in the form of a piece of text Ti, we will update\nthe query model.\nInitially, before we see any user query, we may already have\nsome information about the user. For example, we may have some\ninformation about what documents the user has viewed in the past.\nWe use such information to define a prior on the query model,\nwhich is denoted by \u03c60. After we observe the first query Q1, we\ncan update the query model based on the new observed data Q1.\nThe updated query model \u03c61 can then be used for ranking\ndocuments in response to Q1. As the user views some documents, the\ndisplayed summary text for such documents C1 (i.e., clicked\nsummaries) can serve as some new data for us to further update the\nquery model to obtain \u03c61. As we obtain the second query Q2 from\nthe user, we can update \u03c61 to obtain a new model \u03c62. In general,\nwe may repeat such an updating process to iteratively update the\nquery model.\nClearly, we see two types of updating: (1) updating based on a\nnew query Qi; (2) updating based on a new clicked summary Ci. In\nboth cases, we can treat the current model as a prior of the context\nquery model and treat the new observed query or clicked summary\nas observed data. Thus we have the following updating equations:\np(w|\u03c6i) =\nc(w, Qi) + \u00b5ip(w|\u03c6i\u22121)\n|Qi| + \u00b5i\np(w|\u03c6i) =\nc(w, Ci) + \u03bdip(w|\u03c6i)\n|Ci| + \u03bdi\nwhere \u00b5i is the equivalent sample size for the prior when updating\nthe model based on a query, while \u03bdi is the equivalent sample size\nfor the prior when updating the model based on a clicked summary.\nIf we set \u00b5i = 0 (or \u03bdi = 0) we essentially ignore the prior model,\nthus would start a completely new query model based on the query\nQi (or the clicked summary Ci). On the other hand, if we set \u00b5i =\n+\u221e (or \u03bdi = +\u221e) we essentially ignore the observed query (or\nthe clicked summary) and do not update our model. Thus the model\nremains the same as if we do not observe any new text evidence. In\ngeneral, the parameters \u00b5i and \u03bdi may have different values for\ndifferent i. For example, at the very beginning, we may have very\nsparse query history, thus we could use a smaller \u00b5i, but later as the\nquery history is richer, we can consider using a larger \u00b5i. But in\nour experiments, unless otherwise stated, we set them to the same\nconstants, i.e., \u2200i, j, \u00b5i = \u00b5j, \u03bdi = \u03bdj.\nNote that we can take either p(w|\u03c6i) or p(w|\u03c6i) as our context\nquery model for ranking documents. This suggests that we do not\nhave to wait until a user enters a new query to initiate a new round\nof retrieval; instead, as soon as we collect clicked summary Ci, we\ncan update the query model and use p(w|\u03c6i) to immediately rerank\nany documents that a user has not yet seen.\nTo score documents after seeing query Qk, we use p(w|\u03c6k), i.e.,\np(w|\u03b8k) = p(w|\u03c6k)\n3.5 Batch Bayesian updating (BatchUp)\nIf we set the equivalent sample size parameters to fixed\nconstant, the OnlineUp algorithm would introduce a decaying factor\n- repeated interpolation would cause the early data to have a low\nweight. This may be appropriate for the query history as it is\nreasonable to believe that the user becomes better and better at query\nformulation as time goes on, but it is not necessarily appropriate for\nthe clickthrough information, especially because we use the\ndisplayed summary, rather than the actual content of a clicked\ndocument. One way to avoid applying a decaying interpolation to\nthe clickthrough data is to do OnlineUp only for the query history\nQ = (Q1, ..., Qi\u22121), but not for the clickthrough data C. We first\nbuffer all the clickthrough data together and use the whole chunk\nof clickthrough data to update the model generated through\nrunning OnlineUp on previous queries. The updating equations are as\nfollows.\np(w|\u03c6i) =\nc(w, Qi) + \u00b5ip(w|\u03c6i\u22121)\n|Qi| + \u00b5i\np(w|\u03c8i) =\ni\u22121\nj=1 c(w, Cj) + \u03bdip(w|\u03c6i)\ni\u22121\nj=1 |Cj| + \u03bdi\nwhere \u00b5i has the same interpretation as in OnlineUp, but \u03bdi now\nindicates to what extent we want to trust the clicked summaries. As\nin OnlineUp, we set all \u00b5i\"s and \u03bdi\"s to the same value. And to rank\ndocuments after seeing the current query Qk, we use\np(w|\u03b8k) = p(w|\u03c8k)\n4. DATA COLLECTION\nIn order to quantitatively evaluate our models, we need a data set\nwhich includes not only a text database and testing topics, but also\nquery history and clickthrough history for each topic. Since there\nis no such data set available to us, we have to create one. There\nare two choices. One is to extract topics and any associated query\nhistory and clickthrough history for each topic from the log of a\nretrieval system (e.g., search engine). But the problem is that we\nhave no relevance judgments on such data. The other choice is to\nuse a TREC data set, which has a text database, topic description\nand relevance judgment file. Unfortunately, there are no query\nhistory and clickthrough history data. We decide to augment a TREC\ndata set by collecting query history and clickthrough history data.\nWe select TREC AP88, AP89 and AP90 data as our text database,\nbecause AP data has been used in several TREC tasks and has\nrelatively complete judgments. There are altogether 242918 news\narticles and the average document length is 416 words. Most articles\nhave titles. If not, we select the first sentence of the text as the\ntitle. For the preprocessing, we only do case folding and do not do\nstopword removal or stemming.\nWe select 30 relatively difficult topics from TREC topics 1-150.\nThese 30 topics have the worst average precision performance among\nTREC topics 1-150 according to some baseline experiments using\nthe KL-Divergence model with Bayesian prior smoothing [20]. The\nreason why we select difficult topics is that the user then would\nhave to have several interactions with the retrieval system in order\nto get satisfactory results so that we can expect to collect a\nrelatively richer query history and clickthrough history data from the\nuser. In real applications, we may also expect our models to be\nmost useful for such difficult topics, so our data collection strategy\nreflects the real world applications well.\nWe index the TREC AP data set and set up a search engine and\nweb interface for TREC AP news articles. We use 3 subjects to do\nexperiments to collect query history and clickthrough history data.\nEach subject is assigned 10 topics and given the topic descriptions\nprovided by TREC. For each topic, the first query is the title of\nthe topic given in the original TREC topic description. After the\nsubject submits the query, the search engine will do retrieval and\nreturn a ranked list of search results to the subject. The subject will\nbrowse the results and maybe click one or more results to browse\nthe full text of article(s). The subject may also modify the query to\ndo another search. For each topic, the subject composes at least 4\nqueries. In our experiment, only the first 4 queries for each topic\nare used. The user needs to select the topic number from a\nselection menu before submitting the query to the search engine so that\nwe can easily detect the session boundary, which is not the focus of\nour study. We use a relational database to store user interactions,\nincluding the submitted queries and clicked documents. For each\nquery, we store the query terms and the associated result pages.\nAnd for each clicked document, we store the summary as shown\non the search result page. The summary of the article is query\ndependent and is computed online using fixed-length passage retrieval\n(KL divergence model with Bayesian prior smoothing).\nAmong 120 (4 for each of 30 topics) queries which we study in\nthe experiment, the average query length is 3.71 words. Altogether\nthere are 91 documents clicked to view. So on average, there are\naround 3 clicks per topic. The average length of clicked summary\nFixInt BayesInt OnlineUp BatchUp\nQuery (\u03b1 = 0.1, \u03b2 = 1.0) (\u00b5 = 0.2, \u03bd = 5.0) (\u00b5 = 5.0, \u03bd = 15.0) (\u00b5 = 2.0, \u03bd = 15.0)\nMAP pr@20docs MAP pr@20docs MAP pr@20docs MAP pr@20docs\nq1 0.0095 0.0317 0.0095 0.0317 0.0095 0.0317 0.0095 0.0317\nq2 0.0312 0.1150 0.0312 0.1150 0.0312 0.1150 0.0312 0.1150\nq2 + HQ + HC 0.0324 0.1117 0.0345 0.1117 0.0215 0.0733 0.0342 0.1100\nImprove. 3.8% -2.9% 10.6% -2.9% -31.1% -36.3% 9.6% -4.3%\nq3 0.0421 0.1483 0.0421 0.1483 0.0421 0.1483 0.0421 0.1483\nq3 + HQ + HC 0.0726 0.1967 0.0816 0.2067 0.0706 0.1783 0.0810 0.2067\nImprove 72.4% 32.6% 93.8% 39.4% 67.7% 20.2% 92.4% 39.4%\nq4 0.0536 0.1933 0.0536 0.1933 0.0536 0.1933 0.0536 0.1933\nq4 + HQ + HC 0.0891 0.2233 0.0955 0.2317 0.0792 0.2067 0.0950 0.2250\nImprove 66.2% 15.5% 78.2% 19.9% 47.8% 6.9% 77.2% 16.4%\nTable 1: Effect of using query history and clickthrough data for document ranking.\nis 34.4 words. Among 91 clicked documents, 29 documents are\njudged relevant according to TREC judgment file. This data set is\npublicly available 1\n.\n5. EXPERIMENTS\n5.1 Experiment design\nOur major hypothesis is that using search context (i.e., query\nhistory and clickthrough information) can help improve search\naccuracy. In particular, the search context can provide extra information\nto help us estimate a better query model than using just the current\nquery. So most of our experiments involve comparing the retrieval\nperformance using the current query only (thus ignoring any\ncontext) with that using the current query as well as the search context.\nSince we collected four versions of queries for each topic, we\nmake such comparisons for each version of queries. We use two\nperformance measures: (1) Mean Average Precision (MAP): This\nis the standard non-interpolated average precision and serves as a\ngood measure of the overall ranking accuracy. (2) Precision at 20\ndocuments (pr@20docs): This measure does not average well, but\nit is more meaningful than MAP and reflects the utility for users\nwho only read the top 20 documents. In all cases, the reported\nfigure is the average over all of the 30 topics.\nWe evaluate the four models for exploiting search context (i.e.,\nFixInt, BayesInt, OnlineUp, and BatchUp). Each model has\nprecisely two parameters (\u03b1 and \u03b2 for FixInt; \u00b5 and \u03bd for others).\nNote that \u00b5 and \u03bd may need to be interpreted differently for\ndifferent methods. We vary these parameters and identify the optimal\nperformance for each method. We also vary the parameters to study\nthe sensitivity of our algorithms to the setting of the parameters.\n5.2 Result analysis\n5.2.1 Overall effect of search context\nWe compare the optimal performances of four models with those\nusing the current query only in Table 1. A row labeled with qi is\nthe baseline performance and a row labeled with qi + HQ + HC\nis the performance of using search context. We can make several\nobservations from this table:\n1. Comparing the baseline performances indicates that on average\nreformulated queries are better than the previous queries with the\nperformance of q4 being the best. Users generally formulate better\nand better queries.\n2. Using search context generally has positive effect, especially\nwhen the context is rich. This can be seen from the fact that the\n1\nhttp://sifaka.cs.uiuc.edu/ir/ucair/QCHistory.zip\nimprovement for q4 and q3 is generally more substantial compared\nwith q2. Actually, in many cases with q2, using the context may\nhurt the performance, probably because the history at that point is\nsparse. When the search context is rich, the performance\nimprovement can be quite substantial. For example, BatchUp achieves\n92.4% improvement in the mean average precision over q3 and\n77.2% improvement over q4. (The generally low precisions also\nmake the relative improvement deceptively high, though.)\n3. Among the four models using search context, the performances\nof FixInt and OnlineUp are clearly worse than those of BayesInt\nand BatchUp. Since BayesInt performs better than FixInt and the\nmain difference between BayesInt and FixInt is that the former uses\nan adaptive coefficient for interpolation, the results suggest that\nusing adaptive coefficient is quite beneficial and a Bayesian style\ninterpolation makes sense. The main difference between OnlineUp\nand BatchUp is that OnlineUp uses decaying coefficients to\ncombine the multiple clicked summaries, while BatchUp simply\nconcatenates all clicked summaries. Therefore the fact that BatchUp\nis consistently better than OnlineUp indicates that the weights for\ncombining the clicked summaries indeed should not be decaying.\nWhile OnlineUp is theoretically appealing, its performance is\ninferior to BayesInt and BatchUp, likely because of the decaying\ncoefficient. Overall, BatchUp appears to be the best method when we\nvary the parameter settings.\nWe have two different kinds of search context - query history\nand clickthrough data. We now look into the contribution of each\nkind of context.\n5.2.2 Using query history only\nIn each of four models, we can turn off the clickthrough\nhistory data by setting parameters appropriately. This allows us to\nevaluate the effect of using query history alone. We use the same\nparameter setting for query history as in Table 1. The results are\nshown in Table 2. Here we see that in general, the benefit of using\nquery history is very limited with mixed results. This is different\nfrom what is reported in a previous study [15], where using query\nhistory is consistently helpful. Another observation is that the\ncontext runs perform poorly at q2, but generally perform (slightly)\nbetter than the baselines for q3 and q4. This is again likely because\nat the beginning the initial query, which is the title in the original\nTREC topic description, may not be a good query; indeed, on\naverage, performances of these first-generation queries are clearly\npoorer than those of all other user-formulated queries in the later\ngenerations. Yet another observation is that when using query\nhistory only, the BayesInt model appears to be better than other\nmodels. Since the clickthrough data is ignored, OnlineUp and BatchUp\nFixInt BayesInt OnlineUp BatchUp\nQuery (\u03b1 = 0.1, \u03b2 = 0) (\u00b5 = 0.2,\u03bd = 0) (\u00b5 = 5.0,\u03bd = +\u221e) (\u00b5 = 2.0, \u03bd = +\u221e)\nMAP pr@20docs MAP pr@20docs MAP pr@20docs MAP pr@20docs\nq2 0.0312 0.1150 0.0312 0.1150 0.0312 0.1150 0.0312 0.1150\nq2 + HQ 0.0097 0.0317 0.0311 0.1200 0.0213 0.0783 0.0287 0.0967\nImprove. -68.9% -72.4% -0.3% 4.3% -31.7% -31.9% -8.0% -15.9%\nq3 0.0421 0.1483 0.0421 0.1483 0.0421 0.1483 0.0421 0.1483\nq3 + HQ 0.0261 0.0917 0.0451 0.1517 0.0444 0.1333 0.0455 0.1450\nImprove -38.2% -38.2% 7.1% 2.3% 5.5% -10.1% 8.1% -2.2%\nq4 0.0536 0.1933 0.0536 0.1933 0.0536 0.1933 0.0536 0.1933\nq4 + HQ 0.0428 0.1467 0.0537 0.1917 0.0550 0.1733 0.0552 0.1917\nImprove -20.1% -24.1% 0.2% -0.8% 3.0% -10.3% 3.0% -0.8%\nTable 2: Effect of using query history only for document ranking.\n\u00b5 0 0.5 1 2 3 4 5 6 7 8 9\nq2 + HQ MAP 0.0312 0.0313 0.0308 0.0287 0.0257 0.0231 0.0213 0.0194 0.0183 0.0182 0.0164\nq3 + HQ MAP 0.0421 0.0442 0.0441 0.0455 0.0457 0.0458 0.0444 0.0439 0.0430 0.0390 0.0335\nq4 + HQ MAP 0.0536 0.0546 0.0547 0.0552 0.0544 0.0548 0.0550 0.0541 0.0534 0.0525 0.0513\nTable 3: Average Precision of BatchUp using query history only\nare essentially the same algorithm. The displayed results thus\nreflect the variation caused by parameter \u00b5. A smaller setting of 2.0\nis seen better than a larger value of 5.0. A more complete picture\nof the influence of the setting of \u00b5 can be seen from Table 3, where\nwe show the performance figures for a wider range of values of \u00b5.\nThe value of \u00b5 can be interpreted as how many words we regard\nthe query history is worth. A larger value thus puts more weight\non the history and is seen to hurt the performance more when the\nhistory information is not rich. Thus while for q4 the best\nperformance tends to be achieved for \u00b5 \u2208 [2, 5], only when \u00b5 = 0.5 we\nsee some small benefit for q2. As we would expect, an excessively\nlarge \u00b5 would hurt the performance in general, but q2 is hurt most\nand q4 is barely hurt, indicating that as we accumulate more and\nmore query history information, we can put more and more weight\non the history information. This also suggests that a better strategy\nshould probably dynamically adjust parameters according to how\nmuch history information we have.\nThe mixed query history results suggest that the positive effect\nof using implicit feedback information may have largely come from\nthe use of clickthrough history, which is indeed true as we discuss\nin the next subsection.\n5.2.3 Using clickthrough history only\nWe now turn off the query history and only use the clicked\nsummaries plus the current query. The results are shown in Table 4. We\nsee that the benefit of using clickthrough information is much more\nsignificant than that of using query history. We see an overall\npositive effect, often with significant improvement over the baseline. It\nis also clear that the richer the context data is, the more\nimprovement using clicked summaries can achieve. Other than some\noccasional degradation of precision at 20 documents, the improvement\nis fairly consistent and often quite substantial.\nThese results show that the clicked summary text is in general\nquite useful for inferring a user\"s information need. Intuitively,\nusing the summary text, rather than the actual content of the\ndocument, makes more sense, as it is quite possible that the document\nbehind a seemingly relevant summary is actually non-relevant.\n29 out of the 91 clicked documents are relevant. Updating the\nquery model based on such summaries would bring up the ranks\nof these relevant documents, causing performance improvement.\nHowever, such improvement is really not beneficial for the user as\nthe user has already seen these relevant documents. To see how\nmuch improvement we have achieved on improving the ranks of\nthe unseen relevant documents, we exclude these 29 relevant\ndocuments from our judgment file and recompute the performance of\nBayesInt and the baseline using the new judgment file. The results\nare shown in Table 5. Note that the performance of the baseline\nmethod is lower due to the removal of the 29 relevant documents,\nwhich would have been generally ranked high in the results. From\nTable 5, we see clearly that using clicked summaries also helps\nimprove the ranks of unseen relevant documents significantly.\nQuery BayesInt(\u00b5 = 0, \u03bd = 5.0)\nMAP pr@20docs\nq2 0.0263 0.100\nq2 + HC 0.0314 0.100\nImprove. 19.4% 0%\nq3 0.0331 0.125\nq3 + HC 0.0661 0.178\nImprove 99.7% 42.4%\nq4 0.0442 0.165\nq4 + HC 0.0739 0.188\nImprove 67.2% 13.9%\nTable 5: BayesInt evaluated on unseen relevant documents\nOne remaining question is whether the clickthrough data is still\nhelpful if none of the clicked documents is relevant. To answer\nthis question, we took out the 29 relevant summaries from our\nclickthrough history data HC to obtain a smaller set of clicked\nsummaries HC , and re-evaluated the performance of the BayesInt\nmethod using HC with the same setting of parameters as in\nTable 4. The results are shown in Table 6. We see that although the\nimprovement is not as substantial as in Table 4, the average\nprecision is improved across all generations of queries. These results\nshould be interpreted as very encouraging as they are based on only\n62 non-relevant clickthroughs. In reality, a user would more likely\nclick some relevant summaries, which would help bring up more\nrelevant documents as we have seen in Table 4 and Table 5.\nFixInt BayesInt OnlineUp BatchUp\nQuery (\u03b1 = 0.1, \u03b2 = 1) (\u00b5 = 0, \u03bd = 5.0) (\u00b5k = 5.0, \u03bd = 15, \u2200i < k, \u00b5i = +\u221e) (\u00b5 = 0, \u03bd = 15)\nMAP pr@20docs MAP pr@20docs MAP pr@20docs MAP pr@20docs\nq2 0.0312 0.1150 0.0312 0.1150 0.0312 0.1150 0.0312 0.1150\nq2 + HC 0.0324 0.1117 0.0338 0.1133 0.0358 0.1300 0.0344 0.1167\nImprove. 3.8% -2.9% 8.3% -1.5% 14.7% 13.0% 10.3% 1.5%\nq3 0.0421 0.1483 0.0421 0.1483 0.04210 0.1483 0.0420 0.1483\nq3 + HC 0.0726 0.1967 0.0766 0.2033 0.0622 0.1767 0.0513 0.1650\nImprove 72.4% 32.6% 81.9% 37.1% 47.7% 19.2% 21.9% 11.3%\nq4 0.0536 0.1930 0.0536 0.1930 0.0536 0.1930 0.0536 0.1930\nq4 + HC 0.0891 0.2233 0.0925 0.2283 0.0772 0.2217 0.0623 0.2050\nImprove 66.2% 15.5% 72.6% 18.1% 44.0% 14.7% 16.2% 6.1%\nTable 4: Effect of using clickthrough data only for document ranking.\nQuery BayesInt(\u00b5 = 0, \u03bd = 5.0)\nMAP pr@20docs\nq2 0.0312 0.1150\nq2 + HC 0.0313 0.0950\nImprove. 0.3% -17.4%\nq3 0.0421 0.1483\nq3 + HC 0.0521 0.1820\nImprove 23.8% 23.0%\nq4 0.0536 0.1930\nq4 + HC 0.0620 0.1850\nImprove 15.7% -4.1%\nTable 6: Effect of using only non-relevant clickthrough data\n5.2.4 Additive effect of context information\nBy comparing the results across Table 1, Table 2 and Table 4,\nwe can see that the benefit of the query history information and\nthat of clickthrough information are mostly additive, i.e.,\ncombining them can achieve better performance than using each alone,\nbut most improvement has clearly come from the clickthrough\ninformation. In Table 7, we show this effect for the BatchUp method.\n5.2.5 Parameter sensitivity\nAll four models have two parameters to control the relative weights\nof HQ, HC , and Qk, though the parameterization is different from\nmodel to model. In this subsection, we study the parameter\nsensitivity for BatchUp, which appears to perform relatively better than\nothers. BatchUp has two parameters \u00b5 and \u03bd.\nWe first look at \u00b5. When \u00b5 is set to 0, the query history is not\nused at all, and we essentially just use the clickthrough data\ncombined with the current query. If we increase \u00b5, we will gradually\nincorporate more information from the previous queries. In Table 8,\nwe show how the average precision of BatchUp changes as we vary\n\u00b5 with \u03bd fixed to 15.0, where the best performance of BatchUp is\nachieved. We see that the performance is mostly insensitive to the\nchange of \u00b5 for q3 and q4, but is decreasing as \u00b5 increases for q2.\nThe pattern is also similar when we set \u03bd to other values.\nIn addition to the fact that q1 is generally worse than q2, q3, and\nq4, another possible reason why the sensitivity is lower for q3 and\nq4 may be that we generally have more clickthrough data\navailable for q3 and q4 than for q2, and the dominating influence of the\nclickthrough data has made the small differences caused by \u00b5 less\nvisible for q3 and q4.\nThe best performance is generally achieved when \u00b5 is around\n2.0, which means that the past query information is as useful as\nabout 2 words in the current query. Except for q2, there is clearly\nsome tradeoff between the current query and the previous queries\nQuery MAP pr@20docs\nq2 0.0312 0.1150\nq2 + HQ 0.0287 0.0967\nImprove. -8.0% -15.9%\nq2 + HC 0.0344 0.1167\nImprove. 10.3% 1.5%\nq2 + HQ + HC 0.0342 0.1100\nImprove. 9.6% -4.3%\nq3 0.0421 0.1483\nq3 + HQ 0.0455 0.1450\nImprove 8.1% -2.2%\nq3 + HC 0.0513 0.1650\nImprove 21.9% 11.3%\nq3 + HQ + HC 0.0810 0.2067\nImprove 92.4% 39.4%\nq4 0.0536 0.1930\nq4 + HQ 0.0552 0.1917\nImprove 3.0% -0.8%\nq4 + HC 0.0623 0.2050\nImprove 16.2% 6.1%\nq4 + HQ + HC 0.0950 0.2250\nImprove 77.2% 16.4%\nTable 7: Additive benefit of context information\nand using a balanced combination of them achieves better\nperformance than using each of them alone.\nWe now turn to the other parameter \u03bd. When \u03bd is set to 0, we\nonly use the clickthrough data; When \u03bd is set to +\u221e, we only use\nthe query history and the current query. With \u00b5 set to 2.0, where\nthe best performance of BatchUp is achieved, we vary \u03bd and show\nthe results in Table 9. We see that the performance is also not very\nsensitive when \u03bd \u2264 30, with the best performance often achieved\nat \u03bd = 15. This means that the combined information of query\nhistory and the current query is as useful as about 15 words in the\nclickthrough data, indicating that the clickthrough information is\nhighly valuable.\nOverall, these sensitivity results show that BatchUp not only\nperforms better than other methods, but also is quite robust.\n6. CONCLUSIONS AND FUTURE WORK\nIn this paper, we have explored how to exploit implicit\nfeedback information, including query history and clickthrough history\nwithin the same search session, to improve information retrieval\nperformance. Using the KL-divergence retrieval model as the\nbasis, we proposed and studied four statistical language models for\ncontext-sensitive information retrieval, i.e., FixInt, BayesInt,\nOnlineUp and BatchUp. We use TREC AP Data to create a test set\n\u00b5 0 1 2 3 4 5 6 7 8 9 10\nMAP 0.0386 0.0366 0.0342 0.0315 0.0290 0.0267 0.0250 0.0236 0.0229 0.0223 0.0219\nq2 + HQ + HC pr@20 0.1333 0.1233 0.1100 0.1033 0.1017 0.0933 0.0833 0.0767 0.0783 0.0767 0.0750\nMAP 0.0805 0.0807 0.0811 0.0814 0.0813 0.0808 0.0804 0.0799 0.0795 0.0790 0.0788\nq3 + HQ + HC pr@20 0.210 0.2150 0.2067 0.205 0.2067 0.205 0.2067 0.2067 0.2050 0.2017 0.2000\nMAP 0.0929 0.0947 0.0950 0.0940 0.0941 0.0940 0.0942 0.0937 0.0936 0.0932 0.0929\nq4 + HQ + HC pr@20 0.2183 0.2217 0.2250 0.2217 0.2233 0.2267 0.2283 0.2333 0.2333 0.2350 0.2333\nTable 8: Sensitivity of \u00b5 in BatchUp\n\u03bd 0 1 2 5 10 15 30 100 300 500\nMAP 0.0278 0.0287 0.0296 0.0315 0.0334 0.0342 0.0328 0.0311 0.0296 0.0290\nq2 + HQ + HC pr@20 0.0933 0.0950 0.0950 0.1000 0.1050 0.1100 0.1150 0.0983 0.0967 0.0967\nMAP 0.0728 0.0739 0.0751 0.0786 0.0809 0.0811 0.0770 0.0634 0.0511 0.0491\nq3 + HQ + HC pr@20 0.1917 0.1933 0.1950 0.2100 0.2000 0.2067 0.2017 0.1783 0.1600 0.1550\nMAP 0.0895 0.0903 0.0914 0.0932 0.0944 0.0950 0.0919 0.0761 0.0664 0.0625\nq4 + HQ + HC pr@20 0.2267 0.2233 0.2283 0.2317 0.2233 0.2250 0.2283 0.2200 0.2067 0.2033\nTable 9: Sensitivity of \u03bd in BatchUp\nfor evaluating implicit feedback models. Experiment results show\nthat using implicit feedback, especially clickthrough history, can\nsubstantially improve retrieval performance without requiring any\nadditional user effort.\nThe current work can be extended in several ways: First, we\nhave only explored some very simple language models for\nincorporating implicit feedback information. It would be interesting to\ndevelop more sophisticated models to better exploit query history\nand clickthrough history. For example, we may treat a clicked\nsummary differently depending on whether the current query is a\ngeneralization or refinement of the previous query. Second, the\nproposed models can be implemented in any practical systems. We are\ncurrently developing a client-side personalized search agent, which\nwill incorporate some of the proposed algorithms. We will also do\na user study to evaluate effectiveness of these models in the real\nweb search. Finally, we should further study a general retrieval\nframework for sequential decision making in interactive\ninformation retrieval and study how to optimize some of the parameters in\nthe context-sensitive retrieval models.\n7. ACKNOWLEDGMENTS\nThis material is based in part upon work supported by the\nNational Science Foundation under award numbers IIS-0347933 and\nIIS-0428472. We thank the anonymous reviewers for their useful\ncomments.\n8. REFERENCES\n[1] E. Adar and D. Karger. Haystack: Per-user information\nenvironments. In Proceedings of CIKM 1999, 1999.\n[2] J. Allan and et al. Challenges in information retrieval and\nlanguage modeling. Workshop at University of Amherst,\n2002.\n[3] K. Bharat. Searchpad: Explicit capture of search context to\nsupport web search. In Proceeding of WWW 2000, 2000.\n[4] W. B. Croft, S. Cronen-Townsend, and V. Larvrenko.\nRelevance feedback and personalization: A language\nmodeling perspective. In Proeedings of Second DELOS\nWorkshop: Personalisation and Recommender Systems in\nDigital Libraries, 2001.\n[5] H. Cui, J.-R. Wen, J.-Y. Nie, and W.-Y. Ma. Probabilistic\nquery expansion using query logs. In Proceedings of WWW\n2002, 2002.\n[6] S. T. Dumais, E. Cutrell, R. Sarin, and E. Horvitz. Implicit\nqueries (IQ) for contextualized search (demo description). In\nProceedings of SIGIR 2004, page 594, 2004.\n[7] L. Finkelstein, E. Gabrilovich, Y. Matias, E. Rivlin, Z. Solan,\nG. Wolfman, and E. Ruppin. Placing search in context: The\nconcept revisited. In Proceedings of WWW 2002, 2001.\n[8] C. Huang, L. Chien, and Y. Oyang. Query session based term\nsuggestion for interactive web search. In Proceedings of\nWWW 2001, 2001.\n[9] X. Huang, F. Peng, A. An, and D. Schuurmans. Dynamic\nweb log session identification with statistical language\nmodels. Journal of the American Society for Information\nScience and Technology, 55(14):1290-1303, 2004.\n[10] G. Jeh and J. Widom. Scaling personalized web search. In\nProceeding of WWW 2003, 2003.\n[11] T. Joachims. Optimizing search engines using clickthrough\ndata. In Proceedings of SIGKDD 2002, 2002.\n[12] D. Kelly and N. J. Belkin. Display time as implicit feedback:\nUnderstanding task effects. In Proceedings of SIGIR 2004,\n2004.\n[13] D. Kelly and J. Teevan. Implicit feedback for inferring user\npreference. SIGIR Forum, 32(2), 2003.\n[14] J. Rocchio. Relevance feedback information retrieval. In The\nSmart Retrieval System-Experiments in Automatic Document\nProcessing, pages 313-323, Kansas City, MO, 1971.\nPrentice-Hall.\n[15] X. Shen and C. Zhai. Exploiting query history for document\nranking in interactive information retrieval (poster). In\nProceedings of SIGIR 2003, 2003.\n[16] S. Sriram, X. Shen, and C. Zhai. A session-based search\nengine (poster). In Proceedings of SIGIR 2004, 2004.\n[17] K. Sugiyama, K. Hatano, and M. Yoshikawa. Adaptive web\nsearch based on user profile constructed without any effort\nfrom users. In Proceedings of WWW 2004, 2004.\n[18] R. W. White, J. M. Jose, C. J. van Rijsbergen, and\nI. Ruthven. A simulated study of implicit feedback models.\nIn Proceedings of ECIR 2004, pages 311-326, 2004.\n[19] C. Zhai and J. Lafferty. Model-based feedback in the\nKL-divergence retrieval model. In Proceedings of CIKM\n2001, 2001.\n[20] C. Zhai and J. Lafferty. A study of smoothing methods for\nlanguage models applied to ad-hoc information retrieval. In\nProceedings of SIGIR 2001, 2001.", "keywords": "kl-divergence retrieval model;context-sensitive language;long-term context;interactive retrieval;trec datum set;query expansion;mean average precision;fixed coefficient interpolation;query history information;implicit feedback information;current query;query history;context;retrieval accuracy;relevance feedback;clickthrough information;short-term context;bayesian estimation"}
{"name": "train_H-92", "title": "Improving Web Search Ranking by Incorporating User Behavior Information", "abstract": "We show that incorporating user behavior data can significantly improve ordering of top results in real web search setting. We examine alternatives for incorporating feedback into the ranking process and explore the contributions of user feedback compared to other common web search features. We report results of a large scale evaluation over 3,000 queries and 12 million user interactions with a popular web search engine. We show that incorporating implicit feedback can augment other features, improving the accuracy of a competitive web search ranking algorithms by as much as 31% relative to the original performance.", "fulltext": "1. INTRODUCTION\nMillions of users interact with search engines daily. They issue\nqueries, follow some of the links in the results, click on ads, spend\ntime on pages, reformulate their queries, and perform other\nactions. These interactions can serve as a valuable source of\ninformation for tuning and improving web search result ranking\nand can compliment more costly explicit judgments.\nImplicit relevance feedback for ranking and personalization has\nbecome an active area of research. Recent work by Joachims and\nothers exploring implicit feedback in controlled environments\nhave shown the value of incorporating implicit feedback into the\nranking process. Our motivation for this work is to understand\nhow implicit feedback can be used in a large-scale operational\nenvironment to improve retrieval. How does it compare to and\ncompliment evidence from page content, anchor text, or link-based\nfeatures such as inlinks or PageRank? While it is intuitive that\nuser interactions with the web search engine should reveal at least\nsome information that could be used for ranking, estimating user\npreferences in real web search settings is a challenging problem,\nsince real user interactions tend to be more noisy than\ncommonly assumed in the controlled settings of previous studies.\nOur paper explores whether implicit feedback can be helpful in\nrealistic environments, where user feedback can be noisy (or\nadversarial) and a web search engine already uses hundreds of\nfeatures and is heavily tuned. To this end, we explore different\napproaches for ranking web search results using real user behavior\nobtained as part of normal interactions with the web search\nengine.\nThe specific contributions of this paper include:\n\u2022 Analysis of alternatives for incorporating user behavior\ninto web search ranking (Section 3).\n\u2022 An application of a robust implicit feedback model\nderived from mining millions of user interactions with a\nmajor web search engine (Section 4).\n\u2022 A large scale evaluation over real user queries and search\nresults, showing significant improvements derived from\nincorporating user feedback (Section 6).\nWe summarize our findings and discuss extensions to the current\nwork in Section 7, which concludes the paper.\n2. BACKGROUND AND RELATED WORK\nRanking search results is a fundamental problem in information\nretrieval. Most common approaches primarily focus on similarity\nof query and a page, as well as the overall page quality [3,4,24].\nHowever, with increasing popularity of search engines, implicit\nfeedback (i.e., the actions users take when interacting with the\nsearch engine) can be used to improve the rankings.\nImplicit relevance measures have been studied by several research\ngroups. An overview of implicit measures is compiled in Kelly and\nTeevan [14]. This research, while developing valuable insights\ninto implicit relevance measures, was not applied to improve the\nranking of web search results in realistic settings.\nClosely related to our work, Joachims [11] collected implicit\nmeasures in place of explicit measures, introducing a technique\nbased entirely on clickthrough data to learn ranking functions. Fox\net al. [8] explored the relationship between implicit and explicit\nmeasures in Web search, and developed Bayesian models to\ncorrelate implicit measures and explicit relevance judgments for\nboth individual queries and search sessions. This work considered\na wide range of user behaviors (e.g., dwell time, scroll time,\nreformulation patterns) in addition to the popular clickthrough\nbehavior. However, the modeling effort was aimed at predicting\nexplicit relevance judgments from implicit user actions and not\nspecifically at learning ranking functions. Other studies of user\nbehavior in web search include Pharo and J\u00e4rvelin [19], but were\nnot directly applied to improve ranking.\nMore recently, Joachims et al. [12] presented an empirical\nevaluation of interpreting clickthrough evidence. By performing\neye tracking studies and correlating predictions of their strategies\nwith explicit ratings, the authors showed that it is possible to\naccurately interpret clickthroughs in a controlled, laboratory\nsetting. Unfortunately, the extent to which previous research\napplies to real-world web search is unclear. At the same time,\nwhile recent work (e.g., [26]) on using clickthrough information\nfor improving web search ranking is promising, it captures only\none aspect of the user interactions with web search engines.\nWe build on existing research to develop robust user behavior\ninterpretation techniques for the real web search setting. Instead of\ntreating each user as a reliable expert, we aggregate information\nfrom multiple, unreliable, user search session traces, as we\ndescribe in the next two sections.\n3. INCORPORATING IMPLICIT\nFEEDBACK\nWe consider two complementary approaches to ranking with\nimplicit feedback: (1) treating implicit feedback as independent\nevidence for ranking results, and (2) integrating implicit feedback\nfeatures directly into the ranking algorithm. We describe the two\ngeneral ranking approaches next. The specific implicit feedback\nfeatures are described in Section 4, and the algorithms for\ninterpreting and incorporating implicit feedback are described in\nSection 5.\n3.1 Implicit Feedback as Independent\nEvidence\nThe general approach is to re-rank the results obtained by a web\nsearch engine according to observed clickthrough and other user\ninteractions for the query in previous search sessions. Each result\nis assigned a score according to expected relevance/user\nsatisfaction based on previous interactions, resulting in some\npreference ordering based on user interactions alone.\nWhile there has been significant work on merging multiple\nrankings, we adapt a simple and robust approach of ignoring the\noriginal rankers\" scores, and instead simply merge the rank orders.\nThe main reason for ignoring the original scores is that since the\nfeature spaces and learning algorithms are different, the scores are\nnot directly comparable, and re-normalization tends to remove the\nbenefit of incorporating classifier scores.\nWe experimented with a variety of merging functions on the\ndevelopment set of queries (and using a set of interactions from a\ndifferent time period from final evaluation sets). We found that a\nsimple rank merging heuristic combination works well, and is\nrobust to variations in score values from original rankers. For a\ngiven query q, the implicit score ISd is computed for each result d\nfrom available user interaction features, resulting in the implicit\nrank Id for each result. We compute a merged score SM(d) for d by\ncombining the ranks obtained from implicit feedback, Id with the\noriginal rank of d, Od:\n\n\n\u00a1\n\n\n\u00a2\n\u00a3\n+\n+\n+\n+\n=\notherwise\nO\ndforexistsfeedbackimplicitif\nOI\nw\nwOIdS\nd\ndd\nI\nIddM\n1\n1\n1\n1\n1\n1\n),,,(\nwhere the weight wI is a heuristically tuned scaling factor\nrepresenting the relative importance of the implicit feedback.\nThe query results are ordered in by decreasing values of SM to\nproduce the final ranking. One special case of this model arises\nwhen setting wI to a very large value, effectively forcing clicked\nresults to be ranked higher than un-clicked results - an intuitive\nand effective heuristic that we will use as a baseline. Applying\nmore sophisticated classifier and ranker combination algorithms\nmay result in additional improvements, and is a promising\ndirection for future work.\nThe approach above assumes that there are no interactions\nbetween the underlying features producing the original web search\nranking and the implicit feedback features. We now relax this\nassumption by integrating implicit feedback features directly into\nthe ranking process.\n3.2 Ranking with Implicit Feedback Features\nModern web search engines rank results based on a large number\nof features, including content-based features (i.e., how closely a\nquery matches the text or title or anchor text of the document), and\nquery-independent page quality features (e.g., PageRank of the\ndocument or the domain). In most cases, automatic (or\nsemiautomatic) methods are developed for tuning the specific ranking\nfunction that combines these feature values.\nHence, a natural approach is to incorporate implicit feedback\nfeatures directly as features for the ranking algorithm. During\ntraining or tuning, the ranker can be tuned as before but with\nadditional features. At runtime, the search engine would fetch the\nimplicit feedback features associated with each query-result URL\npair. This model requires a ranking algorithm to be robust to\nmissing values: more than 50% of queries to web search engines\nare unique, with no previous implicit feedback available. We now\ndescribe such a ranker that we used to learn over the combined\nfeature sets including implicit feedback.\n3.3 Learning to Rank Web Search Results\nA key aspect of our approach is exploiting recent advances in\nmachine learning, namely trainable ranking algorithms for web\nsearch and information retrieval (e.g., [5, 11] and classical results\nreviewed in [3]). In our setting, explicit human relevance\njudgments (labels) are available for a set of web search queries\nand results. Hence, an attractive choice to use is a supervised\nmachine learning technique to learn a ranking function that best\npredicts relevance judgments.\nRankNet is one such algorithm. It is a neural net tuning algorithm\nthat optimizes feature weights to best match explicitly provided\npairwise user preferences. While the specific training algorithms\nused by RankNet are beyond the scope of this paper, it is\ndescribed in detail in [5] and includes extensive evaluation and\ncomparison with other ranking methods. An attractive feature of\nRankNet is both train- and run-time efficiency - runtime ranking\ncan be quickly computed and can scale to the web, and training\ncan be done over thousands of queries and associated judged\nresults.\nWe use a 2-layer implementation of RankNet in order to model\nnon-linear relationships between features. Furthermore, RankNet\ncan learn with many (differentiable) cost functions, and hence can\nautomatically learn a ranking function from human-provided\nlabels, an attractive alternative to heuristic feature combination\ntechniques. Hence, we will also use RankNet as a generic ranker\nto explore the contribution of implicit feedback for different\nranking alternatives.\n4. IMPLICIT USER FEEDBACK MODEL\nOur goal is to accurately interpret noisy user feedback obtained as\nby tracing user interactions with the search engine. Interpreting\nimplicit feedback in real web search setting is not an easy task.\nWe characterize this problem in detail in [1], where we motivate\nand evaluate a wide variety of models of implicit user activities.\nThe general approach is to represent user actions for each search\nresult as a vector of features, and then train a ranker on these\nfeatures to discover feature values indicative of relevant (and\nnonrelevant) search results. We first briefly summarize our features\nand model, and the learning approach (Section 4.2) in order to\nprovide sufficient information to replicate our ranking methods\nand the subsequent experiments.\n4.1 Representing User Actions as Features\nWe model observed web search behaviors as a combination of a\n``background\"\" component (i.e., query- and relevance-independent\nnoise in user behavior, including positional biases with result\ninteractions), and a ``relevance\"\" component (i.e., query-specific\nbehavior indicative of relevance of a result to a query). We design\nour features to take advantage of aggregated user behavior. The\nfeature set is comprised of directly observed features (computed\ndirectly from observations for each query), as well as\nqueryspecific derived features, computed as the deviation from the\noverall query-independent distribution of values for the\ncorresponding directly observed feature values.\nThe features used to represent user interactions with web search\nresults are summarized in Table 4.1. This information was\nobtained via opt-in client-side instrumentation from users of a\nmajor web search engine.\nWe include the traditional implicit feedback features such as\nclickthrough counts for the results, as well as our novel derived\nfeatures such as the deviation of the observed clickthrough number\nfor a given query-URL pair from the expected number of clicks on\na result in the given position. We also model the browsing\nbehavior after a result was clicked - e.g., the average page dwell\ntime for a given query-URL pair, as well as its deviation from the\nexpected (average) dwell time. Furthermore, the feature set was\ndesigned to provide essential information about the user\nexperience to make feedback interpretation robust. For example,\nweb search users can often determine whether a result is relevant\nby looking at the result title, URL, and summary - in many cases,\nlooking at the original document is not necessary. To model this\naspect of user experience we include features such as overlap in\nwords in title and words in query (TitleOverlap) and the fraction\nof words shared by the query and the result summary.\nClickthrough features\nPosition Position of the URL in Current ranking\nClickFrequency Number of clicks for this query, URL pair\nClickProbability Probability of a click for this query and URL\nClickDeviation Deviation from expected click probability\nIsNextClicked 1 if clicked on next position, 0 otherwise\nIsPreviousClicked 1 if clicked on previous position, 0 otherwise\nIsClickAbove 1 if there is a click above, 0 otherwise\nIsClickBelow 1 if there is click below, 0 otherwise\nBrowsing features\nTimeOnPage Page dwell time\nCumulativeTimeOnPage\nCumulative time for all subsequent pages after\nsearch\nTimeOnDomain Cumulative dwell time for this domain\nTimeOnShortUrl Cumulative time on URL prefix, no parameters\nIsFollowedLink 1 if followed link to result, 0 otherwise\nIsExactUrlMatch 0 if aggressive normalization used, 1 otherwise\nIsRedirected 1 if initial URL same as final URL, 0 otherwise\nIsPathFromSearch 1 if only followed links after query, 0 otherwise\nClicksFromSearch Number of hops to reach page from query\nAverageDwellTime Average time on page for this query\nDwellTimeDeviation Deviation from average dwell time on page\nCumulativeDeviation Deviation from average cumulative dwell time\nDomainDeviation Deviation from average dwell time on domain\nQuery-text features\nTitleOverlap Words shared between query and title\nSummaryOverlap Words shared between query and snippet\nQueryURLOverlap Words shared between query and URL\nQueryDomainOverlap Words shared between query and URL domain\nQueryLength Number of tokens in query\nQueryNextOverlap Fraction of words shared with next query\nTable 4.1: Some features used to represent post-search\nnavigation history for a given query and search result URL.\nHaving described our feature set, we briefly review our general\nmethod for deriving a user behavior model.\n4.2 Deriving a User Feedback Model\nTo learn to interpret the observed user behavior, we correlate user\nactions (i.e., the features in Table 4.1 representing the actions)\nwith the explicit user judgments for a set of training queries. We\nfind all the instances in our session logs where these queries were\nsubmitted to the search engine, and aggregate the user behavior\nfeatures for all search sessions involving these queries.\nEach observed query-URL pair is represented by the features in\nTable 4.1, with values averaged over all search sessions, and\nassigned one of six possible relevance labels, ranging from\nPerfect to Bad, as assigned by explicit relevance judgments.\nThese labeled feature vectors are used as input to the RankNet\ntraining algorithm (Section 3.3) which produces a trained user\nbehavior model. This approach is particularly attractive as it does\nnot require heuristics beyond feature engineering. The resulting\nuser behavior model is used to help rank web search\nresultseither directly or in combination with other features, as described\nbelow.\n5. EXPERIMENTAL SETUP\nThe ultimate goal of incorporating implicit feedback into ranking\nis to improve the relevance of the returned web search results.\nHence, we compare the ranking methods over a large set of judged\nqueries with explicit relevance labels provided by human judges.\nIn order for the evaluation to be realistic we obtained a random\nsample of queries from web search logs of a major search engine,\nwith associated results and traces for user actions. We describe\nthis dataset in detail next. Our metrics are described in Section 5.2\nthat we use to evaluate the ranking alternatives, listed in Section\n5.3 in the experiments of Section 6.\n5.1 Datasets\nWe compared our ranking methods over a random sample of 3,000\nqueries from the search engine query logs. The queries were\ndrawn from the logs uniformly at random by token without\nreplacement, resulting in a query sample representative of the\noverall query distribution. On average, 30 results were explicitly\nlabeled by human judges using a six point scale ranging from\nPerfect down to Bad. Overall, there were over 83,000 results\nwith explicit relevance judgments. In order to compute various\nstatistics, documents with label Good or better will be\nconsidered relevant, and with lower labels to be non-relevant.\nNote that the experiments were performed over the results already\nhighly ranked by a web search engine, which corresponds to a\ntypical user experience which is limited to the small number of the\nhighly ranked results for a typical web search query.\nThe user interactions were collected over a period of 8 weeks\nusing voluntary opt-in information. In total, over 1.2 million\nunique queries were instrumented, resulting in over 12 million\nindividual interactions with the search engine. The data consisted\nof user interactions with the web search engine (e.g., clicking on a\nresult link, going back to search results, etc.) performed after a\nquery was submitted. These actions were aggregated across users\nand search sessions and converted to features in Table 4.1.\nTo create the training, validation, and test query sets, we created\nthree different random splits of 1,500 training, 500 validation, and\n1000 test queries. The splits were done randomly by query, so that\nthere was no overlap in training, validation, and test queries.\n5.2 Evaluation Metrics\nWe evaluate the ranking algorithms over a range of accepted\ninformation retrieval metrics, namely Precision at K (P(K)),\nNormalized Discounted Cumulative Gain (NDCG), and Mean\nAverage Precision (MAP). Each metric focuses on a deferent\naspect of system performance, as we describe below.\n\u2022 Precision at K: As the most intuitive metric, P(K) reports the\nfraction of documents ranked in the top K results that are\nlabeled as relevant. In our setting, we require a relevant\ndocument to be labeled Good or higher. The position of\nrelevant documents within the top K is irrelevant, and hence\nthis metric measure overall user satisfaction with the top K\nresults.\n\u2022 NDCG at K: NDCG is a retrieval measure devised specifically\nfor web search evaluation [10]. For a given query q, the ranked\nresults are examined from the top ranked down, and the NDCG\ncomputed as:\n\n=\n+\u2212=\nK\nj\njr\nqq jMN\n1\n)(\n)1log(/)12(\nWhere Mq is a normalization constant calculated so that a\nperfect ordering would obtain NDCG of 1; and each r(j) is an\ninteger relevance label (0=Bad and 5=Perfect) of result\nreturned at position j. Note that unlabeled and Bad documents\ndo not contribute to the sum, but will reduce NDCG for the\nquery pushing down the relevant labeled documents, reducing\ntheir contributions. NDCG is well suited to web search\nevaluation, as it rewards relevant documents in the top ranked\nresults more heavily than those ranked lower.\n\u2022 MAP: Average precision for each query is defined as the mean\nof the precision at K values computed after each relevant\ndocument was retrieved. The final MAP value is defined as the\nmean of average precisions of all queries in the test set. This\nmetric is the most commonly used single-value summary of a\nrun over a set of queries.\n5.3 Ranking Methods Compared\nRecall that our goal is to quantify the effectiveness of implicit\nbehavior for real web search. One dimension is to compare the\nutility of implicit feedback with other information available to a\nweb search engine. Specifically, we compare effectiveness of\nimplicit user behaviors with content-based matching, static page\nquality features, and combinations of all features.\n\u2022 BM25F: As a strong web search baseline we used the BM25F\nscoring, which was used in one of the best performing systems\nin the TREC 2004 Web track [23,27]. BM25F and its variants\nhave been extensively described and evaluated in IR literature,\nand hence serve as a strong, reproducible baseline. The BM25F\nvariant we used for our experiments computes separate match\nscores for each field for a result document (e.g., body text,\ntitle, and anchor text), and incorporates query-independent\nlinkbased information (e.g., PageRank, ClickDistance, and URL\ndepth). The scoring function and field-specific tuning is\ndescribed in detail in [23]. Note that BM25F does not directly\nconsider explicit or implicit feedback for tuning.\n\u2022 RN: The ranking produced by a neural net ranker (RankNet,\ndescribed in Section 3.3) that learns to rank web search results\nby incorporating BM25F and a large number of additional static\nand dynamic features describing each search result. This system\nautomatically learns weights for all features (including the\nBM25F score for a document) based on explicit human labels\nfor a large set of queries. A system incorporating an\nimplementation of RankNet is currently in use by a major\nsearch engine and can be considered representative of the state\nof the art in web search.\n\u2022 BM25F-RerankCT: The ranking produced by incorporating\nclickthrough statistics to reorder web search results ranked by\nBM25F above. Clickthrough is a particularly important special\ncase of implicit feedback, and has been shown to correlate with\nresult relevance. This is a special case of the ranking method in\nSection 3.1, with the weight wI set to 1000 and the ranking Id\nis simply the number of clicks on the result corresponding to d.\nIn effect, this ranking brings to the top all returned web search\nresults with at least one click (and orders them in decreasing\norder by number of clicks). The relative ranking of the\nremainder of results is unchanged and they are inserted below\nall clicked results. This method serves as our baseline implicit\nfeedback reranking method.\nBM25F-RerankAll The ranking produced by reordering the\nBM25F results using all user behavior features (Section 4).\nThis method learns a model of user preferences by correlating\nfeature values with explicit relevance labels using the RankNet\nneural net algorithm (Section 4.2). At runtime, for a given\nquery the implicit score Ir is computed for each result r with\navailable user interaction features, and the implicit ranking is\nproduced. The merged ranking is computed as described in\nSection 3.1. Based on the experiments over the development set\nwe fix the value of wI to 3 (the effect of the wI parameter for\nthis ranker turned out to be negligible).\n\u2022 BM25F+All: Ranking derived by training the RankNet\n(Section 3.3) learner over the features set of the BM25F score\nas well as all implicit feedback features (Section 3.2). We used\nthe 2-layer implementation of RankNet [5] trained on the\nqueries and labels in the training and validation sets.\n\u2022 RN+All: Ranking derived by training the 2-layer RankNet\nranking algorithm (Section 3.3) over the union of all content,\ndynamic, and implicit feedback features (i.e., all of the features\ndescribed above as well as all of the new implicit feedback\nfeatures we introduced).\nThe ranking methods above span the range of the information used\nfor ranking, from not using the implicit or explicit feedback at all\n(i.e., BM25F) to a modern web search engine using hundreds of\nfeatures and tuned on explicit judgments (RN). As we will show\nnext, incorporating user behavior into these ranking systems\ndramatically improves the relevance of the returned documents.\n6. EXPERIMENTAL RESULTS\nImplicit feedback for web search ranking can be exploited in a\nnumber of ways. We compare alternative methods of exploiting\nimplicit feedback, both by re-ranking the top results (i.e., the\nBM25F-RerankCT and BM25F-RerankAll methods that reorder\nBM25F results), as well as by integrating the implicit features\ndirectly into the ranking process (i.e., the RN+ALL and\nBM25F+All methods which learn to rank results over the implicit\nfeedback and other features). We compare our methods over strong\nbaselines (BM25F and RN) over the NDCG, Precision at K, and\nMAP measures defined in Section 5.2. The results were averaged\nover three random splits of the overall dataset. Each split\ncontained 1500 training, 500 validation, and 1000 test queries, all\nquery sets disjoint. We first present the results over all 1000 test\nqueries (i.e., including queries for which there are no implicit\nmeasures so we use the original web rankings). We then drill\ndown to examine the effects on reranking for the attempted\nqueries in more detail, analyzing where implicit feedback proved\nmost beneficial.\nWe first experimented with different methods of re-ranking the\noutput of the BM25F search results. Figures 6.1 and 6.2 report\nNDCG and Precision for BM25F, as well as for the strategies\nreranking results with user feedback (Section 3.1). Incorporating\nall user feedback (either in reranking framework or as features to\nthe learner directly) results in significant improvements (using\ntwo-tailed t-test with p=0.01) over both the original BM25F\nranking as well as over reranking with clickthrough alone. The\nimprovement is consistent across the top 10 results and largest for\nthe top result: NDCG at 1 for BM25F+All is 0.622 compared to\n0.518 of the original results, and precision at 1 similarly increases\nfrom 0.5 to 0.63. Based on these results we will use the direct\nfeature combination (i.e., BM25F+All) ranker for subsequent\ncomparisons involving implicit feedback.\n0.5\n0.52\n0.54\n0.56\n0.58\n0.6\n0.62\n0.64\n0.66\n0.68\n1 2 3 4 5 6 7 8 9 10K\nNDCG\nBM25\nBM25-Rerank-CT\nBM25-Rerank-All\nBM25+All\nFigure 6.1: NDCG at K for BM25F, BM25F-RerankCT,\nBM25F-Rerank-All, and BM25F+All for varying K\n0.35\n0.4\n0.45\n0.5\n0.55\n0.6\n0.65\n1 3 5 10\nK\nPrecision\nBM25\nBM25-Rerank-CT\nBM25-Rerank-All\nBM25+All\nFigure 6.2: Precision at K for BM25F, BM25F-RerankCT,\nBM25F-Rerank-All, and BM25F+All for varying K\nInterestingly, using clickthrough alone, while giving significant\nbenefit over the original BM25F ranking, is not as effective as\nconsidering the full set of features in Table 4.1. While we analyze\nuser behavior (and most effective component features) in a\nseparate paper [1], it is worthwhile to give a concrete example of\nthe kind of noise inherent in real user feedback in web search\nsetting.\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n1 2 3 5\nResult position\nRelativeclickfrequency\nPTR=2\nPTR=3\nPTR=5\nFigure 6.3: Relative clickthrough frequency for queries with\nvarying Position of Top Relevant result (PTR).\nIf users considered only the relevance of a result to their query,\nthey would click on the topmost relevant results. Unfortunately, as\nJoachims and others have shown, presentation also influences\nwhich results users click on quite dramatically. Users often click\non results above the relevant one presumably because the short\nsummaries do not provide enough information to make accurate\nrelevance assessments and they have learned that on average\ntopranked items are relevant. Figure 6.3 shows relative clickthrough\nfrequencies for queries with known relevant items at positions\nother than the first position; the position of the top relevant result\n(PTR) ranges from 2-10 in the figure. For example, for queries\nwith first relevant result at position 5 (PTR=5), there are more\nclicks on the non-relevant results in higher ranked positions than\non the first relevant result at position 5. As we will see, learning\nover a richer behavior feature set, results in substantial accuracy\nimprovement over clickthrough alone.\nWe now consider incorporating user behavior into a much richer\nfeature set, RN (Section 5.3) used by a major web search engine.\nRN incorporates BM25F, link-based features, and hundreds of\nother features. Figure 6.4 reports NDCG at K and Figure 6.5\nreports Precision at K. Interestingly, while the original RN\nrankings are significantly more accurate than BM25F alone,\nincorporating implicit feedback features (BM25F+All) results in\nranking that significantly outperforms the original RN rankings. In\nother words, implicit feedback incorporates sufficient information\nto replace the hundreds of other features available to the RankNet\nlearner trained on the RN feature set.\n0.5\n0.52\n0.54\n0.56\n0.58\n0.6\n0.62\n0.64\n0.66\n0.68\n0.7\n1 2 3 4 5 6 7 8 9 10K\nNDCG\nRN\nRN+All\nBM25\nBM25+All\nFigure 6.4: NDCG at K for BM25F, BM25F+All, RN, and\nRN+All for varying K\nFurthermore, enriching the RN features with implicit feedback set\nexhibits significant gain on all measures, allowing RN+All to\noutperform all other methods. This demonstrates the\ncomplementary nature of implicit feedback with other features\navailable to a state of the art web search engine.\n0.4\n0.45\n0.5\n0.55\n0.6\n0.65\n1 3 5 10\nK\nPrecision\nRN\nRN+All\nBM25\nBM25+All\nFigure 6.5: Precision at K for BM25F, BM25F+All, RN, and\nRN+All for varying K\nWe summarize the performance of the different ranking methods\nin Table 6.1. We report the Mean Average Precision (MAP) score\nfor each system. While not intuitive to interpret, MAP allows\nquantitative comparison on a single metric. The gains marked with\n* are significant at p=0.01 level using two tailed t-test.\nMAP Gain P(1) Gain\nBM25F 0.184 -\n0.503BM25F-Rerank-CT 0.215 0.031* 0.577 0.073*\nBM25F-RerankImplicit 0.218 0.003 0.605 0.028*\nBM25F+Implicit 0.222 0.004 0.620 0.015*\nRN 0.215 -\n0.597RN+All 0.248 0.033* 0.629 0.032*\nTable 6.1: Mean Average Precision (MAP) for all strategies.\nSo far we reported results averaged across all queries in the test\nset. Unfortunately, less than half had sufficient interactions to\nattempt reranking. Out of the 1000 queries in test, between 46%\nand 49%, depending on the train-test split, had sufficient\ninteraction information to make predictions (i.e., there was at least\n1 search session in which at least 1 result URL was clicked on by\nthe user). This is not surprising: web search is heavy-tailed, and\nthere are many unique queries. We now consider the performance\non the queries for which user interactions were available. Figure\n6.6 reports NDCG for the subset of the test queries with the\nimplicit feedback features. The gains at top 1 are dramatic. The\nNDCG at 1 of BM25F+All increases from 0.6 to 0.75 (a 31%\nrelative gain), achieving performance comparable to RN+All\noperating over a much richer feature set.\n0.6\n0.65\n0.7\n0.75\n0.8\n1 3 5 10K\nNDCG\nRN RN+All\nBM25 BM25+All\nFigure 6.6: NDCG at K for BM25F, BM25F+All, RN, and\nRN+All on test queries with user interactions\nSimilarly, gains on precision at top 1 are substantial (Figure 6.7),\nand are likely to be apparent to web search users. When implicit\nfeedback is available, the BM25F+All system returns relevant\ndocument at top 1 almost 70% of the time, compared 53% of the\ntime when implicit feedback is not considered by the original\nBM25F system.\n0.45\n0.5\n0.55\n0.6\n0.65\n0.7\n1 3 5 10K\nPrecision\nRN\nRN+All\nBM25\nBM25+All\nFigure 6.7: Precision at K NDCG at K for BM25F,\nBM25F+All, RN, and RN+All on test queries with user\ninteractions\nWe summarize the results on the MAP measure for attempted\nqueries in Table 6.2. MAP improvements are both substantial and\nsignificant, with improvements over the BM25F ranker most\npronounced.\nMethod MAP Gain P(1) Gain\nRN 0.269 0.632\nRN+All 0.321 0.051 (19%) 0.693 0.061(10%)\nBM25F 0.236 0.525\nBM25F+All 0.292 0.056 (24%) 0.687 0.162 (31%)\nTable 6.2: Mean Average Precision (MAP) on attempted\nqueries for best performing methods\nWe now analyze the cases where implicit feedback was shown\nmost helpful. Figure 6.8 reports the MAP improvements over the\nbaseline BM25F run for each query with MAP under 0.6. Note\nthat most of the improvement is for poorly performing queries\n(i.e., MAP < 0.1). Interestingly, incorporating user behavior\ninformation degrades accuracy for queries with high original MAP\nscore. One possible explanation is that these easy queries tend\nto be navigational (i.e., having a single, highly-ranked most\nappropriate answer), and user interactions with lower-ranked\nresults may indicate divergent information needs that are better\nserved by the less popular results (with correspondingly poor\noverall relevance ratings).\n0\n50\n100\n150\n200\n250\n300\n350\n0.1 0.2 0.3 0.4 0.5 0.6\n-0.4\n-0.35\n-0.3\n-0.25\n-0.2\n-0.15\n-0.1\n-0.05\n0\n0.05\n0.1\n0.15\n0.2\nFrequency Average Gain\nFigure 6.8: Gain of BM25F+All over original BM25F ranking\nTo summarize our experimental results, incorporating implicit\nfeedback in real web search setting resulted in significant\nimprovements over the original rankings, using both BM25F and\nRN baselines. Our rich set of implicit features, such as time on\npage and deviations from the average behavior, provides\nadvantages over using clickthrough alone as an indicator of\ninterest. Furthermore, incorporating implicit feedback features\ndirectly into the learned ranking function is more effective than\nusing implicit feedback for reranking. The improvements observed\nover large test sets of queries (1,000 total, between 466 and 495\nwith implicit feedback available) are both substantial and\nstatistically significant.\n7. CONCLUSIONS AND FUTURE WORK\nIn this paper we explored the utility of incorporating noisy implicit\nfeedback obtained in a real web search setting to improve web\nsearch ranking. We performed a large-scale evaluation over 3,000\nqueries and more than 12 million user interactions with a major\nsearch engine, establishing the utility of incorporating noisy\nimplicit feedback to improve web search relevance.\nWe compared two alternatives of incorporating implicit feedback\ninto the search process, namely reranking with implicit feedback\nand incorporating implicit feedback features directly into the\ntrained ranking function. Our experiments showed significant\nimprovement over methods that do not consider implicit feedback.\nThe gains are particularly dramatic for the top K=1 result in the\nfinal ranking, with precision improvements as high as 31%, and\nthe gains are substantial for all values of K. Our experiments\nshowed that implicit user feedback can further improve web\nsearch performance, when incorporated directly with popular\ncontent- and link-based features.\nInterestingly, implicit feedback is particularly valuable for queries\nwith poor original ranking of results (e.g., MAP lower than 0.1).\nOne promising direction for future work is to apply recent research\non automatically predicting query difficulty, and only attempt to\nincorporate implicit feedback for the difficult queries. As\nanother research direction we are exploring methods for extending\nour predictions to the previously unseen queries (e.g., query\nclustering), which should further improve the web search\nexperience of users.\nACKNOWLEDGMENTS\nWe thank Chris Burges and Matt Richardson for an\nimplementation of RankNet for our experiments. We also thank\nRobert Ragno for his valuable suggestions and many discussions.\n8. REFERENCES\n[1] E. Agichtein, E. Brill, S. Dumais, and R.Ragno, Learning\nUser Interaction Models for Predicting Web Search Result\nPreferences. In Proceedings of the ACM Conference on\nResearch and Development on Information Retrieval (SIGIR),\n2006\n[2] J. Allan, HARD Track Overview in TREC 2003, High\nAccuracy Retrieval from Documents, 2003\n[3] R. Baeza-Yates and B. Ribeiro-Neto, Modern Information\nRetrieval, Addison-Wesley, 1999.\n[4] S. Brin and L. Page, The Anatomy of a Large-scale\nHypertextual Web Search Engine, in Proceedings of WWW,\n1997\n[5] C.J.C. Burges, T. Shaked, E. Renshaw, A. Lazier, M. Deeds,\nN. Hamilton, G. Hullender, Learning to Rank using Gradient\nDescent, in Proceedings of the International Conference on\nMachine Learning, 2005\n[6] D.M. Chickering, The WinMine Toolkit, Microsoft Technical\nReport MSR-TR-2002-103, 2002\n[7] M. Claypool, D. Brown, P. Lee and M. Waseda. Inferring\nuser interest. IEEE Internet Computing. 2001\n[8] S. Fox, K. Karnawat, M. Mydland, S. T. Dumais and T.\nWhite. Evaluating implicit measures to improve the search\nexperience. In ACM Transactions on Information Systems,\n2005\n[9] J. Goecks and J. Shavlick. Learning users\" interests by\nunobtrusively observing their normal behavior. In\nProceedings of the IJCAI Workshop on Machine Learning for\nInformation Filtering. 1999.\n[10] K Jarvelin and J. Kekalainen. IR evaluation methods for\nretrieving highly relevant documents. In Proceedings of the\nACM Conference on Research and Development on\nInformation Retrieval (SIGIR), 2000\n[11] T. Joachims, Optimizing Search Engines Using Clickthrough\nData. In Proceedings of the ACM Conference on Knowledge\nDiscovery and Datamining (SIGKDD), 2002\n[12] T. Joachims, L. Granka, B. Pang, H. Hembrooke, and G. Gay,\nAccurately Interpreting Clickthrough Data as Implicit\nFeedback, Proceedings of the ACM Conference on Research\nand Development on Information Retrieval (SIGIR), 2005\n[13] T. Joachims, Making Large-Scale SVM Learning Practical.\nAdvances in Kernel Methods, in Support Vector Learning,\nMIT Press, 1999\n[14] D. Kelly and J. Teevan, Implicit feedback for inferring user\npreference: A bibliography. In SIGIR Forum, 2003\n[15] J. Konstan, B. Miller, D. Maltz, J. Herlocker, L. Gordon, and\nJ. Riedl. GroupLens: Applying collaborative filtering to\nusenet news. In Communications of ACM, 1997.\n[16] M. Morita, and Y. Shinoda, Information filtering based on\nuser behavior analysis and best match text retrieval.\nProceedings of the ACM Conference on Research and\nDevelopment on Information Retrieval (SIGIR), 1994\n[17] D. Oard and J. Kim. Implicit feedback for recommender\nsystems. In Proceedings of the AAAI Workshop on\nRecommender Systems. 1998\n[18] D. Oard and J. Kim. Modeling information content using\nobservable behavior. In Proceedings of the 64th Annual\nMeeting of the American Society for Information Science and\nTechnology. 2001\n[19] N. Pharo, N. and K. J\u00e4rvelin. The SST method: a tool for\nanalyzing web information search processes. In Information\nProcessing & Management, 2004\n[20] P. Pirolli, The Use of Proximal Information Scent to Forage\nfor Distal Content on the World Wide Web. In Working with\nTechnology in Mind: Brunswikian. Resources for Cognitive\nScience and Engineering, Oxford University Press, 2004\n[21] F. Radlinski and T. Joachims, Query Chains: Learning to\nRank from Implicit Feedback. In Proceedings of the ACM\nConference on Knowledge Discovery and Data Mining\n(SIGKDD), 2005.\n[22] F. Radlinski and T. Joachims, Evaluating the Robustness of\nLearning from Implicit Feedback, in Proceedings of the ICML\nWorkshop on Learning in Web Search, 2005\n[23] S. E. Robertson, H. Zaragoza, and M. Taylor, Simple BM25\nextension to multiple weighted fields, in Proceedings of the\nConference on Information and Knowledge Management\n(CIKM), 2004\n[24] G. Salton & M. McGill. Introduction to modern information\nretrieval. McGraw-Hill, 1983\n[25] E.M. Voorhees, D. Harman, Overview of TREC, 2001\n[26] G.R. Xue, H.J. Zeng, Z. Chen, Y. Yu, W.Y. Ma, W.S. Xi,\nand W.G. Fan, Optimizing web search using web\nclickthrough data, in Proceedings of the Conference on\nInformation and Knowledge Management (CIKM), 2004\n[27] H. Zaragoza, N. Craswell, M. Taylor, S. Saria, and S.\nRobertson. Microsoft Cambridge at TREC 13: Web and Hard\nTracks. In Proceedings of TREC 2004", "keywords": "feedback;implicit relevance feedback;document;web search rank;web search;ranking;score;user interaction;information;information retrieval;user behavior;relevance feedback;result"}
{"name": "train_H-95", "title": "Handling Locations in Search Engine Queries", "abstract": "This paper proposes simple techniques for handling place references in search engine queries, an important aspect of geographical information retrieval. We address not only the detection, but also the disambiguation of place references, by matching them explicitly with concepts at an ontology. Moreover, when a query does not reference any locations, we propose to use information from documents matching the query, exploiting geographic scopes previously assigned to these documents. Evaluation experiments, using topics from CLEF campaigns and logs from real search engine queries, show the effectiveness of the proposed approaches.", "fulltext": "1. INTRODUCTION\nSearch engine queries are often associated with geographical\nlocations, either explicitly (i.e. a location reference is given as part of\nthe query) or implicitly (i.e. the location reference is not present in\nthe query string, but the query clearly has a local intent [17]). One\nof the concerns of geographical information retrieval (GIR) lies in\nappropriately handling such queries, bringing better targeted search\nresults and improving user satisfaction.\nNowadays, GIR is getting increasing attention. Systems that\naccess resources on the basis of geographic context are starting to\nappear, both in the academic and commercial domains [4, 7].\nAccurately and effectively detecting location references in search\nengine queries is a crucial aspect of these systems, as they are\ngenerally based on interpreting geographical terms differently from the\nothers. Detecting locations in queries is also important for\ngeneralpropose search engines, as this information can be used to improve\nranking algorithms. Queries with a local intent are best answered\nwith localized pages, while queries without any geographical\nreferences are best answered with broad pages [5].\nText mining methods have been successfully used in GIR to\ndetect and disambiguate geographical references in text [9], or even to\ninfer geographic scopes for documents [1, 13]. However, this body\nof research has been focused on processing Web pages and full-text\ndocuments. Search engine queries are more difficult to handle, in\nthe sense that they are very short and with implicit and subjective\nuser intents. Moreover, the data is also noisier and more versatile\nin form, and we have to deal with misspellings, multilingualism\nand acronyms. How to automatically understand what the user\nintended, given a search query, without putting the burden in the user\nhimself, remains an open text mining problem.\nKey challenges in handling locations over search engine queries\ninclude their detection and disambiguation, the ranking of possible\ncandidates, the detection of false positives (i.e not all contained\nlocation names refer to geographical locations), and the detection of\nimplied locations by the context of the query (i.e. when the query\ndoes not explicitly contain a place reference but it is nonetheless\ngeographical). Simple named entity recognition (NER) algorithms,\nbased on dictionary look-ups for geographical names, may\nintroduce high false positives for queries whose location names do not\nconstitute place references. For example the query Denzel\nWashington contains the place name Washington, but the query is not\ngeographical. Queries can also be geographic without containing\nany explicit reference to locations at the dictionary. In these cases,\nplace name extraction and disambiguation does not give any results,\nand we need to access other sources of information.\nThis paper proposes simple and yet effective techniques for\nhandling place references over queries. Each query is split into a triple\n< what,relation,where >, where what specifies the non-geographic\naspect of the information need, where specifies the geographic\nareas of interest, and relation specifies a spatial relationship\nconnecting what and where. When this is not possible, i.e. the query does\nnot contain any place references, we try using information from\ndocuments matching the query, exploiting geographic scopes\npreviously assigned to these documents.\nDisambiguating place references is one of the most important\naspects. We use a search procedure that combines textual patterns\nwith geographical names defined at an ontology, and we use\nheuristics to disambiguate the discovered references (e.g. more important\nplaces are preferred). Disambiguation results in having the where\nterm, from the triple above, associated with the most likely\ncorresponding concepts from the ontology. When we cannot detect\nany locations, we attempt to use geographical scopes previously\ninferred for the documents at the top search results. By doing this,\nwe assume that the most frequent geographical scope in the results\nshould correspond to the geographical context implicit in the query.\nExperiments with CLEF topics [4] and sample queries from a\nWeb search engine show that the proposed methods are accurate,\nand may have applications in improving search results.\nThe rest of this paper is organized as follows. We first formalize\nthe problem and describe related work to our research. Next, we\ndescribe our approach for handling place names in queries, starting\nwith the general approach for disambiguating place references over\ntextual strings, then presenting the method for splitting a query into\na < what,relation,where > triple, and finally discussing the\ntechnique for exploiting geographic scopes previously assigned to\ndocuments in the result set. Section 4 presents evaluation results.\nFinally, we give some conclusions and directions for future research.\n2. CONCEPTS AND RELATED WORK\nSearch engine performance depends on the ability to capture the\nmost likely meaning of a query as intended by the user [16].\nPrevious studies showed that a significant portion of the queries\nsubmitted to search engines are geographic [8, 14]. A recent enhancement\nto search engine technology is the addition of geographic\nreasoning, combining geographic information systems and information\nretrieval in order to build search engines that find information\nassociated with given locations. The ability to recognize and reason\nabout the geographical terminology, given in the text documents\nand user queries, is a crucial aspect of these geographical\ninformation retrieval (GIR) systems [4, 7].\nExtracting and distinguishing different types of entities in text is\nusually referred to as Named Entity Recognition (NER). For at least\na decade, this has been an important text mining task, and a key\nfeature of the Message Understanding Conferences (MUC) [3]. NER\nhas been successfully automated with near-human performance,\nbut the specific problem of recognizing geographical references\npresents additional challenges [9]. When handling named\nentities with a high level of detail, ambiguity problems arise more\nfrequently. Ambiguity in geographical references is bi-directional [15].\nThe same name can be used for more than one location (referent\nambiguity), and the same location can have more than one name\n(reference ambiguity). The former has another twist, since the same\nname can be used for locations as well as for other class of\nentities, such as persons or company names (referent class ambiguity).\nBesides the recognition of geographical expressions, GIR also\nrequires that the recognized expressions be classified and grounded\nto unique identifiers [11]. Grounding the recognized expressions\n(e.g. associating them to coordinates or concepts at an ontology)\nassures that they can be used in more advanced GIR tasks.\nPrevious works have addressed the tagging and grounding of\nlocations in Web pages, as well as the assignment of geographic\nscopes to these documents [1, 7, 13]. This is a complementary\naspect to the techniques described in this paper, since if we have the\nWeb pages tagged with location information, a search engine can\nconveniently return pages with a geographical scope related to the\nscope of the query. The task of handling geographical references\nover documents is however considerably different from that of\nhandling geographical references over queries. In our case, queries are\nusually short and often do not constitute proper sentences. Text\nmining techniques that make use of context information are\ndifficult to apply for high accuracy.\nPrevious studies have also addressed the use of text mining and\nautomated classification techniques over search engine queries [16,\n10]. However, most of these works did not consider place\nreferences or geographical categories. Again, these previously proposed\nmethods are difficult to apply to the geographic domain.\nGravano et. al. studied the classification of Web queries into two\ntypes, namely local and global [5]. They defined a query as local if\nits best matches on a Web search engine are likely to be local pages,\nsuch as houses for sale. A number of classification algorithms\nhave been evaluated using search engine queries. However, their\nexperimental results showed that only a rather low precision and\nrecall could be achieved. The problem addressed in this paper is\nalso slightly different, since we are trying not only to detect local\nqueries but also to disambiguate the local of interest.\nWang et. al. proposed to go further than detecting local queries,\nby also disambiguating the implicit local of interest [17]. The\nproposed approach works for both queries containing place references\nand queries not containing them, by looking for dominant\ngeographic references over query logs and text from search results.\nIn comparison, we propose simpler techniques based on matching\nnames from a geographic ontology. Our approach looks for spatial\nrelationships at the query string, and it also associates the place\nreferences to ontology concepts. In the case of queries not containing\nexplicit place references, we use geographical scopes previously\nassigned to the documents, whereas Wang et. al. proposed to\nextract locations from the text of the top search results.\nThere are nowadays many geocoding, reverse-geocoding, and\nmapping services on the Web that can be easily integrated with\nother applications. Geocoding is the process of locating points on\nthe surface of the Earth from alphanumeric addressing data. Taking\na string with an address, a geocoder queries a geographical\ninformation system and returns interpolated coordinate values for the\ngiven location. Instead of computing coordinates for a given place\nreference, the technique described in this paper aims at assigning\nreferences to the corresponding ontology concepts. However, if\neach concept at the ontology contains associated coordinate\ninformation, the approach described here could also be used to build a\ngeocoding service. Most of such existing services are commercial\nin nature, and there are no technical publications describing them.\nA number of commercial search services have also started to\nsupport location-based searches. Google Local, for instance, initially\nrequired the user to specify a location qualifier separately from the\nsearch query. More recently, it added location look-up\ncapabilities that extract locations from query strings. For example, in a\nsearch for Pizza Seattle, Google Local returns local results for\npizza near Seattle, WA. However, the intrinsics of their solution\nare not published, and their approach also does not handle\nlocationimplicit queries. Moreover, Google Local does not take spatial\nrelations into account.\nIn sum, there are already some studies on tagging geographical\nreferences, but Web queries pose additional challenges which have\nnot been addressed. In this paper, we explain the proposed\nsolutions for the identified problems.\n3. HANDLINGQUERIESIN GIR SYSTEMS\nMost GIR queries can be parsed to < what,relation,where >\ntriple, where the what term is used to specify the general\nnongeographical aspect of the information need, the where term is used\nto specify the geographical areas of interest, and the relation term\nis used to specify a spatial relationship connecting what and where.\nWhile the what term can assume any form, in order to reflect any\ninformation need, the relation and where terms should be part of a\ncontrolled vocabulary. In particular, the relation term should refer\nto a well-known geographical relation that the underlying GIR\nsystem can interpret (e.g. near or contained at), and the where\nterm should be disambiguated into a set of unique identifiers,\ncorresponding to concepts at the ontology.\nDifferent systems can use alternative schemes to take input queries\nfrom the users. Three general strategies can be identified, and GIR\nsystems often support more than one of the following schemes:\nFigure 1: Strategies for processing queries in Geographical Information Retrieval systems.\n1. Input to the system is a textual query string. This is the\nhardest case, since we need to separate the query into the three\ndifferent components, and then we need to disambiguate the\nwhere term into a set of unique identifiers.\n2. Input to the system is provided in two separate strings, one\nconcerning the what term, and the other concerning the where.\nThe relation term can be either fixed (e.g. always assume the\nnear relation), specified together with the where string,\nor provided separately from the users from a set of\npossible choices. Although there is no need for separating query\nstring into the different components, we still need to\ndisambiguate the where term into a set of unique identifiers.\n3. Input to the system is provided through a query string\ntogether with an unambiguous description of the geographical\narea of interest (e.g. a sketch in a map, spatial coordinates\nor a selection from a set of possible choices). No\ndisambiguation is required, and therefore the techniques described\nin this paper do not have to be applied.\nThe first two schemes depend on place name disambiguation.\nFigure 1 illustrates how we propose to handle geographic queries\nin these first two schemes. A common component is the algorithm\nfor disambiguating place references into corresponding ontology\nconcepts, which is described next.\n3.1 From Place Names to Ontology Concepts\nA required task in handling GIR queries consists of associating\na string containing a geographical reference with the set of\ncorresponding concepts at the geographic ontology. We propose to do\nthis according to the pseudo-code listed at Algorithm 1.\nThe algorithm considers the cases where a second (or even more\nthan one) location is given to qualify a first (e.g. Paris, France).\nIt makes recursive calls to match each location, and relies on\nhierarchical part-of relations to detect if two locations share a common\nhierarchy path. One of the provided locations should be more\ngeneral and the other more specific, in the sense that there must exist\na part-of relationship among the associated concepts at the\nontology (either direct or transitive). The most specific location is a\nsub-region of the most general, and the algorithm returns the most\nspecific one (i.e. for Paris, France the algorithm returns the\nontology concept associated with Paris, the capital city of France).\nWe also consider the cases where a geographical type expression\nis used to qualify a given name (e.g. city of Lisbon or state\nof New York). For instance the name Lisbon can correspond\nto many different concepts at a geographical ontology, and type\nAlgorithm 1 Matching a place name with ontology concepts\nRequire: O = A geographic ontology\nRequire: GN = A string with the geographic name to be matched\n1: L = An empty list\n2: INDEX = The position in GN for the first occurrence of a comma,\nsemi-colon or bracket character\n3: if INDEX is defined then\n4: GN1 = The substring of GN from position 0 to INDEX\n5: GN2 = The substring of GN from INDEX +1 to length(GN)\n6: L1 = Algorithm1(O,GN1)\n7: L2 = Algorithm1(O,GN2)\n8: for each C1 in L1 do\n9: for each C2 in L2 do\n10: if C1 is an ancestor of C2 at O then\n11: L = The list L after adding element C2\n12: else if C1 is a descendant of C2 at O then\n13: L = The list L after adding element C1\n14: end if\n15: end for\n16: end for\n17: else\n18: GN = The string GN after removing case and diacritics\n19: if GN contains a geographic type qualifier then\n20: T = The substring of GN containing the type qualifier\n21: GN = The substring of GN with the type qualifier removed\n22: L = The list of concepts from O with name GN and type T\n23: else\n24: L = The list of concepts from O with name GN\n25: end if\n26: end if\n27: return The list L\nqualifiers can provide useful information for disambiguation. The\nconsidered type qualifiers should also described at the ontologies\n(e.g. each geographic concept should be associated to a type that is\nalso defined at the ontology, such as country, district or city).\nIdeally, the geographical reference provided by the user should\nbe disambiguated into a single ontology concept. However, this is\nnot always possible, since the user may not provide all the required\ninformation (i.e. a type expression or a second qualifying location).\nThe output is therefore a list with the possible concepts being\nreferred to by the user. In a final step, we propose to sort this list,\nso that if a single concept is required as output, we can use the one\nthat is ranked higher. The sorting procedure reflects the likelihood\nof each concept being indeed the one referred to. We propose to\nrank concepts according to the following heuristics:\n1. The geographical type expression associated with the\nontology concept. For the same name, a country is more likely to\nbe referenced than a city, and in turn a city more likely to be\nreferenced than a street.\n2. Number of ancestors at the ontology. Top places at the\nontology tend to be more general, and are therefore more likely\nto be referenced in search engine queries.\n3. Population count. Highly populated places are better known,\nand therefore more likely to be referenced in queries.\n4. Population counts from direct ancestors at the ontology.\nSubregions of highly populated places are better known, and also\nmore likely to be referenced in search engine queries.\n5. Occurrence frequency over Web documents (e.g. Google\ncounts) for the geographical names. Places names that occur\nmore frequently over Web documents are also more likely to\nbe referenced in search engine queries.\n6. Number of descendants at the ontology. Places that have\nmore sub-regions tend to be more general, and are therefore\nmore likely to be mentioned in search engine queries.\n7. String size for the geographical names. Short names are more\nlikely to be mentioned in search engine queries.\nAlgorithm 1, plus the ranking procedure, can already handle GIR\nqueries where the where term is given separately from the what and\nrelation terms. However, if the query is given in a single string, we\nrequire the identification of the associated < what,relation,where >\ntriple, before disambiguating the where term into the corresponding\nontology concepts. This is described in the following Section.\n3.2 Handling Single Query Strings\nAlgorithm 2 provides the mechanism for separating a query string\ninto a < what,relation,where > triple. It uses Algorithm 1 to find\nthe where term, disambiguating it into a set of ontology concepts.\nThe algorithm starts by tokenizing the query string into\nindividual words, also taking care of removing case and diacritics. We\nhave a simple tokenizer that uses the space character as a word\ndelimiter, but we could also have a tokenization approach similar to\nthe proposal of Wang et. al. which relies on Web occurrence\nstatistics to avoid breaking collocations [17]. In the future, we plan on\ntesting if this different tokenization scheme can improve results.\nNext, the algorithm tests different possible splits of the query,\nbuilding the what, relation and where terms through\nconcatenations of the individual tokens. The relation term is matched against\na list of possible values (e.g. near, at, around, or south\nof), corresponding to the operators that are supported by the GIR\nsystem. Note that is also the responsibility of the underlying GIR\nsystem to interpret the actual meaning of the different spatial\nrelations. Algorithm 1 is used to check whether a where term\nconstitutes a geographical reference or not. We also check if the last\nword in the what term belongs to a list of exceptions, containing for\ninstance first names of people in different languages. This ensures\nthat a query like Denzel Washington is appropriately handled.\nIf the algorithm succeeds in finding valid relation and where\nterms, then the corresponding triple is returned. Otherwise, we\nreturn a triple with the what term equaling the query string, and the\nrelation and where terms set as empty. If the entire query string\nconstitutes a geographical reference, we return a triple with the\nwhat term set to empty, the where term equaling the query string,\nand the relation term set the DEFINITION (i.e. these queries\nshould be answered with information about the given place\nreferences). The algorithm also handles query strings where more\nthan one geographical reference is provided, using and or an\nequivalent preposition, together with a recursive call to Algorithm\n2. A query like Diamond trade in Angola and South Africa is\nAlgorithm 2 Get < what,relation,where > from a query string\nRequire: O = A geographical ontology\nRequire: Q = A non-empty string with the query\n1: Q = The string Q after removing case and diacritics\n2: TOKENS[0..N] = An array of strings with the individual words of Q\n3: N = The size of the TOKENS array\n4: for INDEX = 0 to N do\n5: if INDEX = 0 then\n6: WHAT = Concatenation of TOKENS[0..INDEX \u22121]\n7: LASTWHAT = TOKENS[INDEX \u22121]\n8: else\n9: WHAT = An empty string\n10: LASTWHAT = An empty string\n11: end if\n12: WHERE = Concatenation of TOKENS[INDEX..N]\n13: RELATION = An empty string\n14: for INDEX2 = INDEX to N \u22121 do\n15: RELATION2 = Concatenation of TOKENS[INDEX..INDEX2]\n16: if RELATION2 is a valid geographical relation then\n17: WHERE = Concatenation of S[INDEX2 +1..N]\n18: RELATION = RELATION2;\n19: end if\n20: end for\n21: if RELATION = empty AND LASTWHAT in an exception then\n22: TESTGEO = FALSE\n23: else\n24: TESTGEO = TRUE\n25: end if\n26: if TESTGEO AND Algorithm1(WHERE) <> EMPTY then\n27: if WHERE ends with AND SURROUNDINGS then\n28: RELATION = The string NEAR;\n29: WHERE = The substring of WHERE with AND\nSURROUNDINGS removed\n30: end if\n31: if WHAT ends with AND or similar) then\n32: < WHAT,RELATION,WHERE2 >= Algorithm2(WHAT)\n33: WHERE = Concatenation of WHERE with WHERE2\n34: end if\n35: if RELATION = An empty string then\n36: if WHAT = An empty string then\n37: RELATION = The string DEFINITION\n38: else\n39: RELATION = The string CONTAINED-AT\n40: end if\n41: end if\n42: else\n43: WHAT = The string Q\n44: WHERE = An empty string\n45: RELATION = An empty string\n46: end if\n47: end for\n48: return < WHAT,RELATION,WHERE >\ntherefore appropriately handled. Finally, if the geographical\nreference in the query is complemented with an expression similar to\nand its surroundings, the spatial relation (which is assumed to be\nCONTAINED-AT if none is provided) is changed to NEAR.\n3.3 From Search Results to Query Locality\nThe procedures given so far are appropriate for handling queries\nwhere a place reference is explicitly mentioned. However, the fact\nthat a query can be associated with a geographical context may\nnot be directly observable in the query itself, but rather from the\nresults returned. For instance, queries like recommended hotels\nfor SIGIR 2006 or SeaFair 2006 lodging can be seen to refer to\nthe city of Seattle. Although they do not contain an explicit place\nreference, we expect results to be about hotels in Seattle.\nIn the cases where a query does not contain place references, we\nstart by assuming that the top results from a search engine represent\nthe most popular and correct context and usage for the query. We\nTopic What Relation Where TGN concepts ML concepts\nVegetable Exporters of Europe Vegetable Exporters CONTAINED-AT Europe 1 1\nTrade Unions in Europe Trade Unions CONTAINED-AT Europe 1 1\nRoman cities in the UK and Germany Roman cities CONTAINED-AT UK and Germany 6 2\nCathedrals in Europe Cathedrals CONTAINED-AT Europe 1 1\nCar bombings near Madrid Car bombings NEAR Madrid 14 2\nVolcanos around Quito Volcanos NEAR Quito 4 1\nCities within 100km of Frankfurt Cities NEAR Frankfurt 3 1\nRussian troops in south(ern) Caucasus Russian troops in south(ern) CONTAINED-AT Caucasus 2 1\nCities near active volcanoes (This topic could not be appropriately handled - the relation and where terms are returned empty)\nJapanese rice imports (This topic could not be appropriately handled - the relation and where terms are returned empty)\nTable 1: Example topics from the GeoCLEF evaluation campaigns and the corresponding < what,relation,where > triples.\nthen propose to use the distributional characteristics of\ngeographical scopes previously assigned to the documents corresponding to\nthese top results. In a previous work, we presented a text mining\napproach for assigning documents with corresponding\ngeographical scopes, defined at an ontology, that worked as an offline\npreprocessing stage in a GIR system [13]. This pre-processing step is a\nfundamental stage of GIR, and it is reasonable to assume that this\nkind of information would be available on any system. Similarly to\nWang et. al., we could also attempt to process the results on-line,\nin order to detect place references in the documents [17]. However,\na GIR system already requires the offline stage.\nFor the top N documents given at the results, we check the\ngeographic scopes that were assigned to them. If a significant portion\nof the results are assigned to the same scope, than the query can be\nseen to be related to the corresponding geographic concept. This\nassumption could even be relaxed, for instance by checking if the\ndocuments belong to scopes that are hierarchically related.\n4. EVALUATION EXPERIMENTS\nWe used three different ontologies in evaluation experiments,\nnamely the Getty thesaurus of geographic names (TGN) [6] and\ntwo specific resources developed at our group, here referred to as\nthe PT and ML ontologies [2]. TGN and ML include global\ngeographical information in multiple languages (although TGN is\nconsiderably larger), while the PT ontology focuses on the Portuguese\nterritory with a high detail. Place types are also different across\nontologies, as for instance PT includes street names and postal\naddresses, whereas ML only goes to the level of cities. The reader\nshould refer to [2, 6] for a complete description of these resources.\nOur initial experiments used Portuguese and English topics from\nthe GeoCLEF 2005 and 2006 evaluation campaigns. Topics in\nGeoCLEF correspond to query strings that can be used as input to a GIR\nsystem [4]. ImageCLEF 2006 also included topics specifying place\nreferences, and participants were encouraged to run their GIR\nsystems on them. Our experiments also considered this dataset. For\neach topic, we measured if Algorithm 2 was able to find the\ncorresponding < what,relation,where > triple. The ontologies used\nin this experiment were the TGN and ML, as topics were given in\nmultiple languages and covered the whole globe.\nDataset Number of Correct Triples Time per Query\nQueries ML TGN ML TGN\nGeoCLEF05 EN 25 19 20\nGeoCLEF05 PT 25 20 18 288.1 334.5\nGeoCLEF06 EN 32 28 19 msec msec\nGeoCLEF06 PT 25 23 11\nImgCLEF06 EN 24 16 18\nTable 2: Summary of results over CLEF topics.\nTable 1 illustrates some of the topics, and Table 2 summarizes\nthe obtained results. The tables show that the proposed technique\nadequately handles most of these queries. A manual inspection of\nthe ontology concepts that were returned for each case also revealed\nthat the where term was being correctly disambiguated. Note that\nthe TGN ontology indeed added some ambiguity, as for instance\nnames like Madrid can correspond to many different places around\nthe globe. It should also be noted that some of the considered\ntopics are very hard for an automated system to handle. Some of them\nwere ambiguous (e.g. in Japanese rice imports, the query can\nbe said to refer either rice imports in Japan or imports of Japanese\nrice), and others contained no direct geographical references (e.g.\ncities near active volcanoes). Besides these very hard cases, we\nalso missed some topics due to their usage of place adjectives and\nspecific regions that are not defined at the ontologies (e.g.\nenvironmental concerns around the Scottish Trossachs).\nIn a second experiment, we used a sample of around 100,000\nreal search engine queries. The objective was to see if a\nsignificant number of these queries were geographical in nature, also\nchecking if the algorithm did not produce many mistakes by\nclassifying a query as geographical when that was not the case. The\nPortuguese ontology was used in this experiment, and queries were\ntaken from the logs of a Portuguese Web search engine available\nat www.tumba.pt. Table 3 summarizes the obtained results. Many\nqueries were indeed geographical (around 3.4%, although\nprevious studies reported values above 14% [8]). A manual inspection\nshowed that the algorithm did not produce many false positives,\nand the geographical queries were indeed correctly split into correct\n< what,relation,where > triple. The few mistakes we encountered\nwere related to place names that were more frequently used in other\ncontexts (e.g. in Te\u00f3filo Braga we have the problem that Braga\nis a Portuguese district, and Te\u00f3filo Braga was a well known\nPortuguese writer and politician). The addition of more names to the\nexception list can provide a workaround for most of these cases.\nValue\nNum. Queries 110,916\nNum. Queries without Geographical References 107,159 (96.6%)\nNum. Queries with Geographical References 3,757 (3.4%)\nTable 3: Results from an experiment with search engine logs.\nWe also tested the procedure for detecting queries that are\nimplicitly geographical with a small sample of queries from the logs.\nFor instance, for the query Est\u00e1dio do Drag\u00e3o (e.g. home stadium\nfor a soccer team from Porto), the correct geographical context can\nbe discovered from the analysis of the results (more than 75% of\nthe top 20 results are assigned with the scope Porto). For future\nwork, we plan on using a larger collection of queries to evaluate\nthis aspect. Besides queries from the search engine logs, we also\nplan on using the names of well-known buildings, monuments and\nother landmarks, as they have a strong geographical connotation.\nFinally, we also made a comparative experiment with 2 popular\ngeocoders, Maporama and Microsoft\"s Mappoint. The objective\nwas to compare Algorithm 1 with other approaches, in terms of\nbeing able to correctly disambiguate a string with a place reference.\nCivil Parishes from Lisbon Maporama Mappoint Ours\nCoded refs. (out of 53) 9 (16.9%) 30 (56,6%) 15 (28.3%)\nAvg. Time per ref. (msec) 506.23 1235.87 143.43\nCivil Parishes from Porto Maporama Mappoint Ours\nCoded refs. (out of 15) 0 (0%) 2 (13,3%) 5 (33.3%)\nAvg. Time per ref. (msec) 514.45 991.88 132.14\nTable 4: Results from a comparison with geocoding services.\nThe Portuguese ontology was used in this experiment, taking as\ninput the names of civil parishes from the Portuguese municipalities\nof Lisbon and Porto, and checking if the systems were able to\ndisambiguate the full name (e.g. Campo Grande, Lisboa or Foz\ndo Douro, Porto) into the correct geocode. We specifically\nmeasured whether our approach was better at unambiguously returning\ngeocodes given the place reference (i.e. return the single correct\ncode), and providing results rapidly. Table 4 shows the obtained\nresults, and the accuracy of our method seems comparable to the\ncommercial geocoders. Note that for Maporama and Mappoint, the\ntimes given at Table 4 include fetching results from the Web, but we\nhave no direct way of accessing the geocoding algorithms (in both\ncases, fetching static content from the Web servers takes around\n125 milliseconds). Although our approach cannot unambiguously\nreturn the correct geocode in most cases (only 20 out of a total of\n68 cases), it nonetheless returns results that a human user can\ndisambiguate (e.g. for Madalena, Lisboa we return both a street and\na civil parish), as opposed to the other systems that often did not\nproduce results. Moreover, if we consider the top geocode\naccording to the ranking procedure described in Section 3.1, or if we use\na type qualifier in the name (e.g. civil parish of Campo Grande,\nLisboa), our algorithm always returns the correct geocode.\n5. CONCLUSIONS\nThis paper presented simple approaches for handling place\nreferences in search engine queries. This is a hard text mining problem,\nas queries are often ambiguous or underspecify information needs.\nHowever, our initial experiments indicate that for many queries, the\nreferenced places can be determined effectively. Unlike the\ntechniques proposed by Wang et. al. [17], we mainly focused on\nrecognizing spatial relations and associating place names to ontology\nconcepts. The proposed techniques were employed in the prototype\nsystem that we used for participating in GeoCLEF 2006. In queries\nwhere a geographical reference is not explicitly mentioned, we\npropose to use the results for the query, exploiting geographic scopes\npreviously assigned to these documents. In the future, we plan on\ndoing a careful evaluation of this last approach. Another idea that\nwe would like to test involves the integration of a spelling\ncorrection mechanism [12] into Algorithm 1, so that incorrectly spelled\nplace references can be matched to ontology concepts.\nThe proposed techniques for handling geographic queries can\nhave many applications in improving GIR systems or even general\npurpose search engines. After place references are appropriately\ndisambiguated into ontology concepts, a GIR system can use them\nto retrieve relevant results, through the use of appropriate index\nstructures (e.g. indexing the spatial coordinates associated with\nontology concepts) and provided that the documents are also assigned\nto scopes corresponding to ontology concepts. A different GIR\nstrategy can involve query expansion, by taking the where terms\nfrom the query and using the ontology to add names from\nneighboring locations. In a general purpose search engine, and if a local\nquery is detected, we can forward users to a GIR system, which\nshould be better suited for properly handling the query. The regular\nGoogle search interface already does this, by presenting a link to\nGoogle Local when it detects a geographical query.\n6. REFERENCES\n[1] E. Amitay, N. Har\"El, R. Sivan, and A. Soffer. Web-a-Where:\nGeotagging Web content. In Proceedings of SIGIR-04, the\n27th Conference on research and development in information\nretrieval, 2004.\n[2] M. Chaves, M. J. Silva, and B. Martins. A Geographic\nKnowledge Base for Semantic Web Applications. In\nProceedings of SBBD-05, the 20th Brazilian Symposium on\nDatabases, 2005.\n[3] N. A. Chinchor. Overview of MUC-7/MET-2. In\nProceedings of MUC-7, the 7th Message Understanding\nConference, 1998.\n[4] F. Gey, R. Larson, M. Sanderson, H. Joho, and P. Clough.\nGeoCLEF: the CLEF 2005 cross-language geographic\ninformation retrieval track. In Working Notes for the CLEF\n2005 Workshop, 2005.\n[5] L. Gravano, V. Hatzivassiloglou, and R. Lichtenstein.\nCategorizing Web queries according to geographical locality.\nIn Proceedings of CIKM-03, the 12th Conference on\nInformation and knowledge management, 2003.\n[6] P. Harpring. Proper words in proper places: The thesaurus of\ngeographic names. MDA Information, 3, 1997.\n[7] C. Jones, R. Purves, A. Ruas, M. Sanderson, M. Sester,\nM. van Kreveld, and R. Weibel. Spatial information retrieval\nand geographical ontologies: An overview of the SPIRIT\nproject. In Proceedings of SIGIR-02, the 25th Conference on\nResearch and Development in Information Retrieval, 2002.\n[8] J. Kohler. Analyzing search engine queries for the use of\ngeographic terms, 2003. (MSc Thesis).\n[9] A. Kornai and B. Sundheim, editors. Proceedings of the\nNAACL-HLT Workshop on the Analysis of Geographic\nReferences, 2003.\n[10] Y. Li, Z. Zheng, and H. Dai. KDD CUP-2005 report: Facing\na great challenge. SIGKDD Explorations, 7, 2006.\n[11] D. Manov, A. Kiryakov, B. Popov, K. Bontcheva,\nD. Maynard, and H. Cunningham. Experiments with\ngeographic knowledge for information extraction. In\nProceedings of the NAACL-HLT Workshop on the Analysis of\nGeographic References, 2003.\n[12] B. Martins and M. J. Silva. Spelling correction for search\nengine queries. In Proceedings of EsTAL-04, Espa\u00f1a for\nNatural Language Processing, 2004.\n[13] B. Martins and M. J. Silva. A graph-ranking algorithm for\ngeo-referencing documents. In Proceedings of ICDM-05, the\n5th IEEE International Conference on Data Mining, 2005.\n[14] L. Souza, C. J. Davis, K. Borges, T. Delboni, and\nA. Laender. The role of gazetteers in geographic knowledge\ndiscovery on the web. In Proceedings of LA-Web-05, the 3rd\nLatin American Web Congress, 2005.\n[15] E. Tjong, K. Sang, and F. D. Meulder. Introduction to the\nCoNLL-2003 shared task: Language-Independent Named\nEntity Recognition. In Proceedings of CoNLL-2003, the 7th\nConference on Natural Language Learning, 2003.\n[16] D. Vogel, S. Bickel, P. Haider, R. Schimpfky, P. Siemen,\nS. Bridges, and T. Scheffer. Classifying search engine\nqueries using the Web as background knowledge. SIGKDD\nExplorations Newsletter, 7(2):117-122, 2005.\n[17] L. Wang, C. Wang, X. Xie, J. Forman, Y. Lu, W.-Y. Ma, and\nY. Li. Detecting dominant locations from search queries. In\nProceedings of SIGIR-05, the 28th Conference on Research\nand development in information retrieval, 2005.", "keywords": "tokenization scheme;geographical type expression;geographical information retrieval;search engine query;text mine;disambiguation result;search query;geographic ontology;place reference;spelling correction mechanism;named entity recognition algorithm;web search engine;geographic context;query string;textual string;geographic ir;locationimplicit query;query process;ner"}
{"name": "train_H-96", "title": "A Study of Factors Affecting the Utility of Implicit Relevance Feedback", "abstract": "Implicit relevance feedback (IRF) is the process by which a search system unobtrusively gathers evidence on searcher interests from their interaction with the system. IRF is a new method of gathering information on user interest and, if IRF is to be used in operational IR systems, it is important to establish when it performs well and when it performs poorly. In this paper we investigate how the use and effectiveness of IRF is affected by three factors: search task complexity, the search experience of the user and the stage in the search. Our findings suggest that all three of these factors contribute to the utility of IRF.", "fulltext": "1. INTRODUCTION\nInformation Retrieval (IR) systems are designed to help searchers\nsolve problems. In the traditional interaction metaphor employed by\nWeb search systems such as Yahoo! and MSN Search, the system\ngenerally only supports the retrieval of potentially relevant documents\nfrom the collection. However, it is also possible to offer support to\nsearchers for different search activities, such as selecting the terms to\npresent to the system or choosing which search strategy to adopt [3,\n8]; both of which can be problematic for searchers.\nAs the quality of the query submitted to the system directly affects the\nquality of search results, the issue of how to improve search queries\nhas been studied extensively in IR research [6]. Techniques such as\nRelevance Feedback (RF) [11] have been proposed as a way in which\nthe IR system can support the iterative development of a search query\nby suggesting alternative terms for query modification. However, in\npractice RF techniques have been underutilised as they place an\nincreased cognitive burden on searchers to directly indicate relevant\nresults [10].\nImplicit Relevance Feedback (IRF) [7] has been proposed as a way in\nwhich search queries can be improved by passively observing\nsearchers as they interact. IRF has been implemented either through\nthe use of surrogate measures based on interaction with documents\n(such as reading time, scrolling or document retention) [7] or using\ninteraction with browse-based result interfaces [5]. IRF has been\nshown to display mixed effectiveness because the factors that are good\nindicators of user interest are often erratic and the inferences drawn\nfrom user interaction are not always valid [7].\nIn this paper we present a study into the use and effectiveness of IRF\nin an online search environment. The study aims to investigate the\nfactors that affect IRF, in particular three research questions: (i) is the\nuse of and perceived quality of terms generated by IRF affected by the\nsearch task? (ii) is the use of and perceived quality of terms generated\nby IRF affected by the level of search experience of system users? (iii)\nis IRF equally used and does it generate terms that are equally useful\nat all search stages? This study aims to establish when, and under what\ncircumstances, IRF performs well in terms of its use and the query\nmodification terms selected as a result of its use.\nThe main experiment from which the data are taken was designed to\ntest techniques for selecting query modification terms and techniques\nfor displaying retrieval results [13]. In this paper we use data derived\nfrom that experiment to study factors affecting the utility of IRF.\n2. STUDY\nIn this section we describe the user study conducted to address our\nresearch questions.\n2.1 Systems\nOur study used two systems both of which suggested new query terms\nto the user. One system suggested terms based on the user\"s\ninteraction (IRF), the other used Explicit RF (ERF) asking the user to\nexplicitly indicate relevant material. Both systems used the same term\nsuggestion algorithm, [15], and used a common interface.\n2.1.1 Interface Overview\nIn both systems, retrieved documents are represented at the interface\nby their full-text and a variety of smaller, query-relevant\nrepresentations, created at retrieval time. We used the Web as the test\ncollection in this study and Google1\nas the underlying search engine.\nDocument representations include the document title and a summary\nof the document; a list of top-ranking sentences (TRS) extracted from\nthe top documents retrieved, scored in relation to the query, a sentence\nin the document summary, and each summary sentence in the context\nit occurs in the document (i.e., with the preceding and following\nsentence). Each summary sentence and top-ranking sentence is\nregarded as a representation of the document. The default display\ncontains the list of top-ranking sentences and the list of the first ten\ndocument titles. Interacting with a representation guides searchers to a\ndifferent representation from the same document, e.g., moving the\nmouse over a document title displays a summary of the document.\nThis presentation of progressively more information from documents\nto aid relevance assessments has been shown to be effective in earlier\nwork [14, 16]. In Appendix A we show the complete interface to the\nIRF system with the document representations marked and in\nAppendix B we show a fragment from the ERF interface with the\ncheckboxes used by searchers to indicate relevant information. Both\nsystems provide an interactive query expansion feature by suggesting\nnew query terms to the user. The searcher has the responsibility for\nchoosing which, if any, of these terms to add to the query. The\nsearcher can also add or remove terms from the query at will.\n2.1.2 Explicit RF system\nThis version of the system implements explicit RF. Next to each\ndocument representation are checkboxes that allow searchers to mark\nindividual representations as relevant; marking a representation is an\nindication that its contents are relevant. Only the representations\nmarked relevant by the user are used for suggesting new query terms.\nThis system was used as a baseline against which the IRF system\ncould be compared.\n2.1.3 Implicit RF system\nThis system makes inferences about searcher interests based on the\ninformation with which they interact. As described in Section 2.1.1\ninteracting with a representation highlights a new representation from\nthe same document. To the searcher this is a way they can find out\nmore information from a potentially interesting source. To the implicit\nRF system each interaction with a representation is interpreted as an\nimplicit indication of interest in that representation; interacting with a\nrepresentation is assumed to be an indication that its contents are\nrelevant. The query modification terms are selected using the same\nalgorithm as in the Explicit RF system. Therefore the only difference\nbetween the systems is how relevance is communicated to the system.\nThe results of the main experiment [13] indicated that these two\nsystems were comparable in terms of effectiveness.\n2.2 Tasks\nSearch tasks were designed to encourage realistic search behaviour by\nour subjects. The tasks were phrased in the form of simulated work\ntask situations [2], i.e., short search scenarios that were designed to\nreflect real-life search situations and allow subjects to develop\npersonal assessments of relevance. We devised six search topics (i.e.,\napplying to university, allergies in the workplace, art galleries in\nRome, Third Generation mobile phones, Internet music piracy and\npetrol prices) based on pilot testing with a small representative group\nof subjects. These subjects were not involved in the main experiment.\nFor each topic, three versions of each work task situation were\ndevised, each version differing in their predicted level of task\ncomplexity. As described in [1] task complexity is a variable that\naffects subject perceptions of a task and their interactive behaviour,\ne.g., subjects perform more filtering activities with highly complex\nsearch tasks. By developing tasks of different complexity we can\nassess how the nature of the task affects the subjects\" interactive\nbehaviour and hence the evidence supplied to IRF algorithms. Task\ncomplexity was varied according to the methodology described in [1],\nspecifically by varying the number of potential information sources\nand types of information required, to complete a task. In our pilot\ntests (and in a posteriori analysis of the main experiment results) we\nverified that subjects reporting of individual task complexity matched\nour estimation of the complexity of the task.\nSubjects attempted three search tasks: one high complexity, one\nmoderate complexity and one low complexity2\n. They were asked to\nread the task, place themselves in the situation it described and find\nthe information they felt was required to complete the task. Figure 1\nshows the task statements for three levels of task complexity for one\nof the six search topics.\nHC Task: High Complexity\nWhilst having dinner with an American colleague, they comment on the\nhigh price of petrol in the UK compared to other countries, despite large\nvolumes coming from the same source. Unaware of any major differences,\nyou decide to find out how and why petrol prices vary worldwide.\nMC Task: Moderate Complexity\nWhilst out for dinner one night, one of your friends\" guests is complaining\nabout the price of petrol and the factors that cause it. Throughout the night\nthey seem to be complaining about everything they can, reducing the\ncredibility of their earlier statements so you decide to research which\nfactors actually are important in determining the price of petrol in the UK.\nLC Task: Low Complexity\nWhile out for dinner one night, your friend complains about the rising\nprice of petrol. However, as you have not been driving for long, you are\nunaware of any major changes in price. You decide to find out how the\nprice of petrol has changed in the UK in recent years.\nFigure 1. Varying task complexity (Petrol Prices topic).\n2.3 Subjects\n156 volunteers expressed an interest in participating in our study. 48\nsubjects were selected from this set with the aim of populating two\ngroups, each with 24 subjects: inexperienced (infrequent/\ninexperienced searchers) and experienced (frequent/ experienced\nsearchers). Subjects were not chosen and classified into their groups\nuntil they had completed an entry questionnaire that asked them about\ntheir search experience and computer use.\nThe average age of the subjects was 22.83 years (maximum 51,\nminimum 18, \u03c3 = 5.23 years) and 75% had a university diploma or a\nhigher degree. 47.91% of subjects had, or were pursuing, a\nqualification in a discipline related to Computer Science. The subjects\nwere a mixture of students, researchers, academic staff and others,\nwith different levels of computer and search experience. The subjects\nwere divided into the two groups depending on their search\nexperience, how often they searched and the types of searches they\nperformed. All were familiar with Web searching, and some with\nsearching in other domains.\n2.4 Methodology\nThe experiment had a factorial design; with 2 levels of search\nexperience, 3 experimental systems (although we only report on the\nfindings from the ERF and IRF systems) and 3 levels of search task\ncomplexity. Subjects attempted one task of each complexity,\n2\nThe main experiment from which these results are drawn had a third\ncomparator system which had a different interface. Each subject\ncarried out three tasks, one on each system. We only report on the\nresults from the ERF and IRF systems as these are the only pertinent\nones for this paper.\nswitched systems after each task and used each system once. The\norder in which systems were used and search tasks attempted was\nrandomised according to a Latin square experimental design.\nQuestionnaires used Likert scales, semantic differentials and\nopenended questions to elicit subject opinions [4]. System logging was\nalso used to record subject interaction.\nA tutorial carried out prior to the experiment allowed subjects to use a\nnon-feedback version of the system to attempt a practice task before\nusing the first experimental system. Experiments lasted between\noneand-a-half and two hours, dependent on variables such as the time\nspent completing questionnaires. Subjects were offered a 5 minute\nbreak after the first hour. In each experiment:\ni. the subject was welcomed and asked to read an introduction to\nthe experiments and sign consent forms. This set of instructions\nwas written to ensure that each subject received precisely the\nsame information.\nii. the subject was asked to complete an introductory questionnaire.\nThis contained questions about the subject\"s education, general\nsearch experience, computer experience and Web search\nexperience.\niii. the subject was given a tutorial on the interface, followed by a\ntraining topic on a version of the interface with no RF.\niv. the subject was given three task sheets and asked to choose one\ntask from the six topics on each sheet. No guidelines were given\nto subjects when choosing a task other than they could not\nchoose a task from any topic more than once. Task complexity\nwas rotated by the experimenter so each subject attempted one\nhigh complexity task, one moderate complexity task and one low\ncomplexity task.\nv. the subject was asked to perform the search and was given 15\nminutes to search. The subject could terminate a search early if\nthey were unable to find any more information they felt helped\nthem complete the task.\nvi. after completion of the search, the subject was asked to complete\na post-search questionnaire.\nvii. the remaining tasks were attempted by the subject, following\nsteps v. and vi.\nviii. the subject completed a post-experiment questionnaire and\nparticipated in a post-experiment interview.\nSubjects were told that their interaction may be used by the IRF\nsystem to help them as they searched. They were not told which\nbehaviours would be used or how it would be used.\nWe now describe the findings of our analysis.\n3. FINDINGS\nIn this section we use the data derived from the experiment to answer\nour research questions about the effect of search task complexity,\nsearch experience and stage in search on the use and effectiveness of\nIRF. We present our findings per research question. Due to the\nordinal nature of much of the data non-parametric statistical testing is\nused in this analysis and the level of significance is set to p < .05,\nunless otherwise stated. We use the method proposed by [12] to\ndetermine the significance of differences in multiple comparisons and\nthat of [9] to test for interaction effects between experimental\nvariables, the occurrence of which we report where appropriate. All\nLikert scales and semantic differentials were on a 5-point scale where\na rating closer to 1 signifies more agreement with the attitude\nstatement. The category labels HC, MC and LC are used to denote the\nhigh, moderate and low complexity tasks respectively. The highest, or\nmost positive, values in each table are shown in bold. Our analysis\nuses data from questionnaires, post-experiment interviews and\nbackground system logging on the ERF and IRF systems.\n3.1 Search Task\nSearchers attempted three search tasks of varying complexity, each on\na different experimental system. In this section we present an analysis\non the use and usefulness of IRF for search tasks of different\ncomplexities. We present our findings in terms of the RF provided by\nsubjects and the terms recommended by the systems.\n3.1.1 Feedback\nWe use questionnaires and system logs to gather data on subject\nperceptions and provision of RF for different search tasks. In the\npostsearch questionnaire subjects were asked about how RF was conveyed\nusing differentials to elicit their opinion on:\n1. the value of the feedback technique: How you conveyed relevance\nto the system (i.e. ticking boxes or viewing information) was: easy /\ndifficult, effective/ ineffective, useful\"/not useful.\n2. the process of providing the feedback: How you conveyed relevance\nto the system made you feel: comfortable/uncomfortable, in\ncontrol/not in control.\nThe average obtained differential values are shown in Table 1 for IRF\nand each task category. The value corresponding to the differential\nAll represents the mean of all differentials for a particular attitude\nstatement. This gives some overall understanding of the subjects\"\nfeelings which can be useful as the subjects may not answer individual\ndifferentials very precisely. The values for ERF are included for\nreference in this table and all other tables and figures in the Findings\nsection. Since the aim of the paper is to investigate situations in which\nIRF might perform well, not a direct comparison between IRF and\nERF, we make only limited comparisons between these two types of\nfeedback.\nTable 1. Subject perceptions of RF method (lower = better).\nEach cell in Table 1 summarises the subject responses for 16\ntasksystem pairs (16 subjects who ran a high complexity (HC) task on the\nERF system, 16 subjects who ran a medium complexity (MC) task on\nthe ERF system, etc). Kruskal-Wallis Tests were applied to each\ndifferential for each type of RF3\n. Subject responses suggested that\n3\nSince this analysis involved many differentials, we use a Bonferroni\ncorrection to control the experiment-wise error rate and set the alpha\nlevel (\u03b1) to .0167 and .0250 for both statements 1. and 2.\nrespectively, i.e., .05 divided by the number of differentials. This\ncorrection reduces the number of Type I errors i.e., rejecting null\nhypotheses that are true.\nExplicit RF Implicit RF\nDifferential\nHC MC LC HC MC LC\nEasy 2.78 2.47 2.12 1.86 1.81 1.93\nEffective 2.94 2.68 2.44 2.04 2.41 2.66\nUseful 2.76 2.51 2.16 1.91 2.37 2.56\nAll (1) 2.83 2.55 2.24 1.94 2.20 2.38\nComfortable 2.27 2.28 2.35 2.11 2.15 2.16\nIn control 2.01 1.97 1.93 2.73 2.68 2.61\nAll (2) 2.14 2.13 2.14 2.42 2.42 2.39\nIRF was most effective and useful for more complex search tasks4\nand that the differences in all pair-wise comparisons between tasks\nwere significant5\n. Subject perceptions of IRF elicited using the other\ndifferentials did not appear to be affected by the complexity of the\nsearch task6\n. To determine whether a relationship exists between the\neffectiveness and usefulness of the IRF process and task complexity\nwe applied Spearman\"s Rank Order Correlation Coefficient to\nparticipant responses. The results of this analysis suggest that the\neffectiveness of IRF and usefulness of IRF are both related to task\ncomplexity; as task complexity increases subject preference for IRF\nalso increases7\n.\nOn the other hand, subjects felt ERF was more effective and useful\nfor low complexity tasks8\n. Their verbal reporting of ERF, where\nperceived utility and effectiveness increased as task complexity\ndecreased, supports this finding. In tasks of lower complexity the\nsubjects felt they were better able to provide feedback on whether or\nnot documents were relevant to the task.\nWe analyse interaction logs generated by both interfaces to investigate\nthe amount of RF subjects provided. To do this we use a measure of\nsearch precision that is the proportion of all possible document\nrepresentations that a searcher assessed, divided by the total number\nthey could assess. In ERF this is the proportion of all possible\nrepresentations that were marked relevant by the searcher, i.e., those\nrepresentations explicitly marked relevant. In IRF this is the\nproportion of representations viewed by a searcher over all possible\nrepresentations that could have been viewed by the searcher. This\nproportion measures the searcher\"s level of interaction with a\ndocument, we take it to measure the user\"s interest in the document:\nthe more document representations viewed the more interested we\nassume a user is in the content of the document.\nThere are a maximum of 14 representations per document: 4\ntopranking sentences, 1 title, 1 summary, 4 summary sentences and 4\nsummary sentences in document context. Since the interface shows\ndocument representations from the top-30 documents, there are 420\nrepresentations that a searcher can assess. Table 2 shows proportion\nof representations provided as RF by subjects.\nTable 2. Feedback and documents viewed.\nExplicit RF Implicit RF\nMeasure\nHC MC LC HC MC LC\nProportion\nFeedback\n2.14 2.39 2.65 21.50 19.36 15.32\nDocuments\nViewed\n10.63 10.43 10.81 10.84 12.19 14.81\nFor IRF there is a clear pattern: as complexity increases the subjects\nviewed fewer documents but viewed more representations for each\ndocument. This suggests a pattern where users are investigating\nretrieved documents in more depth. It also means that the amount of\n4\neffective: \u03c72\n(2) = 11.62, p = .003; useful: \u03c72\n(2) = 12.43, p = .002\n5\nDunn\"s post-hoc tests (multiple comparison using rank sums); all Z \u2265\n2.88, all p \u2264 .002\n6\nall \u03c72\n(2) \u2264 2.85, all p \u2265 .24 (Kruskal-Wallis Tests)\n7\neffective: all r \u2265 0.644, p \u2264 .002; useful: all r \u2265 0.541, p \u2264 .009\n8\neffective: \u03c72\n(2) = 7.01, p = .03; useful: \u03c72\n(2) = 6.59, p = .037\n(Kruskal-Wallis Test); all pair-wise differences significant, all Z \u2265\n2.34, all p \u2264 .01 (Dunn\"s post-hoc tests)\nfeedback varies based on the complexity of the search task. Since IRF\nis based on the interaction of the searcher, the more they interact, the\nmore feedback they provide. This has no effect on the number of RF\nterms chosen, but may affect the quality of the terms selected.\nCorrelation analysis revealed a strong negative correlation between the\nnumber of documents viewed and the amount of feedback searchers\nprovide9\n; as the number of documents viewed increases the proportion\nof feedback falls (searchers view less representations of each\ndocument). This may be a natural consequence of their being less\ntime to view documents in a time constrained task environment but as\nwe will show as complexity changes, the nature of information\nsearchers interact with also appears to change. In the next section we\ninvestigate the effect of task complexity on the terms chosen as a\nresult of IRF.\n3.1.2 Terms\nThe same RF algorithm was used to select query modification terms in\nall systems [16]. We use subject opinions of terms recommended by\nthe systems as a measure of the effectiveness of IRF with respect to\nthe terms generated for different search tasks. To test this, subjects\nwere asked to complete two semantic differentials that completed the\nstatement: The words chosen by the system were:\nrelevant/irrelevant and useful/not useful. Table 3 presents\naverage responses grouped by search task.\nTable 3. Subject perceptions of system terms (lower = better).\nExplicit RF Implicit RF\nDifferential\nHC MC LC HC MC LC\nRelevant 2.50 2.46 2.41 1.94 2.35 2.68\nUseful 2.61 2.61 2.59 2.06 2.54 2.70\nKruskal-Wallis Tests were applied within each type of RF. The\nresults indicate that the relevance and usefulness of the terms chosen\nby IRF is affected by the complexity of the search task; the terms\nchosen are more relevant and useful when the search task is more\ncomplex. 10\nRelevant here, was explained as being related to their task\nwhereas useful was for terms that were seen as being helpful in the\nsearch task. For ERF, the results indicate that the terms generated are\nperceived to be more relevant and useful for less complex search\ntasks; although differences between tasks were not significant11\n. This\nsuggests that subject perceptions of the terms chosen for query\nmodification are affected by task complexity. Comparison between\nERF and IRF shows that subject perceptions also vary for different\ntypes of RF12\n.\nAs well as using data on relevance and utility of the terms chosen, we\nused data on term acceptance to measure the perceived value of the\nterms suggested. Explicit and Implicit RF systems made\nrecommendations about which terms could be added to the original\nsearch query. In Table 4 we show the proportion of the top six terms\n9\nr = \u22120.696, p = .001 (Pearson\"s Correlation Coefficient)\n10\nrelevant: \u03c72\n(2) = 13.82, p = .001; useful: \u03c72\n(2) = 11.04, p = .004; \u03b1\n= .025\n11\nall \u03c72\n(2) \u2264 2.28, all p \u2265 .32 (Kruskal-Wallis Test)\n12\nall T(16) \u2265 102, all p \u2264 .021, (Wilcoxon Signed-Rank Test)\n13\nthat were shown to the searcher that were added to the search\nquery, for each type of task and each type of RF.\nTable 4. Term Acceptance (percentage of top six terms).\nExplicit RF Implicit RFProportion\nof terms HC MC LC HC MC LC\nAccepted 65.31 67.32 68.65 67.45 67.24 67.59\nThe average number of terms accepted from IRF is approximately the\nsame across all search tasks and generally the same as that of ERF14\n.\nAs Table 2 shows, subjects marked fewer documents relevant for\nhighly complex tasks . Therefore, when task complexity increases the\nERF system has fewer examples of relevant documents and the\nexpansion terms generated may be poorer. This could explain the\ndifference in the proportion of recommended terms accepted in ERF\nas task complexity increases. For IRF there is little difference in how\nmany of the recommended terms were chosen by subjects for each\nlevel of task complexity15\n. Subjects may have perceived IRF terms as\nmore useful for high complexity tasks but this was not reflected in the\nproportion of IRF terms accepted. Differences may reside in the\nnature of the terms accepted; future work will investigate this issue.\n3.1.3 Summary\nIn this section we have presented an investigation on the effect of\nsearch task complexity on the utility of IRF. From the results there\nappears to be a strong relation between the complexity of the task and\nthe subject interaction: subjects preferring IRF for highly complex\ntasks. Task complexity did not affect the proportion of terms accepted\nin either RF method, despite there being a difference in how\nrelevant and useful subjects perceived the terms to be for different\ncomplexities; complexity may affect term selection in ways other than\nthe proportion of terms accepted.\n3.2 Search Experience\nExperienced searchers may interact differently and give different\ntypes of evidence to RF than inexperienced searchers. As such, levels\nof search experience may affect searchers\" use and perceptions of IRF.\nIn our experiment subjects were divided into two groups based on\ntheir level of search experience, the frequency with which they\nsearched and the types of searches they performed. In this section we\nuse their perceptions and logging to address the next research\nquestion; the relationship between the usefulness and use of IRF and\nthe search experience of experimental subjects. The data are the same\nas that analysed in the previous section, but here we focus on search\nexperience rather than the search task.\n3.2.1 Feedback\nWe analyse the results from the attitude statements described at the\nbeginning of Section 3.1.1. (i.e., How you conveyed relevance to the\nsystem was\u2026 and How you conveyed relevance to the system made\nyou feel\u2026). These differentials elicited opinion from experimental\nsubjects about the RF method used. In Table 5 we show the mean\naverage responses for inexperienced and experienced subject groups\non ERF and IRF; 24 subjects per cell.\n13\nThis was the smallest number of query modification terms that were\noffered in both systems.\n14\nall T(16) \u2265 80, all p \u2264 .31, (Wilcoxon Signed-Rank Test)\n15\nERF: \u03c72\n(2) = 3.67, p = .16; IRF: \u03c72\n(2) = 2.55, p = .28\n(KruskalWallis Tests)\nTable 5. Subject perceptions of RF method (lower = better).\nThe results demonstrate a strong preference in inexperienced subjects\nfor IRF; they found it more easy and effective than experienced\nsubjects. 16\nThe differences for all other IRF differentials were not\nstatistically significant. For all differentials, apart from in control,\ninexperienced subjects generally preferred IRF over ERF17\n.\nInexperienced subjects also felt that IRF was more difficult to control\nthan experienced subjects18\n. As these subjects have less search\nexperience they may be less able to understand RF processes and may\nbe more comfortable with the system gathering feedback implicitly\nfrom their interaction. Experienced subjects tended to like ERF more\nthan inexperienced subjects and felt more comfortable with this\nfeedback method19\n. It appears from these results that experienced\nsubjects found ERF more useful and were more at ease with the ERF\nprocess.\nIn a similar way to Section 3.1.1 we analysed the proportion of\nfeedback that searchers provided to the experimental systems. Our\nanalysis suggested that search experience does not affect the amount\nof feedback subjects provide20\n.\n3.2.2 Terms\nWe used questionnaire responses to gauge subject opinion on the\nrelevance and usefulness of the terms from the perspective of\nexperienced and inexperienced subjects. Table 6 shows the average\ndifferential responses obtained from both subject groups.\nTable 6. Subject perceptions of system terms (lower = better).\nExplicit RF Implicit RF\nDifferential\nInexp. Exp. Inexp. Exp.\nRelevant 2.58 2.44 2.33 2.21\nUseful 2.88 2.63 2.33 2.23\nThe differences between subject groups were significant21\n.\nExperienced subjects generally reacted to the query modification\nterms chosen by the system more positively than inexperienced\n16\neasy: U(24) = 391, p = .016; effective: U(24) = 399, p = .011; \u03b1 =\n.0167 (Mann-Whitney Tests)\n17\nall T(24) \u2265 231, all p \u2264 .001 (Wilcoxon Signed-Rank Test)\n18\nU(24) = 390, p = .018; \u03b1 = .0250 (Mann-Whitney Test)\n19\nT(24) = 222, p = .020 (Wilcoxon Signed-Rank Test)\n20\nERF: all U(24) \u2264 319, p \u2265 .26, IRF: all U(24) \u2264 313, p \u2265 .30\n(MannWhitney Tests)\n21\nERF: all U(24) \u2265 388, p \u2264 .020, IRF: all U(24) \u2265 384, p \u2264 .024\nExplicit RF Implicit RF\nDifferential\nInexp. Exp. Inexp. Exp.\nEasy 2.46 2.46 1.84 1.98\nEffective 2.75 2.63 2.32 2.43\nUseful 2.50 2.46 2.28 2.27\nAll (1) 2.57 2.52 2.14 2.23\nComfortable 2.46 2.14 2.05 2.24\nIn control 1.96 1.98 2.73 2.64\nAll (2) 2.21 2.06 2.39 2.44\nsubjects. This finding was supported by the proportion of query\nmodification terms these subjects accepted. In the same way as in\nSection 3.1.2, we analysed the number of query modification terms\nrecommended by the system that were used by experimental subjects.\nTable 7 shows the average number of accepted terms per subject\ngroup.\nTable 7. Term Acceptance (percentage of top six terms).\nExplicit RF Implicit RFProportion\nof terms Inexp. Exp. Inexp. Exp.\nAccepted 63.76 70.44 64.43 71.35\nOur analysis of the data show that differences between subject groups\nfor each type of RF are significant; experienced subjects accepted\nmore expansion terms regardless of type of RF. However, the\ndifferences between the same groups for different types of RF are not\nsignificant; subjects chose roughly the same percentage of expansion\nterms offered irrespective of the type of RF22\n.\n3.2.3 Summary\nIn this section we have analysed data gathered from two subject\ngroups - inexperienced searchers and experienced searchers - on how\nthey perceive and use IRF. The results indicate that inexperienced\nsubjects found IRF more easy and effective than experienced\nsubjects, who in turn found the terms chosen as a result of IRF more\nrelevant and useful. We also showed that inexperienced subjects\ngenerally accepted less recommended terms than experienced\nsubjects, perhaps because they were less comfortable with RF or\ngenerally submitted shorter search queries. Search experience appears\nto affect how subjects use the terms recommended as a result of the\nRF process.\n3.3 Search Stage\nFrom our observations of experimental subjects as they searched we\nconjectured that RF may be used differently at different times during a\nsearch. To test this, our third research question concerned the use and\nusefulness of IRF during the course of a search. In this section we\ninvestigate whether the amount of RF provided by searchers or the\nproportion of terms accepted are affected by how far through their\nsearch they are. For the purposes of this analysis a search begins when\na subject poses the first query to the system and progresses until they\nterminate the search or reach the maximum allowed time for a search\ntask of 15 minutes. We do not divide tasks based on this limit as\nsubjects often terminated their search in less than 15 minutes.\nIn this section we use data gathered from interaction logs and subject\nopinions to investigate the extent to which RF was used and the extent\nto which it appeared to benefit our experimental subjects at different\nstages in their search\n3.3.1 Feedback\nThe interaction logs for all searches on the Explicit RF and Implicit\nRF were analysed and each search is divided up into nine equal length\ntime slices. This number of slices gave us an equal number per stage\nand was a sufficient level of granularity to identify trends in the\nresults. Slices 1 - 3 correspond to the start of the search, 4 - 6 to the\nmiddle of the search and 7 - 9 to the end. In Figure 2 we plot the\nmeasure of precision described in Section 3.1.1 (i.e., the proportion\nof all possible representations that were provided as RF) at each of the\n22\nIRF: U(24) = 403, p = .009, ERF: U(24) = 396, p = .013\nnine slices, per search task, averaged across all subjects; this allows us\nto see how the provision of RF was distributed during a search. The\ntotal amount of feedback for a single RF method/task complexity\npairing across all nine slices corresponds to the value recorded in the\nfirst row of Table 2 (e.g., the sum of the RF for IRF/HC across all nine\nslices of Figure 2 is 21.50%). To simplify the statistical analysis and\ncomparison we use the grouping of start, middle and end.\n0 1 2 3 4 5 6 7 8 9\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\n4.5\nSlice\nSearch\"precision\"(%oftotalrepsprovidedasRF)\nExplicit RF/HC\nExplicit RF/MC\nExplicit RF/LC\nImplicit RF/HC\nImplicit RF/MC\nImplicit RF/LC\nFigure 2. Distribution of RF provision per search task.\nFigure 2 appears to show the existence of a relationship between the\nstage in the search and the amount of relevance information provided\nto the different types of feedback algorithm. These are essentially\ndifferences in the way users are assessing documents. In the case of\nERF subjects provide explicit relevance assessments throughout most\nof the search, but there is generally a steep increase in the end phase\ntowards the completion of the search23\n.\nWhen using the IRF system, the data indicates that at the start of the\nsearch subjects are providing little relevance information24\n, which\ncorresponds to interacting with few document representations. At this\nstage the subjects are perhaps concentrating more on reading the\nretrieved results. Implicit relevance information is generally offered\nextensively in the middle of the search as they interact with results and\nit then tails off towards the end of the search. This would appear to\ncorrespond to stages of initial exploration, detailed analysis of\ndocument representations and storage and presentation of findings.\nFigure 2 also shows the proportion of feedback for tasks of different\ncomplexity. The results appear to show a difference25\nin how IRF is\nused that relates to the complexity of the search task. More\nspecifically, as complexity increases it appears as though subjects take\nlonger to reach their most interactive point. This suggests that task\ncomplexity affects how IRF is distributed during the search and that\nthey may be spending more time initially interpreting search results\nfor more complex tasks.\n23\nIRF: all Z \u2265 1.87, p \u2264 .031, ERF: start vs. end Z = 2.58, p = .005\n(Dunn\"s post-hoc tests).\n24\nAlthough increasing toward the end of the start stage.\n25\nAlthough not statistically significant; \u03c72\n(2) = 3.54, p = .17\n(Friedman Rank Sum Test)\n3.3.2 Terms\nThe terms recommended by the system are chosen based on the\nfrequency of their occurrence in the relevant items. That is,\nnonstopword, non-query terms occurring frequently in search results\nregarded as relevant are likely to be recommended to the searcher for\nquery modification. Since there is a direct association between the RF\nand the terms selected we use the number of terms accepted by\nsearchers at different points in the search as an indication of how\neffective the RF has been up until the current point in the search. In\nthis section we analysed the average number of terms from the top six\nterms recommended by Explicit RF and Implicit RF over the course of\na search. The average proportion of the top six recommended terms\nthat were accepted at each stage are shown in Table 8; each cell\ncontains data from all 48 subjects.\nTable 8. Term Acceptance (proportion of top six terms).\nExplicit RF Implicit RFProportion\nof terms start middle end start middle end\nAccepted 66.87 66.98 67.34 61.85 68.54 73.22\nThe results show an apparent association between the stage in the\nsearch and the number of feedback terms subjects accept. Search\nstage affects term acceptance in IRF but not in ERF26\n. The further\ninto a search a searcher progresses, the more likely they are to accept\nterms recommended via IRF (significantly more than ERF27\n). A\ncorrelation analysis between the proportion of terms accepted at each\nsearch stage and cumulative RF (i.e., the sum of all precision at each\nslice in Figure 2 up to and including the end of the search stage)\nsuggests that in both types of RF the quality of system terms improves\nas more RF is provided28\n.\n3.3.3 Summary\nThe results from this section indicate that the location in a search\naffects the amount of feedback given by the user to the system, and\nhence the amount of information that the RF mechanism has to decide\nwhich terms to offer the user. Further, trends in the data suggest that\nthe complexity of the task affects how subjects provide IRF and the\nproportion of system terms accepted.\n4. DISCUSSION AND IMPLICATIONS\nIn this section we discuss the implications of the findings presented in\nthe previous section for each research question.\n4.1 Search Task\nThe results of our study showed that ERF was preferred for less\ncomplex tasks and IRF for more complex tasks. From observations\nand subject comments we perceived that when using ERF systems\nsubjects generally forgot to provide the feedback but also employed\ndifferent criteria during the ERF process (i.e., they were assessing\nrelevance rather than expressing an interest). When the search was\nmore complex subjects rarely found results they regarded as\ncompletely relevant. Therefore they struggled to find relevant\n26\nERF: \u03c72\n(2) = 2.22, p = .33; IRF: \u03c72\n(2) = 7.73, p = .021 (Friedman\nRank Sum Tests); IRF: all pair-wise comparisons significant at Z \u2265\n1.77, all p \u2264 .038 (Dunn\"s post-hoc tests)\n27\nall T(48) \u2265 786, all p \u2264 .002, (Wilcoxon Signed-Rank Test)\n28\nIRF: r = .712, p < .001, ERF: r = .695, p = .001 (Pearson\nCorrelation Coefficient)\ninformation and were unable to communicate RF to the search system.\nIn these situations subjects appeared to prefer IRF as they do not need\nto make a relevance decision to obtain the benefits of RF, i.e., term\nsuggestions, whereas in ERF they do.\nThe association between RF method and task complexity has\nimplications for the design of user studies of RF systems and the RF\nsystems themselves. It implies that in the design of user studies\ninvolving ERF or IRF systems care should be taken to include tasks of\nvarying complexities, to avoid task bias. Also, in the design of search\nsystems it implies that since different types of RF may be appropriate\nfor different task complexities then a system that could automatically\ndetect complexity could use both ERF and IRF simultaneously to\nbenefit the searcher. For example, on the IRF system we noticed that\nas task complexity falls search behaviour shifts from results interface\nto retrieved documents. Monitoring such interaction across a number\nof studies may lead to a set of criteria that could help IR systems\nautomatically detect task complexity and tailor support to suit.\n4.2 Search Experience\nWe analysed the affect of search experience on the utility of IRF. Our\nanalysis revealed a general preference across all subjects for IRF over\nERF. That is, the average ratings assigned to IRF were generally more\npositive than those assigned to ERF. However, IRF was generally\nliked by both subject groups (perhaps because it removed the burden\nof providing relevance information) and ERF was generally preferred\nby experienced subjects more than inexperienced subjects (perhaps\nbecause it allowed them to specify which results were used by the\nsystem when generating term recommendations).\nAll subjects felt more in control with ERF than IRF, but for\ninexperienced subjects this did not appear to affect their overall\npreferences29\n. These subjects may understand the RF process less, but\nmay be more willing to sacrifice control over feedback in favour of\nIRF, a process that they perceive more positively.\n4.3 Search Stage\nWe also analysed the effects of search stage on the use and usefulness\nof IRF. Through analysis of this nature we can build a more complete\npicture of how searchers used RF and how this varies based on the RF\nmethod. The results suggest that IRF is used more in the middle of\nthe search than at the beginning or end, whereas ERF is used more\ntowards the end. The results also show the effects of task complexity\non the IRF process and how rapidly subjects reach their most\ninteractive point. Without an analysis of this type it would not have\nbeen possible to establish the existence of such patterns of behaviour.\nThe findings suggest that searchers interact differently for IRF and\nERF. Since ERF is not traditionally used until toward the end of the\nsearch it may be possible to incorporate both IRF and ERF into the\nsame IR system, with IRF being used to gather evidence until subjects\ndecide to use ERF. The development of such a system represents part\nof our ongoing work in this area.\n5. CONCLUSIONS\nIn this paper we have presented an investigation of Implicit Relevance\nFeedback (IRF). We aimed to answer three research questions about\nfactors that may affect the provision and usefulness of IRF. These\nfactors were search task complexity, the subjects\" search experience\nand the stage in the search. Our overall conclusion was that all factors\n29\nThis may also be true for experienced subjects, but the data we have\nis insufficient to draw this conclusion.\nappear to have some effect on the use and effectiveness of IRF,\nalthough the interaction effects between factors are not statistically\nsignificant.\nOur conclusions per each research question are: (i) IRF is generally\nmore useful for complex search tasks, where searchers want to focus\non the search task and get new ideas for their search from the system,\n(ii) IRF is preferred to ERF overall and generally preferred by\ninexperienced subjects wanting to reduce the burden of providing RF,\nand (iii) within a single search session IRF is affected by temporal\nlocation in a search (i.e., it is used in the middle, not the beginning or\nend) and task complexity.\nStudies of this nature are important to establish the circumstances\nwhere a promising technique such as IRF are useful and those when it\nis not. It is only after such studies have been run and analysed in this\nway can we develop an understanding of IRF that allow it to be\nsuccessfully implemented in operational IR systems.\n6. REFERENCES\n[1] Bell, D.J. and Ruthven, I. (2004). Searchers' assessments of task\ncomplexity for web searching. Proceedings of the 26th European\nConference on Information Retrieval, 57-71.\n[2] Borlund, P. (2000). Experimental components for the evaluation\nof interactive information retrieval systems. Journal of\nDocumentation. 56(1): 71-90.\n[3] Brajnik, G., Mizzaro, S., Tasso, C., and Venuti, F. (2002).\nStrategic help for user interfaces for information retrieval.\nJournal of the American Society for Information Science and\nTechnology. 53(5): 343-358.\n[4] Busha, C.H. and Harter, S.P., (1980). Research methods in\nlibrarianship: Techniques and interpretation. Library and\ninformation science series. New York: Academic Press.\n[5] Campbell, I. and Van Rijsbergen, C.J. (1996). The ostensive\nmodel of developing information needs. Proceedings of the 3rd\nInternational Conference on Conceptions of Library and\nInformation Science, 251-268.\n[6] Harman, D., (1992). Relevance feedback and other query\nmodification techniques. In Information retrieval: Data\nstructures and algorithms. New York: Prentice-Hall.\n[7] Kelly, D. and Teevan, J. (2003). Implicit feedback for inferring\nuser preference. SIGIR Forum. 37(2): 18-28.\n[8] Koenemann, J. and Belkin, N.J. (1996). A case for interaction: A\nstudy of interactive information retrieval behavior and\neffectiveness. Proceedings of the ACM SIGCHI Conference on\nHuman Factors in Computing Systems, 205-212.\n[9] Meddis, R., (1984). Statistics using ranks: A unified approach.\nOxford: Basil Blackwell, 303-308.\n[10] Morita, M. and Shinoda, Y. (1994). Information filtering based\non user behavior analysis and best match text retrieval.\nProceedings of the 17th Annual ACM SIGIR Conference on\nResearch and Development in Information Retrieval, 272-281.\n[11] Salton, G. and Buckley, C. (1990). Improving retrieval\nperformance by relevance feedback. Journal of the American\nSociety for Information Science. 41(4): 288-297.\n[12] Siegel, S. and Castellan, N.J. (1988). Nonparametric statistics for\nthe behavioural sciences. 2nd ed. Singapore: McGraw-Hill.\n[13] White, R.W. (2004). Implicit feedback for interactive information\nretrieval. Unpublished Doctoral Dissertation, University of\nGlasgow, Glasgow, United Kingdom.\n[14] White, R.W., Jose, J.M. and Ruthven, I. (2005). An implicit\nfeedback approach for interactive information retrieval,\nInformation Processing and Management, in press.\n[15] White, R.W., Jose, J.M., Ruthven, I. and Van Rijsbergen, C.J.\n(2004). A simulated study of implicit feedback models.\nProceedings of the 26th European Conference on Information\nRetrieval, 311-326.\n[16] Zellweger, P.T., Regli, S.H., Mackinlay, J.D., and Chang, B.-W.\n(2000). The impact of fluid documents on reading and browsing:\nAn observational study. Proceedings of the ACM SIGCHI\nConference on Human Factors in Computing Systems, 249-256.\nAppendix B. Checkboxes to mark\nrelevant document titles in the\nExplicit RF system.\nAppendix A. Interface to Implicit RF system.\n1. Top-Ranking Sentence 2. Title 3. Summary 4. Summary Sentence 5. Sentence in Context\n2\n3\n4\n5\n1", "keywords": "implicit relevance feedback;top-ranking sentence;query modification term;interactive query expansion feature;varying complexity;explicit rf system;medium complexity;high complexity whilst;proportion feedback;moderate complexity whilst;search task complexity;browse-based result interface;search precision;relevance feedback;introductory questionnaire"}
{"name": "train_H-97", "title": "Feature Representation for Effective Action-Item Detection", "abstract": "E-mail users face an ever-growing challenge in managing their inboxes due to the growing centrality of email in the workplace for task assignment, action requests, and other roles beyond information dissemination. Whereas Information Retrieval and Machine Learning techniques are gaining initial acceptance in spam filtering and automated folder assignment, this paper reports on a new task: automated action-item detection, in order to flag emails that require responses, and to highlight the specific passage(s) indicating the request(s) for action. Unlike standard topic-driven text classification, action-item detection requires inferring the sender\"s intent, and as such responds less well to pure bag-of-words classification. However, using enriched feature sets, such as n-grams (up to n=4) with chi-squared feature selection, and contextual cues for action-item location improve performance by up to 10% over unigrams, using in both cases state of the art classifiers such as SVMs with automated model selection via embedded cross-validation.", "fulltext": "1. INTRODUCTION\nE-mail users are facing an increasingly difficult task of\nmanaging their inboxes in the face of mounting challenges that result from\nrising e-mail usage. This includes prioritizing e-mails over a range\nof sources from business partners to family members, filtering and\nreducing junk e-mail, and quickly managing requests that demand\nFrom: Henry Hutchins <hhutchins@innovative.company.com>\nTo: Sara Smith; Joe Johnson; William Woolings\nSubject: meeting with prospective customers\nSent: Fri 12/10/2005 8:08 AM\nHi All,\nI\"d like to remind all of you that the group from GRTY will be visiting us\nnext Friday at 4:30 p.m. The current schedule looks like this:\n+ 9:30 a.m. Informal Breakfast and Discussion in Cafeteria\n+ 10:30 a.m. Company Overview\n+ 11:00 a.m. Individual Meetings (Continue Over Lunch)\n+ 2:00 p.m. Tour of Facilities\n+ 3:00 p.m. Sales Pitch\nIn order to have this go off smoothly, I would like to practice the\npresentation well in advance. As a result, I will need each of your parts by\nWednesday.\nKeep up the good work!\n-Henry\nFigure 1: An E-mail with emphasized Action-Item, an explicit\nrequest that requires the recipient\"s attention or action.\nthe receiver\"s attention or action. Automated action-item detection\ntargets the third of these problems by attempting to detect which\ne-mails require an action or response with information, and within\nthose e-mails, attempting to highlight the sentence (or other\npassage length) that directly indicates the action request.\nSuch a detection system can be used as one part of an e-mail\nagent which would assist a user in processing important e-mails\nquicker than would have been possible without the agent. We view\naction-item detection as one necessary component of a successful\ne-mail agent which would perform spam detection, action-item\ndetection, topic classification and priority ranking, among other\nfunctions. The utility of such a detector can manifest as a method of\nprioritizing e-mails according to task-oriented criteria other than\nthe standard ones of topic and sender or as a means of ensuring that\nthe email user hasn\"t dropped the proverbial ball by forgetting to\naddress an action request.\nAction-item detection differs from standard text classification in\ntwo important ways. First, the user is interested both in\ndetecting whether an email contains action items and in locating exactly\nwhere these action item requests are contained within the email\nbody. In contrast, standard text categorization merely assigns a\ntopic label to each text, whether that label corresponds to an e-mail\nfolder or a controlled indexing vocabulary [12, 15, 22]. Second,\naction-item detection attempts to recover the email sender\"s intent\n- whether she means to elicit response or action on the part of the\nreceiver; note that for this task, classifiers using only unigrams as\nfeatures do not perform optimally, as evidenced in our results\nbelow. Instead we find that we need more information-laden features\nsuch as higher-order n-grams. Text categorization by topic, on the\nother hand, works very well using just individual words as features\n[2, 9, 13, 17]. In fact, genre-classification, which one would think\nmay require more than a bag-of-words approach, also works quite\nwell using just unigram features [14]. Topic detection and\ntracking (TDT), also works well with unigram feature sets [1, 20]. We\nbelieve that action-item detection is one of the first clear instances\nof an IR-related task where we must move beyond bag-of-words\nto achieve high performance, albeit not too far, as bag-of-n-grams\nseem to suffice.\nWe first review related work for similar text classification\nproblems such as e-mail priority ranking and speech act identification.\nThen we more formally define the action-item detection problem,\ndiscuss the aspects that distinguish it from more common problems\nlike topic classification, and highlight the challenges in\nconstructing systems that can perform well at the sentence and document\nlevel. From there, we move to a discussion of feature\nrepresentation and selection techniques appropriate for this problem and how\nstandard text classification approaches can be adapted to smoothly\nmove from the sentence-level detection problem to the\ndocumentlevel classification problem. We then conduct an empirical analysis\nthat helps us determine the effectiveness of our feature extraction\nprocedures as well as establish baselines for a number of\nclassification algorithms on this task. Finally, we summarize this paper\"s\ncontributions and consider interesting directions for future work.\n2. RELATED WORK\nSeveral other researchers have considered very similar text\nclassification tasks. Cohen et al. [5] describe an ontology of speech\nacts, such as Propose a Meeting, and attempt to predict when an\ne-mail contains one of these speech acts. We consider action-items\nto be an important specific type of speech act that falls within their\nmore general classification. While they provide results for\nseveral classification methods, their methods only make use of human\njudgments at the document-level. In contrast, we consider whether\naccuracy can be increased by using finer-grained human judgments\nthat mark the specific sentences and phrases of interest.\nCorston-Oliver et al. [6] consider detecting items in e-mail to\nPut on a To-Do List. This classification task is very similar to\nours except they do not consider simple factual questions to\nbelong to this category. We include questions, but note that not all\nquestions are action-items - some are rhetorical or simply social\nconvention, How are you?. From a learning perspective, while\nthey make use of judgments at the sentence-level, they do not\nexplicitly compare what if any benefits finer-grained judgments offer.\nAdditionally, they do not study alternative choices or approaches to\nthe classification task. Instead, they simply apply a standard SVM\nat the sentence-level and focus primarily on a linguistic analysis of\nhow the sentence can be logically reformulated before adding it to\nthe task list. In this study, we examine several alternative\nclassification methods, compare document-level and sentence-level\napproaches and analyze the machine learning issues implicit in these\nproblems.\nInterest in a variety of learning tasks related to e-mail has been\nrapidly growing in the recent literature. For example, in a forum\ndedicated to e-mail learning tasks, Culotta et al. [7] presented\nmethods for learning social networks from e-mail. In this work, we do\nnot focus on peer relationships; however, such methods could\ncomplement those here since peer relationships often influence word\nchoice when requesting an action.\n3. PROBLEM DEFINITION & APPROACH\nIn contrast to previous work, we explicitly focus on the benefits\nthat finer-grained, more costly, sentence-level human judgments\noffer over coarse-grained document-level judgments. Additionally,\nwe consider multiple standard text classification approaches and\nanalyze both the quantitative and qualitative differences that arise\nfrom taking a document-level vs. a sentence-level approach to\nclassification. Finally, we focus on the representation necessary to\nachieve the most competitive performance.\n3.1 Problem Definition\nIn order to provide the most benefit to the user, a system would\nnot only detect the document, but it would also indicate the specific\nsentences in the e-mail which contain the action-items. Therefore,\nthere are three basic problems:\n1. Document detection: Classify a document as to whether or\nnot it contains an action-item.\n2. Document ranking: Rank the documents such that all\ndocuments containing action-items occur as high as possible in\nthe ranking.\n3. Sentence detection: Classify each sentence in a document as\nto whether or not it is an action-item.\nAs in most Information Retrieval tasks, the weight the\nevaluation metric should give to precision and recall depends on the\nnature of the application. In situations where a user will eventually\nread all received messages, ranking (e.g., via precision at recall of\n1) may be most important since this will help encourage shorter\ndelays in communications between users. In contrast, high-precision\ndetection at low recall will be of increasing importance when the\nuser is under severe time-pressure and therefore will likely not read\nall mail. This can be the case for crisis managers during disaster\nmanagement. Finally, sentence detection plays a role in both\ntimepressure situations and simply to alleviate the user\"s required time\nto gist the message.\n3.2 Approach\nAs mentioned above, the labeled data can come in one of two\nforms: a document-labeling provides a yes/no label for each\ndocument as to whether it contains an action-item; a phrase-labeling\nprovides only a yes label for the specific items of interest. We term\nthe human judgments a phrase-labeling since the user\"s view of the\naction-item may not correspond with actual sentence boundaries or\npredicted sentence boundaries. Obviously, it is straightforward to\ngenerate a document-labeling consistent with a phrase-labeling by\nlabeling a document yes if and only if it contains at least one\nphrase labeled yes.\nTo train classifiers for this task, we can take several viewpoints\nrelated to both the basic problems we have enumerated and the form\nof the labeled data. The document-level view treats each e-mail as\na learning instance with an associated class-label. Then, the\ndocument can be converted to a feature-value vector and learning\nprogresses as usual. Applying a document-level classifier to document\ndetection and ranking is straightforward. In order to apply it to\nsentence detection, one must make additional steps. For example,\nif the classifier predicts a document contains an action-item, then\nareas of the document that contain a high-concentration of words\nwhich the model weights heavily in favor of action-items can be\nindicated. The obvious benefit of the document-level approach is\nthat training set collection costs are lower since the user only has\nto specify whether or not an e-mail contains an action-item and not\nthe specific sentences.\nIn the sentence-level view, each e-mail is automatically segmented\ninto sentences, and each sentence is treated as a learning instance\nwith an associated class-label. Since the phrase-labeling provided\nby the user may not coincide with the automatic segmentation, we\nmust determine what label to assign a partially overlapping\nsentence when converting it to a learning instance. Once trained,\napplying the resulting classifiers to sentence detection is now\nstraightforward, but in order to apply the classifiers to document\ndetection and document ranking, the individual predictions over each\nsentence must be aggregated in order to make a document-level\nprediction. This approach has the potential to benefit from\nmorespecific labels that enable the learner to focus attention on the key\nsentences instead of having to learn based on data that the majority\nof the words in the e-mail provide no or little information about\nclass membership.\n3.2.1 Features\nConsider some of the phrases that might constitute part of an\naction item: would like to know, let me know, as soon as\npossible, have you. Each of these phrases consists of common\nwords that occur in many e-mails. However, when they occur in\nthe same sentence, they are far more indicative of an action-item.\nAdditionally, order can be important: consider have you versus\nyou have. Because of this, we posit that n-grams play a larger\nrole in this problem than is typical of problems like topic\nclassification. Therefore, we consider all n-grams up to size 4.\nWhen using n-grams, if we find an n-gram of size 4 in a segment\nof text, we can represent the text as just one occurrence of the\nngram or as one occurrence of the n-gram and an occurrence of each\nsmaller n-gram contained by it. We choose the second of these\nalternatives since this will allow the algorithm itself to smoothly\nback-off in terms of recall. Methods such as na\u00a8\u0131ve Bayes may be\nhurt by such a representation because of double-counting.\nSince sentence-ending punctuation can provide information, we\nretain the terminating punctuation token when it is identifiable.\nAdditionally, we add a beginning-of-sentence and end-of-sentence\ntoken in order to capture patterns that are often indicators at the\nbeginning or end of a sentence. Assuming proper punctuation, these\nextra tokens are unnecessary, but often e-mail lacks proper\npunctuation. In addition, for the sentence-level classifiers that use\nngrams, we additionally code for each sentence a binary encoding\nof the position of the sentence relative to the document. This\nencoding has eight associated features that represent which octile (the\nfirst eighth, second eighth, etc.) contains the sentence.\n3.2.2 Implementation Details\nIn order to compare the document-level to the sentence-level\napproach, we compare predictions at the document-level. We do not\naddress how to use a document-level classifier to make predictions\nat the sentence-level.\nIn order to automatically segment the text of the e-mail, we use\nthe RASP statistical parser [4]. Since the automatically segmented\nsentences may not correspond directly with the phrase-level\nboundaries, we treat any sentence that contains at least 30% of a marked\naction-item segment as an action-item. When evaluating\nsentencedetection for the sentence-level system, we use these class labels\nas ground truth. Since we are not evaluating multiple segmentation\napproaches, this does not bias any of the methods. If multiple\nsegmentation systems were under evaluation, one would need to use a\nmetric that matched predicted positive sentences to phrases labeled\npositive. The metric would need to punish overly long true\npredictions as well as too short predictions. Our criteria for converting\nto labeled instances implicitly includes both criteria. Since the\nsegmentation is fixed, an overly long prediction would be predicting\nyes for many no instances since presumably the extra length\ncorresponds to additional segmented sentences all of which do not\ncontain 30% of action-item. Likewise, a too short prediction must\ncorrespond to a small sentence included in the action-item but not\nconstituting all of the action-item. Therefore, in order to consider\nthe prediction to be too short, there will be an additional\npreceding/following sentence that is an action-item where we incorrectly\npredicted no.\nOnce a sentence-level classifier has made a prediction for each\nsentence, we must combine these predictions to make both a\ndocument-level prediction and a document-level score. We use the\nsimple policy of predicting positive when any of the sentences is\npredicted positive. In order to produce a document score for\nranking, the confidence that the document contains an action-item is:\n\u03c8(d) =\n1\nn(d) s\u2208d|\u03c0(s)=1 \u03c8(s) if for any s \u2208 d, \u03c0(s) = 1\n1\nn(d)\nmaxs\u2208d \u03c8(s) o.w.\nwhere s is a sentence in document d, \u03c0 is the classifier\"s 1/0\nprediction, \u03c8 is the score the classifier assigns as its confidence that\n\u03c0(s) = 1, and n(d) is the greater of 1 and the number of (unigram)\ntokens in the document. In other words, when any sentence is\npredicted positive, the document score is the length normalized sum of\nthe sentence scores above threshold. When no sentence is predicted\npositive, the document score is the maximum sentence score\nnormalized by length. As in other text problems, we are more likely to\nemit false positives for documents with more words or sentences.\nThus we include a length normalization factor.\n4. EXPERIMENTAL ANALYSIS\n4.1 The Data\nOur corpus consists of e-mails obtained from volunteers at an\neducational institution and cover subjects such as: organizing a\nresearch workshop, arranging for job-candidate interviews,\npublishing proceedings, and talk announcements. The messages were\nanonymized by replacing the names of each individual and\ninstitution with a pseudonym.1\nAfter attempting to identify and eliminate\nduplicate e-mails, the corpus contains 744 e-mail messages.\nAfter identity anonymization, the corpora has three basic\nversions. Quoted material refers to the text of a previous e-mail that\nan author often leaves in an e-mail message when responding to the\ne-mail. Quoted material can act as noise when learning since it may\ninclude action-items from previous messages that are no longer\nrelevant. To isolate the effects of quoted material, we have three\nversions of the corpora. The raw form contains the basic messages.\nThe auto-stripped version contains the messages after quoted\nmaterial has been automatically removed. The hand-stripped version\ncontains the messages after quoted material has been removed by\na human. Additionally, the hand-stripped version has had any xml\ncontent and e-mail signatures removed - leaving only the essential\ncontent of the message. The studies reported here are performed\nwith the hand-stripped version. This allows us to balance the\ncognitive load in terms of number of tokens that must be read in the\nuser-studies we report - including quoted material would\ncomplicate the user studies since some users might skip the material while\nothers read it. Additionally, ensuring all quoted material is removed\n1\nWe have an even more highly anonymized version of the\ncorpus that can be made available for some outside experimentation.\nPlease contact the authors for more information on obtaining this\ndata.\nprevents tainting the cross-validation since otherwise a test item\ncould occur as quoted material in a training document.\n4.1.1 Data Labeling\nTwo human annotators labeled each message as to whether or\nnot it contained an action-item. In addition, they identified each\nsegment of the e-mail which contained an action-item. A segment\nis a contiguous section of text selected by the human annotators\nand may span several sentences or a complete phrase contained in\na sentence. They were instructed that an action item is an explicit\nrequest for information that requires the recipient\"s attention or a\nrequired action and told to highlight the phrases or sentences that\nmake up the request.\nAnnotator 1\nNo Yes\nAnnotator 2\nNo 391 26\nYes 29 298\nTable 1: Agreement of Human Annotators at Document Level\nAnnotator One labeled 324 messages as containing action items.\nAnnotator Two labeled 327 messages as containing action items.\nThe agreement of the human annotators is shown in Tables 1 and\n2. The annotators are said to agree at the document-level when\nboth marked the same document as containing no action-items or\nboth marked at least one action-item regardless of whether the text\nsegments were the same. At the document-level, the annotators\nagreed 93% of the time. The kappa statistic [3, 5] is often used to\nevaluate inter-annotator agreement:\n\u03ba =\nA \u2212 R\n1 \u2212 R\nA is the empirical estimate of the probability of agreement. R\nis the empirical estimate of the probability of random agreement\ngiven the empirical class priors. A value close to \u22121 implies the\nannotators agree far less often than would be expected randomly,\nwhile a value close to 1 means they agree more often than randomly\nexpected.\nAt the document-level, the kappa statistic for inter-annotator\nagreement is 0.85. This value is both strong enough to expect the\nproblem to be learnable and is comparable with results for similar tasks\n[5, 6].\nIn order to determine the sentence-level agreement, we use each\njudgment to create a sentence-corpus with labels as described in\nSection 3.2.2, then consider the agreement over these sentences.\nThis allows us to compare agreement over no judgments. We\nperform this comparison over the hand-stripped corpus since that\neliminates spurious no judgments that would come from\nincluding quoted material, etc. Both annotators were free to label the\nsubject as an action-item, but since neither did, we omit the subject\nline of the message as well. This only reduces the number of no\nagreements. This leaves 6301 automatically segmented sentences.\nAt the sentence-level, the annotators agreed 98% of the time, and\nthe kappa statistic for inter-annotator agreement is 0.82.\nIn order to produce one single set of judgments, the human\nannotators went through each annotation where there was\ndisagreement and came to a consensus opinion. The annotators did not\ncollect statistics during this process but anecdotally reported that\nthe majority of disagreements were either cases of clear annotator\noversight or different interpretations of conditional statements. For\nexample, If you would like to keep your job, come to tomorrow\"s\nmeeting implies a required action where If you would like to join\nAnnotator 1\nNo Yes\nAnnotator 2\nNo 5810 65\nYes 74 352\nTable 2: Agreement of Human Annotators at Sentence Level\nthe football betting pool, come to tomorrow\"s meeting does not.\nThe first would be an action-item in most contexts while the\nsecond would not. Of course, many conditional statements are not so\nclearly interpretable. After reconciling the judgments there are 416\ne-mails with no action-items and 328 e-mails containing\nactionitems. Of the 328 e-mails containing action-items, 259 messages\nhave one action-item segment; 55 messages have two action-item\nsegments; 11 messages have three action-item segments. Two\nmessages have four action-item segments, and one message has six\naction-item segments. Computing the sentence-level agreement\nusing the reconciled gold standard judgments with each of the\nannotators\" individual judgments gives a kappa of 0.89 for Annotator\nOne and a kappa of 0.92 for Annotator Two.\nIn terms of message characteristics, there were on average 132\ncontent tokens in the body after stripping. For action-item\nmessages, there were 115. However, by examining Figure 2 we see\nthe length distributions are nearly identical. As would be expected\nfor e-mail, it is a long-tailed distribution with about half the\nmessages having more than 60 tokens in the body (this paragraph has\n65 tokens).\n4.2 Classifiers\nFor this experiment, we have selected a variety of standard text\nclassification algorithms. In selecting algorithms, we have chosen\nalgorithms that are not only known to work well but which differ\nalong such lines as discriminative vs. generative and lazy vs.\neager. We have done this in order to provide both a competitive and\nthorough sampling of learning methods for the task at hand. This\nis important since it is easy to improve a strawman classifier by\nintroducing a new representation. By thoroughly sampling\nalternative classifier choices we demonstrate that representation\nimprovements over bag-of-words are not due to using the information in the\nbag-of-words poorly.\n4.2.1 kNN\nWe employ a standard variant of the k-nearest neighbor\nalgorithm used in text classification, kNN with s-cut score\nthresholding [19]. We use a tfidf-weighting of the terms with a\ndistanceweighted vote of the neighbors to compute the score before\nthresholding it. In order to choose the value of s for thresholding, we\nperform leave-one-out cross-validation over the training set. The\nvalue of k is set to be 2( log2 N + 1) where N is the number of\ntraining points. This rule for choosing k is theoretically motivated\nby results which show such a rule converges to the optimal\nclassifier as the number of training points increases [8]. In practice,\nwe have also found it to be a computational convenience that\nfrequently leads to comparable results with numerically optimizing k\nvia a cross-validation procedure.\n4.2.2 Na\u00a8\u0131ve Bayes\nWe use a standard multinomial na\u00a8\u0131ve Bayes classifier [16]. In\nusing this classifier, we smoothed word and class probabilities using a\nBayesian estimate (with the word prior) and a Laplace m-estimate,\nrespectively.\n0\n20\n40\n60\n80\n100\n120\n140\n160\n0 200 400 600 800 1000 1200 1400\nNumberofMessages\nNumber of Tokens\nAll Messages\nAction-Item Messages\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\n0.14\n0.16\n0.18\n0.2\n0 200 400 600 800 1000 1200 1400\nPercentageofMessages\nNumber of Tokens\nAll Messages\nAction-Item Messages\nFigure 2: The Histogram (left) and Distribution (right) of Message Length. A bin size of 20 words was used. Only tokens in the body\nafter hand-stripping were counted. After stripping, the majority of words left are usually actual message content.\nClassifiers Document Unigram Document Ngram Sentence Unigram Sentence Ngram\nF1\nkNN 0.6670 \u00b1 0.0288 0.7108 \u00b1 0.0699 0.7615 \u00b1 0.0504 0.7790 \u00b1 0.0460\nna\u00a8\u0131ve Bayes 0.6572 \u00b1 0.0749 0.6484 \u00b1 0.0513 0.7715 \u00b1 0.0597 0.7777 \u00b1 0.0426\nSVM 0.6904 \u00b1 0.0347 0.7428 \u00b1 0.0422 0.7282 \u00b1 0.0698 0.7682 \u00b1 0.0451\nVoted Perceptron 0.6288 \u00b1 0.0395 0.6774 \u00b1 0.0422 0.6511 \u00b1 0.0506 0.6798 \u00b1 0.0913\nAccuracy\nkNN 0.7029 \u00b1 0.0659 0.7486 \u00b1 0.0505 0.7972 \u00b1 0.0435 0.8092 \u00b1 0.0352\nna\u00a8\u0131ve Bayes 0.6074 \u00b1 0.0651 0.5816 \u00b1 0.1075 0.7863 \u00b1 0.0553 0.8145 \u00b1 0.0268\nSVM 0.7595 \u00b1 0.0309 0.7904 \u00b1 0.0349 0.7958 \u00b1 0.0551 0.8173 \u00b1 0.0258\nVoted Perceptron 0.6531 \u00b1 0.0390 0.7164 \u00b1 0.0376 0.6413 \u00b1 0.0833 0.7082 \u00b1 0.1032\nTable 3: Average Document-Detection Performance during Cross-Validation for Each Method and the Sample Standard Deviation\n(Sn\u22121) in italics. The best performance for each classifier is shown in bold.\n4.2.3 SVM\nWe have used a linear SVM with a tfidf feature representation\nand L2-norm as implemented in the SVMlight package v6.01 [11].\nAll default settings were used.\n4.2.4 Voted Perceptron\nLike the SVM, the Voted Perceptron is a kernel-based\nlearning method. We use the same feature representation and kernel\nas we have for the SVM, a linear kernel with tfidf-weighting and\nan L2-norm. The voted perceptron is an online-learning method\nthat keeps a history of past perceptrons used, as well as a weight\nsignifying how often that perceptron was correct. With each new\ntraining example, a correct classification increases the weight on\nthe current perceptron and an incorrect classification updates the\nperceptron. The output of the classifier uses the weights on the\nperceptra to make a final voted classification. When used in an\noffline-manner, multiple passes can be made through the training\ndata. Both the voted perceptron and the SVM give a solution from\nthe same hypothesis space - in this case, a linear classifier.\nFurthermore, it is well-known that the Voted Perceptron increases the\nmargin of the solution after each pass through the training data [10].\nSince Cohen et al. [5] obtain worse results using an SVM than a\nVoted Perceptron with one training iteration, they conclude that the\nbest solution for detecting speech acts may not lie in an area with\na large margin. Because their tasks are highly similar to ours, we\nemploy both classifiers to ensure we are not overlooking a\ncompetitive alternative classifier to the SVM for the basic bag-of-words\nrepresentation.\n4.3 Performance Measures\nTo compare the performance of the classification methods, we\nlook at two standard performance measures, F1 and accuracy. The\nF1 measure [18, 21] is the harmonic mean of precision and recall\nwhere Precision = Correct Positives\nPredicted Positives\nand Recall = Correct Positives\nActual Positives\n.\n4.4 Experimental Methodology\nWe perform standard 10-fold cross-validation on the set of\ndocuments. For the sentence-level approach, all sentences in a\ndocument are either entirely in the training set or entirely in the test set\nfor each fold. For significance tests, we use a two-tailed t-test [21]\nto compare the values obtained during each cross-validation fold\nwith a p-value of 0.05.\nFeature selection was performed using the chi-squared\nstatistic. Different levels of feature selection were considered for each\nclassifier. Each of the following number of features was tried:\n10, 25, 50, 100, 250, 750, 1000, 2000, 4000. There are\napproximately 4700 unigram tokens without feature selection. In order to choose\nthe number of features to use for each classifier, we perform nested\ncross-validation and choose the settings that yield the optimal\ndocument-level F1 for that classifier. For this study, only the body of\neach e-mail message was used. Feature selection is always applied\nto all candidate features. That is, for the n-gram representation, the\nn-grams and position features are also subject to removal by the\nfeature selection method.\n4.5 Results\nThe results for document-level classification are given in Table\n3. The primary hypothesis we are concerned with is that n-grams\nare critical for this task; if this is true, we expect to see a significant\ngap in performance between the document-level classifiers that use\nn-grams (denoted Document Ngram) and those using only unigram\nfeatures (denoted Document Unigram). Examining Table 3, we\nobserve that this is indeed the case for every classifier except na\u00a8\u0131ve\nBayes. This difference in performance produced by the n-gram\nrepresentation is statistically significant for each classifier except\nfor na\u00a8\u0131ve Bayes and the accuracy metric for kNN (see Table 4).\nNa\u00a8\u0131ve Bayes poor performance with the n-gram representation is\nnot surprising since the bag-of-n-grams causes excessive\ndoublecounting as mentioned in Section 3.2.1; however, na\u00a8\u0131ve Bayes is\nnot hurt at the sentence-level because the sparse examples provide\nfew chances for agglomerative effects of double counting. In either\ncase, when a language-modeling approach is desired, modeling the\nn-grams directly would be preferable to na\u00a8\u0131ve Bayes. More\nimportantly for the n-gram hypothesis, the n-grams lead to the best\ndocument-level classifier performance as well.\nAs would be expected, the difference between the sentence-level\nn-gram representation and unigram representation is small. This\nis because the window of text is so small that the unigram\nrepresentation, when done at the sentence-level, implicitly picks up\non the power of the n-grams. Further improvement would\nsignify that the order of the words matter even when only\nconsidering a small sentence-size window. Therefore, the finer-grained\nsentence-level judgments allows a unigram representation to\nsucceed but only when performed in a small window - behaving as\nan n-gram representation for all practical purposes.\nDocument Winner Sentence Winner\nkNN Ngram Ngram\nna\u00a8\u0131ve Bayes Unigram Ngram\nSVM Ngram\u2020\nNgram\nVoted Perceptron Ngram\u2020\nNgram\nTable 4: Significance results for n-grams versus unigrams for\ndocument detection using document-level and sentence-level\nclassifiers. When the F1 result is statistically significant, it is\nshown in bold. When the accuracy result is significant, it is\nshown with a \u2020\n.\nF1 Winner Accuracy Winner\nkNN Sentence Sentence\nna\u00a8\u0131ve Bayes Sentence Sentence\nSVM Sentence Sentence\nVoted Perceptron Sentence Document\nTable 5: Significance results for sentence-level classifiers vs.\ndocument-level classifiers for the document detection problem.\nWhen the result is statistically significant, it is shown in bold.\nFurther highlighting the improvement from finer-grained\njudgments and n-grams, Figure 3 graphically depicts the edge the SVM\nsentence-level classifier has over the standard bag-of-words approach\nwith a precision-recall curve. In the high precision area of the\ngraph, the consistent edge of the sentence-level classifier is rather\nimpressive - continuing at precision 1 out to 0.1 recall. This\nwould mean that a tenth of the user\"s action-items would be placed\nat the top of their action-item sorted inbox. Additionally, the large\nseparation at the top right of the curves corresponds to the area\nwhere the optimal F1 occurs for each classifier, agreeing with the\nlarge improvement from 0.6904 to 0.7682 in F1 score. Considering\nthe relative unexplored nature of classification at the sentence-level,\nthis gives great hope for further increases in performance.\nAccuracy F1\nUnigram Ngram Unigram Ngram\nkNN 0.9519 0.9536 0.6540 0.6686\nna\u00a8\u0131ve Bayes 0.9419 0.9550 0.6176 0.6676\nSVM 0.9559 0.9579 0.6271 0.6672\nVoted Perceptron 0.8895 0.9247 0.3744 0.5164\nTable 6: Performance of the Sentence-Level Classifiers at\nSentence Detection\nAlthough Cohen et al. [5] observed that the Voted Perceptron\nwith a single training iteration outperformed SVM in a set of\nsimilar tasks, we see no such behavior here. This further strengthens the\nevidence that an alternate classifier with the bag-of-words\nrepresentation could not reach the same level of performance. The Voted\nPerceptron classifier does improve when the number of training\niterations are increased, but it is still lower than the SVM classifier.\nSentence detection results are presented in Table 6. With regard\nto the sentence detection problem, we note that the F1 measure\ngives a better feel for the remaining room for improvement in this\ndifficult problem. That is, unlike document detection where\nactionitem documents are fairly common, action-item sentences are very\nrare. Thus, as in other text problems, the accuracy numbers are\ndeceptively high sheerly because of the default accuracy attainable by\nalways predicting no. Although, the results here are significantly\nabove-random, it is unclear what level of performance is necessary\nfor sentence detection to be useful in and of itself and not simply\nas a means to document ranking and classification.\nFigure 4: Users find action-items quicker when assisted by a\nclassification system.\nFinally, when considering a new type of classification task, one\nof the most basic questions is whether an accurate classifier built\nfor the task can have an impact on the end-user. In order to\ndemonstrate the impact this task can have on e-mail users, we conducted\na user study using an earlier less-accurate version of the sentence\nclassifier - where instead of using just a single sentence, a\nthreesentence windowed-approach was used. There were three distinct\nsets of e-mail in which users had to find action-items. These sets\nwere either presented in a random order (Unordered), ordered by\nthe classifier (Ordered), or ordered by the classifier and with the\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1\nPrecision\nRecall\nAction-Item Detection SVM Performance (Post Model Selection)\nDocument Unigram\nSentence Ngram\nFigure 3: Both n-grams and a small prediction window lead to consistent improvements over the standard approach.\ncenter sentence in the highest confidence window highlighted\n(Order+help). In order to perform fair comparisons between\nconditions, the overall number of tokens in each message set should be\napproximately equal; that is, the cognitive reading load should be\napproximately the same before the classifier\"s reordering.\nAdditionally, users typically show practice effects by improving at the\noverall task and thus performing better at later message sets. This\nis typically handled by varying the ordering of the sets across users\nso that the means are comparable. While omitting further detail,\nwe note the sets were balanced for the total number of tokens and\na latin square design was used to balance practice effects.\nFigure 4 shows that at intervals of 5, 10, and 15 minutes, users\nconsistently found significantly more action-items when assisted\nby the classifier, but were most critically aided in the first five\nminutes. Although, the classifier consistently aids the users, we did not\ngain an additional end-user impact by highlighting. As mentioned\nabove, this might be a result of the large room for improvement that\nstill exists for sentence detection, but anecdotal evidence suggests\nthis might also be a result of how the information is presented to the\nuser rather than the accuracy of sentence detection. For example,\nhighlighting the wrong sentence near an actual action-item hurts\nthe user\"s trust, but if a vague indicator (e.g., an arrow) points to the\napproximate area the user is not aware of the near-miss. Since the\nuser studies used a three sentence window, we believe this played a\nrole as well as sentence detection accuracy.\n4.6 Discussion\nIn contrast to problems where n-grams have yielded little\ndifference, we believe their power here stems from the fact that many of\nthe meaningful n-grams for action-items consist of common words,\ne.g., let me know. Therefore, the document-level unigram\napproach cannot gain much leverage, even when modeling their joint\nprobability correctly, since these words will often co-occur in the\ndocument but not necessarily in a phrase. Additionally, action-item\ndetection is distinct from many text classification tasks in that a\nsingle sentence can change the class label of the document. As a\nresult, good classifiers cannot rely on aggregating evidence from a\nlarge number of weak indicators across the entire document.\nEven though we discarded the header information, examining\nthe top-ranked features at the document-level reveals that many of\nthe features are names or parts of e-mail addresses that occurred in\nthe body and are highly associated with e-mails that tend to\ncontain many or no action-items. A few examples are terms such as\norg, bob, and gov. We note that these features will be\nsensitive to the particular distribution (senders/receivers) and thus the\ndocument-level approach may produce classifiers that transfer less\nreadily to alternate contexts and users at different institutions. This\npoints out that part of the problem of going beyond bag-of-words\nmay be the methodology, and investigating such properties as\nlearning curves and how well a model transfers may highlight\ndifferences in models which appear to have similar performance when\ntested on the distributions they were trained on. We are currently\ninvestigating whether the sentence-level classifiers do perform\nbetter over different test corpora without retraining.\n5. FUTURE WORK\nWhile applying text classifiers at the document-level is fairly\nwell-understood, there exists the potential for significantly\nincreasing the performance of the sentence-level classifiers. Such methods\ninclude alternate ways of combining the predictions over each\nsentence, weightings other than tfidf, which may not be appropriate\nsince sentences are small, better sentence segmentation, and other\ntypes of phrasal analysis. Additionally, named entity tagging, time\nexpressions, etc., seem likely candidates for features that can\nfurther improve this task. We are currently pursuing some of these\navenues to see what additional gains these offer.\nFinally, it would be interesting to investigate the best methods for\ncombining the document-level and sentence-level classifiers. Since\nthe simple bag-of-words representation at the document-level leads\nto a learned model that behaves somewhat like a context-specific\nprior dependent on the sender/receiver and general topic, a first\nchoice would be to treat it as such when combining probability\nestimates with the sentence-level classifier. Such a model might\nserve as a general example for other problems where bag-of-words\ncan establish a baseline model but richer approaches are needed to\nachieve performance beyond that baseline.\n6. SUMMARY AND CONCLUSIONS\nThe effectiveness of sentence-level detection argues that\nlabeling at the sentence-level provides significant value. Further\nexperiments are needed to see how this interacts with the amount of\ntraining data available. Sentence detection that is then agglomerated to\ndocument-level detection works surprisingly better given low recall\nthan would be expected with sentence-level items. This, in turn,\nindicates that improved sentence segmentation methods could yield\nfurther improvements in classification.\nIn this work, we examined how action-items can be effectively\ndetected in e-mails. Our empirical analysis has demonstrated that\nn-grams are of key importance to making the most of\ndocumentlevel judgments. When finer-grained judgments are available, then\na standard bag-of-words approach using a small (sentence) window\nsize and automatic segmentation techniques can produce results\nalmost as good as the n-gram based approaches.\nAcknowledgments\nThis material is based upon work supported by the Defense\nAdvanced Research Projects Agency (DARPA) under Contract No.\nNBCHD030010. Any opinions, findings and conclusions or\nrecommendations expressed in this material are those of the author(s)\nand do not necessarily reflect the views of the Defense Advanced\nResearch Projects Agency (DARPA), or the Department of\nInteriorNational Business Center (DOI-NBC).\nWe would like to extend our sincerest thanks to Jill Lehman\nwhose efforts in data collection were essential in constructing the\ncorpus, and both Jill and Aaron Steinfeld for their direction of the\nHCI experiments. We would also like to thank Django Wexler for\nconstructing and supporting the corpus labeling tools and Curtis\nHuttenhower\"s support of the text preprocessing package. Finally,\nwe gratefully acknowledge Scott Fahlman for his encouragement\nand useful discussions on this topic.\n7. REFERENCES\n[1] J. Allan, J. Carbonell, G. Doddington, J. Yamron, and\nY. Yang. Topic detection and tracking pilot study: Final\nreport. In Proceedings of the DARPA Broadcast News\nTranscription and Understanding Workshop, Washington,\nD.C., 1998.\n[2] C. Apte, F. Damerau, and S. M. Weiss. Automated learning\nof decision rules for text categorization. ACM Transactions\non Information Systems, 12(3):233-251, July 1994.\n[3] J. Carletta. Assessing agreement on classification tasks: The\nkappa statistic. Computational Linguistics, 22(2):249-254,\n1996.\n[4] J. Carroll. 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{"name": "train_H-98", "title": "Using Asymmetric Distributions to Improve Text Classifier Probability Estimates", "abstract": "Text classifiers that give probability estimates are more readily applicable in a variety of scenarios. For example, rather than choosing one set decision threshold, they can be used in a Bayesian risk model to issue a run-time decision which minimizes a userspecified cost function dynamically chosen at prediction time. However, the quality of the probability estimates is crucial. We review a variety of standard approaches to converting scores (and poor probability estimates) from text classifiers to high quality estimates and introduce new models motivated by the intuition that the empirical score distribution for the extremely irrelevant, hard to discriminate, and obviously relevant items are often significantly different. Finally, we analyze the experimental performance of these models over the outputs of two text classifiers. The analysis demonstrates that one of these models is theoretically attractive (introducing few new parameters while increasing flexibility), computationally efficient, and empirically preferable.", "fulltext": "1. INTRODUCTION\nText classifiers that give probability estimates are more flexible\nin practice than those that give only a simple classification or even a\nranking. For example, rather than choosing one set decision\nthreshold, they can be used in a Bayesian risk model [8] to issue a\nruntime decision which minimizes the expected cost of a user-specified\ncost function dynamically chosen at prediction time. This can be\nused to minimize a linear utility cost function for filtering tasks\nwhere pre-specified costs of relevant/irrelevant are not available\nduring training but are specified at prediction time. Furthermore,\nthe costs can be changed without retraining the model.\nAdditionally, probability estimates are often used as the basis of deciding\nwhich document\"s label to request next during active learning [17,\n23]. Effective active learning can be key in many information\nretrieval tasks where obtaining labeled data can be costly - severely\nreducing the amount of labeled data needed to reach the same\nperformance as when new labels are requested randomly [17]. Finally,\nthey are also amenable to making other types of cost-sensitive\ndecisions [26] and for combining decisions [3]. However, in all of\nthese tasks, the quality of the probability estimates is crucial.\nParametric models generally use assumptions that the data\nconform to the model to trade-off flexibility with the ability to estimate\nthe model parameters accurately with little training data. Since\nmany text classification tasks often have very little training data, we\nfocus on parametric methods. However, most of the existing\nparametric methods that have been applied to this task have an\nassumption we find undesirable. While some of these methods allow the\ndistributions of the documents relevant and irrelevant to the topic\nto have different variances, they typically enforce the unnecessary\nconstraint that the documents are symmetrically distributed around\ntheir respective modes. We introduce several asymmetric\nparametric models that allow us to relax this assumption without\nsignificantly increasing the number of parameters and demonstrate how\nwe can efficiently fit the models. Additionally, these models can be\ninterpreted as assuming the scores produced by the text classifier\nhave three basic types of empirical behavior - one corresponding\nto each of the extremely irrelevant, hard to discriminate, and\nobviously relevant items.\nWe first review related work on improving probability estimates\nand score modeling in information retrieval. Then, we discuss in\nfurther detail the need for asymmetric models. After this, we\ndescribe two specific asymmetric models and, using two standard text\nclassifiers, na\u00a8\u0131ve Bayes and SVMs, demonstrate how they can be\nefficiently used to recalibrate poor probability estimates or produce\nhigh quality probability estimates from raw scores. We then review\nexperiments using previously proposed methods and the\nasymmetric methods over several text classification corpora to demonstrate\nthe strengths and weaknesses of the various methods. Finally, we\nsummarize our contributions and discuss future directions.\n2. RELATED WORK\nParametric models have been employed to obtain probability\nestimates in several areas of information retrieval. Lewis & Gale [17]\nuse logistic regression to recalibrate na\u00a8\u0131ve Bayes though the quality\nof the probability estimates are not directly evaluated; it is simply\nperformed as an intermediate step in active learning. Manmatha\net. al [20] introduced models appropriate to produce probability\nestimates from relevance scores returned from search engines and\ndemonstrated how the resulting probability estimates could be\nsubsequently employed to combine the outputs of several search\nengines. They use a different parametric distribution for the relevant\nand irrelevant classes, but do not pursue two-sided asymmetric\ndistributions for a single class as described here. They also survey the\nlong history of modeling the relevance scores of search engines.\nOur work is similar in flavor to these previous attempts to model\nsearch engine scores, but we target text classifier outputs which we\nhave found demonstrate a different type of score distribution\nbehavior because of the role of training data.\nFocus on improving probability estimates has been growing lately.\nZadrozny & Elkan [26] provide a corrective measure for decision\ntrees (termed curtailment) and a non-parametric method for\nrecalibrating na\u00a8\u0131ve Bayes. In more recent work [27], they investigate\nusing a semi-parametric method that uses a monotonic\npiecewiseconstant fit to the data and apply the method to na\u00a8\u0131ve Bayes and a\nlinear SVM. While they compared their methods to other\nparametric methods based on symmetry, they fail to provide significance\ntest results. Our work provides asymmetric parametric methods\nwhich complement the non-parametric and semi-parametric\nmethods they propose when data scarcity is an issue. In addition, their\nmethods reduce the resolution of the scores output by the classifier\n(the number of distinct values output), but the methods here do not\nhave such a weakness since they are continuous functions.\nThere is a variety of other work that this paper extends. Platt\n[22] uses a logistic regression framework that models noisy class\nlabels to produce probabilities from the raw output of an SVM.\nHis work showed that this post-processing method not only can\nproduce probability estimates of similar quality to SVMs directly\ntrained to produce probabilities (regularized likelihood kernel\nmethods), but it also tends to produce sparser kernels (which generalize\nbetter). Finally, Bennett [1] obtained moderate gains by applying\nPlatt\"s method to the recalibration of na\u00a8\u0131ve Bayes but found there\nwere more problematic areas than when it was applied to SVMs.\nRecalibrating poorly calibrated classifiers is not a new problem.\nLindley et. al [19] first proposed the idea of recalibrating classifiers,\nand DeGroot & Fienberg [5, 6] gave the now accepted standard\nformalization for the problem of assessing calibration initiated by\nothers [4, 24].\n3. PROBLEM DEFINITION & APPROACH\nOur work differs from earlier approaches primarily in three points:\n(1) We provide asymmetric parametric models suitable for use when\nlittle training data is available; (2) We explicitly analyze the quality\nof probability estimates these and competing methods produce and\nprovide significance tests for these results; (3) We target text\nclassifier outputs where a majority of the previous literature targeted the\noutput of search engines.\n3.1 Problem Definition\nThe general problem we are concerned with is highlighted in\nFigure 1. A text classifier produces a prediction about a document\nand gives a score s(d) indicating the strength of its decision that\nthe document belongs to the positive class (relevant to the topic).\nWe assume throughout there are only two classes: the positive and\nthe negative (or irrelevant) class (\"+\" and \"-\" respectively).\nThere are two general types of parametric approaches. The first\nof these tries to fit the posterior function directly, i.e. there is one\np(s|+) p(s|\u2212)\nBayes\" RuleP(+) P(\u2212)\nClassifier\nP(+| s(d))\nPredict class, c(d)={+,\u2212}\nconfidence s(d) that c(d)=+\nDocument, d\nand give unnormalized\nFigure 1: We are concerned with how to perform the box\nhighlighted in grey. The internals are for one type of approach.\nfunction estimator that performs a direct mapping of the score s to\nthe probability P(+|s(d)). The second type of approach breaks the\nproblem down as shown in the grey box of Figure 1. An estimator\nfor each of the class-conditional densities (i.e. p(s|+) and p(s|\u2212))\nis produced, then Bayes\" rule and the class priors are used to obtain\nthe estimate for P(+|s(d)).\n3.2 Motivation for Asymmetric Distributions\nMost of the previous parametric approaches to this problem\neither directly or indirectly (when fitting only the posterior)\ncorrespond to fitting Gaussians to the class-conditional densities; they\ndiffer only in the criterion used to estimate the parameters. We can\nvisualize this as depicted in Figure 2. Since increasing s usually\nindicates increased likelihood of belonging to the positive class, then\nthe rightmost distribution usually corresponds to p(s|+).\nA B\nC\n0\n0.2\n0.4\n0.6\n0.8\n1\n\u221210 \u22125 0 5 10\np(s|Class={+,\u2212})\nUnnormalized Confidence Score s\np(s | Class = +)\np(s | Class = \u2212)\nFigure 2: Typical View of Discrimination based on Gaussians\nHowever, using standard Gaussians fails to capitalize on a basic\ncharacteristic commonly seen. Namely, if we have a raw output\nscore that can be used for discrimination, then the empirical\nbehavior between the modes (label B in Figure 2) is often very different\nthan that outside of the modes (labels A and C in Figure 2).\nIntuitively, the area between the modes corresponds to the hard\nexamples, which are difficult for this classifier to distinguish, while the\nareas outside the modes are the extreme examples that are usually\neasily distinguished. This suggests that we may want to uncouple\nthe scale of the outside and inside segments of the distribution (as\ndepicted by the curve denoted as A-Gaussian in Figure 3). As a\nresult, an asymmetric distribution may be a more appropriate choice\nfor application to the raw output score of a classifier.\nIdeally (i.e. perfect classification) there will exist scores \u03b8\u2212 and\n\u03b8+ such that all examples with score greater than \u03b8+ are relevant\nand all examples with scores less than \u03b8\u2212 are irrelevant.\nFurthermore, no examples fall between \u03b8\u2212 and \u03b8+. The distance\n| \u03b8\u2212 \u2212 \u03b8+ | corresponds to the margin in some classifiers, and\nan attempt is often made to maximize this quantity. Because text\nclassifiers have training data to use to separate the classes, the\nfinal behavior of the score distributions is primarily a factor of the\namount of training data and the consequent separation in the classes\nachieved. This is in contrast to search engine retrieval where the\ndistribution of scores is more a factor of language distribution across\ndocuments, the similarity function, and the length and type of query.\nPerfect classification corresponds to using two very asymmetric\ndistributions, but in this case, the probabilities are actually one and\nzero and many methods will work for typical purposes. Practically,\nsome examples will fall between \u03b8\u2212 and \u03b8+, and it is often\nimportant to estimate the probabilities of these examples well (since they\ncorrespond to the hard examples). Justifications can be given for\nboth why you may find more and less examples between \u03b8\u2212 and \u03b8+\nthan outside of them, but there are few empirical reasons to believe\nthat the distributions should be symmetric.\nA natural first candidate for an asymmetric distribution is to\ngeneralize a common symmetric distribution, e.g. the Laplace or the\nGaussian. An asymmetric Laplace distribution can be achieved by\nplacing two exponentials around the mode in the following manner:\np(x | \u03b8, \u03b2, \u03b3) =\n\uf8f1\n\uf8f4\uf8f2\n\uf8f4\uf8f3\n\u03b2\u03b3\n\u03b2+\u03b3\nexp [\u2212\u03b2 (\u03b8 \u2212 x)] x \u2264 \u03b8\n(\u03b2, \u03b3 > 0)\n\u03b2\u03b3\n\u03b2+\u03b3\nexp [\u2212\u03b3 (x \u2212 \u03b8)] x > \u03b8\n(1)\nwhere \u03b8, \u03b2, and \u03b3 are the model parameters. \u03b8 is the mode of the\ndistribution, \u03b2 is the inverse scale of the exponential to the left of\nthe mode, and \u03b3 is the inverse scale of the exponential to the right.\nWe will use the notation \u039b(X | \u03b8, \u03b2, \u03b3) to refer to this distribution.\n0\n0.002\n0.004\n0.006\n0.008\n0.01\n-300 -200 -100 0 100 200\np(s|Class={+,-})\nUnnormalized Confidence Score s\nGaussian\nA-Gaussian\nFigure 3: Gaussians vs. Asymmetric Gaussians. A\nShortcoming of Symmetric Distributions - The vertical lines show the\nmodes as estimated nonparametrically.\nWe can create an asymmetric Gaussian in the same manner:\np(x | \u03b8, \u03c3l, \u03c3r) =\n\uf8f1\n\uf8f4\uf8f4\uf8f2\n\uf8f4\uf8f4\uf8f3\n2\u221a\n2\u03c0(\u03c3l+\u03c3r)\nexp \u2212(x\u2212\u03b8)2\n2\u03c32\nl\nx \u2264 \u03b8\n(\u03c3l, \u03c3r > 0)\n2\u221a\n2\u03c0(\u03c3l+\u03c3r)\nexp \u2212(x\u2212\u03b8)2\n2\u03c32\nr\nx > \u03b8\n(2)\nwhere \u03b8, \u03c3l, and \u03c3r are the model parameters. To refer to this\nasymmetric Gaussian, we use the notation \u0393(X | \u03b8, \u03c3l, \u03c3r). While\nthese distributions are composed of halves, the resulting function\nis a single continuous distribution.\nThese distributions allow us to fit our data with much greater\nflexibility at the cost of only fitting six parameters. We could\ninstead try mixture models for each component or other extensions,\nbut most other extensions require at least as many parameters (and\ncan often be more computationally expensive). In addition, the\nmotivation above should provide significant cause to believe the\nunderlying distributions actually behave in this way. Furthermore,\nthis family of distributions can still fit a symmetric distribution,\nand finally, in the empirical evaluation, evidence is presented that\ndemonstrates this asymmetric behavior (see Figure 4).\nTo our knowledge, neither family of distributions has been\npreviously used in machine learning or information retrieval. Both are\ntermed generalizations of an Asymmetric Laplace in [14], but we\nrefer to them as described above to reflect the nature of how we\nderived them for this task.\n3.3 Estimating the Parameters of the\nAsymmetric Distributions\nThis section develops the method for finding maximum\nlikelihood estimates (MLE) of the parameters for the above asymmetric\ndistributions. In order to find the MLEs, we have two choices: (1)\nuse numerical estimation to estimate all three parameters at once\n(2) fix the value of \u03b8, and estimate the other two (\u03b2 and \u03b3 or \u03c3l\nand \u03c3r) given our choice of \u03b8, then consider alternate values of \u03b8.\nBecause of the simplicity of analysis in the latter alternative, we\nchoose this method.\n3.3.1 Asymmetric Laplace MLEs\nFor D = {x1, x2, . . . , xN } where the xi are i.i.d. and X \u223c\n\u039b(X | \u03b8, \u03b2, \u03b3), the likelihood is N\ni \u039b(X | \u03b8, \u03b2, \u03b3). Now, we fix\n\u03b8 and compute the maximum likelihood for that choice of \u03b8. Then,\nwe can simply consider all choices of \u03b8 and choose the one with\nthe maximum likelihood over all choices of \u03b8.\nThe complete derivation is omitted because of space but is\navailable in [2]. We define the following values:\nNl = | {x \u2208 D | x \u2264 \u03b8} | Nr = | {x \u2208 D | x > \u03b8} |\nSl =\nx\u2208D|x\u2264\u03b8\nx Sr =\nx\u2208D|x>\u03b8\nx\nDl = Nl\u03b8 \u2212 Sl Dr = Sr \u2212 Nr\u03b8.\nNote that Dl and Dr are the sum of the absolute differences\nbetween the x belonging to the left and right halves of the distribution\n(respectively) and \u03b8. Finally the MLEs for \u03b2 and \u03b3 for a fixed \u03b8 are:\n\u03b2MLE =\nN\nDl +\n\u221a\nDrDl\n\u03b3MLE =\nN\nDr +\n\u221a\nDrDl\n. (3)\nThese estimates are not wholly unexpected since we would obtain\nNl\nDl\nif we were to estimate \u03b2 independently of \u03b3. The elegance of\nthe formulae is that the estimates will tend to be symmetric only\ninsofar as the data dictate it (i.e. the closer Dl and Dr are to being\nequal, the closer the resulting inverse scales).\nBy continuity arguments, when N = 0, we assign \u03b2 = \u03b3 = 0\nwhere 0 is a small constant that acts to disperse the distribution to\na uniform. Similarly, when N = 0 and Dl = 0, we assign \u03b2 = inf\nwhere inf is a very large constant that corresponds to an extremely\nsharp distribution (i.e. almost all mass at \u03b8 for that half). Dr = 0\nis handled similarly.\nAssuming that \u03b8 falls in some range [\u03c6, \u03c8] dependent upon only\nthe observed documents, then this alternative is also easily\ncomputable. Given Nl, Sl, Nr, Sr, we can compute the posterior and\nthe MLEs in constant time. In addition, if the scores are sorted,\nthen we can perform the whole process quite efficiently. Starting\nwith the minimum \u03b8 = \u03c6 we would like to try, we loop through the\nscores once and set Nl, Sl, Nr, Sr appropriately. Then we increase\n\u03b8 and just step past the scores that have shifted from the right side\nof the distribution to the left. Assuming the number of candidate\n\u03b8s are O(n), this process is O(n), and the overall process is\ndominated by sorting the scores, O(n log n) (or expected linear time).\n3.3.2 Asymmetric Gaussian MLEs\nFor D = {x1, x2, . . . , xN } where the xi are i.i.d. and X \u223c\n\u0393(X | \u03b8, \u03c3l, \u03c3r), the likelihood is N\ni \u0393(X | \u03b8, \u03b2, \u03b3). The MLEs\ncan be worked out similar to the above.\nWe assume the same definitions as above (the complete\nderivation omitted for space is available in [2]), and in addition, let:\nSl2 =\nx\u2208D|x\u2264\u03b8\nx2\nSr2 =\nx\u2208D|x>\u03b8\nx2\nDl2 = Sl2 \u2212 Sl\u03b8 + \u03b82\nNl Dr2 = Sr2 \u2212 Sr\u03b8 + \u03b82\nNr.\nThe analytical solution for the MLEs for a fixed \u03b8 is:\n\u03c3l,MLE =\nDl2 + D\n2/3\nl2 D\n1/3\nr2\nN\n(4)\n\u03c3r,MLE =\nDr2 + D\n2/3\nr2 D\n1/3\nl2\nN\n. (5)\nBy continuity arguments, when N = 0, we assign \u03c3r = \u03c3l =\ninf , and when N = 0 and Dl2 = 0 (resp. Dr2 = 0), we\nassign \u03c3l = 0 (resp. \u03c3r = 0). Again, the same computational\ncomplexity analysis applies to estimating these parameters.\n4. EXPERIMENTAL ANALYSIS\n4.1 Methods\nFor each of the methods that use a class prior, we use a smoothed\nadd-one estimate, i.e. P(c) = |c|+1\nN+2\nwhere N is the number of\ndocuments. For methods that fit the class-conditional densities, p(s|+)\nand p(s|\u2212), the resulting densities are inverted using Bayes\" rule as\ndescribed above. All of the methods below are fit using maximum\nlikelihood estimates.\nFor recalibrating a classifier (i.e. correcting poor probability\nestimates output by the classifier), it is usual to use the log-odds of\nthe classifier\"s estimate as s(d). The log-odds are defined to be\nlog P (+|d)\nP (\u2212|d)\n. The normal decision threshold (minimizing error) in\nterms of log-odds is at zero (i.e. P(+|d) = P(\u2212|d) = 0.5).\nSince it scales the outputs to a space [\u2212\u221e, \u221e], the log-odds\nmake normal (and similar distributions) applicable [19]. Lewis &\nGale [17] give a more motivating viewpoint that fitting the log-odds\nis a dampening effect for the inaccurate independence assumption\nand a bias correction for inaccurate estimates of the priors. In\ngeneral, fitting the log-odds can serve to boost or dampen the signal\nfrom the original classifier as the data dictate.\nGaussians\nA Gaussian is fit to each of the class-conditional densities, using\nthe usual maximum likelihood estimates. This method is denoted\nin the tables below as Gauss.\nAsymmetric Gaussians\nAn asymmetric Gaussian is fit to each of the class-conditional\ndensities using the maximum likelihood estimation procedure\ndescribed above. Intervals between adjacent scores are divided by 10\nin testing candidate \u03b8s, i.e. 8 points between actual scores\noccurring in the data set are tested. This method is denoted as A. Gauss.\nLaplace Distributions\nEven though Laplace distributions are not typically applied to\nthis task, we also tried this method to isolate why benefit is gained\nfrom the asymmetric form. The usual MLEs were used for\nestimating the location and scale of a classical symmetric Laplace\ndistribution as described in [14]. We denote this method as Laplace below.\nAsymmetric Laplace Distributions\nAn asymmetric Laplace is fit to each of the class-conditional\ndensities using the maximum likelihood estimation procedure\ndescribed above. As with the asymmetric Gaussian, intervals between\nadjacent scores are divided by 10 in testing candidate \u03b8s. This\nmethod is denoted as A. Laplace below.\nLogistic Regression\nThis method is the first of two methods we evaluated that\ndirectly fit the posterior, P(+|s(d)). Both methods restrict the set\nof families to a two-parameter sigmoid family; they differ\nprimarily in their model of class labels. As opposed to the above\nmethods, one can argue that an additional boon of these methods is they\ncompletely preserve the ranking given by the classifier. When this\nis desired, these methods may be more appropriate. The previous\nmethods will mostly preserve the rankings, but they can deviate if\nthe data dictate it. Thus, they may model the data behavior better at\nthe cost of departing from a monotonicity constraint in the output\nof the classifier.\nLewis & Gale [17] use logistic regression to recalibrate na\u00a8\u0131ve\nBayes for subsequent use in active learning. The model they use is:\nP(+|s(d)) =\nexp(a + b s(d))\n1 + exp(a + b s(d))\n. (6)\nInstead of using the probabilities directly output by the classifier,\nthey use the loglikelihood ratio of the probabilities, log P (d|+)\nP (d|\u2212)\n, as\nthe score s(d). Instead of using this below, we will use the\nlogodds ratio. This does not affect the model as it simply shifts all of\nthe scores by a constant determined by the priors. We refer to this\nmethod as LogReg below.\nLogistic Regression with Noisy Class Labels\nPlatt [22] proposes a framework that extends the logistic\nregression model above to incorporate noisy class labels and uses it to\nproduce probability estimates from the raw output of an SVM.\nThis model differs from the LogReg model only in how the\nparameters are estimated. The parameters are still fit using maximum\nlikelihood estimation, but a model of noisy class labels is used in\naddition to allow for the possibility that the class was mislabeled.\nThe noise is modeled by assuming there is a finite probability of\nmislabeling a positive example and of mislabeling a negative\nexample; these two noise estimates are determined by the number\nof positive examples and the number of negative examples (using\nBayes\" rule to infer the probability of incorrect label).\nEven though the performance of this model would not be\nexpected to deviate much from LogReg, we evaluate it for\ncompleteness. We refer to this method below as LR+Noise.\n4.2 Data\nWe examined several corpora, including the MSN Web Directory,\nReuters, and TREC-AP.\nMSN Web Directory\nThe MSN Web Directory is a large collection of heterogeneous\nweb pages (from a May 1999 web snapshot) that have been\nhierarchically classified. We used the same train/test split of 50078/10024\ndocuments as that reported in [9]. The MSN Web hierarchy is a\nseven-level hierarchy; we used all 13 of the top-level categories.\nThe class proportions in the training set vary from 1.15% to 22.29%.\nIn the testing set, they range from 1.14% to 21.54%. The classes\nare general subjects such as Health & Fitness and Travel & Vacation.\nHuman indexers assigned the documents to zero or more categories.\nFor the experiments below, we used only the top 1000 words with\nhighest mutual information for each class; approximately 195K\nwords appear in at least three training documents.\nReuters\nThe Reuters 21578 corpus [16] contains Reuters news articles\nfrom 1987. For this data set, we used the ModApte standard train/\ntest split of 9603/3299 documents (8676 unused documents). The\nclasses are economic subjects (e.g., acq for acquisitions, earn\nfor earnings, etc.) that human taggers applied to the document;\na document may have multiple subjects. There are actually 135\nclasses in this domain (only 90 of which occur in the training and\ntesting set); however, we only examined the ten most frequent classes\nsince small numbers of testing examples make interpreting some\nperformance measures difficult due to high variance.1\nLimiting to\nthe ten largest classes allows us to compare our results to\npreviously published results [10, 13, 21, 22]. The class proportions in\nthe training set vary from 1.88% to 29.96%. In the testing set, they\nrange from 1.7% to 32.95%.\nFor the experiments below we used only the top 300 words with\nhighest mutual information for each class; approximately 15K words\nappear in at least three training documents.\nTREC-AP\nThe TREC-AP corpus is a collection of AP news stories from\n1988 to 1990. We used the same train/test split of 142791/66992\ndocuments that was used in [18]. As described in [17] (see also\n[15]), the categories are defined by keywords in a keyword field.\nThe title and body fields are used in the experiments below. There\nare twenty categories in total. The class proportions in the training\nset vary from 0.06% to 2.03%. In the testing set, they range from\n0.03% to 4.32%.\nFor the experiments described below, we use only the top 1000\nwords with the highest mutual information for each class;\napproximately 123K words appear in at least 3 training documents.\n4.3 Classifiers\nWe selected two classifiers for evaluation. A linear SVM\nclassifier which is a discriminative classifier that does not normally\noutput probability values, and a na\u00a8\u0131ve Bayes classifier whose\nprobability outputs are often poor [1, 7] but can be improved [1, 26, 27].\n1\nA separate comparison of only LogReg, LR+Noise, and\nA. Laplace over all 90 categories of Reuters was also conducted.\nAfter accounting for the variance, that evaluation also supported\nthe claims made here.\nSVM\nFor linear SVMs, we use the Smox toolkit which is based on\nPlatt\"s Sequential Minimal Optimization algorithm. The features\nwere represented as continuous values. We used the raw output\nscore of the SVM as s(d) since it has been shown to be appropriate\nbefore [22]. The normal decision threshold (assuming we are\nseeking to minimize errors) for this classifier is at zero.\nNa\u00a8\u0131ve Bayes\nThe na\u00a8\u0131ve Bayes classifier model is a multinomial model [21].\nWe smoothed word and class probabilities using a Bayesian\nestimate (with the word prior) and a Laplace m-estimate, respectively.\nWe use the log-odds estimated by the classifier as s(d). The normal\ndecision threshold is at zero.\n4.4 Performance Measures\nWe use log-loss [12] and squared error [4, 6] to evaluate the\nquality of the probability estimates. For a document d with class c(d) \u2208\n{+, \u2212} (i.e. the data have known labels and not probabilities),\nlogloss is defined as \u03b4(c(d), +) log P(+|d) + \u03b4(c(d), \u2212) log P(\u2212|d)\nwhere \u03b4(a, b)\n.\n= 1 if a = b and 0 otherwise. The squared error is\n\u03b4(c(d), +)(1 \u2212 P(+|d))2\n+ \u03b4(c(d), \u2212)(1 \u2212 P(\u2212|d))2\n. When the\nclass of a document is correctly predicted with a probability of one,\nlog-loss is zero and squared error is zero. When the class of a\ndocument is incorrectly predicted with a probability of one, log-loss\nis \u2212\u221e and squared error is one. Thus, both measures assess how\nclose an estimate comes to correctly predicting the item\"s class but\nvary in how harshly incorrect predictions are penalized.\nWe report only the sum of these measures and omit the averages\nfor space. Their averages, average log-loss and mean squared\nerror (MSE), can be computed from these totals by dividing by the\nnumber of binary decisions in a corpus.\nIn addition, we also compare the error of the classifiers at their\ndefault thresholds and with the probabilities. This evaluates how\nthe probability estimates have improved with respect to the\ndecision threshold P(+|d) = 0.5. Thus, error only indicates how the\nmethods would perform if a false positive was penalized the same\nas a false negative and not the general quality of the probability\nestimates. It is presented simply to provide the reader with a more\ncomplete understanding of the empirical tendencies of the methods.\nWe use a a standard paired micro sign test [25] to determine\nstatistical significance in the difference of all measures. Only pairs\nthat the methods disagree on are used in the sign test. This test\ncompares pairs of scores from two systems with the null\nhypothesis that the number of items they disagree on are binomially\ndistributed. We use a significance level of p = 0.01.\n4.5 Experimental Methodology\nAs the categories under consideration in the experiments are not\nmutually exclusive, the classification was done by training n binary\nclassifiers, where n is the number of classes.\nIn order to generate the scores that each method uses to fit its\nprobability estimates, we use five-fold cross-validation on the\ntraining data. We note that even though it is computationally efficient\nto perform leave-one-out cross-validation for the na\u00a8\u0131ve Bayes\nclassifier, this may not be desirable since the distribution of scores can\nbe skewed as a result. Of course, as with any application of n-fold\ncross-validation, it is also possible to bias the results by holding n\ntoo low and underestimating the performance of the final classifier.\n4.6 Results & Discussion\nThe results for recalibrating na\u00a8\u0131ve Bayes are given in Table 1a.\nTable 1b gives results for producing probabilistic outputs for SVMs.\nLog-loss Error2\nErrors\nMSN Web\nGauss -60656.41 10503.30 10754\nA.Gauss -57262.26 8727.47 9675\nLaplace -45363.84 8617.59 10927\nA.Laplace -36765.88 6407.84\u2020\n8350\nLogReg -36470.99 6525.47 8540\nLR+Noise -36468.18 6534.61 8563\nna\u00a8\u0131ve Bayes -1098900.83 17117.50 17834\nReuters\nGauss -5523.14 1124.17 1654\nA.Gauss -4929.12 652.67 888\nLaplace -5677.68 1157.33 1416\nA.Laplace -3106.95\u2021\n554.37\u2021\n726\nLogReg -3375.63 603.20 786\nLR+Noise -3374.15 604.80 785\nna\u00a8\u0131ve Bayes -52184.52 1969.41 2121\nTREC-AP\nGauss -57872.57 8431.89 9705\nA.Gauss -66009.43 7826.99 8865\nLaplace -61548.42 9571.29 11442\nA.Laplace -48711.55 7251.87\u2021\n8642\nLogReg -48250.81 7540.60 8797\nLR+Noise -48251.51 7544.84 8801\nna\u00a8\u0131ve Bayes -1903487.10 41770.21 43661\nLog-loss Error2\nErrors\nMSN Web\nGauss -54463.32 9090.57 10555\nA. Gauss -44363.70 6907.79 8375\nLaplace -42429.25 7669.75 10201\nA. Laplace -31133.83 5003.32 6170\nLogReg -30209.36 5158.74 6480\nLR+Noise -30294.01 5209.80 6551\nLinear SVM N/A N/A 6602\nReuters\nGauss -3955.33 589.25 735\nA. Gauss -4580.46 428.21 532\nLaplace -3569.36 640.19 770\nA. Laplace -2599.28 412.75 505\nLogReg -2575.85 407.48 509\nLR+Noise -2567.68 408.82 516\nLinear SVM N/A N/A 516\nTREC-AP\nGauss -54620.94 6525.71 7321\nA. Gauss -77729.49 6062.64 6639\nLaplace -54543.19 7508.37 9033\nA. Laplace -48414.39 5761.25\u2021\n6572\u2021\nLogReg -48285.56 5914.04 6791\nLR+Noise -48214.96 5919.25 6794\nLinear SVM N/A N/A 6718\nTable 1: (a) Results for na\u00a8\u0131ve Bayes (left) and (b) SVM (right). The best entry for a corpus is in bold. Entries that are statistically\nsignificantly better than all other entries are underlined. A \u2020 denotes the method is significantly better than all other methods except\nfor na\u00a8\u0131ve Bayes. A \u2021 denotes the entry is significantly better than all other methods except for A. Gauss (and na\u00a8\u0131ve Bayes for the table\non the left). The reason for this distinction in significance tests is described in the text.\nWe start with general observations that result from examining\nthe performance of these methods over the various corpora. The\nfirst is that A. Laplace, LR+Noise, and LogReg, quite clearly\noutperform the other methods. There is usually little difference\nbetween the performance of LR+Noise and LogReg (both as shown\nhere and on a decision by decision basis), but this is unsurprising\nsince LR+Noise just adds noisy class labels to the LogReg model.\nWith respect to the three different measures, LR+Noise and\nLogReg tend to perform slightly better (but never significantly) than\nA. Laplace at some tasks with respect to log-loss and squared error.\nHowever, A. Laplace always produces the least number of errors\nfor all of the tasks, though at times the degree of improvement is\nnot significant.\nIn order to give the reader a better sense of the behavior of these\nmethods, Figures 4-5 show the fits produced by the most\ncompetitive of these methods versus the actual data behavior (as estimated\nnonparametrically by binning) for class Earn in Reuters. Figure 4\nshows the class-conditional densities, and thus only A. Laplace is\nshown since LogReg fits the posterior directly. Figure 5 shows the\nestimations of the log-odds, (i.e. log P (Earn|s(d))\nP (\u00acEarn|s(d))\n). Viewing the\nlog-odds (rather than the posterior) usually enables errors in\nestimation to be detected by the eye more easily.\nWe can break things down as the sign test does and just look at\nwins and losses on the items that the methods disagree on. Looked\nat in this way only two methods (na\u00a8\u0131ve Bayes and A. Gauss) ever\nhave more pairwise wins than A. Laplace; those two sometimes\nhave more pairwise wins on log-loss and squared error even though\nthe total never wins (i.e. they are dragged down by heavy penalties).\nIn addition, this comparison of pairwise wins means that for\nthose cases where LogReg and LR+Noise have better scores than\nA. Laplace, it would not be deemed significant by the sign test at\nany level since they do not have more wins. For example, of the\n130K binary decisions over the MSN Web dataset, A. Laplace had\napproximately 101K pairwise wins versus LogReg and LR+Noise.\nNo method ever has more pairwise wins than A. Laplace for the\nerror comparison nor does any method every achieve a better total.\nThe basic observation made about na\u00a8\u0131ve Bayes in previous work\nis that it tends to produce estimates very close to zero and one [1,\n17]. This means if it tends to be right enough of the time, it will\nproduce results that do not appear significant in a sign test that\nignores size of difference (as the one here). The totals of the squared\nerror and log-loss bear out the previous observation that when it\"s\nwrong it\"s really wrong.\nThere are several interesting points about the performance of the\nasymmetric distributions as well. First, A. Gauss performs poorly\nbecause (similar to na\u00a8\u0131ve Bayes) there are some examples where\nit is penalized a large amount. This behavior results from a\ngeneral tendency to perform like the picture shown in Figure 3 (note\nthe crossover at the tails). While the asymmetric Gaussian tends\nto place the mode much more accurately than a symmetric\nGaussian, its asymmetric flexibility combined with its distance function\ncauses it to distribute too much mass to the outside tails while\nfailing to fit around the mode accurately enough to compensate. Figure\n3 is actually a result of fitting the two distributions to real data. As\na result, at the tails there can be a large discrepancy between the\nlikelihood of belonging to each class. Thus when there are no\noutliers A. Gauss can perform quite competitively, but when there is an\n0\n0.002\n0.004\n0.006\n0.008\n0.01\n0.012\n-600 -400 -200 0 200 400\np(s(d)|Class={+,-})\ns(d) = naive Bayes log-odds\nTrain\nTest\nA.Laplace\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\n0.45\n-15 -10 -5 0 5 10 15\np(s(d)|Class={+,-})\ns(d) = linear SVM raw score\nTrain\nTest\nA.Laplace\nFigure 4: The empirical distribution of classifier scores for documents in the training and the test set for class Earn in Reuters.\nAlso shown is the fit of the asymmetric Laplace distribution to the training score distribution. The positive class (i.e. Earn) is the\ndistribution on the right in each graph, and the negative class (i.e. \u00acEarn) is that on the left in each graph.\n-6\n-4\n-2\n0\n2\n4\n6\n8\n-250 -200 -150 -100 -50 0 50 100 150\nLogOdds=logP(+|s(d))-logP(-|s(d))\ns(d) = naive Bayes log-odds\nTrain\nTest\nA.Laplace\nLogReg\n-5\n0\n5\n10\n15\n-4 -2 0 2 4 6\nLogOdds=logP(+|s(d))-logP(-|s(d))\ns(d) = linear SVM raw score\nTrain\nTest\nA.Laplace\nLogReg\nFigure 5: The fit produced by various methods compared to the empirical log-odds of the training data for class Earn in Reuters.\noutlier A. Gauss is penalized quite heavily. There are enough such\ncases overall that it seems clearly inferior to the top three methods.\nHowever, the asymmetric Laplace places much more emphasis\naround the mode (Figure 4) because of the different distance\nfunction (think of the sharp peak of an exponential). As a result most\nof the mass stays centered around the mode, while the asymmetric\nparameters still allow more flexibility than the standard Laplace.\nSince the standard Laplace also corresponds to a piecewise fit in the\nlog-odds space, this highlights that part of the power of the\nasymmetric methods is their sensitivity in placing the knots at the actual\nmodes - rather than the symmetric assumption that the means\ncorrespond to the modes. Additionally, the asymmetric methods have\ngreater flexibility in fitting the slopes of the line segments as well.\nEven in cases where the test distribution differs from the training\ndistribution (Figure 4), A. Laplace still yields a solution that gives\na better fit than LogReg (Figure 5), the next best competitor.\nFinally, we can make a few observations about the usefulness\nof the various performance metrics. First, log-loss only awards a\nfinite amount of credit as the degree to which something is\ncorrect improves (i.e. there are diminishing returns as it approaches\nzero), but it can infinitely penalize for a wrong estimate. Thus, it\nis possible for one outlier to skew the totals, but misclassifying this\nexample may not matter for any but a handful of actual utility\nfunctions used in practice. Secondly, squared error has a weakness in\nthe other direction. That is, its penalty and reward are bounded in\n[0, 1], but if the number of errors is small enough, it is possible for\na method to appear better when it is producing what we generally\nconsider unhelpful probability estimates. For example, consider a\nmethod that only estimates probabilities as zero or one (which na\u00a8\u0131ve\nBayes tends to but doesn\"t quite reach if you use smoothing). This\nmethod could win according to squared error, but with just one\nerror it would never perform better on log-loss than any method that\nassigns some non-zero probability to each outcome. For these\nreasons, we recommend that neither of these are used in isolation as\nthey each give slightly different insights to the quality of the\nestimates produced. These observations are straightforward from the\ndefinitions but are underscored by the evaluation.\n5. FUTURE WORK\nA promising extension to the work presented here is a hybrid\ndistribution of a Gaussian (on the outside slopes) and exponentials\n(on the inner slopes). From the empirical evidence presented in\n[22], the expectation is that such a distribution might allow more\nemphasis of the probability mass around the modes (as with the\nexponential) while still providing more accurate estimates toward\nthe tails.\nJust as logistic regression allows the log-odds of the posterior\ndistribution to be fit directly with a line, we could directly fit the\nlog-odds of the posterior with a three-piece line (a spline) instead of\nindirectly doing the same thing by fitting the asymmetric Laplace.\nThis approach may provide more power since it retains the\nasymmetry assumption but not the assumption that the class-conditional\ndensities are from an asymmetric Laplace.\nFinally, extending these methods to the outputs of other\ndiscriminative classifiers is an open area. We are currently evaluating the\nappropriateness of these methods for the output of a voted\nperceptron [11]. By analogy to the log-odds, the operative score that\nappears promising is log\nweight perceptrons voting +\nweight perceptrons voting \u2212\n.\n6. SUMMARY AND CONCLUSIONS\nWe have reviewed a wide variety of parametric methods for\nproducing probability estimates from the raw scores of a discriminative\nclassifier and for recalibrating an uncalibrated probabilistic\nclassifier. In addition, we have introduced two new families that attempt\nto capitalize on the asymmetric behavior that tends to arise from\nlearning a discrimination function. We have given an efficient way\nto estimate the parameters of these distributions.\nWhile these distributions attempt to strike a balance between the\ngeneralization power of parametric distributions and the flexibility\nthat the added asymmetric parameters give, the asymmetric\nGaussian appears to have too great of an emphasis away from the modes.\nIn striking contrast, the asymmetric Laplace distribution appears to\nbe preferable over several large text domains and a variety of\nperformance measures to the primary competing parametric methods,\nthough comparable performance is sometimes achieved with one\nof two varieties of logistic regression. Given the ease of\nestimating the parameters of this distribution, it is a good first choice for\nproducing quality probability estimates.\nAcknowledgments\nWe are grateful to Francisco Pereira for the sign test code, Anton\nLikhodedov for logistic regression code, and John Platt for the code\nsupport for the linear SVM classifier toolkit Smox. Also, we\nsincerely thank Chris Meek and John Platt for the very useful advice\nprovided in the early stages of this work. Thanks also to Jaime\nCarbonell and John Lafferty for their useful feedback on the final\nversions of this paper.\n7. REFERENCES\n[1] P. N. Bennett. Assessing the calibration of naive bayes\"\nposterior estimates. Technical Report CMU-CS-00-155,\nCarnegie Mellon, School of Computer Science, 2000.\n[2] P. N. Bennett. Using asymmetric distributions to improve\nclassifier probabilities: A comparison of new and standard\nparametric methods. Technical Report CMU-CS-02-126,\nCarnegie Mellon, School of Computer Science, 2002.\n[3] H. Bourlard and N. Morgan. A continuous speech\nrecognition system embedding mlp into hmm. In NIPS \"89,\n1989.\n[4] G. Brier. Verification of forecasts expressed in terms of\nprobability. Monthly Weather Review, 78:1-3, 1950.\n[5] M. H. DeGroot and S. E. Fienberg. The comparison and\nevaluation of forecasters. Statistician, 32:12-22, 1983.\n[6] M. H. DeGroot and S. E. Fienberg. Comparing probability\nforecasters: Basic binary concepts and multivariate\nextensions. In P. Goel and A. Zellner, editors, Bayesian\nInference and Decision Techniques. Elsevier Science\nPublishers B.V., 1986.\n[7] P. Domingos and M. Pazzani. Beyond independence:\nConditions for the optimality of the simple bayesian\nclassifier. In ICML \"96, 1996.\n[8] R. Duda, P. Hart, and D. Stork. Pattern Classification. John\nWiley & Sons, Inc., 2001.\n[9] S. T. Dumais and H. Chen. Hierarchical classification of web\ncontent. 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Reuters-21578, distribution 1.0.\nhttp://www.daviddlewis.com/resources/\ntestcollections/reuters21578, January 1997.\n[17] D. D. Lewis and W. A. Gale. A sequential algorithm for\ntraining text classifiers. In SIGIR \"94, 1994.\n[18] D. D. Lewis, R. E. Schapire, J. P. Callan, and R. Papka.\nTraining algorithms for linear text classifiers. In SIGIR \"96,\n1996.\n[19] D. Lindley, A. Tversky, and R. Brown. On the reconciliation\nof probability assessments. Journal of the Royal Statistical\nSociety, 1979.\n[20] R. Manmatha, T. Rath, and F. Feng. Modeling score\ndistributions for combining the outputs of search engines. In\nSIGIR \"01, 2001.\n[21] A. McCallum and K. Nigam. A comparison of event models\nfor naive bayes text classification. In AAAI \"98, Workshop on\nLearning for Text Categorization, 1998.\n[22] J. C. Platt. Probabilistic outputs for support vector machines\nand comparisons to regularized likelihood methods. In A. J.\nSmola, P. Bartlett, B. Scholkopf, and D. Schuurmans, editors,\nAdvances in Large Margin Classifiers. MIT Press, 1999.\n[23] M. Saar-Tsechansky and F. Provost. Active learning for class\nprobability estimation and ranking. In IJCAI \"01, 2001.\n[24] R. L. Winkler. Scoring rules and the evaluation of probability\nassessors. Journal of the American Statistical Association,\n1969.\n[25] Y. Yang and X. Liu. A re-examination of text categorization\nmethods. In SIGIR \"99, 1999.\n[26] B. Zadrozny and C. Elkan. Obtaining calibrated probability\nestimates from decision trees and naive bayesian classifiers.\nIn ICML \"01, 2001.\n[27] B. Zadrozny and C. Elkan. Reducing multiclass to binary by\ncoupling probability estimates. In KDD \"02, 2002.", "keywords": "classifier combination;parametric model;maximum likelihood estimate;text classification;asymmetric laplace distribution;asymmetric gaussian;cost-sensitive learn;decision threshold;logistic regression framework;posterior function;active learn;class-conditional density;symmetric distribution;text classifier;information retrieval;bayesian risk model;probability estimate;empirical score distribution;search engine retrieval"}
{"name": "train_I-37", "title": "A Framework for Agent-Based Distributed Machine Learning and Data Mining", "abstract": "This paper proposes a framework for agent-based distributed machine learning and data mining based on (i) the exchange of meta-level descriptions of individual learning processes among agents and (ii) online reasoning about learning success and learning progress by learning agents. We present an abstract architecture that enables agents to exchange models of their local learning processes and introduces a number of different methods for integrating these processes. This allows us to apply existing agent interaction mechanisms to distributed machine learning tasks, thus leveraging the powerful coordination methods available in agent-based computing, and enables agents to engage in meta-reasoning about their own learning decisions. We apply this architecture to a real-world distributed clustering application to illustrate how the conceptual framework can be used in practical systems in which different learners may be using different datasets, hypotheses and learning algorithms. We report on experimental results obtained using this system, review related work on the subject, and discuss potential future extensions to the framework.", "fulltext": "1. INTRODUCTION\nIn the areas of machine learning and data mining (cf. [14,\n17] for overviews), it has long been recognised that\nparallelisation and distribution can be used to improve learning\nperformance. Various techniques have been suggested in\nthis respect, ranging from the low-level integration of\nindependently derived learning hypotheses (e.g. combining\ndifferent classifiers to make optimal classification decisions [4,\n7], model averaging of Bayesian classifiers [8], or\nconsensusbased methods for integrating different clusterings [11]), to\nthe high-level combination of learning results obtained by\nheterogeneous learning agents using meta-learning (e.g. [3,\n10, 21]).\nAll of these approaches assume homogeneity of agent\ndesign (all agents apply the same learning algorithm) and/or\nagent objectives (all agents are trying to cooperatively solve\na single, global learning problem). Therefore, the techniques\nthey suggest are not applicable in societies of autonomous\nlearners interacting in open systems. In such systems,\nlearners (agents) may not be able to integrate their datasets or\nlearning results (because of different data formats and\nrepresentations, learning algorithms, or legal restrictions that\nprohibit such integration [11]) and cannot always be\nguaranteed to interact in a strictly cooperative fashion (discovered\nknowledge and collected data might be economic assets that\nshould only be shared when this is deemed profitable;\nmalicious agents might attempt to adversely influence others\"\nlearning results, etc.).\nExamples for applications of this kind abound. Many\ndistributed learning domains involve the use of sensitive data\nand prohibit the exchange of this data (e.g. exchange of\npatient data in distributed brain tumour diagnosis [2]) -\nhowever, they may permit the exchange of local learning\nhypotheses among different learners. In other areas, training\ndata might be commercially valuable, so that agents would\nonly make it available to others if those agents could\nprovide something in return (e.g. in remote ship surveillance\nand tracking, where the different agencies involved are\ncommercial service providers [1]). Furthermore, agents might\nhave a vested interest in negatively affecting other agents\"\nlearning performance. An example for this is that of\nfraudulent agents on eBay which may try to prevent\nreputationlearning agents from the construction of useful models for\ndetecting fraud.\nViewing learners as autonomous, self-directed agents is\nthe only appropriate view one can take in modelling these\ndistributed learning environments: the agent metaphor\nbecomes a necessity as oppossed to preferences for scalability,\ndynamic data selection, interactivity [13], which can also\nbe achieved through (non-agent) distribution and\nparallelisation in principle.\nDespite the autonomy and self-directedness of learning\nagents, many of these systems exhibit a sufficient overlap\nin terms of individual learning goals so that beneficial\ncooperation might be possible if a model for flexible\ninteraction between autonomous learners was available that allowed\nagents to\n1. exchange information about different aspects of their\nown learning mechanism at different levels of detail\nwithout being forced to reveal private information that\nshould not be disclosed,\n2. decide to what extent they want to share information\nabout their own learning processes and utilise\ninformation provided by other learners, and\n3. reason about how this information can best be used to\nimprove their own learning performance.\nOur model is based on the simple idea that autonomous\nlearners should maintain meta-descriptions of their own\nlearning processes (see also [3]) in order to be able to\nexchange information and reason about them in a rational way\n(i.e. with the overall objective of improving their own\nlearning results). Our hypothesis is a very simple one:\nIf we can devise a sufficiently general, abstract\nview of describing learning processes, we will be\nable to utilise the whole range of methods for (i)\nrational reasoning and (ii) communication and\ncoordination offered by agent technology so as to\nbuild effective autonomous learning agents.\nTo test this hypothesis, we introduce such an abstract\narchitecture (section 2) and implement a simple, concrete\ninstance of it in a real-world domain (section 3). We report\non empirical results obtained with this implemented system\nthat demonstrate the viability of our approach (section 4).\nFinally, we review related work (section 5) and conclude\nwith a summary, discussion of our approach and outlook to\nfuture work on the subject (section 6).\n2. ABSTRACT ARCHITECTURE\nOur framework is based on providing formal (meta-level)\ndescriptions of learning processes, i.e. representations of all\nrelevant components of the learning machinery used by a\nlearning agent, together with information about the state of\nthe learning process.\nTo ensure that this framework is sufficiently general, we\nconsider the following general description of a learning\nproblem:\nGiven data D \u2286 D taken from an instance space\nD, a hypothesis space H and an (unknown)\ntarget function c \u2208 H1\n, derive a function h \u2208 H that\napproximates c as well as possible according to\nsome performance measure g : H \u2192 Q where Q\nis a set of possible levels of learning performance.\n1\nBy requiring this we are ensuring that the learning problem\ncan be solved in principle using the given hypothesis space.\nThis very broad definition includes a number of components\nof a learning problem for which more concrete specifications\ncan be provided if we want to be more precise. For the cases\nof classification and clustering, for example, we can further\nspecify the above as follows: Learning data can be described\nin both cases as D = \u00d7n\ni=1[Ai] where [Ai] is the domain of\nthe ith attribute and the set of attributes is A = {1, . . . , n}.\nFor the hypothesis space we obtain\nH \u2286 {h|h : D \u2192 {0, 1}}\nin the case of classification (i.e. a subset of the set of all\npossible classifiers, the nature of which depends on the\nexpressivity of the learning algorithm used) and\nH \u2286 {h|h : D \u2192 N, h is total with range {1, . . . , k}}\nin the case of clustering (i.e. a subset of all sets of possible\ncluster assignments that map data points to a finite number\nof clusters numbered 1 to k). For classification, g might be\ndefined in terms of the numbers of false negatives and false\npositives with respect to some validation set V \u2286 D, and\nclustering might use various measures of cluster validity to\nevaluate the quality of a current hypothesis, so that Q = R\nin both cases (but other sets of learning quality levels can\nbe imagined).\nNext, we introduce a notion of learning step, which\nimposes a uniform basic structure on all learning processes that\nare supposed to exchange information using our framework.\nFor this, we assume that each learner is presented with a\nfinite set of data D = d1, . . . dk in each step (this is an\nordered set to express that the order in which the samples are\nused for training matters) and employs a training/update\nfunction f : H \u00d7 D\u2217\n\u2192 H which updates h given a series of\nsamples d1, . . . , dk. In other words, one learning step always\nconsists of applying the update function to all samples in D\nexactly once. We define a learning step as a tuple\nl = D, H, f, g, h\nwhere we require that H \u2286 H and h \u2208 H.\nThe intuition behind this definition is that each learning\nstep completely describes one learning iteration as shown\nin Figure 1: in step t, the learner updates the current\nhypothesis ht\u22121 with data Dt, and evaluates the resulting new\nhypothesis ht according to the current performance measure\ngt. Such a learning step is equivalent to the following steps\nof computation:\n1. train the algorithm on all samples in D (once), i.e.\ncalculate ft(ht\u22121, Dt) = ht,\n2. calculate the quality gt of the resulting hypothesis\ngt(ht).\nWe denote the set of all possible learning steps by L. For\nease of notation, we denote the components of any l \u2208 L by\nD(l), H(l), f(l) and g(l), respectively. The reason why such\nlearning step specifications use a subset H of H instead of\nH itself is that learners often have explicit knowledge about\nwhich hypotheses are effectively ruled out by f given h in\nthe future (if this is not the case, we can still set H = H).\nA learning process is a finite, non-empty sequence\nl = l1 \u2192 l2 \u2192 . . . \u2192 ln\nof learning steps such that\n\u22001 \u2264 i < n .h(li+1) = f(li)(h(li), D(li))\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 679\ntraining function\nht\nperformance measure solution quality\nqtgtft\ntraining set\nDt\nhypothesis\nhypothesis\nht\u22121\nFigure 1: A generic model of a learning step\ni.e. the only requirement the transition relation \u2192\u2286 L \u00d7 L\nmakes is that the new hypothesis is the result of training the\nold hypothesis on all available sample data that belongs to\nthe current step. We denote the set of all possible learning\nprocesses by L (ignoring, for ease of notation, the fact that\nthis set depends on H, D and the spaces of possible\ntraining and evaluation functions f and g). The performance\ntrace associated with a learning process l is the sequence\nq1, . . . , qn \u2208 Qn\nwhere qi = g(li)(h(li)), i.e. the sequence\nof quality values calculated by the performance measures of\nthe individual learning steps on the respective hypotheses.\nSuch specifications allow agents to provide a\nselfdescription of their learning process. However, in\ncommunication among learning agents, it is often useful to\nprovide only partial information about one\"s internal learning\nprocess rather than its full details, e.g. when advertising\nthis information in order to enter information exchange\nnegotiations with others. For this purpose, we will assume\nthat learners describe their internal state in terms of sets of\nlearning processes (in the sense of disjunctive choice) which\nwe call learning process descriptions (LPDs) rather than by\ngiving precise descriptions about a single, concrete learning\nprocess.\nThis allows us to describe properties of a learning\nprocess without specifying its details exhaustively. As an\nexample, the set {l \u2208 L|\u2200l = l[i].D(l) \u2264 100} describes all\nprocesses that have a training set of at most 100\nsamples (where all the other elements are arbitrary). Likewise,\n{l \u2208 L|\u2200l = l[i].D(l) = {d}} is equivalent to just providing\ninformation about a single sample {d} and no other details\nabout the process (this can be useful to model, for\nexample, data received from the environment). Therefore, we use\n\u2118(L), that is the set of all LPDs, as the basis for\ndesigning content languages for communication in the protocols\nwe specify below.\nIn practice, the actual content language chosen will of\ncourse be more restricted and allow only for a special type\nof subsets of L to be specified in a compact way, and its\nchoice will be crucial for the interactions that can occur\nbetween learning agents. For our examples below, we simply\nassume explicit enumeration of all possible elements of the\nrespective sets and function spaces (D, H, etc.) extended by\nthe use of wildcard symbols \u2217 (so that our second example\nabove would become ({d}, \u2217, \u2217, \u2217, \u2217)).\n2.1 Learning agents\nIn our framework, a learning agent is essentially a\nmetareasoning function that operates on information about\nlearning processes and is situated in an environment co-inhabited\nby other learning agents. This means that it is not only\ncapable of meta-level control on how to learn, but in doing\nso it can take information into account that is provided by\nother agents or the environment. Although purely\ncooperative or hybrid cases are possible, for the purposes of this\npaper we will assume that agents are purely self-interested,\nand that while there may be a potential for cooperation\nconsidering how agents can mutually improve each others\"\nlearning performance, there is no global mechanism that can\nenforce such cooperative behaviour.2\nFormally speaking, an agent\"s learning function is a\nfunction which, given a set of histories of previous learning\nprocesses (of oneself and potentially of learning processes about\nwhich other agents have provided information) and outputs\na learning step which is its next learning action. In the\nmost general sense, our learning agent\"s internal learning\nprocess update can hence be viewed as a function\n\u03bb : \u2118(L) \u2192 L \u00d7 \u2118(L)\nwhich takes a set of learning histories of oneself and others\nas inputs and computes a new learning step to be executed\nwhile updating the set of known learning process histories\n(e.g. by appending the new learning action to one\"s own\nlearning process and leaving all information about others\"\nlearning processes untouched). Note that in \u03bb({l1, . . . ln}) =\n(l, {l1, . . . ln }) some elements li of the input learning process\nset may be descriptions of new learning data received from\nthe environment.\nThe \u03bb-function can essentially be freely chosen by the\nagent as long as one requirement is met, namely that the\nlearning data that is being used always stems from what\nhas been previously observed. More formally,\n\u2200{l1, . . . ln} \u2208 \u2118(L).\u03bb({l1, . . . ln}) = (l, {l1, . . . ln })\n\u21d2\n\u201e\nD(l) \u222a\n[\nl =li[j]\nD(l )\n\u00ab\n\u2286\n[\nl =li[j]\nD(l )\ni.e. whatever \u03bb outputs as a new learning step and updated\nset of learning histories, it cannot invent new data; it has\nto work with the samples that have been made available\nto it earlier in the process through the environment or from\nother agents (and it can of course re-train on previously used\ndata).\nThe goal of the agent is to output an optimal learning\nstep in each iteration given the information that it has. One\npossibility of specifying this is to require that\n\u2200{l1, . . . ln} \u2208 \u2118(L).\u03bb({l1, . . . ln}) = (l, {l1, . . . ln })\n\u21d2 l = arg max\nl \u2208L\ng(l )(h(l ))\nbut since it will usually be unrealistic to compute the\noptimal next learning step in every situation, it is more useful\n2\nNote that our outlook is not only different from common,\ncooperative models of distributed machine learning and data\nmining, but also delineates our approach from multiagent\nlearning systems in which agents learn about other agents\n[25], i.e. the learning goal itself is not affected by agents\"\nbehaviour in the environment.\n680 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\ni j Dj Hj fj gj hj\nDi\npD\u2192D\n1 (Di, Dj)\n.\n..\npD\u2192D\nkD\u2192D\n(Di, Dj)\n. . . . . . n/a . . .\nHi\n.\n..\n... n/a\nfi\n.\n..\n... n/a\ngi\n.\n.. n/a\npg\u2192h\n1 (gi, hj)\n.\n..\npg\u2192h\nkg\u2192h\n(gi, hj)\nhi\n.\n.. n/a\n...\nTable 1: Matrix of integration functions for\nmessages sent from learner i to j\nto simply use g(l )(h(l )) as a running performance measure\nto evaluate how well the agent is performing.\nThis is too abstract and unspecific for our purposes: While\nit describes what agents should do (transform the settings\nfor the next learning step in an optimal way), it doesn\"t\nspecify how this can be achieved in practice.\n2.2 Integrating learning process information\nTo specify how an agent\"s learning process can be affected\nby integrating information received from others, we need to\nflesh out the details of how the learning steps it will perform\ncan be modified using incoming information about learning\nprocesses described by other agents (this includes the\nacquisition of new learning data from the environment as a\nspecial case). In the most general case, we can specify this\nin terms of the potential modifications to the existing\ninformation about learning histories that can be performed using\nnew information. For ease of presentation, we will assume\nthat agents are stationary learning processes that can only\nrecord the previously executed learning step and only\nexchange information about this one individual learning step\n(our model can be easily extended to cater for more complex\nsettings).\nLet lj = Dj, Hj, fj, gj, hj be the current state of\nagent j when receiving a learning process description li =\nDi, Hi, fi, gi, hi from agent i (for the time being, we\nassume that this is a specific learning step and not a more\nvague, disjunctive description of properties of the\nlearning step of i). Considering all possible interactions at an\nabstract level, we basically obtain a matrix of\npossibilities for modifications of j\"s learning step specification as\nshown in Table 1. In this matrix, each entry specifies\na family of integration functions pc\u2192c\n1 , . . . , pc\u2192c\nkc\u2192c\nwhere\nc, c \u2208 {D, H, f, g, h} and which define how agent j\"s\ncomponent cj will be modified using the information ci provided\nabout (the same or a different component of) i\"s learning\nstep by applying pc\u2192c\nr (ci, cj) for some r \u2208 {1, . . . , kc\u2192c }.\nTo put it more simply, the collections of p-functions an agent\nj uses specifies how it will modify its own learning behaviour\nusing information obtained from i.\nFor the diagonal of this matrix, which contains the most\ncommon ways of integrating new information in one\"s own\nlearning model, obvious ways of modifying one\"s own\nlearning process include replacing cj by ci or ignoring ci\naltogether. More complex/subtle forms of learning process\nintegration include:\n\u2022 Modification of Dj: append Di to Dj; filter out all\nelements from Dj which also appear in Di; append\nDi to Dj discarding all elements with attributes\noutside ranges which affect gj, or those elements already\ncorrectly classified by hj;\n\u2022 Modification of Hi: use the union/intersection of Hi\nand Hj; alternatively, discard elements of Hj that are\ninconsistent with Dj in the process of intersection or\nunion, or filter out elements that cannot be obtained\nusing fj (unless fj is modified at the same time)\n\u2022 Modification of fj: modify parameters or background\nknowledge of fj using information about fi; assess\ntheir relevance by simulating previous learning steps\non Dj using gj and discard those that do not help\nimprove own performance\n\u2022 Modification of hj: combine hj with hi using (say)\nlogical or mathematical operators; make the use of hi\ncontingent on a pre-integration assessment of its quality\nusing own data Dj and gj\nWhile this list does not include fully fledged, concrete\nintegration operations for learning processes, it is indicative of\nthe broad range of interactions between individual agents\"\nlearning processes that our framework enables.\nNote that the list does not include any modifications to\ngj. This is because we do not allow modifications to the\nagent\"s own quality measure as this would render the model\nof rational (learning) action useless (if the quality measure\nis relative and volatile, we cannot objectively judge learning\nperformance). Also note that some of the above examples\nrequire consulting other elements of lj than those appearing\nas arguments of the p-operations; we omit these for ease\nof notation, but emphasise that information-rich operations\nwill involve consulting many different aspects of lj.\nApart from operations along the diagonal of the matrix,\nmore exotic integration operations are conceivable that\ncombine information about different components. In theory\nwe could fill most of the matrix with entries for them, but\nfor lack of space we list only a few examples:\n\u2022 Modification of Dj using fi: pre-process samples in\nfi, e.g. to achieve intermediate representations that fj\ncan be applied to\n\u2022 Modification of Dj using hi: filter out samples from\nDj that are covered by hi and build hj using fj only\non remaining samples\n\u2022 Modification of Hj using fi: filter out hypotheses from\nHj that are not realisable using fi\n\u2022 Modification of hj using gi: if hj is composed of several\nsub-components, filter out those sub-components that\ndo not perform well according to gi\n\u2022 . . .\nFinally, many messages received from others describing\nproperties of their learning processes will contain\ninformation about several elements of a learning step, giving rise to\nyet more complex operations that depend on which kinds of\ninformation are available.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 681\nFigure 2: Screenshot of our simulation system,\ndisplaying online vessel tracking data for the North Sea\nregion\n3. APPLICATION EXAMPLE\n3.1 Domain description\nAs an illustration of our framework, we present an\nagentbased data mining system for clustering-based surveillance\nusing AIS (Automatic Identification System [1]) data. In\nour application domain, different commercial and\ngovernmental agencies track the journeys of ships over time\nusing AIS data which contains structured information\nautomatically provided by ships equipped with shipborne\nmobile AIS stations to shore stations, other ships and aircrafts.\nThis data contains the ship\"s identity, type, position, course,\nspeed, navigational status and other safety-related\ninformation. Figure 2 shows a screenshot of our simulation system.\nIt is the task of AIS agencies to detect anomalous\nbehaviour so as to alarm police/coastguard units to further\ninvestigate unusual, potentially suspicious behaviour. Such\nbehaviour might include things such as deviation from the\nstandard routes between the declared origin and destination\nof the journey, unexpected close encounters between\ndifferent vessels on sea, or unusual patterns in the choice of\ndestination over multiple journeys, taking the type of\nvessel and reported freight into account. While the reasons for\nsuch unusual behaviour may range from pure coincidence or\ntechnical problems to criminal activity (such as smuggling,\npiracy, terrorist/military attacks) it is obviously useful to\npre-process the huge amount of vessel (tracking) data that\nis available before engaging in further analysis by human\nexperts.\nTo support this automated pre-processing task, software\nused by these agencies applies clustering methods in order\nto identify outliers and flag those as potentially suspicious\nentities to the human user. However, many agencies active\nin this domain are competing enterprises and use their\n(partially overlapping, but distinct) datasets and learning\nhypotheses (models) as assets and hence cannot be expected\nto collaborate in a fully cooperative way to improve\noverall learning results. Considering that this is the reality of\nthe domain in the real world, it is easy to see that a\nframework like the one we have suggested above might be useful\nto exploit the cooperation potential that is not exploited by\ncurrent systems.\n3.2 Agent-based distributed learning system\ndesign\nTo describe a concrete design for the AIS domain, we need\nto specify the following elements of the overall system:\n1. The datasets and clustering algorithms available to\nindividual agents,\n2. the interaction mechanism used for exchanging\ndescriptions of learning processes, and\n3. the decision mechanism agents apply to make learning\ndecisions.\nRegarding 1., our agents are equipped with their own private\ndatasets in the form of vessel descriptions. Learning samples\nare represented by tuples containing data about individual\nvessels in terms of attributes A = {1, . . . , n} including things\nsuch as width, length, etc. with real-valued domains ([Ai] =\nR for all i).\nIn terms of learning algorithm, we consider clustering\nwith a fixed number of k clusters using the k-means and\nk-medoids clustering algorithms [5] (fixed meaning that\nthe learning algorithm will always output k clusters;\nhowever, we allow agents to change the value of k over different\nlearning cycles). This means that the hypothesis space can\nbe defined as H = { c1, . . . , ck |ci \u2208 R|A|\n} i.e. the set of all\npossible sets of k cluster centroids in |A|-dimensional\nEuclidean space. For each hypothesis h = c1, . . . , ck and any\ndata point d \u2208 \u00d7n\ni=1[Ai] given domain [Ai] for the ith\nattribute of each sample, the assignment to clusters is given\nby\nC( c1, . . . , ck , d) = arg min\n1\u2264j\u2264k\n|d \u2212 cj|\ni.e. d is assigned to that cluster whose centroid is closest to\nthe data point in terms of Euclidean distance.\nFor evaluation purposes, each dataset pertaining to a\nparticular agent i is initially split into a training set Di and a\nvalidation Vi. Then, we generate a set of fake vessels Fi\nsuch that |Fi| = |Vi|. These two sets assess the agent\"s\nability to detect suspicious vessels. For this, we assign a\nconfidence value r(h, d) to every ship d:\nr(h, d) =\n1\n|d \u2212 cC(h,d)|\nwhere C(h, d) is the index of the nearest centroid. Based\non this measure, we classify any vessel in Fi \u222a Vi as fake if\nits r-value is below the median of all the confidences r(h, d)\nfor d \u2208 Fi \u222a Vi. With this, we can compute the quality\ngi(h) \u2208 R as the ratio between all correctly classified vessels\nand all vessels in Fi \u222a Vi.\nAs concerns 2., we use a simple Contract-Net Protocol\n(CNP) [20] based hypothesis trading mechanism: Before\neach learning iteration, agents issue (publicly broadcasted)\nCalls-For-Proposals (CfPs), advertising their own numerical\nmodel quality. In other words, the initiator of a CNP\ndescribes its own current learning state as (\u2217, \u2217, \u2217, gi(h), \u2217)\nwhere h is their current hypothesis/model. We assume that\nagents are sincere when advertising their model quality, but\nnote that this quality might be of limited relevance to other\nagents as they may specialise on specific regions of the data\nspace not related to the test set of the sender of the CfP.\nSubsequently, (some) agents may issue bids in which they\nadvertise, in turn, the quality of their own model. If the\n682 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nbids (if any) are accepted by the initiator of the protocol\nwho issued the CfP, the agents exchange their hypotheses\nand the next learning iteration ensues.\nTo describe what is necessary for 3., we have to specify\n(i) under which conditions agents submit bids in response\nto a CfP, (ii) when they accept bids in the CNP negotiation\nprocess, and (iii) how they integrate the received\ninformation in their own learning process. Concerning (i) and (ii),\nwe employ a very simple rule that is identical in both cases:\nlet g be one\"s own model quality and g that advertised by\nthe CfP (or highest bid, respectively). If g > g we respond\nto the CfP (accept the bid), else respond to the CfP\n(accept the bid) with probability P(g /g) and ignore (reject) it\nelse. If two agents make a deal, they exchange their\nlearning hypotheses (models). In our experiments, g and g are\ncalculated by an additional agent that acts as a global\nvalidation mechanism for all agents (in a more realistic setting a\ncomparison mechanism for different g functions would have\nto be provided).\nAs for (iii), each agent uses a single model merging\noperator taken from the following two classes of operators (hj is\nthe receiver\"s own model and hi is the provider\"s model):\n\u2022 ph\u2192h\n(hi, hj) :\n- m-join: The m best clusters (in terms of coverage\nof Dj) from hypothesis hi are appended to hj.\n- m-select: The set of the m best clusters (in terms\nof coverage of Dj) from the union hi \u222ahj is chosen\nas a new model. (Unlike m-join this method does\nnot prefer own clusters over others\".)\n\u2022 ph\u2192D\n(hi, Dj) :\n- m-filter: The m best clusters (as above) from\nhi are identified and appended to a new model\nformed by using those samples not covered by\nthese clusters applying the own learning\nalgorithm fj.\nWhenever m is large enough to encompass all clusters, we\nsimply write join or filter for them. In section 4 we analyse\nthe performance of each of these two classes for different\nchoices of m.\nIt is noteworthy that this agent-based distributed data\nmining system is one of the simplest conceivable instances\nof our abstract architecture. While we have previously\napplied it also to a more complex market-based architecture\nusing Inductive Logic Programming learners in a transport\nlogistics domain [22], we believe that the system described\nhere is complex enough to illustrate the key design decisions\ninvolved in using our framework and provides simple\nexample solutions for these design issues.\n4. EXPERIMENTAL RESULTS\nFigure 3 shows results obtained from simulations with\nthree learning agents in the above system using the k-means\nand k-medoids clustering methods respectively. We\npartition the total dataset of 300 ships into three disjoint sets of\n100 samples each and assign each of these to one learning\nagent. The Single Agent is learning from the whole dataset.\nThe parameter k is set to 10 as this is the optimal value for\nthe total dataset according to the Davies-Bouldin index [9].\nFor m-select we assume m = k which achieves a constant\nFigure 3: Performance results obtained for different\nintegration operations in homogeneous learner\nsocieties using the k-means (top) and k-medoids\n(bottom) methods\nmodel size. For m-join and m-filter we assume m = 3 to\nlimit the extent to which models increase over time.\nDuring each experiment the learning agents receive ship\ndescriptions in batches of 10 samples. Between these\nbatches, there is enough time to exchange the models among\nthe agents and recompute the models if necessary. Each\nship is described using width, length, draught and speed\nattributes with the goal of learning to detect which vessels\nhave provided fake descriptions of their own properties. The\nvalidation set contains 100 real and 100 randomly generated\nfake ships. To generate sufficiently realistic properties for\nfake ships, their individual attribute values are taken from\nrandomly selected ships in the validation set (so that each\nfake sample is a combination of attribute values of several\nexisting ships).\nIn these experiments, we are mainly interested in\ninvestigating whether a simple form of knowledge sharing between\nself-interested learning agents could improve agent\nperformance compared to a setting of isolated learners. Thereby,\nwe distinguish between homogeneous learner societies where\nall agents use the same clustering algorithm and\nheterogeneous ones where different agents use different algorithms.\nAs can be seen from the performance plots in Figure 3\n(homogeneous case) and 4 (heterogeneous case, two agents\nuse the same method and one agent uses the other) this is\nclearly the case for the (unrestricted) join and filter\nintegration operations (m = k) in both cases. This is quite natural,\nas these operations amount to sharing all available model\nknowledge among agents (under appropriate constraints\ndepending on how beneficial the exchange seems to the agents).\nWe can see that the quality of these operations is very close\nto the Single Agent that has access to all training data.\nFor the restricted (m < k) m-join, m-filter and m-select\nmethods we can also observe an interesting distinction,\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 683\nFigure 4: Performance results obtained for\ndifferent integration operations in heterogeneous societies\nwith the majority of learners using the k-means\n(top) and k-medoids (bottom) methods\nnamely that these perform similarly to the isolated learner\ncase in homogeneous agent groups but better than isolated\nlearners in more heterogeneous societies. This suggests that\nheterogeneous learners are able to benefit even from rather\nlimited knowledge sharing (and this is what using a rather\nsmall m = 3 amounts to given that k = 10) while this is\nnot always true for homogeneous agents. This nicely\nillustrates how different learning or data mining algorithms can\nspecialise on different parts of the problem space and then\nintegrate their local results to achieve better individual\nperformance.\nApart from these obvious performance benefits,\nintegrating partial learning results can also have other advantages:\nThe m-filter operation, for example, decreases the number\nof learning samples and thus can speed up the learning\nprocess. The relative number of filtered examples measured in\nour experiments is shown in the following table.\nk-means k-medoids\nfiltering 30-40 % 10-20 %\nm-filtering 20-30 % 5-15 %\nThe overall conclusion we can draw from these initial\nexperiments with our architecture is that since a very\nsimplistic application of its principles has proven capable of\nimproving the performance of individual learning agents, it is\nworthwhile investigating more complex forms of\ninformation exchange about learning processes among autonomous\nlearners.\n5. RELATED WORK\nWe have already mentioned work on distributed\n(nonagent) machine learning and data mining in the\nintroductory chapter, so in this section we shall restrict ourselves to\napproaches that are more closely related to our outlook on\ndistributed learning systems.\nVery often, approaches that are allegedly agent-based\ncompletely disregard agent autonomy and prescribe local\ndecision-making procedures a priori. A typical example for\nthis type of system is the one suggested by Caragea et al. [6]\nwhich is based on a distributed support-vector machine\napproach where agents incrementally join their datasets\ntogether according to a fixed distributed algorithm. A similar\nexample is the work of Weiss [24], where groups of\nclassifier agents learn to organise their activity so as to optimise\nglobal system behaviour.\nThe difference between this kind of collaborative\nagentbased learning systems [16] and our own framework is that\nthese approaches assume a joint learning goal that is pursued\ncollaboratively by all agents.\nMany approaches rely heavily on a homogeneity\nassumption: Plaza and Ontanon [15] suggest methods for\nagentbased intelligent reuse of cases in case-based reasoning but\nis only applicable to societies of homogeneous learners (and\ncoined towards a specific learning method). An\nagentbased method for integrating distributed cluster analysis\nprocesses using density estimation is presented by Klusch\net al. [13] which is also specifically designed for a\nparticular learning algorithm. The same is true of [22, 23] which\nboth present market-based mechanisms for aggregating the\noutput of multiple learning agents, even though these\napproaches consider more interesting interaction mechanisms\namong learners.\nA number of approaches for sharing learning data [18]\nhave also been proposed: Grecu and Becker [12] suggest an\nexchange of learning samples among agents, and Ghosh et\nal. [11] is a step in the right direction in terms of revealing\nonly partial information about one\"s learning process as it\ndeals with limited information sharing in distributed\nclustering.\nPapyrus [3] is a system that provides a markup language\nfor meta-description of data, hypotheses and intermediate\nresults and allows for an exchange of all this information\namong different nodes, however with a strictly cooperative\ngoal of distributing the load for massively distributed data\nmining tasks.\nThe MALE system [19] was a very early multiagent\nlearning system in which agents used a blackboard approach to\ncommunicate their hypotheses. Agents were able to critique\neach others\" hypotheses until agreement was reached.\nHowever, all agents in this system were identical and the system\nwas strictly cooperative.\nThe ANIMALS system [10] was used to simulate\nmultistrategy learning by combining two or more learning\ntechniques (represented by heterogeneous agents) in order to\novercome weaknesses in the individual algorithms, yet it was\nalso a strictly cooperative system.\nAs these examples show and to the best of our knowledge,\nthere have been no previous attempts to provide a\nframework that can accommodate both independent and\nheterogeneous learning agents and this can be regarded as the main\ncontribution of our work.\n6. CONCLUSION\nIn this paper, we outlined a generic, abstract framework\nfor distributed machine learning and data mining. This\nframework constitutes, to our knowledge, the first attempt\n684 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nto capture complex forms of interaction between\nheterogeneous and/or self-interested learners in an architecture that\ncan be used as the foundation for implementing systems that\nuse complex interaction and reasoning mechanisms to enable\nagents to inform and improve their learning abilities with\ninformation provided by other learners in the system,\nprovided that all agents engage in a sufficiently similar learning\nactivity.\nTo illustrate that the abstract principles of our\narchitecture can be turned into concrete, computational systems,\nwe described a market-based distributed clustering system\nwhich was evaluated in the domain of vessel tracking for\npurposes of identifying deviant or suspicious behaviour.\nAlthough our experimental results only hint at the potential\nof using our architecture, they underline that what we are\nproposing is feasible in principle and can have beneficial\neffects even in its most simple instantiation.\nYet there is a number of issues that we have not addressed\nin the presentation of the architecture and its empirical\nevaluation: Firstly, we have not considered the cost of\ncommunication and made the implicit assumption that the required\ncommunication comes for free. This is of course\ninadequate if we want to evaluate our method in terms of the\ntotal effort required for producing a certain quality of\nlearning results. Secondly, we have not experimented with agents\nusing completely different learning algorithms (e.g. symbolic\nand numerical). In systems composed of completely different\nagents the circumstances under which successful information\nexchange can be achieved might be very different from those\ndescribed here, and much more complex communication and\nreasoning methods may be necessary to achieve a useful\nintegration of different agents\" learning processes. Finally, more\nsophisticated evaluation criteria for such distributed\nlearning architectures have to be developed to shed some light\non what the right measures of optimality for autonomously\nreasoning and communicating agents should be.\nThese issues, together with a more systematic and\nthorough investigation of advanced interaction and\ncommunication mechanisms for distributed, collaborating and\ncompeting agents will be the subject of our future work on the\nsubject.\nAcknowledgement: We gratefully acknowledge the\nsupport of the presented research by Army Research\nLaboratory project N62558-03-0819 and Office for Naval Research\nproject N00014-06-1-0232.\n7. REFERENCES\n[1] http://www.aislive.com.\n[2] http://www.healthagents.com.\n[3] S. Bailey, R. Grossman, H. Sivakumar, and\nA. Turinsky. Papyrus: A System for Data Mining over\nLocal and Wide Area Clusters and Super-Clusters. In\nProc. of the Conference on Supercomputing. 1999.\n[4] E. Bauer and R. Kohavi. 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Distributed Data Mining:\nAlgorithms, Systems, and Applications. In N. Ye,\neditor, Data Mining Handbook, pages 341-358, 2002.\n[18] F. J. Provost and D. N. Hennessy. Scaling up:\nDistributed machine learning with cooperation. In\nProc. of AAAI-96, pages 74-79. AAAI Press, 1996.\n[19] S. Sian. Extending learning to multiple agents: Issues\nand a model for multi-agent machine learning\n(ma-ml). In Y. Kodratoff, editor, Machine\nLearningEWSL-91, pages 440-456. Springer-Verlag, 1991.\n[20] R. Smith. The contract-net protocol: High-level\ncommunication and control in a distributed problem\nsolver. IEEE Transactions on Computers,\nC-29(12):1104-1113, 1980.\n[21] S. J. Stolfo, A. L. Prodromidis, S. Tselepis, W. Lee,\nD. W. Fan, and P. K. Chan. Jam: Java Agents for\nMeta-Learning over Distributed Databases. In Proc. of\nthe KDD-97, pages 74-81, USA, 1997.\n[22] J. To\u02c7zi\u02c7cka, M. Jakob, and M. P\u02c7echou\u02c7cek.\nMarket-Inspired Approach to Collaborative Learning.\nIn Cooperative Information Agents X (CIA 2006),\nvolume 4149 of LNCS, pages 213-227. Springer, 2006.\n[23] Y. Z. Wei, L. Moreau, and N. R. Jennings.\nRecommender systems: a market-based design. In\nProceedings of AAMAS-03), pages 600-607, 2003.\n[24] G. Wei\u00df. A Multiagent Perspective of Parallel and\nDistributed Machine Learning. In Proceedings of\nAgents\"98, pages 226-230, 1998.\n[25] G. Weiss and P. Dillenbourg. What is \"multi\" in\nmulti-agent learning? Collaborative-learning:\nCognitive and Computational Approaches, 64-80, 1999.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 685", "keywords": "unsupervise cluster;distributed clustering application;multiagent learn;framework and architecture;meta-reasoning;unsupervised clustering;agent;bayesian classifier;frameworks and architecture;historical information;distribute machine learn;individual learning process;machine learning;consensusbased method;autonomous learning agent;datum mining;communication and coordination"}
{"name": "train_I-38", "title": "Bidding Algorithms for a Distributed Combinatorial Auction", "abstract": "Distributed allocation and multiagent coordination problems can be solved through combinatorial auctions. However, most of the existing winner determination algorithms for combinatorial auctions are centralized. The PAUSE auction is one of a few efforts to release the auctioneer from having to do all the work (it might even be possible to get rid of the auctioneer). It is an increasing price combinatorial auction that naturally distributes the problem of winner determination amongst the bidders in such a way that they have an incentive to perform the calculation. It can be used when we wish to distribute the computational load among the bidders or when the bidders do not wish to reveal their true valuations unless necessary. PAUSE establishes the rules the bidders must obey. However, it does not tell us how the bidders should calculate their bids. We have developed a couple of bidding algorithms for the bidders in a PAUSE auction. Our algorithms always return the set of bids that maximizes the bidder\"s utility. Since the problem is NP-Hard, run time remains exponential on the number of items, but it is remarkably better than an exhaustive search. In this paper we present our bidding algorithms, discuss their virtues and drawbacks, and compare the solutions obtained by them to the revenue-maximizing solution found by a centralized winner determination algorithm.", "fulltext": "1. INTRODUCTION\nBoth the research and practice of combinatorial auctions\nhave grown rapidly in the past ten years. In a\ncombinatorial auction bidders can place bids on combinations of\nitems, called packages or bidsets, rather than just\nindividual items. Once the bidders place their bids, it is necessary\nto find the allocation of items to bidders that maximizes\nthe auctioneer\"s revenue. This problem, known as the\nwinner determination problem, is a combinatorial optimization\nproblem and is NP-Hard [10]. Nevertheless, several\nalgorithms that have a satisfactory performance for problem\nsizes and structures occurring in practice have been\ndeveloped. The practical applications of combinatorial auctions\ninclude: allocation of airport takeoff and landing time slots,\nprocurement of freight transportation services, procurement\nof public transport services, and industrial procurement [2].\nBecause of their wide applicability, one cannot hope for a\ngeneral-purpose winner determination algorithm that can\nefficiently solve every instance of the problem. Thus,\nseveral approaches and algorithms have been proposed to\naddress the winner determination problem. However, most of\nthe existing winner determination algorithms for\ncombinatorial auctions are centralized, meaning that they require\nall agents to send their bids to a centralized auctioneer who\nthen determines the winners. Examples of these algorithms\nare CASS [3], Bidtree [11] and CABOB [12]. We believe that\ndistributed solutions to the winner determination problem\nshould be studied as they offer a better fit for some\napplications as when, for example, agents do not want to reveal\ntheir valuations to the auctioneer.\nThe PAUSE (Progressive Adaptive User Selection\nEnvironment) auction [4, 5] is one of a few efforts to distribute\nthe problem of winner determination amongst the bidders.\nPAUSE establishes the rules the participants have to adhere\nto so that the work is distributed amongst them. However,\nit is not concerned with how the bidders determine what\nthey should bid.\nIn this paper we present two algorithms, pausebid and\ncachedpausebid, which enable agents in a PAUSE\nauction to find the bidset that maximizes their utility. Our\nalgorithms implement a myopic utility maximizing strategy\nand are guaranteed to find the bidset that maximizes the\nagent\"s utility given the outstanding best bids at a given\ntime. pausebid performs a branch and bound search\ncompletely from scratch every time that it is called.\ncachedpausebid is a caching-based algorithm which explores fewer\nnodes, since it caches some solutions.\n694\n978-81-904262-7-5 (RPS) c 2007 IFAAMAS\n2. THE PAUSE AUCTION\nA PAUSE auction for m items has m stages. Stage 1\nconsists of having simultaneous ascending price open-cry\nauctions and during this stage the bidders can only place bids on\nindividual items. At the end of this state we will know what\nthe highest bid for each individual item is and who placed\nthat bid. Each successive stage k = 2, 3, . . . , m consists of\nan ascending price auction where the bidders must submit\nbidsets that cover all items but each one of the bids must be\nfor k items or less. The bidders are allowed to use bids that\nother agents have placed in previous rounds when building\ntheir bidsets, thus allowing them to find better solutions.\nAlso, any new bidset has to have a sum of bid prices which\nis bigger than that of the currently winning bidset. At the\nend of each stage k all agents know the best bid for every\nsubset of size k or less. Also, at any point in time after stage\n1 has ended there is a standing bidset whose value increases\nmonotonically as new bidsets are submitted. Since in the\nfinal round all agents consider all possible bidsets, we know\nthat the final winning bidset will be one such that no agent\ncan propose a better bidset. Note, however, that this\nbidset is not guaranteed to be the one that maximizes revenue\nsince we are using an ascending price auction so the\nwinning bid for each set will be only slightly bigger than the\nsecond highest bid for the particular set of items. That is,\nthe final prices will not be the same as the prices in a\ntraditional combinatorial auction where all the bidders bid their\ntrue valuation. However, there remains the open question\nof whether the final distribution of items to bidders found\nin a PAUSE auction is the same as the revenue maximizing\nsolution. Our test results provide an answer to this question.\nThe PAUSE auction makes the job of the auctioneer very\neasy. All it has to do is to make sure that each new\nbidset has a revenue bigger than the current winning bidset, as\nwell as make sure that every bid in an agent\"s bidset that\nis not his does indeed correspond to some other agents\"\nprevious bid. The computational problem shifts from one of\nwinner determination to one of bid generation. Each agent\nmust search over the space of all bidsets which contain at\nleast one of its bids. The search is made easier by the fact\nthat the agent needs to consider only the current best bids\nand only wants bidsets where its own utility is higher than\nin the current winning bidset. Each agent also has a clear\nincentive for performing this computation, namely, its\nutility only increases with each bidset it proposes (of course, it\nmight decrease with the bidsets that others propose).\nFinally, the PAUSE auction has been shown to be envy-free in\nthat at the conclusion of the auction no bidder would prefer\nto exchange his allocation with that of any other bidder [2].\nWe can even envision completely eliminating the\nauctioneer and, instead, have every agent perform the task of the\nauctioneer. That is, all bids are broadcast and when an\nagent receives a bid from another agent it updates the set\nof best bids and determines if the new bid is indeed better\nthan the current winning bid. The agents would have an\nincentive to perform their computation as it will increase their\nexpected utility. Also, any lies about other agents\" bids are\neasily found out by keeping track of the bids sent out by\nevery agent (the set of best bids). Namely, the only one that\ncan increase an agent\"s bid value is the agent itself.\nAnyone claiming a higher value for some other agent is lying.\nThe only thing missing is an algorithm that calculates the\nutility-maximizing bidset for each agent.\n3. PROBLEM FORMULATION\nA bid b is composed of three elements bitems\n(the set of\nitems the bid is over), bagent\n(the agent that placed the bid),\nand bvalue\n(the value or price of the bid). The agents\nmaintain a set B of the current best bids, one for each set of items\nof size \u2264 k, where k is the current stage. At any point in the\nauction, after the first round, there will also be a set W \u2286 B\nof currently winning bids. This is the set of bids that covers\nall the items and currently maximizes the revenue, where\nthe revenue of W is given by\nr(W) =\nb\u2208W\nbvalue\n. (1)\nAgent i\"s value function is given by vi(S) \u2208 where S is a\nset of items. Given an agent\"s value function and the current\nwinning bidset W we can calculate the agent\"s utility from\nW as\nui(W) =\nb\u2208W | bagent=i\nvi(bitems\n) \u2212 bvalue\n. (2)\nThat is, the agent\"s utility for a bidset W is the value it\nreceives for the items it wins in W minus the price it must\npay for those items. If the agent is not winning any items\nthen its utility is zero.\nThe goal of the bidding agents in the PAUSE auction is to\nmaximize their utility, subject to the constraint that their\nnext set of bids must have a total revenue that is at least\nbigger than the current revenue, where is the smallest\nincrement allowed in the auction. Formally, given that W is\nthe current winning bidset, agent i must find a g\u2217\ni such that\nr(g\u2217\ni ) \u2265 r(W) + and\ng\u2217\ni = arg max\ng\u22862B\nui(g), (3)\nwhere each g is a set of bids that covers all items and\n\u2200b\u2208g (b \u2208 B) or (bagent\n= i and bvalue\n> B(bitems\n) and\nsize(bitems\n) \u2264 k), and where B(items) is the value of the\nbid in B for the set items (if there is no bid for those items\nit returns zero). That is, each bid b in g must satisfy at least\none of the two following conditions. 1) b is already in B, 2)\nb is a bid of size \u2264 k in which the agent i bids higher than\nthe price for the same items in B.\n4. BIDDING ALGORITHMS\nAccording to the PAUSE auction, during the first stage we\nhave only several English auctions, with the bidders\nsubmitting bids on individual items. In this case, an agent\"s\ndominant strategy is to bid higher than the current winning bid\nuntil it reaches its valuation for that particular item. Our\nalgorithms focus on the subsequent stages: k > 1. When\nk > 1, agents have to find g\u2217\ni . This can be done by\nperforming a complete search on B. However, this approach is\ncomputationally expensive since it produces a large search\ntree. Our algorithms represent alternative approaches to\novercome this expensive search.\n4.1 The PAUSEBID Algorithm\nIn the pausebid algorithm (shown in Figure 1) we\nimplement some heuristics to prune the search tree. Given\nthat bidders want to maximize their utility and that at any\ngiven point there are likely only a few bids within B which\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 695\npausebid(i, k)\n1 my-bids \u2190 \u2205\n2 their-bids \u2190 \u2205\n3 for b \u2208 B\n4 do if bagent\n= i or vi(bitems\n) > bvalue\n5 then my-bids \u2190 my-bids\n+new Bid(bitems\n, i, vi(bitems\n))\n6 else their-bids \u2190 their-bids +b\n7 for S \u2208 subsets of k or fewer items such that\nvi(S) > 0 and \u00ac\u2203b\u2208Bbitems\n= S\n8 do my-bids \u2190 my-bids +new Bid(S, i, vi(S))\n9 bids \u2190 my-bids + their-bids\n10 g\u2217\n\u2190 \u2205 \u00a3 Global variable\n11 u\u2217\n\u2190 ui(W)\u00a3 Global variable\n12 pbsearch(bids, \u2205)\n13 surplus \u2190 b\u2208g\u2217 | bagent=i bvalue\n\u2212 B(bitems\n)\n14 if surplus = 0\n15 then return g\u2217\n16 my-payment \u2190 vi(g\u2217\n) \u2212 u\u2217\n17 for b \u2208 g\u2217\n| bagent\n= i\n18 do if my-payment \u2264 0\n19 then bvalue\n\u2190 B(bitems\n)\n20 else bvalue\n\u2190 B(bitems\n)\n+ my-payment \u00b7bvalue\n\u2212B(bitems\n)\nsurplus\n21 return g\u2217\nFigure 1: The pausebid algorithm which implements\na branch and bound search. i is the agent and k is\nthe current stage of the auction, for k \u2265 2.\nthe agent can dominate, we start by defining my-bids to be\nthe list of bids for which the agent\"s valuation is higher than\nthe current best bid, as given in B. We set the value of\nthese bids to be the agent\"s true valuation (but we won\"t\nnecessarily be bidding true valuation, as we explain later).\nSimilarly, we set their-bids to be the rest of the bids from B.\nFinally, the agent\"s search list is simply the concatenation\nof my-bids and their-bids. Note that the agent\"s own bids\nare placed first on the search list as this will enable us to do\nmore pruning (pausebid lines 3 to 9). The agent can now\nperform a branch and bound search on the branch-on-bids\ntree produced by these bids. This branch and bound search\nis implemented by pbsearch (Figure 2). Our algorithm not\nonly implements the standard bound but it also implements\nother pruning techniques in order to further reduce the size\nof the search tree.\nThe bound we use is the maximum utility that the agent\ncan expect to receive from a given set of bids. We call it u\u2217\n.\nInitially, u\u2217\nis set to ui(W) (pausebid line 11) since that\nis the utility the agent currently receives and any solution\nhe proposes should give him more utility. If pbsearch ever\ncomes across a partial solution where the maximum utility\nthe agent can expect to receive is less than u\u2217\nthen that\nsubtree is pruned (pbsearch line 21). Note that we can\ndetermine the maximum utility only after the algorithm has\nsearched over all of the agent\"s own bids (which are first on\nthe list) because after that we know that the solution will\nnot include any more bids where the agent is the winner\nthus the agent\"s utility will no longer increase. For example,\npbsearch(bids, g)\n1 if bids = \u2205 then return\n2 b \u2190 first(bids)\n3 bids \u2190 bids \u2212b\n4 g \u2190 g + b\n5 \u00afIg \u2190 items not in g\n6 if g does not contain a bid from i\n7 then return\n8 if g includes all items\n9 then min-payment \u2190 max(0, r(W) + \u2212 (r(g) \u2212 ri(g)),\nb\u2208g | bagent=i B(bitems\n))\n10 max-utility \u2190 vi(g) \u2212 min-payment\n11 if r(g) > r(W) and max-utility \u2265 u\u2217\n12 then g\u2217\n\u2190 g\n13 u\u2217\n\u2190 max-utility\n14 pbsearch(bids, g \u2212 b) \u00a3 b is Out\n15 else max-revenue \u2190 r(g) + max(h(\u00afIg), hi(\u00afIg))\n16 if max-revenue \u2264 r(W)\n17 then pbsearch(bids, g \u2212 b) \u00a3 b is Out\n18 elseif bagent\n= i\n19 then min-payment \u2190 (r(W) + )\n\u2212(r(g) \u2212 ri(g)) \u2212 h(\u00afIg)\n20 max-utility \u2190 vi(g) \u2212 min-payment\n21 if max-utility > u\u2217\n22 then pbsearch({x \u2208 bids |\nxitems\n\u2229 bitems\n= \u2205}, g) \u00a3 b is In\n23 pbsearch(bids, g \u2212 b) \u00a3 b is Out\n24 else\n25 pbsearch({x \u2208 bids |\nxitems\n\u2229 bitems\n= \u2205}, g) \u00a3 b is In\n26 pbsearch(bids, g \u2212 b) \u00a3 b is Out\n27 return\nFigure 2: The pbsearch recursive procedure where\nbids is the set of available bids and g is the current\npartial solution.\nif an agent has only one bid in my-bids then the maximum\nutility he can expect is equal to his value for the items in\nthat bid minus the minimum possible payment we can make\nfor those items and still come up with a set of bids that has\nrevenue greater than r(W). The calculation of the minimum\npayment is shown in line 19 for the partial solution case and\nline 9 for the case where we have a complete solution in\npbsearch. Note that in order to calculate the min-payment\nfor the partial solution case we need an upper bound on the\npayments that we must make for each item. This upper\nbound is provided by\nh(S) =\ns\u2208S\nmax\nb\u2208B | s\u2208bitems\nbvalue\nsize(bitems)\n. (4)\nThis function produces a bound identical to the one used by\nthe Bidtree algorithm-it merely assigns to each individual\nitem in S a value equal to the maximum bid in B divided\nby the number of items in that bid.\nTo prune the branches that cannot lead to a solution with\nrevenue greater than the current W, the algorithm considers\nboth the values of the bids in B and the valuations of the\n696 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nagent. Similarly to (4) we define\nhi(S, k) =\ns\u2208S\nmax\nS | size(S )\u2264k and s\u2208S and vi(S )>0\nvi(S )\nsize(S )\n(5)\nwhich assigns to each individual item s in S the maximum\nvalue produced by the valuation of S divided by the size\nof S , where S is a set for which the agent has a valuation\ngreater than zero, contains s, and its size is less or equal\nthan k. The algorithm uses the heuristics h and hi (lines 15\nand 19 of pbsearch), to prune the just mentioned branches\nin the same way an A\u2217\nalgorithm uses its heuristic. A final\npruning technique implemented by the algorithm is ignoring\nany branches where the agent has no bids in the current\nanswer g and no more of the agent\"s bids are in the list\n(pbsearch lines 6 and 7).\nThe resulting g\u2217\nfound by pbsearch is thus the set of bids\nthat has revenue bigger than r(W) and maximizes agent i\"s\nutility. However, agent i\"s bids in g\u2217\nare still set to his own\nvaluation and not to the lowest possible price. Lines 17 to 20\nin pausebid are responsible for setting the agent\"s payments\nso that it can achieve its maximum utility u\u2217\n. If the agent\nhas only one bid in g\u2217\nthen it is simply a matter of reducing\nthe payment of that bid by u\u2217\nfrom the current maximum of\nthe agent\"s true valuation. However, if the agent has more\nthan one bid then we face the problem of how to distribute\nthe agent\"s payments among these bids. There are many\nways of distributing the payments and there does not appear\nto be a dominant strategy for performing this distribution.\nWe have chosen to distribute the payments in proportion to\nthe agent\"s true valuation for each set of items.\npausebid assumes that the set of best bids B and the\ncurrent best winning bidset W remains constant during its\nexecution, and it returns the agent\"s myopic utility-maximizing\nbidset (if there is one) using a branch and bound search.\nHowever it repeats the whole search at every stage. We\ncan minimize this problem by caching the result of previous\nsearches.\n4.2 The CACHEDPAUSEBID Algorithm\nThe cachedpausebid algorithm (shown in Figure 3) is\nour second approach to solve the bidding problem in the\nPAUSE auction. It is based in a cache table called C-Table\nwhere we store some solutions to avoid doing a complete\nsearch every time. The problem is the same; the agent i has\nto find g\u2217\ni . We note that g\u2217\ni is a bidset that contains at least\none bid of the agent i. Let S be a set of items for which the\nagent i has a valuation such that vi(S) \u2265 B(S) > 0, let gS\ni\nbe a bidset over S such that r(gS\ni ) \u2265 r(W) + and\ngS\ni = arg max\ng\u22862B\nui(g), (6)\nwhere each g is a set of bids that covers all items and\n\u2200b\u2208g (b \u2208 B) or (bagent\n= i and bvalue\n> B(bitems\n)) and\n(\u2203b\u2208gbitems\n= S and bagent\n= i). That is, gS\ni is i\"s best\nbidset for all items which includes a bid from i for all S items.\nIn the PAUSE auction we cannot bid for sets of items with\nsize greater than k. So, if we have for each set of items S for\nwhich vi(S) > 0 and size(S) \u2264 k its corresponding gS\ni then\ng\u2217\ni is the gS\ni that maximizes the agent\"s utility. That is\ng\u2217\ni = arg max\n{S | vi(S)>0\u2227size(S)\u2264k}\nui(gS\ni ). (7)\nEach agent i implements a hash table C-Table such that\nC-Table[S] = gS\nfor all S which vi(S) \u2265 B(S) > 0. We can\ncachedpausebid(i, k, k-changed)\n1 for each S in C-Table\n2 do if vi(S) < B(S)\n3 then remove S from C-Table\n4 else if k-changed and size(S) = k\n5 then B \u2190 B + new Bid(i, S, vi(S))\n6 g\u2217\n\u2190 \u2205\n7 u\u2217\n\u2190 ui(W)\n8 for each S with size(S) \u2264 k in C-Table\n9 do \u00afS \u2190 Items \u2212 S\n10 gS\n\u2190 C-Table[S] \u00a3 Global variable\n11 min-payment \u2190 max(r(W) + , b\u2208gS B(bitems\n))\n12 uS\n\u2190 r(gS\n) \u2212 min-payment \u00a3 Global variable\n13 if (k-changed and size(S) = k)\nor (\u2203b\u2208B bitems\n\u2286 \u00afS and bagent\n= i)\n14 then B \u2190 {b \u2208 B |bitems\n\u2286 \u00afS}\n15 bids \u2190 B\n+{b \u2208 B|bitems\n\u2286 \u00afS and b /\u2208 B }\n16 for b \u2208 bids\n17 do if vi(bitems\n) > bvalue\n18 then bagent\n\u2190 i\n19 bvalue\n\u2190 vi(bitems\n)\n20 if k-changed and size(S) = k\n21 then n \u2190 size(bids)\n22 uS\n\u2190 0\n23 else n \u2190 size(B )\n24 g \u2190 \u2205 + new Bid(S, i, vi(S))\n25 cpbsearch(bids, g, n)\n26 C-Table[S] \u2190 gS\n27 if uS\n> u\u2217\nand r(gS\n) \u2265 r(W) +\n28 then surplus \u2190\nb\u2208gS | bagent=i bvalue\n\u2212 B(bitems\n)\n29 if surplus > 0\n30 then my-payment \u2190 vi(gS\n) \u2212 ui(gS\n)\n31 for b \u2208 gS\n| bagent\n= i\n32 do if my-payment \u2264 0\n33 then bvalue\n\u2190 B(bitems\n)\n34 else bvalue\n\u2190 B(bitems\n)+\nmy-payment \u00b7bvalue\n\u2212B(bitems\n)\nsurplus\n35 u\u2217\n\u2190 ui(gS\n)\n36 g\u2217\n\u2190 gS\n37 else if uS\n\u2264 0 and vi(S) < B(S)\n38 then remove S from C-Table\n39 return g\u2217\nFigure 3: The cachedpausebid algorithm that\nimplements a caching based search to find a bidset that\nmaximizes the utility for the agent i. k is the\ncurrent stage of the auction (for k \u2265 2), and k-changed is\na boolean that is true right after the auction moved\nto the next stage.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 697\ncpbsearch(bids, g, n)\n1 if bids = \u2205 or n \u2264 0 then return\n2 b \u2190 first(bids)\n3 bids \u2190 bids \u2212b\n4 g \u2190 g + b\n5 \u00afIg \u2190 items not in g\n6 if g includes all items\n7 then min-payment \u2190 max(0, r(W) + \u2212 (r(g) \u2212 ri(g)),\nb\u2208g | bagent=i B(bitems\n))\n8 max-utility \u2190 vi(g) \u2212 min-payment\n9 if r(g) > r(W) and max-utility \u2265 uS\n10 then gS\n\u2190 g\n11 uS\n\u2190 max-utility\n12 cpbsearch(bids, g \u2212 b, n \u2212 1) \u00a3 b is Out\n13 else max-revenue \u2190 r(g) + max(h(\u00afIg), hi(\u00afIg))\n14 if max-revenue \u2264 r(W)\n15 then cpbsearch(bids, g \u2212 b, n \u2212 1) \u00a3 b is Out\n16 elseif bagent\n= i\n17 then min-payment \u2190 (r(W) + )\n\u2212(r(g) \u2212 ri(g)) \u2212 h(\u00afIg)\n18 max-utility \u2190 vi(g) \u2212 min-payment\n19 if max-utility > uS\n20 then cpbsearch({x \u2208 bids |\nxitems\n\u2229 bitems\n= \u2205}, g, n + 1) \u00a3 b is In\n21 cpbsearch(bids, g \u2212 b, n \u2212 1) \u00a3 b is Out\n22 else\n23 cpbsearch({x \u2208 bids |\nxitems\n\u2229 bitems\n= \u2205}, g, n + 1) \u00a3 b is In\n24 cpbsearch(bids, g \u2212 b, n \u2212 1) \u00a3 b is Out\n25 return\nFigure 4: The cpbsearch recursive procedure where\nbids is the set of available bids, g is the current\npartial solution and n is a value that indicates how deep\nin the list bids the algorithm has to search.\nthen find g\u2217\nby searching for the gS\n, stored in C-Table[S],\nthat maximizes the agent\"s utility, considering only the set\nof items S with size(S) \u2264 k. The problem remains in\nmaintaining the C-Table updated and avoiding to search every\ngS\nevery time. cachedpausebid deals with this and other\ndetails.\nLet B be the set of bids that contains the new best bids,\nthat is, B contains the bids recently added to B and the bids\nthat have changed price (always higher), bidder, or both and\nwere already in B. Let \u00afS = Items \u2212 S be the complement\nof S (the set of items not included in S). cachedpausebid\ntakes three parameters: i the agent, k the current stage of\nthe auction, and k-changed a boolean that is true right after\nthe auction moved to the next stage. Initially C-Table has\none row or entry for each set S for which vi(S) > 0. We\nstart by eliminating the entries corresponding to each set S\nfor which vi(S) < B(S) from C-Table (line 3). Then, in the\ncase that k-changed is true, for each set S with size(S) = k,\nwe add to B a bid for that set with value equal to vi(S)\nand bidder agent i (line 5); this a bid that the agent is now\nallowed to consider. We then search for g\u2217\namongst the gS\nstored in C-Table, for this we only need to consider the sets\nwith size(S) \u2264 k (line 8). But how do we know that the gS\nin C-Table[S] is still the best solution for S? There are only\ntwo cases when we are not sure about that and we need\nto do a search to update C-Table[S]. These cases are: i)\nWhen k-changed is true and size(S) \u2264 k, since there was\nno gS\nstored in C-Table for this S. ii) When there exists at\nleast one bid in B for the set of items \u00afS or a subset of it\nsubmitted by an agent different than i, since it is probable\nthat this new bid can produce a solution better than the one\nstored in C-Table[S].\nWe handle the two cases mentioned above in lines 13 to 26\nof cachedpausebid. In both of these cases, since gS\nmust\ncontain a bid for S we need to find a bidset that cover the\nmissing items, that is \u00afS. Thus, our search space consists\nof all the bids on B for the set of items \u00afS or for a subset\nof it. We build the list bids that contains only those bids.\nHowever, we put the bids from B at the beginning of bids\n(line 14) since they are the ones that have changed. Then,\nwe replace the bids in bids that have a price lower than the\nvaluation the agent i has for those same items with a bid\nfrom agent i for those items and value equal to the agent\"s\nvaluation (lines 16-19).\nThe recursive procedure cpbsearch, called in line 25 of\ncachedpausebid and shown in Figure 4, is the one that\nfinds the new gS\n. cpbsearch is a slightly modified version\nof our branch and bound search implemented in pbsearch.\nThe first modification is that it has a third parameter n that\nindicates how deep on the list bids we want to search, since\nit stops searching when n less or equal to zero and not only\nwhen the list bids is empty (line 1). Each time that there is\na recursive call of cpbsearch n is decreased by one when a\nbid from bids is discarded or out (lines 12, 15, 21, and 24)\nand n remains the same otherwise (lines 20 and 23). We set\nthe value of n before calling cpbsearch, to be the size of the\nlist bids (cachedpausebid line 21) in case i), since we want\ncpbsearch to search over all bids; and we set n to be the\nnumber of bids from B included in bids (cachedpausebid\nline 23) in case ii), since we know that only the those first n\nbids in bids changed and can affect our current gS\n.\nAnother difference with pbsearch is that the bound in\ncpbsearch is uS\nwhich we set to be 0 (cachedpausebid line\n22) when in case i) and r(gS\n)\u2212min-payment (cachedpausebid\nline 12) when in case ii). We call cpbsearch with g already\ncontaining a bid for S. After cpbsearch is executed we\nare sure that we have the right gS\n, so we store it in the\ncorresponding C-Table[S] (cachedpausebid line 26).\nWhen we reach line 27 in cachedpausebid, we are sure\nthat we have the right gS\n. However, agent i\"s bids in gS\nare\nstill set to his own valuation and not to the lowest possible\nprice. If uS\nis greater than the current u\u2217\n, lines 31 to 34\nin cachedpausebid are responsible for setting the agent\"s\npayments so that it can achieve its maximum utility uS\n.\nAs in pausebid, we have chosen to distribute the payments\nin proportion to the agent\"s true valuation for each set of\nitems. In the case that uS\nless than or equal to zero and\nthe valuation that the agent i has for the set of items S is\nlower than the current value of the bid in B for the same\nset of items, we remove the corresponding C-Table[S] since\nwe know that is not worthwhile to keep it in the cache table\n(cachedpausebid line 38).\nThe cachedpausebid function is called when k > 1 and\nreturns the agent\"s myopic utility-maximizing bidset, if there\nis one. It assumes that W and B remains constant during\nits execution.\n698 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\ngeneratevalues(i, items)\n1 for x \u2208 items\n2 do vi(x) = expd(.01)\n3 for n \u2190 1 . . . (num-bids \u2212 items)\n4 do s1, s2 \u2190Two random sets of items with values.\n5 vi(s1 \u222a s2) = vi(s1) + vi(s2) + expd(.01)\nFigure 5: Algorithm for the generation of random\nvalue functions. expd(x) returns a random number\ntaken from an exponential distribution with mean\n1/x.\n0\n20\n40\n60\n80\n100\n2 3 4 5 6 7 8 9 10\nNumber of Items\nCachedPauseBid\n3 3 3 3 3 3\n3 3\n3\n3\nPauseBid\n+ + + + +\n+ + +\n+\n+\nFigure 6: Average percentage of convergence\n(y-axis), which is the percentage of times that our\nalgorithms converge to the revenue-maximizing\nsolution, as function of the number of items in the\nauction.\n5. TEST AND COMPARISON\nWe have implemented both algorithms and performed a\nseries of experiments in order to determine how their\nsolution compares to the revenue-maximizing solution and how\ntheir times compare with each other. In order to do our\ntests we had to generate value functions for the agents1\n.\nThe algorithm we used is shown in Figure 5. The type of\nvaluations it generates correspond to domains where a set\nof agents must perform a set of tasks but there are cost\nsavings for particular agents if they can bundle together certain\nsubsets of tasks. For example, imagine a set of robots which\nmust pick up and deliver items to different locations. Since\neach robot is at a different location and has different\nabilities, each one will have different preferences over how to\nbundle. Their costs for the item bundles are subadditive,\nwhich means that their preferences are superadditive. The\nfirst experiment we performed simply ensured the proper\n1\nNote that we could not use CATS [6] because it generates\nsets of bids for an indeterminate number of agents. It is as\nif you were told the set of bids placed in a combinatorial\nauction but not who placed each bid or even how many\npeople placed bids, and then asked to determine the value\nfunction of every participant in the auction.\n0\n20\n40\n60\n80\n100\n2 3 4 5 6 7 8 9 10\nNumber of Items\nCachedPauseBid\n3\n3\n3 3\n3 3 3 3 3\n3\nPauseBid\n+ +\n+ +\n+\n+ + +\n+\n+\nFigure 7: Average percentage of revenue from our\nalgorithms relative to maximum revenue (y-axis) as\nfunction of the number of items in the auction.\nfunctioning of our algorithms. We then compared the\nsolutions found by both of them to the revenue-maximizing\nsolution as found by CASS when given a set of bids that\ncorresponds to the agents\" true valuation. That is, for each\nagent i and each set of items S for which vi(S) > 0 we\ngenerated a bid. This set of bids was fed to CASS which\nimplements a centralized winner determination algorithm to find\nthe solution which maximizes revenue. Note, however, that\nthe revenue from the PAUSE auction on all the auctions is\nalways smaller than the revenue of the revenue-maximizing\nsolution when the agents bid their true valuations. Since\nPAUSE uses English auctions the final prices (roughly)\nrepresent the second-highest valuation, plus , for that set of\nitems.\nWe fixed the number of agents to be 5 and we\nexperimented with different number of items, namely from 2 to\n10. We ran both algorithms 100 times for each\ncombination. When we compared the solutions of our algorithms\nto the revenue-maximizing solution, we realized that they\ndo not always find the same distribution of items as the\nrevenue-maximizing solution (as shown in Figure 6). The\ncases where our algorithms failed to arrive at the\ndistribution of the revenue-maximizing solution are those where\nthere was a large gap between the first and second\nvaluation for a set (or sets) of items. If the revenue-maximizing\nsolution contains the bid (or bids) using these higher\nvaluation then it is impossible for the PAUSE auction to find this\nsolution because that bid (those bids) is never placed. For\nexample, if agent i has vi(1) = 1000 and the second highest\nvaluation for (1) is only 10 then i only needs to place a bid\nof 11 in order to win that item. If the revenue-maximizing\nsolution requires that 1 be sold for 1000 then that solution\nwill never be found because that bid will never be placed.\nWe also found that average percentage of times that our\nalgorithms converges to the revenue-maximizing solution\ndecreases as the number of items increases. For 2 items is\nalmost 100% but decreases a little bit less than 1 percent as\nthe items increase, so that this average percentage of\nconvergence is around 90% for 10 items. In a few instances our\nalgorithms find different solutions this is due to the different\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 699\n1\n10\n100\n1000\n10000\n2 3 4 5 6 7 8 9 10\nNumber of Items\nCachedPauseBid\n3\n3\n3\n3\n3\n3\n3\n3\n3\nPauseBid\n+\n+\n+\n+\n+\n+\n+\n+\n+\n+\nFigure 8: Average number of expanded nodes\n(y-axis) as function of items in the auction.\nordering of the bids in the bids list which makes them search\nin different order.\nWe know that the revenue generated by the PAUSE\nauction is generally lower than the revenue of the\nrevenuemaximizing solution, but how much lower? To answer this\nquestion we calculated percentage representing the\nproportion of the revenue given by our algorithms relative to the\nrevenue given by CASS. We found that the percentage of\nrevenue of our algorithms increases in average 2.7% as the\nnumber of items increases, as shown in Figure 7. However,\nwe found that cachedpausebid generates a higher revenue\nthan pausebid (4.3% higher in average) except for auctions\nwith 2 items where both have about the same percentage.\nAgain, this difference is produced by the order of the search.\nIn the case of 2 items both algorithms produce in average\na revenue proportion of 67.4%, while in the other extreme\n(10 items), cachedpausebid produced in average a revenue\nproportion of 91.5% while pausebid produced in average a\nrevenue proportion of 87.7%.\nThe scalability of our algorithms can be determined by\ncounting the number of nodes expanded in the search tree.\nFor this we count the number of times that pbsearch gets\ninvoked for each time that pausebid is called and the\nnumber of times that fastpausebidsearch gets invoked for each\ntime that cachedpausebid, respectively for each of our\nalgorithms. As expected since this is an NP-Hard problem,\nthe number of expanded nodes does grow exponentially with\nthe number of items (as shown in Figure 8). However, we\nfound that cachedpausebid outperforms pausebid, since\nit expands in average less than half the number of nodes.\nFor example, the average number of nodes expanded when\n2 items is zero for cachedpausebid while for pausebid is\n2; and in the other extreme (10 items) cachedpausebid\nexpands in average only 633 nodes while pausebid expands in\naverage 1672 nodes, a difference of more than 1000 nodes.\nAlthough the number of nodes expanded by our algorithms\nincreases as function of the number of items, the actual\nnumber of nodes is a much smaller than the worst-case scenario\nof nn\nwhere n is the number of items. For example, for 10\nitems we expand slightly more than 103\nnodes for the case of\npausebid and less than that for the case of\ncachedpause0.1\n1\n10\n100\n1000\n2 3 4 5 6 7 8 9 10\nNumber of Items\nCachedPauseBid\n3\n3\n3\n3\n3\n3\n3\n3\n3\n3\nPauseBid\n+\n+\n+\n+\n+\n+\n+\n+\n+\n+\nFigure 9: Average time in seconds that takes to\nfinish an auction (y-axis) as function of the number of\nitems in the auction.\nbid which are much smaller numbers than 1010\n. Notice also\nthat our value generation algorithm (Figure 5) generates a\nnumber of bids that is exponential on the number of items,\nas might be expected in many situations. As such, these\nresults do not support the conclusion that time grows\nexponentially with the number of items when the number of\nbids is independent of the number of items. We expect that\nboth algorithms will grow exponentially as a function the\nnumber of bids, but stay roughly constant as the number of\nitems grows.\nWe wanted to make sure that less expanded nodes does\nindeed correspond to faster execution, especially since our\nalgorithms execute different operations. We thus ran the\nsame experiment with all the agents in the same machine,\nan Intel Centrino 2.0 GHz laptop PC with 1 GB of RAM and\na 7200 RMP 60 GB hard drive, and calculated the average\ntime that takes to finish an auction for each algorithm. As\nshown in Figure 9, cachedpausebid is faster than\npausebid, the difference in execution speed is even more clear as\nthe number of items increases.\n6. RELATED WORK\nA lot of research has been done on various aspects of\ncombinatorial auctions. We recommend [2] for a good review.\nHowever, the study of distributed winner determination\nalgorithms for combinatorial auctions is still relatively new.\nOne approach is given by the algorithms for distributing\nthe winner determination problem in combinatorial auctions\npresented in [7], but these algorithms assume the\ncomputational entities are the items being sold and thus end up\nwith a different type of distribution. The VSA algorithm\n[3] is another way of performing distributed winner\ndetermination in combinatorial auction but it assumes the bids\nthemselves perform the computation. This algorithm also\nfails to converge to a solution for most cases. In [9] the\nauthors present a distributed mechanism for calculating VCG\npayments in a mechanism design problem. Their\nmechanism roughly amounts to having each agent calculate the\npayments for two other agents and give these to a secure\n700 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\ncentral server which then checks to make sure results from\nall pairs agree, otherwise a re-calculation is ordered. This\ngeneral idea, which they call the redundancy principle, could\nalso be applied to our problem but it requires the existence\nof a secure center agent that everyone trusts. Another\ninteresting approach is given in [8] where the bidding agents\nprioritize their bids, thus reducing the set of bids that the\ncentralized winner determination algorithm must consider,\nmaking that problem easier. Finally, in the computation\nprocuring clock auction [1] the agents are given an\neverincreasing percentage of the surplus achieved by their\nproposed solution over the current best. As such, it assumes\nthe agents are impartial computational entities, not the set\nof possible buyers as assumed by the PAUSE auction.\n7. CONCLUSIONS\nWe believe that distributed solutions to the winner\ndetermination problem should be studied as they offer a better fit\nfor some applications as when, for example, agents do not\nwant to reveal their valuations to the auctioneer or when\nwe wish to distribute the computational load among the\nbidders. The PAUSE auction is one of a few approaches\nto decentralize the winner determination problem in\ncombinatorial auctions. With this auction, we can even envision\ncompletely eliminating the auctioneer and, instead, have\nevery agent performe the task of the auctioneer. However,\nwhile PAUSE establishes the rules the bidders must obey, it\ndoes not tell us how the bidders should calculate their bids.\nWe have presented two algorithms, pausebid and\ncachedpausebid, that bidder agents can use to engage in a PAUSE\nauction. Both algorithms implement a myopic utility\nmaximizing strategy that is guaranteed to find the bidset that\nmaximizes the agent\"s utility given the set of outstanding\nbest bids at any given time, without considering possible\nfuture bids. Both algorithms find, most of the time, the\nsame distribution of items as the revenue-maximizing\nsolution. The cases where our algorithms failed to arrive at that\ndistribution are those where there was a large gap between\nthe first and second valuation for a set (or sets) of items.\nAs it is an NP-Hard problem, the running time of our\nalgorithms remains exponential but it is significantly better than\na full search. pausebid performs a branch and bound search\ncompletely from scratch each time it is invoked.\ncachedpausebid caches partial solutions and performs a branch\nand bound search only on the few portions affected by the\nchanges on the bids between consecutive times.\ncachedpausebid has a better performance since it explores fewer\nnodes (less than half) and it is faster. As expected the\nrevenue generated by a PAUSE auction is lower than the\nrevenue of a revenue-maximizing solution found by a\ncentralized winner determination algorithm, however we found\nthat cachedpausebid generates in average 4.7% higher\nrevenue than pausebid. We also found that the revenue\ngenerated by our algorithms increases as function of the number\nof items in the auction.\nOur algorithms have shown that it is feasible to implement\nthe complex coordination constraints supported by\ncombinatorial auctions without having to resort to a centralized\nwinner determination algorithm. Moreover, because of the\ndesign of the PAUSE auction, the agents in the auction also\nhave an incentive to perform the required computation. Our\nbidding algorithms can be used by any multiagent system\nthat would use combinatorial auctions for coordination but\nwould rather not implement a centralized auctioneer.\n8. REFERENCES\n[1] P. J. Brewer. Decentralized computation procurement\nand computational robustness in a smart market.\nEconomic Theory, 13(1):41-92, January 1999.\n[2] P. Cramton, Y. Shoham, and R. Steinberg, editors.\nCombinatorial Auctions. MIT Press, 2006.\n[3] Y. Fujishima, K. Leyton-Brown, and Y. Shoham.\nTaming the computational complexity of\ncombinatorial auctions: Optimal and approximate\napproaches. In Proceedings of the Sixteenth\nInternational Joint Conference on Artificial\nIntelligence, pages 548-553. Morgan Kaufmann\nPublishers Inc., 1999.\n[4] F. Kelly and R. Stenberg. A combinatorial auction\nwith multiple winners for universal service.\nManagement Science, 46(4):586-596, 2000.\n[5] A. Land, S. Powell, and R. Steinberg. PAUSE: A\ncomputationally tractable combinatorial auction. In\nCramton et al. [2], chapter 6, pages 139-157.\n[6] K. Leyton-Brown, M. Pearson, and Y. Shoham.\nTowards a universal test suite for combinatorial\nauction algorithms. In Proceedings of the 2nd ACM\nconference on Electronic commerce, pages 66-76.\nACM Press, 2000. http://cats.stanford.edu.\n[7] M. V. Narumanchi and J. M. Vidal. Algorithms for\ndistributed winner determination in combinatorial\nauctions. In LNAI volume of AMEC/TADA. Springer,\n2006.\n[8] S. Park and M. H. Rothkopf. Auctions with\nendogenously determined allowable combinations.\nTechnical report, Rutgets Center for Operations\nResearch, January 2001. RRR 3-2001.\n[9] D. C. Parkes and J. Shneidman. Distributed\nimplementations of vickrey-clarke-groves auctions. In\nProceedings of the Third International Joint\nConference on Autonomous Agents and MultiAgent\nSystems, pages 261-268. ACM, 2004.\n[10] M. H. Rothkopf, A. Pekec, and R. M. Harstad.\nComputationally manageable combinational auctions.\nManagement Science, 44(8):1131-1147, 1998.\n[11] T. Sandholm. An algorithm for winner determination\nin combinatorial auctions. Artificial Intelligence,\n135(1-2):1-54, February 2002.\n[12] T. Sandholm, S. Suri, A. Gilpin, and D. Levine.\nCABOB: a fast optimal algorithm for winner\ndetermination in combinatorial auctions. Management\nScience, 51(3):374-391, 2005.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 701", "keywords": "task and resource allocation;bidding algorithm;pause auction;progressive adaptive user selection environment;branch-on-bid tree;combinatorial auction;agent;coordination;search tree;branch and bound search;distributed allocation;combinatorial optimization problem;revenue-maximizing solution"}
{"name": "train_I-42", "title": "A Complete Distributed Constraint Optimization Method For Non-Traditional Pseudotree Arrangements", "abstract": "Distributed Constraint Optimization (DCOP) is a general framework that can model complex problems in multi-agent systems. Several current algorithms that solve general DCOP instances, including ADOPT and DPOP, arrange agents into a traditional pseudotree structure. We introduce an extension to the DPOP algorithm that handles an extended set of pseudotree arrangements. Our algorithm correctly solves DCOP instances for pseudotrees that include edges between nodes in separate branches. The algorithm also solves instances with traditional pseudotree arrangements using the same procedure as DPOP. We compare our algorithm with DPOP using several metrics including the induced width of the pseudotrees, the maximum dimensionality of messages and computation, and the maximum sequential path cost through the algorithm. We prove that for some problem instances it is not possible to generate a traditional pseudotree using edge-traversal heuristics that will outperform a cross-edged pseudotree. We use multiple heuristics to generate pseudotrees and choose the best pseudotree in linear space-time complexity. For some problem instances we observe significant improvements in message and computation sizes compared to DPOP.", "fulltext": "1. INTRODUCTION\nMany historical problems in the AI community can be\ntransformed into Constraint Satisfaction Problems (CSP). With the\nadvent of distributed AI, multi-agent systems became a popular way\nto model the complex interactions and coordination required to\nsolve distributed problems. CSPs were originally extended to\ndistributed agent environments in [9]. Early domains for\ndistributed constraint satisfaction problems (DisCSP) included job\nshop scheduling [1] and resource allocation [2]. Many domains\nfor agent systems, especially teamwork coordination, distributed\nscheduling, and sensor networks, involve overly constrained\nproblems that are difficult or impossible to satisfy for every constraint.\nRecent approaches to solving problems in these domains rely\non optimization techniques that map constraints into multi-valued\nutility functions. Instead of finding an assignment that satisfies all\nconstraints, these approaches find an assignment that produces a\nhigh level of global utility. This extension to the original DisCSP\napproach has become popular in multi-agent systems, and has been\nlabeled the Distributed Constraint Optimization Problem (DCOP)\n[1].\nCurrent algorithms that solve complete DCOPs use two main\napproaches: search and dynamic programming. Search based\nalgorithms that originated from DisCSP typically use some form of\nbacktracking [10] or bounds propagation, as in ADOPT [3].\nDynamic programming based algorithms include DPOP and its\nextensions [5, 6, 7]. To date, both categories of algorithms arrange\nagents into a traditional pseudotree to solve the problem.\nIt has been shown in [6] that any constraint graph can be mapped\ninto a traditional pseudotree. However, it was also shown that\nfinding the optimal pseudotree was NP-Hard. We began to\ninvestigate the performance of traditional pseudotrees generated by\ncurrent edge-traversal heuristics. We found that these heuristics\noften produced little parallelism as the pseudotrees tended to have\nhigh depth and low branching factors. We suspected that there\ncould be other ways to arrange the pseudotrees that would\nprovide increased parallelism and smaller message sizes. After\nexploring these other arrangements we found that cross-edged\npseudotrees provide shorter depths and higher branching factors than\nthe traditional pseudotrees. Our hypothesis was that these\ncrossedged pseudotrees would outperform traditional pseudotrees for\nsome problem types.\nIn this paper we introduce an extension to the DPOP algorithm\nthat handles an extended set of pseudotree arrangements which\ninclude cross-edged pseudotrees. We begin with a definition of\n741\n978-81-904262-7-5 (RPS) c 2007 IFAAMAS\nDCOP, traditional pseudotrees, and cross-edged pseudotrees. We\nthen provide a summary of the original DPOP algorithm and\nintroduce our DCPOP algorithm. We discuss the complexity of our\nalgorithm as well as the impact of pseudotree generation\nheuristics. We then show that our Distributed Cross-edged Pseudotree\nOptimization Procedure (DCPOP) performs significantly better in\npractice than the original DPOP algorithm for some problem\ninstances. We conclude with a selection of ideas for future work and\nextensions for DCPOP.\n2. PROBLEM DEFINITION\nDCOP has been formalized in slightly different ways in recent\nliterature, so we will adopt the definition as presented in [6]. A\nDistributed Constraint Optimization Problem with n nodes and m\nconstraints consists of the tuple < X, D, U > where:\n\u2022 X = {x1,..,xn} is a set of variables, each one assigned to a\nunique agent\n\u2022 D = {d1,..,dn} is a set of finite domains for each variable\n\u2022 U = {u1,..,um} is a set of utility functions such that each\nfunction involves a subset of variables in X and defines a\nutility for each combination of values among these variables\nAn optimal solution to a DCOP instance consists of an assignment\nof values in D to X such that the sum of utilities in U is maximal.\nProblem domains that require minimum cost instead of maximum\nutility can map costs into negative utilities. The utility functions\nrepresent soft constraints but can also represent hard constraints\nby using arbitrarily large negative values. For this paper we only\nconsider binary utility functions involving two variables. Higher\norder utility functions can be modeled with minor changes to the\nalgorithm, but they also substantially increase the complexity.\n2.1 Traditional Pseudotrees\nPseudotrees are a common structure used in search procedures\nto allow parallel processing of independent branches. As defined in\n[6], a pseudotree is an arrangement of a graph G into a rooted tree\nT such that vertices in G that share an edge are in the same branch\nin T. A back-edge is an edge between a node X and any node which\nlies on the path from X to the root (excluding X\"s parent). Figure 1\nshows a pseudotree with four nodes, three edges (A-B, B-C,\nBD), and one back-edge (A-C). Also defined in [6] are four types of\nrelationships between nodes exist in a pseudotree:\n\u2022 P(X) - the parent of a node X: the single node higher in the\npseudotree that is connected to X directly through a tree edge\n\u2022 C(X) - the children of a node X: the set of nodes lower in\nthe pseudotree that are connected to X directly through tree\nedges\n\u2022 PP(X) - the pseudo-parents of a node X: the set of nodes\nhigher in the pseudotree that are connected to X directly\nthrough back-edges (In Figure 1, A = PP(C))\n\u2022 PC(X) - the pseudo-children of a node X: the set of nodes\nlower in the pseudotree that are connected to X directly\nthrough back-edges (In Figure 1, C = PC(A))\nFigure 1: A traditional pseudotree. Solid line edges\nrepresent parent-child relationships and the dashed line represents\na pseudo-parent-pseudo-child relationship.\nFigure 2: A cross-edged pseudotree. Solid line edges represent\nparent-child relationships, the dashed line represents a\npseudoparent-pseudo-child relationship, and the dotted line\nrepresents a branch-parent-branch-child relationship. The bolded\nnode, B, is the merge point for node E.\n2.2 Cross-edged Pseudotrees\nWe define a cross-edge as an edge from node X to a node Y that is\nabove X but not in the path from X to the root. A cross-edged\npseudotree is a traditional pseudotree with the addition of cross-edges.\nFigure 2 shows a cross-edged pseudotree with a cross-edge (D-E).\nIn a cross-edged pseudotree we designate certain edges as primary.\nThe set of primary edges defines a spanning tree of the nodes. The\nparent, child, pseudo-parent, and pseudo-child relationships from\nthe traditional pseudotree are now defined in the context of this\nprimary edge spanning tree. This definition also yields two additional\ntypes of relationships that may exist between nodes:\n\u2022 BP(X) - the branch-parents of a node X: the set of nodes\nhigher in the pseudotree that are connected to X but are not\nin the primary path from X to the root (In Figure 2, D =\nBP(E))\n\u2022 BC(X) - the branch-children of a node X: the set of nodes\nlower in the pseudotree that are connected to X but are not in\nany primary path from X to any leaf node (In Figure 2, E =\nBC(D))\n2.3 Pseudotree Generation\n742 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nCurrent algorithms usually have a pre-execution phase to\ngenerate a traditional pseudotree from a general DCOP instance. Our\nDCPOP algorithm generates a cross-edged pseudotree in the same\nfashion. First, the DCOP instance < X, D, U > translates directly\ninto a graph with X as the set of vertices and an edge for each pair\nof variables represented in U. Next, various heuristics are used to\narrange this graph into a pseudotree. One common heuristic is to\nperform a guided depth-first search (DFS) as the resulting traversal\nis a pseudotree, and a DFS can easily be performed in a distributed\nfashion. We define an edge-traversal based method as any method\nthat produces a pseudotree in which all parent/child pairs share an\nedge in the original graph. This includes DFS, breadth-first search,\nand best-first search based traversals. Our heuristics that generate\ncross-edged pseudotrees use a distributed best-first search traversal.\n3. DPOP ALGORITHM\nThe original DPOP algorithm operates in three main phases. The\nfirst phase generates a traditional pseudotree from the DCOP\ninstance using a distributed algorithm. The second phase joins utility\nhypercubes from children and the local node and propagates them\ntowards the root. The third phase chooses an assignment for each\ndomain in a top down fashion beginning with the agent at the root\nnode.\nThe complexity of DPOP depends on the size of the largest\ncomputation and utility message during phase two. It has been shown\nthat this size directly corresponds to the induced width of the\npseudotree generated in phase one [6]. DPOP uses polynomial time\nheuristics to generate the pseudotree since finding the minimum\ninduced width pseudotree is NP-hard. Several distributed\nedgetraversal heuristics have been developed to find low width\npseudotrees [8]. At the end of the first phase, each agent knows its\nparent, children, pseudo-parents, and pseudo-children.\n3.1 Utility Propagation\nAgents located at leaf nodes in the pseudotree begin the process\nby calculating a local utility hypercube. This hypercube at node\nX contains summed utilities for each combination of values in the\ndomains for P(X) and PP(X). This hypercube has dimensional size\nequal to the number of pseudo-parents plus one. A message\ncontaining this hypercube is sent to P(X). Agents located at non-leaf\nnodes wait for all messages from children to arrive. Once the agent\nat node Y has all utility messages, it calculates its local utility\nhypercube which includes domains for P(Y), PP(Y), and Y. The local\nutility hypercube is then joined with all of the hypercubes from\nthe child messages. At this point all utilities involving node Y are\nknown, and the domain for Y may be safely eliminated from the\njoined hypercube. This elimination process chooses the best utility\nover the domain of Y for each combination of the remaining\ndomains. A message containing this hypercube is now sent to P(Y).\nThe dimensional size of this hypercube depends on the number of\noverlapping domains in received messages and the local utility\nhypercube. This dynamic programming based propagation phase\ncontinues until the agent at the root node of the pseudotree has received\nall messages from its children.\n3.2 Value Propagation\nValue propagation begins when the agent at the root node Z has\nreceived all messages from its children. Since Z has no parents\nor pseudo-parents, it simply combines the utility hypercubes\nreceived from its children. The combined hypercube contains only\nvalues for the domain for Z. At this point the agent at node Z\nsimply chooses the assignment for its domain that has the best utility.\nA value propagation message with this assignment is sent to each\nnode in C(Z). Each other node then receives a value propagation\nmessage from its parent and chooses the assignment for its domain\nthat has the best utility given the assignments received in the\nmessage. The node adds its domain assignment to the assignments it\nreceived and passes the set of assignments to its children. The\nalgorithm is complete when all nodes have chosen an assignment for\ntheir domain.\n4. DCPOP ALGORITHM\nOur extension to the original DPOP algorithm, shown in\nAlgorithm 1, shares the same three phases. The first phase generates the\ncross-edged pseudotree for the DCOP instance. The second phase\nmerges branches and propagates the utility hypercubes. The third\nphase chooses assignments for domains at branch merge points and\nin a top down fashion, beginning with the agent at the root node.\nFor the first phase we generate a pseudotree using several\ndistributed heuristics and select the one with lowest overall\ncomplexity. The complexity of the computation and utility message size\nin DCPOP does not directly correspond to the induced width of\nthe cross-edged pseudotree. Instead, we use a polynomial time\nmethod for calculating the maximum computation and utility\nmessage size for a given cross-edged pseudotree. A description of\nthis method and the pseudotree selection process appears in\nSection 5. At the end of the first phase, each agent knows its\nparent, children, pseudo-parents, pseudo-children, branch-parents, and\nbranch-children.\n4.1 Merging Branches and Utility\nPropagation\nIn the original DPOP algorithm a node X only had utility\nfunctions involving its parent and its pseudo-parents. In DCPOP, a node\nX is allowed to have a utility function involving a branch-parent.\nThe concept of a branch can be seen in Figure 2 with node E\nrepresenting our node X. The two distinct paths from node E to node\nB are called branches of E. The single node where all branches of\nE meet is node B, which is called the merge point of E.\nAgents with nodes that have branch-parents begin by sending\na utility propagation message to each branch-parent. This\nmessage includes a two dimensional utility hypercube with domains for\nthe node X and the branch-parent BP(X). It also includes a branch\ninformation structure which contains the origination node of the\nbranch, X, the total number of branches originating from X, and the\nnumber of branches originating from X that are merged into a\nsingle representation by this branch information structure (this\nnumber starts at 1). Intuitively when the number of merged branches\nequals the total number of originating branches, the algorithm has\nreached the merge point for X. In Figure 2, node E sends a utility\npropagation message to its branch-parent, node D. This message\nhas dimensions for the domains of E and D, and includes branch\ninformation with an origin of E, 2 total branches, and 1 merged\nbranch.\nAs in the original DPOP utility propagation phase, an agent at\nleaf node X sends a utility propagation message to its parent. In\nDCPOP this message contains dimensions for the domains of P(X)\nand PP(X). If node X also has branch-parents, then the utility\npropagation message also contains a dimension for the domain of X,\nand will include a branch information structure. In Figure 2, node\nE sends a utility propagation message to its parent, node C. This\nmessage has dimensions for the domains of E and C, and includes\nbranch information with an origin of E, 2 total branches, and 1\nmerged branch.\nWhen a node Y receives utility propagation messages from all of\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 743\nits children and branch-children, it merges any branches with the\nsame origination node X. The merged branch information structure\naccumulates the number of merged branches for X. If the\ncumulative total number of merged branches equals the total number of\nbranches, then Y is the merge point for X. This means that the\nutility hypercubes present at Y contain all information about the\nvaluations for utility functions involving node X. In addition to the\ntypical elimination of the domain of Y from the utility hypercubes,\nwe can now safely eliminate the domain of X from the utility\nhypercubes. To illustrate this process, we will examine what happens\nin the second phase for node B in Figure 2.\nIn the second phase Node B receives two utility propagation\nmessages. The first comes from node C and includes dimensions\nfor domains E, B, and A. It also has a branch information structure\nwith origin of E, 2 total branches, and 1 merged branch. The second\ncomes from node D and includes dimensions for domains E and B.\nIt also has a branch information structure with origin of E, 2 total\nbranches, and 1 merged branch. Node B then merges the branch\ninformation structures from both messages because they have the\nsame origination, node E. Since the number of merged branches\noriginating from E is now 2 and the total branches originating from\nE is 2, node B now eliminates the dimensions for domain E. Node\nB also eliminates the dimension for its own domain, leaving only\ninformation about domain A. Node B then sends a utility\npropagation message to node A, containing only one dimension for the\ndomain of A.\nAlthough not possible in DPOP, this method of utility\npropagation and dimension elimination may produce hypercubes at node Y\nthat do not share any domains. In DCPOP we do not join domain\nindependent hypercubes, but instead may send multiple hypercubes\nin the utility propagation message sent to the parent of Y. This lazy\napproach to joins helps to reduce message sizes.\n4.2 Value Propagation\nAs in DPOP, value propagation begins when the agent at the root\nnode Z has received all messages from its children. At this point\nthe agent at node Z chooses the assignment for its domain that has\nthe best utility. If Z is the merge point for the branches of some\nnode X, Z will also choose the assignment for the domain of X.\nThus any node that is a merge point will choose assignments for\na domain other than its own. These assignments are then passed\ndown the primary edge hierarchy. If node X in the hierarchy has\nbranch-parents, then the value assignment message from P(X) will\ncontain an assignment for the domain of X. Every node in the\nhierarchy adds any assignments it has chosen to the ones it received\nand passes the set of assignments to its children. The algorithm is\ncomplete when all nodes have chosen or received an assignment for\ntheir domain.\n4.3 Proof of Correctness\nWe will prove the correctness of DCPOP by first noting that\nDCPOP fully extends DPOP and then examining the two cases for\nvalue assignment in DCPOP. Given a traditional pseudotree as\ninput, the DCPOP algorithm execution is identical to DPOP. Using a\ntraditional pseudotree arrangement no nodes have branch-parents\nor branch-children since all edges are either back-edges or tree\nedges. Thus the DCPOP algorithm using a traditional pseudotree\nsends only utility propagation messages that contain domains\nbelonging to the parent or pseudo-parents of a node. Since no node\nhas any branch-parents, no branches exist, and thus no node serves\nas a merge point for any other node. Thus all value propagation\nassignments are chosen at the node of the assignment domain.\nFor DCPOP execution with cross-edged pseudotrees, some\nnodes serve as merge points. We note that any node X that is not a\nmerge point assigns its value exactly as in DPOP. The local utility\nhypercube at X contains domains for X, P(X), PP(X), and BC(X).\nAs in DPOP the value assignment message received at X includes\nthe values assigned to P(X) and PP(X). Also, since X is not a merge\npoint, all assignments to BC(X) must have been calculated at merge\npoints higher in the tree and are in the value assignment message\nfrom P(X). Thus after eliminating domains for which assignments\nare known, only the domain of X is left. The agent at node X can\nnow correctly choose the assignment with maximum utility for its\nown domain.\nIf node X is a merge point for some branch-child Y, we know\nthat X must be a node along the path from Y to the root, and from\nP(Y) and all BP(Y) to the root. From the algorithm, we know that\nY necessarily has all information from C(Y), PC(Y), and BC(Y)\nsince it waits for their messages. Node X has information about all\nnodes below it in the tree, which would include Y, P(Y), BP(Y),\nand those PP(Y) that are below X in the tree. For any PP(Y) above\nX in the tree, X receives the assignment for the domain of PP(Y)\nin the value assignment message from P(X). Thus X has utility\ninformation about all of the utility functions of which Y is a part.\nBy eliminating domains included in the value assignment message,\nnode X is left with a local utility hypercube with domains for X and\nY. The agent at node X can now correctly choose the assignments\nwith maximum utility for the domains of X and Y.\n4.4 Complexity Analysis\nThe first phase of DCPOP sends one message to each P(X),\nPP(X), and BP(X). The second phase sends one value assignment\nmessage to each C(X). Thus, DCPOP produces a linear number of\nmessages with respect to the number of edges (utility functions) in\nthe cross-edged pseudotree and the original DCOP instance. The\nactual complexity of DCPOP depends on two additional\nmeasurements: message size and computation size.\nMessage size and computation size in DCPOP depend on the\nnumber of overlapping branches as well as the number of\noverlapping back-edges. It was shown in [6] that the number of\noverlapping back-edges is equal to the induced width of the pseudotree. In\na poorly constructed cross-edged pseudotree, the number of\noverlapping branches at node X can be as large as the total number\nof descendants of X. Thus, the total message size in DCPOP in a\npoorly constructed instance can be space-exponential in the total\nnumber of nodes in the graph. However, in practice a well\nconstructed cross-edged pseudotree can achieve much better results.\nLater we address the issue of choosing well constructed\ncrossedged pseudotrees from a set.\nWe introduce an additional measurement of the maximum\nsequential path cost through the algorithm. This measurement\ndirectly relates to the maximum amount of parallelism achievable by\nthe algorithm. To take this measurement we first store the total\ncomputation size for each node during phase two and three. This\ncomputation size represents the number of individual accesses to a\nvalue in a hypercube at each node. For example, a join between two\ndomains of size 4 costs 4 \u2217 4 = 16. Two directed acyclic graphs\n(DAG) can then be drawn; one with the utility propagation\nmessages as edges and the phase two costs at nodes, and the other with\nvalue assignment messages and the phase three costs at nodes. The\nmaximum sequential path cost is equal to the sum of the longest\npath on each DAG from the root to any leaf node.\n5. HEURISTICS\nIn our assessment of complexity in DCPOP we focused on the\nworst case possibly produced by the algorithm. We acknowledge\n744 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nAlgorithm 1 DCPOP Algorithm\n1: DCPOP(X; D; U)\nEach agent Xi executes:\nPhase 1: pseudotree creation\n2: elect leader from all Xj \u2208 X\n3: elected leader initiates pseudotree creation\n4: afterwards, Xi knows P(Xi), PP(Xi), BP(Xi), C(Xi), BC(Xi)\nand PC(Xi)\nPhase 2: UTIL message propagation\n5: if |BP(Xi)| > 0 then\n6: BRANCHXi \u2190 |BP(Xi)| + 1\n7: for all Xk \u2208BP(Xi) do\n8: UTILXi (Xk) \u2190Compute utils(Xi, Xk)\n9: Send message(Xk,UTILXi (Xk),BRANCHXi )\n10: if |C(Xi)| = 0(i.e. Xi is a leaf node) then\n11: UTILXi (P(Xi)) \u2190 Compute utils(P(Xi),PP(Xi))\nfor all PP(Xi)\n12: Send message(P(Xi),\nUTILXi (P(Xi)),BRANCHXi )\n13: Send message(PP(Xi), empty UTIL,\nempty BRANCH) to all PP(Xi)\n14: activate UTIL Message handler()\nPhase 3: VALUE message propagation\n15: activate VALUE Message handler()\nEND ALGORITHM\nUTIL Message handler(Xk,UTILXk (Xi),\nBRANCHXk )\n16: store UTILXk (Xi),BRANCHXk (Xi)\n17: if UTIL messages from all children and branch children arrived\nthen\n18: for all Bj \u2208BRANCH(Xi) do\n19: if Bj is merged then\n20: join all hypercubes where Bj \u2208UTIL(Xi)\n21: eliminate Bj from the joined hypercube\n22: if P(Xi) == null (that means Xi is the root) then\n23: v \u2217 i \u2190 Choose optimal(null)\n24: Send VALUE(Xi, v \u2217 i) to all C(Xi)\n25: else\n26: UTILXi (P(Xi)) \u2190 Compute utils(P(Xi),\nPP(Xi))\n27: Send message(P(Xi),UTILXi (P(Xi)),\nBRANCHXi (P(Xi)))\nVALUE Message handler(VALUEXi ,P(Xi))\n28: add all Xk \u2190 v \u2217 k \u2208VALUEXi ,P(Xi) to agent view\n29: Xi \u2190 v \u2217 i =Choose optimal(agent view)\n30: Send VALUEXl , Xi to all Xl \u2208C(Xi)\nthat in real world problems the generation of the pseudotree has\na significant impact on the actual performance. The problem of\nfinding the best pseudotree for a given DCOP instance is NP-Hard.\nThus a heuristic is used for generation, and the performance of the\nalgorithm depends on the pseudotree found by the heuristic. Some\nprevious research focused on finding heuristics to generate good\npseudotrees [8]. While we have developed some heuristics that\ngenerate good cross-edged pseudotrees for use with DCPOP, our\nfocus has been to use multiple heuristics and then select the best\npseudotree from the generated pseudotrees.\nWe consider only heuristics that run in polynomial time with\nrespect to the number of nodes in the original DCOP instance. The\nactual DCPOP algorithm has worst case exponential complexity,\nbut we can calculate the maximum message size, computation size,\nand sequential path cost for a given cross-edged pseudotree in\nlinear space-time complexity. To do this, we simply run the algorithm\nwithout attempting to calculate any of the local utility hypercubes\nor optimal value assignments. Instead, messages include\ndimensional and branch information but no utility hypercubes.\nAfter each heuristic completes its generation of a pseudotree, we\nexecute the measurement procedure and propagate the\nmeasurement information up to the chosen root in that pseudotree. The\nroot then broadcasts the total complexity for that heuristic to all\nnodes. After all heuristics have had a chance to complete, every\nnode knows which heuristic produced the best pseudotree. Each\nnode then proceeds to begin the DCPOP algorithm using its\nknowledge of the pseudotree generated by the best heuristic.\nThe heuristics used to generate traditional pseudotrees perform\na distributed DFS traversal. The general distributed algorithm uses\na token passing mechanism and a linear number of messages.\nImproved DFS based heuristics use a special procedure to choose the\nroot node, and also provide an ordering function over the neighbors\nof a node to determine the order of path recursion. The DFS based\nheuristics used in our experiments come from the work done in [4,\n8].\n5.1 The best-first cross-edged pseudotree\nheuristic\nThe heuristics used to generate cross-edged pseudotrees\nperform a best-first traversal. A general distributed best-first\nalgorithm for node expansion is presented in Algorithm 2. An\nevaluation function at each node provides the values that are used to\ndetermine the next best node to expand. Note that in this\nalgorithm each node only exchanges its best value with its neighbors.\nIn our experiments we used several evaluation functions that took\nas arguments an ordered list of ancestors and a node, which\ncontains a list of neighbors (with each neighbor\"s placement depth in\nthe tree if it was placed). From these we can calculate\nbranchparents, branch-children, and unknown relationships for a potential\nnode placement. The best overall function calculated the value as\nancestors\u2212(branchparents+branchchildren) with the\nnumber of unknown relationships being a tiebreak. After completion\neach node has knowledge of its parent and ancestors, so it can\neasily determine which connected nodes are pseudo-parents,\nbranchparents, pseudo-children, and branch-children.\nThe complexity of the best-first traversal depends on the\ncomplexity of the evaluation function. Assuming a complexity of O(V )\nfor the evaluation function, which is the case for our best\noverall function, the best-first traversal is O(V \u00b7 E) which is at worst\nO(n3\n). For each v \u2208 V we perform a place operation, and find the\nnext node to place using the getBestNeighbor operation. The place\noperation is at most O(V ) because of the sent messages.\nFinding the next node uses recursion and traverses only already placed\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 745\nAlgorithm 2 Distributed Best-First Search Algorithm\nroot \u2190 electedleader\nnext(root, \u2205)\nplace(node, parent)\nnode.parent \u2190 parent\nnode.ancestors \u2190 parent.ancestors \u222a parent\nsend placement message (node, node.ancestors) to all\nneighbors of node\nnext(current, previous)\nif current is not placed then\nplace(current, previous)\nnext(current, \u2205)\nelse\nbest \u2190 getBestNeighbor(current, previous)\nif best = \u2205 then\nif previous = \u2205 then\nterminate, all nodes are placed\nnext(previous, \u2205)\nelse\nnext(best, current)\ngetBestNeighbor(current, previous)\nbest \u2190 \u2205; score \u2190 0\nfor all n \u2208 current.neighbors do\nif n! = previous then\nif n is placed then\nnscore \u2190 getBestNeighbor(n, current)\nelse\nnscore \u2190 evaluate(current, n)\nif nscore > score then\nscore \u2190 nscore\nbest \u2190 n\nreturn best, score\nnodes, so it has O(V ) recursions. Each recursion performs a\nrecursive getBestNeighbor operation that traverses all placed nodes\nand their neighbors. This operation is O(V \u00b7 E), but results can\nbe cached using only O(V ) space at each node. Thus we have\nO(V \u00b7(V +V +V \u00b7E)) = O(V 2\n\u00b7E). If we are smart about evaluating\nlocal changes when each node receives placement messages from\nits neighbors and cache the results the getBestNeighbor operation\nis only O(E). This increases the complexity of the place operation,\nbut for all placements the total complexity is only O(V \u00b7 E). Thus\nwe have an overall complexity of O(V \u00b7E+V \u00b7(V +E)) = O(V \u00b7E).\n6. COMPARISON OF COMPLEXITY IN\nDPOP AND DCPOP\nWe have already shown that given the same input, DCPOP\nperforms the same as DPOP. We also have shown that we can\naccurately predict performance of a given pseudotree in linear\nspacetime complexity. If we use a constant number of heuristics to\ngenerate the set of pseudotrees, we can choose the best pseudotree in\nlinear space-time complexity. We will now show that there exists\na DCOP instance for which a cross-edged pseudotree outperforms\nall possible traditional pseudotrees (based on edge-traversal\nheuristics).\nIn Figure 3(a) we have a DCOP instance with six nodes. This\nis a bipartite graph with each partition fully connected to the other\n(a) (b) (c)\nFigure 3: (a) The DCOP instance (b) A traditional pseudotree\narrangement for the DCOP instance (c) A cross-edged\npseudotree arrangement for the DCOP instance\npartition. In Figure 3(b) we see a traditional pseudotree\narrangement for this DCOP instance. It is easy to see that any\nedgetraversal based heuristic cannot expand two nodes from the same\npartition in succession. We also see that no node can have more\nthan one child because any such arrangement would be an invalid\npseudotree. Thus any traditional pseudotree arrangement for this\nDCOP instance must take the form of Figure 3(b). We can see that\nthe back-edges F-B and F-A overlap node C. Node C also has a\nparent E, and a back-edge with D. Using the original DPOP\nalgorithm (or DCPOP since they are identical in this case), we find that\nthe computation at node C involves five domains: A, B, C, D, and\nE.\nIn contrast, the cross-edged pseudotree arrangement in\nFigure 3(c) requires only a maximum of four domains in any\ncomputation during DCPOP. Since node A is the merge point for branches\nfrom both B and C, we can see that each of the nodes D, E, and F\nhave two overlapping branches. In addition each of these nodes has\nnode A as its parent. Using the DCPOP algorithm we find that the\ncomputation at node D (or E or F) involves four domains: A, B, C,\nand D (or E or F).\nSince no better traditional pseudotree arrangement can be\ncreated using an edge-traversal heuristic, we have shown that DCPOP\ncan outperform DPOP even if we use the optimal pseudotree found\nthrough edge-traversal. We acknowledge that pseudotree\narrangements that allow parent-child relationships without an actual\nconstraint can solve the problem in Figure 3(a) with maximum\ncomputation size of four domains. However, current heuristics used\nwith DPOP do not produce such pseudotrees, and such a heuristic\nwould be difficult to distribute since each node would require\ninformation about nodes with which it has no constraint. Also, while we\ndo not prove it here, cross-edged pseudotrees can produce smaller\nmessage sizes than such pseudotrees even if the computation size\nis similar. In practice, since finding the best pseudotree\narrangement is NP-Hard, we find that heuristics that produce cross-edged\npseudotrees often produce significantly smaller computation and\nmessage sizes.\n7. EXPERIMENTAL RESULTS\n746 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nExisting performance metrics for DCOP algorithms include the\ntotal number of messages, synchronous clock cycles, and message\nsize. We have already shown that the total number of messages is\nlinear with respect to the number of constraints in the DCOP\ninstance. We also introduced the maximum sequential path cost (PC)\nas a measurement of the maximum amount of parallelism\nachievable by the algorithm. The maximum sequential path cost is equal\nto the sum of the computations performed on the longest path from\nthe root to any leaf node. We also include as metrics the\nmaximum computation size in number of dimensions (CD) and\nmaximum message size in number of dimensions (MD). To analyze the\nrelative complexity of a given DCOP instance, we find the\nminimum induced width (IW) of any traditional pseudotree produced\nby a heuristic for the original DPOP.\n7.1 Generic DCOP instances\nFor our initial tests we randomly generated two sets of problems\nwith 3000 cases in each. Each problem was generated by\nassigning a random number (picked from a range) of constraints to each\nvariable. The generator then created binary constraints until each\nvariable reached its maximum number of constraints. The first set\nuses 20 variables, and the best DPOP IW ranges from 1 to 16 with\nan average of 8.5. The second set uses 100 variables, and the best\nDPOP IW ranged from 2 to 68 with an average of 39.3. Since most\nof the problems in the second set were too complex to actually\ncompute the solution, we took measurements of the metrics using the\ntechniques described earlier in Section 5 without actually solving\nthe problem. Results are shown for the first set in Table 1 and for\nthe second set in Table 2.\nFor the two problem sets we split the cases into low density and\nhigh density categories. Low density cases consist of those\nproblems that have a best DPOP IW less than or equal to half of the\ntotal number of nodes (e.g. IW \u2264 10 for the 20 node problems\nand IW \u2264 50 for the 100 node problems). High density problems\nconsist of the remainder of the problem sets.\nIn both Table 1 and Table 2 we have listed performance\nmetrics for the original DPOP algorithm, the DCPOP algorithm using\nonly cross-edged pseudotrees (DCPOP-CE), and the DCPOP\nalgorithm using traditional and cross-edged pseudotrees (DCPOP-All).\nThe pseudotrees used for DPOP were generated using 5\nheuristics: DFS, DFS MCN, DFS CLIQUE MCN, DFS MCN DSTB,\nand DFS MCN BEC. These are all versions of the guided DFS\ntraversal discussed in Section 5. The cross-edged pseudotrees used\nfor DCPOP-CE were generated using 5 heuristics: MCN, LCN,\nMCN A-B, LCN A-B, and LCSG A-B. These are all versions of\nthe best-first traversal discussed in Section 5.\nFor both DPOP and DCPOP-CE we chose the best pseudotree\nproduced by their respective 5 heuristics for each problem in the\nset. For DCPOP-All we chose the best pseudotree produced by all\n10 heuristics for each problem in the set. For the CD and MD\nmetrics the value shown is the average number of dimensions. For the\nPC metric the value shown is the natural logarithm of the\nmaximum sequential path cost (since the actual value grows\nexponentially with the complexity of the problem).\nThe final row in both tables is a measurement of improvement\nof DCPOP-All over DPOP. For the CD and MD metrics the value\nshown is a reduction in number of dimensions. For the PC metric\nthe value shown is a percentage reduction in the maximum\nsequential path cost (% = DP OP \u2212DCP OP\nDCP OP\n\u2217 100). Notice that\nDCPOPAll outperforms DPOP on all metrics. This logically follows from\nour earlier assertion that given the same input, DCPOP performs\nexactly the same as DPOP. Thus given the choice between the\npseudotrees produced by all 10 heuristics, DCPOP-All will always\noutLow Density High Density\nAlgorithm CD MD PC CD MD PC\nDPOP 7.81 6.81 3.78 13.34 12.34 5.34\nDCPOP-CE 7.94 6.73 3.74 12.83 11.43 5.07\nDCPOP-All 7.62 6.49 3.66 12.72 11.36 5.05\nImprovement 0.18 0.32 13% 0.62 0.98 36%\nTable 1: 20 node problems\nLow Density High Density\nAlgorithm CD MD PC CD MD PC\nDPOP 33.35 32.35 14.55 58.51 57.50 19.90\nDCPOP-CE 33.49 29.17 15.22 57.11 50.03 20.01\nDCPOP-All 32.35 29.57 14.10 56.33 51.17 18.84\nImprovement 1.00 2.78 104% 2.18 6.33 256%\nTable 2: 100 node problems\nFigure 4: Computation Dimension Size\nFigure 5: Message Dimension Size\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 747\nFigure 6: Path Cost\nDCPOP Improvement\nAg Mtg Vars Const IW CD MD PC\n10 4 12 13.5 2.25 -0.01 -0.01 5.6%\n30 14 44 57.6 3.63 0.09 0.09 10.9%\n50 24 76 101.3 4.17 0.08 0.09 10.7%\n100 49 156 212.9 5.04 0.16 0.20 30.0%\n150 74 236 321.8 5.32 0.21 0.23 35.8%\n200 99 316 434.2 5.66 0.18 0.22 29.5%\nTable 3: Meeting Scheduling Problems\nperform DPOP. Another trend we notice is that the improvement is\ngreater for high density problems than low density problems. We\nshow this trend in greater detail in Figures 4, 5, and 6. Notice\nhow the improvement increases as the complexity of the problem\nincreases.\n7.2 Meeting Scheduling Problem\nIn addition to our initial generic DCOP tests, we ran a series\nof tests on the Meeting Scheduling Problem (MSP) as described\nin [6]. The problem setup includes a number of people that are\ngrouped into departments. Each person must attend a specified\nnumber of meetings. Meetings can be held within departments or\namong departments, and can be assigned to one of eight time slots.\nThe MSP maps to a DCOP instance where each variable represents\nthe time slot that a specific person will attend a specific meeting.\nAll variables that belong to the same person have mutual exclusion\nconstraints placed so that the person cannot attend more than one\nmeeting during the same time slot. All variables that belong to the\nsame meeting have equality constraints so that all of the\nparticipants choose the same time slot. Unary constraints are placed on\neach variable to account for a person\"s valuation of each meeting\nand time slot.\nFor our tests we generated 100 sample problems for each\ncombination of agents and meetings. Results are shown in Table 3. The\nvalues in the first five columns represent (in left to right order), the\ntotal number of agents, the total number of meetings, the total\nnumber of variables, the average total number of constraints, and the\naverage minimum IW produced by a traditional pseudotree. The\nlast three columns show the same metrics we used for the generic\nDCOP instances, except this time we only show the improvements\nof DCPOP-All over DPOP. Performance is better on average for\nall MSP instances, but again we see larger improvements for more\ncomplex problem instances.\n8. CONCLUSIONS AND FUTURE WORK\nWe presented a complete, distributed algorithm that solves\ngeneral DCOP instances using cross-edged pseudotree arrangements.\nOur algorithm extends the DPOP algorithm by adding additional\nutility propagation messages, and introducing the concept of branch\nmerging during the utility propagation phase. Our algorithm also\nallows value assignments to occur at higher level merge points\nfor lower level nodes. We have shown that DCPOP fully extends\nDPOP by performing the same operations given the same input.\nWe have also shown through some examples and experimental data\nthat DCPOP can achieve greater performance for some problem\ninstances by extending the allowable input set to include cross-edged\npseudotrees.\nWe placed particular emphasis on the role that edge-traversal\nheuristics play in the generation of pseudotrees. We have shown\nthat the performance penalty is minimal to generate multiple\nheuristics, and that we can choose the best generated pseudotree\nin linear space-time complexity. Given the importance of a good\npseudotree for performance, future work will include new\nheuristics to find better pseudotrees. Future work will also include\nadapting existing DPOP extensions [5, 7] that support different problem\ndomains for use with DCPOP.\n9. REFERENCES\n[1] J. Liu and K. P. Sycara. Exploiting problem structure for\ndistributed constraint optimization. In V. Lesser, editor,\nProceedings of the First International Conference on\nMulti-Agent Systems, pages 246-254, San Francisco, CA,\n1995. MIT Press.\n[2] P. J. Modi, H. Jung, M. Tambe, W.-M. Shen, and S. Kulkarni.\nA dynamic distributed constraint satisfaction approach to\nresource allocation. Lecture Notes in Computer Science,\n2239:685-700, 2001.\n[3] P. J. Modi, W. Shen, M. Tambe, and M. Yokoo. An\nasynchronous complete method for distributed constraint\noptimization. In AAMAS 03, 2003.\n[4] A. Petcu. Frodo: A framework for open/distributed\nconstraint optimization. Technical Report No. 2006/001\n2006/001, Swiss Federal Institute of Technology (EPFL),\nLausanne (Switzerland), 2006. http://liawww.epfl.ch/frodo/.\n[5] A. Petcu and B. Faltings. A-dpop: Approximations in\ndistributed optimization. In poster in CP 2005, pages\n802-806, Sitges, Spain, October 2005.\n[6] A. Petcu and B. Faltings. Dpop: A scalable method for\nmultiagent constraint optimization. In IJCAI 05, pages\n266-271, Edinburgh, Scotland, Aug 2005.\n[7] A. Petcu, B. Faltings, and D. Parkes. M-dpop: Faithful\ndistributed implementation of efficient social choice\nproblems. In AAMAS 06, pages 1397-1404, Hakodate,\nJapan, May 2006.\n[8] G. Ushakov. Solving meeting scheduling problems using\ndistributed pseudotree-optimization procedure. Master\"s\nthesis, \u00b4Ecole Polytechnique F\u00b4ed\u00b4erale de Lausanne, 2005.\n[9] M. Yokoo, E. H. Durfee, T. Ishida, and K. Kuwabara.\nDistributed constraint satisfaction for formalizing distributed\nproblem solving. In International Conference on Distributed\nComputing Systems, pages 614-621, 1992.\n[10] M. Yokoo, E. H. Durfee, T. Ishida, and K. Kuwabara. The\ndistributed constraint satisfaction problem: Formalization\nand algorithms. Knowledge and Data Engineering,\n10(5):673-685, 1998.\n748 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)", "keywords": "cross-edged pseudotree;teamwork coordination;distributed constraint optimization;job shop scheduling;agent;pseudotree arrangement;multi-agent coordination;edge-traversal heuristic;maximum sequential path cost;multi-valued utility function;distribute constraint satisfaction and optimization;multi-agent system;resource allocation;global utility"}
{"name": "train_I-43", "title": "Dynamics Based Control with an Application to Area-Sweeping Problems", "abstract": "In this paper we introduce Dynamics Based Control (DBC), an approach to planning and control of an agent in stochastic environments. Unlike existing approaches, which seek to optimize expected rewards (e.g., in Partially Observable Markov Decision Problems (POMDPs)), DBC optimizes system behavior towards specified system dynamics. We show that a recently developed planning and control approach, Extended Markov Tracking (EMT) is an instantiation of DBC. EMT employs greedy action selection to provide an efficient control algorithm in Markovian environments. We exploit this efficiency in a set of experiments that applied multitarget EMT to a class of area-sweeping problems (searching for moving targets). We show that such problems can be naturally defined and efficiently solved using the DBC framework, and its EMT instantiation.", "fulltext": "1. INTRODUCTION\nPlanning and control constitutes a central research area in\nmultiagent systems and artificial intelligence. In recent years, Partially\nObservable Markov Decision Processes (POMDPs) [12] have\nbecome a popular formal basis for planning in stochastic\nenvironments. In this framework, the planning and control problem is often\naddressed by imposing a reward function, and computing a policy\n(of choosing actions) that is optimal, in the sense that it will result\nin the highest expected utility. While theoretically attractive, the\ncomplexity of optimally solving a POMDP is prohibitive [8, 7].\nWe take an alternative view of planning in stochastic\nenvironments. We do not use a (state-based) reward function, but instead\noptimize over a different criterion, a transition-based specification\nof the desired system dynamics. The idea here is to view\nplanexecution as a process that compels a (stochastic) system to change,\nand a plan as a dynamic process that shapes that change according\nto desired criteria. We call this general planning framework\nDynamics Based Control (DBC).\nIn DBC, the goal of a planning (or control) process becomes to\nensure that the system will change in accordance with specific\n(potentially stochastic) target dynamics. As actual system behavior\nmay deviate from that which is specified by target dynamics (due\nto the stochastic nature of the system), planning in such\nenvironments needs to be continual [4], in a manner similar to classical\nclosed-loop controllers [16]. Here, optimality is measured in terms\nof probability of deviation magnitudes.\nIn this paper, we present the structure of Dynamics Based\nControl. We show that the recently developed Extended Markov\nTracking (EMT) approach [13, 14, 15] is subsumed by DBC, with EMT\nemploying greedy action selection, which is a specific\nparameterization among the options possible within DBC. EMT is an efficient\ninstantiation of DBC.\nTo evaluate DBC, we carried out a set of experiments applying\nmulti-target EMT to the Tag Game [11]; this is a variant on the\narea sweeping problem, where an agent is trying to tag a moving\ntarget (quarry) whose position is not known with certainty.\nExperimental data demonstrates that even with a simple model of the\nenvironment and a simple design of target dynamics, high success\nrates can be produced both in catching the quarry, and in surprising\nthe quarry (as expressed by the observed entropy of the controlled\nagent\"s position).\nThe paper is organized as follows. In Section 2 we motivate DBC\nusing area-sweeping problems, and discuss related work. Section 3\nintroduces the Dynamics Based Control (DBC) structure, and its\nspecialization to Markovian environments. This is followed by a\nreview of the Extended Markov Tracking (EMT) approach as a\nDBC-structured control regimen in Section 4. That section also\ndiscusses the limitations of EMT-based control relative to the\ngeneral DBC framework. Experimental settings and results are then\npresented in Section 5. Section 6 provides a short discussion of\nthe overall approach, and Section 7 gives some concluding remarks\nand directions for future work.\n790\n978-81-904262-7-5 (RPS) c 2007 IFAAMAS\n2. MOTIVATION AND RELATED WORK\nMany real-life scenarios naturally have a stochastic target\ndynamics specification, especially those domains where there exists\nno ultimate goal, but rather system behavior (with specific\nproperties) that has to be continually supported. For example, security\nguards perform persistent sweeps of an area to detect any sign of\nintrusion. Cunning thieves will attempt to track these sweeps, and\ntime their operation to key points of the guards\" motion. It is thus\nadvisable to make the guards\" motion dynamics appear irregular\nand random.\nRecent work by Paruchuri et al. [10] has addressed such\nrandomization in the context of single-agent and distributed POMDPs. The\ngoal in that work was to generate policies that provide a measure of\naction-selection randomization, while maintaining rewards within\nsome acceptable levels. Our focus differs from this work in that\nDBC does not optimize expected rewards-indeed we do not\nconsider rewards at all-but instead maintains desired dynamics\n(including, but not limited to, randomization).\nThe Game of Tag is another example of the applicability of the\napproach. It was introduced in the work by Pineau et al. [11]. There\nare two agents that can move about an area, which is divided into a\ngrid. The grid may have blocked cells (holes) into which no agent\ncan move. One agent (the hunter) seeks to move into a cell\noccupied by the other (the quarry), such that they are co-located (this is\na successful tag). The quarry seeks to avoid the hunter agent, and\nis always aware of the hunter\"s position, but does not know how the\nhunter will behave, which opens up the possibility for a hunter to\nsurprise the prey. The hunter knows the quarry\"s probabilistic law\nof motion, but does not know its current location. Tag is an instance\nof a family of area-sweeping (pursuit-evasion) problems.\nIn [11], the hunter modeled the problem using a POMDP. A\nreward function was defined, to reflect the desire to tag the quarry,\nand an action policy was computed to optimize the reward\ncollected over time. Due to the intractable complexity of determining\nthe optimal policy, the action policy computed in that paper was\nessentially an approximation.\nIn this paper, instead of formulating a reward function, we use\nEMT to solve the problem, by directly specifying the target\ndynamics. In fact, any search problem with randomized motion, the\nsocalled class of area sweeping problems, can be described through\nspecification of such target system dynamics. Dynamics Based\nControl provides a natural approach to solving these problems.\n3. DYNAMICS BASED CONTROL\nThe specification of Dynamics Based Control (DBC) can be\nbroken into three interacting levels: Environment Design Level, User\nLevel, and Agent Level.\n\u2022 Environment Design Level is concerned with the formal\nspecification and modeling of the environment. For\nexample, this level would specify the laws of physics within the\nsystem, and set its parameters, such as the gravitation\nconstant.\n\u2022 User Level in turn relies on the environment model produced\nby Environment Design to specify the target system\ndynamics it wishes to observe. The User Level also specifies the\nestimation or learning procedure for system dynamics, and the\nmeasure of deviation. In the museum guard scenario above,\nthese would correspond to a stochastic sweep schedule, and a\nmeasure of relative surprise between the specified and actual\nsweeping.\n\u2022 Agent Level in turn combines the environment model from\nthe Environment Design level, the dynamics estimation\nprocedure, the deviation measure and the target dynamics\nspecification from User Level, to produce a sequence of actions\nthat create system dynamics as close as possible to the\ntargeted specification.\nAs we are interested in the continual development of a stochastic\nsystem, such as happens in classical control theory [16] and\ncontinual planning [4], as well as in our example of museum sweeps,\nthe question becomes how the Agent Level is to treat the\ndeviation measurements over time. To this end, we use a probability\nthreshold-that is, we would like the Agent Level to maximize the\nprobability that the deviation measure will remain below a certain\nthreshold.\nSpecific action selection then depends on system formalization.\nOne possibility would be to create a mixture of available system\ntrends, much like that which happens in Behavior-Based Robotic\narchitectures [1]. The other alternative would be to rely on the\nestimation procedure provided by the User Level-to utilize the\nEnvironment Design Level model of the environment to choose actions,\nso as to manipulate the dynamics estimator into believing that a\ncertain dynamics has been achieved. Notice that this manipulation is\nnot direct, but via the environment. Thus, for strong enough\nestimator algorithms, successful manipulation would mean a successful\nsimulation of the specified target dynamics (i.e., beyond discerning\nvia the available sensory input).\nDBC levels can also have a back-flow of information (see\nFigure 1). For instance, the Agent Level could provide data about\ntarget dynamics feasibility, allowing the User Level to modify the\nrequirement, perhaps focusing on attainable features of system\nbehavior. Data would also be available about the system response to\ndifferent actions performed; combined with a dynamics estimator\ndefined by the User Level, this can provide an important tool for the\nenvironment model calibration at the Environment Design Level.\nUserEnv. Design Agent\nModel\nIdeal Dynamics\nEstimator\nEstimator\nDynamics Feasibility\nSystem Response Data\nFigure 1: Data flow of the DBC framework\nExtending upon the idea of Actor-Critic algorithms [5], DBC\ndata flow can provide a good basis for the design of a learning\nalgorithm. For example, the User Level can operate as an exploratory\ndevice for a learning algorithm, inferring an ideal dynamics target\nfrom the environment model at hand that would expose and verify\nmost critical features of system behavior. In this case, feasibility\nand system response data from the Agent Level would provide key\ninformation for an environment model update. In fact, the\ncombination of feasibility and response data can provide a basis for the\napplication of strong learning algorithms such as EM [2, 9].\n3.1 DBC for Markovian Environments\nFor a Partially Observable Markovian Environment, DBC can\nbe specified in a more rigorous manner. Notice how DBC discards\nrewards, and replaces it by another optimality criterion (structural\ndifferences are summarized in Table 1):\n\u2022 Environment Design level is to specify a tuple\n< S, A, T, O, \u03a9, s0 >, where:\n- S is the set of all possible environment states;\n- s0 is the initial state of the environment (which can also\nbe viewed as a probability distribution over S);\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 791\n- A is the set of all possible actions applicable in the\nenvironment;\n- T is the environment\"s probabilistic transition function:\nT : S \u00d7A \u2192 \u03a0(S). That is, T(s |a, s) is the\nprobability that the environment will move from state s to state\ns under action a;\n- O is the set of all possible observations. This is what\nthe sensor input would look like for an outside observer;\n- \u03a9 is the observation probability function:\n\u03a9 : S \u00d7 A \u00d7 S \u2192 \u03a0(O).\nThat is, \u03a9(o|s , a, s) is the probability that one will\nobserve o given that the environment has moved from\nstate s to state s under action a.\n\u2022 User Level, in the case of Markovian environment, operates\non the set of system dynamics described by a family of\nconditional probabilities F = {\u03c4 : S \u00d7 A \u2192 \u03a0(S)}. Thus\nspecification of target dynamics can be expressed by q \u2208 F,\nand the learning or tracking algorithm can be represented as\na function L : O\u00d7(A\u00d7O)\u2217\n\u2192 F; that is, it maps sequences\nof observations and actions performed so far into an estimate\n\u03c4 \u2208 F of system dynamics.\nThere are many possible variations available at the User Level\nto define divergence between system dynamics; several of\nthem are:\n- Trace distance or L1 distance between two\ndistributions p and q defined by\nD(p(\u00b7), q(\u00b7)) =\n1\n2 x\n|p(x) \u2212 q(x)|\n- Fidelity measure of distance\nF(p(\u00b7), q(\u00b7)) =\nx\np(x)q(x)\n- Kullback-Leibler divergence\nDKL(p(\u00b7) q(\u00b7)) =\nx\np(x) log\np(x)\nq(x)\nNotice that the latter two are not actually metrics over the\nspace of possible distributions, but nevertheless have\nmeaningful and important interpretations. For instance,\nKullbackLeibler divergence is an important tool of information\ntheory [3] that allows one to measure the price of encoding an\ninformation source governed by q, while assuming that it is\ngoverned by p.\nThe User Level also defines the threshold of dynamics\ndeviation probability \u03b8.\n\u2022 Agent Level is then faced with a problem of selecting a\ncontrol signal function a\u2217\nto satisfy a minimization problem as\nfollows:\na\u2217\n= arg min\na\nPr(d(\u03c4a, q) > \u03b8)\nwhere d(\u03c4a, q) is a random variable describing deviation of\nthe dynamics estimate \u03c4a, created by L under control signal\na, from the ideal dynamics q. Implicit in this minimization\nproblem is that L is manipulated via the environment, based\non the environment model produced by the Environment\nDesign Level.\n3.2 DBC View of the State Space\nIt is important to note the complementary view that DBC and\nPOMDPs take on the state space of the environment. POMDPs\nregard state as a stationary snap-shot of the environment;\nwhatever attributes of state sequencing one seeks are reached through\nproperties of the control process, in this case reward accumulation.\nThis can be viewed as if the sequencing of states and the attributes\nof that sequencing are only introduced by and for the controlling\nmechanism-the POMDP policy.\nDBC concentrates on the underlying principle of state\nsequencing, the system dynamics. DBC\"s target dynamics specification can\nuse the environment\"s state space as a means to describe, discern,\nand preserve changes that occur within the system. As a result,\nDBC has a greater ability to express state sequencing properties,\nwhich are grounded in the environment model and its state space\ndefinition.\nFor example, consider the task of moving through rough terrain\ntowards a goal and reaching it as fast as possible. POMDPs would\nencode terrain as state space points, while speed would be ensured\nby negative reward for every step taken without reaching the\ngoalaccumulating higher reward can be reached only by faster motion.\nAlternatively, the state space could directly include the notion of\nspeed. For POMDPs, this would mean that the same concept is\nencoded twice, in some sense: directly in the state space, and\nindirectly within reward accumulation. Now, even if the reward\nfunction would encode more, and finer, details of the properties of\nmotion, the POMDP solution will have to search in a much larger\nspace of policies, while still being guided by the implicit concept\nof the reward accumulation procedure.\nOn the other hand, the tactical target expression of variations and\ncorrelations between position and speed of motion is now grounded\nin the state space representation. In this situation, any further\nconstraints, e.g., smoothness of motion, speed limits in different\nlocations, or speed reductions during sharp turns, are explicitly and\nuniformly expressed by the tactical target, and can result in faster\nand more effective action selection by a DBC algorithm.\n4. EMT-BASED CONTROL AS A DBC\nRecently, a control algorithm was introduced called EMT-based\nControl [13], which instantiates the DBC framework. Although it\nprovides an approximate greedy solution in the DBC sense, initial\nexperiments using EMT-based control have been encouraging [14,\n15]. EMT-based control is based on the Markovian environment\ndefinition, as in the case with POMDPs, but its User and Agent\nLevels are of the Markovian DBC type of optimality.\n\u2022 User Level of EMT-based control defines a limited-case\ntarget system dynamics independent of action:\nqEMT : S \u2192 \u03a0(S).\nIt then utilizes the Kullback-Leibler divergence measure to\ncompose a momentary system dynamics estimator-the\nExtended Markov Tracking (EMT) algorithm. The algorithm\nkeeps a system dynamics estimate \u03c4t\nEMT that is capable of\nexplaining recent change in an auxiliary Bayesian system\nstate estimator from pt\u22121 to pt, and updates it conservatively\nusing Kullback-Leibler divergence. Since \u03c4t\nEMT and pt\u22121,t\nare respectively the conditional and marginal probabilities\nover the system\"s state space, explanation simply means\nthat\npt(s ) =\ns\n\u03c4t\nEMT (s |s)pt\u22121(s),\nand the dynamics estimate update is performed by solving a\n792 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nTable 1: Structure of POMDP vs. Dynamics-Based Control in Markovian Environment\nLevel\nApproach\nMDP Markovian DBC\nEnvironment\n< S, A, T, O, \u03a9 >,where\nS - set of states\nA - set of actions\nDesign\nT : S \u00d7 A \u2192 \u03a0(S) - transition\nO - observation set\n\u03a9 : S \u00d7 A \u00d7 S \u2192 \u03a0(O)\nUser\nr : S \u00d7 A \u00d7 S \u2192 R q : S \u00d7 A \u2192 \u03a0(S)\nF(\u03c0\u2217\n) \u2192 r L(o1, ..., ot) \u2192 \u03c4\nr - reward function q - ideal dynamics\nF - reward remodeling L - dynamics estimator\n\u03b8 - threshold\nAgent \u03c0\u2217\n= arg max\n\u03c0\nE[ \u03b3t\nrt] \u03c0\u2217\n= arg min\n\u03c0\nProb(d(\u03c4 q) > \u03b8)\nminimization problem:\n\u03c4t\nEMT = H[pt, pt\u22121, \u03c4t\u22121\nEMT ]\n= arg min\n\u03c4\nDKL(\u03c4 \u00d7 pt\u22121 \u03c4t\u22121\nEMT \u00d7 pt\u22121)\ns.t.\npt(s ) =\ns\n(\u03c4 \u00d7 pt\u22121)(s , s)\npt\u22121(s) =\ns\n(\u03c4 \u00d7 pt\u22121)(s , s)\n\u2022 Agent Level in EMT-based control is suboptimal with\nrespect to DBC (though it remains within the DBC\nframework), performing greedy action selection based on\nprediction of EMT\"s reaction. The prediction is based on the\nenvironment model provided by the Environment Design level,\nso that if we denote by Ta the environment\"s transition\nfunction limited to action a, and pt\u22121 is the auxiliary Bayesian\nsystem state estimator, then the EMT-based control choice is\ndescribed by\na\u2217\n= arg min\na\u2208A\nDKL(H[Ta \u00d7 pt, pt, \u03c4t\nEMT ] qEMT \u00d7 pt\u22121)\nNote that this follows the Markovian DBC framework precisely:\nthe rewarding optimality of POMDPs is discarded, and in its place\na dynamics estimator (EMT in this case) is manipulated via action\neffects on the environment to produce an estimate close to the\nspecified target system dynamics. Yet as we mentioned, naive\nEMTbased control is suboptimal in the DBC sense, and has several\nadditional limitations that do not exist in the general DBC framework\n(discussed in Section 4.2).\n4.1 Multi-Target EMT\nAt times, there may exist several behavioral preferences. For\nexample, in the case of museum guards, some art items are more\nheavily guarded, requiring that the guards stay more often in their\nclose vicinity. On the other hand, no corner of the museum is to\nbe left unchecked, which demands constant motion. Successful\nmuseum security would demand that the guards adhere to, and\nbalance, both of these behaviors. For EMT-based control, this would\nmean facing several tactical targets {qk}K\nk=1, and the question\nbecomes how to merge and balance them. A balancing mechanism\ncan be applied to resolve this issue.\nNote that EMT-based control, while selecting an action, creates\na preference vector over the set of actions based on their predicted\nperformance with respect to a given target. If these preference\nvectors are normalized, they can be combined into a single unified\npreference. This requires replacement of standard EMT-based action\nselection by the algorithm below [15]:\n\u2022 Given:\n- a set of target dynamics {qk}K\nk=1,\n- vector of weights w(k)\n\u2022 Select action as follows\n- For each action a \u2208 A predict the future state\ndistribution \u00afpa\nt+1 = Ta \u2217 pt;\n- For each action, compute\nDa = H(\u00afpa\nt+1, pt, PDt)\n- For each a \u2208 A and qk tactical target, denote\nV (a, k) = DKL (Da qk) pt\n.\nLet Vk(a) = 1\nZk\nV (a, k), where Zk =\na\u2208A\nV (a, k) is\na normalization factor.\n- Select a\u2217\n= arg min\na\nk\nk=1 w(k)Vk(a)\nThe weights vector w = (w1, ..., wK ) allows the additional\ntuning of importance among target dynamics without the need\nto redesign the targets themselves. This balancing method is also\nseamlessly integrated into the EMT-based control flow of\noperation.\n4.2 EMT-based Control Limitations\nEMT-based control is a sub-optimal (in the DBC sense)\nrepresentative of the DBC structure. It limits the User by forcing EMT to\nbe its dynamic tracking algorithm, and replaces Agent optimization\nby greedy action selection. This kind of combination, however, is\ncommon for on-line algorithms. Although further development of\nEMT-based controllers is necessary, evidence so far suggests that\neven the simplest form of the algorithm possesses a great deal of\npower, and displays trends that are optimal in the DBC sense of the\nword.\nThere are two further, EMT-specific, limitations to EMT-based\ncontrol that are evident at this point. Both already have partial\nsolutions and are subjects of ongoing research.\nThe first limitation is the problem of negative preference. In the\nPOMDP framework for example, this is captured simply, through\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 793\nthe appearance of values with different signs within the reward\nstructure. For EMT-based control, however, negative preference\nmeans that one would like to avoid a certain distribution over\nsystem development sequences; EMT-based control, however,\nconcentrates on getting as close as possible to a distribution. Avoidance is\nthus unnatural in native EMT-based control.\nThe second limitation comes from the fact that standard\nenvironment modeling can create pure sensory actions-actions that do\nnot change the state of the world, and differ only in the way\nobservations are received and the quality of observations received. Since\nthe world state does not change, EMT-based control would not be\nable to differentiate between different sensory actions.\nNotice that both of these limitations of EMT-based control are\nabsent from the general DBC framework, since it may have a\ntracking algorithm capable of considering pure sensory actions and,\nunlike Kullback-Leibler divergence, a distribution deviation measure\nthat is capable of dealing with negative preference.\n5. EMT PLAYING TAG\nThe Game of Tag was first introduced in [11]. It is a single agent\nproblem of capturing a quarry, and belongs to the class of area\nsweeping problems. An example domain is shown in Figure 2.\n0 51 2 3 4 6\n7 8 10 12 13\n161514\n17 18 19\n2221\n23\n9 11Q A\n20\nFigure 2: Tag domain; an agent (A) attempts to seek and\ncapture a quarry (Q)\nThe Game of Tag extremely limits the agent\"s perception, so that\nthe agent is able to detect the quarry only if they are co-located in\nthe same cell of the grid world. In the classical version of the game,\nco-location leads to a special observation, and the \u2018Tag\" action can\nbe performed. We slightly modify this setting: the moment that\nboth agents occupy the same cell, the game ends. As a result, both\nthe agent and its quarry have the same motion capability, which\nallows them to move in four directions, North, South, East, and\nWest. These form a formal space of actions within a Markovian\nenvironment.\nThe state space of the formal Markovian environment is described\nby the cross-product of the agent and quarry\"s positions. For\nFigure 2, it would be S = {s0, ..., s23} \u00d7 {s0, ..., s23}.\nThe effects of an action taken by the agent are deterministic, but\nthe environment in general has a stochastic response due to the\nmotion of the quarry. With probability q0\n1\nit stays put, and with\nprobability 1 \u2212 q0 it moves to an adjacent cell further away from the\n1\nIn our experiments this was taken to be q0 = 0.2.\nagent. So for the instance shown in Figure 2 and q0 = 0.1:\nP(Q = s9|Q = s9, A = s11) = 0.1\nP(Q = s2|Q = s9, A = s11) = 0.3\nP(Q = s8|Q = s9, A = s11) = 0.3\nP(Q = s14|Q = s9, A = s11) = 0.3\nAlthough the evasive behavior of the quarry is known to the\nagent, the quarry\"s position is not. The only sensory information\navailable to the agent is its own location.\nWe use EMT and directly specify the target dynamics. For the\nGame of Tag, we can easily formulate three major trends: catching\nthe quarry, staying mobile, and stalking the quarry. This results in\nthe following three target dynamics:\nTcatch(At+1 = si|Qt = sj, At = sa) \u221d\n1 si = sj\n0 otherwise\nTmobile(At+1 = si|Qt = so, At = sj) \u221d\n0 si = sj\n1 otherwise\nTstalk(At+1 = si|Qt = so, At = sj) \u221d 1\ndist(si,so)\nNote that none of the above targets are directly achievable; for\ninstance, if Qt = s9 and At = s11, there is no action that can move\nthe agent to At+1 = s9 as required by the Tcatch target dynamics.\nWe ran several experiments to evaluate EMT performance in the\nTag Game. Three configurations of the domain shown in Figure 3\nwere used, each posing a different challenge to the agent due to\npartial observability. In each setting, a set of 1000 runs was performed\nwith a time limit of 100 steps. In every run, the initial position of\nboth the agent and its quarry was selected at random; this means\nthat as far as the agent was concerned, the quarry\"s initial position\nwas uniformly distributed over the entire domain cell space.\nWe also used two variations of the environment observability\nfunction. In the first version, observability function mapped all\njoint positions of hunter and quarry into the position of the hunter as\nan observation. In the second, only those joint positions in which\nhunter and quarry occupied different locations were mapped into\nthe hunter\"s location. The second version in fact utilized and\nexpressed the fact that once hunter and quarry occupy the same cell\nthe game ends.\nThe results of these experiments are shown in Table 2.\nBalancing [15] the catch, move, and stalk target dynamics described in\nthe previous section by the weight vector [0.8, 0.1, 0.1], EMT\nproduced stable performance in all three domains.\nAlthough direct comparisons are difficult to make, the EMT\nperformance displayed notable efficiency vis-`a-vis the POMDP\napproach. In spite of a simple and inefficient Matlab implementation\nof the EMT algorithm, the decision time for any given step\naveraged significantly below 1 second in all experiments. For the\nirregular open arena domain, which proved to be the most difficult, 1000\nexperiment runs bounded by 100 steps each, a total of 42411 steps,\nwere completed in slightly under 6 hours. That is, over 4 \u00d7 104\nonline steps took an order of magnitude less time than the offline\ncomputation of POMDP policy in [11]. The significance of this\ndifferential is made even more prominent by the fact that, should the\nenvironment model parameters change, the online nature of EMT\nwould allow it to maintain its performance time, while the POMDP\npolicy would need to be recomputed, requiring yet again a large\noverhead of computation.\nWe also tested the behavior cell frequency entropy, empirical\nmeasures from trial data. As Figure 4 and Figure 5 show,\nempir794 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nA\nQ\nQ A\n0 1 2 3 4\n5 6 7 8 9\n10 11 12\n13 14 15\n16 17 18\nA\nQ\nFigure 3: These configurations of the Tag Game space were used: a) multiple dead-end, b) irregular open arena, c) circular corridor\nTable 2: Performance of the EMT-based solution in three Tag\nGame domains and two observability models: I) omniposition\nquarry, II) quarry is not at hunter\"s position\nModel Domain Capture% E(Steps) Time/Step\nI\nDead-ends 100 14.8 72(mSec)\nArena 80.2 42.4 500(mSec)\nCircle 91.4 34.6 187(mSec)\nII\nDead-ends 100 13.2 91(mSec)\nArena 96.8 28.67 396(mSec)\nCircle 94.4 31.63 204(mSec)\nical entropy grows with the length of interaction. For runs where\nthe quarry was not captured immediately, the entropy reaches\nbetween 0.85 and 0.952\nfor different runs and scenarios. As the agent\nactively seeks the quarry, the entropy never reaches its maximum.\nOne characteristic of the entropy graph for the open arena\nscenario particularly caught our attention in the case of the\nomniposition quarry observation model. Near the maximum limit of trial\nlength (100 steps), entropy suddenly dropped. Further analysis of\nthe data showed that under certain circumstances, a fluctuating\nbehavior occurs in which the agent faces equally viable versions of\nquarry-following behavior. Since the EMT algorithm has greedy\naction selection, and the state space does not encode any form of\ncommitment (not even speed or acceleration), the agent is locked\nwithin a small portion of cells. It is essentially attempting to\nsimultaneously follow several courses of action, all of which are\nconsistent with the target dynamics. This behavior did not occur in our\nsecond observation model, since it significantly reduced the set of\neligible courses of action-essentially contributing to tie-breaking\namong them.\n6. DISCUSSION\nThe design of the EMT solution for the Tag Game exposes the\ncore difference in approach to planning and control between EMT\nor DBC, on the one hand, and the more familiar POMDP approach,\non the other. POMDP defines a reward structure to optimize, and\ninfluences system dynamics indirectly through that optimization.\nEMT discards any reward scheme, and instead measures and\ninfluences system dynamics directly.\n2\nEntropy was calculated using log base equal to the number of\npossible locations within the domain; this properly scales entropy\nexpression into the range [0, 1] for all domains.\nThus for the Tag Game, we did not search for a reward function\nthat would encode and express our preference over the agent\"s\nbehavior, but rather directly set three (heuristic) behavior preferences\nas the basis for target dynamics to be maintained. Experimental\ndata shows that these targets need not be directly achievable via the\nagent\"s actions. However, the ratio between EMT performance and\nachievability of target dynamics remains to be explored.\nThe tag game experiment data also revealed the different\nemphasis DBC and POMDPs place on the formulation of an environment\nstate space. POMDPs rely entirely on the mechanism of reward\naccumulation maximization, i.e., formation of the action selection\nprocedure to achieve necessary state sequencing. DBC, on the\nother hand, has two sources of sequencing specification: through\nthe properties of an action selection procedure, and through direct\nspecification within the target dynamics. The importance of the\nsecond source was underlined by the Tag Game experiment data,\nin which the greedy EMT algorithm, applied to a POMDP-type\nstate space specification, failed, since target description over such a\nstate space was incapable of encoding the necessary behavior\ntendencies, e.g., tie-breaking and commitment to directed motion.\nThe structural differences between DBC (and EMT in\nparticular), and POMDPs, prohibits direct performance comparison, and\nplaces them on complementary tracks, each within a suitable niche.\nFor instance, POMDPs could be seen as a much more natural\nformulation of economic sequential decision-making problems, while\nEMT is a better fit for continual demand for stochastic change, as\nhappens in many robotic or embodied-agent problems.\nThe complementary properties of POMDPs and EMT can be\nfurther exploited. There is recent interest in using POMDPs in hybrid\nsolutions [17], in which the POMDPs can be used together with\nother control approaches to provide results not easily achievable\nwith either approach by itself. DBC can be an effective partner in\nsuch a hybrid solution. For instance, POMDPs have prohibitively\nlarge off-line time requirements for policy computation, but can\nbe readily used in simpler settings to expose beneficial behavioral\ntrends; this can serve as a form of target dynamics that are provided\nto EMT in a larger domain for on-line operation.\n7. CONCLUSIONS AND FUTURE WORK\nIn this paper, we have presented a novel perspective on the\nprocess of planning and control in stochastic environments, in the form\nof the Dynamics Based Control (DBC) framework. DBC\nformulates the task of planning as support of a specified target system\ndynamics, which describes the necessary properties of change within\nthe environment. Optimality of DBC plans of action are measured\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 795\n0 20 40 60 80 100\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nSteps\nEntropy\nDead\u2212ends\n0 20 40 60 80 100\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nSteps\nEntropy\nArena\n0 20 40 60 80 100\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nSteps\nEntropy\nCircle\nFigure 4: Observation Model I: Omniposition quarry. Entropy development with length of Tag Game for the three experiment\nscenarios: a) multiple dead-end, b) irregular open arena, c) circular corridor.\n0 10 20 30 40 50 60\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nSteps\nEntropy\nDead\u2212ends\n0 20 40 60 80 100\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nSteps\nEntropy\nArena\n0 20 40 60 80 100\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nSteps\nEntropy\nCircle\nFigure 5: Observation Model II: quarry not observed at hunter\"s position. Entropy development with length of Tag Game for the\nthree experiment scenarios: a) multiple dead-end, b) irregular open arena, c) circular corridor.\nwith respect to the deviation of actual system dynamics from the\ntarget dynamics.\nWe show that a recently developed technique of Extended Markov\nTracking (EMT) [13] is an instantiation of DBC. In fact, EMT can\nbe seen as a specific case of DBC parameterization, which employs\na greedy action selection procedure.\nSince EMT exhibits the key features of the general DBC\nframework, as well as polynomial time complexity, we used the\nmultitarget version of EMT [15] to demonstrate that the class of area\nsweeping problems naturally lends itself to dynamics-based\ndescriptions, as instantiated by our experiments in the Tag Game\ndomain.\nAs enumerated in Section 4.2, EMT has a number of\nlimitations, such as difficulty in dealing with negative dynamic\npreference. This prevents direct application of EMT to such problems\nas Rendezvous-Evasion Games (e.g., [6]). However, DBC in\ngeneral has no such limitations, and readily enables the formulation\nof evasion games. In future work, we intend to proceed with the\ndevelopment of dynamics-based controllers for these problems.\n8. ACKNOWLEDGMENT\nThe work of the first two authors was partially supported by\nIsrael Science Foundation grant #898/05, and the third author was\npartially supported by a grant from Israel\"s Ministry of Science and\nTechnology.\n9. REFERENCES\n[1] R. C. Arkin. Behavior-Based Robotics. MIT Press, 1998.\n[2] J. A. Bilmes. A gentle tutorial of the EM algorithm and its\napplication to parameter estimation for Gaussian mixture and\nHidden Markov Models. Technical Report TR-97-021,\nDepartment of Electrical Engeineering and Computer\nScience, University of California at Berkeley, 1998.\n[3] T. M. Cover and J. A. Thomas. Elements of information\ntheory. Wiley, 1991.\n[4] M. E. desJardins, E. H. Durfee, C. L. Ortiz, and M. J.\nWolverton. A survey of research in distributed, continual\nplanning. AI Magazine, 4:13-22, 1999.\n[5] V. R. Konda and J. N. Tsitsiklis. Actor-Critic algorithms.\nSIAM Journal on Control and Optimization,\n42(4):1143-1166, 2003.\n[6] W. S. Lim. A rendezvous-evasion game on discrete locations\nwith joint randomization. Advances in Applied Probability,\n29(4):1004-1017, December 1997.\n[7] M. L. Littman, T. L. Dean, and L. P. Kaelbling. On the\ncomplexity of solving Markov decision problems. In\nProceedings of the 11th Annual Conference on Uncertainty\nin Artificial Intelligence (UAI-95), pages 394-402, 1995.\n[8] O. Madani, S. Hanks, and A. Condon. On the undecidability\nof probabilistic planning and related stochastic optimization\nproblems. Artificial Intelligence Journal, 147(1-2):5-34,\nJuly 2003.\n[9] R. M. Neal and G. E. Hinton. A view of the EM algorithm\n796 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nthat justifies incremental, sparse, and other variants. In M. I.\nJordan, editor, Learning in Graphical Models, pages\n355-368. Kluwer Academic Publishers, 1998.\n[10] P. Paruchuri, M. Tambe, F. Ordonez, and S. Kraus. Security\nin multiagent systems by policy randomization. In\nProceeding of AAMAS 2006, 2006.\n[11] J. Pineau, G. Gordon, and S. Thrun. Point-based value\niteration: An anytime algorithm for pomdps. In International\nJoint Conference on Artificial Intelligence (IJCAI), pages\n1025-1032, August 2003.\n[12] M. L. Puterman. Markov Decision Processes. Wiley Series in\nProbability and Mathematical Statistics: Applied Probability\nand Statistics Section. Wiley-Interscience Publication, New\nYork, 1994.\n[13] Z. Rabinovich and J. S. Rosenschein. Extended Markov\nTracking with an application to control. In The Workshop on\nAgent Tracking: Modeling Other Agents from Observations,\nat the Third International Joint Conference on Autonomous\nAgents and Multiagent Systems, pages 95-100, New-York,\nJuly 2004.\n[14] Z. Rabinovich and J. S. Rosenschein. Multiagent\ncoordination by Extended Markov Tracking. In The Fourth\nInternational Joint Conference on Autonomous Agents and\nMultiagent Systems, pages 431-438, Utrecht, The\nNetherlands, July 2005.\n[15] Z. Rabinovich and J. S. Rosenschein. On the response of\nEMT-based control to interacting targets and models. In The\nFifth International Joint Conference on Autonomous Agents\nand Multiagent Systems, pages 465-470, Hakodate, Japan,\nMay 2006.\n[16] R. F. Stengel. Optimal Control and Estimation. Dover\nPublications, 1994.\n[17] M. Tambe, E. Bowring, H. Jung, G. Kaminka,\nR. Maheswaran, J. Marecki, J. Modi, R. Nair, J. Pearce,\nP. Paruchuri, D. Pynadath, P. Scerri, N. Schurr, and\nP. Varakantham. Conflicts in teamwork: Hybrids to the\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 797", "keywords": "dynamics base control;target dynamics;partially observable markov decision problem;reward function;tag game;stochastic environment;area-sweeping problem;environment design level;user level;extended markov tracking;dynamics based control;control;game of tag;multi-agent system;action-selection randomization;agent level;system dynamics;robotic"}
{"name": "train_I-45", "title": "Implementing Commitment-Based Interactions\u2217", "abstract": "Although agent interaction plays a vital role in MAS, and messagecentric approaches to agent interaction have their drawbacks, present agent-oriented programming languages do not provide support for implementing agent interaction that is flexible and robust. Instead, messages are provided as a primitive building block. In this paper we consider one approach for modelling agent interactions: the commitment machines framework. This framework supports modelling interactions at a higher level (using social commitments), resulting in more flexible interactions. We investigate how commitmentbased interactions can be implemented in conventional agent-oriented programming languages. The contributions of this paper are: a mapping from a commitment machine to a collection of BDI-style plans; extensions to the semantics of BDI programming languages; and an examination of two issues that arise when distributing commitment machines (turn management and race conditions) and solutions to these problems.", "fulltext": "1. INTRODUCTION\nAgents are social, and agent interaction plays a vital role in\nmultiagent systems. Consequently, design and implementation of agent\ninteraction is an important research topic.\nThe standard approach for designing agent interactions is\nmessagecentric: interactions are defined by interaction protocols that give\nthe permissible sequences of messages, specified using notations\nsuch as finite state machines, Petri nets, or Agent UML.\nIt has been argued that this message-centric approach to\ninteraction design is not a good match for intelligent agents. Intelligent\nagents should exhibit the ability to persist in achieving their goals\nin the face of failure (robustness) by trying different approaches\n(flexibility). On the other hand, when following an interaction\nprotocol, an agent has limited flexibility and robustness: the ability to\npersistently try alternative means to achieving the interaction\"s aim\nis limited to those options that the protocol\"s designer provided, and\nin practice, message-centric design processes do not tend to lead to\nprotocols that are flexible or robust.\nRecognising these limitations of the traditional approach to\ndesigning agent interactions, a number of approaches have been\nproposed in recent years that move away from message-centric\ninteraction protocols, and instead consider designing agent interactions\nusing higher-level concepts such as social commitments [8, 10,\n18] or interaction goals [2]. There has also been work on richer\nforms of interaction in specific settings, such as teams of\ncooperative agents [5, 11].\nHowever, although there has been work on designing flexible and\nrobust agent interactions, there has been virtually no work on\nproviding programming language support for implementing such\ninteractions. Current Agent Oriented Programming Languages\n(AOPLs) do not provide support for implementing flexible and robust\nagent interactions using higher-level concepts than messages.\nIndeed, modern AOPLs [1], with virtually no exceptions, provide\nonly simple message sending as the basis for implementing agent\ninteraction.\nThis paper presents what, to the best of our knowledge, is the\nsecond AOPL to support high-level, flexible, and robust agent\ninteraction implementation. The first such language, STAPLE, was\nproposed a few years ago [9], but is not described in detail, and is\narguably impractical for use by non-specialists, due to its logical\nbasis and heavy reliance on temporal and modal logic.\nThis paper presents a scheme for extending BDI-like AOPLs\nto support direct implementation of agent interactions that are\ndesigned using Yolum & Singh\"s commitment machine (CM)\nframework [19]. In the remainder of this paper we briefly review\ncommitment machines and present a simple abstraction of BDI AOPLs\nwhich lies in the common subset of languages such as Jason, 3APL,\nand CAN. We then present a scheme for translating commitment\nmachines to this language, and indicate how the language needs\nto be extended to support this. We then extend our scheme to\naddress a range of issues concerned with distribution, including turn\ntracking [7], and race conditions.\n2. BACKGROUND\n2.1 Commitment Machines\nThe aim of the commitment machine framework is to allow for\nthe definition of interactions that are more flexible than traditional\nmessage-centric approaches. A Commitment Machine (CM) [19]\nspecifies an interaction between entities (e.g. agents, services,\nprocesses) in terms of actions that change the interaction state. This\ninteract state consists of fluents (predicates that change value over\ntime), but also social commitments, both base-level and conditional.\nA base-level social commitment is an undertaking by debtor A to\ncreditor B to bring about condition p, denoted C(A, B, p). This is\nsometimes abbreviated to C(p), where it is not important to specify\nthe identities of the entities in question. For example, a\ncommitment by customer C to merchant M to make the fluent paid true\nwould be written as C(C, M, paid).\nA conditional social commitment is an undertaking by debtor A\nto creditor B that should condition q become true, A will then\ncommit to bringing about condition p. This is denoted by CC(A, B, q, p),\nand, where the identity of the entities involved is unimportant (or\nobvious), is abbreviated to CC(q p) where the arrow is a\nreminder of the causal link between q becoming true and the creation\nof a commitment to make p true. For example, a commitment to\nmake the fluent paid true once goods have been received would be\nwritten CC(goods paid).\nThe semantics of commitments (both base-level and conditional)\nis defined with rules that specify how commitments change over\ntime. For example, the commitment C(p) (or CC(q p)) is\ndischarged when p becomes true; and the commitment CC(q p) is\nreplaced by C(p) when q becomes true. In this paper we use the\nmore symmetric semantics proposed by [15] and subsequently\nreformalised by [14]. In brief, these semantics deal with a number of\nmore complex cases, such as where commitments are created when\nconditions already hold: if p holds when CC(p q) is meant to\nbe created, then C(q) is created instead of CC(p q).\nAn interaction is defined by specifying the entities involved, the\npossible contents of the interaction state (both fluents and\ncommitments), and (most importantly) the actions that each entity can\nperform along with the preconditions and effects of each action,\nspecified as add and delete lists.\nA commitment machine (CM) defines a range of possible\ninteractions that each start in some state1\n, and perform actions until\nreaching a final state. A final state is one that has no base-level\ncommitments. One way of visualising the interactions that are\npossible with a given commitment machine is to generate the finite\nstate machine corresponding to the CM. For example, figure 1 gives\nthe FSM2\ncorresponding to the NetBill [18] commitment machine:\na simple CM where a customer (C) and merchant (M) attempt to\ntrade using the following actions3\n:\n1\nUnlike standard interaction protocols, or finite state machines,\nthere is no designated initial state for the interaction.\n2\nThe finite state machine is software-generated: the nodes and\nconnections were computed by an implementation of the axioms\n(available from http://www.winikoff.net/CM) and were then laid out by\ngraphviz (http://www.graphviz.org/).\n3\nWe use the notation A(X) : P \u21d2 E to indicate that action A is\nperformed by entity X, has precondition P (with : P omitted if\nempty) and effect E.\n\u2022 sendRequest(C) \u21d2 request\n\u2022 sendQuote(M) \u21d2 offer\nwhere offer \u2261 promiseGoods \u2227 promiseReceipt and\npromiseGoods \u2261 CC(M, C, accept, goods) and\npromiseReceipt \u2261 CC(M, C, pay, receipt)\n\u2022 sendAccept(C) \u21d2 accept\nwhere accept \u2261 CC(C, M, goods, pay)\n\u2022 sendGoods(M) \u21d2 promiseReceipt \u2227 goods\nwhere promiseReceipt \u2261 CC(M, C, pay, receipt)\n\u2022 sendEPO(C) : goods \u21d2 pay\n\u2022 sendReceipt(M) : pay \u21d2 receipt.\nThe commitment accept is the customer\"s promise to pay once\ngoods have been sent, promiseGoods is the merchant\"s promise\nto send the goods once the customer accepts, and promiseReceipt\nis the merchant\"s promise to send a receipt once payment has been\nmade.\nAs seen in figure 1, commitment machines can support a range\nof interaction sequences.\n2.2 An Abstract Agent ProgrammingLanguage\nAgent programming languages in the BDI tradition (e.g. dMARS,\nJAM, PRS, UM-PRS, JACK, AgentSpeak(L), Jason, 3APL, CAN,\nJadex) define agent behaviour in terms of event-triggered plans,\nwhere each plan specifies what it is triggered by, under what\nsituations it can be considered to be applicable (defined using a so-called\ncontext condition), and a plan body: a sequence of steps that can\ninclude posting events which in turn triggers further plans. Given\na collection of plans and an event e that has been posted the agent\nfirst collects all plans types that are triggered by that event (the\nrelevant plans), then evaluates the context conditions of these plans to\nobtain a set of applicable plan instances. One of these is chosen\nand is executed.\nWe now briefly define the formal syntax and semantics of a\nSimple Abstract (BDI) Agent Programming Language (SAAPL). This\nlanguage is intended to be an abstraction that is in the common\nsubset of such languages as Jason [1, Chapter 1], 3APL [1,\nChapter 2], and CAN [16]. Thus, it is intentionally incomplete in some\nareas, for instance it doesn\"t commit to a particular mechanism for\ndealing with plan failure, since different mechanisms are used by\ndifferent AOPLs.\nAn agent program (denoted by \u03a0) consists of a collection of plan\nclauses of the form e : C \u2190 P where e is an event, C is a context\ncondition (a logical formula over the agent\"s beliefs), and P is the\nplan body. The plan body is built up from the following constructs.\nWe have the empty step which always succeeds and does nothing,\noperations to add (+b) and delete (\u2212b) beliefs, sending a message\nm to agent N (\u2191N\nm), and posting an event4\n(e). These can be\nsequenced (P; P).\nC ::= b | C \u2227 C | C \u2228 C | \u00acC | \u2203x.C\nP ::= | +b | \u2212b | e | \u2191N\nm | P; P\nFormal semantics for this language is given in figure 2. This\nsemantics is based on the semantics for AgentSpeak given by [12],\nwhich in turn is based on the semantics for CAN [16]. The\nsemantics is in the style of Plotkin\"s Structural Operational Semantics,\nand assumes that operations exist that check whether a condition\n4\nWe use \u2193N\nm as short hand for the event corresponding to\nreceiving message m from agent N.\n874 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nFigure 1: Finite State Machine for NetBill (shaded = final states)\nfollows from a belief set, that add a belief to a belief set, and that\ndelete a belief from a belief set. In the case of beliefs being a set of\nground atoms these operations are respectively consequence\nchecking (B |= C), and set addition (B \u222a {b}) and deletion (B \\ {b}).\nMore sophisticated belief management methods may be used, but\nare not considered here.\nWe define a basic configuration S = Q, N, B, P where Q is a\n(global) message queue (modelled as a sequence5\nwhere messages\nare added at one end and removed from the other end), N is the\nname of the agent, B is the beliefs of the agent and P is the plan\nbody being executed (i.e. the intention). We also define an agent\nconfiguration, where instead of a single plan body P there is a set\nof plan instances, \u0393. Finally, a complete MAS is a pair Q, As of a\nglobal message queue Q and a set of agent configurations (without\nthe queue, Q). The global message queue is a sequence of triplets\nof the form sender:recipient:message.\nA transition S0 \u2212\u2192 S1 specifies that executing S0 a single step\nyields S1. We annotate the arrow with an indication of whether\nthe configuration in question is basic, an agent configuration, or a\nMAS configuration. The transition relation is defined using rules\nof the form S \u2212\u2192 S or of the form\nS \u2212\u2192 Sr\nS \u2212\u2192 Sr ; the latter are\nconditional with the top (numerator) being the premise and the bottom\n(denominator) being the conclusion.\nNote that there is non-determinism in SAAPL, e.g. the choice\nof plan to execute from a set of applicable plans. This is resolved\nby using selection functions: SO selects one of the applicable plan\ninstances to handle a given event, SI selects which of the plan\ninstances that can be executed should be executed next, and SA\nselects which agent should execute (a step) next.\n3. IMPLEMENTING COMMITMENT-BASED\nINTERACTIONS\nIn this section we present a mapping from a commitment\nmachine to a collection of SAAPL programs (one for each role). We\nbegin by considering the simple case of two interacting agents, and\n5\nThe + operator is used to denote sequence concatenation.\nassume that the agents take turns to act. In section 4 we relax these\nassumptions.\nEach action A(X) : P \u21d2 E is mapped to a number of plans:\nthere is a plan (for agent X) with context condition P that\nperforms the action (i.e. applies the effects E to the agent\"s beliefs)\nand sends a message to the other agent, and a plan (for the other\nagent) that updates its state when a message is received from X.\nFor example, given the action sendAccept(C) \u21d2 accept we have\nthe following plans, where each plan is preceded by M: or C:\nto indicate which agent that plan belongs to. Note that where the\nidentify of the sender (respectively recipient) is obvious, i.e. the\nother agent, we abbreviate \u2191N\nm to \u2191m (resp. \u2193N\nm to \u2193m). Turn\ntaking is captured through the event \u0131 (short for interact): the\nagent that is active has an \u0131 event that is being handled. Handling\nthe event involves sending a message to the other agent, and then\ndoing nothing until a response is received.\nC: \u0131 : true \u2190 +accept; \u2191sendAccept.\nM: \u2193sendAccept : true \u2190 +accept; \u0131.\nIf the action has a non-trivial precondition then there are two plans\nin the recipient: one to perform the action (if possible), and another\nto report an error if the action\"s precondition doesn\"t hold (we\nreturn to this in section 4). For example, the action sendReceipt(M) :\npay \u21d2 receipt generates the following plans:\nM: \u0131 : pay \u2190 +receipt; \u2191sendReceipt.\nC: \u2193sendReceipt : pay \u2190 +receipt; \u0131.\nC: \u2193sendReceipt : \u00acpay \u2190 . . . report error . . . .\nIn addition to these plans, we also need plans to start and finish\nthe interaction. An interaction can be completed whenever there\nare no base-level commitments, so both agents have the following\nplans:\n\u0131 : \u00ac\u2203p.C(p) \u2190 \u2191done.\n\u2193done : \u00ac\u2203p.C(p) \u2190 .\n\u2193done : \u2203p.C(p) \u2190 . . . report error . . . .\nAn interaction is started by setting up an agent\"s initial beliefs, and\nthen having it begin to interact. Exactly how to do this depends\non the agent platform: e.g. the agent platform in question may\noffer a simple way to load beliefs from a file. A generic approach\nthat is a little cumbersome, but is portable, is to send each of the\nagents involved in the interaction a sequence of init messages, each\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 875\nQ, N, B, +b\nBasic\n\u2212\u2192 Q, N, B \u222a {b},\nQ, N, B, \u2212b\nBasic\n\u2212\u2192 Q, N, B \\ {b},\n\u0394 = {Pi\u03b8|(ti : ci \u2190 Pi) \u2208 \u03a0 \u2227 ti\u03b8 = e \u2227 B |= ci\u03b8}\nQ, N, B, e\nBasic\n\u2212\u2192 Q, N, B, SO(\u0394)\nQ, N, B, P1\nBasic\n\u2212\u2192 Q , N, B , P\nQ, N, B, P1; P2\nBasic\n\u2212\u2192 Q , N, B , P ; P2\nQ, N, B, ; P\nBasic\n\u2212\u2192 Q, N, B, P\nQ, N, B, \u2191NB m\nBasic\n\u2212\u2192 Q + N:NB:m, N, B,\nQ = NA:N:m + Q\nQ, N, B, \u0393\nAgent\n\u2212\u2192 Q , N, B, \u0393 \u222a {\u2193NA m}\nP = SI(\u0393) Q, N, B, P\nBasic\n\u2212\u2192 Q , N, B , P\nQ, N, B, \u0393\nAgent\n\u2212\u2192 Q , N, B , (\u0393 \\ {P}) \u222a {P }\nP = SI(\u0393) P =\nQ, N, B, \u0393\nAgent\n\u2212\u2192 Q, N, B, (\u0393 \\ {P})\nN, B, \u0393 = SA(As) Q, N, B, \u0393\nAgent\n\u2212\u2192 Q , N, B , \u0393\nQ, As\nMAS\n\u2212\u2192 Q , (As \u222a { N, B , \u0393 }) \\ { N, B, \u0393 }\nFigure 2: Operational Semantics for SAAPL\ncontaining a belief to be added; and then send one of the agents a\nstart message which begins the interaction. Both agents thus have\nthe following two plans:\n\u2193init(B) : true \u2190 +B.\n\u2193start : true \u2190 \u0131.\nFigure 3 gives the SAAPL programs for both merchant and\ncustomer that implement the NetBill protocol. For conciseness the\nerror reporting plans are omitted.\nWe now turn to refining the context conditions. There are three\nrefinements that we consider. Firstly, we need to prevent\nperforming actions that have no effect on the interaction state. Secondly,\nan agent may want to specify that certain actions that it is able to\nperform should not be performed unless additional conditions hold.\nFor example, the customer may not want to agree to the merchant\"s\noffer unless the goods have a certain price or property. Thirdly, the\ncontext conditions of the plans that terminate the interaction need to\nbe refined in order to avoid terminating the interaction prematurely.\nFor each plan of the form \u0131 : P \u2190 +E; \u2191m we replace the\ncontext condition P with the enhanced condition P \u2227 P \u2227 \u00acE where\nP is any additional conditions that the agent wishes to impose,\nand \u00acE is the negation of the effects of the action. For\nexample, the customer\"s payment plan becomes (assuming no additional\nconditions, i.e. no P ): \u0131 : goods \u2227 \u00acpay \u2190 +pay; \u2191sendEPO.\nFor each plan of the form \u2193m : P \u2190 +E; \u0131 we could add \u00acE to\nthe precondition, but this is redundant, since it is already checked\nby the performer of the action, and if the action has no effect then\nCustomer\"s plans:\n\u0131 : true \u2190 +request; \u2191sendRequest.\n\u0131 : true \u2190 +accept; \u2191sendAccept.\n\u0131 : goods \u2190 +pay; \u2191sendEPO.\n\u2193sendQuote : true \u2190 +promiseGoods;\n+promiseReceipt; \u0131.\n\u2193sendGoods : true \u2190 +promiseReceipt; +goods; \u0131.\n\u2193sendReceipt : pay \u2190 +receipt; \u0131.\nMerchant\"s plans:\n\u0131 : true \u2190 +promiseGoods;\n+promiseReceipt; \u2191sendQuote.\n\u0131 : true \u2190 +promiseReceipt; +goods; \u2191sendGoods.\n\u0131 : pay \u2190 +receipt; \u2191sendReceipt.\n\u2193sendRequest : true \u2190 +request; \u0131.\n\u2193sendAccept : true \u2190 +accept; \u0131.\n\u2193sendEPO : goods \u2190 +pay; \u0131.\nShared plans (i.e. plans of both agents):\n\u0131 : \u00ac\u2203p.C(p) \u2190 \u2191done.\n\u2193done : \u00ac\u2203p.C(p) \u2190 .\n\u2193init(B) : true \u2190 +B.\n\u2193start : true \u2190 \u0131.\nWhere\naccept \u2261 CC(goods pay)\npromiseGoods \u2261 CC(accept goods)\npromiseReceipt \u2261 CC(pay receipt)\noffer \u2261 promiseGoods \u2227 promiseReceipt\nFigure 3: SAAPL Implementation of NetBill\nthe sender won\"t perform it and send the message (see also the\ndiscussion in section 4).\nWhen specifying additional conditions (P ), some care needs to\nbe taken to avoid situations where progress cannot be made because\nthe only action(s) possible are prevented by additional conditions.\nOne way of indicating preference between actions (in many agent\nplatforms) is to reorder the agent\"s plans. This is clearly safe, since\nactions are not prevented, just considered in a different order.\nThe third refinement of context conditions concerns the plans\nthat terminate the interaction. In the Commitment Machine\nframework any state that has no base-level commitment is final, in that\nthe interaction may end there (or it may continue). However, only\nsome of these final states are desirable final states. Which final\nstates are considered to be desirable depends on the domain and\nthe desired interaction outcome. In the NetBill example, the\ndesirable final state is one where the goods have been sent and paid\nfor, and a receipt issued (i.e. goods \u2227 pay \u2227 receipt). In order to\nprevent an agent from terminating the interaction too early we add\nthis as a precondition to the termination plan:\n\u0131 : goods \u2227 pay \u2227 receipt \u2227 \u00ac\u2203p.C(p) \u2190 \u2191done.\nFigure 4 shows the plans that are changed from figure 3.\nIn order to support the realisation of CMs, we need to change\nSAAPL in a number of ways. These changes, which are discussed\nbelow, can be applied to existing BDI languages to make them\ncommitment machine supportive. We present the three changes,\nexplain what they involve, and for each change explain how the\nchange was implemented using the 3APL agent oriented\nprogramming language. The three changes are:\n1. extending the beliefs of the agent so that they can contain\ncommitments;\n876 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nCustomer\"s plans:\n\u0131 : \u00acrequest \u2190 +request; \u2191sendRequest.\n\u0131 : \u00acaccept \u2190 +accept; \u2191sendAccept.\n\u0131 : goods \u2227 \u00acpay \u2190 +pay; \u2191sendEPO.\nMerchant\"s plans:\n\u0131 : \u00acoffer \u2190 +promiseGoods; +promiseReceipt;\n\u2191sendQuote.\n\u0131 : \u00ac(promiseReceipt \u2227 goods) \u2190\n+promiseReceipt; +goods; \u2191sendGoods.\n\u0131 : pay \u2227 \u00acreceipt \u2190 +receipt; \u2191sendReceipt.\nWhere\naccept \u2261 CC(goods pay)\npromiseGoods \u2261 CC(accept goods)\npromiseReceipt \u2261 CC(pay receipt)\noffer \u2261 promiseGoods \u2227 promiseReceipt\nFigure 4: SAAPL Implementation of NetBill with refined\ncontext conditions (changed plans only)\n2. changing the definition of |= to encompass implied\ncommitments; and\n3. whenever a belief is added, updating existing commitments,\naccording to the rules of commitment dynamics.\nExtending the notion of beliefs to encompass commitments in\nfact requires no change in agent platforms that are prolog-like and\nsupport terms as beliefs (e.g. Jason, 3APL, CAN). However, other\nagent platforms do require an extension. For example, JACK, which\nis an extension of Java, would require changes to support\ncommitments that can be nested. In the case of 3APL no change is needed\nto support this.\nWhenever a context condition contains commitments,\ndetermining whether the context condition is implied by the agent\"s beliefs\n(B |= C) needs to take into account the notion of implied\ncommitments [15]. In brief, a commitment can be considered to follow\nfrom a belief set B if the commitment is in the belief set (C \u2208 B),\nbut also under other conditions. For example, a commitment to pay\nC(pay) can be considered to be implied by a belief set containing\npay because the commitment may have held and been discharged\nwhen pay was made true. Similar rules apply for conditional\ncommitments. These rules, which were introduced in [15] were\nsubsequently re-formalised in a simpler form by [14] resulting in the\nfour inference rules in the bottom part of figure 5.\nThe change that needs to be made to SAAPL to support\ncommitment machine implementations is to extend the definition of |= to\ninclude these four rules. For 3APL this was realised by having each\nagent include the following Prolog clauses:\nholds(X) :- clause(X,true).\nholds(c(P)) :- holds(P).\nholds(c(P)) :- clause(cc(Q,P),true), holds(Q).\nholds(cc(_,Q)) :- holds(Q).\nholds(cc(_,Q)) :- holds(c(Q)).\nThe first clause simply says that anything holds if it is in agent\"s\nbeliefs (clause(X,true) is true if X is a fact). The\nremaining four clauses correspond respectively to the inference rules C1,\nC2, CC1 and CC2. To use these rules we then modify context\nconditions in our program so that instead of writing, for\nexample, cc(m,c, pay, receipt) we write holds(cc(m,c,\npay, receipt)).\nB = norm(B \u222a {b})\nQ, N, B, +b \u2212\u2192 Q, N, B ,\nfunction norm(B)\nB \u2190 B\nfor each b \u2208 B do\nif b = C(p) \u2227 B |= p then B \u2190 B \\ {b}\nelseif b = CC(p q) then\nif B |= q then B \u2190 B \\ {b}\nelseif B |= p then B \u2190 (B \\ {b}) \u222a {C(q)}\nelseif B |= C(q) then B \u2190 B \\ {b}\nendif\nendif\nendfor\nreturn B\nend function\nB |= P\nB |= C(P)\nC1\nCC(Q P) \u2208 B B |= Q\nB |= P\nC2\nB |= CC(P Q)\nB |= Q\nCC1\nB |= C(Q)\nB |= CC(P Q)\nCC2\nFigure 5: New Operational Semantics\nThe final change is to update commitments when a belief is\nadded. Formally, this is done by modifying the semantic rule for\nbelief addition so that it applies an algorithm to update\ncommitments. The modified rule and algorithm (which mirrors the\ndefinition of norm in [14]) can be found in the top part of figure 5.\nFor 3APL this final change was achieved by manually inserting\nupdate() after updating beliefs, and defining the following rules\nfor update():\nupdate() <- c(P) AND holds(P)\n| {Deletec(P) ; update()},\nupdate() <- cc(P,Q) AND holds(Q)\n| {Deletecc(P,Q) ; update()},\nupdate() <- cc(P,Q) AND holds(P)\n| {Deletecc(P,Q) ; Addc(Q) ; update()},\nupdate() <- cc(P,Q) AND holds(c(Q))\n| {Deletecc(P,Q) ; update()},\nupdate() <- true | Skip\nwhere Deletec and Deletecc delete respectively a base-level\nand conditional commitment, and Addc adds a base-level\ncommitment.\nOne aspect that doesn\"t require a change is linking commitments\nand actions. This is because commitments don\"t trigger actions\ndirectly: they may trigger actions indirectly, but in general their effect\nis to prevent completion of an interaction while there are\noutstanding (base level) commitments.\nFigure 6 shows the message sequences from a number of runs of\na 3APL implementation of the NetBill commitment machine6\n. In\norder to illustrate the different possible interactions the code was\nmodified so that each agent selected randomly from the actions\nthat it could perform, and a number of runs were made with the\ncustomer as the initiator, and then with the merchant as the\ninitiator. There are other possible sequences of messages, not shown,\n6\nSource code is available from http://www.winikoff.net/CM\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 877\nFigure 6: Sample runs from 3APL implementation (alternating turns)\nincluding the obvious one: request, quote, accept, goods, payment,\nreceipt, and then done.\nOne minor difference between the 3APL implementation and\nSAAPL concerns the semantics of messages. In the semantics of\nSAAPL (and of most AOPLs), receiving a message is treated as an\nevent. However, in 3APL, receiving a message is modelled as the\naddition to the agent\"s beliefs of a fact indicating that the message\nwas received [6]. Thus in the 3APL implementation we have PG\nrules that are triggered by these beliefs, rather than by any event.\nOne issue with this approach is that the belief remains there, so we\nneed to ensure that the belief in question is either deleted once\nhandled, or that we modify preconditions of plans to avoid handling it\nmore than once. In our implementation we delete these received\nbeliefs when they are handled, to avoid duplicate handling of\nmessages.\n4. BEYOND TWO PARTICIPANTS\nGeneralising to more than two interaction participants requires\nrevisiting how turn management is done, since it is no longer\npossible to assume alternating turns [7].\nIn fact, perhaps surprisingly, even in the two participant setting,\nan alternating turn setup is an unreasonable assumption! For\nexample, consider the path (in figure 1) from state 1 to 15 (sendGoods)\nthen to state 12 (sendAccept). The result, in an alternating turn\nsetup, is a dead-end: there is only a single possible action in state\n12, namely sendEPO, but this action is done by the customer, and\nit is the merchant\"s turn to act! Figure 7 shows the FSM for NetBill\nwith alternating initiative.\nA solution to this problem that works in this example, but doesn\"t\ngeneralise7\n, is to weaken the alternating turn taking regime by\nallowing an agent to act twice in a row if its second action is driven\nby a commitment.\nA general solution is to track whose turn it is to act. This can be\ndone by working out which agents have actions that are able to be\nperformed in the current state. If there is only a single active agent,\nthen it is clearly that agent\"s turn to act. However, if more than\none agent is active then somehow the agents need to work out who\nshould act next. Working this out by negotiation is not a particularly\ngood solution for two reasons. Firstly, this negotiation has to be\ndone at every step of the interaction where more than one agent is\nactive (in the NetBill, this applies to seven out of sixteen states), so\nit is highly desirable to have a light-weight mechanism for doing\nthis. Secondly, it is not clear how the negotiation can avoid an\ninfinite regress situation (you go first, no, you go first, . ..)\nwithout imposing some arbitrary rule. It is also possible to resolve\nwho should act by imposing an arbitrary rule, for example, that the\ncustomer always acts in preference to the merchant, or that each\nagent has a numerical priority (perhaps determined by the order in\nwhich they joined the interaction?) that determines who acts.\nAn alternative solution, which exploits the symmetrical\nproperties of commitment machines, is to not try and manage turn taking.\n7\nConsider actions A1(C) \u21d2 p, A2(C) \u21d2 q, and A3(M) : p \u2227\nq \u21d2 r.\nFigure 7: NetBill with alternating initiative\nInstead of tracking and controlling whose turn it is, we simply allow\nthe agents to act freely, and rely on the properties of the interaction\nspace to ensure that things work out, a notion that we shall make\nprecise, and prove, in the remainder of this section.\nThe issue with having multiple agents be active simultaneously\nis that instead of all agents agreeing on the current interaction state,\nagents can be in different states. This can be visualised as each\nagent having its own copy of the FSM that it navigates through\nwhere it is possible for agents to follow different paths through the\nFSM. The two specific issues that need to be addressed are:\n1. Can agents end up in different final states?\n2. Can an agent be in a position where an error occurs because\nit cannot perform an action corresponding to a received\nmessage?\nWe will show that, because actions commute under certain\nassumptions, agents cannot end up in different final states, and\nfurthermore, that errors cannot occur (again, under certain\nassumptions).\nBy actions commute we mean that the state resulting from\nperforming a sequence of actions A1 . . . An is the same, regardless of\nthe order in which the actions are performed. This means that even\nif agents take different paths through the FSM, they still end up in\nthe same resulting state, because once all messages have been\nprocessed, all agents will have performed the same set of actions. This\naddresses the issue of ending up in different final states. We return\nto the possibility of errors occurring shortly.\nDefinition 1 (Monotonicity) An action is monotonic if it does not\ndelete8\nany fluents or commitments. A Commitment Machine is\n8\nThat is directly deletes, it is fine to discharge commitments by\nadding fluents/commitments.\n878 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nmonotonic if all of its actions are monotonic. (Adapted from [14,\nDefinition 6])\nTheorem 1 If A1 and A2 are monotonic actions, then performing\nA1 followed by A2 has the same effect on the agent\"s beliefs as\nperforming A2 followed by A1. (Adapted from [14, Theorem 2]).\nThis assumes that both actions can be performed. However, it is\npossible for the performance of A1 to disable A2 from being done.\nFor example, if A1 has the effect +p, and A2 has precondition\n\u00acp, then although both actions may be enabled in the initial state,\nthey cannot be performed in either order. We can prevent this by\nensuring that actions\" preconditions do not contain negation (or\nimplication), since a monotonic action cannot result in a precondition\nthat is negation-free becoming false. Note that this restriction only\napplies to the original action precondition, P, not to any additional\npreconditions imposed by the agent (P ). This is because only P\nis used to determine whether another agent is able to perform the\naction.\nThus monotonic CMs with preconditions that do not contain\nnegations have actions that commute. However, in fact, the\nrestriction to monotonic CMs is unnecessarily strong: all that is needed\nis that whenever there is a choice of agent that can act, then the\npossible actions are monotonic. If there is only a single agent that\ncan act, then no restriction is needed on the actions: they may or\nmay not be monotonic.\nDefinition 2 (Locally Monotonic) A commitment machine is\nlocally monotonic if for any state S either (a) only a single agent\nhas actions that can be performed; or (b) all actions that can be\nperformed in S are monotonic.\nTheorem 2 In a locally monotonic CM, once all messages have\nbeen processed, all agents will be in the same state. Furthermore,\nno errors can occur.\nProof: Once all messages have been processed we have that all\nagents will have performed the same action set, perhaps in a\ndifferent order. The essence of the proof is to argue that as long as\nagents haven\"t yet converged to the same state, all actions must\nbe monotonic, and hence that these actions commute, and cannot\ndisable any other actions.\nConsider the first point of divergence, where an agent performs\naction A and at the same time another agent (call it XB) performs\naction B. Clearly, this state has actions of more than one agent\nenabled, so, since the CM is locally monotonic, the relevant actions\nmust be monotonic. Therefore, after doing A, the action B must\nstill be enabled, and so the message to do B can be processed by\nupdating the recipient agent\"s beliefs with the effects of B.\nFurthermore, because monotonic actions commute, the result of doing\nA before B is the same as doing B before A:\nS\nA\n\u2212\u2212\u2212\u2212\u2212\u2192 SA\n?\n?\nyB B\n?\n?\ny\nSB \u2212\u2212\u2212\u2212\u2212\u2192\nA\nSAB\nHowever, what happens if the next action after A is not B, but\nC? Because B is enabled, and C is not done by agent XB (see\nbelow), we must have that C is also monotonic, and hence (a) the\nresult of doing A and B and C is the same regardless of the order\nin which the three actions are done; and (b) C doesn\"t disable B,\nso B can still be done after C.\nS\nA\n\u2212\u2212\u2212\u2212\u2212\u2192 SA\nC\n\u2212\u2212\u2212\u2212\u2212\u2192 SAC\n?\n?\nyB B\n?\n?\ny B\n?\n?\ny\nSB \u2212\u2212\u2212\u2212\u2212\u2192\nA\nSAB \u2212\u2212\u2212\u2212\u2212\u2192\nC\nSABC\nThe reason why C cannot be done by XB is that messages are\nprocessed in the order of their arrival9\n. From the perspective of\nXB the action B was done before C, and therefore from any other\nagent\"s perspective the message saying that B was done must be\nreceived (and processed) before a message saying that C is done.\nThis argument can be extended to show that once agents start\ntaking different paths through the FSM all actions taken until the\npoint where they converge on a single state must be monotonic,\nand hence it is always possible to converge (because actions aren\"t\ndisabled), so the interaction is error free; and the resulting state\nonce convergence occurs is the same (because monotonic actions\ncommute).\nThis theorem gives a strong theoretical guarantee that not\ndoing turn management will not lead to disaster. This is analogous\nto proving that disabling all traffic lights would not lead to any\naccidents, and is only possible because the refined CM axioms are\nsymmetrical.\nBased on this theorem the generic transformation from CM to\ncode should allow agents to act freely, which is achieved by simply\nchanging \u0131 : P \u2227 P \u2227 \u00acE \u2190 +E; \u2191A to\n\u0131 : P \u2227 P \u2227 \u00acE \u2190 +E; \u2191A; \u0131\nFor example, instead of \u0131 : \u00acrequest \u2190 +request; \u2191sendRequest\nwe have \u0131 : \u00acrequest \u2190 +request; \u2191sendRequest; \u0131.\nOne consequence of the theorem is that it is not necessary to\nensure that agents process messages before continuing to\ninteract. However, in order to avoid unnecessary parallelism, which can\nmake debugging harder, it may still be desirable to process\nmessages before performing actions.\nFigure 8 shows a number of runs from the 3APL implementation\nthat has been modified to allow free, non-alternating, interaction.\n5. DISCUSSION\nWe have presented a scheme for mapping commitment machines\nto BDI platforms (using SAAPL as an exemplar), identified three\nchanges that needed to be made to SAAPL to support CM-based\ninteraction, and shown that turn management can be avoided in\nCMbased interaction, provided the CM is locally monotonic. The three\nchanges to SAAPL, and the translation scheme from commitment\nmachine to BDI plans are both applicable to any BDI language.\nAs we have mentioned in section 1, there has been some work\non designing flexible and robust agent interaction, but virtually no\nwork on implementing flexible and robust interactions.\nWe have already discussed STAPLE [9, 10]. Another piece of\nwork that is relevant is the work by Cheong and Winikoff on their\nHermes methodology [2]. Although the main focus of their work is\na pragmatic design methodology, they also provide guidelines for\nimplementing Hermes designs using BDI platforms (specifically\nJadex) [3]. However, since Hermes does not yield a design that is\nformal, it is only possible to generate skeleton code that then needs\nto be completed. Also, they do not address the turn taking issue:\nhow to decide which agent acts when more than one agent is able\nto act.\n9\nWe also assume that the communication medium does not deliver\nmessages out of order, which is the case for (e.g.) TCP.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 879\nFigure 8: Sample runs from 3APL implementation (non-alternating turns)\nThe work of Kremer and Flores (e.g. [8]) also uses\ncommitments, and deals with implementation. However, they provide\ninfrastructure support (CASA) rather than a programming language,\nand do not appear to provide assistance to a programmer seeking to\nimplement agents.\nAlthough we have implemented the NetBill interaction using\n3APL, the changes to the semantics were done by modifying our\nNetBill 3APL program, rather than by modifying the 3APL\nimplementation itself. Clearly, it would be desirable to modify the\nsemantics of 3APL (or of another language) directly, by changing\nthe implementation. Also, although we have not done so, it should\nbe clear that the translation from a CM to its implementation could\neasily be automated.\nAnother area for further work is to look at how the assumptions\nrequired to ensure that actions commute can be relaxed.\nFinally, there is a need to perform empirical evaluation. There\nhas already been some work on comparing Hermes with a\nconventional message-centric approach to designing interaction, and\nthis has shown that using Hermes results in designs that are\nsignificantly more flexible and robust [4]. It would be interesting to\ncompare commitment machines with Hermes, but, since\ncommitment machines are a framework, not a design methodology, we\nneed to compare Hermes with a methodology for designing\ninteractions that results in commitment machines [13, 17].\n6. REFERENCES\n[1] R. H. Bordini, M. Dastani, J. Dix, and A. E. F. Seghrouchni,\neditors. Multi-Agent Programming: Languages, Platforms\nand Applications. Springer, 2005.\n[2] C. Cheong and M. Winikoff. Hermes: Designing\ngoal-oriented agent interactions. In Proceedings of the 6th\nInternational Workshop on Agent-Oriented Software\nEngineering (AOSE-2005), July 2005.\n[3] C. Cheong and M. Winikoff. Hermes: Implementing\ngoal-oriented agent interactions. In Proceedings of the Third\ninternational Workshop on Programming Multi-Agent\nSystems (ProMAS), July 2005.\n[4] C. Cheong and M. Winikoff. Hermes versus prometheus: A\ncomparative evaluation of two agent interaction design\napproaches. Submitted for publication, 2007.\n[5] P. R. Cohen and H. J. Levesque. Teamwork. Nous,\n25(4):487-512, 1991.\n[6] M. Dastani, J. van der Ham, and F. Dignum. Communication\nfor goal directed agents. In Proceedings of the Agent\nCommunication Languages and Conversation Policies\nWorkshop, 2002.\n[7] F. P. Dignum and G. A. Vreeswijk. Towards a testbed for\nmulti-party dialogues. In Advances in Agent Communication,\npages 212-230. Springer, LNCS 2922, 2004.\n[8] R. Kremer and R. Flores. Using a performative subsumption\nlattice to support commitment-based conversations. In\nF. Dignum, V. Dignum, S. Koenig, S. Kraus, M. P. Singh, and\nM. Wooldridge, editors, Autonomous Agents and Multi-Agent\nSystems (AAMAS), pages 114-121. ACM Press, 2005.\n[9] S. Kumar and P. R. Cohen. STAPLE: An agent programming\nlanguage based on the joint intention theory. In Proceedings\nof the Third International Joint Conference on Autonomous\nAgents & Multi-Agent Systems (AAMAS 2004), pages\n1390-1391. ACM Press, July 2004.\n[10] S. Kumar, M. J. Huber, and P. R. Cohen. Representing and\nexecuting protocols as joint actions. In Proceedings of the\nFirst International Joint Conference on Autonomous Agents\nand Multi-Agent Systems, pages 543 - 550, Bologna, Italy,\n15 - 19 July 2002. ACM Press.\n[11] M. Tambe and W. Zhang. Towards flexible teamwork in\npersistent teams: Extended report. Journal of Autonomous\nAgents and Multi-agent Systems, 2000. Special issue on\nBest of ICMAS 98.\n[12] M. Winikoff. An AgentSpeak meta-interpreter and its\napplications. In Third International Workshop on\nProgramming Multi-Agent Systems (ProMAS), pages\n123-138. Springer, LNCS 3862 (post-proceedings, 2006),\n2005.\n[13] M. Winikoff. Designing commitment-based agent\ninteractions. In Proceedings of the 2006 IEEE/WIC/ACM\nInternational Conference on Intelligent Agent Technology\n(IAT-06), 2006.\n[14] M. Winikoff. Implementing flexible and robust agent\ninteractions using distributed commitment machines.\nMultiagent and Grid Systems, 2(4), 2006.\n[15] M. Winikoff, W. Liu, and J. Harland. Enhancing\ncommitment machines. In J. Leite, A. Omicini, P. Torroni,\nand P. Yolum, editors, Declarative Agent Languages and\nTechnologies II, number 3476 in Lecture Notes in Artificial\nIntelligence (LNAI), pages 198-220. Springer, 2004.\n[16] M. Winikoff, L. Padgham, J. Harland, and J. Thangarajah.\nDeclarative & procedural goals in intelligent agent systems.\nIn Proceedings of the Eighth International Conference on\nPrinciples of Knowledge Representation and Reasoning\n(KR2002), Toulouse, France, 2002.\n[17] P. Yolum. Towards design tools for protocol development. In\nF. Dignum, V. Dignum, S. Koenig, S. Kraus, M. P. Singh, and\nM. Wooldridge, editors, Autonomous Agents and Multi-Agent\nSystems (AAMAS), pages 99-105. ACM Press, 2005.\n[18] P. Yolum and M. P. Singh. Flexible protocol specification and\nexecution: Applying event calculus planning using\ncommitments. In Proceedings of the 1st Joint Conference on\nAutonomous Agents and MultiAgent Systems (AAMAS),\npages 527-534, 2002.\n[19] P. Yolum and M. P. Singh. Reasoning about commitments in\nthe event calculus: An approach for specifying and executing\nprotocols. Annals of Mathematics and Artificial Intelligence\n(AMAI), 2004.\n880 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)", "keywords": "social commitment;commitment machine;interaction goal;race condition;agent interaction;agent-oriented programming language;bdi-style plan;bdi;commitment-based interaction;messagecentric approach;agent orient program language;herme design;belief desire intention;netbill interaction;turn tracking;commitment machine framework;belief management method"}
{"name": "train_I-46", "title": "Modular Interpreted Systems", "abstract": "We propose a new class of representations that can be used for modeling (and model checking) temporal, strategic and epistemic properties of agents and their teams. Our representations borrow the main ideas from interpreted systems of Halpern, Fagin et al.; however, they are also modular and compact in the way concurrent programs are. We also mention preliminary results on model checking alternating-time temporal logic for this natural class of models.", "fulltext": "1. INTRODUCTION\nThe logical foundations of multi-agent systems have received\nmuch attention in recent years. Logic has been used to represent\nand reason about, e.g., knowledge [7], time [6], cooperation and\nstrategic ability [3]. Lately, an increasing amount of research has\nfocused on higher level representation languages for models of such\nlogics, motivated mainly by the need for compact representations,\nand for representations that correspond more closely to the actual\nsystems which are modeled. Multi-agent systems are open systems,\nin the sense that agents interact with an environment only partially\nknown in advance. Thus, we need representations of models of\nmulti-agent systems which are modular, in the sense that a\ncomponent, such as an agent, can be replaced, removed, or added, without\nmajor changes to the representation of the whole model. However,\nas we argue in this paper, few existing representation languages are\nboth modular, compact and computationally grounded on the one\nhand, and allow for representing properties of both knowledge and\nstrategic ability, on the other.\nIn this paper we present a new class of representations for\nmodels of open multi-agent systems, which are modular, compact and\ncome with an implicit methodology for modeling and designing\nactual systems.\nThe structure of the paper is as follows. First, in Section 2, we\npresent the background of our work - that is, logics that combine\ntime, knowledge, and strategies. More precisely: modal logics that\ncombine branching time, knowledge, and strategies under\nincomplete information. We start with computation tree logic CTL, then\nwe add knowledge (CTLK), and then we discuss two variants of\nalternating-time temporal logic (ATL): one for the perfect, and one\nfor the imperfect information case. The semantics of logics like the\nones presented in Section 2 are usually defined over explicit models\n(Kripke structures) that enumerate all possible (global) states of the\nsystem. However, enumerating these states is one of the things one\nmostly wants to avoid, because there are too many of them even\nfor simple systems. Thus, we usually need representations that are\nmore compact. Another reason for using a more specialized class of\nmodels is that general Kripke structures do not always give enough\nhelp in terms of methodology, both at the stage of design, nor at\nimplementation. This calls for a semantics which is more grounded, in\nthe sense that the correspondence between elements of the model,\nand the entities that are modeled, is more immediate. In Section 3,\nwe present an overview of representations that have been used for\nmodeling and model checking systems in which time, action (and\npossibly knowledge) are important; we mention especially\nrepresentations used for theoretical analysis. We point out that the\ncompact and/or grounded representations of temporal models do not\nplay their role in a satisfactory way when agents\" strategies are\nconsidered. Finally, in Section 4, we present our framework of\nmodular interpreted systems (MIS), and show where it fits in the\npicture. We conclude with a somewhat surprising hypothesis, that\nmodel checking ability under imperfect information for MIS can be\ncomputationally cheaper than model checking perfect information.\nUntil now, almost all complexity results were distinctly in favor of\nperfect information strategies (and the others were indifferent).\n2. LOGICS OF TIME, KNOWLEDGE, AND\nSTRATEGIC ABILITY\nFirst, we present the logics CTL, CTLK, ATL and ATLir that are\nthe starting point of our study.\n2.1 Branching Time: CTL\nComputation tree logic CTL [6] includes operators for temporal\nproperties of systems: i.e., path quantifier E (there is a path),\ntogether with temporal operators: f(in the next state), 2 (always\nfrom now on) and U (until).1\nEvery occurrence of a temporal\noperator is immediately preceded by exactly one path quantifier\n(this variant of the language is sometimes called vanilla CTL).\nLet \u03a0 be a set of atomic propositions with a typical element p.\nCTL formulae \u03d5 are defined as follows:\n\u03d5 ::= p | \u00ac\u03d5 | \u03d5 \u2227 \u03d5 | E f\u03d5 | E2\u03d5 | E\u03d5 U \u03d5.\nThe semantics of CTL is based on Kripke models M = St, R, \u03c0 ,\nwhich include a nonempty set of states St, a state transition relation\nR \u2286 St \u00d7 St, and a valuation of propositions \u03c0 : \u03a0 \u2192 P(St).\nA path \u03bb in M refers to a possible behavior (or computation) of\nsystem M, and can be represented as an infinite sequence of states\nq0q1q2... such that qiRqi+1 for every i = 0, 1, 2, .... We denote\nthe ith state in \u03bb by \u03bb[i]. A q-path is a path that starts in q.\nInterpretation of a formula in a state q in model M is defined as follows:\nM, q |= p iff q \u2208 \u03c0(p);\nM, q |= \u00ac\u03d5 iff M, q |= \u03d5;\nM, q |= \u03d5 \u2227 \u03c8 iff M, q |= \u03d5 and M, q |= \u03c8;\nM, q |= E f\u03d5 iff there is a q-path \u03bb such that M, \u03bb[1] |= \u03d5;\nM, q |= E2\u03d5 iff there is a q-path \u03bb such that M, \u03bb[i] |= \u03d5 for\nevery i \u2265 0;\nM, q |= E\u03d5 U \u03c8 iff there is a q-path \u03bb and i \u2265 0 such that\nM, \u03bb[i] |= \u03c8 and M, \u03bb[j] |= \u03d5 for every 0 \u2264 j < i.\n2.2 Adding Knowledge: CTLK\nCTLK [19] is a straightforward combination of CTL and standard\nepistemic logic [10, 7]. Let Agt = {1, ..., k} be a set of agents with\na typical element a. Epistemic logic uses operators for representing\nagents\" knowledge: Ka\u03d5 is read as agent a knows that \u03d5. Models\nof CTLK extend models of CTL with epistemic indistinguishability\nrelations \u223ca\u2286 St \u00d7 St (one per agent). We assume that all \u223ca are\nequivalences. The semantics of epistemic operators is defined as\nfollows:\nM, q |= Ka\u03d5 iff M, q |= \u03d5 for every q such that q \u223ca q .\nNote that, when talking about agents\" knowledge, we\nimplicitly assume that agents may have imperfect information about the\nactual current state of the world (otherwise the notion of\nknowledge would be trivial). This does not have influence on the way\nwe model evolution of a system as a single unit, but it will become\nimportant when particular agents and their strategies come to the\nfore.\n2.3 Agents and Their Strategies: ATL\nAlternating-time temporal logic ATL [3] is a logic for\nreasoning about temporal and strategic properties of open computational\nsystems (multi-agent systems in particular). The language of ATL\nconsists of the following formulae:\n\u03d5 ::= p | \u00ac\u03d5 | \u03d5 \u2227 \u03d5 | A f\u03d5 | A 2\u03d5 | A \u03d5 U \u03d5.\nwhere A \u2286 Agt. Informally, A \u03d5 says that agents A have a\ncollective strategy to enforce \u03d5. It should be noted that the CTL path\nquantifiers A, E can be expressed with \u2205 , Agt respectively.\nThe semantics of ATL is defined in so called concurrent game\nstructures (CGSs). A CGS is a tuple\nM = Agt, St, Act, d, o, \u03a0, \u03c0 ,\n1\nAdditional operators A (for every path) and 3 (sometime in\nthe future) are defined in the usual way.\nconsisting of: a set Agt = {1, . . . , k} of agents; set St of states;\nvaluation of propositions \u03c0 : \u03a0 \u2192 P(St); set Act of atomic\nactions. Function d : Agt \u00d7 St \u2192 P(Act) indicates the actions\navailable to agent a \u2208 Agt in state q \u2208 St. Finally, o is a\ndeterministic transition function which maps a state q \u2208 St and an\naction profile \u03b11, . . . , \u03b1k \u2208 Actk\n, \u03b1i \u2208 d(i, q), to another state\nq = o(q, \u03b11, . . . , \u03b1k).\nDEFINITION 1. A (memoryless) strategy of agent a is a function\nsa : St \u2192 Act such that sa(q) \u2208 d(a, q).2\nA collective strategy SA\nfor a team A \u2286 Agt specifies an individual strategy for each agent\na \u2208 A. Finally, the outcome of strategy SA in state q is defined as\nthe set of all computations that may result from executing SA from\nq on:\nout(q, SA) = {\u03bb = q0q1q2... | q0 = q and for every i = 1, 2, ...\nthere exists \u03b1i\u22121\n1 , ..., \u03b1i\u22121\nk such that \u03b1i\u22121\na = SA(a)(qi\u22121)\nfor each a \u2208 A, \u03b1i\u22121\na \u2208 d(a, qi\u22121) for each a /\u2208 A, and\no(qi\u22121, \u03b1i\u22121\n1 , ..., \u03b1i\u22121\nk ) = qi}.\nThe semantics of cooperation modalities is as follows:\nM, q |= A f\u03d5 iff there is a collective strategy SA such that,\nfor every \u03bb \u2208 out(q, SA), we have M, \u03bb[1] |= \u03d5;\nM, q |= A 2\u03d5 iff there exists SA such that, for every \u03bb \u2208\nout(q, SA), we have M, \u03bb[i] for every i \u2265 0;\nM, q |= A \u03d5 U \u03c8 iff there exists SA such that for every \u03bb \u2208\nout(q, SA) there is a i \u2265 0, for which M, \u03bb[i] |= \u03c8, and\nM, \u03bb[j] |= \u03d5 for every 0 \u2264 j < i.\n2.4 Agents with Imperfect Information: ATLir\nAs ATL does not include incomplete information in its scope, it\ncan be seen as a logic for reasoning about agents who always have\ncomplete knowledge about the current state of the whole system.\nATLir [21] includes the same formulae as ATL, except that the\ncooperation modalities are presented with a subscript: A ir indicates\nthat they address agents with imperfect information and imperfect\nrecall. Formally, the recursive definition of ATLir formulae is:\n\u03d5 ::= p | \u00ac\u03d5 | \u03d5 \u2227 \u03d5 | A ir\nf\u03d5 | A ir2\u03d5 | A ir\u03d5 U \u03d5\nModels of ATLir, concurrent epistemic game structures (CEGS),\ncan be defined as tuples M = Agt, St, Act, d, o, \u223c1, ..., \u223ck, \u03a0, \u03c0 ,\nwhere Agt, St, Act, d, o, \u03a0, \u03c0 is a CGS, and \u223c1, ..., \u223ck are\nepistemic (equivalence) relations. It is required that agents have the\nsame choices in indistinguishable states: q \u223ca q implies d(a, q) =\nd(a, q ). ATLir restricts the strategies that can be used by agents\nto uniform strategies, i.e. functions sa : St \u2192 Act, such that: (1)\nsa(q) \u2208 d(a, q), and (2) if q \u223ca q then sa(q) = sa(q ). A collective\nstrategy is uniform if it contains only uniform individual strategies.\nAgain, the function out(q, SA) returns the set of all paths that may\nresult from agents A executing collective strategy SA from state q.\nThe semantics of ATLir formulae can be defined as follows:\nM, q |= A ir\nf\u03d5 iff there is a uniform collective strategy SA\nsuch that, for every a \u2208 A, q such that q \u223ca q , and \u03bb \u2208\nout(SA, q ), we have M, \u03bb[1] |= \u03d5;\n2\nThis is a deviation from the original semantics of ATL [3], where\nstrategies assign agents\" choices to sequences of states, which\nsuggests that agents can by definition recall the whole history of each\ngame. While the choice of one or another notion of strategy affects\nthe semantics of the full ATL\n\u2217\n, and most ATL extensions (e.g. for\ngames with imperfect information), it should be pointed out that\nboth types of strategies yield equivalent semantics for pure ATL\n(cf. [21]).\n898 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nM, q |= A ir2\u03d5 iff there exists SA such that, for every a \u2208 A,\nq such that q \u223ca q , and \u03bb \u2208 out(SA, q ), we have M, \u03bb[i]\nfor every i \u2265 0;\nM, q |= A ir\u03d5 U \u03c8 iff there exist SA such that, for every a \u2208 A,\nq such that q \u223ca q , and \u03bb \u2208 out(SA, q ), there is i \u2265 0 for\nwhich M, \u03bb[i] |= \u03c8, and M, \u03bb[j] |= \u03d5 for every 0 \u2264 j < i.\nThat is, A ir\u03d5 holds iff A have a uniform collective strategy, such\nthat for every path that can possibly result from execution of the\nstrategy according to at least one agent from A, \u03d5 is the case.\n3. MODELS AND MODEL CHECKING\nIn this section, we present and discuss various (existing)\nrepresentations of systems that can be used for modeling and model\nchecking. We believe that the two most important points of\nreference are in this case: (1) the modeling formalism (i.e., the logic\nand the semantics we use), and (2) the phenomenon, or more\ngenerally, the domain we are going to model (to which we will often\nrefer as the real world). Our aim is a representation which is\nreasonably close to the real world (i.e., it is sufficiently compact and\ngrounded), and still not too far away from the formalism (so that\nit e.g. easily allows for theoretical analysis of computational\nproblems). We begin with discussing the merits of explicit\nmodelsin our case, these are transition systems, concurrent game structures\nand CEGSs, presented in the previous section.\n3.1 Explicit Models\nObviously, an advantage of explicit models is that they are very\nclose to the semantics of our logics (simply because they are the\nsemantics). On the other hand, they are in many ways difficult to\nuse to describe an actual system:\n\u2022 Exponential size: temporal models usually have an\nexponential number of states with respect to any higher-level\ndescription (e.g. Boolean variables, n-ary attributes etc.). Also, their\nsize is exponential in the number of processes (or agents)\nif the evolution of a system results from joint (synchronous\nor asynchronous) actions of several active entities [15]. For\nCGSs the situation is even worse: here, also the number of\ntransitions is exponential, even if we fix the number of states.3\nIn practice, this means that such representations are very\nseldom scalable.\n\u2022 Explicit models include no modularity. States in a model\nrefer to global states of the system; transitions in the model\ncorrespond to global transitions as well, i.e., they represent\n(in an atomic way) everything that may happen in one single\nstep, regardless of who has done it, to whom, and in what\nway.\n\u2022 Logics like ATL are often advertised as frameworks for\nmodeling and reasoning about open computational systems.\nIdeally, one would like the elements of such a system to have\nas little interdependencies as possible, so that they can be\nplugged in and out without much hassle, for instance when\nwe want to test various designs or implementations of the\nactive component. In the case of a multi-agent system the\n3\nAnother class of ATL models, alternating transition systems [2]\nrepresent transitions in a more succinct way. While we still have\nexponentially many states in an ATS, the number of transitions is\nsimply quadratic wrt. to states (like for CTL models).\nUnfortunately, ATS are even less modular and harder to design than\nconcurrent game structures, and they cannot be easily extended to handle\nincomplete information (cf. [9]).\nneed is perhaps even more obvious. We do not only need\nto re-plug various designs of a single agent in the overall\narchitecture; we usually also need to change (e.g., increase)\nthe number of agents acting in a given environment without\nnecessarily changing the design of the whole system.\nUnfortunately, ATL models are anything but open in this sense.\nTheoretical complexity results for explicit models are as follows.\nModel checking CTL and CTLK is P-complete, and can be done in\ntime O(ml), where m is the number of transitions in the model,\nand l is the length of the formula [5]. Alternatively, it can be done\nin time O(n2\nl), where n is the number of states. Model checking\nATL is P-complete wrt. m, l and \u0394P\n3 -complete wrt. n, k, l (k being\nthe number of agents) [3, 12, 16]. Model checking ATLir is \u0394P\n\n2complete wrt. m, l and \u0394P\n3 -complete wrt. n, k, l [21, 13].\n3.2 Compressed Representations\nExplicit representation of all states and transitions is inefficient\nin many ways. An alternative is to represent the state/transition\nspace in a symbolic way [17, 18].\nSuch models offer some hope for feasible model checking\nproperties of open/multi-agent systems, although it is well known that\nthey are compact only in a fraction of all cases.4\nFor us, however,\nthey are insufficient for another reason: they are merely optimized\nrepresentations of explicit models. Thus, they are neither more\nopen nor better grounded: they were meant to optimize\nimplementation rather than facilitate design or modeling methodology.\n3.3 Interpreted Systems\nInterpreted systems [11, 7] are held by many as a prime example\nof computationally grounded models of distributed systems. An\ninterpreted system can be defined as a tuple IS = St1, ..., Stk, Stenv, R, \u03c0 .\nSt1, ..., Stk are local state spaces of agents 1, ..., k, and Stenv is the\nset of states of the environment. The set of global states is defined\nas St = St1 \u00d7 ... \u00d7 Stk \u00d7 Stenv; R \u2286 St \u00d7 St is a transition relation,\nand \u03c0 : \u03a0 \u2192 P(St). While the transition relation encapsulates\nthe (possible) evolution of the system over time, the epistemic\ndimension is defined by the local components of each global state:\nq1, ..., qk, qenv \u223ci q1, ..., qk, qenv iff qi = qi .\nIt is easy to see that such a representation is modular and\ncompact as far as we are concerned with states. Moreover, it gives a\nnatural (grounded) approach to knowledge, and suggests an\nintuitive methodology for modeling epistemic states. Unfortunately,\nthe way transitions are represented in interpreted systems is neither\ncompact, nor modular, nor grounded: the temporal aspect of the\nsystem is given by a joint transition function, exactly like in\nexplicit models. This is not without a reason: if we separate activities\nof the agents too much, we cannot model interaction in the\nframework any more, and interaction is the most interesting thing here.\nBut the bottom line is that the temporal dimension of an interpreted\nsystem has exponential representation. And it is almost as difficult\nto plug components in and out of an interpreted system, as for an\nordinary CTL or ATL model, since the local activity of an agent is\ncompletely merged with his interaction with the rest of the system.\n3.4 Concurrent Programs\nThe idea of concurrent programs has been long known in the\nliterature on distributed systems. Here, we use the formulation\nfrom [15]. A concurrent program P is composed of k\nconcurrent processes, each described by a labeled transition system Pi =\nSti, Acti, Ri, \u03a0i, \u03c0i , where Sti is the set of local states of process\n4\nRepresentation R of an explicit model M is compact if the size of\nR is logarithmic with respect to the size of M.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 899\ni, Acti is the set of local actions, Ri \u2286 Sti \u00d7Acti \u00d7Sti is a transition\nrelation, and \u03a0i, \u03c0i are the set of local propositions and their\nvaluation. The behavior of program P is given by the product\nautomaton of P1, ..., Pk under the assumption that processes work\nasynchronously, actions are interleaved, and synchronization is obtained\nthrough common action names.\nConcurrent programs have several advantages. First of all, they\nare modular and compact. They allow for local modeling of\ncomponents - much more so than interpreted systems (not only states,\nbut also actions are local here). Moreover, they allow for\nrepresenting explicit interaction between local transitions of reactive\nprocesses, like willful communication, and synchronization. On the\nother hand, they do not allow for representing implicit,\nincidental, or not entirely benevolent interaction between processes. For\nexample, if we want to represent the act of pushing somebody, the\npushed object must explicitly execute an action of being pushed,\nwhich seems somewhat ridiculous. Side effects of actions are also\nnot easy to model. Still, this is a minor complaint in the context\nof CTL, because for temporal logics we are only interested in the\nflow of transitions, and not in the underlying actions. For temporal\nreasoning about k asynchronous processes with no implicit\ninteraction, concurrent programs seem just about perfect.\nThe situation is different when we talk about autonomous,\nproactive components (like agents), acting together (cooperatively or\nadversely) in a common environment - and we want to address\ntheir strategies and abilities. Now, particular actions are no less\nimportant than the resulting transitions. Actions may influence other\nagents\" local states without their consent, they may have side\neffects on other agents\" states etc. Passing messages and/or calling\nprocedures is by no means the only way of interaction between\nagents. Moreover, the availability of actions (to an agent) should\nnot depend on the actions that will be executed by other agents at\nthe same time - these are the outcome states that may depend on\nthese actions! Finally, we would often like to assume that agents act\nsynchronously. In particular, all agents play simultaneously in\nconcurrent game structures. But, assuming synchrony and autonomy\nof actions, synchronization can no longer be a means of\ncoordination.\nTo sum up, we need a representation which is very much like\nconcurrent programs, but allows for modeling agents that play\nsynchronously, and which enables modeling more sophisticated\ninteraction between agents\" actions. The first postulate is easy to satisfy,\nas we show in the following section. The second will be addressed\nin Section 4.\nWe note that model checking CTL against concurrent programs\nis PSPACE-complete in the number of local states and the length\nof the formula [15].\n3.5 Synchronous CP and Simple Reactive\nModules\nThe semantics of ATL is based on synchronous models where\navailability of actions does not depend on the actions currently\nexecuted by the other players. A slightly different variant of\nconcurrent programs can be defined via synchronous product of programs,\nso that all agents play simultaneously.5\nUnfortunately, under such\ninterpretation, no direct interaction between agents\" actions can be\nmodeled at all.\nDEFINITION 2. A synchronous concurrent program consists of\nk concurrent processes Pi = Sti, Acti, Ri, \u03a0i, \u03c0i with the\nfollow5\nThe concept is not new, of course, and has already existed in folk\nknowledge, although we failed to find an explicit definition in the\nliterature.\ning unfolding to a CGS: Agt = {1, ..., k}, St =\nQk\ni=1 Sti, Act =\nSk\ni=1 Acti, d(i, q1, ..., qk ) = {\u03b1i | qi, \u03b1i, qi \u2208 Ri for some qi \u2208\nSti}, o( q1, ..., qk , \u03b11, ..., \u03b1k) = q1, ..., qk such that qi, \u03b1i, qi \u2208\nRi for every i; \u03a0 =\nSk\ni=1 \u03a0i, and \u03c0(p) = \u03c0i(p) for p \u2208 \u03a0i.\nWe note that the simple reactive modules (SRML) from [22] can\nbe seen as a particular implementation of synchronous concurrent\nprograms.\nDEFINITION 3. A SRML system is a tuple \u03a3, \u03a0, m1, . . . , mk ,\nwhere \u03a3 = {1, . . . , k} is a set of modules (or agents), \u03a0 is a\nset of Boolean variables, and, for each i \u2208 \u03a3, we have mi =\nctri, initi, updatei , where ctri \u2286 \u03a0. Sets initi and updatei consist\nof guarded commands of the form \u03c6 ; v1 := \u03c81; . . . ; vk := \u03c8k,\nwhere every vj \u2208 ctri, and \u03c6, \u03c81, . . . , \u03c8k are propositional\nformulae over \u03a0. It is required that ctr1, . . . ctrk partitions \u03a0.\nThe idea is that agent i controls the variables ctri. The init guarded\ncommands are used to initialize the controlled variables, while the\nupdate guarded commands can change their values in each round.\nA guarded command is enabled if the guard \u03c6 is true in the current\nstate of the system. In each round an enabled update guarded\ncommand is executed: each \u03c8j is evaluated against the current state of\nthe system, and its logical value is assigned to vj. Several guarded\ncommands being enabled at the same time model non-deterministic\nchoice. Model checking ATL for SRML has been proved\nEXPTIMEcomplete in the size of the model and the length of the formula [22].\n3.6 Concurrent Epistemic Programs\nConcurrent programs (both asynchronous and synchronous) can\nbe used to encode epistemic relations too - exactly in the same\nway as interpreted systems do [20]. That is, when unfolding a\nconcurrent program to a model of CTLK or ATLir, we define that\nq1, ..., qk \u223ci q1, ..., qk iff qi = qi . Model checking CTLK\nagainst concurrent epistemic programs is PSPACE-complete [20].\nSRML can be also interpreted in the same way; then, we would\nassume that every agent can see only the variables he controls.\nConcurrent epistemic programs are modular and have a grounded\nsemantics. They are usually compact (albeit not always: for\nexample, an agent with perfect information will always blow up the size\nof such a program). Still, they inherit all the problems of\nconcurrent programs with perfect information, discussed in Section 3.4:\nlimited interaction between components, availability of local\nactions depending on the actual transition etc. The problems were\nalready important for agents with perfect information, but they\nbecome even more crucial when agents have only limited knowledge\nof the current situation. One of the most important applications of\nlogics that combine strategic and epistemic properties is\nverification of communication protocols (e.g., in the context of security).\nNow, we may want to, e.g., check agents\" ability to pass an\ninformation between them, without letting anybody else intercept the\nmessage. The point is that the action of intercepting is by definition\nenabled; we just look for a protocol in which the transition of\nsuccessful interception is never carried out. So, availability of actions\nmust be independent of the actions chosen by the other agents under\nincomplete information. On the other hand, interaction is arguably\nthe most interesting feature of multi-agent systems, and it is really\nhard to imagine models of strategic-epistemic logics, in which it is\nnot possible to represent communication.\n3.7 Reactive Modules\nReactive modules [1] can be seen as a refinement of\nconcurrent epistemic programs (primarily used by the MOCHA model\nchecker [4]), but they are much more powerful, expressive and\n900 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\ngrounded. We have already mentioned a very limited variant of\nRML (i.e., SRML). The vocabulary of RML is very close to\nimplementations (in terms of general computational systems): the\nmodules are essentially collections of variables, states are just\nvaluations of variables; events/actions are variable updates. However,\nthe sets of variables controlled by different agents can overlap,\nthey can change over time etc. Moreover, reactive modules\nsupport incomplete information (through observability of variables),\nalthough it is not the main focus of RML. Again, the relationship\nbetween sets of observable variables (and to sets of controlled\nvariables) is mostly left up to the designer of a system. Agents can act\nsynchronously as well as asynchronously.\nTo sum up, RML define a powerful framework for modeling\ndistributed systems with various kinds of synchrony and asynchrony.\nHowever, we believe that there is still a need for a simpler and\nslightly more abstract class of representations. First, the\nframework of RML is technically complicated, involving a number\nauxiliary concepts and their definitions. Second, it is not always\nconvenient to represent all that is going on in a multi-agent system\nas reading and/or writing from/to program variables. This view\nof a multi-agent system is arguably close to its computer\nimplementation, but usually rather distant from the real world\ndomainhence the need for a more abstract, and more conceptually flexible\nframework. Third, the separation of the local complexity, and the\ncomplexity of interaction is not straightforward. Our new proposal,\nmore in the spirit of interpreted systems, takes these observations\nas the starting point. The proposed framework is presented in\nSection 4.\n4. MODULAR INTERPRETED SYSTEMS\nThe idea behind distributed systems (multi-agent systems even\nmore so) is that we deal with several loosely coupled components,\nwhere most of the processing goes on inside components (i.e.,\nlocally), and only a small fraction of the processing occurs between\nthe components. Interaction is crucial (which makes concurrent\nprograms an insufficient modeling tool), but it usually consumes\nmuch less of the agent\"s resources than local computations (which\nmakes the explicit transition tables of CGS, CEGS, and interpreted\nsystems an overkill). Modular interpreted systems, proposed here,\nextrapolate the modeling idea behind interpreted systems in a way\nthat allows for a tight control of the interaction complexity.\nDEFINITION 4. A modular interpreted system (MIS) is defined\nas a tuple\nS = Agt, env, Act, In ,\nwhere Agt = {a1, ..., ak} is a set of agents, env is the environment,\nAct is a set of actions, and In is a set of symbols called interaction\nalphabet. Each agent has the following internal structure:\nai = Sti, di, outi, ini, oi, \u03a0i, \u03c0i , where:\n\u2022 Sti is a set of local states,\n\u2022 di : Sti \u2192 P(Act) defines local availability of actions; for\nconvenience of the notation, we additionally define the set of\nsituated actions as Di = { qi, \u03b1 | qi \u2208 Sti, \u03b1 \u2208 di(qi)},\n\u2022 outi, ini are interaction functions; outi : Di \u2192 In refers to\nthe influence that a given situated action (of agent ai) may\npossibly have on the external world, and ini : Sti \u00d7Ink\n\u2192 In\ntranslates external manifestations of the other agents (and\nthe environment) into the impression that they make on\nai\"s transition function depending on the local state of ai,\n\u2022 oi : Di \u00d7 In \u2192 Sti is a (deterministic) local transition\nfunction,\n\u2022 \u03a0i is a set of local propositions of agent ai where we require\nthat \u03a0i and \u03a0j are disjunct when i = j, and\n\u2022 \u03c0i : \u03a0i \u2192 P(Sti) is a valuation of these propositions.\nThe environment env = Stenv, outenv, inenv, oenv, \u03a0env, \u03c0env has the\nsame structure as an agent except that it does not perform actions,\nand that thus outenv : Stenv \u2192 In and oenv : Stenv \u00d7 In \u2192 Stenv.\nWithin our framework, we assume that every action is executed\nby an actor, that is, an agent. As a consequence, every actor is\nexplicitly represented in a MIS as an agent, just like in the case of\nCGS and CEGS. The environment, on the other hand, represents the\n(passive) context of agents\" actions. In practice, it serves to capture\nthe aspects of the global state that are not observable by any of the\nagents.\nThe input functions ini seem to be the fragile spots here: when\ngiven explicitly as tables, they have size exponential wrt. the\nnumber of agents (and linear wrt. the size of In). However, we can\nuse, e.g., a construction similar to the one from [16] to represent\ninteraction functions more compactly.\nDEFINITION 5. Implicit input function for state q \u2208 Sti is given\nby a sequence \u03d51, \u03b71 , ..., \u03d5n, \u03b7n , where each \u03b7j \u2208 In is an\ninteraction symbol, and each \u03d5j is a boolean combination of\npropositions \u02c6\u03b7i\n, with \u03b7 \u2208 In; \u02c6\u03b7i\nstands for \u03b7 is the symbol currently\ngenerated by agent i. The input function is now defined as\nfollows: ini(q, 1, ..., k, env) = \u03b7j iff j is the lowest index such that\n{\u02c61\n1, ..., \u02c6k\nk, \u02c6env\nenv} |= \u03d5j. It is required that \u03d5n \u2261 , so that the\nmapping is effective.\nREMARK 1. Every ini can be encoded as an implicit input\nfunction, with each \u03d5j being of polynomial size with respect to the\nnumber of interaction symbols (cf. [16]).\nNote that, for some domains, the MIS representation of a system\nrequires exponentially many symbols in the interaction alphabet In.\nIn such a case, the problem is inherent to the domain, and ini will\nhave size exponential wrt the number of agents.\n4.1 Representing Agent Systems with MIS\nLet Stg = (\nQk\ni=1 Sti)\u00d7Stenv be the set of all possible global states\ngenerated by a modular interpreted system S.\nDEFINITION 6. The unfolding of a MIS S for initial states Q \u2286\nStg to a CEGS cegs(S, Q) = Agt , St , \u03a0 , \u03c0 , Act , d , o , \u223c1, ..., \u223ck\nis defined as follows:\n\u2022 Agt = {1, ..., k} and Act = Act,\n\u2022 St is the set of global states from Stg which are reachable\nfrom some state in Q via the transition relation defined by o\n(below),\n\u2022 \u03a0 =\nSk\ni=1 \u03a0i \u222a \u03a0env,\n\u2022 For each q = q1, . . . , qk, qenv \u2208 St and i = 1, ..., k, env,\nwe define q \u2208 \u03c0 (p) iff p \u2208 \u03a0i and qi \u2208 \u03c0i(p),\n\u2022 d (i, q) = di(qi) for global state q = q1, ..., qk, qenv ,\n\u2022 The transition function is constructed as follows. Let q =\nq1, ..., qk, qenv \u2208 St , and \u03b1 = \u03b11, ..., \u03b1k be an action\nprofile s.t. \u03b1i \u2208 d (i, q). We define inputi(q, \u03b1) =\nini\n`\nqi, out1(q1, \u03b11), . . . , outi\u22121(qi\u22121, \u03b1i\u22121), outi+1(qi+1, \u03b1i+1),\n. . . , outk(qk, \u03b1k), outenv(qenv)\n\u00b4\nfor each agent i = 1, . . . , k,\nand inputenv(q, \u03b1) = inenv\n`\nqenv, out1(q1, \u03b11), . . . , outk(qk, \u03b1k)\n\u00b4\n.\nThen, o (q, \u03b1) = o1( q1, \u03b11 , input1(q, \u03b1)), . . . ,\nok( qk, \u03b1k , inputk(q, \u03b1)), oenv(qenv, inputenv(q, \u03b1)) ;\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 901\n\u2022 For each i = 1, ..., k: q1, ..., qk, qenv \u223ci q1, ..., qk, qenv iff\nqi = qi .6\nREMARK 2. Note that MISs can be used as representations of\nCGSs too. In that case, epistemic relations \u223ci are simply omitted in\nthe unfolding. We denote the unfolding of a MIS S for initial states\nQ into a CGS by cgs(S, Q).\nPropositions 3 and 5 state that modular interpreted systems can\nbe used as representations for explicit models of multi-agent\nsystems. On the other hand, these representations are not always\ncompact, as demonstrated by Propositions 7 and 8.\nPROPOSITION 3. For every CEGS M, there is a MIS SM\nand a\nset of global states Q of SM\nsuch that cegs(SM\n, Q) is isomorphic to\nM.7\nPROOF. Let M = {1, . . . , k}, St, Act, d, o, \u03a0, \u03c0, \u223c1, . . . , \u223ck\nbe a CEGS. We construct a MIS SM\n= {a1, . . . , ak}, env, Act, In\nwith agents ai = Sti, di, outi, ini, oi, \u03a0i, \u03c0i and environment env =\nStenv, outenv, inenv, oenv, \u03a0env, \u03c0env , plus a set Q \u2286 Stg of global\nstates, as follows.\n\u2022 In = Act \u222a St \u222a (Actk\u22121\n\u00d7 St),\n\u2022 Sti = {[q]\u223ci | q \u2208 St} for 1 \u2264 i \u2264 k (i.e., Sti is the set of i\"s\nindistinguishability classes in M),\n\u2022 Stenv = St,\n\u2022 di([q]\u223ci ) = d(i, q) for 1 \u2264 i \u2264 k (this is well-defined since\nd(i, q) = d(i, q ) whenever q \u223ci q ),\n\u2022 outi([q]\u223ci , \u03b1i) = \u03b1i for 1 \u2264 i \u2264 k; outenv(q) = q,\n\u2022 ini([q]\u223ci , \u03b11, . . . , \u03b1i\u22121, \u03b1i+1, . . . , \u03b1k, qenv) =\n\u03b11, . . . , \u03b1i\u22121, \u03b1i+1, . . . , \u03b1k, qenv for i \u2208 {1, . . . , k};\ninenv(q, \u03b11 . . . , \u03b1k) = \u03b11, . . . , \u03b1k ;\nini(x) and inenv(x) are arbitrary for other arguments x,\n\u2022 oi( [q]\u223ci , \u03b1i , \u03b11, . . . , \u03b1i\u22121, \u03b1i+1, . . . , \u03b1k, qenv ) =\n[o(qenv, \u03b11, . . . , \u03b1k)]\u223ci for 1 \u2264 i \u2264 k and \u03b1i \u2208 di([q]\u223ci );\noenv(q, \u03b11, . . . , \u03b1k ) = o(q, \u03b11, . . . , \u03b1k);\noi and oenv are arbitrary for other arguments,\n\u2022 \u03a0i = \u2205 for 1 \u2264 i \u2264 k, and \u03a0env = \u03a0,\n\u2022 \u03c0env(p) = \u03c0(p)\n\u2022 Q = { [q]\u223c1 , . . . , [q]\u223ck , q : q \u2208 St}\nLet M = cegs(SM\n, Q) = Agt , St , Act , d , o , \u03a0 , \u03c0 , \u223c1, . . . , \u223ck .\nWe argue that M and M are isomorphic by establishing a\noneto-one correspondence between the respective sets of states, and\nshowing that the other parts of the structures agree on\ncorresponding states.\nFirst we show that, for any \u02c6q = [q ]\u223c1 , . . . , [q ]\u223ck , q \u2208 Q\nand any \u03b1 = \u03b11, . . . , \u03b1k such that \u03b1i \u2208 d (i, \u02c6q ), we have\no (\u02c6q , \u03b1) = [q]\u223c1 , . . . , [q]\u223ck , q where q = o(q , \u03b1) (1)\nLet \u02c6q = o (\u02c6q , \u03b1). Now, for any i: inputi(\u02c6q , \u03b1) = ini([q ]\u223ci ,\nout1([q ]\u223c1 , \u03b11), ..., outi\u22121([q ]\u223ci\u22121 , \u03b1i\u22121), outi+1([q ]\u223ci+1 , \u03b1i+1),\n. . . , outk([q ]\u223ck , \u03b1k), outenv(q )) = ini([q ]\u223ci , \u03b11, . . . , \u03b1i\u22121, \u03b1i+1,\n6\nThis shows another difference between the environment and the\nagents: the environment does not possess knowledge.\n7\nWe say that two CEGS are isomorphic if they only differ in the\nnames of states and/or actions.\n. . . , \u03b1k, q ) = \u03b11, . . . , \u03b1i\u22121, \u03b1i+1, . . . , \u03b1k, q . Similarly, we get\nthat inputenv(\u02c6q , \u03b1) = \u03b11, . . . , \u03b1k . Thus we get that o (\u02c6q , \u03b1) =\no1( [q ]\u223c1 , \u03b11 , input1(\u02c6q , \u03b1)), . . . , ok( [q ]\u223ck , \u03b1k , inputk(\u02c6q , \u03b1)),\noenv(q , inputenv(\u02c6q , \u03b1)) = [o(q , \u03b11, . . . , \u03b1k)]\u223c1 , . . . ,\n[o(q , \u03b11, . . . , \u03b1k)]\u223ck , o(q , \u03b11, . . . , \u03b1k) . Thus, \u02c6q =\n[q]\u223c1 , . . . , [q]\u223ck , q for q = o(q , \u03b11, . . . , \u03b1k), which completes\nthe proof of (1).\nWe now argue that St = Q. Clearly, Q \u2286 St . Let \u02c6q \u2208 St ;\nwe must show that \u02c6q \u2208 Q. The argument is on induction on the\nlength of the least o path from Q to \u02c6q. The base case, \u02c6q \u2208 Q, is\nimmediate. For the inductive step, \u02c6q = o (\u02c6q , \u03b1) for some \u02c6q \u2208 Q,\nand then we have that \u02c6q \u2208 Q by (1). Thus, St = Q.\nNow we have a one-to-one correspondence between St and St :\nr \u2208 St corresponds to [r]\u223c1 , . . . , [r]\u223ck , r \u2208 St . It remains to\nbe shown that the other parts of the structures M and M agree on\ncorresponding states:\n\u2022 Agt = Agt,\n\u2022 Act = Act,\n\u2022 \u03a0 =\nSk\ni=1 \u03a0i \u222a \u03a0env = \u03a0,\n\u2022 For p \u2208 \u03a0 = \u03a0: [q ]\u223c1 , . . . , [q ]\u223ck , q \u2208 \u03c0 (p) iff q \u2208\n\u03c0env(p) iff q \u2208 \u03c0(p) (same valuations at corresponding states),\n\u2022 d (i, [q ]\u223c1 , . . . , [q ]\u223ck , q ) = di([q ]\u223ci ) = d(i, q),\n\u2022 It follows immediately from (1), and the fact that Q = St ,\nthat o ( [q ]\u223c1 , . . . , [q ]\u223ck , q , \u03b1) = [r ]\u223c1 , . . . , [r ]\u223ck , r\niff o(q , \u03b1) = r (transitions on the same joint action in\ncorresponding states lead to corresponding states),\n\u2022 [q ]\u223c1 , . . . , [q ]\u223ck , q \u223ci [r ]\u223c1 , . . . , [r ]\u223ck , r iff [q ]\u223ci =\n[r ]\u223ci iff q \u223ci r (the accessibility relations relate\ncorresponding states), which completes the proof.\nCOROLLARY 4. For every CEGS M, there is an ATLir-equivalent\nMIS S with initial states Q, that is, for every state q in M there is\na state q in cegs(S, Q) satisfying exactly the same ATLir formulae,\nand vice versa.\nPROPOSITION 5. For every CGS M, there is a MIS SM\nand a set\nof global states Q of SM\nsuch that cgs(SM\n, Q) is isomorphic to M.\nPROOF. Let M = Agt, St, Act, d, o, \u03a0, \u03c0 be given. Now, let\n\u02c6M = Agt, St, Act, d, o, \u03a0, \u03c0, \u223c1, . . . , \u223ck for some arbitrary\naccessibility relations \u223ci over St. By Proposition 3, there exists a MIS\nS\n\u02c6M\nwith global states Q such that \u02c6M = cegs(S\n\u02c6M\n, Q) is isomorphic\nto \u02c6M. Let M be the CGS obtained by removing the accessibility\nrelations from \u02c6M . Clearly, M is isomorphic to M.\nCOROLLARY 6. For every CGS M, there is an ATL-equivalent\nMIS S with initial states Q. That is, for every state q in M there is a\nstate q in cgs(S, Q) satisfying exactly the same ATL formulae, and\nvice versa.\nPROPOSITION 7. The local state spaces in a MIS are not\nalways compact with respect to the underlying concurrent epistemic\ngame structure.\nPROOF. Take a CEGS M in which agent i has always perfect\ninformation about the current global state of the system. When\nconstructing a modular interpreted system S such that M = cegs(S, Q),\nwe have that Sti must be isomorphic with St.\n902 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nThe above property is a part of the interpreted systems heritage.\nThe next proposition stems from the fact that explicit models (and\ninterpreted systems) allow for intensive interaction between agents.\nPROPOSITION 8. The size of In in S is, in general, exponential\nwith respect to the number of local states and local actions. This is\nthe case even when epistemic relations are not relevant (i.e., when\nS is taken as a representation of an ordinary CGS).\nPROOF. Consider a CGS M with agents Agt = {1, ..., k}, global\nstates St =\nQk\ni=1{qi\n0, ..., qi\ni}, and actions Act = {0, 1}, all enabled\neverywhere. The transition function is defined as\no( q1\nj1\n, ..., qk\njk\n, \u03b11, ..., \u03b1k) = q1\nl1\n, ..., qk\nlk\n, where li = (ji + \u03b11 +\n... + \u03b1k) mod i. Note that M can be represented as a modular\ninterpreted system with succinct local state spaces Sti = {qi\n0, ..., qi\ni}.\nStill, the current actions of all agents are relevant to determine the\nresulting local transition of agent i.\nWe will call items In, outi, ini the interaction layer of a\nmodular interpreted system S; the other elements of S constitute the local\nlayer of the MIS. In this paper we are ultimately interested in model\nchecking complexity with respect to the size of the local layer. To\nthis end, we will assume that the size of interaction layer is\npolynomial in the number of local states and actions. Note that, by\nPropositions 7 and 8, not every explicit model submits to compact\nrepresentation with a MIS. Still, as we declared at the beginning of\nSection 4, we are mainly interested in a modeling framework for\nsystems of loosely coupled components, where interaction is\nessential, but most processing is done locally anyway. More\nimportantly, the framework of MIS allows for separating the interaction\nof agents from their local structure to a larger extent. Moreover, we\ncan control and measure the complexity of each layer in a finer way\nthan before. First, we can try to abstract from the complexity of a\nlayer (e.g. like in this paper, by assuming that the other layer is kept\nwithin certain complexity bounds). Second, we can also measure\nseparately the interaction complexity of different agents.\n4.2 Modular Interpreted Systems vs. Simple\nReactive Modules\nIn this section we show that simple reactive modules are (as we\nalready suggested) a specific (and somewhat limited)\nimplementation of modular interpreted systems. First, we define our (quite\nstrong) notion of equivalence of representations.\nDEFINITION 7. Two representations are equivalent if they\nunfold to isomorphic concurrent epistemic game structures. They are\nCGS-equivalent if they unfold to the same CGS.\nPROPOSITION 9. For any SRML there is a CGS-equivalent MIS.\nPROOF. Consider an SRML R with k modules and n variables.\nWe construct S = Agt, Act, In with Agt = {a1, ..., ak}, Act =\n{ 1, ..., n, \u22a51, ..., \u22a5n}, and In =\nSk\ni=1 Sti \u00d7 Sti (the local state\nspaces Sti will be defined in a moment). Let us assume without loss\nof generality that ctri = {x1, ..., xr}. Also, we consider all guarded\ncommands of i to be of type \u03b3i,\u03c8 : \u03c8 ; xi := , or \u03b3\u22a5\ni,\u03c8 : \u03c8 ;\nxi := \u22a5. Now, agent ai in S has the following components: Sti =\nP(ctri) (i.e., local states of ai are valuations of variables controlled\nby i); di(qi) = { 1, ..., r, \u22a51, ..., \u22a5r}; outi(qi, \u03b1) = qi, qi ;\nini(qi, q1, q1 , ..., qi\u22121, qi\u22121 , qi+1, qi+1 , qk, qk ) =\n{xi \u2208 ctri | q1, ..., qk |=\nW\n\u03b3i,\u03c8\n\u03c8}, {xi \u2208 ctri | q1, ..., qk |=\nW\n\u03b3\u22a5\ni,\u03c8\n\u03c8} . To define local transitions, we consider three cases. If\nt = f = \u2205 (no update is enabled), then oi(qi, \u03b1, t, f ) = qi for\nevery action \u03b1. If t = \u2205, we take any arbitrary \u02c6x \u2208 t, and\ndefine oi(qi, j, t, f ) = qi \u222a {xj} if xj \u2208 t, and qi \u222a {\u02c6x} otherwise;\noi(qi, \u22a5j, t, f ) = qi \\ {xj} if xj \u2208 f, and qi \u222a {\u02c6x} otherwise.\nMoreover, if t = \u2205 = f, we take any arbitrary \u02c6x \u2208 f, and\ndefine oi(qi, j, t, f ) = qi \u222a {xj} if xj \u2208 t, and qi \\ {\u02c6x} otherwise;\noi(qi, \u22a5j, t, f ) = qi \\{xj} if xj \u2208 f, and qi \\{\u02c6x} otherwise. Finally,\n\u03a0i = ctri, and qi \u2208 \u03c0i(xj) iff xj \u2208 qi.\nThe above construction shows that SRML have more compact\nrepresentation of states than MIS: ri local variables of agent i give\nrise to 2ri\nlocal states. In a way, reactive modules (both simple\nand full) are two-level representations: first, the system is\nrepresented as a product of modules; next, each module can be seen\nas a product of its variables (together with their update operations).\nNote, however, that specification of updates with respect to a single\nvariable in an SRML may require guarded commands of total length\nO(2\nPk\ni=1 ri\n). Thus, the representation of transitions in SRML is (in\nthe worst case) no more compact than in MIS, despite the two-level\nstructure of SRML. We observe finally that MIS are more general,\nbecause in SRML the current actions of other agents have no\ninfluence on the outcome of agent i\"s current action (although the\noutcome can be influenced by other agents\" current local states).\n4.3 Model Checking Modular Interpreted\nSystems\nOne of our main aims was to study the complexity of symbolic\nmodel checking ATLir in a meaningful way. Following the\nreviewers\" remarks, we state our complexity results only as conjectures.\nPreliminary proofs can be found in [14].\nCONJECTURE 10. Model checking ATL for modular interpreted\nsystems is EXPTIME-complete.\nCONJECTURE 11. Model checking ATLir for the class of\nmodular interpreted systems is PSPACE-complete.\nA summary of complexity results for model checking\ntemporal and strategic logics (with and without epistemic component)\nis given in the table below. The table presents completeness\nresults for various models and settings of input parameters. Symbols\nn, k, m stand for the number of states, agents and transitions in an\nexplicit model; l is the length of the formula, and nlocal is the\nnumber of local states in a concurrent program or modular interpreted\nsystem. The new results, conjectured in this paper, are printed in\nitalics. Note that the result for model checking ATL against modular\ninterpreted systems is an extension of the result from [22].\nm, l n, k, l nlocal, k, l\nCTL P [5] P [5] PSPACE [15]\nCTLK P [5, 8] P [5, 8] PSPACE [20]\nATL P [3] \u0394P\n3 [12, 16] EXPTIME\nATLir \u0394P\n2 [21, 13] \u0394P\n3 [13] PSPACE\nIf we are right, then the results for ATL and ATLir form an\nintriguing pattern. When we compare model checking agents with\nperfect vs. imperfect information, the first problem appears to be\nmuch easier against explicit models measured with the number of\ntransitions; next, we get the same complexity class against explicit\nmodels measured with the number of states and agents; finally,\nmodel checking imperfect information turns out to be easier than\nmodel checking perfect information for modular interpreted\nsystems. Why can it be so?\nFirst, a MIS unfolds into CEGS and CGS in a different way. In\nthe first case, the MIS is assumed to encode the epistemic relations\nexplicitly (which makes it explode when we model agents with\nperfect, or almost perfect information). In the latter case, the epistemic\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 903\naspect is ignored, which gives some extra room for encoding the\ntransition relation more efficiently. Another crucial factor is the\nnumber of available strategies (relative to the size of input\nparameters). The number of all strategies is exponential in the number\nof global states; for uniform strategies, there are usually much less\nof them but still exponentially many in general. Thus, the fact that\nperfect information strategies can be synthesized incrementally has\na substantial impact on the complexity of the problem. However,\nmeasured in terms of local states and agents, the number of all\nstrategies is doubly exponential, while there are only\nexponentially many uniform strategies - which settles the results in favor of\nimperfect information.\n5. CONCLUSIONS\nWe have presented a new class of representations for open\nmultiagent systems. Our representations, called modular interpreted\nsystems, are: modular, in the sense that components can be changed,\nreplaced, removed or added, with as little changes to the whole\nrepresentation as possible; more compact than traditional explicit\nrepresentations; and grounded, in the sense that the correspondences\nbetween the primitives of the model and the entities being\nmodeled are more immediate, giving a methodology for designing and\nimplementing systems. We also conjecture that the complexity of\nmodel checking strategic ability for our representations is higher if\nwe assume perfect information than if we assume imperfect\ninformation.\nThe solutions, proposed in this paper, are not necessarily\nperfect (for example, the impression functions ini seem to be the\nmain source of non-modularity in MIS, and can be perhaps\nimproved), but we believe them to be a step in the right direction.\nWe also do not mean to claim that our representations should\nreplace more elaborate modeling languages like Promela or reactive\nmodules. We only suggest that there is a need for compact, modular\nand reasonably grounded models that are more expressive than\nconcurrent (epistemic) programs, and still allow for easier theoretical\nanalysis than reactive modules. We also suggest that MIS might be\nbetter suited for modeling simple multi-agent domains, especially\nfor human-oriented (as opposed to computer-oriented) design.\n6. ACKNOWLEDGMENTS\nWe thank the anonymous reviewers and Andrzej Tarlecki for\ntheir helpful remarks. Thomas \u00c5gotnes\" work on this paper was\nsupported by grants 166525/V30 and 176853/S10 from the\nResearch Council of Norway.\n7. REFERENCES\n[1] R. Alur and T. A. Henzinger. Reactive modules. Formal\nMethods in System Design, 15(1):7-48, 1999.\n[2] R. Alur, T. A. Henzinger, and O. Kupferman.\nAlternating-time Temporal Logic. Lecture Notes in\nComputer Science, 1536:23-60, 1998.\n[3] R. Alur, T. A. Henzinger, and O. Kupferman.\nAlternating-time Temporal Logic. Journal of the ACM,\n49:672-713, 2002.\n[4] R. Alur, T.A. Henzinger, F.Y.C. Mang, S. Qadeer, S.K.\nRajamani, and S. Tasiran. MOCHA user manual. In\nProceedings of CAV\"98, volume 1427 of Lecture Notes in\nComputer Science, pages 521-525, 1998.\n[5] E.M. Clarke, E.A. Emerson, and A.P. Sistla. Automatic\nverification of finite-state concurrent systems using temporal\nlogic specifications. ACM Transactions on Programming\nLanguages and Systems, 8(2):244-263, 1986.\n[6] E.A. Emerson and J.Y. Halpern. \"sometimes\" and \"not never\"\nrevisited: On branching versus linear time temporal logic. In\nProceedings of the Annual ACM Symposium on Principles of\nProgramming Languages, pages 151-178, 1982.\n[7] R. Fagin, J. Y. Halpern, Y. Moses, and M. Y. Vardi.\nReasoning about Knowledge. MIT Press: Cambridge, MA,\n1995.\n[8] M. Franceschet, A. Montanari, and M. de Rijke. Model\nchecking for combined logics. In Proceedings of the 3rd\nInternational Conference on Temporal Logic (ICTL), 2000.\n[9] V. Goranko and W. Jamroga. Comparing semantics of logics\nfor multi-agent systems. Synthese, 139(2):241-280, 2004.\n[10] J. Y. Halpern. Reasoning about knowledge: a survey. In\nD. M. Gabbay, C. J. Hogger, and J. A. Robinson, editors, The\nHandbook of Logic in Artificial Intelligence and Logic\nProgramming, Volume IV, pages 1-34. Oxford University\nPress, 1995.\n[11] J.Y. Halpern and R. Fagin. Modelling knowledge and action\nin distributed systems. Distributed Computing,\n3(4):159-177, 1989.\n[12] W. Jamroga and J. Dix. Do agents make model checking\nexplode (computationally)? In M. P\u02d8echou\u02d8cek, P. Petta, and\nL.Z. Varga, editors, Proceedings of CEEMAS 2005, volume\n3690 of Lecture Notes in Computer Science, pages 398-407.\nSpringer Verlag, 2005.\n[13] W. Jamroga and J. Dix. Model checking abilities of agents:\nA closer look. Submitted, 2006.\n[14] W. Jamroga and T. \u00c5gotnes. Modular interpreted systems: A\npreliminary report. Technical Report IfI-06-15, Clausthal\nUniversity of Technology, 2006.\n[15] O. Kupferman, M.Y. Vardi, and P. Wolper. An\nautomata-theoretic approach to branching-time model\nchecking. Journal of the ACM, 47(2):312-360, 2000.\n[16] F. Laroussinie, N. Markey, and G. Oreiby. Expressiveness\nand complexity of ATL. Technical Report LSV-06-03, CNRS\n& ENS Cachan, France, 2006.\n[17] K.L. McMillan. Symbolic Model Checking: An Approach to\nthe State Explosion Problem. Kluwer Academic Publishers,\n1993.\n[18] K.L. McMillan. Applying SAT methods in unbounded\nsymbolic model checking. In Proceedings of CAV\"02,\nvolume 2404 of Lecture Notes in Computer Science, pages\n250-264, 2002.\n[19] W. Penczek and A. Lomuscio. Verifying epistemic properties\nof multi-agent systems via bounded model checking. In\nProceedings of AAMAS\"03, pages 209-216, New York, NY,\nUSA, 2003. ACM Press.\n[20] F. Raimondi and A. Lomuscio. The complexity of symbolic\nmodel checking temporal-epistemic logics. In L. Czaja,\neditor, Proceedings of CS&P\"05, 2005.\n[21] P. Y. Schobbens. Alternating-time logic with imperfect\nrecall. Electronic Notes in Theoretical Computer Science,\n85(2), 2004.\n[22] W. van der Hoek, A. Lomuscio, and M. Wooldridge. On the\ncomplexity of practical ATL model checking. In P. Stone and\nG. Weiss, editors, Proceedings of AAMAS\"06, pages\n201-208, 2006.\n904 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)", "keywords": "temporal and strategic logic;synchronous concurrent program;reactive module;model methodology;multi-agent system;higher level representation language;kripke structure;modeling methodology;open computational system;branching time;alternating-time temporal logic;model checking;computation tree logic ctl;model check;modular interpreted system"}
{"name": "train_I-47", "title": "Operational Semantics of Multiagent Interactions", "abstract": "The social stance advocated by institutional frameworks and most multi-agent system methodologies has resulted in a wide spectrum of organizational and communicative abstractions which have found currency in several programming frameworks and software platforms. Still, these tools and frameworks are designed to support a limited range of interaction capabilities that constrain developers to a fixed set of particular, pre-defined abstractions. The main hypothesis motivating this paper is that the variety of multi-agent interaction mechanisms - both, organizational and communicative, share a common semantic core. In the realm of software architectures, the paper proposes a connector-based model of multi-agent interactions which attempts to identify the essential structure underlying multi-agent interactions. Furthermore, the paper also provides this model with a formal execution semantics which describes the dynamics of social interactions. The proposed model is intended as the abstract machine of an organizational programming language which allows programmers to accommodate an open set of interaction mechanisms.", "fulltext": "1. INTRODUCTION\nThe suitability of agent-based computing to manage the\ncomplex patterns of interactions naturally occurring in the\ndevelopment of large scale, open systems, has become one\nof its major assets over the last few years [26, 24, 15].\nParticularly, the organizational or social stance advocated by\ninstitutional frameworks [2] and most multi-agent system\n(MAS) methodologies [26, 10], provides an excellent basis to\ndeal with the complexity and dynamism of the interactions\namong system components. This approach has resulted in\na wide spectrum of organizational and communicative\nabstractions, such as institutions, normative positions, power\nrelationships, organizations, groups, scenes, dialogue games,\ncommunicative actions (CAs), etc., to effectively model the\ninteraction space of MAS. This wealth of computational\nabstractions has found currency in several programming\nframeworks and software platforms (AMELI [9], MadKit [13],\nINGENIAS toolkit [18], etc.), which leverage multi-agent\nmiddlewares built upon raw ACL-based interaction mechanism\n[14], and minimize the gap between organizational\nmetamodels and target implementation languages.\nStill, these tools and frameworks are designed to support\na limited range of interaction capabilities that constrain\ndevelopers to a fixed set of particular, pre-defined abstractions.\nThe main hypothesis motivating this paper is that the\nvariety of multi-agent interaction mechanisms - both,\norganizational and communicative, share a common semantic core.\nThis paper thus focuses on the fundamental building blocks\nof multi-agent interactions: those which may be composed,\nextended or refined in order to define more complex\norganizational or communicative types of interactions.\nIts first goal is to carry out a principled analysis of\nmultiagent interactions, departing from general features commonly\nascribed to agent-based computing: autonomy, situatedness\nand sociality [26]. To approach this issue, we draw on the\nnotion of connector, put forward within the field of software\narchitectures [1, 17]. The outcome of this analysis will be a\nconnector-based model of multi-agent interactions between\nautonomous social and situated components, i.e. agents,\nattempting to identify their essential structure. Furthermore,\nthe paper also provides this model with a formal\nexecution semantics which describes the dynamics of multi-agent\n(or social) interactions. Structural Operational Semantics\n(SOS)[21], a common technique to specify the operational\nsemantics of programming languages, is used for this\npurpose.\nThe paper is structured as follows: first, the major entities\nand relationships which constitute the structure of social\ninteractions are introduced. Next, the dynamics of social\ninteractions will show how these entities and relationships\nevolve. Last, relevant work in the literature is discussed\n889\n978-81-904262-7-5 (RPS) c 2007 IFAAMAS\nwith respect to the proposal, limitations are addressed, and\ncurrent and future work is described.\n2. SOCIAL INTERACTION STRUCTURE\nFrom an architectural point of view, interactions between\nsoftware components are embodied in software connectors:\nfirst-class entities defined on the basis of the different roles\nplayed by software components and the protocols that\nregulate their behaviour [1]. The roles of a connector represent\nits participants, such as the caller and callee roles of an\nRPC connector, or the sender and receiver roles in a\nmessage passing connector. The attachment operation binds a\ncomponent to the role of a given connector.\nThe analysis of social interactions introduced in this\nsection gives rise to a new kind of social connector. It refines the\ngeneric model in several respects, attending to the features\ncommonly ascribed to agent-based computing:\n\u2022 According to the autonomy feature, we may\ndistinguish a first kind of participant (i.e. role) in a\nsocial interaction, so-called agents. Basically, agents are\nthose software components which will be regarded as\nautonomous within the scope of the interaction1\n.\n\u2022 A second group of participants, so-called\nenvironmental resources, may be identified from the situatedness\nfeature. Unlike agents, resources represent those\nnonautonomous components whose state may be\nexternally controlled by other components (agents or\nresources) within the interaction. Moreover, the\nparticipation of resources in an interaction is not\nmandatory.\n\u2022 Last, according to the sociality of agents, the\nspecification of social connector protocols - the glue linking\nagents among themselves and with resources, will rely\non normative concepts such as permissions, obligations\nand empowerments [23].\nBesides agents, resources and social protocols, two other\nkinds of entities are of major relevance in our analysis of\nsocial interactions: actions, which represent the way in which\nagents alter the environmental and social state of the\ninteraction; and events, which represent the changes in the\ninteraction resulting from the performance of actions or the\nactivity of environmental resources.\nIn the following, we describe the basic entities involved in\nsocial interactions. Each kind of entity T will be specified as\na record type T l1 : T1, . . . ln : Tn , possibly followed by\na number of invariants, definitions, and the actions affecting\ntheir state. Instances or values v of a record type T will be\nrepresented as v = v1, . . . , vn : T. The type SetT\nrepresents a collection of values drawn from type T. The type\nQueueT represents a queue of values v : T waiting to be\nprocessed. The value v in the expression [v| ] : Queue[T]\nrepresents the head of the queue. The type Enum {v1, . . . , vn}\n1\nNote that we think of the autonomy feature in a relative,\nrather than absolute, perspective. Basically, this means that\nsoftware components counting as agents in a social\ninteraction may behave non-autonomously in other contexts, e.g.\nin their interactions through human-user interfaces. This\nconceptualization of agenthood resembles the way in which\nobjects are understood in CORBA: as any kind of software\ncomponent (C, Prolog, Cobol, etc.) attached to an ORB.\nrepresents an enumeration type whose values are v1, . . . ,\nvn. Given some value v : T, the term vl\nrefers to the value\nof the field l of a record type T. Given some labels l1, l2,\n. . . , the expression vl1,l2,...\nis syntactic sugar for ((vl1\n)l2\n) . . ..\nThe special term nil will be used to represent the absence\nof proper value for an optional field, so that vl\n= nil will be\ntrue in those cases and false otherwise. The formal model\nwill be illustrated with several examples drawn from the\ndesign of a virtual organization to aid in the management of\nuniversity courses.\n2.1 Social Interactions\nSocial interactions shall be considered as composite\nconnectors [17], structured in terms of a tree of nested\nsubinteractions. Let\"s consider an interaction representing a\nuniversity course (e.g. on data structures). On the one\nhand, this interaction is actually a complex one, made up\nof lower-level interactions. For instance, within the scope\nof the course agents will participate in programming\nassignment groups, lectures, tutoring meetings, examinations and\nso on. Assignment groups, in turn, may hold a number of\nassignment submissions and test requests interactions. A\ntest request may also be regarded as a complex interaction,\nultimately decomposed in the atomic, or bottom-level\ninteractions represented by communicative actions (e.g.\nrequest, agree, refuse, . . . ). On the other hand, courses are\nrun within the scope of a particular degree (e.g. computer\nscience), a higher-level interaction. Traversing upwards from\na degree to its ancestors, we find its faculty, the university\nand, finally, the multi-agent community or agent society.\nThe community is thus the top-level interaction which\nsubsumes any other kind of multi-agent interaction2\n.\nThe organizational and communicative interaction types\nidentified above clearly differ in many ways. However, we\nmay identify four major components in all of them: the\nparticipating agents, the resources that agents manipulate,\nthe protocol regulating the agent activities and the\nsubinteraction space. Accordingly, we may specify the type I\nof social interactions, ranged over by the meta-variable i, as\nfollows:\nI state : SI, ini : A, mem : Set A, env : Set R,\nsub : Set I, prot : P, ch : CH\ndef. : (1) icontext = i1 \u21d4 i \u2208 isub\n1\ninv. : (2) iini = nil \u21d4 icontext = nil\nact. : setUp, join, create, destroy\nwhere the member and environment fields represent the\nagents (A) and local resources (R) participating in the\ninteraction; the sub-interaction field, its set of inner interactions;\nand the protocol field the rules that govern the interaction\n(P). The event channel, to be described in the next\nsection, allows the dispatching of local events to external\ninteractions. The context of some interaction is defined as its\nsuper-interaction (def. 1), so that the context of the\ntoplevel interaction is nil.\nThe type SI Enum {open, closing, closed} represents\nthe possible execution states of the interaction. Any\ninteraction, but the top-level one, is set up within the context of\nanother interaction by an initiator agent. The initiator is\n2\nIn the context of this application, a one-to-one mapping\nbetween human users and software components attached to\nthe community as agents would be a right choice.\n890 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nthus a mandatory feature for any interaction different to the\ncommunity (inv. 2). The life-cycle of the interaction begins\nin the open state. Its sets of agent and resource participants,\ninitially empty, vary as agents join and leave the interaction,\nand as they create and destroy resources from its local\nenvironment. Eventually, the interaction may come to an end\n(according to the protocol\"s rules), or be explicitly closed by\nsome agent, thus prematurely disabling the activity of its\nparticipants. The transient closing state will be described\nin the next section.\n2.2 Agents\nComponents attach themselves as agents in social\ninteractions with the purpose of achieving something. The purpose\ndeclared by some agent when it joins an interaction shall be\nregarded as the institutional goal that it purports to satisfy\nwithin that context3\n. The types of agents participating in\na given interaction are primarily identified from their\npurposes. For instance, students are those agents participating\nin a course who purport to obtain a certificate in the course\"s\nsubject. Other members of the course include lecturers and\nteaching assistants.\nThe type A of agents, ranged over by meta-variable a, is\ndefined as follows:\nA state : SA, player : A, purp : F, att : Queue ACT ,\nev : Queue E, obl : Set O\ndef. : (3) acontext = i \u21d4 a \u2208 imem\n(4) a1 \u2208 aroles \u21d4 aplayer\n1 = a\n(5) i \u2208 apartIn \u21d4 a1 \u2208 imem \u2227 a1 \u2208 aroles\nact. : see\nwhere the purpose is represented as a well-formed boolean\nformula, of a generic type F, which evaluates to true if the\npurpose is satisfied and false otherwise. The context of some\nagent is defined as the interaction in which it participates\n(def. 3).\nThe type SA Enum {playing, leaving, succ, unsuc}\nrepresents the execution state of the agent. Its life-cycle\nbegins in the playing state when its player agent joins the\ninteraction, or some software component is attached as an agent\nto the multi-agent system (in this latter case, the player\nvalue is nil). The derived roles and partIn features\nrepresent the roles played by the agent and the contexts in which\nthese roles are played (def. 4, 5)4\n. An agent may play roles\nat interactions within or outside the scope of its context. For\ninstance, students of a course are played by student agents\nbelonging to the (undergraduate) degree, whereas lecturers\nmay be played by teachers of a given department and the\nassistant role may be played by students of a Ph.D degree\n(both, the department and the Ph.D. degrees, are modelled\nas sub-interactions of the faculty).\nComponents will normally attempt to perform different\nactions (e.g. to set up sub-interactions) in order to satisfy\ntheir purposes within some interaction. Moreover,\ncomponents need to be aware of the current state of the interaction,\nso that they will also be capable of observing certain events\nfrom the interaction. Both, the visibility of the interaction\n3\nThus, it may or may not correspond to actual internal\ngoals or intentions of the component.\n4\nFree variables in the antecedents/consequents of\nimplications shall be understood as universally/existentially\nquantified.\nand the attempts of members, are subject to the rules\ngoverning the interaction. The attempts and events fields of\nthe agent structure represent the queues of attempts to\nexecute some actions (ACT ), and the events (E) received by\nthe agent which have not been observed yet. An agent may\nupdate its event queue by seeing the state of some entity\nof the community. The last field of the structure represents\nthe obligations (O) of agents, to be described later.\nEventually, the participation of some agent in the\ninteraction will be over. This may either happen when certain\nconditions are met (specified by the protocol rules), or when\nthe agent takes the explicit decision of leaving the\ninteraction. In either case, the final state of the agent will be\nsuccessful if its purpose was satisfied; unsuccessful\notherwise. The transient leaving state will be described in the\nnext section.\n2.3 Resources\nResources are software components which may represent\ndifferent types of non-autonomous informational or\ncomputational entities. For instance, objectives, topics,\nassignments, grades and exams are different kinds of informational\nresources created by lecturers and assistants in the context\nof the course interaction. Students may also create programs\nto satisfy the requirements of some assignment. Other types\nof computational resources put at the disposal of students\nby teachers include compilers and interpreters.\nThe type R of resources, ranged over by meta-variable r,\ncan be specified by the following record type:\nR cr : A, owners : Set A, op : Set OP\ndef. : (6) rcontext = i \u21d4 r \u2208 ienv\nact. : take, share, give, invoke\nEssentially, resources can be regarded as objects deployed\nin a social setting. This means that resources are created,\naccessed and manipulated by agents in a social interaction\ncontext (def. 6), according to the rules specified by its\nprotocol. The mandatory feature creator represents the agent\nwho created this resource. Moreover, resources may have\nowners. The ownership relationship between members and\nresources is considered as a normative device aimed at the\nsimplification of the protocol\"s rules that govern the\ninteraction of agents and the environment. Members may gain\nownership of some resource by taking it, and grant\nownership to other agents by giving or sharing their own\nproperties. For instance, the ownership of programs may be shared\nby several students if the assignment can be performed by\ngroups of two or more students.\nThe last operations feature represents the interface of the\nresource, consisting of a set of operations. A resource is\nstructured around several public operations that\nparticipants may invoke, in accordance to the rules specified by the\ninteraction\"s protocol. The set of operations of a resource\nmakes up its interface.\n2.4 Protocols\nThe protocol of any interaction is made up of the rules\nwhich govern its overall state and dynamics. The present\nspecification abstracts away the particular formalism used to\nspecify these rules, and focuses instead on several\nrequirements concerning the structure and interface of protocols.\nAccordingly, the type P of protocols, ranged over by\nmetaThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 891\nvariable p, is defined as follows5\n:\nP emp : A \u00d7 ACT \u2192 Boolean,\nperm : A \u00d7 ACT \u2192 Boolean,\nobl :\u2192 Set (A \u00d7 Set O \u00d7 Set E),\nmonitor : E \u2192 Set A,\nfinish :\u2192 Boolean,\nover : A \u2192 Boolean\ndef. : (7) pcontext = i \u21d4 p = iprot\ninv. : (8) pfinish() \u2227 s \u2208 pcontext,sub \u21d2 sprot,finish()\n(9) pfinish() \u2227 a \u2208 pcontext,mem \u21d2 pover(a)\n(10) pover(a) \u2227 ai \u2208 aroles \u21d2 acontext,prot,over\ni (ai)\n(11) \u03b1add \u222a {a} \u2286 pmonitor( a, \u03b1, )\nact. : Close, Leave\nWe demand from protocols four major kinds of functions.\nFirstly, protocols shall include rules to identify the\nempowerments and permissions of any agent attempting to alter\nthe state of the interaction (e.g. its members, the\nenvironment, etc.) through the execution of some action (e.g. join,\ncreate, etc.). Empowerments shall be regarded as the\ninstitutional capabilities which some agent possesses in order\nto satisfy its purpose. Corresponding rules, encapsulated\nby the empowered function field, shall allow to determine\nwhether some agent is capable to perform a given action\nover the interaction. Empowerments may only be exercised\nunder certain circumstances - that permissions specify.\nPermission rules shall allow to determine whether the attempt\nof an empowered agent to perform some particular action\nis satisfied or not (cf. permitted field). For instance, the\ncourse\"s protocol specifies that the agents empowered to\njoin the interaction as students are those students of the\ndegree who have payed the fee established for the course\"s\nsubject, and own the certificates corresponding to its\nprerequisite subjects. Permission rules, in turn, specify that those\nstudents may only join the course in the admission stage.\nHence, even if some student has paid the fee, the attempt\nto join the course will fail if the course has not entered the\ncorresponding stage6\n.\nSecondly, protocols shall allow to determine the\nobligations of agents towards the interaction. Obligations\nrepresent a normative device of social enforcement, fully\ncompatible with the autonomy of agents, used to bias their\nbehaviour in a certain direction. These kinds of rules shall\nallow to determine whether some agent must perform an\naction of a given type, as well as if some obligation was fulfilled,\nviolated or needs to be revoked. The function obligations of\nthe protocol structure thus identifies the agents whose\nobligation set must be updated. Moreover, it returns for each\nagent a collection of events representing the changes in the\nobligation set. For instance, the course\"s protocol\nestablishes that members of departments must join the course as\nteachers whenever they are assigned to the course\"s subject.\nThirdly, the protocol shall allow to specify monitoring\nrules for the different events originating within the\ninteraction. Corresponding rules shall establish the set of agents\nthat must be awared of some event. For instance, this\nfunc5\nThe formalization assumes that protocol\"s functions\nimplicitly recieve as input the interaction being regulated.\n6\nThe hasPaidFee relationship between (degree) students\nand subject resources is represented by an additional,\napplication-dependent field of the agent structure for this\nkind of roles. Similarly, the admission stage is an additional\nboolean field of the structure for school interactions. The\ngeneric types I, A, R and P are thus extendable.\ntionality is exploited by teachers in order to monitor the\nenrollment of students to the course.\nLast, the protocol shall allow to control the state of the\ninteraction as well as the states of its members. Corresponding\nrules identify the conditions under which some interaction\nwill be automatically finished, and whether the participation\nof some member agent will be automatically over. Thus, the\nfunction field finish returns true if the regulated interaction\nmust finish its execution. If so happens, a well-defined set of\nprotocols must ensure that its sub-interactions and members\nare finished as well (inv. 8,9). Similarly, the function over\nreturns true if the participation of the specified member must\nbe over. Well-formed protocols must ensure the consistency\nbetween these functions across playing roles (inv. 10)7\n. For\ninstance, the course\"s protocol establishes that the\nparticipation of students is over when they gain ownership of the\ncourse\"s certificate or the chances to get it are exhausted.\nIt also establishes that the course must be finished when\nthe admission stage has passed and all the students finished\ntheir participation.\n3. SOCIAL INTERACTION DYNAMICS\nThe dynamics of the multi-agent community is influenced\nby the external actions executed by software components\nand the protocols governing their interactions. This section\nfocuses on the dynamics resulting from a particular kind of\nexternal action: the attempt of some component, attached\nto the community as an agent, to execute a given (internal)\naction. The description of other external actions concerning\nagents (e.g. observe the events from its event queue, enter\nor exit from the community) and resources (e.g. a timer\nresource may signal the pass of time) will be skipped.\nThe processing of some attempt may give rise to changes\nin the scope of the target interaction, such as the\ninstantiation of new participants (agents or resources) or the\nsetting up of new sub-interactions. These resulting events\nmay cause further changes in the state of other interactions\n(the target one included), namely, in its execution state as\nwell as in the execution state, obligations and visibility of\ntheir members. This section will also describe the way in\nwhich these events are processed. The resulting dynamics\ndescribed bellow allows for actions and events corresponding\nto different agents and interactions to be processed\nsimultaneously. Due to lack of space, we only include some of the\noperational rules that formalise the execution semantics.\n3.1 Attempt processing\nAn attempt is defined by the structure AT T perf :\nA, act : ACT , where the performer represents the agent\nin charge of executing the specified action. This action is\nintended to alter the state of some target interaction\n(possibly, the performer\"s context itself), and notify a collection\nof addressees of the changes resulting from a successful\nexecution. Accordingly, the type ACT of actions, ranged over\nby meta-variable \u03b1, is specified as follows:\nACT state : SACT , target : I, add : Set A\ndef. : (12) \u03b1perf = a \u21d4 \u03b1 \u2208 aatt\n7\nThe close and leave actions update the finish and over\nfunction fields as explained in the next section. Additional\nactions, such as permit, forbid, empower, etc., to update other\nprotocol\"s fields are yet to be identified in future work.\n892 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nwhere: the performer is formally defined as the agent who\nstores the action in its queue of attempts, and the state field\nrepresents the current phase of processing. This process\ngoes through four major phases, as specified by the\nenumeration type SACT Enum {emp, perm, exec} :\nempowerment checking, permission checking and action execution,\ndescribed in the sequel.\n3.1.1 Empowerment checking\nThe post-condition of an attempt consists of inserting the\naction in the queue of attempts of the specified performer.\nAs rule 1 specifies8\n, this will only be possible if the\nperformer is empowered to execute that action according to the\nrules that govern the state of the target interaction. If this\ncondition is not met, the attempt will simply be ignored.\nMoreover, the performer agent must be in the playing state\n(this pre-condition is also required for any rule concerning\nthe processing of attempts). If these pre-conditions are\nsatisfied the rule is fired and the processing of the action\ncontinues in the permission checking stage. For instance, when\nthe software component attached as a student in a degree\nattempts to join as a student the course in which some subject\nis teached, the empowerment rules of the course interaction\nare checked. If the (degree) student has passed the course\"s\nprerequisite subjects the join action will be inserted in its\nqueue of attempts and considered for execution.\n\u03b1target,prot,emp(a, \u03b1)\na = playing, , , qACT , ,\na,\u03b1 :AT T\n\u2212\u2192 playing, , , qACT , ,\n(1)\nW here : (\u03b1 )state\n= perm\n(qACT ) = insert(\u03b1 , qACT )\n3.1.2 Permissions checking\nThe processing of the action resumes when the possible\npreceding actions in the performer\"s queue of attempts are\nfully processed and removed from the queue. Moreover,\nthere should be no pending events to be processed in the\ninteraction, for these events may cause the member or the\ninteraction to be finished (as will be shortly explained in the\nnext sub-section). If these conditions are met the\npermissions to execute the given action (and notify the specified\naddressees) are checked (e.g. it will be checked whether the\nstudent paid the fee for the course\"s subject). If the protocol\nof the target interaction grants permission, the processing\nof the attempt moves to the action execution stage (rule 2).\nOtherwise, the action is discharged and removed from the\nqueue. Unlike unempowered attempts, a forbidden one will\ncause an event to be generated and transfered to the event\nchannel for further processing.\n\u03b1state = perm \u2227 acontext,ch,in,ev = \u2205 \u2227 \u03b1target,prot,perm(a, \u03b1)\na = playing, , , [\u03b1| ], , \u2212\u2192 playing, , , [\u03b1 | ], ,\n(2)\nW here : (\u03b1 )state\n= exec\n8\nLabels of record instances are omitted to allow for more\ncompact specifications. Moreover, note that record updates\nin where clauses only affect the specified fields.\n3.1.3 Action execution\nThe transitions fired in this stage are classified\naccording to the different types of actions to be executed. The\nintended effects of some actions may directly be achieved\nin a single step, while others will required an indirect\napproach and possibly several execution steps. Actions of the\nfirst kind are constructive ones such as set up and join.\nThe second group of actions include those, such as close and\nleave, whose effects are indirectly achieved by updating the\ninteraction protocol.\nAs an example of constructive action, let\"s consider the\nexecution of a set up action, whose type is defined as\nfollows9\n:\nSetUp ACT \u00b7 new : I\ninv. : (13) \u03b1new,mem = \u03b1new,res = \u03b1new,sub = \u2205\n(14) \u03b1new,state = open\nwhere the new field represents the new interaction to be\ninitiated. Its sets of participants (agents and resources) and\nsub-interactions must be empty (inv. 13) and its state must\nbe open (inv. 14). The setting up of the new interaction may\nthus affect its protocol and possible application-dependent\nfields (e.g. the subject of a course interaction). According\nto rule 3, the outcome of the execution is threefold: firstly,\nthe performer\"s attempt queue is updated so that the\nexecuting action is removed; secondly, the new interaction is\nadded to the target\"s set of sub-interactions (moreover, its\ninitiator field is set to the performer agent); last, the event\nrepresenting this change (which includes a description of the\nchange, the agent that caused it and the action performed)\nis inserted in the output port of the target\"s event channel.\n\u03b1state = exec \u2227 \u03b1 : SetUp \u2227 \u03b1new = i\na = playing, , , [\u03b1|qACT ], , \u2212\u2192 playing, , , qACT , ,\n\u03b1target = open, , , , , sI , c \u2212\u2192 open, , , , , sI \u222a i , c\n(3)\nW here : (i )ini\n= a\n(c )out,ev\n= insert( a, \u03b1, sub(\u03b1target\n, i ) , cout,ev\n)\nLet\"s consider now the case of a close action. This action\nrepresents an attempt by the performer to force some\ninteraction to finish, thus bypassing its current protocol rules\n(those concerning the finish function). The way to achieve\nthis effect is to cause an update on the protocol so that the\nfinish function returns true afterwards10\n. Accordingly, we\nmay specify this type of action as follows:\nClose ACT \u00b7 upd : (\u2192 Bool) \u2192 (\u2192 Bool)\ninv. : (15) \u03b1target,state = open\n(16) \u03b1target,context = nil\n(17) \u03b1upd(\u03b1target,prot,finish)()\nwhere the inherited target field represents the interaction\nto be closed (which must be open and different to the\ntopinteraction, according to invariants 15 and 16) and the new\n9\nThe resulting type consists of the fields of the ACT record\nextended with an additional new field.\n10\nThis strategy is also followed in the definition of leave and\nmay also be used in the definition of other types of actions\nsuch as fire, permit, forbid, etc.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 893\nupdate field represents a proper higher-order function to\nupdate the target\"s protocol (inv. 17). The transition which\nmodels the execution of this action, specified by rule 4,\ndefines two effects in the target interaction: its protocol is\nupdated and the event representing this change is inserted\nin its output port. This event will actually trigger the\nclosing process of the interaction as described in the next\nsubsection.\n\u03b1state = exec \u2227 \u03b1 : Close\na = playing, , , [\u03b1|qACT ], , \u2212\u2192 playing, , , qACT , ,\n\u03b1target = open, , , , , p, c \u2212\u2192 open, , , , , p , c\n(4)\nW here : (p )finish\n= \u03b1upd\n(pfinish\n)\n(c )out,ev\n= insert( a, \u03b1, finish(\u03b1target\n) , cout,ev\n)\n3.2 Event Processing\nThe processing of events is encapsulated in the event\nchannels of interactions. Channels, ranged over by meta-variable\nc, are defined by two input and output ports, according to\nthe following definition:\nCH out : OutP, in : InP\ninv. : (18) ccontext \u2208 cout,disp( , , finish(ccontext) )\n(19) ccontext \u2208 cout,disp( , , over(a) )\n(20) ccontext,sub \u2286 cout,disp(closing(ccontext))\n(21) apartsIn \u2286 cout,disp(leaving(a))\n(22) ccontext \u2208 cout,disp(closed(i))\n(23) {ccontext, aplayer,context} \u2286 cout,disp(left(a))\nOutP ev : Queue E, disp : E \u2192 Set I, int : Set I, ag : Set A\nInP ev : Queue E, stage : Enum {int, mem, obl}, ag : Set A\nThe output port stores and processes the events originated\nwithin the scope of the channel\"s interaction. Its first\npurpose is to dispatch the local events to the agents\nidentified by the protocol\"s monitoring function. Moreover, since\nthese events may influence the results of the finishing, over\nand obligation functions of certain protocols, they will also\nbe dispatched to the input ports of the interactions\nidentified through a dispatching function - whose invariants will\nbe explained later on. Thus, input ports serve as a\ncoordination mechanism which activate the re-evaluation of the\nabove functios whenever some event is received11\n.\nAccordingly, the processing of some event goes through four major\nstages: event dispatching, interaction state update, member\nstate update and obligations update. The first one takes place\nin the output port of the interaction in which the event\noriginated, whereas the other ones execute in separate control\nthreads associated to the input ports of the interactions to\nwhich the event was dispatched.\n3.2.1 Event dispatching\nThe processing of some event stored in the output port is\ntriggered when all its preceding events have been dispatched.\nAs a first step, the auxiliary int and ag fields are initialised\n11\nAlternatively, we may have assumed that interactions are\nfully aware of any change in the multi-agent community. In\nthis scenario, interactions would trigger themselves without\nrequiring any explicit notification. On the contrary, we\nadhere to the more realistic assumption of limited awareness.\nwith the returned values of the dispatching and protocol\"s\nmonitoring functions, respectively (rule 5). Then, additional\nrules simply iterate over these collections until all agents and\ninteractions have been notified (i.e., both sets are empty).\nLast, the event is removed from the queue and the auxiliary\nfields are re-set to nil.\nThe dispatching function shall identify the set of\ninteractions (possibly, empty) that may be affected by the event\n(which may include the channel\"s interaction itself)12\n. For\ninstance, according to the finishing rule of university courses\nmentioned in the last section, the event representing the\nend of the admission stage, originated within the scope of\nthe school interaction, will be dispatched to every course of\nthe school\"s degrees. Concerning the monitoring function,\naccording to invariant 11 of protocols, if the event is\ngenerated as the result of an action performance, the agents\nto be notified will include the performer and addressees of\nthat action. Thus, according to the monitoring rule of\nuniversity courses, if a student of some degree joins a certain\ncourse and specifies a colleague as addressee of that action,\nthe course\"s teachers and itself will also be notified of the\nsuccessful execution.\nccontext,state\ns = open \u2227 ccontext,prot,monitor\ns = mon\ncs = [e| ], d, nil, nil , \u2212\u2192 [e| ], , d(e), mon(e) ,\n(5)\n3.2.2 Interaction state update\nInput port activity is triggered when a new event is\nreceived. Irrespective of the kind of incoming event, the first\nprocessing action is to check whether the channel\"s\ninteraction must be finished. Thus, the dispatching of the finish\nevent resulting from a close action (inv. 18) serves as a\ntrigger of the closing procedure. If the interaction has not to\nbe finished, the input port stage field is set to the member\nstate update stage and the auxiliary ag field is initialised to\nthe interaction members. Otherwise, we can consider two\npossible scenarios. In the first one, the interaction has no\nmembers and no sub-interactions. In this case, the\ninteraction can be inmediately closed down. As rule 6 shows,\nthe interaction is closed, removed from the context\"s set of\nsub-interactions and a closed event is inserted in its output\nchannel. According to invariant 22, this event will be later\ninserted to its input channel to allow for further treatment.\ncin,ev\n1 = \u2205 \u2227 cin,stage\n1 = int \u2227 pfinish()\n, , , , {i} \u222a sI , , c \u2212\u2192 , , , , sI , , c\ni = , , \u2205, , \u2205, p, c1 \u2212\u2192 closed, , , , , ,\n(6)\nW here : (c )out,ev\n= insert(closed(i), cout,ev\n)\nIn the second scenario, the interaction has some member\nor sub-interaction. In this case, clean-up is required prior to\nthe disposal of the interaction (e.g. if the admission period\nends and no student has matriculated for the course,\nteachers has to be finished before finishing the course itself). As\nrule 7 shows, the interaction is moved to the transient\nclosing state and a corresponding event is inserted in the output\nport. According to invariant 20, the closing event will be\ndispatched to every sub-interaction in order to activate its\nclosing procedure (guaranteed by invariant 8). Moreover,\n12\nThis is essentially determined by the protocol rules of these\ninteractions. The way in which the dispatching function is\ninitialised and updated is out of the scope of this paper.\n894 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nthe stage and ag fields are properly initialised so that the\nprocess goes on in the next member state update stage. This\nstage will further initiate the leaving process of the members\n(according to invariant 9).\ncin,ev = \u2205 \u2227 cin,stage = int \u2227 pfinish() \u2227 (sA = \u2205 \u2228 sI = \u2205)\ni = open, , sA, , sI , p, c \u2212\u2192 closing, , sA, , sI , p, c\n(7)\nW here : (c )out,ev\n= insert(closing(i), cout,ev\n)\n(c )in,stage\n= mem\n(c )in,ag\n= sA\nEventually, every member will leave the interaction and\nevery sub-interaction will be closed. Corresponding events\nwill be received by the interaction (according to invariants\n23 and 22) so that the conditions of the first scenario will\nhold.\n3.2.3 Member state update\nThis stage simply iterates over the members of the\ninteraction to check whether they must be finished according to\nthe protocol\"s over function. When all members have been\nchecked, the stage field will be set to the next obligation\nupdate stage and the auxiliary ag field will be initalised\nwith the agents identified by the protocol\"s obligation\nupdate function.\nIf some member has to end its participation in the\ninteraction and it is not playing any role, it will be inmediately\nabandoned (successfully or unsuccessfully, according to the\nsatisfaction of its purpose). The corresponding event will\nbe forwarded to its interaction and to the interaction of its\nplayer agent to account for further changes (inv. 23).\nOtherwise, the member enters the transient leaving state, thus\npreventing any action performance. Then, it waits for the\ncompletion of the leaving procedures of its played roles,\ntriggered by proper dispatching of the leaving event (inv. 21).\n3.2.4 Obligations update\nIn this stage, the obligations of agents (not necessaryly\nmembers of the interaction) towards the interaction are\nupdated accordingly. When all the identified agents have been\nupdated, the event is removed from the input queue and\nthe stage field is set back to the interaction state update.\nFor instance, when a course interaction receives an event\nrepresenting the assignment of some department member to\nits subject, an obligation to join the course as a teacher is\ncreated for that member. Moreover, the event representing\nthis change is added to the output channel of the department\ninteraction.\n4. DISCUSSION\nThis paper has attempted to expose a possible\nsemantic core underlying the wide spectrum of interaction types\nbetween autonomous, social and situated software\ncomponents. In the realm of software architectures, this core has\nbeen formalised as an operational model of social\nconnectors, intended to describe both the basic structure and\ndynamics of multi-agent interactions, from the largest (the\nagent society itself) down to the smallest ones\n(communicative actions). Thus, top-level interactions may represent the\nkind of agent-web pursued by large-scale initiatives such as\nthe Agentcities/openNet one [25]. Large-scale interactions,\nmodelling complex aggregates of agent interactions such as\nthose represented by e-institutions or virtual organizations\n[2, 26], are also amenable to be conceptualised as\nparticular kinds of first-level social interactions. The last\nlevels of the interaction tree may represent small-scale\nmultiagent interactions such as those represented by interaction\nprotocols [11], dialogue games [16], or scenes [2]. Finally,\nbottom-level interactions may represent communicative\nactions. From this perspective, the member types of a CA\ninclude the speaker and possibly many listeners. The\npurpose of the speaker coincides with the illocutionary purpose\nof the CA [22], whereas the purpose of any listener is to\ndeclare that it (actually, the software component) successfully\nprocessed the meaning of the CA.\nThe analysis of social interactions put forward in this\npaper draws upon current proposals of the literature in\nseveral general respects, such as the institutional and\norganizational character of multi-agent systems [2, 26, 10, 7] and the\nnormative perspective on multi-agent protocols [12, 23, 20].\nThese proposals as well as others focusing in relevant\nabstractions such as power relationships, contracts, trust and\nreputation mechanisms in organizational settings, etc., could\nbe further exploited in order to characterize more accurately\nthe organizational character of some multi-agent\ninteractions. Similarly, the conceptualization of communicative\nactions as atomic interactions may similarly benefit from\npublic semantics of communicative actions such as the one\nintroduced in [3]. Last, the abstract model of protocols may\nbe refined taking into account existing operational models\nof norms [12, 6]. These analyses shall result in new\norganizational and communicative abstractions obtained through\na refinement and/or extension of the general model of\nsocial interactions. Thus, the proposed model is not intended\nto capture every organizational or communicative feature of\nmulti-agent interactions, but to reveal their roots in basic\ninteraction mechanisms. In turn, this would allow for the\nexploitation of common formalisms, particularly concerning\nprotocols.\nUnlike the development of individual agents, which has\ngreatly benefited from the design of several agent\nprogramming languages [4], societal features of multi-agent systems\nare mostly implemented in terms of visual modelling [8, 18]\nand a fixed set of interaction abstractions. We argue that\nthe current field of multi-agent system programming may\ngreatly benefit from multi-agent programming languages that\nallow programmers to accommodate an open set of\ninteraction mechanisms. The model of social interactions put\nforward in this paper is intended as the abstract machine\nof a language of this type. This abstract machine would\nbe independent of particular agent architectures and\nlanguages (i.e. software components may be programmed in a\nBDI language such as Jason [5] or in a non-agent oriented\nlanguage).\nOn top of the presented execution semantics, current and\nfuture work aims at the specification of the type system [19]\nwhich allows to program the abstract machine, the\nspecification of the corresponding surface syntaxes (both textual\nand visual) and the design and implementation of a virtual\nmachine over existing middleware technologies such as FIPA\nplatforms or Web services. We also plan to study particular\nrefinements and limitations to the proposed model,\nparticularly with respect to the dispatching of events, semantics\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 895\nof obligations, dynamic updates of protocols and rule\nformalisms. In this latter aspect, we plan to investigate the\nuse of Answer Set Programming to specify the rules of\nprotocols, attending to the role that incompleteness (rules may\nonly specify either necessary or sufficient conditions, for\ninstance), explicit negation (e.g. prohibitions) and defaults\nplay in this domain.\n5. ACKNOWLEDGMENTS\nThe authors thank anonymous reviewers for their\ncomments and suggestions. Research sponsored by the Spanish\nMinistry of Science and Education (MEC), project\nTIN200615455-C03-03.\n6. REFERENCES\n[1] R. Allen and D. Garlan. A Formal Basis for\nArchitectural Connection. ACM Transactions on\nSoftware Engineering and Methodology, 6(3):213-249,\nJune 1997.\n[2] J. L. Arcos, M. Esteva, P. Noriega, J. A. Rodr\u00b4\u0131guez,\nand C. Sierra. Engineering open environments with\nelectronic institutions. Journal on Engineering\nApplications of Artificial Intelligence, 18(2):191-204,\n2005.\n[3] G. Boella, R. Damiano, J. Hulstijn, and L. W. N.\nvan der Torre. Role-based semantics for agent\ncommunication: embedding of the \"mental attitudes\"\nand \"social commitments\" semantics. In AAMAS,\npages 688-690, 2006.\n[4] R. H. Bordini, L. Braubach, M. Dastani, A. E. F.\nSeghrouchni, J. J. G. Sanz, J. Leite, G. O\"Hare,\nA. Pokahr, and A. Ricci. A survey of programming\nlanguages and platforms for multi-agent systems.\nInformatica, 30:33-44, 2006.\n[5] R. H. Bordini, J. F. H\u00a8ubner, and R. Vieira. Jason and\nthe golden fleece of agent-oriented programming. In\nR. H. Bordini, D. M., J. Dix, and\nA. El Fallah Seghrouchni, editors, Multi-Agent\nProgramming: Languages, Platforms and Applications,\nchapter 1. Springer-Verlag, 2005.\n[6] O. Cliffe, M. D. Vos, and J. A. Padget. Specifying and\nanalysing agent-based social institutions using answer\nset programming. In EUMAS, pages 476-477, 2005.\n[7] V. Dignum, J. V\u00b4azquez-Salceda, and F. Dignum.\nOmni: Introducing social structure, norms and\nontologies into agent organizations. In R. Bordini,\nM. Dastani, J. Dix, and A. Seghrouchni, editors,\nProgramming Multi-Agent Systems Second\nInternational Workshop ProMAS 2004, volume 3346\nof LNAI, pages 181-198. Springer, 2005.\n[8] M. Esteva, D. de la Cruz, and C. Sierra. ISLANDER:\nan electronic institutions editor. In M. Gini, T. Ishida,\nC. Castelfranchi, and W. L. Johnson, editors,\nProceedings of the First International Joint\nConference on Autonomous Agents and Multiagent\nSystems (AAMAS\"02), pages 1045-1052. ACM Press,\nJuly 2002.\n[9] M. Esteva, B. Rosell, J. A. Rodr\u00b4\u0131guez-Aguilar, and\nJ. L. Arcos. AMELI: An agent-based middleware for\nelectronic institutions. In Proceedings of the Third\nInternational Joint Conference on Autonomous Agents\nand Multiagent Systems, volume 1, pages 236-243,\n2004.\n[10] J. Ferber, O. Gutknecht, and F. Michel. From agents\nto organizations: An organizational view of\nmulti-agent systems. In AOSE, pages 214-230, 2003.\n[11] Foundation for Intelligent Physical Agents. FIPA\nInteraction Protocol Library Specification.\nhttp://www.fipa.org/repository/ips.html, 2003.\n[12] A. Garc\u00b4\u0131a-Camino, J. A. Rodr\u00b4\u0131guez-Aguilar, C. Sierra,\nand W. Vasconcelos. Norm-oriented programming of\nelectronic institutions. In AAMAS, pages 670-672,\n2006.\n[13] O. Gutknecht and J. Ferber. The MadKit agent\nplatform architecture. Lecture Notes in Computer\nScience, 1887:48-55, 2001.\n[14] JADE. The JADE project home page.\nhttp://jade.cselt.it, 2005.\n[15] M. Luck, P. McBurney, O. Shehory, and S. Willmott.\nAgent Technology: Computing as Interaction - A\nRoadmap for Agent-Based Computing. AgentLink III,\n2005.\n[16] P. McBurney and S. Parsons. A formal framework for\ninter-agent dialogues. In J. P. M\u00a8uller, E. Andre,\nS. Sen, and C. Frasson, editors, Proceedings of the\nFifth International Conference on Autonomous\nAgents, pages 178-179, Montreal, Canada, May 2001.\nACM Press.\n[17] N. R. Mehta, N. Medvidovic, and S. Phadke. Towards\na taxonomy of software connectors. In Proceedings of\nthe 22nd International Conference on Software\nEngineering, pages 178-187. ACM Press, June 2000.\n[18] J. Pav\u00b4on and J. G\u00b4omez-Sanz. Agent oriented software\nengineering with ingenias. In V. Marik, J. Muller, and\nM. Pechoucek, editors, Proceedings of the 3rd\nInternational Central and Eastern European\nConference on Multi-Agent Systems. Springer Verlag,\n2003.\n[19] B. C. Pierce. Types and Programming Languages. The\nMIT Press, Cambridge, MA, 2002.\n[20] J. Pitt, L. Kamara, M. Sergot, and A. Artikis. Voting\nin multi-agent systems. Feb. 27 2006.\n[21] G. Plotkin. A structural approach to operational\nsemantics. Technical Report DAIMI FN-19, Aarhus\nUniversity, Sept. 1981.\n[22] J. Searle. Speech Acts. Cambridge University Press,\n1969.\n[23] M. Sergot. A computational theory of normative\npositions. ACM Transactions on Computational Logic,\n2(4):581-622, Oct. 2001.\n[24] M. P. Singh. Agent-based abstractions for software\ndevelopment. In F. Bergenti, M.-P. Gleizes, and\nF. Zambonelli, editors, Methodologies and Software\nEngineering for Agent Systems, chapter 1, pages 5-18.\nKluwer, 2004.\n[25] S. Willmot and al. Agentcities / opennet testbed.\nhttp://x-opennet.net, 2004.\n[26] F. Zambonelli, N. R. Jennings, and M. Wooldridge.\nDeveloping multiagent systems: The Gaia\nmethodology. ACM Transactions on Software\nEngineering and Methodology, 12(3):317-370, July\n2003.\n896 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)", "keywords": "social interaction;operational semantics;organizational and communicative abstraction;organizational programming language;structural operational semantics;multi-agent interaction connector-based model;connector-based model of multi-agent interaction;institutional framework;pre-defined abstraction;formal execution semantics;multiagent interaction;software architecture;software connector"}
{"name": "train_I-48", "title": "Normative System Games", "abstract": "We develop a model of normative systems in which agents are assumed to have multiple goals of increasing priority, and investigate the computational complexity and game theoretic properties of this model. In the underlying model of normative systems, we use Kripke structures to represent the possible transitions of a multiagent system. A normative system is then simply a subset of the Kripke structure, which contains the arcs that are forbidden by the normative system. We specify an agent\"s goals as a hierarchy of formulae of Computation Tree Logic (CTL), a widely used logic for representing the properties of Kripke structures: the intuition is that goals further up the hierarchy are preferred by the agent over those that appear further down the hierarchy. Using this scheme, we define a model of ordinal utility, which in turn allows us to interpret our Kripke-based normative systems as games, in which agents must determine whether to comply with the normative system or not. We then characterise the computational complexity of a number of decision problems associated with these Kripke-based normative system games; for example, we show that the complexity of checking whether there exists a normative system which has the property of being a Nash implementation is NP-complete.", "fulltext": "1. INTRODUCTION\nNormative systems, or social laws, have proved to be an attractive\napproach to coordination in multi-agent systems [13, 14, 10, 15, 1].\nAlthough the various approaches to normative systems proposed in\nthe literature differ on technical details, they all share the same\nbasic intuition that a normative system is a set of constraints on the\nbehaviour of agents in the system; by imposing these constraints,\nit is hoped that some desirable objective will emerge. The idea of\nusing social laws to coordinate multi-agent systems was proposed\nby Shoham and Tennenholtz [13, 14]; their approach was extended\nby van der Hoek et al. to include the idea of specifying a desirable\nglobal objective for a social law as a logical formula, with the idea\nbeing that the normative system would be regarded as successful\nif, after implementing it (i.e., after eliminating all forbidden\nactions), the objective formula was guaranteed to be satisfied in the\nsystem [15]. However, this model did not take into account the\npreferences of individual agents, and hence neglected to account\nfor possible strategic behaviour by agents when deciding whether\nto comply with the normative system or not. This model of\nnormative systems was further extended by attributing to each agent\na single goal in [16]. However, this model was still too\nimpoverished to capture the kinds of decision making that take place when\nan agent decides whether or not to comply with a social law. In\nreality, strategic considerations come into play: an agent takes into\naccount not just whether the normative system would be beneficial\nfor itself, but also whether other agents will rationally choose to\nparticipate.\nIn this paper, we develop a model of normative systems in which\nagents are assumed to have multiple goals, of increasing priority.\nWe specify an agent\"s goals as a hierarchy of formulae of\nComputation Tree Logic (CTL), a widely used logic for representing the\nproperties of Kripke structures [8]: the intuition is that goals further\nup the hierarchy are preferred by the agent over those that appear\nfurther down the hierarchy. Using this scheme, we define a model\nof ordinal utility, which in turn allows us to interpret our\nKripkebased normative systems as games, in which agents must determine\nwhether to comply with the normative system or not. We thus\nprovide a very natural bridge between logical structures and languages\nand the techniques and concepts of game theory, which have proved\nto be very powerful for analysing social contract-style scenarios\nsuch as normative systems [3, 4]. We then characterise the\ncomputational complexity of a number of decision problems associated\nwith these Kripke-based normative system games; for example, we\nshow that the complexity of checking whether there exists a\nnormative system which has the property of being a Nash implementation\nis NP-complete.\n2. KRIPKE STRUCTURES AND CTL\nWe use Kripke structures as our basic semantic model for\nmultiagent systems [8]. A Kripke structure is essentially a directed\ngraph, with the vertex set S corresponding to possible states of the\nsystem being modelled, and the relation R \u2286 S \u00d7 S capturing the\n881\n978-81-904262-7-5 (RPS) c 2007 IFAAMAS\npossible transitions of the system; intuitively, these transitions are\ncaused by agents in the system performing actions, although we do\nnot include such actions in our semantic model (see, e.g., [13, 2,\n15] for related models which include actions as first class citizens).\nWe let S0\ndenote the set of possible initial states of the system.\nOur model is intended to correspond to the well-known interleaved\nconcurrency model from the reactive systems literature: thus an\narc corresponds to the execution of an atomic action by one of the\nprocesses in the system, which we call agents.\nIt is important to note that, in contrast to such models as [2, 15],\nwe are therefore here not modelling synchronous action. This\nassumption is not in fact essential for our analysis, but it greatly\nsimplifies the presentation. However, we find it convenient to include\nwithin our model the agents that cause transitions. We therefore\nassume a set A of agents, and we label each transition in R with\nthe agent that causes the transition via a function \u03b1 : R \u2192 A.\nFinally, we use a vocabulary \u03a6 = {p, q, . . .} of Boolean variables\nto express the properties of individual states S: we use a function\nV : S \u2192 2\u03a6\nto label each state with the Boolean variables true (or\nsatisfied) in that state.\nCollecting these components together, an agent-labelled Kripke\nstructure (over \u03a6) is a 6-tuple:\nK = S, S0\n, R, A, \u03b1, V , where:\n\u2022 S is a finite, non-empty set of states,\n\u2022 S0\n\u2286 S (S0\n= \u2205) is the set of initial states;\n\u2022 R \u2286 S \u00d7 S is a total binary relation on S, which we refer to\nas the transition relation1\n;\n\u2022 A = {1, . . . , n} is a set of agents;\n\u2022 \u03b1 : R \u2192 A labels each transition in R with an agent; and\n\u2022 V : S \u2192 2\u03a6\nlabels each state with the set of propositional\nvariables true in that state.\nIn the interests of brevity, we shall hereafter refer to an\nagentlabelled Kripke structure simply as a Kripke structure. A path\nover a transition relation R is an infinite sequence of states \u03c0 =\ns0, s1, . . . which must satisfy the property that \u2200u \u2208 N: (su , su+1) \u2208\nR. If u \u2208 N, then we denote by \u03c0[u] the component indexed by\nu in \u03c0 (thus \u03c0[0] denotes the first element, \u03c0[1] the second, and so\non). A path \u03c0 such that \u03c0[0] = s is an s-path. Let \u03a0R(s) denote\nthe set of s-paths over R; since it will usually be clear from\ncontext, we often omit reference to R, and simply write \u03a0(s). We will\nsometimes refer to and think of an s-path as a possible\ncomputation, or system evolution, from s.\nEXAMPLE 1. Our running example is of a system with a single\nnon-sharable resource, which is desired by two agents. Consider\nthe Kripke structure depicted in Figure 1. We have two states, s and\nt, and two corresponding Boolean variables p1 and p2, which are\n1\nIn the branching time temporal logic literature, a relation R \u2286\nS \u00d7 S is said to be total iff \u2200s \u2203s : (s, s ) \u2208 R. Note that\nthe term total relation is sometimes used to refer to relations\nR \u2286 S \u00d7 S such that for every pair of elements s, s \u2208 S we\nhave either (s, s ) \u2208 R or (s , s) \u2208 R; we are not using the term\nin this way here. It is also worth noting that for some domains,\nother constraints may be more appropriate than simple totality. For\nexample, one might consider the agent totality requirement, that in\nevery state, every agent has at least one possible transition\navailable: \u2200s\u2200i \u2208 A\u2203s : (s, s ) \u2208 R and \u03b1(s, s ) = i.\n2p\nt\np\n2\n2\n1\ns\n1\n1\nFigure 1: The resource control running example.\nmutually exclusive. Think of pi as meaning agent i has currently\ncontrol over the resource. Each agent has two possible actions,\nwhen in possession of the resource: either give it away, or keep it.\nObviously there are infinitely many different s-paths and t-paths.\nLet us say that our set of initial states S0\nequals {s, t}, i.e., we\ndon\"t make any assumptions about who initially has control over\nthe resource.\n2.1 CTL\nWe now define Computation Tree Logic (CTL), a branching time\ntemporal logic intended for representing the properties of Kripke\nstructures [8]. Note that since CTL is well known and widely\ndocumented in the literature, our presentation, though complete, will be\nsomewhat terse. We will use CTL to express agents\" goals.\nThe syntax of CTL is defined by the following grammar:\n\u03d5 ::= | p | \u00ac\u03d5 | \u03d5 \u2228 \u03d5 | E f\u03d5 | E(\u03d5 U \u03d5) | A f\u03d5 | A(\u03d5 U \u03d5)\nwhere p \u2208 \u03a6. We denote the set of CTL formula over \u03a6 by L\u03a6;\nsince \u03a6 is understood, we usually omit reference to it.\nThe semantics of CTL are given with respect to the satisfaction\nrelation |=, which holds between pairs of the form K, s, (where\nK is a Kripke structure and s is a state in K), and formulae of the\nlanguage. The satisfaction relation is defined as follows:\nK, s |= ;\nK, s |= p iff p \u2208 V (s) (where p \u2208 \u03a6);\nK, s |= \u00ac\u03d5 iff not K, s |= \u03d5;\nK, s |= \u03d5 \u2228 \u03c8 iff K, s |= \u03d5 or K, s |= \u03c8;\nK, s |= A f\u03d5 iff \u2200\u03c0 \u2208 \u03a0(s) : K, \u03c0[1] |= \u03d5;\nK, s |= E f\u03d5 iff \u2203\u03c0 \u2208 \u03a0(s) : K, \u03c0[1] |= \u03d5;\nK, s |= A(\u03d5 U \u03c8) iff \u2200\u03c0 \u2208 \u03a0(s), \u2203u \u2208 N, s.t. K, \u03c0[u] |= \u03c8\nand \u2200v, (0 \u2264 v < u) : K, \u03c0[v] |= \u03d5\nK, s |= E(\u03d5 U \u03c8) iff \u2203\u03c0 \u2208 \u03a0(s), \u2203u \u2208 N, s.t. K, \u03c0[u] |= \u03c8\nand \u2200v, (0 \u2264 v < u) : K, \u03c0[v] |= \u03d5\nThe remaining classical logic connectives (\u2227, \u2192, \u2194) are\nassumed to be defined as abbreviations in terms of \u00ac, \u2228, in the\nconventional manner. The remaining CTL temporal operators are\ndefined:\nA\u2666\u03d5 \u2261 A( U \u03d5) E\u2666\u03d5 \u2261 E( U \u03d5)\nA \u03d5 \u2261 \u00acE\u2666\u00ac\u03d5 E \u03d5 \u2261 \u00acA\u2666\u00ac\u03d5\nWe say \u03d5 is satisfiable if K, s |= \u03d5 for some Kripke structure K\nand state s in K; \u03d5 is valid if K, s |= \u03d5 for all Kripke structures\nK and states s in K. The problem of checking whether K, s |= \u03d5\nfor given K, s, \u03d5 (model checking) can be done in deterministic\npolynomial time, while checking whether a given \u03d5 is satisfiable or\nwhether \u03d5 is valid is EXPTIME-complete [8]. We write K |= \u03d5 if\nK, s0 |= \u03d5 for all s0 \u2208 S0\n, and |= \u03d5 if K |= \u03d5 for all K.\n882 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\n3. NORMATIVE SYSTEMS\nFor our purposes, a normative system is simply a set of constraints\non the behaviour of agents in a system [1]. More precisely, a\nnormative system defines, for every possible system transition, whether\nor not that transition is considered to be legal or not. Different\nnormative systems may differ on whether or not a transition is\nlegal. Formally, a normative system \u03b7 (w.r.t. a Kripke structure\nK = S, S0\n, R, A, \u03b1, V ) is simply a subset of R, such that R \\ \u03b7\nis a total relation. The requirement that R\\\u03b7 is total is a\nreasonableness constraint: it prevents normative systems which lead to states\nwith no successor. Let N (R) = {\u03b7 : (\u03b7 \u2286 R) & (R \\ \u03b7 is total)}\nbe the set of normative systems over R. The intended\ninterpretation of a normative system \u03b7 is that (s, s ) \u2208 \u03b7 means transition\n(s, s ) is forbidden in the context of \u03b7; hence R \\ \u03b7 denotes the\nlegal transitions of \u03b7. Since it is assumed \u03b7 is reasonable, we are\nguaranteed that a legal outward transition exists for every state. We\ndenote the empty normative system by \u03b7\u2205, so \u03b7\u2205 = \u2205. Note that\nthe empty normative system \u03b7\u2205 is reasonable with respect to any\ntransition relation R.\nThe effect of implementing a normative system on a Kripke\nstructure is to eliminate from it all transitions that are forbidden\naccording to this normative system (see [15, 1]). If K is a Kripke\nstructure, and \u03b7 is a normative system over K, then K \u2020 \u03b7 denotes the\nKripke structure obtained from K by deleting transitions forbidden\nin \u03b7. Formally, if K = S, S0\n, R, A, \u03b1, V , and \u03b7 \u2208 N (R), then\nlet K\u2020\u03b7 = K be the Kripke structure K = S , S0\n, R , A , \u03b1 , V\nwhere:\n\u2022 S = S , S0\n= S0\n, A = A , and V = V ;\n\u2022 R = R \\ \u03b7; and\n\u2022 \u03b1 is the restriction of \u03b1 to R :\n\u03b1 (s, s ) =\nj\n\u03b1(s, s ) if (s, s ) \u2208 R\nundefined otherwise.\nNotice that for all K, we have K \u2020 \u03b7\u2205 = K.\nEXAMPLE 1. (continued) When thinking in terms of fairness, it\nseems natural to consider normative systems \u03b7 that contain (s, s)\nor (t, t). A normative system with (s, t) would not be fair, in the\nsense that A\u2666A \u00acp1 \u2228 A\u2666A \u00acp2 holds: in all paths, from\nsome moment on, one agent will have control forever. Let us, for\nlater reference, fix \u03b71 = {(s, s)}, \u03b72 = {(t, t)}, and \u03b73 = {(s, s),\n(t, t)}.\nLater, we will address the issue of whether or not agents should\nrationally choose to comply with a particular normative system. In\nthis context, it is useful to define operators on normative systems\nwhich correspond to groups of agents defecting from the\nnormative system. Formally, let K = S, S0\n,R, A,\u03b1, V be a Kripke\nstructure, let C \u2286 A be a set of agents over K, and let \u03b7 be a\nnormative system over K. Then:\n\u2022 \u03b7 C denotes the normative system that is the same as \u03b7\nexcept that it only contains the arcs of \u03b7 that correspond to\nthe actions of agents in C. We call \u03b7 C the restriction of \u03b7\nto C, and it is defined as:\n\u03b7 C = {(s, s ) : (s, s ) \u2208 \u03b7 & \u03b1(s, s ) \u2208 C}.\nThus K \u2020 (\u03b7 C) is the Kripke structure that results if only\nthe agents in C choose to comply with the normative system.\n\u2022 \u03b7 C denotes the normative system that is the same as \u03b7\nexcept that it only contains the arcs of \u03b7 that do not correspond\nto actions of agents in C. We call \u03b7 C the exclusion of C\nfrom \u03b7, and it is defined as:\n\u03b7 C = {(s, s ) : (s, s ) \u2208 \u03b7 & \u03b1(s, s ) \u2208 C}.\nThus K \u2020 (\u03b7 C) is the Kripke structure that results if only\nthe agents in C choose not to comply with the normative\nsystem (i.e., the only ones who comply are those in A \\ C).\nNote that we have \u03b7 C = \u03b7 (A\\C) and \u03b7 C = \u03b7 (A\\C).\nEXAMPLE 1. (Continued) We have \u03b71 {1} = \u03b71 = {(s, s)},\nwhile \u03b71 {1} = \u03b7\u2205 = \u03b71 {2}. Similarly, we have \u03b73 {1} =\n{(s, s)} and \u03b73 {1} = {(t, t)}.\n4. GOALS AND UTILITIES\nNext, we want to be able to capture the goals that agents have, as\nthese will drive an agent\"s strategic considerations - particularly, as\nwe will see, considerations about whether or not to comply with a\nnormative system. We will model an agent\"s goals as a prioritised\nlist of CTL formulae, representing increasingly desired properties\nthat the agent wishes to hold. The intended interpretation of such a\ngoal hierarchy \u03b3i for agent i \u2208 A is that the further up the\nhierarchy a goal is, the more it is desired by i. Note that we assume\nthat if an agent can achieve a goal at a particular level in its goal\nhierarchy, then it is unconcerned about goals lower down the\nhierarchy. Formally, a goal hierarchy, \u03b3, (over a Kripke structure K)\nis a finite, non-empty sequence of CTL formulae\n\u03b3 = (\u03d50, \u03d51, . . . , \u03d5k )\nin which, by convention, \u03d50 = . We use a natural number\nindexing notation to extract the elements of a goal hierarchy, so if\n\u03b3 = (\u03d50, \u03d51, . . . , \u03d5k ) then \u03b3[0] = \u03d50, \u03b3[1] = \u03d51, and so on. We\ndenote the largest index of any element in \u03b3 by |\u03b3|.\nA particular Kripke structure K is said to satisfy a goal at\nindex x in goal hierarchy \u03b3 if K |= \u03b3[x], i.e., if \u03b3[x] is satisfied in all\ninitial states S0\nof K. An obvious potential property of goal\nhierarchies is monotonicity: where goals at higher levels in the hierarchy\nlogically imply those at lower levels in the hierarchy. Formally, a\ngoal hierarchy \u03b3 is monotonic if for all x \u2208 {1, . . . , |\u03b3|} \u2286 N, we\nhave |= \u03b3[x] \u2192 \u03b3[x \u2212 1]. The simplest type of monotonic goal\nhierarchy is where \u03b3[x + 1] = \u03b3[x] \u2227 \u03c8x+1 for some \u03c8x+1, so at\neach successive level of the hierarchy, we add new constraints to\nthe goal of the previous level. Although this is a natural property\nof many goal hierarchies, it is not a property we demand of all goal\nhierarchies.\nEXAMPLE 1. (continued) Suppose the agents have similar, but\nopposing goals: each agent i wants to keep the source as often and\nlong as possible for himself. Define each agent\"s goal hierarchy as:\n\u03b3i = ( \u03d5i\n0 = , \u03d5i\n1 = E\u2666pi ,\n\u03d5i\n2 = E E\u2666pi , \u03d5i\n3 = E\u2666E pi ,\n\u03d5i\n4 = A E\u2666pi , \u03d5i\n5 = E\u2666A pi\n\u03d5i\n6 = A A\u2666pi , \u03d5i\n7 = A (A\u2666pi \u2227 E pi ),\n\u03d5i\n8 = A pi )\nThe most desired goal of agent i is to, in every computation,\nalways have the resource, pi (this is expressed in \u03d5i\n8). Thanks to our\nreasonableness constraint, this goal implies \u03d5i\n7 which says that, no\nmatter how the computation paths evolve, it will always be that all\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 883\ncontinuations will hit a point in which pi , and, moreover, there is a\ncontinuation in which pi always holds. Goal \u03d5i\n6 is a fairness\nconstraint implied by it. Note that A\u2666pi says that every computation\neventually reaches a pi state. This may mean that after pi has\nhappened, it will never happen again. \u03d5i\n6 circumvents this: it says that,\nno matter where you are, there should be a future pi state. The goal\n\u03d5i\n5 is like the strong goal \u03d5i\n8 but it accepts that this is only achieved\nin some computation, eventually. \u03d5i\n4 requires that in every path,\nthere is always a continuation that eventually gives pi . Goal \u03d5i\n3\nsays that pi should be true on some branch, from some moment on.\nIt implies \u03d5i\n2 which expresses that there is a computation such that\neverywhere during it, it is possible to choose a continuation that\neventually satisfies pi . This implies \u03d5i\n1, which says that pi should\nat least not be impossible. If we even drop that demand, we have\nthe trivial goal \u03d5i\n0.\nWe remark that it may seem more natural to express a fairness\nconstraint \u03d5i\n6 as A \u2666pi . However, this is not a proper CTL\nformula. It is in fact a formula in CTL\n\u2217\n[9], and in this logic, the two\nexpressions would be equivalent. However, our basic complexity\nresults in the next sections would not hold for the richer language\nCTL\n\u22172\n, and the price to pay for this is that we have to formulate\nour desired goals in a somewhat more cumbersome manner than\nwe might ideally like. Of course, our basic framework does not\ndemand that goals are expressed in CTL; they could equally well\nbe expressed in CTL\n\u2217\nor indeed ATL [2] (as in [15]). We\ncomment on the implications of alternative goal representations at the\nconclusion of the next section.\nA multi-agent system collects together a Kripke structure\n(representing the basic properties of a system under consideration: its\nstate space, and the possible state transitions that may occur in it),\ntogether with a goal hierarchy, one for each agent, representing the\naspirations of the agents in the system. Formally, a multi-agent\nsystem, M , is an (n + 1)-tuple:\nM = K, \u03b31, . . . , \u03b3n\nwhere K is a Kripke structure, and for each agent i in K, \u03b3i is a\ngoal hierarchy over K.\n4.1 The Utility of Normative Systems\nWe can now define the utility of a Kripke structure for an agent.\nThe idea is that the utility of a Kripke structure is the highest index\nof any goal that is guaranteed for that agent in the Kripke structure.\nWe make this precise in the function ui (\u00b7):\nui (K) = max{j : 0 \u2264 j \u2264 |\u03b3i | & K |= \u03b3i [j ]}\nNote that using these definitions of goals and utility, it never\nmakes sense to have a goal \u03d5 at index n if there is a logically\nweaker goal \u03c8 at index n + k in the hierarchy: by definition of\nutility, it could never be n for any structure K.\nEXAMPLE 1. (continued) Let M = K, \u03b31, \u03b32 be the\nmultiagent system of Figure 1, with \u03b31 and \u03b32 as defined earlier in this\nexample. Recall that we have defined S0\nas {s, t}. Then, u1(K) =\nu2(K) = 4: goal \u03d54 is true in S0\n, but \u03d55 is not. To see that\n\u03d52\n4 = A E\u2666p2 is true in s for instance: note that on ever path it\nis always the case that there is a transition to t, in which p2 is true.\nNotice that since for any goal hierarchy \u03b3i we have \u03b3[0] = ,\nthen for all Kripke structures, ui (K) is well defined, with ui (K) \u2265\n2\nCTL\n\u2217\nmodel checking is PSPACE-complete, and hence much\nworse (under standard complexity theoretic assumptions) than\nmodel checking CTL [8].\n\u03b7 \u03b41(K, \u03b7) \u03b42(K, \u03b7)\n\u03b7\u2205 0 0\n\u03b71 0 3\n\u03b72 3 0\n\u03b73 2 2\nC D\nC (2, 2) (0, 3)\nD (3, 0) (0, 0)\nFigure 2: Benefits of implementing a normative system \u03b7 (left)\nand pay-offs for the game \u03a3M .\n0. Note that this is an ordinal utility measure: it tells us, for any\ngiven agent, the relative utility of different Kripke structures, but\nutility values are not on some standard system-wide scale. The fact\nthat ui (K1) > ui (K2) certainly means that i strictly prefers K1\nover K2, but the fact that ui (K) > uj (K) does not mean that i\nvalues K more highly than j . Thus, it does not make sense to\ncompare utility values between agents, and so for example, some system\nwide measures of utility, (notably those measures that aggregate\nindividual utilities, such as social welfare), do not make sense when\napplied in this setting. However, as we shall see shortly, other\nmeasures - such as Pareto efficiency - can be usefully applied.\nThere are other representations for goals, which would allow us\nto define cardinal utilities. The simplest would be to specify goals \u03b3\nfor an agent as a finite, non-empty, one-to-one relation: \u03b3 \u2286 L\u00d7R.\nWe assume that the x values in pairs (\u03d5, x) \u2208 \u03b3 are specified so\nthat x for agent i means the same as x for agent j , and so we have\ncardinal utility. We then define the utility for i of a Kripke structure\nK asui (K) = max{x : (\u03d5, x) \u2208 \u03b3i & K |= \u03d5}. The results of\nthis paper in fact hold irrespective of which of these representations\nwe actually choose; we fix upon the goal hierarchy approach in the\ninterests of simplicity.\nOur next step is to show how, in much the same way, we can lift\nthe utility function from Kripke structures to normative systems.\nSuppose we are given a multi-agent system M = K, \u03b31, . . . , \u03b3n\nand an associated normative system \u03b7 over K. Let for agent i,\n\u03b4i (K, K ) be the difference in his utility when moving from K to\nK : \u03b4i (K, K ) = ui (K )\u2212 ui (K). Then the utility of \u03b7 to agent i\nwrt K is \u03b4i (K, K \u2020 \u03b7). We will sometimes abuse notation and just\nwrite \u03b4i (K, \u03b7) for this, and refer to it as the benefit for agent i of\nimplementing \u03b7 in K. Note that this benefit can be negative.\nSummarising, the utility of a normative system to an agent is the\ndifference between the utility of the Kripke structure in which the\nnormative system was implemented and the original Kripke\nstructure. If this value is greater than 0, then the agent would be better\noff if the normative system were imposed, while if it is less than\n0 then the agent would be worse off if \u03b7 were imposed than in the\noriginal system. We say \u03b7 is individually rational for i wrt K if\n\u03b4i (K, \u03b7) > 0, and individually rational simpliciter if \u03b7 is\nindividually rational for every agent.\nA social system now is a pair\n\u03a3 = M , \u03b7\nwhere M is a multi-agent system, and \u03b7 is a normative system over\nM .\nEXAMPLE 1. The table at the left hand in Figure 2 displays the\nutilities \u03b4i (K, \u03b7) of implementing \u03b7 in the Kripke structure of our\nrunning example, for the normative systems \u03b7 = \u03b7\u2205, \u03b71, \u03b72 and \u03b73,\nintroduced before. Recall that u1(K) = u2(K) = 4.\n4.2 Universal and Existential Goals\n884 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nKeeping in mind that a norm \u03b7 restricts the possible transitions\nof the model under consideration, we make the following\nobservation, borrowing from [15]. Some classes of goals are monotonic\nor anti-monotonic with respect to adding additional constraints to\na system. Let us therefore define two fragments of the language\nof CTL: the universal language Lu\nwith typical element \u03bc, and the\nexistential fragment Le\nwith typical element \u03b5.\n\u03bc ::= | p | \u00acp | \u03bc \u2228 \u03bc | A f\u03bc | A \u03bc | A(\u03bc U \u03bc)\n\u03b5 ::= | p | \u00acp | \u03b5 \u2228 \u03b5 | E f\u03b5 | E\u2666\u03b5 | E(\u03b5 U \u03b5)\nLet us say, for two Kripke structures K1 = S, S0\n, R1, A, \u03b1, V\nand K2 = S, S0\n, R2, A, \u03b1, V that K1 is a subsystem of K2 and\nK2 is a supersystem of K1, written K1 K2 iff R1 \u2286 R2. Note\nthat typically K \u2020 \u03b7 K. Then we have (cf. [15]).\nTHEOREM 1. Suppose K1 K2, and s \u2208 S. Then\n\u2200\u03b5 \u2208 Le\n: K1, s |= \u03b5 \u21d2 K2, s |= \u03b5\n\u2200\u03bc \u2208 Lu\n: K2, s |= \u03bc \u21d2 K1, s |= \u03bc\nThis has the following effect on imposing a new norm:\nCOROLLARY 1. Let K be a structure, and \u03b7 a normative\nsystem. Let \u03b3i denote a goal hierarchy for agent i.\n1. Suppose agent i\"s utility ui (K) is n, and \u03b3i [n] \u2208 Lu\n, (i.e.,\n\u03b3i [n] is a universal formula). Then, for any normative system\n\u03b7, \u03b4i (K, \u03b7) \u2265 0.\n2. Suppose agent i\"s utility ui (K \u2020 \u03b7) is n, and \u03b3i [n] is an\nexistential formula \u03b5. Then, \u03b4i (K \u2020 \u03b7, K) \u2265 0.\nCorollary 1\"s first item says that an agent whose current\nmaximal goal in a system is a universal formula, need never fear the\nimposition of a new norm \u03b7. The reason is that his current goal will\nat least remain true (in fact a goal higher up in the hierarchy may\nbecome true). It follows from this that an agent with only universal\ngoals can only gain from the imposition of normative systems \u03b7.\nThe opposite is true for existential goals, according to the second\nitem of the corollary: it can never be bad for an agent to undo a\nnorm \u03b7. Hence, an agent with only existential goals might well fear\nany norm \u03b7.\nHowever, these observations implicitly assume that all agents in\nthe system will comply with the norm. Whether they will in fact do\nso, of course, is a strategic decision: it partly depends on what the\nagent thinks that other agents will do. This motivates us to consider\nnormative system games.\n5. NORMATIVE SYSTEM GAMES\nWe now have a principled way of talking about the utility of\nnormative systems for agents, and so we can start to apply the technical\napparatus of game theory to analyse them.\nSuppose we have a multi-agent system M = K, \u03b31, . . . , \u03b3n\nand a normative system \u03b7 over K. It is proposed to the agents\nin M that \u03b7 should be imposed on K, (typically to achieve some\ncoordination objective). Our agent - let\"s say agent i - is then faced\nwith a choice: should it comply with the strictures of the normative\nsystem, or not? Note that this reasoning takes place before the agent\nis in the system - it is a design time consideration.\nWe can understand the reasoning here as a game, as follows. A\ngame in strategic normal form (cf. [11, p.11]) is a structure:\nG = AG, S1, . . . , Sn , U1, . . . , Un where:\n\u2022 AG = {1, . . . , n} is a set of agents - the players of the game;\n\u2022 Si is the set of strategies for each agent i \u2208 AG (a strategy\nfor an agent i is nothing else than a choice between\nalternative actions); and\n\u2022 Ui : (S1 \u00d7 \u00b7 \u00b7 \u00b7 \u00d7 Sn ) \u2192 R is the utility function for agent\ni \u2208 AG, which assigns a utility to every combination of\nstrategy choices for the agents.\nNow, suppose we are given a social system \u03a3 = M , \u03b7 where\nM = K, \u03b31, . . . , \u03b3n . Then we can associate a game - the\nnormative system game - G\u03a3 with \u03a3, as follows. The agents AG in G\u03a3\nare as in \u03a3. Each agent i has just two strategies available to it:\n\u2022 C - comply (cooperate) with the normative system; and\n\u2022 D - do not comply with (defect from) the normative system.\nIf S is a tuple of strategies, one for each agent, and x \u2208 {C, D},\nthen we denote by AGx\nS the subset of agents that play strategy x in\nS. Hence, for a social system \u03a3 = M , \u03b7 , the normative system\n\u03b7 AGC\nS only implements the restrictions for those agents that\nchoose to cooperate in G\u03a3. Note that this is the same as \u03b7 AGD\nS :\nthe normative system that excludes all the restrictions of agents that\nplay D in G\u03a3. We then define the utility functions Ui for each\ni \u2208 AG as:\nUi (S) = \u03b4i (K, \u03b7 AGC\nS ).\nSo, for example, if SD is a collection of strategies in which every\nagent defects (i.e., does not comply with the norm), then\nUi (SD ) = \u03b4i (K, (\u03b7 AGD\nSD\n)) = ui (K \u2020 \u03b7\u2205) \u2212 ui (K) = 0.\nIn the same way, if SC is a collection of strategies in which every\nagent cooperates (i.e., complies with the norm), then\nUi (SC ) = \u03b4i (K, (\u03b7 AGD\nSC\n)) = ui (K \u2020 (\u03b7 \u2205)) = ui (K \u2020 \u03b7).\nWe can now start to investigate some properties of normative\nsystem games.\nEXAMPLE 1. (continued) For our example system, we have\ndisplayed the different U values for our multi agent system with the\nnorm \u03b73, i.e., {(s, s), (t, t)} as the second table of Figure 2. For\ninstance, the pair (0, 3) in the matrix under the entry S = C, D\nis obtained as follows. U1( C, D ) = \u03b41(K, \u03b73 AGC\nC,D ) =\nu1(K \u2020 \u03b73 AGC\nC,D ) \u2212 u1(K). The first term of this is the\nutility of 1 in the system K where we implement \u03b73 for the\ncooperating agent, i.e., 1, only. This means that the transitions are\nR \\ {(s, s)}. In this system, still \u03d51\n4 = A E\u2666p1 is the highest\ngoal for agent 1. This is the same utility for 1 as in K, and hence,\n\u03b41(K, \u03b73 AGC\nC,D ) = 0. Agent 2 of course benefits if agent 1\ncomplies with \u03b73 while 2 does not. His utility would be 3, since\n\u03b73 AGC\nC,D is in fact \u03b71.\n5.1 Individually Rational Normative Systems\nA normative system is individually rational if every agent would\nfare better if the normative system were imposed than otherwise.\nThis is a necessary, although not sufficient condition on a norm to\nexpect that everybody respects it. Note that \u03b73 of our example is\nindividually rational for both 1 and 2, although this is not a stable\nsituation: given that the other plays C, i is better of by playing\nD. We can easily characterise individually rationality with respect\nto the corresponding game in strategic form, as follows. Let \u03a3 =\nM , \u03b7 be a social system. Then the following are equivalent:\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 885\nf(xk)\n...\ns0\ns1\ns2\ns3\ns4\ns(2k\u22121)\ns2k\nt(x1)\nf(x1)\nt(x2)\nf(x2)\nt(xk)\nFigure 3: The Kripke structure produced in the reduction of\nTheorem 2; all transitions are associated with agent 1, the only\ninitial state is s0.\n1. \u03b7 is individually rational in M ;\n2. \u2200i \u2208 AG, Ui (SC ) > Ui (SD ) in the game G\u03a3.\nThe decision problem associated with individually rational\nnormative systems is as follows:\nINDIVIDUALLY RATIONAL NORMATIVE SYSTEM (IRNS):\nGiven: Multi-agent system M .\nQuestion: Does there exist an individually rational\nnormative system for M ?\nTHEOREM 2. IRNS is NP-complete, even in one-agent systems.\nPROOF. For membership of NP, guess a normative system \u03b7,\nand verify that it is individually rational. Since \u03b7 \u2286 R, we will be\nable to guess it in nondeterministic polynomial time. To verify that\nit is individually rational, we check that for all i, we have ui (K \u2020\n\u03b7) > ui (K); computing K \u2020 \u03b7 is just set subtraction, so can be\ndone in polynomial time, while determining the value of ui (K) for\nany K can be done with a polynomial number of model checking\ncalls, each of which requires only time polynomial in the K and \u03b3.\nHence verifying that ui (K \u2020 \u03b7) > ui (K) requires only polynomial\ntime.\nFor NP-hardness, we reduce SAT [12, p.77]. Given a SAT instance\n\u03d5 over Boolean variables x1, . . . , xk , we produce an instance of\nIRNS as follows. First, we define a single agent A = {1}. For each\nBoolean variable xi in the SAT instance, we create two Boolean\nvariables t(xi ) and f (xi ) in the IRNS instance. We then create a\nKripke structure K\u03d5 with 2k + 1 states, as shown in Figure 3: arcs\nin this graph correspond to transitions in K\u03d5. Let \u03d5\u2217\nbe the result\nof systematically substituting for every Boolean variable xi in \u03d5\nthe CTL expression (E ft(xi )). Next, consider the following\nformulae:\nk^\ni=1\nE f(t(xi ) \u2228 f (xi )) (1)\nk^\ni=1\n\u00ac((E ft(xi )) \u2227 (E ff (xi ))) (2)\nWe then define the goal hierarchy for all agent 1 as follows:\n\u03b31[0] =\n\u03b31[1] = (1) \u2227 (2) \u2227 \u03d5\u2217\nWe claim there is an individually rational normative system for the\ninstance so constructed iff \u03d5 is satisfiable. First, notice that any\nindividually rational normative system must force \u03b31[1] to be true,\nsince in the original system, we do not have \u03b31[1].\nFor the \u21d2 direction, if there is an individually rational normative\nsystem \u03b7, then we construct a satisfying assignment for \u03d5 by\nconsidering the arcs that are forbidden by \u03b7: formula (1) ensures that\nwe must forbid an arc to either a t(xi ) or a f (xi ) state for all\nvariables xi , but (2) ensures that we cannot forbid arcs to both. So, if\nwe forbid an arc to a t(xi ) state then in the corresponding valuation\nfor \u03d5 we make xi false, while if we forbid an arc to a f (xi ) state\nthen we make xi true. The fact that \u03d5\u2217\nis part of the goal ensures\nthat the normative system is indeed a valuation for \u03d5.\nFor \u21d0, note that for any satisfying valuation for \u03d5 we can\nconstruct an individually rational normative system \u03b7, as follows: if\nthe valuation makes xi true, we forbid the arc to the f (xi ) state,\nwhile if the valuation makes xi false, we forbid the arc to the t(xi )\nstate. The resulting normative system ensures \u03b31[1], and is thus\nindividually rational.\nNotice that the Kripke structure constructed in the reduction\ncontains just a single agent, and so the Theorem is proven.\n5.2 Pareto Efficient Normative Systems\nPareto efficiency is a basic measure of how good a particular\noutcome is for a group of agents [11, p.7]. Intuitively, an outcome\nis Pareto efficient if there is no other outcome that makes every\nagent better off. In our framework, suppose we are given a social\nsystem \u03a3 = M , \u03b7 , and asked whether \u03b7 is Pareto efficient. This\namounts to asking whether or not there is some other normative\nsystem \u03b7 such that every agent would be better off under \u03b7 than\nwith \u03b7. If \u03b7 makes every agent better off than \u03b7, then we say \u03b7\nPareto dominates \u03b7. The decision problem is as follows:\nPARETO EFFICIENT NORMATIVE SYSTEM (PENS):\nGiven: Multi-agent system M and normative system \u03b7\nover M .\nQuestion: Is \u03b7 Pareto efficient for M ?\nTHEOREM 3. PENS is co-NP-complete, even for one-agent\nsystems.\nPROOF. Let M and \u03b7 be as in the Theorem. We show that the\ncomplement problem to PENS, which we refer to as PARETO\nDOMINATED, is NP-complete. In this problem, we are given M and \u03b7,\nand we are asked whether \u03b7 is Pareto dominated, i.e., whether or not\nthere exists some \u03b7 over M such that \u03b7 makes every agent better\noff than \u03b7. For membership of NP, simply guess a normative system\n\u03b7 , and verify that for all i \u2208 A, we have ui (K \u2020 \u03b7 ) > ui (K \u2020 \u03b7)\n- verifying requires a polynomial number of model checking\nproblems, each of which takes polynomial time. Since \u03b7 \u2286 R, the\nnormative system can be guessed in non-deterministic polynomial\ntime. For NP-hardness, we reduce IRNS, which we know to be\nNPcomplete from Theorem 2. Given an instance M of IRNS, we let M\nin the instance of PARETO DOMINATED be as in the IRNS instance,\nand define the normative system for PARETO DOMINATED to be \u03b7\u2205,\nthe empty normative system. Now, it is straightforward that there\nexists a normative system \u03b7 which Pareto dominates \u03b7\u2205 in M iff\nthere exist an individually rational normative system in M . Since\nthe complement problem is NP-complete, it follows that PENS is\nco-NP-complete.\n886 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\n\u03b70 \u03b71 \u03b72 \u03b73 \u03b74 \u03b75 \u03b76 \u03b77 \u03b78\nu1(K \u2020 \u03b7) 4 4 7 6 5 0 0 8 0\nu2(K \u2020 \u03b7) 4 7 4 6 0 5 8 0 0\nTable 1: Utilities for all possible norms in our example\nHow about Pareto efficient norms for our toy example? Settling\nthis question amounts to finding the dominant normative systems\namong \u03b70 = \u03b7\u2205, \u03b71, \u03b72, \u03b73 defined before, and \u03b74 = {(s, t)}, \u03b75 =\n{(t, s)}, \u03b76 = {(s, s), (t, s)}, \u03b77 = {(t, t), (s, t)} and \u03b78 =\n{(s, t), (t, s)}. The utilities for each system are given in Table 1.\nFrom this, we infer that the Pareto efficient norms are \u03b71, \u03b72, \u03b73, \u03b76\nand \u03b77. Note that \u03b78 prohibits the resource to be passed from one\nagent to another, and this is not good for any agent (since we have\nchosen S0\n= {s, t}, no agent can be sure to ever get the resource,\ni.e., goal \u03d5i\n1 is not true in K \u2020 \u03b78).\n5.3 Nash Implementation Normative Systems\nThe most famous solution concept in game theory is of course\nNash equilibrium [11, p.14]. A collection of strategies, one for each\nagent, is said to form a Nash equilibrium if no agent can benefit by\ndoing anything other than playing its strategy, under the\nassumption that the other agents play theirs. Nash equilibria are important\nbecause they provide stable solutions to the problem of what\nstrategy an agent should play. Note that in our toy example, although\n\u03b73 is individually rational for each agent, it is not a Nash\nequilibrium, since given this norm, it would be beneficial for agent 1 to\ndeviate (and likewise for 2). In our framework, we say a social\nsystem \u03a3 = M , \u03b7 (where \u03b7 = \u03b7\u2205) is a Nash implementation if\nSC (i.e., everyone complying with the normative system) forms a\nNash equilibrium in the game G\u03a3. The intuition is that if \u03a3 is a\nNash implementation, then complying with the normative system\nis a reasonable solution for all concerned: there can be no\nbenefit to deviating from it, indeed, there is a positive incentive for all\nto comply. If \u03a3 is not a Nash implementation, then the normative\nsystem is unlikely to succeed, since compliance is not rational for\nsome agents. (Our choice of terminology is deliberately chosen to\nreflect the way the term Nash implementation is used in\nimplementation theory, or mechanism design [11, p.185], where a game\ndesigner seeks to achieve some outcomes by designing the rules of\nthe game such that these outcomes are equilibria.)\nNASH IMPLEMENTATION (NI) :\nGiven: Multi-agent system M .\nQuestion: Does there exist a non-empty normative\nsystem \u03b7 over M such that M , \u03b7 forms a Nash\nimplementation?\nVerifying that a particular social system forms a Nash\nimplementation can be done in polynomial time - it amounts to checking:\n\u2200i \u2208 A : ui (K \u2020 \u03b7) \u2265 ui (K \u2020 (\u03b7 {i})).\nThis, clearly requires only a polynomial number of model checking\ncalls, each of which requires only polynomial time.\nTHEOREM 4. The NI problem is NP-complete, even for\ntwoagent systems.\nPROOF. For membership of NP, simply guess a normative\nsystem \u03b7 and check that it forms a Nash implementation; since \u03b7 \u2286 R,\nguessing can be done in non-deterministic polynomial time, and as\ns(2k+1)\n1\n1\n1\n1\n1\n1\n11\n1 1\n11\n2\n2\n2\n2\n2\n2\n2\n2\n2\n2\n2\nt(x1)\nf(x1)\nt(x2)\nf(x2)\nt(xk)\nf(xk)\n2\n2\nt(x1)\nf(x1)\nt(x2)\nf(x2)\nt(xk)\nf(xk)\n......\ns0\nFigure 4: Reduction for Theorem 4.\nwe argued above, verifying that it forms a Nash implementation\ncan be done in polynomial time.\nFor NP-hardness, we reduce SAT. Suppose we are given a SAT\ninstance \u03d5 over Boolean variables x1, . . . , xk . Then we construct an\ninstance of NI as follows. We create two agents, A = {1, 2}. For\neach Boolean variable xi we create two Boolean variables, t(xi )\nand f (xi ), and we then define a Kripke structure as shown in\nFigure 4, with s0 being the only initial state; the arc labelling in\nFigure 4 gives the \u03b1 function, and each state is labelled with the\npropositions that are true in that state. For each Boolean variable xi , we\ndefine the formulae xi and x\u22a5\ni as follows:\nxi = E f(t(xi ) \u2227 E f((E f(t(xi ))) \u2227 A f(\u00acf (xi ))))\nx\u22a5\ni = E f(f (xi ) \u2227 E f((E f(f (xi ))) \u2227 A f(\u00act(xi ))))\nLet \u03d5\u2217\nbe the formula obtained from \u03d5 by systematically\nsubstituting xi for xi . Each agent has three goals: \u03b3i [0] = for both\ni \u2208 {1, 2}, while\n\u03b31[1] =\nk^\ni=1\n((E f(t(xi ))) \u2227 (E f(f (xi ))))\n\u03b32[1] = E fE f\nk^\ni=1\n((E f(t(xi ))) \u2227 (E f(f (xi ))))\nand finally, for both agents, \u03b3i [2] being the conjunction of the\nfollowing formulae:\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 887\nk^\ni=1\n(xi \u2228 x\u22a5\ni ) (3)\nk^\ni=1\n\u00ac(xi \u2227 x\u22a5\ni ) (4)\nk^\ni=1\n\u00ac(E f(t(xi )) \u2227 E f(f (xi ))) (5)\n\u03d5\u2217\n(6)\nWe denote the multi-agent system so constructed by M\u03d5. Now,\nwe prove that the SAT instance \u03d5 is satisfiable iff M\u03d5 has a Nash\nimplementation normative system:\nFor the \u21d2 direction, suppose \u03d5 is satisfiable, and let X be a\nsatisfying valuation, i.e., a set of Boolean variables making \u03d5 true.\nWe can extract from X a Nash implementation normative system \u03b7\nas follows: if xi \u2208 X , then \u03b7 includes the arc from s0 to the state\nin which f (xi ) is true, and also includes the arc from s(2k + 1)\nto the state in which f (xi ) is true; if xi \u2208 X , then \u03b7 includes the\narc from s0 to the state in which t(xi ) is true, and also includes\nthe arc from s(2k + 1) to the state in which t(xi ) is true. No\nother arcs, apart from those so defined, as included in \u03b7. Notice\nthat \u03b7 is individually rational for both agents: if they both comply\nwith the normative system, then they will have their \u03b3i [2] goals\nachieved, which they do not in the basic system. To see that \u03b7\nforms a Nash implementation, observe that if either agent defects\nfrom \u03b7, then neither will have their \u03b3i [2] goals achieved: agent 1\nstrictly prefers (C, C) over (D, C), and agent 2 strictly prefers\n(C, C) over (C, D).\nFor the \u21d0 direction, suppose there exists a Nash implementation\nnormative system \u03b7, in which case \u03b7 = \u2205. Then \u03d5 is satisfiable;\nfor suppose not. Then the goals \u03b3i [2] are not achievable by any\nnormative system, (by construction). Now, since \u03b7 must forbid at\nleast one transition, then at least one agent would fail to have its\n\u03b3i [1] goal achieved if it complied, so at least one would do better\nby defecting, i.e., not complying with \u03b7. But this contradicts the\nassumption that \u03b7 is a Nash implementation, i.e., that (C, C) forms\na Nash equilibrium.\nThis result is perhaps of some technical interest beyond the specific\nconcerns of the present paper, since it is related to two problems\nthat are of wider interest: the complexity of mechanism design [5],\nand the complexity of computing Nash equilibria [6, 7]\n5.4 Richer Goal Languages\nIt is interesting to consider what happens to the complexity of\nthe problems we consider above if we allow richer languages for\ngoals: in particular, CTL\n\u2217\n[9]. The main difference is that\ndetermining ui (K) in a given multi-agent system M when such a goal\nlanguage is used involves solving a PSPACE-complete problem (since\nmodel checking for CTL\n\u2217\nis PSPACE-complete [8]). In fact, it seems\nthat for each of the three problems we consider above, the\ncorresponding problem under the assumption of a CTL\n\u2217\nrepresentation\nfor goals is also PSPACE-complete. It cannot be any easier, since\ndetermining the utility of a particular Kripke structure involves\nsolving a PSPACE-complete problem. To see membership in PSPACE\nwe can exploit the fact that PSPACE = NPSPACE [12, p.150], and so\nwe can guess the desired normative system, applying a PSPACE\nverification procedure to check that it has the desired properties.\n6. CONCLUSIONS\nSocial norms are supposed to restrict our behaviour. Of course,\nsuch a restriction does not have to be bad: the fact that an agent\"s\nbehaviour is restricted may seem a limitation, but there may be\nbenefits if he can assume that others will also constrain their behaviour.\nThe question then, for an agent is, how to be sure that others will\ncomply with a norm. And, for a system designer, how to be sure\nthat the system will behave socially, that is, according to its norm.\nGame theory is a very natural tool to analyse and answer these\nquestions, which involve strategic considerations, and we have\nproposed a way to translate key questions concerning logic-based\nnormative systems to game theoretical questions. We have proposed\na logical framework to reason about such scenarios, and we have\ngiven some computational costs for settling some of the main\nquestions about them. Of course, our approach is in many senses open\nfor extension or enrichment. An obvious issue is to consider is the\ncomplexity of the questions we give for more practical\nrepresentations of models (cf. [1]), and to consider other classes of allowable\ngoals.\n7. REFERENCES\n[1] T. Agotnes, W. van der Hoek, J. A. Rodriguez-Aguilar,\nC. Sierra, and M. Wooldridge. On the logic of normative\nsystems. In Proc. IJCAI-07, Hyderabad, India, 2007.\n[2] R. Alur, T. A. Henzinger, and O. Kupferman.\nAlternating-time temporal logic. Jnl. of the ACM,\n49(5):672-713, 2002.\n[3] K. Binmore. Game Theory and the Social Contract Volume\n1: Playing Fair. The MIT Press: Cambridge, MA, 1994.\n[4] K. Binmore. Game Theory and the Social Contract Volume\n2: Just Playing. The MIT Press: Cambridge, MA, 1998.\n[5] V. Conitzer and T. Sandholm. Complexity of mechanism\ndesign. In Proc. UAI, Edmonton, Canada, 2002.\n[6] V. Conitzer and T. Sandholm. Complexity results about nash\nequilibria. In Proc. IJCAI-03, pp. 765-771, Acapulco,\nMexico, 2003.\n[7] C. Daskalakis, P. W. Goldberg, and C. H. Papadimitriou. The\ncomplexity of computing a Nash equilibrium. In Proc.\nSTOC, Seattle, WA, 2006.\n[8] E. A. Emerson. Temporal and modal logic. In Handbook of\nTheor. Comp. Sci. Vol. B, pages 996-1072. Elsevier, 1990.\n[9] E. A. Emerson and J. Y. Halpern. \u2018Sometimes\" and \u2018not\nnever\" revisited: on branching time versus linear time\ntemporal logic. Jnl. of the ACM, 33(1):151-178, 1986.\n[10] D. Fitoussi and M. Tennenholtz. Choosing social laws for\nmulti-agent systems: Minimality and simplicity. Artificial\nIntelligence, 119(1-2):61-101, 2000.\n[11] M. J. Osborne and A. Rubinstein. A Course in Game Theory.\nThe MIT Press: Cambridge, MA, 1994.\n[12] C. H. Papadimitriou. Computational Complexity.\nAddison-Wesley: Reading, MA, 1994.\n[13] Y. Shoham and M. Tennenholtz. On the synthesis of useful\nsocial laws for artificial agent societies. In Proc. AAAI, San\nDiego, CA, 1992.\n[14] Y. Shoham and M. Tennenholtz. On social laws for artificial\nagent societies: Off-line design. In Computational Theories\nof Interaction and Agency, pages 597-618. The MIT Press:\nCambridge, MA, 1996.\n[15] W. van der Hoek, M. Roberts, and M. Wooldridge. Social\nlaws in alternating time: Effectiveness, feasibility, and\nsynthesis. Synthese, 2007.\n[16] M. Wooldridge and W. van der Hoek. On obligations and\nnormative ability. Jnl. of Appl. Logic, 3:396-420, 2005.\n888 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)", "keywords": "social law;constraint;goal;decision making;normative system game;normative system;desirable objective;complexity;kripke structure;logic;computational complexity;game;game theoretic property;ordinal utility;multi-agent system;computation tree logic;nash implementation;multiple goal of increasing priority"}
{"name": "train_I-49", "title": "A Multilateral Multi-issue Negotiation Protocol", "abstract": "In this paper, we present a new protocol to address multilateral multi-issue negotiation in a cooperative context. We consider complex dependencies between multiple issues by modelling the preferences of the agents with a multi-criteria decision aid tool, also enabling us to extract relevant information on a proposal assessment. This information is used in the protocol to help in accelerating the search for a consensus between the cooperative agents. In addition, the negotiation procedure is defined in a crisis management context where the common objective of our agents is also considered in the preferences of a mediator agent.", "fulltext": "1. INTRODUCTION\nMulti-issue negotiation protocols represent an important\nfield of study since negotiation problems in the real world\nare often complex ones involving multiple issues. To date,\nmost of previous work in this area ([2, 3, 19, 13]) dealt\nalmost exclusively with simple negotiations involving\nindependent issues. However, real-world negotiation problems\ninvolve complex dependencies between multiple issues. When\none wants to buy a car, for example, the value of a given\ncar is highly dependent on its price, consumption, comfort\nand so on. The addition of such interdependencies greatly\ncomplicates the agents utility functions and classical\nutility functions, such as the weighted sum, are not sufficient\nto model this kind of preferences. In [10, 9, 17, 14, 20], the\nauthors consider inter-dependencies between issues, most\noften defined with boolean values, except for [9], while we can\ndeal with continuous and discrete dependent issues thanks\nto the modelling power of the Choquet integral. In [17],\nthe authors deal with bilateral negotiation while we are\ninterested in a multilateral negotiation setting. Klein et al.\n[10] present an approach similar to ours, using a mediator\ntoo and information about the strength of the approval or\nrejection that an agent makes during the negotiation. In\nour protocol, we use more precise information to improve\nthe proposals thanks to the multi-criteria methodology and\ntools used to model the preferences of our agents. Lin, in [14,\n20], also presents a mediation service but using an\nevolutionary algorithm to reach optimal solutions and as explained\nin [4], players in the evolutionary models need to repeatedly\ninteract with each other until the stable state is reached.\nAs the population size increases, the time it takes for the\npopulation to stabilize also increases, resulting in excessive\ncomputation, communication, and time overheads that can\nbecome prohibitive, and for one-to-many and many-to-many\nnegotiations, the overheads become higher as the number of\nplayers increases. In [9], the authors consider a non-linear\nutility function by using constraints on the domain of the\nissues and a mediation service to find a combination of bids\nmaximizing the social welfare. Our preference model, a\nnonlinear utility function too, is more complex than [9] one since\nthe Choquet integral takes into account the interactions and\nthe importance of each decision criteria/issue, not only the\ndependencies between the values of the issues, to determine\nthe utility. We also use an iterative protocol enabling us to\nfind a solution even when no bid combination is possible.\nIn this paper, we propose a negotiation protocol suited for\nmultiple agents with complex preferences and taking into\naccount, at the same time, multiple interdependent issues and\nrecommendations made by the agents to improve a proposal.\nMoreover, the preferences of our agents are modelled using\na multi-criteria methodology and tools enabling us to take\ninto account information about the improvements that can\nbe made to a proposal, in order to help in accelerating the\nsearch for a consensus between the agents. Therefore, we\npropose a negotiation protocol consisting of solving our\ndecision problem using a MAS with a multi-criteria decision\naiding modelling at the agent level and a cooperation-based\nmultilateral multi-issue negotiation protocol. This protocol\nis studied under a non-cooperative approach and it is shown\n943\n978-81-904262-7-5 (RPS) c 2007 IFAAMAS\nthat it has subgame perfect equilibria, provided that agents\nbehave rationally in the sense of von Neumann and\nMorgenstern. The approach proposed in this paper has been first\nintroduced and presented in [8]. In this paper, we present\nour first experiments, with some noteworthy results, and a\nmore complex multi-agent system with representatives to\nenable us to have a more robust system.\nIn Section 2, we present our application, a crisis\nmanagement problem. Section 3 deals with the general aspect of the\nproposed approach. The preference modelling is described\nin sect. 4, whereas the motivations of our protocol are\nconsidered in sect. 5 and the agent/multiagent modelling in\nsect. 6. Section 7 presents the formal modelling and\nproperties of our protocol before presenting our first experiments\nin sect. 8. Finally, in Section 9, we conclude and present\nthe future work.\n2. CASE STUDY\nThis protocol is applied to a crisis management problem.\nCrisis management is a relatively new field of management\nand is composed of three types of activities: crisis\nprevention, operational preparedness and management of declared\ncrisis. The crisis prevention aims to bring the risk of crisis\nto an acceptable level and, when possible, avoid that the\ncrisis actually happens. The operational preparedness includes\nstrategic advanced planning, training and simulation to\nensure availability, rapid mobilisation and deployment of\nresources to deal with possible emergencies. The management\nof declared crisis is the response to - including the\nevacuation, search and rescue - and the recovery from the crisis by\nminimising the effects of the crises, limiting the impact on\nthe community and environment and, on a longer term, by\nbringing the community\"s systems back to normal. In this\npaper, we focus on the response part of the management of\ndeclared crisis activity, and particularly on the evacuation\nof the injured people in disaster situations. When a crisis\nis declared, the plans defined during the operational\npreparedness activity are executed. For disasters, master plans\nare executed. These plans are elaborated by the authorities\nwith the collaboration of civil protection agencies, police,\nhealth services, non-governmental organizations, etc.\nWhen a victim is found, several actions follow. First, a\nrescue party is assigned to the victim who is examined and is\ngiven first aid on the spot. Then, the victims can be placed\nin an emergency centre on the ground called the medical\nadvanced post. For all victims, a sorter physician -\ngenerally a hospital physician - examines the seriousness of their\ninjuries and classifies the victims by pathology. The\nevacuation by emergency health transport if necessary can take\nplace after these clinical examinations and classifications.\nNowadays, to evacuate the injured people, the physicians\ncontact the emergency call centre to pass on the medical\nassessments of the most urgent cases. The emergency call\ncentre then searches for available and appropriate spaces in\nthe hospitals to care for these victims. The physicians are\ninformed of the allocations, so they can proceed to the\nevacuations choosing the emergency health transports according\nto the pathologies and the transport modes provided. In\nthis context, we can observe that the evacuation is based\non three important elements: the examination and\nclassification of the victims, the search for an allocation and the\ntransport. In the case of the 11 March 2004 Madrid attacks,\nfor instance, some injured people did not receive the\nappropriate health care because, during the search for space, the\nemergency call centre did not consider the transport\nconstraints and, in particular, the traffic. Therefore, for a large\nscale crisis management problem, there is a need to support\nthe emergency call centre and the physicians in the\ndispatching to take into account the hospitals and the transport\nconstraints and availabilities.\n3. PROPOSED APPROACH\nTo accept a proposal, an agent has to consider several\nissues such as, in the case of the crisis management problem,\nthe availabilities in terms of number of beds by unit,\nmedical and surgical staffs, theatres and so on. Therefore, each\nagent has its own preferences in correlation with its resource\nconstraints and other decision criteria such as, for the case\nstudy, the level of congestion of a hospital. All the agents\nalso make decisions by taking into account the dependencies\nbetween these decision criteria.\nThe first hypothesis of our approach is that there are\nseveral parties involved in and impacted by the decision, and\nso they have to decide together according to their own\nconstraints and decision criteria. Negotiation is the process by\nwhich a group facing a conflict communicates with one\nanother to try and come to a mutually acceptable agreement\nor decision and so, the agents have to negotiate. The\nconflict we have to resolve is finding an acceptable solution for\nall the parties by using a particular protocol. In our\ncontext, multilateral negotiation is a negotiation protocol type\nthat is the best suited for this type of problem : this type\nof protocol enables the hospitals and the physicians to\nnegotiate together. The negotiation also deals with multiple\nissues. Moreover, an other hypothesis is that we are in a\ncooperative context where all the parties have a common\nobjective which is to provide the best possible solution for\neveryone. This implies the use of a negotiation protocol\nencouraging the parties involved to cooperate as satisfying its\npreferences.\nTaking into account these aspects, a Multi-Agent System\n(MAS) seems to be a reliable method in the case of a\ndistributed decision making process. Indeed, a MAS is a suitable\nanswer when the solution has to combine, at least,\ndistribution features and reasoning capabilities. Another motivation\nfor using MAS lies in the fact that MAS is well known for\nfacilitating automated negotiation at the operative decision\nmaking level in various applications.\nTherefore, our approach consists of solving a multiparty\ndecision problem using a MAS with\n\u2022 The preferences of the agents are modelled using a\nmulti-criteria decision aid tool, MYRIAD, also\nenabling us to consider multi-issue problems by evaluating\nproposals on several criteria.\n\u2022 A cooperation-based multilateral and multi-issue\nnegotiation protocol.\n4. THE PREFERENCE MODEL\nWe consider a problem where an agent has several decision\ncriteria, a set Nk = {1, . . . , nk} of criteria for each agent k\ninvolved in the negotiation protocol. These decision criteria\nenable the agents to evaluate the set of issues that are\nnegotiated. The issues correspond directly or not to the decision\ncriteria. However, for the example of the crisis management\n944 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nproblem, the issues are the set of victims to dispatch\nbetween the hospitals. These issues are translated to decision\ncriteria enabling the hospital to evaluate its congestion and\nso to an updated number of available beds, medical teams\nand so on. In order to take into account the complexity that\nexists between the criteria/issues, we use a multi-criteria\ndecision aiding (MCDA) tool named MYRIAD [12] developed\nat Thales for MCDA applications based on a two-additive\nChoquet integral which is a good compromise between\nversatility and ease to understand and model the interactions\nbetween decision criteria [6].\nThe set of the attributes of Nk is denoted by Xk\n1 , . . . , Xk\nnk\n.\nAll the attributes are made commensurate thanks to the\nintroduction of partial utility functions uk\ni : Xk\ni \u2192 [0, 1]. The\n[0, 1] scale depicts the satisfaction of the agent k regarding\nthe values of the attributes. An option x is identified to an\nelement of Xk\n= Xk\n1 \u00d7 \u00b7 \u00b7 \u00b7 \u00d7 Xk\nnk\n, with x = (x1, . . . , xnk ).\nThen the overall assessment of x is given by\nUk(x) = Hk(uk\n1 (x1), . . . , uh\nnk\n(xnk )) (1)\nwhere Hk : [0, 1]nk \u2192 [0, 1] is the aggregation function. The\noverall preference relation over Xk\nis then\nx y \u21d0\u21d2 Uk(x) \u2265 Uk(y) .\nThe two-additive Choquet integral is defined for\n(z1, . . . , znk ) \u2208 [0, 1]nk by [7]\nHk(z1, . . . , znk ) =\nX\ni\u2208Nk\n0\n@vk\ni \u2212\n1\n2\nX\nj=i\n|Ik\ni,j|\n1\nA zi\n+\nX\nIk\ni,j >0\nIk\ni,j zi \u2227 zj +\nX\nIi,j <0\n|Ii,j| zi \u2228 zj (2)\nwhere vk\ni is the relative importance of criterion i for agent\nk and Ik\ni,j is the interaction between criteria i and j, \u2227 and\n\u2228 denote the min and max functions respectively. Assume\nthat zi < zj. A positive interaction between criteria i and\nj depicts complementarity between these criteria (positive\nsynergy) [7]. Hence, the lower score of z on criterion i\nconceals the positive effect of the better score on criterion j to\na larger extent on the overall evaluation than the impact of\nthe relative importance of the criteria taken independently\nof the other ones. In other words, the score of z on criterion\nj is penalized by the lower score on criterion i. Conversely, a\nnegative interaction between criteria i and j depicts\nsubstitutability between these criteria (negative synergy) [7]. The\nscore of z on criterion i is then saved by a better score on\ncriterion j.\nIn MYRIAD, we can also obtain some recommendations\ncorresponding to an indicator \u03c9C (H, x) measuring the worth\nto improve option x w.r.t. Hk on some criteria C \u2286 Nk as\nfollows\n\u03c9C (Hk, x)=\nZ 1\n0\nHk\n`\n(1 \u2212 \u03c4)xC + \u03c4, xNk\\C\n\u00b4\n\u2212 Hk(x)\nEC (\u03c4, x)\nd\u03c4\nwhere ((1\u2212\u03c4)xC +\u03c4, xNk\\C ) is the compound act that equals\n(1 \u2212 \u03c4)xi + \u03c4 if i \u2208 C and equals xi if i \u2208 Nk \\ C. Moreover,\nEC (\u03c4, x) is the effort to go from the profile x to the profile\n((1 \u2212 \u03c4)xC + \u03c4, xNk\\C ). Function \u03c9C (Hk, x) depicts the\naverage improvement of Hk when the criteria of coalition A\nrange from xC to 1C divided by the average effort needed\nfor this improvement. We generally assume that EC is of\norder 1, that is EC (\u03c4, x) = \u03c4\nP\ni\u2208C (1 \u2212 xi). The expression\nof \u03c9C (Hk, x) when Hk is a Choquet integral, is given in [11].\nThe agent is then recommended to improve of coalition C\nfor which \u03c9C (Hk, x) is maximum. This recommendation is\nvery useful in a negotiation protocol since it helps the agents\nto know what to do if they want an offer to be accepted while\nnot revealing their own preference model.\n5. PROTOCOL MOTIVATIONS\nFor multi-issue problems, there are two approaches: a\ncomplete package approach where the issues are\nnegotiated simultaneously in opposition to the sequential approach\nwhere the issues are negotiated one by one. When the issues\nare dependant, then it is the best choice to bargain\nsimultaneously over all issues [5]. Thus, the complete package is\nthe adopted approach so that an offer will be on the\noverall set of injured people while taking into account the other\ndecision criteria.\nWe have to consider that all the parties of the\nnegotiation process have to agree on the decision since they are all\ninvolved in and impacted by this decision and so an\nunanimous agreement is required in the protocol. In addition, no\nparty can leave the process until an agreement is reached,\ni.e. a consensus achieved. This makes sense since a proposal\nconcerns all the parties. Moreover, we have to guarantee the\navailability of the resources needed by the parties to ensure\nthat a proposal is realistic. To this end, the information\nabout these availabilities are used to determine admissible\nproposals such that an offer cannot be made if one of the\nparties has not enough resources to execute/achieve it. At the\nbeginning of the negotiation, each party provides its\nmaximum availabilities, this defining the constraints that have\nto be satisfied for each offer submitted.\nThe negotiation has also to converge quickly on an\nunanimous agreement. We decided to introduce in the negotiation\nprotocol an incentive to cooperate taking into account the\npassed negotiation time. This incentive is defined on the\nbasis of a time dependent penalty, the discounting factor as\nin [18] or a time-dependent threshold. This penalty has to\nbe used in the accept/reject stage of our consensus\nprocedure. In fact, in the case of a discounting factor, each party\nwill accept or reject an offer by evaluating the proposal\nusing its utility function deducted from the discounting factor.\nIn the case of a time-dependent threshold, if the evaluation\nis greater or equal to this threshold, the offer is accepted,\notherwise, in the next period, its threshold is reduced.\nThe use of a penalty is not enough alone since it does\nnot help in finding a solution. Some information about the\nassessments of the parties involved in the negotiation are\nneeded. In particular, it would be helpful to know why an\noffer has been rejected and/or what can be done to make\na proposal that would be accepted. MYRIAD provides an\nanalysis that determines the flaws an option, here a\nproposal. In particular, it gives this type of information: which\ncriteria of a proposal should be improved so as to reach the\nhighest possible overall evaluation [11]. As we use this tool\nto model the parties involved in the negotiation, the\ninformation about the criteria to improve can be used by the\nmediator to elaborate the proposals. We also consider that\nthe dual function can be used to take into account another\ntype of information: on which criteria of a proposal, no\nimprovement is necessary so that the overall evaluation of a\nproposal is still acceptable, do not decrease. Thus, all\ninformation is a constraint to be satisfied as much as possible by\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 945\nFigure 1: An illustration of some system.\nthe parties to make a new proposal.\nWe are in a cooperative context and revealing one\"s\nopinion on what can be improved is not prohibited, on the\ncontrary, it is useful and recommended here seeing that it helps\nin converging on an agreement. Therefore, when one of the\nparties refuses an offer, some information will be\ncommunicated. In order to facilitate and speed up the negotiation,\nwe introduce a mediator. This specific entity is in charge\nof making the proposals to the other parties in the system\nby taking into account their public constraints (e.g. their\navailabilities) and the recommendations they make. This\nmediator can also be considered as the representative of\nthe general interest we can have, in some applications, such\nas in the crisis management problem, the physician will be\nthe mediator and will also have some more information to\nconsider when making an offer (e.g. traffic state, transport\nmode and time). Each party in a negotiation N, a\nnegotiator, can also be a mediator of another negotiation N , this\nparty becoming the representative of N in the negotiation\nN, as illustrated by fig. 1 what can also help in reducing\nthe communication time.\n6. AGENTIFICATION\nHow the problem is transposed in a MAS problem is a\nvery important aspect when designing such a system. The\nagentification has an influence upon the systems efficiency in\nsolving the problem. Therefore, in this section, we describe\nthe elements and constraints taken into account during the\nmodelling phase and for the model itself. However, for this\nnegotiation application, the modelling is quite natural when\none observes the negotiation protocol motivations and main\nproperties.\nFirst of all, it seems obvious that there should be one agent\nfor each player of our multilateral multi-issue negotiation\nprotocol. The agents have the involved parties\" information\nand preferences. These agents are:\n\u2022 Autonomous: they decide for themselves what, when\nand under what conditions actions should be\nperformed;\n\u2022 Rational: they have a means-ends competence to fit\nits decisions, according to its knowledge, preferences\nand goal;\n\u2022 Self-interested: they have their own interests which\nmay conflict with the interests of other agents.\nMoreover, their preferences are modelled and a proposal\nevaluated and analysed using MYRIAD. Each agent has\nprivate information and can access public information as\nknowledge.\nIn fact, there are two types of agents: the mediator type\nfor the agents corresponding to the mediator of our\nnegotiation protocol, the delegated physician in our application,\nand the negotiator type for the agents corresponding to\nthe other parties, the hospitals. The main behaviours that\nan agent of type mediator needs to negotiate in our protocol\nare the following:\n\u2022 convert_improvements: converts the information\ngiven by the other agents involved in the negotiation\nabout the improvements to be done, into constraints\non the next proposal to be made;\n\u2022 convert_no_decrease: converts the information given\nby the other agents involved in the negotiation about\nthe points that should not be changed into constraints\non the next proposal to be made;\n\u2022 construct_proposal: constructs a new proposal\naccording to the constraints obtained with\nconvert_improvements, convert_no_decrease and the agent\npreferences;\nThe main behaviours that an agent of type negotiator\nneeds to negotiate in our protocol are the following:\n\u2022 convert_proposal: converts a proposal to a MYRIAD\noption of the agent according to its preferences model\nand its private data;\n\u2022 convert_improvements_wc: converts the agent\nrecommendations for the improvements of a MYRIAD\noption into general information on the proposal;\n\u2022 convert_no_decrease_wc: converts the agent\nrecommendations about the criteria that should not be\nchanged in the MYRIAD option into general information\non the proposal;\nIn addition to these behaviours, there are, for the two types\nof agents, access behaviours to MYRIAD functionalities\nsuch as the evaluation and improvement functions:\n\u2022 evaluate_option: evaluates the MYRIAD option\nobtained using the agent behaviour convert_proposal;\n\u2022 improvements: gets the agent recommendations to\nimprove a proposal from the MYRIAD option;\n\u2022 no_decrease: gets the agent recommendations to not\nchange some criteria from the MYRIAD option;\nOf course, before running the system with such agents, we\nmust have defined each party preferences model in\nMYRIAD. This model has to be part of the agent so that it could\nbe used to make the assessments and to retrieve the\nimprovements. In addition to these behaviours, the communication\nacts between the agents is as follows.\n1. mediator agent communication acts:\n946 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nm1 m\n1\n1\nm\ninform1 m\nmediator negotiator\naccept\u2212proposal\nl\n1\naccept\u2212proposal\nm\u2212l\nreject\u2212proposal\npropose\npropose\nFigure 2: The protocol diagram in AUML, and\nwhere m is the number of negotiator agents and l\nis the number of agents refusing current proposal.\n(a) propose: sends a message containing a proposal\nto all negotiator agents;\n(b) inform: sends a message to all negotiator agents\nto inform them that an agreement has been\nreached and containing the consensus outcome.\n2. negotiator agent communication acts:\n(a) accept-proposal: sends a message to the\nmediator agent containing the agent recommendations\nto improve the proposal and obtained with\nconvert_improvements_wc;\n(b) reject-proposal: sends a message to the\nmediator agent containing the agent recommendations\nabout the criteria that should not be changed and\nobtained with convert_no_decrease_wc.\nSuch agents are interchangeable, in a case of failure, since\nthey all have the same properties and represent a user with\nhis preference model, not depending on the agent, but on the\nmodel defined in MYRIAD. When the issues and the\ndecision criteria are different from each other, the information\nabout the criteria improvement have to be pre-processed to\ngive some instructions on the directions to take and about\nthe negotiated issues. It is the same for the evaluation of a\nproposal: each agent has to convert the information about\nthe issues to update its private information and to obtain\nthe values of each attribute of the decision criteria.\n7. OUR PROTOCOL\nFormally, we consider negotiations where a set of\nplayers A = {1, 2, . . . , m} and a player a are negotiating over\na set Q of size q. The player a is the protocol\nmediator, the mediator agent of the agentification. The\nutility/preference function of a player k \u2208 A \u222a {a} is Uk,\ndefined using MYRIAD, as presented in Section 4, with a set\nNk of criteria, Xk\nan option, and so on. An offer is a\nvector P = (P1, P2, \u00b7 \u00b7 \u00b7 , Pm), a partition of Q, in which Pk is\nplayer k\"s share of Q. We have P \u2208 P where P is the set of\nadmissible proposals, a finite set. Note that P is determined\nusing all players general constraints on the proposals and Q.\nMoreover, let \u02dcP denote a particular proposal defined as a\"s\npreferred proposal.\nWe also have the following notation: \u03b4k is the\nthreshold decrease factor of player k, \u03a6k : Pk \u2192 Xk\nis player\nk\"s function to convert a proposal to an option and \u03a8k is\nthe function indicating which points P has to be improved,\nwith \u03a8k its dual function - on which points no\nimprovement is necessary. \u03a8k is obtained using the dual function of\n\u03c9C (Hk, x):\ne\u03c9C (Hk, x)=\nZ 1\n0\nHk(x) \u2212 Hk\n`\n\u03c4 xC , xNk\\C\n\u00b4\neEC (\u03c4, x)\nd\u03c4\nWhere eEC (\u03c4, x) is the cost/effort to go from (\u03c4xC , xNk\\C )\nto x.\nIn period t of our consensus procedure, player a proposes\nan agreement P. All players k \u2208 A respond to a by\naccepting or rejecting P. The responses are made simultaneously.\nIf all players k \u2208 A accept the offer, the game ends. If any\nplayer k rejects P, then the next period t+1 begins: player a\nmakes another proposal P by taking into account\ninformation provided by the players and the ones that have rejected\nP apply a penalty. Therefore, our negotiation protocol can\nbe as follows:\nProtocol P1.\n\u2022 At the beginning, we set period t = 0\n\u2022 a makes a proposal P \u2208 P that has not been\nproposed before.\n\u2022 Wait that all players of A give their opinion\nYes or No to the player a. If all players\nagree on P, this later is chosen. Otherwise\nt is incremented and we go back to previous\npoint.\n\u2022 If there is no more offer left from P, the\ndefault offer \u02dcP will be chosen.\n\u2022 The utility of players regarding a given\noffer decreases over time. More precisely, the\nutility of player k \u2208 A at period t regarding\noffer P is Uk(\u03a6k(Pk), t) = ft(Uk(\u03a6k(Pk))),\nwhere one can take for instance ft(x) =\nx.(\u03b4k)t\nor ft(x) = x \u2212 \u03b4k.t, as penalty\nfunction.\nLemma 1. Protocol P1 has at least one subgame perfect\nequilibrium 1\n.\nProof : Protocol P1 is first transformed in a game in\nextensive form. To this end, one shall specify the order in which\nthe responders A react to the offer P of a. However the\norder in which the players answer has no influence on the\ncourse of the game and in particular on their personal\nutility. Hence protocol P1 is strictly equivalent to a game in\n1\nA subgame perfect equilibrium is an equilibrium such that\nplayers\" strategies constitute a Nash equilibrium in every\nsubgame of the original game [18, 16]. A Nash equilibrium\nis a set of strategies, one for each player, such that no player\nhas incentive to unilaterally change his/her action [15].\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 947\nextensive form, considering any order of the players A. This\ngame is clearly finite since P is finite and each offer can\nonly be proposed once. Finally P1 corresponds to a game\nwith perfect information. We end the proof by using a\nclassical result stating that any finite game in extensive form\nwith perfect information has at least one subgame perfect\nequilibrium (see e.g. [16]).\nRational players (in the sense of von Neumann and\nMorgenstern) involved in protocol P1 will necessarily come up\nwith a subgame perfect equilibrium.\nExample 1. Consider an example with A = {1, 2} and\nP = {P1\n, P2\n, P3\n} where the default offer is P1\n. Assume\nthat ft(x) = x \u2212 0.1 t. Consider the following table giving\nthe utilities at t = 0.\nP1\nP2\nP3\na 1 0.8 0.7\n1 0.1 0.7 0.5\n2 0.1 0.3 0.8\nIt is easy to see that there is one single subgame perfect\nequilibrium for protocol P1 corresponding to these values. This\nequilibrium consists of the following choices: first a proposes\nP3\n; player 1 rejects this offer; a proposes then P2\nand both\nplayers 1 and 2 accepts otherwise they are threatened to\nreceive the worse offer P1\nfor them. Finally offer P2\nis\nchosen. Option P1\nis the best one for a but the two other players\nvetoed it. It is interesting to point out that, even though a\nprefers P2\nto P3\n, offer P3\nis first proposed and this make\nP2\nbeing accepted. If a proposes P2\nfirst, then the subgame\nperfect equilibrium in this situation is P3\n. To sum up, the\nworse preferred options have to be proposed first in order to\nget finally the best one. But this entails a waste of time.\nAnalysing the previous example, one sees that the game\noutcome at the equilibrium is P2\nthat is not very attractive\nfor player 2. Option P3\nseems more balanced since no player\njudges it badly. It could be seen as a better solution as a\nconsensus among the agents.\nIn order to introduce this notion of balanceness in the\nprotocol, we introduce a condition under which a player will\nbe obliged to accept the proposal, reducing the autonomy\nof the agents but for increasing rationality and cooperation.\nMore precisely if the utility of a player is larger than a given\nthreshold then acceptance is required. The threshold\ndecreases over time so that players have to make more and\nmore concession. Therefore, the protocol becomes as\nfollows.\nProtocol P2.\n\u2022 At the beginning we set period t = 0\n\u2022 a makes a proposal P \u2208 P that has not been\nproposed before.\n\u2022 Wait that all players of A give their opinion\nYes or No to the player a. A player k must\naccept the offer if Uk(\u03a6k(Pk)) \u2265 \u03c1k(t) where\n\u03c1k(t) tends to zero when t grows.\nMoreover there exists T such that for all t \u2265 T,\n\u03c1k(t) = 0. If all players agree on P, this\nlater is chosen. Otherwise t is incremented\nand we go back to previous point.\n\u2022 If there is no more offer left from P, the\ndefault offer \u02dcP will be chosen.\nOne can show exactly as in Lemma 1 that protocol P2\nhas at least one subgame perfect equilibrium. We expect\nthat protocol P2 provides a solution not to far from P ,\nso it favours fairness among the players. Therefore, our\ncooperation-based multilateral multi-issue protocol is the\nfollowing:\nProtocol P.\n\u2022 At the beginning we set period t = 0\n\u2022 a makes a proposal P \u2208 P that has not\nbeen proposed before, considering \u03a8k(Pt\n)\nand \u03a8k(Pt\n) for all players k \u2208 A.\n\u2022 Wait that all players of A give their opinion\n(Yes , \u03a8k(Pt\n)) or (No , \u03a8k(Pt\n)) to the\nplayer a. A player k must accept the offer\nif Uk(\u03a6k(Pk)) \u2265 \u03c1k(t) where \u03c1k(t) tends to\nzero when t grows. Moreover there exists\nT such that for all t \u2265 T, \u03c1k(t) = 0. If\nall players agree on P, this later is chosen.\nOtherwise t is incremented and we go back\nto previous point.\n\u2022 If there is no more offer left from P, the\ndefault offer \u02dcP will be chosen.\n8. EXPERIMENTS\nWe developed a MAS using the widely used JADE agent\nplatform [1]. This MAS is designed to be as general as\npossible (e.g. a general framework to specialise according to the\napplication) and enable us to make some preliminary\nexperiments. The experiments aim at verifying that our approach\ngives solutions as close as possible to the Maximin solution\nand in a small number of rounds and hopefully in a short\ntime since our context is highly cooperative. We defined\nthe two types of agents and their behaviours as introduced\nin section 6. The agents and their behaviours correspond\nto the main classes of our prototype, NegotiatorAgent\nand NegotiatorBehaviour for the negotiator agents, and\nMediatorAgent and MediatorBehaviour for the mediator\nagent. These classes extend JADE classes and integrate\nMYRIAD into the agents, reducing the amount of\ncommunications in the system. Some functionalities depending on\nthe application have to be implemented according to the\napplication by extending these classes. In particular, all\nconversion parts of the agents have to be specified according to\nthe application since to convert a proposal into decision\ncriteria, we need to know, first, this model and the correlations\nbetween the proposals and this model.\nFirst, to illustrate our protocol, we present a simple\nexample of our dispatch problem. In this example, we have\nthree hospitals, H1, H2 and H3. Each hospital can receive\nvictims having a particular pathology in such a way that\nH1 can receive patients with the pathology burn, surgery\nor orthopedic, H2 can receive patients with the pathology\nsurgery, orthopedic or cardiology and H3 can receive\npatients with the pathology burn or cardiology. All the\nhospitals have similar decision criteria reflecting their preferences\non the level of congestion they can face for the overall\nhospital and the different services available, as briefly explained\nfor hospital H1 hereafter.\nFor hospital H1, the preference model, fig. 3, is composed\nof five criteria. These criteria correspond to the preferences\non the pathologies the hospital can treat. In the case of\n948 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nFigure 3: The H1 preference model in MYRIAD.\nthe pathology burn, the corresponding criterion, also named\nburn as shown in fig. 3, represents the preferences of H1\naccording to the value of Cburn which is the current capacity\nof burn. Therefore, the utility function of this criterion\nrepresents a preference such that the more there are patients of\nthis pathology in the hospital, the less the hospital may\nsatisfy them, and this with an initial capacity. In addition to\nreflecting this kind of viewpoint, the aggregation function as\ndefined in MYRIAD introduces a veto on the criteria burn,\nsurgery, orthopedic and EReceipt, where EReceipt is the\ncriterion for the preferences about the capacity to receive a\nnumber of patients at the same time.\nIn this simplified example, the physician have no\nparticular preferences on the dispatch and the mediator agent\nchooses a proposal randomly in a subset of the set of\nadmissibility. This subset have to satisfy as much as possible the\nrecommendations made by the hospitals. To solve this\nproblem, for this example, we decided to solve a linear problem\nwith the availability constraints and the recommendations\nas linear constraints on the dispatch values. The set of\nadmissibility is then obtained by solving this linear problem\nby the use of Prolog. Moreover, only the recommendations\non how to improve a proposal are taken into account. The\nproblem to solve is then to dispatch to hospital H1, H2 and\nH3, the set of victims composed of 5 victims with the\npathology burn, 10 with surgery, 3 with orthopedic and 7 with\ncardiology. The availabilities of the hospitals are as\npresented in the following table.\nAvailable Overall burn surg. orthop. cardio.\nH1 11 4 8\n10H2 25 - 3 4 10\nH3 7 10 - - 3\nWe obtain a multiagent system with the mediator agent\nand three agents of type negotiator for the three hospital\nin the problem. The hospitals threshold are fixed\napproximatively to the level where an evaluation is considered as\ngood. To start, the negotiator agents send their\navailabilities. The mediator agent makes a proposal chosen randomly\nin admissible set obtained with these availabilities as\nlinear constraints. This proposal is the vector P0 = [[H1,burn,\n3], [H1, surgery, 8], [H1, orthopaedic, 0], [H2, surgery, 2],\n[H2, orthopaedic, 3], [H2, cardiology, 6], [H3, burn, 2], [H3,\ncardiology, 1]] and the mediator sends propose(P0) to H1,\nH2 and H3 for approval. Each negotiator agent evaluates\nthis proposal and answers back by accepting or rejecting P0:\n\u2022 Agent H1 rejects this offer since its evaluation is very\nfar from the threshold (0.29, a bad score) and gives\na recommendation to improve burn and surgery by\nsending the message\nreject_proposal([burn,surgery]);\n\u2022 Agent H2 accepts this offer by sending the message\naccept_proposal(), the proposal evaluation being\ngood;\n\u2022 Agent H3 accepts P0 by sending the message accept_\nproposal(), the proposal evaluation being good.\nJust with the recommendations provided by agent H1, the\nmediator is able to make a new proposal by restricting the\nvalue of burn and surgery. The new proposal obtained is\nthen P1 = [[H1,burn, 0], [H1, surgery, 8], [H1, orthopaedic,\n1], [H2, surgery, 2], [H2, orthopaedic, 2], [H2, cardiology,\n6], [H3, burn, 5], [H3, cardiology, 1]]. The mediator sends\npropose(P1) the negotiator agents. H1, H2 and H3 answer\nback by sending the message accept_proposal(), P1 being\nevaluated with a high enough score to be acceptable, and\nalso considered as a good proposal when using the\nexplanation function of MYRIAD. An agreement is reached with\nP1. Note that the evaluation of P1 by H3 has decreased in\ncomparison with P0, but not enough to be rejected and that\nthis solution is the Pareto one, P\u2217\n.\nOther examples have been tested with the same settings:\nissues in IN, three negotiator agents and the same mediator\nagent, with no preference model but selecting randomly the\nproposal. We obtained solutions either equal or close to the\nMaximin solution, the distance from the standard deviation\nbeing less than 0.0829, the evaluations not far from the ones\nobtained with P\u2217\nand with less than seven proposals made.\nThis shows us that we are able to solve this multi-issue\nmultilateral negotiation problem in a simple and efficient way,\nwith solutions close to the Pareto solution.\n9. CONCLUSION AND FUTURE WORK\nThis paper presents a new protocol to address\nmultilateral multi-issue negotiation in a cooperative context. The\nfirst main contribution is that we take into account complex\ninter-dependencies between multiple issues with the use of\na complex preference modelling. This contribution is\nreinforced by the use of multi-issue negotiation in a multilateral\ncontext. Our second contribution is the use of sharp\nrecommendations in the protocol to help in accelerating the search\nof a consensus between the cooperative agents and in finding\nan optimal solution. We have also shown that the protocol\nhas subgame perfect equilibria and these equilibria converge\nto the usual maximum solution. Moreover, we tested this\nprotocol in a crisis management context where the\nnegotiation aim is where to evacuate a whole set of injured people\nto predefined hospitals.\nWe have already developed a first MAS, in particular\nintegrating MYRIAD, to test this protocol in order to know\nmore about its efficiency in terms of solution quality and\nquickness in finding a consensus. This prototype enabled\nus to solve some examples with our approach and the\nresults we obtained are encouraging since we obtained quickly\ngood agreements, close to the Pareto solution, in the light\nof the initial constraints of the problem: the availabilities.\nWe still have to improve our MAS by taking into account\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 949\nthe two types of recommendations and by adding a\npreference model to the mediator of our system. Moreover, a\ncomparative study has to be done in order to evaluate the\nperformance of our framework against the existing ones and\nagainst some variations on the protocol.\n10. ACKNOWLEDGEMENT\nThis work is partly funded by the ICIS research project\nunder the Dutch BSIK Program (BSIK 03024).\n11. REFERENCES\n[1] JADE. http://jade.tilab.com/.\n[2] P. Faratin, C. Sierra, and N. R. Jennings. Using\nsimilarity criteria to make issue trade-offs in\nautomated negotiations. Artificial Intelligence,\n142(2):205-237, 2003.\n[3] S. S. Fatima, M. Wooldridge, and N. R. Jennings.\nOptimal negotiation of multiple issues in incomplete\ninformation settings. In 3rd International Joint\nConference on Autonomous Agents and Multiagent\nSystems (AAMAS\"04), pages 1080-1087, New York,\nUSA, 2004.\n[4] S. S. Fatima, M. Wooldridge, and N. R. Jennings. A\ncomparative study of game theoretic and evolutionary\nmodels of bargaining for software agents. Artificial\nIntelligence Review, 23:185-203, 2005.\n[5] S. S. Fatima, M. Wooldridge, and N. R. Jennings. On\nefficient procedures for multi-issue negotiation. In 8th\nInternational Workshop on Agent-Mediated Electronic\nCommerce(AMEC\"06), pages 71-84, Hakodate, Japan,\n2006.\n[6] M. Grabisch. The application of fuzzy integrals in\nmulticriteria decision making. European J. of\nOperational Research, 89:445-456, 1996.\n[7] M. Grabisch, T. Murofushi, and M. Sugeno. Fuzzy\nMeasures and Integrals. Theory and Applications\n(edited volume). Studies in Fuzziness. Physica Verlag,\n2000.\n[8] M. Hemaissia, A. El Fallah-Seghrouchni,\nC. Labreuche, and J. Mattioli. Cooperation-based\nmultilateral multi-issue negotiation for crisis\nmanagement. In 2th International Workshop on\nRational, Robust and Secure Negotiation (RRS\"06),\npages 77-95, Hakodate, Japan, May 2006.\n[9] T. Ito, M. Klein, and H. Hattori. A negotiation\nprotocol for agents with nonlinear utility functions. In\nAAAI, 2006.\n[10] M. Klein, P. Faratin, H. Sayama, and Y. Bar-Yam.\nNegotiating complex contracts. Group Decision and\nNegotiation, 12:111-125, March 2003.\n[11] C. Labreuche. Determination of the criteria to be\nimproved first in order to improve as much as possible\nthe overall evaluation. In IPMU 2004, pages 609-616,\nPerugia, Italy, 2004.\n[12] C. Labreuche and F. Le Hu\u00b4ed\u00b4e. MYRIAD: a tool suite\nfor MCDA. In EUSFLAT\"05, pages 204-209,\nBarcelona, Spain, 2005.\n[13] R. Y. K. Lau. Towards genetically optimised\nmulti-agent multi-issue negotiations. In Proceedings of\nthe 38th Annual Hawaii International Conference on\nSystem Sciences (HICSS\"05), Big Island, Hawaii, 2005.\n[14] R. J. Lin. Bilateral multi-issue contract negotiation for\ntask redistribution using a mediation service. In Agent\nMediated Electronic Commerce VI (AMEC\"04), New\nYork, USA, 2004.\n[15] J. F. Nash. Non cooperative games. Annals of\nMathematics, 54:286-295, 1951.\n[16] G. Owen. Game Theory. Academic Press, New York,\n1995.\n[17] V. Robu, D. J. A. Somefun, and J. A. L. Poutr\u00b4e.\nModeling complex multi-issue negotiations using\nutility graphs. In 4th International Joint Conference\non Autonomous agents and multiagent systems\n(AAMAS\"05), pages 280-287, 2005.\n[18] A. Rubinstein. Perfect equilibrium in a bargaining\nmodel. Econometrica, 50:97-109, jan 1982.\n[19] L.-K. Soh and X. Li. Adaptive, confidence-based\nmultiagent negotiation strategy. In 3rd International\nJoint Conference on Autonomous agents and\nmultiagent systems (AAMAS\"04), pages 1048-1055,\nLos Alamitos, CA, USA, 2004.\n[20] H.-W. Tung and R. J. Lin. Automated contract\nnegotiation using a mediation service. In 7th IEEE\nInternational Conference on E-Commerce Technology\n(CEC\"05), pages 374-377, Munich, Germany, 2005.\n950 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)", "keywords": "multi-criterion decision make;decision making;automate negotiation;multi-agent system;cooperative agent;modelling;myriad;multilateral negotiation;negotiation protocol;automated negotiation;multi-issue negotiation;crisis management;negotiation strategy"}
{"name": "train_I-50", "title": "Agents, Beliefs, and Plausible Behavior in a Temporal Setting", "abstract": "Logics of knowledge and belief are often too static and inflexible to be used on real-world problems. In particular, they usually offer no concept for expressing that some course of events is more likely to happen than another. We address this problem and extend CTLK (computation tree logic with knowledge) with a notion of plausibility, which allows for practical and counterfactual reasoning. The new logic CTLKP (CTLK with plausibility) includes also a particular notion of belief. A plausibility update operator is added to this logic in order to change plausibility assumptions dynamically. Furthermore, we examine some important properties of these concepts. In particular, we show that, for a natural class of models, belief is a KD45 modality. We also show that model checking CTLKP is PTIME-complete and can be done in time linear with respect to the size of models and formulae.", "fulltext": "1. INTRODUCTION\nNotions like time, knowledge, and beliefs are very\nimportant for analyzing the behavior of agents and multi-agent\nsystems. In this paper, we extend modal logics of time and\nknowledge with a concept of plausible behavior: this notion\nis added to the language of CTLK [19], which is a\nstraightforward combination of the branching-time temporal logic\nCTL [4, 3] and standard epistemic logic [9, 5].\nIn our approach, plausibility can be seen as a temporal\nproperty of behaviors. That is, some behaviors of the\nsystem can be assumed plausible and others implausible, with\nthe underlying idea that the latter should perhaps be\nignored in practical reasoning about possible future courses\nof action. Moreover, behaviors can be formally understood\nas temporal paths in the Kripke structure modeling a\nmultiagent system. As a consequence, we obtain a language to\nreason about what can (or must) plausibly happen. We\npropose a particular notion of beliefs (inspired by [20, 7]),\ndefined in terms of epistemic relations and plausibility. The\nmain intuition is that beliefs are facts that an agent would\nknow if he assumed that only plausible things could happen.\nWe believe that humans use such a concept of plausibility\nand practical beliefs quite often in their everyday\nreasoning. Restricting one\"s reasoning to plausible possibilities is\nessential to make the reasoning feasible, as the space of all\npossibilities is exceedingly large in real life. We investigate\nsome important properties of plausibility, knowledge, and\nbelief in this new framework. In particular, we show that\nknowledge is an S5 modality, and that beliefs satisfy\naxioms K45 in general, and KD45 for the class of plausibly\nserial models. Finally, we show that the relationship\nbetween knowledge and belief for plausibly serial models is\nnatural and reflects the initial intuition well. We also show\nhow plausibility assumptions can be specified in the object\nlanguage via a plausibility update operator, and we study\nproperties of such updates. Finally, we show that model\nchecking of the new logic is no more complex than model\nchecking CTL and CTLK.\nOur ultimate goal is to come up with a logic that\nallows the study of strategies, time, knowledge, and\nplausible/rational behavior under both perfect and imperfect\ninformation. As combining all these dimensions is highly\nnontrivial (cf. [12, 14]) it seems reasonable to split this task.\nWhile this paper deals with knowledge, plausibility, and\nbelief, the companion paper [11] proposes a general framework\nfor multi-agent systems that regard game-theoretical\nrationality criteria like Nash equilibrium, Pareto optimality, etc.\nThe latter approach is based on the more powerful logic\nATL [1].\nThe paper is structured as follows. Firstly, we briefly\npresent branching-time logic with knowledge, CTLK. In\nSection 3 we present our approach to plausibility and\nformally define CTLK with plausibility. We also show how\n582\n978-81-904262-7-5 (RPS) c 2007 IFAAMAS\ntemporal formulae can be used to describe plausible paths,\nand we compare our logic with existing related work. In\nSection 4, properties of knowledge, belief, and plausibility are\nexplored. Finally, we present verification complexity results\nfor CTLKP in Section 5.\n2. BRANCHING TIME AND KNOWLEDGE\nIn this paper we develop a framework for agents\" beliefs\nabout how the world can (or must) evolve. Thus, we need a\nnotion of time and change, plus a notion of what the agents\nare supposed to know in particular situations. CTLK [19]\nis a straightforward combination of the computation tree\nlogic CTL [4, 3] and standard epistemic logic [9, 5].\nCTL includes operators for temporal properties of\nsystems: i.e., path quantifier E (there is a path), together\nwith temporal operators: f(in the next state), 2\n(always from now on) and U (until).1\nEvery occurrence of\na temporal operator is preceded by exactly one path\nquantifier in CTL (this variant of the language is sometimes called\nvanilla CTL). Epistemic logic uses operators for\nrepresenting agents\" knowledge: Ka\u03d5 is read as agent a knows\nthat \u03d5.\nLet \u03a0 be a set of atomic propositions with a typical\nelement p, and Agt = {1, ..., k} be a set of agents with a typical\nelement a. The language of CTLK consists of formulae \u03d5,\ngiven as follows:\n\u03d5 ::= p | \u00ac\u03d5 | \u03d5 \u2227 \u03d5 | E\u03b3 | Ka\u03d5\n\u03b3 ::= f\u03d5 | 2 \u03d5 | \u03d5U \u03d5.\nWe will sometimes refer to formulae \u03d5 as (vanilla) state\nformulae and to formulae \u03b3 as (vanilla) path formulae.\nThe semantics of CTLK is based on Kripke models M =\nQ, R, \u223c1, ..., \u223ck, \u03c0 , which include a nonempty set of states\nQ, a state transition relation R \u2286 Q \u00d7 Q, epistemic\nindistinguishability relations \u223ca\u2286 Q \u00d7 Q (one per agent), and a\nvaluation of propositions \u03c0 : \u03a0 \u2192 P(Q). We assume that\nrelation R is serial and that all \u223ca are equivalence relations.\nA path \u03bb in M refers to a possible behavior (or\ncomputation) of system M, and can be represented as an infinite\nsequence of states that follow relation R, that is, a sequence\nq0q1q2... such that qiRqi+1 for every i = 0, 1, 2, ... We\ndenote the ith state in \u03bb by \u03bb[i]. The set of all paths in M\nis denoted by \u039bM (if the model is clear from context, M\nwill be omitted). A q-path is a path that starts from q,\ni.e., \u03bb[0] = q. A q-subpath is a sequence of states, starting\nfrom q, which is a subpath of some path in the model, i.e.\na sequence q0q1... such that q = q0 and there are q0\n, ..., qi\nsuch that q0\n...qi\nq0q1... \u2208 \u039bM.2\nThe semantics of CTLK is\ndefined as follows:\nM, q |= p iff q \u2208 \u03c0(p);\nM, q |= \u00ac\u03d5 iff M, q |= \u03d5;\nM, q |= \u03d5 \u2227 \u03c8 iff M, q |= \u03d5 and M, q |= \u03c8;\nM, q |= E f\u03d5 iff there is a q-path \u03bb such that M, \u03bb[1] |= \u03d5;\nM, q |= E2 \u03d5 iff there is a q-path \u03bb such that M, \u03bb[i] |= \u03d5\nfor every i \u2265 0;\n1\nAdditional operators A (for every path) and \u2666\n(sometime in the future) are defined in the usual way.\n2\nFor CTLK models, \u03bb is a q-subpath iff it is a q-path. It\nwill not always be so when plausible paths are introduced.\nM, q |= E\u03d5U \u03c8 iff there is a q-path \u03bb and i \u2265 0 such that\nM, \u03bb[i] |= \u03c8, and M, \u03bb[j] |= \u03d5 for every 0 \u2264 j < i;\nM, q |= Ka\u03d5 iff M, q |= \u03d5 for every q such that q \u223ca q .\n3. EXTENDING TIME AND KNOWLEDGE\nWITH PLAUSIBILITY AND BELIEFS\nIn this section we discuss the central concept of this\npaper, i.e. the concept of plausibility. First, we outline the\nidea informally. Then, we extend CTLK with the notion\nof plausibility by adding plausible path operators Pl a and\nphysical path operator Ph to the logic. Formula Pl a\u03d5 has\nthe intended meaning: according to agent a, it is plausible\nthat \u03d5 holds; formula Ph \u03d5 reads as: \u03d5 holds in all\nphysically possible scenarios (i.e., even in implausible ones). The\nplausible path operator restricts statements only to those\npaths which are defined to be sensible, whereas the\nphysical path operator generates statements about all paths that\nmay theoretically occur. Furthermore, we define beliefs on\ntop of plausibility and knowledge, as the facts that an agent\nwould know if he assumed that only plausible things could\nhappen. Finally, we discuss related work [7, 8, 20, 18, 16],\nand compare it with our approach.\n3.1 The Concept of Plausibility\nIt is well known how knowledge (or beliefs) can be\nmodeled with Kripke structures. However, it is not so obvious\nhow we can capture knowledge and beliefs in a sensible way\nin one framework. Clearly, there should be a connection\nbetween these two notions. Our approach is to use the\nnotion of plausibility for this purpose. Plausibility can serve\nas a primitive concept that helps to define the semantics\nof beliefs, in a similar way as indistinguishability of states\n(represented by relation \u223ca) is the semantic concept that\nunderlies knowledge. In this sense, our work follows [7, 20]:\nessentially, beliefs are what an agent would know if he took\nonly plausible options into account. In our approach,\nhowever, plausibility is explicitly seen as a temporal property.\nThat is, we do not consider states (or possible worlds) to be\nmore plausible than others but rather define some behaviors\nto be plausible, and others implausible. Moreover,\nbehaviors can be formally understood as temporal paths in the\nKripke structure modeling a multi-agent system.\nAn actual notion of plausibility (that is, a particular set of\nplausible paths) can emerge in many different ways. It may\nresult from observations and learning; an agent can learn\nfrom its observations and see specific patterns of events as\nplausible (a lot of people wear black shoes if they wear a\nsuit). Knowledge exchange is another possibility (e.g., an\nagent a can tell agent b that player c always bluffs when he\nis smiling). Game theory, with its rationality criteria\n(undominated strategies, maxmin, Nash equilibrium etc.) is\nanother viable source of plausibility assumptions. Last but not\nleast, folk knowledge can be used to establish\nplausibilityrelated classifications of behavior (players normally want\nto win a game, people want to live).\nIn any case, restricting the reasoning to plausible\npossibilities can be essential if we want to make the reasoning\nfeasible, as the space of all possibilities (we call them physical\npossibilities in the rest of the paper) is exceedingly large in\nreal life. Of course, this does not exclude a more extensive\nanalysis in special cases, e.g. when our plausibility\nassumptions do not seem accurate any more, or when the cost of\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 583\ninaccurate assumptions can be too high (as in the case of\nhigh-budget business decisions). But even in these cases, we\nusually do not get rid of plausibility assumptions completely\n- we only revise them to make them more cautious.3\nTo formalize this idea, we extend models of CTLK with\nsets of plausible paths and add plausibility operators Pl a,\nphysical paths operator Ph , and belief operators Ba to the\nlanguage of CTLK. Now, it is possible to make statements\nthat refer to plausible paths only, as well as statements that\nregard all paths that may occur in the system.\n3.2 CTLK with Plausibility\nIn this section, we extend the logic of CTLK with\nplausibility; we call the resulting logic CTLKP. Formally, the\nlanguage of CTLKP is defined as:\n\u03d5 ::= p | \u00ac\u03d5 | \u03d5 \u2227 \u03d5 | E\u03b3 | Pl a\u03d5 | Ph \u03d5 | Ka\u03d5 | Ba\u03d5\n\u03b3 ::= f\u03d5 | 2 \u03d5 | \u03d5U \u03d5.\nFor instance, we may claim it is plausible to assume that\na shop is closed after the opening hours, though the manager\nmay be physically able to open it at any time: Pl aA2 (late \u2192\n\u00acopen) \u2227 Ph E\u2666 (late \u2227 open).\nThe semantics of CTLKP extends that of CTLK as\nfollows. Firstly, we augment the models with sets of plausible\npaths. A model with plausibility is given as\nM = Q, R, \u223c1, ..., \u223ck, \u03a51, ..., \u03a5k, \u03c0 ,\nwhere Q, R, \u223c1, ..., \u223ck, \u03c0 is a CTLK model, and \u03a5a \u2286 \u039bM\nis the set of paths in M that are plausible according to agent\na. If we want to make it clear that \u03a5a is taken from model\nM, we will write \u03a5M\na . It seems worth emphasizing that this\nnotion of plausibility is subjective and holistic. It is\nsubjective because \u03a5a represents agent a\"s subjective view on what\nis plausible - and indeed, different agents may have\ndifferent ideas on plausibility (i.e., \u03a5a may differ from \u03a5b). It is\nholistic because \u03a5a represents agent a\"s idea of the\nplausible behavior of the whole system (including the behavior of\nother agents).\nRemark 1. In our models, plausibility is also global, i.e.,\nplausibility sets do not depend on the state of the system.\nInvestigating systems, in which plausibility is relativized with\nrespect to states (like in [7]), might be an interesting avenue\nof future work. However, such an approach - while obviously\nmore flexible - allows for potentially counterintuitive system\ndescriptions. For example, it might be the case that path \u03bb\nis plausible in q = \u03bb[0], but the set of plausible paths in\nq = \u03bb[1] is empty. That is, by following plausible path \u03bb we\nare bound to get to an implausible situation. But then, does\nit make sense to consider \u03bb as plausible?\nSecondly, we use a non-standard satisfaction relation |=P ,\nwhich we call plausible satisfaction. Let M be a CTLKP\n3\nThat is, when planning to open an industrial plant in the\nUK, we will probably consider the possibility of our main\ncontractor taking her life, but we will still not take into\naccount the possibilities of: an invasion of UFO, England being\ndestroyed by a meteorite, Fidel Castro becoming the British\nPrime Minister etc. Note that this is fundamentally different\nfrom using a probabilistic model in which all these unlikely\nscenarios are assigned very low probabilities: in that case,\nthey also have a very small influence on our final decision,\nbut we must process the whole space of physical possibilities\nto evaluate the options.\nmodel and P \u2286 \u039bM be an arbitrary subset of paths in M\n(not necessarily any \u03a5M\na ). |=P restricts the evaluation of\ntemporal formulae to the paths given in P only. The\nabsolute satisfaction relation |= is defined as |=\u039bM .\nLet on(P) be the set of all states that lie on at least one\npath in P, i.e. on(P) = {q \u2208 Q | \u2203\u03bb \u2208 P\u2203i (\u03bb[i] = q)}. Now,\nthe semantics of CTLKP can be given through the\nfollowing clauses:\nM, q |=P p iff q \u2208 \u03c0(p);\nM, q |=P \u00ac\u03d5 iff M, q |=P \u03d5;\nM, q |=P \u03d5 \u2227 \u03c8 iff M, q |=P \u03d5 and M, q |=P \u03c8;\nM, q |=P E f\u03d5 iff there is a q-subpath \u03bb \u2208 P such that\nM, \u03bb[1] |=P \u03d5;\nM, q |=P E2 \u03d5 iff there is a q-subpath \u03bb \u2208 P such that\nM, \u03bb[i] |=P \u03d5 for every i \u2265 0;\nM, q |=P E\u03d5U \u03c8 iff there is a q-subpath \u03bb \u2208 P and i \u2265 0\nsuch that M, \u03bb[i] |=P \u03c8, and M, \u03bb[j] |=P \u03d5 for every\n0 \u2264 j < i;\nM, q |=P Pl a\u03d5 iff M, q |=\u03a5a\n\u03d5;\nM, q |=P Ph \u03d5 iff M, q |= \u03d5;\nM, q |=P Ka\u03d5 iff M, q |= \u03d5 for every q such that q \u223ca q ;\nM, q |=P Ba\u03d5 iff for all q \u2208 on(\u03a5a) with q \u223ca q , we have\nthat M, q |=\u03a5a\n\u03d5.\nOne of the main reasons for using the concept of\nplausibility is that we want to define agents\" beliefs out of more\nprimitive concepts - in our case, these are plausibility and\nindistinguishability - in a way analogous to [20, 7]. If an\nagent knows that \u03d5, he must be sure about it. However,\nbeliefs of an agent are not necessarily about reliable facts.\nStill, they should make sense to the agent; if he believes that\n\u03d5, then the formula should at least hold in all futures that\nhe envisages as plausible. Thus, beliefs of an agent may be\nseen as things known to him if he disregards all non-plausible\npossibilities.\nWe say that \u03d5 is M-true (M |= \u03d5) if M, q |= \u03d5 for all\nq \u2208 QM. \u03d5 is valid (|= \u03d5) if M |= \u03d5 for all models M. \u03d5\nis M-strongly true (M |\u2261 \u03d5) if M, q |=P \u03d5 for all q \u2208 QM\nand all P \u2286 \u039bM. \u03d5 is strongly valid ( |\u2261 \u03d5) if M |\u2261 \u03d5 for all\nmodels M.\nProposition 2. Strong truth and strong validity imply\ntruth and validity, respectively. The reverse does not hold.\nUltimately, we are going to be interested in normal (not\nstrong) validity, as parameterizing the satisfaction relation\nwith a set P is just a technical device for propagating sets\nof plausible paths \u03a5a into the semantics of nested formulae.\nThe importance of strong validity, however, lies in the fact\nthat |\u2261 \u03d5 \u2194 \u03c8 makes \u03d5 and \u03c8 completely interchangeable,\nwhile the same is not true for normal validity.\nProposition 3. Let \u03a6[\u03d5/\u03c8] denote formula \u03a6 in which\nevery occurrence of \u03c8 was replaced by \u03d5. Also, let |\u2261 \u03d5 \u2194 \u03c8.\nThen for all M, q, P: M, q |=P \u03a6 iff M, q |=P \u03a6[\u03d5/\u03c8] (in\nparticular, M, q |= \u03a6 iff M, q |= \u03a6[\u03d5/\u03c8]).\nNote that |= \u03d5 \u2194 \u03c8 does not even imply that M, q |= \u03a6 iff\nM, q |= \u03a6[\u03d5/\u03c8].\n584 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nFigure 1: Guessing Robots game\nExample 1 (Guessing Robots). Consider a simple\ngame with two agents a and b, shown in Figure 1. First,\na chooses a real number r \u2208 [0, 1] (without revealing the\nnumber to b); then, b chooses a real number r \u2208 [0, 1].\nThe agents win the game (and collect EUR 1, 000, 000) if\nboth chose 1, otherwise they lose. Formally, we model the\ngame with a CTLKP model M, in which the set of states\nQ includes qs for the initial situation, states qr, r \u2208 [0, 1],\nfor the situations after a has chosen number r, and final\nstates qw, ql for the winning and the losing situation,\nrespectively. The transition relation is as follows: qsRqr and\nqrRql for all r \u2208 [0, 1]; q1Rqw, qwRqw, and qlRql. Moreover,\n\u03c0(one) = {q1} and \u03c0(win) = {qw}. Player a has perfect\ninformation in the game (i.e., q \u223ca q iff q = q ), but player\nb does not distinguish between states qr (i.e., qr \u223cb qr for\nall r, r \u2208 [0, 1]). Obviously, the only sensible thing to do\nfor both agents is to choose 1 (using game-theoretical\nvocabulary, these strategies are strongly dominant for the\nrespective players). Thus, there is only one plausible course of\nevents if we assume that our players are rational, and hence\n\u03a5a = \u03a5b = {qsq1qwqw . . .}.\nNote that, in principle, the outcome of the game is\nuncertain: M, qs |= \u00acA\u2666 win\u2227\u00acA2 \u00acwin. However, assuming\nrationality of the players makes it only plausible that the game\nmust end up with a win: M, qs |= Pla A\u2666 win \u2227 Plb A\u2666 win,\nand the agents believe that this will be the case: M, qs |=\nBaA\u2666 win \u2227 BbA\u2666 win. Note also that, in any of the states\nqr, agent b believes that a (being rational) has played 1:\nM, qr |= Bbone for all r \u2208 [0, 1].\n3.3 Defining Plausible Paths with Formulae\nSo far, we have assumed that sets of plausible paths are\nsomehow given in models. In this section we present a\ndynamic approach where an actual notion of plausibility can\nbe specified in the object language. Note that we want to\nspecify (usually infinite) sets of infinite paths, and we need a\nfinite representation of these structures. One logical solution\nis given by using path formulae \u03b3. These formulae describe\nproperties of paths; therefore, a specific formula can be used\nto characterize a set of paths. For instance, think about a\ncountry in Africa where it has never snowed. Then,\nplausible paths might be defined as ones in which it never snows,\ni.e., all paths that satisfy 2 \u00acsnows. Formally, let \u03b3 be a\nCTLK path formula. We define |\u03b3|M to be the set of paths\nthat satisfy \u03b3 in model M:\n| f\u03d5|M = {\u03bb | M, \u03bb[1] |= \u03d5}\n|2 \u03d5|M = {\u03bb | \u2200i (M, \u03bb[i] |= \u03d5)}\n|\u03d51U \u03d52|M = {\u03bb | \u2203i\n`\nM, \u03bb[i] |= \u03d52 \u2227\n\u2200j(0 \u2264 j < i \u21d2 M, \u03bb[j] |= \u03d51)\n\u00b4\n}.\nMoreover, we define the plausible paths model update as\nfollows. Let M = Q, R, \u223c1, ..., \u223ck, \u03a51, ..., \u03a5k, \u03c0 be a\nCTLKP model, and let P \u2286 \u039bM be a set of paths. Then\nMa,P\n= Q, R, \u223c1, ..., \u223ck, \u03a51, ..., \u03a5a\u22121, P, \u03a5a+1, ..., \u03a5k, \u03c0\ndenotes model M with a\"s set of plausible paths reset to P.\nNow we can extend the language of CTLKP with\nformulae (set-pla \u03b3)\u03d5 with the intuitive reading: suppose that\n\u03b3 exactly characterizes the set of plausible paths, then \u03d5\nholds, and formal semantics given below:\nM, q |=P (set-pla \u03b3)\u03d5 iff Ma,|\u03b3|M , q |=P \u03d5.\nWe observe that this update scheme is similar to the one\nproposed in [13].\n3.4 Comparison to Related Work\nSeveral modal notions of plausibility were already\ndiscussed in the existing literature [7, 8, 20, 18, 16]. In these\npapers, like in ours, plausibility is used as a primitive\nsemantic concept that helps to define beliefs on top of agents\"\nknowledge. A similar idea was introduced by Moses and\nShoham in [18]. Their work preceded both [7, 8] and\n[20]and although Moses and Shoham do not explicitly mention\nthe term plausibility, it seems appropriate to summarize\ntheir idea first.\nMoses and Shoham: Beliefs as Conditional Knowledge\nIn [18], beliefs are relativized with respect to a formula \u03b1\n(which can be seen as a plausibility assumption expressed\nin the object language). More precisely, worlds that satisfy \u03b1\ncan be considered as plausible. This concept is expressed via\nsymbols B\u03b1\ni \u03d5; the index i \u2208 {1, 2, 3} is used to distinguish\nbetween three different implementations of beliefs. The first\nversion is given by B\u03b1\n1 \u03d5 \u2261 K(\u03b1 \u2192 \u03d5).4\nA drawback of\nthis version is that if \u03b1 is false, then everything will be\nbelieved with respect to \u03b1. The second version overcomes\nthis problem: B\u03b1\n2 \u03d5 \u2261 K(\u03b1 \u2192 \u03d5) \u2227 (K\u00ac\u03b1 \u2192 K\u03d5); now \u03d5 is\nonly believed if it is known that \u03d5 follows from assumption\n\u03b1, and \u03d5 must be known if assumption \u03b1 is known to be false.\nFinally, B\u03b1\n3 \u03d5 \u2261 K(\u03b1 \u2192 \u03d5) \u2227 \u00acK\u00ac\u03b1: if the assumption \u03b1 is\nknown to be false, nothing should be believed with respect to\n\u03b1. The strength of these different notions is given as follows:\nB\u03b1\n3 \u03d5 implies B\u03b1\n2 \u03d5, and B\u03b1\n2 \u03d5 implies B\u03b1\n1 \u03d5. In this approach,\nbelief is strongly connected to knowledge in the sense that\nbelief is knowledge with respect to a given assumption.\nFriedman and Halpern: Plausibility Spaces\nThe work of Friedman and Halpern [7] extends the concepts\nof knowledge and belief with an explicit notion of\nplausibility; i.e., some worlds are more plausible for an agent\nthan others. To implement this idea, Kripke models are\nextended with function P which assigns a plausibility space\nP(q, a) = (\u03a9(q,a), (q,a)) to every state, or more generally\nevery possible world q, and agent a. The plausibility space\n4\nUnlike in most approaches, K is interpreted over all worlds\nand not only over the indistinguishable worlds.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 585\nis just a partially ordered subset of states/worlds; that is,\n\u03a9(q, a) \u2286 Q, and (q,a)\u2286 Q \u00d7Q is a reflexive and transitive\nrelation. Let S, T \u2286 \u03a9(q,a) be finite subsets of states; now,\nT is defined to be plausible given S with respect to P(q, a),\ndenoted by S \u2192P (q,a) T, iff all minimal points/states in\nS (with respect to (q,a)) are also in T.5\nFriedman and\nHalpern\"s view to modal plausibility is closely related to\nprobability and, more generally, plausibility measures.\nLogics of plausibility can be seen as a qualitative description of\nagents preferences/knowledge; logics of probability [6, 15],\non the other hand, offer a quantitative description.\nThe logic from [7] is defined by the following grammar:\n\u03d5 ::= p | \u03d5\u2227\u03d5 | \u00ac\u03d5 | Ka\u03d5 | \u03d5 \u2192a \u03d5, where the semantics of\nall operators except \u2192a is given as usual, and formulae \u03d5 \u2192a\n\u03c8 have the meaning that \u03c8 is true in the most plausible\nworlds in which \u03d5 holds. Formally, the semantics for \u2192a\nis given as: M, q |= \u03d5 \u2192a \u03c8 iff S\u03d5\nP (q,a) \u2192P(q,a)\nS\u03c8\nP (q,a),\nwhere S\u03d5\n(q,a) = {q \u2208 \u03a9(q,a) | M, q |= \u03d5} are the states in\n\u03a9(q,a) that satisfy \u03d5. The idea of defining beliefs is given\nby the assumption that an agent believes in something if he\nknows that it is true in the most plausible worlds of \u03a9(q,a);\nformally, this can be stated as Ba\u03d5 \u2261 Ka( \u2192a \u03d5).\nFriedman and Halpern have shown that the KD45\naxioms are valid for operator Ba if plausibility spaces satisfy\nconsistency (for all states q \u2208 Q it holds that \u03a9(q,a) \u2286 { q \u2208\nQ | q \u223ca q }) and normality (for all states q \u2208 Q it holds\nthat \u03a9(q,a) = \u2205).6\nA temporal extension of the language\n(mentioned briefly in [7], and discussed in more detail in [8])\nuses the interpreted systems approach [10, 5]. A system R\nis given by runs, where a run r : N \u2192 Q is a function from\ntime moments (modeled by N) to global states, and a time\npoint (r, i) is given by a time point i \u2208 N and a run r. A\nglobal state is a combination of local states, one per agent.\nAn interpreted system M = (R, \u03c0) is given by a system R\nand a valuation of propositions \u03c0. Epistemic relations are\ndefined over time points, i.e., (r , m ) \u223ca (r, m) iff agent\na\"s local states ra(m ) and ra(m) of (r , m ) and (r, m) are\nequal. Formulae are interpreted in a straightforward way\nwith respect to interpreted systems, e.g. M, r, m |= Ka\u03d5 iff\nM, r , m |= \u03d5 for all (r , m ) \u223ca (r, m). Now, these are time\npoints that play the role of possible worlds; consequently,\nplausibility spaces P(r,m,a) are assigned to each point (r, m)\nand agent a.\nSu et al.: KBC Logic\nSu et al. [20] have developed a multi-modal,\ncomputationally grounded logic with modalities K, B, and C (knowledge,\nbelief, and certainty). The computational model consists of\n(global) states q = (qvis\n, qinv\n, qper\n, Qpls\n) where the\nenvironment is divided into a visible (qvis\n) and an invisible part\n(qinv\n), and qper\ncaptures the agent\"s perception of the visible\npart of the environment. External sources may provide the\nagent with information about the invisible part of a state,\nwhich results in a set of states Qpls\nthat are plausible for\nthe agent.\nGiven a global state q, we additionally define V is(q) =\nqvis\n, Inv(q) = qinv\n, Per(q) = qper\n, and Pls(q) = Qpls\n. The\n5\nWhen there are infinite chains . . . q3 q2 a q1, the\ndefinition is much more sophisticated. An interested reader\nis referred to [7] for more details.\n6\nNote that this normality is essentially seriality of states\nwrt plausibility spaces.\nsemantics is given by an extension of interpreted systems [10,\n5], here, it is called interpreted KBC systems. KBC\nformulae are defined as \u03d5 ::= p | \u00ac\u03d5 | \u03d5 \u2227 \u03d5 | K\u03d5 | B\u03d5 | C\u03d5.\nThe epistemic relation \u223cvis is captured in the following way:\n(r, i) \u223cvis (r , i ) iff V is(r(i)) = V is(r (i )). The semantic\nclauses for belief and certainty are given below.\nM, r, i |= B\u03d5 iff M, r , i |= \u03d5 for all (r , i ) with V is(r (i )) =\nPer(r(i)) and Inv(r (i )) \u2208 Pls(r(i))\nM, r, i |= C\u03d5 iff M, r , i |= \u03d5 for all (r (i )) with V is(r (i )) =\nPer(r(i))\nThus, an agent believes \u03d5 if, and only if, \u03d5 is true in all\nstates which look like what he sees now and seem plausible\nin the current state. Certainty is stronger: if an agent is\ncertain about \u03d5, the formula must hold in all states with\na visible part equal to the current perception, regardless of\nwhether the invisible part is plausible or not.\nThe logic does not include temporal formulae, although\nit might be extended with temporal operators, as time is\nalready present in KBC models.\nWhat Are the Differences to Our Logic?\nIn our approach, plausibility is explicitly seen as a temporal\nproperty, i.e., it is a property of temporal paths rather than\nstates. In the object language, this is reflected by the fact\nthat plausibility assumptions are specified through path\nformulae. In contrast, the approach of [18] and [20] is static:\nnot only the logics do not include operators for talking about\ntime and/or change, but these are states that are assumed\nplausible or not in their semantics.\nThe differences to [7, 8] are more subtle. Firstly, the\nframework of Friedman and Halpern is static in the sense\nthat plausibility is taken as a property of (abstract)\npossible worlds. This formulation is flexible enough to allow for\nincorporating time; still, in our approach, time is inherent\nto plausibility rather than incidental.\nSecondly, our framework is more computationally oriented.\nThe implementation of temporal plausibility in [7, 8] is based\non the interpreted systems approach with time points (r, m)\nbeing subject to plausibility. As runs are included in time\npoints, they can also be defined plausible or implausible.7\nHowever, it also means that time points serve the role of\npossible worlds in the basic formulation, which yields Kripke\nstructures with uncountable possible world spaces in all but\nthe most trivial cases.\nThirdly, [7, 8] build on linear time: a run (more precisely,\na time moment (r, m)) is fixed when a formula is interpreted.\nIn contrast, we use branching time with explicit\nquantification over temporal paths.8\nWe believe that branching time\nis more suitable for non-deterministic domains (cf. e.g. [4]),\nof which multi-agent systems are a prime example. Note\nthat branching time makes our notion of belief different from\nFriedman and Halpern\"s. Most notably, property K\u03d5 \u2192 B\u03d5\nis valid in their approach, but not in ours: an agent may\n7\nFriedman and Halpern even briefly mention how\nplausibility of runs can be embedded in their framework.\n8\nTo be more precise, time in [7] does implicitly branch at\nepistemic states. This is because (r, m) \u223ca (r , m ) iff a\"s\nlocal state corresponding to both time points is the same\n(ra(m) = ra(m )). In consequence, the semantics of Ka\u03d5\ncan be read as for every run, and every moment on this\nrun that yields the same local state as now, \u03d5 holds.\n586 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nknow that some course of events is in principle possible,\nwithout believing that it can really become the case (see\nSection 4.2). As Proposition 13 suggests, such a subtle\ndistinction between knowledge and beliefs is possible in our\napproach because branching time logics allow for existential\nquantification over runs.\nFourthly, while Friedman and Halpern\"s models are very\nflexible, they also enable system descriptions that may seem\ncounterintuitive. Suppose that (r, m) is plausible in itself\n(formally: (r, m) is minimal wrt (r,m,a)), but (r, m + 1) is\nnot plausible in (r, m + 1). This means that following the\nplausible path makes it implausible (cf. Remark 1), which\nis even stranger in the case of linear time. Combining the\nargument with computational aspects, we suggest that our\napproach can be more natural and straightforward for many\napplications.\nLast but not least, our logic provides a mechanism for\nspecifying (and updating) sets of plausible paths in the\nobject language. Thus, plausibility sets can be specified in a\nsuccinct way, which is another feature that makes our\nframework computation-friendly. The model checking results from\nSection 5 are especially encouraging in this light.\n4. PLAUSIBILITY, KNOWLEDGE, AND\nBELIEFS IN CTLKP\nIn this section we study some relevant properties of\nplausibility, knowledge, and beliefs; in particular, axioms KDT45\nare examined. But first, we identify two important\nsubclasses of models with plausibility.\nA CTLKP model is plausibly serial (or p-serial) for agent\na if every state of the system is part of a plausible path\naccording to a, i.e. on(\u03a5a) = Q. As we will see further, a\nweaker requirement is sometimes sufficient. We call a model\nweakly p-serial if every state has at least one\nindistinguishable counterpart which lies on a plausible path, i.e. for each\nq \u2208 Q there is a q \u2208 Q such that q \u223ca q and q \u2208 on(\u03a5a).\nObviously, p-seriality implies weak p-seriality. We get the\nfollowing characterization of both model classes.\nProposition 4. M is plausibly serial for agent a iff\nformula Pl aE f is valid in M. M is weakly p-serial for agent\na iff \u00acKaPl aA f\u22a5 is valid in M.\n4.1 Axiomatic Properties\nTheorem 5. Axioms K, D, 4, and 5 for knowledge are\nstrongly valid, and axiom T is valid. That is, modalities Ka\nform system S5 in the sense of normal validity, and KD45\nin the sense of strong validity.\nWe do not include proofs here due to lack of space. The\ninterested reader is referred to [2], where detailed proofs are\ngiven.\nProposition 6. Axioms K, 4, and 5 for beliefs are\nstrongly valid. That is, we have:\n|\u2261 (Ba\u03d5 \u2227 Ba(\u03d5 \u2192 \u03c8)) \u2192 Ba\u03c8, |\u2261 (Ba\u03d5 \u2192 BaBa\u03d5), and\n|\u2261 (\u00acBa\u03d5 \u2192 Ba\u00acBa\u03d5).\nThe next proposition concerns the consistency axiom\nD: Ba\u03d5 \u2192 \u00acBa\u00ac\u03d5. It is easy to see that the axiom is not\nvalid in general: as we have no restrictions on plausibility\nsets \u03a5a, it may be as well that \u03a5a = \u2205. In that case we have\nBa\u03d5 \u2227 Ba\u00ac\u03d5 for all formulae \u03d5, because the set of states to\nbe considered becomes empty. However, it turns out that D\nis valid for a very natural class of models.\nProposition 7. Axiom D for beliefs is not valid in the\nclass of all CTLKP models. However, it is strongly valid in\nthe class of weak p-serial models (and therefore also in the\nclass of p-serial models).\nMoreover, as one may expect, beliefs do not have to be\nalways true.\nProposition 8. Axiom T for beliefs is not valid; i.e.,\n|= (Ba\u03d5 \u2192 \u03d5). The axiom is not even valid in the class of\np-serial models.\nTheorem 9. Belief modalities Ba form system K45 in\nthe class of all models, and KD45 in the class of weakly\nplausibly serial models (in the sense of both normal and\nstrong validity). Axiom T is not even valid for p-serial\nmodels.\n4.2 Plausibility, Knowledge, and Beliefs\nFirst, we investigate the relationship between knowledge\nand plausibility/physicality operators. Then, we look at the\ninteraction between knowledge and beliefs.\nProposition 10. Let \u03d5 be a CTLKP formula, and M\nbe a CTLKP model. We have the following strong validities:\n(i) |\u2261 Pl aKa\u03d5 \u2194 Ka\u03d5\n(ii) |\u2261 Ph Ka\u03d5 \u2194 KaPh \u03d5 and |\u2261 KaPh \u03d5 \u2194 Ka\u03d5\nWe now want to examine the relationship between\nknowledge and belief. For instance, if agent a believes in\nsomething, he knows that he believes it. Or, if he knows a fact,\nhe also believes that he knows it. On the other hand, for\ninstance, an agent does not necessarily believe in all the\nthings he knows. For example, we may know that an\ninvasion from another galaxy is in principle possible (KaE\u2666\ninvasion), but if we do not take this possibility as plausible\n(\u00acPl aE\u2666 invasion), then we reject the corresponding belief\nin consequence (\u00acBaE\u2666 invasion). Note that this property\nreflects the strong connection between belief and plausibility\nin our framework.\nProposition 11. The following formulae are strongly\nvalid:\n(i) Ba\u03d5 \u2192 KaBa\u03d5, (ii) KaBa\u03d5 \u2192 Ba\u03d5,\n(iii) Ka\u03d5 \u2192 BaKa\u03d5.\nThe following formulae are not valid:\n(iv) Ba\u03d5 \u2192 BaKa\u03d5, (v) Ka\u03d5 \u2192 Ba\u03d5\nThe last invalidity is especially important: it is not the\ncase that knowing something implies believing in it. This\nemphasizes that we study a specific concept of beliefs here.\nNote that its specific is not due to the plausibility-based\ndefinition of beliefs. The reason lies rather in the fact that we\ninvestigate knowledge, beliefs and plausibility in a temporal\nframework, as Proposition 12 shows.\nProposition 12. Let \u03d5 be a CTLKP formula that does\nnot include any temporal operators. Then Ka\u03d5 \u2192 Ba\u03d5 is\nstrongly valid, and in the class of p-serial models we have\neven that |\u2261 Ka\u03d5 \u2194 Ba\u03d5.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 587\nMoreover, it is important that we use branching time with\nexplicit quantification over paths; this observation is\nformalized in Proposition 13.\nDefinition 1. We define the universal sublanguage of\nCTLK in a way similar to [21]:\n\u03d5u ::= p | \u00acp | \u03d5u \u2227 \u03d5u | \u03d5u \u2228 \u03d5u | A\u03b3u | Ka\u03d5u,\n\u03b3u ::= f\u03d5u | 2 \u03d5u | \u03d5uU \u03d5u.\nWe call such \u03d5u universal formulae, and \u03b3u universal path\nformulae.\nProposition 13. Let \u03d5u be a universal CTLK formula.\nThen |\u2261 Ka\u03d5u \u2192 Ba\u03d5u.\nThe following two theorems characterize the relationship\nbetween knowledge and beliefs: first for the class of p-serial\nmodels, and then, finally, for all models.\nTheorem 14. The following formulae are strongly valid\nin the class of plausibly serial CTLKP models:\n(i) Ba\u03d5 \u2194 KaPl a\u03d5, (ii) Ka\u03d5 \u2194 BaPh \u03d5.\nTheorem 15. Formula Ba\u03d5 \u2194 KaPl a(E f \u2192 \u03d5) is\nstrongly valid.\nNote that this characterization has a strong commonsense\nreading: believing in \u03d5 is knowing that \u03d5 plausibly holds in\nall plausibly imaginable situations.\n4.3 Properties of the Update\nThe first notable property of plausibility update is that it\ninfluences only formulae in which plausibility plays a role,\ni.e. ones in which belief or plausibility modalities occur.\nProposition 16. Let \u03d5 be a CTLKP formula that does\nnot include operators Pl a and Ba, and \u03b3 be a CTLKP path\nformula. Then, we have |\u2261 \u03d5 \u2194 (set-pla \u03b3)\u03d5.\nWhat can be said about the result of an update? At first\nsight, formula (set-pla \u03b3)Pl aA\u03b3 seems a natural\ncharacterization; however, it is not valid. This is because, by leaving\nthe other (implausible) paths out of scope, we may leave out\nof |\u03b3| some paths that were needed to satisfy \u03b3 (see the\nexample in Section 4.2). We propose two alternative ways out:\nthe first one restricts the language of the update similarly\nto [21]; the other refers to physical possibilities, in a way\nanalogous to [13].\nProposition 17. The CTLKP formula (set-pla \u03b3)Pl aA\u03b3\nis not valid. However, we have the following validities:\n(i) |\u2261 (set-pla \u03b3u)Pl aA\u03b3u, where \u03b3u is a universal CTLK\npath formula from Definition 1.\n(ii) If \u03d5, \u03d51, \u03d52 are arbitrary CTLK formulae, then:\n|\u2261 (set-pla\nf\u03d5)Pl aA f(Ph \u03d5),\n|\u2261 (set-pla 2 \u03d5)Pl aA2 (Ph \u03d5), and\n|\u2261 (set-pla \u03d51U \u03d52)Pl aA(Ph \u03d51)U (Ph \u03d52).\n5. VERIFICATION OF PLAUSIBILITY,\nTIME AND BELIEFS\nIn this section we report preliminary results on model\nchecking CTLKP formulae. Clearly, verifying CTLKP\nproperties directly against models with plausibility does not\nmake much sense, since these models are inherently infinite;\nwhat we need is a finite representation of plausibility sets.\nOne such representation has been discussed in Section 3.3:\nplausibility sets can be defined by path formulae and the\nupdate operator (set-pla \u03b3).\nWe follow this idea here, studying the complexity of model\nchecking CTLKP formulae against CTLK models (which\ncan be seen as a compact representation of CTLKP\nmodels in which all the paths are assumed plausible), with the\nunderlying idea that plausibility sets, when needed, must be\ndefined explicitly in the object language. Below we sketch\nan algorithm that model-checks CTLKP formulae in time\nlinear wrt the size of the model and the length of the\nformula. This means that we have extended CTLK to a more\nexpressive language with no computational price to pay.\nFirst of all, we get rid of the belief operators (due to\nTheorem 15), replacing every occurrence of Ba\u03d5 with KaPl a(E f\n\u2192 \u03d5). Now, let \u2212\u2192\u03b3 = \u03b31, ..., \u03b3k be a vector of vanilla\npath formulae (one per agent), with the initial vector \u2212\u2192\u03b30 =\n, ..., , and \u2212\u2192\u03b3 [\u03b3 /a] denoting vector \u2212\u2192\u03b3 , in which \u2212\u2192\u03b3 [a]\nis replaced with \u03b3 . Additionally, we define \u2212\u2192\u03b3 [0] = . We\ntranslate the resulting CTLKP formulae to ones without\nplausibility via function tr(\u03d5) = tr\u2212\u2192\u03b30,0(\u03d5), defined as\nfollows:\ntr\u2212\u2192\u03b3 ,i(p) = p,\ntr\u2212\u2192\u03b3 ,i(\u03d51 \u2227 \u03d52) = tr\u2212\u2192\u03b3 ,i(\u03d51) \u2227 tr\u2212\u2192\u03b3 ,i(\u03d52),\ntr\u2212\u2192\u03b3 ,i(\u00ac\u03d5) = \u00actr\u2212\u2192\u03b3 ,i(\u03d5),\ntr\u2212\u2192\u03b3 ,i(Ka\u03d5) = Ka tr\u2212\u2192\u03b3 ,0(\u03d5),\ntr\u2212\u2192\u03b3 ,i(Pla \u03d5) = tr\u2212\u2192\u03b3 ,a(\u03d5),\ntr\u2212\u2192\u03b3 ,i((set-pla \u03b3 )\u03d5) = tr\u2212\u2192\u03b3 [\u03b3 /a],i(\u03d5),\ntr\u2212\u2192\u03b3 ,i(Ph \u03d5) = tr\u2212\u2192\u03b3 ,0(\u03d5),\ntr\u2212\u2192\u03b3 ,i( f\u03d5) = ftr\u2212\u2192\u03b3 ,i(\u03d5),\ntr\u2212\u2192\u03b3 ,i(2 \u03d5) = 2 tr\u2212\u2192\u03b3 ,i(\u03d5),\ntr\u2212\u2192\u03b3 ,i(\u03d51U \u03d52) = tr\u2212\u2192\u03b3 ,i(\u03d51)U tr\u2212\u2192\u03b3 ,i(\u03d52),\ntr\u2212\u2192\u03b3 ,i(E\u03b3 ) = E(\u2212\u2192\u03b3 [i] \u2227 tr\u2212\u2192\u03b3 ,i(\u03b3 )).\nNote that the resulting sentences belong to the logic of\nCTLK+, that is CTL+ (where each path quantifier can be\nfollowed by a Boolean combination of vanilla path\nformulae)9\nwith epistemic modalities. The following proposition\njustifies the translation.\nProposition 18. For any CTLKP formula \u03d5 without\nBa, we have that M, q |=CTLKP \u03d5 iff M, q |=CTLK+ tr(\u03d5).\nIn general, model checking CTL+ (and also CTLK+)\nis \u0394P\n2 -complete. However, in our case, the Boolean\ncombinations of path subformulae are always conjunctions of at\nmost two non-negated elements, which allows us to propose\nthe following model checking algorithm. First, subformulae\nare evaluated recursively: for every subformula \u03c8 of \u03d5, the\nset of states in M that satisfy \u03c8 is computed and labeled\nwith a new proposition p\u03c8. Now, it is enough to define\nchecking M, q |= \u03d5 for \u03d5 in which all (state) subformulae\nare propositions, with the following cases:\nCase M, q |= E(2 p \u2227 \u03b3): If M, q |= p, then return no.\nOtherwise, remove from M all the states that do not satisfy\np (yielding a sparser model M ), and check the CTL\nformula E\u03b3 in M , q with any CTL model-checker.\nCase M, q |= E( fp \u2227 \u03b3): Create M by adding a copy q of\nstate q, in which only the transitions to states\nsatisfying p are kept (i.e., M, q |= r iff M, q |= r; and q Rq\niff qRq and M, q |= p). Then, check E\u03b3 in M , q .\n9\nFor the semantics of CTL+, and discussion of model\nchecking complexity, cf. [17].\n588 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nCase M, q |= E(p1U p2 \u2227 p3U p4): Note that this is\nequivalent to checking E(p1 \u2227 p3)U (p2 \u2227 Ep3U p4) \u2228 E(p1 \u2227\np3)U (p4 \u2227 Ep1U p2), which is a CTL formula.\nOther cases: The above cases cover all possible formulas\nthat begin with a path quantifier. For other cases,\nstandard CTLK model checking can be used.\nTheorem 19. Model checking CTLKP against CTLK\nmodels is PTIME-complete, and can be done in time O(ml),\nwhere m is the number of transitions in the model, and l is\nthe length of the formula to be checked. That is, the\ncomplexity is no worse than for CTLK itself.\n6. CONCLUSIONS\nIn this paper a notion of plausible behavior is considered,\nwith the underlying idea that implausible options should be\nusually ignored in practical reasoning about possible future\ncourses of action. We add the new notion of plausibility to\nthe logic of CTLK [19], and obtain a language which\nenables reasoning about what can (or must) plausibly happen.\nAs a technical device to define the semantics of the resulting\nlogic, we use a non-standard satisfaction relation |=P that\nallows to propagate the current set of plausible paths into\nsubformulae. Furthermore, we propose a non-standard\nnotion of beliefs, defined in terms of indistinguishability and\nplausibility. We also propose how plausibility assumptions\ncan be specified in the object language via a plausibility\nupdate operator (in a way similar to [13]).\nWe use this new framework to investigate some important\nproperties of plausibility, knowledge, beliefs, and updates.\nIn particular, we show that knowledge is an S5 modality,\nand that beliefs satisfy axioms K45 in general, and KD45\nfor the class of plausibly serial models. We also prove that\nbelieving in \u03d5 is knowing that \u03d5 plausibly holds in all\nplausibly possible situations. That is, the relationship between\nknowledge and beliefs is very natural and reflects the\ninitial intuition precisely. Moreover, the model checking\nresults from Section 5 show that verification for CTLKP is\nno more complex than for CTL and CTLK.\nWe would like to stress that we do not see this contribution\nas a mere technical exercise in formal logic. Human agents\nuse a similar concept of plausibility and practical beliefs\nin their everyday reasoning in order to reduce the search\nspace and make the reasoning feasible. As a consequence, we\nsuggest that the framework we propose may prove suitable\nfor modeling, design, and analysis resource-bounded agents\nin general.\nWe would like to thank Juergen Dix for fruitful\ndiscussions, useful comments and improvements.\n7. REFERENCES\n[1] R. Alur, T. A. Henzinger, and O. Kupferman.\nAlternating-time Temporal Logic. Journal of the\nACM, 49:672-713, 2002.\n[2] N. Bulling and W. Jamroga. Agents, beliefs and\nplausible behavior in a temporal setting. Technical\nReport IfI-06-05, Clausthal Univ. of Technology, 2006.\n[3] E. A. Emerson. Temporal and modal logic. In J. van\nLeeuwen, editor, Handbook of Theoretical Computer\nScience, volume B, pages 995-1072. Elsevier, 1990.\n[4] E.A. Emerson and J.Y. Halpern. sometimes and\nnot never revisited: On branching versus linear time\ntemporal logic. Journal of the ACM, 33(1):151-178,\n1986.\n[5] R. Fagin, J. Y. Halpern, Y. Moses, and M. Y. Vardi.\nReasoning about Knowledge. MIT Press: Cambridge,\nMA, 1995.\n[6] R. Fagin and J.Y. Halpern. Reasoning about\nknowledge and probability. Journal of ACM,\n41(2):340-367, 1994.\n[7] N. Friedman and J.Y. Halpern. A knowledge-based\nframework for belief change, Part I: Foundations. In\nProceedings of TARK, pages 44-64, 1994.\n[8] N. Friedman and J.Y. Halpern. A knowledge-based\nframework for belief change, Part II: Revision and\nupdate. In Proceedings of KR\"94, 1994.\n[9] J.Y. Halpern. Reasoning about knowledge: a survey.\nIn Handbook of Logic in Artificial Intelligence and\nLogic Programming. Vol. 4: Epistemic and Temporal\nReasoning, pages 1-34. Oxford University Press,\nOxford, 1995.\n[10] J.Y. Halpern and R. Fagin. Modelling knowledge and\naction in distributed systems. Distributed Computing,\n3(4):159-177, 1989.\n[11] W. Jamroga and N. Bulling. A general framework for\nreasoning about rational agents. In Proceedings of\nAAMAS\"07, 2007. Short paper.\n[12] W. Jamroga and W. van der Hoek. Agents that know\nhow to play. Fundamenta Informaticae,\n63(2-3):185-219, 2004.\n[13] W. Jamroga, W. van der Hoek, and M. Wooldridge.\nIntentions and strategies in game-like scenarios. In\nProgress in Artificial Intelligence: Proceedings of\nEPIA 2005, volume 3808 of LNAI, pages 512-523.\nSpringer Verlag, 2005.\n[14] W. Jamroga and Thomas \u02daAgotnes. Constructive\nknowledge: What agents can achieve under incomplete\ninformation. Technical Report IfI-05-10, Clausthal\nUniversity of Technology, 2005.\n[15] B.P. Kooi. Probabilistic dynamic epistemic logic.\nJournal of Logic, Language and Information,\n12(4):381-408, 2003.\n[16] P. Lamarre and Y. Shoham. Knowledge, certainty,\nbelief, and conditionalisation (abbreviated version). In\nProceedings of KR\"94, pages 415-424, 1994.\n[17] F. Laroussinie, N. Markey, and Ph. Schnoebelen.\nModel checking CTL+ and FCTL is hard. In\nProceedings of FoSSaCS\"01, volume 2030 of LNCS,\npages 318-331. Springer, 2001.\n[18] Y. Moses and Y. Shoham. Belief as defeasible\nknowledge. Artificial Intelligence, 64(2):299-321, 1993.\n[19] W. Penczek and A. Lomuscio. Verifying epistemic\nproperties of multi-agent systems via bounded model\nchecking. In Proceedings of AAMAS\"03, pages\n209-216, New York, NY, USA, 2003. ACM Press.\n[20] K. Su, A. Sattar, G. Governatori, and Q. Chen. A\ncomputationally grounded logic of knowledge, belief\nand certainty. In Proceedings of AAMAS\"05, pages\n149-156. ACM Press, 2005.\n[21] W. van der Hoek, M. Roberts, and M. Wooldridge.\nSocial laws in alternating time: Effectiveness,\nfeasibility and synthesis. Synthese, 2005.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 589", "keywords": "belief notion;notion of plausibility;semantics;notion of belief;belief;plausibility notion;plausibility;reasoning;indistinguishability;logic;temporal logic;plausibility update operator;framework;multi-agent system;computation tree logic"}
{"name": "train_I-51", "title": "Learning and Joint Deliberation through Argumentation in Multi-Agent Systems", "abstract": "In this paper we will present an argumentation framework for learning agents (AMAL) designed for two purposes: (1) for joint deliberation, and (2) for learning from communication. The AMAL framework is completely based on learning from examples: the argument preference relation, the argument generation policy, and the counterargument generation policy are case-based techniques. For join deliberation, learning agents share their experience by forming a committee to decide upon some joint decision. We experimentally show that the argumentation among committees of agents improves both the individual and joint performance. For learning from communication, an agent engages into arguing with other agents in order to contrast its individual hypotheses and receive counterexamples; the argumentation process improves their learning scope and individual performance.", "fulltext": "1. INTRODUCTION\nArgumentation frameworks for multi-agent systems can be used\nfor different purposes like joint deliberation, persuasion,\nnegotiation, and conflict resolution. In this paper we will present an\nargumentation framework for learning agents, and show that it can be\nused for two purposes: (1) joint deliberation, and (2) learning from\ncommunication.\nArgumentation-based joint deliberation involves discussion over\nthe outcome of a particular situation or the appropriate course of\naction for a particular situation. Learning agents are capable of\nlearning from experience, in the sense that past examples (situations and\ntheir outcomes) are used to predict the outcome for the situation\nat hand. However, since individual agents experience may be\nlimited, individual knowledge and prediction accuracy is also limited.\nThus, learning agents that are capable of arguing their individual\npredictions with other agents may reach better prediction accuracy\nafter such an argumentation process.\nMost existing argumentation frameworks for multi-agent\nsystems are based on deductive logic or some other deductive logic\nformalism specifically designed to support argumentation, such as\ndefault logic [3]). Usually, an argument is seen as a logical\nstatement, while a counterargument is an argument offered in opposition\nto another argument [4, 13]; agents use a preference relation to\nresolve conflicting arguments. However, logic-based argumentation\nframeworks assume agents with preloaded knowledge and\npreference relation. In this paper, we focus on an Argumentation-based\nMulti-Agent Learning (AMAL) framework where both knowledge\nand preference relation are learned from experience. Thus, we\nconsider a scenario with agents that (1) work in the same domain using\na shared ontology, (2) are capable of learning from examples, and\n(3) communicate using an argumentative framework.\nHaving learning capabilities allows agents effectively use a\nspecific form of counterargument, namely the use of\ncounterexamples. Counterexamples offer the possibility of agents learning\nduring the argumentation process. Moreover, learning agents allow\ntechniques that use learnt experience to generate adequate\narguments and counterarguments. Specifically, we will need to address\ntwo issues: (1) how to define a technique to generate arguments\nand counterarguments from examples, and (2)how to define a\npreference relation over two conflicting arguments that have been\ninduced from examples.\nThis paper presents a case-based approach to address both\nissues. The agents use case-based reasoning (CBR) [1] to learn from\npast cases (where a case is a situation and its outcome) in order\nto predict the outcome of a new situation. We propose an\nargumentation protocol inside the AMAL framework at supports agents\nin reaching a joint prediction over a specific situation or problem\n- moreover, the reasoning needed to support the argumentation\nprocess will also be based on cases. In particular, we present two\ncase-based measures, one for generating the arguments and\ncounterarguments adequate to a particular situation and another for\ndetermining preference relation among arguments. Finally, we\nevaluate (1) if argumentation between learning agents can produce a\njoint prediction that improves over individual learning performance\nand (2) if learning from the counterexamples conveyed during the\nargumentation process increases the individual performance with\nprecisely those cases being used while arguing among them.\nThe paper is structured as follows. Section 2 discusses the\nrelation among argumentation, collaboration and learning. Then\nSection 3 introduces our multi-agent CBR (MAC) framework and the\nnotion of justified prediction. After that, Section 4 formally\ndefines our argumentation framework. Sections 5 and 6 present our\ncase-based preference relation and argument generation policies\nrespectively. Later, Section 7 presents the argumentation protocol in\nour AMAL framework. After that, Section 8 presents an\nexemplification of the argumentation framework. Finally, Section 9 presents\nan empirical evaluation of our two main hypotheses. The paper\ncloses with related work and conclusions sections.\n2. ARGUMENTATION,COLLABORATION\nAND LEARNING\nBoth learning and collaboration are ways in which an agent can\nimprove individual performance. In fact, there is a clear parallelism\nbetween learning and collaboration in multi-agent systems, since\nboth are ways in which agents can deal with their shortcomings.\nLet us show which are the main motivations that an agent can have\nto learn or to collaborate.\n\u2022 Motivations to learn:\n- Increase quality of prediction,\n- Increase efficiency,\n- Increase the range of solvable problems.\n\u2022 Motivations to collaborate:\n- Increase quality of prediction,\n- Increase efficiency,\n- Increase the range of solvable problems,\n- Increase the range of accessible resources.\nLooking at the above lists of motivation, we can easily see that\nlearning and collaboration are very related in multi-agent systems.\nIn fact, with the exception of the last item in the motivations to\ncollaborate list, they are two extremes of a continuum of strategies\nto improve performance. An agent may choose to increase\nperformance by learning, by collaborating, or by finding an intermediate\npoint that combines learning and collaboration in order to improve\nperformance.\nIn this paper we will propose AMAL, an argumentation\nframework for learning agents, and will also also show how AMAL can be\nused both for learning from communication and for solving\nproblems in a collaborative way:\n\u2022 Agents can solve problems in a collaborative way via\nengaging an argumentation process about the prediction for the\nsituation at hand. Using this collaboration, the prediction\ncan be done in a more informed way, since the information\nknown by several agents has been taken into account.\n\u2022 Agents can also learn from communication with other agents\nby engaging an argumentation process. Agents that engage\nin such argumentation processes can learn from the\narguments and counterexamples received from other agents, and\nuse this information for predicting the outcomes of future\nsituations.\nIn the rest of this paper we will propose an argumentation\nframework and show how it can be used both for learning and for solving\nproblems in a collaborative way.\n3. MULTI-AGENT CBR SYSTEMS\nA Multi-Agent Case Based Reasoning System (MAC) M =\n{(A1, C1), ..., (An, Cn)} is a multi-agent system composed of A =\n{Ai, ..., An}, a set of CBR agents, where each agent Ai \u2208 A\npossesses an individual case base Ci. Each individual agent Ai\nin a MAC is completely autonomous and each agent Ai has\naccess only to its individual and private case base Ci. A case base\nCi = {c1, ..., cm} is a collection of cases. Agents in a MAC\nsystem are able to individually solve problems, but they can also\ncollaborate with other agents to solve problems.\nIn this framework, we will restrict ourselves to analytical tasks,\ni.e. tasks like classification, where the solution of a problem is\nachieved by selecting a solution class from an enumerated set of\nsolution classes. In the following we will note the set of all the\nsolution classes by S = {S1, ..., SK }. Therefore, a case c = P, S is\na tuple containing a case description P and a solution class S \u2208 S.\nIn the following, we will use the terms problem and case\ndescription indistinctly. Moreover, we will use the dot notation to refer to\nelements inside a tuple; e.g., to refer to the solution class of a case\nc, we will write c.S.\nTherefore, we say a group of agents perform joint deliberation,\nwhen they collaborate to find a joint solution by means of an\nargumentation process. However, in order to do so, an agent has to\nbe able to justify its prediction to the other agents (i.e. generate an\nargument for its predicted solution that can be examined and\ncritiqued by the other agents). The next section addresses this issue.\n3.1 Justified Predictions\nBoth expert systems and CBR systems may have an explanation\ncomponent [14] in charge of justifying why the system has\nprovided a specific answer to the user. The line of reasoning of the\nsystem can then be examined by a human expert, thus increasing\nthe reliability of the system.\nMost of the existing work on explanation generation focuses on\ngenerating explanations to be provided to the user. However, in our\napproach we use explanations (or justifications) as a tool for\nimproving communication and coordination among agents. We are\ninterested in justifications since they can be used as arguments.\nFor that purpose, we will benefit from the ability of some machine\nlearning methods to provide justifications.\nA justification built by a CBR method after determining that the\nsolution of a particular problem P was Sk is a description that\ncontains the relevant information from the problem P that the CBR\nmethod has considered to predict Sk as the solution of P. In\nparticular, CBR methods work by retrieving similar cases to the problem\nat hand, and then reusing their solutions for the current problem,\nexpecting that since the problem and the cases are similar, the\nsolutions will also be similar. Thus, if a CBR method has retrieved a set\nof cases C1, ..., Cn to solve a particular problem P the justification\nbuilt will contain the relevant information from the problem P that\nmade the CBR system retrieve that particular set of cases, i.e. it\nwill contain the relevant information that P and C1, ..., Cn have in\ncommon.\nFor example, Figure 1 shows a justification build by a CBR\nsystem for a toy problem (in the following sections we will show\njustifications for real problems). In the figure, a problem has two\nattributes (Traffic_light, and Cars_passing), the retrieval mechanism\nof the CBR system notices that by considering only the attribute\nTraffic_light, it can retrieve two cases that predict the same\nsolution: wait. Thus, since only this attribute has been used, it is the\nonly one appearing in the justification. The values of the rest of\nattributes are irrelevant, since whatever their value the solution class\nwould have been the same.\n976 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nProblem\nTraffic_light: red\nCars_passing: no\nCase 1\nTraffic_light: red\nCars_passing: no\nSolution: wait\nCase 3\nTraffic_light: red\nCars_passing: yes\nSolution: wait\nCase 4\nTraffic_light: green\nCars_passing: yes\nSolution: wait\nCase 2\nTraffic_light: green\nCars_passing: no\nSolution: cross\nRetrieved\ncases\nSolution: wait\nJustification\nTraffic_light: red\nFigure 1: An example of justification generation in a CBR system. Notice that, since the only relevant feature to decide is Traffic_light\n(the only one used to retrieve cases), it is the only one appearing in the justification.\nIn general, the meaning of a justification is that all (or most of)\nthe cases in the case base of an agent that satisfy the justification\n(i.e. all the cases that are subsumed by the justification) belong to\nthe predicted solution class. In the rest of the paper, we will use\nto denote the subsumption relation. In our work, we use LID [2], a\nCBR method capable of building symbolic justifications such as the\none exemplified in Figure 1. When an agent provides a justification\nfor a prediction, the agent generates a justified prediction:\nDEFINITION 3.1. A Justified Prediction is a tuple J = A, P,\nS, D where agent A considers S the correct solution for problem\nP, and that prediction is justified a symbolic description D such\nthat J.D J.P.\nJustifications can have many uses for CBR systems [8, 9]. In this\npaper, we are going to use justifications as arguments, in order to\nallow learning agents to engage in argumentation processes.\n4. ARGUMENTS AND\nCOUNTERARGUMENTS\nFor our purposes an argument \u03b1 generated by an agent A is\ncomposed of a statement S and some evidence D supporting S as\ncorrect. In the remainder of this section we will see how this\ngeneral definition of argument can be instantiated in specific kind of\narguments that the agents can generate. In the context of MAC\nsystems, agents argue about predictions for new problems and can\nprovide two kinds of information: a) specific cases P, S , and b)\njustified predictions: A, P, S, D . Using this information, we can\ndefine three types of arguments: justified predictions,\ncounterarguments, and counterexamples.\nA justified prediction \u03b1 is generated by an agent Ai to argue that\nAi believes that the correct solution for a given problem P is \u03b1.S,\nand the evidence provided is the justification \u03b1.D. In the\nexample depicted in Figure 1, an agent Ai may generate the argument\n\u03b1 = Ai, P, Wait, (Traffic_light = red) , meaning that the agent Ai\nbelieves that the correct solution for P is Wait because the attribute\nTraffic_light equals red.\nA counterargument \u03b2 is an argument offered in opposition to\nanother argument \u03b1. In our framework, a counterargument\nconsists of a justified prediction Aj, P, S , D generated by an agent\nAj with the intention to rebut an argument \u03b1 generated by another\nagent Ai, that endorses a solution class S different from that of\n\u03b1.S for the problem at hand and justifies this with a justification\nD . In the example in Figure 1, if an agent generates the argument\n\u03b1 = Ai, P, Walk, (Cars_passing = no) , an agent that thinks that\nthe correct solution is Wait might answer with the counterargument\n\u03b2 = Aj, P, Wait, (Cars_passing = no \u2227 Traffic_light = red) ,\nmeaning that, although there are no cars passing, the traffic light is red,\nand the street cannot be crossed.\nA counterexample c is a case that contradicts an argument \u03b1.\nThus a counterexample is also a counterargument, one that states\nthat a specific argument \u03b1 is not always true, and the evidence\nprovided is the case c. Specifically, for a case c to be a\ncounterexample of an argument \u03b1, the following conditions have to be met:\n\u03b1.D c and \u03b1.S = c.S, i.e. the case must satisfy the justification\n\u03b1.D and the solution of c must be different than the predicted by\n\u03b1.\nBy exchanging arguments and counterarguments (including\ncounterexamples), agents can argue about the correct solution of a given\nproblem, i.e. they can engage a joint deliberation process.\nHowever, in order to do so, they need a specific interaction protocol, a\npreference relation between contradicting arguments, and a\ndecision policy to generate counterarguments (including\ncounterexamples). In the following sections we will present these elements.\n5. PREFERENCE RELATION\nA specific argument provided by an agent might not be consistent\nwith the information known to other agents (or even to some of the\ninformation known by the agent that has generated the justification\ndue to noise in training data). For that reason, we are going to\ndefine a preference relation over contradicting justified predictions\nbased on cases. Basically, we will define a confidence measure for\neach justified prediction (that takes into account the cases owned by\neach agent), and the justified prediction with the highest confidence\nwill be the preferred one.\nThe idea behind case-based confidence is to count how many of\nthe cases in an individual case base endorse a justified prediction,\nand how many of them are counterexamples of it. The more the\nendorsing cases, the higher the confidence; and the more the\ncounterexamples, the lower the confidence. Specifically, to assess the\nconfidence of a justified prediction \u03b1, an agent obtains the set of\ncases in its individual case base that are subsumed by \u03b1.D. With\nthem, an agent Ai obtains the Y (aye) and N (nay) values:\n\u2022 Y Ai\n\u03b1 = |{c \u2208 Ci| \u03b1.D c.P \u2227 \u03b1.S = c.S}| is the number\nof cases in the agent\"s case base subsumed by the justification\n\u03b1.D that belong to the solution class \u03b1.S,\n\u2022 NAi\n\u03b1 = |{c \u2208 Ci| \u03b1.D c.P \u2227 \u03b1.S = c.S}| is the number\nof cases in the agent\"s case base subsumed by justification\n\u03b1.D that do not belong to that solution class.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 977\n+ +\n+\n+\n+\n+\n\n\n-\n- +\nFigure 2: Confidence of arguments is evaluated by contrasting them against the case bases of the agents.\nAn agent estimates the confidence of an argument as:\nCAi (\u03b1) =\nY Ai\n\u03b1\n1 + Y Ai\n\u03b1 + NAi\n\u03b1\ni.e. the confidence on a justified prediction is the number of\nendorsing cases divided by the number of endorsing cases plus\ncounterexamples. Notice that we add 1 to the denominator, this is to avoid\ngiving excessively high confidences to justified predictions whose\nconfidence has been computed using a small number of cases.\nNotice that this correction follows the same idea than the Laplace\ncorrection to estimate probabilities. Figure 2 illustrates the individual\nevaluation of the confidence of an argument, in particular, three\nendorsing cases and one counterexample are found in the case base\nof agents Ai, giving an estimated confidence of 0.6\nMoreover, we can also define the joint confidence of an argument\n\u03b1 as the confidence computed using the cases present in the case\nbases of all the agents in the group:\nC(\u03b1) = i Y Ai\n\u03b1\n1 + i Y Ai\n\u03b1 + NAi\n\u03b1\nNotice that, to collaboratively compute the joint confidence, the\nagents only have to make public the aye and nay values locally\ncomputed for a given argument.\nIn our framework, agents use this joint confidence as the\npreference relation: a justified prediction \u03b1 is preferred over another one\n\u03b2 if C(\u03b1) \u2265 C(\u03b2).\n6. GENERATION OF ARGUMENTS\nIn our framework, arguments are generated by the agents from\ncases, using learning methods. Any learning method able to\nprovide a justified prediction can be used to generate arguments. For\ninstance, decision trees and LID [2] are suitable learning methods.\nSpecifically, in the experiments reported in this paper agents use\nLID. Thus, when an agent wants to generate an argument\nendorsing that a specific solution class is the correct solution for a problem\nP, it generates a justified prediction as explained in Section 3.1.\nFor instance, Figure 3 shows a real justification generated by\nLID after solving a problem P in the domain of marine sponges\nidentification. In particular, Figure 3 shows how when an agent\nreceives a new problem to solve (in this case, a new sponge to\ndetermine its order), the agent uses LID to generate an argument\n(consisting on a justified prediction) using the cases in the case\nbase of the agent. The justification shown in Figure 3 can be\ninterpreted saying that the predicted solution is hadromerida\nbecause the smooth form of the megascleres of the spiculate\nskeleton of the sponge is of type tylostyle, the spikulate skeleton of the\nsponge has no uniform length, and there is no gemmules in the\nexternal features of the sponge. Thus, the argument generated will\nbe \u03b1 = A1, P, hadromerida, D1 .\n6.1 Generation of Counterarguments\nAs previously stated, agents may try to rebut arguments by\ngenerating counterargument or by finding counterexamples. Let us\nexplain how they can be generated.\nAn agent Ai wants to generate a counterargument \u03b2 to rebut an\nargument \u03b1 when \u03b1 is in contradiction with the local case base of\nAi. Moreover, while generating such counterargument \u03b2, Ai\nexpects that \u03b2 is preferred over \u03b1. For that purpose, we will present\na specific policy to generate counterarguments based on the\nspecificity criterion [10].\nThe specificity criterion is widely used in deductive frameworks\nfor argumentation, and states that between two conflicting\narguments, the most specific should be preferred since it is, in\nprinciple, more informed. Thus, counterarguments generated based on\nthe specificity criterion are expected to be preferable (since they are\nmore informed) to the arguments they try to rebut. However, there\nis no guarantee that such counterarguments will always win, since,\nas we have stated in Section 5, agents in our framework use a\npreference relation based on joint confidence. Moreover, one may think\nthat it would be better that the agents generate counterarguments\nbased on the joint confidence preference relation; however it is not\nobvious how to generate counterarguments based on joint\nconfidence in an efficient way, since collaboration is required in order to\nevaluate joint confidence. Thus, the agent generating the\ncounterargument should constantly communicate with the other agents at\neach step of the induction algorithm used to generate\ncounterarguments (presently one of our future research lines).\nThus, in our framework, when an agent wants to generate a\ncounterargument \u03b2 to an argument \u03b1, \u03b2 has to be more specific than \u03b1\n(i.e. \u03b1.D < \u03b2.D).\nThe generation of counterarguments using the specificity\ncriterion imposes some restrictions over the learning method, although\nLID or ID3 can be easily adapted for this task. For instance, LID is\nan algorithm that generates a description starting from scratch and\nheuristically adding features to that term. Thus, at every step, the\ndescription is made more specific than in the previous step, and the\nnumber of cases that are subsumed by that description is reduced.\nWhen the description covers only (or almost only) cases of a\nsingle solution class LID terminates and predicts that solution class.\nTo generate a counterargument to an argument \u03b1 LID just has to\nuse as starting point the description \u03b1.D instead of starting from\nscratch. In this way, the justification provided by LID will always\nbe subsumed by \u03b1.D, and thus the resulting counterargument will\nbe more specific than \u03b1. However, notice that LID may sometimes\nnot be able to generate counterarguments, since LID may not be\nable to specialize the description \u03b1.D any further, or because the\nagent Ai has no case inCi that is subsumed by \u03b1.D. Figure 4 shows\nhow an agent A2 that disagreed with the argument shown in\nFigure 3, generates a counterargument using LID. Moreover, Figure 4\nshows the generation of a counterargument \u03b21\n2 for the argument \u03b10\n1\n(in Figure 3) that is a specialization of \u03b10\n1.\n978 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nSolution: hadromerida\nJustification: D1\nSponge\nSpikulate\nskeleton\nExternal\nfeatures\nExternal features\nGemmules: no\nSpikulate Skeleton\nMegascleres\nUniform length: no\nMegascleres\nSmooth form: tylostyle\nCase Base\nof A1\nLID\nNew\nsponge\nP\nFigure 3: Example of a real justification generated by LID in the marine sponges data set.\nSpecifically, in our experiments, when an agent Ai wants to rebut\nan argument \u03b1, uses the following policy:\n1. Agent Ai uses LID to try to find a counterargument \u03b2 more\nspecific than \u03b1; if found, \u03b2 is sent to the other agent as a\ncounterargument of \u03b1.\n2. If not found, then Ai searches for a counterexample c \u2208 Ci\nof \u03b1. If a case c is found, then c is sent to the other agent as\na counterexample of \u03b1.\n3. If no counterexamples are found, then Ai cannot rebut the\nargument \u03b1.\n7. ARGUMENTATION-BASED\nMULTI-AGENT LEARNING\nThe interaction protocol of AMAL allows a group of agents A1,\n..., An to deliberate about the correct solution of a problem P by\nmeans of an argumentation process. If the argumentation process\narrives to a consensual solution, the joint deliberation ends;\notherwise a weighted vote is used to determine the joint solution.\nMoreover, AMAL also allows the agents to learn from the\ncounterexamples received from other agents.\nThe AMAL protocol consists on a series of rounds. In the initial\nround, each agent states which is its individual prediction for P.\nThen, at each round an agent can try to rebut the prediction made\nby any of the other agents. The protocol uses a token passing\nmechanism so that agents (one at a time) can send counterarguments or\ncounterexamples if they disagree with the prediction made by any\nother agent. Specifically, each agent is allowed to send one\ncounterargument or counterexample each time he gets the token (notice\nthat this restriction is just to simplify the protocol, and that it does\nnot restrict the number of counterargument an agent can sent, since\nthey can be delayed for subsequent rounds). When an agent\nreceives a counterargument or counterexample, it informs the other\nagents if it accepts the counterargument (and changes its\nprediction) or not. Moreover, agents have also the opportunity to answer\nto counterarguments when they receive the token, by trying to\ngenerate a counterargument to the counterargument.\nWhen all the agents have had the token once, the token returns\nto the first agent, and so on. If at any time in the protocol, all the\nagents agree or during the last n rounds no agent has generated\nany counterargument, the protocol ends. Moreover, if at the end of\nthe argumentation the agents have not reached an agreement, then\na voting mechanism that uses the confidence of each prediction as\nweights is used to decide the final solution (Thus, AMAL follows\nthe same mechanism as human committees, first each individual\nmember of a committee exposes his arguments and discuses those\nof the other members (joint deliberation), and if no consensus is\nreached, then a voting mechanism is required).\nAt each iteration, agents can use the following performatives:\n\u2022 assert(\u03b1): the justified prediction held during the next round\nwill be \u03b1. An agent can only hold a single prediction at each\nround, thus is multiple asserts are send, only the last one is\nconsidered as the currently held prediction.\n\u2022 rebut(\u03b2, \u03b1): the agent has found a counterargument \u03b2 to the\nprediction \u03b1.\nWe will define Ht = \u03b1t\n1, ..., \u03b1t\nn as the predictions that each\nof the n agents hold at a round t. Moreover, we will also define\ncontradict(\u03b1t\ni) = {\u03b1 \u2208 Ht|\u03b1.S = \u03b1t\ni.S} as the set of\ncontradicting arguments for an agent Ai in a round t, i.e. the set of\narguments at round t that support a different solution class than \u03b1t\ni.\nThe protocol is initiated because one of the agents receives a\nproblem P to be solved. After that, the agent informs all the other\nagents about the problem P to solve, and the protocol starts:\n1. At round t = 0, each one of the agents individually solves P,\nand builds a justified prediction using its own CBR method.\nThen, each agent Ai sends the performative assert(\u03b10\ni ) to\nthe other agents. Thus, the agents know H0 = \u03b10\ni , ..., \u03b10\nn .\nOnce all the predictions have been sent the token is given to\nthe first agent A1.\n2. At each round t (other than 0), the agents check whether their\narguments in Ht agree. If they do, the protocol moves to step\n5. Moreover, if during the last n rounds no agent has sent any\ncounterexample or counterargument, the protocol also moves\nto step 5. Otherwise, the agent Ai owner of the token tries\nto generate a counterargument for each of the opposing\narguments in contradict(\u03b1t\ni) \u2286 Ht (see Section 6.1). Then, the\ncounterargument \u03b2t\ni against the prediction \u03b1t\nj with the\nlowest confidence C(\u03b1t\nj) is selected (since \u03b1t\nj is the prediction\nmore likely to be successfully rebutted).\n\u2022 If \u03b2t\ni is a counterargument, then, Ai locally compares\n\u03b1t\ni with \u03b2t\ni by assessing their confidence against its\nindividual case base Ci (see Section 5) (notice that Ai is\ncomparing its previous argument with the\ncounterargument that Ai itself has just generated and that is about\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 979\nSponge\nSpikulate\nskeleton\nExternal\nfeatures\nExternal features\nGemmules: no\nGrowing:\nSpikulate Skeleton\nMegascleres\nUniform length: no\nMegascleres\nSmooth form: tylostyle\nGrowing\nGrow: massive\nCase Base\nof A2\nLID\nSolution: astrophorida\nJustification: D2\nFigure 4: Generation of a counterargument using LID in the sponges data set.\nto send to Aj). If CAi (\u03b2t\ni ) > CAi (\u03b1t\ni), then Ai\nconsiders that \u03b2t\ni is stronger than its previous argument,\nchanges its argument to \u03b2t\ni by sending assert(\u03b2t\ni ) to\nthe rest of the agents (the intuition behind this is that\nsince a counterargument is also an argument, Ai checks\nif the newly counterargument is a better argument than\nthe one he was previously holding) and rebut(\u03b2t\ni ,\n\u03b1t\nj) to Aj. Otherwise (i.e. CAi (\u03b2t\ni ) \u2264 CAi (\u03b1t\ni)), Ai\nwill send only rebut(\u03b2t\ni , \u03b1t\nj) to Aj. In any of the two\nsituations the protocol moves to step 3.\n\u2022 If \u03b2t\ni is a counterexample c, then Ai sends rebut(c, \u03b1t\nj)\nto Aj. The protocol moves to step 4.\n\u2022 If Ai cannot generate any counterargument or\ncounterexample, the token is sent to the next agent, a new\nround t + 1 starts, and the protocol moves to state 2.\n3. The agent Aj that has received the counterargument \u03b2t\ni ,\nlocally compares it against its own argument, \u03b1t\nj, by locally\nassessing their confidence. If CAj (\u03b2t\ni ) > CAj (\u03b1t\nj), then\nAj will accept the counterargument as stronger than its own\nargument, and it will send assert(\u03b2t\ni ) to the other agents.\nOtherwise (i.e. CAj (\u03b2t\ni ) \u2264 CAj (\u03b1t\nj)), Aj will not accept\nthe counterargument, and will inform the other agents\naccordingly. Any of the two situations start a new round t + 1,\nAi sends the token to the next agent, and the protocol moves\nback to state 2.\n4. The agent Aj that has received the counterexample c retains\nit into its case base and generates a new argument \u03b1t+1\nj that\ntakes into account c, and informs the rest of the agents by\nsending assert(\u03b1t+1\nj ) to all of them. Then, Ai sends the\ntoken to the next agent, a new round t + 1 starts, and the\nprotocol moves back to step 2.\n5. The protocol ends yielding a joint prediction, as follows: if\nthe arguments in Ht agree then their prediction is the joint\nprediction, otherwise a voting mechanism is used to decide\nthe joint prediction. The voting mechanism uses the joint\nconfidence measure as the voting weights, as follows:\nS = arg max\nSk\u2208S\n\u03b1i\u2208Ht|\u03b1i.S=Sk\nC(\u03b1i)\nMoreover, in order to avoid infinite iterations, if an agent sends\ntwice the same argument or counterargument to the same agent, the\nmessage is not considered.\n8. EXEMPLIFICATION\nLet us consider a system composed of three agents A1, A2 and\nA3. One of the agents, A1 receives a problem P to solve, and\ndecides to use AMAL to solve it. For that reason, invites A2 and A3 to\ntake part in the argumentation process. They accept the invitation,\nand the argumentation protocol starts.\nInitially, each agent generates its individual prediction for P, and\nbroadcasts it to the other agents. Thus, all of them can compute\nH0 = \u03b10\n1, \u03b10\n2, \u03b10\n3 . In particular, in this example:\n\u2022 \u03b10\n1 = A1, P, hadromerida, D1\n\u2022 \u03b10\n2 = A2, P, astrophorida, D2\n\u2022 \u03b10\n3 = A3, P, axinellida, D3\nA1 starts owning the token and tries to generate\ncounterarguments for \u03b10\n2 and \u03b10\n3, but does not succeed, however it has one\ncounterexample c13 for \u03b10\n3. Thus, A1 sends the the message rebut(\nc13, \u03b10\n3) to A3. A3 incorporates c13 into its case base and tries to\nsolve the problem P again, now taking c13 into consideration. A3\ncomes up with the justified prediction \u03b11\n3 = A3, P, hadromerida,\nD4 , and broadcasts it to the rest of the agents with the message\nassert(\u03b11\n3). Thus, all of them know the new H1 = \u03b10\n1, \u03b10\n2, \u03b11\n3 .\nRound 1 starts and A2 gets the token. A2 tries to generate\ncounterarguments for \u03b10\n1 and \u03b11\n3 and only succeeds to generate a\ncounterargument \u03b21\n2 = A2, P, astrophorida, D5 against \u03b11\n3. The\ncounterargument is sent to A3 with the message rebut(\u03b21\n2 , \u03b11\n3).\nAgent A3 receives the counterargument and assesses its local\nconfidence. The result is that the individual confidence of the\ncounterargument \u03b21\n2 is lower than the local confidence of \u03b11\n3. Therefore, A3\ndoes not accept the counterargument, and thus H2 = \u03b10\n1, \u03b10\n2, \u03b11\n3 .\nRound 2 starts and A3 gets the token. A3 generates a\ncounterargument \u03b22\n3 = A3, P, hadromerida, D6 for \u03b10\n2 and sends it to\nA2 with the message rebut(\u03b22\n3 , \u03b10\n2). Agent A2 receives the\ncounterargument and assesses its local confidence. The result is that the\nlocal confidence of the counterargument \u03b22\n3 is higher than the local\nconfidence of \u03b10\n2. Therefore, A2 accepts the counterargument and\ninforms the rest of the agents with the message assert(\u03b22\n3 ). After\nthat, H3 = \u03b10\n1, \u03b22\n3 , \u03b11\n3 .\nAt Round 3, since all the agents agree (all the justified\npredictions in H3 predict hadromerida as the solution class) The\nprotocol ends, and A1 (the agent that received the problem) considers\nhadromerida as the joint solution for the problem P.\n9. EXPERIMENTAL EVALUATION\n980 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nSPONGE\n75\n77\n79\n81\n83\n85\n87\n89\n91\n2 3 4 5\nAMAL\nVoting\nIndividual\nSOYBEAN\n55\n60\n65\n70\n75\n80\n85\n90\n2 3 4 5\nAMAL\nVoting\nIndividual\nFigure 5: Individual and joint accuracy for 2 to 5 agents.\nIn this section we empirically evaluate the AMAL argumentation\nframework. We have made experiments in two different data sets:\nsoybean (from the UCI machine learning repository) and sponge (a\nrelational data set). The soybean data set has 307 examples and 19\nsolution classes, while the sponge data set has 280 examples and 3\nsolution classes. In an experimental run, the data set is divided in 2\nsets: the training set and the test set. The training set examples are\ndistributed among 5 different agents without replication, i.e. there\nis no example shared by two agents. In the testing stage, problems\nin the test set arrive randomly to one of the agents, and their goal is\nto predict the correct solution.\nThe experiments are designed to test two hypotheses: (H1) that\nargumentation is a useful framework for joint deliberation and can\nimprove over other typical methods such as voting; and (H2) that\nlearning from communication improves the individual performance\nof a learning agent participating in an argumentation process.\nMoreover, we also expect that the improvement achieved from\nargumentation will increase as the number of agents participating in the\nargumentation increases (since more information will be taken into\naccount).\nConcerning H1 (argumentation is a useful framework for joint\ndeliberation), we ran 4 experiments, using 2, 3, 4, and 5 agents\nrespectively (in all experiments each agent has a 20% of the training\ndata, since the training is always distributed among 5 agents).\nFigure 5 shows the result of those experiments in the sponge and\nsoybean data sets. Classification accuracy is plotted in the\nvertical axis, and in the horizontal axis the number of agents that took\npart in the argumentation processes is shown. For each number of\nagents, three bars are shown: individual, Voting, and AMAL. The\nindividual bar shows the average accuracy of individual agents\npredictions; the voting bar shows the average accuracy of the joint\nprediction achieved by voting but without any argumentation; and\nfinally the AMAL bar shows the average accuracy of the joint\nprediction using argumentation. The results shown are the average of\n5 10-fold cross validation runs.\nFigure 5 shows that collaboration (voting and AMAL)\noutperforms individual problem solving. Moreover, as we expected, the\naccuracy improves as more agents collaborate, since more\ninformation is taken into account. We can also see that AMAL always\noutperforms standard voting, proving that joint decisions are based\non better information as provided by the argumentation process.\nFor instance, the joint accuracy for 2 agents in the sponge data\nset is of 87.57% for AMAL and 86.57% for voting (while individual\naccuracy is just 80.07%). Moreover, the improvement achieved by\nAMAL over Voting is even larger in the soybean data set. The\nreason is that the soybean data set is more difficult (in the sense that\nagents need more data to produce good predictions). These\nexperimental results show that AMAL effectively exploits the opportunity\nfor improvement: the accuracy is higher only because more agents\nhave changed their opinion during argumentation (otherwise they\nwould achieve the same result as Voting).\nConcerning H2 (learning from communication in argumentation\nprocesses improves individual prediction ), we ran the following\nexperiment: initially, we distributed a 25% of the training set among\nthe five agents; after that, the rest of the cases in the training set is\nsent to the agents one by one; when an agent receives a new\ntraining case, it has several options: the agent can discard it, the agent\ncan retain it, or the agent can use it for engaging an argumentation\nprocess. Figure 6 shows the result of that experiment for the two\ndata sets. Figure 6 contains three plots, where NL (not learning)\nshows accuracy of an agent with no learning at all; L (learning),\nshows the evolution of the individual classification accuracy when\nagents learn by retaining the training cases they individually\nreceive (notice that when all the training cases have been retained at\n100%, the accuracy should be equal to that of Figure 5 for\nindividual agents); and finally LFC (learning from communication) shows\nthe evolution of the individual classification accuracy of learning\nagents that also learn by retaining those counterexamples received\nduring argumentation (i.e. they learn both from training examples\nand counterexamples).\nFigure 6 shows that if an agent Ai learns also from\ncommunication, Ai can significantly improve its individual performance with\njust a small number of additional cases (those selected as relevant\ncounterexamples for Ai during argumentation). For instance, in\nthe soybean data set, individual agents have achieved an accuracy\nof 70.62% when they also learn from communication versus an\naccuracy of 59.93% when they only learn from their individual\nexperience. The number of cases learnt from communication depends\non the properties of the data set: in the sponges data set, agents\nhave retained only very few additional cases, and significantly\nimproved individual accuracy; namely they retain 59.96 cases in\naverage (compared to the 50.4 cases retained if they do not learn from\ncommunication). In the soybean data set more counterexamples are\nlearnt to significantly improve individual accuracy, namely they\nretain 87.16 cases in average (compared to 55.27 cases retained if\nthey do not learn from communication). Finally, the fact that both\ndata sets show a significant improvement points out the adaptive\nnature of the argumentation-based approach to learning from\ncommunication: the useful cases are selected as counterexamples (and\nno more than those needed), and they have the intended effect.\n10. RELATED WORK\nConcerning CBR in a multi-agent setting, the first research was\non negotiated case retrieval [11] among groups of agents. Our\nwork on multi-agent case-based learning started in 1999 [6]; later\nMc Ginty and Smyth [7] presented a multi-agent collaborative CBR\napproach (CCBR) for planning. Finally, another interesting\napproach is multi-case-base reasoning (MCBR) [5], that deals with\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 981\nSPONGE\n60\n65\n70\n75\n80\n85\n25% 40% 55% 70% 85% 100%\nLFC\nL\nNL\nSOYBEAN\n20\n30\n40\n50\n60\n70\n80\n90\n25% 40% 55% 70% 85% 100%\nLFC\nL\nNL\nFigure 6: Learning from communication resulting from argumentation in a system composed of 5 agents.\ndistributed systems where there are several case bases available for\nthe same task and addresses the problems of cross-case base\nadaptation. The main difference is that our MAC approach is a way to\ndistribute the Reuse process of CBR (using a voting system) while\nRetrieve is performed individually by each agent; the other\nmultiagent CBR approaches, however, focus on distributing the Retrieve\nprocess.\nResearch on MAS argumentation focus on several issues like a)\nlogics, protocols and languages that support argumentation, b)\nargument selection and c) argument interpretation. Approaches for\nlogic and languages that support argumentation include defeasible\nlogic [4] and BDI models [13]. Although argument selection is a\nkey aspect of automated argumentation (see [12] and [13]), most\nresearch has been focused on preference relations among arguments.\nIn our framework we have addressed both argument selection and\npreference relations using a case-based approach.\n11. CONCLUSIONS AND FUTURE WORK\nIn this paper we have presented an argumentation-based\nframework for multi-agent learning. Specifically, we have presented\nAMAL, a framework that allows a group of learning agents to\nargue about the solution of a given problem and we have shown how\nthe learning capabilities can be used to generate arguments and\ncounterarguments. The experimental evaluation shows that the\nincreased amount of information provided to the agents by the\nargumentation process increases their predictive accuracy, and specially\nwhen an adequate number of agents take part in the argumentation.\nThe main contributions of this work are: a) an argumentation\nframework for learning agents; b) a case-based preference relation\nover arguments, based on computing an overall confidence\nestimation of arguments; c) a case-based policy to generate\ncounterarguments and select counterexamples; and d) an argumentation-based\napproach for learning from communication.\nFinally, in the experiments presented here a learning agent would\nretain all counterexamples submitted by the other agent; however,\nthis is a very simple case retention policy, and we will like to\nexperiment with more informed policies - with the goal that individual\nlearning agents could significantly improve using only a small set\nof cases proposed by other agents. Finally, our approach is focused\non lazy learning, and future works aims at incorporating eager\ninductive learning inside the argumentative framework for learning\nfrom communication.\n12. REFERENCES\n[1] Agnar Aamodt and Enric Plaza. Case-based reasoning:\nFoundational issues, methodological variations, and system\napproaches. Artificial Intelligence Communications,\n7(1):39-59, 1994.\n[2] E. Armengol and E. Plaza. Lazy induction of descriptions for\nrelational case-based learning. In ECML\"2001, pages 13-24,\n2001.\n[3] Gerhard Brewka. Dynamic argument systems: A formal\nmodel of argumentation processes based on situation\ncalculus. Journal of Logic and Computation, 11(2):257-282,\n2001.\n[4] Carlos I. Ches\u00f1evar and Guillermo R. Simari. Formalizing\nDefeasible Argumentation using Labelled Deductive\nSystems. Journal of Computer Science & Technology,\n1(4):18-33, 2000.\n[5] D. Leake and R. Sooriamurthi. Automatically selecting\nstrategies for multi-case-base reasoning. In S. Craw and\nA. Preece, editors, ECCBR\"2002, pages 204-219, Berlin,\n2002. Springer Verlag.\n[6] Francisco J. Mart\u00edn, Enric Plaza, and Josep-Lluis Arcos.\nKnowledge and experience reuse through communications\namong competent (peer) agents. International Journal of\nSoftware Engineering and Knowledge Engineering,\n9(3):319-341, 1999.\n[7] Lorraine McGinty and Barry Smyth. Collaborative\ncase-based reasoning: Applications in personalized route\nplanning. In I. Watson and Q. Yang, editors, ICCBR, number\n2080 in LNAI, pages 362-376. Springer-Verlag, 2001.\n[8] Santi Onta\u00f1\u00f3n and Enric Plaza. Justification-based\nmultiagent learning. In ICML\"2003, pages 576-583. Morgan\nKaufmann, 2003.\n[9] Enric Plaza, Eva Armengol, and Santiago Onta\u00f1\u00f3n. The\nexplanatory power of symbolic similarity in case-based\nreasoning. Artificial Intelligence Review, 24(2):145-161,\n2005.\n[10] David Poole. On the comparison of theories: Preferring the\nmost specific explanation. In IJCAI-85, pages 144-147,\n1985.\n[11] M V Nagendra Prassad, Victor R Lesser, and Susan Lander.\nRetrieval and reasoning in distributed case bases. Technical\nreport, UMass Computer Science Department, 1995.\n[12] K. Sycara S. Kraus and A. Evenchik. Reaching agreements\nthrough argumentation: a logical model and implementation.\nArtificial Intelligence Journal, 104:1-69, 1998.\n[13] N. R. Jennings S. Parsons, C. Sierra. Agents that reason and\nnegotiate by arguing. Journal of Logic and Computation,\n8:261-292, 1998.\n[14] Bruce A. Wooley. Explanation component of software\nsystems. ACM CrossRoads, 5.1, 1998.\n982 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)", "keywords": "group;case-base reason;learning agent;multi-agent learn;case-based policy;argumentation framework;predictive accuracy;argumentation;learning from communication;argumentation protocol;multi-agent system;collaboration;joint deliberation"}
{"name": "train_I-52", "title": "A Unified and General Framework for Argumentation-based Negotiation", "abstract": "This paper proposes a unified and general framework for argumentation-based negotiation, in which the role of argumentation is formally analyzed. The framework makes it possible to study the outcomes of an argumentation-based negotiation. It shows what an agreement is, how it is related to the theories of the agents, when it is possible, and how this can be attained by the negotiating agents in this case. It defines also the notion of concession, and shows in which situation an agent will make one, as well as how it influences the evolution of the dialogue.", "fulltext": "1. INTRODUCTION\nRoughly speaking, negotiation is a process aiming at\nfinding some compromise or consensus between two or several\nagents about some matters of collective agreement, such\nas pricing products, allocating resources, or choosing\ncandidates. Negotiation models have been proposed for the\ndesign of systems able to bargain in an optimal way with\nother agents for example, buying or selling products in\necommerce.\nDifferent approaches to automated negotiation have been\ninvestigated, including game-theoretic approaches (which\nusually assume complete information and unlimited\ncomputation capabilities) [11], heuristic-based approaches which try\nto cope with these limitations [6], and argumentation-based\napproaches [2, 3, 7, 8, 9, 12, 13] which emphasize the\nimportance of exchanging information and explanations between\nnegotiating agents in order to mutually influence their\nbehaviors (e.g. an agent may concede a goal having a small\npriority), and consequently the outcome of the dialogue.\nIndeed, the two first types of settings do not allow for the\naddition of information or for exchanging opinions about offers.\nIntegrating argumentation theory in negotiation provides a\ngood means for supplying additional information and also\nhelps agents to convince each other by adequate arguments\nduring a negotiation dialogue. Indeed, an offer supported\nby a good argument has a better chance to be accepted by\nan agent, and can also make him reveal his goals or give\nup some of them. The basic idea behind an\nargumentationbased approach is that by exchanging arguments, the\ntheories of the agents (i.e. their mental states) may evolve, and\nconsequently, the status of offers may change. For instance,\nan agent may reject an offer because it is not acceptable for\nit. However, the agent may change its mind if it receives a\nstrong argument in favor of this offer.\nSeveral proposals have been made in the literature for\nmodeling such an approach. However, the work is still\npreliminary. Some researchers have mainly focused on relating\nargumentation with protocols. They have shown how and\nwhen arguments in favor of offers can be computed and\nexchanged. Others have emphasized on the decision making\nproblem. In [3, 7], the authors argued that selecting an offer\nto propose at a given step of the dialogue is a decision\nmaking problem. They have thus proposed an\nargumentationbased decision model, and have shown how such a model\ncan be related to the dialogue protocol.\nIn most existing works, there is no deep formal analysis\nof the role of argumentation in negotiation dialogues. It is\nnot clear how argumentation can influence the outcome of\nthe dialogue. Moreover, basic concepts in negotiation such\nas agreement (i.e. optimal solutions, or compromise) and\nconcession are neither defined nor studied.\nThis paper aims to propose a unified and general framework\nfor argumentation-based negotiation, in which the role of\nargumentation is formally analyzed, and where the existing\nsystems can be restated. In this framework, a negotiation\ndialogue takes place between two agents on a set O of offers,\nwhose structure is not known. The goal of a negotiation is to\nfind among elements of O, an offer that satisfies more or less\n967\n978-81-904262-7-5 (RPS) c 2007 IFAAMAS\nthe preferences of both agents. Each agent is supposed to\nhave a theory represented in an abstract way. A theory\nconsists of a set A of arguments whose structure and origin are\nnot known, a function specifying for each possible offer in O,\nthe arguments of A that support it, a non specified conflict\nrelation among the arguments, and finally a preference\nrelation between the arguments. The status of each argument is\ndefined using Dung\"s acceptability semantics. Consequently,\nthe set of offers is partitioned into four subsets: acceptable,\nrejected, negotiable and non-supported offers. We show how\nan agent\"s theory may evolve during a negotiation dialogue.\nWe define formally the notions of concession, compromise,\nand optimal solution. Then, we propose a protocol that\nallows agents i) to exchange offers and arguments, and ii) to\nmake concessions when necessary. We show that dialogues\ngenerated under such a protocol terminate, and even reach\noptimal solutions when they exist.\nThis paper is organized as follows: Section 2 introduces the\nlogical language that is used in the rest of the paper.\nSection 3 defines the agents as well as their theories. In section\n4, we study the properties of these agents\" theories.\nSection 5 defines formally an argumentation-based negotiation,\nshows how the theories of agents may evolve during a\ndialogue, and how this evolution may influence the outcome of\nthe dialogue. Two kinds of outcomes: optimal solution and\ncompromise are defined, and we show when such outcomes\nare reached. Section 6 illustrates our general framework\nthrough some examples. Section 7 compares our formalism\nwith existing ones. Section 8 concludes and presents some\nperspectives. Due to lack of space, the proofs are not\nincluded. These last are in a technical report that we will\nmake available online at some later time.\n2. THE LOGICAL LANGUAGE\nIn what follows, L will denote a logical language, and \u2261\nis an equivalence relation associated with it.\nFrom L, a set O = {o1, . . . , on} of n offers is identified, such\nthat oi, oj \u2208 O such that oi \u2261 oj. This means that the\noffers are different. Offers correspond to the different\nalternatives that can be exchanged during a negotiation dialogue.\nFor instance, if the agents try to decide the place of their\nnext meeting, then the set O will contain different towns.\nDifferent arguments can be built from L. The set Args(L)\nwill contain all those arguments. By argument, we mean a\nreason in believing or of doing something. In [3], it has been\nargued that the selection of the best offer to propose at a\ngiven step of the dialogue is a decision problem. In [4], it has\nbeen shown that in an argumentation-based approach for\ndecision making, two kinds of arguments are distinguished:\narguments supporting choices (or decisions), and arguments\nsupporting beliefs. Moreover, it has been acknowledged that\nthe two categories of arguments are formally defined in\ndifferent ways, and they play different roles. Indeed, an\nargument in favor of a decision, built both on an agent\"s\nbeliefs and goals, tries to justify the choice; whereas an\nargument in favor of a belief, built only from beliefs, tries\nto destroy the decision arguments, in particular the beliefs\npart of those decision arguments. Consequently, in a\nnegotiation dialogue, those two kinds of arguments are generally\nexchanged between agents. In what follows, the set Args(L)\nis then divided into two subsets: a subset Argso(L) of\narguments supporting offers, and a subset Argsb(L) of arguments\nsupporting beliefs. Thus, Args(L) = Argso(L) \u222a Argsb(L).\nAs in [5], in what follows, we consider that the structure of\nthe arguments is not known.\nSince the knowledge bases from which arguments are built\nmay be inconsistent, the arguments may be conflicting too.\nIn what follows, those conflicts will be captured by the\nrelation RL, thus RL \u2286 Args(L) \u00d7 Args(L). Three assumptions\nare made on this relation: First the arguments supporting\ndifferent offers are conflicting. The idea behind this\nassumption is that since offers are exclusive, an agent has to choose\nonly one at a given step of the dialogue. Note that, the\nrelation RL is not necessarily symmetric between the\narguments of Argsb(L). The second hypothesis says that\narguments supporting the same offer are also conflicting. The\nidea here is to return the strongest argument among these\narguments. The third condition does not allow an argument\nin favor of an offer to attack an argument supporting a\nbelief. This avoids wishful thinking. Formally:\nDefinition 1. RL \u2286 Args(L) \u00d7 Args(L) is a conflict\nrelation among arguments such that:\n\u2022 \u2200a, a \u2208 Argso(L), s.t. a = a , a RL a\n\u2022 a \u2208 Argso(L) and a \u2208 Argsb(L) such that a RL a\nNote that the relation RL is not symmetric. This is due\nto the fact that arguments of Argsb(L) may be conflicting\nbut not necessarily in a symmetric way. In what follows, we\nassume that the set Args(L) of arguments is finite, and each\nargument is attacked by a finite number of arguments.\n3. NEGOTIATING AGENTS THEORIES AND\nREASONING MODELS\nIn this section we define formally the negotiating agents,\ni.e. their theories, as well as the reasoning model used by\nthose agents in a negotiation dialogue.\n3.1 Negotiating agents theories\nAgents involved in a negotiation dialogue, called\nnegotiating agents, are supposed to have theories. In this paper, the\ntheory of an agent will not refer, as usual, to its mental states\n(i.e. its beliefs, desires and intentions). However, it will be\nencoded in a more abstract way in terms of the arguments\nowned by the agent, a conflict relation among those\narguments, a preference relation between the arguments, and a\nfunction that specifies which arguments support offers of the\nset O. We assume that an agent is aware of all the\narguments of the set Args(L). The agent is even able to express\na preference between any pair of arguments. This does not\nmean that the agent will use all the arguments of Args(L),\nbut it encodes the fact that when an agent receives an\nargument from another agent, it can interpret it correctly, and it\ncan also compare it with its own arguments. Similarly, each\nagent is supposed to be aware of the conflicts between\narguments. This also allows us to encode the fact that an agent\ncan recognize whether the received argument is in conflict\nor not with its arguments. However, in its theory, only the\nconflicts between its own arguments are considered.\nDefinition 2 (Negotiating agent theory). Let O\nbe a set of n offers. A negotiating agent theory is a tuple\nA, F, , R, Def such that:\n\u2022 A \u2286 Args(L).\n968 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\n\u2022 F: O \u2192 2A\ns.t \u2200i, j with i = j, F(oi) \u2229 F(oj) = \u2205.\nLet AO = \u222aF(oi) with i = 1, . . . , n.\n\u2022 \u2286 Args(L) \u00d7 Args(L) is a partial preorder denoting\na preference relation between arguments.\n\u2022 R \u2286 RL such that R \u2286 A \u00d7 A\n\u2022 Def \u2286 A \u00d7 A such that \u2200 a, b \u2208 A, a defeats b, denoted\na Def b iff:\n- a R b, and\n- not (b a)\nThe function F returns the arguments supporting offers in\nO. In [4], it has been argued that any decision may have\narguments supporting it, called arguments PRO, and\narguments against it, called arguments CONS. Moreover, these\ntwo types of arguments are not necessarily conflicting. For\nsimplicity reasons, in this paper we consider only arguments\nPRO. Moreover, we assume that an argument cannot\nsupport two distinct offers. However, it may be the case that an\noffer is not supported at all by arguments, thus F(oi) may\nbe empty.\nExample 1. Let O = {o1, o2, o3} be a set of offers. The\nfollowing theory is the theory of agent i:\n\u2022 A = {a1, a2, a3, a4}\n\u2022 F(o1) = {a1}, F(o2) = {a2}, F(o3) = \u2205. Thus, Ao =\n{a1, a2}\n\u2022 = {(a1, a2), (a2, a1), (a3, a2), (a4, a3)}\n\u2022 R = {a1, a2), (a2, a1), (a3, a2), (a4, a3)}\n\u2022 Def = {(a4, a3), (a3, a2)}\nFrom the above definition of agent theory, the following hold:\nProperty 1.\n\u2022 Def \u2286 R\n\u2022 \u2200a, a \u2208 F(oi), a R a\n3.2 The reasoning model\nFrom the theory of an agent, one can define the\nargumentation system used by that agent for reasoning about the\noffers and the arguments, i.e. for computing the status of\nthe different offers and arguments.\nDefinition 3 (Argumentation system). Let A, F,\n, R, Def be the theory of an agent. The argumentation\nsystem of that agent is the pair A, Def .\nIn [5], different acceptability semantics have been introduced\nfor computing the status of arguments. These are based\non two basic concepts, defence and conflict-free, defined as\nfollows:\nDefinition 4 (Defence/conflict-free). Let S \u2286 A.\n\u2022 S defends an argument a iff each argument that defeats\na is defeated by some argument in S.\n\u2022 S is conflict-free iff there exist no a, a in S such that\na Def a .\nDefinition 5 (Acceptability semantics). Let S be\na conflict-free set of arguments, and let T : 2A\n\u2192 2A\nbe a\nfunction such that T (S) = {a | a is defended by S}.\n\u2022 S is a complete extension iff S = T (S).\n\u2022 S is a preferred extension iff S is a maximal (w.r.t set\n\u2286) complete extension.\n\u2022 S is a grounded extension iff it is the smallest (w.r.t\nset \u2286) complete extension.\nLet E1, . . . , Ex denote the different extensions under a given\nsemantics.\nNote that there is only one grounded extension. It\ncontains all the arguments that are not defeated, and those\narguments that are defended directly or indirectly by\nnondefeated arguments.\nTheorem 1. Let A, Def the argumentation system\ndefined as shown above.\n1. It may have x \u2265 1 preferred extensions.\n2. The grounded extensions is S = i\u22651\nT (\u2205).\nNote that when the grounded extension (or the preferred\nextension) is empty, this means that there is no acceptable\noffer for the negotiating agent.\nExample 2. In example 1, there is one preferred\nextension, E = {a1, a2, a4}.\nNow that the acceptability semantics is defined, we are ready\nto define the status of any argument.\nDefinition 6 (Argument status). Let A, Def be an\nargumentation system, and E1, . . . , Ex its extensions under a\ngiven semantics. Let a \u2208 A.\n1. a is accepted iff a \u2208 Ei, \u2200Ei with i = 1, . . . , x.\n2. a is rejected iff Ei such that a \u2208 Ei.\n3. a is undecided iff a is neither accepted nor rejected.\nThis means that a is in some extensions and not in\nothers.\nNote that A = {a|a is accepted} \u222a {a|a is rejected} \u222a {a|a\nis undecided}.\nExample 3. In example 1, the arguments a1, a2 and a4\nare accepted, whereas the argument a3 is rejected.\nAs said before, agents use argumentation systems for\nreasoning about offers. In a negotiation dialogue, agents propose\nand accept offers that are acceptable for them, and reject\nbad ones. In what follows, we will define the status of an\noffer. According to the status of arguments, one can define\nfour statuses of the offers as follows:\nDefinition 7 (Offers status). Let o \u2208 O.\n\u2022 The offer o is acceptable for the negotiating agent iff\n\u2203 a \u2208 F(o) such that a is accepted. Oa = {oi \u2208 O,\nsuch that oi is acceptable}.\n\u2022 The offer o is rejected for the negotiating agent iff \u2200\na \u2208 F(o), a is rejected. Or = {oi \u2208 O, such that oi is\nrejected}.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 969\n\u2022 The offer o is negotiable iff \u2200 a \u2208 F(o), a is undecided.\nOn = {oi \u2208 O, such that oi is negotiable}.\n\u2022 The offer o is non-supported iff it is neither\nacceptable, nor rejected or negotiable. Ons = {oi \u2208 O, such\nthat oi is non-supported offers}.\nExample 4. In example 1, the two offers o1 and o2 are\nacceptable since they are supported by accepted arguments,\nwhereas the offer o3 is non-supported since it has no\nargument in its favor.\nFrom the above definitions, the following results hold:\nProperty 2. Let o \u2208 O.\n\u2022 O = Oa \u222a Or \u222a On \u222a Ons.\n\u2022 The set Oa may contain more than one offer.\nFrom the above partition of the set O of offers, a preference\nrelation between offers is defined. Let Ox and Oy be two\nsubsets of O. Ox Oy means that any offer in Ox is\npreferred to any offer in the set Oy. We can write also for two\noffers oi, oj, oi oj iff oi \u2208 Ox, oj \u2208 Oy and Ox Oy.\nDefinition 8 (Preference between offers). Let O\nbe a set of offers, and Oa, Or, On, Ons its partition. Oa\nOn Ons Or.\nExample 5. In example 1, we have o1 o3, and o2 o3.\nHowever, o1 and o2 are indifferent.\n4. THE STRUCTURE OF NEGOTIATION\nTHEORIES\nIn this section, we study the properties of the system\ndeveloped above. We first show that in the particular case\nwhere A = AO (ie. all of the agent\"s arguments refer to\noffers), the corresponding argumentation system will return\nat least one non-empty preferred extension.\nTheorem 2. Let A, Def an argumentation system such\nthat A = AO. Then the system returns at least one\nextension E, such that |E| \u2265 1.\nWe now present some results that demonstrate the\nimportance of indifference in negotiating agents, and more\nspecifically its relation to acceptable outcomes. We first show that\nthe set Oa may contain several offers when their\ncorresponding accepted arguments are indifferent w.r.t the preference\nrelation .\nTheorem 3. Let o1, o2 \u2208 O. o1, o2 \u2208 Oa iff \u2203 a1 \u2208\nF(o1), \u2203 a2 \u2208 F(o2), such that a1 and a2 are accepted and\nare indifferent w.r.t (i.e. a b and b a).\nWe now study acyclic preference relations that are defined\nformally as follows.\nDefinition 9 (Acyclic relation). A relation R on\na set A is acyclic if there is no sequence a1, a2, . . . , an \u2208 A,\nwith n > 1, such that (ai, ai+1) \u2208 R and (an, a1) \u2208 R, with\n1 \u2264 i < n.\nNote that acyclicity prohibits pairs of arguments a, b such\nthat a b and b a, ie., an acyclic preference relation\ndisallows indifference.\nTheorem 4. Let A be a set of arguments, R the\nattacking relation of A defined as R \u2286 A \u00d7 A, and an acyclic\nrelation on A. Then for any pair of arguments a, b \u2208 A,\nsuch that (a, b) \u2208 R, either (a, b) \u2208 Def or (b, a) \u2208 Def (or\nboth).\nThe previous result is used in the proof of the following\ntheorem that states that acyclic preference relations\nsanction extensions that support exactly one offer.\nTheorem 5. Let A be a set of arguments, and an\nacyclic relation on A. If E is an extension of <A, Def>,\nthen |E \u2229 AO| = 1.\nAn immediate consequence of the above is the following.\nProperty 3. Let A be a set of arguments such that A =\nAO. If the relation on A is acyclic, then each extension\nEi of <A, Def>, |Ei| = 1.\nAnother direct consequence of the above theorem is that\nin acyclic preference relations, arguments that support offers\ncan participate in only one preferred extension.\nTheorem 6. Let A be a set of arguments, and an\nacyclic relation on A. Then the preferred extensions of\nA, Def are pairwise disjoint w.r.t arguments of AO.\nUsing the above results we can prove the main theorem of\nthis section that states that negotiating agents with acyclic\npreference relations do not have acceptable offers.\nTheorem 7. Let A, F, R, , Def be a negotiating\nagent such that A = AO and is an acyclic relation. Then\nthe set of accepted arguments w.r.t A, Def is emtpy.\nConsequently, the set of acceptable offers, Oa is empty as well.\n5. ARGUMENTATION-BASED NEGOTIATION\nIn this section, we define formally a protocol that\ngenerates argumentation-based negotiation dialogues between\ntwo negotiating agents P and C. The two agents\nnegotiate about an object whose possible values belong to a set\nO. This set O is supposed to be known and the same for\nboth agents. For simplicity reasons, we assume that this\nset does not change during the dialogue. The agents are\nequipped with theories denoted respectively AP\n, FP\n, P\n,\nRP\n, DefP\n, and AC\n, FC\n, C\n, RC\n, DefC\n. Note that the\ntwo theories may be different in the sense that the agents\nmay have different sets of arguments, and different\npreference relations. Worst yet, they may have different\narguments in favor of the same offers. Moreover, these theories\nmay evolve during the dialogue.\n5.1 Evolution of the theories\nBefore defining formally the evolution of an agent\"s theory,\nlet us first introduce the notion of dialogue moves, or moves\nfor short.\nDefinition 10 (Move). A move is a tuple mi = pi,\nai, oi, ti such that:\n\u2022 pi \u2208 {P, C}\n\u2022 ai \u2208 Args(L) \u222a \u03b81\n1\nIn what follows \u03b8 denotes the fact that no argument, or no\noffer is given\n970 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\n\u2022 oi \u2208 O \u222a \u03b8\n\u2022 ti \u2208 N\u2217\nis the target of the move, such that ti < i\nThe function Player (resp. Argument, Offer, Target)\nreturns the player of the move (i.e. pi) (resp. the argument\nof a move, i.e ai, the offer oi, and the target of the move,\nti). Let M denote the set of all the moves that can be built\nfrom {P, C}, Arg(L), O .\nNote that the set M is finite since Arg(L) and O are\nassumed to be finite. Let us now see how an agent\"s theory\nevolves and why. The idea is that if an agent receives an\nargument from another agent, it will add the new argument\nto its theory. Moreover, since an argument may bring new\ninformation for the agent, thus new arguments can emerge.\nLet us take the following example:\nExample 6. Suppose that an agent P has the following\npropositional knowledge base: \u03a3P = {x, y \u2192 z}. From this\nbase one cannot deduce z. Let\"s assume that this agent\nreceives the following argument {a, a \u2192 y} that justifies y.\nIt is clear that now P can build an argument, say {a, a \u2192\ny, y \u2192 z} in favor of z.\nIn a similar way, if a received argument is in conflict with the\narguments of the agent i, then those conflicts are also added\nto its relation Ri\n. Note that new conflicts may arise between\nthe original arguments of the agent and the ones that emerge\nafter adding the received arguments to its theory. Those new\nconflicts should also be considered. As a direct consequence\nof the evolution of the sets Ai\nand Ri\n, the defeat relation\nDefi\nis also updated.\nThe initial theory of an agent i, (i.e. its theory before the\ndialogue starts), is denoted by Ai\n0, Fi\n0, i\n0, Ri\n0, Defi\n0 , with\ni \u2208 {P, C}. Besides, in this paper, we suppose that the\npreference relation i\nof an agent does not change during\nthe dialogue.\nDefinition 11 (Theory evolution). Let m1, . . ., mt,\n. . ., mj be a sequence of moves. The theory of an agent i at\na step t > 0 is: Ai\nt, Fi\nt , i\nt, Ri\nt, Defi\nt such that:\n\u2022 Ai\nt = Ai\n0 \u222a {ai, i = 1, . . . , t, ai = Argument(mi)} \u222a\nA with A \u2286 Args(L)\n\u2022 Fi\nt = O \u2192 2Ai\nt\n\u2022 i\nt = i\n0\n\u2022 Ri\nt = Ri\n0 \u222a {(ai, aj) | ai = Argument(mi),\naj = Argument(mj), i, j \u2264 t, and ai RL aj} \u222a R with\nR \u2286 RL\n\u2022 Defi\nt \u2286 Ai\nt \u00d7 Ai\nt\nThe above definition captures the monotonic aspect of an\nargument. Indeed, an argument cannot be removed.\nHowever, its status may change. An argument that is accepted\nat step t of the dialogue by an agent may become rejected\nat step t + i. Consequently, the status of offers also change.\nThus, the sets Oa, Or, On, and Ons may change from one\nstep of the dialogue to another. That means for example\nthat some offers could move from the set Oa to the set Or\nand vice-versa. Note that in the definition of Rt, the\nrelation RL is used to denote a conflict between exchanged\narguments. The reason is that, such a conflict may not be\nin the set Ri\nof the agent i. Thus, in order to recognize\nsuch conflicts, we have supposed that the set RL is known\nto the agents. This allows us to capture the situation where\nan agent is able to prove an argument that it was unable\nto prove before, by incorporating in its beliefs some\ninformation conveyed through the exchange of arguments with\nanother agent. This, unknown at the beginning of the\ndialogue argument, could give to this agent the possibility to\ndefeat an argument that it could not by using its initial\narguments. This could even lead to a change of the status of\nthese initial arguments and this change would lead to the\none of the associated offers\" status.\nIn what follows, Oi\nt,x denotes the set of offers of type x,\nwhere x \u2208 {a, n, r, ns}, of the agent i at step t of the\ndialogue. In some places, we can use for short the notation Oi\nt\nto denote the partition of the set O at step t for agent i.\nNote that we have: not(Oi\nt,x \u2286 Oi\nt+1,x).\n5.2 The notion of agreement\nAs said in the introduction, negotiation is a process aiming\nat finding an agreement about some matters. By agreement,\none means a solution that satisfies to the largest possible\nextent the preferences of both agents. In case there is no such\nsolution, we say that the negotiation fails. In what follows,\nwe will discuss the different kinds of solutions that may be\nreached in a negotiation. The first one is the optimal\nsolution. An optimal solution is the best offer for both agents.\nFormally:\nDefinition 12 (Optimal solution). Let O be a set\nof offers, and o \u2208 O. The offer o is an optimal solution at\na step t \u2265 0 iff o \u2208 OP\nt,a \u2229 OC\nt,a\nSuch a solution does not always exist since agents may have\nconflicting preferences. Thus, agents make concessions by\nproposing/accepting less preferred offers.\nDefinition 13 (Concession). Let o \u2208 O be an offer.\nThe offer o is a concession for an agent i iff o \u2208 Oi\nx such\nthat \u2203Oi\ny = \u2205, and Oi\ny Oi\nx.\nDuring a negotiation dialogue, agents exchange first their\nmost preferred offers, and if these last are rejected, they\nmake concessions. In this case, we say that their best offers\nare no longer defendable. In an argumentation setting, this\nmeans that the agent has already presented all its arguments\nsupporting its best offers, and it has no counter argument\nagainst the ones presented by the other agent. Formally:\nDefinition 14 (Defendable offer). Let Ai\nt, Fi\nt , i\nt,\nRi\nt, Defi\nt be the theory of agent i at a step t > 0 of the\ndialogue. Let o \u2208 O such that \u2203j \u2264 t with Player(mj) = i and\noffer(mj) = o. The offer o is defendable by the agent i iff:\n\u2022 \u2203a \u2208 Fi\nt (o), and k \u2264 t s.t. Argument(mk) = a, or\n\u2022 \u2203a \u2208 At\n\\Fi\nt (o) s.t. a Defi\nt b with\n- Argument(mk) = b, k \u2264 t, and Player(mk) = i\n- l \u2264 t, Argument(ml) = a\nThe offer o is said non-defendable otherwise and NDi\nt is the\nset of non-defendable offers of agent i at a step t.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 971\n5.3 Negotiation dialogue\nNow that we have shown how the theories of the agents\nevolve during a dialogue, we are ready to define formally\nan argumentation-based negotiation dialogue. For that\npurpose, we need to define first the notion of a legal\ncontinuation.\nDefinition 15 (Legal move). A move m is a legal\ncontinuation of a sequence of moves m1, . . . , ml iff j, k < l,\nsuch that:\n\u2022 Offer(mj) = Offer(mk), and\n\u2022 Player(mj) = Player(mk)\nThe idea here is that if the two agents present the same\noffer, then the dialogue should terminate, and there is no\nlonger possible continuation of the dialogue.\nDefinition 16 (Argumentation-based negotiation).\nAn argumentation-based negotiation dialogue d between two\nagents P and C is a non-empty sequence of moves m1, . . . , ml\nsuch that:\n\u2022 pi = P iff i is even, and pi = C iff i is odd\n\u2022 Player(m1) = P, Argument(m1) = \u03b8, Offer(m1) = \u03b8,\nand Target(m1) = 02\n\u2022 \u2200 mi, if Offer(mi) = \u03b8, then Offer(mi) oj, \u2200 oj \u2208\nO\\(O\nPlayer(mi)\ni,r \u222a ND\nPlayer(mi)\ni )\n\u2022 \u2200i = 1, . . . , l, mi is a legal continuation of m1, . . . , mi\u22121\n\u2022 Target(mi) = mj such that j < i and Player(mi) =\nPlayer(mj)\n\u2022 If Argument(mi) = \u03b8, then:\n- if Offer(mi) = \u03b8 then Argument(mi) \u2208 F(Offer(mi))\n- if Offer(mi) = \u03b8 then Argument(mi) Def\nPlayer(mi)\ni\nArgument(Target(mi))\n\u2022 i, j \u2264 l such that mi = mj\n\u2022 m \u2208 M such that m is a legal continuation of m1, . . . , ml\nLet D be the set of all possible dialogues.\nThe first condition says that the two agents take turn. The\nsecond condition says that agent P starts the negotiation\ndialogue by presenting an offer. Note that, in the first turn,\nwe suppose that the agent does not present an argument.\nThis assumption is made for strategical purposes. Indeed,\narguments are exchanged as soon as a conflict appears. The\nthird condition ensures that agents exchange their best\noffers, but never the rejected ones. This condition takes also\ninto account the concessions that an agent will have to make\nif it was established that a concession is the only option for\nit at the current state of the dialogue. Of course, as we\nhave shown in a previous section, an agent may have several\ngood or acceptable offers. In this case, the agent chooses\none of them randomly. The fourth condition ensures that\nthe moves are legal. This condition allows to terminate the\ndialogue as soon as an offer is presented by both agents.\nThe fifth condition allows agents to backtrack. The sixth\n2\nThe first move has no target.\ncondition says that an agent may send arguments in favor\nof offers, and in this case the offer should be stated in the\nsame move. An agent can also send arguments in order to\ndefeat arguments of the other agent. The next condition\nprevents repeating the same move. This is useful for\navoiding loops. The last condition ensures that all the possible\nlegal moves have been presented.\nThe outcome of a negotiation dialogue is computed as\nfollows:\nDefinition 17 (Dialogue outcome). Let d = m1, . . .,\nml be a argumentation-based negotiation dialogue. The\noutcome of this dialogue, denoted Outcome, is Outcome(d) =\nOffer(ml) iff \u2203j < l s.t. Offer(ml) = Offer(mj), and\nPlayer(ml) = Player(mj). Otherwise, Outcome(d) = \u03b8.\nNote that when Outcome(d) = \u03b8, the negotiation fails, and\nno agreement is reached by the two agents. However, if\nOutcome(d) = \u03b8, the negotiation succeeds, and a solution\nthat is either optimal or a compromise is found.\nTheorem 8. \u2200di \u2208 D, the argumentation-based\nnegotiation di terminates.\nThe above result is of great importance, since it shows that\nthe proposed protocol avoids loops, and dialogues terminate.\nAnother important result shows that the proposed protocol\nensures to reach an optimal solution if it exists. Formally:\nTheorem 9 (Completeness). Let d = m1, . . . , ml be\na argumentation-based negotiation dialogue. If \u2203t \u2264 l such\nthat OP\nt,a \u2229 OC\nt,a = \u2205, then Outcome(d) \u2208 OP\nt,a \u2229 OC\nt,a.\nWe show also that the proposed dialogue protocol is sound\nin the sense that, if a dialogue returns a solution, then that\nsolution is for sure a compromise. In other words, that\nsolution is a common agreement at a given step of the\ndialogue. We show also that if the negotiation fails, then there\nis no possible solution.\nTheorem 10 (Soundness). Let d = m1, . . . , ml be a\nargumentation-based negotiation dialogue.\n1. If Outcome(d) = o, (o = \u03b8), then \u2203t \u2264 l such that o \u2208\nOP\nt,x \u2229 OC\nt,y, with x, y \u2208 {a, n, ns}.\n2. If Outcome(d) = \u03b8, then \u2200t \u2264 l, OP\nt,x \u2229 OC\nt,y = \u2205, \u2200\nx, y \u2208 {a, n, ns}.\nA direct consequence of the above theorem is the following:\nProperty 4. Let d = m1, . . . , ml be a\nargumentationbased negotiation dialogue. If Outcome(d) = \u03b8, then \u2200t \u2264 l,\n\u2022 OP\nt,r = OC\nt,a \u222a OC\nt,n \u222a OC\nt,ns, and\n\u2022 OC\nt,r = OP\nt,a \u222a OP\nt,n \u222a OP\nt,ns.\n6. ILLUSTRATIVE EXAMPLES\nIn this section we will present some examples in order to\nillustrate our general framework.\nExample 7 (No argumentation). Let O = {o1, o2}\nbe the set of all possible offers. Let P and C be two agents,\nequipped with the same theory: A, F, , R, Def such that\nA = \u2205, F(o1) = F(o2) = \u2205, = \u2205, R = \u2205, Def = \u2205. In\nthis case, it is clear that the two offers o1 and o2 are\nnonsupported. The proposed protocol (see Definition 16) will\ngenerate one of the following dialogues:\n972 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nP: m1 = P, \u03b8, o1, 0\nC: m2 = C, \u03b8, o1, 1\nThis dialogue ends with o1 as a compromise. Note that this\nsolution is not considered as optimal since it is not an\nacceptable offer for the agents.\nP: m1 = P, \u03b8, o1, 0\nC: m2 = C, \u03b8, o2, 1\nP: m3 = P, \u03b8, o2, 2\nThis dialogue ends with o2 as a compromise.\nP: m1 = P, \u03b8, o2, 0\nC: m2 = C, \u03b8, o2, 1\nThis dialogue also ends with o2 as a compromise. The last\npossible dialgue is the following that ends with o1 as a\ncompromise.\nP: m1 = P, \u03b8, o2, 0\nC: m2 = C, \u03b8, o1, 1\nP: m3 = P, \u03b8, o1, 2\nNote that in the above example, since there is no exchange\nof arguments, the theories of both agents do not change. Let\nus now consider the following example.\nExample 8 (Static theories). Let O = {o1, o2} be\nthe set of all possible offers. The theory of agent P is AP\n,\nFP\n, P\n, RP\n, DefP\nsuch that: AP\n= {a1, a2}, FP\n(o1) =\n{a1}, FP\n(o2) = {a2}, P\n= {(a1, a2)}, RP\n= {(a1, a2), (a2, a1)},\nDefP\n= {a1, a2}. The argumentation system AP\n, DefP\nof\nthis agent will return a1 as an accepted argument, and a2 as\na rejected one. Consequently, the offer o1 is acceptable and\no2 is rejected.\nThe theory of agent C is AC\n, FC\n, C\n, RC\n, DefC\nsuch\nthat: AC\n= {a1, a2}, FC\n(o1) = {a1}, FC\n(o2) = {a2}, C\n=\n{(a2, a1)}, RC\n= {(a1, a2), (a2, a1)}, DefC\n= {a2, a1}. The\nargumentation system AC\n, DefC\nof this agent will return\na2 as an accepted argument, and a1 as a rejected one.\nConsequently, the offer o2 is acceptable and o1 is rejected.\nThe only possible dialogues that may take place between\nthe two agents are the following:\nP: m1 = P, \u03b8, o1, 0\nC: m2 = C, \u03b8, o2, 1\nP: m3 = P, a1, o1, 2\nC: m4 = C, a2, o2, 3\nThe second possible dialogue is the following:\nP: m1 = P, \u03b8, o1, 0\nC: m2 = C, a2, o2, 1\nP: m3 = P, a1, o1, 2\nC: m4 = C, \u03b8, o2, 3\nBoth dialogues end with failure. Note that in both dialogues,\nthe theories of both agents do not change. The reason is that\nthe exchanged arguments are already known to both agents.\nThe negotiation fails because the agents have conflicting\npreferences.\nLet us now consider an example in which argumentation will\nallow agents to reach an agreement.\nExample 9 (Dynamic theories). Let O = {o1, o2} be\nthe set of all possible offers. The theory of agent P is AP\n,\nFP\n, P\n, RP\n, DefP\nsuch that: AP\n= {a1, a2}, FP\n(o1)\n= {a1}, FP\n(o2) = {a2}, P\n= {(a1, a2), (a3, a1)}, RP\n=\n{(a1, a2), (a2, a1)}, DefP\n= {(a1, a2)}. The argumentation\nsystem AP\n, DefP\nof this agent will return a1 as an accepted\nargument, and a2 as a rejected one. Consequently, the offer\no1 is acceptable and o2 is rejected.\nThe theory of agent C is AC\n, FC\n, C\n, RC\n, DefC\nsuch\nthat: AC\n= {a1, a2, a3}, FC\n(o1) = {a1}, FC\n(o2) = {a2},\nC\n= {(a1, a2), (a3, a1)}, RC\n= {(a1, a2), (a2, a1), (a3, a1)},\nDefC\n= {(a1, a2), (a3, a1)}. The argumentation system\nAC\n, DefC\nof this agent will return a3 and a2 as accepted\narguments, and a1 as a rejected one. Consequently, the offer\no2 is acceptable and o1 is rejected.\nThe following dialogue may take place between the two\nagents:\nP: m1 = P, \u03b8, o1, 0\nC: m2 = C, \u03b8, o2, 1\nP: m3 = P, a1, o1, 2\nC: m4 = C, a3, \u03b8, 3\nC: m5 = P, \u03b8, o2, 4\nAt step 4 of the dialogue, the agent P receives the\nargument a3 from P. Thus, its theory evolves as follows: AP\n= {a1, a2, a3}, RP\n= {(a1, a2), (a2, a1), (a3, a1)}, DefP\n=\n{(a1, a2), (a3, a1)}. At this step, the argument a1 which was\naccepted will become rejected, and the argument a2 which\nwas at the beginning of the dialogue rejected will become\naccepted. Thus, the offer o2 will be acceptable for the agent,\nwhereas o1 will become rejected. At this step 4, the offer o2\nis acceptable for both agents, thus it is an optimal solution.\nThe dialogue ends by returning this offer as an outcome.\n7. RELATED WORK\nArgumentation has been integrated in negotiation\ndialogues at the early nineties by Sycara [12]. In that work, the\nauthor has emphasized the advantages of using\nargumentation in negotiation dialogues, and a specific framework has\nbeen introduced. In [8], the different types of arguments\nthat are used in a negotiation dialogue, such as threats and\nrewards, have been discussed. Moreover, a particular\nframework for negotiation have been proposed. In [9, 13],\ndifferent other frameworks have been proposed. Even if all these\nframeworks are based on different logics, and use different\ndefinitions of arguments, they all have at their heart an\nexchange of offers and arguments. However, none of those\nproposals explain when arguments can be used within a\nnegotiation, and how they should be dealt with by the agent\nthat receives them. Thus the protocol for handling\narguments was missing. Another limitation of the above\nframeworks is the fact that the argumentation frameworks they\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 973\nuse are quite poor, since they use a very simple\nacceptability semantics. In [2] a negotiation framework that fills the\ngap has been suggested. A protocol that handles the\narguments was proposed. However, the notion of concession\nis not modeled in that framework, and it is not clear what\nis the status of the outcome of the dialogue. Moreover, it\nis not clear how an agent chooses the offer to propose at a\ngiven step of the dialogue. In [1, 7], the authors have\nfocused mainly on this decision problem. They have proposed\nan argumentation-based decision framework that is used by\nagents in order to choose the offer to propose or to accept\nduring the dialogue. In that work, agents are supposed to\nhave a beliefs base and a goals base.\nOur framework is more general since it does not impose\nany specific structure for the arguments, the offers, or the\nbeliefs. The negotiation protocol is general as well. Thus this\nframework can be instantiated in different ways by creating,\nin such manner, different specific argumentation-based\nnegotiation frameworks, all of them respecting the same\nproperties. Our framework is also a unified one because frameworks\nlike the ones presented above can be represented within this\nframework. For example the decision making mechanism\nproposed in [7] for the evaluation of arguments and\ntherefore of offers, which is based on a priority relation between\nmutually attacked arguments, can be captured by the\nrelation defeat proposed in our framework. This relation takes\nsimultaneously into account the attacking and preference\nrelations that may exist between two arguments.\n8. CONCLUSIONS AND FUTURE WORK\nIn this paper we have presented a unified and general\nframework for argumentation-based negotiation. Like any\nother argumentation-based negotiation framework, as it is\nevoked in (e.g. [10]), our framework has all the advantages\nthat argumentation-based negotiation approaches present\nwhen related to the negotiation approaches based either on\ngame theoretic models (see e.g. [11]) or heuristics ([6]). This\nwork is a first attempt to formally define the role of\nargumentation in the negotiation process. More precisely, for the\nfirst time, it formally establishes the link that exists between\nthe status of the arguments and the offers they support, it\ndefines the notion of concession and shows how it influences\nthe evolution of the negotiation, it determines how the\ntheories of agents evolve during the dialogue and performs an\nanalysis of the negotiation outcomes. It is also the first time\nwhere a study of the formal properties of the negotiation\ntheories of the agents as well as of an argumentative\nnegotiation dialogue is presented.\nOur future work concerns several points. A first point is\nto relax the assumption that the set of possible offers is the\nsame to both agents. Indeed, it is more natural to assume\nthat agents may have different sets of offers. During a\nnegotiation dialogue, these sets will evolve. Arguments in favor\nof the new offers may be built from the agent theory. Thus,\nthe set of offers will be part of the agent theory. Another\npossible extension of this work would be to allow agents\nto handle both arguments PRO and CONS offers. This is\nmore akin to the way human take decisions. Considering\nboth types of arguments will refine the evaluation of the\noffers status. In the proposed model, a preference relation\nbetween offers is defined on the basis of the partition of the\nset of offers. This preference relation can be refined. For\ninstance, among the acceptable offers, one may prefer the\noffer that is supported by the strongest argument. In [4],\ndifferent criteria have been proposed for comparing decisions.\nOur framework can thus be extended by integrating those\ncriteria. Another interesting point to investigate is that of\nconsidering negotiation dialogues between two agents with\ndifferent profiles. By profile, we mean the criterion used by\nan agent to compare its offers.\n9. REFERENCES\n[1] L. Amgoud, S. Belabbes, and H. Prade. Towards a\nformal framework for the search of a consensus\nbetween autonomous agents. In Proceedings of the 4th\nInternational Joint Conference on Autonomous Agents\nand Multi-Agents systems, pages 537-543, 2005.\n[2] L. Amgoud, S. Parsons, and N. Maudet. Arguments,\ndialogue, and negotiation. In Proceedings of the 14th\nEuropean Conference on Artificial Intelligence, 2000.\n[3] L. Amgoud and H. Prade. Reaching agreement\nthrough argumentation: A possibilistic approach. In 9\nth International Conference on the Principles of\nKnowledge Representation and Reasoning, KR\"2004,\n2004.\n[4] L. Amgoud and H. Prade. Explaining qualitative\ndecision under uncertainty by argumentation. In 21st\nNational Conference on Artificial Intelligence,\nAAAI\"06, pages 16 - 20, 2006.\n[5] P. M. Dung. On the acceptability of arguments and its\nfundamental role in nonmonotonic reasoning, logic\nprogramming and n-person games. Artificial\nIntelligence, 77:321-357, 1995.\n[6] N. R. Jennings, P. Faratin, A. R. Lumuscio,\nS. Parsons, and C. Sierra. Automated negotiation:\nProspects, methods and challenges. International\nJournal of Group Decision and Negotiation, 2001.\n[7] A. Kakas and P. Moraitis. Adaptive agent negotiation\nvia argumentation. In Proceedings of the 5th\nInternational Joint Conference on Autonomous Agents\nand Multi-Agents systems, pages 384-391, 2006.\n[8] S. Kraus, K. Sycara, and A. Evenchik. Reaching\nagreements through argumentation: a logical model\nand implementation. Artificial Intelligence, 104:1-69,\n1998.\n[9] S. Parsons and N. R. Jennings. Negotiation through\nargumentation-a preliminary report. In Proceedings\nof the 2nd International Conference on Multi Agent\nSystems, pages 267-274, 1996.\n[10] I. Rahwan, S. D. Ramchurn, N. R. Jennings,\nP. McBurney, S. Parsons, and E. Sonenberg.\nArgumentation-based negotiation. Knowledge\nEngineering Review, 18 (4):343-375, 2003.\n[11] J. Rosenschein and G. Zlotkin. Rules of Encounter:\nDesigning Conventions for Automated Negotiation\nAmong Computers,. MIT Press, Cambridge,\nMassachusetts, 1994., 1994.\n[12] K. Sycara. Persuasive argumentation in negotiation.\nTheory and Decision, 28:203-242, 1990.\n[13] F. Tohm\u00b4e. Negotiation and defeasible reasons for\nchoice. In Proceedings of the Stanford Spring\nSymposium on Qualitative Preferences in Deliberation\nand Practical Reasoning, pages 95-102, 1997.\n974 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)", "keywords": "outcome;belief;agent;argumentation-based negotiation;concession notion;argument;information;argumentation;decision making mechanism;negotiation;framework;solution;theory;notion of concession"}
{"name": "train_I-53", "title": "A Randomized Method for the Shapley Value for the Voting Game", "abstract": "The Shapley value is one of the key solution concepts for coalition games. Its main advantage is that it provides a unique and fair solution, but its main problem is that, for many coalition games, the Shapley value cannot be determined in polynomial time. In particular, the problem of finding this value for the voting game is known to be #P-complete in the general case. However, in this paper, we show that there are some specific voting games for which the problem is computationally tractable. For other general voting games, we overcome the problem of computational complexity by presenting a new randomized method for determining the approximate Shapley value. The time complexity of this method is linear in the number of players. We also show, through empirical studies, that the percentage error for the proposed method is always less than 20% and, in most cases, less than 5%.", "fulltext": "1. INTRODUCTION\nCoalition formation, a key form of interaction in multi-agent\nsystems, is the process of joining together two or more agents so as\nto achieve goals that individuals on their own cannot, or to achieve\nthem more efficiently [1, 11, 14, 13]. Often, in such situations,\nthere is more than one possible coalition and a player\"s payoff\ndepends on which one it joins. Given this, a key problem is to ensure\nthat none of the parties in a coalition has any incentive to break\naway from it and join another coalition (i.e., the coalitions should\nbe stable). However, in many cases there may be more than one\nsolution (i.e., a stable coalition). In such cases, it becomes difficult\nto select a single solution from among the possible ones, especially\nif the parties are self-interested (i.e., they have different preferences\nover stable coalitions).\nIn this context, cooperative game theory deals with the\nproblem of coalition formation and offers a number of solution\nconcepts that possess desirable properties like stability, fair division\nof joint gains, and uniqueness [16, 14]. Cooperative game theory\ndiffers from its non-cooperative counterpart in that for the former\nthe players are allowed to form binding agreements and so there is\na strong incentive to work together to receive the largest total\npayoff. Also, unlike non-cooperative game theory, cooperative game\ntheory does not specify a game through a description of the\nstrategic environment (including the order of players\" moves and the set\nof actions at each move) and the resulting payoffs, but, instead, it\nreduces this collection of data to the coalitional form where each\ncoalition is represented by a single real number: there are no\nactions, moves, or individual payoffs. The chief advantage of this\napproach, at least in multiple-player environments, is its practical\nusefulness. Thus, many more real-life situations fit more easily into\na coalitional form game, whose structure is more tractable than that\nof a non-cooperative game, whether that be in normal or extensive\nform and it is for this reason that we focus on such forms in this\npaper.\nGiven these observations, a number of multiagent systems\nresearchers have used and extended cooperative game-theoretic\nsolutions to facilitate automated coalition formation [20, 21, 18].\nMoreover, in this work, one of the most extensively studied solution\nconcepts is the Shapley value [19]. A player\"s Shapley value gives an\nindication of its prospects of playing the game - the higher the\nShapley value, the better its prospects. The main advantage of the\nShapley value is that it provides a solution that is both unique and\nfair (see Section 2.1 for a discussion of the property of fairness).\nHowever, while these are both desirable properties, the Shapley\nvalue has one major drawback: for many coalition games, it\ncannot be determined in polynomial time. For instance, finding this\nvalue for the weighted voting game is, in general, #P-complete [6].\nA problem is #P-hard if solving it is as hard as counting\nsatisfying assignments of propositional logic formulae [15, p442]. Since\n#P-completeness thus subsumes NP-completeness, this implies that\ncomputing the Shapley value for the weighted voting game will be\nintractable in general. In other words, it is practically infeasible to\ntry to compute the exact Shapley value. However, the voting game\nhas practical relevance to multi-agent systems as it is an important\nmeans of reaching consensus between multiple agents. Hence, our\nobjective is to overcome the computational complexity of finding\nthe Shapley value for this game. Specifically, we first show that\nthere are some specific voting games for which the exact value can\n959\n978-81-904262-7-5 (RPS) c 2007 IFAAMAS\nbe computed in polynomial time. By identifying such games, we\nshow, for the first tme, when it is feasible to find the exact value and\nwhen it is not. For the computationally complex voting games, we\npresent a new randomised method, along the lines of Monte-Carlo\nsimulation, for computing the approximate Shapley value.\nThe computational complexity of such games has typically been\ntackled using two main approaches. The first is to use\ngenerating functions [3]. This method trades time complexity for\nstorage space. The second uses an approximation technique based on\nMonte Carlo simulation [12, 7]. However the method we propose is\nmore general than either of these (see Section 6 for details).\nMoreover, no work has previously analysed the approximation error. The\napproximation error relates to how close the approximate is to the\ntrue Shapley value. Specifically, it is the difference between the true\nand the approximate Shapley value. It is important to determine\nthis error because the performance of an approximation method is\nevaluated in terms of two criteria: its time complexity, and its\napproximation error. Thus, our contribution lies in also in providing,\nfor the first time, an analysis of the percentage error in the\napproximate Shapley value. This analysis is carried out empirically.\nOur experiments show that the error is always less than 20%,\nand in most cases it is under 5%. Finally, our method has time\ncomplexity linear in the number of players and it does not require\nany arrays (i.e., it is economical in terms of both computing time\nand storage space). Given this, and the fact that software agents\nhave limited computational resources and therefore cannot\ncompute the true Shapley value, our results are especially relevant to\nsuch resource bounded agents.\nThe rest of the paper is organised as follows. Section 2 defines\nthe Shapley value and describes the weighted voting game. In\nSection 3 we describe voting games whose Shapley value can be found\nin polynomial time. In Section 4, we present a randomized method\nfor finding the approximate Shapley value and analyse its\nperformance in Section 5. Section 6 discusses related literature. Finally,\nSection 7 concludes.\n2. BACKGROUND\nWe begin by introducing coalition games and the Shapley value and\nthen define the weighted voting game. A coalition game is a game\nwhere groups of players (coalitions) may enforce cooperative\nbehaviour between their members. Hence the game is a competition\nbetween coalitions of players, rather than between individual\nplayers.\nDepending on how the players measure utility, coalition game\ntheory is split into two parts. If the players measure utility or the\npayoff in the same units and there is a means of exchange of utility\nsuch as side payments, we say the game has transferable utility;\notherwise it has non-transferable utility. More formally, a coalition\ngame with transferable utility, N, v , consists of:\n1. a finite set (N = {1, 2, . . . , n}) of players and\n2. a function (v) that associates with every non-empty subset S\nof N (i.e., a coalition) a real number v(S) (the worth of S).\nFor each coalition S, the number v(S) is the total payoff that is\navailable for division among the members of S (i.e., the set of joint\nactions that coalition S can take consists of all possible divisions\nof v(S) among the members of S). Coalition games with\nnontransferable payoffs differ from ones with transferable payoffs in\nthe following way. For the former, each coalition is associated with\na set of payoff vectors that is not necessarily the set of all possible\ndivisions of some fixed amount. The focus of this paper is on the\nweighted voting game (described in Section 2.1) which is a game\nwith transferable payoffs.\nThus, in either case, the players will only join a coalition if they\nexpect to gain from it. Here, the players are allowed to form\nbinding agreements, and so there is strong incentive to work together to\nreceive the largest total payoff. The problem then is how to split the\ntotal payoff between or among the players. In this context, Shapley\n[19] constructed a solution using an axiomatic approach. Shapley\ndefined a value for games to be a function that assigns to a game\n(N, v), a number \u03d5i(N, v) for each i in N. This function satisfies\nthree axioms [17]:\n1. Symmetry. This axiom requires that the names of players\nplay no role in determining the value.\n2. Carrier. This axiom requires that the sum of \u03d5i(N, v) for all\nplayers i in any carrier C equal v(C). A carrier C is a subset\nof N such that v(S) = v(S \u2229 C) for any subset of players\nS \u2282 N.\n3. Additivity. This axiom specifies how the values of different\ngames must be related to one another. It requires that for\nany games \u03d5i(N, v) and \u03d5i(N, v ), \u03d5i(N, v)+\u03d5i(N, v ) =\n\u03d5i(N, v + v ) for all i in N.\nShapley showed that there is a unique function that satisfies these\nthree axioms.\nShapley viewed this value as an index for measuring the power\nof players in a game. Like a price index or other market indices, the\nvalue uses averages (or weighted averages in some of its\ngeneralizations) to aggregate the power of players in their various cooperation\nopportunities. Alternatively, one can think of the Shapley value as\na measure of the utility of risk neutral players in a game.\nWe first introduce some notation and then define the Shapley\nvalue. Let S denote the set N \u2212 {i} and fi : S \u2192 2N\u2212{i}\nbe\na random variable that takes its values in the set of all subsets of\nN \u2212 {i}, and has the probability distribution function (g) defined\nas:\ng(fi(S) = S) =\n|S|!(n \u2212 |S| \u2212 1)!\nn!\nThe random variable fi is interpreted as the random choice of a\ncoalition that player i joins. Then, a player\"s Shapley value is\ndefined in terms of its marginal contribution. Thus, the marginal\ncontribution of player i to coalition S with i /\u2208 S is a function \u0394iv that\nis defined as follows:\n\u0394iv(S) = v(S \u222a {i}) \u2212 v(S)\nThus a player\"s marginal contribution to a coalition S is the\nincrease in the value of S as a result of i joining it.\nDEFINITION 1. The Shapley value (\u03d5i) of the game N, v for\nplayer i is the expectation (E) of its marginal contribution to a\ncoalition that is chosen randomly:\n\u03d5i(N, v) = E[\u0394iv \u25e6 fi] (1)\nThe Shapley value is interpreted as follows. Suppose that all\nthe players are arranged in some order, all orderings being equally\nlikely. Then \u03d5i(N, v) is the expected marginal contribution, over\nall orderings, of player i to the set of players who precede him.\nThe method for finding a player\"s Shapley value depends on the\ndefinition of the value function (v). This function is different for\ndifferent games, but here we focus specifically on the weighted\nvoting game for the reasons outlined in Section 1.\n960 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\n2.1 The weighted voting game\nWe adopt the definition of the voting game given in [6]. Thus, there\nis a set of n players that may, for example, represent shareholders\nin a company or members in a parliament. The weighted voting\ngame is then a game G = N, v in which:\nv(S) =\nj\n1 if w(S) \u2265 q\n0 otherwise\nfor some q \u2208 IR+ and wi \u2208 IRN\n+ , where:\nw(S) =\nX\ni\u2208S\nwi\nfor any coalition S. Thus wi is the number of votes that player i\nhas and q is the number of votes needed to win the game (i.e., the\nquota).\nNote that for this game (denoted q; w1, . . . , wn ), a player\"s\nmarginal contribution is either zero or one. This is because the\nvalue of any coalition is either zero or one. A coalition with value\nzero is called a losing coalition and with value one a winning\ncoalition. If a player\"s entry to a coalition changes it from losing to\nwinning, then the player\"s marginal contribution for that coalition\nis one; otherwise it is zero.\nThe main advantage of the Shapley value is that it gives a\nsolution that is both unique and fair. The property of uniqueness\nis desirable because it leaves no ambiguity. The property of\nfairness relates to how the gains from cooperation are split between\nthe members of a coalition. In this case, a player\"s Shapley value\nis proportional to the contribution it makes as a member of a\ncoalition; the more contribution it makes, the higher its value. Thus,\nfrom a player\"s perspective, both uniqueness and fairness are\ndesirable properties.\n3. VOTING GAMES WITH POLYNOMIAL\nTIME SOLUTIONS\nHere we describe those voting games for which the Shapley value\ncan be determined in polynomial time. This is achieved using the\ndirect enumeration approach (i.e., listing all possible coalitions and\nfinding a player\"s marginal contribution to each of them). We\ncharacterise such games in terms of the number of players and their\nweights.\n3.1 All players have equal weight\nConsider the game q; j, . . . , j with m parties. Each party has j\nvotes. If q \u2264 j, then there would be no need for the players to form\na coalition. On the other hand, if q = mj (m = |N| is the number\nof players), only the grand coalition is possible. The interesting\ngames are those for which the quota (q) satisfies the constraint:\n(j + 1) \u2264 q \u2264 j(m \u2212 1). For these games, the value of a coalition\nis one if the weight of the coalition is greater than or equal to q,\notherwise it is zero.\nLet \u03d5 denote the Shapley value for a player. Consider any one\nplayer. This player can join a coalition as the ith member where\n1 \u2264 i \u2264 m. However, the marginal contribution of the player is 1\nonly if it joins a coalition as the q/j th member. In all other cases,\nits marginal contribution is zero. Thus, the Shapley value for each\nplayer \u03d5 = 1/m. Since \u03d5 requires one division operation, it can\nbe found in constant time (i.e., O(1)).\n3.2 A single large party\nConsider a game in which there are two types of players: large\n(with weight wl > ws) and small (with weight ws). There is one\nlarge player and m small ones. The quota for this game is q; i.e., we\nhave a game of the form q; wl, ws, ws, . . . , ws . The total number\nof players is (m + 1). The value of a coalition is one if the weight\nof the coalition is greater than or equal to q, otherwise it is zero.\nLet \u03d5l denote the Shapley value for the large player and \u03d5s that for\neach small player.\nWe first consider ws = 1 and then ws > 1. The smallest\npossible value for q is wl + 1. This is because, if q \u2264 wl, then the\nlarge party can win the election on its own without the need for\na coalition. Thus, the quota for the game satisfies the constraint\nwl + 1 \u2264 q \u2264 m + wl \u2212 1. Also, the lower and upper limits for\nwl are 2 and (q \u2212 1) respectively. The lower limit is 2 because\nthe weight of the large party has to be greater than each small one.\nFurthermore, the weight of the large party cannot be greater than\nq, since in that case, there would be no need for the large party\nto form a coalition. Recall that for our voting game, a player\"s\nmarginal contribution to a coalition can only be zero or one.\nConsider the large party. This party can join a coalition as the\nith member where 1 \u2264 i \u2264 (m + 1). However, the marginal\ncontribution of the large party is one if it joins a coalition as the\nith member where (q \u2212 wl) \u2264 i < q. In all the remaining cases,\nits marginal contribution is zero. Thus, out of the total (m + 1)\npossible cases, its marginal contribution is one in wl cases. Hence,\nthe Shapley value of the large party is: \u03d5l = wl/(m + 1). In the\nsame way, we obtain the Shapley value of the large party for the\ngeneral case where ws > 1 as:\n\u03d5l = wl/ws /(m + 1)\nNow consider a small player. We know that the sum of the\nShapley values of all the m+1 players is one. Also, since the small\nparties have equal weights, their Shapley values are the same. Hence,\nwe get:\n\u03d5s =\n1 \u2212 \u03d5l\nm\nThus, both \u03d5l and \u03d5s can be computed in constant time. This\nis because both require a constant number of basic operations\n(addition, subtraction, multiplication, and division). In the same way,\nthe Shapley value for a voting game with a single large party and\nmultiple small parties can be determined in constant time.\n3.3 Multiple large and small parties\nWe now consider a voting game that has two player types: large\nand small (as in Section 3.2), but now there are multiple large and\nmultiple small parties. The set of parties consists of ml large\nparties and ms small parties. The weight of each large party is wl and\nthat of each small one is ws, where ws < wl. We show the\ncomputational tractability for this game by considering the following four\npossible scenarios:\nS1 q \u2264 mlwl and q \u2264 msws\nS2 q \u2264 mlwl and q \u2265 msws\nS3 q \u2265 mlwl and q \u2265 msws\nS4 q \u2265 mlwl and q \u2264 msws\nFor the first scenario, consider a large player. In order to determine\nthe Shapley value for this player, we need to consider the number\nof all possible coalitions that give it a marginal contribution of one.\nIt is possible for the marginal contribution of this player to be one if\nit joins a coalition in which the number of large players is between\nzero and (q \u22121)/wl. In other words, there are (q \u22121)/wl +1 such\ncases and we now consider each of them.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 961\nConsider a coalition such that when the large player joins in,\nthere are i large players and (q \u2212 iwl \u2212 1)/ws small players\nalready in it, and the remaining players join after the large player.\nSuch a coalition gives the large player unit marginal contribution.\nLet C2\nl (i, q) denote the number of all such coalitions. To begin,\nconsider the case i = 0:\nC2\nl (0, q) = C\n\u201e\nms,\nq \u2212 1\nws\n\u00ab\n\u00d7 FACTORIAL\n\u201e\nq \u2212 1\nws\n\u00ab\n\u00d7\nFACTORIAL\n\u201e\nml + ms \u2212\nq \u2212 1\nws\n\u2212 1\n\u00ab\nwhere C(y, x) denotes the number of possible combinations of x\nitems from a set of y items. For i = 1, we get:\nC2\nl (1, q) = C(ml, 1) \u00d7 C\n\u201e\nms,\nq \u2212 wl \u2212 1\nws\n\u00ab\n\u00d7\nFACTORIAL\n\u201e\nq \u2212 wl \u2212 1\nws\n\u00ab\n\u00d7\nFACTORIAL\n\u201e\nml + ms \u2212\nq \u2212 wl \u2212 1\nws\n\u2212 1\n\u00ab\nIn general, for i > 1, we get:\nC2\nl (i, q) = C(ml, i) \u00d7 C\n\u201e\nms,\nq \u2212 iwl \u2212 1\nws\n\u00ab\n\u00d7\nFACTORIAL\n\u201e\nq \u2212 iwl \u2212 1\nws\n\u00ab\n\u00d7\nFACTORIAL\n\u201e\nml + ms \u2212\nq \u2212 wl \u2212 1\nws\n\u2212 1\n\u00ab\nThus the large player\"s Shapley value is:\n\u03d5l =\nq\u22121\nwlX\ni=0\nC2\nl (i, q)/FACTORIAL(ml + ms)\nFor a given i, the time to find C2\nl (i, q) is O(T) where\nT = (mlms(q \u2212 iwl \u2212 1)(ml + ms))/ws\nHence, the time to find the Shapley value is O(T q/wl).\nIn the same way, a small player\"s Shapley value is:\n\u03d5s =\nq\u22121\nwsX\ni=0\nC2\ns (i, q)/FACTORIAL(ml + ms)\nand can be found in time O(T q/ws). Likewise, the remaining three\nscenarios (S2 to S4) can be shown to have the same time\ncomplexity.\n3.4 Three player types\nWe now consider a voting game that has three player types: 1, 2,\nand 3. The set of parties consists of m1 players of type 1 (each\nwith weight w1), m2 players of type 2 (each with weight w2), and\nm3 players of type 3 (each with weight w3).\nFor this voting game, consider a player of type 1. It is possible\nfor the marginal contribution of this player to be one if it joins a\ncoalition in which the number of type 1 players is between zero\nand (q \u2212 1)/w1. In other words, there are (q \u2212 1)/w1 + 1 such\ncases and we now consider each of them.\nConsider a coalition such that when the type 1 player joins in,\nthere are i type 1 players already in it. The remaining players join\nafter the type 1 player. Let C3\nl (i, q) denote the number of all such\ncoalitions that give a marginal contribution of one to the type 1\nplayer where:\nC3\n1 (i, q) =\nq\u22121\nw1X\ni=0\nq\u2212iw1\u22121\nw2X\nj=0\nC2\n1 (j, q \u2212 iw1)\nTherefore the Shapley value of the type 1 player is:\n\u03d51 =\nq\u22121\nw1X\ni=0\nC3\n1 (i, q)/FACTORIAL(m1 + m2 + m3)\nThe time complexity of finding this value is O(T q2\n/w1w2) where:\nT = (\n3Y\ni=1\nmi)(q \u2212 iwl \u2212 1)(\n3X\ni=1\nmi)/(w2 + w3)\nLikewise, for the other two player types (2 and 3).\nThus, we have identified games for which the exact Shapley\nvalue can be easily determined. However, the computational\ncomplexity of the above direct enumeration method increases with the\nnumber of player types. For a voting game with more than three\nplayer types, the time complexity of the above method is a\npolynomial of degree four or more. To deal with such situations, therefore,\nthe following section presents a faster randomised method for\nfinding the approximate Shapley value.\n4. FINDING THE APPROXIMATE SHAPLEY\nVALUE\nWe first give a brief introduction to randomized algorithms and\nthen present our randomized method for finding the approximate\nShapley value. Randomized algorithms are the most commonly\nused approach for finding approximate solutions to\ncomputationally hard problems. A randomized algorithm is an algorithm that,\nduring some of its steps, performs random choices [2]. The\nrandom steps performed by the algorithm imply that by executing the\nalgorithm several times with the same input we are not guaranteed\nto find the same solution. Now, since such algorithms generate\napproximate solutions, their performance is evaluated in terms of two\ncriteria: their time complexity, and their error of approximation.\nThe approximation error refers to the difference between the\nexact solution and its approximation. Against this background, we\npresent a randomized method for finding the approximate Shapley\nvalue and empirically evaluate its error.\nWe first describe the general voting game and then present our\nrandomized algorithm. In its general form, a voting game has more\nthan two types of players. Let wi denote the weight of player\ni. Thus, for m players and for quota q the game is of the form\nq; w1, w2, . . . , wm . The weights are specified in terms of a\nprobability distribution function. For such a game, we want to find the\napproximate Shapley value.\nWe let P denote a population of players. The players\" weights\nin this population are defined by a probability distribution function.\nIrrespective of the actual probability distribution function, let \u03bc be\nthe mean weight for the population of players and \u03bd the variance in\nthe players\" weights. From this population of players we randomly\ndraw samples and find the sum of the players\" weights in the sample\nusing the following rule from Sampling Theory (see [8] p425):\nIf w1, w2, . . . , wn is a random sample of size n drawn\nfrom any distribution with mean \u03bc and variance \u03bd, then\nthe sample sum has an approximate Normal\ndistribution with mean n\u03bc and variance \u03bd\nn\n(the larger the n the\nbetter the approximation).\n962 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nR-SHAPLEYVALUE (P, \u03bc, \u03bd, q, wi)\nP: Population of players\n\u03bc: Mean weight of the population P\n\u03bd: Variance in the weights for poulation P\nq: Quota for the voting game\nwi: Player i\"s weight\n1. Ti \u2190 0; a \u2190 q \u2212 wi; b \u2190 q \u2212\n2. For X from 1 to m repeatedly do the following\n2.1. Select a random sample SX of size X from the\npopulation P\n2.2. Evaluate expected marginal contribution (\u0394X\ni )\nof player i to SX as:\n\u0394X\ni \u2190 1\u221a\n(2\u03c0\u03bd/X)\nR b\na\ne\u2212X\n(x\u2212X\u03bc)2\n2\u03bd dx\n2.3. Ti \u2190 Ti + \u0394X\ni\n3. Evaluate Shapley value of player i as:\n\u03d5i \u2190 Ti/m\nTable 1: Randomized algorithm to find the Shapley value for\nplayer i.\nWe know from Definition 1, that the Shapley value for a player is\nthe expectation (E) of its marginal contribution to a coalition that is\nchosen randomly. We use this rule to determine the Shapley value\nas follows.\nFor player i with weight wi, let \u03d5i denote the Shapley value. Let\nX denote the size of a random sample drawn from a population\nin which the individual player weights have any distribution. The\nmarginal contribution of player i to this random sample is one if the\ntotal weight of the X players in the sample is greater than or equal\nto a = q \u2212wi but less than b = q \u2212 (where is an inifinitesimally\nsmall quantity). Otherwise, its marginal contribution is zero. Thus,\nthe expected marginal contribution of player i (denoted \u0394X\ni ) to the\nsample coalition is the area under the curve defined by N(X\u03bc, \u03bd\nX\n)\nin the interval [a, b]. This area is shown as the region B in Figure 1\n(the dotted line in the figure is X\u03bc). Hence we get:\n\u0394X\ni =\n1\np\n(2\u03c0\u03bd/X)\nZ b\na\ne\u2212X\n(x\u2212X\u03bc)2\n2\u03bd dx (2)\nand the Shapley value is:\n\u03d5i =\n1\nm\nmX\nX=1\n\u0394X\ni (3)\nThe above steps are described in Table 1. In more detail, Step\n1 does the initialization. In Step 2, we vary X between 1 and m\nand repeatedly do the following. In Step 2.1, we randomly select a\nsample SX of size X from the population P. Player i\"s marginal\ncontribution to the random coalition SX is found in Step 2.2. The\naverage marginal contribution is found in Step 3 - and this is the\nShapley value for player i.\nTHEOREM 1. The time complexity of the proposed randomized\nmethod is linear in the number of players.\nPROOF. As per Equation 3, \u0394X\ni must be computed m times.\nThis is done in the for loop of Step 2 in Table 1. Hence, the time\ncomplexity of computing a player\"s Shapley value is O(m).\nThe following section analyses the approximation error for the\nproposed method.\n5. PERFORMANCE OF THE RANDOMIZED\nMETHOD\nWe first derive the formula for measuring the error in the\napproximate Shapley value and then conduct experiments for evaluating\nthis error in a wide range of settings. However, before doing so, we\nintroduce the idea of error.\nThe concept of error relates to a measurement made of a\nquantity which has an accepted value [22, 4]. Obviously, it cannot be\ndetermined exactly how far off a measurement is from the accepted\nvalue; if this could be done, it would be possible to just give a more\naccurate, corrected value. Thus, error has to do with uncertainty in\nmeasurements that nothing can be done about. If a measurement is\nrepeated, the values obtained will differ and none of the results can\nbe preferred over the others. However, although it is not possible\nto do anything about such error, it can be characterized.\nAs described in Section 4, we make measurements on samples\nthat are drawn randomly from a given population (P) of players.\nNow, there are statistical errors associated with sampling which\nare unavoidable and must be lived with. Hence, if the result of a\nmeasurement is to have meaning it cannot consist of the measured\nvalue alone. An indication of how accurate the result is must be\nincluded also. Thus, the result of any physical measurement has\ntwo essential components:\n1. a numerical value giving the best estimate possible of the\nquantity measured, and\n2. the degree of uncertainty associated with this estimated value.\nFor example, if the estimate of a quantity is x and the uncertainty\nis e(x) the quantity would lie in x \u00b1 e(x).\nFor sampling experiments, the standard error is by far the most\ncommon way of characterising uncertainty [22]. Given this, the\nfollowing section defines this error and uses it to evaluate the\nperformance of the proposed randomized method.\n5.1 Approximation error\nThe accuracy of the above randomized method depends on its\nsampling error which is defined as follows [22, 4]:\nDEFINITION 2. The sampling error (or standard error) is\ndefined as the standard deviation for a set of measurements divided\nby the square root of the number of measurements.\nTo this end, let e(\u03c3X\n) be the sampling error in the sum of the\nweights for a sample of size X drawn from the distribution N(X\u03bc, \u03bd\nX\n)\nwhere:\ne(\u03c3X\n) =\np\n(\u03bd/X)/\np\n(X)\n=\np\n(\u03bd)/X (4)\nLet e(\u0394X\ni ) denote the error in the marginal contribution for player\ni (given in Equation 2). This error is obtained by propagating the\nerror in Equation 4 to Equation 2. In Equation 2, a and b are the\nlower and upper limits for the sum of the players\" weights for a\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 963\nb\nC\nB\na \u2212 e (\u03c3X )\na\nA\n)X(\u03c3eb+ Sum of weights\nZ1 Z2\nFigure 1: A normal distribution for the sum of players\" weights\nin a coalition of size X.\n40\n60\n80\n100\n0\n50\n100\n0\n5\n10\n15\n20\n25\nQuotaWeight\nPercentageerrorintheShapleyvalue\nFigure 2: Performance of the randomized method for m = 10\nplayers.\ncoalition of size X. Since the error in this sum is e(\u03c3X\n), the actual\nvalues of a and b lie in the interval a \u00b1 e(\u03c3X\n) and b \u00b1 e(\u03c3X\n)\nrespectively. Hence, the error in Equation 2 is either the probability\nthat the sum lies between the limits a \u2212 e(\u03c3X\n) and a (i.e., the area\nunder the curve defined by N(X\u03bc, \u03bd\nX\n) between a \u2212 e(\u03c3X\n) and a,\nwhich is the shaded region A in Figure 1) or the probability that the\nsum of weights lies between the limits b and b+e(\u03c3X\n) (i.e., the area\nunder the curve defined by N(X\u03bc, \u03bd\nX\n) between b and b + e(\u03c3X\n),\nwhich is the shaded region C in Figure 1). More specifically, the\nerror is the maximum of these two probabilities:\ne(\u0394X\ni ) =\n1\np\n(2\u03c0\u03bd/X)\n\u00d7 MAX\n\u201eZ a\na\u2212e(\u03c3X )\ne\u2212X\n(x\u2212X\u03bc)2\n2\u03bd dx,\nZ b+e(\u03c3X\n)\nb\ne\u2212X\n(x\u2212X\u03bc)2\n2\u03bd dx\n\u00ab\nOn the basis of the above error, we find the error in the Shapley\nvalue by using the following standard error propagation rules [22]:\nR1 If x and y are two random variables with errors e(x) and e(y)\nrespectively, then the error in the random variable z = x + y\nis given by:\ne(z) = e(x) + e(y)\nR2 If x is a random variable with error e(x) and z = kx where\n0\n100\n200\n300\n400\n500\n0\n100\n200\n300\n400\n500\n0\n5\n10\n15\n20\n25\nQuotaWeight\nPercentageerrorintheShapleyvalue\nFigure 3: Performance of the randomized method for m = 50\nplayers.\nthe constant k has no error, then the error in z is:\ne(z) = |k|e(x)\nUsing the above rules, the error in the Shapley value (given in\nEquation 3) is obtained by propagating the error in Equation 4 to\nall coalitions between the sizes X = 1 and X = m. Let e(\u03d5i)\ndenote this error where:\ne(\u03d5i) =\n1\nm\nmX\nX=1\ne(\u0394X\ni )\nWe analyze the performance of our method in terms of the\npercentage error PE in the approximate Shapley value which is defined\nas follows:\nPE = 100 \u00d7 e(\u03d5i)/\u03d5i (5)\n5.2 Experimental Results\nWe now compute the percentage error in the Shapley value using\nthe above equation for PE. Since this error depends on the\nparameters of the voting game, we evaluate it in a range of settings by\nsystematically varying the parameters of the voting game.\nIn particular, we conduct experiments in the following setting.\nFor a player with weight w, the percentage error in a player\"s\nShapley value depends on the following five parameters (see Equation 3):\n1. The number of parties (m).\n2. The mean weight (\u03bc).\n3. The variance in the player\"s weights (\u03bd).\n4. The quota for the voting game (q).\n5. The given player\"s weight (w).\nWe fix \u03bc = 10 and \u03bd = 1. This is because, for the normal\ndistribution, \u03bc = 10 ensures that for almost all the players the\nweight is positive, and \u03bd = 1 is used most commonly in statistical\nexperiments (\u03bd can be higher or lower but PE is increasing in\n\u03bdsee Equations 4 and 5). We then vary m, q, and w as follows. We\nvary m between 5 and 100 (since beyond 100 we found that the\nerror is close to zero), for each m we vary q between 4\u03bc and m\u03bc\n(we impose these limits because they ensure that the size of the\n964 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\n0\n200\n400\n600\n800\n1000\n0\n200\n400\n600\n800\n1000\n0\n5\n10\n15\n20\n25\nQuotaWeight\nPercentageerrorintheShapleyvalue\nFigure 4: Performance of the randomized method for m = 100\nplayers.\nwinning coalition is more than one and less than m - see Section 3\nfor details), and for each q, we vary w between 1 and q\u22121 (because\na winning coalition must contain at least two players). The results\nof these experiments are shown in Figures 2, 3, and 4. As seen in\nthe figures, the maximum PE is around 20% and in most cases it is\nbelow 5%.\nWe now analyse the effect of the three parameters: w, q, and m\non the percentage error in more detail.\n- Effect of w. The PE depends on e(\u03c3X\n) because, in\nEquation 5, the limits of integration depend on e(\u03c3X\n). The\ninterval over which the first integration in Equation 5 is done is\na \u2212 a + e(\u03c3X\n) = e(\u03c3X\n), and the interval over which the\nsecond one is done is b + e(\u03c3X\n) \u2212 b = e(\u03c3X\n). Thus, the\ninterval is the same for both integrations and it is independent\nof wi. Note that each of the two functions that are integrated\nin Equation 5 are the same as the function that is integrated\nin Equation 2. Only the limits of the integration are different.\nAlso, the interval over which the integration for the marginal\ncontribution of Equation 2 is done is b \u2212 a = wi \u2212 (see\nFigure 1). The error in the marginal contribution is either the\narea of the shaded region A (between a \u2212 e(\u03c3X\n) and a) in\nFigure 1, or the shaded area C (between b and b + e(\u03c3X\n)).\nAs per Equation 5, it is the maximum of these two areas.\nSince e(\u03c3X\n) is independent of wi, as wi increases, e(\u03c3X\n)\nremains unchanged. However, the area of the unshaded\nregion B increases. Hence, as wi increases, the error in the\nmarginal contribution decreases and PE also decreases.\n- Effect of q. For a given q, the Shapley value for player i is\nas given in Equation 3. We know that, for a sample of size\nX, the sum of the players\" weights is distributed normally\nwith mean X\u03bc and variance \u03bd/X. Since 99% of a normal\ndistribution lies within two standard deviations of its mean\n[8], player i\"s marginal contribution to a sample of size X is\nalmost zero if:\na < X\u03bc + 2\np\n\u03bd/X or b > X\u03bc \u2212 2\np\n\u03bd/X\nThis is because the three regions A, B, and C (in Figure 1)\nlie either to the right of Z2 or to the left of Z1. However,\nplayer i\"s marginal contribution is greater than zero for those\nX for which the following constraint is satisfied:\nX\u03bc \u2212 2\np\n\u03bd/X < a < b < X\u03bc + 2\np\n\u03bd/X\nFor this constraint, the three regions A, B, and C lie\nsomewhere between Z1 and Z2. Since a = q \u2212wi and b = q \u2212 ,\nEquation 6 can also be written as:\nX\u03bc \u2212 2\np\n\u03bd/X < q \u2212 wi < q \u2212 < X\u03bc + 2\np\n\u03bd/X\nThe smallest X that satisfies the constraint in Equation 6\nstrictly increases with q. As X increases, the error in sum\nof weights in a sample (i.e., e(\u03c3X\n) =\np\n(\u03bd)/X) decreases.\nConsequently, the error in a player\"s marginal contribution\n(see Equation 5) also decreases. This implies that as q\nincreases, the error in the marginal contribution (and\nconsequently the error in the Shapley value) decreases.\n- Effect of m. It is clear from Equation 4 that the error e(\u03c3X\n)\nis highest for X = 1 and it decreases with X. Hence, for\nsmall m, e(\u03c31\n) has a significant effect on PE. But as m\nincreases, the effect of e(\u03c31\n) on PE decreases and, as a result,\nPE decreases.\n6. RELATED WORK\nIn order to overcome the computational complexity of finding the\nShapley value, two main approaches have been proposed in the\nliterature. One approach is to use generating functions [3]. This\nmethod is an exact procedure that overcomes the problem of time\ncomplexity, but its storage requirements are substantial - it requires\nhuge arrays. It also has the limitation (not shared by other\napproaches) that it can only be applied to games with integer weights\nand quotas.\nThe other method uses an approximation technique based on\nMonte Carlo simulation. In [12], for instance, the Shapley value is\ncomputed by considering a random sample from a large population\nof players. The method we propose differs from this in that they\ndefine the Shapley value by treating a player\"s number of swings (if a\nplayer can change a losing coalition to a winning one, then, for the\nplayer, the coalition is counted as a swing) as a random variable,\nwhile we treat the players\" weights as random variables. In [12],\nhowever, the question remains how to get the number of swings\nfrom the definition of a voting game and what is the time\ncomplexity of doing this. Since the voting game is defined in terms of the\nplayers\" weights and the number of swings are obtained from these\nweights, our method corresponds more closely to the definition of\nthe voting game. Our method also differs from [7] in that while [7]\npresents a method for the case where all the players\" weights are\ndistributed normally, our method applies to any type of distribution\nfor these weights. Thus, as stated in Section 1, our method is more\ngeneral than [3, 12, 7]. Also, unlike all the above mentioned work,\nwe provide an analysis of the performance of our method in terms\nof the percentage error in the approximate Shapley value.\nA method for finding the Shapley value was also proposed in\n[5]. This method gives the exact Shapley value, but its time\ncomplexity is exponential. Furthermore, the method can be used only\nif the game is represented in a specific form (viz., the multi-issue\nrepresentation), not otherwise. Finally, [9, 10] present a\npolynomial time method for finding the Shapley value. This method can\nbe used if the coalition game is represented as a marginal\ncontribution net. Furthermore, they assume that the Shapley value of\na component of a given coalition game is given by an oracle, and\non the basis of this assumption aggregate these values to find the\nvalue for the overall game. In contrast, our method is independent\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 965\nof the representation and gives an approximate Shapley value in\nlinear time, without the need for an oracle.\n7. CONCLUSIONS AND FUTURE WORK\nCoalition formation is an important form of interaction in\nmultiagent systems. An important issue in such work is for the agents to\ndecide how to split the gains from cooperation between the\nmembers of a coalition. In this context, cooperative game theory offers\na solution concept called the Shapley value. The main advantage of\nthe Shapley value is that it provides a solution that is both unique\nand fair. However, its main problem is that, for many coalition\ngames, the Shapley value cannot be determined in polynomial time.\nIn particular, the problem of finding this value for the voting game\nis #P-complete. Although this problem is, in general #P-complete,\nwe show that there are some specific voting games for which the\nShapley value can be determined in polynomial time and\ncharacterise such games. By doing so, we have shown when it is\ncomputationally feasible to find the exact Shapley value. For other complex\nvoting games, we presented a new randomized method for\ndetermining the approximate Shapley value. The time complexity of the\nproposed method is linear in the number of players. We analysed\nthe performance of this method in terms of the percentage error in\nthe approximate Shapley value.\nOur experiments show that the percentage error in the Shapley\nvalue is at most 20. Furthermore, in most cases, the error is less\nthan 5%. Finally, we analyse the effect of the different parameters\nof the voting game on this error. Our study shows that the error\ndecreases as\n1. a player\"s weight increases,\n2. the quota increases, and\n3. the number of players increases.\nGiven the fact that software agents have limited computational\nresources and therefore cannot compute the true Shapley value, our\nresults are especially relevant to such resource bounded agents. In\nfuture, we will explore the problem of determining the Shapley\nvalue for other commonly occurring coalition games like the\nproduction economy and the market economy.\n8. REFERENCES\n[1] R. Aumann. Acceptable points in general cooperative\nn-person games. In Contributions to theTheory of Games\nvolume IV. Princeton University Press, 1959.\n[2] G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann,\nA. Marchetti-Spaccamela, and M. Protasi. Complexity and\napproximation: Combinatorial optimization problems and\ntheir approximability properties. Springer, 2003.\n[3] J. M. Bilbao, J. R. Fernandez, A. J. Losada, and J. J. Lopez.\nGenerating functions for computing power indices\nefficiently. Top 8, 2:191-213, 2000.\n[4] P. Bork, H. Grote, D. Notz, and M. Regler. Data Analysis\nTechniques in High Energy Physics Experiments. Cambridge\nUniversity Press, 1993.\n[5] V. Conitzer and T. Sandholm. Computing Shapley values,\nmanipulating value division schemes, and checking core\nmembership in multi-issue domains. In Proceedings of the\nNational Conference on Artificial Intelligence, pages\n219-225, San Jose, California, 2004.\n[6] X. Deng and C. H. Papadimitriou. On the complexity of\ncooperative solution concepts. Mathematics of Operations\nResearch, 19(2):257-266, 1994.\n[7] S. S. Fatima, M. Wooldridge, and N. R. Jennings. An\nanalysis of the shapley value and its uncertainty for the\nvoting game. In Proc. 7th Int. Workshop on Agent Mediated\nElectronic Commerce, pages 39-52, 2005.\n[8] A. Francis. Advanced Level Statistics. Stanley Thornes\nPublishers, 1979.\n[9] S. Ieong and Y. Shoham. Marginal contribution nets: A\ncompact representation scheme for coalitional games. In\nProceedings of the Sixth ACM Conference on Electronic\nCommerce, pages 193-202, Vancouver, Canada, 2005.\n[10] S. Ieong and Y. Shoham. Multi-attribute coalition games. In\nProceedings of the Seventh ACM Conference on Electronic\nCommerce, pages 170-179, Ann Arbor, Michigan, 2006.\n[11] J. P. Kahan and A. Rapoport. Theories of Coalition\nFormation. Lawrence Erlbaum Associates Publishers, 1984.\n[12] I. Mann and L. S. Shapley. Values for large games iv:\nEvaluating the electoral college exactly. Technical report,\nThe RAND Corporation, Santa Monica, 1962.\n[13] A. MasColell, M. Whinston, and J. R. Green.\nMicroeconomic Theory. Oxford University Press, 1995.\n[14] M. J. Osborne and A. Rubinstein. A Course in Game Theory.\nThe MIT Press, 1994.\n[15] C. H. Papadimitriou. Computational Complexity. Addison\nWesley Longman, 1994.\n[16] A. Rapoport. N-person Game Theory : Concepts and\nApplications. Dover Publications, Mineola, NY, 2001.\n[17] A. E. Roth. Introduction to the shapley value. In A. E. Roth,\neditor, The Shapley value, pages 1-27. University of\nCambridge Press, Cambridge, 1988.\n[18] T. Sandholm and V. Lesser. Coalitions among\ncomputationally bounded agents. Artificial Intelligence\nJournal, 94(1):99-137, 1997.\n[19] L. S. Shapley. A value for n person games. In A. E. Roth,\neditor, The Shapley value, pages 31-40. University of\nCambridge Press, Cambridge, 1988.\n[20] O. Shehory and S. Kraus. A kernel-oriented model for\ncoalition-formation in general environments: Implemetation\nand results. In In Proceedings of the National Conference on\nArtificial Intelligence (AAAI-96), pages 131-140, 1996.\n[21] O. Shehory and S. Kraus. Methods for task allocation via\nagent coalition formation. Artificial Intelligence Journal,\n101(2):165-200, 1998.\n[22] J. R. Taylor. An introduction to error analysis: The study of\nuncertainties in physical measurements. University Science\nBooks, 1982.\n966 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)", "keywords": "mean of reaching consensus;approximation;unique and fair solution;polynomial time;reaching consensus mean;generating function;coalition formation;shapley value;game-theory;cooperative game theory;interaction;multi-agent system;randomised method"}
{"name": "train_I-54", "title": "Approximate and Online Multi-Issue Negotiation", "abstract": "This paper analyzes bilateral multi-issue negotiation between selfinterested autonomous agents. The agents have time constraints in the form of both deadlines and discount factors. There are m > 1 issues for negotiation where each issue is viewed as a pie of size one. The issues are indivisible (i.e., individual issues cannot be split between the parties; each issue must be allocated in its entirety to either agent). Here different agents value different issues differently. Thus, the problem is for the agents to decide how to allocate the issues between themselves so as to maximize their individual utilities. For such negotiations, we first obtain the equilibrium strategies for the case where the issues for negotiation are known a priori to the parties. Then, we analyse their time complexity and show that finding the equilibrium offers is an NP-hard problem, even in a complete information setting. In order to overcome this computational complexity, we then present negotiation strategies that are approximately optimal but computationally efficient, and show that they form an equilibrium. We also analyze the relative error (i.e., the difference between the true optimum and the approximate). The time complexity of the approximate equilibrium strategies is O(nm/ 2 ) where n is the negotiation deadline and the relative error. Finally, we extend the analysis to online negotiation where different issues become available at different time points and the agents are uncertain about their valuations for these issues. Specifically, we show that an approximate equilibrium exists for online negotiation and show that the expected difference between the optimum and the approximate is O( \u221a m) . These approximate strategies also have polynomial time complexity.", "fulltext": "1. INTRODUCTION\nNegotiation is a key form of interaction in multiagent systems. It\nis a process in which disputing agents decide how to divide the\ngains from cooperation. Since this decision is made jointly by the\nagents themselves [20, 19, 13, 15], each party can only obtain what\nthe other is prepared to allow them. Now, the simplest form of\nnegotiation involves two agents and a single issue. For example,\nconsider a scenario in which a buyer and a seller negotiate on the\nprice of a good. To begin, the two agents are likely to differ on the\nprice at which they believe the trade should take place, but through\na process of joint decision-making they either arrive at a price that\nis mutually acceptable or they fail to reach an agreement. Since\nagents are likely to begin with different prices, one or both of them\nmust move toward the other, through a series of offers and counter\noffers, in order to obtain a mutually acceptable outcome. However,\nbefore the agents can actually perform such negotiations, they must\ndecide the rules for making offers and counter offers. That is, they\nmust set the negotiation protocol [20]. On the basis of this protocol,\neach agent chooses its strategy (i.e., what offers it should make\nduring the course of negotiation). Given this context, this work\nfocuses on competitive scenarios with self-interested agents. For\nsuch cases, each participant defines its strategy so as to maximise\nits individual utility.\nHowever, in most bilateral negotiations, the parties involved need\nto settle more than one issue. For this case, the issues may be\ndivisible or indivisible [4]. For the former, the problem for the agents\nis to decide how to split each issue between themselves [21]. For\nthe latter, the individual issues cannot be divided. An issue, in its\nentirety, must be allocated to either of the two agents. Since the\nagents value different issues differently, they must come to terms\nabout who will take which issue. To date, most of the existing\nwork on multi-issue negotiation has focussed on the former case\n[7, 2, 5, 23, 11, 6]. However, in many real-world settings, the\nissues are indivisible. Hence, our focus here is on negotiation for\nindivisible issues. Such negotiations are very common in\nmultiagent systems. For example, consider the case of task allocation\nbetween two agents. There is a set of tasks to be carried out and\ndifferent agents have different preferences for the tasks. The tasks\ncannot be partitioned; a task must be carried out by one agent. The\nproblem then is for the agents to negotiate about who will carry out\nwhich task.\nA key problem in the study of multi-issue negotiation is to\ndetermine the equilibrium strategies. An equally important problem,\nespecially in the context of software agents, is to find the time\ncomplexity of computing the equilibrium offers. However, such\ncomputational issues have so far received little attention. As we will\nshow, this is mainly due to the fact that existing work (describe in\nSection 5) has mostly focused on negotiation for divisible issues\n951\n978-81-904262-7-5 (RPS) c 2007 IFAAMAS\nand finding the equilibrium for this case is computationally easier\nthan that for the case of indivisible issues. Our primary objective is,\ntherefore, to answer the computational questions for the latter case\nfor the types of situations that are commonly faced by agents in\nreal-world contexts. Thus, we consider negotiations in which there\nis incomplete information and time constraints. Incompleteness of\ninformation on the part of negotiators is a common feature of most\npractical negotiations. Also, agents typically have time constraints\nin the form of both deadlines and discount factors. Deadlines are an\nessential element since negotiation cannot go on indefinitely, rather\nit must end within a reasonable time limit. Likewise, discount\nfactors are essential since the goods may be perishable or their value\nmay decline due to inflation. Moreover, the strategic behaviour of\nagents with deadlines and discount factors differs from those\nwithout (see [21] for single issue bargaining without deadlines and [23,\n13] for bargaining with deadlines and discount factors in the\ncontext of divisible issues).\nGiven this, we consider indivisible issues and first analyze the\nstrategic behaviour of agents to obtain the equilibrium strategies\nfor the case where all the issues for negotiation are known a priori\nto both agents. For this case, we show that the problem of finding\nthe equilibrium offers is NP-hard, even in a complete information\nsetting. Then, in order to overcome the problem of time\ncomplexity, we present strategies that are approximately optimal but\ncomputationally efficient, and show that they form an equilibrium. We\nalso analyze the relative error (i.e., the difference between the true\noptimum and the approximate). The time complexity of the\napproximate equilibrium strategies is O(nm/ 2\n) where n is the\nnegotiation deadline and the relative error. Finally, we extend the\nanalysis to online negotiation where different issues become\navailable at different time points and the agents are uncertain about their\nvaluations for these issues. Specifically, we show that an\napproximate equilibrium exists for online negotiation and show that the\nexpected difference between the optimum and the approximate is\nO(\n\u221a\nm) . These approximate strategies also have polynomial time\ncomplexity.\nIn so doing, our contribution lies in analyzing the computational\ncomplexity of the above multi-issue negotiation problem, and\nfinding the approximate and online equilibria. No previous work has\ndetermined these equilibria. Since software agents have limited\ncomputational resources, our results are especially relevant to such\nresource bounded agents.\nThe remainder of the paper is organised as follows. We begin by\ngiving a brief overview of single-issue negotiation in Section 2. In\nSection 3, we obtain the equilibrium for multi-issue negotiation and\nshow that finding equilibrium offers is an NP-hard problem. We\nthen present an approximate equilibrium and evaluate its\napproximation error. Section 4 analyzes online multi-issue negotiation.\nSection 5 discusses the related literature and Section 6 concludes.\n2. SINGLE-ISSUE NEGOTIATION\nWe adopt the single issue model of [27] because this is a model\nwhere, during negotiation, the parties are allowed to make offers\nfrom a set of discrete offers. Since our focus is on indivisible issues\n(i.e., parties are allowed to make one of two possible offers: zero\nor one), our scenario fits in well with [27]. Hence we use this basic\nsingle issue model and extend it to multiple issues. Before doing\nso, we give an overview of this model and its equilibrium strategies.\nThere are two strategic agents: a and b. Each agent has time\nconstraints in the form of deadlines and discount factors. The two\nagents negotiate over a single indivisible issue (i). This issue is a\n\u2018pie\" of size 1 and the agents want to determine who gets the pie.\nThere is a deadline (i.e., a number of rounds by which negotiation\nmust end). Let n \u2208 N+\ndenote this deadline. The agents use an\nalternating offers protocol (as the one of Rubinstein [18]), which\nproceeds through a series of time periods. One of the agents, say\na, starts negotiation in the first time period (i.e., t = 1) by making\nan offer (xi = 0 or 1) to b. Agent b can either accept or reject the\noffer. If it accepts, negotiation ends in an agreement with a getting\nxi and b getting yi = 1 \u2212 xi. Otherwise, negotiation proceeds to\nthe next time period, in which agent b makes a counter-offer. This\nprocess of making offers continues until one of the agents either\naccepts an offer or quits negotiation (resulting in a conflict). Thus,\nthere are three possible actions an agent can take during any time\nperiod: accept the last offer, make a new counter-offer, or quit the\nnegotiation.\nAn essential feature of negotiations involving alternating offers\nis that the agents\" utilities decrease with time [21]. Specifically,\nthe decrease occurs at each step of offer and counteroffer. This\ndecrease is represented with a discount factor denoted 0 < \u03b4i \u2264 1\nfor both1\nagents.\nLet [xt\ni, yt\ni ] denote the offer made at time period t where xt\ni and\nyt\ni denote the share for agent a and b respectively. Then, for a given\npie, the set of possible offers is:\n{[xt\ni, yt\ni ] : xt\ni = 0 or 1, yt\ni = 0 or 1, and xt\ni + yt\ni = 1}\nAt time t, if a and b receive a share of xt\ni and yt\ni respectively, then\ntheir utilities are:\nua\ni (xt\ni, t) =\nj\nxt\ni \u00d7 \u03b4t\u22121\nif t \u2264 n\n0 otherwise\nub\ni (yt\ni , t) =\nj\nyt\ni \u00d7 \u03b4t\u22121\nif t \u2264 n\n0 otherwise\nThe conflict utility (i.e., the utility received in the event that no deal\nis struck) is zero for both agents.\nFor the above setting, the agents reason as follows in order to\ndetermine what to offer at t = 1. We let A(1) (B(1)) denote a\"s\n(b\"s) equilibrium offer for the first time period. Let agent a denote\nthe first mover (i.e., at t = 1, a proposes to b who should get the\npie). To begin, consider the case where the deadline for both agents\nis n = 1. If b accepts, the division occurs as agreed; if not, neither\nagent gets anything (since n = 1 is the deadline). Here, a is in a\npowerful position and is able to propose to keep 100 percent of the\npie and give nothing to b 2\n. Since the deadline is n = 1, b accepts\nthis offer and agreement takes place in the first time period.\nNow, consider the case where the deadline is n = 2. In order to\ndecide what to offer in the first round, a looks ahead to t = 2 and\nreasons backwards. Agent a reasons that if negotiation proceeds\nto the second round, b will take 100 percent of the pie by offering\n[0, 1] and leave nothing for a. Thus, in the first time period, if a\noffers b anything less than the whole pie, b will reject the offer.\nHence, during the first time period, agent a offers [0, 1]. Agent b\naccepts this and an agreement occurs in the first time period.\nIn general, if the deadline is n, negotiation proceeds as follows.\nAs before, agent a decides what to offer in the first round by\nlooking ahead as far as t = n and then reasoning backwards. Agent a\"s\n1\nHaving a different discount factor for different agents only makes\nthe presentation more involved without leading to any changes in\nthe analysis of the strategic behaviour of the agents or the time\ncomplexity of finding the equilibrium offers. Hence we have a single\ndiscount factor for both agents.\n2\nIt is possible that b may reject such a proposal. However,\nirrespective of whether b accepts or rejects the proposal, it gets zero utility\n(because the deadline is n = 1). Thus, we assume that b accepts\na\"s offer.\n952 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\noffer for t = 1 depends on who the offering agent is for the last\ntime period. This, in turn, depends on whether n is odd or even.\nSince a makes an offer at t = 1 and the agents use the alternating\noffers protocol, the offering agent for the last time period is b if n\nis even and it is a if n is odd. Thus, depending on whether n is odd\nor even, a makes the following offer at t = 1:\nA(1) =\nj\nOFFER [1, 0] IF ODD n\nACCEPT IF b\"s TURN\nB(1) =\nj\nOFFER [0, 1] IF EVEN n\nACCEPT IF a\"s TURN\nAgent b accepts this offer and negotiation ends in the first time\nperiod. Note that the equilibrium outcome depends on who makes\nthe first move. Since we have two agents and either of them could\nmove first, we get two possible equilibrium outcomes.\nOn the basis of the above equilibrium for single-issue\nnegotiation with complete information, we first obtain the equilibrium for\nmultiple issues and then show that computing these offers is a hard\nproblem. We then present a time efficient approximate equilibrium.\n3. MULTI-ISSUE NEGOTIATION\nWe first analyse the complete information setting. This section\nforms the base which we extend to the case of information\nuncertainty in Section 4.\nHere a and b negotiate over m > 1 indivisible issues. These\nissues are m distinct pies and the agents want to determine how\nto distribute the pies between themselves. Let S = {1, 2, . . . , m}\ndenote the set of m pies. As before, each pie is of size 1. Let the\ndiscount factor for issue c, where 1 \u2264 c \u2264 m, be 0 < \u03b4c \u2264 1.\nFor each issue, let n denote each agent\"s deadline. In the offer for\ntime period t (where 1 \u2264 t \u2264 n), agent a\"s (b\"s) share for each of\nthe m issues is now represented as an m element vector xt\n\u2208 Bm\n(yt\n\u2208 Bm\n) where B denotes the set {0, 1}. Thus, if agent a\"s share\nfor issue c at time t is xt\nc, then agent b\"s share is yt\nc = (1\u2212xt\nc). The\nshares for a and b are together represented as the package [xt\n, yt\n].\nAs is traditional in multi-issue utility theory, we define an agent\"s\ncumulative utility using the standard additive form [12]. The\nfunctions Ua\n: Bm\n\u00d7 Bm\n\u00d7 N+\n\u2192 R and Ub\n: Bm\n\u00d7 Bm\n\u00d7 N+\n\u2192 R\ngive the cumulative utilities for a and b respectively at time t. These\nare defined as follows:\nUa\n([xt\n, yt\n], t) =\n(\n\u03a3m\nc=1ka\nc ua\nc (xt\nc, t) if t \u2264 n\n0 otherwise\n(1)\nUb\n([xt\n, yt\n], t) =\n(\n\u03a3m\nc=1kb\ncub\nc(yt\nc, t) if t \u2264 n\n0 otherwise\n(2)\nwhere ka\n\u2208 Nm\n+ denotes an m element vector of constants for\nagent a and kb\n\u2208 Nm\n+ that for b. Here N+ denotes the set of\npositive integers. These vectors indicate how the agents value different\nissues. For example, if ka\nc > ka\nc+1, then agent a values issue c\nmore than issue c + 1. Likewise for agent b. In other words, the m\nissues are perfect substitutes (i.e., all that matters to an agent is its\ntotal utility for all the m issues and not that for any subset of them).\nIn all the settings we study, the issues will be perfect substitutes.\nTo begin each agent has complete information about all negotiation\nparameters (i.e., n, m, ka\nc , kb\nc, and \u03b4c for 1 \u2264 c \u2264 m).\nNow, multi-issue negotiation can be done using different\nprocedures. Broadly speaking, there are three key procedures for\nnegotiating multiple issues [19]:\n1. the package deal procedure where all the issues are settled\ntogether as a bundle,\n2. the sequential procedure where the issues are discussed one\nafter another, and\n3. the simultaneous procedure where the issues are discussed in\nparallel.\nBetween these three procedures, the package deal is known to\ngenerate Pareto optimal outcomes [19, 6]. Hence we adopt it here. We\nfirst give a brief description of the procedure and then determine\nthe equilibrium strategies for it.\n3.1 The package deal procedure\nIn this procedure, the agents use the same protocol as for\nsingleissue negotiation (described in Section 2). However, an offer for the\npackage deal includes a proposal for each issue under negotiation.\nThus, for m issues, an offer includes m divisions, one for each\nissue. Agents are allowed to either accept a complete offer (i.e., all\nm issues) or reject a complete offer. An agreement can therefore\ntake place either on all m issues or on none of them.\nAs per the single-issue negotiation, an agent decides what to\noffer by looking ahead and reasoning backwards. However, since an\noffer for the package deal includes a share for all the m issues, the\nagents can now make tradeoffs across the issues in order to\nmaximise their cumulative utilities.\nFor 1 \u2264 c \u2264 m, the equilibrium offer for issue c at time t is\ndenoted as [at\nc, bt\nc] where at\nc and bt\nc denote the shares for agent a\nand b respectively. We denote the equilibrium package at time t\nas [at\n, bt\n] where at\n\u2208 Bm\n(bt\n\u2208 Bm\n) is an m element vector\nthat denotes a\"s (b\"s) share for each of the m issues. Also, for\n1 \u2264 c \u2264 m, \u03b4c is the discount factor for issue c. The symbols 0\nand 1 denote m element vectors of zeroes and ones respectively.\nNote that for 1 \u2264 t \u2264 n, at\nc + bt\nc = 1 (i.e., the sum of the agents\"\nshares (at time t) for each pie is one). Finally, for time period t (for\n1 \u2264 t \u2264 n) we let A(t) (respectively B(t)) denote the equilibrium\nstrategy for agent a (respectively b).\n3.2 Equilibrium strategies\nAs mentioned in Section 1, the package deal allows agents to make\ntradeoffs. We let TRADEOFFA (TRADEOFFB) denote agent a\"s (b\"s)\nfunction for making tradeoffs. We let P denote a set of parameters\nto the procedure TRADEOFFA (TRADEOFFB) where P = {ka\n, kb\n, \u03b4, m}.\nGiven this, the following theorem characterises the equilibrium for\nthe package deal procedure.\nTHEOREM 1. For the package deal procedure, the following\nstrategies form a Nash equilibrium. The equilibrium strategy for\nt = n is:\nA(n) =\nj\nOFFER [1, 0] IF a\"s TURN\nACCEPT IF b\"s TURN\nB(n) =\nj\nOFFER [0, 1] IF b\"s TURN\nACCEPT IF a\"s TURN\nFor all preceding time periods t < n, if [xt\n, yt\n] denotes the\noffer made at time t, then the equilibrium strategies are defined as\nfollows:\nA(t) =\n8\n<\n:\nOFFER TRADEOFFA(P, UB(t), t) IF a\"s TURN\nIf (Ua\n([xt\n, yt\n], t) \u2265 UA(t)) ACCEPT\nelse REJECT IF b\"s TURN\nB(t) =\n8\n<\n:\nOFFER TRADEOFFB(P, UA(t), t) IF b\"s TURN\nIf (Ub\n([xt\n, yt\n], t) \u2265 UB(t)) ACCEPT\nelse REJECT IF a\"s TURN\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 953\nwhere UA(t) = Ua\n([at+1\n, bt+1\n], t + 1) and UB(t) = Ub\n([at+1\n,\nbt+1\n], t + 1).\nPROOF. We look ahead to the last time period (i.e., t = n) and\nthen reason backwards. To begin, if negotiation reaches the\ndeadline (n), then the agent whose turn it is takes everything and leaves\nnothing for its opponent. Hence, we get the strategies A(n) and\nB(n) as given in the statement of the theorem.\nIn all the preceding time periods (t < n), the offering agent\nproposes a package that gives its opponent a cumulative utility equal\nto what the opponent would get from its own equilibrium offer for\nthe next time period. During time period t, either a or b could\nbe the offering agent. Consider the case where a makes an offer\nat t. The package that a offers at t gives b a cumulative utility\nof Ub\n([at+1\n, bt+1\n], t + 1). However, since there is more than one\nissue, there is more than one package that gives b this cumulative\nutility. From among these packages, a offers the one that maximises\nits own cumulative utility (because it is a utility maximiser). Thus,\nthe problem for a is to find the package [at\n, bt\n] so as to:\nmaximize\nmX\nc=1\nka\nc (1 \u2212 bt\nc)\u03b4t\u22121\nc (3)\nsuch that\nmX\nc=1\nbt\nckb\nc \u2265 UB(t)\nbt\nc = 0 or 1 for 1 \u2264 c \u2264 m\nwhere UB(t), \u03b4t\u22121\nc , ka\nc , and kb\nc are constants and bt\nc (1 \u2264 c \u2264 m)\nis a variable.\nAssume that the function TRADEOFFA takes parameters P, UB(t),\nand t, to solve the maximisation problem given in Equation 3 and\nreturns the corresponding package. If there is more than one\npackage that solves Equation 3, then TRADEOFFA returns any one of\nthem (because agent a gets equal utility from all such packages\nand so does agent b). The function TRADEOFFB for agent b is\nanalogous to that for a.\nOn the other hand, the equilibrium strategy for the agent that\nreceives an offer is as follows. For time period t, let b denote the\nreceiving agent. Then, b accepts [xt\n, yt\n] if UB(t) \u2264 Ub\n([xt\n, yt\n], t),\notherwise it rejects the offer because it can get a higher utility in\nthe next time period. The equilibrium strategy for a as receiving\nagent is defined analogously.\nIn this way, we reason backwards and obtain the offers for the\nfirst time period. Thus, we get the equilibrium strategies (A(t) and\nB(t)) given in the statement of the theorem.\nThe following example illustrates how the agents make tradeoffs\nusing the above equilibrium strategies.\nEXAMPLE 1. Assume there are m = 2 issues for negotiation,\nthe deadline for both issues is n = 2, and the discount factor for\nboth issues for both agents is \u03b4 = 1/2. Let ka\n1 = 3, ka\n2 = 1,\nkb\n1 = 1, and kb\n2 = 5. Let agent a be the first mover. By\nusing backward reasoning, a knows that if negotiation reaches the\nsecond time period (which is the deadline), then b will get a\nhundred percent of both the issues. This gives b a cumulative utility of\nUB(2) = 1/2 + 5/2 = 3. Thus, in the first time period, if b gets\nanything less than a utility of 3, it will reject a\"s offer. So, at t = 1,\na offers the package where it gets issue 1 and b gets issue 2. This\ngives a cumulative utility of 3 to a and 5 to b. Agent b accepts the\npackage and an agreement takes place in the first time period.\nThe maximization problem in Equation 3 can be viewed as the 0-1\nknapsack problem3\n. In the 0-1 knapsack problem, we have a set\n3\nNote that for the case of divisible issues this is the fractional\nknapof m items where each item has a profit and a weight. There is a\nknapsack with a given capacity. The objective is to fill the knapsack\nwith items so as to maximize the cumulative profit of the items in\nthe knapsack. This problem is analogous to the negotiation problem\nwe want to solve (i.e., the maximization problem of Equation 3).\nSince ka\nc and \u03b4t\u22121\nc are constants, maximizing\nPm\nc=1 ka\nc (1\u2212bt\nc)\u03b4t\u22121\nc\nis the same as minimizing\nPm\nc=1 ka\nc bt\nc. Hence Equation 3 can be\nwritten as:\nminimize\nmX\nc=1\nka\nc bt\nc (4)\nsuch that\nmX\nc=1\nbt\nckb\nc \u2265 UB(t)\nbt\nc = 0 or 1 for 1 \u2264 c \u2264 m\nEquation 4 is a minimization version of the standard 0-1 knapsack\nproblem4\nwith m items where ka\nc represents the profit for item c,\nkb\nc the weight for item c, and UB(t) the knapsack capacity.\nExample 1 was for two issues and so it was easy to find the\nequilibrium offers. But, in general, it is not computationally easy to\nfind the equilibrium offers of Theorem 1. The following theorem\nproves this.\nTHEOREM 2. For the package deal procedure, the problem of\nfinding the equilibrium offers given in Theorem 1 is NP-hard.\nPROOF. Finding the equilibrium offers given in Theorem 1\nrequires solving the 0-1 knapsack problem given in Equation 4. Since\nthe 0-1 knapsack problem is NP-hard [17], the problem of finding\nequilibrium for the package deal is also NP-hard.\n3.3 Approximate equilibrium\nResearchers in the area of algorithms have found time efficient\nmethods for computing approximate solutions to 0-1 knapsack\nproblems [10]. Hence we use these methods to find a solution to our\nnegotiation problem. At this stage, we would like to point out the\nmain difference between solving the 0-1 knapsack problem and\nsolving our negotiation problem. The 0-1 knapsack problem\ninvolves decision making by a single agent regarding which items to\nplace in the knapsack. On the other hand, our negotiation problem\ninvolves two players and they are both strategic. Hence, in our case,\nit is not enough to just find an approximate solution to the knapsack\nproblem, we must also show that such an approximation forms an\nequilibrium.\nThe traditional approach for overcoming the computational\ncomplexity in finding an equilibrium has been to use an approximate\nequilibrium (see [14, 26] for example). In this approach, a strategy\nprofile is said to form an approximate Nash equilibrium if neither\nagent can gain more than the constant by deviating. Hence, our\naim is to use the solution to the 0-1 knapsack problem proposed\nin [10] and show that it forms an approximate equilibrium to our\nnegotiation problem. Before doing so, we give a brief overview of\nthe key ideas that underlie approximation algorithms.\nThere are two key issues in the design of approximate algorithms\n[1]:\nsack problem. The factional knapsack problem is computationally\neasy; it can be solved in time polynomial in the number of items in\nthe knapsack problem [17]. In contrast, the 0-1 knapsack problem\nis computationally hard.\n4\nNote that for the standard 0-1 knapsack problem the weights,\nprofits and the capacity are positive integers. However a 0-1 knapsack\nproblem with fractions and non positive values can easily be\ntransformed to one with positive integers in time linear in m using the\nmethods given in [8, 17].\n954 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\n1. the quality of their solution, and\n2. the time taken to compute the approximation.\nThe quality of an approximate algorithm is determined by\ncomparing its performance to that of the optimal algorithm and measuring\nthe relative error [3, 1]. The relative error is defined as (z\u2212z\u2217\n)/z\u2217\nwhere z is the approximate solution and z\u2217\nthe optimal one. In\ngeneral, we are interested in finding approximate algorithms whose\nrelative error is bounded from above by a certain constant , i.e.,\n(z \u2212 z\u2217\n)/z\u2217\n\u2264 (5)\nRegarding the second issue of time complexity, we are interested in\nfinding fully polynomial approximation algorithms. An\napproximation algorithm is said to be fully polynomial if for any > 0 it finds\na solution satisfying Equation 5 in time polynomially bounded by\nsize of the problem (for the 0-1 knapsack problem, the problem size\nis equal to the number of items) and by 1/ [1].\nFor the 0-1 knapsack problem, Ibarra and Kim [10] presented a\nfully polynomial approximation method. This method is based on\ndynamic programming. It is a parametric method that takes as a\nparameter and for any > 0, finds a heuristic solution z with\nrelative error at most , such that the time and space complexity grow\npolynomially with the number of items m and 1/ . More\nspecifically, the space and time complexity are both O(m/ 2\n) and hence\npolynomial in m and 1/ (see [10] for the detailed approximation\nalgorithm and proof of time and space complexity).\nSince the Ibarra and Kim method is fully polynomial, we use it to\nsolve our negotiation problem. This is done as follows. For agent\na, let APRX-TRADEOFFA(P, UB(t), t, ) denote a procedure that\nreturns an approximate solution to Equation 4 using the Ibarra and\nKim method. The procedure APRX-TRADEOFFB(P, UA(t), t, ) for\nagent b is analogous.\nFor 1 \u2264 c \u2264 m, the approximate equilibrium offer for issue c\nat time t is denoted as [\u00afat\nc,\u00afbt\nc] where \u00afat\nc and \u00afbt\nc denote the shares\nfor agent a and b respectively. We denote the equilibrium package\nat time t as [\u00afat\n,\u00afbt\n] where \u00afat\n\u2208 Bm\n(\u00afbt\n\u2208 Bm\n) is an m element\nvector that denotes a\"s (b\"s) share for each of the m issues. Also,\nas before, for 1 \u2264 c \u2264 m, \u03b4c is the discount factor for issue c.\nNote that for 1 \u2264 t \u2264 n, \u00afat\nc + \u00afbt\nc = 1 (i.e., the sum of the agents\"\nshares (at time t) for each pie is one). Finally, for time period t (for\n1 \u2264 t \u2264 n) we let \u00afA(t) (respectively \u00afB(t)) denote the approximate\nequilibrium strategy for agent a (respectively b).The following\ntheorem uses this notation and characterizes an approximate\nequilibrium for multi-issue negotiation.\nTHEOREM 3. For the package deal procedure, the following\nstrategies form an approximate Nash equilibrium. The\nequilibrium strategy for t = n is:\n\u00afA(n) =\nj\nOFFER [1, 0] IF a\"s TURN\nACCEPT IF b\"s TURN\n\u00afB(n) =\nj\nOFFER [0, 1] IF b\"s TURN\nACCEPT IF a\"s TURN\nFor all preceding time periods t < n, if [xt\n, yt\n] denotes the\noffer made at time t, then the equilibrium strategies are defined as\nfollows:\n\u00afA(t) =\n8\n<\n:\nOFFER APRX-TRADEOFFA(P, UB(t), t, ) IF a\"s TURN\nIf (Ua\n([xt\n, yt\n], t) \u2265 UA(t)) ACCEPT\nelse REJECT IF b\"s TURN\n\u00afB(t) =\n8\n<\n:\nOFFER APRX-TRADEOFFB(P, UA(t), t, ) IF b\"s TURN\nIf (Ub\n([xt\n, yt\n], t) \u2265 UB(t)) ACCEPT\nelse REJECT IF a\"s TURN\nwhere UA(t) = Ua\n([\u00afat+1\n,\u00afbt+1\n], t + 1) and UB(t) = Ub\n([\u00afat+1\n,\n\u00afbt+1\n], t + 1). An agreement takes place at t = 1.\nPROOF. As in the proof for Theorem 1, we use backward\nreasoning. We first obtain the strategies for the last time period t = n.\nIt is straightforward to get these strategies; the offering agent gets\na hundred percent of all the issues.\nThen for t = n \u2212 1, the offering agent must solve the\nmaximization problem of Equation 4 by substituting t = n\u22121 in it. For agent\na (b), this is done by APPROX-TRADEOFFA (APPROX-TRADEOFFB).\nThese two functions are nothing but the Ibarra and Kim\"s\napproximation method for solving the 0-1 knapsack problem. These two\nfunctions take as a parameter and use the Ibarra and Kim\"s\napproximation method to return a package that approximately\nmaximizes Equation 4. Thus, the relative error for these two functions\nis the same as that for Ibarra and Kim\"s method (i.e., it is at most\nwhere is given in Equation 5).\nAssume that a is the offering agent for t = n \u2212 1. Agent a must\noffer a package that gives b a cumulative utility equal to what it\nwould get from its own approximate equilibrium offer for the next\ntime period (i.e., Ub\n([\u00afat+1\n,\u00afbt+1\n], t + 1) where [\u00afat+1\n,\u00afbt+1\n] is the\napproximate equilibrium package for the next time period). Recall\nthat for the last time period, the offering agent gets a hundred\npercent of all the issues. Since a is the offering agent for t = n \u2212 1\nand the agents use the alternating offers protocol, it is b\"s turn at\nt = n. Thus Ub\n([\u00afat+1\n,\u00afbt+1\n], t + 1) is equal to b\"s cumulative\nutility from receiving a hundred percent of all the issues. Using this\nutility as the capacity of the knapsack, a uses APPROX-TRADEOFFA\nand obtains the approximate equilibrium package for t = n \u2212 1.\nOn the other hand, if b is the offering agent at t = n \u2212 1, it uses\nAPPROX-TRADEOFFB to obtain the approximate equilibrium\npackage.\nIn the same way for t < n \u2212 1, the offering agent (say a) uses\nAPPROX-TRADEOFFA to find an approximate equilibrium package\nthat gives b a utility of Ub\n([\u00afat+1\n,\u00afbt+1\n], t + 1). By reasoning\nbackwards, we obtain the offer for time period t = 1. If a (b) is the\noffering agent, it proposes the offer APPROX-TRADEOFFA(P, UB(1), 1, )\n(APPROX-TRADEOFFB(P, UA(1), 1, )). The receiving agent\naccepts the offer. This is because the relative error in its cumulative\nutility from the offer is at most . An agreement therefore takes\nplace in the first time period.\nTHEOREM 4. The time complexity of finding the approximate\nequilibrium offer for the first time period is O(nm/ 2\n).\nPROOF. The time complexity of APPROX-TRADEOFFA and\nAPPROXTRADEOFFB is the same as the time complexity of the Ibarra and\nKim method [10] i.e., O(m/ 2\n)). In order to find the equilibrium\noffer for the first time period using backward reasoning,\nAPPROXTRADEOFFA (or APPROX- TRADEOFFB) is invoked n times. Hence\nthe time complexity of finding the approximate equilibrium offer\nfor the first time period is O(nm/ 2\n).\nThis analysis was done in a complete information setting.\nHowever an extension of this analysis to an incomplete information\nsetting where the agents have probability distributions over some\nuncertain parameter is straightforward, as long as the negotiation is\ndone offline; i.e., the agents know their preference for each\nindividual issue before negotiation begins. For instance, consider the case\nwhere different agents have different discount factors, and each\nagent is uncertain about its opponent\"s discount factor although it\nknows its own. This uncertainty is modelled with a probability\ndistribution over the possible values for the opponent\"s discount factor\nand having this distribution as common knowledge to the agents.\nAll our analysis for the complete information setting still holds for\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 955\nthis incomplete information setting, except for the fact that an agent\nmust now use the given probability distribution and find its\nopponent\"s expected utility instead of its actual utility. Hence, instead of\nanalyzing an incomplete information setting for offline negotiation,\nwe focus on online multi-issue negotiation.\n4. ONLINE MULTI-ISSUE NEGOTIATION\nWe now consider a more general and, arguably more realistic,\nversion of multi-issue negotiation, where the agents are uncertain about\nthe issues they will have to negotiate about in future. In this setting,\nwhen negotiating an issue, the agents know that they will negotiate\nmore issues in the future, but they are uncertain about the details of\nthose issues. As before, let m be the total number of issues that are\nup for negotiation. The agents have a probability distribution over\nthe possible values of ka\nc and kb\nc. For 1 \u2264 c \u2264 m let ka\nc and kb\nc be\nuniformly distributed over [0,1]. This probability distribution, n,\nand m are common knowledge to the agents. However, the agents\ncome to know ka\nc and kb\nc only just before negotiation for issue c\nbegins. Once the agents reach an agreement on issue c, it cannot be\nre-negotiated.\nThis scenario requires online negotiation since the agents must\nmake decisions about an issue prior to having the information about\nthe future issues [3]. We first give a brief introduction to online\nproblems and then draw an analogy between the online knapsack\nproblem and the negotiation problem we want to solve.\nIn an online problem, data is given to the algorithm\nincrementally, one unit at a time [3]. The online algorithm must also\nproduce the output incrementally: after seeing i units of input it must\noutput the ith unit of output. Since decisions about the output are\nmade with incomplete knowledge about the entire input, an\nonline algorithm often cannot produce an optimal solution. Such an\nalgorithm can only approximate the performance of the optimal\nalgorithm that sees all the inputs in advance. In the design of online\nalgorithms, the main aim is to achieve a performance that is close\nto that of the optimal offline algorithm on each input. An online\nalgorithm is said to be stochastic if it makes decisions on the basis of\nthe probability distributions for the future inputs. The performance\nof stochastic online algorithms is assessed in terms of the expected\ndifference between the optimum and the approximate solution\n(denoted E[z\u2217\nm \u2212zm] where z\u2217\nm is the optimal and zm the approximate\nsolution). Note that the subscript m is used to indicate the fact that\nthis difference depends on m.\nWe now describe the protocol for online negotiation and then\nobtain an approximate equilibrium. The protocol is defined as\nfollows. Let agent a denote the first mover (since we focus on the\npackage deal procedure, the first mover is the same for all the m\nissues).\nStep 1. For c = 1, the agents are given the values of ka\nc and kb\nc.\nThese two values are now common5\nknowledge.\nStep 2. The agents settle issue c using the alternating offers\nprotocol described in Section 2. Negotiation for issue c must end\nwithin n time periods from the start of negotiation on the\nissue. If an agreement is not reached within this time, then\nnegotiation fails on this and on all remaining issues.\nStep 3. The above steps are repeated for issues c = 2, 3, . . . , m.\nNegotiation for issue c (2 \u2264 c \u2264 m) begins in the time\nperiod following an agreement on issue c \u2212 1.\n5\nWe assume common knowledge because it simplifies exposition.\nHowever, if ka\nc (kb\nc) is a\"s (b\"s) private knowledge, then our analysis\nwill still hold but now an agent must find its opponent\"s expected\nutility on the basis of the p.d.fs for ka\nc and kb\nc.\nThus, during time period t, the problem for the offering agent (say\na) is to find the optimal offer for issue c on the basis of ka\nc and\nkb\nc and the probability distribution for ka\ni and kb\ni (c < i \u2264 m).\nIn order to solve this online negotiation problem we draw analogy\nwith the online knapsack problem. Before doing so, however, we\ngive a brief overview of the online knapsack problem.\nIn the online knapsack problem, there are m items. The agent\nmust examine the m items one at a time according to the order they\nare input (i.e., as their profit and size coefficients become known).\nHence, the algorithm is required to decide whether or not to\ninclude each item in the knapsack as soon as its weight and profit\nbecome known, without knowledge concerning the items still to be\nseen, except for their total number. Note that since the agents have\na probability distribution over the weights and profits of the future\nitems, this is a case of stochastic online knapsack problem. Our\nonline negotiation problem is analogous to the online knapsack\nproblem. This analogy is described in detail in the proof for Theorem 5.\nAgain, researchers in algorithms have developed time efficient\napproximate solutions to the online knapsack problem [16]. Hence\nwe use this solution and show that it forms an equilibrium.\nThe following theorem characterizes an approximate equilibrium\nfor online negotiation. Here the agents have to choose a\nstrategy without knowing the features of the future issues. Because of\nthis information incompleteness, the relevant equilibrium solution\nis that of a Bayes\" Nash Equilibrium (BNE) in which each agent\nplays the best response to the other agents with respect to their\nexpected utilities [18]. However, finding an agent\"s BNE strategy is\nanalogous to solving the online 0-1 knapsack problem. Also, the\nonline knapsack can only be solved approximately [16]. Hence\nthe relevant equilibrium solution concept is approximate BNE (see\n[26] for example). The following theorem finds this equilibrium\nusing procedures ONLINE- TRADEOFFA and ONLINE-TRADEOFFB\nwhich are defined in the proof of the theorem. For a given time\nperiod, we let zm denote the approximately optimal solution\ngenerated by ONLINE-TRADEOFFA (or ONLINE-TRADEOFFB) and z\u2217\nm\nthe actual optimum.\nTHEOREM 5. For the package deal procedure, the following\nstrategies form an approximate Bayes\" Nash equilibrium. The\nequilibrium strategy for t = n is:\nA(n) =\nj\nOFFER [1, 0] IF a\"s TURN\nACCEPT IF b\"s TURN\nB(n) =\nj\nOFFER [0, 1] IF b\"s TURN\nACCEPT IF a\"s TURN\nFor all preceding time periods t < n, if [xt\n, yt\n] denotes the\noffer made at time t, then the equilibrium strategies are defined as\nfollows:\nA(t) =\n8\n<\n:\nOFFER ONLINE-TRADEOFFA(P, UB(t), t) IF a\"s TURN\nIf (Ua\n([xt\n, yt\n], t) \u2265 UA(t)) ACCEPT\nelse REJECT IF b\"s TURN\nB(t) =\n8\n<\n:\nOFFER ONLINE-TRADEOFFB(P, UA(t), t) IF b\"s TURN\nIf (Ub\n([xt\n, yt\n], t) \u2265 UB(t)) ACCEPT\nelse REJECT IF a\"s TURN\nwhere UA(t) = Ua\n([\u00afat+1\n,\u00afbt+1\n], t + 1) and UB(t) = Ub\n([\u00afat+1\n,\n\u00afbt+1\n], t + 1). An agreement on issue c takes place at t = c. For a\ngiven time period, the expected difference between the solution\ngenerated by the optimal strategy and that by the approximate strategy\nis E[z\u2217\nm \u2212 zm] = O(\n\u221a\nm).\n956 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nPROOF. As in Theorem 1 we find the equilibrium offer for time\nperiod t = 1 using backward induction. Let a be the offering agent\nfor t = 1 for all the m issues. Consider the last time period t = n\n(recall from Step 2 of the online protocol that n is the deadline for\ncompleting negotiation on the first issue). Since the first mover is\nthe same for all the issues, and the agents make offers alternately,\nthe offering agent for t = n is also the same for all the m issues.\nAssume that b is the offering agent for t = n. As in Section 3,\nthe offering agent for t = n gets a hundred percent of all the m\nissues. Since b is the offering agent for t = n, his utility for this\ntime period is:\nUB(n) = kb\n1\u03b4n\u22121\n1 + 1/2\nmX\ni=2\n\u03b4\ni(n\u22121)\ni (6)\nRecall that ka\ni and kb\ni (for c < i \u2264 m) are not known to the\nagents. Hence, the agents can only find their expected utilities from\nthe future issues on the basis of the probability distribution\nfunctions for ka\ni and kb\ni . However, during the negotiation for issue c\nthe agents know ka\nc but not kb\nc (see Step 1 of the online protocol).\nHence, a computes UB(n) as follows. Agent b\"s utility from issue\nc = 1 is kb\n1\u03b4n\u22121\n1 (which is the first term of Equation 6). Then,\non the basis of the probability distribution functions for ka\ni and\nkb\ni , agent a computes b\"s expected utility from each future issue i\nas \u03b4\ni(n\u22121)\ni /2 (since ka\ni and kb\ni are uniformly distributed on [0, 1]).\nThus, b\"s expected cumulative utility from these m \u2212 c issues is\n1/2\nPm\ni=2 \u03b4\ni(n\u22121)\ni (which is the second term of Equation 6).\nNow, in order to decide what to offer for issue c = 1, the offering\nagent for t = n \u2212 1 (i.e., agent a) must solve the following online\nknapsack problem:\nmaximize \u03a3m\ni=1ka\ni (1 \u2212 \u00afbt\ni)\u03b4n\u22121\ni (7)\nsuch that \u03a3m\ni=1kb\ni\n\u00afbt\ni \u2265 UB(n)\n\u00afbt\ni = 0 or 1 for 1 \u2264 i \u2264 m\nThe only variables in the above maximization problem are \u00afbt\ni. Now,\nmaximizing \u03a3m\ni=1ka\ni (1\u2212\u00afbt\ni)\u03b4n\u22121\ni is the same as minimizing \u03a3m\ni=1ka\ni\n\u00afbt\ni\nsince \u03b4n\u22121\ni and ka\ni are constants. Thus, we write Equation 7 as:\nminimize \u03a3m\ni=1ka\ni\n\u00afbt\ni (8)\nsuch that \u03a3m\ni=1kb\ni\n\u00afbt\ni \u2265 UB(n)\n\u00afbt\ni = 0 or 1 for 1 \u2264 i \u2264 m\nThe above optimization problem is analogous to the online 0-1\nknapsack problem. An algorithm to solve the online knapsack\nproblem has already proposed in [16]. This algorithm is called the\nfixed-choice online algorithm. It has time complexity linear in the\nnumber of items (m) in the knapsack problem. We use this to solve\nour online negotiation problem. Thus, our ONLINE-TRADEOFFA\nalgorithm is nothing but the fixed-choice online algorithm and\ntherefore has the same time complexity as the latter. This algorithm takes\nthe values of ka\ni and kb\ni one at a time and generates an approximate\nsolution to the above knapsack problem. The expected difference\nbetween the optimum and approximate solution is E[z\u2217\nm \u2212 zm] =\nO(\n\u221a\nm) [16] (see [16] for the detailed fixed-choice online\nalgorithm and a proof for E[z\u2217\nm \u2212 zm] = O(\n\u221a\nm)).\nThe fixed-choice online algorithm of [16] is a generalization of\nthe basic greedy algorithm for the offline knapsack problem; the\nidea behind it is as follows. A threshold value is determined on the\nbasis of the information regarding weights and profits for the 0-1\nknapsack problem. The method then includes into the knapsack all\nitems whose profit density (profit density of an item is its profit per\nunit weight) exceeds the threshold until either the knapsack is filled\nor all the m items have been considered.\nIn more detail, the algorithm ONLINE-TRADEOFFA works as\nfollows. It first gets the values of ka\n1 and kb\n1 and finds \u00afbt\nc. Since we\nhave a 0-1 knapsack problem, \u00afbt\nc can be either zero or one. Now, if\n\u00afbt\nc = 1 for t = n, then \u00afbt\nc must be one for 1 \u2264 t < n (i.e., a must\noffer \u00afbt\nc = 1 at t = 1). If \u00afbt\nc = 1 for t = n, but a offers \u00afbt\nc = 0\nat t = 1, then agent b gets less utility than what it expects from a\"s\noffer and rejects the proposal. Thus, if \u00afbt\nc = 1 for t = n, then the\noptimal strategy for a is to offer \u00afbt\nc = 1 at t = 1. Agent b accepts\nthe offer. Thus, negotiation on the first issue starts at t = 1 and an\nagreement on it is also reached at t = 1.\nIn the next time period (i.e., t = 2), negotiation proceeds to the\nnext issue. The deadline for the second issue is n time periods from\nthe start of negotiation on the issue. For c = 2, the algorithm\nONLINE-TRADEOFFA is given the values of ka\n2 and kb\n2 and finds \u00afbt\nc\nas described above. Agent offers bc at t = 2 and b accepts. Thus,\nnegotiation on the second issue starts at t = 2 and an agreement\non it is also reached at t = 2.\nThis process repeats for the remaining issues c = 3, . . . , m.\nThus, each issue is agreed upon in the same time period in which\nit starts. As negotiation for the next issue starts in the following\ntime period (see step 3 of the online protocol), agreement on issue\ni occurs at time t = i.\nOn the other hand, if b is the offering agent at t = 1, he uses\nthe algorithm ONLINE-TRADEOFFB which is defined analogously.\nThus, irrespective of who makes the first move, all the m issues are\nsettled at time t = m.\nTHEOREM 6. The time complexity of finding the approximate\nequilibrium offers of Theorem 5 is linear in m.\nPROOF. The time complexity of ONLINE-TRADEOFFA and\nONLINETRADEOFFB is the same as the time complexity of the fixed-choice\nonline algorithm of [16]. Since the latter has time complexity linear\nin m, the time complexity of ONLINE-TRADEOFFA and\nONLINETRADEOFFB is also linear in m.\nIt is worth noting that, for the 0-1 knapsack problem, the lower\nbound on the expected difference between the optimum and the\nsolution found by any online algorithm is \u03a9(1) [16]. Thus, it follows\nthat this lower bound also holds for our negotiation problem.\n5. RELATED WORK\nWork on multi-issue negotiation can be divided into two main types:\nthat for indivisible issues and that for divisible issues. We first\ndescribe the existing work for the case of divisible issues. Since\nSchelling [24] first noted that the outcome of negotiation depends\non the choice of negotiation procedure, much research effort has\nbeen devoted to the study of different procedures for negotiating\nmultiple issues. However, most of this work has focussed on the\nsequential procedure [7, 2]. For this procedure, a key issue is the\nnegotiation agenda. Here the term agenda refers to the order in which\nthe issues are negotiated. The agenda is important because each\nagent\"s cumulative utility depends on the agenda; if we change the\nagenda then these utilities change. Hence, the agents must decide\nwhat agenda they will use. Now, the agenda can be decided before\nnegotiating the issues (such an agenda is called exogenous) or it\nmay be decided during the process of negotiation (such an agenda\nis called endogenous). For instance, Fershtman [7] analyze\nsequential negotiation with exogenous agenda. A number of researchers\nhave also studied negotiations with an endogenous agenda [2].\nIn contrast to the above work that mainly deals with sequential\nnegotiation, [6] studies the equilibrium for the package deal\nprocedure. However, all the above mentioned work differs from ours in\nthat we focus on indivisible issues while others focus on the case\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 957\nwhere each issue is divisible. Specifically, no previous work has\ndetermined an approximate equilibrium for multi-issue negotiation\nor for online negotiation.\nExisting work for the case of indivisible issues has mostly dealt\nwith task allocation problems (for tasks that cannot be partioned)\nto a group of agents. The problem of task allocation has been\npreviously studied in the context of coalitions involving more than\ntwo agents. For example [25] analyze the problem for the case\nwhere the agents act so as to maximize the benefit of the system\nas a whole. In contrast, our focus is on two agents where both of\nthem are self-interested and want to maximize their individual\nutilities. On the other hand [22] focus on the use of contracts for task\nallocation to multiple self interested agents but this work concerns\nfinding ways of decommitting contracts (after the initial allocation\nhas been done) so as to improve an agent\"s utility. In contrast, our\nfocuses on negotiation regarding who will carry out which task.\nFinally, online and approximate mechanisms have been studied\nin the context of auctions [14, 9] but not for bilateral negotiations\n(which is the focus of our work).\n6. CONCLUSIONS\nThis paper has studied bilateral multi-issue negotiation between\nself-interested autonomous agents with time constraints. The issues\nare indivisible and different agents value different issues\ndifferently. Thus, the problem is for the agents to decide how to allocate\nthe issues between themselves so as to maximize their individual\nutilities. Specifically, we first showed that finding the equilibrium\noffers is an NP-hard problem even in a complete information\nsetting. We then presented approximately optimal negotiation\nstrategies and showed that they form an equilibrium. These strategies\nhave polynomial time complexity. We also analysed the difference\nbetween the true optimum and the approximate optimum. Finally,\nwe extended the analysis to online negotiation where the issues\nbecome available at different time points and the agents are uncertain\nabout the features of these issues. Specifically, we showed that an\napproximate equilibrium exists for online negotiation and analysed\nthe approximation error. These approximate strategies also have\npolynomial time complexity.\nThere are several interesting directions for future work. First,\nfor online negotiation, we assumed that the constants ka\nc and kb\nc are\nboth uniformly distributed. It will be interesting to analyze the case\nwhere ka\nc and kb\nc have other, possibly different, probability\ndistributions. Apart from this, we treated the number of issues as being\ncommon knowledge to the agents. In future, it will be interesting\nto treat the number of issues as uncertain.\n7. REFERENCES\n[1] G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann,\nA. Marchetti-Spaccamela, and M. Protasi. Complexity and\napproximation: Combinatorial optimization problems and\ntheir approximability properties. Springer, 2003.\n[2] M. Bac and H. Raff. Issue-by-issue negotiations: the role of\ninformation and time preference. Games and Economic\nBehavior, 13:125-134, 1996.\n[3] A. Borodin and R. El-Yaniv. Online Computation and\nCompetitive Analysis. Cambridge University Press, 1998.\n[4] S. J. Brams. Fair division: from cake cutting to dispute\nresolution. Cambridge University Press, 1996.\n[5] L. A. Busch and I. J. Horstman. Bargaining frictions,\nbargaining procedures and implied costs in multiple-issue\nbargaining. Economica, 64:669-680, 1997.\n[6] S. S. Fatima, M. Wooldridge, and N. R. Jennings.\nMulti-issue negotiation with deadlines. Journal of Artificial\nIntelligence Research, 27:381-417, 2006.\n[7] C. Fershtman. The importance of the agenda in bargaining.\nGames and Economic Behavior, 2:224-238, 1990.\n[8] F. Glover. A multiphase dual algorithm for the zero-one\ninteger programming problem. Operations Research,\n13:879-919, 1965.\n[9] M. T. Hajiaghayi, R. Kleinberg, and D. C. Parkes. Adaptive\nlimited-supply online auctions. In ACM Conference on\nElectronic Commerce (ACMEC-04), pages 71-80, New\nYork, 2004.\n[10] O. H. Ibarra and C. E. Kim. Fast approximation algorithms\nfor the knapsack and sum of subset problems. Journal of\nACM, 22:463-468, 1975.\n[11] R. Inderst. Multi-issue bargaining with endogenous agenda.\nGames and Economic Behavior, 30:64-82, 2000.\n[12] R. Keeney and H. Raiffa. Decisions with Multiple\nObjectives: Preferences and Value Trade-offs. New York:\nJohn Wiley, 1976.\n[13] S. Kraus. Strategic negotiation in multi-agent environments.\nThe MIT Press, Cambridge, Massachusetts, 2001.\n[14] D. Lehman, L. I. O\"Callaghan, and Y. Shoham. Truth\nrevelation in approximately efficient combinatorial auctions.\nJournal of the ACM, 49(5):577-602, 2002.\n[15] A. Lomuscio, M. Wooldridge, and N. R. Jennings. A\nclassification scheme for negotiation in electronic commerce.\nInternational Journal of Group Decision and Negotiation,\n12(1):31-56, 2003.\n[16] A. Marchetti-Spaccamela and C. Vercellis. Stochastic online\nknapsack problems. Mathematical Programming,\n68:73-104, 1995.\n[17] S. Martello and P. Toth. Knapsack problems: Algorithms and\ncomputer implementations. John Wiley and Sons, 1990.\n[18] M. J. Osborne and A. Rubinstein. A Course in Game Theory.\nThe MIT Press, 1994.\n[19] H. Raiffa. The Art and Science of Negotiation. Harvard\nUniversity Press, Cambridge, USA, 1982.\n[20] J. S. Rosenschein and G. Zlotkin. Rules of Encounter. MIT\nPress, 1994.\n[21] A. Rubinstein. Perfect equilibrium in a bargaining model.\nEconometrica, 50(1):97-109, January 1982.\n[22] T. Sandholm and V. Lesser. Levelled commitment contracts\nand strategic breach. Games and Economic Behavior:\nSpecial Issue on AI and Economics, 35:212-270, 2001.\n[23] T. Sandholm and N. Vulkan. Bargaining with deadlines. In\nAAAI-99, pages 44-51, Orlando, FL, 1999.\n[24] T. C. Schelling. An essay on bargaining. American Economic\nReview, 46:281-306, 1956.\n[25] O. Shehory and S. Kraus. Methods for task allocation via\nagent coalition formation. Artificial Intelligence Journal,\n101(1-2):165-200, 1998.\n[26] S. Singh, V. Soni, and M. Wellman. Computing approximate\nBayes Nash equilibria in tree games of incomplete\ninformation. In Proceedings of the ACM Conference on\nElectronic Commerce ACM-EC, pages 81-90, New York,\nMay 2004.\n[27] I. Stahl. Bargaining Theory. Economics Research Institute,\nStockholm School of Economics, Stockholm, 1972.\n958 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)", "keywords": "gain from cooperation;disputing agent;protocol;approximation;relative error;online computation;indivisible issue;game-theory;equilibrium;negotiation;strategy;key form of interaction;multiagent system;time constraint;interaction key form"}
{"name": "train_I-55", "title": "Searching for Joint Gains in Automated Negotiations Based on Multi-criteria Decision Making Theory", "abstract": "It is well established by conflict theorists and others that successful negotiation should incorporate creating value as well as claiming value. Joint improvements that bring benefits to all parties can be realised by (i) identifying attributes that are not of direct conflict between the parties, (ii) tradeoffs on attributes that are valued differently by different parties, and (iii) searching for values within attributes that could bring more gains to one party while not incurring too much loss on the other party. In this paper we propose an approach for maximising joint gains in automated negotiations by formulating the negotiation problem as a multi-criteria decision making problem and taking advantage of several optimisation techniques introduced by operations researchers and conflict theorists. We use a mediator to protect the negotiating parties from unnecessary disclosure of information to their opponent, while also allowing an objective calculation of maximum joint gains. We separate out attributes that take a finite set of values (simple attributes) from those with continuous values, and we show that for simple attributes, the mediator can determine the Pareto-optimal values. In addition we show that if none of the simple attributes strongly dominates the other simple attributes, then truth telling is an equilibrium strategy for negotiators during the optimisation of simple attributes. We also describe an approach for improving joint gains on non-simple attributes, by moving the parties in a series of steps, towards the Pareto-optimal frontier.", "fulltext": "1. INTRODUCTION\nGiven that negotiation is perhaps one of the oldest activities in\nthe history of human communication, it\"s perhaps surprising that\nconducted experiments on negotiations have shown that negotiators\nmore often than not reach inefficient compromises [1, 21]. Raiffa\n[17] and Sebenius [20] provide analyses on the negotiators\" failure\nto achieve efficient agreements in practice and their unwillingness\nto disclose private information due to strategic reasons. According\nto conflict theorists Lax and Sebenius [13], most negotiation\nactually involves both integrative and distributive bargaining which\nthey refer to as creating value and claiming value. They argue\nthat negotiation necessarily includes both cooperative and\ncompetitive elements, and that these elements exist in tension. Negotiators\nface a dilemma in deciding whether to pursue a cooperative or a\ncompetitive strategy at a particular time during a negotiation. They\nrefer to this problem as the Negotiator\"s Dilemma.\nWe argue that the Negotiator\"s Dilemma is essentially\ninformationbased, due to the private information held by the agents. Such\nprivate information contains both the information that implies the\nagent\"s bottom lines (or, her walk-away positions) and the\ninformation that enforces her bargaining strength. For instance, when\nbargaining to sell a house to a potential buyer, the seller would\ntry to hide her actual reserve price as much as possible for she\nhopes to reach an agreement at a much higher price than her\nreserve price. On the other hand, the outside options available to her\n(e.g. other buyers who have expressed genuine interest with fairly\ngood offers) consist in the information that improves her\nbargaining strength about which she would like to convey to her opponent.\nBut at the same time, her opponent is well aware of the fact that it\nis her incentive to boost her bargaining strength and thus will not\naccept every information she sends out unless it is substantiated by\nevidence.\nComing back to the Negotiator\"s Dilemma, it\"s not always\npossible to separate the integrative bargaining process from the\ndistributive bargaining process. In fact, more often than not, the two\nprocesses interplay with each other making information manipulation\nbecome part of the integrative bargaining process. This is because a\nnegotiator could use the information about his opponent\"s interests\nagainst her during the distributive negotiation process. That is, a\nnegotiator may refuse to concede on an important conflicting issue\nby claiming that he has made a major concession (on another\nissue) to meet his opponent\"s interests even though the concession he\nmade could be insignificant to him. For instance, few buyers would\nstart a bargaining with a dealer over a deal for a notebook computer\nby declaring that he is most interested in an extended warranty for\nthe item and therefore prepared to pay a high price to get such an\nextended warranty.\nNegotiation Support Systems (NSSs) and negotiating software\n508\n978-81-904262-7-5 (RPS) c 2007 IFAAMAS\nagents (NSAs) have been introduced either to assist humans in\nmaking decisions or to enable automated negotiation to allow\ncomputer processes to engage in meaningful negotiation to reach\nagreements (see, for instance, [14, 15, 19, 6, 5]). However, because of\nthe Negotiator\"s Dilemma and given even bargaining power and\nincomplete information, the following two undesirable situations\noften arise: (i) negotiators reach inefficient compromises, or (ii)\nnegotiators engage in a deadlock situation in which both\nnegotiators refuse to act upon with incomplete information and at the same\ntime do not want to disclose more information.\nIn this paper, we argue for the role of a mediator to resolve the\nabove two issues. The mediator thus plays two roles in a\nnegotiation: (i) to encourage cooperative behaviour among the negotiators,\nand (ii) to absorb the information disclosure by the negotiators to\nprevent negotiators from using uncertainty and private information\nas a strategic device. To take advantage of existing results in\nnegotiation analysis and operations research (OR) literatures [18], we\nemploy multi-criteria decision making (MCDM) theory to allow\nthe negotiation problem to be represented and analysed. Section 2\nprovides background on MCDM theory and the negotiation\nframework. Section 3 formulates the problem. In Section 4, we discuss\nour approach to integrative negotiation. Section 5 discusses the\nfuture work with some concluding remarks.\n2. BACKGROUND\n2.1 Multi-criteria decision making theory\nLet A denote the set of feasible alternatives available to a\ndecision maker M. As an act, or decision, a in A may involve\nmultiple aspects, we usually describe the alternatives a with a set of\nattributes j; (j = 1, . . . , m). (Attributes are also referred to as\nissues, or decision variables.) A typical decision maker also has\nseveral objectives X1, . . . , Xk. We assume that Xi, (i = 1, . . . , k),\nmaps the alternatives to real numbers. Thus, a tuple (x1, . . . , xk) =\n(X1(a), . . . , Xk(a)) denotes the consequence of the act a to the\ndecision maker M. By definition, objectives are statements that\ndelineate the desires of a decision maker. Thus, M wishes to\nmaximise his objectives. However, as discussed thoroughly by Keeney\nand Raiffa [8], it is quite likely that a decision maker\"s objectives\nwill conflict with each other in that the improved achievement with\none objective can only be accomplished at the expense of another.\nFor instance, most businesses and public services have objectives\nlike minimise cost and maximise the quality of services. Since\nbetter services can often only be attained for a price, these\nobjectives conflict.\nDue to the conflicting nature of a decision maker\"s objectives, M\nusually has to settle at a compromise solution. That is, he may have\nto choose an act a \u2208 A that does not optimise every objective. This\nis the topic of the multi-criteria decision making theory. Part of the\nsolution to this problem is that M has to try to identify the Pareto\nfrontier in the consequence space {(X1(a), . . . , Xk(a))}a\u2208A.\nDEFINITION 1. (Dominant)\nLet x = (x1, . . . , xk) and x = (x1, . . . , xk) be two\nconsequences. x dominates x iff xi > xi for all i, and the inequality is\nstrict for at least one i.\nThe Pareto frontier in a consequence space then consists of all\nconsequences that are not dominated by any other consequence.\nThis is illustrated in Fig. 1 in which an alternative consists of two\nattributes d1 and d2 and the decision maker tries to maximise the\ntwo objectives X1 and X2. A decision a \u2208 A whose consequence\ndoes not lie on the Pareto frontier is inefficient. While the Pareto\n1x\nd2\na (X (a),X (a))\nd1\n1\nx2\n2\nAlternative spaceA\nPareto frontier\nConsequence space\noptimal consequenc\nFigure 1: The Pareto frontier\nfrontier allows M to avoid taking inefficient decisions, M still has\nto decide which of the efficient consequences on the Pareto frontier\nis most preferred by him.\nMCDM theorists introduce a mechanism to allow the objective\ncomponents of consequences to be normalised to the payoff\nvaluations for the objectives. Consequences can then be ordered: if the\ngains in satisfaction brought about by C1 (in comparison to C2)\nequals to the losses in satisfaction brought about by C1 (in\ncomparison to C2), then the two consequences C1 and C2 are considered\nindifferent. M can now construct the set of indifference curves1\nin\nthe consequence space (the dashed curves in Fig. 1). The most\npreferred indifference curve that intersects with the Pareto frontier is\nin focus: its intersection with the Pareto frontier is the sought after\nconsequence (i.e., the optimal consequence in Fig. 1).\n2.2 A negotiation framework\nA multi-agent negotiation framework consists of:\n1. A set of two negotiating agents N = {1, 2}.\n2. A set of attributes Att = {\u03b11, . . . , \u03b1m} characterising the\nissues the agents are negotiating over. Each attribute \u03b1 can take a\nvalue from the set V al\u03b1;\n3. A set of alternative outcomes O. An outcome o \u2208 O is\nrepresented by an assignment of values to the corresponding attributes\nin Att.\n4. Agents\" utility: Based on the theory of multiple-criteria decision\nmaking [8], we define the agents\" utility as follows:\n\u2022 Objectives: Agent i has a set of ni objectives, or interests;\ndenoted by j (j = 1, . . . , ni). To measure how much an\noutcome o fulfills an objective j to an agent i, we use objective\nfunctions: for each agent i, we define i\"s interests using the\nobjective vector function fi = [fij ] : O \u2192 Rni\n.\n\u2022 Value functions: Instead of directly evaluating an outcome o,\nagent i looks at how much his objectives are fulfilled and will\nmake a valuation based on these more basic criteria. Thus,\nfor each agent i, there is a value function \u03c3i : Rni\n\u2192 R.\nIn particular, Raiffa [17] shows how to systematically\nconstruct an additive value function to each party involved in a\nnegotiation.\n\u2022 Utility: Now, given an outcome o \u2208 O, an agent i is able\nto determine its value, i.e., \u03c3i(fi(o)). However, a\nnegotiation infrastructure is usually required to facilitate negotiation.\nThis might involve other mechanisms and factors/parties, e.g.,\na mediator, a legal institution, participation fees, etc. The\nstandard way to implement such a thing is to allow money\n1\nIn fact, given the k-dimensional space, these should be called\nindifference surfaces. However, we will not bog down to that level of\ndetails.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 509\nand side-payments. In this paper, we ignore those side-effects\nand assume that agent i\"s utility function ui is normalised so\nthat ui : O \u2192 [0, 1].\nEXAMPLE 1. There are two agents, A and B. Agent A has\na task T that needs to be done and also 100 units of a resource\nR. Agent B has the capacity to perform task T and would like to\nobtain at least 10 and at most 20 units of the resource R. Agent B is\nindifferent on any amount between 10 and 20 units of the resource\nR. The objective functions for both agents A and B are cost and\nrevenue. And they both aim at minimising costs while maximising\nrevenues. Having T done generates for A a revenue rA,T while\ndoing T incurs a cost cB,T to B. Agent B obtains a revenue rB,R\nfor each unit of the resource R while providing each unit of the\nresource R costs agent A cA,R.\nAssuming that money transfer between agents is possible, the set\nAtt then contains three attributes:\n\u2022 T, taking values from the set {0, 1}, indicates whether the\ntask T is assigned to agent B;\n\u2022 R, taking values from the set of non-negative integer,\nindicates the amount of resource R being allocated to agent B;\nand\n\u2022 MT, taking values from R, indicates the payment p to be\ntransferred from A to B.\nConsider the outcome o = [T = 1, R = k, MT = p], i.e., the\ntask T is assigned to B, and A allocates to B with k units of the\nresource R, and A transfers p dollars to B. Then, costA(o) =\nk.cA,R + p and revA(o) = rA,T ; and costB(o) = cB,T and\nrevA(o) =\nj\nk.rB,R + p if 10 \u2264 k \u2264 20\np otherwise.\nAnd, \u03c3i(costi(o), revi(o)) = revi(o) \u2212 costi(o), (i = A, B).\n3. PROBLEM FORMALISATION\nConsider Example 1, assume that rA,T = $150 and cB,T =\n$100 and rB,R = $10 and cA,R = $7. That is, the revenues\ngenerated for A exceeds the costs incurred to B to do task T, and B\nvalues resource R more highly than the cost for A to provide it.\nThe optimal solution to this problem scenario is to assign task T to\nagent B and to allocate 20 units of resource R (i.e., the maximal\namount of resource R required by agent B) from agent A to agent\nB. This outcome regarding the resource and task allocation\nproblems leaves payoffs of $10 to agent A and $100 to agent B.2\nAny\nother outcome would leave at least one of the agents worse off. In\nother words, the presented outcome is Pareto-efficient and should\nbe part of the solution outcome for this problem scenario.\nHowever, as the agents still have to bargain over the amount of\nmoney transfer p, neither agent would be willing to disclose their\nrespective costs and revenues regarding the task T and the resource\nR. As a consequence, agents often do not achieve the optimal\noutcome presented above in practice. To address this issue, we\nintroduce a mediator to help the agents discover better agreements than\nthe ones they might try to settle on. Note that this problem is\nessentially the problem of searching for joint gains in a multilateral\nnegotiation in which the involved parties hold strategic information,\ni.e., the integrative part in a negotiation. In order to help facilitate\nthis process, we introduce the role of a neutral mediator. Before\nformalising the decision problems faced by the mediator and the\n2\nCertainly, without money transfer to compensate agent A, this\noutcome is not a fair one.\nnegotiating agents, we discuss the properties of the solution\noutcomes to be achieved by the mediator. In a negotiation setting, the\ntwo typical design goals would be:\n\u2022 Efficiency: Avoid the agents from settling on an outcome that\nis not Pareto-optimal; and\n\u2022 Fairness: Avoid agreements that give the most of the gains\nto a subset of agents while leaving the rest with too little.\nThe above goals are axiomatised in Nash\"s seminal work [16] on\ncooperative negotiation games. Essentially, Nash advocates for the\nfollowing properties to be satisfied by solution to the bilateral\nnegotiation problem: (i) it produces only Pareto-optimal outcomes; (ii)\nit is invariant to affine transformation (to the consequence space);\n(iii) it is symmetric; and (iv) it is independent from irrelevant\nalternatives. A solution satisfying Nash\"s axioms is called a Nash\nbargaining solution.\nIt then turns out that, by taking the negotiators\" utilities as its\nobjectives the mediator itself faces a multi-criteria decision making\nproblem. The issues faced by the mediator are: (i) the mediator\nrequires access to the negotiators\" utility functions, and (ii)\nmaking (fair) tradeoffs between different agents\" utilities. Our methods\nallow the agents to repeatedly interact with the mediator so that a\nNash solution outcome could be found by the parties.\nInformally, the problem faced by both the mediator and the\nnegotiators is construction of the indifference curves. Why are the\nindifference curves so important?\n\u2022 To the negotiators, knowing the options available along\nindifference curves opens up opportunities to reach more\nefficient outcomes. For instance, consider an agent A who is\npresenting his opponent with an offer \u03b8A which she refuses\nto accept. Rather than having to concede, A could look at\nhis indifference curve going through \u03b8A and choose another\nproposal \u03b8A. To him, \u03b8A and \u03b8A are indifferent but \u03b8A could\ngive some gains to B and thus will be more acceptable to B.\nIn other words, the outcome \u03b8A is more efficient than \u03b8A to\nthese two negotiators.\n\u2022 To the mediator, constructing indifference curves requires a\nmeasure of fairness between the negotiators. The mediator\nneeds to determine how much utility it needs to take away\nfrom the other negotiators to give a particular negotiator a\nspecific gain G (in utility).\nIn order to search for integrative solutions within the outcome\nspace O, we characterise the relationship between the agents over\nthe set of attributes Att. As the agents hold different objectives and\nhave different capacities, it may be the case that changing between\ntwo values of a specific attribute implies different shifts in utility\nof the agents. However, the problem of finding the exact\nParetooptimal set3\nis NP-hard [2].\nOur approach is thus to solve this optimisation problem in two\nsteps. In the first steps, the more manageable attributes will be\nsolved. These are attributes that take a finite set of values. The\nresult of this step would be a subset of outcomes that contains the\nPareto-optimal set. In the second step, we employ an iterative\nprocedure that allows the mediator to interact with the negotiators to\nfind joint improvements that move towards a Pareto-optimal\noutcome. This approach will not work unless the attributes from Att\n3\nThe Pareto-optimal set is the set of outcomes whose consequences\n(in the consequence space) correspond to the Pareto frontier.\n510 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nare independent. Most works on multi-attribute, or multi-issue,\nnegotiation (e.g. [17]) assume that the attributes or the issues are\nindependent, resulting in an additive value function for each agent.4\nASSUMPTION 1. Let i \u2208 N and S \u2286 Att. Denote by \u00afS the\nset Att \\ S. Assume that vS and vS are two assignments of values\nto the attributes of S and v1\n\u00afS, v2\n\u00afS are two arbitrary value\nassignments to the attributes of \u00afS, then (ui([vS, v1\n\u00afS]) \u2212 ui([vS, v2\n\u00afS])) =\n(ui([vS, v1\n\u00afS])\u2212ui([vS, v2\n\u00afS])). That is, the utility function of agent i\nwill be defined on the attributes from S independently of any value\nassignment to other attributes.\n4. MEDIATOR-BASED BILATERAL\nNEGOTIATIONS\nAs discussed by Lax and Sebenius [13], under incomplete\ninformation the tension between creating and claiming values is the\nprimary cause of inefficient outcomes. This can be seen most\neasily in negotiations involving two negotiators; during the\ndistributive phase of the negotiation, the two negotiators\"s objectives are\ndirectly opposing each other. We will now formally characterise\nthis relationship between negotiators by defining the opposition\nbetween two negotiating parties. The following exposition will be\nmainly reproduced from [9].\nAssuming for the moment that all attributes from Att take values\nfrom the set of real numbers R, i.e., V alj \u2286 R for all j \u2208 Att. We\nfurther assume that the set O = \u00d7j\u2208AttV alj of feasible outcomes\nis defined by constraints that all parties must obey and O is convex.\nNow, an outcome o \u2208 O is just a point in the m-dimensional space\nof real numbers. Then, the questions are: (i) from the point of view\nof an agent i, is o already the best outcome for i? (ii) if o is not\nthe best outcome for i then is there another outcome o such that o\ngives i a better utility than o and o does not cause a utility loss to\nthe other agent j in comparison to o?\nThe above questions can be answered by looking at the directions\nof improvement of the negotiating parties at o, i.e., the directions\nin the outcome space O into which their utilities increase at point\no. Under the assumption that the parties\" utility functions ui are\ndifferentiable concave, the set of all directions of improvement for\na party at a point o can be defined in terms of his most preferred,\nor gradient, direction at that point. When the gradient direction\n\u2207ui(o) of agent i at point o is outright opposing to the gradient\ndirection \u2207uj (o) of agent j at point o then the two parties strongly\ndisagree at o and no joint improvements can be achieved for i and\nj in the locality surrounding o.\nSince opposition between the two parties can vary considerably\nover the outcome space (with one pair of outcomes considered\nhighly antagonistic and another pair being highly cooperative), we\nneed to describe the local properties of the relationship. We begin\nwith the opposition at any point of the outcome space Rm\n. The\nfollowing definition is reproduced from [9]:\nDEFINITION 2. 1. The parties are in local strict opposition\nat a point x \u2208 Rm\niff for all points x \u2208 Rm\nthat are\nsufficiently close to x (i.e., for some > 0 such that\n\u2200x x \u2212x < ), an increase of one utility can be achieved\nonly at the expense of a decrease of the other utility.\n2. The parties are in local non-strict opposition at a point x \u2208\nRm\niff they are not in local strict opposition at x, i.e., iff it is\npossible for both parties to raise their utilities by moving an\ninfinitesimal distance from x.\n4\nKlein et al. [10] explore several implications of complex contracts\nin which attributes are possibly inter-dependent.\n3. The parties are in local weak opposition at a point x \u2208 Rm\niff \u2207u1(x).\u2207u2(x) \u2265 0, i.e., iff the gradients at x of the two\nutility functions form an acute or right angle.\n4. The parties are in local strong opposition at a point x \u2208 Rm\niff \u2207u1(x).\u2207u2(x) < 0, i.e., iff the gradients at x form an\nobtuse angle.\n5. The parties are in global strict (nonstrict, weak, strong)\nopposition iff for every x \u2208 Rm\nthey are in local strict\n(nonstrict, weak, strong) opposition.\nGlobal strict and nonstrict oppositions are complementary cases.\nEssentially, under global strict opposition the whole outcome space\nO becomes the Pareto-optimal set as at no point in O can the\nnegotiating parties make a joint improvement, i.e., every point in O\nis a Pareto-efficient outcome. In other words, under global strict\nopposition the outcome space O can be flattened out into a single\nline such that for each pair of outcomes x, y \u2208 O, u1(x) < u1(y)\niff u2(x) > u2(y), i.e., at every point in O, the gradient of the two\nutility functions point to two different ends of the line.\nIntuitively, global strict opposition implies that there is no way to\nobtain joint improvements for both agents. As a consequence, the\nnegotiation degenerates to a distributive negotiation, i.e., the\nnegotiating parties should try to claim as much shares from the\nnegotiation issues as possible while the mediator should aim for the\nfairness of the division. On the other hand, global nonstrict opposition\nallows room for joint improvements and all parties might be better\noff trying to realise the potential gains by reaching Pareto-efficient\nagreements. Weak and strong oppositions indicate different levels\nof opposition. The weaker the opposition, the more potential gains\ncan be realised making cooperation the better strategy to employ\nduring negotiation. On the other hand, stronger opposition\nsuggests that the negotiating parties tend to behave strategically\nleading to misrepresentation of their respective objectives and utility\nfunctions and making joint gains more difficult to realise.\nWe have been temporarily making the assumption that the\noutcome space O is the subset of Rm\n. In many real-world\nnegotiations, this assumption would be too restrictive. We will continue\nour exposition by lifting this restriction and allowing discrete\nattributes. However, as most negotiations involve only discrete\nissues with a bounded number of options, we will assume that each\nattribute takes values either from a finite set or from the set of real\nnumbers R. In the rest of the paper, we will refer to attributes whose\nvalues are from finite sets as simple attributes and attributes whose\nvalues are from R as continuous attributes. The notions of local\noppositions, i.e., strict, nonstrict, weak and strong, are not\napplicable to outcome spaces that contain simple attributes and nor are the\nnotions of global weak and strong oppositions. However, the\nnotions of global strict and nonstrict oppositions can be generalised\nfor outcome spaces that contain simple attributes.\nDEFINITION 3. Given an outcome space O, the parties are in\nglobal strict opposition iff \u2200x, y \u2208 O, u1(x) < u1(y) iff u2(x) >\nu2(y).\nThe parties are in global nonstrict opposition if they are not in\nglobal strict opposition.\n4.1 Optimisation on simple attributes\nIn order to extract the optimal values for a subset of attributes,\nin the first step of this optimisation process the mediator requests\nthe negotiators to submit their respective utility functions over the\nset of simple attributes. Let Simp \u2286 Att denote the set of all\nsimple attributes from Att. Note that, due to Assumption 1, agent i\"s\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 511\nutility function can be characterised as follows:\nui([vSimp, vSimp]) = wi\n1 \u2217 ui,1([vSimp]) + wi\n2 \u2217 ui,2([vSimp]),\nwhere Simp = Att \\ Simp, and ui,1 and ui,2 are the utility\ncomponents of ui over the sets of attributes Simp and Simp, respectively,\nand 0 < wi\n1, wi\n2 < 1 and wi\n1 + wi\n2 = 1.\nAs attributes are independent of each other regarding the agents\"\nutility functions, the optimisation problem over the attributes from\nSimp can be carried out by fixing ui([vSimp]) to a constant C,\nand then search for the optimal values within the set of attributes\nSimp. Now, how does the mediator determine the optimal values\nfor the attributes in Simp? Several well-known optimisation\nstrategies could be applicable here:\n\u2022 The utilitarian solution: The sum of the agents\" utilities are\nmaximised. Thus, the optimal values are the solution of the\nfollowing optimisation problem:\narg max\nv\u2208V alSimp\nX\ni\u2208N\nui(v)\n\u2022 The Nash solution: The product of the agents\" utilities are\nmaximised. Thus, the optimal values are the solution of the\nfollowing optimisation problem:\narg max\nv\u2208V alSimp\nY\ni\u2208N\nui(v)\n\u2022 The egalitarian solution (aka. the maximin solution): The\nutility of the agent with minimum utility is maximised. Thus,\nthe optimal values are the solution of the following\noptimisation problem:\narg max\nv\u2208V alSimp\nmin\ni\u2208N\nui(v)\nThe question now is of course whether a negotiator has the\nincentive to misrepresent his utility function. First of all, recall that the\nagents\" utility functions are bounded, i.e., \u2200o \u2208 O.0 \u2264 ui(o) \u2264 1.\nThus, the agents have no incentive to overstate their utility\nregarding an outcome o: If o is the most preferred outcome to an agent\ni then he already assigns the maximal utility to o. On the other\nhand, if o is not the most preferred outcome to i then by\noverstating the utility he assigns to o, the agent i runs the risk of having\nto settle on an agreement which would give him less payoffs than\nhe is supposed to receive. However, agents do have an incentive\nto understate their utility if the final settlement will be based on the\nabove solutions alone. Essentially, the mechanism to avoid an agent\nto understate his utility regarding particular outcomes is to\nguarantee a certain measure of fairness for the final settlement. That is,\nthe agents lose the incentive to be dishonest to obtain gains from\ntaking advantage of the known solutions to determine the\nsettlement outcome for they would be offset by the fairness maintenance\nmechanism. Firsts, we state an easy lemma.\nLEMMA 1. When Simp contains one single attributes, the agents\nhave the incentive to understate their utility functions regarding\noutcomes that are not attractive to them.\nBy way of illustration, consider the set Simp containing only one\nattribute that could take values from the finite set {A, B, C, D}.\nAssume that negotiator 1 assigns utilities of 0.4, 0.7, 0.9, and 1\nto A, B, C, and D, respectively. Assume also that negotiator 2\nassigns utilities of 1, 0.9, 0.7, and 0.4 to A, B, C, and D,\nrespectively. If agent 1 misrepresents his utility function to the mediator\nby reporting utility 0 for all values A, B and C and utility 1 for\nvalue D then the agent 2 who plays honestly in his report to the\nmediator will obtain the worst outcome D given any of the above\nsolutions. Note that agent 1 doesn\"t need to know agent 2\"s utility\nfunction, nor does he need to know the strategy employed by agent\n2. As long as he knows that the mediator is going to employ one of\nthe above three solutions, then the above misrepresentation is the\ndominant strategy for this game.\nHowever, when the set Simp contains more than one attribute\nand none of the attributes strongly dominate the other attributes\nthen the above problem disminishes by itself thanks to the\nintegrative solution. We of course have to define clearly what it means\nfor an attribute to strongly dominate other attributes. Intuitively, if\nmost of an agent\"s utility concentrates on one of the attributes then\nthis attribute strongly dominates other attributes. We again appeal\nto the Assumption 1 on additivity of utility functions to achieve a\nmeasure of fairness within this negotiation setting. Due to\nAssumption 1, we can characterise agent i\"s utility component over the set\nof attributes Simp by the following equation:\nui,1([vSimp]) =\nX\nj\u2208Simp\nwi\nj \u2217 ui,j([vj]) (1)\nwhere\nP\nj\u2208Simp wj = 1.\nThen, an attribute \u2208 Simp strongly dominates the rest of the\nattributes in Simp (for agent i) iff wi\n>\nP\nj\u2208(Simp\u2212 ) wi\nj . Attribute\nis said to be strongly dominant (for agent i) wrt. the set of simple\nattributes Simp.\nThe following theorem shows that if the set of attributes Simp\ndoes not contain a strongly dominant attribute then the negotiators\nhave no incentive to be dishonest.\nTHEOREM 1. Given a negotiation framework, if for every agent\nthe set of simple attributes doesn\"t contain a strongly dominant\nattribute, then truth-telling is an equilibrium strategy for the\nnegotiators during the optimisation of simple attributes.\nSo far, we have been concentrating on the efficiency issue while\nleaving the fairness issue aside. A fair framework does not only\nsupport a more satisfactory distribution of utility among the agents,\nbut also often a good measure to prevent misrepresentation of\nprivate information by the agents. Of the three solutions presented\nabove, the utilitarian solution does not support fairness. On the\nother hand, Nash [16] proves that the Nash solution satisfies the\nabove four axioms for the cooperative bargaining games and is\nconsidered a fair solution. The egalitarian solution is another\nmechanism to achieve fairness by essentially helping the worst off. The\nproblem with these solutions, as discussed earlier, is that they are\nvulnerable to strategic behaviours when one of the attributes strongly\ndominates the rest of attributes.\nHowever, there is yet another solution that aims to guarantee\nfairness, the minimax solution. That is, the utility of the agent with\nmaximum utility is minimised. It\"s obvious that the minimax\nsolution produces inefficient outcomes. However, to get around this\nproblem (given that the Pareto-optimal set can be tractably\ncomputed), we can apply this solution over the Pareto-optimal set only.\nLet POSet \u2286 V alSimp be the Pareto-optimal subset of the simple\noutcomes, the minimax solution is defined to be the solution of the\nfollowing optimisation problem.\narg min\nv\u2208P OSet\nmax\ni\u2208N\nui(v)\nWhile overall efficiency often suffers under a minimax solution,\ni.e., the sum of all agents\" utilities are often lower than under other\nsolutions, it can be shown that the minimax solution is less\nvulnerable to manipulation.\n512 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nTHEOREM 2. Given a negotiation framework, under the\nminimax solution, if the negotiators are uncertain about their\nopponents\" preferences then truth-telling is an equilibrium strategy for\nthe negotiators during the optimisation of simple attributes.\nThat is, even when there is only one single simple attribute, if an\nagent is uncertain whether the other agent\"s most preferred\nresolution is also his own most preferred resolution then he should opt for\ntruth-telling as the optimal strategy.\n4.2 Optimisation on continuous attributes\nWhen the attributes take values from infinite sets, we assume that\nthey are continuous. This is similar to the common practice in\noperations research in which linear programming solutions/techniques\nare applied to integer programming problems.\nWe denote the number of continuous attributes by k, i.e., Att =\nSimp \u222a Simp and |Simp| = k. Then, the outcome space O can be\nrepresented as follows: O = (\nQ\nj\u2208Simp V alj) \u00d7 (\nQ\nl\u2208Simp V all),\nwhere\nQ\nl\u2208Simp V all \u2286 Rk\nis the continuous component of O. Let\nOc\ndenote the set\nQ\nl\u2208Simp V all. We\"ll refer to Oc\nas the feasible\nset and assume that Oc\nis closed and convex. After carrying out\nthe optimisation over the set of simple attributes, we are able to\nassign the optimal values to the simple attributes from Simp. Thus,\nwe reduce the original problem to the problem of searching for\noptimal (and fair) outcomes within the feasible set Oc\n. Recall that,\nby Assumption 1, we can characterise agent i\"s utility function as\nfollows:\nui([v\u2217\nSimp, vSimp]) = C + wi\n2 \u2217 ui,2([vSimp]),\nwhere C is the constant wi\n1 \u2217 ui,1([v\u2217\nSimp]) and v\u2217\nSimp denotes the\noptimal values of the simple attributes in Simp. Hence, without loss\nof generality (albeit with a blatant abuse of notation), we can take\nthe agent i\"s utility function as ui : Rk\n\u2192 [0, 1]. Accordingly we\nwill also take the set of outcomes under consideration by the agents\nto be the feasible set Oc\n. We now state another assumption to be\nused in this section:\nASSUMPTION 2. The negotiators\" utility functions can be\ndescribed by continuously differentiable and concave functions ui :\nRk\n\u2192 [0, 1], (i = 1, 2).\nIt should be emphasised that we do not assume that agents\nexplicitly know their utility functions. For the method to be described\nin the following to work, we only assume that the agents know the\nrelevant information, e.g. at certain point within the feasible set Oc\n,\nthe gradient direction of their own utility functions and some\nsection of their respective indifference curves. Assume that a tentative\nagreement (which is a point x \u2208 Rk\n) is currently on the table, the\nprocess for the agents to jointly improve this agreement in order to\nreach a Pareto-optimal agreement can be described as follows. The\nmediator asks the negotiators to discretely submit their respective\ngradient directions at x, i.e., \u2207u1(x) and \u2207u2(x).\nNote that the goal of the process to be described here is to search\nfor agreements that are more efficient than the tentative agreement\ncurrently on the table. That is, we are searching for points x within\nthe feasible set Oc\nsuch that moving to x from the current tentative\nagreement x brings more gains to at least one of the agents while\nnot hurting any of the agents. Due to the assumption made above,\ni.e. the feasible set Oc\nis bounded, the conditions for an alternative\nx \u2208 Oc\nto be efficient vary depending on the position of x. The\nfollowing results are proved in [9]:\nLet B(x) = 0 denote the equation of the boundary of Oc\n,\ndefining x \u2208 Oc\niff B(x) \u2265 0. An alternative x\u2217\n\u2208 Oc\nis efficient iff,\neither\nA. x\u2217\nis in the interior of Oc\nand the parties are in local strict\nopposition at x\u2217\n, i.e.,\n\u2207u1(x\u2217\n) = \u2212\u03b3\u2207u2(x\u2217\n) (2)\nwhere \u03b3 > 0; or\nB. x\u2217\nis on the boundary of Oc\n, and for some \u03b1, \u03b2 \u2265 0:\n\u03b1\u2207u1(x\u2217\n) + \u03b2\u2207u2(x\u2217\n) = \u2207B(x\u2217\n) (3)\nWe are now interested in answering the following questions:\n(i) What is the initial tentative agreement x0?\n(ii) How to find the more efficient agreement xh+1, given the\ncurrent tentative agreement xh?\n4.2.1 Determining a fair initial tentative agreement\nIt should be emphasised that the choice of the initial tentative\nagreement affects the fairness of the final agreement to be reached\nby the presented method. For instance, if the initial tentative\nagreement x0 is chosen to be the most preferred alternative to one of\nthe agents then it is also a Pareto-optimal outcome, making it\nimpossible to find any joint improvement from x0. However, if x0\nwill then be chosen to be the final settlement and if x0 turns out\nto be the worst alternative to the other agent then this outcome is a\nvery unfair one. Thus, it\"s important that the choice of the initial\ntentative agreement be sensibly made.\nEhtamo et al [3] present several methods to choose the initial\ntentative agreement (called reference point in their paper). However,\ntheir goal is to approximate the Pareto-optimal set by\nsystematically choosing a set of reference points. Once an (approximate)\nPareto-optimal set is generated, it is left to the negotiators to decide\nwhich of the generated Pareto-optimal outcomes to be chosen as\nthe final settlement. That is, distributive negotiation will then be\nrequired to settle the issue.\nWe, on the other hand, are interested in a fair initial tentative\nagreement which is not necessarily efficient. Improving a given\ntentative agreement to yield a Pareto-optimal agreement is\nconsidered in the next section. For each attribute j \u2208 Simp, an agent i will\nbe asked to discretely submit three values (from the set V alj): the\nmost preferred value, denoted by pvi,j, the least preferred value,\ndenoted by wvi,j, and a value that gives i an approximately\naverage payoff, denoted by avi,j. (Note that this is possible\nbecause the set V alj is bounded.) If pv1,j and pv2,j are sufficiently\nclose, i.e., |pv1,j \u2212 pv2,j| < \u0394 for some pre-defined \u0394 > 0,\nthen pv1,j and pv2,j are chosen to be the two core values,\ndenoted by cv1 and cv2. Otherwise, between the two values pv1,j\nand av1,j, we eliminate the one that is closer to wv2,j, the\nremaining value is denoted by cv1. Similarly, we obtain cv2 from the\ntwo values pv2,j and av2,j. If cv1 = cv2 then cv1 is selected as\nthe initial value for the attribute j as part of the initial tentative\nagreement. Otherwise, without loss of generality, we assume that\ncv1 < cv2. The mediator selects randomly p values mv1, . . . , mvp\nfrom the open interval (cv1, cv2), where p \u2265 1. The mediator then\nasks the agents to submit their valuations over the set of values\n{cv1, cv2, mv1, . . . , mvp}. The value whose the two valuations of\ntwo agents are closest is selected as the initial value for the attribute\nj as part of the initial tentative agreement.\nThe above procedure guarantees that the agents do not gain by\nbehaving strategically. By performing the above procedure on\nevery attribute j \u2208 Simp, we are able to identify the initial tentative\nagreement x0 such that x0 \u2208 Oc\n. The next step is to compute\na new tentative agreement from an existing tentative agreement so\nthat the new one would be more efficient than the existing one.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 513\n4.2.2 Computing new tentative agreement\nOur procedure is a combination of the method of jointly\nimproving direction introduced by Ehtamo et al [4] and a method we\npropose in the coming section. Basically, the idea is to see how strong\nthe opposition the parties are in. If the two parties are in (local)\nweak opposition at the current tentative agreement xh, i.e., their\nimproving directions at xh are close to each other, then the\ncompromise direction proposed by Ehtamo et al [4] is likely to point to\na better agreement for both agents. However, if the two parties are\nin local strong opposition at the current point xh then it\"s unclear\nwhether the compromise direction would really not hurt one of the\nagents whilst bringing some benefit to the other.\nWe will first review the method proposed by Ehtamo et al [4]\nto compute the compromise direction for a group of negotiators at\na given point x \u2208 Oc\n. Ehtamo et al define a a function T(x)\nthat describes the mediator\"s choice for a compromise direction at\nx. For the case of two-party negotiations, the following bisecting\nfunction, denoted by T BS\n, can be defined over the interior set of Oc\n.\nNote that the closed set Oc\ncontains two disjoint subsets: Oc\n=\nOc\n0 \u222aOc\nB , where Oc\n0 denotes the set of interior points of Oc\nand Oc\nB\ndenotes the boundary of Oc\n. The bisecting compromise is defined\nby a function T BS\n: Oc\n0 \u2192 R2\n,\nT BS\n(x) =\n\u2207u1(x)\n\u2207u1(x)\n+\n\u2207u2(x)\n\u2207u2(x)\n, x \u2208 Oc\n0. (4)\nGiven the current tentative agreement xh (h \u2265 0), the mediator\nhas to choose a point xh+1 along d = T(xh) so that all parties\ngain. Ehtamo et al then define a mechanism to generate a sequence\nof points and prove that when the generated sequence is bounded\nand when all generated points (from the sequence) belong to the\ninterior set Oc\n0 then the sequence converges to a weakly\nParetooptimal agreement [4, pp. 59-60].5\nAs the above mechanism does not work at the boundary points\nof Oc\n, we will introduce a procedure that works everywhere in an\nalternative space Oc\n. Let x \u2208 Oc\nand let \u03b8(x) denote the angle\nbetween the gradients \u2207u1(x) and \u2207u2(x) at x. That is,\n\u03b8(x) = arccos(\n\u2207u1(x).\u2207u2(x)\n\u2207u1(x) . \u2207u2(x)\n)\nFrom Definition 2, it is obvious that the two parties are in local\nstrict opposition (at x) iff \u03b8(x) = \u03c0, and they are in local strong\nopposition iff \u03c0 \u2265 \u03b8(x) > \u03c0/2, and they are in local weak\nopposition iff \u03c0/2 \u2265 \u03b8(x) \u2265 0. Note also that the two vectors \u2207u1(x)\nand \u2207u2(x) define a hyperplane, denoted by h\u2207(x), in the\nkdimensional space Rk\n. Furthermore, there are two indifference\ncurves of agents 1 and 2 going through point x, denoted by IC1(x)\nand IC2(x), respectively. Let hT1(x) and hT2(x) denote the\ntangent hyperplanes to the indifference curves IC1(x) and IC2(x),\nrespectively, at point x. The planes hT1(x) and hT2(x) intersect\nh\u2207(x) in the lines IS1(x) and IS2(x), respectively. Note that\ngiven a line L(x) going through the point x, there are two (unit)\nvectors from x along L(x) pointing to two opposite directions,\ndenoted by L+\n(x) and L\u2212\n(x).\nWe can now informally explain our solution to the problem of\nsearching for joint gains. When it isn\"t possible to obtain a\ncompromise direction for joint improvements at a point x \u2208 Oc\neither\nbecause the compromise vector points to the space outside of the\nfeasible set Oc\nor because the two parties are in local strong\nopposition at x, we will consider to move along the indifference curve of\none party while trying to improve the utility of the other party. As\n5\nLet S be the set of alternatives, x\u2217\nis weakly Pareto optimal if\nthere is no x \u2208 S such that ui(x) > ui(x\u2217\n) for all agents i.\nthe mediator does not know the indifference curves of the parties,\nhe has to use the tangent hyperplanes to the indifference curves of\nthe parties at point x. Note that the tangent hyperplane to a curve\nis a useful approximation of the curve in the immediate vicinity of\nthe point of tangency, x.\nWe are now describing an iteration step to reach the next tentative\nagreement xh+1 from the current tentative agreement xh \u2208 Oc\n. A\nvector v whose tail is xh is said to be bounded in Oc\nif \u2203\u03bb > 0\nsuch that xh +\u03bbv \u2208 Oc\n. To start, the mediator asks the negotiators\nfor their gradients \u2207u1(xh) and \u2207u2(xh), respectively, at xh.\n1. If xh is a Pareto-optimal outcome according to equation 2 or\nequation 3, then the process is terminated.\n2. If 1 \u2265 \u2207u1(xh).\u2207u2(xh) > 0 and the vector T BS\n(xh) is\nbounded in Oc\nthen the mediator chooses the compromise\nimproving direction d = T BS\n(xh) and apply the method\ndescribed by Ehtamo et al [4] to generate the next tentative\nagreement xh+1.\n3. Otherwise, among the four vectors IS\u03c3\ni (xh), i = 1, 2 and\n\u03c3 = +/\u2212, the mediator chooses the vector that (i) is bounded\nin Oc\n, and (ii) is closest to the gradient of the other agent,\n\u2207uj (xh)(j = i). Denote this vector by T G(xh). That is,\nwe will be searching for a point on the indifference curve of\nagent i, ICi(xh), while trying to improve the utility of agent\nj. Note that when xh is an interior point of Oc\nthen the\nsituation is symmetric for the two agents 1 and 2, and the mediator\nhas the choice of either finding a point on IC1(xh) to\nimprove the utility of agent 2, or finding a point on IC2(xh) to\nimprove the utility of agent 1. To decide on which choice to\nmake, the mediator has to compute the distribution of gains\nthroughout the whole process to avoid giving more gains to\none agent than to the other. Now, the point xh+1 to be\ngenerated lies somewhere on the intersection of ICi(xh) and the\nhyperplane defined by \u2207ui(xh) and T G(xh). This\nintersection is approximated by T G(xh). Thus, the sought\nafter point xh+1 can be generated by first finding a point yh\nalong the direction of T G(xh) and then move from yh to the\nsame direction of \u2207ui(xh) until we intersect with ICi(xh).\nMathematically, let \u03b6 and \u03be denote the vectors T G(xh) and\n\u2207ui(xh), respectively, xh+1 is the solution to the following\noptimisation problem:\nmax\n\u03bb1,\u03bb2\u2208L\nuj(xh + \u03bb1\u03b6 + \u03bb2\u03be)\ns.t. xh+\u03bb1\u03b6+\u03bb2\u03be \u2208 Oc\n, and ui(xh+\u03bb1\u03b6+\u03bb2\u03be) = ui(xh),\nwhere L is a suitable interval of positive real numbers; e.g.,\nL = {\u03bb|\u03bb > 0}, or L = {\u03bb|a < \u03bb \u2264 b}, 0 \u2264 a < b.\nGiven an initial tentative agreement x0, the method described\nabove allows a sequence of tentative agreements x1, x2, . . . to be\niteratively generated. The iteration stops whenever a weakly Pareto\noptimal agreement is reached.\nTHEOREM 3. If the sequence of agreements generated by the\nabove method is bounded then the method converges to a point\nx\u2217\n\u2208 Oc\nthat is weakly Pareto optimal.\n5. CONCLUSION AND FUTURE WORK\nIn this paper we have established a framework for negotiation\nthat is based on MCDM theory for representing the agents\"\nobjectives and utilities. The focus of the paper is on integrative\nnegotiation in which agents aim to maximise joint gains, or create value.\n514 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nWe have introduced a mediator into the negotiation in order to\nallow negotiators to disclose information about their utilities,\nwithout providing this information to their opponents. Furthermore, the\nmediator also works toward the goal of achieving fairness of the\nnegotiation outcome.\nThat is, the approach that we describe aims for both efficiency, in\nthe sense that it produces Pareto optimal outcomes (i.e. no aspect\ncan be improved for one of the parties without worsening the\noutcome for another party), and also for fairness, which chooses\noptimal solutions which distribute gains amongst the agents in some\nappropriate manner. We have developed a two step process for\naddressing the NP-hard problem of finding a solution for a set of\nintegrative attributes, which is within the Pareto-optimal set for those\nattributes. For simple attributes (i.e. those which have a finite set\nof values) we use known optimisation techniques to find a\nParetooptimal solution. In order to discourage agents from\nmisrepresenting their utilities to gain an advantage, we look for solutions that\nare least vulnerable to manipulation. We have shown that as long\nas one of the simple attributes does not strongly dominate the\nothers, then truth telling is an equilibrium strategy for the negotiators\nduring the stage of optimising simple attributes. For non-simple\nattributes we propose a mechanism that provides stepwise\nimprovements to move the proposed solution in the direction of a\nParetooptimal solution.\nThe approach presented in this paper is similar to the ideas\nbehind negotiation analysis [18]. Ehtamo et al [4] presents an\napproach to searching for joint gains in multi-party negotiations. The\nrelation of their approach to our approach is discussed in the\npreceding section. Lai et al [12] provide an alternative approach to\nintegrative negotiation. While their approach was clearly described\nfor the case of two-issue negotiations, the generalisation to\nnegotiations with more than two issues is not entirely clear.\nZhang et at [22] discuss the use of integrative negotiation in\nagent organisations. They assume that agents are honest. Their\nmain result is an experiment showing that in some situations, agents\"\ncooperativeness may not bring the most benefits to the organisation\nas a whole, while giving no explanation. Jonker et al [7] consider\nan approach to multi-attribute negotiation without the use of a\nmediator. Thus, their approach can be considered a complement of\nours. Their experimental results show that agents can reach\nParetooptimal outcomes using their approach.\nThe details of the approach have currently been shown only for\nbilateral negotiation, and while we believe they are generalisable to\nmultiple negotiators, this work remains to be done. There is also\nfuture work to be done in more fully characterising the outcomes\nof the determination of values for the non-simple attributes. In\norder to provide a complete framework we are also working on the\ndistributive phase using the mediator.\nAcknowledgement\nThe authors acknowledge financial support by ARC Dicovery Grant\n(2006-2009, grant DP0663147) and DEST IAP grant (2004-2006,\ngrant CG040014). The authors would like to thank Lawrence\nCavedon and the RMIT Agents research group for their helpful\ncomments and suggestions.\n6. REFERENCES\n[1] F. Alemi, P. Fos, and W. Lacorte. A demonstration of\nmethods for studying negotiations between physicians and\nhealth care managers. Decision Science, 21:633-641, 1990.\n[2] M. Ehrgott. Multicriteria Optimization. Springer-Verlag,\nBerlin, 2000.\n[3] H. Ehtamo, R. P. Hamalainen, P. Heiskanen, J. Teich,\nM. Verkama, and S. Zionts. Generating pareto solutions in a\ntwo-party setting: Constraint proposal methods.\nManagement Science, 45(12):1697-1709, 1999.\n[4] H. Ehtamo, E. Kettunen, and R. P. Hmlinen. Searching for\njoint gains in multi-party negotiations. European Journal of\nOperational Research, 130:54-69, 2001.\n[5] P. Faratin. Automated Service Negotiation Between\nAutonomous Computational Agents. PhD thesis, University\nof London, 2000.\n[6] A. Foroughi. Minimizing negotiation process losses with\ncomputerized negotiation support systems. The Journal of\nApplied Business Research, 14(4):15-26, 1998.\n[7] C. M. Jonker, V. Robu, and J. Treur. An agent architecture\nfor multi-attribute negotiation using incomplete preference\ninformation. J. Autonomous Agents and Multi-Agent\nSystems, (to appear).\n[8] R. L. Keeney and H. Raiffa. Decisions with Multiple\nObjectives: Preferences and Value Trade-Offs. John Wiley\nand Sons, Inc., New York, 1976.\n[9] G. Kersten and S. Noronha. Rational agents, contract curves,\nand non-efficient compromises. IEEE Systems, Man, and\nCybernetics, 28(3):326-338, 1998.\n[10] M. Klein, P. Faratin, H. Sayama, and Y. Bar-Yam. Protocols\nfor negotiating complex contracts. IEEE Intelligent Systems,\n18(6):32-38, 2003.\n[11] S. Kraus, J. Wilkenfeld, and G. Zlotkin. Multiagent\nnegotiation under time constraints. Artificial Intelligence\nJournal, 75(2):297-345, 1995.\n[12] G. Lai, C. Li, and K. Sycara. Efficient multi-attribute\nnegotiation with incomplete information. Group Decision\nand Negotiation, 15:511-528, 2006.\n[13] D. Lax and J. Sebenius. The manager as negotiator: The\nnegotiator\"s dilemma: Creating and claiming value, 2nd ed.\nIn S. Goldberg, F. Sander & N. Rogers, editors, Dispute\nResolution, 2nd ed., pages 49-62. Little Brown & Co., 1992.\n[14] M. Lomuscio and N. Jennings. A classification scheme for\nnegotiation in electronic commerce. In Agent-Mediated\nElectronic Commerce: A European Agentlink Perspective.\nSpringer-Verlag, 2001.\n[15] R. Maes and A. Moukas. Agents that buy and sell.\nCommunications of the ACM, 42(3):81-91, 1999.\n[16] J. Nash. Two-person cooperative games. Econometrica,\n21(1):128-140, April 1953.\n[17] H. Raiffa. The Art and Science of Negotiation. Harvard\nUniversity Press, Cambridge, USA, 1982.\n[18] H. Raiffa, J. Richardson, and D. Metcalfe. Negotiation\nAnalysis: The Science and Art of Collaborative Decision\nMaking. Belknap Press, Cambridge, MA, 2002.\n[19] T. Sandholm. Agents in electronic commerce: Component\ntechnologies for automated negotiation and coalition\nformation. JAAMAS, 3(1):73-96, 2000.\n[20] J. Sebenius. Negotiation analysis: A characterization and\nreview. Management Science, 38(1):18-38, 1992.\n[21] L. Weingart, E. Hyder, and M. Pietrula. Knowledge matters:\nThe effect of tactical descriptions on negotiation behavior\nand outcome. Tech. Report, CMU, 1995.\n[22] X. Zhang, V. R. Lesser, and T. Wagner. Integrative\nnegotiation among agents situated in organizations. IEEE\nTrans. on Systems, Man, and Cybernetics, Part C,\n36(1):19-30, 2006.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 515", "keywords": "concession;mediator;uncertainty;multi-criterion decision make;automate negotiation;integrative negotiation;inefficient compromise;dilemma;deadlock situation;creating value;claiming value;mcdm;incomplete information;negotiation"}
{"name": "train_I-56", "title": "Unifying Distributed Constraint Algorithms in a BDI Negotiation Framework", "abstract": "This paper presents a novel, unified distributed constraint satisfaction framework based on automated negotiation. The Distributed Constraint Satisfaction Problem (DCSP) is one that entails several agents to search for an agreement, which is a consistent combination of actions that satisfies their mutual constraints in a shared environment. By anchoring the DCSP search on automated negotiation, we show that several well-known DCSP algorithms are actually mechanisms that can reach agreements through a common Belief-Desire-Intention (BDI) protocol, but using different strategies. A major motivation for this BDI framework is that it not only provides a conceptually clearer understanding of existing DCSP algorithms from an agent model perspective, but also opens up the opportunities to extend and develop new strategies for DCSP. To this end, a new strategy called Unsolicited Mutual Advice (UMA) is proposed. Performance evaluation shows that the UMA strategy can outperform some existing mechanisms in terms of computational cycles.", "fulltext": "1. INTRODUCTION\nAt the core of many emerging distributed applications is the\ndistributed constraint satisfaction problem (DCSP) - one which\ninvolves finding a consistent combination of actions (abstracted as\ndomain values) to satisfy the constraints among multiple agents\nin a shared environment. Important application examples include\ndistributed resource allocation [1] and distributed scheduling [2].\nMany important algorithms, such as distributed breakout (DBO)\n[3], asynchronous backtracking (ABT) [4], asynchronous partial\noverlay (APO) [5] and asynchronous weak-commitment (AWC)\n[4], have been developed to address the DCSP and provide the\nagent solution basis for its applications. Broadly speaking, these\nalgorithms are based on two different approaches, either\nextending from classical backtracking algorithms [6] or introducing\nmediation among the agents.\nWhile there has been no lack of efforts in this promising\nresearch field, especially in dealing with outstanding issues such as\nresource restrictions (e.g., limits on time and communication) [7]\nand privacy requirements [8], there is unfortunately no\nconceptually clear treatment to prise open the model-theoretic workings of\nthe various agent algorithms that have been developed. As a\nresult, for instance, a deeper intellectual understanding on why one\nalgorithm is better than the other, beyond computational issues,\nis not possible.\nIn this paper, we present a novel, unified distributed constraint\nsatisfaction framework based on automated negotiation [9].\nNegotiation is viewed as a process of several agents searching for a\nsolution called an agreement. The search can be realized via a\nnegotiation mechanism (or algorithm) by which the agents follow\na high level protocol prescribing the rules of interactions, using\na set of strategies devised to select their own preferences at each\nnegotiation step.\nAnchoring the DCSP search on automated negotiation, we\nshow in this paper that several well-known DCSP algorithms\n[3] are actually mechanisms that share the same\nBelief-DesireIntention (BDI) interaction protocol to reach agreements, but\nuse different action or value selection strategies. The proposed\nframework provides not only a clearer understanding of existing\nDCSP algorithms from a unified BDI agent perspective, but also\nopens up the opportunities to extend and develop new strategies\nfor DCSP. To this end, a new strategy called Unsolicited Mutual\nAdvice (UMA) is proposed. Our performance evaluation shows\nthat UMA can outperform ABT and AWC in terms of the average\nnumber of computational cycles for both the sparse and critical\ncoloring problems [6].\nThe rest of this paper is organized as follows. In Section 2,\nwe provide a formal overview of DCSP. Section 3 presents a BDI\nnegotiation model by which a DCSP agent reasons. Section 4\npresents the existing algorithms ABT, AWC and DBO as\ndifferent strategies formalized on a common protocol. A new strategy\ncalled Unsolicited Mutual Advice is proposed in Section 5; our\nempirical results and discussion attempt to highlight the merits\nof the new strategy over existing ones. Section 6 concludes the\npaper and points to some future work.\n2. DCSP: PROBLEM FORMALIZATION\nThe DCSP [4] considers the following environment.\n\u2022 There are n agents with k variables x0, x1, \u00b7 \u00b7 \u00b7 , xk\u22121, n \u2264\nk, which have values in domains D1, D2, \u00b7 \u00b7 \u00b7 , Dk,\nrespectively. We define a partial function B over the\nproductrange {0, 1, . . . , (n\u22121)}\u00d7{0, 1, . . . , (k \u22121)} such that, that\nvariable xj belongs to agent i is denoted by B(i, j)!. The\nexclamation mark \u2018!\" means \u2018is defined\".\n\u2022 There are m constraints c0, c1, \u00b7 \u00b7 \u00b7 cm\u22121 to be conjunctively\nsatisfied. In a similar fashion as defined for B(i, j), we use\nE(l, j)!, (0 \u2264 l < m, 0 \u2264 j < k), to denote that xj is\nrelevant to the constraint cl.\nThe DCSP may be formally stated as follows.\nProblem Statement: \u2200i, j (0 \u2264 i < n)(0 \u2264 j < k) where\nB(i, j)!, find the assignment xj = dj \u2208 Dj such that \u2200l (0 \u2264 l <\nm) where E(l, j)!, cl is satisfied.\nA constraint may consist of different variables belonging to\ndifferent agents. An agent cannot change or modify the\nassignment values of other agents\" variables. Therefore, in\ncooperatively searching for a DCSP solution, the agents would need to\ncommunicate with one another, and adjust and re-adjust their\nown variable assignments in the process.\n2.1 DCSP Agent Model\nIn general, all DCSP agents must cooperatively interact, and\nessentially perform the assignment and reassignment of domain\nvalues to variables to resolve all constraint violations. If the\nagents succeed in their resolution, a solution is found.\nIn order to engage in cooperative behavior, a DCSP agent needs\nfive fundamental parameters, namely, (i) a variable [4] or a\nvariable set [10], (ii) domains, (iii) priority, (iv) a neighbor list and\n(v) a constraint list.\nEach variable assumes a range of values called a domain. A\ndomain value, which usually abstracts an action, is a possible\noption that an agent may take. Each agent has an assigned priority.\nThese priority values help decide the order in which they revise\nor modify their variable assignments. An agent\"s priority may be\nfixed (static) or changing (dynamic) when searching for a\nsolution. If an agent has more than one variable, each variable can\nbe assigned a different priority, to help determine which variable\nassignment the agent should modify first.\nAn agent which shares the same constraint with another agent\nis called the latter\"s neighbor. Each agent needs to refer to its list\nof neighbors during the search process. This list may also be kept\nunchanged or updated accordingly in runtime. Similarly, each\nagent maintains a constraint list. The agent needs to ensure that\nthere is no violation of the constraints in this list. Constraints can\nbe added or removed from an agent\"s constraint list in runtime.\nAs with an agent, a constraint can also be associated with a\npriority value. Constraints with a high priority are said to be\nmore important than constraints with a lower priority. To\ndistinguish it from the priority of an agent, the priority of a constraint\nis called its weight.\n3. THE BDI NEGOTIATION MODEL\nThe BDI model originates with the work of M. Bratman [11].\nAccording to [12, Ch.1], the BDI architecture is based on a\nphilosophical model of human practical reasoning, and draws out the\nprocess of reasoning by which an agent decides which actions to\nperform at consecutive moments when pursuing certain goals.\nGrounding the scope to the DCSP framework, the common goal\nof all agents is finding a combination of domain values to satisfy a\nset of predefined constraints. In automated negotiation [9], such\na solution is called an agreement among the agents. Within this\nscope, we found that we were able to unearth the generic behavior\nof a DCSP agent and formulate it in a negotiation protocol,\nprescribed using the powerful concepts of BDI. Thus, our proposed\nnegotiation model can be said to combine the BDI concepts with\nautomated negotiation in a multiagent framework, allowing us\nto conceptually separate DCSP mechanisms into a common BDI\ninteraction protocol and the adopted strategies.\n3.1 The generic protocol\nFigure 1 shows the basic reasoning steps in an arbitrary round\nof negotiation that constitute the new protocol. The solid line\nindicates the common component or transition which always\nexists regardless of the strategy used. The dotted line indicates the\nPercept\nBelief\nDesire\nIntention\nMediation\nExecution\nP\nB\nD\nI\nI\nI\nInfo Message\nInfo Message\nNegotiation Message\nNegotiation Message\nNegotiation Message\nNegotiation Message\nNegotiation Message\nNegotiation Message\nNegotiation Message\nFigure 1: The BDI interaction protocol\ncomponent or transition which may or may not appear depending\non the adopted strategy.\nTwo types of messages are exchanged through this protocol,\nnamely, the info message and the negotiation message.\nAn info message perceived is a message sent by another agent.\nThe message will contain the current selected values and priorities\nof the variables of that sending agent. The main purpose of this\nmessage is to update the agent about the current environment.\nInfo message is sent out at the end of one negotiation round (also\ncalled a negotiation cycle), and received at the beginning of next\nround.\nA negotiation message is a message which may be sent within\na round. This message is for mediation purposes. The agent may\nput different contents into this type of message as long as it is\nagreed among the group. The format of the negotiation message\nand when it is to be sent out are subject to the strategy. A\nnegotiation message can be sent out at the end of one reasoning\nstep and received at the beginning of the next step.\nMediation is a step of the protocol that depends on whether the\nagent\"s interaction with others is synchronous or asynchronous.\nIn synchronous mechanism, mediation is required in every\nnegotiation round. In an asynchronous one, mediation is needed only in\na negotiation round when the agent receives a negotiation\nmessage. A more in-depth view of this mediation step is provided\nlater in this section.\nThe BDI protocol prescribes the skeletal structure for DCSP\nnegotiation. We will show in Section 4 that several well-known\nDCSP mechanisms all inherit this generic model.\nThe details of the six main reasoning steps for the protocol\n(see Figure 1) are described as follows for a DCSP agent. For a\nconceptually clearer description, we assume that there is only one\nvariable per agent.\n\u2022 Percept. In this step, the agent receives info messages\nfrom its neighbors in the environment, and using its Percept\nfunction, returns an image P. This image contains the\ncurrent values assigned to the variables of all agents in its\nneighbor list. The image P will drive the agent\"s actions\nin subsequent steps. The agent also updates its constraint\nlist C using some criteria of the adopted strategy.\n\u2022 Belief. Using the image P and constraint list C, the agent\nwill check if there is any violated constraint. If there is\nno violation, the agent will believe it is choosing a correct\noption and therefore will take no action. The agent will\ndo nothing if it is in a local stable state - a snapshot of\nthe variables assignments of the agent and all its neighbors\nby which they satisfy their shared constraints. When all\nagents are in their local stable states, the whole\nenvironment is said to be in a global stable state and an\nagreeThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 525\nment is found. In case the agent finds its value in conflict\nwith some of its neighbors\", i.e., the combination of values\nassigned to the variables leads to a constraint violation,\nthe agent will first try to reassign its own variable using a\nspecific strategy. If it finds a suitable option which meets\nsome criteria of the adopted strategy, the agent will believe\nit should change to the new option. However it does not\nalways happen that an agent can successfully find such an\noption. If no option can be found, the agent will believe it\nhas no option, and therefore will request its neighbors to\nreconsider their variable assignments.\nTo summarize, there are three types of beliefs that a DCSP\nagent can form: (i) it can change its variable assignment to\nimprove the current situation, (ii) it cannot change its\nvariable assignment and some constraints violations cannot be\nresolved and (iii) it need not change its variable assignment\nas all the constraints are satisfied.\nOnce the beliefs are formed, the agent will determine its\ndesires, which are the options that attempt to resolve the\ncurrent constraint violations.\n\u2022 Desire. If the agent takes Belief (i), it will generate a list of\nits own suitable domain values as its desire set. If the agent\ntakes Belief (ii), it cannot ascertain its desire set, but will\ngenerate a sublist of agents from its neighbor list, whom it\nwill ask to reconsider their variable assignments. How this\nsublist is created depends on the strategy devised for the\nagent. In this situation, the agent will use a virtual desire\nset that it determines based on its adopted strategy. If the\nagent takes Belief (iii), it will have no desire to revise its\ndomain value, and hence no intention.\n\u2022 Intention. The agent will select a value from its desire\nset as its intention. An intention is the best desired\noption that the agent assigns to its variable. The criteria for\nselecting a desire as the agent\"s intention depend on the\nstrategy used. Once the intention is formed, the agent may\neither proceed to the execution step, or undergo mediation.\nAgain, the decision to do so is determined by some criteria\nof the adopted strategy.\n\u2022 Mediation. This is an important function of the agent.\nSince, if the agent executes its intention without\nperforming intention mediation with its neighbors, the constraint\nviolation between the agents may not be resolved. Take\nfor example, suppose two agents have variables, x1 and x2,\nassociated with the same domain {1, 2}, and their shared\nconstraint is (x1 + x2 = 3). Then if both the variables are\ninitialized with value 1, they will both concurrently switch\nbetween the values 2 and 1 in the absence of mediation\nbetween them.\nThere are two types of mediation: local mediation and\ngroup mediation. In the former, the agents exchange their\nintentions. When an agent receives another\"s intention\nwhich conflicts with its own, the agent must mediate\nbetween the intentions, by either changing its own intention\nor informing the other agent to change its intention. In the\nlatter, there is an agent which acts as a group mediator.\nThis mediator will collect the intentions from the group - a\nunion of the agent and its neighbors - and determine which\nintention is to be executed. The result of this mediation is\npassed back to the agents in the group. Following\nmediation, the agent may proceed to the next reasoning step to\nexecute its intention or begin a new negotiation round.\n\u2022 Execution. This is the last step of a negotiation round.\nThe agent will execute by updating its variable assignment\nif the intention obtained at this step is its own. Following\nexecution, the agent will inform its neighbors about its new\nvariable assignment and updated priority. To do so, the\nagent will send out an info message.\n3.2 The strategy\nA strategy plays an important role in the negotiation process.\nWithin the protocol, it will often determine the efficiency of the\nPercept\nBelief\nDesire\nIntention\nMediation\nExecution\nP\nB\nD\nI\nInfo Message\nInfo Message\nNegotiation Message\nNegotiation Message\nNegotiation Message\nFigure 2: BDI protocol with Asynchronous\nBacktracking strategy\nsearch process in terms of computational cycles and message\ncommunication costs.\nThe design space when devising a strategy is influenced by the\nfollowing dimensions: (i) asynchronous or synchronous, (ii)\ndynamic or static priority, (iii) dynamic or static constraint weight,\n(iv) number of negotiation messages to be communicated, (v) the\nnegotiation message format and (vi) the completeness property.\nIn other words, these dimensions provide technical considerations\nfor a strategy design.\n4. DCSP ALGORITHMS: BDI PROTOCOL\n+ STRATEGIES\nIn this section, we apply the proposed BDI negotiation model\npresented in Section 3 to expose the BDI protocol and the\ndifferent strategies used for three well-known algorithms, ABT, AWC\nand DBO. All these algorithms assume that there is only one\nvariable per agent. Under our framework, we call the strategies\napplied the ABT, AWC and DBO strategies, respectively.\nTo describe each strategy formally, the following mathematical\nnotations are used:\n\u2022 n is the number of agents, m is the number of constraints;\n\u2022 xi denotes the variable held by agent i, (0 \u2264 i < n);\n\u2022 Di denotes the domain of variable xi; Fi denotes the\nneighbor list of agent i; Ci denotes its constraint list;\n\u2022 pi denotes the priority of agent i; and Pi = {(xj = vj, pj =\nk) | agent j \u2208 Fi, vj \u2208 Dj is the current value assigned\nto xj and the priority value k is a positive integer } is the\nperception of agent i;\n\u2022 wl denotes the weight of constraint l, (0 \u2264 l < m);\n\u2022 Si(v) is the total weight of the violated constraints in Ci\nwhen its variable has the value v \u2208 Di.\n4.1 Asynchronous Backtracking\nFigure 2 presents the BDI negotiation model incorporating the\nAsynchronous Backtracking (ABT) strategy. As mentioned in\nSection 3, for an asynchronous mechanism that ABT is, the\nmediation step is needed only in a negotiation round when an agent\nreceives a negotiation message.\nFor agent i, beginning initially with (wl = 1, (0 \u2264 l < m);\npi = i, (0 \u2264 i < n)) and Fi contains all the agents who share the\nconstraints with agent i, its BDI-driven ABT strategy is described\nas follows.\nStep 1 - Percept: Update Pi upon receiving the info\nmessages from the neighbors (in Fi). Update Ci to be the list of\n526 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nconstraints which only consists of agents in Fi that have equal or\nhigher priority than this agent.\nStep 2 - Belief: The belief function GB (Pi,Ci) will return a\nvalue bi \u2208 {0, 1, 2}, decided as follows:\n\u2022 bi = 0 when agent i can find an optimal option, i.e., if\n(Si(vi) = 0 or vi is in bad values list) and (\u2203a \u2208 Di)(Si(a) =\n0) and a is not in a list of domain values called bad values\nlist. Initially this list is empty and it will be cleared when a\nneighbor of higher priority changes its variable assignment.\n\u2022 bi = 1 when it cannot find an optimal option, i.e., if (\u2200a \u2208\nDi)(Si(a) = 0) or a is in bad values list.\n\u2022 bi = 2 when its current variable assignment is an optimal\noption, i.e., if Si(vi) = 0 and vi is not in bad value list.\nStep 3 - Desire: The desire function GD (bi) will return a\ndesire set denoted by DS, decided as follows:\n\u2022 If bi = 0, then DS = {a | (a = vi), (Si(a) = 0) and a is not\nin the bad value list }.\n\u2022 If bi = 1, then DS = \u2205, the agent also finds agent k which\nis determined by {k | pk = min(pj) with agent j \u2208 Fi and\npk > pi }.\n\u2022 If bi = 2, then DS = \u2205.\nStep 4 - Intention: The intention function GI (DS) will\nreturn an intention, decided as follows:\n\u2022 If DS = \u2205, then select an arbitrary value (say, vi) from DS\nas the intention.\n\u2022 If DS = \u2205, then assign nil as the intention (to denote its\nlack thereof).\nStep 5 - Execution:\n\u2022 If agent i has a domain value as its intention, the agent will\nupdate its variable assignment with this value.\n\u2022 If bi = 1, agent i will send a negotiation message to agent\nk, then remove k from Fi and begin its next negotiation\nround. The negotiation message will contain the list of\nvariable assignments of those agents in its neighbor list Fi\nthat have a higher priority than agent i in the current image\nPi.\nMediation: When agent i receives a negotiation message,\nseveral sub-steps are carried out, as follows:\n\u2022 If the list of agents associated with the negotiation message\ncontains agents which are not in Fi, it will add these agents\nto Fi, and request these agents to add itself to their\nneighbor lists. The request is considered as a type of negotiation\nmessage.\n\u2022 Agent i will first check if the sender agent is updated with\nits current value vi. The agent will add vi to its bad values\nlist if it is so, or otherwise send its current value to the\nsender agent.\nFollowing this step, agent i proceeds to the next negotiation\nround.\n4.2 Asynchronous Weak Commitment Search\nFigure 3 presents the BDI negotiation model incorporating the\nAsynchronous Weak Commitment (AWC) strategy. The model is\nsimilar to that of incorporating the ABT strategy (see Figure 2).\nThis is not surprising; AWC and ABT are found to be\nstrategically similar, differing only in the details of some reasoning steps.\nThe distinguishing point of AWC is that when the agent cannot\nfind a suitable variable assignment, it will change its priority to\nthe highest among its group members ({i} \u222a Fi).\nFor agent i, beginning initially with (wl = 1, (0 \u2264 l < m);\npi = i, (0 \u2264 i < n)) and Fi contains all the agents who share\nthe constraints with agent i, its BDI-driven AWC strategy is\ndescribed as follows.\nStep 1 - Percept: This step is identical to the Percept step\nof ABT.\nStep 2 - Belief: The belief function GB (Pi,Ci) will return a\nvalue bi \u2208 {0, 1, 2}, decided as follows:\nPercept\nBelief\nDesire\nIntention\nMediation\nExecution\nP\nB\nD\nI\nInfo Message\nInfo Message\nNegotiation Message\nNegotiation Message\nNegotiation Message\nFigure 3: BDI protocol with Asynchronous\nWeakCommitment strategy\n\u2022 bi = 0 when the agent can find an optimal option i.e., if\n(Si(vi) = 0 or the assignment xi = vi and the current\nvariables assignments of the neighbors in Fi who have higher\npriority form a nogood [4]) stored in a list called nogood list\nand \u2203a \u2208 Di, Si(a) = 0 (initially the list is empty).\n\u2022 bi = 1 when the agent cannot find any optimal option i.e.,\nif \u2200a \u2208 Di, Si(a) = 0.\n\u2022 bi = 2 when the current assignment is an optimal option\ni.e., if Si(vi) = 0 and the current state is not a nogood in\nnogood list.\nStep 3 - Desire: The desire function GD (bi) will return a\ndesire set DS, decided as follows:\n\u2022 If bi = 0, then DS = {a | (a = vi), (Si(a) = 0) and the\nnumber of constraint violations with lower priority agents\nis minimized }.\n\u2022 If bi = 1, then DS = {a | a \u2208 Di and the number of\nviolations of all relevant constraints is minimized }.\n\u2022 If bi = 2, then DS = \u2205.\nFollowing, if bi = 1, agent i will find a list Ki of higher priority\nneighbors, defined by Ki = {k | agent k \u2208 Fi and pk > pi}.\nStep 4 - Intention: This step is similar to the Intention step\nof ABT. However, for this strategy, the negotiation message will\ncontain the variable assignments (of the current image Pi) for\nall the agents in Ki. This list of assignment is considered as\na nogood. If the same negotiation message had been sent out\nbefore, agent i will have nil intention. Otherwise, the agent will\nsend the message and save the nogood in the nogood list.\nStep 5 - Execution:\n\u2022 If agent i has a domain value as its intention, the agent will\nupdate its variable assignment with this value.\n\u2022 If bi = 1, it will send the negotiation message to its\nneighbors in Ki, and set pi = max{pj} + 1, with agent j \u2208 Fi.\nMediation: This step is identical to the Mediation step of\nABT, except that agent i will now add the nogood contained in\nthe negotiation message received to its own nogood list.\n4.3 Distributed Breakout\nFigure 4 presents the BDI negotiation model incorporating the\nDistributed Breakout (DBO) strategy. Essentially, by this\nsynchronous strategy, each agent will search iteratively for\nimprovement by reducing the total weight of the violated constraints.\nThe iteration will continue until no agent can improve further,\nat which time if some constraints remain violated, the weights of\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 527\nPercept\nBelief\nDesire\nIntention\nMediation\nExecution\nP\nB\nD\nI\nI\nA\nInfo Message\nInfo Message\nNegotiation Message\nNegotiation Message\nFigure 4: BDI protocol with Distributed Breakout\nstrategy\nthese constraints will be increased by 1 to help \u2018breakout\" from a\nlocal minimum.\nFor agent i, beginning initially with (wl = 1, (0 \u2264 l < m),\npi = i, (0 \u2264 i < n)) and Fi contains all the agents who share the\nconstraints with agent i, its BDI-driven DBO strategy is described\nas follows.\nStep 1 - Percept: Update Pi upon receiving the info\nmessages from the neighbors (in Fi). Update Ci to be the list of its\nrelevant constraints.\nStep 2 - Belief: The belief function GB (Pi,Ci) will return a\nvalue bi \u2208 {0, 1, 2}, decided as follows:\n\u2022 bi = 0 when agent i can find an option to reduce the number\nviolations of the constraints in Ci, i.e., if \u2203a \u2208 Di, Si(a) <\nSi(vi).\n\u2022 bi = 1 when it cannot find any option to improve situation,\ni.e., if \u2200a \u2208 Di, a = vi, Si(a) \u2265 Si(vi).\n\u2022 bi = 2 when its current assignment is an optimal option,\ni.e., if Si(vi) = 0.\nStep 3 - Desire: The desire function GD (bi) will return a\ndesire set DS, decided as follows:\n\u2022 If bi = 0, then DS = {a | a = vi, Si(a) < Si(vi) and\n(Si(vi)\u2212Si(a)) is maximized }. (max{(Si(vi)\u2212Si(a))} will\nbe referenced by hmax\ni in subsequent steps, and it defines\nthe maximal reduction in constraint violations).\n\u2022 Otherwise, DS = \u2205.\nStep 4 - Intention: The intention function GI (DS) will\nreturn an intention, decided as follows:\n\u2022 If DS = \u2205, then select an arbitrary value (say, vi) from DS\nas the intention.\n\u2022 If DS = \u2205, then assign nil as the intention.\nFollowing, agent i will send its intention to all its neighbors.\nIn return, it will receive intentions from these agents before\nproceeding to Mediation step.\nMediation: Agent i receives all the intentions from its\nneighbors. If it finds that the intention received from a neighbor agent\nj is associated with hmax\nj > hmax\ni , the agent will automatically\ncancel its current intention.\nStep 5 - Execution:\n\u2022 If agent i did not cancel its intention, it will update its\nvariable assignment with the intended value.\nPercept\nBelief\nDesire\nIntention\nMediation\nExecution\nP\nB\nD\nI\nI\nA\nInfo Message\nInfo Message\nNegotiation Message\nNegotiation Message\nNegotiation Message\nNegotiation Message\nFigure 5: BDI protocol with Unsolicited Mutual\nAdvice strategy\n\u2022 If all intentions received and its own one are nil intention,\nthe agent will increase the weight of each currently violated\nconstraint by 1.\n5. THE UMA STRATEGY\nFigure 5 presents the BDI negotiation model incorporating the\nUnsolicited Mutual Advice(UMA) strategy.\nUnlike when using the strategies of the previous section, a\nDCSP agent using UMA will not only send out a negotiation\nmessage when concluding its Intention step, but also when\nconcluding its Desire step. The negotiation message that it sends out\nto conclude the Desire step constitutes an unsolicited advice for\nall its neighbors. In turn, the agent will wait to receive unsolicited\nadvices from all its neighbors, before proceeding on to determine\nits intention.\nFor agent i, beginning initially with (wl = 1, (0 \u2264 l < m),\npi = i, (0 \u2264 i < n)) and Fi contains all the agents who share\nthe constraints with agent i, its BDI-driven UMA strategy is\ndescribed as follows.\nStep 1 - Percept: Update Pi upon receiving the info\nmessages from the neighbors (in Fi). Update Ci to be the list of\nconstraints relevant to agent i.\nStep 2 - Belief: The belief function GB (Pi,Ci) will return a\nvalue bi \u2208 {0, 1, 2}, decided as follows:\n\u2022 bi = 0 when agent i can find an option to reduce the number\nviolations of the constraints in Ci, i.e., if \u2203a \u2208 Di, Si(a) <\nSi(vi) and the assignment xi = a and the current variable\nassignments of its neighbors do not form a local state stored\nin a list called bad states list (initially this list is empty).\n\u2022 bi = 1 when it cannot find a value a such as a \u2208 Di, Si(a) <\nSi(vi), and the assignment xi = a and the current variable\nassignments of its neighbors do not form a local state stored\nin the bad states list.\n\u2022 bi = 2 when its current assignment is an optimal option,\ni.e., if Si(vi) = 0.\nStep 3 - Desire: The desire function GD (bi) will return a\ndesire set DS, decided as follows:\n\u2022 If bi = 0, then DS = {a | a = vi, Si(a) < Si(vi) and\n(Si(vi) \u2212 Si(a)) is maximized } and the assignment xi = a\nand the current variable assignments of agent i\"s neighbors\ndo not form a state in the bad states list. In this case, DS is\ncalled a set of voluntary desires. max{(Si(vi)\u2212Si(a))} will\nbe referenced by hmax\ni in subsequent steps, and it defines\n528 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nthe maximal reduction in constraint violations. It is also\nreferred to as an improvement).\n\u2022 If bi = 1, then DS = {a | a = vi, Si(a) is minimized } and\nthe assignment xi = a and the current variable assignments\nof agent i\"s neighbors do not form a state in the bad states\nlist. In this case, DS is called a set of reluctant desires\n\u2022 If bi = 2, then DS = \u2205.\nFollowing, if bi = 0, agent i will send a negotiation message\ncontaining hmax\ni to all its neighbors. This message is called a\nvoluntary advice. If bi = 1, agent i will send a negotiation message\ncalled change advice to the neighbors in Fi who share the violated\nconstraints with agent i.\nAgent i receives advices from all its neighbors and stores them\nin a list called A, before proceeding to the next step.\nStep 4 - Intention: The intention function GI (DS, A) will\nreturn an intention, decided as follows:\n\u2022 If there is a voluntary advice from an agent j which is\nassociated with hmax\nj > hmax\ni , assign nil as the intention.\n\u2022 If DS = \u2205, DS is a set of voluntary desires and hmax\ni is\nthe biggest improvement among those associated with the\nvoluntary advices received, select an arbitrary value (say,\nvi) from DS as the intention. This intention is called a\nvoluntary intention.\n\u2022 If DS = \u2205, DS is a set of reluctant desires and agent i\nreceives some change advices, select an arbitrary value (say,\nvi) from DS as the intention. This intention is called\nreluctant intention.\n\u2022 If DS = \u2205, then assign nil as the intention.\nFollowing, if the improvement hmax\ni is the biggest improvement\nand equal to some improvements associated with the received\nvoluntary advices, agent i will send its computed intention to all\nits neighbors. If agent i has a reluctant intention, it will also\nsend this intention to all its neighbors. In both cases, agent i\nwill attach the number of received change advices in the current\nnegotiation round with its intention. In return, agent i will receive\nthe intentions from its neighbors before proceeding to Mediation\nstep.\nMediation: If agent i does not send out its intention before\nthis step, i.e., the agent has either a nil intention or a voluntary\nintention with biggest improvement, it will proceed to next step.\nOtherwise, agent i will select the best intention among all the\nintentions received, including its own (if any). The criteria to\nselect the best intention are listed, applied in descending order of\nimportance as follows.\n\u2022 A voluntary intention is preferred over a reluctant intention.\n\u2022 A voluntary intention (if any) with biggest improvement is\nselected.\n\u2022 If there is no voluntary intention, the reluctant intention\nwith the lowest number of constraint violations is selected.\n\u2022 The intention from an agent who has received a higher\nnumber of change advices in the current negotiation round is\nselected.\n\u2022 Intention from an agent with highest priority is selected.\nIf the selected intention is not agent i\"s intention, it will cancel\nits intention.\nStep 5 - Execution: If agent i does not cancel its intention,\nit will update its variable assignment with the intended value.\nTermination Condition: Since each agent does not have\nfull information about the global state, it may not know when it\nhas reached a solution, i.e., when all the agents are in a global\nstable state. Hence an observer is needed that will keep track\nof the negotiation messages communicated in the environment.\nFollowing a certain period of time when there is no more message\ncommunication (and this happens when all the agents have no\nmore intention to update their variable assignments), the observer\nwill inform the agents in the environment that a solution has been\nfound.\n1\n2\n3\n4\n5\n6 7\n8\n9\n10\nFigure 6: Example problem\n5.1 An Example\nTo illustrate how UMA works, consider a 2-color graph problem\n[6] as shown in Figure 6. In this example, each agent has a color\nvariable representing a node. There are 10 color variables sharing\nthe same domain {Black, White}.\nThe following records the outcome of each step in every\nnegotiation round executed.\nRound 1:\nStep 1 - Percept: Each agent obtains the current color\nassignments of those nodes (agents) adjacent to it, i.e., its\nneighbors\".\nStep 2 - Belief: Agents which have positive improvements are\nagent 1 (this agent believes it should change its color to\nWhite), agent 2 (this believes should change its color to\nWhite), agent 7 (this agent believes it should change its\ncolor to Black) and agent 10 (this agent believes it should\nchange its value to Black). In this negotiation round, the\nimprovements achieved by these agents are 1. Agents which\ndo not have any improvements are agents 4, 5 and 8. Agents\n3, 6 and 9 need not change as all their relevant constraints\nare satisfied.\nStep 3 - Desire: Agents 1, 2, 7 and 10 have the voluntary desire\n(White color for agents 1, 2 and Black color for agents 7,\n10). These agents will send the voluntary advices to all\ntheir neighbors. Meanwhile, agents 4, 5 and 8 have the\nreluctant desires (White color for agent 4 and Black color\nfor agents 5, 8). Agent 4 will send a change advice to\nagent 2 as agent 2 is sharing the violated constraint with\nit. Similarly, agents 5 and 8 will send change advices to\nagents 7 and 10 respectively. Agents 3, 6 and 9 do not have\nany desire to update their color assignments.\nStep 4 - Intention: Agents 2, 7 and 10 receive the change\nadvices from agents 4, 5 and 8, respectively. They form their\nvoluntary intentions. Agents 4, 5 and 8 receive the\nvoluntary advices from agents 2, 7 and 10, hence they will not\nhave any intention. Agents 3, 6 and 9 do not have any\nintention. Following, the intention from the agents will be\nsent to all their neighbors.\nMediation: Agent 1 finds that the intention from agent 2 is\nbetter than its intention. This is because, although both\nagents have voluntary intentions with improvement of 1,\nagent 2 has received one change advice from agent 4 while\nagent 1 has not received any. Hence agent 1 cancels its\nintention. Agent 2 will keep its intention.\nAgents 7 and 10 keep their intentions since none of their\nneighbors has an intention.\nThe rest of the agents do nothing in this step as they do\nnot have any intention.\nStep 5 - Execution: Agent 2 changes its color to White. Agents\n7 and 10 change their colors to Black.\nThe new state after round 1 is shown in Figure 7.\nRound 2:\nStep 1 - Percept: The agents obtain the current color\nassignments of their neighbors.\nStep 2 - Belief: Agent 3 is the only agent who has a positive\nimprovement which is 1. It believes it should change its\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 529\n1\n2\n3\n4\n5\n6 7\n8\n9\n10\nFigure 7: The graph after round 1\ncolor to Black. Agent 2 does not have any positive\nimprovement. The rest of the agents need not make any change as\nall their relevant constraints are satisfied. They will have\nno desire, and hence no intention.\nStep 3 - Desire: Agent 3 desires to change its color to Black\nvoluntarily, hence it sends out a voluntary advice to its\nneighbor, i.e., agent 2. Agent 2 does not have any value for\nits reluctant desire set as the only option, Black color, will\nbring agent 2 and its neighbors to the previous state which\nis known to be a bad state. Since agent 2 is sharing the\nconstraint violation with agent 3, it sends a change advice\nto agent 3.\nStep 4 - Intention: Agent 3 will have a voluntary intention\nwhile agent 2 will not have any intention as it receives the\nvoluntary advice from agent 3.\nMediation: Agent 3 will keep its intention as its only neighbor,\nagent 2, does not have any intention.\nStep 5 - Execution: Agent 3 changes its color to Black.\nThe new state after round 2 is shown in Figure 8.\nRound 3: In this round, every agent finds that it has no\ndesire and hence no intention to revise its variable assignment.\nFollowing, with no more negotiation message communication in\nthe environment, the observer will inform all the agents that a\nsolution has been found.\n2\n3\n4\n5\n6 7\n8\n91\n10\nFigure 8: The solution obtained\n5.2 Performance Evaluation\nTo facilitate credible comparisons with existing strategies, we\nmeasured the execution time in terms of computational cycles\nas defined in [4], and built a simulator that could reproduce the\npublished results for ABT and AWC. The definition of a\ncomputational cycle is as follows.\n\u2022 In one cycle, each agent receives all the incoming messages,\nperforms local computation and sends out a reply.\n\u2022 A message which is sent at time t will be received at time\nt + 1. The network delay is neglected.\n\u2022 Each agent has it own clock. The initial clock\"s value is\n0. Agents attach their clock value as a time-stamp in the\noutgoing message and use the time-stamp in the incoming\nmessage to update their own clock\"s value.\nFour benchmark problems [6] were considered, namely, n-queens\nand node coloring for sparse, dense and critical graphs. For each\nproblem, a finite number of test cases were generated for\nvarious problem sizes n. The maximum execution time was set to\n0\n200\n400\n600\n800\n1000\n10 50 100\nNumber of queens\nCycles\nAsynchronous\nBacktracking\nAsynchronous Weak\nCommitment\nUnsolicited Mutual\nAdvice\nFigure 9: Relationship between execution time and\nproblem size\n10000 cycles for node coloring for critical graphs and 1000 cycles\nfor other problems. The simulator program was terminated after\nthis period and the algorithm was considered to fail a test case if\nit did not find a solution by then. In such a case, the execution\ntime for the test was counted as 1000 cycles.\n5.2.1 Evaluation with n-queens problem\nThe n-queens problem is a traditional problem of constraint\nsatisfaction. 10 test cases were generated for each problem size\nn \u2208 {10, 50 and 100}.\nFigure 9 shows the execution time for different problem sizes\nwhen ABT, AWC and UMA were run.\n5.2.2 Evaluation with graph coloring problem\nThe graph coloring problem can be characterized by three\nparameters: (i) the number of colors k, the number of nodes/agents\nn and the number of links m. Based on the ratio m/n, the\nproblem can be classified into three types [3]: (i) sparse (with\nm/n = 2), (ii) critical (with m/n = 2.7 or 4.7) and (iii) dense\n(with m/n = (n \u2212 1)/4). For this problem, we did not include\nABT in our empirical results as its failure rate was found to be\nvery high. This poor performance of ABT was expected since\nthe graph coloring problem is more difficult than the n-queens\nproblem, on which ABT already did not perform well (see Figure\n9).\nThe sparse and dense (coloring) problem types are relatively\neasy while the critical type is difficult to solve. In the\nexperiments, we fix k = 3. 10 test cases were created using the method\ndescribed in [13] for each value of n \u2208 {60, 90, 120}, for each\nproblem type.\nThe simulation results for each type of problem are shown in\nFigures 10 - 12.\n0\n40\n80\n120\n160\n200\n60 90 120 150\nNumber of Nodes\nCycles\nAsynchronous\nWeak\nCommitment\nUnsolicited\nMutual Advice\nFigure 10: Comparison between AWC and UMA\n(sparse graph coloring)\n5.3 Discussion\n5.3.1 Comparison with ABT and AWC\n530 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\n0\n1000\n2000\n3000\n4000\n5000\n6000\n60 90 120\nNumber of Nodes\nCycles\nAsynchronous\nWeak\nCommitment\nUnsolicited\nMutual Advice\nFigure 11: Comparison between AWC and UMA\n(critical graph coloring)\n0\n10\n20\n30\n40\n50\n60 90 120\nNumber of Nodes\nCycles\nAsynchronous\nWeak\nCommitment\nUnsolicited\nMutual Advice\nFigure 12: Comparison between AWC and UMA\n(dense graph coloring)\nFigure 10 shows that the average performance of UMA is slightly\nbetter than AWC for the sparse problem. UMA outperforms\nAWC in solving the critical problem as shown in Figure 11. It\nwas observed that the latter strategy failed in some test cases.\nHowever, as seen in Figure 12, both the strategies are very\nefficient when solving the dense problem, with AWC showing slightly\nbetter performance.\nThe performance of UMA, in the worst (time complexity) case,\nis similar to that of all evaluated strategies. The worst case\noccurs when all the possible global states of the search are reached.\nSince only a few agents have the right to change their variable\nassignments in a negotiation round, the number of redundant\ncomputational cycles and info messages is reduced. As we observe\nfrom the backtracking in ABT and AWC, the difference in the\nordering of incoming messages can result in a different number of\ncomputational cycles to be executed by the agents.\n5.3.2 Comparison with DBO\nThe computational performance of UMA is arguably better\nthan DBO for the following reasons:\n\u2022 UMA can guarantee that there will be a variable\nreassignment following every negotiation round whereas DBO\ncannot.\n\u2022 UMA introduces one more communication round trip (that\nof sending a message and awaiting a reply) than DBO,\nwhich occurs due to the need to communicate unsolicited\nadvices. Although this increases the communication cost\nper negotiation round, we observed from our simulations\nthat the overall communication cost incurred by UMA is\nlower due to the significantly lower number of negotiation\nrounds.\n\u2022 Using UMA, in the worst case, an agent will only take 2 or 3\ncommunication round trips per negotiation round, following\nwhich the agent or its neighbor will do a variable\nassignment update. Using DBO, this number of round trips is\nuncertain as each agent might have to increase the weights\nof the violated constraints until an agent has a positive\nimprovement; this could result in a infinite loop [3].\n6. CONCLUSION\nApplying automated negotiation to DCSP, this paper has\nproposed a protocol that prescribes the generic reasoning of a DCSP\nagent in a BDI architecture. Our work shows that several\nwellknown DCSP algorithms, namely ABT, AWC and DBO, can be\ndescribed as mechanisms sharing the same proposed protocol, and\nonly differ in the strategies employed for the reasoning steps per\nnegotiation round as governed by the protocol. Importantly, this\nmeans that it might furnish a unified framework for DCSP that\nnot only provides a clearer BDI agent-theoretic view of existing\nDCSP approaches, but also opens up the opportunities to enhance\nor develop new strategies. Towards the latter, we have proposed\nand formulated a new strategy - the UMA strategy. Empirical\nresults and our discussion suggest that UMA is superior to ABT,\nAWC and DBO in some specific aspects.\nIt was observed from our simulations that UMA possesses the\ncompleteness property. Future work will attempt to formally\nestablish this property, as well as formalize other existing DSCP\nalgorithms as BDI negotiation mechanisms, including the recent\nendeavor that employs a group mediator [5]. The idea of DCSP\nagents using different strategies in the same environment will also\nbe investigated.\n7. REFERENCES\n[1] P. J. Modi, H. Jung, M. Tambe, W.-M. Shen, and\nS. Kulkarni, Dynamic distributed resource allocation: A\ndistributed constraint satisfaction approach, in Lecture\nNotes in Computer Science, 2001, p. 264.\n[2] H. Schlenker and U. Geske, Simulating large railway\nnetworks using distributed constraint satisfaction, in 2nd\nIEEE International Conference on Industrial Informatics\n(INDIN-04), 2004, pp. 441- 446.\n[3] M. Yokoo, Distributed Constraint Satisfaction :\nFoundations of Cooperation in Multi-Agent Systems.\nSpringer Verlag, 2000, springer Series on Agent Technology.\n[4] M. Yokoo, E. H. Durfee, T. Ishida, and K. Kuwabara, The\ndistributed constraint satisfaction problem : Formalization\nand algorithms, IEEE Transactions on Knowledge and\nData Engineering, vol. 10, no. 5, pp. 673-685,\nSeptember/October 1998.\n[5] R. Mailler and V. Lesser, Using cooperative mediation to\nsolve distributed constraint satisfaction problems, in\nProceedings of the Third International Joint Conference on\nAutonomous Agents and Multiagent Systems\n(AAMAS-04), 2004, pp. 446-453.\n[6] E. Tsang, Foundation of Constraint Satisfaction.\nAcademic Press, 1993.\n[7] R. Mailler, R. Vincent, V. Lesser, T. Middlekoop, and\nJ. Shen, Soft Real-Time, Cooperative Negotiation for\nDistributed Resource Allocation, AAAI Fall Symposium\non Negotiation Methods for Autonomous Cooperative\nSystems, November 2001.\n[8] M. Yokoo, K. Suzuki, and K. Hirayama, Secure\ndistributed constraint satisfaction: Reaching agreement\nwithout revealing private information, Artificial\nIntelligence, vol. 161, no. 1-2, pp. 229-246, 2005.\n[9] J. S. Rosenschein and G. Zlotkin, Rules of Encounter.\nThe MIT Press, 1994.\n[10] M. Yokoo and K. Hirayama, Distributed constraint\nsatisfaction algorithm for complex local problems, in\nProceedings of the Third International Conference on\nMultiagent Systems (ICMAS-98), 1998, pp. 372-379.\n[11] M. E. Bratman, Intentions, Plans and Practical Reason.\nHarvard University Press, Cambridge, M.A, 1987.\n[12] G. Weiss, Ed., Multiagent System : A Modern Approach to\nDistributed Artificial Intelligence. The MIT Press,\nLondon, U.K, 1999.\n[13] S. Minton, M. D. Johnson, A. B. Philips, and P. Laird,\nMinimizing conflicts: A heuristic repair method for\nconstraint satisfaction and scheduling problems, Artificial\nIntelligence, vol. e58, no. 1-3, pp. 161-205, 1992.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 531", "keywords": "algorithm;agent negotiation;constraint;resource restriction;privacy requirement;shared environment;bdi;uma;mediation;backtracking;negotiation;dcsp;belief-desireintention model;distribute constraint satisfaction problem"}
{"name": "train_I-57", "title": "Rumours and Reputation: Evaluating Multi-Dimensional Trust within a Decentralised Reputation System", "abstract": "In this paper we develop a novel probabilistic model of computational trust that explicitly deals with correlated multi-dimensional contracts. Our starting point is to consider an agent attempting to estimate the utility of a contract, and we show that this leads to a model of computational trust whereby an agent must determine a vector of estimates that represent the probability that any dimension of the contract will be successfully fulfilled, and a covariance matrix that describes the uncertainty and correlations in these probabilities. We present a formalism based on the Dirichlet distribution that allows an agent to calculate these probabilities and correlations from their direct experience of contract outcomes, and we show that this leads to superior estimates compared to an alternative approach using multiple independent beta distributions. We then show how agents may use the sufficient statistics of this Dirichlet distribution to communicate and fuse reputation within a decentralised reputation system. Finally, we present a novel solution to the problem of rumour propagation within such systems. This solution uses the notion of private and shared information, and provides estimates consistent with a centralised reputation system, whilst maintaining the anonymity of the agents, and avoiding bias and overconfidence.", "fulltext": "1. INTRODUCTION\nThe role of computational models of trust within multi-agent\nsystems in particular, and open distributed systems in general, has\nrecently generated a great deal of research interest. In such systems,\nagents must typically choose between interaction partners, and in\nthis context trust can be viewed to provide a means for agents to\nrepresent and estimate the reliability with which these interaction\npartners will fulfill their commitments. To date, however, much of\nthe work within this area has used domain specific or ad-hoc trust\nmetrics, and has focused on providing heuristics to evaluate and\nupdate these metrics using direct experience and reputation reports\nfrom other agents (see [8] for a review).\nRecent work has attempted to place the notion of computational\ntrust within the framework of probability theory [6, 11]. This\napproach allows many of the desiderata of computational trust models\nto be addressed through principled means. In particular: (i) it\nallows agents to update their estimates of the trustworthiness of a\nsupplier as they acquire direct experience, (ii) it provides a\nnatural framework for agents to express their uncertainty this\ntrustworthiness, and, (iii) it allows agents to exchange, combine and filter\nreputation reports received from other agents.\nWhilst this approach is attractive, it is somewhat limited in that it\nhas so far only considered single dimensional outcomes (i.e. whether\nthe contract has succeeded or failed in its entirety). However, in\nmany real world settings the success or failure of an interaction may\nbe decomposed into several dimensions [7]. This presents the\nchallenge of combining these multiple dimensions into a single metric\nover which a decision can be made. Furthermore, these dimensions\nwill typically also exhibit correlations. For example, a contract\nwithin a supply chain may specify criteria for timeliness, quality\nand quantity. A supplier who is suffering delays may attempt a\ntrade-off between these dimensions by supplying the full amount\nlate, or supplying as much as possible (but less than the quantity\nspecified within the contract) on time. Thus, correlations will\nnaturally arise between these dimensions, and hence, between the\nprobabilities that describe the successful fulfillment of each contract\ndimension. To date, however, no such principled framework exists\nto describe these multi-dimensional contracts, nor the correlations\nbetween these dimensions (although some ad-hoc models do exist\n- see section 2 for more details).\nTo rectify this shortcoming, in this paper we develop a\nprobabilistic model of computational trust that explicitly deals with\ncorrelated multi-dimensional contracts. The starting point for our work\nis to consider how an agent can estimate the utility that it will derive\nfrom interacting with a supplier. Here we use standard approaches\nfrom the literature of data fusion (since this is a well developed\nfield where the notion of multi-dimensional correlated estimates is\nwell established1\n) to show that this naturally leads to a trust model\nwhere the agent must estimate probabilities and correlations over\n1\nIn this context, the multiple dimensions typically represent the\nphysical coordinates of a target being tracked, and correlations arise\nthrough the operation and orientation of sensors.\n1070\n978-81-904262-7-5 (RPS) c 2007 IFAAMAS\nmultiple dimensions. Building upon this, we then devise a novel\ntrust model that addresses the three desiderata discussed above. In\nmore detail, in this paper we extend the state of the art in four key\nways:\n1. We devise a novel multi-dimensional probabilistic trust model\nthat enables an agent to estimate the expected utility of a\ncontract, by estimating (i) the probability that each contract\ndimension will be successfully fulfilled, and (ii) the\ncorrelations between these estimates.\n2. We present an exact probabilistic model based upon the\nDirichlet distribution that allows agents to use their direct\nexperience of contract outcomes to calculate the probabilities and\ncorrelations described above. We then benchmark this\nsolution and show that it leads to good estimates.\n3. We show that agents can use the sufficient statistics of this\nDirichlet distribution in order to exchange reputation reports\nwith one another. The sufficient statistics represent\naggregations of their direct experience, and thus, express contract\noutcomes in a compact format with no loss of information.\n4. We show that, while being efficient, the aggregation of\ncontract outcomes can lead to double counting, and rumour\npropagation, in decentralised reputation systems. Thus, we present\na novel solution based upon the idea of private and shared\ninformation. We show that it yields estimates consistent with a\ncentralised reputation system, whilst maintaining the anonymity\nof the agents, and avoiding overconfidence.\nThe remainder of this paper is organised as follows: in section 2 we\nreview related work. In section 3 we present our notation for a\nsingle dimensional contract, before introducing our multi-dimensional\ntrust model in section 4. In sections 5 and 6 we discuss\ncommunicating reputation, and present our solution to rumour propagation\nin decentralised reputation systems. We conclude in section 7.\n2. RELATED WORK\nThe need for a multi-dimensional trust model has been recognised\nby a number of researchers. Sabater and Sierra present a model of\nreputation, in which agents form contracts based on multiple\nvariables (such as delivery date and quality), and define impressions as\nsubjective evaluations of the outcome of these contracts. They\nprovide heuristic approaches to combining these impressions to form\na measure they call subjective reputation.\nLikewise, Griffiths decomposes overall trust into a number of\ndifferent dimensions such as success, cost, timeliness and\nquality [4]. In his case, each dimension is scored as a real number\nthat represents a comparative value with no strong semantic\nmeaning. He develops an heuristic rule to update these values based\non the direct experiences of the individual agent, and an heuristic\nfunction that takes the individual trust dimensions and generates a\nsingle scalar that is then used to select between suppliers. Whilst,\nhe comments that the trust values could have some associated\nconfidence level, heuristics for updating these levels are not presented.\nGujral et al. take a similar approach and present a trust model\nover multiple domain specific dimensions [5]. They define\nmultidimensional goal requirements, and evaluate an expected payoff\nbased on a supplier\"s estimated behaviour. These estimates are,\nhowever, simple aggregations over the direct experience of several\nagents, and there is no measure of the uncertainty. Nevertheless,\nthey show that agents who select suppliers based on these multiple\ndimensions outperform those who consider just a single one.\nBy contrast, a number of researchers have presented more\nprincipled computational trust models based on probability theory, albeit\nlimited to a single dimension. J\u00f8sang and Ismail describe the Beta\nReputation System whereby the reputation of an agent is compiled\nfrom the positive and negative reports from other agents who have\ninteracted with it [6]. The beta distribution represents a natural\nchoice for representing these binary outcomes, and it provides a\nprincipled means of representing uncertainty. Moreover, they\nprovide a number of extensions to this initial model including an\napproach to exchanging reputation reports using the sufficient\nstatistics of the beta distribution, methods to discount the opinions of\nagents who themselves have low reputation ratings, and techniques\nto deal with reputations that may change over time.\nLikewise, Teacy et al. use the beta distribution to describe an\nagent\"s belief in the probability that another agent will\nsuccessfully fulfill its commitments [11]. They present a formalism using\na beta distribution that allows the agent to estimate this probability\nbased upon its direct experience, and again they use the sufficient\nstatistics of this distribution to communicate this estimate to other\nagents. They provide a number of extensions to this initial model,\nand, in particular, they consider that agents may not always\ntruthfully report their trust estimates. Thus, they present a principled\napproach to detecting and removing inconsistent reports.\nOur work builds upon these more principled approaches.\nHowever, the starting point of our approach is to consider an agent that\nis attempting to estimate the expected utility of a contract. We show\nthat estimating this expected utility requires that an agent must\nestimate the probability with which the supplier will fulfill its contract.\nIn the single-dimensional case, this naturally leads to a trust model\nusing the beta distribution (as per J\u00f8sang and Ismail and Teacy et\nal.). However, we then go on to extend this analysis to multiple\ndimensions, where we use the natural extension of the beta\ndistribution, namely the Dirichlet distribution, to represent the agent\"s\nbelief over multiple dimensions.\n3. SINGLE-DIMENSIONAL TRUST\nBefore presenting our multi-dimensional trust model, we first\nintroduce the notation and formalism that we will use by describing the\nmore familiar single dimensional case. We consider an agent who\nmust decide whether to engage in a future contract with a supplier.\nThis contract will lead to some outcome, o, and we consider that\no = 1 if the contract is successfully fulfilled, and o = 0 if not2\n.\nIn order for the agent to make a rational decision, it should\nconsider the utility that it will derive from this contract. We assume\nthat in the case that the contract is successfully fulfilled, the agent\nderives a utility u(o = 1), otherwise it receives no utility3\n. Now,\ngiven that the agent is uncertain of the reliability with which the\nsupplier will fulfill the contract, it should consider the expected\nutility that it will derive, E[U], and this is given by:\nE[U] = p(o = 1)u(o = 1) (1)\nwhere p(o = 1) is the probability that the supplier will successfully\nfulfill the contract. However, whilst u(o = 1) is known by the\nagent, p(o = 1) is not. The best the agent can do is to determine\na distribution over possible values of p(o = 1) given its direct\nexperience of previous contract outcomes. Given that it has been\nable to do so, it can then determine an estimate of the expected\nutility4\nof the contract, E[E[U]], and a measure of its uncertainty\nin this expected utility, Var(E[U]). This uncertainty is important\nsince a risk averse agent may make a decision regarding a contract,\n2\nNote that we only consider binary contract outcomes, although\nextending this to partial outcomes is part of our future work.\n3\nClearly this can be extended to the case where some utility is\nderived from an unsuccessful outcome.\n4\nNote that this is often called the expected expected utility, and\nthis is the notation that we adopt here [2].\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1071\nnot only on its estimate of the expected utility of the contract, but\nalso on the probability that the expected utility will exceed some\nminimum amount. These two properties are given by:\nE[E[U]] = \u02c6p(o = 1)u(o = 1) (2)\nVar(E[U]) = Var(p(o = 1))u(o = 1)2\n(3)\nwhere \u02c6p(o = 1) and Var(p(o = 1)) are the estimate and\nuncertainty of the probability that a contract will be successfully\nfulfilled, and are calculated from the distribution over possible values\nof p(o = 1) that the agent determines from its direct experience.\nThe utility based approach that we present here provides an\nattractive motivation for this model of Teacy et al. [11].\nNow, in the case of binary contract outcomes, the beta\ndistribution is the natural choice to represent the distribution over possible\nvalues of p(o = 1) since within Bayesian statistics this well known\nto be the conjugate prior for binomial observations [3]. By adopting\nthe beta distribution, we can calculate \u02c6p(o = 1) and Var(p(o = 1))\nusing standard results, and thus, if an agent observed N previous\ncontracts of which n were successfully fulfilled, then:\n\u02c6p(o = 1) =\nn + 1\nN + 2\nand:\nVar(p(o = 1)) =\n(n + 1)(N \u2212 n + 1)\n(N + 2)2(N + 3)\nNote that as expected, the greater the number of contracts the agent\nobserves, the smaller the variance term Var(p(o = 1)), and, thus,\nthe less the uncertainty regarding the probability that a contract will\nbe successfully fulfilled, \u02c6p(o = 1).\n4. MULTI-DIMENSIONAL TRUST\nWe now extend the description above, to consider contracts\nbetween suppliers and agents that are represented by multiple\ndimensions, and hence the success or failure of a contract can be\ndecomposed into the success or failure of each separate\ndimension. Consider again the example of the supply chain that\nspecifies the timeliness, quantity, and quality of the goods that are to\nbe delivered. Thus, within our trust model oa = 1 now\nindicates a successful outcome over dimension a of the contract and\noa = 0 indicates an unsuccessful one. A contract outcome, X,\nis now composed of a vector of individual contract part outcomes\n(e.g. X = {oa = 1, ob = 0, oc = 0, . . .}).\nGiven a multi-dimensional contract whose outcome is described\nby the vector X, we again consider that in order for an agent to\nmake a rational decision, it should consider the utility that it will\nderive from this contract. To this end, we can make the general\nstatement that the expected utility of a contract is given by:\nE[U] = p(X)U(X)T\n(4)\nwhere p(X) is a joint probability distribution over all possible\ncontract outcomes:\np(X) =\n\u239b\n\u239c\n\u239c\n\u239c\n\u239d\np(oa = 1, ob = 0, oc = 0, . . .)\np(oa = 1, ob = 1, oc = 0, . . .)\np(oa = 0, ob = 1, oc = 0, . . .)\n...\n\u239e\n\u239f\n\u239f\n\u239f\n\u23a0\n(5)\nand U(X) is the utility derived from these possible outcomes:\nU(X) =\n\u239b\n\u239c\n\u239c\n\u239c\n\u239d\nu(oa = 1, ob = 0, oc = 0, . . .)\nu(oa = 1, ob = 1, oc = 0, . . .)\nu(oa = 0, ob = 1, oc = 0, . . .)\n...\n\u239e\n\u239f\n\u239f\n\u239f\n\u23a0\n(6)\nAs before, whilst U(X) is known to the agent, the probability\ndistribution p(X) is not. Rather, given the agent\"s direct experience\nof the supplier, the agent can determine a distribution over possible\nvalues for p(X). In the single dimensional case, a beta distribution\nwas the natural choice over possible values of p(o = 1). In the\nmulti-dimensional case, where p(X) itself is a vector of\nprobabilities, the corresponding natural choice is the Dirichlet distribution,\nsince this is a conjugate prior for multinomial proportions [3].\nGiven this distribution, the agent is then able to calculate an\nestimate of the expected utility of a contract. As before, this estimate\nis itself represented by an expected value given by:\nE[E[U]] = \u02c6p(X)U(X)T\n(7)\nand a variance, describing the uncertainty in this expected utility:\nVar(E[U]) = U(X)Cov(p(X))U(X)T\n(8)\nwhere:\nCov(p(X)) E[(p(X) \u2212 \u02c6p(X))(p(X) \u2212 \u02c6p(X))T\n] (9)\nThus, whilst the single dimensional case naturally leads to a trust\nmodel in which the agents attempt to derive an estimate of\nprobability that a contract will be successfully fulfilled, \u02c6p(o = 1), along\nwith a scalar variance that describes the uncertainty in this\nprobability, Var(p(o = 1)), in this case, the agents must derive an\nestimate of a vector of probabilities, \u02c6p(X), along with a covariance\nmatrix, Cov(p(X)), that represents the uncertainty in p(X) given\nthe observed contractual outcomes. At this point, it is interesting\nto note that the estimate in the single dimensional case, \u02c6p(o = 1),\nhas a clear semantic meaning in relation to trust; it is the agent\"s\nbelief in the probability of a supplier successfully fulfilling a\ncontract. However, in the multi-dimensional case the agent must\ndetermine \u02c6p(X), and since this describes the probability of all possible\ncontract outcomes, including those that are completely un-fulfilled,\nthis direct semantic interpretation is not present. In the next\nsection, we describe the exemplar utility function that we shall use in\nthe remainder of this paper.\n4.1 Exemplar Utility Function\nThe approach described so far is completely general, in that it\napplies to any utility function of the form described above, and also\napplies to the estimation of any joint probability distribution. In\nthe remainder of this paper, for illustrative purposes, we shall limit\nthe discussion to the simplest possible utility function that exhibits\na dependence upon the correlations between the contract\ndimensions. That is, we consider the case that expected utility is\ndependent only on the marginal probabilities of each contract dimension\nbeing successfully fulfilled, rather than the full joint probabilities:\nU(X) =\n\u239b\n\u239c\n\u239c\n\u239c\n\u239d\nu(oa = 1)\nu(ob = 1)\nu(oc = 1)\n...\n\u239e\n\u239f\n\u239f\n\u239f\n\u23a0\n(10)\nThus, \u02c6p(X) is a vector estimate of the probability of each contract\ndimension being successfully fulfilled, and maintains the clear\nsemantic interpretation seen in the single dimensional case:\n\u02c6p(X) =\n\u239b\n\u239c\n\u239c\n\u239c\n\u239d\n\u02c6p(oa = 1)\n\u02c6p(ob = 1)\n\u02c6p(oc = 1)\n...\n\u239e\n\u239f\n\u239f\n\u239f\n\u23a0\n(11)\nThe correlations between the contract dimensions affect the\nuncertainty in the expected utility. To see this, consider the covariance\n1072 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nmatrix that describes this uncertainty, Cov(p(X)), is now given by:\nCov(p(X)) =\n\u239b\n\u239c\n\u239c\n\u239c\n\u239d\nVa Cab Cac . . .\nCab Vb Cbc . . .\nCac Cbc Vc . . .\n...\n...\n...\n\u239e\n\u239f\n\u239f\n\u239f\n\u23a0\n(12)\nIn this matrix, the diagonal terms, Va, Vb and Vc, represent the\nuncertainties in p(oa = 1), p(ob = 1) and p(oc = 1) within\np(X). The off-diagonal terms, Cab, Cac and Cbc, represent the\ncorrelations between these probabilities. In the next section, we use\nthe Dirichlet distribution to calculate both \u02c6p(X) and Cov(p(X))\nfrom an agent\"s direct experience of previous contract outcomes.\nWe first illustrate why this is necessary by considering an\nalternative approach to modelling multi-dimensional contracts whereby\nan agent na\u00a8\u0131vely assumes that the dimensions are independent, and\nthus, it models each individually by separate beta distributions (as\nin the single dimensional case we presented in section 3). This\nis actually equivalent to setting the off-diagonal terms within the\ncovariance matrix, Cov(p(X)), to zero. However, doing so can\nlead an agent to assume that its estimate of the expected utility of\nthe contract is more accurate than it actually is. To illustrate this,\nconsider a specific scenario with the following values: u(oa =\n1) = u(ob = 1) = 1 and Va = Vb = 0.2. In this case,\nVar(E[U]) = 0.4(1 + Cab), and thus, if the correlation Cab is\nignored then the variance in the expected utility is 0.4. However, if\nthe contract outcomes are completely correlated then Cab = 1 and\nVar(E[U]) is actually 0.8. Thus, in order to have an accurate\nestimate of the variance of the expected contract utility, and to make\na rational decision, it is essential that the agent is able to\nrepresent and calculate these correlation terms. In the next section, we\ndescribe how an agent may do so using the Dirichlet distribution.\n4.2 The Dirichlet Distribution\nIn this section, we describe how the agent may use its direct\nexperience of previous contracts, and the standard results of the Dirichlet\ndistribution, to determine an estimate of the probability that each\ncontract dimension will be successful fulfilled, \u02c6p(X), and a\nmeasure of the uncertainties in these probabilities that expresses the\ncorrelations between the contract dimensions, Cov(p(X)).\nWe first consider the calculation of \u02c6p(X) and the diagonal terms\nof the covariance matrix Cov(p(X)). As described above, the\nderivation of these results is identical to the case of the single\ndimensional beta distribution, where out of N contract outcomes,\nn are successfully fulfilled. In the multi-dimensional case,\nhowever, we have a vector {na, nb, nc, . . .} that represents the number\nof outcomes for which each of the individual contract dimensions\nwere successfully fulfilled. Thus, in terms of the standard Dirichlet\nparameters where \u03b1a = na + 1 and \u03b10 = N + 2, the agent can\nestimate the probability of this contract dimension being successfully\nfulfilled:\n\u02c6p(oa = 1) =\n\u03b1a\n\u03b10\n=\nna + 1\nN + 2\nand can also calculate the variance in any contract dimension:\nVa =\n\u03b1a(\u03b10 \u2212 \u03b1a)\n\u03b12\n0(1 + \u03b10)\n=\n(na + 1)(N \u2212 na + 1)\n(N + 2)2(N + 3)\nHowever, calculating the off-diagonal terms within Cov(p(X)) is\nmore complex since it is necessary to consider the correlations\nbetween the contract dimensions. Thus, for each pair of dimensions\n(i.e. a and b), we must consider all possible combinations of\ncontract outcomes, and thus we define nab\nij as the number of contract\noutcomes for which both oa = i and ob = j. For example, nab\n10\nrepresents the number of contracts for which oa = 1 and ob = 0.\nNow, using the standard Dirichlet notation, we can define \u03b1ab\nij\nnab\nij + 1 for all i and j taking values 0 and 1, and then, to calculate\nthe cross-correlations between contract pairs a and b, we note that\nthe Dirichlet distribution over pair-wise joint probabilities is:\nProb(pab) = Kab\ni\u2208{0,1} j\u2208{0,1}\np(oa = i, ob = j)\u03b1ab\nij \u22121\nwhere:\ni\u2208{0,1} j\u2208{0,1}\np(oa = i, ob = j) = 1\nand Kab is a normalising constant [3]. From this we can derive\npair-wise probability estimates and variances:\nE[p(oa = i, ob = j)] =\n\u03b1ab\nij\n\u03b10\n(13)\nV [p(oa = i, ob = j)] =\n\u03b1ab\nij (\u03b10 \u2212 \u03b1ab\nij )\n\u03b12\n0(1 + \u03b10)\n(14)\nwhere:\n\u03b10 =\ni\u2208{0,1} j\u2208{0,1}\n\u03b1ab\nij (15)\nand in fact, \u03b10 = N + 2, where N is the total number of contracts\nobserved. Likewise, we can express the covariance in these\npairwise probabilities in similar terms:\nC[p(oa = i, ob = j), p(oa = m, ob = n)] =\n\u2212\u03b1ab\nij \u03b1ab\nmn\n\u03b12\n0(1 + \u03b10)\nFinally, we can use the expression:\np(oa = 1) =\nj\u2208{0,1}\np(oa = 1, ob = j)\nto determine the covariance Cab. To do so, we first simplify the\nnotation by defining V ab\nij V [p(oa = i, ob = j)] and Cab\nijmn\nC[p(oa = i, ob = j), p(oa = m, ob = n)]. The covariance for the\nprobability of positive contract outcomes is then the covariance\nbetween j\u2208{0,1} p(oa = 1, ob = j) and i\u2208{0,1} p(oa = i, ob =\n1), and thus:\nCab = Cab\n1001 + Cab\n1101 + Cab\n1011 + V ab\n11 .\nThus, given a set of contract outcomes that represent the agent\"s\nprevious interactions with a supplier, we may use the Dirichlet\ndistribution to calculate the mean and variance of the probability of\nany contract dimension being successfully fulfilled (i.e. \u02c6p(oa = 1)\nand Va). In addition, by a somewhat more complex procedure we\ncan also calculate the correlations between these probabilities (i.e.\nCab). This allows us to calculate an estimate of the probability that\nany contract dimension will be successfully fulfilled, \u02c6p(X), and\nalso represent the uncertainty and correlations in these probabilities\nby the covariance matrix, Cov(p(X)). In turn, these results may be\nused to calculate the estimate and uncertainty in the expected\nutility of the contract. In the next section we present empirical results\nthat show that in practise this formalism yields significant\nimprovements in these estimates compared to the na\u00a8\u0131ve approximation\nusing multiple independent beta distributions.\n4.3 Empirical Comparison\nIn order to evaluate the effectiveness of our formalism, and show\nthe importance of the off-diagonal terms in Cov(p(X)), we\ncompare two approaches:\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1073\n\u22121 \u22120.5 0 0.5 1\n0.2\n0.4\n0.6\n0.8\nCorrelation (\u03c1)\nVar(E[U])\nDirichlet Distribution\nIndepedent Beta Distributions\n\u22121 \u22120.5 0 0.5 1\n0.5\n1\n1.5\n2\n2.5\nx 10\n4\nCorrelation (\u03c1)\nInformation(I)\nDirichlet Distribution\nIndepedent Beta Distributions\nFigure 1: Plots showing (i) the variance of the expected contract\nutility and (ii) the information content of the estimates\ncomputed using the Dirichlet distribution and multiple independent\nbeta distributions. Results are averaged over 106\nruns, and the\nerror bars show the standard error in the mean.\n\u2022 Dirichlet Distribution: We use the full Dirichlet\ndistribution, as described above, to calculate \u02c6p(X) and Cov(p(X))\nincluding all its off-diagonal terms that represent the\ncorrelations between the contract dimensions.\n\u2022 Independent Beta Distributions: We use independent beta\ndistributions to represent each contract dimension, in order\nto calculate \u02c6p(X), and then, as described earlier, we\napproximate Cov(p(X)) and ignore the correlations by setting all\nthe off-diagonal terms to zero.\nWe consider a two-dimensional case where u(oa = 1) = 6 and\nu(ob = 1) = 2, since this allows us to plot \u02c6p(X) and Cov(p(X))\nas ellipses in a two-dimensional plane, and thus explain the\ndifferences between the two approaches. Specifically, we initially\nallocate the agent some previous contract outcomes that represents its\ndirect experience with a supplier. The number of contracts is drawn\nuniformly between 10 and 20, and the actual contract outcomes are\ndrawn from an arbitrary joint distribution intended to induce\ncorrelations between the contract dimensions. For each set of\ncontracts, we use the approaches described above to calculate \u02c6p(X)\nand Cov(p(X)), and hence, the variance in the expected contract\nutility, Var(E[U]). In addition, we calculate a scalar measure of the\ninformation content, I, of the covariance matrix Cov(p(X)), which\nis a standard way of measuring the uncertainty encoded within the\ncovariance matrix [1]. More specifically, we calculate the\ndeterminant of the inverse of the covariance matrix:\nI = det(Cov(p(X))\u22121\n) (16)\nand note that the larger the information content, the more precise\n\u02c6p(X) will be, and thus, the better the estimate of the expected\nutility that the agent is able to calculate. Finally, we use the results\n0.3 0.4 0.5 0.6 0.7 0.8\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\np(o =1)\np(o=1)\na\nb\nDirichlet Distribution\nIndepedent Beta Distributions\nFigure 2: Examples of \u02c6p(X) and Cov(p(X)) plotted as second\nstandard error ellipses.\npresented in section 4.2 to calculate the actual correlation, \u03c1,\nassociated with this particular set of contract outcomes:\n\u03c1 =\nCab\n\u221a\nVaVb\n(17)\nwhere Cab, Va and Vb are calculated as described in section 4.2.\nThe results of this analysis are shown in figure 1. Here we show\nthe values of I and Var(E[U]) calculated by the agents, plotted\nagainst the correlation of the contract outcomes, \u03c1, that constituted\ntheir direct experience. The results are averaged over 106\n\nsimulation runs. Note that as expected, when the dimensions of the\ncontract outcomes are uncorrelated (i.e. \u03c1 = 0), then both approaches\ngive the same results. However, the value of using our formalism\nwith the full Dirichlet distribution is shown when the correlation\nbetween the dimensions increases (either negatively or positively).\nAs can be seen, if we approximate the Dirichlet distribution with\nmultiple independent beta distributions, all of the correlation\ninformation contained within the covariance matrix, Cov(p(X)), is\nlost, and thus, the information content of the matrix is much lower.\nThe loss of this correlation information leads the variance of the\nexpected utility of the contract to be incorrect (either over or under\nestimated depending on the correlation)5\n, with the exact amount of\nmis-estimation depending on the actual utility function chosen (i.e.\nthe values of u(oa = 1) and u(ob = 1)).\nIn addition, in figure 2 we illustrate an example of the estimates\ncalculated through both methods, for a single exemplar set of\ncontract outcomes. We represent the probability estimates, \u02c6p(X), and\nthe covariance matrix, Cov(p(X)), in the standard way as an\nellipse [1]. That is, \u02c6p(X) determines the position of the center of\nthe ellipse, Cov(p(X)) defines its size and shape. Note that whilst\nthe ellipse resulting from the full Dirichlet formalism accurately\nreflects the true distribution (samples of which are plotted as points),\nthat calculated by using multiple independent Beta distributions\n(and thus ignoring the correlations) results in a much larger ellipse\nthat does not reflect the true distribution. The larger size of this\nellipse is a result of the off-diagonal terms of the covariance matrix\nbeing set to zero, and corresponds to the agent miscalculating the\nuncertainty in the probability of each contract dimension being\nfulfilled. This, in turn, leads it to miscalculate the uncertainty in the\nexpected utility of a contract (shown in figure 1 as Var(E[U]).\n5. COMMUNICATING REPUTATION\nHaving described how an individual agent can use its own direct\nexperience of contract outcomes in order to estimate the\nprobabil5\nNote that the plots are not smooth due to the fact that given a\nlimited number of contract outcomes, then the mean of Va and Vb\ndo not vary smoothly with \u03c1.\n1074 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nity that a multi-dimensional contract will be successfully fulfilled,\nwe now go on to consider how agents within an open multi-agent\nsystem can communicate these estimates to one another. This is\ncommonly referred to as reputation and allows agents with limited\ndirect experience of a supplier to make rational decisions.\nBoth J\u00f8sang and Ismail, and Teacy et al. present models whereby\nreputation is communicated between agents using the sufficient\nstatistics of the beta distribution [6, 11]. This approach is attractive since\nthese sufficient statistics are simple aggregations of contract\noutcomes (more precisely, they are simply the total number of\ncontracts observed, N, and the number of these that were successfully\nfulfilled, n). Under the probabilistic framework of the beta\ndistribution, reputation reports in this form may simply be aggregated with\nan agent\"s own direct experience, in order to gain a more precise\nestimate based on a larger set of contract outcomes.\nWe can immediately extend this approach to the multi-dimensional\ncase considered here, by requiring that the agents exchange the\nsufficient statistics of the Dirichlet distribution instead of the beta\ndistribution. In this case, for each pair of dimensions (i.e. a and b), the\nagents must communicate a vector of contract outcomes, N, which\nare the sufficient statistics of the Dirichlet distribution, given by:\nN =< nab\nij > \u2200a, b, i \u2208 {0, 1}, j \u2208 {0, 1} (18)\nThus, an agent is able to communicate the sufficient statistics of\nits own Dirichlet distribution in terms of just 2d(d \u2212 1) numbers\n(where d is the number of contract dimensions). For instance, in\nthe case of three dimensions, N, is given by:\nN =< nab\n00, nab\n01, nab\n10, nab\n11, nac\n00, nac\n01, nac\n10, nac\n11, nbc\n00, nbc\n01, nbc\n10, nbc\n11 >\nand, hence, large sets of contract outcomes may be communicated\nwithin a relatively small message size, with no loss of information.\nAgain, agents receiving these sufficient statistics may simply\naggregate them with their own direct experience in order to gain a\nmore precise estimate of the trustworthiness of a supplier.\nFinally, we note that whilst it is not the focus of our work here,\nby adopting the same principled approach as J\u00f8sang and Ismail, and\nTeacy et al., many of the techniques that they have developed (such\nas discounting reports from unreliable agents, and filtering\ninconsistent reports from selfish agents) may be directly applied within\nthis multi-dimensional model. However, we now go on to consider\na new issue that arises in both the single and multi-dimensional\nmodels, namely the problems that arise when such aggregated\nsufficient statistics are propagated within decentralised agent networks.\n6. RUMOUR PROPAGATION\nWITHIN REPUTATION SYSTEMS\nIn the previous section, we described the use of sufficient\nstatistics to communicate reputation, and we showed that by aggregating\ncontract outcomes together into these sufficient statistics, a large\nnumber of contract outcomes can be represented and\ncommunicated in a compact form. Whilst, this is an attractive property, it\ncan be problematic in practise, since the individual provenance of\neach contract outcome is lost in the aggregation. Thus, to ensure an\naccurate estimate, the reputation system must ensure that each\nobservation of a contract outcome is included within the aggregated\nstatistics no more than once.\nWithin a centralised reputation system, where all agents report\ntheir direct experience to a trusted center, such double counting of\ncontract outcomes is easy to avoid. However, in a decentralised\nreputation system, where agents communicate reputation to one\nanother, and aggregate their direct experience with these reputation\nreports on-the-fly, avoiding double counting is much more difficult.\na1 a2\na3\n\u00a8\n\u00a8\u00a8\n\u00a8\u00a8\n\u00a8\u00a8B\nE\nT\nN1\nN1\nN1 + N2\nFigure 3: Example of rumour propagation in a decentralised\nreputation system.\nFor example, consider the case shown in figure 3 where three\nagents (a1 . . . a3), each with some direct experience of a supplier,\nshare reputation reports regarding this supplier. If agent a1 were\nto provide its estimate to agents a2 and a3 in the form of the\nsufficient statistics of its Dirichlet distribution, then these agents can\naggregate these contract outcomes with their own, and thus obtain\nmore precise estimates. If at a later stage, agent a2 were to send\nits aggregate vector of contract outcomes to agent a3, then agent\na3 being unaware of the full history of exchanges, may attempt to\ncombine these contract outcomes with its own aggregated vector.\nHowever, since both vectors contain a contribution from agent a1,\nthese will be counted twice in the final aggregated vector, and will\nresult in a biased and overconfident estimate. This is termed\nrumour propagation or data incest in the data fusion literature [9].\nOne possible solution would be to uniquely identify the source of\neach contract outcome, and then propagate each vector, along with\nits label, through the network. Agents can thus identify identical\nobservations that have arrived through different routes, and after\nremoving the duplicates, can aggregate these together to form their\nestimates. Whilst this appears to be attractive in principle, for a\nnumber of reasons, it is not always a viable solution in practise [12].\nFirstly, agents may not actually wish to have their uniquely labelled\ncontract outcomes passed around an open system, since such\ninformation may have commercial or practical significance that could\nbe used to their disadvantage. As such, agents may only be willing\nto exchange identifiable contract outcomes with a small number of\nother agents (perhaps those that they have some sort of reciprocal\nrelationship with). Secondly, the fact that there is no aggregation\nof the contract outcomes as they pass around the network means\nthat the message size increases over time, and the ultimate size of\nthese messages is bounded only by the number of agents within the\nsystem (possibly an extremely large number for a global system).\nFinally, it may actually be difficult to assign globally agreeable,\nconsistent, and unique labels for each agent within an open system.\nIn the next section, we develop a novel solution to the problem of\nrumour propagation within decentralised reputation systems. Our\nsolution is based on an approach developed within the area of target\ntracking and data fusion [9]. It avoids the need to uniquely identify\nan agent, it allows agents to restrict the number of other agents\nwho they reveal their private estimates to, and yet it still allows\ninformation to propagate throughout the network.\n6.1 Private and Shared Information\nOur solution to rumour propagation within decentralised reputation\nsystems introduces the notion of private information that an agent\nknows it has not communicated to any other agent, and shared\ninformation that has been communicated to, or received from,\nanother agent. Thus, the agent can decompose its contract outcome\nvector, N, into two vectors, a private one, Np, that has not been\ncommunicated to another agent, and a shared one, Ns, that has\nbeen shared with, or received from, another agent:\nN = Np + Ns (19)\nNow, whenever an agent communicates reputation, it\ncommunicates both its private and shared vectors separately. Both the\norigThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1075\ninating and receiving agents then update their two vectors\nappropriately. To understand this, consider the case that agent a\u03b1 sends\nits private and shared contract outcome vectors, N\u03b1\np and N\u03b1\ns , to\nagent a\u03b2 that itself has private and shared contract outcomes N\u03b2\np\nand N\u03b2\ns . Each agent updates its vectors of contract outcomes\naccording to the following procedure:\n\u2022 Originating Agent: Once the originating agent has sent both\nits shared and private contract outcome vectors to another\nagent, its private information is no longer private. Thus, it\nmust remove the contract outcomes that were in its private\nvector, and add them into its shared vector:\nN\u03b1\ns \u2190 N\u03b1\ns + N\u03b1\np\nN\u03b1\np \u2190 \u2205.\n\u2022 Receiving Agent: The goal of the receiving agent is to\naccumulate the largest number contract outcomes (since this will\nresult in the most precise estimate) without including shared\ninformation from both itself and the other agent (since this\nmay result in double counting of contract outcomes). It has\ntwo choices depending on the total number of contract\noutcomes6\nwithin its own shared vector, N\u03b2\ns , and within that of\nthe originating agent, N\u03b1\ns . Thus, it updates its vector\naccording to the procedure below:\n- N\u03b2\ns > N\u03b1\ns : If the receiving agent\"s shared vector\nrepresents a greater number of contract outcomes than that\nof the shared vector of the originating agent, then the\nagent combines its shared vector with the private\nvector of the originating agent:\nN\u03b2\ns \u2190 N\u03b2\ns + N\u03b1\np\nN\u03b2\np unchanged.\n- N\u03b2\ns < N\u03b1\ns : Alternatively if the receiving agent\"s shared\nvector represents a smaller number contract outcomes\nthan that of the shared vector of the originating agent,\nthen the receiving agent discards its own shared vector\nand forms a new one from both the private and shared\nvectors of the originating agent:\nN\u03b2\ns \u2190 N\u03b1\ns + N\u03b1\np\nN\u03b2\np unchanged.\nIn the case that N\u03b2\ns = N\u03b1\ns then either option is\nappropriate. Once the receiving agent has updated its sets, it uses the\ncontract outcomes within both to form its trust estimate. If\nagents receive several vectors simultaneously, this approach\ngeneralises to the receiving agent using the largest shared\nvector, and the private vectors of itself and all the originating\nagents to form its new shared vector.\nThis procedure has a number of attractive properties. Firstly, since\ncontract outcomes in an agent\"s shared vector are never combined\nwith those in the shared vector of another agent, outcomes that\noriginated from the same agent are never combined together, and\nthus, rumour propagation is completely avoided. However, since\nthe receiving agent may discard its own shared vector, and adopt\nthe shared vector of the originating agent, information is still\npropagated around the network. Moreover, since contract outcomes are\naggregated together within the private and shared vectors, the\nmessage size is constant and does not increase as the number of\ninteractions increases. Finally, an agent only communicates its own\nprivate contract outcomes to its immediate neighbours. If this agent\n6\nNote that this may be calculated from N = nab\n00 +nab\n01 +nab\n10 +nab\n11.\nsubsequently passes it on, it does so as unidentifiable aggregated\ninformation within its shared information. Thus, an agent may limit\nthe number of agents with which it is willing to reveal\nidentifiable contract outcomes, and yet these contract outcomes can still\npropagate within the network, and thus, improve estimates of other\nagents. Next, we demonstrate empirically that these properties can\nindeed be realised in practise.\n6.2 Empirical Comparison\nIn order to evaluate the effectiveness of this procedure we\nsimulated random networks consisting of ten agents. Each agent has\nsome direct experience of interacting with a supplier (as described\nin section 4.3). At each iteration of the simulation, it interacts with\nits immediate neighbours and exchanges reputation reports through\nthe sufficient statistics of their Dirichlet distributions. We compare\nour solution to two of the most obvious decentralised alternatives:\n\u2022 Private and Shared Information: The agents follow the\nprocedure described in the previous section. That is, they\nmaintain separate private and shared vectors of contract\noutcomes, and at each iteration they communicate both these\nvectors to their immediate neighbours.\n\u2022 Rumour Propagation: The agents do not differentiate\nbetween private and shared contract outcomes. At the first\niteration they communicate all of the contract outcomes that\nconstitute their direct experience. In subsequent iterations,\nthey propagate contract outcomes that they receive from any\nof the neighbours, to all their other immediate neighbours.\n\u2022 Private Information Only: The agents only communicate\nthe contract outcomes that constitute their direct experience.\nIn all cases, at each iteration, the agents use the Dirichlet\ndistribution in order to calculate their trust estimates. We compare these\nthree decentralised approaches to a centralised reputation system:\n\u2022 Centralised Reputation: All the agents pass their direct\nexperience to a centralised reputation system that aggregates\nthem together, and passes this estimate back to each agent.\nThis centralised solution makes the most effective use of\ninformation available in the network. However, most real world\nproblems demand decentralised solutions due to scalability,\nmodularity and communication concerns. Thus, this centralised solution\nis included since it represents the optimal case, and allows us to\nbenchmark our decentralised solution.\nThe results of these comparisons are shown in figure 4. Here\nwe show the sum of the information content of each agent\"s\ncovariance matrix (calculated as discussed earlier in section 4.3), for\neach of these four different approaches. We first note that where\nprivate information only is communicated, there is no change in\ninformation after the first iteration. Once each agent has received the\ndirect experience of its immediate neighbours, no further increase\nin information can be achieved. This represents the minimum\ncommunication, and it exhibits the lowest total information of the four\ncases. Next, we note that in the case of rumour propagation, the\ninformation content increases continually, and rapidly exceeds the\ncentralised reputation result. The fact that the rumour propagation\ncase incorrectly exceeds this limit, indicates that it is continuously\ncounting the same contract outcomes as they cycle around the\nnetwork, in the belief that they are independent events. Finally, we\nnote that using private and shared information represents a\ncompromise between the private information only case and the centralised\nreputation case. Information is still allowed to propagate around\nthe network, however rumours are eliminated.\nAs before, we also plot a single instance of the trust estimates\nfrom one agent (i.e. \u02c6p(X) and Cov(p(X))) as a set of ellipses on a\n1076 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\n1 2 3 4 5\n10\n4\n10\n6\n10\n8\n10\n10\nIteration\nInformation(I)\nPrivate & Shared Information\nRumour Propagation\nPrivate Information Only\nCentralised Reputation\nFigure 4: Sum of information over all agents as a function of\nthe communication iteration.\ntwo-dimensional plane (along with samples from the true\ndistribution). As expected, the centralised reputation system achieves the\nbest estimate of the true distribution, since it uses the direct\nexperience of all agents. The private information only case shows the\nlargest ellipse since it propagates the least information around the\nnetwork. The rumour propagation case shows the smallest ellipse,\nbut it is inconsistent with the actual distribution p(X). Thus,\npropagating rumours around the network and double counting contract\noutcomes in the belief that they are independent events, results in\nan overconfident estimate. However, we note that our solution,\nusing separate vectors of private and shared information, allows us to\npropagate more information than the private information only case,\nbut we completely avoid the problems of rumour propagation.\nFinally, we consider the effect that this has on the agents\"\ncalculation of the expected utility of the contract. We assume the same\nutility function as used in section 4.3 (i.e. u(oa = 1) = 6 and\nu(ob = 1) = 2), and in table 1 we present the estimate of the\nexpected utility, and its standard deviation calculated for all four cases\nby a single agent at iteration five (after communication has ceased\nto have any further effect for all methods other than rumour\npropagation). We note that the rumour propagation case is clearly\ninconsistent with the centralised reputation system, since its standard\ndeviation is too small and does not reflect the true uncertainty in\nthe expected utility, given the contract outcomes. However, we\nobserve that our solution represents the closest case to the centralised\nreputation system, and thus succeeds in propagating information\nthroughout the network, whilst also avoiding bias and\noverconfidence. The exact difference between it and the centralised\nreputation system depends upon the topology of the network, and the\nhistory of exchanges that take place within it.\n7. CONCLUSIONS\nIn this paper we addressed the need for a principled probabilistic\nmodel of computational trust that deals with contracts that have\nmultiple correlated dimensions. Our starting point was an agent\nestimating the expected utility of a contract, and we showed that this\nleads to a model of computational trust that uses the Dirichlet\ndistribution to calculate a trust estimate from the direct experience of an\nagent. We then showed how agents may use the sufficient statistics\nof this Dirichlet distribution to represent and communicate\nreputation within a decentralised reputation system, and we presented a\nsolution to rumour propagation within these systems.\nOur future work in this area is to extend the exchange of\nreputation to the case where contracts are not homogeneous. That\nis, not all agents observe the same contract dimensions. This is\na challenging extension, since in this case, the sufficient statistics\nof the Dirichlet distribution can not be used directly. However, by\n0.2 0.3 0.4 0.5 0.6 0.7\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\np(o =1)\np(o=1)\na\nb\nPrivate & Shared Information\nRumour Propagation\nPrivate Information Only\nCentralised Reputation\nFigure 5: Instances of \u02c6p(X) and Cov(p(X)) plotted as second\nstandard error ellipses after 5 communication iterations.\nMethod E[E[U]] \u00b1 Var(E[U])\nPrivate and Shared Information 3.18 \u00b1 0.54\nRumour Propagation 3.33 \u00b1 0.07\nPrivate Information Only 3.20 \u00b1 0.65\nCentralised Reputation 3.17 \u00b1 0.42\nTable 1: Estimated expected utility and its standard error as\ncalculated by a single agent after 5 communication iterations.\naddressing this challenge, we hope to be able to apply these\ntechniques to a setting in which a suppliers provides a range of services\nwhose failures are correlated, and agents only have direct\nexperiences of different subsets of these services.\n8. ACKNOWLEDGEMENTS\nThis research was undertaken as part of the ALADDIN (Autonomous\nLearning Agents for Decentralised Data and Information Networks)\nproject and is jointly funded by a BAE Systems and EPSRC\nstrategic partnership (EP/C548051/1).\n9. REFERENCES\n[1] Y. Bar-Shalom, X. R. Li, and T. Kirubarajan. Estimation with Applications to\nTracking and Navigation. Wiley Interscience, 2001.\n[2] C. Boutilier. The foundations of expected expected utility. In Proc. of the 4th\nInt. Joint Conf. on on Artificial Intelligence, pages 285-290, Acapulco,\nMexico, 2003.\n[3] M. Evans, N. Hastings, and B. Peacock. Statistical Distributions. John Wiley\n& Sons, Inc., 1993.\n[4] N. Griffiths. Task delegation using experience-based multi-dimensional trust.\nIn Proc. of the 4th Int. Joint Conf. on Autonomous Agents and Multiagent\nSystems, pages 489-496, New York, USA, 2005.\n[5] N. Gukrai, D. DeAngelis, K. K. Fullam, and K. S. Barber. Modelling\nmulti-dimensional trust. In Proc. of the 9th Int. Workshop on Trust in Agent\nSystems, Hakodate, Japan, 2006.\n[6] A. J\u00f8sang and R. Ismail. The beta reputation system. In Proc. of the 15th Bled\nElectronic Commerce Conf., pages 324-337, Bled, Slovenia, 2002.\n[7] E. M. Maximilien and M. P. Singh. Agent-based trust model involving\nmultiple qualities. In Proc. of the 4th Int. Joint Conf. on Autonomous Agents\nand Multiagent Systems, pages 519-526, Utrecht, The Netherlands, 2005.\n[8] S. D. Ramchurn, D. Hunyh, and N. R. Jennings. Trust in multi-agent systems.\nKnowledge Engineering Review, 19(1):1-25, 2004.\n[9] S. Reece and S. Roberts. Robust, low-bandwidth, multi-vehicle mapping. In\nProc. of the 8th Int. Conf. on Information Fusion, Philadelphia, USA, 2005.\n[10] J. Sabater and C. Sierra. REGRET: A reputation model for gregarious\nsocieties. In Proc. of the 4th Workshop on Deception, Fraud and Trust in Agent\nSocieties, pages 61-69, Montreal, Canada, 2001.\n[11] W. T. L. Teacy, J. Patel, N. R. Jennings, and M. Luck. TRAVOS: Trust and\nreputation in the context of inaccurate information sources. Autonomous\nAgents and Multi-Agent Systems, 12(2):183-198, 2006.\n[12] S. Utete. Network Management in Decentralised Sensing Systems. PhD thesis,\nUniversity of Oxford, UK, 1994.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1077", "keywords": "dirichlet distribution;rumour propogation;double counting;datum fusion;overconfidence;multi-dimensional trust;trust model;probability theory;reputation system;correlation;rumour propagation;heuristic;anonymity"}
{"name": "train_I-58", "title": "An Efficient Heuristic Approach for Security Against Multiple Adversaries", "abstract": "In adversarial multiagent domains, security, commonly defined as the ability to deal with intentional threats from other agents, is a critical issue. This paper focuses on domains where these threats come from unknown adversaries. These domains can be modeled as Bayesian games; much work has been done on finding equilibria for such games. However, it is often the case in multiagent security domains that one agent can commit to a mixed strategy which its adversaries observe before choosing their own strategies. In this case, the agent can maximize reward by finding an optimal strategy, without requiring equilibrium. Previous work has shown this problem of optimal strategy selection to be NP-hard. Therefore, we present a heuristic called ASAP, with three key advantages to address the problem. First, ASAP searches for the highest-reward strategy, rather than a Bayes-Nash equilibrium, allowing it to find feasible strategies that exploit the natural first-mover advantage of the game. Second, it provides strategies which are simple to understand, represent, and implement. Third, it operates directly on the compact, Bayesian game representation, without requiring conversion to normal form. We provide an efficient Mixed Integer Linear Program (MILP) implementation for ASAP, along with experimental results illustrating significant speedups and higher rewards over other approaches.", "fulltext": "1. INTRODUCTION\nIn many multiagent domains, agents must act in order to\nprovide security against attacks by adversaries. A common issue that\nagents face in such security domains is uncertainty about the\nadversaries they may be facing. For example, a security robot may\nneed to make a choice about which areas to patrol, and how often\n[16]. However, it will not know in advance exactly where a robber\nwill choose to strike. A team of unmanned aerial vehicles (UAVs)\n[1] monitoring a region undergoing a humanitarian crisis may also\nneed to choose a patrolling policy. They must make this decision\nwithout knowing in advance whether terrorists or other adversaries\nmay be waiting to disrupt the mission at a given location. It may\nindeed be possible to model the motivations of types of adversaries\nthe agent or agent team is likely to face in order to target these\nadversaries more closely. However, in both cases, the security robot\nor UAV team will not know exactly which kinds of adversaries may\nbe active on any given day.\nA common approach for choosing a policy for agents in such\nscenarios is to model the scenarios as Bayesian games. A Bayesian\ngame is a game in which agents may belong to one or more types;\nthe type of an agent determines its possible actions and payoffs.\nThe distribution of adversary types that an agent will face may\nbe known or inferred from historical data. Usually, these games\nare analyzed according to the solution concept of a Bayes-Nash\nequilibrium, an extension of the Nash equilibrium for Bayesian\ngames. However, in many settings, a Nash or Bayes-Nash\nequilibrium is not an appropriate solution concept, since it assumes that\nthe agents\" strategies are chosen simultaneously [5].\nIn some settings, one player can (or must) commit to a strategy\nbefore the other players choose their strategies. These scenarios are\nknown as Stackelberg games [6]. In a Stackelberg game, a leader\ncommits to a strategy first, and then a follower (or group of\nfollowers) selfishly optimize their own rewards, considering the action\nchosen by the leader. For example, the security agent (leader) must\nfirst commit to a strategy for patrolling various areas. This strategy\ncould be a mixed strategy in order to be unpredictable to the\nrobbers (followers). The robbers, after observing the pattern of patrols\nover time, can then choose their strategy (which location to rob).\nOften, the leader in a Stackelberg game can attain a higher\nreward than if the strategies were chosen simultaneously. To see the\nadvantage of being the leader in a Stackelberg game, consider a\nsimple game with the payoff table as shown in Table 1. The leader\nis the row player and the follower is the column player. Here, the\nleader\"s payoff is listed first.\n1 2 3\n1 5,5 0,0 3,10\n2 0,0 2,2 5,0\nTable 1: Payoff table for example normal form game.\nThe only Nash equilibrium for this game is when the leader plays\n2 and the follower plays 2 which gives the leader a payoff of 2.\n311\n978-81-904262-7-5 (RPS) c 2007 IFAAMAS\nHowever, if the leader commits to a uniform mixed strategy of\nplaying 1 and 2 with equal (0.5) probability, the follower\"s best\nresponse is to play 3 to get an expected payoff of 5 (10 and 0 with\nequal probability). The leader\"s payoff would then be 4 (3 and 5\nwith equal probability). In this case, the leader now has an\nincentive to deviate and choose a pure strategy of 2 (to get a payoff of\n5). However, this would cause the follower to deviate to strategy\n2 as well, resulting in the Nash equilibrium. Thus, by committing\nto a strategy that is observed by the follower, and by avoiding the\ntemptation to deviate, the leader manages to obtain a reward higher\nthan that of the best Nash equilibrium.\nThe problem of choosing an optimal strategy for the leader to\ncommit to in a Stackelberg game is analyzed in [5] and found to\nbe NP-hard in the case of a Bayesian game with multiple types of\nfollowers. Thus, efficient heuristic techniques for choosing\nhighreward strategies in these games is an important open issue.\nMethods for finding optimal leader strategies for non-Bayesian games\n[5] can be applied to this problem by converting the Bayesian game\ninto a normal-form game by the Harsanyi transformation [8]. If, on\nthe other hand, we wish to compute the highest-reward Nash\nequilibrium, new methods using mixed-integer linear programs (MILPs)\n[17] may be used, since the highest-reward Bayes-Nash\nequilibrium is equivalent to the corresponding Nash equilibrium in the\ntransformed game. However, by transforming the game, the\ncompact structure of the Bayesian game is lost. In addition, since the\nNash equilibrium assumes a simultaneous choice of strategies, the\nadvantages of being the leader are not considered.\nThis paper introduces an efficient heuristic method for\napproximating the optimal leader strategy for security domains, known as\nASAP (Agent Security via Approximate Policies). This method has\nthree key advantages. First, it directly searches for an optimal\nstrategy, rather than a Nash (or Bayes-Nash) equilibrium, thus allowing\nit to find high-reward non-equilibrium strategies like the one in the\nabove example. Second, it generates policies with a support which\ncan be expressed as a uniform distribution over a multiset of fixed\nsize as proposed in [12]. This allows for policies that are simple\nto understand and represent [12], as well as a tunable parameter\n(the size of the multiset) that controls the simplicity of the policy.\nThird, the method allows for a Bayes-Nash game to be expressed\ncompactly without conversion to a normal-form game, allowing for\nlarge speedups over existing Nash methods such as [17] and [11].\nThe rest of the paper is organized as follows. In Section 2 we\nfully describe the patrolling domain and its properties. Section 3\nintroduces the Bayesian game, the Harsanyi transformation, and\nexisting methods for finding an optimal leader\"s strategy in a\nStackelberg game. Then, in Section 4 the ASAP algorithm is presented\nfor normal-form games, and in Section 5 we show how it can be\nadapted to the structure of Bayesian games with uncertain\nadversaries. Experimental results showing higher reward and faster\npolicy computation over existing Nash methods are shown in Section\n6, and we conclude with a discussion of related work in Section 7.\n2. THE PATROLLING DOMAIN\nIn most security patrolling domains, the security agents (like\nUAVs [1] or security robots [16]) cannot feasibly patrol all areas all\nthe time. Instead, they must choose a policy by which they patrol\nvarious routes at different times, taking into account factors such as\nthe likelihood of crime in different areas, possible targets for crime,\nand the security agents\" own resources (number of security agents,\namount of available time, fuel, etc.). It is usually beneficial for\nthis policy to be nondeterministic so that robbers cannot safely rob\ncertain locations, knowing that they will be safe from the security\nagents [14]. To demonstrate the utility of our algorithm, we use a\nsimplified version of such a domain, expressed as a game.\nThe most basic version of our game consists of two players: the\nsecurity agent (the leader) and the robber (the follower) in a world\nconsisting of m houses, 1 . . . m. The security agent\"s set of pure\nstrategies consists of possible routes of d houses to patrol (in an\norder). The security agent can choose a mixed strategy so that the\nrobber will be unsure of exactly where the security agent may\npatrol, but the robber will know the mixed strategy the security agent\nhas chosen. For example, the robber can observe over time how\noften the security agent patrols each area. With this knowledge, the\nrobber must choose a single house to rob. We assume that the\nrobber generally takes a long time to rob a house. If the house chosen\nby the robber is not on the security agent\"s route, then the robber\nsuccessfully robs it. Otherwise, if it is on the security agent\"s route,\nthen the earlier the house is on the route, the easier it is for the\nsecurity agent to catch the robber before he finishes robbing it.\nWe model the payoffs for this game with the following variables:\n\u2022 vl,x: value of the goods in house l to the security agent.\n\u2022 vl,q: value of the goods in house l to the robber.\n\u2022 cx: reward to the security agent of catching the robber.\n\u2022 cq: cost to the robber of getting caught.\n\u2022 pl: probability that the security agent can catch the robber at\nthe lth house in the patrol (pl < pl \u21d0\u21d2 l < l).\nThe security agent\"s set of possible pure strategies (patrol routes)\nis denoted by X and includes all d-tuples i =< w1, w2, ..., wd >\nwith w1 . . . wd = 1 . . . m where no two elements are equal (the\nagent is not allowed to return to the same house). The robber\"s\nset of possible pure strategies (houses to rob) is denoted by Q and\nincludes all integers j = 1 . . . m. The payoffs (security agent,\nrobber) for pure strategies i, j are:\n\u2022 \u2212vl,x, vl,q, for j = l /\u2208 i.\n\u2022 plcx +(1\u2212pl)(\u2212vl,x), \u2212plcq +(1\u2212pl)(vl,q), for j = l \u2208 i.\nWith this structure it is possible to model many different types\nof robbers who have differing motivations; for example, one robber\nmay have a lower cost of getting caught than another, or may value\nthe goods in the various houses differently. If the distribution of\ndifferent robber types is known or inferred from historical data,\nthen the game can be modeled as a Bayesian game [6].\n3. BAYESIAN GAMES\nA Bayesian game contains a set of N agents, and each agent n\nmust be one of a given set of types \u03b8n. For our patrolling domain,\nwe have two agents, the security agent and the robber. \u03b81 is the set\nof security agent types and \u03b82 is the set of robber types. Since there\nis only one type of security agent, \u03b81 contains only one element.\nDuring the game, the robber knows its type but the security agent\ndoes not know the robber\"s type. For each agent (the security agent\nor the robber) n, there is a set of strategies \u03c3n and a utility function\nun : \u03b81 \u00d7 \u03b82 \u00d7 \u03c31 \u00d7 \u03c32 \u2192 .\nA Bayesian game can be transformed into a normal-form game\nusing the Harsanyi transformation [8]. Once this is done, new,\nlinear-program (LP)-based methods for finding high-reward\nstrategies for normal-form games [5] can be used to find a strategy in the\ntransformed game; this strategy can then be used for the Bayesian\ngame. While methods exist for finding Bayes-Nash equilibria\ndirectly, without the Harsanyi transformation [10], they find only a\n312 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nsingle equilibrium in the general case, which may not be of high\nreward. Recent work [17] has led to efficient mixed-integer linear\nprogram techniques to find the best Nash equilibrium for a given\nagent. However, these techniques do require a normal-form game,\nand so to compare the policies given by ASAP against the optimal\npolicy, as well as against the highest-reward Nash equilibrium, we\nmust apply these techniques to the Harsanyi-transformed matrix.\nThe next two subsections elaborate on how this is done.\n3.1 Harsanyi Transformation\nThe first step in solving Bayesian games is to apply the Harsanyi\ntransformation [8] that converts the Bayesian game into a normal\nform game. Given that the Harsanyi transformation is a standard\nconcept in game theory, we explain it briefly through a simple\nexample in our patrolling domain without introducing the\nmathematical formulations. Let us assume there are two robber types a and\nb in the Bayesian game. Robber a will be active with probability\n\u03b1, and robber b will be active with probability 1 \u2212 \u03b1. The rules\ndescribed in Section 2 allow us to construct simple payoff tables.\nAssume that there are two houses in the world (1 and 2) and\nhence there are two patrol routes (pure strategies) for the agent:\n{1,2} and {2,1}. The robber can rob either house 1 or house 2\nand hence he has two strategies (denoted as 1l, 2l for robber type\nl). Since there are two types assumed (denoted as a and b), we\nconstruct two payoff tables (shown in Table 2) corresponding to\nthe security agent playing a separate game with each of the two\nrobber types with probabilities \u03b1 and 1 \u2212 \u03b1. First, consider robber\ntype a. Borrowing the notation from the domain section, we assign\nthe following values to the variables: v1,x = v1,q = 3/4, v2,x =\nv2,q = 1/4, cx = 1/2, cq = 1, p1 = 1, p2 = 1/2. Using these\nvalues we construct a base payoff table as the payoff for the game\nagainst robber type a. For example, if the security agent chooses\nroute {1,2} when robber a is active, and robber a chooses house 1,\nthe robber receives a reward of -1 (for being caught) and the agent\nreceives a reward of 0.5 for catching the robber. The payoffs for the\ngame against robber type b are constructed using different values.\nSecurity agent: {1,2} {2,1}\nRobber a\n1a -1, .5 -.375, .125\n2a -.125, -.125 -1, .5\nRobber b\n1b -.9, .6 -.275, .225\n2b -.025, -.025 -.9, .6\nTable 2: Payoff tables: Security Agent vs Robbers a and b\nUsing the Harsanyi technique involves introducing a chance node,\nthat determines the robber\"s type, thus transforming the security\nagent\"s incomplete information regarding the robber into imperfect\ninformation [3]. The Bayesian equilibrium of the game is then\nprecisely the Nash equilibrium of the imperfect information game. The\ntransformed, normal-form game is shown in Table 3. In the\ntransformed game, the security agent is the column player, and the set\nof all robber types together is the row player. Suppose that robber\ntype a robs house 1 and robber type b robs house 2, while the\nsecurity agent chooses patrol {1,2}. Then, the security agent and the\nrobber receive an expected payoff corresponding to their payoffs\nfrom the agent encountering robber a at house 1 with probability \u03b1\nand robber b at house 2 with probability 1 \u2212 \u03b1.\n3.2 Finding an Optimal Strategy\nAlthough a Nash equilibrium is the standard solution concept for\ngames in which agents choose strategies simultaneously, in our\nsecurity domain, the security agent (the leader) can gain an advantage\nby committing to a mixed strategy in advance. Since the followers\n(the robbers) will know the leader\"s strategy, the optimal response\nfor the followers will be a pure strategy. Given the common\nassumption, taken in [5], in the case where followers are indifferent,\nthey will choose the strategy that benefits the leader, there must\nexist a guaranteed optimal strategy for the leader [5].\nFrom the Bayesian game in Table 2, we constructed the Harsanyi\ntransformed bimatrix in Table 3. The strategies for each player\n(security agent or robber) in the transformed game correspond to all\ncombinations of possible strategies taken by each of that player\"s\ntypes. Therefore, we denote X = \u03c3\u03b81\n1 = \u03c31 and Q = \u03c3\u03b82\n2 as the\nindex sets of the security agent and robbers\" pure strategies\nrespectively, with R and C as the corresponding payoff matrices. Rij is\nthe reward of the security agent and Cij is the reward of the\nrobbers when the security agent takes pure strategy i and the robbers\ntake pure strategy j. A mixed strategy for the security agent is a\nprobability distribution over its set of pure strategies and will be\nrepresented by a vector x = (px1, px2, . . . , px|X|), where pxi \u2265 0\nand\nP\npxi = 1. Here, pxi is the probability that the security agent\nwill choose its ith pure strategy.\nThe optimal mixed strategy for the security agent can be found\nin time polynomial in the number of rows in the normal form game\nusing the following linear program formulation from [5].\nFor every possible pure strategy j by the follower (the set of all\nrobber types),\nmax\nP\ni\u2208X pxiRij\ns.t. \u2200j \u2208 Q,\nP\ni\u2208\u03c31\npxiCij \u2265\nP\ni\u2208\u03c31\npxiCij\nP\ni\u2208X pxi = 1\n\u2200i\u2208X , pxi >= 0\n(1)\nThen, for all feasible follower strategies j, choose the one that\nmaximizes\nP\ni\u2208X pxiRij, the reward for the security agent (leader).\nThe pxi variables give the optimal strategy for the security agent.\nNote that while this method is polynomial in the number of rows\nin the transformed, normal-form game, the number of rows\nincreases exponentially with the number of robber types. Using this\nmethod for a Bayesian game thus requires running |\u03c32||\u03b82|\n\nseparate linear programs. This is no surprise, since finding the leader\"s\noptimal strategy in a Bayesian Stackelberg game is NP-hard [5].\n4. HEURISTIC APPROACHES\nGiven that finding the optimal strategy for the leader is NP-hard,\nwe provide a heuristic approach. In this heuristic we limit the\npossible mixed strategies of the leader to select actions with\nprobabilities that are integer multiples of 1/k for a predetermined integer\nk. Previous work [14] has shown that strategies with high entropy\nare beneficial for security applications when opponents\" utilities\nare completely unknown. In our domain, if utilities are not\nconsidered, this method will result in uniform-distribution strategies.\nOne advantage of such strategies is that they are compact to\nrepresent (as fractions) and simple to understand; therefore they can\nbe efficiently implemented by real organizations. We aim to\nmaintain the advantage provided by simple strategies for our security\napplication problem, incorporating the effect of the robbers\"\nrewards on the security agent\"s rewards. Thus, the ASAP heuristic\nwill produce strategies which are k-uniform. A mixed strategy is\ndenoted k-uniform if it is a uniform distribution on a multiset S of\npure strategies with |S| = k. A multiset is a set whose elements\nmay be repeated multiple times; thus, for example, the mixed\nstrategy corresponding to the multiset {1, 1, 2} would take strategy 1\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 313\n{1,2} {2,1}\n{1a, 1b} \u22121\u03b1 \u2212 .9(1 \u2212 \u03b1), .5\u03b1 + .6(1 \u2212 \u03b1) \u2212.375\u03b1 \u2212 .275(1 \u2212 \u03b1), .125\u03b1 + .225(1 \u2212 \u03b1)\n{1a, 2b} \u22121\u03b1 \u2212 .025(1 \u2212 \u03b1), .5\u03b1 \u2212 .025(1 \u2212 \u03b1) \u2212.375\u03b1 \u2212 .9(1 \u2212 \u03b1), .125\u03b1 + .6(1 \u2212 \u03b1)\n{2a, 1b} \u2212.125\u03b1 \u2212 .9(1 \u2212 \u03b1), \u2212.125\u03b1 + .6(1 \u2212 \u03b1) \u22121\u03b1 \u2212 .275(1 \u2212 \u03b1), .5\u03b1 + .225(1 \u2212 \u03b1)\n{2a, 2b} \u2212.125\u03b1 \u2212 .025(1 \u2212 \u03b1), \u2212.125\u03b1 \u2212 .025(1 \u2212 \u03b1) \u22121\u03b1 \u2212 .9(1 \u2212 \u03b1), .5\u03b1 + .6(1 \u2212 \u03b1)\nTable 3: Harsanyi Transformed Payoff Table\nwith probability 2/3 and strategy 2 with probability 1/3. ASAP\nallows the size of the multiset to be chosen in order to balance the\ncomplexity of the strategy reached with the goal that the identified\nstrategy will yield a high reward.\nAnother advantage of the ASAP heuristic is that it operates\ndirectly on the compact Bayesian representation, without requiring\nthe Harsanyi transformation. This is because the different follower\n(robber) types are independent of each other. Hence, evaluating\nthe leader strategy against a Harsanyi-transformed game matrix\nis equivalent to evaluating against each of the game matrices for\nthe individual follower types. This independence property is\nexploited in ASAP to yield a decomposition scheme. Note that the LP\nmethod introduced by [5] to compute optimal Stackelberg policies\nis unlikely to be decomposable into a small number of games as it\nwas shown to be NP-hard for Bayes-Nash problems. Finally, note\nthat ASAP requires the solution of only one optimization problem,\nrather than solving a series of problems as in the LP method of [5].\nFor a single follower type, the algorithm works the following\nway. Given a particular k, for each possible mixed strategy x for the\nleader that corresponds to a multiset of size k, evaluate the leader\"s\npayoff from x when the follower plays a reward-maximizing pure\nstrategy. We then take the mixed strategy with the highest payoff.\nWe need only to consider the reward-maximizing pure\nstrategies of the followers (robbers), since for a given fixed strategy x\nof the security agent, each robber type faces a problem with fixed\nlinear rewards. If a mixed strategy is optimal for the robber, then\nso are all the pure strategies in the support of that mixed strategy.\nNote also that because we limit the leader\"s strategies to take on\ndiscrete values, the assumption from Section 3.2 that the followers\nwill break ties in the leader\"s favor is not significant, since ties will\nbe unlikely to arise. This is because, in domains where rewards are\ndrawn from any random distribution, the probability of a follower\nhaving more than one pure optimal response to a given leader\nstrategy approaches zero, and the leader will have only a finite number\nof possible mixed strategies.\nOur approach to characterize the optimal strategy for the security\nagent makes use of properties of linear programming. We briefly\noutline these results here for completeness, for detailed discussion\nand proofs see one of many references on the topic, such as [2].\nEvery linear programming problem, such as:\nmax cT\nx | Ax = b, x \u2265 0,\nhas an associated dual linear program, in this case:\nmin bT\ny | AT\ny \u2265 c.\nThese primal/dual pairs of problems satisfy weak duality: For any x\nand y primal and dual feasible solutions respectively, cT\nx \u2264 bT\ny.\nThus a pair of feasible solutions is optimal if cT\nx = bT\ny, and\nthe problems are said to satisfy strong duality. In fact if a linear\nprogram is feasible and has a bounded optimal solution, then the\ndual is also feasible and there is a pair x\u2217\n, y\u2217\nthat satisfies cT\nx\u2217\n=\nbT\ny\u2217\n. These optimal solutions are characterized with the following\noptimality conditions (as defined in [2]):\n\u2022 primal feasibility: Ax = b, x \u2265 0\n\u2022 dual feasibility: AT\ny \u2265 c\n\u2022 complementary slackness: xi(AT\ny \u2212 c)i = 0 for all i.\nNote that this last condition implies that\ncT\nx = xT\nAT\ny = bT\ny,\nwhich proves optimality for primal dual feasible solutions x and y.\nIn the following subsections, we first define the problem in its\nmost intuititive form as a mixed-integer quadratic program (MIQP),\nand then show how this problem can be converted into a\nmixedinteger linear program (MILP).\n4.1 Mixed-Integer Quadratic Program\nWe begin with the case of a single type of follower. Let the\nleader be the row player and the follower the column player. We\ndenote by x the vector of strategies of the leader and q the vector\nof strategies of the follower. We also denote X and Q the index\nsets of the leader and follower\"s pure strategies, respectively. The\npayoff matrices R and C correspond to: Rij is the reward of the\nleader and Cij is the reward of the follower when the leader takes\npure strategy i and the follower takes pure strategy j. Let k be the\nsize of the multiset.\nWe first fix the policy of the leader to some k-uniform policy\nx. The value xi is the number of times pure strategy i is used in\nthe k-uniform policy, which is selected with probability xi/k. We\nformulate the optimization problem the follower solves to find its\noptimal response to x as the following linear program:\nmax\nX\nj\u2208Q\nX\ni\u2208X\n1\nk\nCijxi qj\ns.t.\nP\nj\u2208Q qj = 1\nq \u2265 0.\n(2)\nThe objective function maximizes the follower\"s expected reward\ngiven x, while the constraints make feasible any mixed strategy q\nfor the follower. The dual to this linear programming problem is\nthe following:\nmin a\ns.t. a \u2265\nX\ni\u2208X\n1\nk\nCijxi j \u2208 Q. (3)\nFrom strong duality and complementary slackness we obtain that\nthe follower\"s maximum reward value, a, is the value of every pure\nstrategy with qj > 0, that is in the support of the optimal mixed\nstrategy. Therefore each of these pure strategies is optimal.\nOptimal solutions to the follower\"s problem are characterized by linear\nprogramming optimality conditions: primal feasibility constraints\nin (2), dual feasibility constraints in (3), and complementary\nslackness\nqj a \u2212\nX\ni\u2208X\n1\nk\nCijxi\n!\n= 0 j \u2208 Q.\nThese conditions must be included in the problem solved by the\nleader in order to consider only best responses by the follower to\nthe k-uniform policy x.\n314 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nThe leader seeks the k-uniform solution x that maximizes its\nown payoff, given that the follower uses an optimal response q(x).\nTherefore the leader solves the following integer problem:\nmax\nX\ni\u2208X\nX\nj\u2208Q\n1\nk\nRijq(x)j xi\ns.t.\nP\ni\u2208X xi = k\nxi \u2208 {0, 1, . . . , k}.\n(4)\nProblem (4) maximizes the leader\"s reward with the follower\"s best\nresponse (qj for fixed leader\"s policy x and hence denoted q(x)j)\nby selecting a uniform policy from a multiset of constant size k. We\ncomplete this problem by including the characterization of q(x)\nthrough linear programming optimality conditions. To simplify\nwriting the complementary slackness conditions, we will constrain\nq(x) to be only optimal pure strategies by just considering integer\nsolutions of q(x). The leader\"s problem becomes:\nmaxx,q\nX\ni\u2208X\nX\nj\u2208Q\n1\nk\nRijxiqj\ns.t.\nP\ni xi = kP\nj\u2208Q qj = 1\n0 \u2264 (a \u2212\nP\ni\u2208X\n1\nk\nCijxi) \u2264 (1 \u2212 qj)M\nxi \u2208 {0, 1, ...., k}\nqj \u2208 {0, 1}.\n(5)\nHere, the constant M is some large number. The first and fourth\nconstraints enforce a k-uniform policy for the leader, and the\nsecond and fifth constraints enforce a feasible pure strategy for the\nfollower. The third constraint enforces dual feasibility of the\nfollower\"s problem (leftmost inequality) and the complementary\nslackness constraint for an optimal pure strategy q for the follower\n(rightmost inequality). In fact, since only one pure strategy can be\nselected by the follower, say qh = 1, this last constraint enforces that\na =\nP\ni\u2208X\n1\nk\nCihxi imposing no additional constraint for all other\npure strategies which have qj = 0.\nWe conclude this subsection noting that Problem (5) is an\ninteger program with a non-convex quadratic objective in general,\nas the matrix R need not be positive-semi-definite. Efficient\nsolution methods for non-linear, non-convex integer problems remains\na challenging research question. In the next section we show a\nreformulation of this problem as a linear integer programming\nproblem, for which a number of efficient commercial solvers exist.\n4.2 Mixed-Integer Linear Program\nWe can linearize the quadratic program of Problem 5 through the\nchange of variables zij = xiqj, obtaining the following problem\nmaxq,z\nP\ni\u2208X\nP\nj\u2208Q\n1\nk\nRijzij\ns.t.\nP\ni\u2208X\nP\nj\u2208Q zij = k\nP\nj\u2208Q zij \u2264 k\nkqj \u2264\nP\ni\u2208X zij \u2264 k\nP\nj\u2208Q qj = 1\n0 \u2264 (a \u2212\nP\ni\u2208X\n1\nk\nCij(\nP\nh\u2208Q zih)) \u2264 (1 \u2212 qj)M\nzij \u2208 {0, 1, ...., k}\nqj \u2208 {0, 1}\n(6)\nPROPOSITION 1. Problems (5) and (6) are equivalent.\nProof: Consider x, q a feasible solution of (5). We will show\nthat q, zij = xiqj is a feasible solution of (6) of same objective\nfunction value. The equivalence of the objective functions, and\nconstraints 4, 6 and 7 of (6) are satisfied by construction. The fact\nthat\nP\nj\u2208Q zij = xi as\nP\nj\u2208Q qj = 1 explains constraints 1, 2, and\n5 of (6). Constraint 3 of (6) is satisfied because\nP\ni\u2208X zij = kqj.\nLet us now consider q, z feasible for (6). We will show that q and\nxi =\nP\nj\u2208Q zij are feasible for (5) with the same objective value.\nIn fact all constraints of (5) are readily satisfied by construction. To\nsee that the objectives match, notice that if qh = 1 then the third\nconstraint in (6) implies that\nP\ni\u2208X zih = k, which means that\nzij = 0 for all i \u2208 X and all j = h. Therefore,\nxiqj =\nX\nl\u2208Q\nzilqj = zihqj = zij.\nThis last equality is because both are 0 when j = h. This shows\nthat the transformation preserves the objective function value,\ncompleting the proof.\nGiven this transformation to a mixed-integer linear program (MILP),\nwe now show how we can apply our decomposition technique on\nthe MILP to obtain significant speedups for Bayesian games with\nmultiple follower types.\n5. DECOMPOSITION FOR MULTIPLE\nADVERSARIES\nThe MILP developed in the previous section handles only one\nfollower. Since our security scenario contains multiple follower\n(robber) types, we change the response function for the follower\nfrom a pure strategy into a weighted combination over various pure\nfollower strategies where the weights are probabilities of\noccurrence of each of the follower types.\n5.1 Decomposed MIQP\nTo admit multiple adversaries in our framework, we modify the\nnotation defined in the previous section to reason about multiple\nfollower types. We denote by x the vector of strategies of the leader\nand ql\nthe vector of strategies of follower l, with L denoting the\nindex set of follower types. We also denote by X and Q the index\nsets of leader and follower l\"s pure strategies, respectively. We also\nindex the payoff matrices on each follower l, considering the\nmatrices Rl\nand Cl\n.\nUsing this modified notation, we characterize the optimal\nsolution of follower l\"s problem given the leaders k-uniform policy x,\nwith the following optimality conditions:\nX\nj\u2208Q\nql\nj = 1\nal\n\u2212\nX\ni\u2208X\n1\nk\nCl\nijxi \u2265 0\nql\nj(al\n\u2212\nX\ni\u2208X\n1\nk\nCl\nijxi) = 0\nql\nj \u2265 0\nAgain, considering only optimal pure strategies for follower l\"s\nproblem we can linearize the complementarity constraint above.\nWe incorporate these constraints on the leader\"s problem that\nselects the optimal k-uniform policy. Therefore, given a priori\nprobabilities pl\n, with l \u2208 L of facing each follower, the leader solves\nthe following problem:\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 315\nmaxx,q\nX\ni\u2208X\nX\nl\u2208L\nX\nj\u2208Q\npl\nk\nRl\nijxiql\nj\ns.t.\nP\ni xi = kP\nj\u2208Q ql\nj = 1\n0 \u2264 (al\n\u2212\nP\ni\u2208X\n1\nk\nCl\nijxi) \u2264 (1 \u2212 ql\nj)M\nxi \u2208 {0, 1, ...., k}\nql\nj \u2208 {0, 1}.\n(7)\nProblem (7) for a Bayesian game with multiple follower types\nis indeed equivalent to Problem (5) on the payoff matrix obtained\nfrom the Harsanyi transformation of the game. In fact, every pure\nstrategy j in Problem (5) corresponds to a sequence of pure\nstrategies jl, one for each follower l \u2208 L. This means that qj = 1 if\nand only if ql\njl\n= 1 for all l \u2208 L. In addition, given the a\npriori probabilities pl\nof facing player l, the reward in the Harsanyi\ntransformation payoff table is Rij =\nP\nl\u2208L pl\nRl\nijl\n. The same\nrelation holds between C and Cl\n. These relations between a pure\nstrategy in the equivalent normal form game and pure strategies in\nthe individual games with each followers are key in showing these\nproblems are equivalent.\n5.2 Decomposed MILP\nWe can linearize the quadratic programming problem 7 through\nthe change of variables zl\nij = xiql\nj, obtaining the following\nproblem\nmaxq,z\nP\ni\u2208X\nP\nl\u2208L\nP\nj\u2208Q\npl\nk\nRl\nijzl\nij\ns.t.\nP\ni\u2208X\nP\nj\u2208Q zl\nij = k\nP\nj\u2208Q zl\nij \u2264 k\nkql\nj \u2264\nP\ni\u2208X zl\nij \u2264 k\nP\nj\u2208Q ql\nj = 1\n0 \u2264 (al\n\u2212\nP\ni\u2208X\n1\nk\nCl\nij(\nP\nh\u2208Q zl\nih)) \u2264 (1 \u2212 ql\nj)M\nP\nj\u2208Q zl\nij =\nP\nj\u2208Q z1\nij\nzl\nij \u2208 {0, 1, ...., k}\nql\nj \u2208 {0, 1}\n(8)\nPROPOSITION 2. Problems (7) and (8) are equivalent.\nProof: Consider x, ql\n, al\nwith l \u2208 L a feasible solution of (7).\nWe will show that ql\n, al\n, zl\nij = xiql\nj is a feasible solution of (8)\nof same objective function value. The equivalence of the objective\nfunctions, and constraints 4, 7 and 8 of (8) are satisfied by\nconstruction. The fact that\nP\nj\u2208Q zl\nij = xi as\nP\nj\u2208Q ql\nj = 1 explains\nconstraints 1, 2, 5 and 6 of (8). Constraint 3 of (8) is satisfied\nbecause\nP\ni\u2208X zl\nij = kql\nj.\nLets now consider ql\n, zl\n, al\nfeasible for (8). We will show that\nql\n, al\nand xi =\nP\nj\u2208Q z1\nij are feasible for (7) with the same\nobjective value. In fact all constraints of (7) are readily satisfied by\nconstruction. To see that the objectives match, notice for each l\none ql\nj must equal 1 and the rest equal 0. Let us say that ql\njl\n= 1,\nthen the third constraint in (8) implies that\nP\ni\u2208X zl\nijl\n= k, which\nmeans that zl\nij = 0 for all i \u2208 X and all j = jl. In particular this\nimplies that\nxi =\nX\nj\u2208Q\nz1\nij = z1\nij1\n= zl\nijl\n,\nthe last equality from constraint 6 of (8). Therefore xiql\nj = zl\nijl\nql\nj =\nzl\nij. This last equality is because both are 0 when j = jl.\nEffectively, constraint 6 ensures that all the adversaries are calculating\ntheir best responses against a particular fixed policy of the agent.\nThis shows that the transformation preserves the objective function\nvalue, completing the proof.\nWe can therefore solve this equivalent linear integer program\nwith efficient integer programming packages which can handle\nproblems with thousands of integer variables. We implemented the\ndecomposed MILP and the results are shown in the following section.\n6. EXPERIMENTAL RESULTS\nThe patrolling domain and the payoffs for the associated game\nare detailed in Sections 2 and 3. We performed experiments for this\ngame in worlds of three and four houses with patrols consisting of\ntwo houses. The description given in Section 2 is used to generate\na base case for both the security agent and robber payoff functions.\nThe payoff tables for additional robber types are constructed and\nadded to the game by adding a random distribution of varying size\nto the payoffs in the base case. All games are normalized so that,\nfor each robber type, the minimum and maximum payoffs to the\nsecurity agent and robber are 0 and 1, respectively.\nUsing the data generated, we performed the experiments using\nfour methods for generating the security agent\"s strategy:\n\u2022 uniform randomization\n\u2022 ASAP\n\u2022 the multiple linear programs method from [5] (to find the true\noptimal strategy)\n\u2022 the highest reward Bayes-Nash equilibrium, found using the\nMIP-Nash algorithm [17]\nThe last three methods were applied using CPLEX 8.1. Because\nthe last two methods are designed for normal-form games rather\nthan Bayesian games, the games were first converted using the\nHarsanyi transformation [8]. The uniform randomization method is\nsimply choosing a uniform random policy over all possible patrol\nroutes. We use this method as a simple baseline to measure the\nperformance of our heuristics. We anticipated that the uniform policy\nwould perform reasonably well since maximum-entropy policies\nhave been shown to be effective in multiagent security domains\n[14]. The highest-reward Bayes-Nash equilibria were used in order\nto demonstrate the higher reward gained by looking for an optimal\npolicy rather than an equilibria in Stackelberg games such as our\nsecurity domain.\nBased on our experiments we present three sets of graphs to\ndemonstrate (1) the runtime of ASAP compared to other common\nmethods for finding a strategy, (2) the reward guaranteed by ASAP\ncompared to other methods, and (3) the effect of varying the\nparameter k, the size of the multiset, on the performance of ASAP.\nIn the first two sets of graphs, ASAP is run using a multiset of\n80 elements; in the third set this number is varied. The first set of\ngraphs, shown in Figure 1 shows the runtime graphs for three-house\n(left column) and four-house (right column) domains. Each of the\nthree rows of graphs corresponds to a different randomly-generated\nscenario. The x-axis shows the number of robber types the\nsecurity agent faces and the y-axis of the graph shows the runtime in\nseconds. All experiments that were not concluded in 30 minutes\n(1800 seconds) were cut off. The runtime for the uniform policy\nis always negligible irrespective of the number of adversaries and\nhence is not shown.\nThe ASAP algorithm clearly outperforms the optimal,\nmultipleLP method as well as the MIP-Nash algorithm for finding the\nhighestreward Bayes-Nash equilibrium with respect to runtime. For a\n316 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nFigure 1: Runtimes for various algorithms on problems of 3\nand 4 houses.\ndomain of three houses, the optimal method cannot reach a\nsolution for more than seven robber types, and for four houses it\ncannot solve for more than six types within the cutoff time in any of\nthe three scenarios. MIP-Nash solves for even fewer robber types\nwithin the cutoff time. On the other hand, ASAP runs much faster,\nand is able to solve for at least 20 adversaries for the three-house\nscenarios and for at least 12 adversaries in the four-house\nscenarios within the cutoff time. The runtime of ASAP does not increase\nstrictly with the number of robber types for each scenario, but in\ngeneral, the addition of more types increases the runtime required.\nThe second set of graphs, Figure 2, shows the reward to the patrol\nagent given by each method for three scenarios in the three-house\n(left column) and four-house (right column) domains. This reward\nis the utility received by the security agent in the patrolling game,\nand not as a percentage of the optimal reward, since it was not\npossible to obtain the optimal reward as the number of robber types\nincreased. The uniform policy consistently provides the lowest\nreward in both domains; while the optimal method of course\nproduces the optimal reward. The ASAP method remains consistently\nclose to the optimal, even as the number of robber types increases.\nThe highest-reward Bayes-Nash equilibria, provided by the\nMIPNash method, produced rewards higher than the uniform method,\nbut lower than ASAP. This difference clearly illustrates the gains in\nthe patrolling domain from committing to a strategy as the leader\nin a Stackelberg game, rather than playing a standard Bayes-Nash\nstrategy.\nThe third set of graphs, shown in Figure 3 shows the effect of the\nmultiset size on runtime in seconds (left column) and reward (right\ncolumn), again expressed as the reward received by the security\nagent in the patrolling game, and not a percentage of the optimal\nFigure 2: Reward for various algorithms on problems of 3 and\n4 houses.\nreward. Results here are for the three-house domain. The trend is\nthat as as the multiset size is increased, the runtime and reward level\nboth increase. Not surprisingly, the reward increases monotonically\nas the multiset size increases, but what is interesting is that there is\nrelatively little benefit to using a large multiset in this domain. In\nall cases, the reward given by a multiset of 10 elements was within\nat least 96% of the reward given by an 80-element multiset. The\nruntime does not always increase strictly with the multiset size;\nindeed in one example (scenario 2 with 20 robber types), using a\nmultiset of 10 elements took 1228 seconds, while using 80 elements\nonly took 617 seconds. In general, runtime should increase since a\nlarger multiset means a larger domain for the variables in the MILP,\nand thus a larger search space. However, an increase in the number\nof variables can sometimes allow for a policy to be constructed\nmore quickly due to more flexibility in the problem.\n7. SUMMARY AND RELATED WORK\nThis paper focuses on security for agents patrolling in hostile\nenvironments. In these environments, intentional threats are caused\nby adversaries about whom the security patrolling agents have\nincomplete information. Specifically, we deal with situations where\nthe adversaries\" actions and payoffs are known but the exact\nadversary type is unknown to the security agent. Agents acting in the\nreal world quite frequently have such incomplete information about\nother agents. Bayesian games have been a popular choice to model\nsuch incomplete information games [3]. The Gala toolkit is one\nmethod for defining such games [9] without requiring the game to\nbe represented in normal form via the Harsanyi transformation [8];\nGala\"s guarantees are focused on fully competitive games. Much\nwork has been done on finding optimal Bayes-Nash equilbria for\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 317\nFigure 3: Reward for ASAP using multisets of 10, 30, and 80\nelements\nsubclasses of Bayesian games, finding single Bayes-Nash\nequilibria for general Bayesian games [10] or approximate Bayes-Nash\nequilibria [18]. Less attention has been paid to finding the optimal\nstrategy to commit to in a Bayesian game (the Stackelberg scenario\n[15]). However, the complexity of this problem was shown to be\nNP-hard in the general case [5], which also provides algorithms for\nthis problem in the non-Bayesian case.\nTherefore, we present a heuristic called ASAP, with three key\nadvantages towards addressing this problem. First, ASAP searches\nfor the highest reward strategy, rather than a Bayes-Nash\nequilibrium, allowing it to find feasible strategies that exploit the\nnatural first-mover advantage of the game. Second, it provides\nstrategies which are simple to understand, represent, and implement.\nThird, it operates directly on the compact, Bayesian game\nrepresentation, without requiring conversion to normal form. We provide\nan efficient Mixed Integer Linear Program (MILP) implementation\nfor ASAP, along with experimental results illustrating significant\nspeedups and higher rewards over other approaches.\nOur k-uniform strategies are similar to the k-uniform strategies\nof [12]. While that work provides epsilon error-bounds based on\nthe k-uniform strategies, their solution concept is still that of a\nNash equilibrium, and they do not provide efficient algorithms for\nobtaining such k-uniform strategies. This contrasts with ASAP,\nwhere our emphasis is on a highly efficient heuristic approach that\nis not focused on equilibrium solutions.\nFinally the patrolling problem which motivated our work has\nrecently received growing attention from the multiagent community\ndue to its wide range of applications [4, 13]. However most of this\nwork is focused on either limiting energy consumption involved in\npatrolling [7] or optimizing on criteria like the length of the path\ntraveled [4, 13], without reasoning about any explicit model of an\nadversary[14].\nAcknowledgments : This research is supported by the United States\nDepartment of Homeland Security through Center for Risk and Economic\nAnalysis of Terrorism Events (CREATE). It is also supported by the\nDefense Advanced Research Projects Agency (DARPA), through the\nDepartment of the Interior, NBC, Acquisition Services Division, under Contract\nNo. NBCHD030010. Sarit Kraus is also affiliated with UMIACS.\n8. REFERENCES\n[1] R. W. Beard and T. McLain. Multiple UAV cooperative\nsearch under collision avoidance and limited range\ncommunication constraints. In IEEE CDC, 2003.\n[2] D. Bertsimas and J. Tsitsiklis. Introduction to Linear\nOptimization. Athena Scientific, 1997.\n[3] J. Brynielsson and S. Arnborg. Bayesian games for threat\nprediction and situation analysis. In FUSION, 2004.\n[4] Y. Chevaleyre. Theoretical analysis of multi-agent patrolling\nproblem. In AAMAS, 2004.\n[5] V. Conitzer and T. Sandholm. Choosing the best strategy to\ncommit to. In ACM Conference on Electronic Commerce,\n2006.\n[6] D. Fudenberg and J. Tirole. Game Theory. MIT Press, 1991.\n[7] C. Gui and P. Mohapatra. Virtual patrol: A new power\nconservation design for surveillance using sensor networks.\nIn IPSN, 2005.\n[8] J. C. Harsanyi and R. Selten. A generalized Nash solution for\ntwo-person bargaining games with incomplete information.\nManagement Science, 18(5):80-106, 1972.\n[9] D. Koller and A. Pfeffer. Generating and solving imperfect\ninformation games. In IJCAI, pages 1185-1193, 1995.\n[10] D. Koller and A. Pfeffer. Representations and solutions for\ngame-theoretic problems. Artificial Intelligence,\n94(1):167-215, 1997.\n[11] C. Lemke and J. Howson. Equilibrium points of bimatrix\ngames. Journal of the Society for Industrial and Applied\nMathematics, 12:413-423, 1964.\n[12] R. J. Lipton, E. Markakis, and A. Mehta. Playing large\ngames using simple strategies. In ACM Conference on\nElectronic Commerce, 2003.\n[13] A. Machado, G. Ramalho, J. D. Zucker, and A. Drougoul.\nMulti-agent patrolling: an empirical analysis on alternative\narchitectures. In MABS, 2002.\n[14] P. Paruchuri, M. Tambe, F. Ordonez, and S. Kraus. Security\nin multiagent systems by policy randomization. In AAMAS,\n2006.\n[15] T. Roughgarden. Stackelberg scheduling strategies. In ACM\nSymposium on TOC, 2001.\n[16] S. Ruan, C. Meirina, F. Yu, K. R. Pattipati, and R. L. Popp.\nPatrolling in a stochastic environment. In 10th Intl.\nCommand and Control Research Symp., 2005.\n[17] T. Sandholm, A. Gilpin, and V. Conitzer. Mixed-integer\nprogramming methods for finding nash equilibria. In AAAI,\n2005.\n[18] S. Singh, V. Soni, and M. Wellman. Computing approximate\nBayes-Nash equilibria with tree-games of incomplete\ninformation. In ACM Conference on Electronic Commerce,\n2004.\n318 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)", "keywords": "heuristic approach;game theory;security of agent system;decomposition for multiple adversary;bayesian game;agent system security;patrolling domain;bayesian and stackelberg game;bayes-nash equilibrium;adversarial multiagent domain;mixed-integer linear program;np-hard;agent security via approximate policy"}
{"name": "train_I-59", "title": "An Agent-Based Approach for Privacy-Preserving Recommender Systems", "abstract": "Recommender Systems are used in various domains to generate personalized information based on personal user data. The ability to preserve the privacy of all participants is an essential requirement of the underlying Information Filtering architectures, because the deployed Recommender Systems have to be accepted by privacy-aware users as well as information and service providers. Existing approaches neglect to address privacy in this multilateral way. We have developed an approach for privacy-preserving Recommender Systems based on Multi-Agent System technology which enables applications to generate recommendations via various filtering techniques while preserving the privacy of all participants. We describe the main modules of our solution as well as an application we have implemented based on this approach.", "fulltext": "1. INTRODUCTION\nInformation Filtering (IF) systems aim at countering\ninformation overload by extracting information that is\nrelevant for a given user out of a large body of information\navailable via an information provider. In contrast to\nInformation Retrieval (IR) systems, where relevant information\nis extracted based on search queries, IF architectures\ngenerate personalized information based on user profiles\ncontaining, for each given user, personal data, preferences, and\nrated items. The provided body of information is usually\nstructured and collected in provider profiles. Filtering\ntechniques operate on these profiles in order to generate\nrecommendations of items that are probably relevant for a given\nuser, or in order to determine users with similar interests,\nor both. Depending on the respective goal, the resulting\nsystems constitute Recommender Systems [5], Matchmaker\nSystems [10], or a combination thereof.\nThe aspect of privacy is an essential issue in all IF systems:\nGenerating personalized information obviously requires the\nuse of personal data. According to surveys indicating major\nprivacy concerns of users in the context of Recommender\nSystems and e-commerce in general [23], users can be\nexpected to be less reluctant to provide personal information\nif they trust the system to be privacy-preserving with regard\nto personal data. Similar considerations also apply to the\ninformation provider, who may want to control the\ndissemination of the provided information, and to the provider of the\nfiltering techniques, who may not want the details of the\nutilized filtering algorithms to become common knowledge. A\nprivacy-preserving IF system should therefore balance these\nrequirements and protect the privacy of all parties involved\nin a multilateral way, while addressing general requirements\nregarding performance, security and quality of the\nrecommendations as well. As described in the following section,\nthere are several approaches with similar goals, but none of\nthese provide a generic approach in which the privacy of all\nparties is preserved.\nWe have developed an agent-based approach for\nprivacypreserving IF which has been utilized for realizing a\ncombined Recommender/Matchmaker System as part of an\napplication supporting users in planning entertainment-related\nactivities. In this paper, we focus on the Recommender\nSystem functionality. Our approach is based on Multi-Agent\nSystem (MAS) technology because fundamental features of\nagents such as autonomy, adaptability and the ability to\ncommunicate are essential requirements of our approach. In\nother words, the realized approach does not merely\nconstitute a solution for privacy-preserving IF within a MAS\ncontext, but rather utilizes a MAS architecture in order to\nrealize a solution for privacy-preserving IF, which could not\nbe realized easily otherwise.\nThe paper is structured as follows: Section 2 describes\nrelated work. Section 3 describes the general ideas of our\napproach. In Section 4, we describe essential details of the\n319\n978-81-904262-7-5 (RPS) c 2007 IFAAMAS\nmodules of our approach and their implementation. In\nSection 5, we evaluate the approach, mainly via the realized\napplication. Section 6 concludes the paper with an outlook\nand outlines further work.\n2. RELATED WORK\nThere is a large amount of work in related areas, such as\nPrivate Information Retrieval [7], Privacy-Preserving Data\nMining [2], and other privacy-preserving protocols [4, 16],\nmost of which is based on Secure Multi-Party Computation\n[27]. We have ruled out Secure Multi-Party Computation\napproaches mainly because of their complexity, and because\nthe algorithm that is computed securely is not considered to\nbe private in these approaches.\nVarious enforcement mechanisms have been suggested\nthat are applicable in the context of privacy-preserving\nInformation Filtering, such as enterprise privacy policies [17]\nor hippocratic databases [1], both of which annotate user\ndata with additional meta-information specifying how the\ndata is to be handled on the provider side. These approaches\nultimately assume that the provider actually intends to\nprotect the privacy of the user data, and offer support for this\ntask, but they are not intended to prevent the provider\nfrom acting in a malicious manner. Trusted computing, as\nspecified by the Trusted Computing Group, aims at\nrealizing trusted systems by increasing the security of open\nsystems to a level comparable with the level of security that\nis achievable in closed systems. It is based on a\ncombination of tamper-proof hardware and various software\ncomponents. Some example applications, including peer-to-peer\nnetworks, distributed firewalls, and distributed computing\nin general, are listed in [13].\nThere are some approaches for privacy-preserving\nRecommender Systems based on distributed collaborative filtering,\nin which recommendations are generated via a public model\naggregating the distributed user profiles without containing\nexplicit information about user profiles themselves. This\nis achieved via Secure Multi-Party Computation [6], or via\nrandom perturbation of the user data [20]. In [19],\nvarious approaches are integrated within a single architecture.\nIn [10], an agent-based approach is described in which user\nagents representing similar users are discovered via a\ntransitive traversal of user agents. Privacy is preserved through\npseudonymous interaction between the agents and through\nadding obfuscating data to personal information. More\nrecent related approaches are described in [18].\nIn [3], an agent-based architecture for privacy-preserving\ndemographic filtering is described which may be\ngeneralized in order to support other kinds of filtering techniques.\nWhile in some aspects similar to our approach, this\narchitecture addresses at least two aspects inadequately, namely\nthe protection of the filter against manipulation attempts,\nand the prevention of collusions between the filter and the\nprovider.\n3. PRIVACY-PRESERVING\nINFORMATION FILTERING\nWe identify three main abstract entities participating in\nan information filtering process within a distributed system:\nA user entity, a provider entity, and a filter entity. Whereas\nin some applications the provider and filter entities\nexplicitly trust each other, because they are deployed by the same\nparty, our solution is applicable more generically because it\ndoes not require any trust between the main abstract\nentities. In this paper, we focus on aspects related to the\ninformation filtering process itself, and omit all aspects\nrelated to information collection and processing, i.e. the stages\nin which profiles are generated and maintained, mainly\nbecause these stages are less critical with regard to privacy, as\nthey involve fewer different entities.\n3.1 Requirements\nOur solution aims at meeting the following requirements\nwith regard to privacy:\n\u2022 User Privacy: No linkable information about user\nprofiles should be acquired permanently by any other\nentity or external party, including other user entities.\nSingle user profile items, however, may be acquired\npermanently if they are unlinkable, i.e. if they\ncannot be attributed to a specific user or linked to other\nuser profile items. Temporary acquisition of private\ninformation is permitted as well. Sets of\nrecommendations may be acquired permanently by the provider,\nbut they should not be linkable to a specific user.\nThese concessions simplify the resulting protocol and\nallow the provider to obtain recommendations and\nsingle unlinkable user profile items, and thus to determine\nfrequently requested information and optimize the\noffered information accordingly.\n\u2022 Provider Privacy: No information about provider\nprofiles, with the exception of the recommendations,\nshould be acquired permanently by other entities or\nexternal parties. Again, temporary acquisition of\nprivate information is permitted. Additionally, the\npropagation of provider information is entirely under the\ncontrol of the provider. Thus, the provider is enabled\nto prevent misuse such as the automatic large-scale\nextraction of information.\n\u2022 Filter Privacy: Details of the algorithms applied by\nthe filtering techniques should not be acquired\npermanently by any other entity or external party. General\ninformation about the algorithm may be provided by\nthe filter entity in order to help other entities to reach\na decision on whether to apply the respective filtering\ntechnique.\nIn addition, general requirements regarding the quality\nof the recommendations as well as security aspects,\nperformance and broadness of the resulting system have to be\naddressed as well. While minor trade-offs may be acceptable,\nthe resulting system should reach a level similar to regular\nRecommender Systems with regard to these requirements.\n3.2 Outline of the Solution\nThe basic idea for realizing a protocol fulfilling these\nprivacy-related requirements in Recommender Systems is\nimplied by allowing the temporary acquisition of private\ninformation (see [8] for the original approach): User and\nprovider entity both propagate the respective profile data to\nthe filter entity. The filter entity provides the\nrecommendations, and subsequently deletes all private information, thus\nfulfilling the requirement regarding permanent acquisition\nof private information.\n320 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nThe entities whose private information is propagated have\nto be certain that the respective information is actually\nacquired temporarily only. Trust in this regard may be\nestablished in two main ways:\n\u2022 Trusted Software: The respective entity itself is trusted\nto remove the respective information as specified.\n\u2022 Trusted Environment: The respective entity operates\nin an environment that is trusted to control the\ncommunication and life cycle of the entity to an extent\nthat the removal of the respective information may\nbe achieved regardless of the attempted actions of the\nentity itself. Additionally, the environment itself is\ntrusted not to act in a malicious manner (e.g. it is\ntrusted not to acquire and propagate the respective\ninformation itself).\nIn both cases, trust may be established in various ways.\nReputation-based mechanisms, additional trusted third\nparties certifying entities or environments, or trusted\ncomputing mechanisms may be used. Our approach is based on a\ntrusted environment realized via trusted computing\nmechanisms, because we see this solution as the most generic\nand realistic approach. This decision is discussed briefly in\nSection 5.\nWe are now able to specify the abstract information\nfiltering protocol as shown in Figure 1: The filter entity deploys a\nTemporary Filter Entity (TFE) operating in a trusted\nenvironment. The user entity deploys an additional relay entity\noperating in the same environment. Through mechanisms\nprovided by this environment, the relay entity is able to\ncontrol the communication of the TFE, and the provider entity\nis able to control the communication of both relay entity\nand the TFE. Thus, it is possible to ensure that the\ncontrolled entities are only able to propagate recommendations,\nbut no other private information. In the first stage (steps\n1.1 to 1.3 of Figure 1), the relay entity establishes control of\nthe TFE, and thus prevents it from propagating user profile\ninformation. User profile data is propagated without\nparticipation of the provider entity from the user entity to the\nTFE via the relay entity. In the second stage (steps 2.1 to\n2.3 of Figure 1), the provider entity establishes control of\nboth relay and TFE, and thus prevents them from\npropagating provider profile information. Provider profile data is\npropagated from the provider entity to the TFE via the\nrelay entity. In the third stage (steps 3.1 to 3.5 of Figure 1),\nthe TFE returns the recommendations via the relay entity,\nand the controlled entities are terminated. Taken together,\nthese steps ensure that all private information is acquired\ntemporarily only by the other main entities. The problems\nof determining acceptable queries on the provider profile and\nensuring unlinkability of the recommendations are discussed\nin the following section.\nOur approach requires each entity in the distributed\narchitecture to have the following five main abilities: The ability\nto perform certain well-defined tasks (such as carrying out a\nfiltering process) with a high degree of autonomy, i.e. largely\nindependent of other entities (e.g. because the respective\nentity is not able to communicate in an unrestricted manner),\nthe ability to be deployable dynamically in a well-defined\nenvironment, the ability to communicate with other entities,\nthe ability to achieve protection against external\nmanipulation attempts, and the ability to control and restrict the\ncommunication of other entities.\nFigure 1: The abstract privacy-preserving\ninformation filtering protocol. All communication across\nthe environments indicated by dashed lines is\nprevented with the exception of communication with\nthe controlling entity.\nMAS architectures are an ideal solution for realizing a\ndistributed system characterized by these features, because\nthey provide agents constituting entities that are actually\ncharacterized by autonomy, mobility and the ability to\ncommunicate [26], as well as agent platforms as environments\nproviding means to realize the security of agents. In this\ncontext, the issue of malicious hosts, i.e. hosts attacking\nagents, has to be addressed explicitly. Furthermore, existing\nMAS architectures generally do not allow agents to control\nthe communication of other agents. It is possible, however,\nto expand a MAS architecture and to provide designated\nagents with this ability. For these reasons, our solution is\nbased on a FIPA[11]-compliant MAS architecture. The\nentities introduced above are mapped directly to agents, and\nthe trusted environment in which they exist is realized in\nthe form of agent platforms.\nIn addition to the MAS architecture itself, which is\nassumed as given, our solution consists of the following five\nmain modules:\n\u2022 The Controller Module described in Section 4.1\nprovides functionality for controlling the communication\ncapabilities of agents.\n\u2022 The Transparent Persistence Module facilitates\nthe use of different data storage mechanisms, and\nprovides a uniform interface for accessing persistent\ninformation, which may be utilized for monitoring critical\ninteractions involving potentially private information\ne.g. as part of queries. Its description is outside the\nscope of this paper.\n\u2022 The Recommender Module, details of which are\ndescribed in Section 4.2, provides Recommender System\nfunctionality.\n\u2022 The Matchmaker Module provides Matchmaker\nSystem functionality. It additionally utilizes social\naspects of MAS technology. Its description is outside the\nscope of this paper.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 321\n\u2022 Finally, a separate module described in Section 4.4\nprovides Exemplary Filtering Techniques in order\nto show that various restrictions imposed on filtering\ntechniques by our approach may actually be fulfilled.\nThe trusted environment introduced above encompasses\nthe MAS architecture itself and the Controller Module,\nwhich have to be trusted to act in a non-malicious manner\nin order to rule out the possibility of malicious hosts.\n4. MAIN MODULES AND\nIMPLEMENTATION\nIn this section, we describe the main modules of our\napproach, and outline the implementation. While we have\nchosen a specific architecture for the implementation, the\nspecification of the module is applicable to any FIPA-compliant\nMAS architecture. A module basically encompasses\nontologies, functionality provided by agents via agent services, and\ninternal functionality. Throughout this paper, {m}KX\ndenotes a message m encrypted via a non-specified symmetric\nencryption scheme with a secret key KX used for\nencryption and decryption which is initially known only to\nparticipant X. A key KXY is a key shared by participants\nX and Y . A cryptographic hash function is used at\nvarious points of the protocol, i.e. a function returning a hash\nvalue h(x) for given data x that is both preimage-resistant\nand collision-resistant1\n. We denote a set of hash values for\na data set X = {x1, .., xn} as H(X) = {h(x1), .., h(xn)},\nwhereas h(X) denotes a single hash value of a data set.\n4.1 Controller Module\nAs noted above, the ability to control the communication\nof agents is generally not a feature of existing MAS\narchitectures2\nbut at the same time a central requirement of our\napproach for privacy-preserving Information Filtering. The\nrequired functionality cannot be realized based on regular\nagent services or components, because an agent on a\nplatform is usually not allowed to interfere with the actions of\nother agents in any way. Therefore, we add additional\ninfrastructure providing the required functionality to the MAS\narchitecture itself, resulting in an agent environment with\nextended functionality and responsibilities.\nControlling the communication capabilities of an agent is\nrealized by restricting via rules, in a manner similar to a\nfirewall, but with the consent of the respective agent, its\nincoming and outgoing communication to specific platforms\nor agents on external platforms as well as other possible\ncommunication channels, such as the file system. Consent\nis required because otherwise the overall security would be\ncompromised, as attackers could arbitrarily block various\ncommunication channels. Our approach does not require\ncontrolling the communication between agents on the same\nplatform, and therefore this aspect is not addressed.\nConsequently, all rules addressing communication capabilities\nhave to be enforced across entire platforms, because\notherwise a controlled agent could just use a non-controlled agent\n1\nIn the implementation, we have used the Advanced\nEncryption Standard (AES) as the symmetric encryption scheme\nand SHA-1 as the cryptographic hash function.\n2\nA recent survey on agent environments [24] concludes that\naspects related to agent environments are often neglected,\nand does not indicate any existing work in this particular\narea.\non the same platform as a relay for communicating with\nagents residing on external platforms. Various agent services\nprovide functionality for adding and revoking control of\nplatforms, including functionality required in complex scenarios\nwhere controlled agents in turn control further platforms.\nThe implementation of the actual control mechanism\ndepends on the actual MAS architecture. In our\nimplementation, we have utilized methods provided via the Java\nSecurity Manager as part of the Java security model. Thus,\nthe supervisor agent is enabled to define custom security\npolicies, thereby granting or denying other agents access to\nresources required for communication with other agents as\nwell as communication in general, such as files or sockets for\nTCP/IP-based communication.\n4.2 Recommender Module\nThe Recommender Module is mainly responsible for\ncarrying out information filtering processes, according to the\nprotocol described in Table 1. The participating entities are\nrealized as agents, and the interactions as agent services. We\nassume that mechanisms for secure agent communication are\navailable within the respective MAS architecture. Two\nissues have to be addressed in this module: The relevant parts\nof the provider profile have to be retrieved without\ncompromising the user\"s privacy, and the recommendations have to\nbe propagated in a privacy-preserving way.\nOur solution is based on a threat model in which no main\nabstract entity may safely assume any other abstract entity\nto act in an honest manner: Each entity has to assume that\nother entities may attempt to obtain private information,\neither while following the specified protocol or even by\ndeviating from the protocol. According to [15], we classify the\nformer case as honest-but-curious behavior (as an example,\nthe TFE may propagate recommendations as specified, but\nmay additionally attempt to propagate private information),\nand the latter case as malicious behavior (as an example, the\nfilter may attempt to propagate private information instead\nof the recommendations).\n4.2.1 Retrieving the Provider Profile\nAs outlined above, the relay agent relays data between\nthe TFE agent and the provider agent. These agents are\nnot allowed to communicate directly, because the TFE agent\ncannot be assumed to act in an honest manner. Unlike the\nuser profile, which is usually rather small, the provider\nprofile is often too voluminous to be propagated as a whole\nefficiently. A typical example is a user profile containing\nratings of about 100 movies, while the provider profile\ncontains some 10,000 movies. Retrieving only the relevant part\nof the provider profile, however, is problematic because it\nhas to be done without leaking sensitive information about\nthe user profile. Therefore, the relay agent has to analyze all\nqueries on the provider profile, and reject potentially critical\nqueries, such as queries containing a set of user profile items.\nBecause the propagation of single unlinkable user profile\nitems is assumed to be uncritical, we extend the\ninformation filtering protocol as follows: The relevant parts of the\nprovider profile are retrieved based on single anonymous\ninteractions between the relay and the provider. If the MAS\narchitecture used for the implementation does not provide\nan infrastructure for anonymous agent communication, this\nfeature has to be provided explicitly: The most\nstraightforward way is to use additional relay agents deployed via\n322 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nTable 1: The basic information filtering protocol\nwith participants U = user agent, P = provider\nagent, F = TFE agent, R = relay agent, based on the\nabstract protocol shown in Figure 1. UP denotes the\nuser profile with UP = {up1, .., upn}, PP denotes the\nprovider profile, and REC denotes the set of\nrecommendations with REC = {rec1, .., recm}.\nPhase. Sender \u2192 Message or Action\nStep Receiver\n1.1 R \u2192 F establish control\n1.2 U \u2192 R UP\n1.3 R \u2192 F UP\n2.1 P \u2192 R, F establish control\n2.2 P \u2192 R PP\n2.3 R \u2192 F PP\n3.1 F \u2192 R REC\n3.2 R \u2192 P REC\n3.3 P \u2192 U REC\n3.4 R \u2192 F terminate F\n3.5 P \u2192 R terminate R\nthe main relay agent and used once for a single anonymous\ninteraction. Obviously, unlinkability is only achieved if\nmultiple instances of the protocol are executed simultaneously\nbetween the provider and different users. Because agents\non controlled platforms are unable to communicate\nanonymously with the respective controlling agent, control has to\nbe established after the anonymous interactions have been\ncompleted. To prevent the uncontrolled relay agents from\npropagating provider profile data, the respective data is\nencrypted and the key is provided only after control has been\nestablished. Therefore, the second phase of the protocol\ndescribed in Table 1 is replaced as described in Table 2.\nAdditionally, the relay agent may allow other interactions\nas long as no user profile items are used within the queries.\nIn this case, the relay agent has to ensure that the provider\ndoes not obtain any information exceeding the information\ndeducible via the recommendations themselves. The\nclusterbased filtering technique described in Section 4.3 is an\nexample for a filtering technique operating in this manner.\n4.2.2 Recommendation Propagation\nThe propagation of the recommendations is even more\nproblematic mainly because more participants are involved:\nRecommendations have to be propagated from the TFE\nagent via the relay and provider agent to the user agent. No\nparticipant should be able to alter the recommendations or\nuse them for the propagation of private information.\nTherefore, every participant in this chain has to obtain and verify\nthe recommendations in unencrypted form prior to the next\nagent in the chain, i.e. the relay agent has to verify the\nrecommendations before the provider obtains them, and so on.\nTherefore, the final phase of the protocol described in Table\n1 is replaced as described in Table 3. It basically consists of\ntwo parts (Step 3.1 to 3.4, and Step 3.5 to Step 3.8), each of\nwhich provide a solution for a problem related to the\nprisoners\" problem [22], in which two participants (the prisoners)\nintend to exchange a message via a third, untrusted\nparticipant (the warden) who may read the message but must not\nbe able to alter it in an undetectable manner. There are\nvarious solutions for protocols addressing the prisoners\"\nprobTable 2: The updated second stage of the\ninformation filtering protocol with definitions as above. PPq\nis the part of the provider profile PP returned as the\nresult of the query q.\nPhase. Sender \u2192 Message or Action\nStep Receiver\nrepeat 2.1 to 2.3 \u2200 up \u2208 UP:\n2.1 F \u2192 R q(up) (a query based on up)\n2.2 R anon\n\u2192 P q(up) (R remains anonymous)\n2.3 P \u2192 R anon\n{PPq(up)}KP\n2.4 P \u2192 R, F establish control\n2.5 P \u2192 R KP\n2.6 R \u2192 F PPq(UP )\nTable 3: The updated final stage of the information\nfiltering protocol with definitions as above.\nPhase. Sender \u2192 Message or Action\nStep Receiver\n3.1 F \u2192 R REC, {H(REC)}KPF\n3.2 R \u2192 P h(KR), {{H(REC)}KPF }KR\n3.3 P \u2192 R KP F\n3.4 R \u2192 P KR\nrepeat 3.5 \u2200 rec \u2208 REC:\n3.5 R \u2192 P {rec}KURrec\nrepeat 3.6 \u2200 rec \u2208 REC:\n3.6 P \u2192 U h(KPrec ), {{rec}KURrec\n}KPrec\nrepeat 3.7 to 3.8 \u2200 rec \u2208 REC:\n3.7 U \u2192 P KURrec\n3.8 P \u2192 U KPrec\n3.9 U \u2192 F terminate F\n3.10 P \u2192 U terminate U\nlem. The more obvious of these, however, such as protocols\nbased on the use of digital signatures, introduce additional\nthreats e.g. via the possibility of additional subliminal\nchannels [22]. In order to minimize the risk of possible threats,\nwe have decided to use a protocol that only requires a\nsymmetric encryption scheme.\nThe first part of the final phase is carried out as follows:\nIn order to prevent the relay from altering\nrecommendations, they are propagated by the filter together with an\nencrypted hash in Step 3.1. Thus, the relay is able to verify\nthe recommendations before they are propagated further.\nThe relay, however, may suspect the data propagated as\nthe encrypted hash to contain private information instead\nof the actual hash value. Therefore, the encrypted hash is\nencrypted again and propagated together with a hash on\nthe respective key in Step 3.2. In Step 3.3, the key KP F\nis revealed to the relay, allowing the relay to validate the\nencrypted hash. In Step 3.4, the key KR is revealed to the\nprovider, allowing the provider to decrypt the data received\nin Step 3.2 and thus to obtain H(REC). Propagating the\nhash of the key KR prevents the relay from altering the\nrecommendations to REC after Step 3.3, which would be\nundetectable otherwise because the relay could choose a key\nKR so that {{H(REC)}KPF }KR = {{H(REC )}KPF }KR\n.\nThe encryption scheme used for encrypting the hash has to\nbe secure against known-plaintext attacks, because\notherwise the relay may be able to obtain KP F after Step 3.1 and\nsubsequently alter the recommendations in an undetectable\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 323\nway. Additionally, the encryption scheme must not be\ncommutative for similar reasons.\nThe remaining protocol steps are interactions between\nrelay, provider and user agent. The interactions of Step 3.5\nto Step 3.8 ensure, via the same mechanisms used in Step\n3.1 to 3.4, that the provider is able to analyze the\nrecommendations before the user obtains them, but at the same\ntime prevent the provider from altering the\nrecommendations. Additionally, the recommendations are not processed\nat once, but rather one at a time, to prevent the provider\nfrom withholding all recommendations.\nUpon completion of the protocol, both user and provider\nhave obtained a set of recommendations. If the user wants\nthese recommendations to be unlinkable to himself, the user\nagent has to carry out the entire protocol anonymously.\nAgain, the most straightforward way to achieve this is to use\nadditional relay agents deployed via the user agent which are\nused once for a single information filtering process.\n4.3 Exemplary Filtering Techniques\nThe filtering technique applied by the TFE agent cannot\nbe chosen freely: All collaboration-based approaches, such\nas collaborative filtering techniques based on the profiles\nof a set of users, are not applicable because the provider\nprofile does not contain user profile data (unless this data\nhas been collected externally). Instead, these approaches\nare realized via the Matchmaker Module, which is outside\nthe scope of this paper. Learning-based approaches are not\napplicable because the TFE agent cannot propagate any\nacquired data to the filter, which effectively means that the\nfilter is incapable of learning. Filtering techniques that are\nactually applicable are feature-based approaches, such as\ncontent-based filtering (in which profile items are compared\nvia their attributes) and knowledge-based filtering (in which\ndomain-specific knowledge is applied in order to match user\nand provider profile items). An overview of different classes\nand hybrid combinations of filtering techniques is given in\n[5]. We have implemented two generic content-based\nfiltering approaches that are applicable within our approach:\nA direct content-based filtering technique based on the\nclass of item-based top-N recommendation algorithms [9] is\nused in cases where the user profile contains items that are\nalso contained in the provider profile. In a preprocessing\nstage, i.e. prior to the actual information filtering processes,\na model is generated containing the k most similar items for\neach provider profile item. While computationally rather\ncomplex, this approach is feasible because it has to be done\nonly once, and it is carried out in a privacy-preserving way\nvia interactions between the provider agent and a TFE\nagent. The resulting model is stored by the provider agent\nand can be seen as an additional part of the provider\nprofile. In the actual information filtering process, the k most\nsimilar items are retrieved for each single user profile item\nvia queries on the model (as described in Section 4.2.1, this\nis possible in a privacy-preserving way via anonymous\ncommunication). Recommendations are generated by selecting\nthe n most frequent items from the result sets that are not\nalready contained within the user profile.\nAs an alternative approach applicable when the user\nprofile contains information in addition to provider profile\nitems, we provide a cluster-based approach in which provider\nprofile items are clustered in a preprocessing stage via an\nagglomerative hierarchical clustering approach. Each cluster is\nrepresented by a centroid item, and the cluster elements are\neither sub-clusters or, on the lowest level, the items\nthemselves. In the information filtering stage, the relevant items\nare retrieved by descending through the cluster hierarchy in\nthe following manner: The cluster items of the highest level\nare retrieved independent of the user profile. By\ncomparing these items with the user profile data, the most relevant\nsub-clusters are determined and retrieved in a subsequent\niteration. This process is repeated until the lowest level\nis reached, which contains the items themselves as\nrecommendations. Throughout the process, user profile items are\nnever propagated to the provider as such. The\ninformation deducible about the user profile does not exceed the\ninformation deducible via the recommendations themselves\n(because essentially only a chain of cluster centroids leading\nto the recommendations is retrieved), and therefore it is not\nregarded as privacy-critical.\n4.4 Implementation\nWe have implemented the approach for privacy-preserving\nIF based on JIAC IV [12], a FIPA-compliant MAS\narchitecture. JIAC IV integrates fundamental aspects of\nautonomous agents regarding pro-activeness, intelligence,\ncommunication capabilities and mobility by providing a scalable\ncomponent-based architecture. Additionally, JIAC IV offers\ncomponents realizing management and security\nfunctionality, and provides a methodology for Agent-Oriented\nSoftware Engineering. JIAC IV stands out among MAS\narchitectures as the only security-certified architecture, since it\nhas been certified by the German Federal Office for\nInformation Security according to the EAL3 of the Common Criteria\nfor Information Technology Security standard [14]. JIAC IV\noffers several security features in the areas of access control\nfor agent services, secure communication between agents,\nand low-level security based on Java security policies [21],\nand thus provides all security-related functionality required\nfor our approach.\nWe have extended the JIAC IV architecture by adding the\nmechanisms for communication control described in Section\n4.1. Regarding the issue of malicious hosts, we currently\nassume all providers of agent platforms to be trusted. We\nare additionally developing a solution that is actually based\non a trusted computing infrastructure.\n5. EVALUATION\nFor the evaluation of our approach, we have examined\nwhether and to which extent the requirements (mainly\nregarding privacy, performance, and quality) are actually met.\nPrivacy aspects are directly addressed by the modules and\nprotocols described above and therefore not evaluated\nfurther here. Performance is a critical issue, mainly because of\nthe overhead caused by creating additional agents and agent\nplatforms for controlling communication, and by the\nadditional interactions within the Recommender Module.\nOverall, a single information filtering process takes about ten\ntimes longer than a non-privacy-preserving information\nfiltering process leading to the same results, which is a\nconsiderable overhead but still acceptable under certain conditions,\nas described in the following section.\n5.1 The Smart Event Assistant\nAs a proof of concept, and in order to evaluate\nperformance and quality under real-life conditions, we have\nap324 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nFigure 2: The Smart Event Assistant, a\nprivacypreserving Recommender System supporting users\nin planning entertainment-related activities.\nplied our approach within the Smart Event Assistant, a\nMAS-based Recommender System which integrates various\npersonalized services for entertainment planning in\ndifferent German cities, such as a restaurant finder and a movie\nfinder [25]. Additional services, such as a calendar, a\nrouting service and news services complement the information\nservices. An intelligent day planner integrates all\nfunctionality by providing personalized recommendations for the\nvarious information services, based on the user\"s preferences\nand taking into account the location of the user as well as\nthe potential venues. All services are accessible via mobile\ndevices as well3\n. Figure 2 shows a screenshot of the\nintelligent day planner\"s result dialog. The Smart Event\nAssistant is entirely realized as a MAS system providing, among\nother functionality, various filter agents and different service\nprovider agents, which together with the user agents utilize\nthe functionality provided by our approach.\nRecommendations are generated in two ways: A push\nservice delivers new recommendations to the user in regular\nintervals (e.g. once per day) via email or SMS. Because the\nuser is not online during these interactions, they are less\ncritical with regard to performance and the protracted\nduration of the information filtering process is acceptable in\nthis case. Recommendations generated for the intelligent\nday planner, however, have to be delivered with very little\nlatency because the process is triggered by the user, who\nexpects to receive results promptly. In this scenario, the\noverall performance is substantially improved by setting up\nthe relay agent and the TFE agent o\ufb04ine, i.e. prior to the\nuser\"s request, and by an efficient retrieval of the relevant\n3\nThe Smart Event Assistant may be accessed online via\nhttp://www.smarteventassistant.de.\nTable 4: Complexity of typical privacy-preserving\n(PP) vs. non-privacy-preserving (NPP) filtering\nprocesses in the realized application. In the\nnonprivacy-preserving version, an agent retrieves the\nprofiles directly and propagates the result to a\nprovider agent.\nscenario push day planning\nversion NPP PP NPP PP\nprofile size (retrieved/total amount of items)\nuser 25/25 25/25\nprovider 125/10,000 500/10,000\nelapsed time in filtering process (in seconds)\nsetup n/a 2.2 n/a o\ufb04ine\ndatabase access 0.2 0.5 0.4 0.4\nprofile propagation n/a 0.8 n/a 0.3\nfiltering algorithm 0.2 0.2 0.2 0.2\nresult propagation 0.1 1.1 0.1 1.1\ncomplete time 0.5 4.8 0.7 2.0\npart of the provider profile: Because the user is only\ninterested in items, such as movies, available within a certain\ntime period and related to specific locations, such as\nscreenings at cinemas in a specific city, the relevant part of the\nprovider profile is usually small enough to be propagated\nentirely. Because these additional parameters are not seen\nas privacy-critical (as they are not based on the user\nprofile, but rather constitute a short-term information need),\nthe relevant part of the provider profile may be propagated\nas a whole, with no need for complex interactions. Taken\ntogether, these improvements result in a filtering process\nthat takes about three times as long as the respective\nnonprivacy-preserving filtering process, which we regard as an\nacceptable trade-off for the increased level of privacy. Table\n4 shows the results of the performance evaluation in more\ndetail. In these scenarios, a direct content-based filtering\ntechnique similar to the one described in Section 4.3 is\napplied. Because equivalent filtering techniques have been\napplied successfully in regular Recommender Systems [9], there\nare no negative consequences with regard to the quality of\nthe recommendations.\n5.2 Alternative Approaches\nAs described in Section 3.2, our solution is based on\ntrusted computing. There are more straightforward ways\nto realize privacy-preserving IF, e.g. by utilizing a\ncentralized architecture in which the privacy-preserving\nproviderside functionality is realized as trusted software based on\ntrusted computing. However, we consider these approaches\nto be unsuitable because they are far less generic: Whenever\nsome part of the respective software is patched, upgraded or\nreplaced, the entire system has to be analyzed again in order\nto determine its trustworthiness, a process that is\nproblematic in itself due to its complexity. In our solution, only a\ncomparatively small part of the overall system is based on\ntrusted computing. Because agent platforms can be utilized\nfor a large variety of tasks, and because we see trusted\ncomputing as the most promising approach to realize secure and\ntrusted agent environments, it seems reasonable to assume\nthat these respective mechanisms will be generally available\nin the future, independent of specific solutions such as the\none described here.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 325\n6. CONCLUSION & FURTHER WORK\nWe have developed an agent-based approach for\nprivacypreserving Recommender Systems. By utilizing\nfundamental features of agents such as autonomy, adaptability and\nthe ability to communicate, by extending the capabilities\nof agent platform managers regarding control of agent\ncommunication, by providing a privacy-preserving protocol for\ninformation filtering processes, and by utilizing suitable\nfiltering techniques we have been able to realize an approach\nwhich actually preserves privacy in Information Filtering\narchitectures in a multilateral way. As a proof of concept, we\nhave used the approach within an application supporting\nusers in planning entertainment-related activities.\nWe envision various areas of future work: To achieve\ncomplete user privacy, the protocol should be extended in order\nto keep the recommendations themselves private as well.\nGenerally, the feedback we have obtained from users of the\nSmart Event Assistant indicates that most users are\nindifferent to privacy in the context of entertainment-related\npersonal information. Therefore, we intend to utilize the\napproach to realize a Recommender System in a more\nprivacysensitive domain, such as health or finance, which would\nenable us to better evaluate user acceptance.\n7. ACKNOWLEDGMENTS\nWe would like to thank our colleagues Andreas Rieger\nand Nicolas Braun, who co-developed the Smart Event\nAssistant. The Smart Event Assistant is based on a project\nfunded by the German Federal Ministry of Education and\nResearch under Grant No. 01AK037, and a project funded\nby the German Federal Ministry of Economics and Labour\nunder Grant No. 01MD506.\n8. REFERENCES\n[1] R. Agrawal, J. Kiernan, R. Srikant, and Y. Xu.\nHippocratic databases. In 28th Int\"l Conf. on Very\nLarge Databases (VLDB), Hong Kong, 2002.\n[2] R. Agrawal and R. Srikant. Privacy-preserving data\nmining. In Proc. of the ACM SIGMOD Conference on\nManagement of Data, pages 439-450. ACM Press,\nMay 2000.\n[3] E. A\u00a8\u0131meur, G. Brassard, J. M. Fernandez, and F. S.\nMani Onana. Privacy-preserving demographic\nfiltering. In SAC \"06: Proceedings of the 2006 ACM\nsymposium on Applied computing, pages 872-878, New\nYork, NY, USA, 2006. ACM Press.\n[4] M. Bawa, R. Bayardo, Jr., and R. Agrawal.\nPrivacy-preserving indexing of documents on the\nnetwork. In Proc. of the 2003 VLDB, 2003.\n[5] R. Burke. Hybrid recommender systems: Survey and\nexperiments. User Modeling and User-Adapted\nInteraction, 12(4):331-370, 2002.\n[6] J. Canny. Collaborative filtering with privacy. In\nIEEE Symposium on Security and Privacy, pages\n45-57, 2002.\n[7] B. Chor, O. Goldreich, E. Kushilevitz, and M. Sudan.\nPrivate information retrieval. In IEEE Symposium on\nFoundations of Computer Science, pages 41-50, 1995.\n[8] R. Ciss\u00b4ee. An architecture for agent-based\nprivacy-preserving information filtering. In Proceedings\nof the 6th International Workshop on Trust, Privacy,\nDeception and Fraud in Agent Systems, 2003.\n[9] M. Deshpande and G. Karypis. Item-based top-N\nrecommendation algorithms. ACM Trans. Inf. Syst.,\n22(1):143-177, 2004.\n[10] L. Foner. Political artifacts and personal privacy: The\nyenta multi-agent distributed matchmaking system.\nPhD thesis, MIT, 1999.\n[11] Foundation for Intelligent Physical Agents. FIPA\nAbstract Architecture Specification, Version L, 2002.\n[12] S. Fricke, K. Bsufka, J. Keiser, T. Schmidt,\nR. Sesseler, and S. Albayrak. Agent-based telematic\nservices and telecom applications. Communications of\nthe ACM, 44(4), April 2001.\n[13] T. Garfinkel, M. Rosenblum, and D. Boneh. Flexible\nOS support and applications for trusted computing. In\nProceedings of HotOS-IX, May 2003.\n[14] T. Geissler and O. Kroll-Peters. Applying security\nstandards to multi agent systems. In AAMAS\nWorkshop: Safety & Security in Multiagent Systems, 2004.\n[15] O. Goldreich, S. Micali, and A. Wigderson. How to\nplay any mental game. In Proc. of STOC \"87, pages\n218-229, New York, NY, USA, 1987. ACM Press.\n[16] S. Jha, L. Kruger, and P. McDaniel. Privacy\npreserving clustering. In ESORICS 2005, volume 3679\nof LNCS. Springer, 2005.\n[17] G. Karjoth, M. Schunter, and M. Waidner. The\nplatform for enterprise privacy practices:\nPrivacy-enabled management of customer data. In\nPET 2002, volume 2482 of LNCS. Springer, 2003.\n[18] H. Link, J. Saia, T. Lane, and R. A. LaViolette. The\nimpact of social networks on multi-agent recommender\nsystems. In Proc. of the Workshop on Cooperative\nMulti-Agent Learning (ECML/PKDD \"05), 2005.\n[19] B. N. Miller, J. A. Konstan, and J. Riedl. PocketLens:\nToward a personal recommender system. ACM Trans.\nInf. Syst., 22(3):437-476, 2004.\n[20] H. Polat and W. Du. SVD-based collaborative filtering\nwith privacy. In Proc. of SAC \"05, pages 791-795,\nNew York, NY, USA, 2005. ACM Press.\n[21] T. Schmidt. Advanced Security Infrastructure for\nMulti-Agent-Applications in the Telematic Area. PhD\nthesis, Technische Universit\u00a8at Berlin, 2002.\n[22] G. J. Simmons. The prisoners\" problem and the\nsubliminal channel. In D. Chaum, editor, Proc. of\nCrypto \"83, pages 51-67. Plenum Press, 1984.\n[23] M. Teltzrow and A. Kobsa. Impacts of user privacy\npreferences on personalized systems: a comparative\nstudy. In Designing personalized user experiences in\neCommerce, pages 315-332. 2004.\n[24] D. Weyns, H. Parunak, F. Michel, T. Holvoet, and\nJ. Ferber. Environments for multiagent systems:\nState-of-the-art and research challenges. In\nEnvironments for Multiagent Systems, volume 3477 of\nLNCS. Springer, 2005.\n[25] J. Wohltorf, R. Ciss\u00b4ee, and A. Rieger. Berlintainment:\nAn agent-based context-aware entertainment planning\nsystem. IEEE Communications Magazine, 43(6), 2005.\n[26] M. Wooldridge and N. R. Jennings. Intelligent agents:\nTheory and practice. Knowledge Engineering Review,\n10(2):115-152, 1995.\n[27] A. Yao. Protocols for secure computation. In Proc. of\nIEEE FOGS \"82, pages 160-164, 1982.\n326 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)", "keywords": "privacy;secure multi-party computation;privacy-preserving recommender system;information filter;recommender system;multi-agent system;distributed artificial intelligence-multiagent system;trusted software;java security model;feature-based approach;learning-based approach;trust;information search;multi-agent system technology;retrieval-information filtering"}
{"name": "train_I-60", "title": "On the Benefits of Cheating by Self-Interested Agents in Vehicular Networks", "abstract": "As more and more cars are equipped with GPS and Wi-Fi transmitters, it becomes easier to design systems that will allow cars to interact autonomously with each other, e.g., regarding traffic on the roads. Indeed, car manufacturers are already equipping their cars with such devices. Though, currently these systems are a proprietary, we envision a natural evolution where agent applications will be developed for vehicular systems, e.g., to improve car routing in dense urban areas. Nonetheless, this new technology and agent applications may lead to the emergence of self-interested car owners, who will care more about their own welfare than the social welfare of their peers. These car owners will try to manipulate their agents such that they transmit false data to their peers. Using a simulation environment, which models a real transportation network in a large city, we demonstrate the benefits achieved by self-interested agents if no counter-measures are implemented.", "fulltext": "1. INTRODUCTION\nAs technology advances, more and more cars are being\nequipped with devices, which enable them to act as\nautonomous agents. An important advancement in this\nrespect is the introduction of ad-hoc communication networks\n(such as Wi-Fi), which enable the exchange of information\nbetween cars, e.g., for locating road congestions [1] and\noptimal routes [15] or improving traffic safety [2].\nVehicle-To-Vehicle (V2V) communication is already\nonboard by some car manufactures, enabling the\ncollaboration between different cars on the road. For example, GM\"s\nproprietary algorithm [6], called the threat assessment\nalgorithm, constantly calculates, in real time, other vehicles\"\npositions and speeds, and enables messaging other cars when\na collision is imminent; Also, Honda has began testing its\nsystem in which vehicles talk with each other and with the\nhighway system itself [7].\nIn this paper, we investigate the attraction of being a\nselfish agent in vehicular networks. That is, we investigate the\nbenefits achieved by car owners, who tamper with on-board\ndevices and incorporate their own self-interested agents in\nthem, which act for their benefit. We build on the notion\nof Gossip Networks, introduced by Shavitt and Shay [15], in\nwhich the agents can obtain road congestion information by\ngossiping with peer agents using ad-hoc communication.\nWe recognize two typical behaviors that the self-interested\nagents could embark upon, in the context of vehicular\nnetworks. In the first behavior, described in Section 4, the\nobjective of the self-interested agents is to maximize their\nown utility, expressed by their average journey duration on\nthe road. This situation can be modeled in real life by car\nowners, whose aim is to reach their destination as fast as\npossible, and would like to have their way free of other cars. To\nthis end they will let their agents cheat the other agents, by\ninjecting false information into the network. This is achieved\nby reporting heavy traffic values for the roads on their route\nto other agents in the network in the hope of making the\nother agents believe that the route is jammed, and causing\nthem to choose a different route.\nThe second type of behavior, described in Section 5, is\nmodeled by the self-interested agents\" objective to cause\ndisorder in the network, more than they are interested in\nmaximizing their own utility. This kind of behavior could\nbe generated, for example, by vandalism or terrorists, who\naim to cause as much mayhem in the network as possible.\nWe note that the introduction of self-interested agents to\nthe network, would most probably motivate other agents to\ntry and detect these agents in order to minimize their effect.\nThis is similar, though in a different context, to the problem\nintroduced by Lamport et al. [8] as the Byzantine Generals\nProblem. However, the introduction of mechanisms to deal\nwith self-interested agents is costly and time consuming. In\nthis paper we focus mainly on the attractiveness of selfish\nbehavior by these agents, while we also provide some insights\n327\n978-81-904262-7-5 (RPS) c 2007 IFAAMAS\ninto the possibility of detecting self-interested agents and\nminimizing their effect.\nTo demonstrate the benefits achieved by self-interested\nagents, we have used a simulation environment, which\nmodels the transportation network in a central part of a large\nreal city. The simulation environment is further described in\nSection 3. Our simulations provide insights to the benefits\nof self-interested agents cheating. Our findings can motivate\nfuture research in this field in order to minimize the effect\nof selfish-agents.\nThe rest of this paper is organized as follows. In Section 2\nwe review related work in the field of self-interested agents\nand V2V communications. We continue and formally\ndescribe our environment and simulation settings in Section 3.\nSections 4 and 5 describe the different behaviors of the\nselfinterested agents and our findings. Finally, we conclude the\npaper with open questions and future research directions.\n2. RELATED WORK\nIn their seminal paper, Lamport et al. [8] describe the\nByzantine Generals problem, in which processors need to\nhandle malfunctioning components that give conflicting\ninformation to different parts of the system. They also present\na model in which not all agents are connected, and thus an\nagent cannot send a message to all the other agents. Dolev et\nal. [5] has built on this problem and has analyzed the number\nof faulty agents that can be tolerated in order to eventually\nreach the right conclusion about true data. Similar work\nis presented by Minsky et al. [11], who discuss techniques\nfor constructing gossip protocols that are resilient to up to\nt malicious host failures. As opposed to the above works,\nour work focuses on vehicular networks, in which the agents\nare constantly roaming the network and exchanging data.\nAlso, the domain of transportation networks introduces\ndynamic data, as the load of the roads is subject to change. In\naddition, the system in transportation networks has a\nfeedback mechanism, since the load in the roads depends on the\nreports and the movement of the agents themselves.\nMalkhi et al. [10] present a gossip algorithm for\npropagating information in a network of processors, in the presence\nof malicious parties. Their algorithm prevents the spreading\nof spurious gossip and diffuses genuine data. This is done\nin time, which is logarithmic in the number of processes\nand linear in the number of corrupt parties. Nevertheless,\ntheir work assumes that the network is static and also that\nthe agents are static (they discuss a network of processors).\nThis is not true for transportation networks. For example,\nin our model, agents might gossip about heavy traffic load\nof a specific road, which is currently jammed, yet this\ninformation might be false several minutes later, leaving the\nagents to speculate whether the spreading agents are indeed\nmalicious or not. In addition, as the agents are constantly\nmoving, each agent cannot choose with whom he interacts\nand exchanges data.\nIn the context of analyzing the data and deciding whether\nthe data is true or not, researchers have focused on\ndistributed reputation systems or decision mechanisms to decide\nwhether or not to share data.\nYu and Singh [18] build a social network of agents\"\nreputations. Every agent keeps a list of its neighbors, which can\nbe changed over time, and computes the trustworthiness of\nother agents by updating the current values of testimonies\nobtained from reliable referral chains. After a bad\nexperience with another agent every agent decreases the rating of\nthe \"bad\" agent and propagates this bad experience\nthroughout the network so that other agents can update their\nratings accordingly. This approach might be implemented in\nour domain to allow gossip agents to identify self-interested\nagents and thus minimize their effect. However, the\nimplementation of such a mechanism is an expensive addition\nto the infrastructure of autonomous agents in\ntransportation networks. This is mainly due to the dynamic nature of\nthe list of neighbors in transportation networks. Thus, not\nonly does it require maintaining the neighbors\" list, since the\nneighbors change frequently, but it is also harder to build a\ngood reputation system.\nLeckie et al. [9] focus on the issue of when to share\ninformation between the agents in the network. Their domain\ninvolves monitoring distributed sensors. Each agent\nmonitors a subset of the sensors and evaluates a hypothesis based\non the local measurements of its sensors. If the agent\nbelieves that a hypothesis is sufficient likely he exchanges this\ninformation with the other agents. In their domain, the\ngoal of all the agents is to reach a global consensus about\nthe likelihood of the hypothesis. In our domain, however, as\nthe agents constantly move, they have many samples, which\nthey exchange with each other. Also, the data might also\nvary (e.g., a road might be reported as jammed, but a few\nminutes later it could be free), thus making it harder to\ndecide whether to trust the agent, who sent the data.\nMoreover, the agent might lie only about a subset of its samples,\nthus making it even harder to detect his cheating.\nSome work has been done in the context of gossip networks\nor transportation networks regarding the spreading of data\nand its dissemination.\nDatta et al. [4] focus on information dissemination in\nmobile ad-hoc networks (MANET). They propose an\nautonomous gossiping algorithm for an infrastructure-less\nmobile ad-hoc networking environment. Their autonomous\ngossiping algorithm uses a greedy mechanism to spread data\nitems in the network. The data items are spread to\nimmediate neighbors that are interested in the information, and\navoid ones that are not interested. The decision which node\nis interested in the information is made by the data item\nitself, using heuristics. However, their work concentrates on\nthe movement of the data itself, and not on the agents who\npropagate the data. This is different from our scenario in\nwhich each agent maintains the data it has gathered, while\nthe agent itself roams the road and is responsible (and has\nthe capabilities) for spreading the data to other agents in\nthe network.\nDas et al. [3] propose a cooperative strategy for content\ndelivery in vehicular networks. In their domain, peers\ndownload a file from a mesh and exchange pieces of the file among\nthemselves. We, on the other hand, are interested in\nvehicular networks in which there is no rule forcing the agents to\ncooperate among themselves.\nShibata et al. [16] propose a method for cars to\ncooperatively and autonomously collect traffic jam statistics to\nestimate arrival time to destinations for each car. The\ncommunication is based on IEEE 802.11, without using a fixed\ninfrastructure on the ground. While we use the same\ndomain, we focus on a different problem. Shibata et al. [16]\nmainly focus on efficiently broadcasting the data between\nagents (e.g., avoid duplicates and communication overhead),\nas we focus on the case where agents are not cooperative in\n328 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nnature, and on how selfish agents affect other agents and the\nnetwork load.\nWang et al. [17] also assert, in the context of wireless\nnetworks, that individual agents are likely to do what is most\nbeneficial for their owners, and will act selfishly. They design\na protocol for communication in networks in which all agents\nare selfish. Their protocol motivates every agent to\nmaximize its profit only when it behaves truthfully (a mechanism\nof incentive compatibility). However, the domain of wireless\nnetworks is quite different from the domain of\ntransportation networks. In the wireless network, the wireless terminal\nis required to contribute its local resources to transmit data.\nThus, Wang et al. [17] use a payment mechanism, which\nattaches costs to terminals when transmitting data, and thus\nenables them to maximize their utility when transmitting\ndata, instead of acting selfishly. Unlike this, in the context\nof transportation networks, constructing such a mechanism\nis not quite a straightforward task, as self-interested agents\nand regular gossip agents might incur the same cost when\ntransmitting data. The difference between the two types of\nagents only exists regarding the credibility of the data they\nexchange.\nIn the next section, we will describe our transportation\nnetwork model and gossiping between the agents. We will\nalso describe the different agents in our system.\n3. MODEL AND SIMULATIONS\nWe first describe the formal transportation network model,\nand then we describe the simulations designs.\n3.1 Formal Model\nFollowing Shavitt and Shay [15] and Parshani [13], the\ntransportation network is represented by a directed graph\nG(V, E), where V is the set of vertices representing\njunctions, and E is the set of edges, representing roads. An edge\ne \u2208 E is associated with a weight w > 0, which specifies\nthe time it takes to traverse the road associated with that\nedge. The roads\" weights vary in time according to the\nnetwork (traffic) load. Each car, which is associated with an\nautonomous agent, is given a pair of origin and destination\npoints (vertices). A journey is defined as the (not\nnecessarily simple) path taken by an agent between the origin vertex\nand the destination vertex. We assume that there is always\na path between a source and a destination. A journey length\nis defined as the sum of all weights of the edges constituting\nthis path. Every agent has to travel between its origin and\ndestination points and aims to minimize its journey length.\nInitially, agents are ignorant about the state of the roads.\nRegular agents are only capable of gathering information\nabout the roads as they traverse them. However, we assume\nthat some agents have means of inter-vehicle\ncommunication (e.g., IEEE 802.11) with a given communication range,\nwhich enables them to communicate with other agents with\nthe same device. Those agents are referred to as gossip\nagents. Since the communication range is limited, the\nexchange of information using gossiping is done in one of two\nways: (a) between gossip agents passing one another, or (b)\nbetween gossip agents located at the same junction. We\nassume that each agent stores the most recent information it\nhas received or gathered around the edges in the network.\nA subset of the gossip agents are those agents who are\nselfinterested and manipulate the devices for their own benefit.\nWe will refer to these agents as self-interested agents. A\ndetailed description of their behavior is given in Sections 4\nand 5.\n3.2 Simulation Design\nBuilding on [13], the network in our simulations replicates\na central part of a large city, and consists of 50 junctions\nand 150 roads, which are approximately the number of main\nstreets in the city. Each simulation consists of 6 iterations.\nThe basic time unit of the iteration is a step, which\nequivalents to about 30 seconds. Each iteration simulates six hours\nof movements. The average number of cars passing through\nthe network during the iteration is about 70,000 and the\naverage number of cars in the network at a specific time unit\nis about 3,500 cars. In each iteration the same agents are\nused with the same origin and destination points, whereas\nthe data collected in earlier iterations is preserved in the\nfuture iterations (referred to as the history of the agent).\nThis allows us to simulate somewhat a daily routine in the\ntransportation network (e.g., a working week).\nEach of the experiments that we describe below is run\nwith 5 different traffic scenarios. Each such traffic scenario\ndiffers from one another by the initial load of the roads and\nthe designated routes of the agents (cars) in the network.\nFor each such scenario 5 simulations are run, creating a total\nof 25 simulations for each experiment.\nIt has been shown by Parshani et al. [13, 14] that the\ninformation propagation in the network is very efficient when\nthe percentage of gossiping agents is 10% or more. Yet, due\nto congestion caused by too many cars rushing to what is\nreported as the less congested part of the network 20-30%\nof gossiping agents leads to the most efficient routing results\nin their experiments. Thus, in our simulation, we focus only\non simulations in which the percentage of gossip agents is\n20%.\nThe simulations were done with different percentages of\nself-interested agents. To gain statistical significance we ran\neach simulation with changes in the set of the gossip agents,\nand the set of the self-interested agents.\nIn order to gain a similar ordinal scale, the results were\nnormalized. The normalized values were calculated by\ncomparing each agent\"s result to his results when the same\nscenario was run with no self-interested agents. This was done\nfor all of the iterations. Using the normalized values enabled\nus to see how worse (or better) each agent would perform\ncompared to the basic setting. For example, if an average\njourney length of a certain agent in iteration 1 with no\nselfinterested agent was 50, and the length was 60 in the same\nscenario and iteration in which self-interested agents were\ninvolved, then the normalized value for that agent would be\n60/50 = 1.2.\nMore details regarding the simulations are described in\nSections 4 and 5.\n4. SPREADING LIES, MAXIMIZING\nUTILITY\nIn the first set of experiments we investigated the benefits\nachieved by the self-interested agents, whose aim was to\nminimize their own journey length. The self-interested agents\nadopted a cheating approach, in which they sent false data\nto their peers.\nIn this section we first describe the simulations with the\nself-interested agents. Then, we model the scenario as a\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 329\ngame with two types of agents, and prove that the\nequilibrium result can only be achieved when there is no efficient\nexchange of gossiping information in the network.\n4.1 Modeling the Self-Interested Agents\"\nBehavior\nWhile the gossip agents gather data and send it to other\nagents, the self-interested agents\" behavior is modeled as\nfollows:\n1. Calculate the shortest path from origin to destination.\n2. Communicate the following data to other agents:\n(a) If the road is not in the agent\"s route - send the\ntrue data about it (e.g., data about roads it has\nreceived from other agents)\n(b) For all roads in the agent\"s route, which the agent\nhas not yet traversed, send a random high weight.\nBasically, the self-interested agent acts the same as the\ngossip agent. It collects data regarding the weight of the roads\n(either by traversing the road or by getting the data from\nother agents) and sends the data it has collected to other\nagents. However, the self-interested agent acts differently\nwhen the road is in its route. Since the agent\"s goal is to\nreach its destination as fast as possible, the agent will falsely\nreport that all the roads in its route are heavily congested.\nThis is in order to free the path for itself, by making other\nagents recalculate their paths, this time without including\nroads on the self-interested agent\"s route. To this end, for\nall the roads in its route, which the agent has not yet passed,\nthe agent generates a random weight, which is above the\naverage weight of the roads in the network. It then associates\nthese new weights with the roads in its route and sends them\nto the other agents.\nWhile an agent can also divert cars from its route by\nfalsely reporting congested roads in parallel to its route as\nfree, this behavior is not very likely since other agents,\nattempting to use the roads, will find the mistake within a\nshort time and spread the true congestion on the road. On\nthe other hand, if an agent manages to persuade other agents\nnot to use a road, it will be harder for them to detect that\nthe said roads are not congested.\nIn addition, to avoid being influenced by its own lies and\nother lies spreading in the network, all self-interested agents\nwill ignore data received about roads with heavy traffic (note\nthat data about roads that are not heavily traffic will not\nbe ignored)1\n.\nIn the next subsection we describe the simulation results,\ninvolving the self-interested agents.\n4.2 Simulation Results\nTo test the benefits of cheating by the self-interested agents\nwe ran several experiments. In the first set of experiments,\nwe created a scenario, in which a small group of self-interested\nagents spread lies on the same route, and tested its\neffect on the journey length of all the agents in the network.\n1\nIn other simulations we have run, in which there had been\nseveral real congestions in the network, we indeed saw that\neven when the roads are jammed, the self-interested agents\nwere less affected if they ignored all reported heavy traffic,\nsince by such they also discarded all lies roaming the network\nTable 1: Normalized journey length values,\nselfinterested agents with the same route\nIteration Self-Interested Gossip - Gossip - Regular\nNumber Agents SR Others Agents\n1 1.38 1.27 1.06 1.06\n2 0.95 1.56 1.18 1.14\n3 1.00 1.86 1.28 1.17\n4 1.06 2.93 1.35 1.16\n5 1.13 2.00 1.40 1.17\n6 1.08 2.02 1.43 1.18\nThus, several cars, which had the same origin and\ndestination points, were designated as self-interested agents. In this\nsimulation, we selected only 6 agents to be part of the group\nof the self-interested agents, as we wanted to investigate the\neffect achieved by only a small number of agents.\nIn each simulation in this experiment, 6 different agents\nwere randomly chosen to be part of the group of self-interested\nagents, as described above. In addition, one road, on the\nroute of these agents, was randomly selected to be partially\nblocked, letting only one car go through that road at each\ntime step. About 8,000 agents were randomly selected as\nregular gossip agents, and the other 32,000 agents were\ndesignated as regular agents.\nWe analyzed the average journey length of the self-interested\nagents as opposed to the average journey length of other\nregular gossip agents traveling along the same route. Table\n1 summarizes the normalized results for the self-interested\nagents, the gossip agents (those having the same origin and\ndestination points as the self-interested agents, denoted\nGossip - SR, and all other gossip agents, denoted Gossip -\nOthers) and the regular agents, as a function of the iteration\nnumber.\nWe can see from the results that the first time the\nselfinterested agents traveled the route while spreading the false\ndata about the roads did not help them (using the paired\nt-test we show that those agents had significantly lower\njourney lengths in the scenario in which they did not spread any\nlies, with p < 0.01). This is mainly due to the fact that\nthe lies do not bypass the self-interested agent and reach\nother cars that are ahead of the self-interested car on the\nsame route. Thus, spreading the lies in the first iteration\ndoes not help the self-interested agent to free the route he\nis about to travel, in the first iteration.\nOnly when the self-interested agents had repeated their\njourney in the next iteration (iteration 2) did it help them\nsignificantly (p = 0.04). The reason for this is that other\ngossip agents received this data and used it to recalculate their\nshortest path, thus avoiding entrance to the roads, for which\nthe self-interested agents had spread false information about\ncongestion. It is also interesting to note the large value\nattained by the self-interested agents in the first iteration.\nThis is mainly due to several self-interested agents, who\nentered the jammed road. This situation occurred since the\nself-interested agents ignored all heavy traffic data, and thus\nignored the fact that the road was jammed. As they started\nspreading lies about this road, more cars shifted from this\nroute, thus making the road free for the future iterations.\nHowever, we also recall that the self-interested agents\nignore all information about the heavy traffic roads. Thus,\n330 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nTable 2: Normalized journey length values,\nspreading lies for a beneficiary agent\nIteration Beneficiary Gossip - Gossip - Regular\nNumber Agent SR Others Agents\n1 1.10 1.05 0.94 1.11\n2 1.09 1.14 0.99 1.14\n3 1.04 1.19 1.02 1.14\n4 1.03 1.26 1.03 1.14\n5 1.05 1.32 1.05 1.12\n6 0.92 1.40 1.06 1.11\nwhen the network becomes congested, more self-interested\ncars are affected, since they might enter jammed roads,\nwhich they would otherwise not have entered. This can be\nseen, for example, in iterations 4-6, in which the normalized\nvalue of the self-interested agents increased above 1.00.\nUsing the paired t-test to compare these values with the values\nachieved by these agents when no lies are used, we see that\nthere is no significant difference between the two scenarios.\nAs opposed to the gossip agents, we can see how little\neffect the self-interested agents have on the regular agents.\nAs compared to the gossip agents on the same route that\nhave traveled as much as 193% more, when self-interested\nagents are introduced, the average journey length for the\nregular agents has only increased by about 15%. This result\nis even lower than the effect on other gossip agents in the\nentire network.\nSince we noticed that cheating by the self-interested agents\ndoes not benefit them in the first iteration, we devised\nanother set of experiments. In the second set of experiments,\nthe self-interested agents have the objective to help another\nagent, who is supposed to enter the network some time\nafter the self-interested agent entered. We refer to the latter\nagent as the beneficiary agent. Just like a self-interested\nagent, the beneficiary agent also ignores all data regarding\nheavy traffic. In real-life this can be modeled, for\nexample, by a husband, who would like to help his wife find a\nfaster route to her destination. Table 2 summarizes the\nnormalized values for the different agents. As in the first set\nof experiments, 5 simulations were run for each scenario,\nwith a total of 25 simulations. In each of these simulation\none agent was randomly selected as a self-interested agent,\nand then another agent, with the same origin as the\nselfinterested agent, was randomly selected as the beneficiary\nagent. The other 8,000 and 32,000 agents were designated\nas regular gossip agents and regular agents, respectively.\nWe can see that as the number of iterations advances, the\nlower the normalized value for the beneficiary agent. In this\nscenario, just like the previous one, in the first iterations,\nnot only does the beneficiary agent not avoid the jammed\nroads, since he ignores all heavy traffic, he also does not\nbenefit from the lies spread by the self-interested agent. This\nis due to the fact that the lies are not yet incorporated by\nother gossip agents. Thus, if we compare the average journey\nlength in the first iteration when lies are spread and when\nthere are no lies, the average is significantly lower when there\nare no lies (p < 0.03). On the other hand, if we compare\nthe average journey length in all of the iterations, there is\nno significant difference between the two settings. Still, in\nmost of the iterations, the average journey length of the\nbeneficiary agent is longer than in the case when no lies are\nspread.\nWe can also see the impact on the other agents in the\nsystem. While the gossip agents, which are not on the\nroute of the beneficiary agent, virtually are not affected by\nthe self-interested agent, those on the route and the\nregular agents are affected and have higher normalized values.\nThat is, even with just one self-interested car, we can see\nthat both the gossip agents that follow the same route as\nthe lies spread by the self-interested agents, and other\nregular agents, increase their journey length by more than 14%.\nIn our third set of experiments we examined a setting in\nwhich there was an increasing number of agents, and the\nagents did not necessarily have the same origin and\ndestination points. To model this we randomly selected\nselfinterested agents, whose objective was to minimize their\naverage journey length, assuming the cars were repeating\ntheir journeys (that is, more than one iteration was made).\nAs opposed to the first set of experiments, in this set the\nself-interested agents were selected randomly, and we did\nnot enforce the constraint that they will all have the same\norigin and destination points.\nAs in the previous sets of experiments we ran 5\ndifferent simulations per scenario. In each simulation 11 runs\nwere made, each run with different numbers of self-interested\nagents: 0 (no self-interested agents), 1, 2, 4, 8, and 16. Each\nagent adopted the behavior modeled in Section 4.1. Figure\n1 shows the normalized value achieved by the self-interested\nagents as a function of their number. The figure shows these\nvalues for iterations 2-6. The first iteration is not shown\nintentionally, as we assume repeated journeys. Also, we have\nseen in the previous set of experiments and we have\nprovided explanations as to why the self-interested agents do\nnot gain much from their behavior in the first iteration.\n0.955\n0.96\n0.965\n0.97\n0.975\n0.98\n0.985\n0.99\n0.995\n1\n1.005\n1.01\n1.015\n1.02\n1.025\n1.03\n0 1 2 3 4 5 6 7 8 9 10111213141516\nSelf-Interested Agents Number\nNormalizedValue\nIteration 2 Iteration 3 Iteration 4\nIteration 5 Iteration 6\nFigure 1: Self-interested agents normalized values as\na function of the number of self-interested agents.\nUsing these simulations we examined what the threshold\ncould be for the number of randomly selected self-interested\nagents in order to allow themselves to benefit from their\nselfish behavior. We can see that up to 8 self-interested\nagents, the average normalized value is below 1. That is,\nthey benefit from their malicious behavior. In the case of\none self-interested agent there is a significant difference\nbetween the average journey length of when the agent spread\nlies and when no lies are spread (p < 0.001), while when\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 331\nthere are 2, 4, 8 and 16 self-interested agents there is no\nsignificance difference. Yet, as the number of self-interested\nagents increases, the normalized value also increases. In\nsuch cases, the normalized value is larger than 1, and the\nself-interested agents journey length becomes significantly\nhigher than their journey length, in cases where there are\nno self-interested agents in the system.\nIn the next subsection we analyze the scenario as a game\nand show that when in equilibrium the exchange of gossiping\nbetween the agents becomes inefficient.\n4.3 When Gossiping is Inefficient\nWe continued and modeled our scenario as a game, in\norder to find the equilibrium. There are two possible types for\nthe agents: (a) regular gossip agents, and (b) self-interested\nagents. Each of these agents is a representative of its group,\nand thus all agents in the same group have similar behavior.\nWe note that the advantage of using gossiping in\ntransportation networks is to allow the agents to detect anomalies\nin the network (e.g., traffic jams) and to quickly adapt to\nthem by recalculating their routes [14]. We also assume that\nthe objective of the self-interested agents is to minimize their\nown journey length, thus they spread lies on their routes, as\ndescribed in Section 4.1. We also assume that sophisticated\nmethods for identifying the self-interested agents or\nmanaging reputation are not used. This is mainly due to the\ncomplexity of incorporating and maintaining such mechanisms,\nas well as due to the dynamics of the network, in which\ninteractions between different agents are frequent, agents may\nleave the network, and data about the road might change as\ntime progresses (e.g., a road might be reported by a regular\ngossip agent as free at a given time, yet it may currently be\njammed due to heavy traffic on the road).\nLet Tavg be the average time it takes to traverse an edge\nin the transportation network (that is, the average load of\nan edge). Let Tmax be the maximum time it takes to\ntraverse an edge. We will investigate the game, in which the\nself-interested and the regular gossip agents can choose the\nfollowing actions. The self-interested agents can choose how\nmuch to lie, that is, they can choose to spread how long (not\nnecessarily the true duration) it takes to traverse certain\nroads. Since the objective of the self-interested agents is to\nspread messages as though some roads are jammed, the\ntraversal time they report is obviously larger than the average\ntime. We denote the time the self-interested agents spread\nas Ts, such that Tavg \u2264 Ts \u2264 Tmax. Motivated by the\nresults of the simulations we have described above, we saw that\nthe agents are less affected if they discard the heavy traffic\nvalues. Thus, the regular gossip cars, attempting to\nmitigate the effect of the liars, can choose a strategy to ignore\nabnormal congestion values above a certain threshold, Tg.\nObviously, Tavg \u2264 Tg \u2264 Tmax. In order to prevent the\ngossip agents from detecting the lies and just discarding those\nvalues, the self-interested agents send lies in a given range,\n[Ts, Tmax], with an inverse geometric distribution, that is,\nthe higher the T value, the higher its frequency.\nNow we construct the utility functions for each type of\nagents, which is defined by the values of Ts and Tg. If the\nself-interested agents spread traversal times higher than or\nequal to the regular gossip cars\" threshold, they will not\nbenefit from those lies. Thus, the utility value of the\nselfinterested agents in this case is 0. On the other hand, if the\nself-interested agents spread traversal time which is lower\nthan the threshold, they will gain a positive utility value.\nFrom the regular gossip agents point-of-view, if they accept\nmessages from the self-interested agents, then they\nincorporate the lies in their calculation, thus they will lose utility\npoints. On the other hand, if they discard the false values\nthe self-interested agents send, that is, they do not\nincorporate the lies, they will gain utility values. Formally, we use\nus\nto denote the utility of the self-interested agents and ug\nto denote the utility of the regular gossip agents. We also\ndenote the strategy profile in the game as {Ts, Tg}. The\nutility functions are defined as:\nus\n=\n0 if Ts \u2265 Tg\nTs \u2212 Tavg + 1 if Ts < Tg\n(1)\nug\n=\nTg \u2212 Tavg if Ts \u2265 Tg\nTs \u2212 Tg if Ts < Tg\n(2)\nWe are interested in finding the Nash equilibrium. We\nrecall from [12], that the Nash equilibrium is a strategy\nprofile, where no player has anything to gain by deviating from\nhis strategy, given that the other agent follows his strategy\nprofile. Formally, let (S, u) denote the game, where S is\nthe set of strategy profiles and u is the set of utility\nfunctions. When each agent i \u2208 {regular gossip, self-interested}\nchooses a strategy Ti resulting in a strategy profile T =\n(Ts, Tg) then agent i obtains a utility of ui\n(T). A strategy\nprofile T\u2217\n\u2208 S is a Nash equilibrium if no deviation in the\nstrategy by any single agent is profitable, that is, if for all i,\nui\n(T\u2217\n) \u2265 ui\n(Ti, T\u2217\n\u2212i). That is, (Ts, Tg) is a Nash equilibrium\nif the self-interested agents have no other value Ts such that\nus\n(Ts, Tg) > us\n(Ts, Tg), and similarly for the gossip agents.\nWe now have the following theorem.\nTheorem 4.1. (Tavg, Tavg) is the only Nash equilibrium.\nProof. First we will show that (Tavg, Tavg) is a Nash\nequilibrium. Assume, by contradiction, that the gossip agents\nchoose another value Tg > Tavg. Thus, ug\n(Tavg, Tg ) =\nTavg \u2212 Tg < 0. On the other hand, ug\n(Tavg, Tavg) = 0.\nThus, the regular gossip agents have no incentive to\ndeviate from this strategy. The self-interested agents also have\nno incentive to deviate from this strategy. By\ncontradiction, again assume that the self-interested agents choose\nanother value Ts > Tavg. Thus, us\n(Ts , Tavg) = 0, while\nus\n(Tavg, Tavg) = 0.\nWe will now show that the above solution is unique. We\nwill show that any other tuple (Ts, Tg), such that Tavg <\nTg \u2264 Tmax and Tavg < Ts \u2264 Tmax is not a Nash equilibrium.\nWe have three cases. In the first Tavg < Tg < Ts \u2264 Tmax.\nThus, us\n(Ts, Tg) = 0 and ug\n(Ts, Tg) = Tg \u2212 Tavg. In this\ncase, the regular gossip agents have an incentive to deviate\nand choose another strategy Tg + 1, since by doing so they\nincrease their own utility: ug\n(Ts, Tg + 1) = Tg + 1 \u2212 Tavg.\nIn the second case we have Tavg < Ts < Tg \u2264 Tmax. Thus,\nug\n(Ts, Tg) = Ts \u2212 Tg < 0. Also, the regular gossip agents\nhave an incentive to deviate and choose another strategy\nTg \u22121, in which their utility value is higher: ug\n(Ts, Tg \u22121) =\nTs \u2212 Tg + 1.\nIn the last case we have Tavg < Ts = Tg \u2264 Tmax. Thus,\nus\n(Ts, Tg) = Ts \u2212 Tg = 0. In this case, the self-interested\nagents have an incentive to deviate and choose another\nstrategy Tg \u2212 1, in which their utility value is higher: us\n(Tg \u2212\n1, Tg) = Tg \u2212 1 \u2212 Tavg + 1 = Tg \u2212 Tavg > 0.\n332 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nTable 3: Normalized journey length values for the\nfirst iteration\nSelf-Interested Self-Interested Gossip Regular\nAgents Number Agents Agents Agents\n1 0.98 1.01 1.05\n2 1.09 1.02 1.05\n4 1.07 1.02 1.05\n8 1.06 1.04 1.05\n16 1.03 1.08 1.06\n32 1.07 1.17 1.08\n50 1.12 1.28 1.1\n64 1.14 1.4 1.13\n80 1.15 1.5 1.14\n100 1.17 1.63 1.16\nTable 4: Normalized journey length values for all\niterations\nSelf-Interested Self-Interested Gossip Regular\nAgents Number Agents Agents Agents\n1 0.98 1.02 1.06\n2 1.0 1.04 1.07\n4 1.0 1.08 1.07\n8 1.01 1.33 1.11\n16 1.02 1.89 1.17\n32 1.06 2.46 1.25\n50 1.13 2.24 1.29\n64 1.21 2.2 1.32\n80 1.21 2.13 1.27\n100 1.26 2.11 1.27\nThe above theorem proves that the equilibrium point is\nreached only when the self-interested agents send the time\nto traverse certain edges equals the average time, and on\nthe other hand the regular gossip agents discard all data\nregarding roads that are associated with an average time or\nhigher. Thus, for this equilibrium point the exchange of\ngossiping information between agents is inefficient, as the gossip\nagents are unable to detect any anomalies in the network.\nIn the next section we describe another scenario for the\nself-interested agents, in which they are not concerned with\ntheir own utility, but rather interested in maximizing the\naverage journey length of other gossip agents.\n5. SPREADING LIES, CAUSING CHAOS\nAnother possible behavior that can be adopted by\nselfinterested agents is characterized by their goal to cause\ndisorder in the network. This can be achieved, for example, by\nmaximizing the average journey length of all agents, even at\nthe cost of maximizing their own journey length.\nTo understand the vulnerability of the gossip based\ntransportation support system, we ran 5 different simulations for\neach scenario. In each simulation different agents were\nrandomly chosen (using a uniform distribution) to act as\ngossip agents, among them self-interested agents were chosen.\nEach self-interested agent behaved in the same manner as\ndescribed in Section 4.1.\nEvery simulation consisted of 11 runs with each run\ncomprising different numbers of self-interested agents: 0 (no\nselfinterested agents), 1, 2, 4, 8, 16, 32, 50, 64, 80 and 100.\nAlso, in each run the number of self-interested agents was\nincreased incrementally. For example: the run with 50\nselfinterested agents consisted of all the self-interested agents\nthat were used in the run with 32 self-interested agents, but\nwith an additional 18 self-interested agents.\nTables 3 and 4 summarize the normalized journey length\nfor the self-interested agents, the regular gossip agents and\nthe regular (non-gossip) agents. Table 3 summarizes the\ndata for the first iteration and Table 4 summarizes the data\nfor the average of all iterations. Figure 2 demonstrates\nthe changes in the normalized values for the regular gossip\nagents and the regular agents, as a function of the iteration\nnumber. Similar to the results in our first set of experiments,\ndescribed in Section 4.2, we can see that randomly selected\nself-interested agents who follow different randomly selected\nroutes do not benefit from their malicious behavior (that is,\ntheir average journey length does not decrease). However,\nwhen only one self-interested agent is involved, it does\nbenefit from the malicious behavior, even in the first iteration.\nThe results also indicate that the regular gossip agents are\nmore sensitive to malicious behavior than regular\nagentsthe average journey length for the gossip agents increases\nsignificantly (e.g., with 32 self-interested agents the average\njourney length for the gossip agents was 146% higher than\nin the setting with no self-interested agents at all, as\nopposed to an increase of only 25% for the regular agents). In\ncontrast, these results also indicate that the self-interested\nagents do not succeed in causing a significant load in the\nnetwork by their malicious behavior.\n1\n1.1\n1.2\n1.3\n1.4\n1.5\n1.6\n1.7\n1.8\n1.9\n2\n2.1\n2.2\n2.3\n2.4\n2.5\n2.6\n2.7\n2.8\n2.9\n1 2 3 4 5 6\nIteration Number\nNormalizedValue\n32 self-interested agents, gossip agents normalized value\n100 self-interested agents, gossip agents normalized value\n32 self-interested agents, regular agents normalized value\n100 self-interested agents, regular agents normalized value\nFigure 2: Gossip and regular agents normalized\nvalues, as a function of the iteration.\nSince the goal of the self-interested agents in this case is\nto cause disorder in the network rather than use the lies for\ntheir own benefits, the question arises as to why would the\nbehavior of the self-interested agents be to send lies about\ntheir routes only. Furthermore, we hypothesize that if they\nall send lies about the same major roads the damage they\nmight inflict on the entire network would be larger that had\neach of them sent lies about its own route. To examine this\nhypothesis, we designed another set of experiments. In this\nset of experiments, all the self-interested agents spread lies\nabout the same 13 main roads in the network. However, the\nresults show quite a smaller impact on other gossip and\nreguThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 333\nTable 5: Normalized journey length values for all\niterations. Network with congestions.\nSelf-Interested Self-Interested Gossip Regular\nAgents Number Agents Agents Agents\n1 1.04 1.02 1.22\n2 1.06 1.04 1.22\n4 1.04 1.06 1.23\n8 1.07 1.15 1.26\n16 1.09 1.55 1.39\n32 1.12 2.25 1.56\n50 1.24 2.25 1.60\n64 1.28 2.47 1.63\n80 1.50 2.41 1.64\n100 1.69 2.61 1.75\nlar agents in the network. The average normalized value for\nthe gossip agents in these simulations was only about 1.07,\nas opposed to 1.7 in the original scenario. When analyzing\nthe results we saw that although the false data was spread,\nit did not cause other gossip cars to change their route. The\nmain reason was that the lies were spread on roads that were\nnot on the route of the self-interested agents. Thus, it took\nthe data longer to reach agents on the main roads, and when\nthe agents reached the relevant roads this data was too old\nto be incorporated in the other agents calculations.\nWe also examined the impact of sending lies in order to\ncause chaos when there are already congestions in the\nnetwork. To this end, we simulated a network in which 13 main\nroads are jammed. The behavior of the self-interested agents\nis as described in Section 4.1, and the self-interested agents\nspread lies about their own route. The simulation results,\ndetailed in Table 5, show that there is a greater incentive\nfor the self-interested agents to cheat when the network is\nalready congested, as their cheating causes more damage\nto the other agents in the network. For example, whereas\nthe average journey length of the regular agents increased\nonly by about 15% in the original scenario, in which the\nnetwork was not congested, in this scenario the average journey\nlength of the agents had increased by about 60%.\n6. CONCLUSIONS\nIn this paper we investigated the benefits achieved by\nself-interested agents in vehicular networks. Using\nsimulations we investigated two behaviors that might be taken\nby self-interested agents: (a) trying to minimize their\njourney length, and (b) trying to cause chaos in the network.\nOur simulations indicate that in both behaviors the\nselfinterested agents have only limited success achieving their\ngoal, even if no counter-measures are taken. This is in\ncontrast to the greater impact inflicted by self-interested agents\nin other domains (e.g., E-Commerce). Some reasons for this\nare the special characteristics of vehicular networks and their\ndynamic nature. While the self-interested agents spread lies,\nthey cannot choose which agents with whom they will\ninteract. Also, by the time their lies reach other agents, they\nmight become irrelevant, as more recent data has reached\nthe same agents.\nMotivated by the simulation results, future research in\nthis field will focus on modeling different behaviors of the\nself-interested agents, which might cause more damage to\nthe network. Another research direction would be to find\nways of minimizing the effect of selfish-agents by using\ndistributed reputation or other measures.\n7. REFERENCES\n[1] A. Bejan and R. Lawrence. Peer-to-peer cooperative\ndriving. In Proceedings of ISCIS, pages 259-264,\nOrlando, USA, October 2002.\n[2] I. Chisalita and N. Shahmehri. 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Hugue\n(Eds.). IEEE Computer Society Press, 1982.\n[9] C. Leckie and R. Kotagiri. Policies for sharing\ndistributed probabilistic beliefs. In Proceedings of\nACSC, pages 285-290, Adelaide, Australia, 2003.\n[10] D. Malkhi, E. Pavlov, and Y. Sella. Gossip with\nmalicious parties. Technical report: 2003-9, School of\nComputer Science and Engineering - The Hebrew\nUniversity of Jerusalem, Israel, March 2003.\n[11] Y. M. Minsky and F. B. Schneider. Tolerating\nmalicious gossip. Distributed Computing, 16(1):49-68,\nFebruary 2003.\n[12] M. J. Osborne and A. Rubinstein. A Course In Game\nTheory. MIT Press, Cambridge MA, 1994.\n[13] R. Parshani. Routing in gossip networks. Master\"s\nthesis, Department of Computer Science, Bar-Ilan\nUniversity, Ramat-Gan, Israel, October 2004.\n[14] R. Parshani, S. Kraus, and Y. Shavitt. A study of\ngossiping in transportation networks. Submitted for\npublication, 2006.\n[15] Y. Shavitt and A. Shay. Optimal routing in gossip\nnetworks. IEEE Transactions on Vehicular\nTechnology, 54(4):1473-1487, July 2005.\n[16] N. Shibata, T. Terauchi, T. Kitani, K. Yasumoto,\nM. Ito, and T. Higashino. A method for sharing traffic\njam information using inter-vehicle communication. In\nProceedings of V2VCOM, USA, 2006.\n[17] W. Wang, X.-Y. Li, and Y. Wang. Truthful multicast\nrouting in selfish wireless networks. In Proceedings of\nMobiCom, pages 245-259, USA, 2004.\n[18] B. Yu and M. P. Singh. A social mechanism of\nreputation management in electronic communities. In\nProceedings of CIA, 2000.\n334 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)", "keywords": "artificial social system;chaos;vehicular network;intelligent agent;journey length;social network;self-interested agent;selfinterested agent;agent-base deploy application"}
{"name": "train_I-61", "title": "Distributed Agent-Based Air Traffic Flow Management", "abstract": "Air traffic flow management is one of the fundamental challenges facing the Federal Aviation Administration (FAA) today. The FAA estimates that in 2005 alone, there were over 322,000 hours of delays at a cost to the industry in excess of three billion dollars. Finding reliable and adaptive solutions to the flow management problem is of paramount importance if the Next Generation Air Transportation Systems are to achieve the stated goal of accommodating three times the current traffic volume. This problem is particularly complex as it requires the integration and/or coordination of many factors including: new data (e.g., changing weather info), potentially conflicting priorities (e.g., different airlines), limited resources (e.g., air traffic controllers) and very heavy traffic volume (e.g., over 40,000 flights over the US airspace). In this paper we use FACET - an air traffic flow simulator developed at NASA and used extensively by the FAA and industry - to test a multi-agent algorithm for traffic flow management. An agent is associated with a fix (a specific location in 2D space) and its action consists of setting the separation required among the airplanes going though that fix. Agents use reinforcement learning to set this separation and their actions speed up or slow down traffic to manage congestion. Our FACET based results show that agents receiving personalized rewards reduce congestion by up to 45% over agents receiving a global reward and by up to 67% over a current industry approach (Monte Carlo estimation).", "fulltext": "1. INTRODUCTION\nThe efficient, safe and reliable management of our ever\nincreasing air traffic is one of the fundamental challenges\nfacing the aerospace industry today. On a typical day, more\nthan 40,000 commercial flights operate within the US airspace\n[14]. In order to efficiently and safely route this air traffic,\ncurrent traffic flow control relies on a centralized,\nhierarchical routing strategy that performs flow projections ranging\nfrom one to six hours. As a consequence, the system is\nslow to respond to developing weather or airport conditions\nleading potentially minor local delays to cascade into large\nregional congestions. In 2005, weather, routing decisions\nand airport conditions caused 437,667 delays, accounting for\n322,272 hours of delays. The total cost of these delays was\nestimated to exceed three billion dollars by industry [7].\nFurthermore, as the traffic flow increases, the current\nprocedures increase the load on the system, the airports, and\nthe air traffic controllers (more aircraft per region)\nwithout providing any of them with means to shape the traffic\npatterns beyond minor reroutes. The Next Generation Air\nTransportation Systems (NGATS) initiative aims to address\nthis issues and, not only account for a threefold increase in\ntraffic, but also for the increasing heterogeneity of aircraft\nand decreasing restrictions on flight paths. Unlike many\nother flow problems where the increasing traffic is to some\nextent absorbed by improved hardware (e.g., more servers\nwith larger memories and faster CPUs for internet routing)\nthe air traffic domain needs to find mainly algorithmic\nsolutions, as the infrastructure (e.g., number of the airports) will\nnot change significantly to impact the flow problem. There\nis therefore a strong need to explore new, distributed and\nadaptive solutions to the air flow control problem.\nAn adaptive, multi-agent approach is an ideal fit to this\nnaturally distributed problem where the complex interaction\namong the aircraft, airports and traffic controllers renders a\npre-determined centralized solution severely suboptimal at\nthe first deviation from the expected plan. Though a truly\ndistributed and adaptive solution (e.g., free flight where\naircraft can choose almost any path) offers the most potential\nin terms of optimizing flow, it also provides the most\nradical departure from the current system. As a consequence, a\nshift to such a system presents tremendous difficulties both\nin terms of implementation (e.g., scheduling and airport\ncapacity) and political fallout (e.g., impact on air traffic\ncontrollers). In this paper, we focus on agent based system that\ncan be implemented readily. In this approach, we assign an\n342\n978-81-904262-7-5 (RPS) c 2007 IFAAMAS\nagent to a fix, a specific location in 2D. Because aircraft\nflight plans consist of a sequence of fixes, this\nrepresentation allows localized fixes (or agents) to have direct impact\non the flow of air traffic1\n. In this approach, the agents\"\nactions are to set the separation that approaching aircraft\nare required to keep. This simple agent-action pair allows\nthe agents to slow down or speed up local traffic and allows\nagents to a have significant impact on the overall air traffic\nflow. Agents learn the most appropriate separation for their\nlocation using a reinforcement learning (RL) algorithm [15].\nIn a reinforcement learning approach, the selection of the\nagent reward has a large impact on the performance of the\nsystem. In this work, we explore four different agent reward\nfunctions, and compare them to simulating various changes\nto the system and selecting the best solution (e.g,\nequivalent to a Monte-Carlo search). The first explored reward\nconsisted of the system reward. The second reward was a\npersonalized agent reward based on collectives [3, 17, 18].\nThe last two rewards were personalized rewards based on\nestimations to lower the computational burden of the\nreward computation. All three personalized rewards aim to\nalign agent rewards with the system reward and ensure that\nthe rewards remain sensitive to the agents\" actions.\nPrevious work in this domain fell into one of two distinct\ncategories: The first principles based modeling approaches\nused by domain experts [5, 8, 10, 13] and the algorithmic\napproaches explored by the learning and/or agents\ncommunity [6, 9, 12]. Though our approach comes from the second\ncategory, we aim to bridge the gap by using FACET to test\nour algorithms, a simulator introduced and widely used (i.e.,\nover 40 organizations and 5000 users) by work in the first\ncategory [4, 11].\nThe main contribution of this paper is to present a\ndistributed adaptive air traffic flow management algorithm that\ncan be readily implemented and test that algorithm using\nFACET. In Section 2, we describe the air traffic flow problem\nand the simulation tool, FACET. In Section 3, we present\nthe agent-based approach, focusing on the selection of the\nagents and their action space along with the agents\" learning\nalgorithms and reward structures. In Section 4 we present\nresults in domains with one and two congestions, explore\ndifferent trade-offs of the system objective function, discuss\nthe scaling properties of the different agent rewards and\ndiscuss the computational cost of achieving certain levels of\nperformance. Finally, in Section 5, we discuss the\nimplications of these results and provide and map the required work\nto enable the FAA to reach its stated goal of increasing the\ntraffic volume by threefold.\n2. AIR TRAFFIC FLOW MANAGEMENT\nWith over 40,000 flights operating within the United States\nairspace on an average day, the management of traffic flow\nis a complex and demanding problem. Not only are there\nconcerns for the efficiency of the system, but also for\nfairness (e.g., different airlines), adaptability (e.g., developing\nweather patterns), reliability and safety (e.g., airport\nmanagement). In order to address such issues, the management\nof this traffic flow occurs over four hierarchical levels:\n1. Separation assurance (2-30 minute decisions);\n1\nWe discuss how flight plans with few fixes can be handled\nin more detail in Section 2.\n2. Regional flow (20 minutes to 2 hours);\n3. National flow (1-8 hours); and\n4. Dynamic airspace configuration (6 hours to 1 year).\nBecause of the strict guidelines and safety concerns\nsurrounding aircraft separation, we will not address that control\nlevel in this paper. Similarly, because of the business and\npolitical impact of dynamic airspace configuration, we will\nnot address the outermost flow control level either. Instead,\nwe will focus on the regional and national flow management\nproblems, restricting our impact to decisions with time\nhorizons between twenty minutes and eight hours. The proposed\nalgorithm will fit between long term planning by the FAA\nand the very short term decisions by air traffic controllers.\nThe continental US airspace consists of 20 regional centers\n(handling 200-300 flights on a given day) and 830 sectors\n(handling 10-40 flights). The flow control problem has to\naddress the integration of policies across these sectors and\ncenters, account for the complexity of the system (e.g., over\n5200 public use airports and 16,000 air traffic controllers)\nand handle changes to the policies caused by weather\npatterns. Two of the fundamental problems in addressing the\nflow problem are: (i) modeling and simulating such a large\ncomplex system as the fidelity required to provide reliable\nresults is difficult to achieve; and (ii) establishing the method\nby which the flow management is evaluated, as directly\nminimizing the total delay may lead to inequities towards\nparticular regions or commercial entities. Below, we discuss\nhow we addressed both issues, namely, we present FACET\na widely used simulation tool and discuss our system\nevaluation function.\nFigure 1: FACET screenshot displaying traffic\nroutes and air flow statistics.\n2.1 FACET\nFACET (Future ATM Concepts Evaluation Tool), a physics\nbased model of the US airspace was developed to accurately\nmodel the complex air traffic flow problem [4]. It is based on\npropagating the trajectories of proposed flights forward in\ntime. FACET can be used to either simulate and display air\ntraffic (a 24 hour slice with 60,000 flights takes 15 minutes to\nsimulate on a 3 GHz, 1 GB RAM computer) or provide rapid\nstatistics on recorded data (4D trajectories for 10,000 flights\nincluding sectors, airports, and fix statistics in 10 seconds\non the same computer) [11]. FACET is extensively used by\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 343\nthe FAA, NASA and industry (over 40 organizations and\n5000 users) [11].\nFACET simulates air traffic based on flight plans and\nthrough a graphical user interface allows the user to analyze\ncongestion patterns of different sectors and centers (Figure\n1). FACET also allows the user to change the flow patterns\nof the aircraft through a number of mechanisms, including\nmetering aircraft through fixes. The user can then observe\nthe effects of these changes to congestion. In this paper,\nagents use FACET directly through batch mode, where\nagents send scripts to FACET asking it to simulate air\ntraffic based on metering orders imposed by the agents. The\nagents then produce their rewards based on receive feedback\nfrom FACET about the impact of these meterings.\n2.2 System Evaluation\nThe system performance evaluation function we select\nfocuses on delay and congestion but does not account for\nfairness impact on different commercial entities. Instead it\nfocuses on the amount of congestion in a particular sector and\non the amount of measured air traffic delay. The linear\ncombination of these two terms gives the full system evaluation\nfunction, G(z) as a function of the full system state z. More\nprecisely, we have:\nG(z) = \u2212((1 \u2212 \u03b1)B(z) + \u03b1C(z)) , (1)\nwhere B(z) is the total delay penalty for all aircraft in the\nsystem, and C(z) is the total congestion penalty. The\nrelative importance of these two penalties is determined by the\nvalue of \u03b1, and we explore various trade-offs based on \u03b1 in\nSection 4.\nThe total delay, B, is a sum of delays over a set of sectors\nS and is given by:\nB(z) =\nX\ns\u2208S\nBs(z) (2)\nwhere\nBs(z) =\nX\nt\n\u0398(t \u2212 \u03c4s)kt,s(t \u2212 \u03c4s) , (3)\nwhere ks,t is the number of aircraft in sector s at a\nparticular time, \u03c4s is a predetermined time, and \u0398(\u00b7) is the\nstep function that equals 1 when its argument is greater or\nequal to zero, and has a value of zero otherwise. Intuitively,\nBs(z) provides the total number of aircraft that remain in\na sector s past a predetermined time \u03c4s, and scales their\ncontribution to count by the amount by which they are late.\nIn this manner Bs(z) provides a delay factor that not only\naccounts for all aircraft that are late, but also provides a\nscale to measure their lateness. This definition is based\non the assumption that most aircraft should have reached\nthe sector by time \u03c4s and that aircraft arriving after this\ntime are late. In this paper the value of \u03c4s is determined by\nassessing aircraft counts in the sector in the absence of any\nintervention or any deviation from predicted paths.\nSimilarly, the total congestion penalty is a sum over the\ncongestion penalties over the sectors of observation, S:\nC(z) =\nX\ns\u2208S\nCs(z) (4)\nwhere\nCs(z) = a\nX\nt\n\u0398(ks,t \u2212 cs)eb(ks,t\u2212cs)\n, (5)\nwhere a and b are normalizing constants, and cs is the\ncapacity of sector s as defined by the FAA. Intuitively, Cs(z)\npenalizes a system state where the number of aircraft in a\nsector exceeds the FAAs official sector capacity. Each sector\ncapacity is computed using various metrics which include the\nnumber of air traffic controllers available. The exponential\npenalty is intended to provide strong feedback to return the\nnumber of aircraft in a sector to below the FAA mandated\ncapacities.\n3. AGENT BASED AIR TRAFFIC FLOW\nThe multi agent approach to air traffic flow management\nwe present is predicated on adaptive agents taking\nindependent actions that maximize the system evaluation function\ndiscussed above. To that end, there are four critical\ndecisions that need to be made: agent selection, agent action\nset selection, agent learning algorithm selection and agent\nreward structure selection.\n3.1 Agent Selection\nSelecting the aircraft as agents is perhaps the most\nobvious choice for defining an agent. That selection has the\nadvantage that agent actions can be intuitive (e.g., change\nof flight plan, increase or decrease speed and altitude) and\noffer a high level of granularity, in that each agent can have\nits own policy. However, there are several problems with\nthat approach. First, there are in excess of 40,000 aircraft\nin a given day, leading to a massively large multi-agent\nsystem. Second, as the agents would not be able to sample their\nstate space sufficiently, learning would be prohibitively slow.\nAs an alternative, we assign agents to individual ground\nlocations throughout the airspace called fixes. Each agent is\nthen responsible for any aircraft going through its fix. Fixes\noffer many advantages as agents:\n1. Their number can vary depending on need. The\nsystem can have as many agents as required for a given\nsituation (e.g., agents coming live around an area\nwith developing weather conditions).\n2. Because fixes are stationary, collecting data and\nmatching behavior to reward is easier.\n3. Because aircraft flight plans consist of fixes, agent will\nhave the ability to affect traffic flow patterns.\n4. They can be deployed within the current air traffic\nrouting procedures, and can be used as tools to help air\ntraffic controllers rather than compete with or replace\nthem.\nFigure 2 shows a schematic of this agent based system.\nAgents surrounding a congestion or weather condition affect\nthe flow of traffic to reduce the burden on particular regions.\n3.2 Agent Actions\nThe second issue that needs to be addressed, is\ndetermining the action set of the agents. Again, an obvious choice\nmay be for fixes to bid on aircraft, affecting their flight\nplans. Though appealing from a free flight perspective, that\napproach makes the flight plans too unreliable and\nsignificantly complicates the scheduling problem (e.g., arrival at\nairports and the subsequent gate assignment process).\nInstead, we set the actions of an agent to determining\nthe separation (distance between aircraft) that aircraft have\n344 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nto maintain, when going through the agent\"s fix. This is\nknown as setting the Miles in Trail or MIT. When an agent\nsets the MIT value to d, aircraft going towards its fix are\ninstructed to line up and keep d miles of separation (though\naircraft will always keep a safe distance from each other\nregardless of the value of d). When there are many aircraft\ngoing through a fix, the effect of issuing higher MIT values\nis to slow down the rate of aircraft that go through the fix.\nBy increasing the value of d, an agent can limit the amount\nof air traffic downstream of its fix, reducing congestion at\nthe expense of increasing the delays upstream.\nFigure 2: Schematic of agent architecture. The\nagents corresponding to fixes surrounding a\npossible congestion become live and start setting new\nseparation times.\n3.3 Agent Learning\nThe objective of each agent is to learn the best values of\nd that will lead to the best system performance, G. In this\npaper we assume that each agent will have a reward\nfunction and will aim to maximize its reward using its own\nreinforcement learner [15] (though alternatives such as\nevolving neuro-controllers are also effective [1]). For complex\ndelayed-reward problems, relatively sophisticated\nreinforcement learning systems such as temporal difference may have\nto be used. However, due to our agent selection and agent\naction set, the air traffic congestion domain modeled in this\npaper only needs to utilize immediate rewards. As a\nconsequence, simple table-based immediate reward reinforcement\nlearning is used. Our reinforcement learner is equivalent to\nan -greedy Q-learner with a discount rate of 0 [15]. At every\nepisode an agent takes an action and then receives a reward\nevaluating that action. After taking action a and receiving\nreward R an agent updates its Q table (which contains its\nestimate of the value for taking that action [15]) as follows:\nQ (a) = (1 \u2212 l)Q(a) + l(R), (6)\nwhere l is the learning rate. At every time step the agent\nchooses the action with the highest table value with\nprobability 1 \u2212 and chooses a random action with probability\n. In the experiments described in this paper, \u03b1 is equal\nto 0.5 and is equal to 0.25. The parameters were chosen\nexperimentally, though system performance was not overly\nsensitive to these parameters.\n3.4 Agent Reward Structure\nThe final issue that needs to be addressed is selecting the\nreward structure for the learning agents. The first and most\ndirect approach is to let each agent receive the system\nperformance as its reward. However, in many domains such\na reward structure leads to slow learning. We will\ntherefore also set up a second set of reward structures based on\nagent-specific rewards. Given that agents aim to maximize\ntheir own rewards, a critical task is to create good agent\nrewards, or rewards that when pursued by the agents lead\nto good overall system performance. In this work we focus\non difference rewards which aim to provide a reward that is\nboth sensitive to that agent\"s actions and aligned with the\noverall system reward [2, 17, 18].\n3.4.1 Difference Rewards\nConsider difference rewards of the form [2, 17, 18]:\nDi \u2261 G(z) \u2212 G(z \u2212 zi + ci) , (7)\nwhere zi is the action of agent i. All the components of\nz that are affected by agent i are replaced with the fixed\nconstant ci\n2\n.\nIn many situations it is possible to use a ci that is\nequivalent to taking agent i out of the system. Intuitively this\ncauses the second term of the difference reward to\nevaluate the performance of the system without i and therefore\nD evaluates the agent\"s contribution to the system\nperformance. There are two advantages to using D: First, because\nthe second term removes a significant portion of the impact\nof other agents in the system, it provides an agent with\na cleaner signal than G. This benefit has been dubbed\nlearnability (agents have an easier time learning) in\nprevious work [2, 17]. Second, because the second term does not\ndepend on the actions of agent i, any action by agent i that\nimproves D, also improves G. This term which measures the\namount of alignment between two rewards has been dubbed\nfactoredness in previous work [2, 17].\n3.4.2 Estimates of Difference Rewards\nThough providing a good compromise between aiming\nfor system performance and removing the impact of other\nagents from an agent\"s reward, one issue that may plague D\nis computational cost. Because it relies on the computation\nof the counterfactual term G(z \u2212 zi + ci) (i.e., the system\nperformance without agent i) it may be difficult or\nimpossible to compute, particularly when the exact mathematical\nform of G is not known. Let us focus on G functions in the\nfollowing form:\nG(z) = Gf (f(z)), (8)\nwhere Gf () is non-linear with a known functional form and,\nf(z) =\nX\ni\nfi(zi) , (9)\nwhere each fi is an unknown non-linear function. We\nassume that we can sample values from f(z), enabling us to\ncompute G, but that we cannot sample from each fi(zi).\n2\nThis notation uses zero padding and vector addition rather\nthan concatenation to form full state vectors from partial\nstate vectors. The vector zi in our notation would be ziei\nin standard vector notation, where ei is a vector with a value\nof 1 in the ith component and is zero everywhere else.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 345\nIn addition, we assume that Gf is much easier to compute\nthan f(z), or that we may not be able to even compute\nf(z) directly and must sample it from a black box\ncomputation. This form of G matches our system evaluation\nin the air traffic domain. When we arrange agents so that\neach aircraft is typically only affected by a single agent, each\nagent\"s impact of the counts of the number of aircraft in a\nsector, kt,s, will be mostly independent of the other agents.\nThese values of kt,s are the f(z)s in our formulation and\nthe penalty functions form Gf . Note that given aircraft\ncounts, the penalty functions (Gf ) can be easily computed\nin microseconds, while aircraft counts (f) can only be\ncomputed by running FACET taking on the order of seconds.\nTo compute our counterfactual G(z \u2212 zi + ci) we need to\ncompute:\nGf (f(z \u2212 zi + ci)) = Gf\n0\n@\nX\nj=i\nfj(zj) + fi(ci)\n1\nA (10)\n= Gf (f(z) \u2212 fi(zi) + fi(ci)) .(11)\nUnfortunately, we cannot compute this directly as the values\nof fi(zi) are unknown. However, if agents take actions\nindependently (it does not observe how other agents act before\ntaking its own action) we can take advantage of the linear\nform of f(z) in the fis with the following equality:\nE(f\u2212i(z\u2212i)|zi) = E(f\u2212i(z\u2212i)|ci) (12)\nwhere E(f\u2212i(z\u2212i)|zi) is the expected value of all of the fs\nother than fi given the value of zi and E(f\u2212i(z\u2212i)|ci) is the\nexpected value of all of the fs other than fi given the value\nof zi is changed to ci. We can then estimate f(z \u2212 zi + ci):\nf(z) \u2212 fi(zi) + fi(ci) = f(z) \u2212 fi(zi) + fi(ci)\n+ E(f\u2212i(z\u2212i)|ci) \u2212 E(f\u2212i(z\u2212i)|zi)\n= f(z) \u2212 E(fi(zi)|zi) + E(fi(ci)|ci)\n+ E(f\u2212i(z\u2212i)|ci) \u2212 E(f\u2212i(z\u2212i)|zi)\n= f(z) \u2212 E(f(z)|zi) + E(f(z)|ci) .\nTherefore we can evaluate Di = G(z) \u2212 G(z \u2212 zi + ci) as:\nDest1\ni = Gf (f(z)) \u2212 Gf (f(z) \u2212 E(f(z)|zi) + E(f(z)|ci)) , (13)\nleaving us with the task of estimating the values of E(f(z)|zi)\nand E(f(z)|ci)). These estimates can be computed by\nkeeping a table of averages where we average the values of the\nobserved f(z) for each value of zi that we have seen. This\nestimate should improve as the number of samples increases. To\nimprove our estimates, we can set ci = E(z) and if we make\nthe mean squared approximation of f(E(z)) \u2248 E(f(z)) then\nwe can estimate G(z) \u2212 G(z \u2212 zi + ci) as:\nDest2\ni = Gf (f(z)) \u2212 Gf (f(z) \u2212 E(f(z)|zi) + E(f(z))) . (14)\nThis formulation has the advantage in that we have more\nsamples at our disposal to estimate E(f(z)) than we do to\nestimate E(f(z)|ci)).\n4. SIMULATION RESULTS\nIn this paper we test the performance of our agent based\nair traffic optimization method on a series of simulations\nusing the FACET air traffic simulator. In all experiments\nwe test the performance of five different methods. The first\nmethod is Monte Carlo estimation, where random policies\nare created, with the best policy being chosen. The other\nfour methods are agent based methods where the agents are\nmaximizing one of the following rewards:\n1. The system reward, G(z), as define in Equation 1.\n2. The difference reward, Di(z), assuming that agents\ncan calculate counterfactuals.\n3. Estimation to the difference reward, Dest1\ni (z), where\nagents estimate the counterfactual using E(f(z)|zi)\nand E(f(z)|ci).\n4. Estimation to the difference reward, Dest2\ni (z), where\nagents estimate the counterfactual using E(f(z)|zi)\nand E(f(z)).\nThese methods are first tested on an air traffic domain with\n300 aircraft, where 200 of the aircraft are going through\na single point of congestion over a four hour simulation.\nAgents are responsible for reducing congestion at this single\npoint, while trying to minimize delay. The methods are then\ntested on a more difficult problem, where a second point of\ncongestion is added with the 100 remaining aircraft going\nthrough this second point of congestion.\nIn all experiments the goal of the system is to maximize\nthe system performance given by G(z) with the parameters,\na = 50, b = 0.3, \u03c4s1 equal to 200 minutes and \u03c4s1 equal to\n175 minutes. These values of \u03c4 are obtained by examining\nthe time at which most of the aircraft leave the sectors, when\nno congestion control is being performed. Except where\nnoted, the trade-off between congestion and lateness, \u03b1 is\nset to 0.5. In all experiments to make the agent results\ncomparable to the Monte Carlo estimation, the best policies\nchosen by the agents are used in the results. All results are\nan average of thirty independent trials with the differences\nin the mean (\u03c3/\n\u221a\nn) shown as error bars, though in most\ncases the error bars are too small to see.\nFigure 3: Performance on single congestion\nproblem, with 300 Aircraft , 20 Agents and \u03b1 = .5.\n4.1 Single Congestion\nIn the first experiment we test the performance of the five\nmethods when there is a single point of congestion, with\ntwenty agents. This point of congestion is created by setting\nup a series of flight plans that cause the number of aircraft in\n346 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nthe sector of interest to be significantly more than the\nnumber allowed by the FAA. The results displayed in Figures\n3 and 4 show the performance of all five algorithms on two\ndifferent system evaluations. In both cases, the agent based\nmethods significantly outperform the Monte Carlo method.\nThis result is not surprising since the agent based methods\nintelligently explore their space, where as the Monte Carlo\nmethod explores the space randomly.\nFigure 4: Performance on single congestion\nproblem, with 300 Aircraft , 20 Agents and \u03b1 = .75.\nAmong the agent based methods, agents using difference\nrewards perform better than agents using the system\nreward. Again this is not surprising, since with twenty agents,\nan agent directly trying to maximize the system reward has\ndifficulty determining the effect of its actions on its own\nreward. Even if an agent takes an action that reduces\ncongestion and lateness, other agents at the same time may\ntake actions that increase congestion and lateness, causing\nthe agent to wrongly believe that its action was poor. In\ncontrast agents using the difference reward have more\ninfluence over the value of their own reward, therefore when an\nagent takes a good action, the value of this action is more\nlikely to be reflected in its reward.\nThis experiment also shows that estimating the difference\nreward is not only possible, but also quite effective, when\nthe true value of the difference reward cannot be computed.\nWhile agents using the estimates do not achieve as high of\nresults as agents using the true difference reward, they still\nperform significantly better than agents using the system\nreward. Note, however, that the benefit of the estimated\ndifference rewards are only present later in learning. Earlier\nin learning, the estimates are poor, and agents using the\nestimated difference rewards perform no better then agents\nusing the system reward.\n4.2 Two Congestions\nIn the second experiment we test the performance of the\nfive methods on a more difficult problem with two points of\ncongestion. On this problem the first region of congestion is\nthe same as in the previous problem, and the second region\nof congestion is added in a different part of the country.\nThe second congestion is less severe than the first one, so\nagents have to form different policies depending which point\nof congestion they are influencing.\nFigure 5: Performance on two congestion problem,\nwith 300 Aircraft, 20 Agents and \u03b1 = .5.\nFigure 6: Performance on two congestion problem,\nwith 300 Aircraft, 50 Agents and \u03b1 = .5.\nThe results displayed in Figure 5 show that the relative\nperformance of the five methods is similar to the single\ncongestion case. Again agent based methods perform better\nthan the Monte Carlo method and the agents using\ndifference rewards perform better than agents using the system\nreward. To verify that the performance improvement of our\nmethods is maintained when there are a different number of\nagents, we perform additional experiments with 50 agents.\nThe results displayed in Figure 6 show that indeed the\nrelative performances of the methods are comparable when the\nnumber of agents is increased to 50. Figure 7 shows scaling\nresults and demonstrates that the conclusions hold over a\nwide range of number of agents. Agents using Dest2\n\nperform slightly better than agents using Dest1\nin all cases but\nfor 50 agents. This slight advantage stems from Dest2\n\nproviding the agents with a cleaner signal, since its estimate\nuses more data points.\n4.3 Penalty Tradeoffs\nThe system evaluation function used in the experiments is\nG(z) = \u2212((1\u2212\u03b1)D(z)+\u03b1C(z)), which comprises of penalties\nfor both congestion and lateness. This evaluation function\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 347\nFigure 7: Impact of number of agents on system\nperformance. Two congestion problem, with 300\nAircraft and \u03b1 = .5.\nforces the agents to tradeoff these relative penalties\ndepending on the value of \u03b1. With high \u03b1 the optimization focuses\non reducing congestion, while with low \u03b1 the system focuses\non reducing lateness. To verify that the results obtained\nabove are not specific to a particular value of \u03b1, we repeat\nthe experiment with 20 agents for \u03b1 = .75. Figure 8 shows\nthat qualitatively the relative performance of the algorithms\nremain the same.\nNext, we perform a series of experiments where \u03b1 ranges\nfrom 0.0 to 1.0 . Figure 9 shows the results which lead to\nthree interesting observations:\n\u2022 First, there is a zero congestion penalty solution. This\nsolution has agents enforce large MIT values to block\nall air traffic, which appears viable when the system\nevaluation does not account for delays. All algorithms\nfind this solution, though it is of little interest in\npractice due to the large delays it would cause.\n\u2022 Second, if the two penalties were independent, an\noptimal solution would be a line from the two end points.\nTherefore, unless D is far from being optimal, the two\npenalties are not independent. Note that for \u03b1 = 0.5\nthe difference between D and this hypothetical line is\nas large as it is anywhere else, making \u03b1 = 0.5 a\nreasonable choice for testing the algorithms in a difficult\nsetting.\n\u2022 Third, Monte Carlo and G are particularly poor at\nhandling multiple objectives. For both algorithms, the\nperformance degrades significantly for mid-ranges of \u03b1.\n4.4 Computational Cost\nThe results in the previous section show the performance\nof the different algorithms after a specific number of episodes.\nThose results show that D is significantly superior to the\nother algorithms. One question that arises, though, is what\ncomputational overhead D puts on the system, and what\nresults would be obtained if the additional computational\nexpense of D is made available to the other algorithms.\nThe computation cost of the system evaluation, G\n(Equation 1) is almost entirely dependent on the computation of\nFigure 8: Performance on two congestion problem,\nwith 300 Aircraft, 20 Agents and \u03b1 = .75.\nFigure 9: Tradeoff Between Objectives on two\ncongestion problem, with 300 Aircraft and 20 Agents.\nNote that Monte Carlo and G are particularly bad\nat handling multiple objectives.\nthe airplane counts for the sectors kt,s, which need to be\ncomputed using FACET. Except when D is used, the\nvalues of k are computed once per episode. However, to\ncompute the counterfactual term in D, if FACET is treated as\na black box, each agent would have to compute their own\nvalues of k for their counterfactual resulting in n + 1\ncomputations of k per episode. While it may be possible to\nstreamline the computation of D with some knowledge of\nthe internals of FACET, given the complexity of the FACET\nsimulation, it is not unreasonable in this case to treat it as\na black box.\nTable 1 shows the performance of the algorithms after\n2100 G computations for each of the algorithms for the\nsimulations presented in Figure 5 where there were 20 agents,\n2 congestions and \u03b1 = .5. All the algorithms except the\nfully computed D reach 2100 k computations at time step\n2100. D however computes k once for the system, and then\nonce for each agent, leading to 21 computations per time\nstep. It therefore reaches 2100 computations at time step\n100. We also show the results of the full D computation\nat t=2100, which needs 44100 computations of k as D44K\n.\n348 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nTable 1: System Performance for 20 Agents, 2\ncongestions and \u03b1 = .5, after 2100 G evaluations (except\nfor D44K\nwhich has 44100 G evaluations at t=2100).\nReward G \u03c3/\n\u221a\nn time\nDest2\n-232.5 7.55 2100\nDest1\n-234.4 6.83 2100\nD -277.0 7.8 100\nD44K\n-219.9 4.48 2100\nG -412.6 13.6 2100\nMC -639.0 16.4 2100\nAlthough D44K\nprovides the best result by a slight margin,\nit is achieved at a considerable computational cost. Indeed,\nthe performance of the two D estimates is remarkable in this\ncase as they were obtained with about twenty times fewer\ncomputations of k. Furthermore, the two D estimates,\nsignificantly outperform the full D computation for a given\nnumber of computations of k and validate the assumptions\nmade in Section 3.4.2. This shows that for this domain, in\npractice it is more fruitful to perform more learning steps\nand approximate D, than few learning steps with full D\ncomputation when we treat FACET as a black box.\n5. DISCUSSION\nThe efficient, safe and reliable management of air traffic\nflow is a complex problem, requiring solutions that integrate\ncontrol policies with time horizons ranging from minutes\nup to a year. The main contribution of this paper is to\npresent a distributed adaptive air traffic flow management\nalgorithm that can be readily implemented and to test that\nalgorithm using FACET, a simulation tool widely used by\nthe FAA, NASA and the industry. Our method is based on\nagents representing fixes and having each agent determine\nthe separation between aircraft approaching its fix. It offers\nthe significant benefit of not requiring radical changes to\nthe current air flow management structure and is therefore\nreadily deployable. The agents use reinforcement learning to\nlearn control policies and we explore different agent reward\nfunctions and different ways of estimating those functions.\nWe are currently extending this work in three directions.\nFirst, we are exploring new methods of estimating agent\nrewards, to further speed up the simulations. Second we are\ninvestigating deployment strategies and looking for\nmodifications that would have larger impact. One such\nmodification is to extend the definition of agents from fixes to\nsectors, giving agents more opportunity to control the\ntraffic flow, and allow them to be more efficient in eliminating\ncongestion. Finally, in cooperation with domain experts,\nwe are investigating different system evaluation functions,\nabove and beyond the delay and congestion dependent G\npresented in this paper.\nAcknowledgments: The authors thank Banavar\nSridhar for his invaluable help in describing both current air\ntraffic flow management and NGATS, and Shon Grabbe for\nhis detailed tutorials on FACET.\n6. REFERENCES\n[1] A. Agogino and K. Tumer. Efficient evaluation\nfunctions for multi-rover systems. In The Genetic and\nEvolutionary Computation Conference, pages 1-12,\nSeatle, WA, June 2004.\n[2] A. Agogino and K. Tumer. Multi agent reward\nanalysis for learning in noisy domains. In Proceedings\nof the Fourth International Joint Conference on\nAutonomous Agents and Multi-Agent Systems,\nUtrecht, Netherlands, July 2005.\n[3] A. K. Agogino and K. Tumer. Handling communiction\nrestrictions and team formation in congestion games.\nJournal of Autonous Agents and Multi Agent Systems,\n13(1):97-115, 2006.\n[4] K. D. Bilimoria, B. Sridhar, G. B. Chatterji, K. S.\nShethand, and S. R. Grabbe. FACET: Future ATM\nconcepts evaluation tool. Air Traffic Control\nQuarterly, 9(1), 2001.\n[5] Karl D. Bilimoria. A geometric optimization approach\nto aircraft conflict resolution. In AIAA Guidance,\nNavigation, and Control Conf, Denver, CO, 2000.\n[6] Martin S. Eby and Wallace E. Kelly III. Free flight\nseparation assurance using distributed algorithms. In\nProc of Aerospace Conf, 1999, Aspen, CO, 1999.\n[7] FAA OPSNET data Jan-Dec 2005. US Department of\nTransportation website.\n[8] S. Grabbe and B. Sridhar. Central east pacific flight\nrouting. In AIAA Guidance, Navigation, and Control\nConference and Exhibit, Keystone, CO, 2006.\n[9] Jared C. Hill, F. Ryan Johnson, James K. Archibald,\nRichard L. Frost, and Wynn C. Stirling. A cooperative\nmulti-agent approach to free flight. In AAMAS \"05:\nProceedings of the fourth international joint conference\non Autonomous agents and multiagent systems, pages\n1083-1090, New York, NY, USA, 2005. ACM Press.\n[10] P. K. Menon, G. D. Sweriduk, and B. Sridhar.\nOptimal strategies for free flight air traffic conflict\nresolution. Journal of Guidance, Control, and\nDynamics, 22(2):202-211, 1999.\n[11] 2006 NASA Software of the Year Award Nomination.\nFACET: Future ATM concepts evaluation tool. Case\nno. ARC-14653-1, 2006.\n[12] M. Pechoucek, D. Sislak, D. Pavlicek, and M. Uller.\nAutonomous agents for air-traffic deconfliction. In\nProc of the Fifth Int Jt Conf on Autonomous Agents\nand Multi-Agent Systems, Hakodate, Japan, May 2006.\n[13] B. Sridhar and S. Grabbe. Benefits of direct-to in\nnational airspace system. In AIAA Guidance,\nNavigation, and Control Conf, Denver, CO, 2000.\n[14] B. Sridhar, T. Soni, K. Sheth, and G. B. Chatterji.\nAggregate flow model for air-traffic management.\nJournal of Guidance, Control, and Dynamics,\n29(4):992-997, 2006.\n[15] R. S. Sutton and A. G. Barto. Reinforcement\nLearning: An Introduction. MIT Press, Cambridge,\nMA, 1998.\n[16] C. Tomlin, G. Pappas, and S. Sastry. Conflict\nresolution for air traffic management. IEEE Tran on\nAutomatic Control, 43(4):509-521, 1998.\n[17] K. Tumer and D. Wolpert, editors. Collectives and the\nDesign of Complex Systems. Springer, New York,\n2004.\n[18] D. H. Wolpert and K. Tumer. Optimal payoff\nfunctions for members of collectives. Advances in\nComplex Systems, 4(2/3):265-279, 2001.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 349", "keywords": "reinforcement learning;air traffic control;optimization;new method of estimating agent reward;reinforcement learn;traffic flow;congestion;deployment strategy;multiagent system;future atm concept evaluation tool"}
{"name": "train_I-62", "title": "A Q-decomposition and Bounded RTDP Approach to Resource Allocation", "abstract": "This paper contributes to solve effectively stochastic resource allocation problems known to be NP-Complete. To address this complex resource management problem, a Qdecomposition approach is proposed when the resources which are already shared among the agents, but the actions made by an agent may influence the reward obtained by at least another agent. The Q-decomposition allows to coordinate these reward separated agents and thus permits to reduce the set of states and actions to consider. On the other hand, when the resources are available to all agents, no Qdecomposition is possible and we use heuristic search. In particular, the bounded Real-time Dynamic Programming (bounded rtdp) is used. Bounded rtdp concentrates the planning on significant states only and prunes the action space. The pruning is accomplished by proposing tight upper and lower bounds on the value function. Categories and Subject Descriptors", "fulltext": "1. INTRODUCTION\nThis paper aims to contribute to solve complex stochastic\nresource allocation problems. In general, resource\nallocation problems are known to be NP-Complete [12]. In such\nproblems, a scheduling process suggests the action (i.e.\nresources to allocate) to undertake to accomplish certain tasks,\naccording to the perfectly observable state of the\nenvironment. When executing an action to realize a set of tasks,\nthe stochastic nature of the problem induces probabilities\non the next visited state. In general, the number of states\nis the combination of all possible specific states of each task\nand available resources. In this case, the number of\npossible actions in a state is the combination of each individual\npossible resource assignment to the tasks. The very high\nnumber of states and actions in this type of problem makes\nit very complex.\nThere can be many types of resource allocation problems.\nFirstly, if the resources are already shared among the agents,\nand the actions made by an agent does not influence the\nstate of another agent, the globally optimal policy can be\ncomputed by planning separately for each agent. A second\ntype of resource allocation problem is where the resources\nare already shared among the agents, but the actions made\nby an agent may influence the reward obtained by at least\nanother agent. To solve this problem efficiently, we adapt\nQdecomposition proposed by Russell and Zimdars [9]. In our\nQ-decomposition approach, a planning agent manages each\ntask and all agents have to share the limited resources. The\nplanning process starts with the initial state s0. In s0, each\nagent computes their respective Q-value. Then, the\nplanning agents are coordinated through an arbitrator to find\nthe highest global Q-value by adding the respective possible\nQ-values of each agents. When implemented with heuristic\nsearch, since the number of states and actions to consider\nwhen computing the optimal policy is exponentially reduced\ncompared to other known approaches, Q-decomposition\nallows to formulate the first optimal decomposed heuristic\nsearch algorithm in a stochastic environments.\nOn the other hand, when the resources are available to\nall agents, no Q-decomposition is possible. A common\nway of addressing this large stochastic problem is by\nusing Markov Decision Processes (mdps), and in particular\nreal-time search where many algorithms have been\ndeveloped recently. For instance Real-Time Dynamic\nProgramming (rtdp) [1], lrtdp [4], hdp [3], and lao [5] are all\nstate-of-the-art heuristic search approaches in a stochastic\nenvironment. Because of its anytime quality, an interesting\napproach is rtdp introduced by Barto et al. [1] which\nupdates states in trajectories from an initial state s0 to a goal\nstate sg. rtdp is used in this paper to solve efficiently a\nconstrained resource allocation problem.\nrtdp is much more effective if the action space can be\npruned of sub-optimal actions. To do this, McMahan et\n1212\n978-81-904262-7-5 (RPS) c 2007 IFAAMAS\nal. [6], Smith and Simmons [11], and Singh and Cohn [10]\nproposed solving a stochastic problem using a rtdp type\nheuristic search with upper and lower bounds on the value\nof states. McMahan et al. [6] and Smith and Simmons [11]\nsuggested, in particular, an efficient trajectory of state\nupdates to further speed up the convergence, when given upper\nand lower bounds. This efficient trajectory of state updates\ncan be combined to the approach proposed here since this\npaper focusses on the definition of tight bounds, and efficient\nstate update for a constrained resource allocation problem.\nOn the other hand, the approach by Singh and Cohn is\nsuitable to our case, and extended in this paper using, in\nparticular, the concept of marginal revenue [7] to elaborate\ntight bounds. This paper proposes new algorithms to define\nupper and lower bounds in the context of a rtdp heuristic\nsearch approach. Our marginal revenue bounds are\ncompared theoretically and empirically to the bounds proposed\nby Singh and Cohn. Also, even if the algorithm used to\nobtain the optimal policy is rtdp, our bounds can be used\nwith any other algorithm to solve an mdp. The only\ncondition on the use of our bounds is to be in the context of\nstochastic constrained resource allocation. The problem is\nnow modelled.\n2. PROBLEM FORMULATION\nA simple resource allocation problem is one where there\nare the following two tasks to realize: ta1 = {wash the\ndishes}, and ta2 = {clean the floor}. These two tasks are\neither in the realized state, or not realized state. To realize the\ntasks, two type of resources are assumed: res1 = {brush},\nand res2 = {detergent}. A computer has to compute the\noptimal allocation of these resources to cleaner robots to realize\ntheir tasks. In this problem, a state represents a\nconjunction of the particular state of each task, and the available\nresources. The resources may be constrained by the amount\nthat may be used simultaneously (local constraint), and in\ntotal (global constraint). Furthermore, the higher is the\nnumber of resources allocated to realize a task, the higher is\nthe expectation of realizing the task. For this reason, when\nthe specific states of the tasks change, or when the number\nof available resources changes, the value of this state may\nchange.\nWhen executing an action a in state s, the specific states\nof the tasks change stochastically, and the remaining\nresource are determined with the resource available in s,\nsubtracted from the resources used by action a, if the resource\nis consumable. Indeed, our model may consider\nconsumable and non-consumable resource types. A consumable\nresource type is one where the amount of available resource\nis decreased when it is used. On the other hand, a\nnonconsumable resource type is one where the amount of\navailable resource is unchanged when it is used. For example, a\nbrush is a non-consumable resource, while the detergent is\na consumable resource.\n2.1 Resource Allocation as a MDPs\nIn our problem, the transition function and the reward\nfunction are both known. A Markov Decision Process (mdp)\nframework is used to model our stochastic resource\nallocation problem. mdps have been widely adopted by researchers\ntoday to model a stochastic process. This is due to the fact\nthat mdps provide a well-studied and simple, yet very\nexpressive model of the world. An mdp in the context of a\nresource allocation problem with limited resources is defined\nas a tuple Res, T a, S, A, P, W, R, , where:\n\u2022 Res = res1, ..., res|Res| is a finite set of resource\ntypes available for a planning process. Each resource\ntype may have a local resource constraint Lres on\nthe number that may be used in a single step, and\na global resource constraint Gres on the number that\nmay be used in total. The global constraint only\napplies for consumable resource types (Resc) and the\nlocal constraints always apply to consumable and\nnonconsumable resource types.\n\u2022 T a is a finite set of tasks with ta \u2208 T a to be\naccomplished.\n\u2022 S is a finite set of states with s \u2208 S. A state s is\na tuple T a, res1, ..., res|Resc| , which is the\ncharacteristic of each unaccomplished task ta \u2208 T a in the\nenvironment, and the available consumable resources.\nsta is the specific state of task ta. Also, S contains a\nnon empty set sg \u2286 S of goal states. A goal state is a\nsink state where an agent stays forever.\n\u2022 A is a finite set of actions (or assignments). The\nactions a \u2208 A(s) applicable in a state are the\ncombination of all resource assignments that may be executed,\naccording to the state s. In particular, a is simply an\nallocation of resources to the current tasks, and ata is\nthe resource allocation to task ta. The possible actions\nare limited by Lres and Gres.\n\u2022 Transition probabilities Pa(s |s) for s \u2208 S and a \u2208\nA(s).\n\u2022 W = [wta] is the relative weight (criticality) of each\ntask.\n\u2022 State rewards R = [rs] :\nta\u2208T a\nrsta \u2190 sta \u00d7 wta. The\nrelative reward of the state of a task rsta is the product\nof a real number sta by the weight factor wta. For\nour problem, a reward of 1 \u00d7 wta is given when the\nstate of a task (sta) is in an achieved state, and 0 in\nall other cases.\n\u2022 A discount (preference) factor \u03b3, which is a real\nnumber between 0 and 1.\nA solution of an mdp is a policy \u03c0 mapping states s into\nactions a \u2208 A(s). In particular, \u03c0ta(s) is the action (i.e.\nresources to allocate) that should be executed on task ta,\nconsidering the global state s. In this case, an optimal\npolicy is one that maximizes the expected total reward for\naccomplishing all tasks. The optimal value of a state, V (s), is\ngiven by:\nV (s) = R(s) + max\na\u2208A(s)\n\u03b3\ns \u2208S\nPa(s |s)V (s ) (1)\nwhere the remaining consumable resources in state s are\nResc \\ res(a), where res(a) are the consumable resources\nused by action a. Indeed, since an action a is a resource\nassignment, Resc \\ res(a) is the new set of available resources\nafter the execution of action a. Furthermore, one may\ncompute the Q-Values Q(a, s) of each state action pair using the\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1213\nfollowing equation:\nQ(a, s) = R(s) + \u03b3\ns \u2208S\nPa(s |s) max\na \u2208A(s )\nQ(a , s ) (2)\nwhere the optimal value of a state is V (s) = max\na\u2208A(s)\nQ(a, s).\nThe policy is subjected to the local resource constraints\nres(\u03c0(s)) \u2264 Lres\u2200 s \u2208 S , and \u2200 res \u2208 Res. The global\nconstraint is defined according to all system trajectories\ntra \u2208 T RA. A system trajectory tra is a possible sequence\nof state-action pairs, until a goal state is reached under the\noptimal policy \u03c0. For example, state s is entered, which may\ntransit to s or to s , according to action a. The two\npossible system trajectories are (s, a), (s ) and (s, a), (s ) .\nThe global resource constraint is res(tra) \u2264 Gres\u2200 tra \u2208\nT RA ,and \u2200 res \u2208 Resc where res(tra) is a function which\nreturns the resources used by trajectory tra. Since the\navailable consumable resources are represented in the state space,\nthis condition is verified by itself. In other words, the model\nis Markovian as the history has not to be considered in the\nstate space. Furthermore, the time is not considered in the\nmodel description, but it may also include a time horizon\nby using a finite horizon mdp. Since resource allocation in\na stochastic environment is NP-Complete, heuristics should\nbe employed. Q-decomposition which decomposes a\nplanning problem to many agents to reduce the computational\ncomplexity associated to the state and/or action spaces is\nnow introduced.\n2.2 Q-decomposition for Resource Allocation\nThere can be many types of resource allocation problems.\nFirstly, if the resources are already shared among the agents,\nand the actions made by an agent does not influence the\nstate of another agent, the globally optimal policy can be\ncomputed by planning separately for each agent.\nA second type of resource allocation problem is where\nthe resources are already shared among the agents, but the\nactions made by an agent may influence the reward obtained\nby at least another agent. For instance, a group of agents\nwhich manages the oil consummated by a country falls in\nthis group. These agents desire to maximize their specific\nreward by consuming the right amount of oil. However, all\nthe agents are penalized when an agent consumes oil because\nof the pollution it generates. Another example of this type\ncomes from our problem of interest, explained in Section\n3, which is a naval platform which must counter incoming\nmissiles (i.e. tasks) by using its resources (i.e. weapons,\nmovements). In some scenarios, it may happens that the\nmissiles can be classified in two types: Those requiring a\nset of resources Res1 and those requiring a set of resources\nRes2. This can happen depending on the type of missiles,\ntheir range, and so on. In this case, two agents can plan for\nboth set of tasks to determine the policy. However, there\nare interaction between the resource of Res1 and Res2, so\nthat certain combination of resource cannot be assigned. IN\nparticular, if an agent i allocate resources Resi to the first\nset of tasks T ai, and agent i allocate resources Resi to\nsecond set of tasks T ai , the resulting policy may include\nactions which cannot be executed together.\nTo result these conflicts, we use Q-decomposition\nproposed by Russell and Zimdars [9] in the context of\nreinforcement learning. The primary assumption underlying\nQdecomposition is that the overall reward function R can be\nadditively decomposed into separate rewards Ri for each\ndistinct agent i \u2208 Ag, where |Ag| is the number of agents. That\nis, R = i\u2208Ag Ri. It requires each agent to compute a value,\nfrom its perspective, for every action. To coordinate with\neach other, each agent i reports its action values Qi(ai, si)\nfor each state si \u2208 Si to an arbitrator at each learning\niteration. The arbitrator then chooses an action maximizing\nthe sum of the agent Q-values for each global state s \u2208 S.\nThe next time state s is updated, an agent i considers the\nvalue as its respective contribution, or Q-value, to the global\nmaximal Q-value. That is, Qi(ai, si) is the value of a state\nsuch that it maximizes maxa\u2208A(s) i\u2208Ag Qi(ai, si). The fact\nthat the agents use a determined Q-value as the value of a\nstate is an extension of the Sarsa on-policy algorithm [8] to\nQ-decomposition. Russell and Zimdars called this approach\nlocal Sarsa. In this way, an ideal compromise can be found\nfor the agents to reach a global optimum. Indeed, rather\nthan allowing each agent to choose the successor action, each\nagent i uses the action ai executed by the arbitrator in the\nsuccessor state si:\nQi(ai, si) = Ri(si) + \u03b3\nsi\u2208Si\nPai (si|si)Qi(ai, si)\n(3)\nwhere the remaining consumable resources in state si are\nResci \\ resi(ai) for a resource allocation problem. Russell\nand Zimdars [9] demonstrated that local Sarsa converges\nto the optimum. Also, in some cases, this form of agent\ndecomposition allows the local Q-functions to be expressed\nby a much reduced state and action space.\nFor our resource allocation problem described briefly in\nthis section, Q-decomposition can be applied to generate an\noptimal solution. Indeed, an optimal Bellman backup can\nbe applied in a state as in Algorithm 1. In Line 5 of the\nQdec-backup function, each agent managing a task\ncomputes its respective Q-value. Here, Qi (ai, s ) determines the\noptimal Q-value of agent i in state s . An agent i uses as\nthe value of a possible state transition s the Q-value for\nthis agent which determines the maximal global Q-value for\nstate s as in the original Q-decomposition approach. In\nbrief, for each visited states s \u2208 S, each agent computes its\nrespective Q-values with respect to the global state s. So\nthe state space is the joint state space of all agents. Some\nof the gain in complexity to use Q-decomposition resides in\nthe\nsi\u2208Si\nPai (si|s) part of the equation. An agent considers\nas a possible state transition only the possible states of the\nset of tasks it manages. Since the number of states is\nexponential with the number of tasks, using Q-decomposition\nshould reduce the planning time significantly. Furthermore,\nthe action space of the agents takes into account only their\navailable resources which is much less complex than a\nstandard action space, which is the combination of all possible\nresource allocation in a state for all agents.\nThen, the arbitrator functionalities are in Lines 8 to 20.\nThe global Q-value is the sum of the Q-values produced by\neach agent managing each task as shown in Line 11,\nconsidering the global action a. In this case, when an action of an\nagent i cannot be executed simultaneously with an action\nof another agent i , the global action is simply discarded\nfrom the action space A(s). Line 14 simply allocate the\ncurrent value with respect to the highest global Q-value, as in\na standard Bellman backup. Then, the optimal policy and\nQ-value of each agent is updated in Lines 16 and 17 to the\nsub-actions ai and specific Q-values Qi(ai, s) of each agent\n1214 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nfor action a.\nAlgorithm 1 The Q-decomposition Bellman Backup.\n1: Function Qdec-backup(s)\n2: V (s) \u2190 0\n3: for all i \u2208 Ag do\n4: for all ai \u2208 Ai(s) do\n5: Qi(ai, s) \u2190 Ri(s) + \u03b3\nsi\n\u2208Si\nPai (si|s)Qi (ai, s )\n{where Qi (ai, s ) = hi(s ) when s is not yet visited,\nand s has Resci \\ resi(ai) remaining consumable\nresources for each agent i}\n6: end for\n7: end for\n8: for all a \u2208 A(s) do\n9: Q(a, s) \u2190 0\n10: for all i \u2208 Ag do\n11: Q(a, s) \u2190 Q(a, s) + Qi(ai, s)\n12: end for\n13: if Q(a, s) > V (s) then\n14: V (s) \u2190 Q(a, s)\n15: for all i \u2208 Ag do\n16: \u03c0i(s) \u2190 ai\n17: Qi (ai, s) \u2190 Qi(ai, s)\n18: end for\n19: end if\n20: end for\nA standard Bellman backup has a complexity of O(|A| \u00d7\n|SAg|), where |SAg| is the number of joint states for all agents\nexcluding the resources, and |A| is the number of joint\nactions. On the other hand, the Q-decomposition Bellman\nbackup has a complexity of O((|Ag| \u00d7 |Ai| \u00d7 |Si)|) + (|A| \u00d7\n|Ag|)), where |Si| is the number of states for an agent i,\nexcluding the resources and |Ai| is the number of actions\nfor an agent i. Since |SAg| is combinatorial with the\nnumber of tasks, so |Si| |S|. Also, |A| is combinatorial with\nthe number of resource types. If the resources are already\nshared among the agents, the number of resource type for\neach agent will usually be lower than the set of all\navailable resource types for all agents. In these circumstances,\n|Ai| |A|. In a standard Bellman backup, |A| is multiplied\nby |SAg|, which is much more complex than multiplying |A|\nby |Ag| with the Q-decomposition Bellman backup. Thus,\nthe Q-decomposition Bellman backup is much less complex\nthan a standard Bellman backup. Furthermore, the\ncommunication cost between the agents and the arbitrator is\nnull since this approach does not consider a geographically\nseparated problem.\nHowever, when the resources are available to all agents,\nno Q-decomposition is possible. In this case, Bounded\nRealTime Dynamic Programming (bounded-rtdp) permits to\nfocuss the search on relevant states, and to prune the action\nspace A by using lower and higher bound on the value of\nstates. bounded-rtdp is now introduced.\n2.3 Bounded-RTDP\nBonet and Geffner [4] proposed lrtdp as an improvement\nto rtdp [1]. lrtdp is a simple dynamic programming\nalgorithm that involves a sequence of trial runs, each starting in\nthe initial state s0 and ending in a goal or a solved state.\nEach lrtdp trial is the result of simulating the policy \u03c0 while\nupdating the values V (s) using a Bellman backup (Equation\n1) over the states s that are visited. h(s) is a heuristic which\ndefine an initial value for state s. This heuristic has to be\nadmissible - The value given by the heuristic has to\noverestimate (or underestimate) the optimal value V (s) when\nthe objective function is maximized (or minimized). For\nexample, an admissible heuristic for a stochastic shortest\npath problem is the solution of a deterministic shortest path\nproblem. Indeed, since the problem is stochastic, the\noptimal value is lower than for the deterministic version. It has\nbeen proven that lrtdp, given an admissible initial\nheuristic on the value of states cannot be trapped in loops, and\neventually yields optimal values [4]. The convergence is\naccomplished by means of a labeling procedure called\ncheckSolved(s, ). This procedure tries to label as solved each\ntraversed state in the current trajectory. When the initial\nstate is labelled as solved, the algorithm has converged.\nIn this section, a bounded version of rtdp\n(boundedrtdp) is presented in Algorithm 2 to prune the action space\nof sub-optimal actions. This pruning enables to speed up the\nconvergence of lrtdp. bounded-rtdp is similar to rtdp\nexcept there are two distinct initial heuristics for unvisited\nstates s \u2208 S; hL(s) and hU (s). Also, the checkSolved(s,\n) procedure can be omitted because the bounds can provide\nthe labeling of a state as solved. On the one hand, hL(s)\ndefines a lower bound on the value of s such that the optimal\nvalue of s is higher than hL(s). For its part, hU (s) defines an\nupper bound on the value of s such that the optimal value\nof s is lower than hU (s).\nThe values of the bounds are computed in Lines 3 and\n4 of the bounded-backup function. Computing these two\nQ-values is made simultaneously as the state transitions are\nthe same for both Q-values. Only the values of the state\ntransitions change. Thus, having to compute two Q-values\ninstead of one does not augment the complexity of the\napproach. In fact, Smith and Simmons [11] state that the\nadditional time to compute a Bellman backup for two bounds,\ninstead of one, is no more than 10%, which is also what we\nobtained. In particular, L(s) is the lower bound of state s,\nwhile U(s) is the upper bound of state s. Similarly, QL(a, s)\nis the Q-value of the lower bound of action a in state s, while\nQU (a, s) is the Q-value of the upper bound of action a in\nstate s. Using these two bounds allow significantly\nreducing the action space A. Indeed, in Lines 5 and 6 of the\nbounded-backup function, if QU (a, s) \u2264 L(s) then action\na may be pruned from the action space of s. In Line 13\nof this function, a state can be labeled as solved if the\ndifference between the lower and upper bounds is lower than\n. When the execution goes back to the bounded-rtdp\nfunction, the next state in Line 10 has a fixed number of\nconsumable resources available Resc, determined in Line 9.\nIn brief, pickNextState(res) selects a none-solved state\ns reachable under the current policy which has the highest\nBellman error (|U(s) \u2212 L(s)|). Finally, in Lines 12 to 15, a\nbackup is made in a backward fashion on all visited state\nof a trajectory, when this trajectory has been made. This\nstrategy has been proven as efficient [11] [6].\nAs discussed by Singh and Cohn [10], this type of\nalgorithm has a number of desirable anytime characteristics: if\nan action has to be picked in state s before the algorithm\nhas converged (while multiple competitive actions remains),\nthe action with the highest lower bound is picked. Since\nthe upper bound for state s is known, it may be estimated\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1215\nAlgorithm 2 The bounded-rtdp algorithm. Adapted\nfrom [4] and [10].\n1: Function bounded-rtdp(S)\n2: returns a value function V\n3: repeat\n4: s \u2190 s0\n5: visited \u2190 null\n6: repeat\n7: visited.push(s)\n8: bounded-backup(s)\n9: Resc \u2190 Resc \\ {\u03c0(s)}\n10: s \u2190 s.pickNextState(Resc)\n11: until s is a goal\n12: while visited = null do\n13: s \u2190 visited.pop()\n14: bounded-backup(s)\n15: end while\n16: until s0 is solved or |A(s)| = 1 \u2200 s \u2208 S reachable from\ns0\n17: return V\nAlgorithm 3 The bounded Bellman backup.\n1: Function bounded-backup(s)\n2: for all a \u2208 A(s) do\n3: QU (a, s) \u2190 R(s) + \u03b3\ns \u2208S\nPa(s |s)U(s )\n4: QL(a, s) \u2190 R(s) + \u03b3\ns \u2208S\nPa(s |s)L(s )\n{where L(s ) \u2190 hL(s ) and U(s ) \u2190 hU (s ) when s\nis not yet visited and s has Resc \\ res(a) remaining\nconsumable resources}\n5: if QU (a, s) \u2264 L(s) then\n6: A(s) \u2190 A(s) \\ res(a)\n7: end if\n8: end for\n9: L(s) \u2190 max\na\u2208A(s)\nQL(a, s)\n10: U(s) \u2190 max\na\u2208A(s)\nQU (a, s)\n11: \u03c0(s) \u2190 arg max\na\u2208A(s)\nQL(a, s)\n12: if |U(s) \u2212 L(s)| < then\n13: s \u2190 solved\n14: end if\nhow far the lower bound is from the optimal. If the\ndifference between the lower and upper bound is too high, one\ncan choose to use another greedy algorithm of one\"s choice,\nwhich outputs a fast and near optimal solution.\nFurthermore, if a new task dynamically arrives in the environment,\nit can be accommodated by redefining the lower and\nupper bounds which exist at the time of its arrival. Singh\nand Cohn [10] proved that an algorithm that uses\nadmissible lower and upper bounds to prune the action space is\nassured of converging to an optimal solution.\nThe next sections describe two separate methods to define\nhL(s) and hU (s). First of all, the method of Singh and Cohn\n[10] is briefly described. Then, our own method proposes\ntighter bounds, thus allowing a more effective pruning of\nthe action space.\n2.4 Singh and Cohn\"s Bounds\nSingh and Cohn [10] defined lower and upper bounds to\nprune the action space. Their approach is pretty\nstraightforward. First of all, a value function is computed for all\ntasks to realize, using a standard rtdp approach. Then,\nusing these task-value functions, a lower bound hL, and\nupper bound hU can be defined. In particular, hL(s) =\nmax\nta\u2208T a\nVta(sta), and hU (s) =\nta\u2208T a\nVta(sta). For readability,\nthe upper bound by Singh and Cohn is named SinghU, and\nthe lower bound is named SinghL. The admissibility of these\nbounds has been proven by Singh and Cohn, such that, the\nupper bound always overestimates the optimal value of each\nstate, while the lower bound always underestimates the\noptimal value of each state. To determine the optimal policy\n\u03c0, Singh and Cohn implemented an algorithm very similar\nto bounded-rtdp, which uses the bounds to initialize L(s)\nand U(s). The only difference between bounded-rtdp, and\nthe rtdp version of Singh and Cohn is in the stopping\ncriteria. Singh and Cohn proposed that the algorithm terminates\nwhen only one competitive action remains for each state, or\nwhen the range of all competitive actions for any state are\nbounded by an indifference parameter . bounded-rtdp\nlabels states for which |U(s) \u2212 L(s)| < as solved and the\nconvergence is reached when s0 is solved or when only one\ncompetitive action remains for each state. This stopping\ncriteria is more effective since it is similar to the one used\nby Smith and Simmons [11] and McMahan et al. brtdp [6].\nIn this paper, the bounds defined by Singh and Cohn and\nimplemented using bounded-rtdp define the Singh-rtdp\napproach. The next sections propose to tighten the bounds\nof Singh-rtdp to permit a more effective pruning of the\naction space.\n2.5 Reducing the Upper Bound\nSinghU includes actions which may not be possible to\nexecute because of resource constraints, which overestimates\nthe upper bound. To consider only possible actions, our\nupper bound, named maxU is introduced:\nhU (s) = max\na\u2208A(s)\nta\u2208T a\nQta(ata, sta) (4)\nwhere Qta(ata, sta) is the Q-value of task ta for state sta,\nand action ata computed using a standard lrtdp approach.\nTheorem 2.1. The upper bound defined by Equation 4 is\nadmissible.\nProof: The local resource constraints are satisfied because\nthe upper bound is computed using all global possible\nactions a. However, hU (s) still overestimates V (s) because\nthe global resource constraint is not enforced. Indeed, each\ntask may use all consumable resources for its own purpose.\nDoing this produces a higher value for each task, than the\none obtained when planning for all tasks globally with the\nshared limited resources.\nComputing the maxU bound in a state has a\ncomplexity of O(|A| \u00d7 |T a|), and O(|T a|) for SinghU. A standard\nBellman backup has a complexity of O(|A| \u00d7 |S|). Since\n|A|\u00d7|T a| |A|\u00d7|S|, the computation time to determine the\nupper bound of a state, which is done one time for each\nvisited state, is much less than the computation time required\nto compute a standard Bellman backup for a state, which is\nusually done many times for each visited state. Thus, the\ncomputation time of the upper bound is negligible.\n1216 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\n2.6 Increasing the Lower Bound\nThe idea to increase SinghL is to allocate the resources\na priori among the tasks. When each task has its own set\nof resources, each task may be solved independently. The\nlower bound of state s is hL(s) =\nta\u2208T a\nLowta(sta), where\nLowta(sta) is a value function for each task ta \u2208 T a, such\nthat the resources have been allocated a priori. The\nallocation a priori of the resources is made using marginal revenue,\nwhich is a highly used concept in microeconomics [7], and\nhas recently been used for coordination of a Decentralized\nmdp [2]. In brief, marginal revenue is the extra revenue that\nan additional unit of product will bring to a firm. Thus,\nfor a stochastic resource allocation problem, the marginal\nrevenue of a resource is the additional expected value it\ninvolves. The marginal revenue of a resource res for a task ta\nin a state sta is defined as following:\nmrta(sta) = max\nata\u2208A(sta)\nQta(ata, sta)\u2212\nmax\nata\u2208A(sta)\nQta(ata|res /\u2208 ata, sta) (5)\nThe concept of marginal revenue of a resource is used in\nAlgorithm 4 to allocate the resources a priori among the\ntasks which enables to define the lower bound value of a\nstate. In Line 4 of the algorithm, a value function is\ncomputed for all tasks in the environment using a standard\nlrtdp [4] approach. These value functions, which are also\nused for the upper bound, are computed considering that\neach task may use all available resources. The Line 5\ninitializes the valueta variable. This variable is the estimated\nvalue of each task ta \u2208 T a. In the beginning of the\nalgorithm, no resources are allocated to a specific task, thus the\nvalueta variable is initialized to 0 for all ta \u2208 T a. Then, in\nLine 9, a resource type res (consumable or non-consumable)\nis selected to be allocated. Here, a domain expert may\nseparate all available resources in many types or parts to be\nallocated. The resources are allocated in the order of its\nspecialization. In other words, the more a resource is\nefficient on a small group of tasks, the more it is allocated early.\nAllocating the resources in this order improves the quality\nof the resulting lower bound. The Line 12 computes the\nmarginal revenue of a consumable resource res for each task\nta \u2208 T a. For a non-consumable resource, since the resource\nis not considered in the state space, all other reachable states\nfrom sta consider that the resource res is still usable. The\napproach here is to sum the difference between the real value\nof a state to the maximal Q-value of this state if resource res\ncannot be used for all states in a trajectory given by the\npolicy of task ta. This heuristic proved to obtain good results,\nbut other ones may be tried, for example Monte-Carlo\nsimulation. In Line 21, the marginal revenue is updated in\nfunction of the resources already allocated to each task. R(sgta )\nis the reward to realize task ta. Thus, Vta(sta)\u2212valueta\nR(sgta )\nis\nthe residual expected value that remains to be achieved,\nknowing current allocation to task ta, and normalized by\nthe reward of realizing the tasks. The marginal revenue is\nmultiplied by this term to indicate that, the more a task\nhas a high residual value, the more its marginal revenue is\ngoing to be high. Then, a task ta is selected in Line 23 with\nthe highest marginal revenue, adjusted with residual value.\nIn Line 24, the resource type res is allocated to the group\nof resources Resta of task ta. Afterwards, Line 29\nrecomAlgorithm 4 The marginal revenue lower bound algorithm.\n1: Function revenue-bound(S)\n2: returns a lower bound LowT a\n3: for all ta \u2208 T a do\n4: Vta \u2190lrtdp(Sta)\n5: valueta \u2190 0\n6: end for\n7: s \u2190 s0\n8: repeat\n9: res \u2190 Select a resource type res \u2208 Res\n10: for all ta \u2208 T a do\n11: if res is consumable then\n12: mrta(sta) \u2190 Vta(sta) \u2212 Vta(sta(Res \\ res))\n13: else\n14: mrta(sta) \u2190 0\n15: repeat\n16: mrta(sta) \u2190 mrta(sta) +\nVta(sta)max\n(ata\u2208A(sta)|res/\u2208ata)\nQta(ata, sta)\n17: sta \u2190 sta.pickNextState(Resc)\n18: until sta is a goal\n19: s \u2190 s0\n20: end if\n21: mrrvta(sta) \u2190 mrta(sta) \u00d7 Vta(sta)\u2212valueta\nR(sgta )\n22: end for\n23: ta \u2190 Task ta \u2208 T a which maximize mrrvta(sta)\n24: Resta \u2190 Resta {res}\n25: temp \u2190 \u2205\n26: if res is consumable then\n27: temp \u2190 res\n28: end if\n29: valueta \u2190 valueta + ((Vta(sta) \u2212 valueta)\u00d7\nmax\nata\u2208A(sta,res)\nQta(ata,sta(temp))\nVta(sta)\n)\n30: until all resource types res \u2208 Res are assigned\n31: for all ta \u2208 T a do\n32: Lowta \u2190lrtdp(Sta, Resta)\n33: end for\n34: return LowT a\nputes valueta. The first part of the equation to compute\nvalueta represents the expected residual value for task ta.\nThis term is multiplied by\nmax\nata\u2208A(sta)\nQta(ata,sta(res))\nVta(sta)\n, which\nis the ratio of the efficiency of resource type res. In other\nwords, valueta is assigned to valueta + (the residual value\n\u00d7 the value ratio of resource type res). For a consumable\nresource, the Q-value consider only resource res in the state\nspace, while for a non-consumable resource, no resources are\navailable.\nAll resource types are allocated in this manner until Res is\nempty. All consumable and non-consumable resource types\nare allocated to each task. When all resources are allocated,\nthe lower bound components Lowta of each task are\ncomputed in Line 32. When the global solution is computed,\nthe lower bound is as follow:\nhL(s) = max(SinghL, max\na\u2208A(s)\nta\u2208T a\nLowta(sta)) (6)\nWe use the maximum of the SinghL bound and the sum\nof the lower bound components Lowta, thus\nmarginalrevenue \u2265 SinghL. In particular, the SinghL bound may\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1217\nbe higher when a little number of tasks remain. As the\ncomponents Lowta are computed considering s0; for example, if\nin a subsequent state only one task remains, the bound of\nSinghL will be higher than any of the Lowta components.\nThe main difference of complexity between SinghL and\nrevenue-bound is in Line 32 where a value for each task\nhas to be computed with the shared resource. However,\nsince the resource are shared, the state space and action\nspace is greatly reduced for each task, reducing greatly the\ncalculus compared to the value functions computed in Line\n4 which is done for both SinghL and revenue-bound.\nTheorem 2.2. The lower bound of Equation 6 is\nadmissible.\nProof: Lowta(sta) is computed with the resource being\nshared. Summing the Lowta(sta) value functions for each\nta \u2208 T a does not violates the local and global resource\nconstraints. Indeed, as the resources are shared, the tasks\ncannot overuse them. Thus, hL(s) is a realizable policy, and an\nadmissible lower bound.\n3. DISCUSSION AND EXPERIMENTS\nThe domain of the experiments is a naval platform which\nmust counter incoming missiles (i.e. tasks) by using its\nresources (i.e. weapons, movements). For the experiments,\n100 randomly resource allocation problems were generated\nfor each approach, and possible number of tasks. In our\nproblem, |Sta| = 4, thus each task can be in four distinct\nstates. There are two types of states; firstly, states where\nactions modify the transition probabilities; and then, there\nare goal states. The state transitions are all stochastic\nbecause when a missile is in a given state, it may always transit\nin many possible states. In particular, each resource type\nhas a probability to counter a missile between 45% and 65%\ndepending on the state of the task. When a missile is not\ncountered, it transits to another state, which may be\npreferred or not to the current state, where the most preferred\nstate for a task is when it is countered. The effectiveness\nof each resource is modified randomly by \u00b115% at the start\nof a scenario. There are also local and global resource\nconstraints on the amount that may be used. For the local\nconstraints, at most 1 resource of each type can be\nallocated to execute tasks in a specific state. This constraint is\nalso present on a real naval platform because of sensor and\nlauncher constraints and engagement policies. Furthermore,\nfor consumable resources, the total amount of available\nconsumable resource is between 1 and 2 for each type. The\nglobal constraint is generated randomly at the start of a\nscenario for each consumable resource type. The number of\nresource type has been fixed to 5, where there are 3\nconsumable resource types and 2 non-consumable resources types.\nFor this problem a standard lrtdp approach has been\nimplemented. A simple heuristic has been used where the\nvalue of an unvisited state is assigned as the value of a goal\nstate such that all tasks are achieved. This way, the value\nof each unvisited state is assured to overestimate its real\nvalue since the value of achieving a task ta is the highest\nthe planner may get for ta. Since this heuristic is pretty\nstraightforward, the advantages of using better heuristics are\nmore evident. Nevertheless, even if the lrtdp approach uses\na simple heuristic, still a huge part of the state space is not\nvisited when computing the optimal policy. The approaches\ndescribed in this paper are compared in Figures 1 and 2.\nLets summarize these approaches here:\n\u2022 Qdec-lrtdp: The backups are computed using the\nQdec-backup function (Algorithm 1), but in a lrtdp\ncontext. In particular the updates made in the\ncheckSolved function are also made using the the\nQdecbackup function.\n\u2022 lrtdp-up: The upper bound of maxU is used for\nlrtdp.\n\u2022 Singh-rtdp: The SinghL and SinghU bounds are\nused for bounded-rtdp.\n\u2022 mr-rtdp: The revenue-bound and maxU bounds\nare used for bounded-rtdp.\nTo implement Qdec-lrtdp, we divided the set of tasks\nin two equal parts. The set of task T ai, managed by agent\ni, can be accomplished with the set of resources Resi, while\nthe second set of task T ai , managed by agent Agi , can be\naccomplished with the set of resources Resi . Resi had one\nconsumable resource type and one non-consumable resource\ntype, while Resi had two consumable resource types and\none non-consumable resource type. When the number of\ntasks is odd, one more task was assigned to T ai . There are\nconstraint between the group of resource Resi and Resi\nsuch that some assignments are not possible. These\nconstraints are managed by the arbitrator as described in\nSection 2.2. Q-decomposition permits to diminish the planning\ntime significantly in our problem settings, and seems a very\nefficient approach when a group of agents have to allocate\nresources which are only available to themselves, but the\nactions made by an agent may influence the reward obtained\nby at least another agent.\nTo compute the lower bound of revenue-bound, all\navailable resources have to be separated in many types or\nparts to be allocated. For our problem, we allocated each\nresource of each type in the order of of its specialization like\nwe said when describing the revenue-bound function.\nIn terms of experiments, notice that the lrtdp lrtdp-up\nand approaches for resource allocation, which doe not prune\nthe action space, are much more complex. For instance, it\ntook an average of 1512 seconds to plan for the lrtdp-up\napproach with six tasks (see Figure 1). The Singh-rtdp\napproach diminished the planning time by using a lower\nand upper bound to prune the action space. mr-rtdp\nfurther reduce the planning time by providing very tight\ninitial bounds. In particular, Singh-rtdp needed 231 seconds\nin average to solve problem with six tasks and mr-rtdp\nrequired 76 seconds. Indeed, the time reduction is quite\nsignificant compared to lrtdp-up, which demonstrates the\nefficiency of using bounds to prune the action space.\nFurthermore, we implemented mr-rtdp with the SinghU\nbound, and this was slightly less efficient than with the\nmaxU bound. We also implemented mr-rtdp with the\nSinghL bound, and this was slightly more efficient than\nSingh-rtdp. From these results, we conclude that the\ndifference of efficiency between mr-rtdp and Singh-rtdp is\nmore attributable to the marginal-revenue lower bound\nthat to the maxU upper bound. Indeed, when the number\nof task to execute is high, the lower bounds by Singh-rtdp\ntakes the values of a single task. On the other hand, the\nlower bound of mr-rtdp takes into account the value of all\n1218 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\n0.01\n0.1\n1\n10\n100\n1000\n10000\n100000\n1 2 3 4 5 6 7 8 9 10 11 12 13\nTimeinseconds\nNumber of tasks\nLRTDP\nQDEC-LRTDP\nFigure 1: Efficiency of Q-decomposition LRTDP\nand LRTDP.\n0.01\n0.1\n1\n10\n100\n1000\n10000\n1 2 3 4 5 6 7 8\nTimeinseconds\nNumber of tasks\nLRTDP\nLRTDP-up\nSingh-RTDP\nMR-RTDP\nFigure 2: Efficiency of MR-RTDP compared to\nSINGH-RTDP.\ntask by using a heuristic to distribute the resources.\nIndeed, an optimal allocation is one where the resources are\ndistributed in the best way to all tasks, and our lower bound\nheuristically does that.\n4. CONCLUSION\nThe experiments have shown that Q-decomposition seems\na very efficient approach when a group of agents have to\nallocate resources which are only available to themselves,\nbut the actions made by an agent may influence the reward\nobtained by at least another agent.\nOn the other hand, when the available resource are\nshared, no Q-decomposition is possible and we proposed\ntight bounds for heuristic search. In this case, the\nplanning time of bounded-rtdp, which prunes the action space,\nis significantly lower than for lrtdp. Furthermore, The\nmarginal revenue bound proposed in this paper compares\nfavorably to the Singh and Cohn [10] approach.\nboundedrtdp with our proposed bounds may apply to a wide range\nof stochastic environments. The only condition for the use\nour bounds is that each task possesses consumable and/or\nnon-consumable limited resources.\nAn interesting research avenue would be to experiment\nour bounds with other heuristic search algorithms. For\ninstance, frtdp [11], and brtdp [6] are both efficient\nheuristic search algorithms. In particular, both these approaches\nproposed an efficient state trajectory updates, when given\nupper and lower bounds. Our tight bounds would enable,\nfor both frtdp and brtdp, to reduce the number of backup\nto perform before convergence. Finally, the bounded-rtdp\nfunction prunes the action space when QU (a, s) \u2264 L(s), as\nSingh and Cohn [10] suggested. frtdp and brtdp could\nalso prune the action space in these circumstances to\nfurther reduce their planning time.\n5. REFERENCES\n[1] A. Barto, S. Bradtke, and S. Singh. Learning to act\nusing real-time dynamic programming. Artificial\nIntelligence, 72(1):81-138, 1995.\n[2] A. Beynier and A. I. Mouaddib. An iterative algorithm\nfor solving constrained decentralized markov decision\nprocesses. In Proceeding of the Twenty-First National\nConference on Artificial Intelligence (AAAI-06), 2006.\n[3] B. Bonet and H. Geffner. Faster heuristic search\nalgorithms for planning with uncertainty and full\nfeedback. In Proceedings of the Eighteenth\nInternational Joint Conference on Artificial\nIntelligence (IJCAI-03), August 2003.\n[4] B. Bonet and H. Geffner. Labeled lrtdp approach:\nImproving the convergence of real-time dynamic\nprogramming. In Proceeding of the Thirteenth\nInternational Conference on Automated Planning &\nScheduling (ICAPS-03), pages 12-21, Trento, Italy,\n2003.\n[5] E. A. Hansen and S. Zilberstein. lao : A heuristic\nsearch algorithm that finds solutions with loops.\nArtificial Intelligence, 129(1-2):35-62, 2001.\n[6] H. B. McMahan, M. Likhachev, and G. J. Gordon.\nBounded real-time dynamic programming: rtdp with\nmonotone upper bounds and performance guarantees.\nIn ICML \"05: Proceedings of the Twenty-Second\nInternational Conference on Machine learning, pages\n569-576, New York, NY, USA, 2005. ACM Press.\n[7] R. S. Pindyck and D. L. Rubinfeld. Microeconomics.\nPrentice Hall, 2000.\n[8] G. A. Rummery and M. Niranjan. On-line Q-learning\nusing connectionist systems. Technical report\nCUED/FINFENG/TR 166, Cambridge University\nEngineering Department, 1994.\n[9] S. J. Russell and A. Zimdars. Q-decomposition for\nreinforcement learning agents. In ICML, pages\n656-663, 2003.\n[10] S. Singh and D. Cohn. How to dynamically merge\nmarkov decision processes. In Advances in Neural\nInformation Processing Systems, volume 10, pages\n1057-1063, Cambridge, MA, USA, 1998. MIT Press.\n[11] T. Smith and R. Simmons. Focused real-time dynamic\nprogramming for mdps: Squeezing more out of a\nheuristic. In Proceedings of the Twenty-First National\nConference on Artificial Intelligence (AAAI), Boston,\nUSA, 2006.\n[12] W. Zhang. Modeling and solving a resource allocation\nproblem with soft constraint techniques. Technical\nreport: wucs-2002-13, Washington University,\nSaint-Louis, Missouri, 2002.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1219", "keywords": "planning agent;real-time dynamic programming;heuristic search;reward separated agent;stochastic environment;marginal revenue;markov decision process;complex stochastic resource allocation problem;marginal revenue bound;resource management;resource allocation;q-decomposition"}
{"name": "train_I-63", "title": "Combinatorial Resource Scheduling for Multiagent MDPs", "abstract": "Optimal resource scheduling in multiagent systems is a computationally challenging task, particularly when the values of resources are not additive. We consider the combinatorial problem of scheduling the usage of multiple resources among agents that operate in stochastic environments, modeled as Markov decision processes (MDPs). In recent years, efficient resource-allocation algorithms have been developed for agents with resource values induced by MDPs. However, this prior work has focused on static resource-allocation problems where resources are distributed once and then utilized in infinite-horizon MDPs. We extend those existing models to the problem of combinatorial resource scheduling, where agents persist only for finite periods between their (predefined) arrival and departure times, requiring resources only for those time periods. We provide a computationally efficient procedure for computing globally optimal resource assignments to agents over time. We illustrate and empirically analyze the method in the context of a stochastic jobscheduling domain.", "fulltext": "1. INTRODUCTION\nThe tasks of optimal resource allocation and scheduling\nare ubiquitous in multiagent systems, but solving such\noptimization problems can be computationally difficult, due to\na number of factors. In particular, when the value of a set of\nresources to an agent is not additive (as is often the case with\nresources that are substitutes or complements), the utility\nfunction might have to be defined on an exponentially large\nspace of resource bundles, which very quickly becomes\ncomputationally intractable. Further, even when each agent has\na utility function that is nonzero only on a small subset of\nthe possible resource bundles, obtaining optimal allocation\nis still computationally prohibitive, as the problem becomes\nNP-complete [14].\nSuch computational issues have recently spawned several\nthreads of work in using compact models of agents\"\npreferences. One idea is to use any structure present in utility\nfunctions to represent them compactly, via, for example,\nlogical formulas [15, 10, 4, 3]. An alternative is to directly model\nthe mechanisms that define the agents\" utility functions and\nperform resource allocation directly with these models [9]. A\nway of accomplishing this is to model the processes by which\nan agent might utilize the resources and define the utility\nfunction as the payoff of these processes. In particular, if\nan agent uses resources to act in a stochastic environment,\nits utility function can be naturally modeled with a Markov\ndecision process, whose action set is parameterized by the\navailable resources. This representation can then be used to\nconstruct very efficient resource-allocation algorithms that\nlead to an exponential speedup over a straightforward\noptimization problem with flat representations of combinatorial\npreferences [6, 7, 8].\nHowever, this existing work on resource allocation with\npreferences induced by resource-parameterized MDPs makes\nan assumption that the resources are only allocated once and\nare then utilized by the agents independently within their\ninfinite-horizon MDPs. This assumption that no reallocation\nof resources is possible can be limiting in domains where\nagents arrive and depart dynamically.\nIn this paper, we extend the work on resource allocation\nunder MDP-induced preferences to discrete-time scheduling\nproblems, where agents are present in the system for finite\ntime intervals and can only use resources within these\nintervals. In particular, agents arrive and depart at arbitrary\n(predefined) times and within these intervals use resources\nto execute tasks in finite-horizon MDPs. We address the\nproblem of globally optimal resource scheduling, where the\nobjective is to find an allocation of resources to the agents\nacross time that maximizes the sum of the expected rewards\nthat they obtain.\nIn this context, our main contribution is a\nmixed-integerprogramming formulation of the scheduling problem that\nchooses globally optimal resource assignments, starting times,\nand execution horizons for all agents (within their\narrival1220\n978-81-904262-7-5 (RPS) c 2007 IFAAMAS\ndeparture intervals). We analyze and empirically compare\ntwo flavors of the scheduling problem: one, where agents\nhave static resource assignments within their finite-horizon\nMDPs, and another, where resources can be dynamically\nreallocated between agents at every time step.\nIn the rest of the paper, we first lay down the necessary\ngroundwork in Section 2 and then introduce our model and\nformal problem statement in Section 3. In Section 4.2, we\ndescribe our main result, the optimization program for\nglobally optimal resource scheduling. Following the discussion of\nour experimental results on a job-scheduling problem in\nSection 5, we conclude in Section 6 with a discussion of possible\nextensions and generalizations of our method.\n2. BACKGROUND\nSimilarly to the model used in previous work on\nresourceallocation with MDP-induced preferences [6, 7], we define\nthe value of a set of resources to an agent as the value of the\nbest MDP policy that is realizable, given those resources.\nHowever, since the focus of our work is on scheduling\nproblems, and a large part of the optimization problem is to\ndecide how resources are allocated in time among agents\nwith finite arrival and departure times, we model the agents\"\nplanning problems as finite-horizon MDPs, in contrast to\nprevious work that used infinite-horizon discounted MDPs.\nIn the rest of this section, we first introduce some\nnecessary background on finite-horizon MDPs and present a\nlinear-programming formulation that serves as the basis for\nour solution algorithm developed in Section 4. We also\noutline the standard methods for combinatorial resource\nscheduling with flat resource values, which serve as a comparison\nbenchmark for the new model developed here.\n2.1 Markov Decision Processes\nA stationary, finite-domain, discrete-time MDP (see, for\nexample, [13] for a thorough and detailed development) can\nbe described as S, A, p, r , where: S is a finite set of\nsystem states; A is a finite set of actions that are available to\nthe agent; p is a stationary stochastic transition function,\nwhere p(\u03c3|s, a) is the probability of transitioning to state \u03c3\nupon executing action a in state s; r is a stationary reward\nfunction, where r(s, a) specifies the reward obtained upon\nexecuting action a in state s.\nGiven such an MDP, a decision problem under a finite\nhorizon T is to choose an optimal action at every time step\nto maximize the expected value of the total reward accrued\nduring the agent\"s (finite) lifetime. The agent\"s optimal\npolicy is then a function of current state s and the time until\nthe horizon. An optimal policy for such a problem is to act\ngreedily with respect to the optimal value function, defined\nrecursively by the following system of finite-time Bellman\nequations [2]:\nv(s, t) = max\na\nr(s, a) +\nX\n\u03c3\np(\u03c3|s, a)v(\u03c3, t + 1),\n\u2200s \u2208 S, t \u2208 [1, T \u2212 1];\nv(s, T) = 0, \u2200s \u2208 S;\nwhere v(s, t) is the optimal value of being in state s at time\nt \u2208 [1, T].\nThis optimal value function can be easily computed using\ndynamic programming, leading to the following optimal\npolicy \u03c0, where \u03c0(s, a, t) is the probability of executing action\na in state s at time t:\n\u03c0(s, a, t) =\n(\n1, a = argmaxa r(s, a) +\nP\n\u03c3 p(\u03c3|s, a)v(\u03c3, t + 1),\n0, otherwise.\nThe above is the most common way of computing the\noptimal value function (and therefore an optimal policy) for\na finite-horizon MDP. However, we can also formulate the\nproblem as the following linear program (similarly to the\ndual LP for infinite-horizon discounted MDPs [13, 6, 7]):\nmax\nX\ns\nX\na\nr(s, a)\nX\nt\nx(s, a, t)\nsubject to:\nX\na\nx(\u03c3, a, t + 1) =\nX\ns,a\np(\u03c3|s, a)x(s, a, t) \u2200\u03c3, t \u2208 [1, T \u2212 1];\nX\na\nx(s, a, 1) = \u03b1(s), \u2200s \u2208 S;\n(1)\nwhere \u03b1(s) is the initial distribution over the state space, and\nx is the (non-stationary) occupation measure (x(s, a, t) \u2208\n[0, 1] is the total expected number of times action a is\nexecuted in state s at time t). An optimal (non-stationary)\npolicy is obtained from the occupation measure as follows:\n\u03c0(s, a, t) = x(s, a, t)/\nX\na\nx(s, a, t) \u2200s \u2208 S, t \u2208 [1, T]. (2)\nNote that the standard unconstrained finite-horizon MDP,\nas described above, always has a uniformly-optimal\nsolution (optimal for any initial distribution \u03b1(s)). Therefore,\nan optimal policy can be obtained by using an arbitrary\nconstant \u03b1(s) > 0 (in particular, \u03b1(s) = 1 will result in\nx(s, a, t) = \u03c0(s, a, t)).\nHowever, for MDPs with resource constraints (as defined\nbelow in Section 3), uniformly-optimal policies do not in\ngeneral exist. In such cases, \u03b1 becomes a part of the\nproblem input, and a resulting policy is only optimal for that\nparticular \u03b1. This result is well known for infinite-horizon\nMDPs with various types of constraints [1, 6], and it also\nholds for our finite-horizon model, which can be easily\nestablished via a line of reasoning completely analogous to the\narguments in [6].\n2.2 Combinatorial Resource Scheduling\nA straightforward approach to resource scheduling for a\nset of agents M, whose values for the resources are induced\nby stochastic planning problems (in our case, finite-horizon\nMDPs) would be to have each agent enumerate all possible\nresource assignments over time and, for each one, compute\nits value by solving the corresponding MDP. Then, each\nagent would provide valuations for each possible resource\nbundle over time to a centralized coordinator, who would\ncompute the optimal resource assignments across time based\non these valuations.\nWhen resources can be allocated at different times to\ndifferent agents, each agent must submit valuations for\nevery combination of possible time horizons. Let each agent\nm \u2208 M execute its MDP within the arrival-departure time\ninterval \u03c4 \u2208 [\u03c4a\nm, \u03c4d\nm]. Hence, agent m will execute an MDP\nwith time horizon no greater than Tm = \u03c4d\nm\u2212\u03c4a\nm+1. Let b\u03c4 be\nthe global time horizon for the problem, before which all of\nthe agents\" MDPs must finish. We assume \u03c4d\nm < b\u03c4, \u2200m \u2208 M.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1221\nFor the scheduling problem where agents have static\nresource requirements within their finite-horizon MDPs, the\nagents provide a valuation for each resource bundle for each\npossible time horizon (from [1, Tm]) that they may use. Let\n\u03a9 be the set of resources to be allocated among the agents.\nAn agent will get at most one resource bundle for one of the\ntime horizons. Let the variable \u03c8 \u2208 \u03a8m enumerate all\npossible pairs of resource bundles and time horizons for agent\nm, so there are 2|\u03a9|\n\u00d7 Tm values for \u03c8 (the space of bundles\nis exponential in the number of resource types |\u03a9|).\nThe agent m must provide a value v\u03c8\nm for each \u03c8, and\nthe coordinator will allocate at most one \u03c8 (resource, time\nhorizon) pair to each agent. This allocation is expressed as\nan indicator variable z\u03c8\nm \u2208 {0, 1} that shows whether \u03c8 is\nassigned to agent m. For time \u03c4 and resource \u03c9, the function\nnm(\u03c8, \u03c4, \u03c9) \u2208 {0, 1} indicates whether the bundle in \u03c8 uses\nresource \u03c9 at time \u03c4 (we make the assumption that agents\nhave binary resource requirements). This allocation problem\nis NP-complete, even when considering only a single time\nstep, and its difficulty increases significantly with multiple\ntime steps because of the increasing number of values of \u03c8.\nThe problem of finding an optimal allocation that satisfies\nthe global constraint that the amount of each resource \u03c9\nallocated to all agents does not exceed the available amount\nb\u03d5(\u03c9) can be expressed as the following integer program:\nmax\nX\nm\u2208M\nX\n\u03c8\u2208\u03a8m\nz\u03c8\nmv\u03c8\nm\nsubject to:\nX\n\u03c8\u2208\u03a8m\nz\u03c8\nm \u2264 1, \u2200m \u2208 M;\nX\nm\u2208M\nX\n\u03c8\u2208\u03a8m\nz\u03c8\nmnm(\u03c8, \u03c4, \u03c9) \u2264 b\u03d5(\u03c9), \u2200\u03c4 \u2208 [1, b\u03c4], \u2200\u03c9 \u2208 \u03a9;\n(3)\nThe first constraint in equation 3 says that no agent can\nreceive more than one bundle, and the second constraint\nensures that the total assignment of resource \u03c9 does not, at\nany time, exceed the resource bound.\nFor the scheduling problem where the agents are able to\ndynamically reallocate resources, each agent must specify\na value for every combination of bundles and time steps\nwithin its time horizon. Let the variable \u03c8 \u2208 \u03a8m in this case\nenumerate all possible resource bundles for which at most\none bundle may be assigned to agent m at each time step.\nTherefore, in this case there are\nP\nt\u2208[1,Tm](2|\u03a9|\n)t\n\u223c 2|\u03a9|Tm\npossibilities of resource bundles assigned to different time\nslots, for the Tm different time horizons.\nThe same set of equations (3) can be used to solve this\ndynamic scheduling problem, but the integer program is\ndifferent because of the difference in how \u03c8 is defined. In this\ncase, the number of \u03c8 values is exponential in each agent\"s\nplanning horizon Tm, resulting in a much larger program.\nThis straightforward approach to solving both of these\nscheduling problems requires an enumeration and solution\nof either 2|\u03a9|\nTm (static allocation) or\nP\nt\u2208[1,Tm] 2|\u03a9|t\n\n(dynamic reallocation) MDPs for each agent, which very quickly\nbecomes intractable with the growth of the number of\nresources |\u03a9| or the time horizon Tm.\n3. MODEL AND PROBLEM STATEMENT\nWe now formally introduce our model of the\nresourcescheduling problem. The problem input consists of the\nfollowing components:\n\u2022 M, \u03a9, b\u03d5, \u03c4a\nm, \u03c4d\nm, b\u03c4 are as defined above in Section 2.2.\n\u2022 {\u0398m} = {S, A, pm, rm, \u03b1m} are the MDPs of all agents\nm \u2208 M. Without loss of generality, we assume that state\nand action spaces of all agents are the same, but each has\nits own transition function pm, reward function rm, and\ninitial conditions \u03b1m.\n\u2022 \u03d5m : A\u00d7\u03a9 \u2192 {0, 1} is the mapping of actions to resources\nfor agent m. \u03d5m(a, \u03c9) indicates whether action a of agent\nm needs resource \u03c9. An agent m that receives a set of\nresources that does not include resource \u03c9 cannot execute\nin its MDP policy any action a for which \u03d5m(a, \u03c9) = 0. We\nassume all resource requirements are binary; as discussed\nbelow in Section 6, this assumption is not limiting.\nGiven the above input, the optimization problem we\nconsider is to find the globally optimal-maximizing the sum\nof expected rewards-mapping of resources to agents for all\ntime steps: \u0394 : \u03c4 \u00d7 M \u00d7 \u03a9 \u2192 {0, 1}. A solution is feasible\nif the corresponding assignment of resources to the agents\ndoes not violate the global resource constraint:\nX\nm\n\u0394m(\u03c4, \u03c9) \u2264 b\u03d5(\u03c9), \u2200\u03c9 \u2208 \u03a9, \u03c4 \u2208 [1, b\u03c4]. (4)\nWe consider two flavors of the resource-scheduling\nproblem. The first formulation restricts resource assignments to\nthe space where the allocation of resources to each agent is\nstatic during the agent\"s lifetime. The second formulation\nallows reassignment of resources between agents at every time\nstep within their lifetimes.\nFigure 1 depicts a resource-scheduling problem with three\nagents M = {m1, m2, m3}, three resources \u03a9 = {\u03c91, \u03c92, \u03c93},\nand a global problem horizon of b\u03c4 = 11. The agents\" arrival\nand departure times are shown as gray boxes and are {1, 6},\n{3, 7}, and {2, 11}, respectively. A solution to this problem\nis shown via horizontal bars within each agents\" box, where\nthe bars correspond to the allocation of the three resource\ntypes. Figure 1a shows a solution to a static scheduling\nproblem. According to the shown solution, agent m1 begins the\nexecution of its MDP at time \u03c4 = 1 and has a lock on all\nthree resources until it finishes execution at time \u03c4 = 3. Note\nthat agent m1 relinquishes its hold on the resources before\nits announced departure time of \u03c4d\nm1\n= 6, ostensibly because\nother agents can utilize the resources more effectively. Thus,\nat time \u03c4 = 4, resources \u03c91 and \u03c93 are allocated to agent\nm2, who then uses them to execute its MDP (using only\nactions supported by resources \u03c91 and \u03c93) until time \u03c4 = 7.\nAgent m3 holds resource \u03c93 during the interval \u03c4 \u2208 [4, 10].\nFigure 1b shows a possible solution to the dynamic version\nof the same problem. There, resources can be reallocated\nbetween agents at every time step. For example, agent m1\ngives up its use of resource \u03c92 at time \u03c4 = 2, although it\ncontinues the execution of its MDP until time \u03c4 = 6. Notice\nthat an agent is not allowed to stop and restart its MDP, so\nagent m1 is only able to continue executing in the interval\n\u03c4 \u2208 [3, 4] if it has actions that do not require any resources\n(\u03d5m(a, \u03c9) = 0).\nClearly, the model and problem statement described above\nmake a number of assumptions about the problem and the\ndesired solution properties. We discuss some of those\nassumptions and their implications in Section 6.\n1222 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\n(a) (b)\nFigure 1: Illustration of a solution to a resource-scheduling problem with three agents and three resources: a) static\nresource assignments (resource assignments are constant within agents\" lifetimes; b) dynamic assignment (resource\nassignments are allowed to change at every time step).\n4. RESOURCE SCHEDULING\nOur resource-scheduling algorithm proceeds in two stages.\nFirst, we perform a preprocessing step that augments the\nagent MDPs; this process is described in Section 4.1.\nSecond, using these augmented MDPs we construct a global\noptimization problem, which is described in Section 4.2.\n4.1 Augmenting Agents\" MDPs\nIn the model described in the previous section, we assume\nthat if an agent does not possess the necessary resources to\nperform actions in its MDP, its execution is halted and the\nagent leaves the system. In other words, the MDPs cannot\nbe paused and resumed. For example, in the problem\nshown in Figure 1a, agent m1 releases all resources after time\n\u03c4 = 3, at which point the execution of its MDP is halted.\nSimilarly, agents m2 and m3 only execute their MDPs in the\nintervals \u03c4 \u2208 [4, 6] and \u03c4 \u2208 [4, 10], respectively. Therefore, an\nimportant part of the global decision-making problem is to\ndecide the window of time during which each of the agents\nis active (i.e., executing its MDP).\nTo accomplish this, we augment each agent\"s MDP with\ntwo new states (start and finish states sb\n, sf\n,\nrespectively) and a new start/stop action a\u2217\n, as illustrated in\nFigure 2. The idea is that an agent stays in the start state\nsb\nuntil it is ready to execute its MDP, at which point it\nperforms the start/stop action a\u2217\nand transitions into the\nstate space of the original MDP with the transition\nprobability that corresponds to the original initial distribution\n\u03b1(s). For example, in Figure 1a, for agent m2 this would\nhappen at time \u03c4 = 4. Once the agent gets to the end of its\nactivity window (time \u03c4 = 6 for agent m2 in Figure 1a), it\nperforms the start/stop action, which takes it into the sink\nfinish state sf\nat time \u03c4 = 7.\nMore precisely, given an MDP S, A, pm, rm, \u03b1m , we\ndefine an augmented MDP S , A , pm, rm, \u03b1m as follows:\nS = S \u222a sb\n\u222a sf\n; A = A \u222a a\u2217\n;\np (s|sb\n, a\u2217\n) = \u03b1(s), \u2200s \u2208 S; p (sb\n|sb\n, a) = 1.0, \u2200a \u2208 A;\np (sf\n|s, a\u2217\n) = 1.0, \u2200s \u2208 S;\np (\u03c3|s, a) = p(\u03c3|s, a), \u2200s, \u03c3 \u2208 S, a \u2208 A;\nr (sb\n, a) = r (sf\n, a) = 0, \u2200a \u2208 A ;\nr (s, a) = r(s, a), \u2200s \u2208 S, a \u2208 A;\n\u03b1 (sb\n) = 1; \u03b1 (s) = 0, \u2200s \u2208 S;\nwhere all non-specified transition probabilities are assumed\nto be zero. Further, in order to account for the new starting\nstate, we begin the MDP one time-step earlier, setting \u03c4a\nm \u2190\n\u03c4a\nm \u2212 1. This will not affect the resource allocation due to\nthe resource constraints only being enforced for the original\nMDP states, as will be discussed in the next section. For\nexample, the augmented MDPs shown in Figure 2b (which\nstarts in state sb\nat time \u03c4 = 2) would be constructed from\nan MDP with original arrival time \u03c4 = 3. Figure 2b also\nshows a sample trajectory through the state space: the agent\nstarts in state sb\n, transitions into the state space S of the\noriginal MDP, and finally exists into the sink state sf\n.\nNote that if we wanted to model a problem where agents\ncould pause their MDPs at arbitrary time steps (which might\nbe useful for domains where dynamic reallocation is\npossible), we could easily accomplish this by including an extra\naction that transitions from each state to itself with zero\nreward.\n4.2 MILP for Resource Scheduling\nGiven a set of augmented MDPs, as defined above, the\ngoal of this section is to formulate a global optimization\nprogram that solves the resource-scheduling problem. In this\nsection and below, all MDPs are assumed to be the\naugmented MDPs as defined in Section 4.1.\nOur approach is similar to the idea used in [6]: we\nbegin with the linear-program formulation of agents\" MDPs\n(1) and augment it with constraints that ensure that the\ncorresponding resource allocation across agents and time is\nvalid. The resulting optimization problem then\nsimultaneously solves the agents\" MDPs and resource-scheduling\nproblems. In the rest of this section, we incrementally develop a\nmixed integer program (MILP) that achieves this.\nIn the absence of resource constraints, the agents\"\nfinitehorizon MDPs are completely independent, and the globally\noptimal solution can be trivially obtained via the following\nLP, which is simply an aggregation of single-agent\nfinitehorizon LPs:\nmax\nX\nm\nX\ns\nX\na\nrm(s, a)\nX\nt\nxm(s, a, t)\nsubject to:\nX\na\nxm(\u03c3, a, t + 1) =\nX\ns,a\npm(\u03c3|s, a)xm(s, a, t),\n\u2200m \u2208 M, \u03c3 \u2208 S, t \u2208 [1, Tm \u2212 1];\nX\na\nxm(s, a, 1) = \u03b1m(s), \u2200m \u2208 M, s \u2208 S;\n(12)\nwhere xm(s, a, t) is the occupation measure of agent m, and\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1223\n(a) (b)\nFigure 2: Illustration of augmenting an MDP to allow for variable starting and stopping times: a) (left) the original\ntwo-state MDP with a single action; (right) the augmented MDP with new states sb and sf and the new action a\u2217\n(note that the origianl transitions are not changed in the augmentation process); b) the augmented MDP displayed as\na trajectory through time (grey lines indicate all transitions, while black lines indicate a given trajectory.\nObjective Function\n(sum of expected rewards over all agents)\nmax\nX\nm\nX\ns\nX\na\nrm(s, a)\nX\nt\nxm(s, a, t) (5)\nMeaning Implication Linear Constraints\nTie x to \u03b8. Agent is\nonly active when\noccupation measure is nonzero\nin original MDP states.\n\u03b8m(\u03c4) = 0 =\u21d2 xm(s, a, \u03c4 \u2212\u03c4a\nm+1) = 0\n\u2200s /\u2208 {sb\n, sf\n}, a \u2208 A\nX\ns/\u2208{sb,sf }\nX\na\nxm(s, a, t) \u2264 \u03b8m(\u03c4a\nm + t \u2212 1)\n\u2200m \u2208 M, \u2200t \u2208 [1, Tm]\n(6)\nAgent can only be active\nin \u03c4 \u2208 (\u03c4a\nm, \u03c4d\nm) \u03b8m(\u03c4) = 0 \u2200m \u2208 M, \u03c4 /\u2208 (\u03c4a\nm, \u03c4d\nm) (7)\nCannot use resources\nwhen not active\n\u03b8m(\u03c4) = 0 =\u21d2 \u0394m(\u03c4, \u03c9) = 0\n\u2200\u03c4 \u2208 [0, b\u03c4], \u03c9 \u2208 \u03a9 \u0394m(\u03c4, \u03c9) \u2264 \u03b8m(\u03c4) \u2200m \u2208 M, \u03c4 \u2208 [0, b\u03c4], \u03c9 \u2208 \u03a9 (8)\nTie x to \u0394 (nonzero x\nforces corresponding \u0394\nto be nonzero.)\n\u0394m(\u03c4, \u03c9) = 0, \u03d5m(a, \u03c9) = 1 =\u21d2\nxm(s, a, \u03c4 \u2212 \u03c4a\nm + 1) = 0\n\u2200s /\u2208 {sb\n, sf\n}\n1/|A|\nX\na\n\u03d5m(a, \u03c9)\nX\ns/\u2208{sb,sf }\nxm(s, a, t) \u2264 \u0394m(t + \u03c4a\nm \u2212 1, \u03c9)\n\u2200m \u2208 M, \u03c9 \u2208 \u03a9, t \u2208 [1, Tm]\n(9)\nResource bounds\nX\nm\n\u0394m(\u03c4, \u03c9) \u2264 b\u03d5(\u03c9) \u2200\u03c9 \u2208 \u03a9, \u03c4 \u2208 [0, b\u03c4] (10)\nAgent cannot change\nresources while\nactive. Only enabled for\nscheduling with static\nassignments.\n\u03b8m(\u03c4) = 1 and \u03b8m(\u03c4 + 1) = 1 =\u21d2\n\u0394m(\u03c4, \u03c9) = \u0394m(\u03c4 + 1, \u03c9)\n\u0394m(\u03c4, \u03c9) \u2212 Z(1 \u2212 \u03b8m(\u03c4 + 1)) \u2264\n\u0394m(\u03c4 + 1, \u03c9) + Z(1 \u2212 \u03b8m(\u03c4))\n\u0394m(\u03c4, \u03c9) + Z(1 \u2212 \u03b8m(\u03c4 + 1)) \u2265\n\u0394m(\u03c4 + 1, \u03c9) \u2212 Z(1 \u2212 \u03b8m(\u03c4))\n\u2200m \u2208 M, \u03c9 \u2208 \u03a9, \u03c4 \u2208 [0, b\u03c4]\n(11)\nTable 1: MILP for globally optimal resource scheduling.\nTm = \u03c4d\nm \u2212 \u03c4a\nm + 1 is the time horizon for the agent\"s MDP.\nUsing this LP as a basis, we augment it with constraints\nthat ensure that the resource usage implied by the agents\"\noccupation measures {xm} does not violate the global\nresource requirements b\u03d5 at any time step \u03c4 \u2208 [0, b\u03c4]. To\nformulate these resource constraints, we use the following binary\nvariables:\n\u2022 \u0394m(\u03c4, \u03c9) = {0, 1}, \u2200m \u2208 M, \u03c4 \u2208 [0, b\u03c4], \u03c9 \u2208 \u03a9, which\nserve as indicator variables that define whether agent m\npossesses resource \u03c9 at time \u03c4. These are analogous to\nthe static indicator variables used in the one-shot static\nresource-allocation problem in [6].\n\u2022 \u03b8m = {0, 1}, \u2200m \u2208 M, \u03c4 \u2208 [0, b\u03c4] are indicator variables\nthat specify whether agent m is active (i.e., executing\nits MDP) at time \u03c4.\nThe meaning of resource-usage variables \u0394 is illustrated in\nFigure 1: \u0394m(\u03c4, \u03c9) = 1 only if resource \u03c9 is allocated to\nagent m at time \u03c4. The meaning of the activity\nindicators \u03b8 is illustrated in Figure 2b: when agent m is in either\nthe start state sb\nor the finish state sf\n, the corresponding\n\u03b8m = 0, but once the agent becomes active and enters one\nof the other states, we set \u03b8m = 1 . This meaning of \u03b8 can be\nenforced with a linear constraint that synchronizes the\nvalues of the agents\" occupation measures xm and the activity\n1224 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nindicators \u03b8, as shown in (6) in Table 1.\nAnother constraint we have to add-because the activity\nindicators \u03b8 are defined on the global timeline \u03c4-is to\nenforce the fact that the agent is inactive outside of its\narrivaldeparture window. This is accomplished by constraint (7) in\nTable 1.\nFurthermore, agents should not be using resources while\nthey are inactive. This constraint can also be enforced via a\nlinear inequality on \u03b8 and \u0394, as shown in (8).\nConstraint (6) sets the value of \u03b8 to match the policy\ndefined by the occupation measure xm. In a similar fashion,\nwe have to make sure that the resource-usage variables \u0394 are\nalso synchronized with the occupation measure xm. This is\ndone via constraint (9) in Table 1, which is nearly identical\nto the analogous constraint from [6].\nAfter implementing the above constraint, which enforces\nthe meaning of \u0394, we add a constraint that ensures that the\nagents\" resource usage never exceeds the amounts of\navailable resources. This condition is also trivially expressed as\na linear inequality (10) in Table 1.\nFinally, for the problem formulation where resource\nassignments are static during a lifetime of an agent, we add a\nconstraint that ensures that the resource-usage variables \u0394\ndo not change their value while the agent is active (\u03b8 = 1).\nThis is accomplished via the linear constraint (11), where\nZ \u2265 2 is a constant that is used to turn off the constraints\nwhen \u03b8m(\u03c4) = 0 or \u03b8m(\u03c4 + 1) = 0. This constraint is not\nused for the dynamic problem formulation, where resources\ncan be reallocated between agents at every time step.\nTo summarize, Table 1 together with the\nconservationof-flow constraints from (12) defines the MILP that\nsimultaneously computes an optimal resource assignment for all\nagents across time as well as optimal finite-horizon MDP\npolicies that are valid under that resource assignment.\nAs a rough measure of the complexity of this MILP, let\nus consider the number of optimization variables and\nconstraints. Let TM =\nP\nTm =\nP\nm(\u03c4a\nm \u2212 \u03c4d\nm + 1) be the sum\nof the lengths of the arrival-departure windows across all\nagents. Then, the number of optimization variables is:\nTM + b\u03c4|M||\u03a9| + b\u03c4|M|,\nTM of which are continuous (xm), and b\u03c4|M||\u03a9| + b\u03c4|M| are\nbinary (\u0394 and \u03b8). However, notice that all but TM|M| of\nthe \u03b8 are set to zero by constraint (7), which also\nimmediately forces all but TM|M||\u03a9| of the \u0394 to be zero via the\nconstraints (8). The number of constraints (not including\nthe degenerate constraints in (7)) in the MILP is:\nTM + TM|\u03a9| + b\u03c4|\u03a9| + b\u03c4|M||\u03a9|.\nDespite the fact that the complexity of the MILP is, in the\nworst case, exponential1\nin the number of binary variables,\nthe complexity of this MILP is significantly (exponentially)\nlower than that of the MILP with flat utility functions,\ndescribed in Section 2.2. This result echos the efficiency gains\nreported in [6] for single-shot resource-allocation problems,\nbut is much more pronounced, because of the explosion of\nthe flat utility representation due to the temporal aspect of\nthe problem (recall the prohibitive complexity of the\ncombinatorial optimization in Section 2.2). We empirically analyze\nthe performance of this method in Section 5.\n1\nStrictly speaking, solving MILPs to optimality is\nNPcomplete in the number of integer variables.\n5. EXPERIMENTAL RESULTS\nAlthough the complexity of solving MILPs is in the worst\ncase exponential in the number of integer variables, there\nare many efficient methods for solving MILPs that allow\nour algorithm to scale well for parameters common to\nresource allocation and scheduling problems. In particular,\nthis section introduces a problem domain-the repairshop\nproblem-used to empirically evaluate our algorithm\"s\nscalability in terms of the number of agents |M|, the number of\nshared resources |\u03a9|, and the varied lengths of global time\nb\u03c4 during which agents may enter and exit the system.\nThe repairshop problem is a simple parameterized MDP\nadopting the metaphor of a vehicular repair shop. Agents\nin the repair shop are mechanics with a number of\nindependent tasks that yield reward only when completed. In our\nMDP model of this system, actions taken to advance through\nthe state space are only allowed if the agent holds certain\nresources that are publicly available to the shop. These\nresources are in finite supply, and optimal policies for the shop\nwill determine when each agent may hold the limited\nresources to take actions and earn individual rewards. Each\ntask to be completed is associated with a single action,\nalthough the agent is required to repeat the action numerous\ntimes before completing the task and earning a reward.\nThis model was parameterized in terms of the number\nof agents in the system, the number of different types of\nresources that could be linked to necessary actions, a global\ntime during which agents are allowed to arrive and depart,\nand a maximum length for the number of time steps an agent\nmay remain in the system.\nAll datapoints in our experiments were obtained with 20\nevaluations using CPLEX to solve the MILPs on a\nPentium4 computer with 2Gb of RAM. Trials were conducted on\nboth the static and the dynamic version of the\nresourcescheduling problem, as defined earlier.\nFigure 3 shows the runtime and policy value for\nindependent modifications to the parameter set. The top row\nshows how the solution time for the MILP scales as we\nincrease the number of agents |M|, the global time horizon b\u03c4,\nand the number of resources |\u03a9|. Increasing the number of\nagents leads to exponential complexity scaling, which is to\nbe expected for an NP-complete problem. However,\nincreasing the global time limit b\u03c4 or the total number of resource\ntypes |\u03a9|-while holding the number of agents\nconstantdoes not lead to decreased performance. This occurs because\nthe problems get easier as they become under-constrained,\nwhich is also a common phenomenon for NP-complete\nproblems. We also observe that the solution to the dynamic\nversion of the problem can often be computed much faster than\nthe static version.\nThe bottom row of Figure 3 shows the joint policy value\nof the policies that correspond to the computed optimal\nresource-allocation schedules. We can observe that the\ndynamic version yields higher reward (as expected, since the\nreward for the dynamic version is always no less than the\nreward of the static version). We should point out that these\ngraphs should not be viewed as a measure of performance of\ntwo different algorithms (both algorithms produce optimal\nsolutions but to different problems), but rather as\nobservations about how the quality of optimal solutions change as\nmore flexibility is allowed in the reallocation of resources.\nFigure 4 shows runtime and policy value for trials in which\ncommon input variables are scaled together. This allows\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1225\n2 4 6 8 10\n10\n\u22123\n10\n\u22122\n10\n\u22121\n10\n0\n10\n1\n10\n2\n10\n3\n10\n4\nNumber of Agents |M|\nCPUTime,sec\n|\u03a9| = 5, \u03c4 = 50\nstatic\ndynamic\n50 100 150 200\n10\n\u22122\n10\n\u22121\n10\n0\n10\n1\n10\n2\n10\n3\nGlobal Time Boundary \u03c4\nCPUTime,sec\n|M| = 5, |\u03a9| = 5\nstatic\ndynamic\n10 20 30 40 50\n10\n\u22122\n10\n\u22121\n10\n0\n10\n1\n10\n2\nNumber of Resources |\u03a9|\nCPUTime,sec\n|M| = 5, \u03c4 = 50\nstatic\ndynamic\n2 4 6 8 10\n200\n400\n600\n800\n1000\n1200\n1400\n1600\nNumber of Agents |M|\nValue\n|\u03a9| = 5, \u03c4 = 50\nstatic\ndynamic\n50 100 150 200\n400\n500\n600\n700\n800\n900\n1000\n1100\n1200\n1300\n1400\nGlobal Time Boundary \u03c4\nValue\n|M| = 5, |\u03a9| = 5\nstatic\ndynamic\n10 20 30 40 50\n500\n600\n700\n800\n900\n1000\n1100\n1200\n1300\n1400\nNumber of Resources |\u03a9|\nValue\n|M| = 5, \u03c4 = 50\nstatic\ndynamic\nFigure 3: Evaluation of our MILP for variable numbers of agents (column 1), lengths of global-time window (column\n2), and numbers of resource types (column 3). Top row shows CPU time, and bottom row shows the joint reward of\nagents\" MDP policies. Error bars show the 1st and 3rd quartiles (25% and 75%).\n2 4 6 8 10\n10\n\u22123\n10\n\u22122\n10\n\u22121\n10\n0\n10\n1\n10\n2\n10\n3\nNumber of Agents |M|\nCPUTime,sec\n\u03c4 = 10|M|\nstatic\ndynamic\n2 4 6 8 10\n10\n\u22123\n10\n\u22122\n10\n\u22121\n10\n0\n10\n1\n10\n2\n10\n3\n10\n4\nNumber of Agents |M|\nCPUTime,sec\n|\u03a9| = 2|M|\nstatic\ndynamic\n2 4 6 8 10\n10\n\u22123\n10\n\u22122\n10\n\u22121\n10\n0\n10\n1\n10\n2\n10\n3\n10\n4\nNumber of Agents |M|\nCPUTime,sec\n|\u03a9| = 5|M|\nstatic\ndynamic\n2 4 6 8 10\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n1800\n2000\n2200\nNumber of Agents |M|\nValue\n\u03c4 = 10|M|\nstatic\ndynamic\n2 4 6 8 10\n200\n400\n600\n800\n1000\n1200\n1400\n1600\n1800\n2000\nNumber of Agents |M|\nValue\n|\u03a9| = 2|M|\nstatic\ndynamic\n2 4 6 8 10\n0\n500\n1000\n1500\n2000\n2500\nNumber of Agents |M|\nValue\n|\u03a9| = 5|M|\nstatic\ndynamic\nFigure 4: Evaluation of our MILP using correlated input variables. The left column tracks the performance and CPU\ntime as the number of agents and global-time window increase together (b\u03c4 = 10|M|). The middle and the right column\ntrack the performance and CPU time as the number of resources and the number of agents increase together as\n|\u03a9| = 2|M| and |\u03a9| = 5|M|, respectively. Error bars show the 1st and 3rd quartiles (25% and 75%).\n1226 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nus to explore domains where the total number of agents\nscales proportionally to the total number of resource types\nor the global time horizon, while keeping constant the\naverage agent density (per unit of global time) or the average\nnumber of resources per agent (which commonly occurs in\nreal-life applications).\nOverall, we believe that these experimental results\nindicate that our MILP formulation can be used to effectively\nsolve resource-scheduling problems of nontrivial size.\n6. DISCUSSION AND CONCLUSIONS\nThroughout the paper, we have made a number of\nassumptions in our model and solution algorithm; we discuss\ntheir implications below.\n\u2022 Continual execution. We assume that once an agent\nstops executing its MDP (transitions into state sf\n), it\nexits the system and cannot return. It is easy to relax\nthis assumption for domains where agents\" MDPs can be\npaused and restarted. All that is required is to include an\nadditional pause action which transitions from a given\nstate back to itself, and has zero reward.\n\u2022 Indifference to start time. We used a reward model\nwhere agents\" rewards depend only on the time horizon\nof their MDPs and not the global start time. This is a\nconsequence of our MDP-augmentation procedure from\nSection 4.1. It is easy to extend the model so that the\nagents incur an explicit penalty for idling by assigning a\nnon-zero negative reward to the start state sb\n.\n\u2022 Binary resource requirements. For simplicity, we have\nassumed that resource costs are binary: \u03d5m(a, \u03c9) = {0, 1},\nbut our results generalize in a straightforward manner to\nnon-binary resource mappings, analogously to the\nprocedure used in [5].\n\u2022 Cooperative agents. The optimization procedure\ndiscussed in this paper was developed in the context of\ncooperative agents, but it can also be used to design a\nmechanism for scheduling resources among self-interested agents.\nThis optimization procedure can be embedded in a\nVickreyClarke-Groves auction, completely analogously to the way\nit was done in [7]. In fact, all the results of [7] about the\nproperties of the auction and information privacy directly\ncarry over to the scheduling domain discussed in this\npaper, requiring only slight modifications to deal with\nfinitehorizon MDPs.\n\u2022 Known, deterministic arrival and departure times.\nFinally, we have assumed that agents\" arrival and\ndeparture times (\u03c4a\nm and \u03c4d\nm) are deterministic and known a\npriori. This assumption is fundamental to our solution\nmethod. While there are many domains where this\nassumption is valid, in many cases agents arrive and\ndepart dynamically and their arrival and departure times\ncan only be predicted probabilistically, leading to online\nresource-allocation problems. In particular, in the case of\nself-interested agents, this becomes an interesting version\nof an online-mechanism-design problem [11, 12].\nIn summary, we have presented an MILP formulation for\nthe combinatorial resource-scheduling problem where agents\"\nvalues for possible resource assignments are defined by\nfinitehorizon MDPs. This result extends previous work ([6, 7])\non static one-shot resource allocation under MDP-induced\npreferences to resource-scheduling problems with a temporal\naspect. As such, this work takes a step in the direction of\ndesigning an online mechanism for agents with combinatorial\nresource preferences induced by stochastic planning\nproblems. Relaxing the assumption about deterministic arrival\nand departure times of the agents is a focus of our future\nwork.\nWe would like to thank the anonymous reviewers for their\ninsightful comments and suggestions.\n7. REFERENCES\n[1] E. Altman and A. Shwartz. Adaptive control of\nconstrained Markov chains: Criteria and policies.\nAnnals of Operations Research, special issue on\nMarkov Decision Processes, 28:101-134, 1991.\n[2] R. Bellman. Dynamic Programming. Princeton\nUniversity Press, 1957.\n[3] C. Boutilier. Solving concisely expressed combinatorial\nauction problems. In Proc. of AAAI-02, pages\n359-366, 2002.\n[4] C. Boutilier and H. H. Hoos. Bidding languages for\ncombinatorial auctions. In Proc. of IJCAI-01, pages\n1211-1217, 2001.\n[5] D. Dolgov. Integrated Resource Allocation and\nPlanning in Stochastic Multiagent Environments. PhD\nthesis, Computer Science Department, University of\nMichigan, February 2006.\n[6] D. A. Dolgov and E. H. Durfee. Optimal resource\nallocation and policy formulation in loosely-coupled\nMarkov decision processes. In Proc. of ICAPS-04,\npages 315-324, June 2004.\n[7] D. A. Dolgov and E. H. Durfee. Computationally\nefficient combinatorial auctions for resource allocation\nin weakly-coupled MDPs. In Proc. of AAMAS-05,\nNew York, NY, USA, 2005. ACM Press.\n[8] D. A. Dolgov and E. H. Durfee. Resource allocation\namong agents with preferences induced by factored\nMDPs. In Proc. of AAMAS-06, 2006.\n[9] K. Larson and T. Sandholm. Mechanism design and\ndeliberative agents. In Proc. of AAMAS-05, pages\n650-656, New York, NY, USA, 2005. ACM Press.\n[10] N. Nisan. Bidding and allocation in combinatorial\nauctions. In Electronic Commerce, 2000.\n[11] D. C. Parkes and S. Singh. An MDP-based approach\nto Online Mechanism Design. In Proc. of the\nSeventeenths Annual Conference on Neural\nInformation Processing Systems (NIPS-03), 2003.\n[12] D. C. Parkes, S. Singh, and D. Yanovsky.\nApproximately efficient online mechanism design. In\nProc. of the Eighteenths Annual Conference on Neural\nInformation Processing Systems (NIPS-04), 2004.\n[13] M. L. Puterman. Markov Decision Processes. John\nWiley & Sons, New York, 1994.\n[14] M. H. Rothkopf, A. Pekec, and R. M. Harstad.\nComputationally manageable combinational auctions.\nManagement Science, 44(8):1131-1147, 1998.\n[15] T. Sandholm. An algorithm for optimal winner\ndetermination in combinatorial auctions. In Proc. of\nIJCAI-99, pages 542-547, San Francisco, CA, USA,\n1999. Morgan Kaufmann Publishers Inc.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1227", "keywords": "multiagent system;multiagent plan;resource-scheduling;optimal allocation;markov decision process;utility function;resource;resource allocation;scheduling;discrete-time scheduling problem;resource-scheduling algorithm;task and resource allocation in agent system;optimal resource scheduling;optimization problem;combinatorial resource scheduling"}
{"name": "train_I-64", "title": "Organizational Self-Design in Semi-dynamic Environments", "abstract": "Organizations are an important basis for coordination in multiagent systems. However, there is no best way to organize and all ways of organizing are not equally effective. Attempting to optimize an organizational structure depends strongly on environmental features including problem characteristics, available resources, and agent capabilities. If the environment is dynamic, the environmental conditions or the problem task structure may change over time. This precludes the use of static, design-time generated, organizational structures in such systems. On the other hand, for many real environments, the problems are not totally unique either: certain characteristics and conditions change slowly, if at all, and these can have an important effect in creating stable organizational structures. Organizational-Self Design (OSD) has been proposed as an approach for constructing suitable organizational structures at runtime. We extend the existing OSD approach to include worthoriented domains, model other resources in addition to only processor resources and build in robustness into the organization. We then evaluate our approach against the contract-net approach and show that our OSD agents perform better, are more efficient, and more flexible to changes in the environment.", "fulltext": "1. INTRODUCTION\nIn this paper, we are primarily interested in the organizational\ndesign of a multiagent system - the roles enacted by the agents,\n\u2217Primary author is a student\nthe coordination between the roles and the number and assignment\nof roles and resources to the individual agents. The organizational\ndesign is complicated by the fact that there is no best way to\norganize and all ways of organizing are not equally effective [2].\nInstead, the optimal organizational structure depends both on the\nproblem at hand and the environmental conditions under which the\nproblem needs to be solved. The environmental conditions may\nnot be known a priori, or may change over time, which would\npreclude the use of a static organizational structure. On the other hand,\nall problem instances and environmental conditions are not always\nunique, which would render inefficient the use of a new, bespoke\norganizational structure for every problem instance.\nOrganizational Self-Design (OSD) [4, 10] has been proposed\nas an approach to designing organizations at run-time in which\nthe agents are responsible for generating their own organizational\nstructures. We believe that OSD is especially suited to the above\nscenario in which the environment is semi-dynamic as the agents\ncan adapt to changes in the task structures and environmental\nconditions, while still being able to generate relatively stable\norganizational structures that exploit the common characteristics across\nproblem instances.\nIn our approach (as in [10]), we define two operators for OSD\n- agent spawning and composition - when an agent becomes\noverloaded, it spawns off a new agent to handle part of its task\nload/responsibility; when an agent lies idle for an extended period\nof time, it may decide to compose with another agent.\nWe use T\u00c6MS as the underlying representation for our\nproblem solving requests. T\u00c6MS [11] (Task Analysis, Environment\nModeling and Simulation) is a computational framework for\nrepresenting and reasoning about complex task environments in which\ntasks (problems) are represented using extended hierarchical task\nstructures [3]. The root node of the task structure represents the\nhigh-level goal that the agent is trying to achieve. The sub-nodes of\na node represent the subtasks and methods that make up the\nhighlevel task. The leaf nodes are at the lowest level of abstraction and\nrepresent executable methods - the primitive actions that the agents\ncan perform. The executable methods, themselves, may have\nmultiple outcomes, with different probabilities and different\ncharacteristics such as quality, cost and duration. T\u00c6MS also allows\nvarious mechanisms for specifying subtask variations and alternatives,\ni.e. each node in T\u00c6MS is labeled with a characteristic\naccumulation function that describes how many or which subgoals or sets of\nsubgoals need to be achieved in order to achieve a particular\nhigherlevel goal. T\u00c6MS has been used to model many different\nproblemsolving environments including distributed sensor networks,\ninformation gathering, hospital scheduling, EMS, and military planning.\n[5, 6, 3, 15].\nThe main contributions of this paper are as follows:\n1. We extend existing OSD approaches to use T\u00c6MS as the\nunderlying problem representation, which allows us to model\nand use OSD for worth-oriented domains. This in turn\nallows us to reason about (1) alternative task and role\nassignments that make different quality/cost tradeoffs and generate\ndifferent organizational structures and (2) uncertainties in the\nexecution of tasks.\n2. We model the use of resources other than only processor\nresources.\n3. We incorporate robustness into the organizational structures.\n2. RELATED WORK\nThe concept of OSD is not new and has been around since\nthe work of Corkill and Lesser on the DVMT system[4], even\nthough the concept was not fully developed by them. More\nrecently Dignum et. al.[8] have described OSD in the context of the\nreorganization of agent societies and attempt to classify the various\nkinds of reorganization possible according to the the reason for\nreorganization, the type of reorganization and who is responsible for\nthe reorganization decision. According to their scheme, the type of\nreorganization done by our agents falls into the category of\nstructural changes and the reorganization decision can be described as\nshared command.\nOur research primarily builds on the work done by Gasser and\nIshida [10], in which they use OSD in the context of a\nproduction system in order to perform adaptive work allocation and load\nbalancing. In their approach, they define two organizational\nprimitives - composition and decomposition, which are similar to our\norganizational primitives for agent spawning and composition. The\nmain difference between their work and our work is that we use\nT\u00c6MS as the underlying representation for our problems, which\nallows, firstly, the representation of a larger, more general class of\nproblems and, secondly, quantitative reasoning over task structures.\nThe latter also allows us to incorporate different design-to-criteria\nschedulers [16].\nHorling and Lesser [9] present a different, top-down approach to\nOSD that also uses T\u00c6MS as the underlying representation.\nHowever, their approach assumes a fixed number of agents with\ndesignated (and fixed) roles. OSD is used in their work to change the\ninteraction patterns between the agents and results in the agents\nusing different subtasks or different resources to achieve their goals.\nWe also extend on the work done by Sycara et. al.,[13] on Agent\nCloning, which is another approach to resource allocation and load\nbalancing. In this approach, the authors present agent cloning as\na possible response to agent overload - if an agent detects that it\nis overloaded and that there are spare (unused) resources in the\nsystem, the agent clones itself and gives its clone some part of its\ntask load. Hence, agent cloning can be thought of as akin to agent\nspawning in our approach. However, the two approaches are\ndifferent in that there is no specialization of the agents in the\nformerthe cloned agents are perfect replicas of the original agents and\nfulfill the same roles and responsibilities as the original agents. In our\napproach, on the other hand, the spawned agents are specialized on\na subpart of the spawning agent\"s task structure, which is no longer\nthe responsibility of the spawning agent. Hence, our approach also\ndeals with explicit organization formation and the coordination of\nthe agents\" tasks which are not handled by their approach.\nOther approaches to OSD include the work of So and Durfee\n[14], who describe a top-down model of OSD in the context of\nCooperative Distributive Problem Solving (CDPS) and Barber and\nMartin [1], who describe an adaptive decision making framework\nin which agents are able to reorganize decision-making groups by\ndynamically changing (1) who makes the decisions for a particular\ngoal and (2) who must carry out these decisions.The latter work is\nprimarily concerned with coordination decisions and can be used\nto complement our OSD work, which primarily deals with task and\nresource allocation.\n3. TASK AND RESOURCE MODEL\nTo ground our discussion of OSD, we now formally describe\nour task and resource model. In our model, the primary input to\nthe multi-agent system (MAS) is an ordered set of problem\nsolving requests or task instances, < P1, P2, P3, ..., Pn >, where each\nproblem solving request, Pi, can be represented using the tuple\n< ti, ai, di >. In this scheme, ti is the underlying T\u00c6MS task\nstructure, ai \u2208 N+\nis the arrival time and di \u2208 N+\nis the deadline\nof the ith\ntask instance1\n. The MAS has no prior knowledge about\nthe task ti before the arrival time, ai. In order for the MAS to\naccrue quality, the task ti must be completed before the deadline,\ndi.\nFurthermore, every underlying task structure, ti, can be\nrepresented using the tuple < T, \u03c4, M, Q, E, R, \u03c1, C >, where:\n\u2022 T is the set of tasks. The tasks are non-leaf nodes in a\nT\u00c6MS task structure and are used to denote goals that the\nagents must achieve. Tasks have a characteristic\naccumulation function (see below) and are themselves composed of\nother subtasks and/or methods that need to be achieved in\norder to achieve the goal represented by that task. Formally,\neach task Tj can be represented using the pair (qj, sj), where\nqj \u2208 Q and sj \u2282 (T \u222a M). For our convenience, we\ndefine two functions SUBTASKS(Task) : T \u2192 P(T \u222a M) and\nSUPERTASKS(T\u00c6MS node) : T \u222a M \u2192 P(T), that return\nthe subtasks and supertasks of a T\u00c6MS node respectively2\n.\n\u2022 \u03c4 \u2208 T, is the root of the task structure, i.e. the highest level\ngoal that the organization is trying to achieve. The quality\naccrued on a problem is equal to the quality of task \u03c4.\n\u2022 M is the set executable methods, i.e., M =\n{m1, m2, ..., mn}, where each method, mk,\nis represented using the outcome distribution,\n{(o1, p1), (o2, p2), ..., (om, pm)}. In the pair (ol, pl),\nol is an outcome and pl is the probability that executing mk\nwill result in the outcome ol. Furthermore, each outcome,\nol is represented using the triple (ql, cl, dl), where ql is the\nquality distribution, cl is the cost distribution and dl is the\nduration distribution of outcome ol. Each discrete\ndistribution is itself a set of pairs, {(n1, p1), (n2, p2), ..., (nn, pn)},\nwhere pi \u2208 +\nis the probability that the outcome will have\na quality/cost/duration of nl \u2208 N depending on the type of\ndistribution and\nPm\ni=1 pl = 1.\n\u2022 Q is the set of quality/characteristic accumulation functions\n(CAFs). The CAFs determine how a task group accrues\nquality given the quality accrued by its subtasks/methods. For\nour research, we use four CAFs: MIN, MAX, SUM and\nEXACTLY ONE. See [5] for formal definitions.\n\u2022 E is the set of (non-local) effects. Again, see [5] for formal\ndefinitions.\n\u2022 R is the set of resources.\n\u2022 \u03c1 is a mapping from an executable method and resource to\nthe quantity of that resource needed (by an agent) to\nschedule/execute that method. That is \u03c1(method, resource) :\nM \u00d7 R \u2192 N.\n1\nN is the set of natural numbers including zero and N+\nis the set\nof positive natural numbers excluding zero.\n2\nP is the power set of set, i.e., the set of all subsets of a set\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1229\n\u2022 C is a mapping from a resource to the cost of that resource,\nthat is C(resource) : R \u2192 N+\nWe also make the following set of assumptions in our research:\n1. The agents in the MAS are drawn from the infinite set A =\n{a1, a2, a3, ...}. That is, we do not assume a fixed set of\nagents - instead agents are created (spawned) and destroyed\n(combined) as needed.\n2. All problem solving requests have the same underlying task\nstructure, i.e. \u2203t\u2200iti = t, where t is the task structure of\nthe problem that the MAS is trying to solve. We believe that\nthis assumption holds for many of the practical problems that\nwe have in mind because T\u00c6MS task structures are\nbasically high-level plans for achieving some goal in which the\nsteps required for achieving the goal-as well as the possible\ncontingency situations-have been pre-computed offline and\nrepresented in the task structure. Because it represents many\ncontingencies, alternatives, uncertain characteristics and\nruntime flexible choices, the same underlying task structure\ncan play out very differently across specific instances.\n3. All resources are exclusive, i.e., only one agent may use a\nresource at any given time. Furthermore, we assume that\neach agent has to own the set of resources that it\nneedseven though the resource ownership can change during the\nevolution of the organization.\n4. All resources are non-consumable.\n4. ORGANIZATIONAL SELF DESIGN\n4.1 Agent Roles and Relationships\nThe organizational structure is primarily composed of roles and\nthe relationships between the roles. One or more agents may enact\na particular role and one or more roles must be enacted by every\nagent. The roles may be thought of as the parts played by the agents\nenacting the roles in the solution to the problem and reflect the\nlong-term commitments made by the agents in question to a certain\ncourse of action (that includes task responsibility, authority, and\nmechanisms for coordination). The relationships between the roles\nare the coordination relationships that exist between the subparts of\na problem.\nIn our approach, the organizational design is directly contingent\non the task structure and the environmental conditions under which\nthe problems need to be solved. We define a role as a T\u00c6MS\nsubtree rooted at a particular node. Hence, the set (T \u222a M)\nencompasses the space of all possible roles. Note, by definition, a role\nmay consist of one or more other (sub-) roles as a particular T\u00c6MS\nnode may itself be made up of one or more subtrees. Hence, we will\nuse the terms role, task node and task interchangeably.\nWe, also, differentiate between local and managed (non-local)\nroles. Local roles are roles that are the sole responsibility of a\nsingle agent, that is, the agent concerned is responsible for solving all\nthe subproblems of the tree rooted at that node. For such roles, the\nagent concerned can do one or more subtasks, solely at its\ndiscretion and without consultation with any other agent. Managed roles,\non the other hand, must be coordinated between two or more agents\nas such roles will have two or more descendent local roles that are\nthe responsibility of two or more separate agents. Any of the\nexisting coordination mechanisms (such as GPGP [11]) can be used to\nachieve this coordination.\nFormally, if the function TYPE(Agent, T\u00c6MS Node) : A\u00d7(T \u222a\nM) \u2192 {Local, Managed, Unassigned}, returns the type of the\nresponsibility of the agent towards the specified role, then\nTYPE(a, r) = Local \u21d0\u21d2\n\u2200ri\u2208SUBTASKS(r)TYPE(a, ri) = Local\nTYPE(a, r) = Managed \u21d0\u21d2\n[\u2203a1\u2203r1(r1 \u2208 SUBTASKS(r)) \u2227 (TYPE(a1, r1) = Managed)] \u2228\n[\u2203a2\u2203a3\u2203r2\u2203r3(a2 = a3) \u2227 (r2 = r3) \u2227\n(r2 \u2208 SUBTASKS(r)) \u2227 (r3 \u2208 SUBTASKS(r)) \u2227\n(TYPE(a2, r2) = Local) \u2227 (TYPE(a3, r3) = Local)]\n4.2 Organization Formation and Adaptation\nTo form or adapt their organizational structure, the agents use\ntwo organizational primitives: agent spawning and composition.\nThese two primitives result in a change in the assignment of roles\nto the agents. Agent spawning is the generation of a new agent to\nhandle a subset of the roles of the spawning agent. Agent\ncomposition, on the other hand, is orthogonal to agent spawning and\ninvolves the merging of two or more agents together - the\ncombined agent is responsible for enacting all the roles of the agents\nbeing merged.\nIn order to participate in the formation and adaption of an\norganization, the agents need to explicitly represent and reason about\nthe role assignments. Hence, as a part of its organizational\nknowledge, each agent keeps a list of the local roles that it is enacting and\nthe non-local roles that it is managing. Note that each agent only\nhas limited organizational knowledge and is individually\nresponsible for spawning off or combining with another agent, as needed,\nbased on its estimate of its performance so far.\nTo see how the organizational primitives work, we first describe\nfour rules that can be thought of as the organizational invariants\nwhich will always hold before and after any organizational change:\n1. For a local role, all the descendent nodes of that role will be\nlocal.\nTYPE(a, r) = Local =\u21d2\n\u2200ri\u2208SUBTASKS(r)TYPE(a, ri) = Local\n2. Similarly, for a managed (non-local) role, all the ascendent\nnodes of that role will be managed.\nTYPE(a, r) = Managed =\u21d2\n\u2200ri\u2208SUPERTASKS(r)\u2203ai(ai \u2208 A) \u2227 (TYPE(ai, ri) = Managed)\n3. If two local roles that are enacted by two different agents\nshare a common ancestor, that ancestor will be a managed\nrole.\n(TYPE(a1, r1) = Local) \u2227 (TYPE(a2, r2) = Local)\u2227\n(a1 = a2) \u2227 (r1 = r2) =\u21d2\n\u2200ri\u2208(SUPERTASKS(r1)\u2229SUPERTASKS(r2))\u2203ai(ai \u2208 A)\u2227\n(TYPE(ai, ri) = Managed)\n4. If all the direct descendants of a role are local and the sole\nresponsibility of a single agent, that role will be a local role.\n\u2203a\u2203r\u2200ri\u2208SUBTASKS(r)(a \u2208 A) \u2227 (r \u2208 (T \u222a M))\u2227\n(TYPE(a, ri) = Local) =\u21d2\n(TYPE(a, r) = Local)\nWhen a new agent is spawned, the agent doing the spawning will\nassign one or more of its local roles to the newly spawned agent\n(Algorithm 1). To preserve invariant rules 2 and 3, the spawning\nagent will change the type of all the ascendent roles of the nodes\nassigned to the newly spawned agent from local to managed. Note\nthat the spawning agent is only changing its local organizational\nknowledge and not the global organizational knowledge. At the\n1230 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nsame time, the spawning agent is taking on the task of managing\nthe previously local roles. Similarly, the newly spawned agent will\nonly know of its just assigned local roles.\nWhen an agent (the composing agent) decides to compose with\nanother agent (the composed agent), the organizational knowledge\nof the composing agent is merged with the organizational\nknowledge of the composed agent. To do this, the composed agent takes\non the roles of all the local and managed tasks of the composing\nagent. Care is taken to preserve the organizational invariant rules 1\nand 4.\nAlgorithm 1 SpawnAgent(SpawningAgent) : A \u2192 A\n1: LocalRoles \u2190 {r \u2286 (T \u222a M) | TYPE(SpawningAgent,\nr)= Local}\n2: NewAgent \u2190 CREATENEWAGENT()\n3: NewAgentRoles \u2190 FINDROLESFORSPAWNEDAGENT\n(LocalRoles)\n4: for role in NewAgentRoles do\n5: TYPE(NewAgent, role) \u2190 Local\n6: TYPE(SpawningAgent, role) \u2190 Unassigned\n7: PRESERVEORGANIZATIONALINVARIANTS()\n8: return NewAgent\nAlgorithm 2 FINDROLESFORSPAWNEDAGENT\n(SpawningAgentRoles) : (T \u222a M) \u2192 (T \u222a M)\n1: R \u2190 SpawningAgentRoles\n2: selectedRoles \u2190 nil\n3: for roleSet in [P(R) \u2212 {\u03c6, R}] do\n4: if COST(R, roleSet) < COST(R, selectedRoles) then\n5: selectedRoles \u2190 roleSet\n6: return selectedRoles\nAlgorithm 3 GETRESOURCECOST(Roles) : (T \u222a M) \u2192\n1: M \u2190 (Roles \u2229 M)\n2: cost \u2190 0\n3: for resource in R do\n4: maxResourceUsage \u2190 0\n5: for method in M do\n6: if \u03c1(method, resource) > maxResourceUsage then\n7: max \u2190 \u03c1(method, resource)\n8: cost \u2190 cost +\n[C(resource) \u00d7 maxResourceUsage]\n9: return cost\n4.2.1 Role allocation during spawning\nOne of the key questions that the agent doing the spawning needs\nto answer is - which of its local-roles should it assign to the newly\nspawned agent and which of its local roles should it keep to\nitself? The onus of answering this question falls on the\nFINDROLESFORSPAWNEDAGENT() function, shown in Algorithm 2 above. This\nfunction takes the set of local roles that are the responsibility of the\nspawning agent and returns a subset of those roles for allocation\nto the newly spawned agent. This subset is selected based on the\nresults of a cost function as is evident from line 4 of the algorithm.\nSince the use of different cost functions will result in different\norganizational structures and since we have no a priori reason to believe\nthat one cost function will out-perform the other, we evaluated the\nperformance of three different cost functions based on the\nfollowing three different heuristics:\nAlgorithm 4 GETEXPECTEDDURATION(Roles) : (T \u222a M) \u2192 N+\n1: M \u2190 (Roles \u2229 M)\n2: exptDuration \u2190 0\n3: for [outcome =< (q, c, d), outcomeProb >] in M do\n4: exptOutcomeDuration \u2190 0\n5: for (n,p) in d do\n6: exptOutcomeDuration \u2190 n \u00d7 p\n7: exptDuration \u2190 exptDuration +\n[exptOutcomeDuration \u00d7 outcomeProb]\n8: return exptDuration\nAllocating top-most roles first: This heuristic always breaks\nup at the top-most nodes first. That is, if the nodes of a task\nstructure were numbered, starting from the root, in a breadth-first\nfashion, then this heuristic would select the local-role of the spawning\nagent that had the lowest number and breakup that node (by\nallocating one of its subtasks to the newly spawned agent). We\nselected this heuristic because (a) it is the simplest to implement, (b)\nfastest to run (the role allocation can be done in constant time\nwithout the need of a search through the task structure) and (c) it makes\nsense from a human-organizational perspective as this heuristic\ncorresponds to dividing an organization along functional lines.\nMinimizing total resources: This heuristic attempts to\nminimize the total cost of the resources needed by the agents in the\norganization to execute their roles. If R be the local roles of the\nspawning agent and R be the subset of roles being evaluated for\nallocation to the newly spawned agent, the cost function for this\nheuristic is given by: COST(R, R ) \u2190 GETRESOURCECOST(R \u2212\nR )+GETRESOURCECOST(R )\nBalancing execution time: This heuristic attempts to allocate\nroles in a way that tries to ensure that each agent has an equal\namount of work to do. For each potential role allocation, this\nheuristic works by calculating the absolute value of the difference\nbetween the expected duration of its own roles after spawning and\nthe expected duration of the roles of the newly spawned agent.\nIf this difference is close to zero, then the both the agents have\nroughly the same amount of work to do. Formally, if R be the\nlocal roles of the spawning agent and R be the subset of roles\nbeing evaluated for allocation to the newly spawned agent, then\nthe cost function for this heuristic is given by: COST(R, R ) \u2190\n|GETEXPECTEDDURATION(R\u2212R )\u2212GETEXPECTEDDURATION(R )|\nTo evaluate these heuristics, we ran a series of experiments that\ntested the performance of the resultant organization on randomly\ngenerated task structures. The results are given in Section 6.\n4.3 Reasons for Organizational Change\nAs organizational change is expensive (requiring clock cycles,\nallocation/deallocation of resources, etc.) we want a stable\norganizational structure that is suited to the task and environmental\nconditions at hand. Hence, we wish to change the organizational\nstructure only if the task structure and/or environmental conditions\nchange. Also to allow temporary changes to the environmental\nconditions to be overlooked, we want the probability of an\norganizational change to be inversely proportional to the time since the last\norganizational change. If this time is relatively short, the agents are\nstill adjusting to the changes in the environment - hence the\nprobability of an agent initiating an organizational change should be\nhigh. Similarly, if the time since the last organizational change is\nrelatively large, we wish to have a low probability of organizational\nchange.\nTo allow this variation in probability of organizational change,\nwe use simulated annealing to determine the probability of\nkeepThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1231\ning an existing organizational structure. This probability is\ncalculated using the annealing formula: p = e\u2212 \u0394E\nkT where \u0394E is the\namount of overload/underload, T is the time since the last\norganizational change and k is a constant. The mechanism of\ncomputing \u0394E is different for agent spawning than for agent composition\nand is described below. From this formula, if T is large, p, or the\nprobability of keeping the existing organizational structure is large.\nNote that the value of p is capped at a certain threshold in order to\nprevent the organization from being too sluggish in its reaction to\nenvironmental change.\nTo compute if agent spawning is necessary, we use the annealing\nequation with \u0394E = 1\n\u03b1\u2217Slack\nwhere \u03b1 is a constant and Slack is\nthe difference between the total time available for completion of\nthe outstanding tasks and the sum of the expected time required for\ncompletion of each task on the task queue. Also, if the amount of\nSlack is negative, immediate agent spawning will occur without use\nof the annealing equation.\nTo calculate if agent composition is necessary, we again use the\nsimulated annealing equation. However, in this case, \u0394E = \u03b2 \u2217\nIdle Time, where \u03b2 is a constant and Idle Time is the amount\nof time for which the agent was idle. If the agent has been sitting\nidle for a long period of time, \u0394E is large, which implies that p,\nthe probability of keeping the existing organizational structure, is\nlow.\n5. ORGANIZATION AND ROBUSTNESS\nThere are two approaches commonly used to achieve robustness\nin multiagent systems:\n1. the Survivalist Approach [12], which involves replicating\ndomain agents in order to allow the replicas to take over should\nthe original agents fail; and\n2. the Citizen Approach [7], which involves the use of special\nmonitoring agents (called Sentinel Agents) in order to detect\nagent failure and dynamically startup new agents in lieu of\nthe failed ones.\nThe advantage of the survivalist approach is that recovery is\nrelatively fast, since the replicas are pre-existing in the organization\nand can take over as soon as a failure is detected. The advantages\nof the citizen approach are that it requires fewer resources, little\nmodification to the existing organizational structure and\ncoordination protocol and is simpler to implement.\nBoth of these approaches can be applied to achieve robustness in\nour OSD agents and it is not clear which approach would be better.\nRather a thorough empirical evaluation of both approaches would\nbe required. In this paper, we present the citizen approach as it has\nbeen shown by [7], to have a better performance than the survivalist\napproach in the Contract Net protocol, and leave the presentation\nand evaluation of the survivalist approach to a future paper.\nTo implement the citizen approach, we designed special\nmonitoring agents, that periodically poll the domain agents by sending\nthem are you alive messages that the agents must respond to. If\nan agent fails, it will not respond to such messages - the\nmonitoring agents can then create a new agent and delegate the\nresponsibilities of the dead agent to the new agent.\nThis delegation of responsibilities is non-trivial as the\nmonitoring agents do not have access to the internal state of the domain\nagents, which is itself composed of two components - the\norganizational knowledge and the task information. The former consists\nof the information about the local and managerial roles of the agent\nwhile the latter is composed of the methods that are being\nscheduled and executed and the tasks that have been delegated to other\nagents. This state information can only be deduced by monitoring\nand recording the messages being sent and received by the domain\nagents. For example, in order to deduce the organizational\nknowledge, the monitoring agents need to keep a track of the spawn and\ncompose messages sent by the agents in order to trigger the\nspawning and composition operations respectively. The deduction\nprocess is particularly complicated in the case of the task information\nas the monitoring agents do not have access to the private\nschedules of the domain agents. The details are beyond the scope of this\npaper.\n6. EVALUATION\nTo evaluate our approach, we ran a series of experiments that\nsimulated the operation of both the OSD agents and the Contract\nNet agents on various task structures with varied arrival rates and\ndeadlines. At the start of each experiment, a random T\u00c6MS task\nstructure was generated with a specified depth and branching\nfactor. During the course of the experiment, a series of task instances\n(problems) arrive at the organization and must be completed by the\nagents before their specified deadlines.\nTo directly compare the OSD approach with the Contract Net\napproach, each experiment was repeated several times - using OSD\nagents on the first run and a different number of Contract Net agents\non each subsequent run. We were careful to use the same task\nstructure, task arrival times, task deadlines and random numbers for each\nof these trials.\nWe divided the experiments into two groups: experiments in\nwhich the environment was static (fixed task arrival rates and\ndeadlines) and experiments in which the environment was dynamic\n(varying arrival rates and/or deadlines).\nThe two graphs in Figure 1, show the average performance of the\nOSD organization against the Contract Net organizations with 8,\n10, 12 and 14 agents. The results shown are the averages of running\n40 experiments. 20 of those experiments had a static environment\nwith a fixed task arrival time of 15 cycles and a deadline window of\n20 cycles. The remaining 20 experiments had a varying task arrival\nrate - the task arrival rate was changed from 15 cycles to 30 cycles\nand back to 15 cycles after every 20 tasks. In all the experiments,\nthe task structures were randomly generated with a maximum depth\nof 4 and a maximum branching factor of 3. The runtime of all the\nexperiments was 2500 cycles.\nWe tested several hypotheses relating to the comparative\nperformance of our OSD approach using the Wilcoxon Matched-Pair\nSigned-Rank tests. Matched-Pair signifies that we are comparing\nthe performance of each system on precisely the same randomized\ntask set within each separate experiment. The tested hypothesis are:\nThe OSD organization requires fewer agents to complete an\nequal or larger number of tasks when compared to the\nContract Net organization: To test this hypothesis, we tested the\nstronger null hypothesis that states that the contract net agents\ncomplete more tasks. This null hypothesis is rejected for all contract\nnet organizations with less than 14 agents (static: p < 0.0003;\ndynamic: p < 0.03). For large contract net organizations, the number\nof tasks completed is statistically equivalent to the number\ncompleted by the OSD agents, however the number of agents used by\nthe OSD organization is smaller: 9.59 agents (in the static case) and\n7.38 agents (in the dynamic case) versus 14 contract net agents3\n.\nThus the original hypothesis, that OSD requires fewer agents to\n3\nThese values should not be construed as an indication of the\nscalability of our approach. We have tested our approach on\norganizations with more than 300 agents, which is significantly greater than\nthe number of agents needed for the kind of applications that we\nhave in mind (i.e. web service choreography, efficient dynamic use\nof grid computing, distributed information gathering, etc.).\n1232 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nFigure 1: Graph comparing the average performance of the\nOSD organization with the Contract Net organizations (with\n8, 10, 12 and 14 agents). The error bars show the standard\ndeviations.\ncomplete an equal or larger number of tasks, is upheld.\nThe OSD organizations achieve an equal or greater average\nquality than the Contract Net organizations: The null\nhypothesis is that the Contract Net agents achieve a greater average quality.\nWe can reject the null hypothesis for contract net organizations with\nless than 12 agents (static: p < 0.01; dynamic: p < 0.05). For\nlarger contract net organizations, the average quality is statistically\nequivalent to that achieved by OSD.\nThe OSD agents have a lower average response time as\ncompared to the Contract Net agents: The null hypothesis that OSD\nhas the same or higher response time is rejected for all contract net\norganizations (static: p < 0.0002; dynamic: p < 0.0004).\nThe OSD agents send less messages than the Contract Net\nAgents: The null hypothesis that OSD sends the same or more\nmessages is rejected for all contract net organizations (p < .0003\nin all cases except 8 contract net agents in a static environment\nwhere p < 0.02)\nHence, as demonstrated by the above tests, our agents perform\nbetter than the contract net agents as they complete a larger number\nof tasks, achieve a greater quality and also have a lower response\ntime and communication overhead. These results make intuitive\nsense given our goals for the OSD approach. We expected the OSD\norganizations to have a faster average response time and to send\nless messages because the agents in the OSD organization are not\nwasting time and messages sending bid requests and replying to\nbids. The quality gained on the tasks is directly dependent on the\nCriteria/Heuristic BET TF MR Rand\nNumber of Agents 572 567 100 139\nNo-Org-Changes 641 51 5 177\nTotal-Messages-Sent 586 499 13 11\nResource-Cost 346 418 337 66\nTasks-Completed 427 560 154 166\nAverage-Quality 367 492 298 339\nAverage-Response-Time 356 321 370 283\nAverage-Runtime 543 323 74 116\nAverage-Turnaround-Time 560 314 74 126\nTable 1: The number of times that each heuristic performed\nthe best or statistically equivalent to the best for each of the\nperformance criteria. Heuristic Key: BET is Balancing\nExecution Time, TF is Topmost First, MR is Minimizing Resources and\nRand is a random allocation strategy, in which every T\u00c6MS\nnode has a uniform probability of being selected for allocation.\nnumber of tasks completed, hence the more the number of tasks\ncompleted, the greater average quality. The results of testing the\nfirst hypothesis were slightly more surprising. It appears that due\nto the inherent inefficiency of the contract net protocol in bidding\nfor each and every task instance, a greater number of agents are\nneeded to complete an equal number of tasks.\nNext, we evaluated the performance of the three heuristics for\nallocating tasks. Some preliminary experiments (that are not reported\nhere due to space constraints) demonstrated the lack of a clear\nwinner amongst the three heuristics for most of the performance\ncriteria that we evaluated. We suspected this to be the case because\ndifferent heuristics are better for different task structures and\nenvironmental conditions, and since each experiment starts with a different\nrandom task structure, we couldn\"t find one allocation strategy that\nalways dominated the other for all the performance criteria.\nTo determine which heuristic performs the best, given a set of\ntask structures, environmental conditions and performance criteria,\nwe performed a series of experiments that were controlled using\nthe following five variables:\n\u2022 The depth of the task structure was varied from 3 to 5.\n\u2022 The branching factor was varied from 3 to 5.\n\u2022 The probability of any given task node having a MIN CAF\nwas varied from 0.0 to 1.0 in increments of 0.2. The\nprobability of any node having a SUM CAF was in turn modified\nto ensure that the probabilities add up to 14\n.\n\u2022 The arrival rate: from 10 to 40 cycles in increments of 10.\n\u2022 The deadline slack: from 5 to 15 in increments of 5.\nEach experiment was repeated 20 times, with a new task\nstructure being generated each time - these 20 experiments formed an\nexperimental set. Hence, all the experiments in an experimental set\nhad the same values for the exogenous variables that were used to\ncontrol the experiment. Note that a static environment was used in\neach of these experiments, as we wanted to see the performance of\nthe arrival rate and deadline slack on each of the three heuristics.\nAlso the results of any experiment in which the OSD organization\nconsisted of a single agent ware culled from the results. Similarly,\n4\nSince our preliminary analysis led is to believe that the number\nof MAX and EXACTLY ONE CAFs in a task structure have a\nminimal effect on the performance of the allocation strategies being\nevaluated, we set the probabilities of the MAX and EXACTLY ONE\nCAFs to 0 in order to reduce the combinatorial explosion of the full\nfactorial experimental design.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1233\nexperiments in which the generated task structures were\nunsatisfiable (given the deadline constraints), were removed from the final\nresults. If any experimental set had more than 15 experiments thus\nremoved, the whole set was ignored for performing the evaluation.\nThe final evaluation was done on 673 experimental sets.\nWe tested the potential of these three heuristics on the following\nperformance criteria:\n1. The average number of agents used.\n2. The total number of organizational changes.\n3. The total messages sent by all the agents.\n4. The total resource cost of the organization.\n5. The number of tasks completed.\n6. The average quality accrued. The average quality is defined\nas the total quality accrued during the experimental run\ndivided by the sum of the number of tasks completed and the\nnumber of tasks failed.\n7. The average response time of the organization. The response\ntime of a task is defined as the difference between the time\nat which any agent in the organization starts working on\nthe task (the start time) and the time at which the task was\ngenerated (the generation time). Hence, the response time\nis equivalent to the wait time. For tasks that are never\nattempted/started, the response time is set at final runtime\nminus the generation time.\n8. The average runtime of the tasks attempted by the\norganization. This time is defined as the difference between the time\nat which the task completed or failed and the start time. For\ntasks that were never stated, this time is set to zero.\n9. The turnaround time is defined as the sum of the response\ntime and runtime of a task.\nExcept for the number of tasks completed and the average\nquality accrued, lower values for the various performance criteria\nindicate better performance. Again we ran the Wilcoxon Matched-Pair\nSigned-Rank tests on the experiments in each of the experimental\nsets. The null hypothesis in each case was that there is no\ndifference between the pair of heuristics for the performance criteria\nunder consideration. We were interested in the cases in which we\ncould reject the null hypothesis with 95% confidence (p < 0.05).\nWe noted the number of times that a heuristic performed the best\nor was in a group that performed statistically better than the rest.\nThese counts are given in Tables 1 and 2.\nThe number of experimental sets in which each heuristic\nperformed the best or statistically equivalent to the best is shown in\nTable 1. The breakup of these numbers into (1) the number of times\nthat each heuristic performed better than all the other heuristics and\n(2) the number of times each heuristic was statistically equivalent\nto another group of heuristics, all of which performed the best, is\nshown in Table 2. Both of these tables allow us to glean important\ninformation about the performance of the three heuristics.\nParticularly interesting were the following results:\n\u2022 Whereas Balancing Execution Time (BET) used the\nlowest number of agents in largest number of experimental sets\n(572), in most of these cases (337 experimental sets) it was\nstatistically equivalent to Topmost First (TF). When these\ntwo heuristics didn\"t perform equally, there was an almost\neven split between the number of experimental sets in which\none outperformed the other.\nWe believe this was the case because BET always bifurcates\nthe agents into two agents that have a more or less equal task\nload. This often results in organizations that have an even\nFigure 2: Graph demonstrating the robustness of the citizen\napproach. The baseline shows the number of tasks completed\nin the absence of any failure.\nnumber of agents - none of which are small5\nenough to\ncombine into a larger agent. With TF, on the other hand, a\nlarge agent can successively spawn off smaller agents until it\nand the spawned agents are small enough to complete their\ntasks before the deadlines - this often results in\norganizations with an odd number of agents that is less than those\nused by BET.\n\u2022 As expected, BET achieved the lowest number of\norganizational changes in the largest number of experimental sets. In\nfact, it was over ten times as good as its second best\ncompetitor (TF). This shows that if the agents are conscientious\nin their initial task allocation, there is a lesser need for\norganizational change later on, especially for static environments.\n\u2022 A particularly interesting, yet easily explainable, result was\nthat of the average response time. We found that the\nMinimizing Resources (MR) heuristic performed the best when it\ncame to minimizing the average response time! This can be\nexplained by the fact the MR heuristic is extremely greedy\nand prefers to spawn off small agents that have a tiny\nresource footprint (so as to minimize the total increase in the\nresource cost to the organization at the time of spawning).\nWhereas most of these small agents might compose with\nother agents over time, the presence of a single small agent\nis sufficient to reduce the response time.\nIn fact the MR heuristic is not the most effective heuristic\nwhen it comes to minimizing the resource-cost of the\norganization - in fact, it only outperforms a random task/resource\nallocation. We believe this is in part due to the greedy\nnature of this heuristic and in part because of the fact that all\nspawning and composition operations only use local\ninformation. We believe that using some non-local information\nabout the resource allocation might help in making better\ndecisions, something that we plan to look at in the future.\nFinally we evaluated the performance of the citizens approach to\nrobustness as applied to our OSD mechanism (Figure 2). As\nexpected, as the probability of failure increases, the number of agents\nfailing during a run also increases. This results in a slight decrease\nin the number of tasks completed, which can be explained by the\nfact that whenever an agent fails, its looses whatever work it was\ndoing at the time. The newly created agent that fills in for the failed\n5\nFor this discussion small agents are agents that have a low\nexpected duration for their local roles (as calculated by Algorithm 4).\n1234 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nCriteria/Heuristic BET TF MR Rand BET+TF BET+Rand MR+Rand TF+MR BET+TF+MR All\nNumber of Agents 94 88 3 7 337 2 0 0 12 85\nNo-Org-Changes 480 0 0 29 16 113 0 0 0 5\nTotal-Messages-Sent 170 85 0 2 399 1 0 0 7 5\nResource-Cost 26 100 170 42 167 0 7 6 128 15\nTasks-Completed 77 197 4 28 184 1 3 9 36 99\nAverage-Quality 38 147 26 104 76 0 11 11 34 208\nAverage-Response-Time 104 74 162 43 31 20 16 8 7 169\nAverage-Runtime 322 110 0 12 121 13 1 1 1 69\nAverage-Turnaround-Time 318 94 1 11 125 26 1 0 7 64\nTable 2: Table showing the number of times that each individual heuristic performed the best and the number of times that a certain\ngroup of statistically equivalent heuristics performed the best. Only the more interesting heuristic groupings are shown. All shows\nthe number of experimental sets in which there was no statistical difference between the three heuristics and a random allocation\nstrategy\none must redo the work, thus wasting precious time which might\nnot be available close to a deadline.\nAs a part of our future research, we wish to, firstly, evaluate the\nsurvivalist approach to robustness. The survivalist approach might\nactually be better than the citizen approach for higher\nprobabilities of agent failure, as the replicated agents may be processing the\ntask structures in parallel and can take over the moment the\noriginal agents fail - thus saving time around tight deadlines. Also,\nwe strongly believe that the optimal organizational structure may\nvary, depending on the probability of failure and the desired level\nof robustness. For example, one way of achieving a higher level\nof robustness in the survivalist approach, given a large numbers of\nagent failures, would be to relax the task deadlines. However, such\na relaxation would result in the system using fewer agents in order\nto conserve resources, which in turn would have a detrimental\neffect on the robustness. Therefore, towards this end, we have begun\nexploring the robustness properties of task structures and the ways\nin which the organizational design can be modified to take such\nproperties into account.\n7. CONCLUSION\nIn this paper, we have presented a run-time approach to\norganization in which the agents use Organizational Self-Design to come up\nwith a suitable organizational structure. We have also evaluated the\nperformance of the organizations generated by the agents following\nour approach with the bespoke organization formation that takes\nplace in the Contract Net protocol and have demonstrated that our\napproach is better than the Contract Net approach as evident by the\nlarger number of tasks completed, larger quality achieved and lower\nresponse time. Finally, we tested the performance of three different\nresource allocation heuristics on various performance metrics and\nalso evaluated the robustness of our approach.\n8. REFERENCES\n[1] K. S. Barber and C. E. Martin. Dynamic reorganization of\ndecision-making groups. In AGENTS \"01, pages 513-520,\nNew York, NY, USA, 2001.\n[2] K. M. Carley and L. Gasser. Computational organization\ntheory. In G. Wiess, editor, Multiagent Systems: A Modern\nApproach to Distributed Artificial Intelligence, pages\n299-330, MIT Press, 1999.\n[3] W. Chen and K. S. Decker. The analysis of coordination in\nan information system application - emergency medical\nservices. In Lecture Notes in Computer Science (LNCS),\nnumber 3508, pages 36-51. Springer-Verlag, May 2005.\n[4] D. Corkill and V. Lesser. The use of meta-level control for\ncoordination in a distributed problem solving network.\nProceedings of the Eighth International Joint Conference on\nArtificial Intelligence, pages 748-756, August 1983.\n[5] K. S. Decker. Environment centered analysis and design of\ncoordination mechanisms. Ph.D. Thesis, Dept. of Comp.\nScience, University of Massachusetts, Amherst, May 1995.\n[6] K. S. Decker and J. Li. Coordinating mutually exclusive\nresources using GPGP. Autonomous Agents and Multi-Agent\nSystems, 3(2):133-157, 2000.\n[7] C. Dellarocas and M. Klein. An experimental evaluation of\ndomain-independent fault handling services in open\nmulti-agent systems. Proceedings of the International\nConference on Multi-Agent Systems (ICMAS-2000), July\n2000.\n[8] V. Dignum, F. Dignum, and L. Sonenberg. Towards Dynamic\nReorganization of Agent Societies. In Proceedings of CEAS:\nWorkshop on Coordination in Emergent Agent Societies at\nECAI, pages 22-27, Valencia, Spain, September 2004.\n[9] B. Horling, B. Benyo, and V. Lesser. Using self-diagnosis to\nadapt organizational structures. In AGENTS \"01, pages\n529-536, New York, NY, USA, 2001. ACM Press.\n[10] T. Ishida, L. Gasser, and M. Yokoo. Organization self-design\nof distributed production systems. IEEE Transactions on\nKnowledge and Data Engineering, 4(2):123-134, 1992.\n[11] V. R. Lesser et. al. Evolution of the gpgp/t\u00e6ms\ndomain-independent coordination framework. Autonomous\nAgents and Multi-Agent Systems, 9(1-2):87-143, 2004.\n[12] O. Marin, P. Sens, J. Briot, and Z. Guessoum. Towards\nadaptive fault tolerance for distributed multi-agent systems.\nProceedings of ERSADS 2001, May 2001.\n[13] O. Shehory, K. Sycara, et. al. Agent cloning: an approach to\nagent mobility and resource allocation. IEEE\nCommunications Magazine, 36(7):58-67, 1998.\n[14] Y. So and E. Durfee. An organizational self-design model for\norganizational change. In AAAI-93 Workshop on AI and\nTheories of Groups and Organizations, pages 8-15,\nWashington, D.C., July 1993.\n[15] T. Wagner. Coordination decision support assistants\n(coordinators). Technical Report 04-29, BAA, 2004.\n[16] T. Wagner and V. Lesser. Design-to-criteria scheduling:\nReal-time agent control. Proc. of AAAI 2000 Spring\nSymposium on Real-Time Autonomous Systems, 89-96.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1235", "keywords": "organization;organizational-self design;task and resource allocation;agent spawning;robustness;organizational structure;extended hierarchical task structure;environment modeling;composition;task analysis;coordination;simulation;multiagent system;organizational self-design"}
{"name": "train_I-65", "title": "Graphical Models for Online Solutions to Interactive POMDPs", "abstract": "We develop a new graphical representation for interactive partially observable Markov decision processes (I-POMDPs) that is significantly more transparent and semantically clear than the previous representation. These graphical models called interactive dynamic influence diagrams (I-DIDs) seek to explicitly model the structure that is often present in real-world problems by decomposing the situation into chance and decision variables, and the dependencies between the variables. I-DIDs generalize DIDs, which may be viewed as graphical representations of POMDPs, to multiagent settings in the same way that I-POMDPs generalize POMDPs. I-DIDs may be used to compute the policy of an agent online as the agent acts and observes in a setting that is populated by other interacting agents. Using several examples, we show how I-DIDs may be applied and demonstrate their usefulness.", "fulltext": "1. INTRODUCTION\nInteractive partially observable Markov decision processes\n(IPOMDPs) [9] provide a framework for sequential decision-making\nin partially observable multiagent environments. They generalize\nPOMDPs [13] to multiagent settings by including the other agents\"\ncomputable models in the state space along with the states of the\nphysical environment. The models encompass all information\ninfluencing the agents\" behaviors, including their preferences,\ncapabilities, and beliefs, and are thus analogous to types in Bayesian\ngames [11]. I-POMDPs adopt a subjective approach to\nunderstanding strategic behavior, rooted in a decision-theoretic framework that\ntakes a decision-maker\"s perspective in the interaction.\nIn [15], Polich and Gmytrasiewicz introduced interactive\ndynamic influence diagrams (I-DIDs) as the computational\nrepresentations of I-POMDPs. I-DIDs generalize DIDs [12], which may\nbe viewed as computational counterparts of POMDPs, to\nmultiagents settings in the same way that I-POMDPs generalize POMDPs.\nI-DIDs contribute to a growing line of work [19] that includes\nmulti-agent influence diagrams (MAIDs) [14], and more recently,\nnetworks of influence diagrams (NIDs) [8]. These formalisms seek\nto explicitly model the structure that is often present in real-world\nproblems by decomposing the situation into chance and decision\nvariables, and the dependencies between the variables. MAIDs\nprovide an alternative to normal and extensive game forms using\na graphical formalism to represent games of imperfect information\nwith a decision node for each agent\"s actions and chance nodes\ncapturing the agent\"s private information. MAIDs objectively\nanalyze the game, efficiently computing the Nash equilibrium profile\nby exploiting the independence structure. NIDs extend MAIDs to\ninclude agents\" uncertainty over the game being played and over\nmodels of the other agents. Each model is a MAID and the network\nof MAIDs is collapsed, bottom up, into a single MAID for\ncomputing the equilibrium of the game keeping in mind the different\nmodels of each agent. Graphical formalisms such as MAIDs and NIDs\nopen up a promising area of research that aims to represent\nmultiagent interactions more transparently. However, MAIDs provide an\nanalysis of the game from an external viewpoint and the\napplicability of both is limited to static single play games. Matters are more\ncomplex when we consider interactions that are extended over time,\nwhere predictions about others\" future actions must be made using\nmodels that change as the agents act and observe. I-DIDs address\nthis gap by allowing the representation of other agents\" models as\nthe values of a special model node. Both, other agents\" models and\nthe original agent\"s beliefs over these models are updated over time\nusing special-purpose implementations.\nIn this paper, we improve on the previous preliminary\nrepresentation of the I-DID shown in [15] by using the insight that the static\nI-ID is a type of NID. Thus, we may utilize NID-specific language\nconstructs such as multiplexers to represent the model node, and\nsubsequently the I-ID, more transparently. Furthermore, we clarify\nthe semantics of the special purpose policy link introduced in the\nrepresentation of I-DID by [15], and show that it could be replaced\nby traditional dependency links. In the previous representation of\nthe I-DID, the update of the agent\"s belief over the models of others\nas the agents act and receive observations was denoted using a\nspecial link called the model update link that connected the model\nnodes over time. We explicate the semantics of this link by\nshowing how it can be implemented using the traditional dependency\nlinks between the chance nodes that constitute the model nodes.\nThe net result is a representation of I-DID that is significantly more\ntransparent, semantically clear, and capable of being implemented\nusing the standard algorithms for solving DIDs. We show how\nIDIDs may be used to model an agent\"s uncertainty over others\"\nmodels, that may themselves be I-DIDs. Solution to the I-DID is\na policy that prescribes what the agent should do over time, given\nits beliefs over the physical state and others\" models. Analogous to\nDIDs, I-DIDs may be used to compute the policy of an agent online\nas the agent acts and observes in a setting that is populated by other\ninteracting agents.\n2. BACKGROUND: FINITELY NESTED\nIPOMDPS\nInteractive POMDPs generalize POMDPs to multiagent settings\nby including other agents\" models as part of the state space [9].\nSince other agents may also reason about others, the interactive\nstate space is strategically nested; it contains beliefs about other\nagents\" models and their beliefs about others. For simplicity of\npresentation we consider an agent, i, that is interacting with one\nother agent, j.\nA finitely nested I-POMDP of agent i with a strategy level l is\ndefined as the tuple:\nI-POMDPi,l = ISi,l, A, Ti, \u03a9i, Oi, Ri\nwhere: \u2022 ISi,l denotes a set of interactive states defined as, ISi,l =\nS \u00d7 Mj,l\u22121, where Mj,l\u22121 = {\u0398j,l\u22121 \u222a SMj}, for l \u2265 1, and\nISi,0 = S, where S is the set of states of the physical\nenvironment. \u0398j,l\u22121 is the set of computable intentional models of agent\nj: \u03b8j,l\u22121 = bj,l\u22121, \u02c6\u03b8j where the frame, \u02c6\u03b8j = A, \u03a9j, Tj, Oj, Rj,\nOCj . Here, j is Bayes rational and OCj is j\"s optimality criterion.\nSMj is the set of subintentional models of j. Simple examples of\nsubintentional models include a no-information model [10] and a\nfictitious play model [6], both of which are history independent.\nWe give a recursive bottom-up construction of the interactive state\nspace below.\nISi,0 = S, \u0398j,0 = { bj,0, \u02c6\u03b8j | bj,0 \u2208 \u0394(ISj,0)}\nISi,1 = S \u00d7 {\u0398j,0 \u222a SMj}, \u0398j,1 = { bj,1, \u02c6\u03b8j | bj,1 \u2208 \u0394(ISj,1)}\n.\n.\n.\n.\n.\n.\nISi,l = S \u00d7 {\u0398j,l\u22121 \u222a SMj}, \u0398j,l = { bj,l, \u02c6\u03b8j | bj,l \u2208 \u0394(ISj,l)}\nSimilar formulations of nested spaces have appeared in [1, 3].\n\u2022 A = Ai \u00d7 Aj is the set of joint actions of all agents in the\nenvironment; \u2022 Ti : S \u00d7A\u00d7S \u2192 [0, 1], describes the effect of the\njoint actions on the physical states of the environment; \u2022 \u03a9i is the\nset of observations of agent i; \u2022 Oi : S \u00d7 A \u00d7 \u03a9i \u2192 [0, 1] gives\nthe likelihood of the observations given the physical state and joint\naction; \u2022 Ri : ISi \u00d7 A \u2192 R describes agent i\"s preferences over\nits interactive states. Usually only the physical states will matter.\nAgent i\"s policy is the mapping, \u03a9\u2217\ni \u2192 \u0394(Ai), where \u03a9\u2217\ni is\nthe set of all observation histories of agent i. Since belief over the\ninteractive states forms a sufficient statistic [9], the policy can also\nbe represented as a mapping from the set of all beliefs of agent i to\na distribution over its actions, \u0394(ISi) \u2192 \u0394(Ai).\n2.1 Belief Update\nAnalogous to POMDPs, an agent within the I-POMDP\nframework updates its belief as it acts and observes. However, there are\ntwo differences that complicate the belief update in multiagent\nsettings when compared to single agent ones. First, since the state of\nthe physical environment depends on the actions of both agents, i\"s\nprediction of how the physical state changes has to be made based\non its prediction of j\"s actions. Second, changes in j\"s models have\nto be included in i\"s belief update. Specifically, if j is intentional\nthen an update of j\"s beliefs due to its action and observation has\nto be included. In other words, i has to update its belief based on\nits prediction of what j would observe and how j would update\nits belief. If j\"s model is subintentional, then j\"s probable\nobservations are appended to the observation history contained in the\nmodel. Formally, we have:\nPr(ist\n|at\u22121\ni , bt\u22121\ni,l ) = \u03b2 ISt\u22121:mt\u22121\nj =\u03b8t\nj\nbt\u22121\ni,l (ist\u22121\n)\n\u00d7 at\u22121\nj\nPr(at\u22121\nj |\u03b8t\u22121\nj,l\u22121)Oi(st\n, at\u22121\ni , at\u22121\nj , ot\ni)\n\u00d7Ti(st\u22121\n, at\u22121\ni , at\u22121\nj , st\n) ot\nj\nOj(st\n, at\u22121\ni , at\u22121\nj , ot\nj)\n\u00d7\u03c4(SE\u03b8t\nj\n(bt\u22121\nj,l\u22121, at\u22121\nj , ot\nj) \u2212 bt\nj,l\u22121)\n(1)\nwhere \u03b2 is the normalizing constant, \u03c4 is 1 if its argument is 0\notherwise it is 0, Pr(at\u22121\nj |\u03b8t\u22121\nj,l\u22121) is the probability that at\u22121\nj is\nBayes rational for the agent described by model \u03b8t\u22121\nj,l\u22121, and SE(\u00b7)\nis an abbreviation for the belief update. For a version of the belief\nupdate when j\"s model is subintentional, see [9].\nIf agent j is also modeled as an I-POMDP, then i\"s belief update\ninvokes j\"s belief update (via the term SE\u03b8t\nj\n( bt\u22121\nj,l\u22121 , at\u22121\nj , ot\nj)),\nwhich in turn could invoke i\"s belief update and so on. This\nrecursion in belief nesting bottoms out at the 0th\nlevel. At this level, the\nbelief update of the agent reduces to a POMDP belief update. 1\nFor\nillustrations of the belief update, additional details on I-POMDPs,\nand how they compare with other multiagent frameworks, see [9].\n2.2 Value Iteration\nEach belief state in a finitely nested I-POMDP has an associated\nvalue reflecting the maximum payoff the agent can expect in this\nbelief state:\nUn\n( bi,l, \u03b8i ) = max\nai\u2208Ai is\u2208ISi,l\nERi(is, ai)bi,l(is)+\n\u03b3\noi\u2208\u03a9i\nPr(oi|ai, bi,l)Un\u22121\n( SE\u03b8i\n(bi,l, ai, oi), \u03b8i )\n(2)\nwhere, ERi(is, ai) = aj\nRi(is, ai, aj)Pr(aj|mj,l\u22121) (since\nis = (s, mj,l\u22121)). Eq. 2 is a basis for value iteration in I-POMDPs.\nAgent i\"s optimal action, a\u2217\ni , for the case of finite horizon with\ndiscounting, is an element of the set of optimal actions for the belief\nstate, OPT(\u03b8i), defined as:\nOPT( bi,l, \u03b8i ) = argmax\nai\u2208Ai is\u2208ISi,l\nERi(is, ai)bi,l(is)\n+\u03b3\noi\u2208\u03a9i\nPr(oi|ai, bi,l)Un\n( SE\u03b8i\n(bi,l, ai, oi), \u03b8i )\n(3)\n3. INTERACTIVEINFLUENCEDIAGRAMS\nA naive extension of influence diagrams (IDs) to settings\npopulated by multiple agents is possible by treating other agents as\nautomatons, represented using chance nodes. However, this approach\nassumes that the agents\" actions are controlled using a probability\ndistribution that does not change over time. Interactive influence\ndiagrams (I-IDs) adopt a more sophisticated approach by\ngeneralizing IDs to make them applicable to settings shared with other\nagents who may act and observe, and update their beliefs.\n3.1 Syntax\nIn addition to the usual chance, decision, and utility nodes,\nIIDs include a new type of node called the model node. We show a\ngeneral level l I-ID in Fig. 1(a), where the model node (Mj,l\u22121) is\ndenoted using a hexagon. We note that the probability distribution\nover the chance node, S, and the model node together represents\nagent i\"s belief over its interactive states. In addition to the model\n1\nThe 0th\nlevel model is a POMDP: Other agent\"s actions are treated\nas exogenous events and folded into the T, O, and R functions.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 815\nFigure 1: (a) A generic level l I-ID for agent i situated with one other agent j. The hexagon is the model node (Mj,l\u22121) whose structure we show in\n(b). Members of the model node are I-IDs themselves (m1\nj,l\u22121, m2\nj,l\u22121; diagrams not shown here for simplicity) whose decision nodes are mapped to\nthe corresponding chance nodes (A1\nj , A2\nj ). Depending on the value of the node, Mod[Mj], the distribution of each of the chance nodes is assigned to\nthe node Aj. (c) The transformed I-ID with the model node replaced by the chance nodes and the relationships between them.\nnode, I-IDs differ from IDs by having a dashed link (called the\npolicy link in [15]) between the model node and a chance node,\nAj, that represents the distribution over the other agent\"s actions\ngiven its model. In the absence of other agents, the model node and\nthe chance node, Aj, vanish and I-IDs collapse into traditional IDs.\nThe model node contains the alternative computational models\nascribed by i to the other agent from the set, \u0398j,l\u22121 \u222a SMj, where\n\u0398j,l\u22121 and SMj were defined previously in Section 2. Thus, a\nmodel in the model node may itself be an I-ID or ID, and the\nrecursion terminates when a model is an ID or subintentional. Because\nthe model node contains the alternative models of the other agent\nas its values, its representation is not trivial. In particular, some of\nthe models within the node are I-IDs that when solved generate the\nagent\"s optimal policy in their decision nodes. Each decision node\nis mapped to the corresponding chance node, say A1\nj , in the\nfollowing way: if OPT is the set of optimal actions obtained by solving\nthe I-ID (or ID), then Pr(aj \u2208 A1\nj ) = 1\n|OP T |\nif aj \u2208 OPT, 0\notherwise.\nBorrowing insights from previous work [8], we observe that the\nmodel node and the dashed policy link that connects it to the\nchance node, Aj, could be represented as shown in Fig. 1(b). The\ndecision node of each level l \u2212 1 I-ID is transformed into a chance\nnode, as we mentioned previously, so that the actions with the\nlargest value in the decision node are assigned uniform\nprobabilities in the chance node while the rest are assigned zero probability.\nThe different chance nodes (A1\nj , A2\nj ), one for each model, and\nadditionally, the chance node labeled Mod[Mj] form the parents of the\nchance node, Aj. Thus, there are as many action nodes (A1\nj , A2\nj )\nin Mj,l\u22121 as the number of models in the support of agent i\"s\nbeliefs. The conditional probability table of the chance node, Aj,\nis a multiplexer that assumes the distribution of each of the action\nnodes (A1\nj , A2\nj ) depending on the value of Mod[Mj]. The values of\nMod[Mj] denote the different models of j. In other words, when\nMod[Mj] has the value m1\nj,l\u22121, the chance node Aj assumes the\ndistribution of the node A1\nj , and Aj assumes the distribution of A2\nj\nwhen Mod[Mj] has the value m2\nj,l\u22121. The distribution over the\nnode, Mod[Mj], is the agent i\"s belief over the models of j given a\nphysical state. For more agents, we will have as many model nodes\nas there are agents. Notice that Fig. 1(b) clarifies the semantics of\nthe policy link, and shows how it can be represented using the\ntraditional dependency links.\nIn Fig. 1(c), we show the transformed I-ID when the model node\nis replaced by the chance nodes and relationships between them. In\ncontrast to the representation in [15], there are no special-purpose\npolicy links, rather the I-ID is composed of only those types of\nnodes that are found in traditional IDs and dependency\nrelationships between the nodes. This allows I-IDs to be represented and\nimplemented using conventional application tools that target IDs.\nNote that we may view the level l I-ID as a NID. Specifically, each\nof the level l \u2212 1 models within the model node are blocks in the\nNID (see Fig. 2). If the level l = 1, each block is a traditional ID,\notherwise if l > 1, each block within the NID may itself be a NID.\nNote that within the I-IDs (or IDs) at each level, there is only a\nsingle decision node. Thus, our NID does not contain any MAIDs.\nFigure 2: A level l I-ID represented as a NID. The probabilities\nassigned to the blocks of the NID are i\"s beliefs over j\"s models\nconditioned on a physical state.\n3.2 Solution\nThe solution of an I-ID proceeds in a bottom-up manner, and is\nimplemented recursively. We start by solving the level 0 models,\nwhich, if intentional, are traditional IDs. Their solutions provide\nprobability distributions over the other agents\" actions, which are\nentered in the corresponding chance nodes found in the model node\nof the level 1 I-ID. The mapping from the level 0 models\" decision\nnodes to the chance nodes is carried out so that actions with the\nlargest value in the decision node are assigned uniform\nprobabilities in the chance node while the rest are assigned zero probability.\nGiven the distributions over the actions within the different chance\nnodes (one for each model of the other agent), the level 1 I-ID is\ntransformed as shown in Fig. 1(c). During the transformation, the\nconditional probability table (CPT) of the node, Aj, is populated\nsuch that the node assumes the distribution of each of the chance\nnodes depending on the value of the node, Mod[Mj]. As we\nmentioned previously, the values of the node Mod[Mj] denote the\ndifferent models of the other agent, and its distribution is the agent i\"s\nbelief over the models of j conditioned on the physical state. The\ntransformed level 1 I-ID is a traditional ID that may be solved\nus816 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\n(a) (b)\nFigure 3: (a) A generic two time-slice level l I-DID for agent i in a setting with one other agent j. Notice the dotted model update link that denotes\nthe update of the models of j and the distribution over the models over time. (b) The semantics of the model update link.\ning the standard expected utility maximization method [18]. This\nprocedure is carried out up to the level l I-ID whose solution gives\nthe non-empty set of optimal actions that the agent should perform\ngiven its belief. Notice that analogous to IDs, I-IDs are suitable for\nonline decision-making when the agent\"s current belief is known.\n4. INTERACTIVE DYNAMIC INFLUENCE\nDIAGRAMS\nInteractive dynamic influence diagrams (I-DIDs) extend I-IDs\n(and NIDs) to allow sequential decision-making over several time\nsteps. Just as DIDs are structured graphical representations of POMDPs,\nI-DIDs are the graphical online analogs for finitely nested I-POMDPs.\nI-DIDs may be used to optimize over a finite look-ahead given\ninitial beliefs while interacting with other, possibly similar, agents.\n4.1 Syntax\nWe depict a general two time-slice I-DID in Fig. 3(a). In\naddition to the model nodes and the dashed policy link, what\ndifferentiates an I-DID from a DID is the model update link shown as a\ndotted arrow in Fig. 3(a). We explained the semantics of the model\nnode and the policy link in the previous section; we describe the\nmodel updates next.\nThe update of the model node over time involves two steps: First,\ngiven the models at time t, we identify the updated set of models\nthat reside in the model node at time t + 1. Recall from Section 2\nthat an agent\"s intentional model includes its belief. Because the\nagents act and receive observations, their models are updated to\nreflect their changed beliefs. Since the set of optimal actions for\na model could include all the actions, and the agent may receive\nany one of |\u03a9j| possible observations, the updated set at time step\nt + 1 will have at most |Mt\nj,l\u22121||Aj||\u03a9j| models. Here, |Mt\nj,l\u22121|\nis the number of models at time step t, |Aj| and |\u03a9j| are the largest\nspaces of actions and observations respectively, among all the\nmodels. Second, we compute the new distribution over the updated\nmodels given the original distribution and the probability of the\nagent performing the action and receiving the observation that led\nto the updated model. These steps are a part of agent i\"s belief\nupdate formalized using Eq. 1.\nIn Fig. 3(b), we show how the dotted model update link is\nimplemented in the I-DID. If each of the two level l \u2212 1 models\nascribed to j at time step t results in one action, and j could make\none of two possible observations, then the model node at time step\nt + 1 contains four updated models (mt+1,1\nj,l\u22121 ,mt+1,2\nj,l\u22121 , mt+1,3\nj,l\u22121 , and\nmt+1,4\nj,l\u22121 ). These models differ in their initial beliefs, each of which\nis the result of j updating its beliefs due to its action and a possible\nobservation. The decision nodes in each of the I-DIDs or DIDs that\nrepresent the lower level models are mapped to the corresponding\nFigure 4: Transformed I-DID with the model nodes and model update\nlink replaced with the chance nodes and the relationships (in bold).\nchance nodes, as mentioned previously. Next, we describe how the\ndistribution over the updated set of models (the distribution over the\nchance node Mod[Mt+1\nj ] in Mt+1\nj,l\u22121) is computed. The probability\nthat j\"s updated model is, say mt+1,1\nj,l\u22121 , depends on the probability\nof j performing the action and receiving the observation that led to\nthis model, and the prior distribution over the models at time step\nt. Because the chance node At\nj assumes the distribution of each\nof the action nodes based on the value of Mod[Mt\nj ], the\nprobability of the action is given by this chance node. In order to obtain\nthe probability of j\"s possible observation, we introduce the chance\nnode Oj, which depending on the value of Mod[Mt\nj ] assumes the\ndistribution of the observation node in the lower level model\ndenoted by Mod[Mt\nj ]. Because the probability of j\"s observations\ndepends on the physical state and the joint actions of both agents,\nthe node Oj is linked with St+1\n, At\nj, and At\ni. 2\nAnalogous to At\nj,\nthe conditional probability table of Oj is also a multiplexer\nmodulated by Mod[Mt\nj ]. Finally, the distribution over the prior models\nat time t is obtained from the chance node, Mod[Mt\nj ] in Mt\nj,l\u22121.\nConsequently, the chance nodes, Mod[Mt\nj ], At\nj, and Oj, form the\nparents of Mod[Mt+1\nj ] in Mt+1\nj,l\u22121. Notice that the model update\nlink may be replaced by the dependency links between the chance\nnodes that constitute the model nodes in the two time slices. In\nFig. 4 we show the two time-slice I-DID with the model nodes\nreplaced by the chance nodes and the relationships between them.\nChance nodes and dependency links that not in bold are standard,\nusually found in DIDs.\nExpansion of the I-DID over more time steps requires the\nrepetition of the two steps of updating the set of models that form the\n2\nNote that Oj represents j\"s observation at time t + 1.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 817\nvalues of the model node and adding the relationships between the\nchance nodes, as many times as there are model update links. We\nnote that the possible set of models of the other agent j grows\nexponentially with the number of time steps. For example, after T steps,\nthere may be at most |Mt=1\nj,l\u22121|(|Aj||\u03a9j|)T \u22121\ncandidate models\nresiding in the model node.\n4.2 Solution\nAnalogous to I-IDs, the solution to a level l I-DID for agent i\nexpanded over T time steps may be carried out recursively. For the\npurpose of illustration, let l=1 and T=2. The solution method uses\nthe standard look-ahead technique, projecting the agent\"s action\nand observation sequences forward from the current belief state [17],\nand finding the possible beliefs that i could have in the next time\nstep. Because agent i has a belief over j\"s models as well, the\nlookahead includes finding out the possible models that j could have in\nthe future. Consequently, each of j\"s subintentional or level 0\nmodels (represented using a standard DID) in the first time step must be\nsolved to obtain its optimal set of actions. These actions are\ncombined with the set of possible observations that j could make in that\nmodel, resulting in an updated set of candidate models (that include\nthe updated beliefs) that could describe the behavior of j. Beliefs\nover this updated set of candidate models are calculated using the\nstandard inference methods using the dependency relationships\nbetween the model nodes as shown in Fig. 3(b). We note the recursive\nnature of this solution: in solving agent i\"s level 1 I-DID, j\"s level 0\nDIDs must be solved. If the nesting of models is deeper, all models\nat all levels starting from 0 are solved in a bottom-up manner.\nWe briefly outline the recursive algorithm for solving agent i\"s\nAlgorithm for solving I-DID\nInput : level l \u2265 1 I-ID or level 0 ID, T\nExpansion Phase\n1. For t from 1 to T \u2212 1 do\n2. If l \u2265 1 then\nPopulate Mt+1\nj,l\u22121\n3. For each mt\nj in Range(Mt\nj,l\u22121) do\n4. Recursively call algorithm with the l \u2212 1 I-ID (or ID)\nthat represents mt\nj and the horizon, T \u2212 t + 1\n5. Map the decision node of the solved I-ID (or ID),\nOPT(mt\nj), to a chance node Aj\n6. For each aj in OPT(mt\nj) do\n7. For each oj in Oj (part of mt\nj) do\n8. Update j\"s belief, bt+1\nj \u2190 SE(bt\nj, aj, oj)\n9. mt+1\nj \u2190 New I-ID (or ID) with bt+1\nj as the\ninitial belief\n10. Range(Mt+1\nj,l\u22121)\n\u222a\n\u2190 {mt+1\nj }\n11. Add the model node, Mt+1\nj,l\u22121, and the dependency links\nbetween Mt\nj,l\u22121 and Mt+1\nj,l\u22121 (shown in Fig. 3(b))\n12. Add the chance, decision, and utility nodes for t + 1 time\nslice and the dependency links between them\n13. Establish the CPTs for each chance node and utility node\nLook-Ahead Phase\n14. Apply the standard look-ahead and backup method to solve\nthe expanded I-DID\nFigure 5: Algorithm for solving a level l \u2265 0 I-DID.\nlevel l I-DID expanded over T time steps with one other agent j in\nFig. 5. We adopt a two-phase approach: Given an I-ID of level l\n(described previously in Section 3) with all lower level models also\nrepresented as I-IDs or IDs (if level 0), the first step is to expand\nthe level l I-ID over T time steps adding the dependency links and\nthe conditional probability tables for each node. We particularly\nfocus on establishing and populating the model nodes (lines 3-11).\nNote that Range(\u00b7) returns the values (lower level models) of the\nrandom variable given as input (model node). In the second phase,\nwe use a standard look-ahead technique projecting the action and\nobservation sequences over T time steps in the future, and backing\nup the utility values of the reachable beliefs. Similar to I-IDs, the\nI-DIDs reduce to DIDs in the absence of other agents.\nAs we mentioned previously, the 0-th level models are the\ntraditional DIDs. Their solutions provide probability distributions over\nactions of the agent modeled at that level to I-DIDs at level 1. Given\nprobability distributions over other agent\"s actions the level 1\nIDIDs can themselves be solved as DIDs, and provide probability\ndistributions to yet higher level models. Assume that the number\nof models considered at each level is bound by a number, M.\nSolving an I-DID of level l in then equivalent to solving O(Ml\n) DIDs.\n5. EXAMPLE APPLICATIONS\nTo illustrate the usefulness of I-DIDs, we apply them to three\nproblem domains. We describe, in particular, the formulation of\nthe I-DID and the optimal prescriptions obtained on solving it.\n5.1 Followership-Leadership in the Multiagent\nTiger Problem\nWe begin our illustrations of using I-IDs and I-DIDs with a slightly\nmodified version of the multiagent tiger problem discussed in [9].\nThe problem has two agents, each of which can open the right door\n(OR), the left door (OL) or listen (L). In addition to hearing growls\n(from the left (GL) or from the right (GR)) when they listen, the\nagents also hear creaks (from the left (CL), from the right (CR), or\nno creaks (S)), which noisily indicate the other agent\"s opening one\nof the doors. When any door is opened, the tiger persists in its\noriginal location with a probability of 95%. Agent i hears growls with\na reliability of 65% and creaks with a reliability of 95%. Agent j,\non the other hand, hears growls with a reliability of 95%. Thus,\nthe setting is such that agent i hears agent j opening doors more\nreliably than the tiger\"s growls. This suggests that i could use j\"s\nactions as an indication of the location of the tiger, as we discuss\nbelow. Each agent\"s preferences are as in the single agent game\ndiscussed in [13]. The transition, observation, and reward\nfunctions are shown in [16].\nA good indicator of the usefulness of normative methods for\ndecision-making like I-DIDs is the emergence of realistic social\nbehaviors in their prescriptions. In settings of the persistent\nmultiagent tiger problem that reflect real world situations, we demonstrate\nfollowership between the agents and, as shown in [15], deception\namong agents who believe that they are in a follower-leader type\nof relationship. In particular, we analyze the situational and\nepistemological conditions sufficient for their emergence. The\nfollowership behavior, for example, results from the agent knowing its own\nweaknesses, assessing the strengths, preferences, and possible\nbehaviors of the other, and realizing that its best for it to follow the\nother\"s actions in order to maximize its payoffs.\nLet us consider a particular setting of the tiger problem in which\nagent i believes that j\"s preferences are aligned with its own - both\nof them just want to get the gold - and j\"s hearing is more reliable\nin comparison to itself. As an example, suppose that j, on listening\ncan discern the tiger\"s location 95% of the times compared to i\"s\n65% accuracy. Additionally, agent i does not have any initial\ninformation about the tiger\"s location. In other words, i\"s single-level\nnested belief, bi,1, assigns 0.5 to each of the two locations of the\ntiger. In addition, i considers two models of j, which differ in j\"s\nflat level 0 initial beliefs. This is represented in the level 1 I-ID\nshown in Fig. 6(a). According to one model, j assigns a\nprobability of 0.9 that the tiger is behind the left door, while the other\n818 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nFigure 6: (a) Level 1 I-ID of agent i, (b) two level 0 IDs of agent j\nwhose decision nodes are mapped to the chance nodes, A1\nj , A2\nj , in (a).\nmodel assigns 0.1 to that location (see Fig. 6(b)). Agent i is\nundecided on these two models of j. If we vary i\"s hearing ability,\nand solve the corresponding level 1 I-ID expanded over three time\nsteps, we obtain the normative behavioral policies shown in Fig 7\nthat exhibit followership behavior. If i\"s probability of correctly\nhearing the growls is 0.65, then as shown in the policy in Fig. 7(a),\ni begins to conditionally follow j\"s actions: i opens the same door\nthat j opened previously iff i\"s own assessment of the tiger\"s\nlocation confirms j\"s pick. If i loses the ability to correctly interpret\nthe growls completely, it blindly follows j and opens the same door\nthat j opened previously (Fig. 7(b)).\nFigure 7: Emergence of (a) conditional followership, and (b) blind\nfollowership in the tiger problem. Behaviors of interest are in bold. * is\na wildcard, and denotes any one of the observations.\nWe observed that a single level of belief nesting - beliefs about\nthe other\"s models - was sufficient for followership to emerge in the\ntiger problem. However, the epistemological requirements for the\nemergence of leadership are more complex. For an agent, say j, to\nemerge as a leader, followership must first emerge in the other agent\ni. As we mentioned previously, if i is certain that its preferences\nare identical to those of j, and believes that j has a better sense\nof hearing, i will follow j\"s actions over time. Agent j emerges\nas a leader if it believes that i will follow it, which implies that\nj\"s belief must be nested two levels deep to enable it to recognize\nits leadership role. Realizing that i will follow presents j with an\nopportunity to influence i\"s actions in the benefit of the collective\ngood or its self-interest alone. For example, in the tiger problem,\nlet us consider a setting in which if both i and j open the correct\ndoor, then each gets a payoff of 20 that is double the original. If\nj alone selects the correct door, it gets the payoff of 10. On the\nother hand, if both agents pick the wrong door, their penalties are\ncut in half. In this setting, it is in both j\"s best interest as well as the\ncollective betterment for j to use its expertise in selecting the\ncorrect door, and thus be a good leader. However, consider a slightly\ndifferent problem in which j gains from i\"s loss and is penalized\nif i gains. Specifically, let i\"s payoff be subtracted from j\"s,\nindicating that j is antagonistic toward i - if j picks the correct door\nand i the wrong one, then i\"s loss of 100 becomes j\"s gain. Agent\nj believes that i incorrectly thinks that j\"s preferences are those\nthat promote the collective good and that it starts off by believing\nwith 99% confidence where the tiger is. Because i believes that its\npreferences are similar to those of j, and that j starts by believing\nalmost surely that one of the two is the correct location (two level\n0 models of j), i will start by following j\"s actions. We show i\"s\nnormative policy on solving its singly-nested I-DID over three time\nsteps in Fig. 8(a). The policy demonstrates that i will blindly\nfollow j\"s actions. Since the tiger persists in its original location with\na probability of 0.95, i will select the same door again. If j begins\nthe game with a 99% probability that the tiger is on the right,\nsolving j\"s I-DID nested two levels deep, results in the policy shown in\nFig. 8(b). Even though j is almost certain that OL is the correct\naction, it will start by selecting OR, followed by OL. Agent j\"s\nintention is to deceive i who, it believes, will follow j\"s actions, so\nas to gain $110 in the second time step, which is more than what j\nwould gain if it were to be honest.\nFigure 8: Emergence of deception between agents in the tiger\nproblem. Behaviors of interest are in bold. * denotes as before. (a) Agent\ni\"s policy demonstrating that it will blindly follow j\"s actions. (b) Even\nthough j is almost certain that the tiger is on the right, it will start by\nselecting OR, followed by OL, in order to deceive i.\n5.2 Altruism and Reciprocity in the Public\nGood Problem\nThe public good (PG) problem [7], consists of a group of M\nagents, each of whom must either contribute some resource to a\npublic pot or keep it for themselves. Since resources contributed to\nthe public pot are shared among all the agents, they are less\nvaluable to the agent when in the public pot. However, if all agents\nchoose to contribute their resources, then the payoff to each agent\nis more than if no one contributes. Since an agent gets its share of\nthe public pot irrespective of whether it has contributed or not, the\ndominating action is for each agent to not contribute, and instead\nfree ride on others\" contributions. However, behaviors of human\nplayers in empirical simulations of the PG problem differ from the\nnormative predictions. The experiments reveal that many players\ninitially contribute a large amount to the public pot, and continue\nto contribute when the PG problem is played repeatedly, though\nin decreasing amounts [4]. Many of these experiments [5] report\nthat a small core group of players persistently contributes to the\npublic pot even when all others are defecting. These experiments\nalso reveal that players who persistently contribute have altruistic\nor reciprocal preferences matching expected cooperation of others.\nFor simplicity, we assume that the game is played between M =\n2 agents, i and j. Let each agent be initially endowed with XT\namount of resources. While the classical PG game formulation\npermits each agent to contribute any quantity of resources (\u2264 XT ) to\nthe public pot, we simplify the action space by allowing two\npossible actions. Each agent may choose to either contribute (C) a fixed\namount of the resources, or not contribute. The latter action is\ndeThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 819\nnoted as defect (D). We assume that the actions are not observable\nto others. The value of resources in the public pot is discounted\nby ci for each agent i, where ci is the marginal private return. We\nassume that ci < 1 so that the agent does not benefit enough that\nit contributes to the public pot for private gain. Simultaneously,\nciM > 1, making collective contribution pareto optimal.\ni/j C D\nC 2ciXT , 2cjXT ciXT \u2212 cp, XT + cjXT \u2212 P\nD XT + ciXT \u2212 P, cjXT \u2212 cp XT , XT\nTable 1: The one-shot PG game with punishment.\nIn order to encourage contributions, the contributing agents\npunish free riders but incur a small cost for administering the\npunishment. Let P be the punishment meted out to the defecting agent\nand cp the non-zero cost of punishing for the contributing agent.\nFor simplicity, we assume that the cost of punishing is same for\nboth the agents. The one-shot PG game with punishment is shown\nin Table. 1. Let ci = cj, cp > 0, and if P > XT \u2212 ciXT , then\ndefection is no longer a dominating action. If P < XT \u2212 ciXT , then\ndefection is the dominating action for both. If P = XT \u2212 ciXT ,\nthen the game is not dominance-solvable.\nFigure 9: (a) Level 1 I-ID of agent i, (b) level 0 IDs of agent j with\ndecision nodes mapped to the chance nodes, A1\nj and A2\nj , in (a).\nWe formulate a sequential version of the PG problem with\npunishment from the perspective of agent i. Though in the repeated PG\ngame, the quantity in the public pot is revealed to all the agents after\neach round of actions, we assume in our formulation that it is\nhidden from the agents. Each agent may contribute a fixed amount, xc,\nor defect. An agent on performing an action receives an observation\nof plenty (PY) or meager (MR) symbolizing the state of the\npublic pot. Notice that the observations are also indirectly indicative of\nagent j\"s actions because the state of the public pot is influenced by\nthem. The amount of resources in agent i\"s private pot, is perfectly\nobservable to i. The payoffs are analogous to Table. 1.\nBorrowing from the empirical investigations of the PG problem [5], we\nconstruct level 0 IDs for j that model altruistic and non-altruistic\ntypes (Fig. 9(b)). Specifically, our altruistic agent has a high\nmarginal private return (cj is close to 1) and does not punish others\nwho defect. Let xc = 1 and the level 0 agent be punished half the\ntimes it defects. With one action remaining, both types of agents\nchoose to contribute to avoid being punished. With two actions\nto go, the altruistic type chooses to contribute, while the other\ndefects. This is because cj for the altruistic type is close to 1, thus the\nexpected punishment, 0.5P > (1 \u2212 cj), which the altruistic type\navoids. Because cj for the non-altruistic type is less, it prefers not\nto contribute. With three steps to go, the altruistic agent contributes\nto avoid punishment (0.5P > 2(1 \u2212 cj)), and the non-altruistic\ntype defects. For greater than three steps, while the altruistic agent\ncontinues to contribute to the public pot depending on how close\nits marginal private return is to 1, the non-altruistic type prescribes\ndefection.\nWe analyzed the decisions of an altruistic agent i modeled using\na level 1 I-DID expanded over 3 time steps. i ascribes the two level\n0 models, mentioned previously, to j (see Fig. 9). If i believes with\na probability 1 that j is altruistic, i chooses to contribute for each of\nthe three steps. This behavior persists when i is unaware of whether\nj is altruistic (Fig. 10(a)), and when i assigns a high probability to\nj being the non-altruistic type. However, when i believes with a\nprobability 1 that j is non-altruistic and will thus surely defect, i\nchooses to defect to avoid being punished and because its marginal\nprivate return is less than 1. These results demonstrate that the\nbehavior of our altruistic type resembles that found experimentally.\nThe non-altruistic level 1 agent chooses to defect regardless of how\nlikely it believes the other agent to be altruistic. We analyzed the\nbehavior of a reciprocal agent type that matches expected\ncooperation or defection. The reciprocal type\"s marginal private return\nis similar to that of the non-altruistic type, however, it obtains a\ngreater payoff when its action is similar to that of the other. We\nconsider the case when the reciprocal agent i is unsure of whether\nj is altruistic and believes that the public pot is likely to be half\nfull. For this prior belief, i chooses to defect. On receiving an\nobservation of plenty, i decides to contribute, while an observation of\nmeager makes it defect (Fig. 10(b)). This is because an\nobservation of plenty signals that the pot is likely to be greater than half\nfull, which results from j\"s action to contribute. Thus, among the\ntwo models ascribed to j, its type is likely to be altruistic making\nit likely that j will contribute again in the next time step. Agent i\ntherefore chooses to contribute to reciprocate j\"s action. An\nanalogous reasoning leads i to defect when it observes a meager pot.\nWith one action to go, i believing that j contributes, will choose to\ncontribute too to avoid punishment regardless of its observations.\nFigure 10: (a) An altruistic level 1 agent always contributes. (b) A\nreciprocal agent i starts off by defecting followed by choosing to\ncontribute or defect based on its observation of plenty (indicating that j is\nlikely altruistic) or meager (j is non-altruistic).\n5.3 Strategies in Two-Player Poker\nPoker is a popular zero sum card game that has received much\nattention among the AI research community as a testbed [2]. Poker is\nplayed among M \u2265 2 players in which each player receives a hand\nof cards from a deck. While several flavors of Poker with\nvarying complexity exist, we consider a simple version in which each\nplayer has three plys during which the player may either exchange\na card (E), keep the existing hand (K), fold (F) and withdraw from\nthe game, or call (C), requiring all players to show their hands. To\nkeep matters simple, let M = 2, and each player receive a hand\nconsisting of a single card drawn from the same suit. Thus, during\na showdown, the player who has the numerically larger card (2 is\nthe lowest, ace is the highest) wins the pot. During an exchange of\ncards, the discarded card is placed either in the L pile, indicating to\nthe other agent that it was a low numbered card less than 8, or in the\n820 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nH pile, indicating that the card had a rank greater than or equal to\n8. Notice that, for example, if a lower numbered card is discarded,\nthe probability of receiving a low card in exchange is now reduced.\nWe show the level 1 I-ID for the simplified two-player Poker in\nFig. 11. We considered two models (personality types) of agent j.\nThe conservative type believes that it is likely that its opponent has\na high numbered card in its hand. On the other hand, the\naggressive agent j believes with a high probability that its opponent has\na lower numbered card. Thus, the two types differ in their beliefs\nover their opponent\"s hand. In both these level 0 models, the\nopponent is assumed to perform its actions following a fixed, uniform\ndistribution. With three actions to go, regardless of its hand\n(unless it is an ace), the aggressive agent chooses to exchange its card,\nwith the intent of improving on its current hand. This is because it\nbelieves the other to have a low card, which improves its chances\nof getting a high card during the exchange. The conservative agent\nchooses to keep its card, no matter its hand because its chances of\ngetting a high card are slim as it believes that its opponent has one.\nFigure 11: (a) Level 1 I-ID of agent i. The observation reveals\ninformation about j\"s hand of the previous time step, (b) level 0 IDs of agent\nj whose decision nodes are mapped to the chance nodes, A1\nj , A2\nj , in (a).\nThe policy of a level 1 agent i who believes that each card\nexcept its own has an equal likelihood of being in j\"s hand (neutral\npersonality type) and j could be either an aggressive or\nconservative type, is shown in Fig. 12. i\"s own hand contains the card\nnumbered 8. The agent starts by keeping its card. On seeing that\nj did not exchange a card (N), i believes with probability 1 that j\nis conservative and hence will keep its cards. i responds by either\nkeeping its card or exchanging it because j is equally likely to have\na lower or higher card. If i observes that j discarded its card into\nthe L or H pile, i believes that j is aggressive. On observing L,\ni realizes that j had a low card, and is likely to have a high card\nafter its exchange. Because the probability of receiving a low card\nis high now, i chooses to keep its card. On observing H,\nbelieving that the probability of receiving a high numbered card is high,\ni chooses to exchange its card. In the final step, i chooses to call\nregardless of its observation history because its belief that j has a\nhigher card is not sufficiently high to conclude that its better to fold\nand relinquish the payoff. This is partly due to the fact that an\nobservation of, say, L resets the agent i\"s previous time step beliefs\nover j\"s hand to the low numbered cards only.\n6. DISCUSSION\nWe showed how DIDs may be extended to I-DIDs that enable\nonline sequential decision-making in uncertain multiagent settings.\nOur graphical representation of I-DIDs improves on the previous\nFigure 12: A level 1 agent i\"s three step policy in the Poker problem.\ni starts by believing that j is equally likely to be aggressive or\nconservative and could have any card in its hand with equal probability.\nwork significantly by being more transparent, semantically clear,\nand capable of being solved using standard algorithms that target\nDIDs. I-DIDs extend NIDs to allow sequential decision-making\nover multiple time steps in the presence of other interacting agents.\nI-DIDs may be seen as concise graphical representations for\nIPOMDPs providing a way to exploit problem structure and carry\nout online decision-making as the agent acts and observes given its\nprior beliefs. We are currently investigating ways to solve I-DIDs\napproximately with provable bounds on the solution quality.\nAcknowledgment: We thank Piotr Gmytrasiewicz for some\nuseful discussions related to this work. The first author would like\nto acknowledge the support of a UGARF grant.\n7. REFERENCES\n[1] R. J. Aumann. Interactive epistemology i: Knowledge. International\nJournal of Game Theory, 28:263-300, 1999.\n[2] D. Billings, A. Davidson, J. Schaeffer, and D. Szafron. The challenge\nof poker. AIJ, 2001.\n[3] A. Brandenburger and E. Dekel. Hierarchies of beliefs and common\nknowledge. Journal of Economic Theory, 59:189-198, 1993.\n[4] C. Camerer. Behavioral Game Theory: Experiments in Strategic\nInteraction. Princeton University Press, 2003.\n[5] E. Fehr and S. Gachter. Cooperation and punishment in public goods\nexperiments. American Economic Review, 90(4):980-994, 2000.\n[6] D. Fudenberg and D. K. Levine. The Theory of Learning in Games.\nMIT Press, 1998.\n[7] D. Fudenberg and J. Tirole. Game Theory. MIT Press, 1991.\n[8] Y. Gal and A. Pfeffer. A language for modeling agent\"s\ndecision-making processes in games. In AAMAS, 2003.\n[9] P. Gmytrasiewicz and P. Doshi. A framework for sequential planning\nin multiagent settings. JAIR, 24:49-79, 2005.\n[10] P. Gmytrasiewicz and E. Durfee. Rational coordination in\nmulti-agent environments. JAAMAS, 3(4):319-350, 2000.\n[11] J. C. Harsanyi. Games with incomplete information played by\nbayesian players. Management Science, 14(3):159-182, 1967.\n[12] R. A. Howard and J. E. Matheson. Influence diagrams. In R. A.\nHoward and J. E. Matheson, editors, The Principles and Applications\nof Decision Analysis. Strategic Decisions Group, Menlo Park, CA\n94025, 1984.\n[13] L. Kaelbling, M. Littman, and A. Cassandra. Planning and acting in\npartially observable stochastic domains. Artificial Intelligence\nJournal, 2, 1998.\n[14] D. Koller and B. Milch. Multi-agent influence diagrams for\nrepresenting and solving games. In IJCAI, pages 1027-1034, 2001.\n[15] K. Polich and P. Gmytrasiewicz. Interactive dynamic influence\ndiagrams. In GTDT Workshop, AAMAS, 2006.\n[16] B. Rathnas., P. Doshi, and P. J. Gmytrasiewicz. Exact solutions to\ninteractive pomdps using behavioral equivalence. In Autonomous\nAgents and Multi-Agent Systems Conference (AAMAS), 2006.\n[17] S. Russell and P. Norvig. Artificial Intelligence: A Modern Approach\n(Second Edition). Prentice Hall, 2003.\n[18] R. D. Shachter. Evaluating influence diagrams. Operations Research,\n34(6):871-882, 1986.\n[19] D. Suryadi and P. Gmytrasiewicz. Learning models of other agents\nusing influence diagrams. In UM, 1999.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 821", "keywords": "influence diagram;multiagent environment;influence diagram network;dynamic in\ufb02uence diagram;multiplexer;independence structure;dependency link;decision-make;online sequential decision-making;interactive dynamic influence diagram;nash equilibrium profile;agent online;network of influence diagram;policy link;multi-agent influence diagram;partially observable multiagent environment;interactive influence diagram;sequential decision-making;agent model;interactive partially observable markov decision process;graphical model"}
{"name": "train_I-66", "title": "Letting loose a SPIDER on a network of POMDPs: Generating quality guaranteed policies", "abstract": "Distributed Partially Observable Markov Decision Problems (Distributed POMDPs) are a popular approach for modeling multi-agent systems acting in uncertain domains. Given the significant complexity of solving distributed POMDPs, particularly as we scale up the numbers of agents, one popular approach has focused on approximate solutions. Though this approach is efficient, the algorithms within this approach do not provide any guarantees on solution quality. A second less popular approach focuses on global optimality, but typical results are available only for two agents, and also at considerable computational cost. This paper overcomes the limitations of both these approaches by providing SPIDER, a novel combination of three key features for policy generation in distributed POMDPs: (i) it exploits agent interaction structure given a network of agents (i.e. allowing easier scale-up to larger number of agents); (ii) it uses a combination of heuristics to speedup policy search; and (iii) it allows quality guaranteed approximations, allowing a systematic tradeoff of solution quality for time. Experimental results show orders of magnitude improvement in performance when compared with previous global optimal algorithms.", "fulltext": "1. INTRODUCTION\nDistributed Partially Observable Markov Decision Problems\n(Distributed POMDPs) are emerging as a popular approach for\nmodeling sequential decision making in teams operating under\nuncertainty [9, 4, 1, 2, 13]. The uncertainty arises on account of\nnondeterminism in the outcomes of actions and because the world state\nmay only be partially (or incorrectly) observable. Unfortunately, as\nshown by Bernstein et al. [3], the problem of finding the optimal\njoint policy for general distributed POMDPs is NEXP-Complete.\nResearchers have attempted two different types of approaches\ntowards solving these models. The first category consists of highly\nefficient approximate techniques, that may not reach globally\noptimal solutions [2, 9, 11]. The key problem with these techniques\nhas been their inability to provide any guarantees on the quality\nof the solution. In contrast, the second less popular category of\napproaches has focused on a global optimal result [13, 5, 10]. Though\nthese approaches obtain optimal solutions, they typically consider\nonly two agents. Furthermore, they fail to exploit structure in the\ninteractions of the agents and hence are severely hampered with\nrespect to scalability when considering more than two agents.\nTo address these problems with the existing approaches, we\npropose approximate techniques that provide guarantees on the\nquality of the solution while focussing on a network of more than two\nagents. We first propose the basic SPIDER (Search for Policies\nIn Distributed EnviRonments) algorithm. There are two key novel\nfeatures in SPIDER: (i) it is a branch and bound heuristic search\ntechnique that uses a MDP-based heuristic function to search for an\noptimal joint policy; (ii) it exploits network structure of agents by\norganizing agents into a Depth First Search (DFS) pseudo tree and\ntakes advantage of the independence in the different branches of the\nDFS tree. We then provide three enhancements to improve the\nefficiency of the basic SPIDER algorithm while providing guarantees\non the quality of the solution. The first enhancement uses\nabstractions for speedup, but does not sacrifice solution quality. In\nparticular, it initially performs branch and bound search on abstract\npolicies and then extends to complete policies. The second\nenhancement obtains speedups by sacrificing solution quality, but within\nan input parameter that provides the tolerable expected value\ndifference from the optimal solution. The third enhancement is again\nbased on bounding the search for efficiency, however with a\ntolerance parameter that is provided as a percentage of optimal.\nWe experimented with the sensor network domain presented in\nNair et al. [10], a domain representative of an important class of\nproblems with networks of agents working in uncertain\nenvironments. In our experiments, we illustrate that SPIDER dominates\nan existing global optimal approach called GOA [10], the only\nknown global optimal algorithm with demonstrated experimental\nresults for more than two agents. Furthermore, we demonstrate\nthat abstraction improves the performance of SPIDER significantly\n(while providing optimal solutions). We finally demonstrate a key\nfeature of SPIDER: by utilizing the approximation enhancements\nit enables principled tradeoffs in run-time versus solution quality.\n822\n978-81-904262-7-5 (RPS) c 2007 IFAAMAS\n2. DOMAIN: DISTRIBUTED SENSOR NETS\nDistributed sensor networks are a large, important class of\ndomains that motivate our work. This paper focuses on a set of target\ntracking problems that arise in certain types of sensor networks [6]\nfirst introduced in [10]. Figure 1 shows a specific problem instance\nwithin this type consisting of three sensors. Here, each sensor node\ncan scan in one of four directions: North, South, East or West (see\nFigure 1). To track a target and obtain associated reward, two\nsensors with overlapping scanning areas must coordinate by scanning\nthe same area simultaneously. In Figure 1, to track a target in\nLoc11, sensor1 needs to scan \u2018East\" and sensor2 needs to scan \u2018West\"\nsimultaneously. Thus, sensors have to act in a coordinated fashion.\nWe assume that there are two independent targets and that each\ntarget\"s movement is uncertain and unaffected by the sensor agents.\nBased on the area it is scanning, each sensor receives observations\nthat can have false positives and false negatives. The sensors\"\nobservations and transitions are independent of each other\"s actions\ne.g.the observations that sensor1 receives are independent of\nsensor2\"s actions. Each agent incurs a cost for scanning whether the\ntarget is present or not, but no cost if it turns off. Given the sensors\"\nobservational uncertainty, the targets\" uncertain transitions and the\ndistributed nature of the sensor nodes, these sensor nets provide a\nuseful domains for applying distributed POMDP models.\nFigure 1: A 3-chain sensor configuration\n3. BACKGROUND\n3.1 Model: Network Distributed POMDP\nThe ND-POMDP model was introduced in [10], motivated by\ndomains such as the sensor networks introduced in Section 2. It is\ndefined as the tuple S, A, P, \u03a9, O, R, b , where S = \u00d71\u2264i\u2264nSi \u00d7\nSu is the set of world states. Si refers to the set of local states of\nagent i and Su is the set of unaffectable states. Unaffectable state\nrefers to that part of the world state that cannot be affected by the\nagents\" actions, e.g. environmental factors like target locations that\nno agent can control. A = \u00d71\u2264i\u2264nAi is the set of joint actions,\nwhere Ai is the set of action for agent i.\nND-POMDP assumes transition independence, where the\ntransition function is defined as P(s, a, s ) = Pu(su, su) \u00b7 1\u2264i\u2264n\nPi(si, su, ai, si), where a = a1, . . . , an is the joint action\nperformed in state s = s1, . . . , sn, su and s = s1, . . . , sn, su is\nthe resulting state.\n\u03a9 = \u00d71\u2264i\u2264n\u03a9i is the set of joint observations where \u03a9i is\nthe set of observations for agents i. Observational independence\nis assumed in ND-POMDPs i.e., the joint observation function is\ndefined as O(s, a, \u03c9) = 1\u2264i\u2264n Oi(si, su, ai, \u03c9i), where s =\ns1, . . . , sn, su is the world state that results from the agents\nperforming a = a1, . . . , an in the previous state, and\n\u03c9 = \u03c91, . . . , \u03c9n \u2208 \u03a9 is the observation received in state s. This\nimplies that each agent\"s observation depends only on the\nunaffectable state, its local action and on its resulting local state.\nThe reward function, R, is defined as\nR(s, a) = l Rl(sl1, . . . , slr, su, al1, . . . , alr ), where each l\ncould refer to any sub-group of agents and r = |l|. Based on\nthe reward function, an interaction hypergraph is constructed. A\nhyper-link, l, exists between a subset of agents for all Rl that\ncomprise R. The interaction hypergraph is defined as G = (Ag, E),\nwhere the agents, Ag, are the vertices and E = {l|l \u2286 Ag \u2227\nRl is a component of R} are the edges.\nThe initial belief state (distribution over the initial state), b, is\ndefined as b(s) = bu(su) \u00b7 1\u2264i\u2264n bi(si), where bu and bi refer\nto the distribution over initial unaffectable state and agent i\"s initial\nbelief state, respectively. The goal in ND-POMDP is to compute\nthe joint policy \u03c0 = \u03c01, . . . , \u03c0n that maximizes team\"s expected\nreward over a finite horizon T starting from the belief state b.\nAn ND-POMDP is similar to an n-ary Distributed Constraint\nOptimization Problem (DCOP)[8, 12] where the variable at each\nnode represents the policy selected by an individual agent, \u03c0i with\nthe domain of the variable being the set of all local policies, \u03a0i.\nThe reward component Rl where |l| = 1 can be thought of as a\nlocal constraint while the reward component Rl where l > 1\ncorresponds to a non-local constraint in the constraint graph.\n3.2 Algorithm: Global Optimal Algorithm (GOA)\nIn previous work, GOA has been defined as a global optimal\nalgorithm for ND-POMDPs [10]. We will use GOA in our\nexperimental comparisons, since GOA is a state-of-the-art global optimal\nalgorithm, and in fact the only one with experimental results\navailable for networks of more than two agents. GOA borrows from a\nglobal optimal DCOP algorithm called DPOP[12]. GOA\"s message\npassing follows that of DPOP. The first phase is the UTIL\npropagation, where the utility messages, in this case values of policies,\nare passed up from the leaves to the root. Value for a policy at an\nagent is defined as the sum of best response values from its\nchildren and the joint policy reward associated with the parent policy.\nThus, given a policy for a parent node, GOA requires an agent to\niterate through all its policies, finding the best response policy and\nreturning the value to the parent - while at the parent node, to find\nthe best policy, an agent requires its children to return their best\nresponses to each of its policies. This UTIL propagation process\nis repeated at each level in the tree, until the root exhausts all its\npolicies. In the second phase of VALUE propagation, where the\noptimal policies are passed down from the root till the leaves.\nGOA takes advantage of the local interactions in the interaction\ngraph, by pruning out unnecessary joint policy evaluations\n(associated with nodes not connected directly in the tree). Since the\ninteraction graph captures all the reward interactions among agents\nand as this algorithm iterates through all the relevant joint policy\nevaluations, this algorithm yields a globally optimal solution.\n4. SPIDER\nAs mentioned in Section 3.1, an ND-POMDP can be treated as a\nDCOP, where the goal is to compute a joint policy that maximizes\nthe overall joint reward. The brute-force technique for computing\nan optimal policy would be to examine the expected values for all\npossible joint policies. The key idea in SPIDER is to avoid\ncomputation of expected values for the entire space of joint policies, by\nutilizing upper bounds on the expected values of policies and the\ninteraction structure of the agents.\nAkin to some of the algorithms for DCOP [8, 12], SPIDER has a\npre-processing step that constructs a DFS tree corresponding to the\ngiven interaction structure. Note that these DFS trees are pseudo\ntrees [12] that allow links between ancestors and children. We\nemploy the Maximum Constrained Node (MCN) heuristic used in the\nDCOP algorithm, ADOPT [8], however other heuristics (such as\nMLSP heuristic from [7]) can also be employed. MCN heuristic\ntries to place agents with more number of constraints at the top of\nthe tree. This tree governs how the search for the optimal joint\npolThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 823\nicy proceeds in SPIDER. The algorithms presented in this paper are\neasily extendable to hyper-trees, however for expository purposes,\nwe assume binary trees.\nSPIDER is an algorithm for centralized planning and distributed\nexecution in distributed POMDPs. In this paper, we employ the\nfollowing notation to denote policies and expected values:\nAncestors(i) \u21d2 agents from i to the root (not including i).\nTree(i) \u21d2 agents in the sub-tree (not including i) for which i is\nthe root.\n\u03c0root+\n\u21d2 joint policy of all agents.\n\u03c0i+\n\u21d2 joint policy of all agents in Tree(i) \u222a i.\n\u03c0i\u2212\n\u21d2 joint policy of agents that are in Ancestors(i).\n\u03c0i \u21d2 policy of the ith agent.\n\u02c6v[\u03c0i, \u03c0i\u2212\n] \u21d2 upper bound on the expected value for \u03c0i+\ngiven \u03c0i\nand policies of ancestor agents i.e. \u03c0i\u2212\n.\n\u02c6vj[\u03c0i, \u03c0i\u2212\n] \u21d2 upper bound on the expected value for \u03c0i+\nfrom the\njth child.\nv[\u03c0i, \u03c0i\u2212\n] \u21d2 expected value for \u03c0i given policies of ancestor agents,\n\u03c0i\u2212\n.\nv[\u03c0i+\n, \u03c0i\u2212\n] \u21d2 expected value for \u03c0i+\ngiven policies of ancestor\nagents, \u03c0i\u2212\n.\nvj[\u03c0i+\n, \u03c0i\u2212\n] \u21d2 expected value for \u03c0i+\nfrom the jth child.\nFigure 2: Execution of SPIDER, an example\n4.1 Outline of SPIDER\nSPIDER is based on the idea of branch and bound search, where\nthe nodes in the search tree represent partial/complete joint\npolicies. Figure 2 shows an example search tree for the SPIDER\nalgorithm, using an example of the three agent chain. Before SPIDER\nbegins its search we create a DFS tree (i.e. pseudo tree) from the\nthree agent chain, with the middle agent as the root of this tree.\nSPIDER exploits the structure of this DFS tree while engaging in\nits search. Note that in our example figure, each agent is assigned\na policy with T=2. Thus, each rounded rectange (search tree node)\nindicates a partial/complete joint policy, a rectangle indicates an\nagent and the ovals internal to an agent show its policy. Heuristic\nor actual expected value for a joint policy is indicated in the top\nright corner of the rounded rectangle. If the number is italicized\nand underlined, it implies that the actual expected value of the joint\npolicy is provided.\nSPIDER begins with no policy assigned to any of the agents\n(shown in the level 1 of the search tree). Level 2 of the search tree\nindicates that the joint policies are sorted based on upper bounds\ncomputed for root agent\"s policies. Level 3 shows one SPIDER\nsearch node with a complete joint policy (a policy assigned to each\nof the agents). The expected value for this joint policy is used to\nprune out the nodes in level 2 (the ones with upper bounds < 234)\nWhen creating policies for each non-leaf agent i, SPIDER\npotentially performs two steps:\n1. Obtaining upper bounds and sorting: In this step, agent i\ncomputes upper bounds on the expected values, \u02c6v[\u03c0i, \u03c0i\u2212\n] of the\njoint policies \u03c0i+\ncorresponding to each of its policy \u03c0i and fixed\nancestor policies. An MDP based heuristic is used to compute these\nupper bounds on the expected values. Detailed description about\nthis MDP heuristic is provided in Section 4.2. All policies of agent\ni, \u03a0i are then sorted based on these upper bounds (also referred to\nas heuristic values henceforth) in descending order. Exploration of\nthese policies (in step 2 below) are performed in this descending\norder. As indicated in the level 2 of the search tree (of Figure 2), all\nthe joint policies are sorted based on the heuristic values, indicated\nin the top right corner of each joint policy. The intuition behind\nsorting and then exploring policies in descending order of upper\nbounds, is that the policies with higher upper bounds could yield\njoint policies with higher expected values.\n2. Exploration and Pruning: Exploration implies computing\nthe best response joint policy \u03c0i+,\u2217\ncorresponding to fixed\nancestor policies of agent i, \u03c0i\u2212\n. This is performed by iterating through\nall policies of agent i i.e. \u03a0i and summing two quantities for each\npolicy: (i) the best response for all of i\"s children (obtained by\nperforming steps 1 and 2 at each of the child nodes); (ii) the expected\nvalue obtained by i for fixed policies of ancestors. Thus,\nexploration of a policy \u03c0i yields actual expected value of a joint policy,\n\u03c0i+\nrepresented as v[\u03c0i+\n, \u03c0i\u2212\n]. The policy with the highest\nexpected value is the best response policy.\nPruning refers to avoiding exploring all policies (or computing\nexpected values) at agent i by using the current best expected value,\nvmax\n[\u03c0i+\n, \u03c0i\u2212\n]. Henceforth, this vmax\n[\u03c0i+\n, \u03c0i\u2212\n] will be referred\nto as threshold. A policy, \u03c0i need not be explored if the upper\nbound for that policy, \u02c6v[\u03c0i, \u03c0i\u2212\n] is less than the threshold. This is\nbecause the expected value for the best joint policy attainable for\nthat policy will be less than the threshold.\nOn the other hand, when considering a leaf agent, SPIDER\ncomputes the best response policy (and consequently its expected value)\ncorresponding to fixed policies of its ancestors, \u03c0i\u2212\n. This is\naccomplished by computing expected values for each of the policies\n(corresponding to fixed policies of ancestors) and selecting the highest\nexpected value policy. In Figure 2, SPIDER assigns best response\npolicies to leaf agents at level 3. The policy for the left leaf agent is\nto perform action East at each time step in the policy, while the\npolicy for the right leaf agent is to perform Off at each time step.\nThese best response policies from the leaf agents yield an actual\nexpected value of 234 for the complete joint policy.\nAlgorithm 1 provides the pseudo code for SPIDER. This\nalgorithm outputs the best joint policy, \u03c0i+,\u2217\n(with an expected value\ngreater than threshold) for the agents in Tree(i). Lines 3-8\ncompute the best response policy of a leaf agent i, while lines 9-23\ncomputes the best response joint policy for agents in Tree(i). This\nbest response computation for a non-leaf agent i includes: (a)\nSorting of policies (in descending order) based on heuristic values on\nline 11; (b) Computing best response policies at each of the\nchildren for fixed policies of agent i in lines 16-20; and (c) Maintaining\n824 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nAlgorithm 1 SPIDER(i, \u03c0i\u2212\n, threshold)\n1: \u03c0i+,\u2217 \u2190 null\n2: \u03a0i \u2190 GET-ALL-POLICIES (horizon, Ai, \u03a9i)\n3: if IS-LEAF(i) then\n4: for all \u03c0i \u2208 \u03a0i do\n5: v[\u03c0i, \u03c0i\u2212] \u2190 JOINT-REWARD (\u03c0i, \u03c0i\u2212)\n6: if v[\u03c0i, \u03c0i\u2212] > threshold then\n7: \u03c0i+,\u2217 \u2190 \u03c0i\n8: threshold \u2190 v[\u03c0i, \u03c0i\u2212]\n9: else\n10: children \u2190 CHILDREN (i)\n11: \u02c6\u03a0i \u2190 UPPER-BOUND-SORT(i, \u03a0i, \u03c0i\u2212)\n12: for all \u03c0i \u2208 \u02c6\u03a0i do\n13: \u02dc\u03c0i+ \u2190 \u03c0i\n14: if \u02c6v[\u03c0i, \u03c0i\u2212] < threshold then\n15: Go to line 12\n16: for all j \u2208 children do\n17: jThres \u2190 threshold \u2212 v[\u03c0i, \u03c0i\u2212]\u2212\n\u03a3k\u2208children,k=j \u02c6vk[\u03c0i, \u03c0i\u2212]\n18: \u03c0j+,\u2217 \u2190 SPIDER(j, \u03c0i \u03c0i\u2212, jThres)\n19: \u02dc\u03c0i+ \u2190 \u02dc\u03c0i+ \u03c0j+,\u2217\n20: \u02c6vj[\u03c0i, \u03c0i\u2212] \u2190 v[\u03c0j+,\u2217, \u03c0i \u03c0i\u2212]\n21: if v[\u02dc\u03c0i+, \u03c0i\u2212] > threshold then\n22: threshold \u2190 v[\u02dc\u03c0i+, \u03c0i\u2212]\n23: \u03c0i+,\u2217 \u2190 \u02dc\u03c0i+\n24: return \u03c0i+,\u2217\nAlgorithm 2 UPPER-BOUND-SORT(i, \u03a0i, \u03c0i\u2212\n)\n1: children \u2190 CHILDREN (i)\n2: \u02c6\u03a0i \u2190 null /* Stores the sorted list */\n3: for all \u03c0i \u2208 \u03a0i do\n4: \u02c6v[\u03c0i, \u03c0i\u2212] \u2190 JOINT-REWARD (\u03c0i, \u03c0i\u2212)\n5: for all j \u2208 children do\n6: \u02c6vj[\u03c0i, \u03c0i\u2212] \u2190 UPPER-BOUND(i, j, \u03c0i \u03c0i\u2212)\n7: \u02c6v[\u03c0i, \u03c0i\u2212]\n+\n\u2190 \u02c6vj[\u03c0i, \u03c0i\u2212]\n8: \u02c6\u03a0i \u2190 INSERT-INTO-SORTED (\u03c0i, \u02c6\u03a0i)\n9: return \u02c6\u03a0i\nbest expected value, joint policy in lines 21-23.\nAlgorithm 2 provides the pseudo code for sorting policies based\non the upper bounds on the expected values of joint policies.\nExpected value for an agent i consists of two parts: value obtained\nfrom ancestors and value obtained from its children. Line 4\ncomputes the expected value obtained from ancestors of the agent\n(using JOINT-REWARD function), while lines 5-7 compute the\nheuristic value from the children. The sum of these two parts yields an\nupper bound on the expected value for agent i, and line 8 of the\nalgorithm sorts the policies based on these upper bounds.\n4.2 MDP based heuristic function\nThe heuristic function quickly provides an upper bound on the\nexpected value obtainable from the agents in Tree(i). The\nsubtree of agents is a distributed POMDP in itself and the idea here\nis to construct a centralized MDP corresponding to the (sub-tree)\ndistributed POMDP and obtain the expected value of the optimal\npolicy for this centralized MDP. To reiterate this in terms of the\nagents in DFS tree interaction structure, we assume full\nobservability for the agents in Tree(i) and for fixed policies of the agents in\n{Ancestors(i) \u222a i}, we compute the joint value \u02c6v[\u03c0i+\n, \u03c0i\u2212\n] .\nWe use the following notation for presenting the equations for\ncomputing upper bounds/heuristic values (for agents i and k):\nLet Ei\u2212\ndenote the set of links between agents in {Ancestors(i)\u222a\ni} and Tree(i), Ei+\ndenote the set of links between agents in\nTree(i). Also, if l \u2208 Ei\u2212\n, then l1 is the agent in {Ancestors(i)\u222a\ni} and l2 is the agent in Tree(i), that l connects together. We first\ncompact the standard notation:\not\nk =Ok(st+1\nk , st+1\nu , \u03c0k(\u03c9t\nk), \u03c9t+1\nk ) (1)\npt\nk =Pk(st\nk, st\nu, \u03c0k(\u03c9t\nk), st+1\nk ) \u00b7 ot\nk\npt\nu =P(st\nu, st+1\nu )\nst\nl = st\nl1\n, st\nl2\n, st\nu ; \u03c9t\nl = \u03c9t\nl1\n, \u03c9t\nl2\nrt\nl =Rl(st\nl , \u03c0l1\n(\u03c9t\nl1\n), \u03c0l2\n(\u03c9t\nl2\n))\nvt\nl =V t\n\u03c0l\n(st\nl , st\nu, \u03c9t\nl1\n, \u03c9t\nl2\n)\nDepending on the location of agent k in the agent tree we have the following\ncases:\nIF k \u2208 {Ancestors(i) \u222a i}, \u02c6pt\nk = pt\nk, (2)\nIF k \u2208 Tree(i), \u02c6pt\nk = Pk(st\nk, st\nu, \u03c0k(\u03c9t\nk), st+1\nk )\nIF l \u2208 Ei\u2212\n, \u02c6rt\nl = max\n{al2\n}\nRl(st\nl , \u03c0l1\n(\u03c9t\nl1\n), al2\n)\nIF l \u2208 Ei+\n, \u02c6rt\nl = max\n{al1\n,al2\n}\nRl(st\nl , al1\n, al2\n)\nThe value function for an agent i executing the joint policy \u03c0i+\nat\ntime \u03b7 \u2212 1 is provided by the equation:\nV \u03b7\u22121\n\u03c0i+ (s\u03b7\u22121\n, \u03c9\u03b7\u22121\n) = l\u2208Ei\u2212 v\u03b7\u22121\nl + l\u2208Ei+ v\u03b7\u22121\nl (3)\nwhere v\u03b7\u22121\nl = r\u03b7\u22121\nl + \u03c9\n\u03b7\nl\n,s\u03b7 p\u03b7\u22121\nl1\np\u03b7\u22121\nl2\np\u03b7\u22121\nu v\u03b7\nl\nAlgorithm 3 UPPER-BOUND (i, j, \u03c0j\u2212\n)\n1: val \u2190 0\n2: for all l \u2208 Ej\u2212 \u222a Ej+ do\n3: if l \u2208 Ej\u2212 then \u03c0l1\n\u2190 \u03c6\n4: for all s0\nl do\n5: val\n+\n\u2190 startBel[s0\nl ]\u00b7 UPPER-BOUND-TIME\n(i, s0\nl , j, \u03c0l1\n, )\n6: return val\nAlgorithm 4 UPPER-BOUND-TIME (i, st\nl , j, \u03c0l1 , \u03c9t\nl1\n)\n1: maxV al \u2190 \u2212\u221e\n2: for all al1\n, al2\ndo\n3: if l \u2208 Ei\u2212 and l \u2208 Ej\u2212 then al1\n\u2190 \u03c0l1\n(\u03c9t\nl1\n)\n4: val \u2190 GET-REWARD(st\nl , al1\n, al2\n)\n5: if t < \u03c0i.horizon \u2212 1 then\n6: for all st+1\nl , \u03c9t+1\nl1\ndo\n7: futV al\u2190pt\nu \u02c6pt\nl1\n\u02c6pt\nl2\n8: futV al\n\u2217\n\u2190 UPPER-BOUND-TIME(st+1\nl , j, \u03c0l1\n, \u03c9t\nl1\n\u03c9t+1\nl1\n)\n9: val\n+\n\u2190 futV al\n10: if val > maxV al then maxV al \u2190 val\n11: return maxV al\nUpper bound on the expected value for a link is computed by\nmodifying the equation 3 to reflect the full observability\nassumption. This involves removing the observational probability term\nfor agents in Tree(i) and maximizing the future value \u02c6v\u03b7\nl over the\nactions of those agents (in Tree(i)). Thus, the equation for the\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 825\ncomputation of the upper bound on a link l, is as follows:\nIF l \u2208 Ei\u2212\n, \u02c6v\u03b7\u22121\nl =\u02c6r\u03b7\u22121\nl + max\nal2\n\u03c9\n\u03b7\nl1\n,s\n\u03b7\nl\n\u02c6p\u03b7\u22121\nl1\n\u02c6p\u03b7\u22121\nl2\np\u03b7\u22121\nu \u02c6v\u03b7\nl\nIF l \u2208 Ei+\n, \u02c6v\u03b7\u22121\nl =\u02c6r\u03b7\u22121\nl + max\nal1\n,al2\ns\n\u03b7\nl\n\u02c6p\u03b7\u22121\nl1\n\u02c6p\u03b7\u22121\nl2\np\u03b7\u22121\nu \u02c6v\u03b7\nl\nAlgorithm 3 and Algorithm 4 provide the algorithm for computing\nupper bound for child j of agent i, using the equations descirbed\nabove. While Algorithm 4 computes the upper bound on a link\ngiven the starting state, Algorithm 3 sums the upper bound values\ncomputed over each of the links in Ei\u2212\n\u222a Ei+\n.\n4.3 Abstraction\nAlgorithm 5 SPIDER-ABS(i, \u03c0i\u2212\n, threshold)\n1: \u03c0i+,\u2217 \u2190 null\n2: \u03a0i \u2190 GET-POLICIES (<>, 1)\n3: if IS-LEAF(i) then\n4: for all \u03c0i \u2208 \u03a0i do\n5: absHeuristic \u2190 GET-ABS-HEURISTIC (\u03c0i, \u03c0i\u2212)\n6: absHeuristic\n\u2217\n\u2190 (timeHorizon \u2212 \u03c0i.horizon)\n7: if \u03c0i.horizon = timeHorizon and \u03c0i.absNodes = 0 then\n8: v[\u03c0i, \u03c0i\u2212] \u2190 JOINT-REWARD (\u03c0i, \u03c0i\u2212)\n9: if v[\u03c0i, \u03c0i\u2212] > threshold then\n10: \u03c0i+,\u2217 \u2190 \u03c0i; threshold \u2190 v[\u03c0i, \u03c0i\u2212]\n11: else if v[\u03c0i, \u03c0i\u2212] + absHeuristic > threshold then\n12: \u02c6\u03a0i \u2190 EXTEND-POLICY (\u03c0i, \u03c0i.absNodes + 1)\n13: \u03a0i\n+\n\u2190 INSERT-SORTED-POLICIES ( \u02c6\u03a0i)\n14: REMOVE(\u03c0i)\n15: else\n16: children \u2190 CHILDREN (i)\n17: \u03a0i \u2190 UPPER-BOUND-SORT(i, \u03a0i, \u03c0i\u2212)\n18: for all \u03c0i \u2208 \u03a0i do\n19: \u02dc\u03c0i+ \u2190 \u03c0i\n20: absHeuristic \u2190 GET-ABS-HEURISTIC (\u03c0i, \u03c0i\u2212)\n21: absHeuristic\n\u2217\n\u2190 (timeHorizon \u2212 \u03c0i.horizon)\n22: if \u03c0i.horizon = timeHorizon and \u03c0i.absNodes = 0 then\n23: if \u02c6v[\u03c0i, \u03c0i\u2212] < threshold and \u03c0i.absNodes = 0 then\n24: Go to line 19\n25: for all j \u2208 children do\n26: jThres \u2190 threshold \u2212 v[\u03c0i, \u03c0i\u2212]\u2212\n\u03a3k\u2208children,k=j \u02c6vk[\u03c0i, \u03c0i\u2212]\n27: \u03c0j+,\u2217 \u2190 SPIDER(j, \u03c0i \u03c0i\u2212, jThres)\n28: \u02dc\u03c0i+ \u2190 \u02dc\u03c0i+ \u03c0j+,\u2217; \u02c6vj[\u03c0i, \u03c0i\u2212] \u2190 v[\u03c0j+,\u2217, \u03c0i \u03c0i\u2212]\n29: if v[\u02dc\u03c0i+, \u03c0i\u2212] > threshold then\n30: threshold \u2190 v[\u02dc\u03c0i+, \u03c0i\u2212]; \u03c0i+,\u2217 \u2190 \u02dc\u03c0i+\n31: else if \u02c6v[\u03c0i+, \u03c0i\u2212] + absHeuristic > threshold then\n32: \u02c6\u03a0i \u2190 EXTEND-POLICY (\u03c0i, \u03c0i.absNodes + 1)\n33: \u03a0i\n+\n\u2190 INSERT-SORTED-POLICIES (\u02c6\u03a0i)\n34: REMOVE(\u03c0i)\n35: return \u03c0i+,\u2217\nIn SPIDER, the exploration/pruning phase can only begin after\nthe heuristic (or upper bound) computation and sorting for the\npolicies has ended. We provide an approach to possibly circumvent the\nexploration of a group of policies based on heuristic computation\nfor one abstract policy, thus leading to an improvement in runtime\nperformance (without loss in solution quality). The important steps\nin this technique are defining the abstract policy and how heuristic\nvalues are computated for the abstract policies. In this paper, we\npropose two types of abstraction:\n1. Horizon Based Abstraction (HBA): Here, the abstract policy is\ndefined as a shorter horizon policy. It represents a group of longer\nhorizon policies that have the same actions as the abstract policy\nfor times less than or equal to the horizon of the abstract policy.\nIn Figure 3(a), a T=1 abstract policy that performs East action,\nrepresents a group of T=2 policies, that perform East in the first\ntime step.\nFor HBA, there are two parts to heuristic computation:\n(a) Computing the upper bound for the horizon of the abstract\npolicy. This is same as the heuristic computation defined by the\nGETHEURISTIC() algorithm for SPIDER, however with a shorter time\nhorizon (horizon of the abstract policy).\n(b) Computing the maximum possible reward that can be\naccumulated in one time step (using GET-ABS-HEURISTIC()) and\nmultiplying it by the number of time steps to time horizon. This\nmaximum possible reward (for one time step) is obtained by iterating\nthrough all the actions of all the agents in Tree(i) and computing\nthe maximum joint reward for any joint action.\nSum of (a) and (b) is the heuristic value for a HBA abstract policy.\n2. Node Based Abstraction (NBA): Here an abstract policy is\nobtained by not associating actions to certain nodes of the policy tree.\nUnlike in HBA, this implies multiple levels of abstraction. This is\nillustrated in Figure 3(b), where there are T=2 policies that do not\nhave an action for observation \u2018TP\". These incomplete T=2\npolicies are abstractions for T=2 complete policies. Increased levels of\nabstraction leads to faster computation of a complete joint policy,\n\u03c0root+\nand also to shorter heuristic computation and exploration,\npruning phases. For NBA, the heuristic computation is similar to\nthat of a normal policy, except in cases where there is no action\nassociated with policy nodes. In such cases, the immediate reward\nis taken as Rmax (maximum reward for any action).\nWe combine both the abstraction techniques mentioned above\ninto one technique, SPIDER-ABS. Algorithm 5 provides the\nalgorithm for this abstraction technique. For computing optimal joint\npolicy with SPIDER-ABS, a non-leaf agent i initially examines all\nabstract T=1 policies (line 2) and sorts them based on abstract\npolicy heuristic computations (line 17). The abstraction horizon is\ngradually increased and these abstract policies are then explored\nin descending order of heuristic values and ones that have heuristic\nvalues less than the threshold are pruned (lines 23-24). Exploration\nin SPIDER-ABS has the same definition as in SPIDER if the policy\nbeing explored has a horizon of policy computation which is equal\nto the actual time horizon and if all the nodes of the policy have an\naction associated with them (lines 25-30). However, if those\nconditions are not met, then it is substituted by a group of policies that it\nrepresents (using EXTEND-POLICY () function) (lines 31-32).\nEXTEND-POLICY() function is also responsible for\ninitializing the horizon and absNodes of a policy. absNodes\nrepresents the number of nodes at the last level in the policy tree,\nthat do not have an action assigned to them. If \u03c0i.absNodes =\n|\u03a9i|\u03c0i.horizon\u22121\n(i.e. total number of policy nodes possible at\n\u03c0i.horizon) , then \u03c0i.absNodes is set to zero and \u03c0i.horizon is\nincreased by 1. Otherwise, \u03c0i.absNodes is increased by 1. Thus,\nthis function combines both HBA and NBA by using the policy\nvariables, horizon and absNodes. Before substituting the abstract\npolicy with a group of policies, those policies are sorted based on\nheuristic values (line 33). Similar type of abstraction based best\nresponse computation is adopted at leaf agents (lines 3-14).\n4.4 Value ApproXimation (VAX)\nIn this section, we present an approximate enhancement to\nSPIDER called VAX. The input to this technique is an approximation\nparameter , which determines the difference from the optimal\nsolution quality. This approximation parameter is used at each agent\nfor pruning out joint policies. The pruning mechanism in SPIDER\nand SPIDER-Abs dictates that a joint policy be pruned only if the\nthreshold is exactly greater than the heuristic value. However, the\n826 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nFigure 3: Example of abstraction for (a) HBA (Horizon Based Abstraction) and (b) NBA (Node Based Abstraction)\nidea in this technique is to prune out joint a policy if the following\ncondition is satisfied: threshold + > \u02c6v[\u03c0i\n, \u03c0i\u2212\n]. Apart from the\npruning condition, VAX is the same as SPIDER/SPIDER-ABS.\nIn the example of Figure 2, if the heuristic value for the second\njoint policy (or second search tree node) in level 2 were 238 instead\nof 232, then that policy could not be be pruned using SPIDER or\nSPIDER-Abs. However, in VAX with an approximation parameter\nof 5, the joint policy in consideration would also be pruned. This is\nbecause the threshold (234) at that juncture plus the approximation\nparameter (5), i.e. 239 would have been greater than the heuristic\nvalue for that joint policy (238). It can be noted from the example\n(just discussed) that this kind of pruning can lead to fewer\nexplorations and hence lead to an improvement in the overall run-time\nperformance. However, this can entail a sacrifice in the quality of\nthe solution because this technique can prune out a candidate\noptimal solution. A bound on the error introduced by this approximate\nalgorithm as a function of , is provided by Proposition 3.\n4.5 Percentage ApproXimation (PAX)\nIn this section, we present the second approximation\nenhancement over SPIDER called PAX. Input to this technique is a\nparameter, \u03b4 that represents the minimum percentage of the optimal\nsolution quality that is desired. Output of this technique is a policy\nwith an expected value that is at least \u03b4% of the optimal solution\nquality. A policy is pruned if the following condition is satisfied:\nthreshold > \u03b4\n100\n\u02c6v[\u03c0i\n, \u03c0i\u2212\n]. Like in VAX, the only difference\nbetween PAX and SPIDER/SPIDER-ABS is this pruning condition.\nAgain in Figure 2, if the heuristic value for the second search\ntree node in level 2 were 238 instead of 232, then PAX with an\ninput parameter of 98% would be able to prune that search tree node\n(since 98\n100\n\u2217238 < 234). This type of pruning leads to fewer\nexplorations and hence an improvement in run-time performance, while\npotentially leading to a loss in quality of the solution. Proposition 4\nprovides the bound on quality loss.\n4.6 Theoretical Results\nPROPOSITION 1. Heuristic provided using the centralized MDP\nheuristic is admissible.\nProof. For the value provided by the heuristic to be admissible,\nit should be an over estimate of the expected value for a joint policy.\nThus, we need to show that: For l \u2208 Ei+\n\u222a Ei\u2212\n: \u02c6vt\nl \u2265 vt\nl (refer to\nnotation in Section 4.2)\nWe use mathematical induction on t to prove this.\nBase case: t = T \u2212 1. Irrespective of whether l \u2208 Ei\u2212\nor l \u2208\nEi+\n, \u02c6rt\nl is computed by maximizing over all actions of the agents\nin Tree(i), while rt\nl is computed for fixed policies of the same\nagents. Hence, \u02c6rt\nl \u2265 rt\nl and also \u02c6vt\nl \u2265 vt\nl .\nAssumption: Proposition holds for t = \u03b7, where 1 \u2264 \u03b7 < T \u2212 1.\nWe now have to prove that the proposition holds for t = \u03b7 \u2212 1.\nWe show the proof for l \u2208 Ei\u2212\nand similar reasoning can be\nadopted to prove for l \u2208 Ei+\n. The heuristic value function for\nl \u2208 Ei\u2212\nis provided by the following equation:\n\u02c6v\u03b7\u22121\nl =\u02c6r\u03b7\u22121\nl + max\nal2\n\u03c9\n\u03b7\nl1\n,s\n\u03b7\nl\n\u02c6p\u03b7\u22121\nl1\n\u02c6p\u03b7\u22121\nl2\np\u03b7\u22121\nu \u02c6v\u03b7\nl\nRewriting the RHS and using Eqn 2 (in Section 4.2)\n=\u02c6r\u03b7\u22121\nl + max\nal2\n\u03c9\n\u03b7\nl1\n,s\n\u03b7\nl\np\u03b7\u22121\nu p\u03b7\u22121\nl1\n\u02c6p\u03b7\u22121\nl2\n\u02c6v\u03b7\nl\n=\u02c6r\u03b7\u22121\nl +\n\u03c9\n\u03b7\nl1\n,s\n\u03b7\nl\np\u03b7\u22121\nu p\u03b7\u22121\nl1\nmax\nal2\n\u02c6p\u03b7\u22121\nl2\n\u02c6v\u03b7\nl\nSince maxal2\n\u02c6p\u03b7\u22121\nl2\n\u02c6v\u03b7\nl \u2265 \u03c9l2\no\u03b7\u22121\nl2\n\u02c6p\u03b7\u22121\nl2\n\u02c6v\u03b7\nl and p\u03b7\u22121\nl2\n= o\u03b7\u22121\nl2\n\u02c6p\u03b7\u22121\nl2\n\u2265\u02c6r\u03b7\u22121\nl +\n\u03c9\n\u03b7\nl1\n,s\n\u03b7\nl\np\u03b7\u22121\nu p\u03b7\u22121\nl1\n\u03c9l2\np\u03b7\u22121\nl2\n\u02c6v\u03b7\nl\nSince \u02c6v\u03b7\nl \u2265 v\u03b7\nl (from the assumption)\n\u2265\u02c6r\u03b7\u22121\nl +\n\u03c9\n\u03b7\nl1\n,s\n\u03b7\nl\np\u03b7\u22121\nu p\u03b7\u22121\nl1\n\u03c9l2\np\u03b7\u22121\nl2\nv\u03b7\nl\nSince \u02c6r\u03b7\u22121\nl \u2265 r\u03b7\u22121\nl (by definition)\n\u2265r\u03b7\u22121\nl +\n\u03c9\n\u03b7\nl1\n,s\n\u03b7\nl\np\u03b7\u22121\nu p\u03b7\u22121\nl1\n\u03c9l2\np\u03b7\u22121\nl2\nv\u03b7\nl\n=r\u03b7\u22121\nl +\n(\u03c9\n\u03b7\nl\n,s\n\u03b7\nl\n)\np\u03b7\u22121\nu p\u03b7\u22121\nl1\np\u03b7\u22121\nl2\nv\u03b7\nl = v\u03b7\u22121\nl\nThus proved.\nPROPOSITION 2. SPIDER provides an optimal solution.\nProof. SPIDER examines all possible joint policies given the\ninteraction structure of the agents. The only exception being when\na joint policy is pruned based on the heuristic value. Thus, as long\nas a candidate optimal policy is not pruned, SPIDER will return an\noptimal policy. As proved in Proposition 1, the expected value for\na joint policy is always an upper bound. Hence when a joint policy\nis pruned, it cannot be an optimal solution.\nPROPOSITION 3. Error bound on the solution quality for VAX\n(implemented over SPIDER-ABS) with an approximation\nparameter of is \u03c1 , where \u03c1 is the number of leaf nodes in the DFS tree.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 827\nProof. We prove this proposition using mathematical induction\non the depth of the DFS tree.\nBase case: depth = 1 (i.e. one node). Best response is\ncomputed by iterating through all policies, \u03a0k. A policy,\u03c0k is pruned\nif \u02c6v[\u03c0k, \u03c0k\u2212\n] < threshold + . Thus the best response policy\ncomputed by VAX would be at most away from the optimal best\nresponse. Hence the proposition holds for the base case.\nAssumption: Proposition holds for d, where 1 \u2264 depth \u2264 d.\nWe now have to prove that the proposition holds for d + 1.\nWithout loss of generality, lets assume that the root node of this\ntree has k children. Each of this children is of depth \u2264 d, and hence\nfrom the assumption, the error introduced in kth child is \u03c1k , where\n\u03c1k is the number of leaf nodes in kth child of the root. Therefore,\n\u03c1 = k \u03c1k, where \u03c1 is the number of leaf nodes in the tree.\nIn SPIDER-ABS, threshold at the root agent, thresspider =\nk v[\u03c0k+\n, \u03c0k\u2212\n]. However, with VAX the threshold at the root\nagent will be (in the worst case), threshvax = k v[\u03c0k+\n, \u03c0k\u2212\n]\u2212\nk \u03c1k . Hence, with VAX a joint policy is pruned at the root\nagent if \u02c6v[\u03c0root, \u03c0root\u2212\n] < threshvax + \u21d2 \u02c6v[\u03c0root, \u03c0root\u2212\n] <\nthreshspider \u2212 (( k \u03c1k) \u2212 1) \u2264 threshspider \u2212 ( k \u03c1k) \u2264\nthreshspider \u2212 \u03c1 . Hence proved.\nPROPOSITION 4. For PAX (implemented over SPIDER-ABS) with\nan input parameter of \u03b4, the solution quality is at least \u03b4\n100\nv[\u03c0root+,\u2217\n],\nwhere v[\u03c0root+,\u2217\n] denotes the optimal solution quality.\nProof. We prove this proposition using mathematical induction\non the depth of the DFS tree.\nBase case: depth = 1 (i.e. one node). Best response is\ncomputed by iterating through all policies, \u03a0k. A policy,\u03c0k is pruned\nif \u03b4\n100\n\u02c6v[\u03c0k, \u03c0k\u2212\n] < threshold. Thus the best response policy\ncomputed by PAX would be at least \u03b4\n100\ntimes the optimal best\nresponse. Hence the proposition holds for the base case.\nAssumption: Proposition holds for d, where 1 \u2264 depth \u2264 d.\nWe now have to prove that the proposition holds for d + 1.\nWithout loss of generality, lets assume that the root node of\nthis tree has k children. Each of this children is of depth \u2264 d,\nand hence from the assumption, the solution quality in the kth\nchild is at least \u03b4\n100\nv[\u03c0k+,\u2217\n, \u03c0k\u2212\n] for PAX. With SPIDER-ABS,\na joint policy is pruned at the root agent if \u02c6v[\u03c0root, \u03c0root\u2212\n] <\nk v[\u03c0k+,\u2217\n, \u03c0k\u2212\n]. However with PAX, a joint policy is pruned if\n\u03b4\n100\n\u02c6v[\u03c0root, \u03c0root\u2212\n] < k\n\u03b4\n100\nv[\u03c0k+,\u2217\n, \u03c0k\u2212\n] \u21d2 \u02c6v[\u03c0root, \u03c0root\u2212\n] <\nk v[\u03c0k+,\u2217\n, \u03c0k\u2212\n]. Since the pruning condition at the root agent in\nPAX is the same as the one in SPIDER-ABS, there is no error\nintroduced at the root agent and all the error is introduced in the\nchildren. Thus, overall solution quality is at least \u03b4\n100\nof the optimal\nsolution. Hence proved.\n5. EXPERIMENTAL RESULTS\nAll our experiments were conducted on the sensor network\ndomain from Section 2. The five network configurations employed\nare shown in Figure 4. Algorithms that we experimented with\nare GOA, SPIDER, SPIDER-ABS, PAX and VAX. We compare\nagainst GOA because it is the only global optimal algorithm that\nconsiders more than two agents. We performed two sets of\nexperiments: (i) firstly, we compared the run-time performance of the\nabove algorithms and (ii) secondly, we experimented with PAX and\nVAX to study the tradeoff between run-time and solution quality.\nExperiments were terminated after 10000 seconds1\n.\nFigure 5(a) provides run-time comparisons between the optimal\nalgorithms GOA, SPIDER, SPIDER-Abs and the approximate\nalgorithms, PAX ( of 30) and VAX(\u03b4 of 80). X-axis denotes the\n1\nMachine specs for all experiments: Intel Xeon 3.6 GHZ processor,\n2GB RAM\nsensor network configuration used, while Y-axis indicates the\nruntime (on a log-scale). The time horizon of policy computation was\n3. For each configuration (3-chain, 4-chain, 4-star and 5-star), there\nare five bars indicating the time taken by GOA, SPIDER,\nSPIDERAbs, PAX and VAX. GOA did not terminate within the time limit\nfor 4-star and 5-star configurations. SPIDER-Abs dominated the\nSPIDER and GOA for all the configurations. For instance, in the\n3chain configuration, SPIDER-ABS provides 230-fold speedup over\nGOA and 2-fold speedup over SPIDER and for the 4-chain\nconfiguration it provides 58-fold speedup over GOA and 2-fold speedup\nover SPIDER. The two approximation approaches, VAX and PAX\nprovided further improvement in performance over SPIDER-Abs.\nFor instance, in the 5-star configuration VAX provides a 15-fold\nspeedup and PAX provides a 8-fold speedup over SPIDER-Abs.\nFigures 5(b) provides a comparison of the solution quality\nobtained using the different algorithms for the problems tested in\nFigure 5(a). X-axis denotes the sensor network configuration while\nY-axis indicates the solution quality. Since GOA, SPIDER, and\nSPIDER-Abs are all global optimal algorithms, the solution\nquality is the same for all those algorithms. For 5-P configuration,\nthe global optimal algorithms did not terminate within the limit of\n10000 seconds, so the bar for optimal quality indicates an upper\nbound on the optimal solution quality. With both the\napproximations, we obtained a solution quality that was close to the optimal\nsolution quality. In 3-chain and 4-star configurations, it is\nremarkable that both PAX and VAX obtained almost the same actual\nquality as the global optimal algorithms, despite the approximation\nparameter and \u03b4. For other configurations as well, the loss in quality\nwas less than 20% of the optimal solution quality.\nFigure 5(c) provides the time to solution with PAX (for\nvarying epsilons). X-axis denotes the approximation parameter, \u03b4\n(percentage to optimal) used, while Y-axis denotes the time taken to\ncompute the solution (on a log-scale). The time horizon for all\nthe configurations was 4. As \u03b4 was decreased from 70 to 30, the\ntime to solution decreased drastically. For instance, in the 3-chain\ncase there was a total speedup of 170-fold when the \u03b4 was changed\nfrom 70 to 30. Interestingly, even with a low \u03b4 of 30%, the actual\nsolution quality remained equal to the one obtained at 70%.\nFigure 5(d) provides the time to solution for all the\nconfigurations with VAX (for varying epsilons). X-axis denotes the\napproximation parameter, used, while Y-axis denotes the time taken to\ncompute the solution (on a log-scale). The time horizon for all the\nconfigurations was 4. As was increased, the time to solution\ndecreased drastically. For instance, in the 4-star case there was a total\nspeedup of 73-fold when the was changed from 60 to 140. Again,\nthe actual solution quality did not change with varying epsilon.\nFigure 4: Sensor network configurations\n828 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nFigure 5: Comparison of GOA, SPIDER, SPIDER-Abs and VAX for T = 3 on (a) Runtime and (b) Solution quality; (c) Time to solution for PAX\nwith varying percentage to optimal for T=4 (d) Time to solution for VAX with varying epsilon for T=4\n6. SUMMARY AND RELATED WORK\nThis paper presents four algorithms SPIDER, SPIDER-ABS, PAX\nand VAX that provide a novel combination of features for\npolicy search in distributed POMDPs: (i) exploiting agent interaction\nstructure given a network of agents (i.e. easier scale-up to larger\nnumber of agents); (ii) using branch and bound search with an MDP\nbased heuristic function; (iii) utilizing abstraction to improve\nruntime performance without sacrificing solution quality; (iv)\nproviding a priori percentage bounds on quality of solutions using PAX;\nand (v) providing expected value bounds on the quality of solutions\nusing VAX. These features allow for systematic tradeoff of solution\nquality for run-time in networks of agents operating under\nuncertainty. Experimental results show orders of magnitude\nimprovement in performance over previous global optimal algorithms.\nResearchers have typically employed two types of techniques\nfor solving distributed POMDPs. The first set of techniques\ncompute global optimal solutions. Hansen et al. [5] present an\nalgorithm based on dynamic programming and iterated elimination of\ndominant policies, that provides optimal solutions for distributed\nPOMDPs. Szer et al. [13] provide an optimal heuristic search\nmethod for solving Decentralized POMDPs. This algorithm is based\non the combination of a classical heuristic search algorithm, A\u2217\nand\ndecentralized control theory. The key differences between SPIDER\nand MAA* are: (a) Enhancements to SPIDER (VAX and PAX)\nprovide for quality guaranteed approximations, while MAA* is a\nglobal optimal algorithm and hence involves significant\ncomputational complexity; (b) Due to MAA*\"s inability to exploit\ninteraction structure, it was illustrated only with two agents. However,\nSPIDER has been illustrated for networks of agents; and (c)\nSPIDER explores the joint policy one agent at a time, while MAA*\nexpands it one time step at a time (simultaneously for all the agents).\nThe second set of techniques seek approximate policies.\nEmeryMontemerlo et al. [4] approximate POSGs as a series of one-step\nBayesian games using heuristics to approximate future value,\ntrading off limited lookahead for computational efficiency, resulting in\nlocally optimal policies (with respect to the selected heuristic). Nair\net al. [9]\"s JESP algorithm uses dynamic programming to reach a\nlocal optimum solution for finite horizon decentralized POMDPs.\nPeshkin et al. [11] and Bernstein et al. [2] are examples of policy\nsearch techniques that search for locally optimal policies. Though\nall the above techniques improve the efficiency of policy\ncomputation considerably, they are unable to provide error bounds on the\nquality of the solution. This aspect of quality bounds differentiates\nSPIDER from all the above techniques.\nAcknowledgements. This material is based upon work\nsupported by the Defense Advanced Research Projects Agency (DARPA),\nthrough the Department of the Interior, NBC, Acquisition Services\nDivision under Contract No. NBCHD030010. The views and\nconclusions contained in this document are those of the authors, and\nshould not be interpreted as representing the official policies, either\nexpressed or implied, of the Defense Advanced Research Projects\nAgency or the U.S. Government.\n7. REFERENCES\n[1] R. Becker, S. Zilberstein, V. Lesser, and C.V. Goldman.\nSolving transition independent decentralized Markov\ndecision processes. JAIR, 22:423-455, 2004.\n[2] D. S. Bernstein, E.A. Hansen, and S. Zilberstein. Bounded\npolicy iteration for decentralized POMDPs. In IJCAI, 2005.\n[3] D. S. Bernstein, S. Zilberstein, and N. Immerman. The\ncomplexity of decentralized control of MDPs. In UAI, 2000.\n[4] R. Emery-Montemerlo, G. Gordon, J. Schneider, and\nS. Thrun. Approximate solutions for partially observable\nstochastic games with common payoffs. In AAMAS, 2004.\n[5] E. Hansen, D. Bernstein, and S. Zilberstein. Dynamic\nprogramming for partially observable stochastic games. In\nAAAI, 2004.\n[6] V. Lesser, C. Ortiz, and M. Tambe. Distributed sensor nets:\nA multiagent perspective. Kluwer, 2003.\n[7] R. Maheswaran, M. Tambe, E. Bowring, J. Pearce, and\nP. Varakantham. Taking dcop to the real world : Efficient\ncomplete solutions for distributed event scheduling. In\nAAMAS, 2004.\n[8] P. J. Modi, W. Shen, M. Tambe, and M. Yokoo. An\nasynchronous complete method for distributed constraint\noptimization. In AAMAS, 2003.\n[9] R. Nair, D. Pynadath, M. Yokoo, M. Tambe, and S. Marsella.\nTaming decentralized POMDPs: Towards efficient policy\ncomputation for multiagent settings. In IJCAI, 2003.\n[10] R. Nair, P. Varakantham, M. Tambe, and M. Yokoo.\nNetworked distributed POMDPs: A synthesis of distributed\nconstraint optimization and POMDPs. In AAAI, 2005.\n[11] L. Peshkin, N. Meuleau, K.-E. Kim, and L. Kaelbling.\nLearning to cooperate via policy search. In UAI, 2000.\n[12] A. Petcu and B. Faltings. A scalable method for multiagent\nconstraint optimization. In IJCAI, 2005.\n[13] D. Szer, F. Charpillet, and S. Zilberstein. MAA*: A heuristic\nsearch algorithm for solving decentralized POMDPs. In\nIJCAI, 2005.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 829", "keywords": "quality guaranteed approximation;policy search;branch and bound heuristic search technique;globally optimal solution;distributed partially observable markov decision problem;global optimality;network structure;heuristic;partially observable markov decision process;distributed sensor network;pomdp;approximate solution;multi-agent system;network of agent;maximum constrained node;distribute pomdp;agent network;depth first search;overall joint reward;quality guaranteed policy;optimal joint policy;heuristic function;network;uncertain domain;agent interaction structure"}
{"name": "train_I-68", "title": "On Opportunistic Techniques for Solving Decentralized Markov Decision Processes with Temporal Constraints", "abstract": "Decentralized Markov Decision Processes (DEC-MDPs) are a popular model of agent-coordination problems in domains with uncertainty and time constraints but very difficult to solve. In this paper, we improve a state-of-the-art heuristic solution method for DEC-MDPs, called OC-DEC-MDP, that has recently been shown to scale up to larger DEC-MDPs. Our heuristic solution method, called Value Function Propagation (VFP), combines two orthogonal improvements of OC-DEC-MDP. First, it speeds up OC-DECMDP by an order of magnitude by maintaining and manipulating a value function for each state (as a function of time) rather than a separate value for each pair of sate and time interval. Furthermore, it achieves better solution qualities than OC-DEC-MDP because, as our analytical results show, it does not overestimate the expected total reward like OC-DEC- MDP. We test both improvements independently in a crisis-management domain as well as for other types of domains. Our experimental results demonstrate a significant speedup of VFP over OC-DEC-MDP as well as higher solution qualities in a variety of situations.", "fulltext": "1. INTRODUCTION\nThe development of algorithms for effective coordination of\nmultiple agents acting as a team in uncertain and time critical domains\nhas recently become a very active research field with potential\napplications ranging from coordination of agents during a hostage\nrescue mission [11] to the coordination of Autonomous Mars\nExploration Rovers [2]. Because of the uncertain and dynamic\ncharacteristics of such domains, decision-theoretic models have received\na lot of attention in recent years, mainly thanks to their\nexpressiveness and the ability to reason about the utility of actions over\ntime.\nKey decision-theoretic models that have become popular in the\nliterature include Decentralized Markov Decision Processes\n(DECMDPs) and Decentralized, Partially Observable Markov Decision\nProcesses (DEC-POMDPs). Unfortunately, solving these models\noptimally has been proven to be NEXP-complete [3], hence more\ntractable subclasses of these models have been the subject of\nintensive research. In particular, Network Distributed POMDP [13]\nwhich assume that not all the agents interact with each other,\nTransition Independent DEC-MDP [2] which assume that transition\nfunction is decomposable into local transition functions or DEC-MDP\nwith Event Driven Interactions [1] which assume that interactions\nbetween agents happen at fixed time points constitute good\nexamples of such subclasses. Although globally optimal algorithms for\nthese subclasses have demonstrated promising results, domains on\nwhich these algorithms run are still small and time horizons are\nlimited to only a few time ticks.\nTo remedy that, locally optimal algorithms have been proposed\n[12] [4] [5]. In particular, Opportunity Cost DEC-MDP [4] [5],\nreferred to as OC-DEC-MDP, is particularly notable, as it has been\nshown to scale up to domains with hundreds of tasks and double\ndigit time horizons. Additionally, OC-DEC-MDP is unique in its\nability to address both temporal constraints and uncertain method\nexecution durations, which is an important factor for real-world\ndomains. OC-DEC-MDP is able to scale up to such domains mainly\nbecause instead of searching for the globally optimal solution, it\ncarries out a series of policy iterations; in each iteration it performs\na value iteration that reuses the data computed during the previous\npolicy iteration. However, OC-DEC-MDP is still slow, especially\nas the time horizon and the number of methods approach large\nvalues. The reason for high runtimes of OC-DEC-MDP for such\ndomains is a consequence of its huge state space, i.e., OC-DEC-MDP\nintroduces a separate state for each possible pair of method and\nmethod execution interval. Furthermore, OC-DEC-MDP\noverestimates the reward that a method expects to receive for enabling\nthe execution of future methods. This reward, also referred to as\nthe opportunity cost, plays a crucial role in agent decision making,\nand as we show later, its overestimation leads to highly suboptimal\npolicies.\nIn this context, we present VFP (= Value Function P ropagation),\nan efficient solution technique for the DEC-MDP model with\ntemporal constraints and uncertain method execution durations, that\nbuilds on the success of OC-DEC-MDP. VFP introduces our two\northogonal ideas: First, similarly to [7] [9] and [10], we maintain\n830\n978-81-904262-7-5 (RPS) c 2007 IFAAMAS\nand manipulate a value function over time for each method rather\nthan a separate value for each pair of method and time interval.\nSuch representation allows us to group the time points for which\nthe value function changes at the same rate (= its slope is\nconstant), which results in fast, functional propagation of value\nfunctions. Second, we prove (both theoretically and empirically) that\nOC-DEC- MDP overestimates the opportunity cost, and to remedy\nthat, we introduce a set of heuristics, that correct the opportunity\ncost overestimation problem.\nThis paper is organized as follows: In section 2 we motivate this\nresearch by introducing a civilian rescue domain where a team of\nfire- brigades must coordinate in order to rescue civilians trapped in\na burning building. In section 3 we provide a detailed description of\nour DEC-MDP model with Temporal Constraints and in section 4\nwe discuss how one could solve the problems encoded in our model\nusing globally optimal and locally optimal solvers. Sections 5 and\n6 discuss the two orthogonal improvements to the state-of-the-art\nOC-DEC-MDP algorithm that our VFP algorithm implements.\nFinally, in section 7 we demonstrate empirically the impact of our two\northogonal improvements, i.e., we show that: (i) The new\nheuristics correct the opportunity cost overestimation problem leading to\nhigher quality policies, and (ii) By allowing for a systematic\ntradeoff of solution quality for time, the VFP algorithm runs much faster\nthan the OC-DEC-MDP algorithm\n2. MOTIVATING EXAMPLE\nWe are interested in domains where multiple agents must\ncoordinate their plans over time, despite uncertainty in plan execution\nduration and outcome. One example domain is large-scale disaster,\nlike a fire in a skyscraper. Because there can be hundreds of\ncivilians scattered across numerous floors, multiple rescue teams have\nto be dispatched, and radio communication channels can quickly\nget saturated and useless. In particular, small teams of fire-brigades\nmust be sent on separate missions to rescue the civilians trapped in\ndozens of different locations.\nPicture a small mission plan from Figure (1), where three\nfirebrigades have been assigned a task to rescue the civilians trapped\nat site B, accessed from site A (e.g. an office accessed from the\nfloor)1\n. General fire fighting procedures involve both: (i) putting\nout the flames, and (ii) ventilating the site to let the toxic, high\ntemperature gases escape, with the restriction that ventilation should\nnot be performed too fast in order to prevent the fire from spreading.\nThe team estimates that the civilians have 20 minutes before the fire\nat site B becomes unbearable, and that the fire at site A has to be\nput out in order to open the access to site B. As has happened in\nthe past in large scale disasters, communication often breaks down;\nand hence we assume in this domain that there is no\ncommunication between the fire-brigades 1,2 and 3 (denoted as FB1, FB2 and\nFB3). Consequently, FB2 does not know if it is already safe to\nventilate site A, FB1 does not know if it is already safe to enter site A\nand start fighting fire at site B, etc. We assign the reward 50 for\nevacuating the civilians from site B, and a smaller reward 20 for\nthe successful ventilation of site A, since the civilians themselves\nmight succeed in breaking out from site B.\nOne can clearly see the dilemma, that FB2 faces: It can only\nestimate the durations of the Fight fire at site A methods to be\nexecuted by FB1 and FB3, and at the same time FB2 knows that time\nis running out for civilians. If FB2 ventilates site A too early, the\nfire will spread out of control, whereas if FB2 waits with the\nventilation method for too long, fire at site B will become unbearable for\nthe civilians. In general, agents have to perform a sequence of such\n1\nWe explain the EST and LET notation in section 3\nFigure 1: Civilian rescue domain and a mission plan. Dotted\narrows represent implicit precedence constraints within an agent.\ndifficult decisions; in particular, decision process of FB2 involves\nfirst choosing when to start ventilating site A, and then\n(depending on the time it took to ventilate site A), choosing when to start\nevacuating the civilians from site B. Such sequence of decisions\nconstitutes the policy of an agent, and it must be found fast because\ntime is running out.\n3. MODEL DESCRIPTION\nWe encode our decision problems in a model which we refer to as\nDecentralized MDP with Temporal Constraints 2\n. Each instance of\nour decision problems can be described as a tuple M, A, C, P, R\nwhere M = {mi}\n|M|\ni=1 is the set of methods, and A = {Ak}\n|A|\nk=1\nis the set of agents. Agents cannot communicate during mission\nexecution. Each agent Ak is assigned to a set Mk of methods,\nsuch that\nS|A|\nk=1 Mk = M and \u2200i,j;i=jMi \u2229 Mj = \u00f8. Also, each\nmethod of agent Ak can be executed only once, and agent Ak can\nexecute only one method at a time. Method execution times are\nuncertain and P = {pi}\n|M|\ni=1 is the set of distributions of method\nexecution durations. In particular, pi(t) is the probability that the\nexecution of method mi consumes time t. C is a set of\ntemporal constraints in the system. Methods are partially ordered and\neach method has fixed time windows inside which it can be\nexecuted, i.e., C = C\u227a \u222a C[ ] where C\u227a is the set of predecessor\nconstraints and C[ ] is the set of time window constraints. For\nc \u2208 C\u227a, c = mi, mj means that method mi precedes method\nmj i.e., execution of mj cannot start before mi terminates. In\nparticular, for an agent Ak, all its methods form a chain linked by\npredecessor constraints. We assume, that the graph G = M, C\u227a\nis acyclic, does not have disconnected nodes (the problem cannot\nbe decomposed into independent subproblems), and its source and\nsink vertices identify the source and sink methods of the system.\nFor c \u2208 C[ ], c = mi, EST, LET means that execution of mi\ncan only start after the Earliest Starting Time EST and must\nfinish before the Latest End Time LET; we allow methods to have\nmultiple disjoint time window constraints. Although distributions\npi can extend to infinite time horizons, given the time window\nconstraints, the planning horizon \u0394 = max m,\u03c4,\u03c4 \u2208C[ ] \u03c4 is\nconsidered as the mission deadline. Finally, R = {ri}\n|M|\ni=1 is the set of\nnon-negative rewards, i.e., ri is obtained upon successful\nexecution of mi.\nSince there is no communication allowed, an agent can only\nestimate the probabilities that its methods have already been enabled\n2\nOne could also use the OC-DEC-MDP framework, which models\nboth time and resource constraints\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 831\nby other agents. Consequently, if mj \u2208 Mk is the next method\nto be executed by the agent Ak and the current time is t \u2208 [0, \u0394],\nthe agent has to make a decision whether to Execute the method\nmj (denoted as E), or to Wait (denoted as W). In case agent Ak\ndecides to wait, it remains idle for an arbitrary small time , and\nresumes operation at the same place (= about to execute method mj)\nat time t + . In case agent Ak decides to Execute the next method,\ntwo outcomes are possible:\nSuccess: The agent Ak receives reward rj and moves on to its\nnext method (if such method exists) so long as the following\nconditions hold: (i) All the methods {mi| mi, mj \u2208 C\u227a} that\ndirectly enable method mj have already been completed, (ii)\nExecution of method mj started in some time window of method mj, i.e.,\n\u2203 mj ,\u03c4,\u03c4 \u2208C[ ]\nsuch that t \u2208 [\u03c4, \u03c4 ], and (iii) Execution of method\nmj finished inside the same time window, i.e., agent Ak completed\nmethod mj in time less than or equal to \u03c4 \u2212 t.\nFailure: If any of the above-mentioned conditions does not hold,\nagent Ak stops its execution. Other agents may continue their\nexecution, but methods mk \u2208 {m| mj, m \u2208 C\u227a} will never become\nenabled.\nThe policy \u03c0k of an agent Ak is a function \u03c0k : Mk \u00d7 [0, \u0394] \u2192\n{W, E}, and \u03c0k( m, t ) = a means, that if Ak is at method m\nat time t, it will choose to perform the action a. A joint policy\n\u03c0 = [\u03c0k]\n|A|\nk=1 is considered to be optimal (denoted as \u03c0\u2217\n), if it\nmaximizes the sum of expected rewards for all the agents.\n4. SOLUTION TECHNIQUES\n4.1 Optimal Algorithms\nOptimal joint policy \u03c0\u2217\nis usually found by using the Bellman\nupdate principle, i.e., in order to determine the optimal policy for\nmethod mj, optimal policies for methods mk \u2208 {m| mj, m \u2208\nC\u227a} are used. Unfortunately, for our model, the optimal\npolicy for method mj also depends on policies for methods mi \u2208\n{m| m, mj \u2208 C\u227a}. This double dependency results from the\nfact, that the expected reward for starting the execution of method\nmj at time t also depends on the probability that method mj will be\nenabled by time t. Consequently, if time is discretized, one needs to\nconsider \u0394|M|\ncandidate policies in order to find \u03c0\u2217\n. Thus,\nglobally optimal algorithms used for solving real-world problems are\nunlikely to terminate in reasonable time [11]. The complexity of\nour model could be reduced if we considered its more restricted\nversion; in particular, if each method mj was allowed to be\nenabled at time points t \u2208 Tj \u2282 [0, \u0394], the Coverage Set Algorithm\n(CSA) [1] could be used. However, CSA complexity is double\nexponential in the size of Ti, and for our domains Tj can store all\nvalues ranging from 0 to \u0394.\n4.2 Locally Optimal Algorithms\nFollowing the limited applicability of globally optimal algorithms\nfor DEC-MDPs with Temporal Constraints, locally optimal\nalgorithms appear more promising. Specially, the OC-DEC-MDP\nalgorithm [4] is particularly significant, as it has shown to easily scale\nup to domains with hundreds of methods. The idea of the\nOC-DECMDP algorithm is to start with the earliest starting time policy \u03c00\n(according to which an agent will start executing the method m as\nsoon as m has a non-zero chance of being already enabled), and\nthen improve it iteratively, until no further improvement is\npossible. At each iteration, the algorithm starts with some policy \u03c0,\nwhich uniquely determines the probabilities Pi,[\u03c4,\u03c4 ] that method\nmi will be performed in the time interval [\u03c4, \u03c4 ]. It then performs\ntwo steps:\nStep 1: It propagates from sink methods to source methods the\nvalues Vi,[\u03c4,\u03c4 ], that represent the expected utility for executing\nmethod mi in the time interval [\u03c4, \u03c4 ]. This propagation uses the\nprobabilities Pi,[\u03c4,\u03c4 ] from previous algorithm iteration. We call\nthis step a value propagation phase.\nStep 2: Given the values Vi,[\u03c4,\u03c4 ] from Step 1, the algorithm chooses\nthe most profitable method execution intervals which are stored in\na new policy \u03c0 . It then propagates the new probabilities Pi,[\u03c4,\u03c4 ]\nfrom source methods to sink methods. We call this step a\nprobability propagation phase. If policy \u03c0 does not improve \u03c0, the\nalgorithm terminates.\nThere are two shortcomings of the OC-DEC-MDP algorithm that\nwe address in this paper. First, each of OC-DEC-MDP states is a\npair mj, [\u03c4, \u03c4 ] , where [\u03c4, \u03c4 ] is a time interval in which method\nmj can be executed. While such state representation is beneficial,\nin that the problem can be solved with a standard value iteration\nalgorithm, it blurs the intuitive mapping from time t to the expected\ntotal reward for starting the execution of mj at time t.\nConsequently, if some method mi enables method mj, and the values\nVj,[\u03c4,\u03c4 ]\u2200\u03c4,\u03c4 \u2208[0,\u0394] are known, the operation that calculates the\nvalues Vi,[\u03c4,\u03c4 ]\u2200\u03c4, \u03c4 \u2208 [0, \u0394] (during the value propagation phase),\nruns in time O(I2\n), where I is the number of time intervals 3\n. Since\nthe runtime of the whole algorithm is proportional to the runtime of\nthis operation, especially for big time horizons \u0394, the OC-\nDECMDP algorithm runs slow.\nSecond, while OC-DEC-MDP emphasizes on precise calculation\nof values Vj,[\u03c4,\u03c4 ], it fails to address a critical issue that determines\nhow the values Vj,[\u03c4,\u03c4 ] are split given that the method mj has\nmultiple enabling methods. As we show later, OC-DEC-MDP splits\nVj,[\u03c4,\u03c4 ] into parts that may overestimate Vj,[\u03c4,\u03c4 ] when summed up\nagain. As a result, methods that precede the method mj\noverestimate the value for enabling mj which, as we show later, can have\ndisastrous consequences. In the next two sections, we address both\nof these shortcomings.\n5. VALUE FUNCTION PROPAGATION (VFP)\nThe general scheme of the VFP algorithm is identical to the\nOCDEC-MDP algorithm, in that it performs a series of policy\nimprovement iterations, each one involving a Value and Probability\nPropagation Phase. However, instead of propagating separate\nvalues, VFP maintains and propagates the whole functions, we\ntherefore refer to these phases as the value function propagation phase\nand the probability function propagation phase. To this end, for\neach method mi \u2208 M, we define three new functions:\nValue Function, denoted as vi(t), that maps time t \u2208 [0, \u0394] to the\nexpected total reward for starting the execution of method mi at\ntime t.\nOpportunity Cost Function, denoted as Vi(t), that maps time\nt \u2208 [0, \u0394] to the expected total reward for starting the execution\nof method mi at time t assuming that mi is enabled.\nProbability Function, denoted as Pi(t), that maps time t \u2208 [0, \u0394]\nto the probability that method mi will be completed before time\nt.\nSuch functional representation allows us to easily read the current\npolicy, i.e., if an agent Ak is at method mi at time t, then it will\nwait as long as value function vi(t) will be greater in the future.\nFormally:\n\u03c0k( mi, t ) =\nj\nW if \u2203t >t such that vi(t) < vi(t )\nE otherwise.\nWe now develop an analytical technique for performing the value\nfunction and probability function propagation phases.\n3\nSimilarly for the probability propagation phase\n832 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\n5.1 Value Function Propagation Phase\nSuppose, that we are performing a value function propagation phase\nduring which the value functions are propagated from the sink\nmethods to the source methods. At any time during this phase we\nencounter a situation shown in Figure 2, where opportunity cost\nfunctions [Vjn ]N\nn=0 of methods [mjn ]N\nn=0 are known, and the\nopportunity cost Vi0 of method mi0 is to be derived. Let pi0 be the\nprobability distribution function of method mi0 execution\nduration, and ri0 be the immediate reward for starting and\ncompleting the execution of method mi0 inside a time interval [\u03c4, \u03c4 ] such\nthat mi0 \u03c4, \u03c4 \u2208 C[ ]. The function Vi0 is then derived from ri0\nand opportunity costs Vjn,i0 (t) n = 1, ..., N from future methods.\nFormally:\nVi0 (t) =\n8\n>><\n>>:\nR \u03c4 \u2212t\n0\npi0 (t )(ri0 +\nPN\nn=0 Vjn,i0 (t + t ))dt\nif \u2203 mi0\n\u03c4,\u03c4 \u2208C[ ]\nsuch that t \u2208 [\u03c4, \u03c4 ]\n0 otherwise\n(1)\nNote, that for t \u2208 [\u03c4, \u03c4 ], if h(t) := ri0 +\nPN\nn=0 Vjn,i0 (\u03c4 \u2212t) then\nVi0 is a convolution of p and h: vi0 (t) = (pi0 \u2217h)(\u03c4 \u2212t).\nAssume for now, that Vjn,i0 represents a full opportunity cost,\npostponing the discussion on different techniques for splitting the\nopportunity cost Vj0 into [Vj0,ik ]K\nk=0 until section 6. We now show\nhow to derive Vj0,i0 (derivation of Vjn,i0 for n = 0 follows the\nsame scheme).\nFigure 2: Fragment of an MDP of agent Ak. Probability\nfunctions propagate forward (left to right) whereas value functions\npropagate backward (right to left).\nLet V j0,i0 (t) be the opportunity cost of starting the execution of\nmethod mj0 at time t given that method mi0 has been completed.\nIt is derived by multiplying Vi0 by the probability functions of all\nmethods other than mi0 that enable mj0 . Formally:\nV j0,i0 (t) = Vj0 (t) \u00b7\nKY\nk=1\nPik (t).\nWhere similarly to [4] and [5] we ignored the dependency of [Plk ]K\nk=1.\nObserve that V j0,i0 does not have to be monotonically\ndecreasing, i.e., delaying the execution of the method mi0 can sometimes\nbe profitable. Therefore the opportunity cost Vj0,i0 (t) of enabling\nmethod mi0 at time t must be greater than or equal to V j0,i0 .\nFurthermore, Vj0,i0 should be non-increasing. Formally:\nVj0,i0 = min\nf\u2208F\nf (2)\nWhere F = {f | f \u2265 V j0,i0 and f(t) \u2265 f(t ) \u2200t<t }.\nKnowing the opportunity cost Vi0 , we can then easily derive the\nvalue function vi0 . Let Ak be an agent assigned to the method mi0 .\nIf Ak is about to start the execution of mi0 it means, that Ak must\nhave completed its part of the mission plan up to the method mi0 .\nSince Ak does not know if other agents have completed methods\n[mlk ]k=K\nk=1 , in order to derive vi0 , it has to multiply Vi0 by the\nprobability functions of all methods of other agents that enable mi0 .\nFormally:\nvi0 (t) = Vi0 (t) \u00b7\nKY\nk=1\nPlk (t)\nWhere the dependency of [Plk ]K\nk=1 is also ignored.\nWe have consequently shown a general scheme how to propagate\nthe value functions: Knowing [vjn ]N\nn=0 and [Vjn ]N\nn=0 of methods\n[mjn ]N\nn=0 we can derive vi0 and Vi0 of method mi0 . In general, the\nvalue function propagation scheme starts with sink nodes. It then\nvisits at each time a method m, such that all the methods that m\nenables have already been marked as visited. The value function\npropagation phase terminates when all the source methods have\nbeen marked as visited.\n5.2 Reading the Policy\nIn order to determine the policy of agent Ak for the method mj0\nwe must identify the set Zj0 of intervals [z, z ] \u2282 [0, ..., \u0394], such\nthat:\n\u2200t\u2208[z,z ] \u03c0k( mj0 , t ) = W.\nOne can easily identify the intervals of Zj0 by looking at the time\nintervals in which the value function vj0 does not decrease\nmonotonically.\n5.3 Probability Function Propagation Phase\nAssume now, that value functions and opportunity cost values have\nall been propagated from sink methods to source nodes and the sets\nZj for all methods mj \u2208 M have been identified. Since value\nfunction propagation phase was using probabilities Pi(t) for\nmethods mi \u2208 M and times t \u2208 [0, \u0394] found at previous algorithm\niteration, we now have to find new values Pi(t), in order to prepare\nthe algorithm for its next iteration. We now show how in the general\ncase (Figure 2) propagate the probability functions forward through\none method, i.e., we assume that the probability functions [Pik ]K\nk=0\nof methods [mik ]K\nk=0 are known, and the probability function Pj0\nof method mj0 must be derived. Let pj0 be the probability\ndistribution function of method mj0 execution duration, and Zj0 be the\nset of intervals of inactivity for method mj0 , found during the last\nvalue function propagation phase. If we ignore the dependency of\n[Pik ]K\nk=0 then the probability Pj0 (t) that the execution of method\nmj0 starts before time t is given by:\nPj0 (t) =\n(QK\nk=0 Pik (\u03c4) if \u2203(\u03c4, \u03c4 ) \u2208 Zj0 s.t. t \u2208 (\u03c4, \u03c4 )\nQK\nk=0 Pik (t) otherwise.\nGiven Pj0 (t), the probability Pj0 (t) that method mj0 will be\ncompleted by time t is derived by:\nPj0 (t) =\nZ t\n0\nZ t\n0\n(\n\u2202Pj0\n\u2202t\n)(t ) \u00b7 pj0 (t \u2212 t )dt dt (3)\nWhich can be written compactly as\n\u2202Pj0\n\u2202t\n= pj0 \u2217\n\u2202P j0\n\u2202t\n.\nWe have consequently shown how to propagate the probability\nfunctions [Pik ]K\nk=0 of methods [mik ]K\nk=0 to obtain the probability\nfunction Pj0 of method mj0 . The general, the probability function\npropagation phase starts with source methods msi for which we\nknow that Psi = 1 since they are enabled by default. We then\nvisit at each time a method m such that all the methods that enable\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 833\nm have already been marked as visited. The probability function\npropagation phase terminates when all the sink methods have been\nmarked as visited.\n5.4 The Algorithm\nSimilarly to the OC-DEC-MDP algorithm, VFP starts the policy\nimprovement iterations with the earliest starting time policy \u03c00\n.\nThen at each iteration it: (i) Propagates the value functions [vi]\n|M|\ni=1\nusing the old probability functions [Pi]\n|M|\ni=1 from previous algorithm\niteration and establishes the new sets [Zi]\n|M|\ni=1 of method inactivity\nintervals, and (ii) propagates the new probability functions [Pi ]\n|M|\ni=1\nusing the newly established sets [Zi]\n|M|\ni=1. These new functions\n[Pi ]\n|M|\ni=1 are then used in the next iteration of the algorithm.\nSimilarly to OC-DEC-MDP, VFP terminates if a new policy does not\nimprove the policy from the previous algorithm iteration.\n5.5 Implementation of Function Operations\nSo far, we have derived the functional operations for value function\nand probability function propagation without choosing any\nfunction representation. In general, our functional operations can\nhandle continuous time, and one has freedom to choose a desired\nfunction approximation technique, such as piecewise linear [7] or\npiecewise constant [9] approximation. However, since one of our goals\nis to compare VFP with the existing OC-DEC- MDP algorithm, that\nworks only for discrete time, we also discretize time, and choose to\napproximate value functions and probability functions with\npiecewise linear (PWL) functions.\nWhen the VFP algorithm propagates the value functions and\nprobability functions, it constantly carries out operations represented by\nequations (1) and (3) and we have already shown that these\noperations are convolutions of some functions p(t) and h(t). If time is\ndiscretized, functions p(t) and h(t) are discrete; however, h(t) can\nbe nicely approximated with a PWL function bh(t), which is exactly\nwhat VFP does. As a result, instead of performing O(\u03942\n)\nmultiplications to compute f(t), VFP only needs to perform O(k \u00b7 \u0394)\nmultiplications to compute f(t), where k is the number of linear\nsegments of bh(t) (note, that since h(t) is monotonic, bh(t) is\nusually close to h(t) with k \u0394). Since Pi values are in range\n[0, 1] and Vi values are in range [0,\nP\nmi\u2208M ri], we suggest to\napproximate Vi(t) with bVi(t) within error V , and Pi(t) with bPi(t)\nwithin error P . We now prove that the overall approximation error\naccumulated during the value function propagation phase can be\nexpressed in terms of P and V :\nTHEOREM 1. Let C\u227a be a set of precedence constraints of a\nDEC-MDP with Temporal Constraints, and P and V be the\nprobability function and value function approximation errors\nrespectively. The overall error \u03c0 = maxV supt\u2208[0,\u0394]|V (t) \u2212 bV (t)| of\nvalue function propagation phase is then bounded by:\n|C\u227a|\n\nV + ((1 + P )|C\u227a|\n\u2212 1)\nP\nmi\u2208M ri\n\n.\nPROOF. In order to establish the bound for \u03c0, we first prove\nby induction on the size of C\u227a, that the overall error of\nprobability function propagation phase, \u03c0(P ) = maxP supt\u2208[0,\u0394]|P(t) \u2212\nbP(t)| is bounded by (1 + P )|C\u227a|\n\u2212 1.\nInduction base: If n = 1 only two methods are present, and we\nwill perform the operation identified by Equation (3) only once,\nintroducing the error \u03c0(P ) = P = (1 + P )|C\u227a|\n\u2212 1.\nInduction step: Suppose, that \u03c0(P ) for |C\u227a| = n is bounded by\n(1 + P )n\n\u2212 1, and we want to prove that this statement holds for\n|C\u227a| = n. Let G = M, C\u227a be a graph with at most n + 1\nedges, and G = M, C\u227a be a subgraph of G, such that C\u227a =\nC\u227a \u2212 { mi, mj }, where mj \u2208 M is a sink node in G. From the\ninduction assumption we have, that C\u227a introduces the probability\npropagation phase error bounded by (1 + P )n\n\u2212 1. We now add\nback the link { mi, mj } to C\u227a, which affects the error of only\none probability function, namely Pj, by a factor of (1 + P ). Since\nprobability propagation phase error in C\u227a was bounded by (1 +\nP )n\n\u2212 1, in C\u227a = C\u227a \u222a { mi, mj } it can be at most ((1 +\nP )n\n\u2212 1)(1 + P ) < (1 + P )n+1\n\u2212 1. Thus, if opportunity cost\nfunctions are not overestimated, they are bounded by\nP\nmi\u2208M ri\nand the error of a single value function propagation operation will\nbe at most\nZ \u0394\n0\np(t)( V +((1+ P )\n|C\u227a|\n\u22121)\nX\nmi\u2208M\nri) dt < V +((1+ P )\n|C\u227a|\n\u22121)\nX\nmi\u2208M\nri.\nSince the number of value function propagation operations is |C\u227a|,\nthe total error \u03c0 of the value function propagation phase is bounded\nby: |C\u227a|\n\nV + ((1 + P )|C\u227a|\n\u2212 1)\nP\nmi\u2208M ri\n\n.\n6. SPLITTING THE OPPORTUNITY COST\nFUNCTIONS\nIn section 5 we left out the discussion about how the\nopportunity cost function Vj0 of method mj0 is split into opportunity cost\nfunctions [Vj0,ik ]K\nk=0 sent back to methods [mik ]K\nk=0 , that\ndirectly enable method mj0 . So far, we have taken the same\napproach as in [4] and [5] in that the opportunity cost function Vj0,ik\nthat the method mik sends back to the method mj0 is a\nminimal, non-increasing function that dominates function V j0,ik (t) =\n(Vj0 \u00b7\nQ\nk \u2208{0,...,K}\nk =k\nPik\n)(t). We refer to this approach, as\nheuristic H 1,1 . Before we prove that this heuristic overestimates the\nopportunity cost, we discuss three problems that might occur when\nsplitting the opportunity cost functions: (i) overestimation, (ii)\nunderestimation and (iii) starvation. Consider the situation in Figure\nFigure 3: Splitting the value function of method mj0 among\nmethods [mik ]K\nk=0.\n(3) when value function propagation for methods [mik ]K\nk=0 is\nperformed. For each k = 0, ..., K, Equation (1) derives the\nopportunity cost function Vik from immediate reward rk and\nopportunity cost function Vj0,ik . If m0 is the only methods that precedes\nmethod mk, then V ik,0 = Vik is propagated to method m0, and\nconsequently the opportunity cost for completing the method m0 at\ntime t is equal to\nPK\nk=0 Vik,0(t). If this cost is overestimated, then\nan agent A0 at method m0 will have too much incentive to finish\nthe execution of m0 at time t. Consequently, although the\nprobability P(t) that m0 will be enabled by other agents by time t is low,\nagent A0 might still find the expected utility of starting the\nexecution of m0 at time t higher than the expected utility of doing it later.\nAs a result, it will choose at time t to start executing method m0\ninstead of waiting, which can have disastrous consequences.\nSimilarly, if\nPK\nk=0 Vik,0(t) is underestimated, agent A0 might loose\ninterest in enabling the future methods [mik ]K\nk=0 and just focus on\n834 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nmaximizing the chance of obtaining its immediate reward r0. Since\nthis chance is increased when agent A0 waits4\n, it will consider at\ntime t to be more profitable to wait, instead of starting the\nexecution of m0, which can have similarly disastrous consequences.\nFinally, if Vj0 is split in a way, that for some k, Vj0,ik = 0, it is the\nmethod mik that underestimates the opportunity cost of enabling\nmethod mj0 , and the similar reasoning applies. We call such\nproblem a starvation of method mk. That short discussion shows the\nimportance of splitting the opportunity cost function Vj0 in such a\nway, that overestimation, underestimation, and starvation problem\nis avoided. We now prove that:\nTHEOREM 2. Heuristic H 1,1 can overestimate the\nopportunity cost.\nPROOF. We prove the theorem by showing a case where the\noverestimation occurs. For the mission plan from Figure (3), let\nH 1,1 split Vj0 into [V j0,ik = Vj0 \u00b7\nQ\nk \u2208{0,...,K}\nk =k\nPik\n]K\nk=0 sent to\nmethods [mik ]K\nk=0 respectively. Also, assume that methods [mik ]K\nk=0\nprovide no local reward and have the same time windows, i.e.,\nrik = 0; ESTik = 0, LETik = \u0394 for k = 0, ..., K. To prove the\noverestimation of opportunity cost, we must identify t0 \u2208 [0, ..., \u0394]\nsuch that the opportunity cost\nPK\nk=0 Vik (t) for methods [mik ]K\nk=0\nat time t \u2208 [0, .., \u0394] is greater than the opportunity cost Vj0 (t).\nFrom Equation (1) we have:\nVik\n(t) =\nZ \u0394\u2212t\n0\npik\n(t )Vj0,ik\n(t + t )dt\nSumming over all methods [mik ]K\nk=0 we obtain:\nKX\nk=0\nVik\n(t) =\nKX\nk=0\nZ \u0394\u2212t\n0\npik\n(t )Vj0,ik\n(t + t )dt (4)\n\u2265\nKX\nk=0\nZ \u0394\u2212t\n0\npik\n(t )V j0,ik\n(t + t )dt\n=\nKX\nk=0\nZ \u0394\u2212t\n0\npik\n(t )Vj0 (t + t )\nY\nk \u2208{0,...,K}\nk =k\nPik\n(t + t )dt\nLet c \u2208 (0, 1] be a constant and t0 \u2208 [0, \u0394] be such that \u2200t>t0\nand \u2200k=0,..,K we have\nQ\nk \u2208{0,...,K}\nk =k\nPik\n(t) > c. Then:\nKX\nk=0\nVik\n(t0) >\nKX\nk=0\nZ \u0394\u2212t0\n0\npik\n(t )Vj0 (t0 + t ) \u00b7 c dt\nBecause Pjk\nis non-decreasing. Now, suppose there exists t1 \u2208\n(t0, \u0394], such that\nPK\nk=0\nR t1\u2212t0\n0\npik (t )dt >\nVj0\n(t0)\nc\u00b7Vj0\n(t1)\n. Since\ndecreasing the upper limit of the integral over positive function also\ndecreases the integral, we have:\nKX\nk=0\nVik\n(t0) > c\nKX\nk=0\nZ t1\nt0\npik\n(t \u2212 t0)Vj0 (t )dt\nAnd since Vj0 (t ) is non-increasing we have:\nKX\nk=0\nVik\n(t0) > c \u00b7 Vj0 (t1)\nKX\nk=0\nZ t1\nt0\npik\n(t \u2212 t0)dt (5)\n= c \u00b7 Vj0 (t1)\nKX\nk=0\nZ t1\u2212t0\n0\npik\n(t )dt\n> c \u00b7 Vj0 (t1)\nVj(t0)\nc \u00b7 Vj(t1)\n= Vj(t0)\n4\nAssuming LET0 t\nConsequently, the opportunity cost\nPK\nk=0 Vik (t0) of starting the\nexecution of methods [mik ]K\nk=0 at time t \u2208 [0, .., \u0394] is greater\nthan the opportunity cost Vj0 (t0) which proves the theorem.Figure\n4 shows that the overestimation of opportunity cost is easily\nobservable in practice.\nTo remedy the problem of opportunity cost overestimation, we\npropose three alternative heuristics that split the opportunity cost\nfunctions:\n\u2022 Heuristic H 1,0 : Only one method, mik gets the full\nexpected reward for enabling method mj0 , i.e., V j0,ik\n(t) = 0\nfor k \u2208 {0, ..., K}\\{k} and V j0,ik (t) = (Vj0 \u00b7\nQ\nk \u2208{0,...,K}\nk =k\nPik\n)(t).\n\u2022 Heuristic H 1/2,1/2 : Each method [mik ]K\nk=0 gets the full\nopportunity cost for enabling method mj0 divided by the\nnumber K of methods enabling the method mj0 , i.e., V j0,ik (t) =\n1\nK\n(Vj0 \u00b7\nQ\nk \u2208{0,...,K}\nk =k\nPik\n)(t) for k \u2208 {0, ..., K}.\n\u2022 Heuristic bH 1,1 : This is a normalized version of the H 1,1\nheuristic in that each method [mik ]K\nk=0 initially gets the full\nopportunity cost for enabling the method mj0 . To avoid\nopportunity cost overestimation, we normalize the split\nfunctions when their sum exceeds the opportunity cost function\nto be split. Formally:\nV j0,ik (t) =\n8\n><\n>:\nV\nH 1,1\nj0,ik\n(t) if\nPK\nk=0 V\nH 1,1\nj0,ik\n(t) < Vj0 (t)\nVj0 (t)\nV\nH 1,1\nj0,ik\n(t)\nPK\nk=0\nV\nH 1,1\nj0,ik\n(t)\notherwise\nWhere V\nH 1,1\nj0,ik\n(t) = (Vj0 \u00b7\nQ\nk \u2208{0,...,K}\nk =k\nPjk\n)(t).\nFor the new heuristics, we now prove, that:\nTHEOREM 3. Heuristics H 1,0 , H 1/2,1/2 and bH 1,1 do not\noverestimate the opportunity cost.\nPROOF. When heuristic H 1,0 is used to split the opportunity\ncost function Vj0 , only one method (e.g. mik ) gets the opportunity\ncost for enabling method mj0 . Thus:\nKX\nk =0\nVik\n(t) =\nZ \u0394\u2212t\n0\npik\n(t )Vj0,ik\n(t + t )dt (6)\nAnd since Vj0 is non-increasing\n\u2264\nZ \u0394\u2212t\n0\npik\n(t )Vj0 (t + t ) \u00b7\nY\nk \u2208{0,...,K}\nk =k\nPjk\n(t + t )dt\n\u2264\nZ \u0394\u2212t\n0\npik\n(t )Vj0 (t + t )dt \u2264 Vj0 (t)\nThe last inequality is also a consequence of the fact that Vj0 is\nnon-increasing.\nFor heuristic H 1/2,1/2 we similarly have:\nKX\nk=0\nVik\n(t) \u2264\nKX\nk=0\nZ \u0394\u2212t\n0\npik\n(t )\n1\nK\nVj0 (t + t )\nY\nk \u2208{0,...,K}\nk =k\nPjk\n(t + t )dt\n\u2264\n1\nK\nKX\nk=0\nZ \u0394\u2212t\n0\npik\n(t )Vj0 (t + t )dt\n\u2264\n1\nK\n\u00b7 K \u00b7 Vj0 (t) = Vj0 (t).\nFor heuristic bH 1,1 , the opportunity cost function Vj0 is by\ndefinition split in such manner, that\nPK\nk=0 Vik (t) \u2264 Vj0 (t).\nConsequently, we have proved, that our new heuristics H 1,0 , H 1/2,1/2\nand bH 1,1 avoid the overestimation of the opportunity cost.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 835\nThe reason why we have introduced all three new heuristics is the\nfollowing: Since H 1,1 overestimates the opportunity cost, one\nhas to choose which method mik will receive the reward from\nenabling the method mj0 , which is exactly what the heuristic H 1,0\ndoes. However, heuristic H 1,0 leaves K \u2212 1 methods that\nprecede the method mj0 without any reward which leads to starvation.\nStarvation can be avoided if opportunity cost functions are split\nusing heuristic H 1/2,1/2 , that provides reward to all enabling\nmethods. However, the sum of split opportunity cost functions for the\nH 1/2,1/2 heuristic can be smaller than the non-zero split\nopportunity cost function for the H 1,0 heuristic, which is clearly\nundesirable. Such situation (Figure 4, heuristic H 1,0 ) occurs because\nthe mean f+g\n2\nof two functions f, g is not smaller than f nor g\nonly if f = g. This is why we have proposed the bH 1,1 heuristic,\nwhich by definition avoids the overestimation, underestimation and\nstarvation problems.\n7. EXPERIMENTAL EVALUATION\nSince the VFP algorithm that we introduced provides two\northogonal improvements over the OC-DEC-MDP algorithm, the\nexperimental evaluation we performed consisted of two parts: In part 1,\nwe tested empirically the quality of solutions that an locally optimal\nsolver (either OC-DEC-MDP or VFP) finds, given it uses different\nopportunity cost function splitting heuristic, and in part 2, we\ncompared the runtimes of the VFP and OC-DEC- MDP algorithms for\na variety of mission plan configurations.\nPart 1: We first ran the VFP algorithm on a generic mission plan\nconfiguration from Figure 3 where only methods mj0 , mi1 , mi2\nand m0 were present. Time windows of all methods were set to\n400, duration pj0 of method mj0 was uniform, i.e., pj0 (t) = 1\n400\nand durations pi1 , pi2 of methods mi1 , mi2 were normal\ndistributions, i.e., pi1 = N(\u03bc = 250, \u03c3 = 20), and pi2 = N(\u03bc =\n200, \u03c3 = 100). We assumed that only method mj0 provided\nreward, i.e. rj0 = 10 was the reward for finishing the execution of\nmethod mj0 before time t = 400. We show our results in Figure\n(4) where the x-axis of each of the graphs represents time whereas\nthe y-axis represents the opportunity cost. The first graph confirms,\nthat when the opportunity cost function Vj0 was split into\nopportunity cost functions Vi1 and Vi2 using the H 1,1 heuristic, the\nfunction Vi1 +Vi2 was not always below the Vj0 function. In particular,\nVi1 (280) + Vi2 (280) exceeded Vj0 (280) by 69%. When\nheuristics H 1,0 , H 1/2,1/2 and bH 1,1 were used (graphs 2,3 and 4),\nthe function Vi1 + Vi2 was always below Vj0 .\nWe then shifted our attention to the civilian rescue domain\nintroduced in Figure 1 for which we sampled all action execution\ndurations from the normal distribution N = (\u03bc = 5, \u03c3 = 2)). To\nobtain the baseline for the heuristic performance, we implemented\na globally optimal solver, that found a true expected total reward\nfor this domain (Figure (6a)). We then compared this reward with\na expected total reward found by a locally optimal solver guided\nby each of the discussed heuristics. Figure (6a), which plots on\nthe y-axis the expected total reward of a policy complements our\nprevious results: H 1,1 heuristic overestimated the expected total\nreward by 280% whereas the other heuristics were able to guide the\nlocally optimal solver close to a true expected total reward.\nPart 2: We then chose H 1,1 to split the opportunity cost\nfunctions and conducted a series of experiments aimed at testing the\nscalability of VFP for various mission plan configurations, using\nthe performance of the OC-DEC-MDP algorithm as a benchmark.\nWe began the VFP scalability tests with a configuration from Figure\n(5a) associated with the civilian rescue domain, for which method\nexecution durations were extended to normal distributions N(\u03bc =\nFigure 5: Mission plan configurations: (a) civilian rescue\ndomain, (b) chain of n methods, (c) tree of n methods with\nbranching factor = 3 and (d) square mesh of n methods.\nFigure 6: VFP performance in the civilian rescue domain.\n30, \u03c3 = 5), and the deadline was extended to \u0394 = 200.\nWe decided to test the runtime of the VFP algorithm running with\nthree different levels of accuracy, i.e., different approximation\nparameters P and V were chosen, such that the cumulative error\nof the solution found by VFP stayed within 1%, 5% and 10% of\nthe solution found by the OC- DEC-MDP algorithm. We then run\nboth algorithms for a total of 100 policy improvement iterations.\nFigure (6b) shows the performance of the VFP algorithm in the\ncivilian rescue domain (y-axis shows the runtime in milliseconds).\nAs we see, for this small domain, VFP runs 15% faster than\nOCDEC-MDP when computing the policy with an error of less than\n1%. For comparison, the globally optimal solved did not terminate\nwithin the first three hours of its runtime which shows the strength\nof the opportunistic solvers, like OC-DEC-MDP.\nWe next decided to test how VFP performs in a more difficult\ndomain, i.e., with methods forming a long chain (Figure (5b)). We\ntested chains of 10, 20 and 30 methods, increasing at the same\ntime method time windows to 350, 700 and 1050 to ensure that\nlater methods can be reached. We show the results in Figure (7a),\nwhere we vary on the x-axis the number of methods and plot on\nthe y-axis the algorithm runtime (notice the logarithmic scale). As\nwe observe, scaling up the domain reveals the high performance of\nVFP: Within 1% error, it runs up to 6 times faster than\nOC-DECMDP.\nWe then tested how VFP scales up, given that the methods are\narranged into a tree (Figure (5c)). In particular, we considered trees\nwith branching factor of 3, and depth of 2, 3 and 4, increasing at\nthe same time the time horizon from 200 to 300, and then to 400.\nWe show the results in Figure (7b). Although the speedups are\nsmaller than in case of a chain, the VFP algorithm still runs up to 4\ntimes faster than OC-DEC-MDP when computing the policy with\nan error of less than 1%.\nWe finally tested how VFP handles the domains with methods\narranged into a n \u00d7 n mesh, i.e., C\u227a = { mi,j, mk,j+1 } for i =\n1, ..., n; k = 1, ..., n; j = 1, ..., n \u2212 1. In particular, we consider\n836 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nFigure 4: Visualization of heuristics for opportunity costs splitting.\nFigure 7: Scalability experiments for OC-DEC-MDP and VFP for different network configurations.\nmeshes of 3\u00d73, 4\u00d74, and 5\u00d75 methods. For such configurations\nwe have to greatly increase the time horizon since the\nprobabilities of enabling the final methods by a particular time decrease\nexponentially. We therefore vary the time horizons from 3000 to\n4000, and then to 5000. We show the results in Figure (7c) where,\nespecially for larger meshes, the VFP algorithm runs up to one\norder of magnitude faster than OC-DEC-MDP while finding a policy\nthat is within less than 1% from the policy found by OC-\nDECMDP.\n8. CONCLUSIONS\nDecentralized Markov Decision Process (DEC-MDP) has been very\npopular for modeling of agent-coordination problems, it is very\ndifficult to solve, especially for the real-world domains. In this\npaper, we improved a state-of-the-art heuristic solution method for\nDEC-MDPs, called OC-DEC-MDP, that has recently been shown\nto scale up to large DEC-MDPs. Our heuristic solution method,\ncalled Value Function Propagation (VFP), provided two\northogonal improvements of OC-DEC-MDP: (i) It speeded up\nOC-DECMDP by an order of magnitude by maintaining and manipulating a\nvalue function for each method rather than a separate value for each\npair of method and time interval, and (ii) it achieved better solution\nqualities than OC-DEC-MDP because it corrected the\noverestimation of the opportunity cost of OC-DEC-MDP.\nIn terms of related work, we have extensively discussed the\nOCDEC-MDP algorithm [4]. Furthermore, as discussed in Section 4,\nthere are globally optimal algorithms for solving DEC-MDPs with\ntemporal constraints [1] [11]. Unfortunately, they fail to scale up to\nlarge-scale domains at present time. Beyond OC-DEC-MDP, there\nare other locally optimal algorithms for DEC-MDPs and\nDECPOMDPs [8] [12], [13], yet, they have traditionally not dealt with\nuncertain execution times and temporal constraints. Finally, value\nfunction techniques have been studied in context of single agent\nMDPs [7] [9]. However, similarly to [6], they fail to address the\nlack of global state knowledge, which is a fundamental issue in\ndecentralized planning.\nAcknowledgments\nThis material is based upon work supported by the DARPA/IPTO\nCOORDINATORS program and the Air Force Research\nLaboratory under Contract No. FA875005C0030. The authors also want\nto thank Sven Koenig and anonymous reviewers for their valuable\ncomments.\n9. REFERENCES\n[1] R. Becker, V. Lesser, and S. Zilberstein. Decentralized MDPs with\nEvent-Driven Interactions. In AAMAS, pages 302-309, 2004.\n[2] R. Becker, S. Zilberstein, V. Lesser, and C. V. Goldman.\nTransition-Independent Decentralized Markov Decision Processes. In\nAAMAS, pages 41-48, 2003.\n[3] D. S. Bernstein, S. Zilberstein, and N. Immerman. The complexity of\ndecentralized control of Markov decision processes. In UAI, pages\n32-37, 2000.\n[4] A. Beynier and A. Mouaddib. A polynomial algorithm for\ndecentralized Markov decision processes with temporal constraints.\nIn AAMAS, pages 963-969, 2005.\n[5] A. Beynier and A. Mouaddib. An iterative algorithm for solving\nconstrained decentralized Markov decision processes. In AAAI, pages\n1089-1094, 2006.\n[6] C. Boutilier. Sequential optimality and coordination in multiagent\nsystems. In IJCAI, pages 478-485, 1999.\n[7] J. Boyan and M. Littman. Exact solutions to time-dependent MDPs.\nIn NIPS, pages 1026-1032, 2000.\n[8] C. Goldman and S. Zilberstein. Optimizing information exchange in\ncooperative multi-agent systems, 2003.\n[9] L. Li and M. Littman. Lazy approximation for solving continuous\nfinite-horizon MDPs. In AAAI, pages 1175-1180, 2005.\n[10] Y. Liu and S. Koenig. Risk-sensitive planning with one-switch utility\nfunctions: Value iteration. In AAAI, pages 993-999, 2005.\n[11] D. Musliner, E. Durfee, J. Wu, D. Dolgov, R. Goldman, and\nM. Boddy. Coordinated plan management using multiagent MDPs. In\nAAAI Spring Symposium, 2006.\n[12] R. Nair, M. Tambe, M. Yokoo, D. Pynadath, and S. Marsella. Taming\ndecentralized POMDPs: Towards efficient policy computation for\nmultiagent settings. In IJCAI, pages 705-711, 2003.\n[13] R. Nair, P. Varakantham, M. Tambe, and M. Yokoo. Networked\ndistributed POMDPs: A synergy of distributed constraint\noptimization and POMDPs. In IJCAI, pages 1758-1760, 2005.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 837", "keywords": "locally optimal solution;rescue mission;agent-coordination problem;decentralized partially observable markov decision process;decentralize markov decision process;temporal constraint;decision-theoretic model;multiplication;policy iteration;heuristic performance;probability function propagation;opportunity cost;value function propagation;multi-agent system;decentralized markov decision process"}
{"name": "train_I-70", "title": "A Multi-Agent System for Building Dynamic Ontologies", "abstract": "Ontologies building from text is still a time-consuming task which justifies the growth of Ontology Learning. Our system named Dynamo is designed along this domain but following an original approach based on an adaptive multi-agent architecture. In this paper we present a distributed hierarchical clustering algorithm, core of our approach. It is evaluated and compared to a more conventional centralized algorithm. We also present how it has been improved using a multi-criteria approach. With those results in mind, we discuss the limits of our system and add as perspectives the modifications required to reach a complete ontology building solution.", "fulltext": "1. INTRODUCTION\nNowadays, it is well established that ontologies are needed for\nsemantic web, knowledge management, B2B... For knowledge\nmanagement, ontologies are used to annotate documents and to\nenhance the information retrieval. But building an ontology manually\nis a slow, tedious, costly, complex and time consuming process.\nCurrently, a real challenge lies in building them automatically or\nsemi-automatically and keeping them up to date. It would mean\ncreating dynamic ontologies [10] and it justifies the emergence of\nontology learning techniques [14] [13].\nOur research focuses on Dynamo (an acronym of DYNAMic\nOntologies), a tool based on an adaptive multi-agent system to\nconstruct and maintain an ontology from a domain specific set of texts.\nOur aim is not to build an exhaustive, general hierarchical ontology\nbut a domain specific one. We propose a semi-automated tool since\nan external resource is required: the \"ontologist\". An ontologist is\na kind of cognitive engineer, or analyst, who is using information\nfrom texts and expert interviews to design ontologies.\nIn the multi-agent field, ontologies generally enable agents to\nunderstand each other [12]. They\"re sometimes used to ease the\nontology building process, in particular for collaborative contexts [3],\nbut they rarely represent the ontology itself [16]. Most works\ninterested in the construction of ontologies [7] propose the refinement of\nontologies. This process consists in using an existing ontology and\nbuilding a new one from it. This approach is different from our\napproach because Dynamo starts from scratch. Researchers, working\non the construction of ontologies from texts, claim that the work to\nbe automated requires external resources such as a dictionary [14],\nor web access [5]. In our work, we propose an interaction between\nthe ontologist and the system, our external resource lies both in the\ntexts and the ontologist.\nThis paper first presents, in section 2, the big picture of the\nDynamo system. In particular the motives that led to its creation and\nits general architecture. Then, in section 3 we discuss the\ndistributed clustering algorithm used in Dynamo and compare it to\na more classic centralized approach. Section 4 is dedicated to some\nenhancement of the agents behavior that got designed by taking\ninto account criteria ignored by clustering. And finally, in section\n5, we discuss the limitations of our approach and explain how it\nwill be addressed in further work.\n2. DYNAMO OVERVIEW\n2.1 Ontology as a Multi-Agent System\nDynamo aims at reducing the need for manual actions in\nprocessing the text analysis results and at suggesting a concept\nnetwork kick-off in order to build ontologies more efficiently. The\nchosen approach is completely original to our knowledge and uses\nan adaptive multi-agent system. This choice comes from the\nqualities offered by multi-agent system: they can ease the interactive\ndesign of a system [8] (in our case, a conceptual network), they\nallow its incremental building by progressively taking into account\nnew data (coming from text analysis and user interaction), and last\nbut not least they can be easily distributed across a computer\nnetwork.\nDynamo takes a syntactical and terminological analysis of texts\nas input. It uses several criteria based on statistics computed from\nthe linguistic contexts of terms to create and position the concepts.\nAs output, Dynamo provides to the analyst a hierarchical\norganization of concepts (the multi-agent system itself) that can be\nvalidated, refined of modified, until he/she obtains a satisfying state of\n1286\n978-81-904262-7-5 (RPS) c 2007 IFAAMAS\nthe semantic network.\nAn ontology can be seen as a stable map constituted of\nconceptual entities, represented here by agents, linked by labelled\nrelations. Thus, our approach considers an ontology as a type of\nequilibrium between its concept-agents where their forces are\ndefined by their potential relationships. The ontology modification\nis a perturbation of the previous equilibrium by the appearance or\ndisappearance of agents or relationships. In this way, a dynamic\nontology is a self-organizing process occurring when new texts are\nincluded into the corpus, or when the ontologist interacts with it.\nTo support the needed flexibility of such a system we use a\nselforganizing multi-agent system based on a cooperative approach [9].\nWe followed the ADELFE method [4] proposed to drive the design\nof this kind of multi-agent system. It justifies how we designed\nsome of the rules used by our agents in order to maximize the\ncooperation degree within Dynamo\"s multi-agent system.\n2.2 Proposed Architecture\nIn this section, we present our system architecture. It addresses\nthe needs of Knowledge Engineering in the context of dynamic\nontology management and maintenance when the ontology is linked\nto a document collection.\nThe Dynamo system consists of three parts (cf. figure 1):\n\u2022 a term network, obtained thanks to a term extraction tool\nused to preprocess the textual corpus,\n\u2022 a multi-agent system which uses the term network to make a\nhierarchical clustering in order to obtain a taxonomy of\nconcepts,\n\u2022 an interface allowing the ontologist to visualize and control\nthe clustering process.\n??\nOntologist\nInterface\nSystem\nConcept Agent Term\nTerm network\nTerms\nExtraction\nTool\nFigure 1: System architecture\nThe term extractor we use is Syntex, a software that has\nefficiently been used for ontology building tasks [11]. We mainly\nselected it because of its robustness and the great amount of\ninformation extracted. In particular, it creates a \"Head-Expansion\" network\nwhich has already proven to be interesting for a clustering system\n[1]. In such a network, each term is linked to its head term1\nand\n1\ni.e. the maximum sub-phrase located as head of the term\nits expansion term2\n, and also to all the terms for which it is a head\nor an expansion term. For example, \"knowledge engineering from\ntext\" has \"knowledge engineering\" as head term and \"text\" as\nexpansion term. Moreover, \"knowledge engineering\" is composed of\n\"knowledge\" as head term and \"engineering\" as expansion term.\nWith Dynamo, the term network obtained as the output of the\nextractor is stored in a database. For each term pair, we assume that it\nis possible to compute a similarity value in order to make a\nclustering [6] [1]. Because of the nature of the data, we are only focusing\non similarity computation between objects described thanks to\nbinary variables, that means that each item is described by the\npresence or absence of a characteristic set [15]. In the case of terms\nwe are generally dealing with their usage contexts. With Syntex,\nthose contexts are identified by terms and characterized by some\nsyntactic relations.\nThe Dynamo multi-agent system implements the distributed\nclustering algorithm described in detail in section 3 and the rules\ndescribed in section 4. It is designed to be both the system\nproducing the resulting structure and the structure itself. It means that\neach agent represent a class in the taxonomy. Then, the system\noutput is the organization obtained from the interaction between\nagents, while taking into account feedback coming from the\nontologist when he/she modifies the taxonomy given his needs or\nexpertise.\n3. DISTRIBUTED CLUSTERING\nThis section presents the distributed clustering algorithm used in\nDynamo. For the sake of understanding, and because of its\nevaluation in section 3.1, we recall the basic centralized algorithm used\nfor a hierarchical ascending clustering in a non metric space, when\na symmetrical similarity measure is available [15] (which is the\ncase of the measures used in our system).\nAlgorithm 1: Centralized hierarchical ascending clustering\nalgorithm\nData: List L of items to organize as a hierarchy\nResult: Root R of the hierarchy\nwhile length(L) > 1 do\nmax \u2190 0;\nA \u2190 nil;\nB \u2190 nil;\nfor i \u2190 1 to length(L) do\nI \u2190 L[i];\nfor j \u2190 i + 1 to length(L) do\nJ \u2190 L[j];\nsim \u2190 similarity(I, J);\nif sim > max then\nmax \u2190 sim;\nA \u2190 I;\nB \u2190 J;\nend\nend\nend\nremove(A, L);\nremove(B, L);\nappend((A, B), L);\nend\nR \u2190 L[1];\nIn algorithm 1, for each clustering step, the pair of the most\nsimilar elements is determined. Those two elements are grouped in a\ncluster, and the resulting class is appended to the list of remaining\nelements. This algorithm stops when the list has only one element\nleft.\n2\ni.e. the maximum sub-phrase located as tail of the term\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1287\nThe hierarchy resulting from algorithm 1 is always a binary tree\nbecause of the way grouping is done. Moreover grouping the most\nsimilar elements is equivalent to moving them away from the least\nsimilar ones. Our distributed algorithm is designed relying on those\ntwo facts. It is executed concurrently in each of the agents of the\nsystem.\nNote that, in the following of this paper, we used for both\nalgorithms an Anderberg similarity (with \u03b1 = 0.75) and an average\nlink clustering strategy [15]. Those choices have an impact on the\nresulting tree, but they impact neither the global execution of the\nalgorithm nor its complexity.\nWe now present the distributed algorithm used in our system. It\nis bootstrapped in the following way:\n\u2022 a TOP agent having no parent is created, it will be the root of\nthe resulting taxonomy,\n\u2022 an agent is created for each term to be positioned in the\ntaxonomy, they all have TOP as parent.\nOnce this basic structure is set, the algorithm runs until it reaches\nequilibrium and then provides the resulting taxonomy.\nAk\u22121 Ak AnA2A1\nP\n...... ......\nA1\nFigure 2: Distributed classification: Step 1\nThe process first step (figure 2) is triggered when an agent (here\nAk) has more than one brother (since we want to obtain a binary\ntree). Then it sends a message to its parent P indicating its most\ndissimilar brother (here A1). Then P receives the same kind of\nmessage from each of its children. In the following, this kind of\nmessage will be called a \"vote\".\nAk\u22121 Ak AnA2A1\nP\nP\"\n...... ......\nP\"\nP\"\nFigure 3: Distributed clustering: Step 2\nNext, when P has got messages from all its children, it starts the\nsecond step (figure 3). Thanks to the received messages indicating\nthe preferences of its children, P can determine three sub-groups\namong its children:\n\u2022 the child which got the most \"votes\" by its brothers, that is\nthe child being the most dissimilar from the greatest number\nof its brothers. In case of a draw, one of the winners is chosen\nrandomly (here A1),\n\u2022 the children that allowed the \"election\" of the first group, that\nis the agents which chose their brother of the first group as\nbeing the most dissimilar one (here Ak to An),\n\u2022 the remaining children (here A2 to Ak\u22121).\nThen P creates a new agent P (having P as parent) and asks\nagents from the second group (here agents Ak to An) to make it\ntheir new parent.\nAk\u22121 Ak AnA2A1\nP\nP\"\n...... ......\nFigure 4: Distributed clustering: Step 3\nFinally, step 3 (figure 4) is trivial. The children rejected by P\n(here agent A2 to An) take its message into account and choose P\nas their new parent. The hierarchy just created a new intermediate\nlevel.\nNote that this algorithm generally converges, since the number of\nbrothers of an agent drops. When an agent has only one remaining\nbrother, its activity stops (although it keeps processing messages\ncoming from its children). However in a few cases we can reach\na \"circular conflict\" in the voting procedure when for example A\nvotes against B, B against C and C against A. With the current\nsystem no decision can be taken. The current procedure should be\nimproved to address this, probably using a ranked voting method.\n3.1 Quantitative Evaluation\nNow, we evaluate the properties of our distributed algorithm. It\nrequires to begin with a quantitative evaluation, based on its\ncomplexity, while comparing it with the algorithm 1 from the previous\nsection.\nIts theoretical complexity is calculated for the worst case, by\nconsidering the similarity computation operation as elementary. For\nthe distributed algorithm, the worst case means that for each run,\nonly a two-item group can be created. Under those conditions, for a\ngiven dataset of n items, we can determine the amount of similarity\ncomputations.\nFor algorithm 1, we note l = length(L), then the most enclosed\n\"for\" loop is run l \u2212 i times. And its body has the only similarity\ncomputation, so its cost is l\u2212i. The second \"for\" loop is ran l times\nfor i ranging from 1 to l. Then its cost is\nPl\ni=1(l \u2212 i) which can\nbe simplified in l\u00d7(l\u22121)\n2\n. Finally for each run of the \"while\" loop,\nl is decreased from n to 1 which gives us t1(n) as the amount of\nsimilarity computations for algorithm 1:\nt1(n) =\nnX\nl=1\nl \u00d7 (l \u2212 1)\n2\n(1)\nFor the distributed algorithm, at a given step, each one of the l\nagents evaluates the similarity with its l \u22121 brothers. So each steps\nhas a l \u00d7 (l \u2212 1) cost. Then, groups are created and another vote\noccurs with l decreased by one (since we assume worst case, only\ngroups of size 2 or l \u22121 are built). Since l is equal to n on first run,\nwe obtain tdist(n) as the amount of similarity computations for the\ndistributed algorithm:\ntdist(n) =\nnX\nl=1\nl \u00d7 (l \u2212 1) (2)\nBoth algorithms then have an O(n3\n) complexity. But in the\nworst case, the distributed algorithm does twice the number of\nel1288 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nementary operations done by the centralized algorithm. This gap\ncomes from the local decision making in each agent. Because of\nthis, the similarity computations are done twice for each agent pair.\nWe could conceive that an agent sends its computation result to its\npeer. But, it would simply move the problem by generating more\ncommunication in the system.\n0\n20000\n40000\n60000\n80000\n100000\n120000\n140000\n160000\n180000\n10 20 30 40 50 60 70 80 90 100\nAmountofcomparisons\nAmount of input terms\n1. Distributed algorithm (on average, with min and max)\n2. Logarithmic polynomial\n3. Centralized algorithm\nFigure 5: Experimental results\nIn a second step, the average complexity of the algorithm has\nbeen determined by experiments. The multi-agent system has been\nexecuted with randomly generated input data sets ranging from ten\nto one hundred terms. The given value is the average of\ncomparisons made for one hundred of runs without any user interaction.\nIt results in the plots of figure 5. The algorithm is then more\nefficient on average than the centralized algorithm, and its average\ncomplexity is below the worst case. It can be explained by the low\nprobability that a data set forces the system to create only minimal\ngroups (two items) or maximal (n \u2212 1 elements) for each step of\nreasoning. Curve number 2 represents the logarithmic polynomial\nminimizing the error with curve number 1. The highest degree term\nof this polynomial is in n2\nlog(n), then our distributed algorithm\nhas a O(n2\nlog(n)) complexity on average. Finally, let\"s note the\nreduced variation of the average performances with the maximum\nand the minimum. In the worst case for 100 terms, the variation is\nof 1,960.75 for an average of 40,550.10 (around 5%) which shows\nthe good stability of the system.\n3.2 Qualitative Evaluation\nAlthough the quantitative results are interesting, the real\nadvantage of this approach comes from more qualitative characteristics\nthat we will present in this section. All are advantages obtained\nthanks to the use of an adaptive multi-agent system.\nThe main advantage to the use of a multi-agent system for a\nclustering task is to introduce dynamic in such a system. The ontologist\ncan make modifications and the hierarchy adapts depending on the\nrequest. It is particularly interesting in a knowledge engineering\ncontext. Indeed, the hierarchy created by the system is meant to be\nmodified by the ontologist since it is the result of a statistic\ncomputation. During the necessary look at the texts to examine the\nusage contexts of terms [2], the ontologist will be able to interpret\nthe real content and to revise the system proposal. It is extremely\ndifficult to realize this with a centralized \"black-box\" approach. In\nmost cases, one has to find which reasoning step generated the error\nand to manually modify the resulting class. Unfortunately, in this\ncase, all the reasoning steps that occurred after the creation of the\nmodified class are lost and must be recalculated by taking the\nmodification into account. That is why a system like ASIUM [6] tries to\nsoften the problem with a system-user collaboration by showing to\nthe ontologist the created classes after each step of reasoning. But,\nthe ontologist can make a mistake, and become aware of it too late.\nFigure 6: Concept agent tree after autonomous stabilization of\nthe system\nIn order to illustrate our claims, we present an example thanks to\na few screenshots from the working prototype tested on a medical\nrelated corpus. By using test data and letting the system work by\nitself, we obtain the hierarchy from figure 6 after stabilization. It is\nclear that the concept described by the term \"l\u00e9sion\" (lesion) is\nmisplaced. It happens that the similarity computations place it closer to\n\"femme\" (woman) and \"chirurgien\" (surgeon) than to \"infection\",\n\"gastro-ent\u00e9rite\" (gastro-enteritis) and \"h\u00e9patite\" (hepatitis). This\nwrong position for \"lesion\" is explained by the fact that without\nontologist input the reasoning is only done on statistics criteria.\nFigure 7: Concept agent tree after ontologist modification\nThen, the ontologist replaces the concept in the right branch, by\naffecting \"ConceptAgent:8\" as its new parent. The name\n\"ConceptAgent:X\" is automatically given to a concept agent that is not\ndescribed by a term. The system reacts by itself and refines the\nclustering hierarchy to obtain a binary tree by creating\n\"ConceptAgent:11\". The new stable state if the one of figure 7.\nThis system-user coupling is necessary to build an ontology, but\nno particular adjustment to the distributed algorithm principle is\nneeded since each agent does an autonomous local processing and\ncommunicates with its neighborhood by messages.\nMoreover, this algorithm can de facto be distributed on a\ncomputer network. The communication between agents is then done by\nsending messages and each one keeps its decision autonomy. Then,\na system modification to make it run networked would not require\nto adjust the algorithm. On the contrary, it would only require to\nrework the communication layer and the agent creation process since\nin our current implementation those are not networked.\n4. MULTI-CRITERIA HIERARCHY\nIn the previous sections, we assumed that similarity can be\ncomputed for any term pair. But, as soon as one uses real data this\nproperty is not verified anymore. Some terms do not have any\nsimilarity value with any extracted term. Moreover for leaf nodes it is\nsometimes interesting to use other means to position them in the\nhierarchy. For this low level structuring, ontologists generally base\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1289\ntheir choices on simple heuristics. Using this observation, we built\na new set of rules, which are not based on similarity to support low\nlevel structuring.\n4.1 Adding Head Coverage Rules\nIn this case, agents can act with a very local point of view simply\nby looking at the parent/child relation. Each agent can try to\ndetermine if its parent is adequate. It is possible to guess this because\neach concept agent is described by a set of terms and thanks to the\n\"Head-Expansion\" term network.\nIn the following TX will be the set of terms describing concept\nagent X and head(TX ) the set of all the terms that are head of at\nleast one element of TX . Thanks to those two notations we can\ndescribe the parent adequacy function a(P, C) between a parent P\nand a child C:\na(P, C) =\n|TP \u2229 head(TC )|\n|TP \u222a head(TC )|\n(3)\nThen, the best parent for C is the P agent that maximizes a(P, C).\nAn agent unsatisfied by its parent can then try to find a better one\nby evaluating adequacy with candidates. We designed a\ncomplementary algorithm to drive this search:\nWhen an agent C is unsatisfied by its parent P, it evaluates\na(Bi, C) with all its brothers (noted Bi) the one maximizing a(Bi, C)\nis then chosen as the new parent.\nFigure 8: Concept agent tree after autonomous stabilization of\nthe system without head coverage rule\nWe now illustrate this rule behavior with an example. Figure 8\nshows the state of the system after stabilization on test data. We\ncan notice that \"h\u00e9patite viral\" (viral hepatitis) is still linked to the\ntaxonomy root. It is caused by the fact that there is no similarity\nvalue between the \"viral hepatitis\" term and any of the term of the\nother concept agents.\nFigure 9: Concept agent tree after activation of the head\ncoverage rule\nAfter activating the head coverage rule and letting the system\nstabilize again we obtain figure 9. We can see that \"viral hepatitis\"\nslipped through the branch leading to \"hepatitis\" and chose it as its\nnew parent. It is a sensible default choice since \"viral hepatitis\" is\na more specific term than \"hepatitis\".\nThis rule tends to push agents described by a set of term to\nbecome leafs of the concept tree. It addresses our concern to improve\nthe low level structuring of our taxonomy. But obviously our agents\nlack a way to backtrack in case of modifications in the taxonomy\nwhich would make them be located in the wrong branch. That is\none of the point where our system still has to be improved by adding\nanother set of rules.\n4.2 On Using Several Criteria\nIn the previous sections and examples, we only used one\nalgorithm at a time. The distributed clustering algorithm tends to\nintroduce new layers in the taxonomy, while the head coverage\nalgorithm tends to push some of the agents toward the leafs of the\ntaxonomy. It obviously raises the question on how to deal with\nmultiple criteria in our taxonomy building, and how agents\ndetermine their priorities at a given time.\nThe solution we chose came from the search for minimizing non\ncooperation within the system in accordance with the ADELFE\nmethod. Each agent computes three non cooperation degrees and\nchooses its current priority depending on which degree is the\nhighest. For a given agent A having a parent P, a set of brothers Bi\nand which received a set of messages Mk having the priority pk\nthe three non cooperation degrees are:\n\u2022 \u03bcH (A) = 1 \u2212 a(P, A), is the \"head coverage\" non\ncooperation degree, determined by the head coverage of the parent,\n\u2022 \u03bcB(A) = max(1 \u2212 similarity(A, Bi)), is the\n\"brotherhood\" non cooperation degree, determined by the worst brother\nof A regarding similarities,\n\u2022 \u03bcM (A) = max(pk), is the \"message\" non cooperation\ndegree, determined by the most urgent message received.\nThen, the non cooperation degree \u03bc(A) of agent A is:\n\u03bc(A) = max(\u03bcH (A), \u03bcB(A), \u03bcM (A)) (4)\nThen, we have three cases determining which kind of action A will\nchoose:\n\u2022 if \u03bc(A) = \u03bcH (A) then A will use the head coverage\nalgorithm we detailed in the previous subsection\n\u2022 if \u03bc(A) = \u03bcB(A) then A will use the distributed clustering\nalgorithm (see section 3)\n\u2022 if \u03bc(A) = \u03bcM (A) then A will process Mk immediately in\norder to help its sender\nThose three cases summarize the current activities of our agents:\nthey have to find the best parent for them (\u03bc(A) = \u03bcH (A)),\nimprove the structuring through clustering (\u03bc(A) = \u03bcB(A)) and\nprocess other agent messages (\u03bc(A) = \u03bcM (A)) in order to help them\nfulfill their own goals.\n4.3 Experimental Complexity Revisited\nWe evaluated the experimental complexity of the whole\nmultiagent system when all the rules are activated. In this case, the\nmetric used is the number of messages exchanged in the system. Once\nagain the system has been executed with input data sets ranging\nfrom ten to one hundred terms. The given value is the average of\nmessage amount sent in the system as a whole for one hundred runs\nwithout user interaction. It results in the plots of figure 10.\nCurve number 1 represents the average of the value obtained.\nCurve number 2 represents the average of the value obtained when\nonly the distributed clustering algorithm is activated, not the full\nrule set. Curve number 3 represents the polynomial minimizing the\nerror with curve number 1. The highest degree term of this\npolynomial is in n3\n, then our multi-agent system has a O(n3\n) complexity\n1290 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\n0\n5000\n10000\n15000\n20000\n25000\n10 20 30 40 50 60 70 80 90 100\nAmountofmessages\nAmount of input terms\n1. Dynamo, all rules (on average, with min and max)\n2. Distributed clustering only (on average)\n2. Cubic polynomial\nFigure 10: Experimental results\non average. Moreover, let\"s note the very small variation of the\naverage performances with the maximum and the minimum. In the\nworst case for 100 terms, the variation is of 126.73 for an average\nof 20,737.03 (around 0.6%) which proves the excellent stability of\nthe system.\nFinally the extra head coverage rules are a real improvement on\nthe distributed algorithm alone. They introduce more constraints\nand stability point is reached with less interactions and decision\nmaking by the agents. It means that less messages are exchanged\nin the system while obtaining a tree of higher quality for the\nontologist.\n5. DISCUSSION & PERSPECTIVES\n5.1 Current Limitation of our Approach\nThe most important limitation of our current algorithm is that\nthe result depends on the order the data gets added. When the\nsystem works by itself on a fixed data set given during initialization,\nthe final result is equivalent to what we could obtain with a\ncentralized algorithm. On the contrary, adding a new item after a first\nstabilization has an impact on the final result.\nFigure 11: Concept agent tree after autonomous stabilization\nof the system\nTo illustrate our claims, we present another example of the\nworking system. By using test data and letting the system work by itself,\nwe obtain the hierarchy of figure 11 after stabilization.\nFigure 12: Concept agent tree after taking in account\n\"hepatitis\"\nThen, the ontologist interacts with the system and adds a new\nconcept described by the term \"hepatitis\" and linked to the root.\nThe system reacts and stabilizes, we then obtain figure 12 as a\nresult. \"hepatitis\" is located in the right branch, but we have not\nobtained the same organization as the figure 6 of the previous\nexample. We need to improve our distributed algorithm to allow a\nconcept to move along a branch. We are currently working on the\nrequired rules, but the comparison with centralized algorithm will\nbecome very difficult. In particular since they will take into account\ncriteria ignored by the centralized algorithm.\n5.2 Pruning for Ontologies Building\nIn section 3, we presented the distributed clustering algorithm\nused in the Dynamo system. Since this work was first based on this\nalgorithm, it introduced a clear bias toward binary trees as a result.\nBut we have to keep in mind that we are trying to obtain taxonomies\nwhich are more refined and concise. Although the head coverage\nrule is an improvement because it is based on how the ontologists\ngenerally work, it only addresses low level structuring but not the\nintermediate levels of the tree.\nBy looking at figure 7, it is clear that some pruning could be\ndone in the taxonomy. In particular, since \"l\u00e9sion\" moved,\n\"ConceptAgent:9\" could be removed, it is not needed anymore.\nMoreover the branch starting with \"ConceptAgent:8\" clearly respects the\nconstraint to make a binary tree, but it would be more useful to the\nuser in a more compact and meaningful form. In this case\n\"ConceptAgent:10\" and \"ConceptAgent:11\" could probably be merged.\nCurrently, our system has the necessary rules to create\nintermediate levels in the taxonomy, or to have concepts shifting towards\nthe leaf. As we pointed, it is not enough, so new rules are needed to\nallow removing nodes from the tree, or move them toward the root.\nMost of the work needed to develop those rules consists in finding\nthe relevant statistic information that will support the ontologist.\n6. CONCLUSION\nAfter being presented as a promising solution, ensuring model\nquality and their terminological richness, ontology building from\ntextual corpus analysis is difficult and costly. It requires analyst\nsupervising and taking in account the ontology aim. Using\nnatural languages processing tools ease the knowledge localization in\ntexts through language uses. That said, those tools produce a huge\namount of lexical or grammatical data which is not trivial to\nexamine in order to define conceptual elements. Our contribution lies in\nthis step of the modeling process from texts, before any attempts to\nnormalize or formalize the result.\nWe proposed an approach based on an adaptive multi-agent\nsystem to provide the ontologist with a first taxonomic structure of\nconcepts. Our system makes use of a terminological network\nresulting from an analysis made by Syntex. The current state of our\nsoftware allows to produce simple structures, to propose them to\nthe ontologist and to make them evolve depending on the\nmodifications he made. Performances of the system are interesting and\nsome aspects are even comparable to their centralized counterpart.\nIts strengths are mostly qualitative since it allows more subtle user\ninteractions and a progressive adaptation to new linguistic based\ninformation.\nFrom the point of view of ontology building, this work is a first\nstep showing the relevance of our approach. It must continue, both\nto ensure a better robustness during classification, and to obtain\nricher structures semantic wise than simple trees. From this\nimprovements we are mostly focusing on the pruning to obtain better\ntaxonomies. We\"re currently working on the criterion to trigger\nthe complementary actions of the structure changes applied by our\nclustering algorithm. In other words this algorithm introduces\ninThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1291\ntermediate levels, and we need to be able to remove them if\nnecessary, in order to reach a dynamic equilibrium.\nAlso from the multi-agent engineering point of view, their use\nin a dynamic ontology context has shown its relevance. This\ndynamic ontologies can be seen as complex problem solving, in such\na case self-organization through cooperation has been an efficient\nsolution. And, more generally it\"s likely to be interesting for other\ndesign related tasks, even if we\"re focusing only on knowledge\nengineering in this paper. Of course, our system still requires more\nevaluation and validation work to accurately determine the\nadvantages and flaws of this approach. We\"re planning to work on such\nbenchmarking in the near future.\n7. REFERENCES\n[1] H. Assadi. Construction of a regional ontology from text and\nits use within a documentary system. Proceedings of the\nInternational Conference on Formal Ontology and\nInformation Systems - FOIS\"98, pages 236-249, 1998.\n[2] N. Aussenac-Gilles and D. S\u00f6rgel. Text analysis for ontology\nand terminology engineering. Journal of Applied Ontology,\n2005.\n[3] J. Bao and V. Honavar. Collaborative ontology building with\nwiki@nt. Proceedings of the Workshop on Evaluation of\nOntology-Based Tools (EON2004), 2004.\n[4] C. Bernon, V. Camps, M.-P. Gleizes, and G. Picard.\nAgent-Oriented Methodologies, chapter 7. Engineering\nSelf-Adaptive Multi-Agent Systems : the ADELFE\nMethodology, pages 172-202. Idea Group Publishing, 2005.\n[5] C. Brewster, F. Ciravegna, and Y. Wilks. Background and\nforeground knowledge in dynamic ontology construction.\nSemantic Web Workshop, SIGIR\"03, August 2003.\n[6] D. Faure and C. Nedellec. A corpus-based conceptual\nclustering method for verb frames and ontology acquisition.\nLREC workshop on adapting lexical and corpus resources to\nsublanguages and applications, 1998.\n[7] F. Gandon. Ontology Engineering: a Survey and a Return on\nExperience. INRIA, 2002.\n[8] J.-P. Georg\u00e9, G. Picard, M.-P. Gleizes, and P. Glize. Living\nDesign for Open Computational Systems. 12th IEEE\nInternational Workshops on Enabling Technologies,\nInfrastructure for Collaborative Enterprises, pages 389-394,\nJune 2003.\n[9] M.-P. Gleizes, V. Camps, and P. Glize. A Theory of emergent\ncomputation based on cooperative self-organization for\nadaptive artificial systems. Fourth European Congress of\nSystems Science, September 1999.\n[10] J. Heflin and J. Hendler. Dynamic ontologies on the web.\nAmerican Association for Artificial Intelligence Conference,\n2000.\n[11] S. Le Moigno, J. Charlet, D. Bourigault, and M.-C. Jaulent.\nTerminology extraction from text to build an ontology in\nsurgical intensive care. Proceedings of the AMIA 2002\nannual symposium, 2002.\n[12] K. Lister, L. Sterling, and K. Taveter. Reconciling\nOntological Differences by Assistant Agents. AAMAS\"06,\nMay 2006.\n[13] A. Maedche. Ontology learning for the Semantic Web.\nKluwer Academic Publisher, 2002.\n[14] A. Maedche and S. Staab. Mining Ontologies from Text.\nEKAW 2000, pages 189-202, 2000.\n[15] C. D. Manning and H. Sch\u00fctze. Foundations of Statistical\nNatural Language Processing. The MIT Press, Cambridge,\nMassachusetts, 1999.\n[16] H. V. D. Parunak, R. Rohwer, T. C. Belding, and\nS. Brueckner. Dynamic decentralized any-time hierarchical\nclustering. 29th Annual International ACM SIGIR\nConference on Research & Development on Information\nRetrieval, August 2006.\n1292 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)", "keywords": "cooperation;parent adequacy function;ontology;dynamic equilibrium;hepatitis;emergent behavior;quantitative evaluation;black-box;model quality;multi-agent field;dynamo;terminological richness"}
{"name": "train_I-71", "title": "A Formal Model for Situated Semantic Alignment", "abstract": "Ontology matching is currently a key technology to achieve the semantic alignment of ontological entities used by knowledge-based applications, and therefore to enable their interoperability in distributed environments such as multiagent systems. Most ontology matching mechanisms, however, assume matching prior integration and rely on semantics that has been coded a priori in concept hierarchies or external sources. In this paper, we present a formal model for a semantic alignment procedure that incrementally aligns differing conceptualisations of two or more agents relative to their respective perception of the environment or domain they are acting in. It hence makes the situation in which the alignment occurs explicit in the model. We resort to Channel Theory to carry out the formalisation.", "fulltext": "1. INTRODUCTION\nAn ontology is commonly defined as a specification of the\nconceptualisation of a particular domain. It fixes the\nvocabulary used by knowledge engineers to denote concepts and\ntheir relations, and it constrains the interpretation of this\nvocabulary to the meaning originally intended by knowledge\nengineers. As such, ontologies have been widely adopted as\na key technology that may favour knowledge sharing in\ndistributed environments, such as multi-agent systems,\nfederated databases, or the Semantic Web. But the proliferation\nof many diverse ontologies caused by different\nconceptualisations of even the same domain -and their subsequent\nspecification using varying terminology- has highlighted\nthe need of ontology matching techniques that are\ncapable of computing semantic relationships between entities of\nseparately engineered ontologies. [5, 11]\nUntil recently, most ontology matching mechanisms\ndeveloped so far have taken a classical functional approach\nto the semantic heterogeneity problem, in which ontology\nmatching is seen as a process taking two or more\nontologies as input and producing a semantic alignment of\nontological entities as output [3]. Furthermore, matching\noften has been carried out at design-time, before\nintegrating knowledge-based systems or making them interoperate.\nThis might have been successful for clearly delimited and\nstable domains and for closed distributed systems, but it is\nuntenable and even undesirable for the kind of applications\nthat are currently deployed in open systems. Multi-agent\ncommunication, peer-to-peer information sharing, and\nwebservice composition are all of a decentralised, dynamic, and\nopen-ended nature, and they require ontology matching to\nbe locally performed during run-time. In addition, in many\nsituations peer ontologies are not even open for inspection\n(e.g., when they are based on commercially confidential\ninformation).\nCertainly, there exist efforts to efficiently match\nontological entities at run-time, taking only those ontology\nfragment that are necessary for the task at hand [10, 13, 9, 8].\nNevertheless, the techniques used by these systems to\nestablish the semantic relationships between ontological entities\n-even though applied at run-time- still exploit a priori\ndefined concept taxonomies as they are represented in the\ngraph-based structures of the ontologies to be matched, use\npreviously existing external sources such as thesauri (e.g.,\nWordNet) and upper-level ontologies (e.g., CyC or SUMO),\nor resort to additional background knowledge repositories or\nshared instances.\nWe claim that semantic alignment of ontological\nterminology is ultimately relative to the particular situation in which\nthe alignment is carried out, and that this situation should\nbe made explicit and brought into the alignment\nmechanism. Even two agents with identical conceptualisation\ncapabilities, and using exactly the same vocabulary to specify\ntheir respective conceptualisations may fail to interoperate\n1278\n978-81-904262-7-5 (RPS) c 2007 IFAAMAS\nin a concrete situation because of their differing perception\nof the domain. Imagine a situation in which two agents\nare facing each other in front of a checker board. Agent\nA1 may conceptualise a figure on the board as situated on\nthe left margin of the board, while agent A2 may\nconceptualise the same figure as situated on the right. Although\nthe conceptualisation of \u2018left\" and \u2018right\" is done in exactly\nthe same manner by both agents, and even if both use the\nterms left and right in their communication, they still will\nneed to align their respective vocabularies if they want to\nsuccessfully communicate to each other actions that change\nthe position of figures on the checker board. Their semantic\nalignment, however, will only be valid in the scope of their\ninteraction within this particular situation or environment.\nThe same agents situated differently may produce a different\nalignment.\nThis scenario is reminiscent to those in which a group of\ndistributed agents adapt to form an ontology and a shared\nlexicon in an emergent, bottom-up manner, with only local\ninteractions and no central control authority [12]. This sort\nof self-organised emergence of shared meaning is namely\nultimately grounded on the physical interaction of agents with\nthe environment. In this paper, however, we address the\ncase in which agents are already endowed with a top-down\nengineered ontology (it can even be the same one), which\nthey do not adapt or refine, but for which they want to\nfind the semantic relationships with separate ontologies of\nother agents on the grounds of their communication within a\nspecific situation. In particular, we provide a formal model\nthat formalises situated semantic alignment as a sequence of\ninformation-channel refinements in the sense of Barwise and\nSeligman\"s theory of information flow [1]. This theory is\nparticularly useful for our endeavour because it models the flow\nof information occurring in distributed systems due to the\nparticular situations -or tokens- that carry information.\nAnalogously, the semantic alignment that will allow\ninformation to flow ultimately will be carried by the particular\nsituation agents are acting in.\nWe shall therefore consider a scenario with two or more\nagents situated in an environment. Each agent will have its\nown viewpoint of the environment so that, if the\nenvironment is in a concrete state, both agents may have different\nperceptions of this state. Because of these differences there\nmay be a mismatch in the meaning of the syntactic\nentities by which agents describe their perceptions (and which\nconstitute the agents\" respective ontologies). We state that\nthese syntactic entities can be related according to the\nintrinsic semantics provided by the existing relationship\nbetween the agents\" viewpoint of the environment. The\nexistence of this relationship is precisely justified by the fact that\nthe agents are situated and observe the same environment.\nIn Section 2 we describe our formal model for Situated\nSemantic Alignment (SSA). First, in Section 2.1 we associate\na channel to the scenario under consideration and show how\nthe distributed logic generated by this channel provides the\nlogical relationships between the agents\" viewpoints of the\nenvironment. Second, in Section 2.2 we present a method by\nwhich agents obtain approximations of this distributed logic.\nThese approximations gradually become more reliable as the\nmethod is applied. In Section 3 we report on an application\nof our method. Conclusions and further work are analyzed\nin Section 4. Finally, an appendix summarizes the terms and\ntheorems of Channel theory used along the paper. We do not\nassume any knowledge of Channel Theory; we restate basic\ndefinitions and theorems in the appendix, but any detailed\nexposition of the theory is outside the scope of this paper.\n2. A FORMAL MODEL FOR SSA\n2.1 The Logic of SSA\nConsider a scenario with two agents A1 and A2 situated\nin an environment E (the generalization to any numerable\nset of agents is straightforward). We associate a numerable\nset S of states to E and, at any given instant, we suppose\nE to be in one of these states. We further assume that\neach agent is able to observe the environment and has its\nown perception of it. This ability is faithfully captured by\na surjective function seei : S \u2192 Pi, where i \u2208 {1, 2}, and\ntypically see1 and see2 are different.\nAccording to Channel Theory, information is only viable\nwhere there is a systematic way of classifying some range\nof things as being this way or that, in other words, where\nthere is a classification (see appendix A). So in order to be\nwithin the framework of Channel Theory, we must associate\nclassifications to the components of our system.\nFor each i \u2208 {1, 2}, we consider a classification Ai that\nmodels Ai\"s viewpoint of E. First, tok(Ai) is composed of\nAi\"s perceptions of E states, that is, tok(Ai) = Pi. Second,\ntyp(Ai) contains the syntactic entities by which Ai describes\nits perceptions, the ones constituting the ontology of Ai.\nFinally, |=Ai synthesizes how Ai relates its perceptions with\nthese syntactic entities.\nNow, with the aim of associating environment E with a\nclassification E we choose the power classification of S as E,\nwhich is the classification whose set of types is equal to 2S\n,\nwhose tokens are the elements of S, and for which a token\ne is of type \u03b5 if e \u2208 \u03b5. The reason for taking the power\nclassification is because there are no syntactic entities that\nmay play the role of types for E since, in general, there is no\nglobal conceptualisation of the environment. However, the\nset of types of the power classification includes all possible\ntoken configurations potentially described by types. Thus\ntok(E) = S, typ(E) = 2S\nand e |=E \u03b5 if and only if e \u2208 \u03b5.\nThe notion of channel (see appendix A) is fundamental in\nBarwise and Seligman\"s theory. The information flow among\nthe components of a distributed system is modelled in terms\nof a channel and the relationships among these components\nare expressed via infomorphisms (see appendix A) which\nprovide a way of moving information between them.\nThe information flow of the scenario under consideration\nis accurately described by channel E = {fi : Ai \u2192 E}i\u2208{1,2}\ndefined as follows:\n\u2022 \u02c6fi(\u03b1) = {e \u2208 tok(E) | seei(e) |=Ai \u03b1} for each \u03b1 \u2208\ntyp(Ai)\n\u2022 \u02c7fi(e) = seei(e) for each e \u2208 tok(E)\nwhere i \u2208 {1, 2}. Definition of \u02c7fi seems natural while \u02c6fi is\ndefined in such a way that the fundamental property of the\ninfomorphisms is fulfilled:\n\u02c7fi(e) |=Ai \u03b1 iff seei(e) |=Ai \u03b1 (by definition of \u02c7fi)\niff e \u2208 \u02c6fi(\u03b1) (by definition of \u02c6fi)\niff e |=E\n\u02c6fi(\u03b1) (by definition of |=E)\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1279\nConsequently, E is the core of channel E and a state\ne \u2208 tok(E) connects agents\" perceptions \u02c7f1(e) and \u02c7f2(e) (see\nFigure 1).\ntyp(E)\ntyp(A1)\n\u02c6f1\n99ttttttttt\ntyp(A2)\n\u02c6f2\neeJJJJJJJJJ\ntok(E)\n|=E\n\n\n\n\n\n\n\n\u02c7f1yyttttttttt\n\u02c7f2 %%JJJJJJJJJ\ntok(A1)\n|=A1\n\n\n\n\n\n\n\ntok(A2)\n|=A2\n\n\n\n\n\n\n\nFigure 1: Channel E\nE explains the information flow of our scenario by virtue\nof agents A1 and A2 being situated and perceiving the same\nenvironment E. We want to obtain meaningful relations\namong agents\" syntactic entities, that is, agents\" types. We\nstate that meaningfulness must be in accord with E.\nThe sum operation (see appendix A) gives us a way of\nputting the two agents\" classifications of channel E together\ninto a single classification, namely A1 +A2, and also the two\ninfomorphisms together into a single infomorphism, f1 +f2 :\nA1 + A2 \u2192 E.\nA1 + A2 assembles agents\" classifications in a very coarse\nway. tok(A1 + A2) is the cartesian product of tok(A1) and\ntok(A2), that is, tok(A1 + A2) = { p1, p2 | pi \u2208 Pi}, so a\ntoken of A1 + A2 is a pair of agents\" perceptions with no\nrestrictions. typ(A1 + A2) is the disjoint union of typ(A1)\nand typ(A2), and p1, p2 is of type i, \u03b1 if pi is of type\n\u03b1. We attach importance to take the disjoint union because\nA1 and A2 could use identical types with the purpose of\ndescribing their respective perceptions of E.\nClassification A1 + A2 seems to be the natural place in\nwhich to search for relations among agents\" types. Now,\nChannel Theory provides a way to make all these relations\nexplicit in a logical fashion by means of theories and local\nlogics (see appendix A). The theory generated by the sum\nclassification, Th(A1 + A2), and hence its logic generated,\nLog(A1 + A2), involve all those constraints among agents\"\ntypes valid according to A1 +A2. Notice however that these\nconstraints are obvious. As we stated above, meaningfulness\nmust be in accord with channel E.\nClassifications A1 + A2 and E are connected via the sum\ninfomorphism, f = f1 + f2, where:\n\u2022 \u02c6f( i, \u03b1 ) = \u02c6fi(\u03b1) = {e \u2208 tok(E) | seei(e) |=Ai \u03b1} for\neach i, \u03b1 \u2208 typ(A1 + A2)\n\u2022 \u02c7f(e) = \u02c7f1(e), \u02c7f2(e) = see1(e), see2(e) for each e \u2208\ntok(E)\nMeaningful constraints among agents\" types are in accord\nwith channel E because they are computed making use of f\nas we expound below.\nAs important as the notion of channel is the concept of\ndistributed logic (see appendix A). Given a channel C and\na logic L on its core, DLogC(L) represents the reasoning\nabout relations among the components of C justified by L.\nIf L = Log(C), the distributed logic, we denoted by Log(C),\ncaptures in a logical fashion the information flow inherent\nin the channel.\nIn our case, Log(E) explains the relationship between the\nagents\" viewpoints of the environment in a logical fashion.\nOn the one hand, constraints of Th(Log(E)) are defined by:\n\u0393 Log(E) \u0394 if \u02c6f[\u0393] Log(E)\n\u02c6f[\u0394] (1)\nwhere \u0393, \u0394 \u2286 typ(A1 + A2). On the other hand, the set of\nnormal tokens, NLog(E), is equal to the range of function \u02c7f:\nNLog(E) = \u02c7f[tok(E)]\n= { see1(e), see2(e) | e \u2208 tok(E)}\nTherefore, a normal token is a pair of agents\" perceptions\nthat are restricted by coming from the same environment\nstate (unlike A1 + A2 tokens).\nAll constraints of Th(Log(E)) are satisfied by all normal\ntokens (because of being a logic). In this particular case, this\ncondition is also sufficient (the proof is straightforward); as\nalternative to (1) we have:\n\u0393 Log(E) \u0394 iff for all e \u2208 tok(E),\nif (\u2200 i, \u03b3 \u2208 \u0393)[seei(e) |=Ai \u03b3]\nthen (\u2203 j, \u03b4 \u2208 \u0394)[seej(e) |=Aj \u03b4] (2)\nwhere \u0393, \u0394 \u2286 typ(A1 + A2).\nLog(E) is the logic of SSA. Th(Log(E)) comprises the\nmost meaningful constraints among agents\" types in accord\nwith channel E. In other words, the logic of SSA contains\nand also justifies the most meaningful relations among those\nsyntactic entities that agents use in order to describe their\nown environment perceptions.\nLog(E) is complete since Log(E) is complete but it is not\nnecessarily sound because although Log(E) is sound, \u02c7f is\nnot surjective in general (see appendix B). If Log(E) is also\nsound then Log(E) = Log(A1 +A2) (see appendix B). That\nmeans there is no significant relation between agents\" points\nof view of the environment according to E. It is just the fact\nthat Log(E) is unsound what allows a significant relation\nbetween the agents\" viewpoints. This relation is expressed\nat the type level in terms of constraints by Th(Log(E)) and\nat the token level by NLog(E).\n2.2 Approaching the logic of SSA\nthrough communication\nWe have dubbed Log(E) the logic of SSA. Th(Log(E))\ncomprehends the most meaningful constraints among agents\"\ntypes according to E. The problem is that neither agent\ncan make use of this theory because they do not know E\ncompletely. In this section, we present a method by which\nagents obtain approximations to Th(Log(E)). We also prove\nthese approximations gradually become more reliable as the\nmethod is applied.\nAgents can obtain approximations to Th(Log(E)) through\ncommunication. A1 and A2 communicate by exchanging\ninformation about their perceptions of environment states.\nThis information is expressed in terms of their own\nclassification relations. Specifically, if E is in a concrete state e,\nwe assume that agents can convey to each other which types\nare satisfied by their respective perceptions of e and which\nare not. This exchange generates a channel C = {fi : Ai \u2192\n1280 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nC}i\u2208{1,2} and Th(Log(C)) contains the constraints among\nagents\" types justified by the fact that agents have observed\ne. Now, if E turns to another state e and agents proceed\nas before, another channel C = {fi : Ai \u2192 C }i\u2208{1,2} gives\naccount of the new situation considering also the previous\ninformation. Th(Log(C )) comprises the constraints among\nagents\" types justified by the fact that agents have observed\ne and e . The significant point is that C is a refinement of\nC (see appendix A). Theorem 2.1 below ensures that the\nrefined channel involves more reliable information.\nThe communication supposedly ends when agents have\nobserved all the environment states. Again this situation can\nbe modeled by a channel, call it C\u2217\n= {f\u2217\ni : Ai \u2192 C\u2217\n}i\u2208{1,2}.\nTheorem 2.2 states that Th(Log(C\u2217\n)) = Th(Log(E)).\nTheorem 2.1 and Theorem 2.2 assure that applying the\nmethod agents can obtain approximations to Th(Log(E))\ngradually more reliable.\nTheorem 2.1. Let C = {fi : Ai \u2192 C}i\u2208{1,2} and C =\n{fi : Ai \u2192 C }i\u2208{1,2} be two channels. If C is a refinement\nof C then:\n1. Th(Log(C )) \u2286 Th(Log(C))\n2. NLog(C ) \u2287 NLog(C)\nProof. Since C is a refinement of C then there exists a\nrefinement infomorphism r from C to C; so fi = r \u25e6 fi . Let\nA =def A1 + A2, f =def f1 + f2 and f =def f1 + f2.\n1. Let \u0393 and \u0394 be subsets of typ(A) and assume that\n\u0393 Log(C ) \u0394, which means \u02c6f [\u0393] C\n\u02c6f [\u0394]. We have\nto prove \u0393 Log(C) \u0394, or equivalently, \u02c6f[\u0393] C\n\u02c6f[\u0394].\nWe proceed by reductio ad absurdum. Suppose c \u2208\ntok(C) does not satisfy the sequent \u02c6f[\u0393], \u02c6f[\u0394] . Then\nc |=C\n\u02c6f(\u03b3) for all \u03b3 \u2208 \u0393 and c |=C\n\u02c6f(\u03b4) for all \u03b4 \u2208 \u0394.\nLet us choose an arbitrary \u03b3 \u2208 \u0393. We have that\n\u03b3 = i, \u03b1 for some \u03b1 \u2208 typ(Ai) and i \u2208 {1, 2}. Thus\n\u02c6f(\u03b3) = \u02c6f( i, \u03b1 ) = \u02c6fi(\u03b1) = \u02c6r \u25e6 \u02c6fi (\u03b1) = \u02c6r( \u02c6fi (\u03b1)).\nTherefore:\nc |=C\n\u02c6f(\u03b3) iff c |=C \u02c6r( \u02c6fi (\u03b1))\niff \u02c7r(c) |=C\n\u02c6fi (\u03b1)\niff \u02c7r(c) |=C\n\u02c6f ( i, \u03b1 )\niff \u02c7r(c) |=C\n\u02c6f (\u03b3)\nConsequently, \u02c7r(c) |=C\n\u02c6f (\u03b3) for all \u03b3 \u2208 \u0393. Since\n\u02c6f [\u0393] C\n\u02c6f [\u0394] then there exists \u03b4\u2217\n\u2208 \u0394 such that\n\u02c7r(c) |=C\n\u02c6f (\u03b4\u2217\n). A sequence of equivalences similar to\nthe above one justifies c |=C\n\u02c6f(\u03b4\u2217\n), contradicting that c\nis a counterexample to \u02c6f[\u0393], \u02c6f[\u0394] . Hence \u0393 Log(C) \u0394\nas we wanted to prove.\n2. Let a1, a2 \u2208 tok(A) and assume a1, a2 \u2208 NLog(C).\nTherefore, there exists c token in C such that a1, a2 =\n\u02c7f(c). Then we have ai = \u02c7fi(c) = \u02c7fi \u25e6 \u02c7r(c) = \u02c7fi (\u02c7r(c)),\nfor i \u2208 {1, 2}. Hence a1, a2 = \u02c7f (\u02c7r(c)) and a1, a2 \u2208\nNLog(C ). Consequently, NLog(C ) \u2287 NLog(C) which\nconcludes the proof.\nRemark 2.1. Theorem 2.1 asserts that the more refined\nchannel gives more reliable information. Even though its\ntheory has less constraints, it has more normal tokens to\nwhich they apply.\nIn the remainder of the section, we explicitly describe the\nprocess of communication and we conclude with the proof\nof Theorem 2.2.\nLet us assume that typ(Ai) is finite for i \u2208 {1, 2} and S\nis infinite numerable, though the finite case can be treated\nin a similar form. We also choose an infinite numerable set\nof symbols {cn\n| n \u2208 N}1\n.\nWe omit informorphisms superscripts when no confusion\narises. Types are usually denoted by greek letters and tokens\nby latin letters so if f is an infomorphism, f(\u03b1) \u2261 \u02c6f(\u03b1) and\nf(a) \u2261 \u02c7f(a).\nAgents communication starts from the observation of E.\nLet us suppose that E is in state e1\n\u2208 S = tok(E). A1\"s\nperception of e1\nis f1(e1\n) and A2\"s perception of e1\nis f2(e1\n).\nWe take for granted that A1 can communicate A2 those\ntypes that are and are not satisfied by f1(e1\n) according to\nits classification A1. So can A2 do. Since both typ(A1) and\ntyp(A2) are finite, this process eventually finishes. After\nthis communication a channel C1\n= {f1\ni : Ai \u2192 C1\n}i=1,2\narises (see Figure 2).\nC1\nA1\nf1\n1\n==||||||||\nA2\nf1\n2\naaCCCCCCCC\nFigure 2: The first communication stage\nOn the one hand, C1\nis defined by:\n\u2022 tok(C1\n) = {c1\n}\n\u2022 typ(C1\n) = typ(A1 + A2)\n\u2022 c1\n|=C1 i, \u03b1 if fi(e1\n) |=Ai \u03b1\n(for every i, \u03b1 \u2208 typ(A1 + A2))\nOn the other hand, f1\ni , with i \u2208 {1, 2}, is defined by:\n\u2022 f1\ni (\u03b1) = i, \u03b1\n(for every \u03b1 \u2208 typ(Ai))\n\u2022 f1\ni (c1\n) = fi(e1\n)\nLog(C1\n) represents the reasoning about the first stage of\ncommunication. It is easy to prove that Th(Log(C1\n)) =\nTh(C1\n). The significant point is that both agents know C1\nas the result of the communication. Hence they can compute\nseparately theory Th(C1\n) = typ(C1\n), C1 which contains\nthe constraints among agents\" types justified by the fact that\nagents have observed e1\n.\nNow, let us assume that E turns to a new state e2\n. Agents\ncan proceed as before, exchanging this time information\nabout their perceptions of e2\n. Another channel C2\n= {f2\ni :\nAi \u2192 C2\n}i\u2208{1,2} comes up. We define C2\nso as to take also\ninto account the information provided by the previous stage\nof communication.\nOn the one hand, C2\nis defined by:\n\u2022 tok(C2\n) = {c1\n, c2\n}\n1\nWe write these symbols with superindices because we limit\nthe use of subindices for what concerns to agents. Note this\nset is chosen with the same cardinality of S.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1281\n\u2022 typ(C2\n) = typ(A1 + A2)\n\u2022 ck\n|=C2 i, \u03b1 if fi(ek\n) |=Ai \u03b1\n(for every k \u2208 {1, 2} and i, \u03b1 \u2208 typ(A1 + A2))\nOn the other hand, f2\ni , with i \u2208 {1, 2}, is defined by:\n\u2022 f2\ni (\u03b1) = i, \u03b1\n(for every \u03b1 \u2208 typ(Ai))\n\u2022 f2\ni (ck\n) = fi(ek\n)\n(for every k \u2208 {1, 2})\nLog(C2\n) represents the reasoning about the former and\nthe later communication stages. Th(Log(C2\n)) is equal to\nTh(C2\n) = typ(C2\n), C2 , then it contains the constraints\namong agents\" types justified by the fact that agents have\nobserved e1\nand e2\n. A1 and A2 knows C2\nso they can use\nthese constraints. The key point is that channel C2\nis a\nrefinement of C1\n. It is easy to check that f1\ndefined as\nthe identity function on types and the inclusion function on\ntokens is a refinement infomorphism (see at the bottom of\nFigure 3). By Theorem 2.1, C2\nconstraints are more reliable\nthan C1\nconstraints.\nIn the general situation, once the states e1\n, e2\n, . . . , en\u22121\n(n \u2265 2) have been observed and a new state en\nappears,\nchannel Cn\n= {fn\ni : Ai \u2192 Cn\n}i\u2208{1,2} informs about agents\ncommunication up to that moment. Cn\ndefinition is\nsimilar to the previous ones and analogous remarks can be\nmade (see at the top of Figure 3). Theory Th(Log(Cn\n)) =\nTh(Cn\n) = typ(Cn\n), Cn contains the constraints among\nagents\" types justified by the fact that agents have observed\ne1\n, e2\n, . . . , en\n.\nCn\nfn\u22121\n\u0015\u0015\nA1\nfn\u22121\n1\n99PPPPPPPPPPPPP\nfn\n1\nUUnnnnnnnnnnnnn\nf2\n1\n%%44444444444444444444444444\nf1\n1\n\"\",,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, A2\nfn\n2\nggPPPPPPPPPPPPP\nfn\u22121\n2\nwwnnnnnnnnnnnnn\nf2\n2\n\u00d5\u00d5\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nf1\n2\n\u00d8\u00d8\u0012\u0012\u0012\u0012\u0012\u0012\u0012\u0012\u0012\u0012\u0012\u0012\u0012\u0012\u0012\u0012\u0012\u0012\u0012\u0012\u0012\u0012\u0012\u0012\u0012\u0012\u0012\u0012\u0012\u0012\u0012\u0012\u0012\u0012\u0012\u0012\u0012\u0012\nCn\u22121\n\u0015\u0015\n.\n.\n.\n\u0015\u0015\nC2\nf1\n\u0015\u0015\nC1\nFigure 3: Agents communication\nRemember we have assumed that S is infinite numerable.\nIt is therefore unpractical to let communication finish when\nall environment states have been observed by A1 and A2.\nAt that point, the family of channels {Cn\n}n\u2208N would inform\nof all the communication stages. It is therefore up to the\nagents to decide when to stop communicating should a good\nenough approximation have been reached for the purposes of\ntheir respective tasks. But the study of possible termination\ncriteria is outside the scope of this paper and left for future\nwork. From a theoretical point of view, however, we can\nconsider the channel C\u2217\n= {f\u2217\ni : Ai \u2192 C\u2217\n}i\u2208{1,2} which\ninforms of the end of the communication after observing all\nenvironment states.\nOn the one hand, C\u2217\nis defined by:\n\u2022 tok(C\u2217\n) = {cn\n| n \u2208 N}\n\u2022 typ(C\u2217\n) = typ(A1 + A2)\n\u2022 cn\n|=C\u2217 i, \u03b1 if fi(en\n) |=Ai \u03b1\n(for n \u2208 N and i, \u03b1 \u2208 typ(A1 + A2))\nOn the other hand, f\u2217\ni , with i \u2208 {1, 2}, is defined by:\n\u2022 f\u2217\ni (\u03b1) = i, \u03b1\n(for \u03b1 \u2208 typ(Ai))\n\u2022 f\u2217\ni (cn\n) = fi(en\n)\n(for n \u2208 N)\nTheorem below constitutes the cornerstone of the model\nexposed in this paper. It ensures, together with Theorem\n2.1, that at each communication stage agents obtain a theory\nthat approximates more closely to the theory generated by\nthe logic of SSA.\nTheorem 2.2. The following statements hold:\n1. For all n \u2208 N, C\u2217\nis a refinement of Cn\n.\n2. Th(Log(E)) = Th(C\u2217\n) = Th(Log(C\u2217\n)).\nProof.\n1. It is easy to prove that for each n \u2208 N, gn\ndefined as the\nidentity function on types and the inclusion function\non tokens is a refinement infomorphism from C\u2217\nto Cn\n.\n2. The second equality is straightforward; the first one\nfollows directly from:\ncn\n|=C\u2217 i, \u03b1 iff \u02c7fi(en\n) |=Ai \u03b1\n(by definition of |=C\u2217 )\niff en\n|=E\n\u02c6fi(\u03b1)\n(because fi is infomorphim)\niff en\n|=E\n\u02c6f( i, \u03b1 )\n(by definition of \u02c6f)\nE\nC\u2217\ngn\n\u0015\u0015\nA1\nfn\n1\n99OOOOOOOOOOOOO\nf\u2217\n1\nUUooooooooooooo\nf1\ncc\u007f\u007f\u007f\u007f\u007f\u007f\u007f\u007f\u007f\u007f\u007f\u007f\u007f\u007f\u007f\u007f\u007f\nA2\nf\u2217\n2\nggOOOOOOOOOOOOO\nfn\n2\nwwooooooooooooo\nf2\n\u0095\u0095?????????????????\nCn\n1282 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\n3. AN EXAMPLE\nIn the previous section we have described in great detail\nour formal model for SSA. However, we have not tackled\nthe practical aspect of the model yet. In this section, we\ngive a brushstroke of the pragmatic view of our approach.\nWe study a very simple example and explain how agents\ncan use those approximations of the logic of SSA they can\nobtain through communication.\nLet us reflect on a system consisting of robots located in\na two-dimensional grid looking for packages with the aim of\nmoving them to a certain destination (Figure 4). Robots\ncan carry only one package at a time and they can not move\nthrough a package.\nFigure 4: The scenario\nRobots have a partial view of the domain and there exist\ntwo kinds of robots according to the visual field they have.\nSome robots are capable of observing the eight adjoining\nsquares but others just observe the three squares they have\nin front (see Figure 5). We call them URDL (shortened\nform of Up-Right-Down-Left) and LCR (abbreviation for\nLeft-Center-Right) robots respectively.\nDescribing the environment states as well as the robots\"\nperception functions is rather tedious and even unnecessary.\nWe assume the reader has all those descriptions in mind.\nAll robots in the system must be able to solve package\ndistribution problems cooperatively by communicating their\nintentions to each other. In order to communicate, agents\nsend messages using some ontology. In our scenario, there\ncoexist two ontologies, the UDRL and LCR ontologies. Both\nof them are very simple and are just confined to describe\nwhat robots observe.\nFigure 5: Robots field of vision\nWhen a robot carrying a package finds another package\nobstructing its way, it can either go around it or, if there is\nanother robot in its visual field, ask it for assistance. Let\nus suppose two URDL robots are in a situation like the one\ndepicted in Figure 6. Robot1 (the one carrying a package)\ndecides to ask Robot2 for assistance and sends a request.\nThis request is written below as a KQML message and it\nshould be interpreted intuitively as: Robot2, pick up the\npackage located in my Up square, knowing that you are\nlocated in my Up-Right square.\n`\nrequest\n:sender Robot1\n:receiver Robot2\n:language Packages distribution-language\n:ontology URDL-ontology\n:content (pick up U(Package) because UR(Robot2)\n\u00b4\nFigure 6: Robot assistance\nRobot2 understands the content of the request and it can\nuse a rule represented by the following constraint:\n1, UR(Robot2) , 2, UL(Robot1) , 1, U(Package)\n2, U(Package)\nThe above constraint should be interpreted intuitively as:\nif Robot2 is situated in Robot1\"s Up-Right square, Robot1\nis situated in Robot2\"s Up-Left square and a package is\nlocated in Robot1\"s Up square, then a package is located\nin Robot2\"s Up square.\nNow, problems arise when a LCR robot and a URDL\nrobot try to interoperate. See Figure 7. Robot1 sends a\nrequest of the form:\n`\nrequest\n:sender Robot1\n:receiver Robot2\n:language Packages distribution-language\n:ontology LCR-ontology\n:content (pick up R(Robot2) because C(Package)\n\u00b4\nRobot2 does not understand the content of the request but\nthey decide to begin a process of alignment -corresponding\nwith a channel C1\n. Once finished, Robot2 searches in Th(C1\n)\nfor constraints similar to the expected one, that is, those of\nthe form:\n1, R(Robot2) , 2, UL(Robot1) , 1, C(Package)\nC1 2, \u03bb(Package)\nwhere \u03bb \u2208 {U, R, D, L, UR, DR, DL, UL}. From these, only\nthe following constraints are plausible according to C1\n:\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1283\nFigure 7: Ontology mismatch\n1, R(Robot2) , 2, UL(Robot1) , 1, C(Package)\nC1 2, U(Package)\n1, R(Robot2) , 2, UL(Robot1) , 1, C(Package)\nC1 2, L(Package)\n1, R(Robot2) , 2, UL(Robot1) , 1, C(Package)\nC1 2, DR(Package)\nIf subsequently both robots adopting the same roles take\npart in a situation like the one depicted in Figure 8, a new\nprocess of alignment -corresponding with a channel C2\n- takes\nplace. C2\nalso considers the previous information and hence\nrefines C1\n. The only constraint from the above ones that\nremains plausible according to C2\nis :\n1, R(Robot2) , 2, UL(Robot1) , 1, C(Package)\nC2 2, U(Package)\nNotice that this constraint is an element of the theory of the\ndistributed logic. Agents communicate in order to cooperate\nsuccessfully and success is guaranteed using constrains of the\ndistributed logic.\nFigure 8: Refinement\n4. CONCLUSIONS AND FURTHER WORK\nIn this paper we have exposed a formal model of semantic\nalignment as a sequence of information-channel refinements\nthat are relative to the particular states of the environment\nin which two agents communicate and align their respective\nconceptualisations of these states. Before us, Kent [6] and\nKalfoglou and Schorlemmer [4, 10] have applied Channel\nTheory to formalise semantic alignment using also Barwise\nand Seligman\"s insight to focus on tokens as the enablers\nof information flow. Their approach to semantic alignment,\nhowever, like most ontology matching mechanisms\ndeveloped to date (regardless of whether they follow a functional,\ndesign-time-based approach, or an interaction-based,\nruntime-based approach), still defines semantic alignment in\nterms of a priori design decisions such as the concept\ntaxonomy of the ontologies or the external sources brought into\nthe alignment process. Instead the model we have presented\nin this paper makes explicit the particular states of the\nenvironment in which agents are situated and are attempting\nto gradually align their ontological entities.\nIn the future, our effort will focus on the practical side of\nthe situated semantic alignment problem. We plan to\nfurther refine the model presented here (e.g., to include\npragmatic issues such as termination criteria for the alignment\nprocess) and to devise concrete ontology negotiation\nprotocols based on this model that agents may be able to enact.\nThe formal model exposed in this paper will constitute a\nsolid base of future practical results.\nAcknowledgements\nThis work is supported under the UPIC project, sponsored\nby Spain\"s Ministry of Education and Science under grant\nnumber TIN2004-07461-C02- 02 and also under the\nOpenKnowledge Specific Targeted Research Project (STREP),\nsponsored by the European Commission under contract\nnumber FP6-027253. Marco Schorlemmer is supported by a\nRam\u00b4on y Cajal Research Fellowship from Spain\"s Ministry\nof Education and Science, partially funded by the European\nSocial Fund.\n5. REFERENCES\n[1] J. Barwise and J. Seligman. Information Flow: The\nLogic of Distributed Systems. Cambridge University\nPress, 1997.\n[2] C. Ghidini and F. Giunchiglia. Local models\nsemantics, or contextual reasoning = locality +\ncompatibility. Artificial Intelligence, 127(2):221-259,\n2001.\n[3] F. Giunchiglia and P. Shvaiko. Semantic matching.\nThe Knowledge Engineering Review, 18(3):265-280,\n2004.\n[4] Y. Kalfoglou and M. Schorlemmer. IF-Map: An\nontology-mapping method based on information-flow\ntheory. In Journal on Data Semantics I, LNCS 2800,\n2003.\n[5] Y. Kalfoglou and M. Schorlemmer. Ontology mapping:\nThe sate of the art. The Knowledge Engineering\nReview, 18(1):1-31, 2003.\n[6] R. E. Kent. Semantic integration in the Information\nFlow Framework. In Semantic Interoperability and\nIntegration, Dagstuhl Seminar Proceedings 04391,\n2005.\n[7] D. Lenat. CyC: A large-scale investment in knowledge\ninfrastructure. Communications of the ACM, 38(11),\n1995.\n[8] V. L\u00b4opez, M. Sabou, and E. Motta. PowerMap:\nMapping the real Semantic Web on the fly.\nProceedings of the ISWC\"06, 2006.\n[9] F. McNeill. Dynamic Ontology Refinement. PhD\n1284 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nthesis, School of Informatics, The University of\nEdinburgh, 2006.\n[10] M. Schorlemmer and Y. Kalfoglou. Progressive\nontology alignment for meaning coordination: An\ninformation-theoretic foundation. In 4th Int. Joint\nConf. on Autonomous Agents and Multiagent Systems,\n2005.\n[11] P. Shvaiko and J. Euzenat. A survey of schema-based\nmatching approaches. In Journal on Data Semantics\nIV, LNCS 3730, 2005.\n[12] L. Steels. The Origins of Ontologies and\nCommunication Conventions in Multi-Agent Systems.\nIn Journal of Autonomous Agents and Multi-Agent\nSystems, 1(2), 169-194, 1998.\n[13] J. van Diggelen et al. ANEMONE: An Effective\nMinimal Ontology Negotiation Environment In 5th\nInt. Joint Conf. on Autonomous Agents and\nMultiagent Systems, 2006\nAPPENDIX\nA. CHANNEL THEORY TERMS\nClassification: is a tuple A = tok(A), typ(A), |=A where\ntok(A) is a set of tokens, typ(A) is a set of types and\n|=A is a binary relation between tok(A) and typ(A). If\na |=A \u03b1 then a is said to be of type \u03b1.\nInfomorphism: f : A \u2192 B from classifications A to B is\na contravariant pair of functions f = \u02c6f, \u02c7f , where \u02c6f :\ntyp(A) \u2192 typ(B) and \u02c7f : tok(B) \u2192 tok(A), satisfying\nthe following fundamental property:\n\u02c7f(b) |=A \u03b1 iff b |=B\n\u02c6f(\u03b1)\nfor each token b \u2208 tok(B) and each type \u03b1 \u2208 typ(A).\nChannel: consists of two infomorphisms C = {fi : Ai \u2192\nC}i\u2208{1,2} with a common codomain C, called the core\nof C. C tokens are called connections and a connection\nc is said to connect tokens \u02c7f1(c) and \u02c7f2(c).2\nSum: given classifications A and B, the sum of A and B,\ndenoted by A + B, is the classification with tok(A +\nB) = tok(A) \u00d7 tok(B) = { a, b | a \u2208 tok(A) and b \u2208\ntok(B)}, typ(A + B) = typ(A) typ(B) = { i, \u03b3 |\ni = 1 and \u03b3 \u2208 typ(A) or i = 2 and \u03b3 \u2208 typ(B)} and\nrelation |=A+B defined by:\na, b |=A+B 1, \u03b1 if a |=A \u03b1\na, b |=A+B 2, \u03b2 if b |=B \u03b2\nGiven infomorphisms f : A \u2192 C and g : B \u2192 C,\nthe sum f + g : A + B \u2192 C is defined on types by\n\u02c6(f + g)( 1, \u03b1 ) = \u02c6f(\u03b1) and \u02c6(f + g)( 2, \u03b2 ) = \u02c6g(\u03b2), and\non tokens by \u02c7(f + g)(c) = \u02c7f(c), \u02c7g(c) .\nTheory: given a set \u03a3, a sequent of \u03a3 is a pair \u0393, \u0394 of\nsubsets of \u03a3. A binary relation between subsets of\n\u03a3 is called a consequence relation on \u03a3. A theory is a\npair T = \u03a3, where is a consequence relation on\n\u03a3. A sequent \u0393, \u0394 of \u03a3 for which \u0393 \u0394 is called a\nconstraint of the theory T. T is regular if it satisfies:\n1. Identity: \u03b1 \u03b1\n2. Weakening: if \u0393 \u0394, then \u0393, \u0393 \u0394, \u0394\n2\nIn fact, this is the definition of a binary channel. A channel\ncan be defined with an arbitrary index set.\n3. Global Cut: if \u0393, \u03a00 \u0394, \u03a01 for each partition\n\u03a00, \u03a01 of \u03a0 (i.e., \u03a00 \u222a \u03a01 = \u03a0 and \u03a00 \u2229 \u03a01 = \u2205),\nthen \u0393 \u0394\nfor all \u03b1 \u2208 \u03a3 and all \u0393, \u0393 , \u0394, \u0394 , \u03a0 \u2286 \u03a3.3\nTheory generated by a classification: let A be a\nclassification. A token a \u2208 tok(A) satisfies a sequent \u0393, \u0394\nof typ(A) provided that if a is of every type in \u0393 then\nit is of some type in \u0394. The theory generated by A,\ndenoted by Th(A), is the theory typ(A), A where\n\u0393 A \u0394 if every token in A satisfies \u0393, \u0394 .\nLocal logic: is a tuple L = tok(L), typ(L), |=L , L , NL\nwhere:\n1. tok(L), typ(L), |=L is a classification denoted by\nCla(L),\n2. typ(L), L is a regular theory denoted by Th(L),\n3. NL is a subset of tok(L), called the normal tokens\nof L, which satisfy all constraints of Th(L).\nA local logic L is sound if every token in Cla(L) is\nnormal, that is, NL = tok(L). L is complete if every\nsequent of typ(L) satisfied by every normal token is a\nconstraint of Th(L).\nLocal logic generated by a classification: given a\nclassification A, the local logic generated by A, written\nLog(A), is the local logic on A (i.e., Cla(Log(A)) =\nA), with Th(Log(A)) = Th(A) and such that all its\ntokens are normal, i.e., NLog(A) = tok(A).\nInverse image: given an infomorphism f : A \u2192 B and\na local logic L on B, the inverse image of L under\nf, denoted f\u22121\n[L], is the local logic on A such that\n\u0393 f\u22121[L] \u0394 if \u02c6f[\u0393] L\n\u02c6f[\u0394] and Nf\u22121[L] = \u02c7f[NL ] =\n{a \u2208 tok(A) | a = \u02c7f(b) for some b \u2208 NL }.\nDistributed logic: let C = {fi : Ai \u2192 C}i\u2208{1,2} be a\nchannel and L a local logic on its core C, the distributed\nlogic of C generated by L, written DLogC(L), is the\ninverse image of L under the sum f1 + f2.\nRefinement: let C = {fi : Ai \u2192 C}i\u2208{1,2} and C = {fi :\nAi \u2192 C }i\u2208{1,2} be two channels with the same\ncomponent classifications A1 and A2. A refinement\ninfomorphism from C to C is an infomorphism r : C \u2192 C\nsuch that for each i \u2208 {1, 2}, fi = r \u25e6fi (i.e., \u02c6fi = \u02c6r \u25e6 \u02c6fi\nand \u02c7fi = \u02c7fi \u25e6\u02c7r). Channel C is a refinement of C if there\nexists a refinement infomorphism r from C to C.\nB. CHANNEL THEORY THEOREMS\nTheorem B.1. The logic generated by a classification is\nsound and complete. Furthermore, given a classification A\nand a logic L on A, L is sound and complete if and only if\nL = Log(A).\nTheorem B.2. Let L be a logic on a classification B and\nf : A \u2192 B an infomorphism.\n1. If L is complete then f\u22121\n[L] is complete.\n2. If L is sound and \u02c7f is surjective then f\u22121\n[L] is sound.\n3\nAll theories considered in this paper are regular.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1285", "keywords": "constraint;information-channel refinement;ontology;distributed logic;semantic alignment;distribute logic;knowledge-based system;channel refinement;sum infomorphism;multi-agent system;semantic web;disjoint union;federated database"}
{"name": "train_I-72", "title": "Learning Consumer Preferences Using Semantic Similarity", "abstract": "In online, dynamic environments, the services requested by consumers may not be readily served by the providers. This requires the service consumers and providers to negotiate their service needs and offers. Multiagent negotiation approaches typically assume that the parties agree on service content and focus on finding a consensus on service price. In contrast, this work develops an approach through which the parties can negotiate the content of a service. This calls for a negotiation approach in which the parties can understand the semantics of their requests and offers and learn each other\"s preferences incrementally over time. Accordingly, we propose an architecture in which both consumers and producers use a shared ontology to negotiate a service. Through repetitive interactions, the provider learns consumers\" needs accurately and can make better targeted offers. To enable fast and accurate learning of preferences, we develop an extension to Version Space and compare it with existing learning techniques. We further develop a metric for measuring semantic similarity between services and compare the performance of our approach using different similarity metrics.", "fulltext": "1. INTRODUCTION\nCurrent approaches to e-commerce treat service price as the\nprimary construct for negotiation by assuming that the service content\nis fixed [9]. However, negotiation on price presupposes that other\nproperties of the service have already been agreed upon.\nNevertheless, many times the service provider may not be offering the exact\nrequested service due to lack of resources, constraints in its\nbusiness policy, and so on [3]. When this is the case, the producer and\nthe consumer need to negotiate the content of the requested service\n[15].\nHowever, most existing negotiation approaches assume that all\nfeatures of a service are equally important and concentrate on the\nprice [5, 2]. However, in reality not all features may be relevant and\nthe relevance of a feature may vary from consumer to consumer.\nFor instance, completion time of a service may be important for one\nconsumer whereas the quality of the service may be more important\nfor a second consumer. Without doubt, considering the preferences\nof the consumer has a positive impact on the negotiation process.\nFor this purpose, evaluation of the service components with\ndifferent weights can be useful. Some studies take these weights as a\npriori and uses the fixed weights [4]. On the other hand, mostly\nthe producer does not know the consumer\"s preferences before the\nnegotiation. Hence, it is more appropriate for the producer to learn\nthese preferences for each consumer.\nPreference Learning: As an alternative, we propose an\narchitecture in which the service providers learn the relevant features\nof a service for a particular customer over time. We represent\nservice requests as a vector of service features. We use an ontology\nin order to capture the relations between services and to construct\nthe features for a given service. By using a common ontology, we\nenable the consumers and producers to share a common\nvocabulary for negotiation. The particular service we have used is a wine\nselling service. The wine seller learns the wine preferences of the\ncustomer to sell better targeted wines. The producer models the\nrequests of the consumer and its counter offers to learn which\nfeatures are more important for the consumer. Since no information is\npresent before the interactions start, the learning algorithm has to\nbe incremental so that it can be trained at run time and can revise\nitself with each new interaction.\nService Generation: Even after the producer learns the important\nfeatures for a consumer, it needs a method to generate offers that\nare the most relevant for the consumer among its set of possible\nservices. In other words, the question is how the producer uses the\ninformation that was learned from the dialogues to make the best\noffer to the consumer. For instance, assume that the producer has\nlearned that the consumer wants to buy a red wine but the producer\ncan only offer rose or white wine. What should the producer\"s offer\n1301\n978-81-904262-7-5 (RPS) c 2007 IFAAMAS\ncontain; white wine or rose wine? If the producer has some domain\nknowledge about semantic similarity (e.g., knows that the red and\nrose wines are taste-wise more similar than white wine), then it can\ngenerate better offers. However, in addition to domain knowledge,\nthis derivation requires appropriate metrics to measure similarity\nbetween available services and learned preferences.\nThe rest of this paper is organized as follows: Section 2 explains\nour proposed architecture. Section 3 explains the learning\nalgorithms that were studied to learn consumer preferences. Section 4\nstudies the different service offering mechanisms. Section 5\ncontains the similarity metrics used in the experiments. The details of\nthe developed system is analyzed in Section 6. Section 7 provides\nour experimental setup, test cases, and results. Finally, Section 8\ndiscusses and compares our work with other related work.\n2. ARCHITECTURE\nOur main components are consumer and producer agents, which\ncommunicate with each other to perform content-oriented\nnegotiation. Figure 1 depicts our architecture. The consumer agent\nrepresents the customer and hence has access to the preferences of the\ncustomer. The consumer agent generates requests in accordance\nwith these preferences and negotiates with the producer based on\nthese preferences. Similarly, the producer agent has access to the\nproducer\"s inventory and knows which wines are available or not.\nA shared ontology provides the necessary vocabulary and hence\nenables a common language for agents. This ontology describes\nthe content of the service. Further, since an ontology can represent\nconcepts, their properties and their relationships semantically, the\nagents can reason the details of the service that is being negotiated.\nSince a service can be anything such as selling a car, reserving a\nhotel room, and so on, the architecture is independent of the\nontology used. However, to make our discussion concrete, we use the\nwell-known Wine ontology [19] with some modification to\nillustrate our ideas and to test our system. The wine ontology describes\ndifferent types of wine and includes features such as color, body,\nwinery of the wine and so on. With this ontology, the service that\nis being negotiated between the consumer and the producer is that\nof selling wine.\nThe data repository in Figure 1 is used solely by the producer\nagent and holds the inventory information of the producer. The\ndata repository includes information on the products the producer\nowns, the number of the products and ratings of those products.\nRatings indicate the popularity of the products among customers.\nThose are used to decide which product will be offered when there\nexists more than one product having same similarity to the request\nof the consumer agent.\nThe negotiation takes place in a turn-taking fashion, where the\nconsumer agent starts the negotiation with a particular service\nrequest. The request is composed of significant features of the\nservice. In the wine example, these features include color, winery and\nso on. This is the particular wine that the customer is interested in\npurchasing. If the producer has the requested wine in its inventory,\nthe producer offers the wine and the negotiation ends. Otherwise,\nthe producer offers an alternative wine from the inventory. When\nthe consumer receives a counter offer from the producer, it will\nevaluate it. If it is acceptable, then the negotiation will end.\nOtherwise, the customer will generate a new request or stick to the\nprevious request. This process will continue until some service is\naccepted by the consumer agent or all possible offers are put\nforward to the consumer by the producer.\nOne of the crucial challenges of the content-oriented negotiation\nis the automatic generation of counter offers by the service\nproducer. When the producer constructs its offer, it should consider\nFigure 1: Proposed Negotiation Architecture\nthree important things: the current request, consumer preferences\nand the producer\"s available services. Both the consumer\"s current\nrequest and the producer\"s own available services are accessible by\nthe producer. However, the consumer\"s preferences in most cases\nwill not be available. Hence, the producer will have to understand\nthe needs of the consumer from their interactions and generate a\ncounter offer that is likely to be accepted by the consumer. This\nchallenge can be studied in three stages:\n\u2022 Preference Learning: How can the producers learn about\neach customer\"s preferences based on requests and counter\noffers? (Section 3)\n\u2022 Service Offering: How can the producers revise their offers\nbased on the consumer\"s preferences that they have learned\nso far? (Section 4)\n\u2022 Similarity Estimation: How can the producer agent estimate\nsimilarity between the request and available services?\n(Section 5)\n3. PREFERENCE LEARNING\nThe requests of the consumer and the counter offers of the\nproducer are represented as vectors, where each element in the vector\ncorresponds to the value of a feature. The requests of the consumers\nrepresent individual wine products whereas their preferences are\nconstraints over service features. For example, a consumer may\nhave preference for red wine. This means that the consumer is\nwilling to accept any wine offered by the producers as long as the\ncolor is red. Accordingly, the consumer generates a request where\nthe color feature is set to red and other features are set to arbitrary\nvalues, e.g. (Medium, Strong, Red).\nAt the beginning of negotiation, the producer agent does not\nknow the consumer\"s preferences but will need to learn them\nusing information obtained from the dialogues between the producer\nand the consumer. The preferences denote the relative importance\nof the features of the services demanded by the consumer agents.\nFor instance, the color of the wine may be important so the\nconsumer insists on buying the wine whose color is red and rejects all\n1302 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nTable 1: How DCEA works\nType Sample The most The most\ngeneral set specific set\n+ (Full,Strong,White) {(?, ?, ?)} {(Full,Strong,White)}\n{{(?-Full), ?, ? },\n- (Full,Delicate,Rose) {?, (?-Delicate), ?}, {(Full,Strong,White)}\n{?, ?, (?-Rose)}}\n{{(?-Full), ?, ?}, {{(Full,Strong,White)},\n+ (Medium,Moderate,Red) {?,(?-Delicate), ?}, {(Medium,Moderate,Red)}}\n{?, ?, (?-Rose)}}\nthe offers involving the wine whose color is white or rose. On the\ncontrary, the winery may not be as important as the color for this\ncustomer, so the consumer may have a tendency to accept wines\nfrom any winery as long as the color is red.\nTo tackle this problem, we propose to use incremental learning\nalgorithms [6]. This is necessary since no training data is\navailable before the interactions start. We particularly investigate two\napproaches. The first one is inductive learning. This technique is\napplied to learn the preferences as concepts. We elaborate on\nCandidate Elimination Algorithm (CEA) for Version Space [10]. CEA\nis known to perform poorly if the information to be learned is\ndisjunctive. Interestingly, most of the time consumer preferences are\ndisjunctive. Say, we are considering an agent that is buying wine.\nThe consumer may prefer red wine or rose wine but not white wine.\nTo use CEA with such preferences, a solid modification is\nnecessary. The second approach is decision trees. Decision trees can\nlearn from examples easily and classify new instances as positive\nor negative. A well-known incremental decision tree is ID5R [18].\nHowever, ID5R is known to suffer from high computational\ncomplexity. For this reason, we instead use the ID3 algorithm [13] and\niteratively build decision trees to simulate incremental learning.\n3.1 CEA\nCEA [10] is one of the inductive learning algorithms that learns\nconcepts from observed examples. The algorithm maintains two\nsets to model the concept to be learned. The first set is the most\ngeneral set G. G contains hypotheses about all the possible values\nthat the concept may obtain. As the name suggests, it is a\ngeneralization and contains all possible values unless the values have\nbeen identified not to represent the concept. The second set is the\nmost specific set S. S contains only hypotheses that are known to\nidentify the concept that is being learned. At the beginning of the\nalgorithm, G is initialized to cover all possible concepts while S is\ninitialized to be empty.\nDuring the interactions, each request of the consumer can be\nconsidered as a positive example and each counter offer generated by\nthe producer and rejected by the consumer agent can be thought of\nas a negative example. At each interaction between the producer\nand the consumer, both G and S are modified. The negative\nsamples enforce the specialization of some hypotheses so that G does\nnot cover any hypothesis accepting the negative samples as\npositive. When a positive sample comes, the most specific set S should\nbe generalized in order to cover the new training instance. As a\nresult, the most general hypotheses and the most special hypotheses\ncover all positive training samples but do not cover any negative\nones. Incrementally, G specializes and S generalizes until G and\nS are equal to each other. When these sets are equal, the algorithm\nconverges by means of reaching the target concept.\n3.2 Disjunctive CEA\nUnfortunately, CEA is primarily targeted for conjunctive\nconcepts. On the other hand, we need to learn disjunctive concepts in\nthe negotiation of a service since consumer may have several\nalternative wishes. There are several studies on learning disjunctive\nconcepts via Version Space. Some of these approaches use multiple\nversion space. For instance, Hong et al. maintain several version\nspaces by split and merge operation [7]. To be able to learn\ndisjunctive concepts, they create new version spaces by examining the\nconsistency between G and S.\nWe deal with the problem of not supporting disjunctive concepts\nof CEA by extending our hypothesis language to include\ndisjunctive hypothesis in addition to the conjunctives and negation. Each\nattribute of the hypothesis has two parts: inclusive list, which holds\nthe list of valid values for that attribute and exclusive list, which is\nthe list of values which cannot be taken for that feature.\nEXAMPLE 1. Assume that the most specific set is {(Light,\nDelicate, Red)} and a positive example, (Light, Delicate, White) comes.\nThe original CEA will generalize this as (Light, Delicate, ?),\nmeaning the color can take any value. However, in fact, we only know\nthat the color can be red or white. In the DCEA, we generalize it as\n{(Light, Delicate, [White, Red] )}. Only when all the values exist\nin the list, they will be replaced by ?. In other words, we let the\nalgorithm generalize more slowly than before.\nWe modify the CEA algorithm to deal with this change. The\nmodified algorithm, DCEA, is given as Algorithm 1. Note that\ncompared to the previous studies of disjunctive versions, our\napproach uses only a single version space rather than multiple version\nspace. The initialization phase is the same as the original algorithm\n(lines 1, 2). If any positive sample comes, we add the sample to the\nspecial set as before (line 4). However, we do not eliminate the\nhypotheses in G that do not cover this sample since G now contains a\ndisjunction of many hypotheses, some of which will be conflicting\nwith each other. Removing a specific hypothesis from G will result\nin loss of information, since other hypotheses are not guaranteed\nto cover it. After some time, some hypotheses in S can be merged\nand can construct one hypothesis (lines 6, 7).\nWhen a negative sample comes, we do not change S as before.\nWe only modify the most general hypotheses not to cover this\nnegative sample (lines 11-15). Different from the original CEA, we\ntry to specialize the G minimally. The algorithm removes the\nhypothesis covering the negative sample (line 13). Then, we generate\nnew hypotheses as the number of all possible attributes by using\nthe removed hypothesis.\nFor each attribute in the negative sample, we add one of them\nat each time to the exclusive list of the removed hypothesis. Thus,\nall possible hypotheses that do not cover the negative sample are\ngenerated (line 14). Note that, exclusive list contains the values that\nthe attribute cannot take. For example, consider the color attribute.\nIf a hypothesis includes red in its exclusive list and ? in its inclusive\nlist, this means that color may take any value except red.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1303\nAlgorithm 1 Disjunctive Candidate Elimination Algorithm\n1: G \u2190the set of maximally general hypotheses in H\n2: S \u2190the set of maximally specific hypotheses in H\n3: For each training example, d\n4: if d is a positive example then\n5: Add d to S\n6: if s in S can be combined with d to make one element then\n7: Combine s and d into sd {sd is the rule covers s and d}\n8: end if\n9: end if\n10: if d is a negative example then\n11: For each hypothesis g in G does cover d\n12: * Assume : g = (x1, x2, ..., xn) and d = (d1, d2, ..., dn)\n13: - Remove g from G\n14: - Add hypotheses g1, g2, gn where g1= (x1-d1, x2,..., xn),\ng2= (x1, x2-d2,..., xn),..., and gn= (x1, x2,..., xn-dn)\n15: - Remove from G any hypothesis that is less general than\nanother hypothesis in G\n16: end if\nEXAMPLE 2. Table 1 illustrates the first three interactions and\nthe workings of DCEA. The most general set and the most specific\nset show the contents of G and S after the sample comes in. After\nthe first positive sample, S is generalized to also cover the instance.\nThe second sample is negative. Thus, we replace (?, ?, ?) by three\ndisjunctive hypotheses; each hypothesis being minimally\nspecialized. In this process, at each time one attribute value of negative\nsample is applied to the hypothesis in the general set. The third\nsample is positive and generalizes S even more.\nNote that in Table 1, we do not eliminate {(?-Full), ?, ?} from\nthe general set while having a positive sample such as (Full, Strong,\nWhite). This stems from the possibility of using this rule in the\ngeneration of other hypotheses. For instance, if the example continues\nwith a negative sample (Full, Strong, Red), we can specialize the\nprevious rule such as {(?-Full), ?, (?-Red)}. By Algorithm 1, we\ndo not miss any information.\n3.3 ID3\nID3 [13] is an algorithm that constructs decision trees in a\ntopdown fashion from the observed examples represented in a vector\nwith attribute-value pairs. Applying this algorithm to our system\nwith the intention of learning the consumer\"s preferences is\nappropriate since this algorithm also supports learning disjunctive\nconcepts in addition to conjunctive concepts.\nThe ID3 algorithm is used in the learning process with the\npurpose of classification of offers. There are two classes: positive and\nnegative. Positive means that the service description will possibly\nbe accepted by the consumer agent whereas the negative implies\nthat it will potentially be rejected by the consumer. Consumer\"s\nrequests are considered as positive training examples and all rejected\ncounter-offers are thought as negative ones.\nThe decision tree has two types of nodes: leaf node in which the\nclass labels of the instances are held and non-leaf nodes in which\ntest attributes are held. The test attribute in a non-leaf node is one of\nthe attributes making up the service description. For instance, body,\nflavor, color and so on are potential test attributes for wine service.\nWhen we want to find whether the given service description is\nacceptable, we start searching from the root node by examining the\nvalue of test attributes until reaching a leaf node.\nThe problem with this algorithm is that it is not an\nincremental algorithm, which means all the training examples should exist\nbefore learning. To overcome this problem, the system keeps\nconsumer\"s requests throughout the negotiation interaction as positive\nexamples and all counter-offers rejected by the consumer as\nnegative examples. After each coming request, the decision tree is\nrebuilt. Without doubt, there is a drawback of reconstruction such\nas additional process load. However, in practice we have evaluated\nID3 to be fast and the reconstruction cost to be negligible.\n4. SERVICE OFFERING\nAfter learning the consumer\"s preferences, the producer needs to\nmake a counter offer that is compatible with the consumer\"s\npreferences.\n4.1 Service Offering via CEA and DCEA\nTo generate the best offer, the producer agent uses its service\nontology and the CEA algorithm. The service offering mechanism\nis the same for both the original CEA and DCEA, but as explained\nbefore their methods for updating G and S are different.\nWhen producer receives a request from the consumer, the\nlearning set of the producer is trained with this request as a positive\nsample. The learning components, the most specific set S and the\nmost general set G are actively used in offering service. The most\ngeneral set, G is used by the producer in order to avoid offering the\nservices, which will be rejected by the consumer agent. In other\nwords, it filters the service set from the undesired services, since\nG contains hypotheses that are consistent with the requests of the\nconsumer. The most specific set, S is used in order to find best\noffer, which is similar to the consumer\"s preferences. Since the most\nspecific set S holds the previous requests and the current request,\nestimating similarity between this set and every service in the\nservice list is very convenient to find the best offer from the service\nlist.\nWhen the consumer starts the interaction with the producer agent,\nproducer agent loads all related services to the service list object.\nThis list constitutes the provider\"s inventory of services. Upon\nreceiving a request, if the producer can offer an exactly matching\nservice, then it does so. For example, for a wine this corresponds\nto selling a wine that matches the specified features of the\nconsumer\"s request identically. When the producer cannot offer the\nservice as requested, it tries to find the service that is most similar\nto the services that have been requested by the consumer during the\nnegotiation. To do this, the producer has to compute the similarity\nbetween the services it can offer and the services that have been\nrequested (in S).\nWe compute the similarities in various ways as will be explained\nin Section 5. After the similarity of the available services with the\ncurrent S is calculated, there may be more than one service with\nthe maximum similarity. The producer agent can break the tie in a\nnumber of ways. Here, we have associated a rating value with each\nservice and the producer prefers the higher rated service to others.\n4.2 Service Offering via ID3\nIf the producer learns the consumer\"s preferences with ID3, a\nsimilar mechanism is applied with two differences. First, since ID3\ndoes not maintain G, the list of unaccepted services that are\nclassified as negative are removed from the service list. Second, the\nsimilarities of possible services are not measured with respect to S,\nbut instead to all previously made requests.\n4.3 Alternative Service Offering Mechanisms\nIn addition to these three service offering mechanisms (Service\nOffering with CEA, Service Offering with DCEA, and Service\nOffering with ID3), we include two other mechanisms..\n1304 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\n\u2022 Random Service Offering (RO): The producer generates a\ncounter offer randomly from the available service list,\nwithout considering the consumer\"s preferences.\n\u2022 Service Offering considering only the current request (SCR):\nThe producer selects a counter offer according to the\nsimilarity of the consumer\"s current request but does not consider\nprevious requests.\n5. SIMILARITY ESTIMATION\nSimilarity can be estimated with a similarity metric that takes\ntwo entries and returns how similar they are. There are several\nsimilarity metrics used in case based reasoning system such as weighted\nsum of Euclidean distance, Hamming distance and so on [12].\nThe similarity metric affects the performance of the system while\ndeciding which service is the closest to the consumer\"s request. We\nfirst analyze some existing metrics and then propose a new\nsemantic similarity metric named RP Similarity.\n5.1 Tversky\"s Similarity Metric\nTversky\"s similarity metric compares two vectors in terms of\nthe number of exactly matching features [17]. In Equation (1),\ncommon represents the number of matched attributes whereas\ndifferent represents the number of the different attributes. Our\ncurrent assumption is that \u03b1 and \u03b2 is equal to each other.\nSMpq =\n\u03b1(common)\n\u03b1(common) + \u03b2(different)\n(1)\nHere, when two features are compared, we assign zero for\ndissimilarity and one for similarity by omitting the semantic closeness\namong the feature values.\nTversky\"s similarity metric is designed to compare two feature\nvectors. In our system, whereas the list of services that can be\noffered by the producer are each a feature vector, the most specific\nset S is not a feature vector. S consists of hypotheses of feature\nvectors. Therefore, we estimate the similarity of each hypothesis\ninside the most specific set S and then take the average of the\nsimilarities.\nEXAMPLE 3. Assume that S contains the following two\nhypothesis: { {Light, Moderate, (Red, White)} , {Full, Strong, Rose}}.\nTake service s as (Light, Strong, Rose). Then the similarity of the\nfirst one is equal to 1/3 and the second one is equal to 2/3 in\naccordance with Equation (1). Normally, we take the average of it\nand obtain (1/3 + 2/3)/2, equally 1/2. However, the first\nhypothesis involves the effect of two requests and the second hypothesis\ninvolves only one request. As a result, we expect the effect of the\nfirst hypothesis to be greater than that of the second. Therefore,\nwe calculate the average similarity by considering the number of\nsamples that hypotheses cover.\nLet ch denote the number of samples that hypothesis h covers\nand (SM(h,service)) denote the similarity of hypothesis h with the\ngiven service. We compute the similarity of each hypothesis with\nthe given service and weight them with the number of samples they\ncover. We find the similarity by dividing the weighted sum of the\nsimilarities of all hypotheses in S with the service by the number\nof all samples that are covered in S.\nAV G\u2212SM(service,S) =\n|S|\n|h| (ch \u2217 SM(h,service))\n|S|\n|h| ch\n(2)\nFigure 2: Sample taxonomy for similarity estimation\nEXAMPLE 4. For the above example, the similarity of (Light,\nStrong, Rose) with the specific set is (2 \u2217 1/3 + 2/3)/3, equally\n4/9. The possible number of samples that a hypothesis covers can\nbe estimated with multiplying cardinalities of each attribute. For\nexample, the cardinality of the first attribute is two and the others\nis equal to one for the given hypothesis such as {Light, Moderate,\n(Red, White)}. When we multiply them, we obtain two (2 \u2217 1 \u2217 1 =\n2).\n5.2 Lin\"s Similarity Metric\nA taxonomy can be used while estimating semantic similarity\nbetween two concepts. Estimating semantic similarity in a Is-A\ntaxonomy can be done by calculating the distance between the nodes\nrelated to the compared concepts. The links among the nodes can\nbe considered as distances. Then, the length of the path between the\nnodes indicates how closely similar the concepts are. An\nalternative estimation to use information content in estimation of semantic\nsimilarity rather than edge counting method, was proposed by Lin\n[8]. The equation (3) [8] shows Lin\"s similarity where c1 and c2\nare the compared concepts and c0 is the most specific concept that\nsubsumes both of them. Besides, P(C) represents the probability\nof an arbitrary selected object belongs to concept C.\nSimilarity(c1, c2) =\n2 \u00d7 log P(c0)\nlog P(c1) + log P(c2)\n(3)\n5.3 Wu & Palmer\"s Similarity Metric\nDifferent from Lin, Wu and Palmer use the distance between the\nnodes in IS-A taxonomy [20]. The semantic similarity is\nrepresented with Equation (4) [20]. Here, the similarity between c1 and\nc2 is estimated and c0 is the most specific concept subsuming these\nclasses. N1 is the number of edges between c1 and c0. N2 is the\nnumber of edges between c2 and c0. N0 is the number of IS-A\nlinks of c0 from the root of the taxonomy.\nSimW u&P almer(c1, c2) =\n2 \u00d7 N0\nN1 + N2 + 2 \u00d7 N0\n(4)\n5.4 RP Semantic Metric\nWe propose to estimate the relative distance in a taxonomy\nbetween two concepts using the following intuitions. We use Figure\n2 to illustrate these intuitions.\n\u2022 Parent versus grandparent: Parent of a node is more\nsimilar to the node than grandparents of that. Generalization of\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1305\na concept reasonably results in going further away that\nconcept. The more general concepts are, the less similar they\nare. For example, AnyWineColor is parent of ReddishColor\nand ReddishColor is parent of Red. Then, we expect the\nsimilarity between ReddishColor and Red to be higher than that\nof the similarity between AnyWineColor and Red.\n\u2022 Parent versus sibling: A node would have higher similarity\nto its parent than to its sibling. For instance, Red and Rose\nare children of ReddishColor. In this case, we expect the\nsimilarity between Red and ReddishColor to be higher than\nthat of Red and Rose.\n\u2022 Sibling versus grandparent: A node is more similar to it\"s\nsibling then to its grandparent. To illustrate, AnyWineColor\nis grandparent of Red, and Red and Rose are siblings.\nTherefore, we possibly anticipate that Red and Rose are more\nsimilar than AnyWineColor and Red.\nAs a taxonomy is represented in a tree, that tree can be traversed\nfrom the first concept being compared through the second concept.\nAt starting node related to the first concept, the similarity value is\nconstant and equal to one. This value is diminished by a constant\nat each node being visited over the path that will reach to the node\nincluding the second concept. The shorter the path between the\nconcepts, the higher the similarity between nodes.\nAlgorithm 2 Estimate-RP-Similarity(c1,c2)\nRequire: The constants should be m > n > m2\nwhere m, n \u2208\nR[0, 1]\n1: Similarity \u2190 1\n2: if c1 is equal to c2 then\n3: Return Similarity\n4: end if\n5: commonParent \u2190 findCommonParent(c1, c2)\n{commonParent is the most specific concept that covers\nboth c1 and c2}\n6: N1 \u2190 findDistance(commonParent, c1)\n7: N2 \u2190 findDistance(commonParent, c2) {N1 & N2 are\nthe number of links between the concept and parent concept}\n8: if (commonParent == c1) or (commonParent == c2) then\n9: Similarity \u2190 Similarity \u2217 m(N1+N2)\n10: else\n11: Similarity \u2190 Similarity \u2217 n \u2217 m(N1+N2\u22122)\n12: end if\n13: Return Similarity\nRelative distance between nodes c1 and c2 is estimated in the\nfollowing way. Starting from c1, the tree is traversed to reach c2.\nAt each hop, the similarity decreases since the concepts are getting\nfarther away from each other. However, based on our intuitions,\nnot all hops decrease the similarity equally.\nLet m represent the factor for hopping from a child to a parent\nand n represent the factor for hopping from a sibling to another\nsibling. Since hopping from a node to its grandparent counts as\ntwo parent hops, the discount factor of moving from a node to its\ngrandparent is m2\n. According to the above intuitions, our constants\nshould be in the form m > n > m2\nwhere the value of m and n\nshould be between zero and one. Algorithm 2 shows the distance\ncalculation.\nAccording to the algorithm, firstly the similarity is initialized\nwith the value of one (line 1). If the concepts are equal to each other\nthen, similarity will be one (lines 2-4). Otherwise, we compute the\ncommon parent of the two nodes and the distance of each concept\nto the common parent without considering the sibling (lines 5-7).\nIf one of the concepts is equal to the common parent, then there\nis no sibling relation between the concepts. For each level, we\nmultiply the similarity by m and do not consider the sibling factor\nin the similarity estimation. As a result, we decrease the similarity\nat each level with the rate of m (line9). Otherwise, there has to be\na sibling relation. This means that we have to consider the effect of\nn when measuring similarity. Recall that we have counted N1+N2\nedges between the concepts. Since there is a sibling relation, two of\nthese edges constitute the sibling relation. Hence, when calculating\nthe effect of the parent relation, we use N1+N2 \u22122 edges (line 11).\nSome similarity estimations related to the taxonomy in Figure 2\nare given in Table 2. In this example, m is taken as 2/3 and n is\ntaken as 4/7.\nTable 2: Sample similarity estimation over sample taxonomy\nSimilarity(ReddishColor, Rose) = 1 \u2217 (2/3) = 0.6666667\nSimilarity(Red, Rose) = 1 \u2217 (4/7) = 0.5714286\nSimilarity(AnyW ineColor,Rose) = 1 \u2217 (2/3)2\n= 0.44444445\nSimilarity(W hite,Rose) = 1 \u2217 (2/3) \u2217 (4/7) = 0.3809524\nFor all semantic similarity metrics in our architecture, the\ntaxonomy for features is held in the shared ontology. In order to evaluate\nthe similarity of feature vector, we firstly estimate the similarity for\nfeature one by one and take the average sum of these similarities.\nThen the result is equal to the average semantic similarity of the\nentire feature vector.\n6. DEVELOPED SYSTEM\nWe have implemented our architecture in Java. To ease testing\nof the system, the consumer agent has a user interface that allows\nus to enter various requests. The producer agent is fully automated\nand the learning and service offering operations work as explained\nbefore. In this section, we explain the implementation details of the\ndeveloped system.\nWe use OWL [11] as our ontology language and JENA as our\nontology reasoner. The shared ontology is the modified version of\nthe Wine Ontology [19]. It includes the description of wine as a\nconcept and different types of wine. All participants of the\nnegotiation use this ontology for understanding each other. According\nto the ontology, seven properties make up the wine concept. The\nconsumer agent and the producer agent obtain the possible values\nfor the these properties by querying the ontology. Thus, all\npossible values for the components of the wine concept such as color,\nbody, sugar and so on can be reached by both agents. Also a\nvariety of wine types are described in this ontology such as Burgundy,\nChardonnay, CheninBlanc and so on. Intuitively, any wine type\ndescribed in the ontology also represents a wine concept. This allows\nus to consider instances of Chardonnay wine as instances of Wine\nclass.\nIn addition to wine description, the hierarchical information of\nsome features can be inferred from the ontology. For instance,\nwe can represent the information Europe Continent covers\nWestern Country. Western Country covers French Region, which covers\nsome territories such as Loire, Bordeaux and so on. This\nhierarchical information is used in estimation of semantic similarity. In this\npart, some reasoning can be made such as if a concept X covers Y\nand Y covers Z, then concept X covers Z. For example, Europe\nContinent covers Bordeaux.\n1306 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nFor some features such as body, flavor and sugar, there is no\nhierarchical information, but their values are semantically leveled.\nWhen that is the case, we give the reasonable similarity values for\nthese features. For example, the body can be light, medium, or\nstrong. In this case, we assume that light is 0.66 similar to medium\nbut only 0.33 to strong.\nWineStock Ontology is the producer\"s inventory and describes\na product class as WineProduct. This class is necessary for the\nproducer to record the wines that it sells. Ontology involves the\nindividuals of this class. The individuals represent available services\nthat the producer owns. We have prepared two separate WineStock\nontologies for testing. In the first ontology, there are 19 available\nwine products and in the second ontology, there are 50 products.\n7. PERFORMANCE EVALUATION\nWe evaluate the performance of the proposed systems in respect\nto learning technique they used, DCEA and ID3, by comparing\nthem with the CEA, RO (for random offering), and SCR (offering\nbased on current request only).\nWe apply a variety of scenarios on this dataset in order to see the\nperformance differences. Each test scenario contains a list of\npreferences for the user and number of matches from the product list.\nTable 3 shows these preferences and availability of those products\nin the inventory for first five scenarios. Note that these preferences\nare internal to the consumer and the producer tries to learn these\nduring negotiation.\nTable 3: Availability of wines in different test scenarios\nID Preference of consumer Availability (out of 19)\n1 Dry wine 15\n2 Red and dry wine 8\n3 Red, dry and moderate wine 4\n4 Red and strong wine 2\n5 Red or rose, and strong 3\n7.1 Comparison of Learning Algorithms\nIn comparison of learning algorithms, we use the five scenarios\nin Table 3. Here, first we use Tversky\"s similarity measure. With\nthese test cases, we are interested in finding the number of\niterations that are required for the producer to generate an acceptable\noffer for the consumer. Since the performance also depends on the\ninitial request, we repeat our experiments with different initial\nrequests. Consequently, for each case, we run the algorithms five\ntimes with several variations of the initial requests. In each\nexperiment, we count the number of iterations that were needed to reach\nan agreement. We take the average of these numbers in order to\nevaluate these systems fairly. As is customary, we test each\nalgorithm with the same initial requests.\nTable 4 compares the approaches using different learning\nalgorithm. When the large parts of inventory is compatible with the\ncustomer\"s preferences as in the first test case, the performance of\nall techniques are nearly same (e.g., Scenario 1). As the number of\ncompatible services drops, RO performs poorly as expected. The\nsecond worst method is SCR since it only considers the customer\"s\nmost recent request and does not learn from previous requests.\nCEA gives the best results when it can generate an answer but\ncannot handle the cases containing disjunctive preferences, such as the\none in Scenario 5. ID3 and DCEA achieve the best results. Their\nperformance is comparable and they can handle all cases including\nScenario 5.\nTable 4: Comparison of learning algorithms in terms of average\nnumber of interactions\nRun DCEA SCR RO CEA ID3\nScenario 1: 1.2 1.4 1.2 1.2 1.2\nScenario 2: 1.4 1.4 2.6 1.4 1.4\nScenario 3: 1.4 1.8 4.4 1.4 1.4\nScenario 4: 2.2 2.8 9.6 1.8 2\nScenario 5: 2 2.6 7.6 1.75+ No offer 1.8\nAvg. of all cases: 1.64 2 5.08 1.51+No offer 1.56\n7.2 Comparison of Similarity Metrics\nTo compare the similarity metrics that were explained in\nSection 5, we fix the learning algorithm to DCEA. In addition to the\nscenarios shown in Table 3, we add following five new scenarios\nconsidering the hierarchical information.\n\u2022 The customer wants to buy wine whose winery is located in\nCalifornia and whose grape is a type of white grape.\nMoreover, the winery of the wine should not be expensive. There\nare only four products meeting these conditions.\n\u2022 The customer wants to buy wine whose color is red or rose\nand grape type is red grape. In addition, the location of wine\nshould be in Europe. The sweetness degree is wished to be\ndry or off dry. The flavor should be delicate or moderate\nwhere the body should be medium or light. Furthermore, the\nwinery of the wine should be an expensive winery. There are\ntwo products meeting all these requirements.\n\u2022 The customer wants to buy moderate rose wine, which is\nlocated around French Region. The category of winery should\nbe Moderate Winery. There is only one product meeting\nthese requirements.\n\u2022 The customer wants to buy expensive red wine, which is\nlocated around California Region or cheap white wine, which\nis located in around Texas Region. There are five available\nproducts.\n\u2022 The customer wants to buy delicate white wine whose\nproducer in the category of Expensive Winery. There are two\navailable products.\nThe first seven scenarios are tested with the first dataset that\ncontains a total of 19 services and the last three scenarios are tested\nwith the second dataset that contains 50 services.\nTable 5 gives the performance evaluation in terms of the number\nof interactions needed to reach a consensus. Tversky\"s metric gives\nthe worst results since it does not consider the semantic similarity.\nLin\"s performance are better than Tversky but worse than others.\nWu Palmer\"s metric and RP similarity measure nearly give the same\nperformance and better than others. When the results are examined,\nconsidering semantic closeness increases the performance.\n8. DISCUSSION\nWe review the recent literature in comparison to our work. Tama\net al. [16] propose a new approach based on ontology for\nnegotiation. According to their approach, the negotiation protocols used\nin e-commerce can be modeled as ontologies. Thus, the agents can\nperform negotiation protocol by using this shared ontology without\nthe need of being hard coded of negotiation protocol details. While\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1307\nTable 5: Comparison of similarity metrics in terms of number\nof interactions\nRun Tversky Lin Wu Palmer RP\nScenario 1: 1.2 1.2 1 1\nScenario 2: 1.4 1.4 1.6 1.6\nScenario 3: 1.4 1.8 2 2\nScenario 4: 2.2 1 1.2 1.2\nScenario 5: 2 1.6 1.6 1.6\nScenario 6: 5 3.8 2.4 2.6\nScenario 7: 3.2 1.2 1 1\nScenario 8: 5.6 2 2 2.2\nScenario 9: 2.6 2.2 2.2 2.6\nScenario 10: 4.4 2 2 1.8\nAverage of all cases: 2.9 1.82 1.7 1.76\nTama et al. model the negotiation protocol using ontologies, we\nhave instead modeled the service to be negotiated. Further, we have\nbuilt a system with which negotiation preferences can be learned.\nSadri et al. study negotiation in the context of resource\nallocation [14]. Agents have limited resources and need to require\nmissing resources from other agents. A mechanism which is based on\ndialogue sequences among agents is proposed as a solution. The\nmechanism relies on observe-think-action agent cycle. These\ndialogues include offering resources, resource exchanges and offering\nalternative resource. Each agent in the system plans its actions to\nreach a goal state. Contrary to our approach, Sadri et al.\"s study is\nnot concerned with learning preferences of each other.\nBrzostowski and Kowalczyk propose an approach to select an\nappropriate negotiation partner by investigating previous multi-attribute\nnegotiations [1]. For achieving this, they use case-based reasoning.\nTheir approach is probabilistic since the behavior of the partners\ncan change at each iteration. In our approach, we are interested in\nnegotiation the content of the service. After the consumer and\nproducer agree on the service, price-oriented negotiation mechanisms\ncan be used to agree on the price.\nFatima et al. study the factors that affect the negotiation such as\npreferences, deadline, price and so on, since the agent who\ndevelops a strategy against its opponent should consider all of them [5].\nIn their approach, the goal of the seller agent is to sell the service\nfor the highest possible price whereas the goal of the buyer agent\nis to buy the good with the lowest possible price. Time interval\naffects these agents differently. Compared to Fatima et al. our focus\nis different. While they study the effect of time on negotiation, our\nfocus is on learning preferences for a successful negotiation.\nFaratin et al. propose a multi-issue negotiation mechanism, where\nthe service variables for the negotiation such as price, quality of\nthe service, and so on are considered traded-offs against each other\n(i.e., higher price for earlier delivery) [4]. They generate a\nheuristic model for trade-offs including fuzzy similarity estimation and a\nhill-climbing exploration for possibly acceptable offers. Although\nwe address a similar problem, we learn the preferences of the\ncustomer by the help of inductive learning and generate counter-offers\nin accordance with these learned preferences. Faratin et al. only\nuse the last offer made by the consumer in calculating the\nsimilarity for choosing counter offer. Unlike them, we also take into\naccount the previous requests of the consumer. In their experiments,\nFaratin et al. assume that the weights for service variables are fixed\na priori. On the contrary, we learn these preferences over time.\nIn our future work, we plan to integrate ontology reasoning into\nthe learning algorithm so that hierarchical information can be learned\nfrom subsumption hierarchy of relations. Further, by using\nrelationships among features, the producer can discover new\nknowledge from the existing knowledge. These are interesting directions\nthat we will pursue in our future work.\n9. REFERENCES\n[1] J. Brzostowski and R. Kowalczyk. On possibilistic\ncase-based reasoning for selecting partners for\nmulti-attribute agent negotiation. In Proceedings of the 4th\nIntl. Joint Conference on Autonomous Agents and\nMultiAgent Systems (AAMAS), pages 273-278, 2005.\n[2] L. Busch and I. Horstman. A comment on issue-by-issue\nnegotiations. Games and Economic Behavior, 19:144-148,\n1997.\n[3] J. K. Debenham. Managing e-market negotiation in context\nwith a multiagent system. In Proceedings 21st International\nConference on Knowledge Based Systems and Applied\nArtificial Intelligence, ES\"2002:, 2002.\n[4] P. Faratin, C. Sierra, and N. R. Jennings. Using similarity\ncriteria to make issue trade-offs in automated negotiations.\nArtificial Intelligence, 142:205-237, 2002.\n[5] S. Fatima, M. Wooldridge, and N. Jennings. Optimal agents\nfor multi-issue negotiation. In Proceeding of the 2nd Intl.\nJoint Conference on Autonomous Agents and MultiAgent\nSystems (AAMAS), pages 129-136, 2003.\n[6] C. Giraud-Carrier. A note on the utility of incremental\nlearning. AI Communications, 13(4):215-223, 2000.\n[7] T.-P. Hong and S.-S. Tseng. Splitting and merging version\nspaces to learn disjunctive concepts. IEEE Transactions on\nKnowledge and Data Engineering, 11(5):813-815, 1999.\n[8] D. Lin. An information-theoretic definition of similarity. In\nProc. 15th International Conf. on Machine Learning, pages\n296-304. Morgan Kaufmann, San Francisco, CA, 1998.\n[9] P. Maes, R. H. Guttman, and A. G. Moukas. Agents that buy\nand sell. Communications of the ACM, 42(3):81-91, 1999.\n[10] T. M. Mitchell. Machine Learning. McGraw Hill, NY, 1997.\n[11] OWL. OWL: Web ontology language guide, 2003.\nhttp://www.w3.org/TR/2003/CR-owl-guide-20030818/.\n[12] S. K. Pal and S. C. K. Shiu. Foundations of Soft Case-Based\nReasoning. John Wiley & Sons, New Jersey, 2004.\n[13] J. R. Quinlan. Induction of decision trees. Machine Learning,\n1(1):81-106, 1986.\n[14] F. Sadri, F. Toni, and P. Torroni. Dialogues for negotiation:\nAgent varieties and dialogue sequences. In ATAL 2001,\nRevised Papers, volume 2333 of LNAI, pages 405-421.\nSpringer-Verlag, 2002.\n[15] M. P. Singh. Value-oriented electronic commerce. IEEE\nInternet Computing, 3(3):6-7, 1999.\n[16] V. Tamma, S. Phelps, I. Dickinson, and M. Wooldridge.\nOntologies for supporting negotiation in e-commerce.\nEngineering Applications of Artificial Intelligence,\n18:223-236, 2005.\n[17] A. Tversky. Features of similarity. Psychological Review,\n84(4):327-352, 1977.\n[18] P. E. Utgoff. Incremental induction of decision trees.\nMachine Learning, 4:161-186, 1989.\n[19] Wine, 2003.\nhttp://www.w3.org/TR/2003/CR-owl-guide20030818/wine.rdf.\n[20] Z. Wu and M. Palmer. Verb semantics and lexical selection.\nIn 32nd. Annual Meeting of the Association for\nComputational Linguistics, pages 133 -138, 1994.\n1308 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)", "keywords": "incremental decision tree;candidate elimination algorithm;rp similarity;disjunctive cea;consumer preference;disjunctive hypothesis;service;ontology;decision tree;semantic similarity;price;datum repository;negotiation;preference learning;inductive learn;multiple version space;learning set;similarity metric;consumer agent;id3"}
{"name": "train_I-73", "title": "Exchanging Reputation Values among Heterogeneous Agent Reputation Models: An Experience on ART Testbed", "abstract": "In open MAS it is often a problem to achieve agents' interoperability. The heterogeneity of its components turns the establishment of interaction or cooperation among them into a non trivial task, since agents may use different internal models and the decision about trust other agents is a crucial condition to the formation of agents' cooperation. In this paper we propose the use of an ontology to deal with this issue. We experiment this idea by enhancing the ART reputation model with semantic data obtained from this ontology. This data is used during interaction among heterogeneous agents when exchanging reputation values and may be used for agents that use different reputation models.", "fulltext": "1. INTRODUCTION\nOpen multiagent systems (MAS) are composed of autonomous\ndistributed agents that may enter and leave the agent society at\ntheir will because open systems have no centralized control over\nthe development of its parts [1]. Since agents are considered as\nautonomous entities, we cannot assume that there is a way to\ncontrol their internal behavior. These features are interesting to\nobtain flexible and adaptive systems but they also create new risks\nabout the reliability and the robustness of the system. Solutions to\nthis problem have been proposed by the way of trust models\nwhere agents are endowed with a model of other agents that\nallows them to decide if they can or cannot trust another agent.\nSuch trust decision is very important because it is an essential\ncondition to the formation of agents' cooperation. The trust\ndecision processes use the concept of reputation as the basis of a\ndecision. Reputation is a subject that has been studied in several\nworks [4][5][8][9] with different approaches, but also with\ndifferent semantics attached to the reputation concept. Casare and\nSichman [2][3] proposed a Functional Ontology of Reputation\n(FORe) and some directions about how it could be used to allow\nthe interoperability among different agent reputation models. This\npaper describes how the FORe can be applied to allow\ninteroperability among agents that have different reputation\nmodels. An outline of this approach is sketched in the context of a\ntestbed for the experimentation and comparison of trust models,\nthe ART testbed [6].\n2. THE FUNCTIONAL ONTOLOGY OF\nREPUTATION (FORe)\nIn the last years several computational models of reputation have\nbeen proposed [7][10][13][14]. As an example of research\nproduced in the MAS field we refer to three of them: a cognitive\nreputation model [5], a typology of reputation [7] and the\nreputation model used in the ReGret system [9][10]. Each model\nincludes its own specific concepts that may not exist in other\nmodels, or exist with a different name. For instance, Image and\nReputation are two central concepts in the cognitive reputation\nmodel. These concepts do not exist in the typology of reputation\nor in the ReGret model. In the typology of reputation, we can find\nsome similar concepts such as direct reputation and indirect\nreputation but there are some slight semantic differences. In the\nsame way, the ReGret model includes four kinds of reputation\n(direct, witness, neighborhood and system) that overlap with the\nconcepts of other models but that are not exactly the same.\nThe Functional Ontology of Reputation (FORe) was defined as a\ncommon semantic basis that subsumes the concepts of the main\nreputation models. The FORe includes, as its kernel, the following\nconcepts: reputation nature, roles involved in reputation formation\nand propagation, information sources for reputation, evaluation of\nreputation, and reputation maintenance. The ontology concept\nReputationNature is composed of concepts such as\nIndividualReputation, GroupReputation and ProductReputation.\nReputation formation and propagation involves several roles,\nplayed by the entities or agents that participate in those processes.\nThe ontology defines the concepts ReputationProcess and\nReputationRole. Moreover, reputation can be classified according\nto the origin of beliefs and opinions that can derive from several\nsources. The ontology defines the concept ReputationType which\ncan be PrimaryReputation or SecondaryReputation.\nPrimaryReputation is composed of concepts ObservedReputation\nand DirectReputation and the concept SecondaryReputation is\ncomposed of concepts such as PropagatedReputation and\nCollectiveReputation. More details about the FORe can be found\non [2][3].\n3. MAPPING THE AGENT REPUTATION\nMODELS TO THE FORe\nVisser et al [12] suggest three different ways to support semantic\nintegration of different sources of information: a centralized\napproach, where each source of information is related to one\ncommon domain ontology; a decentralized approach, where every\nsource of information is related to its own ontology; and a hybrid\napproach, where every source of information has its own ontology\nand the vocabulary of these ontologies are related to a common\nontology. This latter organizes the common global vocabulary in\norder to support the source ontologies comparison. Casare and\nSichman [3] used the hybrid approach to show that the FORe\nserves as a common ontology for several reputation models.\nTherefore, considering the ontologies which describe the agent\nreputation models we can define a mapping between these\nontologies and the FORe whenever the ontologies use a common\nvocabulary. Also, the information concerning the mappings\nbetween the agent reputation models and the FORe can be directly\ninferred by simply classifying the resulting ontology from the\nintegration of a given reputation model ontology and the FORe in\nan ontology tool with reasoning engine.\nFor instance, a mapping between the Cognitive Reputation Model\nontology and the FORe relates the concepts Image and Reputation\nto PrimaryReputation and SecondaryReputation from FORe,\nrespectively. Also, a mapping between the Typology of\nReputation and the FORe relates the concepts Direct Reputation\nand Indirect Reputation to PrimaryReputation and\nSecondaryReputation from FORe, respectively. Nevertheless, the\nconcepts Direct Trust and Witness Reputation from the Regret\nSystem Reputation Model are mapped to PrimaryReputation and\nPropagatedReputation from FORe. Since PropagatedReputation is\na sub-concept of SecondaryReputation, it can be inferred that\nWitness Reputation is also mapped to SecondaryReputation.\n4. EXPERIMENTAL SCENARIOS USING\nTHE ART TESTBED\nTo exemplify the use of mappings from last section, we define a\nscenario where several agents are implemented using different\nagent reputation models. This scenario includes the agents\"\ninteraction during the simulation of the game defined by ART [6]\nin order to describe the ways interoperability is possible between\ndifferent trust models using the FORe.\n4.1 The ART testbed\nThe ART testbed provides a simulation engine on which several\nagents, using different trust models, may run. The simulation\nconsists in a game where the agents have to decide to trust or not\nother agents. The game\"s domain is art appraisal, in which agents\nare required to evaluate the value of paintings based on\ninformation exchanged among other agents during agents\"\ninteraction. The information can be an opinion transaction, when\nan agent asks other agents to help it in its evaluation of a painting;\nor a reputation transaction, when the information required is\nabout the reputation of another agent (a target) for a given era.\nMore details about the ART testbed can be found in [6].\nThe ART common reputation model was enhanced with semantic\ndata obtained from FORe. A general agent architecture for\ninteroperability was defined [11] to allow agents to reason about\nthe information received from reputation interactions. This\narchitecture contains two main modules: the Reputation Mapping\nModule (RMM) which is responsible for mapping concepts\nbetween an agent reputation model and FORe; and the Reputation\nReasoning Module (RRM) which is responsible for deal with\ninformation about reputation according to the agent reputation\nmodel.\n4.2 Reputation transaction scenarios\nWhile including the FORe to the ART common reputation model,\nwe have incremented it to allow richer interactions that involve\nreputation transaction. In this section we describe scenarios\nconcerning reputation transactions in the context of ART testbed,\nbut the first is valid for any kind of reputation transaction and the\nsecond is specific for the ART domain.\n4.2.1 General scenario\nSuppose that agents A, B and C are implemented according to the\naforementioned general agent architecture with the enhanced ART\ncommon reputation model, using different reputation models.\nAgent A uses the Typology of Reputation model, agent B uses the\nCognitive Reputation Model and agent C uses the ReGret System\nmodel. Consider the interaction about reputation where agents A\nand B receive from agent C information about the reputation of\nagent Y. A big picture of this interaction is showed in Figure 2.\nReGret\nOntology\n(Y, value=0.8,\nwitnessreputation)\nC\nTypol.\nOntology\n(Y, value=0.8,\npropagatedreputation)\nA\nCogMod.\nOntology\n(Y, value=0.8,\nreputation)\nB\n(Y, value=0.8,\nPropagatedReputation)\n(Y, value=0.8,\nPropagatedReputation)\nReGret\nOntology\n(Y, value=0.8,\nwitnessreputation)\nC\nReGret\nOntology\n(Y, value=0.8,\nwitnessreputation)\nReGret\nOntology\n(Y, value=0.8,\nwitnessreputation)\n(Y, value=0.8,\nwitnessreputation)\nC\nTypol.\nOntology\n(Y, value=0.8,\npropagatedreputation)\nA\nTypol.\nOntology\n(Y, value=0.8,\npropagatedreputation)\nTypol.\nOntology\n(Y, value=0.8,\npropagatedreputation)\n(Y, value=0.8,\npropagatedreputation)\nA\nCogMod.\nOntology\n(Y, value=0.8,\nreputation)\nB\nCogMod.\nOntology\n(Y, value=0.8,\nreputation)\nCogMod.\nOntology\n(Y, value=0.8,\nreputation)\n(Y, value=0.8,\nreputation)\nB\n(Y, value=0.8,\nPropagatedReputation)\n(Y, value=0.8,\nPropagatedReputation)\n(Y, value=0.8,\nPropagatedReputation)\n(Y, value=0.8,\nPropagatedReputation)\nFigure 1. Interaction about reputation\nThe information witness reputation from agent C is treated by its\nRMM and is sent as PropagatedReputation to both agents. The\ncorresponding information in agent A reputation model is\npropagated reputation and in agent B reputation model is\nreputation. The way agents A and B make use of the information\ndepends on their internal reputation model and their RRM\nimplementation.\n1048 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\n4.2.2 ART scenario\nConsidering the same agents A and B and the art appraisal domain\nof ART, another interesting scenario describes the following\nsituation: agent A asks to agent B information about agents it\nknows that have skill on some specific painting era. In this case\nagent A wants information concerning the direct reputation agent\nB has about agents that have skill on an specific era, such as\ncubism. Following the same steps of the previous scenario, agent\nA message is prepared in its RRM using information from its\ninternal model. A big picture of this interaction is in Figure 2.\nTypol.\nOntology\n(agent = ?, value = ?,\nskill = cubism,\nreputation = directreputation)\nA\n(agent = ?, value = ?, skill = cubism,\nreputation = PrimaryReputation)\nCogMod.\nOntology\n(agent = ?, value = ?,\nskill = cubism,\nreputation = image)\nB\nTypol.\nOntology\n(agent = ?, value = ?,\nskill = cubism,\nreputation = directreputation)\nA\n(agent = ?, value = ?, skill = cubism,\nreputation = PrimaryReputation)\nCogMod.\nOntology\n(agent = ?, value = ?,\nskill = cubism,\nreputation = image)\nB\nFigure 2. Interaction about specific types of reputation values\nAgent B response to agent A is processed in its RRM and it is\ncomposed of tuples (agent, value, cubism, image) , where\nthe pair (agent, value) is composed of all agents and associated\nreputation values whose agent B knows their expertise about\ncubism by its own opinion. This response is forwarded to the\nRMM in order to be translated to the enriched common model and\nto be sent to agent A. After receiving the information sent by\nagent B, agent A processes it in its RMM and translates it to its\nown reputation model to be analyzed by its RRM.\n5. CONCLUSION\nIn this paper we present a proposal for reducing the\nincompatibility between reputation models by using a general\nagent architecture for reputation interaction which relies on a\nfunctional ontology of reputation (FORe), used as a globally\nshared reputation model. A reputation mapping module allows\nagents to translate information from their internal reputation\nmodel into the shared model and vice versa. The ART testbed has\nbeen enriched to use the ontology during agent transactions. Some\nscenarios were described to illustrate our proposal and they seem\nto be a promising way to improve the process of building\nreputation just using existing technologies.\n6. ACKNOWLEDGMENTS\nAnarosa A. F. Brand\u00e3o is supported by CNPq/Brazil grant\n310087/2006-6 and Jaime Sichman is partially supported by\nCNPq/Brazil grants 304605/2004-2, 482019/2004-2 and\n506881/2004-1. Laurent Vercouter was partially supported by\nFAPESP grant 2005/02902-5.\n7. REFERENCES\n[1] Agha, G. A. Abstracting Interaction Patterns: A\nProgramming Paradigm for Open Distributed Systems, In\n(Eds) E. Najm and J.-B. Stefani, Formal Methods for Open\nObject-based Distributed Systems IFIP Transactions, 1997,\nChapman Hall.\n[2] Casare,S. and Sichman, J.S. Towards a Functional Ontology\nof Reputation, In Proc of the 4th\nIntl Joint Conference on\nAutonomous Agents and Multi Agent Systems (AAMAS\"05),\nUtrecht, The Netherlands, 2005, v.2, pp. 505-511.\n[3] Casare, S. and Sichman, J.S. Using a Functional Ontology of\nReputation to Interoperate Different Agent Reputation\nModels, Journal of the Brazilian Computer Society, (2005),\n11(2), pp. 79-94.\n[4] Castelfranchi, C. and Falcone, R. Principles of trust in MAS:\ncognitive anatomy, social importance and quantification. In\nProceedings of ICMAS\"98, Paris, 1998, pp. 72-79.\n[5] Conte, R. and Paolucci, M. Reputation in Artificial Societies:\nSocial Beliefs for Social Order, Kluwer Publ., 2002.\n[6] Fullam, K.; Klos, T.; Muller, G.; Sabater, J.; Topol, Z.;\nBarber, S.;Rosenchein, J.; Vercouter, L. and Voss, M. A\nspecification of the agent reputation and trust (art) testbed:\nexperimentation and competition for trust in agent societies.\nIn Proc. of the 4th\nIntl. Joint Conf on Autonomous Agents\nand Multiagent Systems (AAMAS\"05), ACM, 2005, 512-158.\n[7] Mui, L.; Halberstadt, A.; Mohtashemi, M. Notions of\nReputation in Multi-Agents Systems: A Review. In: Proc of\n1st Intl. Joint Conf. on Autonomous Agents and Multi-agent\nSystems (AAMAS 2002), Bologna, Italy, 2002, 1, 280-287.\n[8] Muller, G. and Vercouter, L. Decentralized monitoring of\nagent communication with a reputation model. In Trusting\nAgents for Trusting Electronic Societies, LNCS 3577, 2005,\npp. 144-161.\n[9] Sabater, J. and Sierra, C. ReGret: Reputation in gregarious\nsocieties. In M\u00fcller, J. et al (Eds) Proc. of the 5th\nIntl. Conf.\non Autonomous Agents, Canada, 2001, ACM, 194-195.\n[10] Sabater, J. and Sierra, C. Review on Computational Trust\nand Reputation Models. In: Artificial Intelligence Review,\nKluwer Acad. Publ., (2005), v. 24, n. 1, pp. 33 - 60.\n[11] Vercouter,L, Casare, S., Sichman, J. and Brand\u00e3o, A. An\nexperience on reputation models interoperability based on a\nfunctional ontology In Proc. of the 20th\nIJCAI, Hyderabad,\nIndia, 2007, pp.617-622.\n[12] Visser, U.; Stuckenschmidt, H.; Wache, H. and Vogele, T.\nEnabling technologies for inter-operability. In: In U. Visser\nand H. Pundt, Eds, Workshop on the 14th Intl Symp. of\nComputer Science for Environmental Protection, Bonn,\nGermany, 2000, pp. 35-46.\n[13] Yu, B. and Singh, M.P. An Evidential Model of Distributed\nReputation Management. In: Proc. of the 1st Intl Joint Conf.\non Autonomous Agents and Multi-agent Systems (AAMAS\n2002), Bologna, Italy, 2002, part 1, pp. 294 - 301.\n[14] Zacharia, G. and Maes, P. Trust Management Through\nReputation Mechanisms. In: Applied Artificial Intelligence,\n14(9), 2000, pp. 881-907.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1049", "keywords": "interoperability;reputation model;agent architecture;functional ontology of reputation;ontology;heterogeneous agent;reputation value;autonomous distributed agent;reputation formation;reputation;art testbed;trust;art testb;multiagent system"}
{"name": "train_I-74", "title": "On the relevance of utterances in formal inter-agent dialogues", "abstract": "Work on argumentation-based dialogue has defined frameworks within which dialogues can be carried out, established protocols that govern dialogues, and studied different properties of dialogues. This work has established the space in which agents are permitted to interact through dialogues. Recently, there has been increasing interest in the mechanisms agents might use to choose how to act - the rhetorical manoeuvring that they use to navigate through the space defined by the rules of the dialogue. Key in such considerations is the idea of relevance, since a usual requirement is that agents stay focussed on the subject of the dialogue and only make relevant remarks. Here we study several notions of relevance, showing how they can be related to both the rules for carrying out dialogues and to rhetorical manoeuvring.", "fulltext": "1. INTRODUCTION\nFinding ways for agents to reach agreements in\nmultiagent systems is an area of active research. One mechanism\nfor achieving agreement is through the use of argumentation\n- where one agent tries to convince another agent of\nsomething during the course of some dialogue. Early examples of\nargumentation-based approaches to multiagent agreement\ninclude the work of Dignum et al. [7], Kraus [14],\nParsons and Jennings [16], Reed [23], Schroeder et al. [25] and\nSycara [26].\nThe work of Walton and Krabbe [27], popularised in the\nmultiagent systems community by Reed [23], has been\nparticularly influential in the field of argumentation-based\ndialogue. This work influenced the field in a number of ways,\nperhaps most deeply in framing multi-agent interactions as\ndialogue games in the tradition of Hamblin [13]. Viewing\ndialogues in this way, as in [2, 21], provides a powerful\nframework for analysing the formal properties of dialogues, and\nfor identifying suitable protocols under which dialogues can\nbe conducted [18, 20]. The dialogue game view overlaps with\nwork on conversation policies (see, for example, [6, 10]), but\ndiffers in considering the entire dialogue rather than dialogue\nsegments.\nIn this paper, we extend the work of [18] by considering\nthe role of relevance - the relationship between utterances\nin a dialogue. Relevance is a topic of increasing interest\nin argumentation-based dialogue because it relates to the\nscope that an agent has for applying strategic manoeuvering\nto obtain the outcomes that it requires [19, 22, 24]. Our\nwork identifes the limits on such rhetorical manoeuvering,\nshowing when it can and cannot have an effect.\n2. BACKGROUND\nWe begin by introducing the formal system of\nargumentation that underpins our approach, as well as the\ncorresponding terminology and notation, all taken from [2, 8, 17].\nA dialogue is a sequence of messages passed between two\nor more members of a set of agents A. An agent \u03b1 maintains\na knowledge base, \u03a3\u03b1, containing formulas of a propositional\nlanguage L and having no deductive closure. Agent \u03b1 also\nmaintains the set of its past utterances, called the\ncommitment store, CS\u03b1. We refer to this as an agent\"s public\nknowledge, since it contains information that is shared with\nother agents. In contrast, the contents of \u03a3\u03b1 are private\nto \u03b1.\nNote that in the description that follows, we assume that\nis the classical inference relation, that \u2261 stands for logical\nequivalence, and we use \u0394 to denote all the information\navailable to an agent. Thus in a dialogue between two agents\n\u03b1 and \u03b2, \u0394\u03b1 = \u03a3\u03b1 \u222a CS\u03b1 \u222a CS\u03b2, so the commitment store\nCS\u03b1 can be loosely thought of as a subset of \u0394\u03b1 consisting of\nthe assertions that have been made public. In some dialogue\ngames, such as those in [18] anything in CS\u03b1 is either in \u03a3\u03b1\nor can be derived from it. In other dialogue games, such as\n1006\n978-81-904262-7-5 (RPS) c 2007 IFAAMAS\nthose in [2], CS\u03b1 may contain things that cannot be derived\nfrom \u03a3\u03b1.\nDefinition 2.1. An argument A is a pair (S, p) where p\nis a formula of L and S a subset of \u0394 such that (i) S is\nconsistent; (ii) S p; and (iii) S is minimal, so no proper\nsubset of S satisfying both (1) and (2) exists.\nS is called the support of A, written S = Support(A) and p\nis the conclusion of A, written p = Conclusion(A). Thus we\ntalk of p being supported by the argument (S, p).\nIn general, since \u0394 may be inconsistent, arguments in\nA(\u0394), the set of all arguments which can be made from \u0394,\nmay conflict, and we make this idea precise with the notion\nof undercutting:\nDefinition 2.2. Let A1 and A2 be arguments in A(\u0394).\nA1 undercuts A2 iff \u2203\u00acp \u2208 Support(A2) such that p \u2261\nConclusion(A1).\nIn other words, an argument is undercut if and only if there\nis another argument which has as its conclusion the negation\nof an element of the support for the first argument.\nTo capture the fact that some beliefs are more strongly\nheld than others, we assume that any set of beliefs has a\npreference order over it. We consider all information\navailable to an agent, \u0394, to be stratified into non-overlapping\nsubsets \u03941, . . . , \u0394n such that beliefs in \u0394i are all equally\npreferred and are preferred over elements in \u0394j where i > j.\nThe preference level of a nonempty subset S \u2282 \u0394, where\ndifferent elements s \u2208 S may belong to different layers \u0394i,\nis valued at the highest numbered layer which has a member\nin S and is referred to as level(S). In other words, S is only\nas strong as its weakest member. Note that the strength of\na belief as used in this context is a separate concept from\nthe notion of support discussed earlier.\nDefinition 2.3. Let A1 and A2 be arguments in A(\u0394).\nA1 is preferred to A2 according to Pref , A1\nPref\nA2, iff\nlevel(Support(A1)) > level(Support(A2)). If A1 is\npreferred to A2, we say that A1 is stronger than A2.\nWe can now define the argumentation system we will use:\nDefinition 2.4. An argumentation system is a triple:\nA(\u0394), Undercut, Pref\nsuch that:\n\u2022 A(\u0394) is a set of the arguments built from \u0394,\n\u2022 Undercut is a binary relation representing the defeat\nrelationship between arguments, Undercut \u2286 A(\u0394) \u00d7\nA(\u0394), and\n\u2022 Pref is a pre-ordering on A(\u0394) \u00d7 A(\u0394).\nThe preference order makes it possible to distinguish\ndifferent types of relations between arguments:\nDefinition 2.5. Let A1, A2 be two arguments of A(\u0394).\n\u2022 If A2 undercuts A1 then A1 defends itself against A2\niff A1\nPref\nA2. Otherwise, A1 does not defend itself.\n\u2022 A set of arguments A defends A1 iff for every A2 that\nundercuts A1, where A1 does not defend itself against\nA2, then there is some A3 \u2208 A such that A3 undercuts\nA2 and A2 does not defend itself against A3.\nWe write AUndercut,Pref to denote the set of all non-undercut\narguments and arguments defending themselves against all\ntheir undercutting arguments. The set A(\u0394) of acceptable\narguments of the argumentation system\nA(\u0394), Undercut, Pref\nis [1] the least fixpoint of a function F:\nA \u2286 A(\u0394)\nF(A) = {(S, p) \u2208 A(\u0394) | (S, p) is defended by A}\nDefinition 2.6. The set of acceptable arguments for an\nargumentation system A(\u0394), Undercut, Pref is recursively\ndefined as:\nA(\u0394) =\n[\nFi\u22650(\u2205)\n= AUndercut,Pref \u222a\nh[\nFi\u22651(AUndercut,Pref )\ni\nAn argument is acceptable if it is a member of the acceptable\nset, and a proposition is acceptable if it is the conclusion of\nan acceptable argument.\nAn acceptable argument is one which is, in some sense,\nproven since all the arguments which might undermine it\nare themselves undermined.\nDefinition 2.7. If there is an acceptable argument for a\nproposition p, then the status of p is accepted, while if there\nis not an acceptable argument for p, the status of p is not\naccepted.\nArgument A is said to affect the status of another argument\nA if changing the status of A will change the status of A .\n3. DIALOGUES\nSystems like those described in [2, 18], lay down sets of\nlocutions that agents can make to put forward propositions\nand the arguments that support them, and protocols that\ndefine precisely which locutions can be made at which points\nin the dialogue. We are not concerned with such a level\nof detail here. Instead we are interested in the interplay\nbetween arguments that agents put forth. As a result, we\nwill consider only that agents are allowed to put forward\narguments. We do not discuss the detail of the mechanism\nthat is used to put these arguments forward - we just\nassume that arguments of the form (S, p) are inserted into\nan agent\"s commitment store where they are then visible to\nother agents.\nWe then have a typical definition of a dialogue:\nDefinition 3.1. A dialogue D is a sequence of moves:\nm1, m2, . . . , mn.\nA given move mi is a pair \u03b1, Ai where Ai is an argument\nthat \u03b1 places into its commitment store CS\u03b1.\nMoves in an argumentation-based dialogue typically attack\nmoves that have been made previously. While, in general,\na dialogue can include moves that undercut several\narguments, in the remainder of this paper, we will only consider\ndialogues that put forward moves that undercut at most\none argument. For now we place no additional constraints\non the moves that make up a dialogue. Later we will see\nhow different restrictions on moves lead to different kinds of\ndialogue.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1007\nThe sequence of arguments put forward in the dialogue\nis determined by the agents who are taking part in the\ndialogue, but they are usually not completely free to choose\nwhat arguments they make. As indicated earlier, their choice\nis typically limited by a protocol. If we write the sequence\nof n moves m1, m2, . . . , mn as mn, and denote the empty\nsequence as m0, then we can define a profocol in the following\nway:\nDefinition 3.2. A protocol P is a function on a sequence\nof moves mi in a dialogue D that, for all i \u2265 0, identifies\na set of possible moves Mi+1 from which the mi+1th move\nmay be drawn:\nP : mi \u2192 Mi+1\nIn other words, for our purposes here, at every point in\na dialogue, a protocol determines a set of possible moves\nthat agents may make as part of the dialogue. If a dialogue\nD always picks its moves m from the set M identified by\nprotocol P, then D is said to conform to P.\nEven if a dialogue conforms to a protocol, it is typically\nthe case that the agent engaging in the dialogue has to make\na choice of move - it has to choose which of the moves in M\nto make. This excercise of choice is what we refer to as an\nagent\"s use of rhetoric (in its oratorical sense of influencing\nthe thought and conduct of an audience). Some of our\nresults will give a sense of how much scope an agent has to\nexercise rhetoric under different protocols.\nAs arguments are placed into commitment stores, and\nhence become public, agents can determine the relationships\nbetween them. In general, after several moves in a\ndialogue, some arguments will undercut others. We will denote\nthe set of arguments {A1, A2, . . . , Aj} asserted after moves\nm1, m2, . . . , mj of a dialogue to be Aj - the relationship of\nthe arguments in Aj can be described as an argumentation\ngraph, similar to those described in, for example, [3, 4, 9]:\nDefinition 3.3. An argumentation graph AG over a set\nof arguments A is a directed graph (V, E) such that every\nvertex v, v \u2208 V denotes one argument A \u2208 A, every\nargument A is denoted by one vertex v, and every directed edge\ne \u2208 E from v to v denotes that v undercuts v .\nWe will use the term argument graph as a synonym for\nargumentation graph.\nNote that we do not require that the argumentation graph\nis connected. In other words the notion of an argumentation\ngraph allows for the representation of arguments that do\nnot relate, by undercutting or being undercut, to any other\narguments (we will come back to this point very shortly).\nWe adapt some standard graph theoretic notions in order\nto describe various aspects of the argumentation graph. If\nthere is an edge e from vertex v to vertex v , then v is said\nto be the parent of v and v is said to be the child of v.\nIn a reversal of the usual notion, we define a root of an\nargumentation graph1\nas follows:\nDefinition 3.4. A root of an argumentation graph AG =\n(V, E) is a node v \u2208 V that has no children.\nThus a root of a graph is a node to which directed edges\nmay be connected, but from which no directed edges\nconnect to other nodes. Thus a root is a node representing an\n1\nNote that we talk of a root rather than the root - as defined,\nan argumentation graph need not be a tree.\nv v\"\nFigure 1: An example argument graph\nargument that is undercut, but which itself does no\nundercutting. Similarly:\nDefinition 3.5. A leaf of an argumentation graph AG =\n(V, E) is a node v \u2208 V that has no parents.\nThus a leaf in an argumentation graph represents an\nargument that undercuts another argument, but does no\nundercutting. Thus in Figure 1, v is a root, and v is a leaf. The\nreason for the reversal of the usual notions of root and leaf\nis that, as we shall see, we will consider dialogues to\nconstruct argumentation graphs from the roots (in our sense)\nto the leaves. The reversal of the terminology means that it\nmatches the natural process of tree construction.\nSince, as described above, argumentation graphs are\nallowed to be not connected (in the usual graph theory sense),\nit is helpful to distinguish nodes that are connected to other\nnodes, in particular to the root of the tree. We say that node\nv is connected to node v if and only if there is a path from\nv to v . Since edges represent undercut relations, the notion\nof connectedness between nodes captures the influence that\none argument may have on another:\nProposition 3.1. Given an argumentation graph AG, if\nthere is any argument A, denoted by node v that affects the\nstatus of another argument A , denoted by v , then v is\nconnected to v . The converse does not hold.\nProof. Given Definitions 2.5 and 2.6, the only ways in\nwhich A can affect the status of A is if A either undercuts\nA , or if A undercuts some argument A that undercuts A ,\nor if A undercuts some A that undercuts some A that\nundercuts A , and so on. In all such cases, a sequence of\nundercut relations relates the two arguments, and if they are\nboth in an argumentation graph, this means that they are\nconnected.\nSince the notion of path ignores the direction of the\ndirected arcs, nodes v and v are connected whether the edge\nbetween them runs from v to v or vice versa. Since A only\nundercuts A if the edge runs from v to v , we cannot infer\nthat A will affect the status of A from information about\nwhether or not they are connected.\nThe reason that we need the concept of the argumentation\ngraph is that the properties of the argumentation graph tell\nus something about the set of arguments A the graph\nrepresents. When that set of arguments is constructed through a\ndialogue, there is a relationship between the structure of the\nargumentation graph and the protocol that governs the\ndialogue. It is the extent of the relationship between structure\nand protocol that is the main subject of this paper. To study\nthis relationship, we need to establish a correspondence\nbetween a dialogue and an argumentation graph. Given the\ndefinitions we have so far, this is simple:\nDefinition 3.6. A dialogue D, consisting of a sequence\nof moves mn, and an argument graph AG = (V, E)\ncorrespond to one another iff \u2200m \u2208 mn, the argument Ai that\n1008 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nis advanced at move mi is represented by exactly one node\nv \u2208 V , and \u2200v \u2208 V , v represents exactly one argument Ai\nthat has been advanced by a move m \u2208 mn.\nThus a dialogue corresponds to an argumentation graph if\nand only if every argument made in the dialogue corresponds\nto a node in the graph, and every node in the graph\ncorresponds to an argument made in the dialogue. This\none-toone correspondence allows us to consider each node v in the\ngraph to have an index i which is the index of the move in\nthe dialogue that put forward the argument which that node\nrepresents. Thus we can, for example, refer to the third\nnode in the argumentation graph, meaning the node that\nrepresents the argument put forward in the third move of\nthe dialogue.\n4. RELEVANCE\nMost work on dialogues is concerned with what we might\ncall coherent dialogues, that is dialogues in which the\nparticipants are, as in the work of Walton and Krabbe [27],\nfocused on resolving some question through the dialogue2\nTo capture this coherence, it seems we need a notion of\nrelevance to constrain the statements made by agents. Here\nwe study three notions of relevance:\nDefinition 4.1. Consider a dialogue D, consisting of a\nsequence of moves mi, with a corresponding argument graph\nAG. The move mi+1, i > 1, is said to be relevant if one or\nmore of the following hold:\nR1 Making mi+1 will change the status of the argument\ndenoted by the first node of AG.\nR2 Making mi+1 will add a node vi+1 that is connected to\nthe first node of AG.\nR3 Making mi+1 will add a node vi+1 that is connected to\nthe last node to be added to AG.\nR2-relevance is the form of relevance defined by [3] in their\nstudy of strategic and tactical reasoning3\n. R1-relevance was\nsuggested by the notion used in [15], and though it differs\nsomewhat from that suggested there, we believe it captures\nthe essence of its predecessor.\nNote that we only define relevance for the second move\nof the dialogue onwards because the first move is taken to\nidentify the subject of the dialogue, that is, the central\nquestion that the dialogue is intended to answer, and hence it\nmust be relevant to the dialogue, no matter what it is. In\nassuming this, we focus our attention on the same kind of\ndialogues as [18].\nWe can think of relevance as enforcing a form of\nparsimony on a dialogue - it prevents agents from making\nstatements that do not bear on the current state of the dialogue.\nThis promotes efficiency, in the sense of limiting the\nnumber of moves in the dialogue, and, as in [15], prevents agents\nrevealing information that they might better keep hidden.\nAnother form of parsimony is to insist that agents are not\nallowed to put forward arguments that will be undercut by\narguments that have already been made during the dialogue.\nWe therefore distinguish such arguments.\n2\nSee [11, 12] for examples of dialogues where this is not the case.\n3\nWe consider such reasoning sub-types of rhetoric.\nDefinition 4.2. Consider a dialogue D, consisting of a\nsequence of moves mi, with a corresponding argument graph\nAG. The move mi+1 and the argument it puts forward,\nAi+1, are both said to be pre-empted, if Ai+1 is undercut by\nsome A \u2208 Ai.\nWe use the term pre-empted because if such an argument\nis put forward, it can seem as though another agent\nanticipated the argument being made, and already made an\nargument that would render it useless. In the rest of this\npaper, we will only deal with protocols that permit moves\nthat are relevant, in any of the senses introduced above, and\nare not allowed to be pre-empted. We call such protocols\nbasic protocols, and dialogues carried out under such protocols\nbasic dialogues.\nThe argument graph of a basic dialogue is somewhat\nrestricted.\nProposition 4.1. Consider a basic dialogue D. The\nargumentation graph AG that corresponds to D is a tree with\na single root.\nProof. Recall that Definition 3.3 requires only that AG\nbe a directed graph. To show that it is a tree, we have to\nshow that it is acyclic and connected.\nThat the graph is connected follows from the construction\nof the graph under a protocol that enforces relevance. If the\nnotion of relevance is R3, each move adds a node that is\nconnected to the previous node. If the notion of relevance is\nR2, then every move adds a node that is connected to the\nroot, and thus is connected to some node in the graph. If the\nnotion of relevance is R1, then every move has to change the\nstatus of the argument denoted by the root. Proposition 3.1\ntells us that to affect the status of an argument A , the node\nv representing the argument A that is effecting the change\nhas to be connected to v , the node representing A , and so\nit follows that every new node added as a result of an\nR1relevant move will be connected to the argumentation graph.\nThus AG is connected.\nSince a basic dialogue does not allow moves that are\npreempted, every edge that is added during construction is\ndirected from the node that is added to one already in the graph\n(thus denoting that the argument A denoted by the added\nnode, v, undercuts the argument A denoted by the node to\nwhich the connection is made, v , rather than the other way\naround). Since every edge that is added is directed from the\nnew node to the rest of the graph, there can be no cycles.\nThus AG is a tree.\nTo show that AG has a single root, consider its\nconstruction from the initial node. After m1 the graph has one node,\nv1 that is both a root and a leaf. After m2, the graph is two\nnodes connected by an edge, and v1 is now a root and not a\nleaf. v2 is a leaf and not a root. However the third node is\nadded, the argument earlier in this proof demonstrates that\nthere will be a directed edge from it to some other node,\nmaking it a leaf. Thus v1 will always be the only root. The ruling\nout of pre-empted moves means that v1 will never cease to\nbe a root, and so the argumentation graph will always have\none root.\nSince every argumentation graph constructed by a basic\ndialogue is a tree with a single root, this means that the first\nnode of every argumentation graph is the root.\nAlthough these results are straightforward to obtain, they\nallow us to show how the notions of relevance are related.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1009\nProposition 4.2. Consider a basic dialogue D,\nconsisting of a sequence of moves mi, with a corresponding\nargument graph AG.\n1. Every move mi+1 that is R1-relevant is R2-relevant.\nThe converse does not hold.\n2. Every move mi+1 that is R3-relevant is R2-relevant.\nThe converse does not hold.\n3. Not every move mi+1 that is R1-relevant is R3-relevant,\nand not every move mi+1 that is R3-relevant is\nR1relevant\nProof. For 1, consider how move mi+1 can satisfy R1.\nProposition 3.1 tells us that if Ai+1 can change the status\nof the argument denoted by the root v1 (which, as observed\nabove, is the first node) of AG, then vi+1 must be connected\nto the root. This is precisely what is required to satisfy R2,\nand the relatiosnhip is proved to hold.\nTo see that the converse does not hold, we have to consider\nwhat it takes to change the status of r (since Proposition 3.1\ntells us that connectedness is not enough to ensure a change\nof status - if it did, R1 and R2 relevance would coincide).\nFor mi+1 to change the status of the root, it will have to (1)\nmake the argument A represented by r either unacceptable,\nif it were acceptable before the move, or (2) acceptable if it\nwere unacceptable before the move. Given the definition of\nacceptability, it can achieve (1) either by directly\nundercutting the argument represented by r, in which case vi+1 will\nbe directly connected to r by some edge, or by undercutting\nsome argument A that is part of the set of non-undercut\narguments defending A. In the latter case, vi+1 will be\ndirectly connected to the node representing A and by\nProposition 4.1 to r. To achieve (2), vi+1 will have to undercut\nan argument A that is either currently undercutting A, or\nis undercutting an argument that would otherwise defend A.\nNow, further consider that mi+1 puts forward an argument\nAi+1 that undercuts the argument denoted by some node v ,\nbut this latter argument defends itself against Ai+1. In such\na case, the set of acceptable arguments will not change, and\nso the status of Ar will not change. Thus a move that is\nR2-relevant need not be R1-relevant.\nFor 2, consider that mi+1 can satisfy R3 simply by adding\na node that is connected to vi, the last node to be added\nto AG. By Proposition 4.1, it is connected to r and so is\nR2-relevant.\nTo see that the converse does not hold, consider that an\nR2-relevant move can connect to any node in AG.\nThe first part of 3 follows by a similar argument to that we\njust used - an R1-relevant move does not have to connect to\nvi, just to some v that is part of the graph - and the second\npart follows since a move that is R3-relevant may introduce\nan argument Ai+1 that undercuts the argument Ai put\nforward by the previous move (and so vi+1 is connected to vi),\nbut finds that Ai defends itself against Ai+1, preventing a\nchange of status at the root.\nWhat is most interesting is not so much the results but\nwhy they hold, since this reveals some aspects of the\ninterplay between relevance and the structure of argument\ngraphs. For example, to restate a case from the proof of\nProposition 4.2, a move that is R3-relevant by definition has\nto add a node to the argument graph that is connected to the\nlast node that was added. Since a move that is R2-relevant\ncan add a node that connects anywhere on an argument\ngraph, any move that is R3-relevant will be R2-relevant,\nbut the converse does not hold.\nIt turns out that we can exploit the interplay between\nstructure and relevance that Propositions 4.1 and 4.2 have\nstarted to illuminate to establish relationships between the\nprotocols that govern dialogues and the argument graphs\nconstructed during such dialogues. To do this we need to\ndefine protocols in such a way that they refer to the structure\nof the graph. We have:\nDefinition 4.3. A protocol is single-path if all dialogues\nthat conform to it construct argument graphs that have only\none branch.\nProposition 4.3. A basic protocol P is single-path if, for\nall i, the set of permitted moves Mi at move i are all\nR3relevant. The converse does not hold.\nProof. R3-relevance requires that every node added to\nthe argument graph be connected to the previous node.\nStarting from the first node this recursively constructs a tree with\njust one branch, and the relationship holds. The converse\ndoes not hold because even if one or more moves in the\nprotocol are R1- or R2-relevant, it may be the case that, because\nof an agent\"s rhetorical choice or because of its knowledge,\nevery argument that is chosen to be put forward will\nundercut the previous argument and so the argument graph is a\none-branch tree.\nLooking for more complex kinds of protocol that construct\nmore complex kinds of argument graph, it is an obvious\nmove to turn to:\nDefinition 4.4. A basic protocol is multi-path if all\ndialogues that conform to it can construct argument graphs that\nare trees.\nBut, on reflection, since any graph with only one branch is\nalso a tree:\nProposition 4.4. Any single-path protocol is an instance\nof a multi-path protocol.\nand, furthermore:\nProposition 4.5. Any basic protocol P is multi-path.\nProof. Immediate from Proposition 4.1\nSo the notion of a multi-path protocol does not have much\ntraction. As a result we distinguish multi-path protocols\nthat permit dialogues that can construct trees that have\nmore than one branch as bushy protocols. We then have:\nProposition 4.6. A basic protocol P is bushy if, for some\ni, the set of permitted moves Mi at move i are all R1- or\nR2-relevant.\nProof. From Proposition 4.3 we know that if all moves\nare R3-relevant then we\"ll get a tree with one branch, and\nfrom Proposition 4.1 we know that all basic protocols will\nbuild an argument graph that is a tree, so providing we\nexclude R3-relevant moves, we will get protocols that can build\nmulti-branch trees.\n1010 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nOf course, since, by Proposition 4.2, any move that is\nR3relevant is R2-relevant and can quite possibly be R1-relevant\n(all that Proposition 4.2 tells us is that there is no\nguarantee that it will be), all that Proposition 4.6 tells us is that\ndialogues that conform to bushy protocols may have more\nthan one branch. All we can do is to identify a bound on\nthe number of branches:\nProposition 4.7. Consider a basic dialogue D that\nincludes m moves that are not R3-relevant, and has a\ncorresponding argumentation graph AG. The number of branches\nin AG is less than or equal to m + 1.\nProof. Since it must connect a node to the last node\nadded to AG, an R3-relevant move can only extend an\nexisting branch. Since they do not have the same restriction,\nR1 and R2-relevant moves may create a new branch by\nconnecting to a node that is not the last node added. Every\nsuch move could create a new branch, and if they do, we\nwill have m branches. If there were R3-relevant moves\nbefore any of these new-branch-creating moves, then these m\nbranches are in addition to the initial branch created by the\nR3-relevant moves, and we have a maximum of m + 1\npossible branches.\nWe distinguish bushy protocols from multi-path protocols,\nand hence R1- and R2-relevance from R3-relevance, because\nof the kinds of dialogue that R3-relevance enforces. In a\ndialogue in which all moves must be R3-relevant, the\nargumentation graph has a single branch - the dialogue consists of\na sequence of arguments each of which undercuts the\nprevious one and the last move to be made is the one that settles\nthe dialogue. This, as we will see next, means that such a\ndialogue only allows a subset of all the moves that would\notherwise be possible.\n5. COMPLETENESS\nThe above discussion of the difference between dialogues\ncarried out under single-path and bushy protocols brings us\nto the consideration of what [18] called predeterminism,\nbut we now prefer to describe using the term\ncompleteness. The idea of predeterminism, as described in [18],\ncaptures the notion that, under some circumstances, the\nresult of a dialogue can be established without actually having\nthe dialogue - the agents have sufficiently little room for\nrhetorical manoeuver that were one able to see the contents\nof all the \u03a3i of all the \u03b1i \u2208 A, one would be able to\nidentify the outcome of any dialogue on a given subject4\n. We\ndevelop this idea by considering how the argument graphs\nconstructed by dialogues under different protocols compare\nto benchmark complete dialogues. We start by developing\nideas of what complete might mean. One reasonable\ndefinition is that:\nDefinition 5.1. A basic dialogue D between the set of\nagents A with a corresponding argumentation graph AG is\ntopic-complete if no agent can construct an argument A that\nundercuts any argument A represented by a node in AG.\nThe argumentation graph constructed by a topic-complete\ndialogue is called a topic-complete argumentation graph and\nis denoted AG(D)T .\n4\nAssuming that the \u03a3i do not change during the dialogue, which is\nthe usual assumption in this kind of dialogue.\nA dialogue is topic-complete when no agent can add\nanything that is directly connected to the subject of the\ndialogue. Some protocols will prevent agents from making\nmoves even though the dialogue is not topic-complete. To\ndistinguish such cases we have:\nDefinition 5.2. A basic dialogue D between the set of\nagents A with a corresponding argumentation graph AG is\nprotocol-complete under a protocol P if no agent can make\na move that adds a node to the argumentation graph that is\npermitted by P.\nThe argumentation graph constructed by a protocol-complete\ndialogue is called a protocol-complete argumentation graph\nand is denoted AG(D)P . Clearly:\nProposition 5.1. Any dialogue D under a basic protocol\nP is protocol-complete if it is topic-complete. The converse\ndoes not hold in general.\nProof. If D is topic-complete, no agent can make a move\nthat will extend the argumentation graph. This means that\nno agent can make a move that is permitted by a basic\nprotocol, and so D is also protocol complete.\nThe converse does not hold since some basic dialogues\n(under a protocol that only permits R3-relevant moves, for\nexample) will not permit certain moves (like the addition of\na node that connects to the root of the argumentation graph\nafter more than two moves) that would be allowed in a\ntopiccomplete dialogue.\nCorollary 5.1. For a basic dialogue D, AG(D)P is a\nsub-graph of AG(D)T .\nObviously, from the definition of a sub-graph, the converse\nof Corollary 5.1 does not hold in general.\nThe important distinction between topic- and\nprotocolcompleteness is that the former is determined purely by the\nstate of the dialogue - as captured by the argumentation\ngraph - and is thus independent of the protocol, while the\nlatter is determined entirely by the protocol. Any time that\na dialogue ends in a state of protocol-completeness rather\nthan topic completeness, it is ending when agents still have\nthings to say but can\"t because the protocol won\"t allow\nthem to.\nWith these definitions of completeness, our task is to\nrelate topic-completeness - the property that ensures that\nagents can say everything that they have to say in a dialogue\nthat is, in some sense, important - to the notions of\nrelevance we have developed - which determine what agents\nare allowed to say. When we need very specific conditions to\nmake protocol-complete dialogues topic-complete, it means\nthat agents have lots of room for rhetorical maneouver when\nthose conditions are not in force. That is there are many\nways they can bring dialogues to a close before everything\nthat can be said has been said. Where few conditions are\nrequired, or conditions are absent, then dialogues between\nagents with the same knowledge will always play out the\nsame way, and rhetoric has no place. We have:\nProposition 5.2. A protocol-complete basic dialogue D\nunder a protocol which only allows R3-relevant moves will\nbe topic-complete only when AG(D)T has a single branch\nin which the nodes are labelled in increasing order from the\nroot.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1011\nProof. Given what we know about R3-relevance, the\ncondition on AG(D)P having a single branch is obvious. This\nis not a sufficient condition on its own because certain\nprotocols may prevent - through additional restrictions, like\nstrict turn-taking in a multi-party dialogue - all the nodes\nin AG(D)T , which is not subject to such restrictions, being\nadded to the graph. Only when AG(D)T includes the nodes\nin the exact order that the corresponding arguments are put\nforward is it necessary that a topic-complete argumentation\ngraph be constructed.\nGiven Proposition 5.1, these are the conditions under which\ndialogues conducted under the notion of R3-relevance will\nalways be predetermined, and given how restrictive the\nconditions are, such dialogues seem to have plenty of room for\nrhetoric to play a part.\nTo find similar conditions for dialogues composed of\nR1and R2-relevant moves, we first need to distinguish between\nthem. We can do this in terms of the structure of the\nargumentation graph:\nProposition 5.3. Consider a basic dialogue D, with\nargumentation graph AG which has root r denoting an\nargument A. If argument A , denoted by node v is an an\nR2relevant move m, m is not R1-relevant if and only if:\n1. there are two nodes v and v on the path between v\nand r, and the argument denoted by v defends itself\nagainst the argument denoted by v ; or\n2. there is an argument A , denoted by node v , that\naffects the status of A, and the path from v to r has one\nor more nodes in common with the path from v to r.\nProof. For the first condition, consider that since AG is\na tree, v is connected to r. Thus there is a series of undercut\nrelations between A and A , and this corrresponds to a path\nthrough AG. If this path is the only branch in the tree, then\nA will affect the status of A unless the chain of affect\nis broken by an undercut that can\"t change the status of the\nundercut argument because the latter defends itself.\nFor the second condition, as for the first, the only way\nthat A cannot affect the status of A is if something is\nblocking its influence. If this is not due to defending against,\nit must be because there is some node u on the path that\nrepresents an argument whose status is fixed somehow, and\nthat must mean that there is another chain of undercut\nrelations, another branch of the tree, that is incident at u. Since\nthis second branch denotes another chain of arguments, and\nthese affect the status of the argument denoted by u, they\nmust also affect the status of A. Any of these are the A in\nthe condition.\nSo an R2-relevant move m is not R1-relevant if either its\neffect is blocked because an argument upstream is not strong\nenough, or because there is another line of argument that\nis currently determining the status of the argument at the\nroot. This, in turn, means that if the effect is not due to\ndefending against, then there is an alternative move that\nis R1-relevant - a move that undercuts A in the second\ncondition above5\n. We can now show\n5\nThough whether the agent in question can make such a move is\nanother question.\nProposition 5.4. A protocol-complete basic dialogue D\nwill always be topic-complete under a protocol which only\nincludes R2-relevant moves and allows every R2-relevant move\nto be made.\nThe restriction on R2-relevant rules is exactly that for\ntopiccompleteness, so a dialogue that has only R2-relevant moves\nwill continue until every argument that any agent can make\nhas been put forward. Given this, and what we revealed\nabout R1-relevance in Proposition 5.3, we can see that:\nProposition 5.5. A protocol-complete basic dialogue D\nunder a protocol which only includes R1-relevant moves will\nbe topic-complete if AG(D)T :\n1. includes no path with adjacent nodes v, denoting A,\nand v , denoting A , such that A undercuts A and A\nis stronger that A; and\n2. is such that the nodes in every branch have consecutive\nindices and no node with degree greater than two is an\nodd number of arcs from a leaf node.\nProof. The first condition rules out the first condition\nin Proposition 5.3, and the second deals with the situation\nthat leads to the second condition in Proposition 5.3. The\nsecond condition ensures that each branch is constructed in\nfull before any new branch is added, and when a new branch\nis added, the argument that is undercut as part of the\naddition will be acceptable, and so the addition will change the\nstatus of the argument denoted by that node, and hence the\nroot. With these conditions, every move required to\nconstruct AG(D)T will be permitted and so the dialogue will be\ntopic-complete when every move has been completed.\nThe second part of this result only identifies one possible\nway to ensure that the second condition in Proposition 5.3\nis met, so the converse of this result does not hold.\nHowever, what we have is sufficient to answer the\nquestion about predetermination that we started with. For\ndialogues to be predetermined, every move that is R2-relevant\nmust be made. In such cases every dialogue is topic\ncomplete. If we do not require that all R2-relevant moves are\nmade, then there is some room for rhetoric - the way in\nwhich alternative lines of argument are presented becomes\nan issue. If moves are forced to be R3-relevant, then there\nis considerable room for rhetorical play.\n6. SUMMARY\nThis paper has studied the different ideas of relevance in\nargumentation-based dialogue, identifying the relationship\nbetween these ideas, and showing how they can impact the\nextent to which the way that agents choose moves in a\ndialogue - what some authors have called the strategy and\ntactics of a dialogue. This extends existing work on\nrelvance, such as [3, 15] by showing how different notions of\nrelevance can have an effect on the outcome of a dialogue,\nin particular when they render the outcome predetermined.\nThis connection extends the work of [18] which considered\ndialogue outcome, but stopped short of identifying the\nconditions under which it is predetermined.\nThere are two ways we are currently trying to extend this\nwork, both of which will generalise the results and extend its\napplicability. First, we want to relax the restrictions that\n1012 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nwe have imposed, the exclusion of moves that attack\nseveral arguments (without which the argument graph can be\nmulitply-connected) and the exclusion of pre-empted moves,\nwithout which the argument graph can have cycles.\nSecond, we want to extend the ideas of relevance to cope with\nmoves that do not only add undercutting arguments, but\nalso supporting arguments, thus taking account of bipolar\nargumentation frameworks [5].\nAcknowledgments\nThe authors are grateful for financial support received from\nthe EC, through project IST-FP6-002307, and from the NSF\nunder grants REC-02-19347 and NSF IIS-0329037. They are\nalso grateful to Peter Stone for a question, now several years\nold, which this paper has finally answered.\n7. REFERENCES\n[1] L. Amgoud and C. Cayrol. On the acceptability of\narguments in preference-based argumentation\nframework. In Proceedings of the 14th Conference on\nUncertainty in Artificial Intelligence, pages 1-7, 1998.\n[2] L. Amgoud, S. Parsons, and N. Maudet. Arguments,\ndialogue, and negotiation. In W. Horn, editor,\nProceedings of the Fourteenth European Conference on\nArtificial Intelligence, pages 338-342, Berlin,\nGermany, 2000. IOS Press.\n[3] J. Bentahar, M. Mbarki, and B. Moulin. Strategic and\ntactic reasoning for communicating agents. In\nN. Maudet, I. Rahwan, and S. Parsons, editors,\nProceedings of the Third Workshop on Argumentation\nin Muliagent Systems, Hakodate, Japan, 2006.\n[4] P. Besnard and A. Hunter. A logic-based theory of\ndeductive arguments. Artificial Intelligence,\n128:203-235, 2001.\n[5] C. Cayrol, C. Devred, and M.-C. Lagasquie-Schiex.\nHandling controversial arguments in bipolar\nargumentation frameworks. In P. E. Dunne and\nT. J. M. Bench-Capon, editors, Computational Models\nof Argument: Proceedings of COMMA 2006, pages\n261-272. IOS Press, 2006.\n[6] B. 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Wooldridge, and L. Amgoud. On the\noutcomes of formal inter-agent dialogues. In 2nd\nInternational Conference on Autonomous Agents and\nMulti-Agent Systems. ACM Press, 2003.\n[19] H. Prakken. On dialogue systems with speech acts,\narguments, and counterarguments. In Proceedings of\nthe Seventh European Workshop on Logic in Artificial\nIntelligence, Berlin, Germany, 2000. Springer Verlag.\n[20] H. Prakken. Relating protocols for dynamic dispute\nwith logics for defeasible argumentation. Synthese,\n127:187-219, 2001.\n[21] H. Prakken and G. Sartor. Modelling reasoning with\nprecedents in a formal dialogue game. Artificial\nIntelligence and Law, 6:231-287, 1998.\n[22] I. Rahwan, P. McBurney, and E. Sonenberg. Towards\na theory of negotiation strategy. In I. Rahwan,\nP. Moraitis, and C. Reed, editors, Proceedings of the\n1st International Workshop on Argumentation in\nMultiagent Systems, New York, NY, 2004.\n[23] C. Reed. Dialogue frames in agent communications. In\nY. Demazeau, editor, Proceedings of the Third\nInternational Conference on Multi-Agent Systems,\npages 246-253. IEEE Press, 1998.\n[24] M. Rovatsos, I. Rahwan, F. Fisher, and G. Weiss.\nAdaptive strategies for practical argument-based\nnegotiation. In I. Rahwan, P. Moraitis, and C. Reed,\neditors, Proceedings of the 1st International Workshop\non Argumentation in Multiagent Systems, New York,\nNY, 2004.\n[25] M. Schroeder, D. A. Plewe, and A. Raab. Ultima\nratio: should Hamlet kill Claudius. In Proceedings of\nthe 2nd International Conference on Autonomous\nAgents, pages 467-468, 1998.\n[26] K. Sycara. Argumentation: Planning other agents\"\nplans. In Proceedings of the Eleventh Joint Conference\non Artificial Intelligence, pages 517-523, 1989.\n[27] D. N. Walton and E. C. W. Krabbe. Commitment in\nDialogue: Basic Concepts of Interpersonal Reasoning.\nState University of New York Press, Albany, NY,\nUSA, 1995.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1013", "keywords": "node;status;relevance;graph;tree;leaf;dialogue;argument;argumentation;multiagent system"}
{"name": "train_I-75", "title": "Hypotheses Refinement under Topological Communication Constraints", "abstract": "We investigate the properties of a multiagent system where each (distributed) agent locally perceives its environment. Upon perception of an unexpected event, each agent locally computes its favoured hypothesis and tries to propagate it to other agents, by exchanging hypotheses and supporting arguments (observations). However, we further assume that communication opportunities are severely constrained and change dynamically. In this paper, we mostly investigate the convergence of such systems towards global consistency. We first show that (for a wide class of protocols that we shall define), the communication constraints induced by the topology will not prevent the convergence of the system, at the condition that the system dynamics guarantees that no agent will ever be isolated forever, and that agents have unlimited time for computation and arguments exchange. As this assumption cannot be made in most situations though, we then set up an experimental framework aiming at comparing the relative efficiency and effectiveness of different interaction protocols for hypotheses exchange. We study a critical situation involving a number of agents aiming at escaping from a burning building. The results reported here provide some insights regarding the design of optimal protocol for hypotheses refinement in this context.", "fulltext": "1. INTRODUCTION\nWe consider a multiagent system where each (distributed)\nagent locally perceives its environment, and we assume that\nsome unexpected event occurs in that system. If each agent\ncomputes only locally its favoured hypothesis, it is only\nnatural to assume that agents will seek to coordinate and\nrefine their hypotheses by confronting their observations with\nother agents. If, in addition, the communication\nopportunities are severely constrained (for instance, agents can\nonly communicate when they are close enough to some other\nagent), and dynamically changing (for instance, agents may\nchange their locations), it becomes crucial to carefully\ndesign protocols that will allow agents to converge to some\ndesired state of global consistency. In this paper we\nexhibit some sufficient conditions on the system dynamics and\non the protocol/strategy structures that allow to guarantee\nthat property, and we experimentally study some contexts\nwhere (some of) these assumptions are relaxed.\nWhile problems of diagnosis are among the venerable\nclassics in the AI tradition, their multiagent counterparts have\nmuch more recently attracted some attention. Roos and\ncolleagues [8, 9] in particular study a situation where a number\nof distributed entities try to come up with a satisfying global\ndiagnosis of the whole system. They show in particular that\nthe number of messages required to establish this global\ndiagnosis is bound to be prohibitive, unless the communication\nis enhanced with some suitable protocol. However, they do\nnot put any restrictions on agents\" communication options,\nand do not assume either that the system is dynamic.\nThe benefits of enhancing communication with supporting\ninformation to make convergence to a desired global state\nof a system more efficient has often been put forward in the\nliterature. This is for instance one of the main idea\nunderlying the argumentation-based negotiation approach [7], where\nthe desired state is a compromise between agents with\nconflicting preferences. Many of these works however make the\nassumption that this approach is beneficial to start with,\nand study the technical facets of the problem (or instead\nemphasize other advantages of using argumentation).\nNotable exceptions are the works of [3, 4, 2, 5], which studied in\ncontexts different from ours the efficiency of argumentation.\nThe rest of the paper is as follows. Section 2 specifies\nthe basic elements of our model, and Section 3 goes on to\npresenting the different protocols and strategies used by the\nagents to exchange hypotheses and observations. We put\nspecial attention at clearly emphasizing the conditions on\nthe system dynamics and protocols/strategies that will be\nexploited in the rest of the paper. Section 4 details one of\n998\n978-81-904262-7-5 (RPS) c 2007 IFAAMAS\nthe main results of the paper, namely the fact that under the\naforementioned conditions, the constraints that we put on\nthe topology will not prevent the convergence of the system\ntowards global consistency, at the condition that no agent\never gets completely lost forever in the system, and that\nunlimited time is allowed for computation and argument\nexchange. While the conditions on protocols and strategies are\nfairly mild, it is also clear that these system requirements\nlook much more problematic, even frankly unrealistic in\ncritical situations where distributed approaches are precisely\nadvocated. To get a clearer picture of the situation induced\nwhen time is a critical factor, we have set up an\nexperimental framework that we introduce and discuss in Section 5.\nThe critical situation involves a number of agents aiming\nat escaping from a burning building. The results reported\nhere show that the effectiveness of argument exchange\ncrucially depends upon the nature of the building, and provide\nsome insights regarding the design of optimal protocol for\nhypotheses refinement in this context.\n2. BASIC NOTIONS\nWe start by defining the basic elements of our system.\nEnvironment\nLet O be the (potentially infinite) set of possible\nobservations. We assume the sensors of our agents to be perfect,\nhence the observations to be certain. Let H be the set of\nhypotheses, uncertain and revisable. Let Cons(h, O) be the\nconsistency relation, a binary relation between a hypothesis\nh \u2208 H and a set of observations O \u2286 O. In most cases, Cons\nwill refer to classical consistency relation, however, we may\noverload its meaning and add some additional properties to\nthat relation (in which case we will mention it).\nThe environment may include some dynamics, and change\nover the course of time. We define below sequences of time\npoints to deal with it:\nDefinition 1 (Sequence of time points). A\nsequence of time points t1, t2, . . . , tn from t is an ordered\nset of time points t1, t2, . . . , tn such that t1 \u2265 t and\n\u2200i \u2208 [1, n \u2212 1], ti+1 \u2265 ti.\nAgent\nWe take a system populated by n agents a1, . . . , an. Each\nagent is defined as a tuple F, Oi, hi , where:\n\u2022 F, the set of facts, common knowledge to all agents.\n\u2022 Oi \u2208 2O\n, the set of observations made by the agent\nso far. We assume a perfect memory, hence this set\ngrows monotonically.\n\u2022 hi \u2208 H, the favourite hypothesis of the agent.\nA key notion governing the formation of hypotheses is that\nof consistency, defined below:\nDefinition 2 (Consistency). We say that:\n\u2022 An agent is consistent (Cons(ai)) iff Cons(hi, Oi)\n(that is, its hypothesis is consistent with its\nobservation set).\n\u2022 An agent ai consistent with a partner agent aj iff\nCons(ai) and Cons(hi, Oj) (that is, this agent is\nconsistent and its hypothesis can explain the observation\nset of the other agent).\n\u2022 Two agents ai and aj are mutually consistent\n(MCons(ai, aj)) iff Cons(ai, aj) and Cons(aj, ai).\n\u2022 A system is consistent iff \u2200(i, j)\u2208[1, n]2\nit is the case\nthat MCons(ai, aj).\nTo ensure its consistency, each agent is equipped with an\nabstract reasoning machinery that we shall call the\nexplanation function Eh. This (deterministic) function takes a\nset of observation and returns a single prefered hypothesis\n(2O\n\u2192 H). We assume h = Eh(O) to be consistent with\nO by definition of Eh, so using this function on its\nobservation set to determine its favourite hypothesis is a sure way\nfor the agent to achieve consistency. Note however that an\nhypothesis does not need to be generated by Eh to be\nconsistent with an observation set. As a concrete example of such\na function, and one of the main inspiration of this work,\none can cite the Theorist reasoning system [6] -as long as\nit is coupled with a filter selecting a single prefered theory\namong the ones initially selected by Theorist.\nNote also that hi may only be modified as a consequence\nof the application Eh. We refer to this as the autonomy of the\nagent: no other agent can directly impose a given\nhypothesis to an agent. As a consequence, only a new observation\n(being it a new perception, or an observation communicated\nby a fellow agent) can result in a modification of its prefered\nhypothesis hi (but not necessarily of course).\nWe finally define a property of the system that we shall\nuse in the rest of the paper:\nDefinition 3 (Bounded Perceptions). A system\ninvolves a bounded perception for agents iff \u2203n0 s.t.\n\u2200t| \u222aN\ni=1 Oi| \u2264 n0. (That is, the number of observations to\nbe made by the agents in the system is not infinite.)\nAgent Cycle\nNow we need to see how these agents will evolve and interact\nin their environment. In our context, agents evolve in a\ndynamic environment, and we classicaly assume the following\nsystem cycle:\n1. Environment dynamics: the environment evolves\naccording to the defined rules of the system dynamics.\n2. Perception step : agents get perceptions from the\nenvironment. These perceptions are typically partial (e.g.\nthe agent can only see a portion of a map).\n3. Reasoning step: agents compare perception with\npredictions, seek explanations for (potential)\ndifference(s), refine their hypothesis, draw new conclusions.\n4. Communication step: agents can communicate\nhypotheses and observations with other agents through\na defined protocol. Any agent can only be involved in\none communication with another agent by step.\n5. Action step: agents do some practical reasoning using\nthe models obtained from the previous steps and select\nan action. They can then modify the environment by\nexecuting it.\nThe communication of the agents will be further\nconstrained by topological consideration. At a given time, an\nagent will only be able to communicate with a number of\nneighbours. Its connexions with these others agents may\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 999\nevolve with its situation in the environment. Typically, an\nagent can only communicate with agents that it can sense,\nbut one could imagine evolving topological constraints on\ncommunication based on a network of communications\nbetween agents where the links are not always active.\nCommunication\nIn our system, agents will be able to communicate with each\nother. However, due to the aforementionned topological\nconstraints, they will not be able to communicate with any\nagents at anytime. Who an agent can communicate with\nwill be defined dynamically (for instance, this can be a\nconsequence of the agents being close enough to get in touch).\nWe will abstractly denote by C(ai, aj, t) the communication\nproperty, in other words, the fact that agents ai and aj can\ncommunicate at time t (note that this relation is assumed\nto be symetric, but of course not transitive). We are now in\na position to define two essential properties of our system.\nDefinition 4 (Temporal Path). There exists a\ntemporal communication path at horizon tf (noted Ltf (aI , aJ ))\nbetween ai and aj iff there exists a sequence of time points\nt1, t2, . . . , tn from tf and a sequence of agents k1, k2, . . . , kn\ns.t. (i) C(aI , ak1 , t1), (ii) C(akn , aJ , tn+1), (iii) \u2200i \u2208 [1, n],\nC(aki , aki+1 , ti)\nIntuitively, what this property says is that it is possible to\nfind a temporal path in the future that would allow to link\nagent ai and aj via a sequence of intermediary agents. Note\nthat the time points are not necessarily successive, and that\nthe sequence of agents may involve the same agents several\ntimes.\nDefinition 5 (Temporal Connexity). A system is\ntemporaly connex iff \u2200t \u2200(i, j)\u2208[1, n]2\nLt(ai, aj)\nIn short, a temporaly connex system guarantees that any\nagent will be able to communicate with any other agents,\nno matter how long it might take to do so, at any time. To\nput it another way, it is never the case that an agent will be\nisolated for ever from another agent of the system.\nWe will next discuss the detail of how communication\nconcretely takes place in our system. Remember that in this\npaper, we only consider the case of bilateral exchanges (an\nagent can only speak to a single other agent), and that we\nalso assume that any agent can only engage in a single\nexchange in a given round.\n3. PROTOCOLS AND STRATEGIES\nIn this section, we discuss the requirements of the\ninteraction protocols that govern the exchange of messages between\nagents, and provide some example instantiation of such\nprotocols. To clarify the presentation, we distinguish two\nlevels: the local level, which is concerned with the regulation\nof bilateral exchanges; and the global level,which essentially\nregulates the way agents can actually engage into a\nconversation. At each level, we separate what is specified by the\nprotocol, and what is left to agents\" strategies.\nLocal Protocol and Strategies\nWe start by inspecting local protocols and strategies that\nwill regulate the communication between the agents of the\nsystem. As we limit ourselves to bilateral communication,\nthese protocols will simply involve two agents. Such protocol\nwill have to meet one basic requirement to be satisfying.\n\u2022 consistency (CONS)- a local protocol has to\nguarantee the mutual consistency of agents upon termination\n(which implies termination of course).\nFigure 1: A Hypotheses Exchange Protocol [1]\nOne example such protocol is the protocol described in [1]\nthat is pictured in Fig. 1. To further illustrate how such\nprotocol can be used by agents, we give some details on a\npossible strategy: upon receiving a hypothesis h1 (propose(h1) or\ncounterpropose(h1)) from a1, agent a2 is in state 2 and has\nthe following possible replies: counterexample (if the agent\nknows an example contradicting the hypothesis, or not\nexplained by this hypothesis), challenge (if the agents lacks\nevidence to accept this hypothesis), counterpropose (if the\nagent agrees with the hypothesis but prefers another one),\nor accept (if it is indeed as good as its favourite\nhypothesis). This strategy guarantees, among other properties, the\neventual mutual logical consistency of the involved agents\n[1].\nGlobal Protocol\nThe global protocol regulates the way bilateral exchanges\nwill be initiated between agents. At each turn, agents will\nconcurrently send one weighted request to communicate to\nother agents. This weight is a value measuring the agent\"s\nwillingness to converse with the targeted agent (in practice,\nthis can be based on different heuristics, but we shall make\nsome assumptions on agents\" strategies, see below). Sending\nsuch a request is a kind of conditional commitment for the\nagent. An agent sending a weighted request commits to\nengage in conversation with the target if he does not receive\nand accept himself another request. Once all request have\nbeen received, each agent replies with either an acccept or\na reject. By answering with an accept, an agent makes a\nfull commitment to engage in conversation with the sender.\nTherefore, it can only send one accept in a given round, as an\nagent can only participate in one conversation per time step.\nWhen all response have been received, each agent receiving\nan accept can either initiate a conversation using the local\nprotocol or send a cancel if it has accepted another request.\nAt the end of all the bilateral exchanges, the agents\nengaged in conversation are discarded from the protocol. Then\neach of the remaining agents resends a request and the\nprocess iterates until no more requests are sent.\nGlobal Strategy\nWe now define four requirements for the strategies used by\nagents, depending on their role in the protocol: two are\nconcerned with the requestee role (how to decide who the\n1000 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nagent wishes to communicate with?), the other two with the\nresponder role (how to decide which communication request\nto accept or not?).\n\u2022 Willingness to solve inconsistancies (SOLVE)-agents\nwant to communicate with any other agents unless\nthey know they are mutually consistent.\n\u2022 Focus on solving inconsistencies (FOCUS)-agents do\nnot request communication with an agent with whom\nthey know they are mutually consistent.\n\u2022 Willingness to communicate (COMM)-agents cannot\nrefuse a weighted communication request, unless they\nhave just received or send a request with a greater\nweight.\n\u2022 Commitment to communication request\n(REQU)agents cannot accept a weighted communication\nrequest if they have themselves sent a communication\nrequest with a greater weight. Therefore, they will\nnot cancel their request unless they have received a\ncommunicational request with greater weight.\nNow the protocol structure, together with the properties\nCOMM+REQU, ensure that a request can only be rejected\nif its target agent engages in communication with another\nagent. Suppose indeed that agent ai wants to communicate\nwith aj by sending a request with weight w. COMM\nguarantees that an agent receiving a weighted request will either\naccept this communication, accept a communication with a\ngreater weight or wait for the answer to a request with a\ngreater weight. This ensures that the request with\nmaximal weight will be accepted and not cancelled (as REQU\nensures that an agent sending a request can only cancel it if\nhe accepts another request with greater weight). Therefore\nat least two agents will engage in conversation per round\nof the global protocol. As the protocol ensures that ai can\nresend its request while aj is not engaged in a conversation,\nthere will be a turn in which aj must engage in a\nconversation, either with ai or another agent.\nThese requirements concern request sending and\nacceptation, but agents also need some strategy of weight\nattribution. We describe below an altruist strategy, used in our\nexperiments. Being cooperative, an agent may want to know\nmore of the communication wishes of other agents in order to\nimprove the overall allocation of exchanges to agents. A\ncontext request step is then added to the global protocol. Before\nsending their chosen weighted request, agents attribute a\nweight to all agents they are prepared to communicate with,\naccording to some internal factors. In the simplest case, this\nweight will be 1 for all agent with whom the agent is not\nsure of being mutually consistent (ensuring SOLVE), other\nagent being not considered for communication (ensuring\nFOCUS). The agent then sends a context request to all agents\nwith whom communication is considered. This request also\nprovides information about the sender (list of considered\ncommunications along with their weight). After reception\nof all the context requests, agents will either reply with a\ndeny, iff they are already engaged in a conversation (in which\ncase, the requesting agent will not consider communication\nwith them anymore in this turn), or an inform giving the\nrequester information about the requests it has sent and\nreceived. When all replies have been received, each agent can\ncalculate the weight of all requests concerning it. It does so\nby substracting from the weight of its request the weight of\nall requests concerning either it or its target (that is, the\nfinal weight of the request from ai to aj is Wi,j = wi,j +wj,i \u2212\n(\nP\nk\u2208R(i)\u2212{j} wi,k +\nP\nk\u2208S(i)\u2212{j} wk,i +\nP\nk\u2208R(j)\u2212{i} wj,k +\nP\nk\u2208S(j)\u2212{i} wk,j) where wi,j is the weight of the request of\nai to aj, R(i) is the set of indice of agents having received a\nrequest from ai and S(i) is the set of indice of agents\nhaving send a request to ai). It then finally sends a weighted\nrequest to the agents who maximise this weight (or wait for\na request) as described in the global protocol.\n4. (CONDITIONAL) CONVERGENCE TO\nGLOBAL CONSISTENCY\nIn this section we will show that the requirements\nregarding protocols and strategies just discussed will be sufficient\nto ensure that the system will eventually converge towards\nglobal consistency, under some conditions. We first show\nthat, if two agents are not mutually consistent at some time,\nthen there will be necessarily a time in the future such that\nan agent will learn a new observation, being it because it is\nnew for the system, or by learning it from another agent.\nLemma 1. Let S be a system populated by n agents\na1, a2, ..., an, temporaly connex, and involving bounded\nperceptions for these agents. Let n1 be the sum of\ncardinalities of the intersection of pairwise observation sets.\n(n1 =\nP\n(i,j)\u2208[1,n]2 |Oi \u2229 Oj|) Let n2 be the cardinality of\nthe union of all agents\" observations sets. (n2 = | \u222aN\ni=1 Oi|).\nIf \u00acMCons(ai, aj) at time t0, there is necessarily a time\nt > t0 s.t. either n1 or n2 will increase.\nProof. Suppose that there exist a time t0\nand indices (i, j) s.t. \u00acMCons(ai, aj). We will\nuse mt0 =\nP\n(k,l)\u2208[1,n]2 \u03b5Comm(ak, al, t0) where\n\u03b5Comm(ak, al, t0) = 1 if ak and al have\ncommunicated at least once since t0, and 0 otherwise.\nTemporal connexity guarantees that there exist t1, ..., tm+1\nand k1, ..., km s.t. C(ai, ak1 , t1), C(akm , aj, tm+1), and\n\u2200p \u2208 [1, m], C(akp , akp+1 , tp). Clearly, if MCons(ai, ak1 ),\nMCons(akm , aj) and \u2200p, MCons(akp , akp+1 ), we have\nMCons(ai, aj) which contradicts our hypothesis (MCons\nbeing transitive, MCons(ai, ak1 )\u2227MCons(ak1 , ak2 ) implies\nthat MCons(ai, ak2 ) and so on till MCons(ai, akm )\u2227\nMCons(akm , aj) which implies MCons(ai, aj) ).\nAt least two agents are then necessarily\ninconsistent (\u00acMCons(ai, ak1 ), or \u00acMCons(akm , aj), or \u2203p0 t.q.\n\u00acMCons(akp0\n, akp0+1 )). Let ak and al be these two\nneighbours at a time t > t0\n1\n. The SOLVE property ensures\nthat either ak or al will send a communication request to\nthe other agent at time t . As shown before, this in turn\nensures that at least one of these agents will be involved in\na communication. Then there are two possibilities:\n(case i) ak and al communicate at time t . In this case,\nwe know that \u00acMCons(ak, al). This and the CONS\nproperty ensures that at least one of the agents must change its\n1\nStrictly speaking, the transitivity of MCons only ensure\nthat ak and al are inconsistent at a time t \u2265 t0 that can\nbe different from the time t at which they can\ncommunicate. But if they become consistent between t and t (or\ninconsistent between t and t ), it means that at least one\nof them have changed its hypothesis between t and t , that\nis, after t0. We can then apply the reasoning of case iib.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1001\nhypothesis, which in turn, since agents are autonomous,\nimplies at least one exchange of observation. But then |Ok \u2229Ol|\nis bound to increase: n1(t ) > n1(t0).\n(case ii) ak communicates with ap at time t . We then have\nagain two possibilities:\n(case iia) ak and ap did not communicate since t0. But then\n\u03b5Comm(ak, ap, t0) had value 0 and takes value 1. Hence mt0\nincreases.\n(case iib) ak and ap did communicate at some time t0 >\nt0. The CONS property of the protocol ensures that\nMCons(ak, ap) at that time. Now the fact that they\ncommunicate and FOCUS implies that at least one of them did\nchange its hypothesis in the meantime. The fact that agents\nare autonomous implies in turn that a new observation\n(perceived or received from another agent) necessarily provoked\nthis change. The latter case would ensure the existence of a\ntime t > t0 and an agent aq s.t. either |Op \u2229Oq| or |Ok \u2229Oq|\nincreases of 1 at that time (implying n1(t ) > n1(t0)). The\nformer case means that the agent gets a new perception o\nat time t . If that observation was unknown in the system\nbefore, then n2(t ) > n2(t0). If some agent aq already knew\nthis observation before, then either Op \u2229 Oq or Ok \u2229 Oq\nincreases of 1 at time t (which implies that n1(t ) > n1(t0)).\nHence, \u00acMCons(ai, aj) at time t0 guarantees that, either:\n\u2212\u2203t > t0 t.q. n1(t ) > n1(t0); or\n\u2212\u2203t > t0 t.q. n2(t ) > n2(t0); or\n\u2212\u2203t > t0 t.q. mt0 increases of 1 at time t .\nBy iterating the reasoning with t (but keeping t0 as the\ntime reference for mt0 ), we can eliminate the third case\n(mt0 is integer and bounded by n2\n, which means that\nafter a maximum of n2\niterations, we necessarily will be in\none of two other cases.) As a result, we have proven that if\n\u00acMCons(ai, aj) at time t0, there is necessarily a time t s.t.\neither n1 or n2 will increase.\nTheorem 1 (Global consistency). Let S be a\nsystem populated by n agents a1, a2, ..., an, temporaly connex,\nand involving bounded perceptions for these agents. Let\nCons(ai, aj) be a transitive consistency property. Then any\nprotocol and strategies satisfying properties CONS, SOLVE,\nFOCUS, COMM and REQU guarantees that the system will\nconverge towards global consistency.\nProof. For the sake of contradiction, let us assume\n\u2203I, J \u2208 [1, N] s.t. \u2200t, \u2203t0 > t, t.q. \u00acCons(aI , aJ , t0).\nUsing the lemma, this implies that \u2203t > t0 s.t. either\nn1(t ) > n1(t0) or n2(t ) > n2(t0). But we can apply\nthe same reasoning taking t = t , which would give us\nt1 > t > t0 s.t. \u00acCons(aI , aJ , t1), which gives us t > t1\ns.t. either n1(t ) > n1(t1) or n2(t ) > n2(t1). By\nsuccessive iterations we can then construct a sequence t0, t1, ..., tn,\nwhich can be divided in two sub-sequences t0, t1, ...tn and\nt0 , t1 , ..., tn s.t. n1(t0) < n1(t1) < ... < n1(tn) and\nn2(t0 ) < n2(t1 ) < ... < n2(tn). One of these sub-sequences\nhas to be infinite. However, n1(ti) and n2(ti ) are strictly\ngrowing, integer, and bounded, which implies that both are\nfinite. Contradiction.\nWhat the previous result essentially shows is that, in a\nsystem where no agent will be isolated from the rest of the\nagents for ever, only very mild assumptions on the protocols\nand strategies used by agents suffice to guarantee\nconvergence towards system consistency in a finite amount of time\n(although it might take very long). Unfortunately, in many\ncritical situations, it will not be possible to assume this\ntemporal connexity. As distributed approaches as the one\nadvocated in this paper are precisely often presented as a\ngood way to tackle problems of reliability or problems of\ndependence to a center that are of utmost importance in these\ncritical applications, it is certainly interesting to further\nexplore how such a system would behave when we relax this\nassumption.\n5. EXPERIMENTAL STUDY\nThis experiment involves agents trying to escape from a\nburning building. The environment is described as a spatial\ngrid with a set of walls and (thankfully) some exits. Time\nand space are considered discrete. Time is divided in rounds.\nAgents are localised by their position on the spatial grid.\nThese agents can move and communicate with other agents.\nIn a round, an agent can move of one cell in any of the four\ncardinal directions, provided it is not blocked by a wall. In\nthis application, agents communicate with any other agent\n(but, recall, a single one) given that this agent is in view,\nand that they have not yet exchanged their current favoured\nhypothesis. Suddenly, a fire erupts in these premises. From\nthis moment, the fire propagates. Each round, for each cases\nwhere there is fire, the fire propagates in the four directions.\nHowever, the fire cannot propagate through a wall. If the\nfire propagates in a case where an agent is positioned, that\nagent burns and is considered dead. It can of course no\nlonger move nor communicate. If an agent gets to an exit,\nit is considered saved, and can no longer be burned. Agents\nknow the environment and the rules governing the\ndynamics of this environment, that is, they know the map as well\nas the rules of fire propagation previously described. They\nalso locally perceive this environment, but cannot see\nfurther than 3 cases away, in any direction. Walls also block\nthe line of view, preventing agents from seeing behind them.\nWithin their sight, they can see other agents and whether\nor not the cases they see are on fire. All these perceptions\nare memorised.\nWe now show how this instantiates the abstract\nframework presented the paper.\n\u2022 O = {Fire(x, y, t), NoFire(x, y, t), Agent(ai, x, y, t)}\nObservations can then be positive (o \u2208 P(O) iff \u2203h \u2208\nH s.t. h |= o) or negative (o \u2208 N(O) iff \u2203h \u2208 H s.t.\nh |= \u00aco).\n\u2022 H={FireOrigin(x1, y1, t1)\u2227...\u2227FireOrigin(xl, yl, tl)}\nHypotheses are conjunctions of FireOrigins.\n\u2022 Cons(h, O) consistency relation satisfies:\n- coherence : \u2200o \u2208 N(O), h |= \u00aco.\n- completeness : \u2200o \u2208 P(O), h |= o.\n- minimality : For all h \u2208 H, if h is coherent and\ncomplete for O, then h is prefered to h according\nto the preference relation (h \u2264p h ).2\n2\nSelects first the minimal number of origins, then the most\nrecent (least preemptive strategy [6]), then uses some\narbitrary fixed ranking to discriminate ex-aequo. The resulting\nrelation is a total order, hence minimality implies that there\nwill be a single h s.t.Cons(O, h) for a given O. This in\nturn means that MCons(ai, aj) iff Cons(ai), Cons(aj), and\nhi = hj. This relation is then transitive and symmetric.\n1002 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\n\u2022 Eh takes O as argument and returns min\u2264p of the\ncoherent and complete hypothesis for O\n5.1 Experimental Evaluation\nWe will classically (see e.g. [3, 4]) assess the effectiveness\nand efficiency of different interaction protocols.\nEffectiveness of a protocol\nThe proportion of agents surviving the fire over the initial\nnumber of agents involved in the experiment will determine\nthe effectiveness of a given protocol. If this value is high,\nthe protocol has been effective to propagate the information\nand/or for the agents to refine their hypotheses and\ndetermine the best way to the exit.\nEfficiency of a protocol\nTypically, the use of supporting information will involve a\ncommunication overhead. We will assume here that the\nefficiency of a given protocol is characterised by the data flow\ninduced by this protocol. In this paper we will only discuss\nthis aspect wrt. local protocols. The main measure that we\nshall then use here is the mean total size of messages that\nare exchanged by agents per exchange (hence taking into\naccount both the number of messages and the actual size of the\nmessages, because it could be that messages happen to be\nvery big, containing e.g. a large number of observations,\nwhich could counter-balance a low number of messages).\n5.2 Experimental Settings\nThe chosen experimental settings are the following:\n\u2022 Environmental topology- Performances of\ninformation propagation are highly constrained by the\nenvironment topology. The perception skills of the agents\ndepend on the openness of the environment. With\na large number of walls the perceptions of agents are\nlimited, and also the number of possible inter-agent\ncommunications, whereas an open environment will\nprovide optimal possibilities of perception and\ninformation propagation. Thus, we propose a topological\nindex (see below) as a common basis to charaterize the\nenvironments (maps) used during experimentations.\nThe topological index (TI) is the ratio of the number of\ncells that can be perceived by agents summed up from\nall possible positions, divided by the number of cells\nthat would be perceived from the same positions but\nwithout any walls. (The closer to 1, the more open the\nenvironment). We shall also use two additional, more\nclassical [10], measures: the characteristic path length3\n(CPL) and the clustering coefficient4\n(CC).\n\u2022 Number of agents- The propagation of information\nalso depends on the initial number of agents involved\nduring an experimentation. For instance, the more\nagents, the more potential communications there is.\nThis means that there will be more potential for\npropagation, but also that the bilateral exchange restriction\nwill be more crucial.\n3\nThe CPL is the median of the means of the shortest path\nlengths connecting each node to all other nodes.\n4\ncharacterising the isolation degree of a region of an\nenvironment in terms of acessibility (number of roads still usable\nto reach this region).\nMap T.I. (%) C.P.L. C.C.\n69-1 69,23 4,5 0,69\n69-2 68,88 4,38 0,65\n69-3 69,80 4,25 0,67\n53-1 53,19 5,6 0,59\n53-2 53,53 6,38 0,54\n53-3 53,92 6,08 0,61\n38-1 38,56 8,19 0,50\n38-2 38,56 7,3 0,50\n38-3 38,23 8,13 0,50\nTable 1: Topological Characteristics of the Maps\n\u2022 Initial positions of the agents- Initial positions of the\nagents have a significant influence on the overall\nbehavior of an instance of our system: being close from\nan exit will (in general) ease the escape.\n5.3 Experimental environments\nWe choose to realize experiments on three very\ndifferent topological indexes (69% for open environments, 53%\nfor mixed environments, and 38% for labyrinth-like\nenvironments).\nFigure 2: Two maps (left: TI=69%, right TI=38%)\nWe designed three different maps for each index (Fig. 2\nshows two of them), containing the same maximum number\nof agents (36 agents max.) with a maximum density of one\nagent per cell, the same number of exits and a similar fire\norigin (e.g. starting time and position). The three differents\nmaps of a given index are designed as follows. The first map\nis a model of an existing building floor. The second map has\nthe same enclosure, exits and fire origin as the first one,\nbut the number and location of walls are different (wall\nlocations are designed by an heuristic which randomly creates\nwalls on the spatial grid such that no fully closed rooms are\ncreated and that no exit is closed). The third map is\ncharacterised by geometrical enclosure in wich walls location\nis also designed with the aforementioned heuristic. Table 1\nsummarizes the different topological measures\ncharacterizing these different maps. It is worth pointing out that the\nvalues confirm the relevance of TI (maps with a high TI\nhave a low CPL and a high CC. However the CPL and CC\nallows to further refine the difference between the maps, e.g.\nbetween 53-1 and 53-2).\n5.4 Experimental Results\nFor each triple of maps defined as above we conduct the\nsame experiments. In each experiment, the society differs in\nterms of its initial proportion of involved agents, from 1%\nto 100%. This initial proportion represents the percentage\nof involved agents with regards to the possible maximum\nnumber of agents. For each map and each initial proportion,\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1003\nwe select randomly 100 different initial agents\" locations.\nFor each of those different locations we execute the system\none time for each different interaction protocol.\nEffectiveness of Communication and Argumentation\nThe first experiment that we set up aims at testing how\neffective is hypotheses exchange (HE), and in particular how\nthe topological aspects will affect this effectiveness. In order\nto do so, we have computed the ratio of improvement offered\nby that protocol over a situation where agents could simply\nnot communicate (no comm). To get further insights as\nto what extent the hypotheses exchange was really crucial,\nwe also tested a much less elaborated protocol consisting\nof mere observation exchanges (OE). More precisely, this\nprotocol requires that each agent stores any unexpected\nobservation that it perceives, and agents simply exchange\ntheir respective lists of observations when they discuss. In\nthis case, the local protocol is different (note in\nparticular that it does not guarantee mutual consistency), but the\nglobal protocol remains the same (at the only exception that\nagents\" motivation to communicate is to synchronise their\nlist of observations, not their hypothesis). If this protocol is\nat best as effective as HE, it has the advantage of being more\nefficient (this is obvious wrt the number of messages which\nwill be limited to 2, less straightforward as far as the size of\nmessages is concerned, but the rough observation that the\nexchange of observations can be viewed as a flat version\nof the challenge is helpful to see this). The results of these\nexperiments are reported in Fig. 3.\nFigure 3: Comparative effectiveness ratio gain of\nprotocols when the proportion of agents augments\nThe first observation that needs to be made is that\ncommunication improves the effectiveness of the process, and\nthis ratio increases as the number of agents grows in the\nsystem. The second lesson that we learn here is that\ncloseness relatively makes communication more effective over non\ncommunication. Maps exhibiting a T.I. of 38% are\nconstantly above the two others, and 53% are still slightly but\nsignificantly better than 69%. However, these curves also\nsuggest, perhaps surprisingly, that HE outperforms OE in\nprecisely those situations where the ratio gain is less\nimportant (the only noticeable difference occurs for rather open\nmaps where T.I. is 69%). This may be explained as follows:\nwhen a map is open, agents have many potential explanation\ncandidates, and argumentation becomes useful to\ndiscriminate between those. When a map is labyrinth-like, there are\nfewer possible explanations to an unexpected event.\nImportance of the Global Protocol\nThe second set of experiments seeks to evaluate the\nimportance of the design of the global protocol. We tested our\nprotocol against a local broadcast (LB) protocol. Local\nbroadcast means that all the neighbours agents perceived\nby an agent will be involved in a communication with that\nagent in a given round -we alleviate the constraint of a\nsingle communication by agent. This gives us a rough upper\nbound upon the possible ratio gain in the system (for a given\nlocal protocol). Again, we evaluated the ratio gain induced\nby that LB over our classical HE, for the three different\nclasses of maps. The results are reported in Fig. 4.\nFigure 4: Ratio gain of local broadcast over\nhypotheses exchange\nNote to begin with that the ratio gain is 0 when the\nproportion of agents is 5%, which is easily explained by the fact\nthat it corresponds to situations involving only two agents.\nWe first observe that all classes of maps witness a ratio\ngain increasing when the proportion of agents augments: the\ngain reaches 10 to 20%, depending on the class of maps\nconsidered. If one compares this with the improvement reported\nin the previous experiment, it appears to be of the same\nmagnitude. This illustrates that the design of the global\nprotocol cannot be ignored, especially when the proportion\nof agents is high. However, we also note that the\neffectiveness ratio gain curves have very different shapes in both\ncases: the gain induced by the accuracy of the local protocol\nincreases very quickly with the proportion of agents, while\nthe curve is really smooth for the global one.\nNow let us observe more carefully the results reported\nhere: the curve corresponding to a TI of 53% is above that\ncorresponding to 38%. This is so because the more open\na map, the more opportunities to communicate with more\nthan one agent (and hence benefits from broadcast).\nHowever, we also observe that curve for 69% is below that for\n53%. This is explained as follows: in the case of 69%, the\npotential gain to be made in terms of surviving agents is\nmuch lower, because our protocols already give rather\nefficient outcomes anyway (quickly reaching 90%, see Fig. 3).\nA simple rule of thumb could be that when the number of\nagents is small, special attention should be put on the local\n1004 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nprotocol, whereas when that number is large, one should\ncarefully design the global one (unless the map is so open\nthat the protocol is already almost optimally efficient).\nEfficiency of the Protocols\nThe final experiment reported here is concerned with the\nanalysis of the efficiency of the protocols. We analysis here\nthe mean size of the totality of the messages that are\nexchanged by agents (mean size of exchanges, for short) using\nthe following protocols: HE, OE, and two variant\nprotocols. The first one is an intermediary restricted hypotheses\nexchange protocol (RHE). RHE is as follows: it does not\ninvolve any challenge nor counter-propose, which means that\nagents cannot switch their role during the protocol (this\ndiffers from RE in that respect). In short, RHE allows an agent\nto exhaust its partner\"s criticism, and eventually this\npartner will come to adopt the agent\"s hypothesis. Note that this\nmeans that the autonomy of the agent is not preserved here\n(as an agent will essentially accept any hypothesis it cannot\nundermine), with the hope that the gain in efficiency will be\nsignificant enough to compensate a loss in effectiveness. The\nsecond variant protocol is a complete observation exchange\nprotocol (COE). COE uses the same principles as OE, but\nincludes in addition all critical negative examples (nofire) in\nthe exchange (thus giving all examples used as arguments\nby the hypotheses exchanges protocol), hence improving\neffectiveness. Results for map 69-1 are shown on Fig. 5.\nFigure 5: Mean size of exchanges\nFirst we can observe the fact that the ordering of the\nprotocols, from the least efficient to the most efficient, is COE,\nHE, RHE and then OE. HE being more efficient than COE\nproves that the argumentation process gains efficiency by\nselecting when it is needed to provide negative example, which\nhave less impact that positive ones in our specific testbed.\nHowever, by communicating hypotheses before eventually\ngiving observation to support it (HE) instead of directly\ngiving the most crucial observations (OE), the argumentation\nprocess doubles the size of data exchanges. It is the cost for\nensuring consistency at the end of the exchange (a property\nthat OE does not support). Also significant is the fact the\nthe mean size of exchanges is slightly higher when the\nnumber of agents is small. This is explained by the fact that in\nthese cases only a very few agents have relevant informations\nin their possession, and that they will need to communicate\na lot in order to come up with a common view of the\nsituation. When the number of agents increases, this knowledge\nis distributed over more agents which need shorter\ndiscussions to get to mutual consistency. As a consequence, the\nrelative gain in efficiency of using RHE appears to be better\nwhen the number of agents is small: when it is high, they\nwill hardly argue anyway. Finally, it is worth noticing that\nthe standard deviation for these experiments is rather high,\nwhich means that the conversation do not converge to any\nstereotypic pattern.\n6. CONCLUSION\nThis paper has investigated the properties of a\nmultiagent system where each (distributed) agent locally perceives\nits environment, and tries to reach consistency with other\nagents despite severe communication restrictions. In\nparticular we have exhibited conditions allowing convergence, and\nexperimentally investigated a typical situation where those\nconditions cannot hold. There are many possible extensions\nto this work, the first being to further investigate the\nproperties of different global protocols belonging to the class we\nidentified, and their influence on the outcome. There are in\nparticular many heuristics, highly dependent on the context\nof the study, that could intuitively yield interesting results\n(in our study, selecting the recipient on the basis of what can\nbe inferred from his observed actions could be such a\nheuristic). One obvious candidate for longer term issues concern\nthe relaxation of the assumption of perfect sensing.\n7. REFERENCES\n[1] G. Bourgne, N. Maudet, and S. Pinson. When agents\ncommunicate hypotheses in critical situations. In\nProceedings of DALT-2006, May 2006.\n[2] P. Harvey, C. F. Chang, and A. Ghose. Support-based\ndistributed search: a new approach for multiagent\nconstraint processing. In Proceedings of AAMAS06,\n2006.\n[3] H. Jung and M. Tambe. Argumentation as distributed\nconstraint satisfaction: Applications and results. In\nProceedings of AGENTS01, 2001.\n[4] N. C. Karunatillake and N. R. Jennings. Is it worth\narguing? In Proceedings of ArgMAS 2004, 2004.\n[5] S. Onta\u02dcn\u00b4on and E. Plaza. Arguments and\ncounterexamples in case-based joint deliberation. In\nProceedings of ArgMAS-2006, May 2006.\n[6] D. Poole. Explanation and prediction: An architecture\nfor default and abductive reasoning. Computational\nIntelligence, 5(2):97-110, 1989.\n[7] I. Rahwan, S. D. Ramchurn, N. R. Jennings,\nP. McBurney, S. Parsons, and L. Sonenberg.\nArgumention-based negotiation. The Knowledge\nEngineering Review, 4(18):345-375, 2003.\n[8] N. Roos, A. ten Tije, and C. Witteveen. A protocol\nfor multi-agent diagnosis with spatially distributed\nknowledge. In Proceedings of AAMAS03, 2003.\n[9] N. Roos, A. ten Tije, and C. Witteveen. Reaching\ndiagnostic agreement in multiagent diagnosis. In\nProceedings of AAMAS04, 2004.\n[10] T. Takahashi, Y. Kaneda, and N. Ito. Preliminary\nstudy - using robocuprescue simulations for disasters\nprevention. In Proceedings of SRMED2004, 2004.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1005", "keywords": "global consistency;hypothesis exchange protocol;inter-agent communication;favoured hypothesis;bounded perception;context request step;negotiation and argumentation;bilateral exchange;temporal path;sequence of time point;agent communication language and protocol;time point sequence;topological constraint;mutual consistency;multiagent system;consistency;observation set"}
{"name": "train_I-76", "title": "Negotiation by Abduction and Relaxation", "abstract": "This paper studies a logical framework for automated negotiation between two agents. We suppose an agent who has a knowledge base represented by a logic program. Then, we introduce methods of constructing counter-proposals in response to proposals made by an agent. To this end, we combine the techniques of extended abduction in artificial intelligence and relaxation in cooperative query answering for databases. These techniques are respectively used for producing conditional proposals and neighborhood proposals in the process of negotiation. We provide a negotiation protocol based on the exchange of these proposals and develop procedures for computing new proposals.", "fulltext": "1. INTRODUCTION\nAutomated negotiation has been received increasing\nattention in multi-agent systems, and a number of frameworks\nhave been proposed in different contexts ([1, 2, 3, 5, 10, 11,\n13, 14], for instance). Negotiation usually proceeds in a\nseries of rounds and each agent makes a proposal at every\nround. An agent that received a proposal responds in two\nways. One is a critique which is a remark as to whether\nor not (parts of) the proposal is accepted. The other is a\ncounter-proposal which is an alternative proposal made in\nresponse to a previous proposal [13].\nTo see these proposals in one-to-one negotiation, suppose\nthe following negotiation dialogue between a buyer agent B\nand a seller agent S. (Bi (or Si) represents an utterance of\nB (or S) in the i-th round.)\nB1: I want to buy a personal computer of the brand b1,\nwith the specification of CPU:1GHz, Memory:512MB,\nHDD: 80GB, and a DVD-RW driver. I want to get it\nat the price under 1200 USD.\nS1: We can provide a PC with the requested specification\nif you pay for it by cash. In this case, however, service\npoints are not added for this special discount.\nB2: I cannot pay it by cash.\nS2: In a normal price, the requested PC costs 1300 USD.\nB3: I cannot accept the price. My budget is under 1200\nUSD.\nS3: We can provide another computer with the requested\nspecification, except that it is made by the brand b2.\nThe price is exactly 1200 USD.\nB4: I do not want a PC of the brand b2. Instead, I can\ndowngrade a driver from DVD-RW to CD-RW in my\ninitial proposal.\nS4: Ok, I accept your offer.\nIn this dialogue, in response to the opening proposal B1,\nthe counter-proposal S1 is returned. In the rest of the\ndialogue, B2, B3, S4 are critiques, while S2, S3, B4 are\ncounterproposals.\nCritiques are produced by evaluating a proposal in a\nknowledge base of an agent. In contrast, making counter-proposals\ninvolves generating an alternative proposal which is more\nfavorable to the responding agent than the original one.\nIt is known that there are two ways of producing\ncounterproposals: extending the initial proposal or amending part\nof the initial proposal. According to [13], the first type\nappears in the dialogue: A: I propose that you provide me\nwith service X. B: I propose that I provide you with\nservice X if you provide me with service Z. The second type\nis in the dialogue: A: I propose that I provide you with\nservice Y if you provide me with service X. B: I propose\nthat I provide you with service X if you provide me with\nservice Z. A negotiation proceeds by iterating such\ngive-andtake dialogues until it reaches an agreement/disagreement.\nIn those dialogues, agents generate (counter-)proposals by\nreasoning on their own goals or objectives. The objective\nof the agent A in the above dialogues is to obtain service\nX. The agent B proposes conditions to provide the\nservice. In the process of negotiation, however, it may happen\nthat agents are obliged to weaken or change their initial\ngoals to reach a negotiated compromise. In the dialogue of\n1022\n978-81-904262-7-5 (RPS) c 2007 IFAAMAS\na buyer agent and a seller agent presented above, a buyer\nagent changes its initial goal by downgrading a driver from\nDVD-RW to CD-RW. Such behavior is usually represented\nas specific meta-knowledge of an agent or specified as\nnegotiation protocols in particular problems. Currently, there is\nno computational logic for automated negotiation which has\ngeneral inference rules for producing (counter-)proposals.\nThe purpose of this paper is to mechanize a process of\nbuilding (counter-)proposals in one-to-one negotiation\ndialogues. We suppose an agent who has a knowledge base\nrepresented by a logic program. We then introduce\nmethods for generating three different types of proposals. First,\nwe use the technique of extended abduction in artificial\nintelligence [8, 15] to construct a conditional proposal as an\nextension of the original one. Second, we use the technique\nof relaxation in cooperative query answering for databases\n[4, 6] to construct a neighborhood proposal as an amendment\nof the original one. Third, combining extended abduction\nand relaxation, conditional neighborhood proposals are\nconstructed as amended extensions of the original proposal. We\ndevelop a negotiation protocol between two agents based on\nthe exchange of these counter-proposals and critiques. We\nalso provide procedures for computing proposals in logic\nprogramming.\nThis paper is organized as follows. Section 2 introduces\na logical framework used in this paper. Section 3 presents\nmethods for constructing proposals, and provides a\nnegotiation protocol. Section 4 provides methods for computing\nproposals in logic programming. Section 5 discusses related\nworks, and Section 6 concludes the paper.\n2. PRELIMINARIES\nLogic programs considered in this paper are extended\ndisjunctive programs (EDP) [7]. An EDP (or simply a program)\nis a set of rules of the form:\nL1 ; \u00b7 \u00b7 \u00b7 ; Ll \u2190 Ll+1 , . . . , Lm, not Lm+1 , . . . , not Ln\n(n \u2265 m \u2265 l \u2265 0) where each Li is a positive/negative\nliteral, i.e., A or \u00acA for an atom A, and not is negation as\nfailure (NAF). not L is called an NAF-literal. The symbol\n; represents disjunction. The left-hand side of the rule\nis the head, and the right-hand side is the body. For each\nrule r of the above form, head(r), body+\n(r) and body\u2212\n(r)\ndenote the sets of literals {L1, . . . , Ll}, {Ll+1, . . . , Lm}, and\n{Lm+1, . . . , Ln}, respectively. Also, not body\u2212\n(r) denotes\nthe set of NAF-literals {not Lm+1, . . . , not Ln}. A\ndisjunction of literals and a conjunction of (NAF-)literals in a rule\nare identified with its corresponding sets of literals. A rule\nr is often written as head(r) \u2190 body+\n(r), not body\u2212\n(r) or\nhead(r) \u2190 body(r) where body(r) = body+\n(r)\u222anot body\u2212\n(r).\nA rule r is disjunctive if head(r) contains more than one\nliteral. A rule r is an integrity constraint if head(r) = \u2205; and\nr is a fact if body(r) = \u2205. A program is NAF-free if no\nrule contains NAF-literals. Two rules/literals are identified\nwith respect to variable renaming. A substitution is a\nmapping from variables to terms \u03b8 = {x1/t1, . . . , xn/tn}, where\nx1, . . . , xn are distinct variables and each ti is a term\ndistinct from xi. Given a conjunction G of (NAF-)literals, G\u03b8\ndenotes the conjunction obtained by applying \u03b8 to G. A\nprogram, rule, or literal is ground if it contains no variable.\nA program P with variables is a shorthand of its ground\ninstantiation Ground(P), the set of ground rules obtained\nfrom P by substituting variables in P by elements of its\nHerbrand universe in every possible way.\nThe semantics of an EDP is defined by the answer set\nsemantics [7]. Let Lit be the set of all ground literals in\nthe language of a program. Suppose a program P and a\nset of literals S(\u2286 Lit). Then, the reduct P S\nis the\nprogram which contains the ground rule head(r) \u2190 body+\n(r)\niff there is a rule r in Ground(P) such that body\u2212\n(r)\u2229S = \u2205.\nGiven an NAF-free EDP P, Cn(P) denotes the smallest set\nof ground literals which is (i) closed under P, i.e., for\nevery ground rule r in Ground(P), body(r) \u2286 Cn(P) implies\nhead(r) \u2229 Cn(P) = \u2205; and (ii) logically closed, i.e., it is\neither consistent or equal to Lit. Given an EDP P and a set\nS of literals, S is an answer set of P if S = Cn(P S\n). A\nprogram has none, one, or multiple answer sets in general.\nAn answer set is consistent if it is not Lit. A program P is\nconsistent if it has a consistent answer set; otherwise, P is\ninconsistent.\nAbductive logic programming [9] introduces a mechanism\nof hypothetical reasoning to logic programming. An\nabductive framework used in this paper is the extended\nabduction introduced by Inoue and Sakama [8, 15]. An abductive\nprogram is a pair P, H where P is an EDP and H is\na set of literals called abducibles. When a literal L \u2208 H\ncontains variables, any instance of L is also an abducible.\nAn abductive program P, H is consistent if P is\nconsistent. Throughout the paper, abductive programs are\nassumed to be consistent unless stated otherwise. Let G =\nL1, . . . , Lm, not Lm+1, . . . , not Ln be a conjunction, where\nall variables in G are existentially quantified at the front and\nrange-restricted, i.e., every variable in Lm+1, . . . , Ln appears\nin L1, . . . , Lm. A set S of ground literals satisfies the\nconjunction G if { L1\u03b8, . . . , Lm\u03b8 } \u2286 S and { Lm+1\u03b8, . . . , Ln\u03b8 }\u2229\nS = \u2205 for some ground instance G\u03b8 with a substitution \u03b8.\nLet P, H be an abductive program and G a conjunction\nas above. A pair (E, F) is an explanation of an observation\nG in P, H if1\n1. (P \\ F) \u222a E has an answer set which satisfies G,\n2. (P \\ F) \u222a E is consistent,\n3. E and F are sets of ground literals such that E \u2286 H\\P\nand F \u2286 H \u2229 P.\nWhen (P \\ F) \u222a E has an answer set S satisfying the above\nthree conditions, S is called a belief set of an abductive\nprogram P, H satisfying G (with respect to (E, F)). Note\nthat if P has a consistent answer set S satisfying G, S\nis also a belief set of P, H satisfying G with respect to\n(E, F) = (\u2205, \u2205). Extended abduction introduces/removes\nhypotheses to/from a program to explain an observation.\nNote that normal abduction (as in [9]) considers only\nintroducing hypotheses to explain an observation. An\nexplanation (E, F) of an observation G is called minimal if for\nany explanation (E , F ) of G, E \u2286 E and F \u2286 F imply\nE = E and F = F.\nExample 2.1. Consider the abductive program P, H :\nP : flies(x) \u2190 bird(x), not ab(x) ,\nab(x) \u2190 broken-wing(x) ,\nbird(tweety) \u2190 , bird(opus) \u2190 ,\nbroken-wing(tweety) \u2190 .\nH : broken-wing(x) .\nThe observation G = flies(tweety) has the minimal\nexplanation (E, F) = (\u2205, {broken-wing(tweety)}).\n1\nThis defines credulous explanations [15]. Skeptical\nexplanations are used in [8].\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1023\n3. NEGOTIATION\n3.1 Conditional Proposals by Abduction\nWe suppose an agent who has a knowledge base\nrepresented by an abductive program P, H . A program P\nconsists of two types of knowledge, belief B and desire D,\nwhere B represents objective knowledge of an agent, while\nD represents subjective knowledge in general. We define\nP = B \u222a D, but do not distinguish B and D if such\ndistinction is not important in the context. In contrast, abducibles\nH are used for representing permissible conditions to make\na compromise in the process of negotiation.\nDefinition 3.1. A proposal G is a conjunction of literals\nand NAF-literals:\nL1, . . . , Lm, not Lm+1, . . . , not Ln\nwhere every variable in G is existentially quantified at the\nfront and range-restricted. In particular, G is called a\ncritique if G = accept or G = reject where accept and reject\nare the reserved propositions. A counter-proposal is a\nproposal made in response to a proposal.\nDefinition 3.2. A proposal G is accepted in an\nabductive program P, H if P has an answer set satisfying G.\nWhen a proposal is not accepted, abduction is used for\nseeking conditions to make it acceptable.\nDefinition 3.3. Let P, H be an abductive program\nand G a proposal. If (E, F) is a minimal explanation of\nG\u03b8 for some substitution \u03b8 in P, H , the conjunction G :\nG\u03b8, E, not F\nis called a conditional proposal (for G), where E, not F\nrepresents the conjunction: A1, . . . , Ak, not Ak+1, . . . , not Al\nfor E = {A1, . . . , Ak} and F = { Ak+1, . . . , Al }.\nProposition 3.1. Let P, H be an abductive program\nand G a proposal. If G is a conditional proposal, there is a\nbelief set S of P, H satisfying G .\nProof. When G = G\u03b8, E, not F, (P \\ F) \u222a E has a\nconsistent answer set S satisfying G\u03b8 and E \u2229 F = \u2205. In\nthis case, S satisfies G\u03b8, E, not F.\nA conditional proposal G provides a minimal requirement\nfor accepting the proposal G. If G\u03b8 has multiple minimal\nexplanations, several conditional proposals exist accordingly.\nWhen (E, F) = (\u2205, \u2205), a conditional proposal is used as a\nnew proposal made in response to the proposal G.\nExample 3.1. An agent seeks a position of a research\nassistant at the computer department of a university with\nthe condition that the salary is at least 50,000 USD per year.\nThe agent makes his/her request as the proposal:2\nG = assist(compt dept), salary(x), x \u2265 50, 000.\nThe university has the abductive program P, H :\nP : salary(40, 000) \u2190 assist(compt dept), not has PhD,\nsalary(60, 000) \u2190 assist(compt dept), has PhD,\nsalary(50, 000) \u2190 assist(math dept),\nsalary(55, 000) \u2190 system admin(compt dept),\n2\nFor notational convenience, we often include mathematical\n(in)equations in proposals/programs. They are written by\nliterals, for instance, x \u2265 y by geq(x, y) with a suitable\ndefinition of the predicate geq.\nemployee(x) \u2190 assist(x),\nemployee(x) \u2190 system admin(x),\nassist(compt dept); assist(math dept)\n; system admin(compt dept) \u2190,\nH : has PhD,\nwhere available positions are represented by disjunction.\nAccording to P, the base salary of a research assistant at the\ncomputer department is 40,000 USD, but if he/she has PhD,\nit is 60,000 USD. In this case, (E, F) = ({has PhD}, \u2205)\nbecomes the minimal explanation of G\u03b8 = assist(compt dept),\nsalary(60, 000) with \u03b8 = { x/60, 000 }. Then, the\nconditional proposal made by the university becomes\nassist(compt dept), salary(60, 000), has PhD .\n3.2 Neighborhood Proposals by Relaxation\nWhen a proposal is unacceptable, an agent tries to\nconstruct a new counter-proposal by weakening constraints in\nthe initial proposal. We use techniques of relaxation for\nthis purpose. Relaxation is used as a technique of\ncooperative query answering in databases [4, 6]. When an original\nquery fails in a database, relaxation expands the scope of\nthe query by relaxing the constraints in the query. This\nallows the database to return neighborhood answers which\nare related to the original query. We use the technique for\nproducing proposals in the process of negotiation.\nDefinition 3.4. Let P, H be an abductive program\nand G a proposal. Then, G is relaxed to G in the following\nthree ways:\nAnti-instantiation: Construct G such that G \u03b8 = G for\nsome substitution \u03b8.\nDropping conditions: Construct G such that G \u2282 G.\nGoal replacement: If G is a conjunction G1, G2, where\nG1 and G2 are conjunctions, and there is a rule L \u2190\nG1 in P such that G1\u03b8 = G1 for some substitution \u03b8,\nthen build G as L\u03b8, G2. Here, L\u03b8 is called a replaced\nliteral.\nIn each case, every variable in G is existentially quantified\nat the front and range-restricted.\nAnti-instantiation replaces constants (or terms) with fresh\nvariables. Dropping conditions eliminates some conditions\nin a proposal. Goal replacement replaces the condition G1\nin G with a literal L\u03b8 in the presence of a rule L \u2190 G1 in P\nunder the condition G1\u03b8 = G1. All these operations\ngeneralize proposals in different ways. Each G obtained by these\noperations is called a relaxation of G. It is worth noting\nthat these operations are also used in the context of\ninductive generalization [12]. The relaxed proposal can produce\nnew offers which are neighbor to the original proposal.\nDefinition 3.5. Let P, H be an abductive program\nand G a proposal.\n1. Let G be a proposal obtained by anti-instantiation. If\nP has an answer set S which satisfies G \u03b8 for some\nsubstitution \u03b8 and G \u03b8 = G, G \u03b8 is called a neighborhood\nproposal by anti-instantiation.\n2. Let G be a proposal obtained by dropping conditions.\nIf P has an answer set S which satisfies G \u03b8 for some\nsubstitution \u03b8, G \u03b8 is called a neighborhood proposal by\ndropping conditions.\n1024 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\n3. Let G be a proposal obtained by goal replacement.\nFor a replaced literal L \u2208 G and a rule H \u2190 B in\nP such that L = H\u03c3 and (G \\ {L}) \u222a B\u03c3 = G for\nsome substitution \u03c3, put G = (G \\ {L}) \u222a B\u03c3. If\nP has an answer set S which satisfies G \u03b8 for some\nsubstitution \u03b8, G \u03b8 is called a neighborhood proposal\nby goal replacement.\nExample 3.2. (cont. Example 3.1) Given the proposal\nG = assist(compt dept), salary(x), x \u2265 50, 000,\n\u2022 G1 = assist(w), salary(x), x \u2265 50, 000 is produced by\nsubstituting compt dept with a variable w. As\nG1\u03b81 = assist(math dept), salary(50, 000)\nwith \u03b81 = { w/math dept } is satisfied by an answer\nset of P, G1\u03b81 becomes a neighborhood proposal by\nanti-instantiation.\n\u2022 G2 = assist(compt dept), salary(x) is produced by\ndropping the salary condition x \u2265 50, 000. As\nG2\u03b82 = assist(compt dept), salary(40, 000)\nwith \u03b82 = { x/40, 000 } is satisfied by an answer set of\nP, G2\u03b82 becomes a neighborhood proposal by\ndropping conditions.\n\u2022 G3 = employee(compt dept), salary(x), x \u2265 50, 000 is\nproduced by replacing assist(compt dept) with\nemployee(compt dept) using the rule employee(x) \u2190\nassist(x) in P. By G3 and the rule employee(x) \u2190\nsystem admin(x) in P, G3 = sys admin(compt dept),\nsalary(x), x \u2265 50, 000 is produced. As\nG3 \u03b83 = sys admin(compt dept), salary(55, 000)\nwith \u03b83 = { x/55, 000 } is satisfied by an answer set\nof P, G3 \u03b83 becomes a neighborhood proposal by goal\nreplacement.\nFinally, extended abduction and relaxation are combined to\nproduce conditional neighborhood proposals.\nDefinition 3.6. Let P, H be an abductive program\nand G a proposal.\n1. Let G be a proposal obtained by either anti-instantiation\nor dropping conditions. If (E, F) is a minimal\nexplanation of G \u03b8(= G) for some substitution \u03b8, the\nconjunction G \u03b8, E, not F is called a conditional neighborhood\nproposal by anti-instantiation/dropping conditions.\n2. Let G be a proposal obtained by goal replacement.\nSuppose G as in Definition 3.5(3). If (E, F) is a\nminimal explanation of G \u03b8 for some substitution \u03b8,\nthe conjunction G \u03b8, E, not F is called a conditional\nneighborhood proposal by goal replacement.\nA conditional neighborhood proposal reduces to a\nneighborhood proposal when (E, F) = (\u2205, \u2205).\n3.3 Negotiation Protocol\nA negotiation protocol defines how to exchange proposals\nin the process of negotiation. This section presents a\nnegotiation protocol in our framework. We suppose one-to-one\nnegotiation between two agents who have a common\nontology and the same language for successful communication.\nDefinition 3.7. A proposal L1, ..., Lm, not Lm+1, ..., not Ln\nviolates an integrity constraint \u2190 body+\n(r), not body\u2212\n(r) if\nfor any substitution \u03b8, there is a substitution \u03c3 such that\nbody+\n(r)\u03c3 \u2286 { L1\u03b8, . . . , Lm\u03b8 }, body\u2212\n(r)\u03c3\u2229{ L1\u03b8, . . . , Lm\u03b8 } =\n\u2205, and body\u2212\n(r)\u03c3 \u2286 { Lm+1\u03b8, . . . , Ln\u03b8 }.\nIntegrity constraints are conditions which an agent should\nsatisfy, so that they are used to explain why an agent does\nnot accept a proposal.\nA negotiation proceeds in a series of rounds. Each i-th\nround (i \u2265 1) consists of a proposal Gi\n1 made by one agent\nAg1 and another proposal Gi\n2 made by the other agent Ag2.\nDefinition 3.8. Let P1, H1 be an abductive program\nof an agent Ag1 and Gi\n2 a proposal made by Ag2 at the i-th\nround. A critique set of Ag1 (at the i-th round) is a set\nCSi\n1(P1, Gj\n2) = CSi\u22121\n1 (P1, Gj\u22121\n2 ) \u222a { r | r is an integrity\nconstraint in P1 and Gj\n2 violates r }\nwhere j = i \u2212 1 or i, and CS0\n1 (P1, G0\n2) = CS1\n1 (P1, G0\n2) = \u2205.\nA critique set of an agent Ag1 accumulates integrity\nconstraints which are violated by proposals made by another\nagent Ag2. CSi\n2(P2, Gj\n1) is defined in the same manner.\nDefinition 3.9. Let Pk, Hk be an abductive program\nof an agent Agk and Gj\na proposal, which is not a critique,\nmade by any agent at the j(\u2264 i)-th round. A negotiation set\nof Agk (at the i-th round) is a triple NSi\nk = (Si\nc, Si\nn, Si\ncn),\nwhere Si\nc is the set of conditional proposals, Si\nn is the set\nof neighborhood proposals, and Si\ncn is the set of conditional\nneighborhood proposals, produced by Gj\nand Pk, Hk .\nA negotiation set represents the space of possible proposals\nmade by an agent. Si\nx (x \u2208 {c, n, cn}) accumulates proposals\nproduced by Gj\n(1 \u2264 j \u2264 i) according to Definitions 3.3, 3.5,\nand 3.6. Note that an agent can construct counter-proposals\nby modifying its own previous proposals or another agent\"s\nproposals. An agent Agk accumulates proposals that are\nmade by Agk but are rejected by another agent, in the failed\nproposal set FP i\nk (at the i-th round), where FP 0\nk = \u2205.\nSuppose two agents Ag1 and Ag2 who have abductive\nprograms P1, H1 and P2, H2 , respectively. Given a\nproposal G1\n1 which is satisfied by an answer set of P1, a\nnegotiation starts. In response to the proposal Gi\n1 made by Ag1\nat the i-th round, Ag2 behaves as follows.\n1. If Gi\n1 = accept, an agreement is reached and\nnegotiation ends in success.\n2. Else if Gi\n1 = reject, put FP i\n2 = FPi\u22121\n2 \u222a{Gi\u22121\n2 } where\n{G0\n2} = \u2205. Proceed to the step 4(b).\n3. Else if P2 has an answer set satisfying Gi\n1, Ag2 returns\nGi\n2 = accept to Ag1. Negotiation ends in success.\n4. Otherwise, Ag2 behaves as follows. Put FP i\n2 = FPi\u22121\n2 .\n(a) If Gi\n1 violates an integrity constraint in P2, return\nthe critique Gi\n2 = reject to Ag1, together with the\ncritique set CSi\n2(P2, Gi\n1).\n(b) Otherwise, construct NSi\n2 as follows.\n(i) Produce Si\nc. Let \u03bc(Si\nc) = { p | p \u2208 Si\nc \\ FPi\n2 and\np satisfies the constraints in CSi\n1(P1, Gi\u22121\n2 )}.\nIf \u03bc(Si\nc) = \u2205, select one from \u03bc(Si\nc) and propose\nit as Gi\n2 to Ag1; otherwise, go to (ii).\n(ii) Produce Si\nn. If \u03bc(Si\nn) = \u2205, select one from \u03bc(Si\nn)\nand propose it as Gi\n2 to Ag1; otherwise, go to (iii).\n(iii) Produce Si\ncn. If \u03bc(Si\ncn) = \u2205, select one from\n\u03bc(Si\ncn) and propose it as Gi\n2 to Ag1; otherwise,\nnegotiation ends in failure. This means that Ag2\ncan make no counter-proposal or every\ncounterproposal made by Ag2 is rejected by Ag1.\nIn the step 4(a), Ag2 rejects the proposal Gi\n1 and returns\nthe reason of rejection as a critique set. This helps for Ag1\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1025\nin preparing a next counter-proposal. In the step 4(b), Ag2\nconstructs a new proposal. In its construction, Ag2 should\ntake care of the critique set CSi\n1(P1, Gi\u22121\n2 ), which\nrepresents integrity constraints, if any, accumulated in previous\nrounds, that Ag1 must satisfy. Also, FP i\n2 is used for\nremoving proposals which have been rejected. Construction of\nSi\nx (x \u2208 {c, n, cn}) in NSi\n2 is incrementally done by adding\nnew counter-proposals produced by Gi\n1 or Gi\u22121\n2 to Si\u22121\nx . For\ninstance, Si\nn in NSi\n2 is computed as\nSi\nn = Si\u22121\nn \u222a{ p | p is a neighborhood proposal made by Gi\n1 }\n\u222a { p | p is a neighborhood proposal made by Gi\u22121\n2 },\nwhere S0\nn = \u2205. That is, Si\nn is constructed from Si\u22121\nn by\nadding new proposals which are obtained by modifying the\nproposal Gi\n1 made by Ag1 at the i-th round or modifying\nthe proposal Gi\u22121\n2 made by Ag2 at the (i \u2212 1)-th round. Si\nc\nand Si\ncn are obtained as well.\nIn the above protocol, an agent produces Si\nc at first,\nsecondly Si\nn, and finally Si\ncn. This strategy seeks conditions\nwhich satisfy the given proposal, prior to neighborhood\nproposals which change the original one. Another strategy,\nwhich prefers neighborhood proposals to conditional ones,\nis also considered. Conditional neighborhood proposals are\nto be considered in the last place, since they differ from the\noriginal one to the maximal extent. The above protocol\nproduces the candidate proposals in Si\nx for each x \u2208 {c, n, cn}\nat once. We can consider a variant of the protocol in which\neach proposal in Si\nx is constructed one by one (see\nExample 3.3).\nThe above protocol is repeatedly applied to each one of\nthe two negotiating agents until a negotiation ends in\nsuccess/failure. Formally, the above negotiation protocol has\nthe following properties.\nTheorem 3.2. Let Ag1 and Ag2 be two agents having\nabductive programs P1, H1 and P2, H2 , respectively.\n1. If P1, H1 and P2, H2 are function-free (i.e., both\nPi and Hi contain no function symbol), any\nnegotiation will terminate.\n2. If a negotiation terminates with agreement on a\nproposal G, both P1, H1 and P2, H2 have belief sets\nsatisfying G.\nProof. 1. When an abductive program is function-free,\nabducibles and negotiation sets are both finite. Moreover, if\na proposal is once rejected, it is not proposed again by the\nfunction \u03bc. Thus, negotiation will terminate in finite steps.\n2. When a proposal G is made by Ag1, P1, H1 has a\nbelief set satisfying G. If the agent Ag2 accepts the proposal\nG, it is satisfied by an answer set of P2 which is also a belief\nset of P2, H2 .\nExample 3.3. Suppose a buying-selling situation in the\nintroduction. A seller agent has the abductive program\nPs, Hs in which Ps consists of belief Bs and desire Ds:\nBs : pc(b1, 1G, 512M, 80G) ; pc(b2, 1G, 512M, 80G) \u2190,(1)\ndvd-rw ; cd-rw \u2190, (2)\nDs : normal price(1300) \u2190\npc(b1, 1G, 512M, 80G), dvd-rw, (3)\nnormal price(1200) \u2190\npc(b1, 1G, 512M, 80G), cd-rw, (4)\nnormal price(1200) \u2190\npc(b2, 1G, 512M, 80G), dvd-rw, (5)\nprice(x) \u2190 normal price(x), add point, (6)\nprice(x \u2217 0.9) \u2190\nnormal price(x), pay cash, not add point,(7)\nadd point \u2190, (8)\nHs : add point, pay cash.\nHere, (1) and (2) represent selection of products. The atom\npc(b1, 1G, 512M, 80G) represents that the seller agent has\na PC of the brand b1 such that CPU is 1GHz, memory is\n512MB, and HDD is 80GB. Prices of products are\nrepresented as desire of the seller. The rules (3) - (5) are normal\nprices of products. A normal price is a selling price on the\ncondition that service points are added (6). On the other\nhand, a discount price is applied if the paying method is cash\nand no service point is added (7). The fact (8) represents\nthe addition of service points. This service would be\nwithdrawn in case of discount prices, so add point is specified as\nan abducible.\nA buyer agent has the abductive program Pb, Hb in\nwhich Pb consists of belief Bb and desire Db:\nBb : drive \u2190 dvd-rw, (9)\ndrive \u2190 cd-rw, (10)\nprice(x) \u2190, (11)\nDb : pc(b1, 1G, 512M, 80G) \u2190, (12)\ndvd-rw \u2190, (13)\ncd-rw \u2190 not dvd-rw, (14)\n\u2190 pay cash, (15)\n\u2190 price(x), x > 1200, (16)\nHb : dvd-rw.\nRules (12) - (16) are the buyer\"s desire. Among them, (15)\nand (16) impose constraints for buying a PC. A DVD-RW\nis specified as an abducible which is subject to concession.\n(1st round) First, the following proposal is given by the\nbuyer agent:\nG1\nb : pc(b1, 1G, 512M, 80G), dvd-rw, price(x), x \u2264 1200.\nAs Ps has no answer set which satisfies G1\nb , the seller agent\ncannot accept the proposal. The seller takes an action of\nmaking a counter-proposal and performs abduction. As a\nresult, the seller finds the minimal explanation (E, F) =\n({ pay cash }, { add point }) which explains G1\nb \u03b81 with \u03b81 =\n{ x/1170 }. The seller constructs the conditional proposal:\nG1\ns : pc(b1, 1G, 512M, 80G), dvd-rw, price(1170),\npay cash, not add point\nand offers it to the buyer.\n(2nd round) The buyer does not accept G1\ns because he/she\ncannot pay it by cash (15). The buyer then returns the\ncritique G2\nb = reject to the seller, together with the critique set\nCS2\nb (Pb, G1\ns) = {(15)}. In response to this, the seller tries\nto make another proposal which satisfies the constraint in\nthis critique set. As G1\ns is stored in FP 2\ns and no other\nconditional proposal satisfying the buyer\"s requirement exists,\nthe seller produces neighborhood proposals. He/she relaxes\nG1\nb by dropping x \u2264 1200 in the condition, and produces\npc(b1, 1G, 512M, 80G), dvd-rw, price(x).\nAs Ps has an answer set which satisfies\nG2\ns : pc(b1, 1G, 512M, 80G), dvd-rw, price(1300),\n1026 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nthe seller offers G2\ns as a new counter-proposal.\n(3rd round) The buyer does not accept G2\ns because he/she\ncannot pay more than 1200USD (16). The buyer again\nreturns the critique G3\nb = reject to the seller, together with\nthe critique set CS3\nb (Pb, G2\ns) = CS2\nb (Pb, G1\ns) \u222a {(16)}. The\nseller then considers another proposal by replacing b1 with\na variable w, G1\nb now becomes\npc(w, 1G, 512M, 80G), dvd-rw, price(x), x \u2264 1200.\nAs Ps has an answer set which satisfies\nG3\ns : pc(b2, 1G, 512M, 80G), dvd-rw, price(1200),\nthe seller offers G3\ns as a new counter-proposal.\n(4th round) The buyer does not accept G3\ns because a PC of\nthe brand b2 is out of his/her interest and Pb has no answer\nset satisfying G3\ns. Then, the buyer makes a concession by\nchanging his/her original goal. The buyer relaxes G1\nb by goal\nreplacement using the rule (9) in Pb, and produces\npc(b1, 1G, 512M, 80G), drive, price(x), x \u2264 1200.\nUsing (10), the following proposal is produced:\npc(b1, 1G, 512M, 80G), cd-rw, price(x), x \u2264 1200.\nAs Pb \\ { dvd-rw } has a consistent answer set satisfying the\nabove proposal, the buyer proposes the conditional\nneighborhood proposal\nG4\nb : pc(b1, 1G, 512M, 80G), cd-rw, not dvd-rw,\nprice(x), x \u2264 1200\nto the seller agent. Since Ps also has an answer set satisfying\nG4\nb , the seller accepts it and sends the message G4\ns = accept\nto the buyer. Thus, the negotiation ends in success.\n4. COMPUTATION\nIn this section, we provide methods of computing\nproposals in terms of answer sets of programs. We first introduce\nsome definitions from [15].\nDefinition 4.1. Given an abductive program P, H , the\nset UR of update rules is defined as:\nUR = { L \u2190 not L, L \u2190 not L | L \u2208 H }\n\u222a { +L \u2190 L | L \u2208 H \\ P }\n\u222a { \u2212L \u2190 not L | L \u2208 H \u2229 P } ,\nwhere L, +L, and \u2212L are new atoms uniquely associated\nwith every L \u2208 H. The atoms +L and \u2212L are called update\natoms.\nBy the definition, the atom L becomes true iff L is not\ntrue. The pair of rules L \u2190 not L and L \u2190 not L specify\nthe situation that an abducible L is true or not. When\np(x) \u2208 H and p(a) \u2208 P but p(t) \u2208 P for t = a, the rule\n+L \u2190 L precisely becomes +p(t) \u2190 p(t) for any t = a. In\nthis case, the rule is shortly written as +p(x) \u2190 p(x), x = a.\nGenerally, the rule becomes +p(x) \u2190 p(x), x = t1, . . . , x =\ntn for n such instances. The rule +L \u2190 L derives the atom\n+L if an abducible L which is not in P is to be true. In\ncontrast, the rule \u2212L \u2190 not L derives the atom \u2212L if an\nabducible L which is in P is not to be true. Thus, update\natoms represent the change of truth values of abducibles in\na program. That is, +L means the introduction of L, while\n\u2212L means the deletion of L. When an abducible L contains\nvariables, the associated update atom +L or \u2212L is supposed\nto have exactly the same variables. In this case, an update\natom is semantically identified with its ground instances.\nThe set of all update atoms associated with the abducibles\nin H is denoted by UH, and UH = UH+\n\u222a UH\u2212\nwhere\nUH+\n(resp. UH\u2212\n) is the set of update atoms of the form\n+L (resp. \u2212L).\nDefinition 4.2. Given an abductive program P, H , its\nupdate program UP is defined as the program\nUP = (P \\ H) \u222a UR .\nAn answer set S of UP is called U-minimal if there is no\nanswer set T of UP such that T \u2229 UH \u2282 S \u2229 UH.\nBy the definition, U-minimal answer sets exist whenever\nUP has answer sets. Update programs are used for\ncomputing (minimal) explanations of an observation. Given an\nobservation G as a conjunction of literals and NAF-literals\npossibly containing variables, we introduce a new ground\nliteral O together with the rule O \u2190 G. In this case, O\nhas an explanation (E, F) iff G has the same explanation.\nWith this replacement, an observation is assumed to be a\nground literal without loss of generality. In what follows,\nE+\n= { +L | L \u2208 E } and F \u2212\n= { \u2212L | L \u2208 F } for E \u2286 H\nand F \u2286 H.\nProposition 4.1. ([15]) Let P, H be an abductive\nprogram, UP its update program, and G a ground literal\nrepresenting an observation. Then, a pair (E, F) is an\nexplanation of G iff UP \u222a { \u2190 not G } has a consistent answer set\nS such that E+\n= S \u2229 UH+\nand F\u2212\n= S \u2229 UH\u2212\n. In\nparticular, (E, F) is a minimal explanation iff S is a U-minimal\nanswer set.\nExample 4.1. To explain the observation G = flies(t)\nin the program P of Example 2.1, first construct the update\nprogram UP of P:3\nUP : flies(x) \u2190 bird(x), not ab(x),\nab(x) \u2190 broken-wing(x) ,\nbird(t) \u2190 , bird(o) \u2190 ,\nbroken-wing(x) \u2190 not broken-wing(x),\nbroken-wing(x) \u2190 not broken-wing(x),\n+broken-wing(x) \u2190 broken-wing(x), x = t ,\n\u2212broken-wing(t) \u2190 not broken-wing(t) .\nNext, consider the program UP \u222a { \u2190 not flies(t) }. It has\nthe single U-minimal answer set: S = { bird(t), bird(o), flies(t),\nflies(o), broken-wing(t), broken-wing(o), \u2212broken-wing(t) }.\nThe unique minimal explanation (E, F) = (\u2205, {broken-wing(t)})\nof G is expressed by the update atom \u2212broken-wing(t) in\nS \u2229 UH\u2212\n.\nProposition 4.2. Let P, H be an abductive program\nand G a ground literal representing an observation. If P \u222a\n{ \u2190 not G } has a consistent answer set S, G has the\nminimal explanation (E, F) = (\u2205, \u2205) and S satisfies G.\nNow we provide methods for computing (counter-)proposals.\nFirst, conditional proposals are computed as follows.\ninput : an abductive program P, H , a proposal G;\noutput : a set Sc of proposals.\nIf G is a ground literal, compute its minimal\nexplanation (E, F) in P, H using the update program. Put\nG, E, not F in Sc. Else if G is a conjunction possibly\ncontaining variables, consider the abductive program\n3\nt represents tweety and o represents opus.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1027\nP \u222a{ O \u2190 G }, H with a ground literal O. Compute\na minimal explanation of O in P \u222a { O \u2190 G }, H\nusing its update program. If O has a minimal\nexplanation (E, F) with a substitution \u03b8 for variables in G,\nput G\u03b8, E, not F in Sc.\nNext, neighborhood proposals are computed as follows.\ninput : an abductive program P, H , a proposal G;\noutput : a set Sn of proposals.\n% neighborhood proposals by anti-instantiation;\nConstruct G by anti-instantiation. For a ground\nliteral O, if P \u222a { O \u2190 G } \u222a { \u2190 not O } has a\nconsistent answer set satisfying G \u03b8 with a substitution \u03b8\nand G \u03b8 = G, put G \u03b8 in Sn.\n% neighborhood proposals by dropping conditions;\nConstruct G by dropping conditions. If G is a ground\nliteral and the program P \u222a { \u2190 not G } has a\nconsistent answer set, put G in Sn. Else if G is a\nconjunction possibly containing variables, do the following.\nFor a ground literal O, if P \u222a{ O \u2190 G }\u222a{ \u2190 not O }\nhas a consistent answer set satisfying G \u03b8 with a\nsubstitution \u03b8, put G \u03b8 in Sn.\n% neighborhood proposals by goal replacement;\nConstruct G by goal replacement. If G is a ground\nliteral and there is a rule H \u2190 B in P such that G = H\u03c3\nand B\u03c3 = G for some substitution \u03c3, put G = B\u03c3.\nIf P \u222a { \u2190 not G } has a consistent answer set\nsatisfying G \u03b8 with a substitution \u03b8, put G \u03b8 in Sn. Else\nif G is a conjunction possibly containing variables,\ndo the following. For a replaced literal L \u2208 G , if\nthere is a rule H \u2190 B in P such that L = H\u03c3 and\n(G \\ {L}) \u222a B\u03c3 = G for some substitution \u03c3, put\nG = (G \\ {L}) \u222a B\u03c3. For a ground literal O, if\nP \u222a { O \u2190 G } \u222a { \u2190 not O } has a consistent answer\nset satisfying G \u03b8 with a substitution \u03b8, put G \u03b8 in\nSn.\nTheorem 4.3. The set Sc (resp. Sn) computed above\ncoincides with the set of conditional proposals (resp.\nneighborhood proposals).\nProof. The result for Sc follows from Definition 3.3 and\nProposition 4.1. The result for Sn follows from Definition 3.5\nand Proposition 4.2.\nConditional neighborhood proposals are computed by\ncombining the above two procedures. Those proposals are\ncomputed at each round. Note that the procedure for computing\nSn contains some nondeterministic choices. For instance,\nthere are generally several candidates of literals to relax in\na proposal. Also, there might be several rules in a program\nfor the usage of goal replacement. In practice, an agent can\nprespecify literals in a proposal for possible relaxation or\nrules in a program for the usage of goal replacement.\n5. RELATED WORK\nAs there are a number of literature on automated\nnegotiation, this section focuses on comparison with negotiation\nframeworks based on logic and argumentation.\nSadri et al. [14] use abductive logic programming as a\nrepresentation language of negotiating agents. Agents negotiate\nusing common dialogue primitives, called dialogue moves.\nEach agent has an abductive logic program in which a\nsequence of dialogues are specified by a program, a dialogue\nprotocol is specified as constraints, and dialogue moves are\nspecified as abducibles. The behavior of agents is regulated\nby an observe-think-act cycle. Once a dialogue move is\nuttered by an agent, another agent that observed the utterance\nthinks and acts using a proof procedure. Their approach\nand ours both employ abductive logic programming as a\nplatform of agent reasoning, but the use of it is quite\ndifferent. First, they use abducibles to specify dialogue primitives\nof the form tell(utterer, receiver, subject, identifier, time),\nwhile we use abducibles to specify arbitrary permissible\nhypotheses to construct conditional proposals. Second, a\nprogram pre-specifies a plan to carry out in order to achieve a\ngoal, together with available/missing resources in the\ncontext of resource-exchanging problems. This is in contrast\nwith our method in which possible counter-proposals are\nnewly constructed in response to a proposal made by an\nagent. Third, they specify a negotiation policy inside a\nprogram (as integrity constraints), while we give a protocol\nindependent of individual agents. They provide an\noperational model that completely specifies the behavior of agents\nin terms of agent cycle. We do not provide such a complete\nspecification of the behavior of agents. Our primary interest\nis to mechanize construction of proposals.\nBracciali and Torroni [2] formulate abductive agents that\nhave knowledge in abductive logic programs. To explain\nan observation, two agents communicate by exchanging\nintegrity constraints. In the process of communication, an\nagent can revise its own integrity constraints according to\nthe information provided by the other agent. A set IC\nof integrity constraints relaxes a set IC (or IC tightens\nIC ) if any observation that can be proved with respect to\nIC can also be proved with respect to IC . For instance,\nIC : \u2190 a, b, c relaxes IC : \u2190 a, b. Thus, they use relaxation\nfor weakening the constraints in an abductive logic program.\nIn contrast, we use relaxation for weakening proposals and\nthree different relaxation methods, anti-instantiation,\ndropping conditions, and goal replacement, are considered. Their\ngoal is to explain an observation by revising integrity\nconstraints of an agent through communication, while we use\nintegrity constraints for communication to explain critiques\nand help other agents in making counter-proposals.\nMeyer et al. [11] introduce a logical framework for\nnegotiating agents. They introduce two different modes of\nnegotiation: concession and adaptation. They provide rational\npostulates to characterize negotiated outcomes between two\nagents, and describe methods for constructing outcomes.\nThey provide logical conditions for negotiated outcomes to\nsatisfy, but they do not describe a process of negotiation nor\nnegotiation protocols. Moreover, they represent agents by\nclassical propositional theories, which is different from our\nabductive logic programming framework.\nFoo et al. [5] model one-to-one negotiation as a one-time\nencounter between two extended logic programs. An agent\noffers an answer set of its program, and their mutual deal is\nregarded as a trade on their answer sets. Starting from the\ninitial agreement set S\u2229T for an answer set S of an agent and\nan answer set T of another agent, each agent extends this\nset to reflect its own demand while keeping consistency with\ndemand of the other agent. Their algorithm returns new\nprograms having answer sets which are consistent with each\nother and keep the agreement set. The work is extended to\nrepeated encounters in [3]. In their framework, two agents\nexchange answer sets to produce a common belief set, which\nis different from our framework of exchanging proposals.\nThere are a number of proposals for negotiation based\n1028 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\non argumentation. An advantage of argumentation-based\nnegotiation is that it constructs a proposal with arguments\nsupporting the proposal [1]. The existence of arguments is\nuseful to convince other agents of reasons why an agent offers\n(counter-)proposals or returns critiques. Parsons et al. [13]\ndevelop a logic of argumentation-based negotiation among\nBDI agents. In one-to-one negotiation, an agent A generates\na proposal together with its arguments, and passes it to\nanother agent B. The proposal is evaluated by B which\nattempts to build arguments against it. If it conflicts with\nB\"s interest, B informs A of its objection by sending back\nits attacking argument. In response to this, A tries to find\nan alternative way of achieving its original objective, or a\nway of persuading B to drop its objection. If either type of\nargument can be found, A will submit it to B. If B finds no\nreason to reject the new proposal, it will be accepted and\nthe negotiation ends in success. Otherwise, the process is\niterated. In this negotiation processes, the agent A never\nchanges its original objective, so that negotiation ends in\nfailure if A fails to find an alternative way of achieving the\noriginal objective. In our framework, when a proposal is\nrejected by another agent, an agent can weaken or change\nits objective by abduction and relaxation. Our framework\ndoes not have a mechanism of argumentation, but reasons\nfor critiques can be informed by responding critique sets.\nKakas and Moraitis [10] propose a negotiation protocol\nwhich integrates abduction within an argumentation\nframework. A proposal contains an offer corresponding to the\nnegotiation object, together with supporting information\nrepresenting conditions under which this offer is made.\nSupporting information is computed by abduction and is used\nfor constructing conditional arguments during the process\nof negotiation. In their negotiation protocol, when an agent\ncannot satisfy its own goal, the agent considers the other\nagent\"s goal and searches for conditions under which the\ngoal is acceptable. Our present approach differs from theirs\nin the following points. First, they use abduction to seek\nconditions to support arguments, while we use abduction\nto seek conditions for proposals to accept. Second, in their\nnegotiation protocol, counter-proposals are chosen among\ncandidates based on preference knowledge of an agent at\nmeta-level, which represents policy under which an agent\nuses its object-level decision rules according to situations.\nIn our framework, counter-proposals are newly constructed\nusing abduction and relaxation. The method of\nconstruction is independent of particular negotiation protocols. As\n[2, 10, 14], abduction or abductive logic programming used\nin negotiation is mostly based on normal abduction. In\ncontrast, our approach is based on extended abduction which\ncan not only introduce hypotheses but remove them from a\nprogram. This is another important difference.\nRelaxation and neighborhood query answering are devised\nto make databases cooperative with their users [4, 6]. In this\nsense, those techniques have the spirit similar to cooperative\nproblem solving in multi-agent systems. As far as the\nauthors know, however, there is no study which applies those\ntechnique to agent negotiation.\n6. CONCLUSION\nIn this paper we proposed a logical framework for\nnegotiating agents. To construct proposals in the process of\nnegotiation, we combined the techniques of extended abduction\nand relaxation. It was shown that these two operations are\nused for general inference rules in producing proposals. We\ndeveloped a negotiation protocol between two agents based\non exchange of proposals and critiques, and provided\nprocedures for computing proposals in abductive logic\nprogramming. This enables us to realize automated negotiation on\ntop of the existing answer set solvers. The present\nframework does not have a mechanism of selecting an optimal\n(counter-)proposal among different alternatives. To\ncompare and evaluate proposals, an agent must have preference\nknowledge of candidate proposals. Further elaboration to\nmaximize the utility of agents is left for future study.\n7. REFERENCES\n[1] L. Amgoud, S. Parsons, and N. Maudet. Arguments,\ndialogue, and negotiation. In: Proc. ECAI-00,\npp. 338-342, IOS Press, 2000.\n[2] A. Bracciali and P. Torroni. A new framework for\nknowledge revision of abductive agents through their\ninteraction. In: Proc. CLIMA-IV, Computational Logic\nin Multi-Agent Systems, LNAI 3259, pp. 159-177, 2004.\n[3] W. Chen, M. Zhang, and N. Foo. Repeated negotiation\nof logic programs. In: Proc. 7th Workshop on\nNonmonotonic Reasoning, Action and Change, 2006.\n[4] W. W. Chu, Q. Chen, and R.-C. Lee. Cooperative\nquery answering via type abstraction hierarchy. In:\nCooperating Knowledge Based Systems, S. M. Deen ed.,\npp. 271-290, Springer, 1990.\n[5] N. Foo, T. Meyer, Y. Zhang, and D. Zhang.\nNegotiating logic programs. In: Proc. 6th Workshop on\nNonmonotonic Reasoning, Action and Change, 2005.\n[6] T. Gaasterland, P. Godfrey, and J. Minker. Relaxation\nas a platform for cooperative answering. Journal of\nIntelligence Information Systems 1(3/4):293-321, 1992.\n[7] M. Gelfond and V. Lifschitz. Classical negation in logic\nprograms and disjunctive databases. New Generation\nComputing 9:365-385, 1991.\n[8] K. Inoue and C. Sakama. Abductive framework for\nnonmonotonic theory change. In: Proc. IJCAI-95,\npp. 204-210, Morgan Kaufmann.\n[9] A. C. Kakas, R. A. Kowalski, and F. Toni, The role of\nabduction in logic programming. In: Handbook of Logic\nin AI and Logic Programming, D. M. Gabbay, et al.\n(eds), vol. 5, pp. 235-324, Oxford University Press, 1998.\n[10] A. C. Kakas and P. Moraitis. Adaptive agent\nnegotiation via argumentation. In: Proc. AAMAS-06,\npp. 384-391, ACM Press.\n[11] T. Meyer, N. Foo, R. Kwok, and D. Zhang. Logical\nfoundation of negotiation: outcome, concession and\nadaptation. In: Proc. AAAI-04, pp. 293-298, MIT Press.\n[12] R. S. Michalski. A theory and methodology of\ninductive learning. In: Machine Learning: An Artificial\nIntelligence Approach, R. S. Michalski, et al. (eds),\npp. 83-134, Morgan Kaufmann, 1983.\n[13] S. Parsons, C. Sierra and N. Jennings. Agents that\nreason and negotiate by arguing. Journal of Logic and\nComputation, 8(3):261-292, 1988.\n[14] F. Sadri, F. Toni, and P. Torroni, An abductive logic\nprogramming architecture for negotiating agents. In:\nProc. 8th European Conf. on Logics in AI, LNAI 2424,\npp. 419-431, Springer, 2002.\n[15] C. Sakama and K. Inoue. An abductive framework for\ncomputing knowledge base updates. Theory and Practice\nof Logic Programming 3(6):671-715, 2003.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1029", "keywords": "relaxation;logic program;anti-instantiation;abductive program;abductive framework;dropping condition;specific meta-knowledge;inductive generalization;one-to-one negotiation;minimal explanation;conditional proposal;integrity constraint;negotiation;extend abduction;automated negotiation;multi-agent system;alternative proposal"}
{"name": "train_I-77", "title": "The LOGIC Negotiation Model", "abstract": "Successful negotiators prepare by determining their position along five dimensions: Legitimacy, Options, Goals, Independence, and Commitment, (LOGIC). We introduce a negotiation model based on these dimensions and on two primitive concepts: intimacy (degree of closeness) and balance (degree of fairness). The intimacy is a pair of matrices that evaluate both an agent\"s contribution to the relationship and its opponent\"s contribution each from an information view and from a utilitarian view across the five LOGIC dimensions. The balance is the difference between these matrices. A relationship strategy maintains a target intimacy for each relationship that an agent would like the relationship to move towards in future. The negotiation strategy maintains a set of Options that are in-line with the current intimacy level, and then tactics wrap the Options in argumentation with the aim of attaining a successful deal and manipulating the successive negotiation balances towards the target intimacy.", "fulltext": "1. INTRODUCTION\nIn this paper we propose a new negotiation model to deal\nwith long term relationships that are founded on successive\nnegotiation encounters. The model is grounded on results\nfrom business and psychological studies [1, 16, 9], and\nacknowledges that negotiation is an information exchange\nprocess as well as a utility exchange process [15, 14]. We\nbelieve that if agents are to succeed in real application domains\nthey have to reconcile both views: informational and\ngametheoretical. Our aim is to model trading scenarios where\nagents represent their human principals, and thus we want\ntheir behaviour to be comprehensible by humans and to\nrespect usual human negotiation procedures, whilst being\nconsistent with, and somehow extending, game theoretical and\ninformation theoretical results. In this sense, agents are not\njust utility maximisers, but aim at building long lasting\nrelationships with progressing levels of intimacy that determine\nwhat balance in information and resource sharing is\nacceptable to them. These two concepts, intimacy and balance are\nkey in the model, and enable us to understand competitive\nand co-operative game theory as two particular theories of\nagent relationships (i.e. at different intimacy levels). These\ntwo theories are too specific and distinct to describe how\na (business) relationship might grow because interactions\nhave some aspects of these two extremes on a continuum in\nwhich, for example, agents reveal increasing amounts of\nprivate information as their intimacy grows. We don\"t follow\nthe \"Co-Opetition\" aproach [4] where co-operation and\ncompetition depend on the issue under negotiation, but instead\nwe belief that the willingness to co-operate/compete affect\nall aspects in the negotiation process. Negotiation strategies\ncan naturally be seen as procedures that select tactics used\nto attain a successful deal and to reach a target intimacy\nlevel. It is common in human settings to use tactics that\ncompensate for unbalances in one dimension of a\nnegotiation with unbalances in another dimension. In this sense,\nhumans aim at a general sense of fairness in an interaction.\nIn Section 2 we outline the aspects of human negotiation\nmodelling that we cover in this work. Then, in Section 3\nwe introduce the negotiation language. Section 4 explains\nin outline the architecture and the concepts of intimacy and\nbalance, and how they influence the negotiation. Section 5\ncontains a description of the different metrics used in the\nagent model including intimacy. Finally, Section 6 outlines\nhow strategies and tactics use the LOGIC framework,\nintimacy and balance.\n2. HUMAN NEGOTIATION\nBefore a negotiation starts human negotiators prepare the\ndialogic exchanges that can be made along the five LOGIC\ndimensions [7]:\n\u2022 Legitimacy. What information is relevant to the\nnegotiation process? What are the persuasive arguments\nabout the fairness of the options?\n1030\n978-81-904262-7-5 (RPS) c 2007 IFAAMAS\n\u2022 Options. What are the possible agreements we can\naccept?\n\u2022 Goals. What are the underlying things we need or care\nabout? What are our goals?\n\u2022 Independence. What will we do if the negotiation fails?\nWhat alternatives have we got?\n\u2022 Commitment. What outstanding commitments do we\nhave?\nNegotiation dialogues, in this context, exchange\ndialogical moves, i.e. messages, with the intention of getting\ninformation about the opponent or giving away information\nabout us along these five dimensions: request for\ninformation, propose options, inform about interests, issue promises,\nappeal to standards . . . A key part of any negotiation process\nis to build a model of our opponent(s) along these\ndimensions. All utterances agents make during a negotiation give\naway information about their current LOGIC model, that\nis, about their legitimacy, options, goals, independence, and\ncommitments. Also, several utterances can have a\nutilitarian interpretation in the sense that an agent can associate\na preferential gain to them. For instance, an offer may\ninform our negotiation opponent about our willingness to sign\na contract in the terms expressed in the offer, and at the\nsame time the opponent can compute what is its associated\nexpected utilitarian gain. These two views:\ninformationbased and utility-based, are central in the model proposed\nin this paper.\n2.1 Intimacy and Balance in relationships\nThere is evidence from psychological studies that humans\nseek a balance in their negotiation relationships. The\nclassical view [1] is that people perceive resource allocations as\nbeing distributively fair (i.e. well balanced) if they are\nproportional to inputs or contributions (i.e. equitable).\nHowever, more recent studies [16, 17] show that humans follow\na richer set of norms of distributive justice depending on\ntheir intimacy level: equity, equality, and need. Equity\nbeing the allocation proportional to the effort (e.g. the profit\nof a company goes to the stock holders proportional to their\ninvestment), equality being the allocation in equal amounts\n(e.g. two friends eat the same amount of a cake cooked by\none of them), and need being the allocation proportional to\nthe need for the resource (e.g. in case of food scarcity, a\nmother gives all food to her baby). For instance, if we are in\na purely economic setting (low intimacy) we might request\nequity for the Options dimension but could accept equality\nin the Goals dimension.\nThe perception of a relation being in balance (i.e. fair)\ndepends strongly on the nature of the social relationships\nbetween individuals (i.e. the intimacy level). In purely\neconomical relationships (e.g., business), equity is perceived as\nmore fair; in relations where joint action or fostering of social\nrelationships are the goal (e.g. friends), equality is perceived\nas more fair; and in situations where personal development\nor personal welfare are the goal (e.g. family), allocations are\nusually based on need.\nWe believe that the perception of balance in dialogues (in\nnegotiation or otherwise) is grounded on social relationships,\nand that every dimension of an interaction between humans\ncan be correlated to the social closeness, or intimacy,\nbetween the parties involved. According to the previous\nstudies, the more intimacy across the five LOGIC dimensions the\nmore the need norm is used, and the less intimacy the more\nthe equity norm is used. This might be part of our social\nevolution. There is ample evidence that when human\nsocieties evolved from a hunter-gatherer structure1\nto a\nshelterbased one2\nthe probability of survival increased when food\nwas scarce.\nIn this context, we can clearly see that, for instance,\nfamilies exchange not only goods but also information and\nknowledge based on need, and that few families would consider\ntheir relationships as being unbalanced, and thus unfair,\nwhen there is a strong asymmetry in the exchanges (a mother\nexplaining everything to her children, or buying toys, does\nnot expect reciprocity). In the case of partners there is some\nevidence [3] that the allocations of goods and burdens (i.e.\npositive and negative utilities) are perceived as fair, or in\nbalance, based on equity for burdens and equality for goods.\nSee Table 1 for some examples of desired balances along the\nLOGIC dimensions.\nThe perceived balance in a negotiation dialogue allows\nnegotiators to infer information about their opponent, about\nits LOGIC stance, and to compare their relationships with\nall negotiators. For instance, if we perceive that every time\nwe request information it is provided, and that no significant\nquestions are returned, or no complaints about not\nreceiving information are given, then that probably means that\nour opponent perceives our social relationship to be very\nclose. Alternatively, we can detect what issues are causing\na burden to our opponent by observing an imbalance in the\ninformation or utilitarian senses on that issue.\n3. COMMUNICATION MODEL\n3.1 Ontology\nIn order to define a language to structure agent dialogues we\nneed an ontology that includes a (minimum) repertoire of\nelements: a set of concepts (e.g. quantity, quality, material)\norganised in a is-a hierarchy (e.g. platypus is a mammal,\nAustralian-dollar is a currency), and a set of relations over\nthese concepts (e.g. price(beer,AUD)).3\nWe model\nontologies following an algebraic approach [8] as:\nAn ontology is a tuple O = (C, R, \u2264, \u03c3) where:\n1. C is a finite set of concept symbols (including basic\ndata types);\n2. R is a finite set of relation symbols;\n3. \u2264 is a reflexive, transitive and anti-symmetric relation\non C (a partial order)\n4. \u03c3 : R \u2192 C+\nis the function assigning to each relation\nsymbol its arity\n1\nIn its purest form, individuals in these societies collect food\nand consume it when and where it is found. This is a pure\nequity sharing of the resources, the gain is proportional to\nthe effort.\n2\nIn these societies there are family units, around a shelter,\nthat represent the basic food sharing structure. Usually,\nfood is accumulated at the shelter for future use. Then the\nfood intake depends more on the need of the members.\n3\nUsually, a set of axioms defined over the concepts and\nrelations is also required. We will omit this here.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1031\nElement A new trading partner my butcher my boss my partner my children\nLegitimacy equity equity equity equality need\nOptions equity equity equity mixeda\nneed\nGoals equity need equity need need\nIndependence equity equity equality need need\nCommitment equity equity equity mixed need\na\nequity on burden, equality on good\nTable 1: Some desired balances (sense of fairness) examples depending on the relationship.\nwhere \u2264 is the traditional is-a hierarchy. To simplify\ncomputations in the computing of probability distributions we\nassume that there is a number of disjoint is-a trees covering\ndifferent ontological spaces (e.g. a tree for types of fabric,\na tree for shapes of clothing, and so on). R contains\nrelations between the concepts in the hierarchy, this is needed\nto define \u2018objects\" (e.g. deals) that are defined as a tuple of\nissues.\nThe semantic distance between concepts within an\nontology depends on how far away they are in the structure\ndefined by the \u2264 relation. Semantic distance plays a\nfundamental role in strategies for information-based agency. How\nsigned contracts, Commit(\u00b7), about objects in a particular\nsemantic region, and their execution, Done(\u00b7), affect our\ndecision making process about signing future contracts in\nnearby semantic regions is crucial to modelling the common\nsense that human beings apply in managing trading\nrelationships. A measure [10] bases the semantic similarity\nbetween two concepts on the path length induced by \u2264 (more\ndistance in the \u2264 graph means less semantic similarity), and\nthe depth of the subsumer concept (common ancestor) in the\nshortest path between the two concepts (the deeper in the\nhierarchy, the closer the meaning of the concepts). Semantic\nsimilarity is then defined as:\nSim(c, c ) = e\u2212\u03ba1l\n\u00b7\ne\u03ba2h\n\u2212 e\u2212\u03ba2h\ne\u03ba2h + e\u2212\u03ba2h\nwhere l is the length (i.e. number of hops) of the\nshortest path between the concepts, h is the depth of the deepest\nconcept subsuming both concepts, and \u03ba1 and \u03ba2 are\nparameters scaling the contributions of the shortest path length\nand the depth respectively.\n3.2 Language\nThe shape of the language that \u03b1 uses to represent the\ninformation received and the content of its dialogues depends on\ntwo fundamental notions. First, when agents interact within\nan overarching institution they explicitly or implicitly accept\nthe norms that will constrain their behaviour, and accept\nthe established sanctions and penalties whenever norms are\nviolated. Second, the dialogues in which \u03b1 engages are built\naround two fundamental actions: (i) passing information,\nand (ii) exchanging proposals and contracts. A contract\n\u03b4 = (a, b) between agents \u03b1 and \u03b2 is a pair where a and b\nrepresent the actions that agents \u03b1 and \u03b2 are responsible\nfor respectively. Contracts signed by agents and\ninformation passed by agents, are similar to norms in the sense that\nthey oblige agents to behave in a particular way, so as to\nsatisfy the conditions of the contract, or to make the world\nconsistent with the information passed. Contracts and\nInformation can thus be thought of as normative statements\nthat restrict an agent\"s behaviour.\nNorms, contracts, and information have an obvious\ntemporal dimension. Thus, an agent has to abide by a norm\nwhile it is inside an institution, a contract has a validity\nperiod, and a piece of information is true only during an\ninterval in time. The set of norms affecting the behaviour of\nan agent defines the context that the agent has to take into\naccount.\n\u03b1\"s communication language has two fundamental\nprimitives: Commit(\u03b1, \u03b2, \u03d5) to represent, in \u03d5, the world that \u03b1\naims at bringing about and that \u03b2 has the right to verify,\ncomplain about or claim compensation for any deviations\nfrom, and Done(\u03bc) to represent the event that a certain\naction \u03bc4\nhas taken place. In this way, norms, contracts,\nand information chunks will be represented as instances of\nCommit(\u00b7) where \u03b1 and \u03b2 can be individual agents or\ninstitutions. C is:\n\u03bc ::= illoc(\u03b1, \u03b2, \u03d5, t) | \u03bc; \u03bc |\nLet context In \u03bc End\n\u03d5 ::= term | Done(\u03bc) | Commit(\u03b1, \u03b2, \u03d5) | \u03d5 \u2227 \u03d5 |\n\u03d5 \u2228 \u03d5 | \u00ac\u03d5 | \u2200v.\u03d5v | \u2203v.\u03d5v\ncontext ::= \u03d5 | id = \u03d5 | prolog clause | context; context\nwhere \u03d5v is a formula with free variable v, illoc is any\nappropriate set of illocutionary particles, \u2018;\" means sequencing,\nand context represents either previous agreements, previous\nillocutions, the ontological working context, that is a\nprojection of the ontological trees that represent the focus of\nthe conversation, or code that aligns the ontological\ndifferences between the speakers needed to interpret an action\na. Representing an ontology as a set predicates in Prolog\nis simple. The set term contains instances of the ontology\nconcepts and relations.5\nFor example, we can represent the following offer: If you\nspend a total of more than e100 in my shop during\nOctober then I will give you a 10% discount on all goods in\nNovember, as:\nOffer( \u03b1, \u03b2,spent(\u03b2, \u03b1, October, X) \u2227 X \u2265 e100 \u2192\n\u2200 y. Done(Inform(\u03be, \u03b1, pay(\u03b2, \u03b1, y), November)) \u2192\nCommit(\u03b1, \u03b2, discount(y,10%)))\n\u03be is an institution agent that reports the payment.\n4\nWithout loss of generality we will assume that all actions\nare dialogical.\n5\nWe assume the convention that C(c) means that c is an\ninstance of concept C and r(c1, . . . , cn) implicitly determines\nthat ci is an instance of the concept in the i-th position of\nthe relation r.\n1032 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nFigure 1: The LOGIC agent architecture\n4. AGENT ARCHITECTURE\nA multiagent system {\u03b1, \u03b21, . . . , \u03b2n, \u03be, \u03b81, . . . , \u03b8t}, contains\nan agent \u03b1 that interacts with other argumentation agents,\n\u03b2i, information providing agents, \u03b8j, and an institutional\nagent, \u03be, that represents the institution where we assume\nthe interactions happen [2]. The institutional agent reports\npromptly and honestly on what actually occurs after an\nagent signs a contract, or makes some other form of\ncommitment. In Section 4.1 this enables us to measure the\ndifference between an utterance and a subsequent observation.\nThe communication language C introduced in Section 3.2\nenables us both to structure the dialogues and to structure the\nprocessing of the information gathered by agents. Agents\nhave a probabilistic first-order internal language L used to\nrepresent a world model, Mt\n. A generic information-based\narchitecture is described in detail in [15].\nThe LOGIC agent architecture is shown in Figure 1. Agent\n\u03b1 acts in response to a need that is expressed in terms of the\nontology. A need may be exogenous such as a need to trade\nprofitably and may be triggered by another agent offering to\ntrade, or endogenous such as \u03b1 deciding that it owns more\nwine than it requires. Needs trigger \u03b1\"s goal/plan\nproactive reasoning, while other messages are dealt with by \u03b1\"s\nreactive reasoning.6\nEach plan prepares for the negotiation\nby assembling the contents of a \u2018LOGIC briefcase\" that the\nagent \u2018carries\" into the negotiation7\n. The relationship\nstrategy determines which agent to negotiate with for a given\nneed; it uses risk management analysis to preserve a\nstrategic set of trading relationships for each mission-critical need\n- this is not detailed here. For each trading relationship\nthis strategy generates a relationship target that is expressed\nin the LOGIC framework as a desired level of intimacy to\nbe achieved in the long term.\nEach negotiation consists of a dialogue, \u03a8t\n, between two\nagents with agent \u03b1 contributing utterance \u03bc and the\npart6\nEach of \u03b1\"s plans and reactions contain constructors for an\ninitial world model Mt\n. Mt\nis then maintained from\npercepts received using update functions that transform\npercepts into constraints on Mt\n- for details, see [14, 15].\n7\nEmpirical evidence shows that in human negotiation,\nbetter outcomes are achieved by skewing the opening Options\nin favour of the proposer. We are unaware of any\nempirical investigation of this hypothesis for autonomous agents\nin real trading scenarios.\nner \u03b2 contributing \u03bc using the language described in\nSection 3.2. Each dialogue, \u03a8t\n, is evaluated using the LOGIC\nframework in terms of the value of \u03a8t\nto both \u03b1 and \u03b2 - see\nSection 5.2. The negotiation strategy then determines the\ncurrent set of Options {\u03b4i}, and then the tactics, guided by\nthe negotiation target, decide which, if any, of these Options\nto put forward and wraps them in argumentation dialogue\n- see Section 6. We now describe two of the distributions\nin Mt\nthat support offer exchange.\nPt\n(acc(\u03b1, \u03b2, \u03c7, \u03b4)) estimates the probability that \u03b1 should\naccept proposal \u03b4 in satisfaction of her need \u03c7, where \u03b4 =\n(a, b) is a pair of commitments, a for \u03b1 and b for \u03b2. \u03b1 will\naccept \u03b4 if: Pt\n(acc(\u03b1, \u03b2, \u03c7, \u03b4)) > c, for level of certainty c.\nThis estimate is compounded from subjective and objective\nviews of acceptability. The subjective estimate takes account\nof: the extent to which the enactment of \u03b4 will satisfy \u03b1\"s\nneed \u03c7, how much \u03b4 is \u2018worth\" to \u03b1, and the extent to which\n\u03b1 believes that she will be in a position to execute her\ncommitment a [14, 15]. S\u03b1(\u03b2, a) is a random variable denoting\n\u03b1\"s estimate of \u03b2\"s subjective valuation of a over some finite,\nnumerical evaluation space. The objective estimate captures\nwhether \u03b4 is acceptable on the open market, and variable\nU\u03b1(b) denotes \u03b1\"s open-market valuation of the enactment\nof commitment b, again taken over some finite numerical\nvaluation space. We also consider needs, the variable T\u03b1(\u03b2, a)\ndenotes \u03b1\"s estimate of the strength of \u03b2\"s motivating need\nfor the enactment of commitment a over a valuation space.\nThen for \u03b4 = (a, b): Pt\n(acc(\u03b1, \u03b2, \u03c7, \u03b4)) =\nPt\n\u201e\nT\u03b1(\u03b2, a)\nT\u03b1(\u03b1, b)\n\u00abh\n\u00d7\n\u201e\nS\u03b1(\u03b1, b)\nS\u03b1(\u03b2, a)\n\u00abg\n\u00d7\nU\u03b1(b)\nU\u03b1(a)\n\u2265 s\n!\n(1)\nwhere g \u2208 [0, 1] is \u03b1\"s greed, h \u2208 [0, 1] is \u03b1\"s degree of\naltruism, and s \u2248 1 is derived from the stance8\ndescribed in\nSection 6. The parameters g and h are independent. We can\nimagine a relationship that begins with g = 1 and h = 0.\nThen as the agents share increasing amounts of their\ninformation about their open market valuations g gradually\nreduces to 0, and then as they share increasing amounts of\ninformation about their needs h increases to 1. The basis\nfor the acceptance criterion has thus developed from equity\nto equality, and then to need.\nPt\n(acc(\u03b2, \u03b1, \u03b4)) estimates the probability that \u03b2 would\naccept \u03b4, by observing \u03b2\"s responses. For example, if \u03b2\nsends the message Offer(\u03b41) then \u03b1 derives the constraint:\n{Pt\n(acc(\u03b2, \u03b1, \u03b41)) = 1} on the distribution Pt\n(\u03b2, \u03b1, \u03b4), and\nif this is a counter offer to a former offer of \u03b1\"s, \u03b40, then:\n{Pt\n(acc(\u03b2, \u03b1, \u03b40)) = 0}. In the not-atypical special case of\nmulti-issue bargaining where the agents\" preferences over the\nindividual issues only are known and are complementary to\neach other\"s, maximum entropy reasoning can be applied\nto estimate the probability that any multi-issue \u03b4 will be\nacceptable to \u03b2 by enumerating the possible worlds that\nrepresent \u03b2\"s limit of acceptability [6].\n4.1 Updating the World Model Mt\n\u03b1\"s world model consists of probability distributions that\nrepresent its uncertainty in the world state. \u03b1 is interested\n8\nIf \u03b1 chooses to inflate her opening Options then this is\nachieved in Section 6 by increasing the value of s. If s 1\nthen a deal may not be possible. This illustrates the\nwellknown inefficiency of bilateral bargaining established\nanalytically by Myerson and Satterthwaite in 1983.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1033\nin the degree to which an utterance accurately describes\nwhat will subsequently be observed. All observations about\nthe world are received as utterances from an all-truthful\ninstitution agent \u03be. For example, if \u03b2 communicates the goal\nI am hungry and the subsequent negotiation terminates\nwith \u03b2 purchasing a book from \u03b1 (by \u03be advising \u03b1 that a\ncertain amount of money has been credited to \u03b1\"s account)\nthen \u03b1 may conclude that the goal that \u03b2 chose to satisfy\nwas something other than hunger. So, \u03b1\"s world model\ncontains probability distributions that represent its uncertain\nexpectations of what will be observed on the basis of\nutterances received.\nWe represent the relationship between utterance, \u03d5, and\nsubsequent observation, \u03d5 , by Pt\n(\u03d5 |\u03d5) \u2208 Mt\n, where \u03d5 and\n\u03d5 may be ontological categories in the interest of\ncomputational feasibility. For example, if \u03d5 is I will deliver a bucket\nof fish to you tomorrow then the distribution P(\u03d5 |\u03d5) need\nnot be over all possible things that \u03b2 might do, but could\nbe over ontological categories that summarise \u03b2\"s possible\nactions.\nIn the absence of in-coming utterances, the conditional\nprobabilities, Pt\n(\u03d5 |\u03d5), should tend to ignorance as\nrepresented by a decay limit distribution D(\u03d5 |\u03d5). \u03b1 may have\nbackground knowledge concerning D(\u03d5 |\u03d5) as t \u2192 \u221e,\notherwise \u03b1 may assume that it has maximum entropy whilst\nbeing consistent with the data. In general, given a\ndistribution, Pt\n(Xi), and a decay limit distribution D(Xi), Pt\n(Xi)\ndecays by:\nPt+1\n(Xi) = \u0394i(D(Xi), Pt\n(Xi)) (2)\nwhere \u0394i is the decay function for the Xi satisfying the\nproperty that limt\u2192\u221e Pt\n(Xi) = D(Xi). For example, \u0394i\ncould be linear: Pt+1\n(Xi) = (1 \u2212 \u03bdi) \u00d7 D(Xi) + \u03bdi \u00d7 Pt\n(Xi),\nwhere \u03bdi < 1 is the decay rate for the i\"th distribution.\nEither the decay function or the decay limit distribution\ncould also be a function of time: \u0394t\ni and Dt\n(Xi).\nSuppose that \u03b1 receives an utterance \u03bc = illoc(\u03b1, \u03b2, \u03d5, t)\nfrom agent \u03b2 at time t. Suppose that \u03b1 attaches an\nepistemic belief Rt\n(\u03b1, \u03b2, \u03bc) to \u03bc - this probability takes account\nof \u03b1\"s level of personal caution. We model the update of\nPt\n(\u03d5 |\u03d5) in two cases, one for observations given \u03d5, second\nfor observations given \u03c6 in the semantic neighbourhood of\n\u03d5.\n4.2 Update of Pt\n(\u03d5 |\u03d5) given \u03d5\nFirst, if \u03d5k is observed then \u03b1 may set Pt+1\n(\u03d5k|\u03d5) to some\nvalue d where {\u03d51, \u03d52, . . . , \u03d5m} is the set of all possible\nobservations. We estimate the complete posterior\ndistribution Pt+1\n(\u03d5 |\u03d5) by applying the principle of minimum\nrelative entropy9\nas follows. Let p(\u03bc) be the distribution:\n9\nGiven a probability distribution q, the minimum relative\nentropy distribution p = (p1, . . . , pI ) subject to a set of J\nlinear constraints g = {gj(p) = aj \u00b7 p \u2212 cj = 0}, j = 1, . . . , J\n(that must include the constraint\nP\ni pi \u2212 1 = 0) is: p =\narg minr\nP\nj rj log\nrj\nqj\n. This may be calculated by\nintroducing Lagrange multipliers \u03bb: L(p, \u03bb) =\nP\nj pj log\npj\nqj\n+ \u03bb \u00b7 g.\nMinimising L, { \u2202L\n\u2202\u03bbj\n= gj(p) = 0}, j = 1, . . . , J is the set of\ngiven constraints g, and a solution to \u2202L\n\u2202pi\n= 0, i = 1, . . . , I\nleads eventually to p. Entropy-based inference is a form of\nBayesian inference that is convenient when the data is sparse\n[5] and encapsulates common-sense reasoning [12].\narg minx\nP\nj xj log\nxj\nPt(\u03d5 |\u03d5)j\nthat satisfies the constraint p(\u03bc)k\n= d. Then let q(\u03bc) be the distribution:\nq(\u03bc) = Rt\n(\u03b1, \u03b2, \u03bc) \u00d7 p(\u03bc) + (1 \u2212 Rt\n(\u03b1, \u03b2, \u03bc)) \u00d7 Pt\n(\u03d5 |\u03d5)\nand then let:\nr(\u03bc) =\n(\nq(\u03bc) if q(\u03bc) is more interesting than Pt\n(\u03d5 |\u03d5)\nPt\n(\u03d5 |\u03d5) otherwise\nA general measure of whether q(\u03bc) is more interesting than\nPt\n(\u03d5 |\u03d5) is: K(q(\u03bc) D(\u03d5 |\u03d5)) > K(Pt\n(\u03d5 |\u03d5) D(\u03d5 |\u03d5)), where\nK(x y) =\nP\nj xj ln\nxj\nyj\nis the Kullback-Leibler distance\nbetween two probability distributions x and y [11].\nFinally incorporating Eqn. 2 we obtain the method for\nupdating a distribution Pt\n(\u03d5 |\u03d5) on receipt of a message \u03bc:\nPt+1\n(\u03d5 |\u03d5) = \u0394i(D(\u03d5 |\u03d5), r(\u03bc)) (3)\nThis procedure deals with integrity decay, and with two\nprobabilities: first, the probability z in the utterance \u03bc, and\nsecond the belief Rt\n(\u03b1, \u03b2, \u03bc) that \u03b1 attached to \u03bc.\n4.3 Update of Pt\n(\u03c6 |\u03c6) given \u03d5\nThe sim method: Given as above \u03bc = illoc(\u03b1, \u03b2, \u03d5, t) and\nthe observation \u03d5k we define the vector t by\nti = Pt\n(\u03c6i|\u03c6) + (1\u2212 | Sim(\u03d5k, \u03d5) \u2212 Sim(\u03c6i, \u03c6) |) \u00b7 Sim(\u03d5k, \u03c6)\nwith {\u03c61, \u03c62, . . . , \u03c6p} the set of all possible observations in\nthe context of \u03c6 and i = 1, . . . , p. t is not a probability\ndistribution. The multiplying factor Sim(\u03d5 , \u03c6) limits the\nvariation of probability to those formulae whose\nontological context is not too far away from the observation. The\nposterior Pt+1\n(\u03c6 |\u03c6) is obtained with Equation 3 with r(\u03bc)\ndefined to be the normalisation of t.\nThe valuation method: For a given \u03c6k, wexp\n(\u03c6k) =Pm\nj=1 Pt\n(\u03c6j|\u03c6k) \u00b7 w(\u03c6j) is \u03b1\"s expectation of the value of\nwhat will be observed given that \u03b2 has stated that \u03c6k will\nbe observed, for some measure w. Now suppose that, as\nbefore, \u03b1 observes \u03d5k after agent \u03b2 has stated \u03d5. \u03b1 revises\nthe prior estimate of the expected valuation wexp\n(\u03c6k) in the\nlight of the observation \u03d5k to:\n(wrev\n(\u03c6k) | (\u03d5k|\u03d5)) =\ng(wexp\n(\u03c6k), Sim(\u03c6k, \u03d5), w(\u03c6k), w(\u03d5), wi(\u03d5k))\nfor some function g - the idea being, for example, that if the\nexecution, \u03d5k, of the commitment, \u03d5, to supply cheese was\ndevalued then \u03b1\"s expectation of the value of a commitment,\n\u03c6, to supply wine should decrease. We estimate the posterior\nby applying the principle of minimum relative entropy as for\nEquation 3, where the distribution p(\u03bc) = p(\u03c6 |\u03c6) satisfies the\nconstraint:\np\nX\nj=1\np(\u03d5 ,\u03d5)j \u00b7 wi(\u03c6j) =\ng(wexp\n(\u03c6k), Sim(\u03c6k, \u03d5), w(\u03c6k), w(\u03d5), wi(\u03d5k))\n5. SUMMARY MEASURES\nA dialogue, \u03a8t\n, between agents \u03b1 and \u03b2 is a sequence of\ninter-related utterances in context. A relationship, \u03a8\u2217t\n, is a\nsequence of dialogues. We first measure the confidence that\nan agent has for another by observing, for each utterance,\nthe difference between what is said (the utterance) and what\n1034 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nsubsequently occurs (the observation). Second we evaluate\neach dialogue as it progresses in terms of the LOGIC\nframework - this evaluation employs the confidence measures.\nFinally we define the intimacy of a relationship as an\naggregation of the value of its component dialogues.\n5.1 Confidence\nConfidence measures generalise what are commonly called\ntrust, reliability and reputation measures into a single\ncomputational framework that spans the LOGIC categories. In\nSection 5.2 confidence measures are applied to valuing\nfulfilment of promises in the Legitimacy category - we formerly\ncalled this honour [14], to the execution of commitments\n- we formerly called this trust [13], and to valuing\ndialogues in the Goals category - we formerly called this\nreliability [14].\nIdeal observations. Consider a distribution of\nobservations that represent \u03b1\"s ideal in the sense that it is the\nbest that \u03b1 could reasonably expect to observe. This\ndistribution will be a function of \u03b1\"s context with \u03b2 denoted\nby e, and is Pt\nI (\u03d5 |\u03d5, e). Here we measure the relative\nentropy between this ideal distribution, Pt\nI (\u03d5 |\u03d5, e), and the\ndistribution of expected observations, Pt\n(\u03d5 |\u03d5). That is:\nC(\u03b1, \u03b2, \u03d5) = 1 \u2212\nX\n\u03d5\nPt\nI (\u03d5 |\u03d5, e) log\nPt\nI (\u03d5 |\u03d5, e)\nPt(\u03d5 |\u03d5)\n(4)\nwhere the 1 is an arbitrarily chosen constant being the\nmaximum value that this measure may have. This equation\nmeasures confidence for a single statement \u03d5. It makes sense\nto aggregate these values over a class of statements, say over\nthose \u03d5 that are in the ontological context o, that is \u03d5 \u2264 o:\nC(\u03b1, \u03b2, o) = 1 \u2212\nP\n\u03d5:\u03d5\u2264o Pt\n\u03b2(\u03d5) [1 \u2212 C(\u03b1, \u03b2, \u03d5)]\nP\n\u03d5:\u03d5\u2264o Pt\n\u03b2(\u03d5)\nwhere Pt\n\u03b2(\u03d5) is a probability distribution over the space of\nstatements that the next statement \u03b2 will make to \u03b1 is \u03d5.\nSimilarly, for an overall estimate of \u03b2\"s confidence in \u03b1:\nC(\u03b1, \u03b2) = 1 \u2212\nX\n\u03d5\nPt\n\u03b2(\u03d5) [1 \u2212 C(\u03b1, \u03b2, \u03d5)]\nPreferred observations. The previous measure requires\nthat an ideal distribution, Pt\nI (\u03d5 |\u03d5, e), has to be specified for\neach \u03d5. Here we measure the extent to which the\nobservation \u03d5 is preferable to the original statement \u03d5. Given a\npredicate Prefer(c1, c2, e) meaning that \u03b1 prefers c1 to c2 in\nenvironment e. Then if \u03d5 \u2264 o:\nC(\u03b1, \u03b2, \u03d5) =\nX\n\u03d5\nPt\n(Prefer(\u03d5 , \u03d5, o))Pt\n(\u03d5 |\u03d5)\nand:\nC(\u03b1, \u03b2, o) =\nP\n\u03d5:\u03d5\u2264o Pt\n\u03b2(\u03d5)C(\u03b1, \u03b2, \u03d5)\nP\n\u03d5:\u03d5\u2264o Pt\n\u03b2(\u03d5)\nCertainty in observation. Here we measure the\nconsistency in expected acceptable observations, or the lack of\nexpected uncertainty in those possible observations that are\nbetter than the original statement. If \u03d5 \u2264 o let: \u03a6+(\u03d5, o, \u03ba) =\u02d8\n\u03d5 | Pt\n(Prefer(\u03d5 , \u03d5, o)) > \u03ba\n\u00af\nfor some constant \u03ba, and:\nC(\u03b1, \u03b2, \u03d5) = 1 +\n1\nB\u2217\n\u00b7\nX\n\u03d5 \u2208\u03a6+(\u03d5,o,\u03ba)\nPt\n+(\u03d5 |\u03d5) log Pt\n+(\u03d5 |\u03d5)\nwhere Pt\n+(\u03d5 |\u03d5) is the normalisation of Pt\n(\u03d5 |\u03d5) for \u03d5 \u2208\n\u03a6+(\u03d5, o, \u03ba),\nB\u2217\n=\n(\n1 if |\u03a6+(\u03d5, o, \u03ba)| = 1\nlog |\u03a6+(\u03d5, o, \u03ba)| otherwise\nAs above we aggregate this measure for observations in a\nparticular context o, and measure confidence as before.\nComputational Note. The various measures given above\ninvolve extensive calculations. For example, Eqn. 4 containsP\n\u03d5 that sums over all possible observations \u03d5 . We obtain\na more computationally friendly measure by appealing to\nthe structure of the ontology described in Section 3.2, and\nthe right-hand side of Eqn. 4 may be approximated to:\n1 \u2212\nX\n\u03d5 :Sim(\u03d5 ,\u03d5)\u2265\u03b7\nPt\n\u03b7,I (\u03d5 |\u03d5, e) log\nPt\n\u03b7,I (\u03d5 |\u03d5, e)\nPt\n\u03b7(\u03d5 |\u03d5)\nwhere Pt\n\u03b7,I (\u03d5 |\u03d5, e) is the normalisation of Pt\nI (\u03d5 |\u03d5, e) for\nSim(\u03d5 , \u03d5) \u2265 \u03b7, and similarly for Pt\n\u03b7(\u03d5 |\u03d5). The extent\nof this calculation is controlled by the parameter \u03b7. An\neven tighter restriction may be obtained with: Sim(\u03d5 , \u03d5) \u2265\n\u03b7 and \u03d5 \u2264 \u03c8 for some \u03c8.\n5.2 Valuing negotiation dialogues\nSuppose that a negotiation commences at time s, and by\ntime t a string of utterances, \u03a6t\n= \u03bc1, . . . , \u03bcn has been\nexchanged between agent \u03b1 and agent \u03b2. This\nnegotiation dialogue is evaluated by \u03b1 in the context of \u03b1\"s world\nmodel at time s, Ms\n, and the environment e that includes\nutterances that may have been received from other agents\nin the system including the information sources {\u03b8i}. Let\n\u03a8t\n= (\u03a6t\n, Ms\n, e), then \u03b1 estimates the value of this dialogue\nto itself in the context of Ms\nand e as a 2 \u00d7 5 array V\u03b1(\u03a8t\n)\nwhere:\nVx(\u03a8t\n) =\n\u201e\nIL\nx (\u03a8t\n) IO\nx (\u03a8t\n) IG\nx (\u03a8t\n) II\nx(\u03a8t\n) IC\nx (\u03a8t\n)\nUL\nx (\u03a8t\n) UO\nx (\u03a8t\n) UG\nx (\u03a8t\n) UI\nx(\u03a8t\n) UC\nx (\u03a8t\n)\n\u00ab\nwhere the I(\u00b7) and U(\u00b7) functions are information-based and\nutility-based measures respectively as we now describe. \u03b1\nestimates the value of this dialogue to \u03b2 as V\u03b2(\u03a8t\n) by\nassuming that \u03b2\"s reasoning apparatus mirrors its own.\nIn general terms, the information-based valuations\nmeasure the reduction in uncertainty, or information gain, that\nthe dialogue gives to each agent, they are expressed in terms\nof decrease in entropy that can always be calculated. The\nutility-based valuations measure utility gain are expressed in\nterms of some suitable utility evaluation function U(\u00b7) that\ncan be difficult to define. This is one reason why the\nutilitarian approach has no natural extension to the management\nof argumentation that is achieved here by our\ninformationbased approach. For example, if \u03b1 receives the utterance\nToday is Tuesday then this may be translated into a\nconstraint on a single distribution, and the resulting decrease\nin entropy is the information gain. Attaching a utilitarian\nmeasure to this utterance may not be so simple.\nWe use the term 2 \u00d7 5 array loosely to describe V\u03b1 in\nthat the elements of the array are lists of measures that will\nbe determined by the agent\"s requirements. Table 2 shows\na sample measure for each of the ten categories, in it the\ndialogue commences at time s and terminates at time t.\nIn that Table, U(\u00b7) is a suitable utility evaluation function,\nneeds(\u03b2, \u03c7) means agent \u03b2 needs the need \u03c7, cho(\u03b2, \u03c7, \u03b3)\nmeans agent \u03b2 satisfies need \u03c7 by choosing to negotiate\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1035\nwith agent \u03b3, N is the set of needs chosen from the\nontology at some suitable level of abstraction, Tt\nis the set\nof offers on the table at time t, com(\u03b2, \u03b3, b) means agent\n\u03b2 has an outstanding commitment with agent \u03b3 to execute\nthe commitment b where b is defined in the ontology at\nsome suitable level of abstraction, B is the number of such\ncommitments, and there are n + 1 agents in the system.\n5.3 Intimacy and Balance\nThe balance in a negotiation dialogue, \u03a8t\n, is defined as:\nB\u03b1\u03b2(\u03a8t\n) = V\u03b1(\u03a8t\n) V\u03b2(\u03a8t\n) for an element-by-element\ndifference operator that respects the structure of V (\u03a8t\n).\nThe intimacy between agents \u03b1 and \u03b2, I\u2217t\n\u03b1\u03b2, is the pattern\nof the two 2 \u00d7 5 arrays V \u2217t\n\u03b1 and V \u2217t\n\u03b2 that are computed by\nan update function as each negotiation round terminates,\nI\u2217t\n\u03b1\u03b2 =\n`\nV \u2217t\n\u03b1 , V \u2217t\n\u03b2\n\u00b4\n. If \u03a8t\nterminates at time t:\nV \u2217t+1\nx = \u03bd \u00d7 Vx(\u03a8t\n) + (1 \u2212 \u03bd) \u00d7 V \u2217t\nx (5)\nwhere \u03bd is the learning rate, and x = \u03b1, \u03b2. Additionally,\nV \u2217t\nx continually decays by: V \u2217t+1\nx = \u03c4 \u00d7 V \u2217t\nx + (1 \u2212 \u03c4) \u00d7\nDx, where x = \u03b1, \u03b2; \u03c4 is the decay rate, and Dx is a 2 \u00d7\n5 array being the decay limit distribution for the value to\nagent x of the intimacy of the relationship in the absence\nof any interaction. Dx is the reputation of agent x. The\nrelationship balance between agents \u03b1 and \u03b2 is: B\u2217t\n\u03b1\u03b2 = V \u2217t\n\u03b1\nV \u2217t\n\u03b2 . In particular, the intimacy determines values for the\nparameters g and h in Equation 1. As a simple example, if\nboth IO\n\u03b1 (\u03a8\u2217t\n) and IO\n\u03b2 (\u03a8\u2217t\n) increase then g decreases, and as\nthe remaining eight information-based LOGIC components\nincrease, h increases.\nThe notion of balance may be applied to pairs of\nutterances by treating them as degenerate dialogues. In simple\nmulti-issue bargaining the equitable information revelation\nstrategy generalises the tit-for-tat strategy in single-issue\nbargaining, and extends to a tit-for-tat argumentation\nstrategy by applying the same principle across the LOGIC\nframework.\n6. STRATEGIES AND TACTICS\nEach negotiation has to achieve two goals. First it may\nbe intended to achieve some contractual outcome. Second\nit will aim to contribute to the growth, or decline, of the\nrelationship intimacy.\nWe now describe in greater detail the contents of the\nNegotiation box in Figure 1. The negotiation literature\nconsistently advises that an agent\"s behaviour should not be\npredictable even in close, intimate relationships. The\nrequired variation of behaviour is normally described as\nvarying the negotiation stance that informally varies from\nfriendly guy to tough guy. The stance is shown in Figure 1,\nit injects bounded random noise into the process, where the\nbound tightens as intimacy increases. The stance, St\n\u03b1\u03b2, is a\n2 \u00d7 5 matrix of randomly chosen multipliers, each \u2248 1, that\nperturbs \u03b1\"s actions. The value in the (x, y) position in the\nmatrix, where x = I, U and y = L, O, G, I, C, is chosen at\nrandom from [ 1\nl(I\u2217t\n\u03b1\u03b2\n,x,y)\n, l(I\u2217t\n\u03b1\u03b2, x, y)] where l(I\u2217t\n\u03b1\u03b2, x, y) is the\nbound, and I\u2217t\n\u03b1\u03b2 is the intimacy.\nThe negotiation strategy is concerned with maintaining a\nworking set of Options. If the set of options is empty then\n\u03b1 will quit the negotiation. \u03b1 perturbs the acceptance\nmachinery (see Section 4) by deriving s from the St\n\u03b1\u03b2 matrix\nsuch as the value at the (I, O) position. In line with the\ncomment in Footnote 7, in the early stages of the\nnegotiation \u03b1 may decide to inflate her opening Options. This is\nachieved by increasing the value of s in Equation 1. The\nfollowing strategy uses the machinery described in Section 4.\nFix h, g, s and c, set the Options to the empty set, let\nDt\ns = {\u03b4 | Pt\n(acc(\u03b1, \u03b2, \u03c7, \u03b4) > c}, then:\n\u2022 repeat the following as many times as desired: add\n\u03b4 = arg maxx{Pt\n(acc(\u03b2, \u03b1, x)) | x \u2208 Dt\ns} to Options,\nremove {y \u2208 Dt\ns | Sim(y, \u03b4) < k} for some k from Dt\ns\nBy using Pt\n(acc(\u03b2, \u03b1, \u03b4)) this strategy reacts to \u03b2\"s history\nof Propose and Reject utterances.\nNegotiation tactics are concerned with selecting some\nOptions and wrapping them in argumentation. Prior\ninteractions with agent \u03b2 will have produced an intimacy pattern\nexpressed in the form of\n`\nV \u2217t\n\u03b1 , V \u2217t\n\u03b2\n\u00b4\n. Suppose that the\nrelationship target is (T\u2217t\n\u03b1 , T\u2217t\n\u03b2 ). Following from Equation 5, \u03b1\nwill want to achieve a negotiation target, N\u03b2(\u03a8t\n) such that:\n\u03bd \u00b7 N\u03b2(\u03a8t\n) + (1 \u2212 \u03bd) \u00b7 V \u2217t\n\u03b2 is a bit on the T\u2217t\n\u03b2 side of V \u2217t\n\u03b2 :\nN\u03b2(\u03a8t\n) =\n\u03bd \u2212 \u03ba\n\u03bd\nV \u2217t\n\u03b2 \u2295\n\u03ba\n\u03bd\nT\u2217t\n\u03b2 (6)\nfor small \u03ba \u2208 [0, \u03bd] that represents \u03b1\"s desired rate of\ndevelopment for her relationship with \u03b2. N\u03b2(\u03a8t\n) is a 2 \u00d7 5\nmatrix containing variations in the LOGIC dimensions that\n\u03b1 would like to reveal to \u03b2 during \u03a8t\n(e.g. I\"ll pass a bit\nmore information on options than usual, I\"ll be stronger\nin concessions on options, etc.). It is reasonable to\nexpect \u03b2 to progress towards her target at the same rate and\nN\u03b1(\u03a8t\n) is calculated by replacing \u03b2 by \u03b1 in Equation 6.\nN\u03b1(\u03a8t\n) is what \u03b1 hopes to receive from \u03b2 during \u03a8t\n. This\ngives a negotiation balance target of: N\u03b1(\u03a8t\n) N\u03b2(\u03a8t\n) that\ncan be used as the foundation for reactive tactics by\nstriving to maintain this balance across the LOGIC dimensions.\nA cautious tactic could use the balance to bound the\nresponse \u03bc to each utterance \u03bc from \u03b2 by the constraint:\nV\u03b1(\u03bc ) V\u03b2(\u03bc) \u2248 St\n\u03b1\u03b2 \u2297 (N\u03b1(\u03a8t\n) N\u03b2(\u03a8t\n)), where \u2297 is\nelement-by-element matrix multiplication, and St\n\u03b1\u03b2 is the\nstance. A less neurotic tactic could attempt to achieve the\ntarget negotiation balance over the anticipated complete\ndialogue. If a balance bound requires negative information\nrevelation in one LOGIC category then \u03b1 will contribute\nnothing to it, and will leave this to the natural decay to the\nreputation D as described above.\n7. DISCUSSION\nIn this paper we have introduced a novel approach to\nnegotiation that uses information and game-theoretical\nmeasures grounded on business and psychological studies. It\nintroduces the concepts of intimacy and balance as key\nelements in understanding what is a negotiation strategy and\ntactic. Negotiation is understood as a dialogue that affect\nfive basic dimensions: Legitimacy, Options, Goals,\nIndependence, and Commitment. Each dialogical move produces a\nchange in a 2\u00d75 matrix that evaluates the dialogue along five\ninformation-based measures and five utility-based measures.\nThe current Balance and intimacy levels and the desired, or\ntarget, levels are used by the tactics to determine what to\nsay next. We are currently exploring the use of this model as\nan extension of a currently widespread eProcurement\nsoftware commercialised by iSOCO, a spin-off company of the\nlaboratory of one of the authors.\n1036 The Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07)\nIL\n\u03b1(\u03a8t\n) =\nX\n\u03d5\u2208\u03a8t\nCt\n(\u03b1, \u03b2, \u03d5) \u2212 Cs\n(\u03b1, \u03b2, \u03d5) UL\n\u03b1 (\u03a8t\n) =\nX\n\u03d5\u2208\u03a8t\nX\n\u03d5\nPt\n\u03b2(\u03d5 |\u03d5) \u00d7 U\u03b1(\u03d5 )\nIO\n\u03b1 (\u03a8t\n) =\nP\n\u03b4\u2208T t Hs\n(acc(\u03b2, \u03b1, \u03b4)) \u2212\nP\n\u03b4\u2208T t Ht\n(acc(\u03b2, \u03b1, \u03b4))\n|Tt|\nUO\n\u03b1 (\u03a8t\n) =\nX\n\u03b4\u2208T t\nPt\n(acc(\u03b2, \u03b1, \u03b4)) \u00d7\nX\n\u03b4\nPt\n(\u03b4 |\u03b4)U\u03b1(\u03b4 )\nIG\n\u03b1 (\u03a8t\n) =\nP\n\u03c7\u2208N Hs\n(needs(\u03b2, \u03c7)) \u2212 Ht\n(needs(\u03b2, \u03c7))\n|N|\nUG\n\u03b1 (\u03a8t\n) =\nX\n\u03c7\u2208N\nPt\n(needs(\u03b2, \u03c7)) \u00d7 Et\n(U\u03b1(needs(\u03b2, \u03c7)))\nII\n\u03b1(\u03a8t\n) =\nPo\ni=1\nP\n\u03c7\u2208N Hs\n(cho(\u03b2, \u03c7, \u03b2i)) \u2212 Ht\n(cho(\u03b2, \u03c7, \u03b2i))\nn \u00d7 |N|\nUI\n\u03b1(\u03a8t\n) =\noX\ni=1\nX\n\u03c7\u2208N\nUt\n(cho(\u03b2, \u03c7, \u03b2i)) \u2212 Us\n(cho(\u03b2, \u03c7, \u03b2i))\nIC\n\u03b1 (\u03a8t\n) =\nPo\ni=1\nP\n\u03b4\u2208B Hs\n(com(\u03b2, \u03b2i, b)) \u2212 Ht\n(com(\u03b2, \u03b2i, b))\nn \u00d7 |B|\nUC\n\u03b1 (\u03a8t\n) =\noX\ni=1\nX\n\u03b4\u2208B\nUt\n(com(\u03b2, \u03b2i, b)) \u2212 Us\n(com(\u03b2, \u03b2i, b))\nTable 2: Sample measures for each category in V\u03b1(\u03a8t\n). (Similarly for V\u03b2(\u03a8t\n).)\nAcknowledgements Carles Sierra is partially supported\nby the OpenKnowledge European STREP project and by\nthe Spanish IEA Project.\n8. REFERENCES\n[1] Adams, J. S. Inequity in social exchange. In Advances\nin experimental social psychology, L. Berkowitz, Ed.,\nvol. 2. New York: Academic Press, 1965.\n[2] Arcos, J. L., Esteva, M., Noriega, P.,\nRodr\u00b4\u0131guez, J. A., and Sierra, C. Environment\nengineering for multiagent systems. Journal on\nEngineering Applications of Artificial Intelligence 18\n(2005).\n[3] Bazerman, M. H., Loewenstein, G. F., and\nWhite, S. B. Reversal of preference in allocation\ndecisions: judging an alternative versus choosing\namong alternatives. Administration Science Quarterly,\n37 (1992), 220-240.\n[4] Brandenburger, A., and Nalebuff, B.\nCo-Opetition : A Revolution Mindset That Combines\nCompetition and Cooperation. Doubleday, New York,\n1996.\n[5] Cheeseman, P., and Stutz, J. Bayesian Inference\nand Maximum Entropy Methods in Science and\nEngineering. American Institute of Physics, Melville,\nNY, USA, 2004, ch. On The Relationship between\nBayesian and Maximum Entropy Inference, pp.\n445461.\n[6] Debenham, J. Bargaining with information. In\nProceedings Third International Conference on\nAutonomous Agents and Multi Agent Systems\nAAMAS-2004 (July 2004), N. Jennings, C. Sierra,\nL. Sonenberg, and M. Tambe, Eds., ACM Press, New\nYork, pp. 664 - 671.\n[7] Fischer, R., Ury, W., and Patton, B. Getting to\nYes: Negotiating agreements without giving in.\nPenguin Books, 1995.\n[8] Kalfoglou, Y., and Schorlemmer, M. IF-Map:\nAn ontology-mapping method based on\ninformation-flow theory. In Journal on Data\nSemantics I, S. Spaccapietra, S. March, and\nK. Aberer, Eds., vol. 2800 of Lecture Notes in\nComputer Science. Springer-Verlag: Heidelberg,\nGermany, 2003, pp. 98-127.\n[9] Lewicki, R. J., Saunders, D. M., and Minton,\nJ. W. Essentials of Negotiation. McGraw Hill, 2001.\n[10] Li, Y., Bandar, Z. A., and McLean, D. An\napproach for measuring semantic similarity between\nwords using multiple information sources. IEEE\nTransactions on Knowledge and Data Engineering 15,\n4 (July / August 2003), 871 - 882.\n[11] MacKay, D. Information Theory, Inference and\nLearning Algorithms. Cambridge University Press,\n2003.\n[12] Paris, J. Common sense and maximum entropy.\nSynthese 117, 1 (1999), 75 - 93.\n[13] Sierra, C., and Debenham, J. An\ninformation-based model for trust. In Proceedings\nFourth International Conference on Autonomous\nAgents and Multi Agent Systems AAMAS-2005\n(Utrecht, The Netherlands, July 2005), F. Dignum,\nV. Dignum, S. Koenig, S. Kraus, M. Singh, and\nM. Wooldridge, Eds., ACM Press, New York, pp. 497\n- 504.\n[14] Sierra, C., and Debenham, J. Trust and honour in\ninformation-based agency. In Proceedings Fifth\nInternational Conference on Autonomous Agents and\nMulti Agent Systems AAMAS-2006 (Hakodate, Japan,\nMay 2006), P. Stone and G. Weiss, Eds., ACM Press,\nNew York, pp. 1225 - 1232.\n[15] Sierra, C., and Debenham, J. Information-based\nagency. In Proceedings of Twentieth International\nJoint Conference on Artificial Intelligence IJCAI-07\n(Hyderabad, India, January 2007), pp. 1513-1518.\n[16] Sondak, H., Neale, M. A., and Pinkley, R. The\nnegotiated allocations of benefits and burdens: The\nimpact of outcome valence, contribution, and\nrelationship. Organizational Behaviour and Human\nDecision Processes, 3 (December 1995), 249-260.\n[17] Valley, K. L., Neale, M. A., and Mannix, E. A.\nFriends, lovers, colleagues, strangers: The effects of\nrelationships on the process and outcome of\nnegotiations. In Research in Negotiation in\nOrganizations, R. Bies, R. Lewicki, and B. Sheppard,\nEds., vol. 5. JAI Press, 1995, pp. 65-94.\nThe Sixth Intl. Joint Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 1037", "keywords": "set predicate;confidence measure;ontology;view of acceptability;acceptability view;acceptance criterion;component dialogue;long term relationship;utilitarian interpretation;utterance;successive negotiation encounter;negotiation;logic agent architecture;multiagent system;negotiation strategy"}
{"name": "train_J-33", "title": "Bid Expressiveness and Clearing Algorithms in Multiattribute Double Auctions", "abstract": "We investigate the space of two-sided multiattribute auctions, focusing on the relationship between constraints on the offers traders can express through bids, and the resulting computational problem of determining an optimal set of trades. We develop a formal semantic framework for characterizing expressible offers, and show conditions under which the allocation problem can be separated into first identifying optimal pairwise trades and subsequently optimizing combinations of those trades. We analyze the bilateral matching problem while taking into consideration relevant results from multiattribute utility theory. Network flow models we develop for computing global allocations facilitate classification of the problem space by computational complexity, and provide guidance for developing solution algorithms. Experimental trials help distinguish tractable problem classes for proposed solution techniques.", "fulltext": "1. BACKGROUND\nA multiattribute auction is a market-based mechanism where\ngoods are described by vectors of features, or attributes [3, 5, 8,\n19]. Such mechanisms provide traders with the ability to negotiate\nover a multidimensional space of potential deals, delaying\ncommitment to specific configurations until the most promising candidates\nare identified. For example, in a multiattribute auction for\ncomputers, the good may be defined by attributes such as processor speed,\nmemory, and hard disk capacity. Agents have varying preferences\n(or costs) associated with the possible configurations. For example,\na buyer may be willing to purchase a computer with a 2 GHz\nprocessor, 500 MB of memory, and a 50 GB hard disk for a price no\ngreater than $500, or the same computer with 1GB of memory for\na price no greater than $600.\nExisting research in multiattribute auctions has focused\nprimarily on one-sided mechanisms, which automate the process whereby\na single agent negotiates with multiple potential trading partners\n[8, 7, 19, 5, 23, 22]. Models of procurement typically assume\nthe buyer has a value function, v, ranging over the possible\nconfigurations, X, and that each seller i can similarly be associated\nwith a cost function ci over this domain. The role of the auction is\nto elicit these functions (possibly approximate or partial versions),\nand identify the surplus-maximizing deal. In this case, such an\noutcome would be arg maxi,x v(x) \u2212 ci(x). This problem can be\ntranslated into the more familiar auction for a single good without\nattributes by computing a score for each attribute vector based on\nthe seller valuation function, and have buyers bid scores. Analogs\nof the classic first- and second-price auctions correspond to\nfirstand second-score auctions [8, 7].\nIn the absence of a published buyer scoring function, agents on\nboth sides may provide partial specifications of the deals they are\nwilling to engage. Research on such auctions has, for example,\nproduced iterative mechanisms for eliciting cost functions\nincrementally [19]. Other efforts focus on the optimization problem facing\nthe bid taker, for example considering side constraints on the\ncombination of trades comprising an overall deal [4]. Side constraints\nhave also been analyzed in the context of combinatorial auctions\n[6, 20].\nOur emphasis is on two-sided multiattribute auctions, where\nmultiple buyers and sellers submit bids, and the objective is to construct\na set of deals maximizing overall surplus. Previous research on\nsuch auctions includes works by Fink et al. [12] and Gong [14],\nboth of which consider a matching problem for continuous double\nauctions (CDAs), where deals are struck whenever a pair of\ncompatible bids is identified.\nIn a call market, in contrast, bids accumulate until designated\ntimes (e.g., on a periodic or scheduled basis) at which the auction\nclears by determining a comprehensive match over the entire set\nof bids. Because the optimization is performed over an aggregated\nscope, call markets often enjoy liquidity and efficiency advantages\nover CDAs [10].1\nClearing a multiattribute CDA is much like clearing a one-sided\nmultiattribute auction. Because nothing happens between bids, the\nproblem is to match a given new bid (say, an offer to buy) with the\nexisting bids on the other (sell) side. Multiattribute call markets are\npotentially much more complex. Constructing an optimal overall\nmatching may require consideration of many different\ncombina1\nIn the interim between clears, call markets may also disseminate\nprice quotes providing summary information about the state of the\nauction [24]. Such price quotes are often computed based on\nhypothetical clears, and so the clearing algorithm may be invoked more\nfrequently than actual market clearing operations.\n110\ntions of trades, among the various potential trading-partner\npairings. The problem can be complicated by restrictions on overall\nassignments, as expressed in side constraints [16].\nThe goal of the present work is to develop a general framework\nfor multiattribute call markets, to enable investigation of design\nissues and possibilities. In particular, we use the framework to\nexplore tradeoffs between expressive power of agent bids and\ncomputational properties of auction clearing. We conduct our\nexploration independent of any consideration of strategic issues bearing\non mechanism design. As with analogous studies of combinatorial\nauctions [18], we intend that tradeoffs quantified in this work can\nbe combined with incentive factors within a comprehensive overall\napproach to multiattribute auction design.\nWe provide the formal semantics of multiattribute offers in our\nframework in the next section. We abstract, where appropriate,\nfrom the specific language used to express offers, characterizing\nexpressiveness semantically in terms of what deals may be offered.\nThis enables us to identify some general conditions under which\nthe problem of multilateral matching can be decomposed into\nbilateral matching problems. We then develop a family of network\nflow problems that capture corresponding classes of multiattribute\ncall market optimizations. Experimental trials provide preliminary\nconfirmation that the network formulations provide useful structure\nfor implementing clearing algorithms.\n2. MULTIATTRIBUTE OFFERS\n2.1 Basic Definitions\nThe distinguishing feature of a multiattribute auction is that the\ngoods are defined by vectors of attributes, x = (x1, . . . , xm),\nxj \u2208 Xj . A configuration is a particular attribute vector, x \u2208\nX =\nQm\nj=1 Xj . The outcome of the auction is a set of bilateral\ntrades. Trade t takes the form t = (x, q, b, s, \u03c0), signifying that\nagent b buys q > 0 units of configuration x from seller s, for\npayment \u03c0 > 0. For convenience, we use the notation xt to denote the\nconfiguration associated with trade t (and similarly for other\nelements of t). For a set of trades T, we denote by Ti that subset of T\ninvolving agent i (i.e., b = i or s = i). Let T denote the set of all\npossible trades.\nA bid expresses an agent\"s willingness to participate in trades.\nWe specify the semantics of a bid in terms of offer sets. Let OT\ni \u2286\nTi denote agent i\"s trade offer set. Intuitively, this represents the\ntrades in which i is willing to participate. However, since the\noutcome of the auction is a set of trades, several of which may involve\nagent i, we must in general consider willingness to engage in trade\ncombinations. Accordingly, we introduce the combination offer set\nof agent i, OC\ni \u2286 2Ti .\n2.2 Specifying Offer Sets\nA fully expressive bid language would allow specification of\narbitrary combination offer sets. We instead consider a more limited\nclass which, while restrictive, still captures most forms of\nmultiattribute bidding proposed in the literature. Our bids directly specify\npart of the agent\"s trade offer set, and include further directives\ncontrolling how this can be extended to the full trade and combination\noffer sets.\nFor example, one way to specify a trade (buy) offer set would\nbe to describe a set of configurations and quantities, along with the\nmaximal payment one would exchange for each (x, q) specified.\nThis description could be by enumeration, or any available means\nof defining such a mapping.\nAn explicit set of trades in the offer set generally entails inclusion\nof many more implicit trades. We assume payment monotonicity,\nwhich means that agents always prefer more money. That is, for\n\u03c0 > \u03c0 > 0,\n(x, q, i, s, \u03c0) \u2208 OT\ni \u21d2 (x, q, i, s, \u03c0 ) \u2208 OT\ni ,\n(x, q, b, i, \u03c0 ) \u2208 OT\ni \u21d2 (x, q, b, i, \u03c0) \u2208 OT\ni .\nWe also assume free disposal, which dictates that for all i, q >\nq > 0,\n(x, q , i, s, \u03c0) \u2208 OT\ni \u21d2 (x, q, i, s, \u03c0) \u2208 OT\ni ,\n(x, q, b, i, \u03c0) \u2208 OT\ni \u21d2 (x, q , b, i, \u03c0) \u2208 OT\ni .\nNote that the conditions for agents in the role of buyers and sellers\nare analogous. Henceforth, for expository simplicity, we present\nall definitions with respect to buyers only, leaving the definition\nfor sellers as understood. Allowing agents\" bids to comprise offers\nfrom both buyer and seller perspectives is also straightforward.\nAn assertion that offers are divisible entails further implicit\nmembers in the trade offer set.\nDEFINITION 1 (DIVISIBLE OFFER). Agent i\"s offer is\ndivisible down to q iff\n\u2200q < q < q. (x, q, i, s, \u03c0) \u2208 OT\ni \u21d2 (x, q , i, s, q\nq\n\u03c0) \u2208 OT\ni .\nWe employ the shorthand divisible to mean divisible down to 0.\nThe definition above specifies arbitrary divisibility. It would\nlikewise be possible to define divisibility with respect to integers, or to\nany given finite granularity. Note that when offers are divisible, it\nsuffices to specify one offer corresponding to the maximal quantity\none is willing to trade for any given configuration, trading partner,\nand per-unit payment (called the price).\nAt the extreme of indivisibility are all-or-none offers.\nDEFINITION 2 (AON OFFER). Agent i\"s offer is all-or-none\n(AON) iff\n(x, q, i, s, \u03c0) \u2208 OT\ni \u2227 (x, q , i, s, \u03c0 ) \u2208 OT\ni \u21d2 [q = q \u2228 \u03c0 = \u03c0 ].\nIn many cases, the agent will be indifferent with respect to\ndifferent trading partners. In that event, it may omit the partner element\nfrom trades directly specified in its offer set, and simply assert that\nits offer is anonymous.\nDEFINITION 3 (ANONYMITY). Agent i\"s offer is anonymous\niff \u2200s, s , b, b . (x, q, i, s, \u03c0) \u2208 OT\ni \u21d4 (x, q, i, s , \u03c0) \u2208 OT\ni \u2227\n(x, q, b, i, \u03c0) \u2208 OT\ni \u21d4 (x, q, b , i, \u03c0) \u2208 OT\ni .\nBecause omitting trading partner qualifications simplifies the\nexposition, we generally assume in the following that all offers are\nanonymous unless explicitly specified otherwise. Extending to the\nnon-anonymous case is conceptually straightforward. We employ\nthe wild-card symbol \u2217 in place of an agent identifier to indicate\nthat any agent is acceptable.\nTo specify a trade offer set, a bidder directly specifies a set of\nwilling trades, along with any regularity conditions (e.g.,\ndivisibility, anonymity) that implicitly extend the set. The full trade offer\nset is then defined by the closure of this direct set with respect to\npayment monotonicity, free disposal, and any applicable\ndivisibility assumptions.\nWe next consider the specification of combination offer sets.\nWithout loss of generality, we restrict each trade set T \u2208 OC\ni to\ninclude at most one trade for any combination of configuration and\ntrading partner (multiple such trades are equivalent to one net trade\naggregating the quantities and payments). The key question is to\nwhat extent the agent is willing to aggregate deals across\nconfigurations or trading partners. One possibility is disallowing any\naggregation.\n111\nDEFINITION 4 (NO AGGREGATION). The no-aggregation\ncombinations are given by ONA\ni = {\u2205} \u222a {{t} | t \u2208 OT\ni }. Agent i\"s\noffer exhibits non-aggregation iff OC\ni = ONA\ni .\nWe require in general that OC\ni \u2287 ONA\ni .\nA more flexible policy is to allow aggregation across trading\npartners, keeping configuration constant.\nDEFINITION 5 (PARTNER AGGREGATION). Suppose a\nparticular trade is offered in the same context (set of additional trades,\nT) with two different sellers, s and s . That is,\n{(x, q, i, s, \u03c0)} \u222a T \u2208 OC\ni \u2227 {(x, q, i, s , \u03c0)} \u222a T \u2208 OC\ni .\nAgent i\"s offer allows seller aggregation iff in all such cases,\n{(x, q , i, s, \u03c0 ), (x, q \u2212 q , i, s , \u03c0 \u2212 \u03c0 )} \u222a T \u2208 OC\ni .\nIn other words, we may create new trade offer combinations by\nsplitting the common trade (quantity and payment, not necessarily\nproportionately) between the two sellers.\nIn some cases, it might be reasonable to form combinations by\naggregating different configurations.\nDEFINITION 6 (CONFIGURATION AGGREGATION). Suppose\nagent i offers, in the same context, the same quantity of two (not\nnecessarily different) configurations, x and x . That is,\n{(x, q, i, \u2217, \u03c0)} \u222a T \u2208 OC\ni \u2227 {(x , q, i, \u2217, \u03c0 )} \u222a T \u2208 OC\ni .\nAgent i\"s offer allows configuration aggregation iff in all such cases\n(and analogously when it is a seller),\n{(x, q , i, \u2217,\nq\nq\n\u03c0), (x , q \u2212 q , i, \u2217,\nq \u2212 q\nq\n\u03c0 )} \u222a T \u2208 OC\ni .\nNote that combination offer sets can accommodate offerings of\nconfiguration bundles. However, classes of bundles formed by\npartner or configuration aggregation are highly regular, covering only a\nspecific type of bundle formed by splitting a desired quantity across\nconfigurations. This is quite restrictive compared to the general\ncombinatorial case.\n2.3 Willingness to Pay\nAn agent\"s offer trade set implicitly defines the agent\"s\nwillingness to pay for any given configuration and quantity. We assume\nanonymity to avoid conditioning our definitions on trading partner.\nDEFINITION 7 (WILLINGNESS TO PAY). Agent i\"s willingness\nto pay for quantity q of configuration x is given by\n\u02c6uB\ni (x, q) = max \u03c0 s.t. (x, q, i, \u2217, \u03c0) \u2208 OT\ni .\nWe use the symbol \u02c6u to recognize that willingness to pay can be\nviewed as a proxy for the agent\"s utility function, measured in\nmonetary units. The superscript B distinguishes the buyer\"s\nwillingnessto-pay function from, a seller\"s willingness to accept, \u02c6uS\ni (x, q),\ndefined as the minimum payment seller i will accept for q units of\nconfiguration x. We omit the superscript where the distinction is\ninessential or clear from context.\nDEFINITION 8 (TRADE QUANTITY BOUNDS). Agent i\"s\nminimum trade quantity for configuration x is given by\nqi(x) = min q s.t. \u2203\u03c0. (x, q, i, \u2217, \u03c0) \u2208 OT\ni .\nThe agent\"s maximum trade quantity for x is\n\u00afqi(x) = max q s.t.\n\u2203\u03c0. (x, q, i, \u2217, \u03c0) \u2208 OT\ni \u2227 \u00ac\u2203q < q. (x, q , i, \u2217, \u03c0) \u2208 OT\ni .\nWhen the agent has no offers involving x, we take qi(x) = \u00afqi(x) =\n0.\nIt is useful to define a special case where all configurations are\noffered in the same quantity range.\nDEFINITION 9 (CONFIGURATION PARITY). Agent i\"s offers\nexhibit configuration parity iff\nqi(x) > 0 \u2227 qi(x ) > 0 \u21d2 qi(x) = qi(x ) \u2227 \u00afqi(x) = \u00afqi(x ).\nUnder configuration parity we drop the arguments from trade\nquantity bounds, yielding the constants \u00afq and q which apply to all offers.\nDEFINITION 10 (LINEAR PRICING). Agent i\"s offers exhibit\nlinear pricing iff for all qi(x) \u2264 q \u2264 \u00afqi(x),\n\u02c6ui(x, q) =\nq\n\u00afqi(x)\n\u02c6ui(x, \u00afqi(x)).\nNote that linear pricing assumes divisibility down to qi(x). Given\nlinear pricing, we can define the unit willingness to pay, \u02c6ui(x) =\n\u02c6ui(x, \u00afqi(x))/\u00afqi(x), and take \u02c6ui(x, q) = q\u02c6ui(x) for all qi(x) \u2264\nq \u2264 \u00afqi(x).\nIn general, an agent\"s willingness to pay may depend on a context\nof other trades the agent is engaging in.\nDEFINITION 11 (WILLINGNESS TO PAY IN CONTEXT). Agent\ni\"s willingness to pay for quantity q of configuration x in the\ncontext of other trades T is given by\n\u02c6uB\ni (x, q; T) = max \u03c0 s.t. {(x, q, i, s, \u03c0)} \u222a Ti \u2208 OC\ni .\nLEMMA 1. If OC\ni is either non aggregating, or exhibits linear\npricing, then\n\u02c6uB\ni (x, q; T) = \u02c6uB\ni (x, q).\n3. MULTIATTRIBUTE ALLOCATION\nDEFINITION 12 (TRADE SURPLUS). The surplus of trade t =\n(x, q, b, s, \u03c0) is given by\n\u03c3(t) = \u02c6uB\nb (x, q) \u2212 \u02c6uS\ns (x, q).\nNote that the trade surplus does not depend on the payment, which\nis simply a transfer from buyer to seller.\nDEFINITION 13 (TRADE UNIT SURPLUS). The unit surplus\nof trade t = (x, q, b, s, \u03c0) is given by \u03c31\n(t) = \u03c3(t)/q.\nUnder linear pricing, we can equivalently write \u03c31\n(t) = \u02c6uB\nb (x) \u2212\n\u02c6uS\ns (x).\nDEFINITION 14 (SURPLUS OF A TRADE IN CONTEXT). The\nsurplus of trade t = (x, q, b, s, \u03c0) in the context of other trades T,\n\u03c3(t; T), is given by\n\u02c6uB\nb (x, q; T) \u2212 \u02c6uS\ns (x, q; T).\nDEFINITION 15 (GMAP). The Global Multiattribute\nAllocation Problem (GMAP) is to find the set of acceptable trades\nmaximizing total surplus,\nmax\nT \u22082T\nX\nt\u2208T\n\u03c3(t; T \\ {t}) s.t. \u2200i. Ti \u2208 OC\ni .\nDEFINITION 16 (MMP). The Multiattribute Matching\nProblem (MMP) is to find a best trade for a given pair of traders,\nMMP(b, s) = arg max\nt\u2208OT\nb\n\u2229OT\ns\n\u03c3(t).\nIf OT\nb \u2229 OT\ns is empty, we say that MMP has no solution.\n112\nProofs of all the following results are provided in an extended\nversion of this paper available from the authors.\nTHEOREM 2. Suppose all agents\" offers exhibit no aggregation\n(Definition 4). Then the solution to GMAP consists of a set of\ntrades, each of which is a solution to MMP for its specified pair\nof traders.\nTHEOREM 3. Suppose that each agent\"s offer set satisfies one\nof the following (not necessarily the same) sets of conditions.\n1. No aggregation and configuration parity (Definitions 4 and 9).\n2. Divisibility, linear pricing, and configuration parity\n(Definitions 1, 10, and 9), with combination offer set defined as the\nminimal set consistent with configuration aggregation\n(Definition 6).2\nThen the solution to GMAP consists of a set of trades, each of\nwhich employs a configuration that solves MMP for its specified\npair of traders.\nLet MMPd\n(b, s) denote a modified version of MMP, where OT\nb\nand OT\ns are extended to assume divisibility (i.e., the offer sets are\ntaken to be their closures under Definition 1). Then we can extend\nTheorem 3 to allow aggregating agents to maintain AON or\nminquantity offers as follows.\nTHEOREM 4. Suppose offer sets as in Theorem 3, except that\nagents i satisfying configuration aggregation need be divisible only\ndown to qi, rather than down to 0. Then the solution to GMAP\nconsists of a set of trades, each of which employs the same\nconfiguration as a solution to MMPd\nfor its specified pair of traders.\nTHEOREM 5. Suppose agents b and s exhibit configuration\nparity, divisibility, and linear pricing, and there exists configuration x\nsuch that \u02c6ub(x) \u2212 \u02c6us(x) > 0. Then t \u2208 MMPd\n(b, s) iff\nxt = arg max\nx\n{\u02c6ub(x) \u2212 \u02c6us(x)}\nqt = min(\u00afqb, \u00afqs).\n(1)\nThe preceding results signify that under certain conditions, we\ncan divide the global optimization problem into two parts: first find\na bilateral trade that maximizes unit surplus for each pair of traders\n(or total surplus in the non-aggregation case), and then use the\nresults to find a globally optimal set of trades. In the following two\nsections we investigate each of these subproblems.\n4. UTILITY REPRESENTATION AND MMP\nWe turn next to consider the problem of finding a best deal\nbetween pairs of traders. The complexity of MMP depends pivotally\non the representation by bids of offer sets, an issue we have\npostponed to this point.\nNote that issues of utility representation and MMP apply to a\nbroad class of multiattribute mechanisms, beyond the multiattribute\ncall markets we emphasize. For example, the complexity results\ncontained in this section apply equally to the bidding problem faced\nby sellers in reverse auctions, given a published buyer scoring\nfunction.\nThe simplest representation of an offer set is a direct\nenumeration of configurations and associated quantities and payments. This\napproach treats the configurations as atomic entities, making no use\n2\nThat is, for such an agent i, OC\ni is the closure under configuration\naggregation of ONA\ni .\nof attribute structure. A common and inexpensive enhancement is\nto enable a trader to express sets of configurations, by specifying\nsubsets of the domains of component attributes. Associating a\nsingle quantity and payment with a set of configurations expresses\nindifference among them; hence we refer to such a set as an\nindifference range.3\nIndifference ranges include the case of attributes\nwith a natural ordering, in which a bid specifies a minimum or\nmaximum acceptable attribute level. The use of indifference ranges\ncan be convenient for MMP. The compatibility of two indifference\nranges is simply found by testing set intersection for each attribute,\nas demonstrated by the decision-tree algorithm of Fink et al. [12].\nAlternatively, bidders may specify willingness-to-pay functions\n\u02c6u in terms of compact functional forms. Enumeration based\nrepresentations, even when enhanced with indifference ranges, are\nultimately limited by the exponential size of attribute space.\nFunctional forms may avoid this explosion, but only if \u02c6u reflects\nstructure among the attributes. Moreover, even given a compact\nspecification of \u02c6u, we gain computational benefits only if we can\nperform the matching without expanding the \u02c6u values of an\nexponential number of configuration points.\n4.1 Additive Forms\nOne particularly useful multiattribute representation is known as\nthe additive scoring function. Though this form is widely used in\npractice and in the academic literature, it is important to stress the\nassumptions behind it. The theory of multiattribute representation\nis best developed in the context where \u02c6u is interpreted as a\nutility function representing an underlying preference order [17]. We\npresent the premises of additive utility theory in this section, and\ndiscuss some generalizations in the next.\nDEFINITION 17. A set of attributes Y \u2282 X is preferentially\nindependent (PI) of its complement Z = X \\ Y if the conditional\npreference order over Y given a fixed level Z0\nof Z is the same\nregardless of the choice of Z0\n.\nIn other words, the preference order over the projection of X on\nthe attributes in Y is the same for any instantiation of the attributes\nin Z.\nDEFINITION 18. X = {x1, . . . , xm} is mutually preferentially\nindependent (MPI) if any subset of X is preferentially independent\nof its complement.\nTHEOREM 6 ([9]). A preference order over set of attributes\nX has an additive utility function representation\nu(x1, . . . , xm) =\nmX\ni=1\nui(xi)\niff X is mutually preferential independent.\nA utility function over outcomes including money is quasi-linear\nif the function can be represented as a function over non-monetary\nattributes plus payments, \u03c0. Interpreting \u02c6u as a utility function over\nnon-monetary attributes is tantamount to assuming quasi-linearity.\nEven when quasi-linearity is assumed, however, MPI over\nnonmonetary attributes is not sufficient for the quasi-linear utility\nfunction to be additive. For this, we also need that each of the pairs\n(\u03c0, Xi) for any attribute Xi would be PI of the rest of the attributes.\n3\nThese should not be mistaken with indifference curves, which\nexpress dependency between the attributes. Indifference curves can\nbe expressed by the more elaborate utility representations discussed\nbelow.\n113\nThis (by MAUT) in turn implies that the set of attributes including\nmoney is MPI and the utility function can be represented as\nu(x1, . . . , xm, \u03c0) =\nmX\ni=1\nui(xi) + \u03c0.\nGiven that form, a willingness-to-pay function reflecting u can be\nrepresented additively, as\n\u02c6u(x) =\nmX\ni=1\nui(xi)\nIn many cases the additivity assumption provides practically\ncrucial simplification of offer set elicitation. In addition to\ncompactness, additivity dramatically simplifies MMP. If both sides provide\nadditive \u02c6u representations, the globally optimal match reduces to\nfinding the optimal match separately for each attribute.\nA common scenario in procurement has the buyer define an\nadditive scoring function, while suppliers submit enumerated offer\npoints or indifference ranges. This model is still very amenable to\nMMP: for each element in a supplier\"s enumerated set, we optimize\neach attribute by finding the point in the supplier\"s allowable range\nthat is most preferred by the buyer.\nA special type of scoring (more particularly, cost) function was\ndefined by Bichler and Kalagnanam [4] and called a configurable\noffer. This idea is geared towards procurement auctions: assuming\nsuppliers are usually comfortable with expressing their preferences\nin terms of cost that is quasi-linear in every attribute, they can\nspecify a price for a base offer, and additional cost for every change in\na specific attribute level. This model is essentially a pricing out\napproach [17]. For this case, MMP can still be optimized on a\nper-attribute basis. A similar idea has been applied to one-sided\niterative mechanisms [19], in which sellers refine prices on a\nperattribute basis at each iteration.\n4.2 Multiattribute Utility Theory\nUnder MPI, the tradeoffs between the attributes in each subset\ncannot be affected by the value of other attributes. For example,\nwhen buying a PC, a weaker CPU may increase the importance of\nthe RAM compared to, say, the type of keyboard. Such\nrelationships cannot be expressed under an additive model.\nMultiattribute utility theory (MAUT) develops various compact\nrepresentations of utility functions that are based on weaker\nstructural assumptions [17, 2]. There are several challenges in adapting\nthese techniques to multiattribute bidding. First, as noted above,\nthe theory is developed for utility functions, which may behave\ndifferently from willingness-to-pay functions. Second, computational\nefficiency of matching has not been an explicit goal of most work\nin the area. Third, adapting such representations to iterative\nmechanisms may be more challenging.\nOne representation that employs somewhat weaker assumptions\nthan additivity, yet retains the summation structure is the\ngeneralized additive (GA) decomposition:\nu(x) =\nJX\nj=1\nfj(xj\n), xj\n\u2208 Xj\n, (2)\nwhere the Xj\nare potentially overlapping sets of attributes, together\nexhausting the space X.\nA key point from our perspective is that the complexity of the\nmatching is similar to the complexity of optimizing a single\nfunction, since the sum function is in the form (2) as well. Recent work\nby Gonzales and Perny [15] provides an elicitation process for GA\ndecomposable preferences under certainty, as well as an\noptimization algorithm for the GA decomposed function. The complexity of\nexact optimization is exponential in the induced width of the graph.\nHowever, to become operational for multiattribute bidding this\ndecomposition must be detectable and verifiable by statements over\npreferences with respect to price outcomes. We are exploring this\ntopic in ongoing work [11].\n5. SOLVING GMAP UNDER ALLOCATION\nCONSTRAINTS\nTheorems 2, 3, and 4 establish conditions under which GMAP\nsolutions must comprise elements from constituent MMP solutions.\nIn Sections 5.1 and 5.2, we show how to compute these GMAP\nsolutions, given the MMP solutions, under these conditions. In these\nsettings, traders that aggregate partners also aggregate\nconfigurations; hence we refer to them simply as aggregating or\nnonaggregating. Section 5.3 suggests a means to relax the linear\npricing restriction employed in these constructions. Section 5.4\nprovides strategies for allowing traders to aggregate partners and\nrestrict configuration aggregation at the same time.\n5.1 Notation and Graphical Representation\nOur clearing algorithms are based on network flow formulations\nof the underlying optimization problem [1]. The network model is\nbased on a bipartite graph, in which nodes on the left side represent\nbuyers, and nodes on the right represent sellers. We denote the sets\nof buyers and sellers by B and S, respectively.\nWe define two graph families, one for the case of non-aggregating\ntraders (called single-unit), and the other for the case of\naggregating traders (called multi-unit).4\nFor both types, a single directed\narc is placed from a buyer i \u2208 B to a seller j \u2208 S if and only if\nMMP(i, j) is nonempty. We denote by T(i) the set of potential\ntrading partners of trader i (i.e., the nodes connected to buyer or\nseller i in the bipartite graph.\nIn the single-unit case, we define the weight of an arc (i, j) as\nwij = \u03c3(MMP(i, j)). Note that free disposal lets a buy offer\nreceive a larger quantity than desired (and similarly for sell offers).\nFor the multi-unit case, the weights are wij = \u03c31\n(MMP(i, j)),\nand we associate the quantity \u00afqi with the node for trader i. We also\nuse the notation qij for the mathematical formulations to denote\npartial fulfillment of qt for t = MMP(i, j).\n5.2 Handling Indivisibility and Aggregation\nConstraints\nUnder the restrictions of Theorems 2, 3, or 4, and when the\nsolution to MMP is given, GMAP exhibits strong similarity to the\nproblem of clearing double auctions with assignment constraints\n[16]. A match in our bipartite representation corresponds to a\npotential trade in which assignment constraints are satisfied. Network\nflow formulations have been shown to model this problem under\nthe assumption of indivisibility and aggregation for all traders. The\nnovelty in this part of our work is the use of generalized network\nflow formulations for more complex cases where aggregation and\ndivisibility may be controlled by traders.\nInitially we examine the simple case of no aggregation\n(Theorem 2). Observe that the optimal allocation is simply the solution\nto the well known weighted assignment problem [1] on the\nsingleunit bipartite graph described above. The set of matches that\nmaximizes the total weight of arcs corresponds to the set of trades that\nmaximizes total surplus. Note that any form of (in)divisibility can\n4\nIn the next section, we introduce a hybrid form of graph\naccommodating mixes of the two trader categories.\n114\nalso be accommodated in this model via the constituent MMP\nsubproblems.\nThe next formulation solves the case in which all traders fall\nunder case 2 of Theorem 3-that is, all traders are aggregating and\ndivisible, and exhibit linear pricing. This case can be represented\nusing the following linear program, corresponding to our multi-unit\ngraph:\nmax\nX\ni\u2208B,j\u2208S\nwij qij\ns.t.\nX\ni\u2208T (j)\nqij \u2264 \u00afqj j \u2208 S\nX\nj\u2208T (i)\nqij \u2264 \u00afqi i \u2208 B\nqij \u2265 0 j \u2208 S, i \u2208 B\nRecall that the qij variables in the solution represent the number\nof units that buyer i procures from seller j. This formulation is\nknown as the network transportation problem with inequality\nconstraints, for which efficient algorithms are available [1]. It is a\nwell known property of the transportation problem (and flow\nproblems on pure networks in general) that given integer input values,\nthe optimal solution is guaranteed to be integer as well. Figure 1\ndemonstrates the transformation of a set of bids to a transportation\nproblem instance.\nFigure 1: Multi-unit matching with two boolean attributes.\n(a) Bids, with offers to buy in the left column and offers to\nsell at right. q@p indicates an offer to trade q units at price p\nper unit. Configurations are described in terms of constraints\non attribute values. (b) Corresponding multi-unit assignment\nmodel. W represents arc weights (unit surplus), s represents\nsource (exogenous) flow, and t represents sink quantity.\nThe problem becomes significantly harder when aggregation is\ngiven as an option to bidders, requiring various enhancements to\nthe basic multi-unit bipartite graph described above. In general,\nwe consider traders that are either aggregating or not, with either\ndivisible or AON offers.\nInitially we examine a special case, which at the same time\ndemonstrates the hardness of the problem but still carries computational\nadvantages. We designate one side (e.g., buyers) as restrictive (AON\nand non-aggregating), and the other side (sellers) as unrestrictive\n(divisible and aggregating). This problem can be represented using\nthe following integer programming formulation:\nmax\nX\ni\u2208B,j\u2208S\nwij qij\ns.t.\nX\ni\u2208T (j)\n\u00afqiqij \u2264 \u00afqj j \u2208 S\nX\nj\u2208T (i)\nqij \u2264 1 i \u2208 B\nqij \u2208 {0, 1} j \u2208 S, i \u2208 B\n(3)\nThis formulation is a restriction of the generalized assignment\nproblem (GAP) [13]. Although GAP is known to be NP-hard, it can\nbe solved relatively efficiently by exact or approximate algorithms.\nGAP is more general than the formulation above as it allows\nbuyside quantities (\u00afqi above) to be different for each potential seller.\nThat this formulation is NP-hard as well (even the case of a single\nseller corresponds to the knapsack problem), illustrates the drastic\nincrease in complexity when traders with different constraints are\nadmitted to the same problem instance.\nOther than the special case above, we found no advantage in\nlimiting AON constraints when traders may specify aggregation\nconstraints. Therefore, the next generalization allows any combination\nof the two boolean constraints, that is, any trader chooses among\nfour bid types:\nNI Bid AON and not aggregating.\nAD Bid allows aggregation and divisibility.\nAI Bid AON, allows aggregation (quantity can be aggregated across\nconfigurations, as long as it sums to the whole amount).\nND No aggregation, divisibility (one trade, but smaller quantities\nare acceptable).\nTo formulate an integer programming representation for the\nproblem, we introduce the following variables. Boolean (0/1) variables\nri and rj indicate whether buyer i and seller j participate in the\nsolution (used for AON traders). Another indicator variable, yij ,\napplied to non-aggregating buyer i and seller j, is one iff i trades\nwith j. For aggregating traders, yij is not constrained.\nmax\nX\ni\u2208B,j\u2208S\nWij qij (4a)\ns.t.\nX\nj\u2208T (i)\nqij = \u00afqiri i \u2208 AIb (4b)\nX\nj\u2208T (i)\nqij \u2264 \u00afqiri i \u2208 ADb (4c)\nX\ni\u2208T (j)\nqij = \u00afqirj j \u2208 AIs (4d)\nX\ni\u2208T (j)\nqij \u2264 qj rj j \u2208 ADs (4e)\nxij \u2264 \u00afqiyij i \u2208 NDb , j \u2208 T(i) (4f)\nxij \u2264 \u00afqj yij j \u2208 NIs , i \u2208 T(j) (4g)\nX\nj\u2208T (i)\nyij \u2264 ri i \u2208 NIb \u222a NDb (4h)\nX\ni\u2208T (j)\nyij \u2264 rj j \u2208 NIs \u222a NDs (4i)\nint qij (4j)\nyij , rj, ri \u2208 {0, 1} (4k)\n115\nFigure 2: Generalized network flow model. B1 is a buyer in\nAD, B2 \u2208 NI, B3 \u2208 AI, B4 \u2208 ND. V 1 is a seller in ND,\nV 2 \u2208 AI, V 4 \u2208 AD. The g values represent arc gains.\nProblem (4) has additional structure as a generalized min-cost\nflow problem with integral flow.5\nA generalized flow network is\na network in which each arc may have a gain factor, in addition\nto the pure network parameters (which are flow limits and costs).\nFlow in an arc is then multiplied by its gain factor, so that the flow\nthat enters the end node of an arc equals the flow that entered from\nits start node, multiplied by the gain factor of the arc. The network\nmodel can in turn be translated into an IP formulation that captures\nsuch structure.\nThe generalized min-cost flow problem is well-studied and has\na multitude of efficient algorithms [1]. The faster algorithms are\npolynomial in the number of arcs and the logarithm of the maximal\ngain, that is, performance is not strongly polynomial but is\npolynomial in the size of the input. The main benefit of this graphical\nformulation to our matching problem is that it provides a very\nefficient linear relaxation. Integer programming algorithms such as\nbranch-and-bound use solutions to the linear relaxation instance to\nbound the optimal integer solution. Since network flow algorithms\nare much faster than arbitrary linear programs (generalized network\nflow simplex algorithms have been shown to run in practice only 2\nor 3 times slower than pure network min-cost flow [1]), we expect\na branch-and-bound solver for the matching problem to show\nimproved performance when taking advantage of network flow\nmodeling.\nThe network flow formulation is depicted in Figure 2.\nNonrestrictive traders are treated as in Figure 1. For a non-aggregating\nbuyer, a single unit from the source will saturate up to one of the\nyij for all j, and be multiplied by \u00afqi. If i \u2208 ND, the end node of\nyij will function as a sink that may drain up to \u00afqi of the entering\nflow. For i \u2208 NI we use an indicator (0/1) arc ri, on which the\nflow is multiplied by \u00afqi. Trader i trades the full quantity iff ri = 1.\nAt the seller side, the end node of a qij arc functions as a source\nfor sellers j \u2208 ND, in order to let the flow through yij\narcs be 0\nor \u00afqj. The flow is then multiplied by 1\n\u00afqj\nso 0/1 flows enter an end\nnode which can drain either 1 or 0 units. for sellers j \u2208 NI arcs rj\nensure AON similarly to arcs rj for buyers.\nHaving established this framework, we are ready to\naccommo5\nConstraint (4j) could be omitted (yielding computational savings)\nif non-integer quantities are allowed. Here and henceforth we\nassume the harder problem, where divisibility is with respect to\nintegers.\ndate more flexible versions of side constraints. The first\ngeneralization is to replace the boolean AON constraint with divisibility down\nto q, the minimal quantity. In our network flow instance we simply\nneed to turn the node of the constrained trader i (e.g., the node B3\nin Figure 2) to a sink that can drain up to \u00afqi \u2212 qi units of flow. The\ninteger program (4) can be also easily changed to accommodate\nthis extension.\nUsing gains, we can also apply batch size constraints. If a trader\nspecifies a batch size \u03b2, we change the gain on the r arcs to \u03b2, and\nset the available flow of its origin to the maximal number of batches\n\u00afqi/\u03b2.\n5.3 Nonlinear Pricing\nA key assumption in handling aggregation up to this point is\nlinear pricing, which enables us to limit attention to a single unit\nprice. Divisibility without linear pricing allows expression of\nconcave willingness-to-pay functions, corresponding to convex\npreference relations. Bidders may often wish to express non-convex offer\nsets, for example, due to fixed costs or switching costs in\nproduction settings [21].\nWe consider nonlinear pricing in the form of enumerated\npayment schedules-that is, defining values \u02c6u(x, q) for a select set of\nquantities q. For the indivisible case, these points are distinguished\nin the offer set by satisfying the following:\n\u2203\u03c0. (x, q, i, \u2217, \u03c0) \u2208 OT\ni \u2227 \u00ac\u2203q < q. (x, q , i, \u2217, \u03c0) \u2208 OT\ni .\n(cf. Definition 8, which defines the maximum quantity, \u00afq, as the\nlargest of these.) For the divisible case, the distinguished quantities\nare those where the unit price changes, which can be formalized\nsimilarly.\nTo handle nonlinear pricing, we augment the network to include\nflow possibilities corresponding to each of the enumerated\nquantities, plus additional structure to enforce exclusivity among them.\nIn other words, the network treats the offer for a given quantity as\nin Section 5.2, and embeds this in an XOR relation to ensure that\neach trader picks only one of these quantities. Since for each such\nquantity choice we can apply Theorem 3 or 4, the solution we get\nis in fact the solution to GMAP.\nThe network representation of the XOR relation (which can be\nembedded into the network of Figure 2) is depicted in Figure 3. For\na trader i with K XOR quantity points, we define dummy variables,\nzk\ni , k = 1, . . . , K. Since we consider trades between every pair\nof quantity points we also have qk\nij\n, k = 1, . . . , K. For buyer\ni \u2208 AI with XOR points at quantities \u00afqk\ni , we replace (4b) with the\nfollowing constraints:\nX\nj\u2208T (i)\nqk\nij\n= \u00afqk\ni zk\ni k = 1, . . . , K\nKX\nk=1\nzk\ni = ri\nzk\ni \u2208 {0, 1} k = 1, . . . , K\n(5)\n5.4 Homogeneity Constraints\nThe model (4) handles constraints over the aggregation of\nquantities from different trading partners. When aggregation is allowed,\nthe formulation permits trades involving arbitrary combinations of\nconfigurations. A homogeneity constraint [4] restricts such\ncombinations, by requiring that configurations aggregated in an overall\ndeal must agree on some or all attributes.\n116\nFigure 3: Extending the network flow model to express an XOR\nover quantities. B2 has 3 XOR points for 6, 3, or 5 units.\nIn the presence of homogeneity constraints, we can no longer\napply the convenient separation of GMAP into MMP plus global\nbipartite optimization, as the solution to GMAP may include trades\nnot part of any MMP solution. For example, let buyer b specify\nan offer for maximum quantity 10 of various acceptable\nconfigurations, with a homogeneity constraint over the attribute color.\nThis means b is willing to aggregate deals over different trading\npartners and configurations, as long as all are the same color. If\nseller s can provide 5 blue units or 5 green units, and seller s can\nprovide only 5 green units, we may prefer that b and s trade on\ngreen units, even if the local surplus of a blue trade is greater.\nLet {x1, . . . , xH} be attributes that some trader constrains to\nbe homogeneous. To preserve the network flow framework, we\nneed to consider, for each trader, every point in the product domain\nof these homogeneous attributes. Thus, for every assignment \u02c6x\nto the homogeneous attributes, we compute MMP(b, s) under the\nconstraint that configurations are consistent with \u02c6x. We apply the\nsame approach as in Section 5.3: solve the global optimization,\nsuch that the alternative \u02c6x assignments for each trader are combined\nunder XOR semantics, thus enforcing homogeneity constraints.\nThe size of this network is exponential in the number of\nhomogeneous attributes, since we need a node for each point in the product\ndomain of all the homogeneous attributes of each trader.6\nHence\nthis solution method will only be tractable in applications were the\ntraders can be limited to a small number of homogeneous attributes.\nIt is important to note that the graph needs to include a node only\nfor each point that potentially matches a point of the other side. It\nis therefore possible to make the problem tractable by limiting one\nof the sides to a less expressive bidding language, and by that limit\nthe set of potential matches. For example, if sellers submit bounded\nsets of XOR points, we only need to consider the points in the\ncombined set offered by the sellers, and the reduction to network flow\nis polynomial regardless of the number of homogeneous attributes.\nIf such simplifications do not apply, it may be preferable to solve\nthe global problem directly as a single optimization problem. We\nprovide the formulation for the special case of divisibility (with\nrespect to integers) and configuration parity. Let i index buyers, j\nsellers, and H homogeneous attributes. Variable xh\nij\n\u2208 Xh\nrepresents the value of attribute Xh in the trade between buyer i and\nseller j. Integer variable qij represents the quantity of the trade\n(zero for no trade) between i and j.\n6\nIf traders differ on which attributes they express such constraints,\nwe can limit consideration to the relevant alternatives. The\ncomplexity will still be exponential, but in the maximum number of\nhomogeneous attributes for any pair of traders.\nmax\nX\ni\u2208B,j\u2208S\n[\u02c6uB\ni (xij , qij ) \u2212 \u02c6uS\nj (xij , qij )]\nX\nj\u2208S\nqij \u2264 \u00afqi i \u2208 B\nX\ni\u2208B\nqij \u2264 \u00afqj j \u2208 S\nxh\n1j\n= xh\n2j\n= \u00b7 \u00b7 \u00b7 = x|B|j\nj \u2208 S, h \u2208 {1, . . . , H}\nxh\ni1\n= xh\ni2\n= \u00b7 \u00b7 \u00b7 = xi|S|\ni \u2208 B, h \u2208 {1, . . . , H}\n(6)\nTable 1 summarizes the mapping we presented from allocation\nconstraints to the complexity of solving GMAP. Configuration\nparity is assumed for all cases but the first.\n6. EXPERIMENTAL RESULTS\nWe approach the experimental aspect of this work with two\nobjectives. First, we seek a general idea of the sizes and types of\nclearing problems that can be solved under given time constraints. We\nalso look to compare the performance of a straightforward integer\nprogram as in (4) with an integer program that is based on the\nnetwork formulations developed here. Since we used CPLEX, a\ncommercial optimization tool, the second objective could be achieved\nto the extent that CPLEX can take advantage of network structure\npresent in a model.\nWe found that in addition to the problem size (in terms of number\nof traders), the number of aggregating traders plays a crucial role in\ndetermining complexity. When most of the traders are aggregating,\nproblems of larger sizes can be solved quickly. For example, our\nIP model solved instances with 600 buyers and 500 sellers, where\n90% of them are aggregating, in less than two minutes. When the\naggregating ratio was reduced to 80% for the same data, solution\ntime was just under five minutes.\nThese results motivated us to develop a new network model.\nRather than treat non-aggregating traders as a special case, the new\nmodel takes advantage of the single-unit nature of non-aggregating\ntrades (treating the aggregating traders as a special case). This new\nmodel outperformed our other models on most problem instances,\nexceptions being those where aggregating traders constitute a vast\nmajority (at least 80%).\nThis new model (Figure 4) has a single node for each non\naggregating trader, with a single-unit arc designating a match to another\nnon-aggregating trader. An aggregating trader has a node for each\npotential match, connected (via y arcs) to a mutual source node.\nUnlike the previous model we allow fractional flow for this case,\nrepresenting the traded fraction of the buyer\"s total quantity.7\nWe tested all three models on random data in the form of\nbipartite graphs encoding MMP solutions. In our experiments, each\ntrader has a maximum quantity uniformly distributed over [30, 70],\nand minimum quantity uniformly distributed from zero to maximal\nquantity. Each buyer/seller pair is selected as matching with\nprobability 0.75, with matches assigned a surplus uniformly distributed\nover [10, 70]. Whereas the size of the problem is defined by the\nnumber of traders on each side, the problem complexity depends\non the product |B| \u00d7 |S|. The tests depicted in Figures 5-7 are\nfor the worst case |B| = |S|, with each data point averaged over\nsix samples. In the figures, the direct IP (4) is designated SW,\nour first network model (Figure 2) NW, and our revised network\nmodel (Figure 4) NW 2.\n7\nTraded quantity remains integer.\n117\nAggregation Hom. attr. Divisibility linear pricing Technique Complexity\nNo aggregation N/A Any Not required Assignment problem Polynomial\nAll aggregate None Down to 0 Required Transpor. problem Polynomial\nOne side None Aggr side div. Aggr. side GAP NP-hard\nOptional None Down to q, batch Required Generalized ntwrk flow NP-hard\nOptional Bounded Down to q, batch Bounded size schdl. Generalized ntwrk flow NP-hard\nOptional Not bounded Down to q, batch Not required Nonlinear opt Depends on \u02c6u(x, q)\nTable 1: Mapping from combinations of allocation constraints to the solution methods of GMAP. One Side means that one side\naggregates and divisible, and the other side is restrictive. Batch means that traders may submit batch sizes.\nFigure 4: Generalized network flow model. B1 is a buyer in\nAD, B2 \u2208 AI, B3 \u2208 NI, B4 \u2208 ND. V 1 is a seller in AD,\nV 2 \u2208 AI, V 4 \u2208 ND. The g values represent arc gains, and W\nvalues represent weights.\nFigure 5: Average performance of models when 30% of traders\naggregate.\nFigure 6: Average performance of models when 50% of traders\naggregate.\nFigure 7: Average performance of models when 70% of traders\naggregate.\n118\nFigure 8: Performance of models when varying percentage of\naggregating traders\nFigure 8 shows how the various models are affected by a change\nin the percentage of aggregating traders, holding problem size fixed.8\nDue to the integrality constraints, we could not test available\nalgorithms specialized for network-flow problems on our test\nproblems. Thus, we cannot fully evaluate the potential gain attributable\nto network structure. However, the model we built based on the\ninsight from the network structure clearly provided a significant\nspeedup, even without using a special-purpose algorithm. Model\nNW 2 provided speedups of a factor of 4-10 over the model SW.\nThis was consistent throughout the problem sizes, including the\nsmaller sizes for which the speedup is not visually apparent on the\nchart.\n7. CONCLUSIONS\nThe implementation and deployment of market exchanges\nrequires the development of bidding languages, information feedback\npolicies, and clearing algorithms that are suitable for the target\ndomain, while paying heed to the incentive properties of the resulting\nmechanisms. For multiattribute exchanges, the space of feasible\nsuch mechanisms is constrained by computational limitations\nimposed by the clearing process. The extent to which the space of\nfeasible mechanisms may be quantified a priori will facilitate the\nsearch for such exchanges in the full mechanism design problem.\nIn this work, we investigate the space of two-sided multiattribute\nauctions, focusing on the relationship between constraints on the\noffers traders can express through bids, and the resulting\ncomputational problem of determining an optimal set of trades. We\ndeveloped a formal semantic framework for characterizing expressible\noffers, and introduced some basic classes of restrictions. Our key\ntechnical results identify sets of conditions under which the\noverall matching problem can be separated into first identifying\noptimal pairwise trades and subsequently optimizing combinations of\nthose trades. Based on these results, we developed network flow\nmodels for the overall clearing problem, which facilitate\nclassification of problem versions by computational complexity, and provide\nguidance for developing solution algorithms and relaxing bidding\nconstraints.\n8. ACKNOWLEDGMENTS\nThis work was supported in part by NSF grant IIS-0205435, and\nthe STIET program under NSF IGERT grant 0114368. We are\n8\nAll tests were performed on Intel 3.4 GHz processors with 2048\nKB cache. Test that did not complete by the one-hour time limit\nwere recorded as 4000 seconds.\ngrateful to comments from an anonymous reviewer. Some of the\nunderlying ideas were developed while the first two authors worked\nat TradingDynamics Inc. and Ariba Inc. in 1999-2001 (cf. US\nPatent 6,952,682). We thank Yoav Shoham, Kumar Ramaiyer, and\nGopal Sundaram for fruitful discussions about multiattribute\nauctions in that time frame.\n9. REFERENCES\n[1] R. K. Ahuja, T. L. Magnanti, and J. B. Orlin. Network Flows.\nPrentice-Hall, 1993.\n[2] F. Bacchus and A. Grove. Graphical models for preference and\nutility. In Eleventh Conference on Uncertainty in Artificial\nIntelligence, pages 3-10, Montreal, 1995.\n[3] M. Bichler. The Future of e-Markets: Multi-Dimensional Market\nMechanisms. Cambridge U. Press, New York, NY, USA, 2001.\n[4] M. Bichler and J. Kalagnanam. Configurable offers and winner\ndetermination in multi-attribute auctions. European Journal of\nOperational Research, 160:380-394, 2005.\n[5] M. Bichler, M. Kaukal, and A. Segev. Multi-attribute auctions for\nelectronic procurement. In Proceedings of the 1st IBM IAC\nWorkshop on Internet Based Negotiation Technologies, 1999.\n[6] C. Boutilier, T. Sandholm, and R. Shields. Eliciting bid taker\nnon-price preferences in (combinatorial) auctions. In Nineteenth\nNatl. Conf. on Artificial Intelligence, pages 204-211, San Jose, 2004.\n[7] F. Branco. The design of multidimensional auctions. RAND Journal\nof Economics, 28(1):63-81, 1997.\n[8] Y.-K. Che. Design competition through multidimensional auctions.\nRAND Journal of Economics, 24(4):668-680, 1993.\n[9] G. Debreu. Topological methods in cardinal utility theory. In\nK. Arrow, S. Karlin, and P. Suppes, editors, Mathematical Methods\nin the Social Sciences. Stanford University Press, 1959.\n[10] N. Economides and R. A. Schwartz. Electronic call market trading.\nJournal of Portfolio Management, 21(3), 1995.\n[11] Y. Engel and M. P. Wellman. Multiattribute utility representation for\nwillingness-to-pay functions. Tech. report, Univ. of Michigan, 2006.\n[12] E. Fink, J. Johnson, and J. Hu. Exchange market for complex goods:\nTheory and experiments. Netnomics, 6(1):21-42, 2004.\n[13] M. L. Fisher, R. Jaikumar, and L. N. Van Wassenhove. A multiplier\nadjustment method for the generalized assignment problem.\nManagement Science, 32(9):1095-1103, 1986.\n[14] J. Gong. Exchanges for complex commodities: Search for optimal\nmatches. Master\"s thesis, University of South Florida, 2002.\n[15] C. Gonzales and P. Perny. GAI networks for decision making under\ncertainty. In IJCAI-05 workshop on preferences, Edinburgh, 2005.\n[16] J. R. Kalagnanam, A. J. Davenport, and H. S. Lee. Computational\naspects of clearing continuous call double auctions with assignment\nconstraints and indivisible demand. Electronic Commerce Research,\n1(3):221-238, 2001.\n[17] R. L. Keeney and H. Raiffa. Decisions with Multiple Objectives:\nPreferences and Value Tradeoffs. Wiley, 1976.\n[18] N. Nisan. Bidding and allocation in combinatorial auctions. In\nSecond ACM Conference on Electronic Commerce, pages 1-12,\nMinneapolis, MN, 2000.\n[19] D. C. Parkes and J. Kalagnanam. Models for iterative multiattribute\nprocurement auctions. Management Science, 51:435-451, 2005.\n[20] T. Sandholm and S. Suri. Side constraints and non-price attributes in\nmarkets. In IJCAI-01 Workshop on Distributed Constraint\nReasoning, Seattle, 2001.\n[21] L. J. Schvartzman and M. P. Wellman. Market-based allocation with\nindivisible bids. In AAMAS-05 Workshop on Agent-Mediated\nElectronic Commerce, Utrecht, 2005.\n[22] J. Shachat and J. T. Swarthout. Procurement auctions for\ndifferentiated goods. Technical Report 0310004, Economics\nWorking Paper Archive at WUSTL, Oct. 2003.\n[23] A. V. Sunderam and D. C. Parkes. Preference elicitation in proxied\nmultiattribute auctions. In Fourth ACM Conference on Electronic\nCommerce, pages 214-215, San Diego, 2003.\n[24] P. R. Wurman, M. P. Wellman, and W. E. Walsh. A parametrization\nof the auction design space. Games and Economic Behavior,\n35:304-338, 2001.\n119", "keywords": "bid;constraint;one-sided mechanism;partial specification;multiattribute auction;combinatorial auction;auction;global allocation;seller valuation function;preference;continuous double auction;multiattribute utility theory;semantic framework"}
{"name": "train_J-34", "title": "(In)Stability Properties of Limit Order Dynamics", "abstract": "We study the stability properties of the dynamics of the standard continuous limit-order mechanism that is used in modern equity markets. We ask whether such mechanisms are susceptible to butterfly effects - the infliction of large changes on common measures of market activity by only small perturbations of the order sequence. We show that the answer depends strongly on whether the market consists of absolute traders (who determine their prices independent of the current order book state) or relative traders (who determine their prices relative to the current bid and ask). We prove that while the absolute trader model enjoys provably strong stability properties, the relative trader model is vulnerable to great instability. Our theoretical results are supported by large-scale experiments using limit order data from INET, a large electronic exchange for NASDAQ stocks.", "fulltext": "1. INTRODUCTION\nIn recent years there has been an explosive increase in\nthe automation of modern equity markets. This increase\nhas taken place both in the exchanges, which are\nincreasingly computerized and offer sophisticated interfaces for\norder placement and management, and in the trading\nactivity itself, which is ever more frequently undertaken by\nsoftware. The so-called Electronic Communication Networks (or\nECNs) that dominate trading in NASDAQ stocks are a\ncommon example of the automation of the exchanges. On the\ntrading side, computer programs now are entrusted not only\nwith the careful execution of large block trades for clients\n(sometimes referred to on Wall Street as program trading),\nbut with the autonomous selection of stocks, direction (long\nor short) and volumes to trade for profit (commonly referred\nto as statistical arbitrage).\nThe vast majority of equity trading is done via the\nstandard limit order market mechanism. In this mechanism,\ncontinuous trading takes place via the arrival of limit\norders specifying whether the party wishes to buy or sell, the\nvolume desired, and the price offered. Arriving limit orders\nthat are entirely or partially executable with the best offers\non the other side are executed immediately, with any\nvolume not immediately executable being placed in an queue\n(or book) ordered by price on the appropriate side (buy or\nsell). (A detailed description of the limit order mechanism is\ngiven in Section 3.) While traders have always been able to\nview the prices at the top of the buy and sell books (known\nas the bid and ask), a relatively recent development in\ncertain exchanges is the real-time revelation of the entire order\nbook - the complete distribution of orders, prices and\nvolumes on both sides of the exchange. With this revelation\nhas come the opportunity - and increasingly, the\nneedfor modeling and exploiting limit order data and\ndynamics. It is fair to say that market microstructure, as this area\nis generally known, is a topic commanding great interest\nboth in the real markets and in the academic finance\nliterature. The opportunities and needs span the range from\nthe optimized execution of large trades to the creation of\nstand-alone proprietary strategies that attempt to profit\nfrom high-frequency microstructure signals.\nIn this paper we investigate a previously unexplored but\nfundamental aspect of limit order microstructure: the\nstability properties of the dynamics. Specifically, we are\ninterested in the following natural question: To what extent\nare simple models of limit order markets either susceptible\nor immune to butterfly effects - that is, the infliction of\nlarge changes in important activity statistics (such as the\n120\nnumber of shares traded or the average price per share) by\nonly minor perturbations of the order sequence?\nTo examine this question, we consider two stylized but\nnatural models of the limit order arrival process. In the\nabsolute price model, buyers and sellers arrive with limit order\nprices that are determined independently of the current state\nof the market (as represented by the order books), though\nthey may depend on all manner of exogenous information\nor shocks, such as time, news events, announcements from\nthe company whose shares are being traded, private signals\nor state of the individual traders, etc. This process models\ntraditional fundamentals-based trading, in which market\nparticipants each have some inherent but possibly varying\nvaluation for the good that in turn determines their limit\nprice.\nIn contrast, in the relative price model, traders express\ntheir limit order prices relative to the best price offered in\ntheir respective book (buy or sell). Thus, a buyer would\nencode their limit order price as an offset \u2206 (which may be\npositive, negative, or zero) from the current bid pb, which is\nthen translated to the limit price pb +\u2206. Again, in addition\nto now depending on the state of the order books, prices\nmay also depend on all manner of exogenous information.\nThe relative price model can be viewed as modeling traders\nwho, in addition to perhaps incorporating fundamental\nexternal information on the stock, may also position their\norders strategically relative to the other orders on their side\nof the book. A common example of such strategic\nbehavior is known as penny-jumping on Wall Street, in which\na trader who has in interest in buying shares quickly, but\nstill at a discount to placing a market order, will\ndeliberately position their order just above the current bid. More\ngenerally, the entire area of modern execution optimization\n[9, 10, 8] has come to rely heavily on the careful positioning\nof limit orders relative to the current order book state. Note\nthat such positioning may depend on more complex features\nof the order books than just the current bid and ask, but\nthe relative model is a natural and simplified starting point.\nWe remark that an alternate view of the two models is that\nall traders behave in a relative manner, but with absolute\ntraders able to act only on a considerably slower time scale\nthan the faster relative traders.\nHow do these two models differ? Clearly, given any fixed\nsequence of arriving limit order prices, we can choose to\nexpress these prices either as their original (absolute) values,\nor we can run the order book dynamical process and\ntransform each order into a relative difference with the top of\nits book, and obtain identical results. The differences arise\nwhen we consider the stability question introduced above.\nIntuitively, in the absolute model a small perturbation in\nthe arriving limit price sequence should have limited (but\nstill some) effects on the subsequent evolution of the order\nbooks, since prices are determined independently. For the\nrelative model this intuition is less clear. It seems possible\nthat a small perturbation could (for example) slightly\nmodify the current bid, which in turn could slightly modify the\nprice of the next arriving order, which could then slightly\nmodify the price of the subsequent order, and so on, leading\nto an amplifying sequence of events.\nOur main results demonstrate that these two models do\nindeed have dramatically different stability properties. We\nfirst show that for any fixed sequence of prices in the\nabsolute model, the modification of a single order has a bounded\nand extremely limited impact on the subsequent evolution\nof the books. In particular, we define a natural notion of\ndistance between order books and show that small\nmodifications can result in only constant distance to the original\nbooks for all subsequent time steps. We then show that this\nimplies that for almost any standard statistic of market\nactivity - the executed volume, the average price execution\nprice, and many others - the statistic can be influenced\nonly infinitesimally by small perturbations.\nIn contrast, we show that the relative model enjoys no\nsuch stability properties. After giving specific (worst-case)\nrelative price sequences in which small perturbations\ngenerate large changes in basic statistics (for example, altering the\nnumber of shares traded by a factor of two), we proceed to\ndemonstrate that the difference in stability properties of the\ntwo models is more than merely theoretical. Using\nextensive INET (a major ECN for NASDAQ stocks) limit order\ndata and order book reconstruction code, we investigate the\nempirical stability properties when the data is interpreted\nas containing either absolute prices, relative prices, or\nmixtures of the two. The theoretical predictions of stability and\ninstability are strongly borne out by the subsequent\nexperiments.\nIn addition to stability being of fundamental interest in\nany important dynamical system, we believe that the\nresults described here provide food for thought on the\ntopics of market impact and the backtesting of quantitative\ntrading strategies (the attempt to determine hypothetical\npast performance using historical data). They suggest that\none\"s confidence that trading quietly and in small\nvolumes will have minimal market impact is linked to an\nimplicit belief in an absolute price model. Our results and the\nfact that in the real markets there is a large and increasing\namount of relative behavior such as penny-jumping would\nseem to cast doubts on such beliefs. Similarly, in a purely or\nlargely relative-price world, backtesting even low-frequency,\nlow-volume strategies could result in historical estimates of\nperformance that are not only unrelated to future\nperformance (the usual concern), but are not even accurate\nmeasures of a hypothetical past.\nThe outline of the paper follows. In Section 2 we briefly\nreview the large literature on market microstructure. In\nSection 3 we describe the limit order mechanism and our\nformal models. Section 4 presents our most important\ntheoretical results, the 1-Modification Theorem for the absolute\nprice model. This theorem is applied in Section 5 to derive a\nnumber of strong stability properties in the absolute model.\nSection 6 presents specific examples establishing the\nworstcase instability of the relative model. Section 7 contains\nthe simulation studies that largely confirm our theoretical\nfindings on INET market data.\n2. RELATED WORK\nAs was mentioned in the Introduction, market\nmicrostructure is an important and timely topic both in academic\nfinance and on Wall Street, and consequently has a large and\nvaried recent literature. Here we have space only to\nsummarize the main themes of this literature and to provide\npointers to further readings. To our knowledge the stability\nproperties of detailed limit order microstructure dynamics\nhave not been previously considered. (However, see Farmer\nand Joshi [6] for an example and survey of other price\ndynamic stability studies.)\n121\nOn the more theoretical side, there is a rich line of work\nexamining what might be considered the game-theoretic\nproperties of limit order markets. These works model traders\nand market-makers (who provide liquidity by offering both\nbuy and sell quotes, and profit on the difference) by utility\nfunctions incorporating tolerance for risks of price\nmovement, large positions and other factors, and examine the\nresulting equilibrium prices and behaviors. Common\nfindings predict negative price impacts for large trades, and price\neffects for large inventory holdings by market-makers. An\nexcellent and comprehensive survey of results in this area\ncan be found in [2].\nThere is a similarly large body of empirical work on\nmicrostructure. Major themes include the measurement of\nprice impacts, statistical properties of limit order books, and\nattempts to establish the informational value of order books\n[4]. A good overview of the empirical work can be found in\n[7]. Of particular note for our interests is [3], which\nempirically studies the distribution of arriving limit order prices in\nseveral prominent markets. This work takes a view of\narriving prices analogous to our relative model, and establishes\na power-law form for the resulting distributions.\nThere is also a small but growing number of works\nexamining market microstructure topics from a computer\nscience perspective, including some focused on the use of\nmicrostructure in algorithms for optimized trade execution.\nKakade et al. [9] introduced limit order dynamics in\ncompetitive analysis for one-way and volume-weighted average\nprice (VWAP) trading. Some recent papers have applied\nreinforcement learning methods to trade execution using order\nbook properties as state variables [1, 5, 10].\n3. MICROSTRUCTURE PRELIMINARIES\nThe following expository background material is adapted\nfrom [9]. The market mechanism we examine in this paper\nis driven by the simple and standard concept of a limit\norder. Suppose we wish to purchase 1000 shares of Microsoft\n(MSFT) stock. In a limit order, we specify not only the\ndesired volume (1000 shares), but also the desired price.\nSuppose that MSFT is currently trading at roughly $24.07\na share (see Figure 1, which shows an actual snapshot of an\nMSFT order book on INET), but we are only willing to buy\nthe 1000 shares at $24.04 a share or lower. We can choose to\nsubmit a limit order with this specification, and our order\nwill be placed in a queue called the buy order book, which\nis ordered by price, with the highest offered unexecuted buy\nprice at the top (often referred to as the bid). If there are\nmultiple limit orders at the same price, they are ordered\nby time of arrival (with older orders higher in the book).\nIn the example provided by Figure 1, our order would be\nplaced immediately after the extant order for 5,503 shares\nat $24.04; though we offer the same price, this order has\narrived before ours. Similarly, a sell order book for sell limit\norders is maintained, this time with the lowest sell price\noffered (often referred to as the ask) at its top.\nThus, the order books are sorted from the most\ncompetitive limit orders at the top (high buy prices and low sell\nprices) down to less competitive limit orders. The bid and\nask prices together are sometimes referred to as the inside\nmarket, and the difference between them as the spread. By\ndefinition, the order books always consist exclusively of\nunexecuted orders - they are queues of orders hopefully\nwaiting for the price to move in their direction.\nFigure 1: Sample INET order books for MSFT.\nHow then do orders get (partially) executed? If a buy\n(sell, respectively) limit order comes in above the ask\n(below the bid, respectively) price, then the order is matched\nwith orders on the opposing books until either the incoming\norder\"s volume is filled, or no further matching is possible,\nin which case the remaining incoming volume is placed in\nthe books.\nFor instance, suppose in the example of Figure 1 a buy\norder for 2000 shares arrived with a limit price of $24.08.\nThis order would be partially filled by the two 500-share\nsell orders at $24.069 in the sell books, the 500-share sell\norder at $24.07, and the 200-share sell order at $24.08, for\na total of 1700 shares executed. The remaining 300 shares\nof the incoming buy order would become the new bid of\nthe buy book at $24.08. It is important to note that the\nprices of executions are the prices specified in the limit orders\nalready in the books, not the prices of the incoming order\nthat is immediately executed. Thus in this example, the\n1700 executed shares would be at different prices. Note that\nthis also means that in a pure limit order exchange such as\nINET, market orders can be simulated by limit orders\nwith extreme price values. In exchanges such as INET, any\norder can be withdrawn or canceled by the party that placed\nit any time prior to execution.\nEvery limit order arrives atomically and instantaneously\n- there is a strict temporal sequence in which orders arrive,\nand two orders can never arrive simultaneously. This gives\nrise to the definition of the last price of the exchange, which\nis simply the last price at which the exchange executed an\norder. It is this quantity that is usually meant when people\ncasually refer to the (ticker) price of a stock.\n3.1 Formal Definitions\nWe now provide a formal model for the limit order\npro122\ncess described above. In this model, limit orders arrive in a\ntemporal sequence, with each order specifying its limit price\nand an indication of its type (buy or sell). Like the actual\nexchanges, we also allow cancellation of a standing\n(unexecuted) order in the books any time prior to its execution.\nWithout loss of generality we limit attention to a model in\nwhich every order is for a single share; large order volumes\ncan be represented by 1-share sequences.\nDefinition 3.1. Let \u03a3 = \u03c31, ...\u03c3n be a sequence of limit\norders, where each \u03c3i has the form ni, ti, vi . Here ni is an\norder identifier, ti is the order type (buy, sell, or cancel), and\nvi is the limit order value. In the case that ti is a cancel, ni\nmatches a previously placed order and vi is ignored.\nWe have deliberately called vi in the definition above the\nlimit order value rather than price, since our two models\nwill differ in their interpretation of vi (as being absolute or\nrelative). In the absolute model, we do indeed interpret vi\nas simply being the price of the limit order. In the\nrelative model, if the current order book configuration is (A, B)\n(where A is the sell and B the buy book), the price of the\norder is ask(A) + vi if ti is sell, and bid(B) + vi if ti is buy,\nwhere by ask(X) and bid(X) we denote the price of the\norder at the top of the book X. (Note vi can be negative.)\nOur main interest in this paper is the effects that the\nmodification of a small number of limit orders can have on the\nresulting dynamics. For simplicity we consider only\nmodifications to the limit order values, but our results generalize\nto any modification.\nDefinition 3.2. A k-modification of \u03a3 is a sequence \u03a3\nsuch that for exactly k indices i1, ..., ik vij = vij\n, tij = tij\n,\nand nij = nij\n. For every = ij , j \u2208 {1, . . . , k} \u03c3 = \u03c3 .\nWe now define the various quantities whose stability\nproperties we examine in the absolute and relative models. All of\nthese are standard quantities of common interest in financial\nmarkets.\n\u2022 volume(\u03a3): Number of shares executed (traded) in the\nsequence \u03a3.\n\u2022 average(\u03a3): Average execution price.\n\u2022 close(\u03a3): Price of the last (closing) execution.\n\u2022 lastbid(\u03a3): Bid at the end of the sequence.\n\u2022 lastask(\u03a3): Ask at end of the sequence.\n4. THE 1-MODIFICATION THEOREM\nIn this section we provide our most important technical\nresult. It shows that in the absolute model, the effects that\nthe modification of a single order has on the resulting\nevolution of the order books is extremely limited. We then apply\nthis result to derive strong stability results for all of the\naforementioned quantities in the absolute model.\nThroughout this section, we consider an arbitrary order\nsequence \u03a3 in the absolute model, and any 1-modification\n\u03a3 of \u03a3. At any point (index) i in the two sequences we shall\nuse (A1, B1) to denote the sell and buy books (respectively)\nin \u03a3, and (A2, B2) to denote the sell and buy books in \u03a3 ;\nfor notational convenience we omit explicitly superscripting\nby the current index i. We will shortly establish that at all\ntimes i, (A1, B1) and (A2, B2) are very close.\nAlthough the order books are sorted by price, we will use\n(for example) A1 \u222a {a2} = A2 to indicate that A2 contains\nan order at some price a2 that is not present in A1, but that\notherwise A1 and A2 are identical; thus deleting the order\nat a2 in A2 would render the books the same. Similarly,\nB1 \u222a {b2} = B2 \u222a {b1} means B1 contains an order at price\nb1 not present in B2, B2 contains an order at price b2 not\npresent in B1, and that otherwise B1 and B2 are identical.\nUsing this notation, we now define a set of stable system\nstates, where each state is composed from the order books\nof the original and the modified sequences. Shortly we show\nthat if we change only one order\"s value (price), we remain\nin this set for any sequence of limit orders.\nDefinition 4.1. Let ab be the set of all states (A1, B1)\nand (A2, B2) such that A1 = A2 and B1 = B2. Let \u00afab be\nthe set of states such that A1 \u222a {a2} = A2 \u222a {a1}, where\na1 = a2, and B1 = B2. Let a\u00afb be the set of states such that\nB1\u222a{b2} = B2\u222a{b1}, where b1 = b2, and A1 = A2. Let \u00afa\u00afb be\nthe set of states in which A1 = A2\u222a{a1} and B1 = B2\u222a{b1},\nor in which A2 = A1 \u222a {a2} and B2 = B1 \u222a {b2}. Finally\nwe define S = ab \u222a \u00afab \u222a \u00afba \u222a \u00afa\u00afb as the set of stable states.\nTheorem 4.1. (1-Modification Theorem) Consider any\nsequence of orders \u03a3 and any 1-modification \u03a3 of \u03a3. Then\nthe order books (A1, B1) and (A2, B2) determined by \u03a3 and\n\u03a3 lie in the set S of stable states at all times.\nab\n\u00afa\u00afb\na\u00afb\u00afab\nFigure 2: Diagram representing the set S of stable\nstates and the possible movements transitions in it\nafter the change.\nThe idea of the proof of this theorem is contained in\nFigure 2, which shows a state transition diagram labeled by the\ncategories of stable states. This diagram describes all\ntransitions that can take place after the arrival of the order on\nwhich \u03a3 and \u03a3 differ. The following establishes that\nimmediately after the arrival of this differing order, the state lies\nin S.\nLemma 4.2. If at any time the current books (A1, B1) and\n(A2, B2) are in the set ab (and thus identical), then\nmodifying the price of the next order keeps the state in S.\nProof. Suppose the arriving order is a sell order and we\nchange it from a1 to a2; assume without loss of generality\nthat a1 > a2. If neither order is executed immediately, then\nwe move to state \u00afab; if both of them are executed then we\nstay in state ab; and if only a2 is executed then we move to\nstate \u00afa\u00afb. The analysis of an arriving buy order is similar.\nFollowing the arrival of their only differing order, \u03a3 and\n\u03a3 are identical. We now give a sequence of lemmas showing\n123\nExecuted with two orders\nNot executed in both\nArrivng buy order\nArriving buy order\nArriving buy order\nArriving sell order\n\u00afab\nab\n\u00afa\u00afb\nExecuted only with a1\n(not a1 and a2)\nExecuted with a1 and a2\nFigure 3: The state diagram when starting at state\n\u00afab. This diagram provides the intuition of Lemma\n4.3\nthat following the initial difference covered by Lemma 4.2,\nthe state remains in S forever on the remaining (identical)\nsequence. We first show that from state \u00afab we remain in\nS regardless the next order. The intuition of this lemma is\ndemonstrated in Figure 3.\nLemma 4.3. If the current state is in the set \u00afab, then for\nany order the state will remain in S.\nProof. We first provide the analysis for the case of an\narriving sell order. Note that in \u00afab the buy books are identical\n(B1 = B2). Thus either the arriving sell order is executed\nwith the same buy order in both buy books, or it is not\nexecuted in both buy books. For the first case, the buy\nbooks remain identical (the bid is executed in both) and the\nsell books remain unchanged. For the second case, the buy\nbooks remain unchanged and identical, and the sell books\nhave the new sell order added to both of them (and thus\nstill differ by one order).\nNext we provide an analysis of the more subtle case where\nthe arriving item is a buy order. For this case we need to\ntake care of several different scenarios. The first is when the\ntop of both sell books (the ask) is identical. Then\nregardless of whether the new buy order is executed or not, the\nstate remains in \u00afab (the analysis is similar to an arriving\nsell order).\nWe are left to deal with case where ask(A1) and ask(A2)\nare different. Here we discuss two subcases: (a) ask(A1) =\na1 and ask(A2) = a2, and (b) ask(A1) = a1 and ask(A2) =\na . Here a1 and a2 are as in the definition of \u00afab in\nDefinition 4.1, and a is some other price. For subcase (a), by our\nassumption a1 < a2, then either (1) both asks get executed,\nthe sell books become identical, and we move to state ab;\n(2) neither ask is executed and we remain in state \u00afab; or (3)\nonly ask(A1) = a1 is executed, in which case we move to\nstate \u00afa\u00afb with A2 = A1 \u222a {a2} and B2 = B1 \u222a {b2}, where\nb2 is the arriving buy order price. For subcase (b), either\n(1) buy order is executed in neither sell book we remain in\nstate \u00afab; or (2) the buy order is executed in both sell books\nand stay in state \u00afab with A1 \u222a {a } = A2 \u222a {a2}; or (3) only\nask(A1) = a1 is executed and we move to state \u00afa\u00afb.\nLemma 4.4. If the current state is in the set a\u00afb, then for\nany order the state will remain in S.\nLemma 4.5. If the current configuration is in the set \u00afa\u00afb,\nthen for any order the state will remain in S\nThe proofs of these two lemmas are omitted, but are\nsimilar in spirit to that of Lemma 4.3. The next and final lemma\ndeals with cancellations.\nLemma 4.6. If the current order book state lies in S, then\nfollowing the arrival of a cancellation it remains in S.\nProof. When a cancellation order arrives, one of the\nfollowing possibilities holds: (1) the order is still in both sets of\nbooks, (2) it is not in either of them and (3) it is only in one\nof them. For the first two cases it is easy to see that the\ncancellation effect is identical on both sets of books, and thus\nthe state remains unchanged. For the case when the order\nappears only in one set of books, without loss of generality\nwe assume that the cancellation cancels a buy order at b1.\nRather than removing b1 from the book we can change it to\nhave price 0, meaning this buy order will never be executed\nand is effectively canceled. Now regardless the state that we\nwere in, b1 is still only in one buy book (but with a different\nprice), and thus we remain in the same state in S.\nThe proof of Theorem 4.1 follows from the above lemmas.\n5. ABSOLUTE MODEL STABILITY\nIn this section we apply the 1-Modification Theorem to\nshow strong stability properties for the absolute model. We\nbegin with an examination of the executed volume.\nLemma 5.1. Let \u03a3 be any sequence and \u03a3 be any\n1modification of \u03a3. Then the set of the executed orders (ID\nnumbers) generated by the two sequences differs by at most\n2.\nProof. By Theorem 4.1 we know that at each stage the\nbooks differ by at most two orders. Now since the union of\nthe IDs of the executed orders and the order books is always\nidentical for both sequences, this implies that the executed\norders can differ by at most two.\nCorollary 5.2. Let \u03a3 be any sequence and \u03a3 be any\nkmodification of \u03a3. Then the set of the executed orders (ID\nnumbers) generated by the two sequences differs by at most\n2k.\nAn order sequence \u03a3 is a k-extension of \u03a3 if \u03a3 can be\nobtained by deleting any k orders in \u03a3 .\nLemma 5.3. Let \u03a3 be any sequence and let \u03a3 be any\nkextension of \u03a3. Then the set of the executed orders generated\nby \u03a3 and \u03a3 differ by at most 2k.\nThis lemma is the key to obtain our main absolute model\nvolume result below. We use edit(\u03a3, \u03a3 ) to denote the\nstandard edit distance between the sequences \u03a3 and \u03a3 - the\nminimal number of substitutions, insertions and deletions or\norders needed to change \u03a3 to \u03a3 .\nTheorem 5.4. Let \u03a3 and \u03a3 be any absolute model order\nsequences. Then if edit(\u03a3, \u03a3 ) \u2264 k, the set of the executed\norders generated by \u03a3 and \u03a3 differ by at most 4k. In\nparticular, |volume(\u03a3) \u2212 volume(\u03a3 )| \u2264 4k.\nProof. We first define the sequence \u02dc\u03a3 which is the\nintersection of \u03a3 and \u03a3 . Since \u03a3 and \u03a3 are at most k apart,we\nhave that by k insertions we change \u02dc\u03a3 to either \u03a3 or \u03a3 , and\nby Lemma 5.3 its set of executed orders is at most 2k from\neach. Thus the set of executed orders in \u03a3 and \u03a3 is at most\n4k apart.\n124\n5.1 Spread Bounds\nTheorem 5.4 establishes strong stability for executed\nvolume in the absolute model. We now turn to the quantities\nthat involve execution prices as opposed to volume alone\n- namely, average(\u03a3), close(\u03a3), lastbid(\u03a3) and lastask(\u03a3).\nFor these results, unlike executed volume, a condition must\nhold on \u03a3 in order for stability to occur. This condition\nis expressed in terms of a natural measure of the spread of\nthe market, or the gap between the buyers and sellers. We\nmotivate this condition by first showing that without it, by\nchanging one order, we can change average(\u03a3) by any\npositive value x.\nLemma 5.5. There exists \u03a3 such that for any x \u2265 0,\nthere is a 1-modification \u03a3 of \u03a3 such that average(\u03a3 ) =\naverage(\u03a3) + x.\nProof. Let \u03a3 be a sequence of alternating sell and buy\norders in which each seller offers p and each buyer p + x,\nand the first order is a sell. Then all executions take place\nat the ask, which is always p, and thus average(\u03a3) = p.\nNow suppose we modify only the first sell order to be at\nprice p+1+x. This initial sell order will never be executed,\nand now all executions take place at the bid, which is always\np + x.\nSimilar instability results can be shown to hold for the\nother price-based quantities. This motivates the\nintroduction of a quantity we call the second spread of the order\nbooks, which is defined as the difference between the prices\nof the second order in the sell book and the second order in\nthe buy book (as opposed to the bid-ask difference, which is\ncommonly called the spread). We note that in a liquid stock,\nsuch as those we examine experimentally in Section 7, the\nsecond spread will typically be quite small and in fact almost\nalways equal to the spread.\nIn this subsection we consider changes in the sequence\nonly after an initialization period, and sequences such that\nthe second spread is always defined after the time we make a\nchange. We define s2(\u03a3) to be the maximum second spread\nin the sequence \u03a3 following the change.\nTheorem 5.6. Let \u03a3 be a sequence and let \u03a3 be any\n1modification of \u03a3. Then\n1. |lastbid(\u03a3) \u2212 lastbid(\u03a3 )| \u2264 s2(\u03a3)\n2. |lastask(\u03a3) \u2212 lastask(\u03a3 )| \u2264 s2(\u03a3)\nwhere s2(\u03a3) is the maximum over the second spread in \u03a3\nfollowing the 1-modification.\nProof. We provide the proof for the last bid; the proof\nfor the last ask is similar. The proof relies on Theorem 4.1\nand considers states in the stable set S. For states ab and \u00afab,\nwe have that the bid is identical. Let bid(X), sb(X), ask(X),\nbe the bid, the second highest buy order, and the ask of a\nsequence X. Now recall that in state a\u00afb we have that the sell\nbooks are identical, and that the two buy books are identical\nexcept one different order. Thus\nbid(\u03a3)+s2(\u03a3) \u2265 sb(\u03a3)+s2(\u03a3) \u2265 ask(\u03a3) = ask(\u03a3 ) \u2265 bid(\u03a3 ).\nNow it remains to bound bid(\u03a3). Here we use the fact that\nthe bid of the modified sequence is at least the second\nhighest buy order in the original sequence, due to the fact that\nthe books are different only in one order. Since\nbid(\u03a3 ) \u2265 sb(\u03a3) \u2265 ask(\u03a3) \u2212 s2(\u03a3) \u2265 bid(\u03a3) \u2212 s2(\u03a3)\nwe have that |bid(\u03a3) \u2212 bid(\u03a3 )| \u2264 s2(\u03a3) as desired.\nIn state \u00afa\u00afb we have that for one sequence the books\ncontain an additional buy order and an additional sell order.\nFirst suppose that the books containing the additional\norders are the original sequence \u03a3. Now if the bid is not the\nadditional order we are done, otherwise we have the\nfollowing:\nbid(\u03a3) \u2264 ask(\u03a3) \u2264 sb(\u03a3) + s2(\u03a3) = bid(\u03a3 ) + s2(\u03a3),\nwhere sb(\u03a3) \u2264 bid(\u03a3 ) since the original buy book has only\none additional order.\nNow assume that the books with the additional orders are\nfor the modified sequence \u03a3 . We have\nbid(\u03a3) + s2(\u03a3) \u2265 ask(\u03a3) \u2265 ask(\u03a3 ) \u2265 bid(\u03a3 ),\nwhere we used the fact that ask(\u03a3) \u2265 ask(\u03a3 ) since the\nmodified sequence has an additional order. Similarly we\nhave that bid(\u03a3) \u2264 bid(\u03a3 ) since the modified buy book\ncontains an additional order.\nWe note that the proof of Theorem 5.6 actually establishes\nthat the bid and ask of the original and modified sequences\nare within s2(\u03a3) at all times.\nNext we provide a technical lemma which relates the (first)\nspread of the modified sequence to the second spread of the\noriginal sequence.\nLemma 5.7. Let \u03a3 be a sequence and let \u03a3 be any\n1modification of \u03a3. Then the spread of \u03a3 is bounded by\ns2(\u03a3).\nProof. By the 1-Modification Theorem, we know that\nthe books of the modified sequence and the original sequence\ncan differ by at most one order in each book (buy and sell).\nTherefore, the second-highest buy order in the original\nsequence is always at most the bid in the modified sequence,\nand the second-lowest sell order in the original sequence is\nalways at least the ask of the modified sequence.\nWe are now ready to state a stability result for the average\nexecution price in the absolute model. It establishes that in\nhighly liquid markets, where the executed volume is large\nand the spread small, the average price is highly stable.\nTheorem 5.8. Let \u03a3 be a sequence and let \u03a3 be any\n1modification of \u03a3. Then\n|average(\u03a3) \u2212 average(\u03a3 )| \u2264\n2(pmax + s2(\u03a3))\nvolume(\u03a3)\n+ s2(\u03a3)\nwhere pmax is the highest execution price in \u03a3.\nProof. The proof will show that every execution in \u03a3\nbesides the execution of the modified order and the last\nexecution has a matching execution in \u03a3 with a price different\nby at most s2(\u03a3), and will use the fact that pmax + s2(\u03a3) is\na bound on the price in \u03a3 .\nReferring to the proof of the 1-Modification Theorem,\nsuppose we are in state \u00afa\u00afb, where we have in one sequence\n(which can be either \u03a3 or \u03a3 ) an additional buy order b\nand an additional sell order a. Without loss of generality\nwe assume that the sequence with the additional orders is\n\u03a3. If the next execution does not involve a or b then clearly\nwe have the same execution in both \u03a3 and \u03a3 . Suppose\nthat it involves a; there are two possibilities. Either a is the\nmodified order, in which case we change the average price\n125\ndifference by (pmax +s2(\u03a3))/volume(\u03a3), and this can happen\nonly once; or a was executed before in \u03a3 and the executions\nboth involve an order whose limit price is a. By Lemma 5.7\nthe spread of both sequences is bounded by s2(\u03a3), which\nimplies that the price of the execution in \u03a3 was at most\na + s2(\u03a3), while execution is in \u03a3 is at price a, and thus the\nprices are different by at most s2(\u03a3).\nIn states \u00afab, a\u00afb as long as we have concurrent executions\nin the two sequences, we know that the prices can differ\nby at most s2(\u03a3). If we have an execution only in one\nsequence, we either match it in state \u00afa\u00afb, or charge it by\n(pmax + s2(\u03a3))/volume(\u03a3) if we end at state \u00afa\u00afb.\nIf we end in state ab, \u00afab or a\u00afb, then every execution in\nstates \u00afab or a\u00afb were matched to an execution in state \u00afa\u00afb. If\nwe end up in state \u00afa\u00afb, we have the one execution that is not\nmatched and thus we charge it (pmax +s2(\u03a3))/volume(\u03a3).\nWe next give a stability result for the closing price. We\nfirst provide a technical lemma regarding the prices of\nconsecutive executions.\nLemma 5.9. Let \u03a3 be any sequence. Then the prices of\ntwo consecutive executions in \u03a3 differ by at most s2(\u03a3).\nProof. Suppose the first execution is taken at time t;\nits price is bounded below by the current bid and above by\nthe current ask. Now after this execution the bid is at least\nthe second highest buy order at time t, if the former bid\nwas executed and no higher buy orders arrived, and higher\notherwise. Similarly, the ask is at most the second lowest\nsell order at time t. Therefore, the next execution price is\nat least the second bid at time t and at most the second ask\nat time t, which is at most s2(\u03a3) away from the bid/ask at\ntime t.\nLemma 5.10. Let \u03a3 be any sequence and let \u03a3 be a\n1modification of \u03a3. If the volume(\u03a3) \u2265 2, then\n|close(\u03a3) \u2212 close(\u03a3 )| \u2264 s2(\u03a3)\nProof. We first deal with case where the last execution\noccurs in both sequences simultaneously. By Theorem 5.6,\nboth the ask and the bid of \u03a3 and \u03a3 are at most s2(\u03a3)\napart at every time t. Since the price of the last execution\nis their asks (bids) at time t we are done.\nNext we deal with the case where the last execution among\nthe two sequences occurs only in \u03a3. In this case we know\nthat either the previous execution happened simultaneously\nin both sequences at time t, and thus all three executions are\nwithin the second spread of \u03a3 at time t (the first execution\nin \u03a3 by definition, the execution at \u03a3 from identical\narguments as in the former case, and the third by Lemma 5.9).\nOtherwise the previous execution happened only in \u03a3 at\ntime t, in which case the two executions are within the the\nspread of \u03a3 at time t (the execution of \u03a3 from the same\narguments as before, and the execution in \u03a3 must be inside\nits spread in time t).\nIf the last execution happens only in \u03a3 we know that\nthe next execution of \u03a3 will be at most s2(\u03a3) away from\nits previous execution by Lemma 5.9. Together with the\nfact that if an execution happens only in one sequence it\nimplies that the order is in the spread of the second sequence\nas long as the sequences are 1-modification, the proof is\ncompleted.\n5.2 Spread Bounds for k-Modifications\nAs in the case of executed volume, we would like to extend\nthe absolute model stability results for price-based\nquantities to the case where multiple orders are modified. Here our\nresults are weaker and depend on the k-spread, the distance\nbetween the kth highest buy order and the kth lowest sell\norder, instead of the second spread. (Looking ahead to\nSection 7, we note that in actual market data for liquid stocks,\nthis quantity is often very small as well.) We use sk(\u03a3) to\ndenote the k-spread. As before, we assume that the k-spread\nis always defined after an initialization period.\nWe first state the following generalization of Lemma 5.7.\nLemma 5.11. Let \u03a3 be a sequence and let \u03a3 be any\n1modification of \u03a3. For \u2265 1, if s +1(\u03a3) is always defined\nafter the change, then s (\u03a3 ) \u2264 s +1(\u03a3).\nThe proof is similar to the proof of Lemma 5.7 and\nomitted. A simple application of this lemma is the following: Let\n\u03a3 be any sequence which is an -modification of \u03a3. Then\nwe have s2(\u03a3 ) \u2264 s +2(\u03a3). Now using the above lemma and\nby simple induction we can obtain the following theorem.\nTheorem 5.12. Let \u03a3 be a sequence and let \u03a3 be any\nk-modification of \u03a3. Then\n1. |lastbid(\u03a3) \u2212 lastbid(\u03a3 )| \u2264\nPk\n=1 s +1(\u03a3) \u2264 ksk+1(\u03a3)\n2. |lastask(\u03a3)\u2212lastask(\u03a3 )| \u2264\nPk\n=1 s +1(\u03a3) \u2264 ksk+1(\u03a3)\n3. |close(\u03a3) \u2212 close(\u03a3 )| \u2264\nPk\n=1 s +1(\u03a3) \u2264 ksk+1(\u03a3)\n4. |average(\u03a3) \u2212 average(\u03a3 )| \u2264\nPk\n=1\n\n2(pmax +s +1(\u03a3))\nvolume(\u03a3)\n+ s +1(\u03a3)\n\nwhere s (\u03a3) is the maximum over the -spread in \u03a3 following\nthe first modification.\nWe note that while these bounds depend on deeper\nmeasures of spread for more modifications, we are working in\na 1-share order model. Thus in an actual market, where\nsingle orders contain hundreds or thousands of shares, the\nk-spread even for large k might be quite small and close to\nthe standard 1-spread in liquid stocks.\n6. RELATIVE MODEL INSTABILITY\nIn the relative model the underlying assumption is that\ntraders try to exploit their knowledge of the books to\nstrategically place their orders. Thus if a trader wants her buy\norder to be executed quickly, she may position it above the\ncurrent bid and be the first in the queue; if the trader is\npatient and believes that the price trend is going to be\ndownward she will place orders deeper in the buy book, and so\non.\nWhile in the previous sections we showed stability results\nfor the absolute model, here we provide simple examples\nwhich show instability in the relative model for the\nexecuted volume, last bid, last ask, average execution price and\nthe last execution price. In Section 7 we provide many\nsimulations on actual market data that demonstrate that this\ninstability is inherent to the relative model, and not due\nto artificial constructions. In the relative model we assume\nthat for every sequence the ask and bid are always defined,\nso the books have a non-empty initial configuration.\n126\nWe begin by showing that in the relative model, even a\nsingle modification can double the number of shares\nexecuted.\nTheorem 6.1. There is a sequence \u03a3 and a 1-modification\n\u03a3 of \u03a3 such that volume(\u03a3 ) \u2265 2volume(\u03a3).\nProof. For concreteness we assume that at the\nbeginning the ask is 10 and the bid is 8. The sequence \u03a3 is\ncomposed from n buy orders with \u2206 = 0, followed by n sell\norders with \u2206 = 0, and finally an alternating sequence of\nbuy orders with \u2206 = +1 and sell orders with \u2206 = \u22121 of\nlength 2n. Since the books before the alternating sequence\ncontain n + 1 sell orders at 10 and n + 1 buy orders at 8, we\nhave that each pair of buy sell order in the alternating part\nis matched and executed, but none of the initial 2n orders\nis executed, and thus volume(\u03a3) = n. Now we change the\nfirst buy order to have \u2206 = +1. After the first 2n orders\nthere are still no executions; however, the books are\ndifferent. Now there are n + 1 sell orders at 10, n buy orders at 9\nand one buy order at 8. Now each order in the alternating\nsequence is executed with one of the former orders and we\nhave volume(\u03a3 ) = 2n.\nThe next theorem shows that the spread-based stability\nresults of Section 5.1 do not also hold in the relative model.\nBefore providing the proof, we give its intuition. At the\nbeginning the sell book contains only two prices which are far\napart and both contain only two orders, now several buy\norders arrive, at the original sequence they are not being\nexecuted, while in the modified sequence they will be\nexecuted and leave the sell book with only the orders at the high\nprice. Now many sell orders followed by many buy orders\nwill arrive, such that in the original sequence they will be\nexecuted only at the low price and in the modified sequence\nthey will executed at the high price.\nTheorem 6.2. For any positive numbers s and x, there\nis sequence \u03a3 such that s2(\u03a3) = s and a 1-modification \u03a3\nof \u03a3 such that\n\u2022 |close(\u03a3) \u2212 close(\u03a3 )| \u2265 x\n\u2022 |average(\u03a3) \u2212 average(\u03a3 )| \u2265 x\n\u2022 |lastbid(\u03a3) \u2212 lastbid(\u03a3 )| \u2265 x\n\u2022 |lastask(\u03a3) \u2212 lastask(\u03a3 )| \u2265 x\nProof. Without loss of generality let us consider sequences\nin which all prices are integer-valued, in which case the\nsmallest possible value for the second spread is 1; we provide\nthe proof for the case s2(\u03a3) = 2, but the s2(\u03a3) = 1 case is\nsimilar.\nWe consider a sequence \u03a3 such that after an initialization\nperiod there have been no executions, the buy book has\n2 orders at price 10, and the sell book has two orders at\nprice 12 and 2 orders with value 12+y, where y is a positive\ninteger that will be determined by the analysis. The original\nsequence \u03a3 is a buy order with \u2206 = 0, followed by two\nbuy orders with \u2206 = +1, then 2y sell orders with \u2206 = 0,\nand then 2y buy orders with \u2206 = +1. We first note that\ns2(\u03a3) = 2, there are 2y executions, all at price 12, the last\nbid is 11 and the last ask is 12. Next we analyze a modified\nsequence. We change the first buy order from \u2206 = 0 to\n\u2206 = +1. Therefore, the next two buy orders with \u2206 = +1\nare executed, and afterwards we have that the bid is 11 and\nthe ask is 12 + y. Now the 2y sell orders are accumulated at\n12+y, and after the next y buy orders the bid is at 12+y\u22121.\nTherefore, at the end we have that lastbid(\u03a3 ) = 12 + y \u2212 1,\nlastask(\u03a3 ) = 12 + y, close(\u03a3 ) = 12 + y, and average(\u03a3 ) =\ny\ny+2\n(12 + y) + 2\ny+2\n(12). Setting y = x + 2, we obtain the\nlemma for every property.\nWe note that while this proof was based on the fact that\nthere are two consecutive orders in the books which are far\n(y) apart, we can provide a slightly more complicated\nexample in which all orders are close (at most 2 apart), yet still\none change results in large differences.\n7. SIMULATION STUDIES\nThe results presented so far paint a striking contrast\nbetween the absolute and relative price models: while the\nabsolute model enjoys provably strong stability over any fixed\nevent sequence, there exist at least specific sequences\ndemonstrating great instability in the relative model. The\nworstcase nature of these results raises the question of the extent\nto which such differences could actually occur in real\nmarkets. In this section we provide indirect evidence on this\nquestion by presenting simulation results exploiting a rich\nsource of real-market historical limit order sequence data.\nBy interpreting arriving limit order prices as either\nabsolute values, or by transforming them into differences with\nthe current bid and ask (relative model), we can perform\nsmall modifications on the sequences and examine how\ndifferent various outcomes (volume traded, average price, etc.)\nwould be from what actually occurred in the market. These\nsimulations provide an empirical counterpart to the theory\nwe have developed. We emphasize that all such simulations\ninterpret the actual historical data as falling into either the\nabsolute or relative model, and are meaningful only within\nthe confines of such an interpretation. Nevertheless, we feel\nthey provide valuable empirical insight into the potential\n(in)stability properties of modern equity limit order\nmarkets, and demonstrate that one\"s belief or hope in stability\nlargely relies on an absolute model interpretation. We also\ninvestigate the empirical behavior of mixtures of absolute\nand relative prices.\n7.1 Data\nThe historical data used in our simulations is\ncommercially available limit order data from INET, the previously\nmentioned electronic exchange for NASDAQ stocks. Broadly\nspeaking, this data consists of practically every single event\non INET regarding the trading of an individual\nstockevery arriving limit order (price, volume, and sequence ID\nnumber), every execution, and every cancellation of a\nstanding order - all timestamped in milliseconds. It is data\nsufficient to recreate the precise INET order book in a given\nstock on a given day and time.\nWe will report stability properties for three stocks:\nAmazon, Nvidia, and Qualcomm (identified in the sequel by their\ntickers, AMZN, NVDA and QCOM). These three provide\nsome range of liquidities (with QCOM having the greatest\nand NVDA the least liquidity on INET) and other trading\nproperties. We note that the qualitative results of our\nsimulations were similar for several other stocks we examined.\n127\n7.2 Methodology\nFor our simulations we employed order-book\nreconstruction code operating on the underlying raw data. The basic\nformat of each experiment was the following:\n1. Run the order book reconstruction code on the\noriginal INET data and compute the quantity of interest\n(volume traded, average price, etc.)\n2. Make a small modification to a single order, and\nrecompute the resulting value of the quantity of interest.\nIn the absolute model case, Step 2 is as simple as\nmodifying the order in the original data and re-running the order\nbook reconstruction. For the relative model, we must first\npre-process the raw data and convert its prices to relative\nvalues, then make the modification and re-run the order\nbook reconstruction on the relative values.\nThe type of modification we examined was extremely small\ncompared to the volume of orders placed in these stocks:\nnamely, the deletion of a single randomly chosen order from\nthe sequence. Although a deletion is not 1-modification,\nits edit distance is 1 and we can apply Theorem 5.4. For\neach trading day examined,this single deleted order was\nselected among those arriving between 10 AM and 3 PM, and\nthe quantities of interest were measured and compared at 3\nPM. These times were chosen to include the busiest part of\nthe trading day but avoid the half hour around the opening\nand closing of the official NASDAQ market (9:30 AM and\n3:30 PM respectively), which are known to have different\ndynamics than the central portion of the day.\nWe run the absolute and relative model simulations on\nboth the raw INET data and on a cleaned version of\nthis data. In the cleaned we remove all limit orders that\nwere canceled in the actual market prior to their execution\n(along with the cancellations themselves). The reason is\nthat such cancellations may often be the first step in the\nrepositioning of orders - that is, cancellations of the\norder that are followed by the submission of a replacement\norder at a different price. Not removing canceled orders\nallows the possibility of modified simulations in which the\nsame order 1\nis executed twice, which may magnify\ninstability effects. Again, it is clear that neither the raw nor\nthe cleaned data can perfectly reflect what would have\nhappened under the deleted orders in the actual market.\nHowever, the results both from the raw data and the clean\ndata are qualitatively similar. The results mainly differ, as\nexpected, in the executed volume, where the instability\nresults for the relative model are much more dramatic in the\nraw data.\n7.3 Results\nWe begin with summary statistics capturing our overall\nstability findings. Each row of the tables below contains a\nticker (e.g. AMZN) followed by either -R (for the uncleaned\nor raw data) or -C (for the data with canceled orders\nremoved). For each of the approximately 250 trading days\nin 2003, 1000 trials were run in which a randomly selected\norder was deleted from the INET event sequence. For each\nquantity of interest (volume executed, average price, closing\nprice and last bid), we show for the both the absolute and\n1\nHere same is in quotes since the two orders will actually\nhave different sequence ID numbers, which is what makes\nsuch repositioning activity impossible to reliably detect in\nthe data.\nrelative model the average percentage change in the quantity\ninduced by the deletion.\nThe results confirm rather strikingly the qualitative\nconclusions of the theory we have developed. In virtually every\ncase (stock, raw or cleaned data, and quantity) the\npercentage change induced by a single deletion in the relative\nmodel is many orders of magnitude greater than in the\nabsolute model, and shows that indeed butterfly effects may\noccur in a relative model market. As just one specific\nrepresentative example, notice that for QCOM on the cleaned\ndata, the relative model effect of just a single deletion on the\nclosing price is in excess of a full percentage point. This is\na variety of market impact entirely separate from the more\ntraditional and expected kind generated by trading a large\nvolume of shares.\nStock Date volume average\nRel Abs Rel Abs\nAMZN-R 2003 15.1% 0.04% 0.3% 0.0002%\nAMZN-C 2003 0.69% 0.087% 0.36% 0.0007%\nNVDA-R 2003 9.09% 0.05 % 0.17% 0.0003%\nNVDA-C 2003 0.73% 0.09 % 0.35% 0.001%\nQCOM-R 2003 16.94% 0.035% 0.21% 0.0002%\nQCOM-C 2003 0.58% 0.06% 0.35% 0.0005%\nStock Date close lastbid\nRel Abs Rel Abs\nAMZN-R 2003 0.78% 0.0001% 0.78% 0.0007%\nAMZN-C 2003 1.10% 0.077% 1.11% 0.001%\nNVDA-R 2003 1.17% 0.002 % 1.18 % 0.08%\nNVDA-C 2003 0.45% 0.0003% 0.45% 0.0006%\nQCOM-R 2003 0.58% 0.0001% 0.58% 0.0004%\nQCOM-C 2003 1.05% 0.0006% 1.05% 0.06%\nIn Figure 4 we examine how the change to one the\nquantities, the average execution price, grows with the\nintroduction of greater perturbations of the event sequence in the two\nmodels. Rather than deleting only a single order between\n10 AM and 3 PM, in these experiments a growing number\nof randomly chosen deletions was performed, and the\npercentage change to the average price measured. As suggested\nby the theory we have developed, for the absolute model the\nchange to the average price grows linearly with the number\nof deletions and remains very small (note the vastly\ndifferent scales of the y-axis in the panels for the absolute and\nrelative models in the figure). For the relative model, it is\ninteresting to note that while small numbers of changes have\nlarge effects (often causing average execution price changes\nwell in excess of 0.1 percent), the effects of large numbers of\nchanges levels off quite rapidly and consistently.\nWe conclude with an examination of experiments with a\nmixture model. Even if one accepts a world in which traders\nbehave in either an absolute or relative manner, one would\nbe likely to claim that the market contains a mixture of both.\nWe thus ran simulations in which each arriving order in the\nINET event streams was treated as an absolute price with\nprobability \u03b1, and as a relative price with probability 1\u2212\u03b1.\nRepresentative results for the average execution price in this\nmixture model are shown in Figure 5 for AMZN and NVDA.\nPerhaps as expected, we see a monotonic decrease in the\npercentage change (instability) as the fraction of absolute\ntraders increases, with most of the reduction already being\nrealized by the introduction of just a small population of\nabsolute traders. Thus even in a largely relative-price world, a\n128\n0 10 20 30 40 50 60 70 80 90 100\n0\n0.5\n1\n1.5\n2\n2.5\nx 10\n\u22123 QCOM\u2212R June 2004: Absolute\nNumber of changes\nAverageprice\n0 10 20 30 40 50 60 70 80 90 100\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\nQCOM\u2212R June 2004: Relative\nNumber of changes\nAverageprice\nFigure 4: Percentage change to the average\nexecution price (y-axis) as a function of the number of\ndeletions to the sequence (x-axis). The left panel is\nfor the absolute model, the right panel for the\nrelative model, and each curve corresponds to a single\nday of QCOM trading in June 2004. Curves\nrepresent averages over 1000 trials.\nsmall minority of absolute traders can have a greatly\nstabilizing effect. Similar behavior is found for closing price and\nlast bid.\n0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\nAMZN\u2212R Feburary 2004\n\u03b1\nAverageprice\n0 0.2 0.4 0.6 0.8 1\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\n0.4\nNVDA\u2212R June 2004\n\u03b1\nAverageprice\nFigure 5: Percentage change to the average\nexecution price (y-axis) vs. probability of treating\narriving INET orders as absolute prices (x-axis). Each\ncurve corresponds to a single day of trading during\na month of 2004. Curves represent averages over\n1000 trials.\nFor the executed volume in the mixture model, however,\nthe findings are more curious. In Figure 6, we show how\nthe percentage change to the executed volume varies with\nthe absolute trader fraction \u03b1, for NVDA data that is both\nraw and cleaned of cancellations. We first see that for this\nquantity, unlike the others, the difference induced by the\ncleaned and uncleaned data is indeed dramatic, as already\nsuggested by the summary statistics table above. But most\nintriguing is the fact that the stability is not monotonically\nincreasing with \u03b1 for either the cleaned or uncleaned\ndatathe market with maximum instability is not a pure relative\nprice market, but occurs at some nonzero value for \u03b1. It was\nin fact not obvious to us that sequences with this property\ncould even be artificially constructed, much less that they\nwould occur as actual market data. We have yet to find a\nsatisfying explanation for this phenomenon and leave it to\nfuture research.\n8. ACKNOWLEDGMENTS\nWe are grateful to Yuriy Nevmyvaka of Lehman Brothers\nin New York for the use of his INET order book\nreconstruction code, and for valuable comments on the work presented\n0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1\n0\n0.5\n1\n1.5\n2\n2.5\n3\n3.5\n4\nNVDA\u2212C June 2004\n\u03b1\nVolume\n0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1\n0\n2\n4\n6\n8\n10\n12\n14\n16\n18\nNVDA\u2212R June 2004\n\u03b1\nVolume\nFigure 6: Percentage change to the executed volume\n(y-axis) vs. probability of treating arriving INET\norders as absolute prices (x-axis). The left panel is\nfor NVDA using the raw data that includes\ncancellations, while the right panel is on the cleaned data.\nEach curve corresponds to a single day of trading\nduring June 2004. Curves represent averages over\n1000 trials.\nhere. Yishay Mansour was supported in part by the IST\nProgramme of the European Community, under the PASCAL\nNetwork of Excellence, IST-2002-506778, by a grant from\nthe Israel Science Foundation and an IBM faculty award.\n9. REFERENCES\n[1] D. Bertsimas and A. Lo. Optimal control of execution\ncosts. Journal of Financial Markets, 1:1-50, 1998.\n[2] B. Biais, L. Glosten, and C. Spatt. Market\nmicrostructure: a survey of microfoundations,\nempirical results and policy implications. Journal of\nFinancial Markets, 8:217-264, 2005.\n[3] J.-P. Bouchaud, M. Mezard, and M. Potters.\nStatistical properties of stock order books: empirical\nresults and models. Quantitative Finance, 2:251-256,\n2002.\n[4] C. Cao, O.Hansch, and X. Wang. The informational\ncontent of an open limit order book, 2004. AFA 2005\nPhiladelphia Meetings, EFA Maastricht Meetings\nPaper No. 4311.\n[5] R. Coggins, A. Blazejewski, and M. Aitken. Optimal\ntrade execution of equities in a limit order market. In\nInternational Conference on Computational\nIntelligence for Financial Engineering, pages 371-378,\nMarch 2003.\n[6] D. Farmer and S. Joshi. The price dynamics of\ncommon trading strategies. Journal of Economic\nBehavior and Organization, 29:149-171, 2002.\n[7] J. Hasbrouck. Empirical market microstructure:\nEconomic and statistical perspectives on the dynamics\nof trade in securities markets, 2004. Course notes,\nStern School of Business, New York University.\n[8] R. Kissell and M. Glantz. Optimal Trading Strategies.\nAmacom, 2003.\n[9] S.Kakade, M. Kearns, Y. Mansour, and L. Ortiz.\nCompetitive algorithms for VWAP and limit order\ntrading. In Proceedings of the ACM Conference on\nElectronic Commerce, pages 189-198, 2004.\n[10] Y.Nevmyvaka, Y. Feng, and M. Kearns. Reinforcement\nlearning for optimized trade execution, 2006. Preprint.\n129", "keywords": "bid;market microstructure;absolute trader model;computational finance;penny-jumping;standard continuous limit-order mechanism;modern execution optimization;relative trader model;modern equity market;high-frequency microstructure signal;relative price model;quantitative trading strategy;electronic communication network"}
{"name": "train_J-35", "title": "Efficiency and Nash Equilibria in a Scrip System for P2P Networks", "abstract": "A model of providing service in a P2P network is analyzed. It is shown that by adding a scrip system, a mechanism that admits a reasonable Nash equilibrium that reduces free riding can be obtained. The effect of varying the total amount of money (scrip) in the system on efficiency (i.e., social welfare) is analyzed, and it is shown that by maintaining the appropriate ratio between the total amount of money and the number of agents, efficiency is maximized. The work has implications for many online systems, not only P2P networks but also a wide variety of online forums for which scrip systems are popular, but formal analyses have been lacking.", "fulltext": "1. INTRODUCTION\nA common feature of many online distributed systems is\nthat individuals provide services for each other.\nPeer-topeer (P2P) networks (such as Kazaa [25] or BitTorrent [3])\nhave proved popular as mechanisms for file sharing, and\napplications such as distributed computation and file storage\nare on the horizon; systems such as Seti@home [24] provide\ncomputational assistance; systems such as Slashdot [21]\nprovide content, evaluations, and advice forums in which people\nanswer each other\"s questions. Having individuals provide\neach other with service typically increases the social welfare:\nthe individual utilizing the resources of the system derives a\ngreater benefit from it than the cost to the individual\nproviding it. However, the cost of providing service can still be\nnontrivial. For example, users of Kazaa and BitTorrent may\nbe charged for bandwidth usage; in addition, in some\nfilesharing systems, there is the possibility of being sued, which\ncan be viewed as part of the cost. Thus, in many systems\nthere is a strong incentive to become a free rider and\nbenefit from the system without contributing to it. This is not\nmerely a theoretical problem; studies of the Gnutella [22]\nnetwork have shown that almost 70 percent of users share\nno files and nearly 50 percent of responses are from the top\n1 percent of sharing hosts [1].\nHaving relatively few users provide most of the service\ncreates a point of centralization; the disappearance of a small\npercentage of users can greatly impair the functionality of\nthe system. Moreover, current trends seem to be leading\nto the elimination of the altruistic users on which these\nsystems rely. These heavy users are some of the most\nexpensive customers ISPs have. Thus, as the amount of traffic has\ngrown, ISPs have begun to seek ways to reduce this traffic.\nSome universities have started charging students for\nexcessive bandwidth usage; others revoke network access for it\n[5]. A number of companies have also formed whose service\nis to detect excessive bandwidth usage [19].\nThese trends make developing a system that encourages\na more equal distribution of the work critical for the\ncontinued viability of P2P networks and other distributed online\nsystems. A significant amount of research has gone into\ndesigning reputation systems to give preferential treatment\nto users who are sharing files. Some of the P2P networks\ncurrently in use have implemented versions of these\ntechniques. However, these approaches tend to fall into one of\ntwo categories: either they are barter-like or reputational.\nBy barter-like, we mean that each agent bases its decisions\nonly on information it has derived from its own interactions.\nPerhaps the best-known example of a barter-like system is\nBitTorrent, where clients downloading a file try to find other\nclients with parts they are missing so that they can trade,\nthus creating a roughly equal amount of work. Since the\nbarter is restricted to users currently interested in a\nsingle file, this works well for popular files, but tends to have\nproblems maintaining availability of less popular ones. An\nexample of a barter-like system built on top of a more\ntraditional file-sharing system is the credit system used by eMule\n140\n[8]. Each user tracks his history of interactions with other\nusers and gives priority to those he has downloaded from in\nthe past. However, in a large system, the probability that\na pair of randomly-chosen users will have interacted before\nis quite small, so this interaction history will not be\nterribly helpful. Anagnostakis and Greenwald [2] present a more\nsophisticated version of this approach, but it still seems to\nsuffer from similar problems.\nA number of attempts have been made at providing\ngeneral reputation systems (e.g. [12, 13, 17, 27]). The basic idea\nis to aggregate each user\"s experience into a global number\nfor each individual that intuitively represents the system\"s\nview of that individual\"s reputation. However, these\nattempts tend to suffer from practical problems because they\nimplicitly view users as either good or bad, assume that\nthe good users will act according to the specified protocol,\nand that there are relatively few bad users. Unfortunately,\nif there are easy ways to game the system, once this\ninformation becomes widely available, rational users are likely to\nmake use of it. We cannot count on only a few users being\nbad (in the sense of not following the prescribed protocol).\nFor example, Kazaa uses a measure of the ratio of the\nnumber of uploads to the number of downloads to identify good\nand bad users. However, to avoid penalizing new users, they\ngave new users an average rating. Users discovered that they\ncould use this relatively good rating to free ride for a while\nand, once it started to get bad, they could delete their stored\ninformation and effectively come back as a new user, thus\ncircumventing the system (see [2] for a discussion and [11]\nfor a formal analysis of this whitewashing). Thus Kazaa\"s\nreputation system is ineffective.\nThis is a simple case of a more general vulnerability of\nsuch systems to sybil attacks [6], where a single user\nmaintains multiple identities and uses them in a coordinated\nfashion to get better service than he otherwise would. Recent\nwork has shown that most common reputation systems are\nvulnerable (in the worst case)to such attacks [4]; however,\nthe degree of this vulnerability is still unclear. The\nanalyses of the practical vulnerabilities and the existence of such\nsystems that are immune to such attacks remains an area of\nactive research (e.g., [4, 28, 14]).\nSimple economic systems based on a scrip or money seem\nto avoid many of these problems, are easy to implement and\nare quite popular (see, e.g., [13, 15, 26]). However, they\nhave a different set of problems. Perhaps the most common\ninvolve determining the amount of money in the system.\nRoughly speaking, if there is too little money in the system\nrelative to the number of agents, then relatively few users\ncan afford to make request. On the other hand, if there is\ntoo much money, then users will not feel the need to\nrespond to a request; they have enough money already. A\nrelated problem involves handling newcomers. If newcomers\nare each given a positive amount of money, then the system\nis open to sybil attacks. Perhaps not surprisingly, scrip\nsystems end up having to deal with standard economic woes\nsuch as inflation, bubbles, and crashes [26].\nIn this paper, we provide a formal model in which to\nanalyze scrip systems. We describe a simple scrip system\nand show that, under reasonable assumptions, for each fixed\namount of money there is a nontrivial Nash equilibrium\ninvolving threshold strategies, where an agent accepts a request\nif he has less than $k for some threshold k.1\nAn interesting\naspect of our analysis is that, in equilibrium, the\ndistribution of users with each amount of money is the distribution\nthat maximizes entropy (subject to the money supply\nconstraint). This allows us to compute the money supply that\nmaximizes efficiency (social welfare), given the number of\nagents. It also leads to a solution for the problem of\ndealing with newcomers: we simply assume that new users come\nin with no money, and adjust the price of service (which is\nequivalent to adjusting the money supply) to maintain the\nratio that maximizes efficiency. While assuming that new\nusers come in with no money will not work in all settings,\nwe believe the approach will be widely applicable. In\nsystems where the goal is to do work, new users can acquire\nmoney by performing work. It should also work in\nKazaalike system where a user can come in with some resources\n(e.g., a private collection of MP3s).\nThe rest of the paper is organized as follows. In Section 2,\nwe present our formal model and observe that it can be used\nto understand the effect of altruists. In Section 3, we\nexamine what happens in the game under nonstrategic play, if all\nagents use the same threshold strategy. We show that, in\nthis case, the system quickly converges to a situation where\nthe distribution of money is characterized by maximum\nentropy. Using this analysis, we show in Section 4 that, under\nminimal assumptions, there is a nontrivial Nash equilibrium\nin the game where all agents use some threshold strategy.\nMoreover, we show in Section 5 that the analysis leads to\nan understanding of how to choose the amount of money\nin the system (or, equivalently, the cost to fulfill a request)\nso as to maximize efficiency, and also shows how to handle\nnew users. In Section 6, we discuss the extent to which our\napproach can handle sybils and collusion. We conclude in\nSection 7.\n2. THE MODEL\nTo begin, we formalize providing service in a P2P network\nas a non-cooperative game. Unlike much of the modeling in\nthis area, our model will model the asymmetric interactions\nin a file sharing system in which the matching of players\n(those requesting a file with those who have that particular\nfile) is a key part of the system. This is in contrast with\nmuch previous work which uses random matching in a\nprisoner\"s dilemma. Such models were studied in the economics\nliterature [18, 7] and first applied to online reputations in\n[11]; an application to P2P is found in [9].\nThis random-matching model fails to capture some salient\naspects of a number of important settings. When a request\nis made, there are typically many people in the network who\ncan potentially satisfy it (especially in a large P2P network),\nbut not all can. For example, some people may not have\nthe time or resources to satisfy the request. The\nrandommatching process ignores the fact that some people may not\nbe able to satisfy the request. Presumably, if the person\nmatched with the requester could not satisfy the match, he\nwould have to defect. Moreover, it does not capture the fact\nthat the decision as to whether to volunteer to satisfy\nthe request should be made before the matching process,\nnot after. That is, the matching process does not capture\n1\nAlthough we refer to our unit of scrip as the dollar, these\nare not real dollars nor do we view them as convertible to\ndollars.\n141\nthe fact that if someone is unwilling to satisfy the request,\nthere will doubtless be others who can satisfy it. Finally, the\nactions and payoffs in the prisoner\"s dilemma game do not\nobviously correspond to actual choices that can be made.\nFor example, it is not clear what defection on the part of\nthe requester means. In our model we try to deal with all\nthese issues.\nSuppose that there are n agents. At each round, an agent\nis picked uniformly at random to make a request. Each other\nagent is able to satisfy this request with probability \u03b2 > 0 at\nall times, independent of previous behavior. The term \u03b2 is\nintended to capture the probability that an agent is busy, or\ndoes not have the resources to fulfill the request. Assuming\nthat \u03b2 is time-independent does not capture the intution\nthat being an unable to fulfill a request at time t may well\nbe correlated with being unable to fulfill it at time t+1. We\nbelieve that, in large systems, we should be able to drop the\nindependence assumption, but we leave this for future work.\nIn any case, those agents that are able to satisfy the request\nmust choose whether or not to volunteer to satisfy it. If\nat least one agent volunteers, the requester gets a benefit\nof 1 util (the job is done) and one of volunteers is chosen\nat random to fulfill the request. The agent that fulfills the\nrequest pays a cost of \u03b1 < 1. As is standard in the literature,\nwe assume that agents discount future payoffs by a factor of\n\u03b4 per time unit. This captures the intuition that a util now is\nworth more than a util tomorrow, and allows us to compute\nthe total utility derived by an agent in an infinite game.\nLastly, we assume that with more players requests come\nmore often. Thus we assume that the time between rounds\nis 1/n. This captures the fact that the systems we want\nto model are really processing many requests in parallel, so\nwe would expect the number of concurrent requests to be\nproportional to the number of users.2\nLet G(n, \u03b4, \u03b1, \u03b2) denote this game with n agents, a\ndiscount factor of \u03b4, a cost to satisfy requests of \u03b1, and a\nprobability of being able to satisfy requests of \u03b2. When the\nlatter two parameters are not relevant, we sometimes write\nG(n, \u03b4).\nWe use the following notation throughout the paper:\n\u2022 pt\ndenotes the agent chosen in round t.\n\u2022 Bt\ni \u2208 {0, 1} denotes whether agent i can satisfy the\nrequest in round t. Bt\ni = 1 with probability \u03b2 > 0 and\nBt\ni is independent of Bt\ni for all t = t.\n\u2022 V t\ni \u2208 {0, 1} denotes agent i\"s decision about whether\nto volunteer in round t; 1 indicates volunteering. V t\ni\nis determined by agent i\"s strategy.\n\u2022 vt\n\u2208 {j | V t\nj Bt\nj = 1} denotes the agent chosen to satisfy\nthe request. This agent is chosen uniformly at random\nfrom those who are willing (V t\nj = 1) and able (Bt\nj = 1)\nto satisfy the request.\n\u2022 ut\ni denotes agent i\"s utility in round t.\nA standard agent is one whose utility is determined as\ndiscussed in the introduction; namely, the agent gets\n2\nFor large n, our model converges to one in which players\nmake requests in real time, and the time between a player\"s\nrequests are exponentially distributed with mean 1. In\naddition, the time between requests served by a single player\nis also exponentially distributed.\na utility of 1 for a fulfilled request and utility \u2212\u03b1 for\nfulfilling a request. Thus, if i is a standard agent, then\nut\ni =\n8\n<\n:\n1 if i = pt and\nP\nj=i V t\nj Bt\nj > 0\n\u2212\u03b1 if i = vt\n0 otherwise.\n\u2022 Ui =\nP\u221e\nt=0 \u03b4t/n\nut\ni denotes the total utility for agent\ni. It is the discounted total of agent i\"s utility in each\nround. Note that the effective discount factor is \u03b41/n\nsince an increase in n leads to a shortening of the time\nbetween rounds.\nNow that we have a model of making and satisfying\nrequests, we use it to analyze free riding. Take an altruist to\nbe someone who always fulfills requests. Agent i might\nrationally behave altruistically if agent i\"s utility function has\nthe following form, for some \u03b1 > 0:\nut\ni =\n8\n<\n:\n1 if i = pt and\nP\nj=i V t\nj Bt\nj > 0\n\u03b1 if i = vt\n0 otherwise.\nThus, rather than suffering a loss of utility when satisfying\na request, an agent derives positive utility from satisfying\nit. Such a utility function is a reasonable representation of\nthe pleasure that some people get from the sense that they\nprovide the music that everyone is playing. For such\naltruistic agents, playing the strategy that sets V t\ni = 1 for all t\nis dominant. While having a nonstandard utility function\nmight be one reason that a rational agent might use this\nstrategy, there are certainly others. For example a naive\nuser of filesharing software with a good connection might\nwell follow this strategy. All that matters for the\nfollowing discussion is that there are some agents that use this\nstrategy, for whatever reason.\nAs we have observed, such users seem to exist in some\nlarge systems. Suppose that our system has a altruists.\nIntuitively, if a is moderately large, they will manage to satisfy\nmost of the requests in the system even if other agents do\nno work. Thus, there is little incentive for any other agent\nto volunteer, because he is already getting full advantage of\nparticipating in the system. Based on this intuition, it is a\nrelatively straightforward calculation to determine a value\nof a that depends only on \u03b1, \u03b2, and \u03b4, but not the number\nn of players in the system, such that the dominant strategy\nfor all standard agents i is to never volunteer to satisfy any\nrequests (i.e., V t\ni = 0 for all t).\nProposition 2.1. There exists an a that depends only on\n\u03b1, \u03b2, and \u03b4 such that, in G(n, \u03b4, \u03b1, \u03b2) with at least a altruists,\nnot volunteering in every round is a dominant strategy for\nall standard agents.\nProof. Consider the strategy for a standard player j in\nthe presence of a altruists. Even with no money, player\nj will get a request satisfied with probability 1 \u2212 (1 \u2212 \u03b2)a\njust through the actions of these altruists. Thus, even if j is\nchosen to make a request in every round, the most additional\nexpected utility he can hope to gain by having money isP\u221e\nk=1(1 \u2212 \u03b2)a\n\u03b4k\n= (1 \u2212 \u03b2)a\n/(1 \u2212 \u03b4). If (1 \u2212 \u03b2)a\n/(1 \u2212 \u03b4) > \u03b1\nor, equivalently, if a > log1\u2212\u03b2(\u03b1(1 \u2212 \u03b4)), never volunteering\nis a dominant strategy.\nConsider the following reasonable values for our\nparameters: \u03b2 = .01 (so that each player can satisfy 1% of the\nrequests), \u03b1 = .1 (a low but non-negligible cost), \u03b4 = .9999/day\n142\n(which corresponds to a yearly discount factor of\napproximately 0.95), and an average of 1 request per day per player.\nThen we only need a > 1145. While this is a large number,\nit is small relative to the size of a large P2P network.\nCurrent systems all have a pool of users behaving like our\naltruists. This means that attempts to add a reputation\nsystem on top of an existing P2P system to influence users\nto cooperate will have no effect on rational users. To have\na fair distribution of work, these systems must be\nfundamentally redesigned to eliminate the pool of altruistic users.\nIn some sense, this is not a problem at all. In a system\nwith altruists, the altruists are presumably happy, as are\nthe standard agents, who get almost all their requests\nsatisfied without having to do any work. Indeed, current P2P\nnetwork work quite well in terms of distributing content to\npeople. However, as we said in the introduction, there is\nsome reason to believe these altruists may not be around\nforever. Thus, it is worth looking at what can be done to\nmake these systems work in their absence. For the rest of\nthis paper we assume that all agents are standard, and try\nto maximize expected utility.\nWe are interested in equilibria based on a scrip system.\nEach time an agent has a request satisfied he must pay the\nperson who satisfied it some amount. For now, we assume\nthat the payment is fixed; for simplicity, we take the amount\nto be $1. We denote by M the total amount of money in\nthe system. We assume that M > 0 (otherwise no one will\never be able to get paid).\nIn principle, agents are free to adopt a very wide\nvariety of strategies. They can make decisions based on the\nnames of other agents or use a strategy that is heavily\nhistory dependant, and mix these strategies freely. To aid our\nanalysis, we would like to be able to restrict our attention to\na simpler class of strategies. The class of strategies we are\ninterested in is easy to motivate. The intuitive reason for\nwanting to earn money is to cater for the possibility that an\nagent will run out before he has a chance to earn more. On\nthe other hand, a rational agent with plenty of mone would\nnot want to work, because by the time he has managed to\nspend all his money, the util will have less value than the\npresent cost of working. The natural balance between these\ntwo is a threshold strategy. Let Sk be the strategy where\nan agent volunteers whenever he has less than k dollars and\nnot otherwise. Note that S0 is the strategy where the agent\nnever volunteers. While everyone playing S0 is a Nash\nequilibrium (nobody can do better by volunteering if no one else\nis willing to), it is an uninteresting one. As we will show\nin Section 4, it is sufficient to restrict our attention to this\nclass of strategies.\nWe use Kt\ni to denote the amount of money agent i has\nat time t. Clearly Kt+1\ni = Kt\ni unless agent i has a request\nsatisfied, in which case Kt+1\ni = Kt+1\ni \u2212 1 or agent i fulfills a\nrequest, in which case Kt+1\ni = Kt+1\ni + 1. Formally,\nKt+1\ni =\n8\n<\n:\nKt\ni \u2212 1 if i = pt\n,\nP\nj=i V t\nj Bt\nj > 0, and Kt\ni > 0\nKt\ni + 1 if i = vt\nand Kt\npt > 0\nKt\ni otherwise.\nThe threshold strategy Sk is the strategy such that\nV t\ni =\n\uf6be\n1 if Kt\npt > 0 and Kt\ni < k\n0 otherwise.\n3. THE GAME UNDER NONSTRATEGIC\nPLAY\nBefore we consider strategic play, we examine what\nhappens in the system if everyone just plays the same strategy\nSk. Our overall goal is to show that there is some\ndistribution over money (i.e., the fraction of people with each\namount of money) such that the system converges to this\ndistribution in a sense to be made precise shortly.\nSuppose that everyone plays Sk. For simplicity, assume\nthat everyone has at most k dollars. We can make this\nassumption with essentially no loss of generality, since if\nsomeone has more than k dollars, he will just spend money\nuntil he has at most k dollars. After this point he will never\nacquire more than k. Thus, eventually the system will be\nin such a state. If M \u2265 kn, no agent will ever be willing to\nwork. Thus, for the purposes of this section we assume that\nM < kn.\nFrom the perspective of a single agent, in (stochastic)\nequilibrium, the agent is undergoing a random walk.\nHowever, the parameters of this random walk depend on the\nrandom walks of the other agents and it is quite complicated\nto solve directly. Thus we consider an alternative analysis\nbased on the evolution of the system as a whole.\nIf everyone has at most k dollars, then the amount of\nmoney that an agent has is an element of {0, . . . , k}. If there\nare n agents, then the state of the game can be described\nby identifying how much money each agent has, so we can\nrepresent it by an element of Sk,n = {0, . . . , k}{1,...,n}\n. Since\nthe total amount of money is constant, not all of these states\ncan arise in the game. For example the state where each\nplayer has $0 is impossible to reach in any game with money\nin the system. Let mS(s) =\nP\ni\u2208{1...n} s(i) denote the total\nmount of money in the game at state s, where s(i) is the\nnumber of dollars that agent i has in state s. We want\nto consider only those states where the total money in the\nsystem is M, namely\nSk,n,M = {s \u2208 Sk,n | mS(s) = M}.\nUnder the assumption that all agents use strategy Sk, the\nevolution of the system can be treated as a Markov chain\nMk,n,M over the state space Sk,n,M . It is possible to move\nfrom one state to another in a single round if by choosing\na particular agent to make a request and a particular agent\nto satisfy it, the amounts of money possesed by each agent\nbecome those in the second state. Therefore the\nprobability of a transition from a state s to t is 0 unless there exist\ntwo agents i and j such that s(i ) = t(i ) for all i /\u2208 {i, j},\nt(i) = s(i) + 1, and t(j) = s(j) \u2212 1. In this case the\nprobability of transitioning from s to t is the probability of j\nbeing chosen to spend a dollar and has someone willing and\nable to satisfy his request ((1/n)(1 \u2212 (1 \u2212 \u03b2)|{i |s(i )=k}|\u2212Ij\n)\nmultiplied by the probability of i being chosen to satisfy his\nrequest (1/(|({i | s(i ) = k}| \u2212 Ij )). Ij is 0 if j has k dollars\nand 1 otherwise (it is just a correction for the fact that j\ncannot satisfy his own request.)\nLet \u2206k\ndenote the set of probability distributions on {0, . . . , k}.\nWe can think of an element of \u2206k\nas describing the fraction\nof people with each amount of money. This is a useful way\nof looking at the system, since we typically don\"t care who\nhas each amount of money, but just the fraction of people\nthat have each amount. As before, not all elements of \u2206k\nare possible, given our constraint that the total amount of\n143\nmoney is M. Rather than thinking in terms of the total\namount of money in the system, it will prove more useful to\nthink in terms of the average amount of money each player\nhas. Of course, the total amount of money in a system\nwith n agents is M iff the average amount that each player\nhas is m = M/n. Let \u2206k\nm denote all distributions d \u2208 \u2206k\nsuch that E(d) = m (i.e.,\nPk\nj=0 d(j)j = m). Given a state\ns \u2208 Sk,n,M , let ds\n\u2208 \u2206k\nm denote the distribution of money\nin s. Our goal is to show that, if n is large, then there is\na distribution d\u2217\n\u2208 \u2206k\nm such that, with high probability,\nthe Markov chain Mk,n,M will almost always be in a state\ns such that ds\nis close to d\u2217\n. Thus, agents can base their\ndecisions about what strategy to use on the assumption that\nthey will be in such a state.\nWe can in fact completely characterize the distribution\nd\u2217\n. Given a distribution d \u2208 \u2206k\n, let\nH(d) = \u2212\nX\n{j:d(j)=0}\nd(j) log(d(j))\ndenote the entropy of d. If \u2206 is a closed convex set of\ndistributions, then it is well known that there is a unique\ndistribution in \u2206 at which the entropy function takes its maximum\nvalue in \u2206. Since \u2206k\nm is easily seen to be a closed convex set\nof distributions, it follows that there is a unique distribution\nin \u2206k\nm that we denote d\u2217\nk,m whose entropy is greater than\nthat of all other distributions in \u2206k\nm. We now show that,\nfor n sufficiently large, the Markov chain Mk,n,M is almost\nsurely in a state s such that ds\nis close to d\u2217\nk,M/n. The\nstatement is correct under a number of senses of close.\nFor definiteness, we consider the Euclidean distance. Given\n> 0, let Sk,n,m, denote the set of states s in Sk,n,mn such\nthat\nPk\nj=0 |ds\n(j) \u2212 d\u2217\nk,m|2\n< .\nGiven a Markov chain M over a state space S and S \u2286 S,\nlet Xt,s,S be the random variable that denotes that M is in\na state of S at time t, when started in state s.\nTheorem 3.1. For all > 0, all k, and all m, there exists\nn such that for all n > n and all states s \u2208 Sk,n,mn, there\nexists a time t\u2217\n(which may depend on k, n, m, and ) such\nthat for t > t\u2217\n, we have Pr(Xt,s,Sk,n,m, ) > 1 \u2212 .\nProof. (Sketch) Suppose that at some time t, Pr(Xt,s,s )\nis uniform for all s . Then the probability of being in a set of\nstates is just the size of the set divided by the total number of\nstates. A standard technique from statistical mechanics is to\nshow that there is a concentration phenomenon around the\nmaximum entropy distribution [16]. More precisely, using\na straightforward combinatorial argument, it can be shown\nthat the fraction of states not in Sk,n,m, is bounded by\np(n)/ecn\n, where p is a polynomial. This fraction clearly\ngoes to 0 as n gets large. Thus, for sufficiently large n,\nPr(Xt,s,Sk,n,m, ) > 1 \u2212 if Pr(Xt,s,s ) is uniform.\nIt is relatively straightforward to show that our Markov\nChain has a limit distribution \u03c0 over Sk,n,mn, such that for\nall s, s \u2208 Sk,n,mn, limt\u2192\u221e Pr(Xt,s,s ) = \u03c0s . Let Pij denote\nthe probability of transitioning from state i to state j. It\nis easily verified by an explicit computation of the\ntransition probabilities that Pij = Pji for all states i and j. It\nimmediatly follows from this symmetry that \u03c0s = \u03c0s , so\n\u03c0 is uniform. After a sufficient amount of time, the\ndistribution will be close enough to \u03c0, that the probabilities are\nagain bounded by constant, which is sufficient to complete\nthe theorem.\n0 0.002 0.004 0.006 0.008 0.01\nEuclidean Distance\n2000\n2500\n3000\n3500\n4000\nNumberofSteps\nFigure 1: Distance from maximum-entropy\ndistribution with 1000 agents.\n5000 10000 15000 20000 25000\nNumber of Agents\n0.001\n0.002\n0.003\n0.004\n0.005\nMaximumDistance\nFigure 2: Maximum distance from\nmaximumentropy distribution over 106\ntimesteps.\n0 5000 10000 15000 20000 25000\nNumber of Agents\n0\n20000\n40000\n60000\nTimetoDistance.001\nFigure 3: Average time to get within .001 of the\nmaximum-entropy distribution.\n144\nWe performed a number of experiments that show that\nthe maximum entropy behavior described in Theorem 3.1\narises quickly for quite practical values of n and t. The\nfirst experiment showed that, even if n = 1000, we reach\nthe maximum-entropy distribution quickly. We averaged 10\nruns of the Markov chain for k = 5 where there is enough\nmoney for each agent to have $2 starting from a very extreme\ndistribution (every agent has either $0 or $5) and considered\nthe average time needed to come within various distances\nof the maximum entropy distribution. As Figure 1 shows,\nafter 2,000 steps, on average, the Euclidean distance from\nthe average distribution of money to the maximum-entropy\ndistribution is .008; after 3,000 steps, the distance is down\nto .001. Note that this is really only 3 real time units since\nwith 1000 players we have 1000 transactions per time unit.\nWe then considered how close the distribution stays to\nthe maximum entropy distribution once it has reached it.\nTo simplify things, we started the system in a state whose\ndistribution was very close to the maximum-entropy\ndistribution and ran it for 106\nsteps, for various values of n.\nAs Figure 2 shows, the system does not move far from the\nmaximum-entropy distribution once it is there. For\nexample, if n = 5000, the system is never more than distance .001\nfrom the maximum-entropy distribution; if n = 25, 000, it is\nnever more than .0002 from the maximum-entropy\ndistribution.\nFinally, we considered how more carefully how quickly\nthe system converges to the maximum-entropy distribution\nfor various values of n. There are approximately kn\n\npossible states, so the convergence time could in principle be\nquite large. However, we suspect that the Markov chain\nthat arises here is rapidly mixing, which means that it will\nconverge significantly faster (see [20] for more details about\nrapid mixing). We believe that the actually time needed is\nO(n). This behavior is illustrated in Figure 3, which shows\nthat for our example chain (again averaged over 10 runs),\nafter 3n steps, the Euclidean distance between the actual\ndistribution of money in the system and the maximum-entropy\ndistribution is less than .001.\n4. THE GAME UNDER STRATEGIC PLAY\nWe have seen that the system is well behaved if the agents\nall follow a threshold strategy; we now want to show that\nthere is a nontrivial Nash equilibrium where they do so (that\nis, a Nash equilibrium where all the agents use Sk for some\nk > 0.) This is not true in general. If \u03b4 is small, then agents\nhave no incentive to work. Intuitively, if future utility is\nsufficiently discounted, then all that matters is the present,\nand there is no point in volunteering to work. With small\n\u03b4, S0 is the only equilibrium. However, we show that for \u03b4\nsufficiently large, there is another equilibrium in threshold\nstrategies. We do this by first showing that, if every other\nagent is playing a threshold strategy, then there is a best\nresponse that is also a threshold strategy (although not\nnecessarily the same one). We then show that there must be\nsome (mixed) threshold strategy for which this best response\nis the same strategy. It follows that this tuple of threshold\nstrategies is a Nash equilibrium.\nAs a first step, we show that, for all k, if everyone other\nthan agent i is playing Sk, then there is a threshold\nstrategy Sk that is a best response for agent i. To prove this,\nwe need to assume that the system is close to the\nsteadystate distribution (i.e., the maximum-entropy distribution).\nHowever, as long as \u03b4 is sufficiently close to 1, we can ignore\nwhat happens during the period that the system is not in\nsteady state.3\nWe have thus far considered threshold strategies of the\nform Sk, where k is a natural number; this is a discrete set\nof strategies. For a later proof, it will be helpful to have\na continuous set of strategies. If \u03b3 = k + \u03b3 , where k is\na natural number and 0 \u2264 \u03b3 < 1, let S\u03b3 be the strategy\nthat performs Sk with probability 1 \u2212 \u03b3 and Sk+1 with\nprobability \u03b3. (Note that we are not considering arbitrary\nmixed threshold strategies here, but rather just mixing\nbetween adjacent strategies for the sole purpose of making out\nstrategies continuous in a natural way.) Theorem 3.1\napplies to strategies S\u03b3 (the same proof goes through without\nchange), where \u03b3 is an arbitrary nonnegative real number.\nTheorem 4.1. Fix a strategy S\u03b3 and an agent i. There\nexists \u03b4\u2217\n< 1 and n\u2217\nsuch that if \u03b4 > \u03b4\u2217\n, n > n\u2217\n, and every\nagent other than i is playing S\u03b3 in game G(n, \u03b4), then there\nis an integer k such that the best response for agent i is Sk .\nEither k is unique (that is, there is a unique best response\nthat is also a threshold strategy), or there exists an integer\nk such that S\u03b3 is a best response for agent i for all \u03b3 in\nthe interval [k , k +1] (and these are the only best responses\namong threshold strategies).\nProof. (Sketch:) If \u03b4 is sufficiently large, we can ignore\nwhat happens before the system converges to the\nmaximumentropy distribution. If n is sufficiently large, then the\nstrategy played by one agent will not affect the distribution of\nmoney significantly. Thus, the probability of i moving from\none state (dollar amount) to another depends only on i\"s\nstrategy (since we can take the probability that i will be\nchosen to make a request and the probability that i will\nbe chosen to satisfy a request to be constant). Thus, from\ni\"s point of view, the system is a Markov decision process\n(MDP), and i needs to compute the optimal policy\n(strategy) for this MDP. It follows from standard results [23,\nTheorem 6.11.6] that there is an optimal policy that is a\nthreshold policy.\nThe argument that the best response is either unique or\nthere is an interval of best responses follows from a more\ncareful analysis of the value function for the MDP.\nWe remark that there may be best responses that are not\nthreshold strategies. All that Theorem 4.1 shows is that,\namong best responses, there is at least one that is a threshold\nstrategy. Since we know that there is a best response that\nis a threshold strategy, we can look for a Nash equilibrium\nin the space of threshold strategies.\nTheorem 4.2. For all M, there exists \u03b4\u2217\n< 1 and n\u2217\nsuch\nthat if \u03b4 > \u03b4\u2217\nand n > n\u2217\n, there exists a Nash equilibrium in\nthe game G(n, \u03b4) where all agents play S\u03b3 for some integer\n\u03b3 > 0.\nProof. It follows easily from the proof Theorem 4.1 that\nif br(\u03b4, \u03b3) is the minimal best response threshold strategy if\nall the other agents are playing S\u03b3 and the discount factor is\n\u03b4 then, for fixed \u03b4, br(\u03b4, \u00b7) is a step function. It also follows\n3\nFormally, we need to define the strategies when the system\nis far from equilibrium. However, these far from (stochastic)\nequilibrium strategies will not affect the equilibrium\nbehavior when n is large and deviations from stochastic\nequilibrium are extremely rare.\n145\nfrom the theorem that if there are two best responses, then\na mixture of them is also a best response. Therefore, if we\ncan join the steps by a vertical line, we get a best-response\ncurve. It is easy to see that everywhere that this\nbestresponse curve crosses the diagonal y = x defines a Nash\nequilibrium where all agents are using the same threshold\nstrategy. As we have already observed, one such\nequilibrium occurs at 0. If there are only $M in the system, we can\nrestrict to threshold strategies Sk where k \u2264 M + 1. Since\nno one can have more than $M, all strategies Sk for k > M\nare equivalent to SM ; these are just the strategies where\nthe agent always volunteers in response to request made by\nsomeone who can pay. Clearly br(\u03b4, SM ) \u2264 M for all \u03b4, so\nthe best response function is at or below the equilibrium at\nM. If k \u2264 M/n, every player will have at least k dollars\nand so will be unwilling to work and the best response is\njust 0. Consider k\u2217\n, the smallest k such that k > M/n. It\nis not hard to show that for k\u2217\nthere exists a \u03b4\u2217\nsuch that\nfor all \u03b4 \u2265 \u03b4\u2217\n, br(\u03b4, k\u2217\n) \u2265 k\u2217\n. It follows by continuity that if\n\u03b4 \u2265 \u03b4\u2217\n, there must be some \u03b3 such that br(\u03b4, \u03b3) = \u03b3. This\nis the desired Nash equilibrium.\nThis argument also shows us that we cannot in general\nexpect fixed points to be unique. If br(\u03b4, k\u2217\n) = k\u2217\nand\nbr(\u03b4, k + 1) > k + 1 then our argument shows there must be\na second fixed point. In general there may be multiple fixed\npoints even when br(\u03b4, k\u2217\n) > k\u2217\n, as illustrated in the Figure\n4 with n = 1000 and M = 3000.\n0 5 10 15 20 25\nStrategy of Rest of Agents\n0\n5\n10\n15\n20\n25\nBestResponse\nFigure 4: The best response function for n = 1000\nand M = 3000.\nTheorem 4.2 allows us to restrict our design to agents\nusing threshold strategies with the confidence that there will\nbe a nontrivial equilibrium. However, it does not rule out\nthe possibility that there may be other equilibria that do\nnot involve threshold stratgies. It is even possible (although\nit seems unlikely) that some of these equilibria might be\nbetter.\n5. SOCIAL WELFARE AND SCALABITY\nOur theorems show that for each value of M and n, for\nsufficiently large \u03b4, there is a nontrivial Nash equilibrium\nwhere all the agents use some threshold strategy S\u03b3(M,n).\nFrom the point of view of the system designer, not all\nequilibria are equally good; we want an equilibrium where as few\nas possible agents have $0 when they get a chance to make a\nrequest (so that they can pay for the request) and relatively\nfew agents have more than the threshold amount of money\n(so that there are always plenty of agents to fulfill the\nrequest). There is a tension between these objectives. It is not\nhard to show that as the fraction of agents with $0 increases\nin the maximum entropy distribution, the fraction of agents\nwith the maximum amount of money decreases. Thus, our\ngoal is to understand what the optimal amount of money\nshould be in the system, given the number of agents. That\nis, we want to know the amount of money M that maximizes\nefficiency, i.e., the total expected utility if all the agents use\nS\u03b3(M,n). 4\nWe first observe that the most efficient equilibrium\ndepends only on the ratio of M to n, not on the actual values\nof M and n.\nTheorem 5.1. There exists n\u2217\nsuch that for all games\nG(n1, \u03b4) and G(n2, \u03b4) where n1, n2 > n\u2217\n, if M1/n1 = M2/n2,\nthen S\u03b3(M1,n1) = S\u03b3(M2,n2).\nProof. Fix M/n = r. Theorem 3.1 shows that the\nmaximum-entropy distribution depends only on k and the\nratio M/n, not on M and n separately. Thus, given r, for\neach choice of k, there is a unique maximum entropy\ndistribution dk,r. The best response br(\u03b4, k) depends only on the\ndistribution dk,r, not M or n. Thus, the Nash equilibrium\ndepends only on the ratio r. That is, for all choices of M\nand n such that n is sufficiently large (so that Theorem 3.1\napplies) and M/n = r, the equilibrium strategies are the\nsame.\nIn light of Theorem 5.1, the system designer should ensure\nthat there is enough money M in the system so that the\nratio between M/n is optimal. We are currently exploring\nexactly what the optimal ratio is. As our very preliminary\nresults for \u03b2 = 1 show in Figure 5, the ratio appears to be\nmonotone increasing in \u03b4, which matches the intuition that\nwe should provide more patient agents with the opportunity\nto save more money. Additionally, it appears to be relatively\nsmooth, which suggests that it may have a nice analytic\nsolution.\n0.9 0.91 0.92 0.93 0.94 0.95\nDiscount Rate \u2206\n5\n5.5\n6\n6.5\n7\nOptimalRatioofMn\nFigure 5: Optimal average amount of money to the\nnearest .25 for \u03b2 = 1\nWe remark that, in practice, it may be easier for the\ndesigner to vary the price of fulfilling a request rather than\n4\nIf there are multiple equilibria, we take S\u03b3(M,n) to be the\nNash equilibrium that has highest efficiency for fixed M and\nn.\n146\ninjecting money in the system. This produces the same\neffect. For example, changing the cost of fulfilling a request\nfrom $1 to $2 is equivalent to halving the amount of money\nthat each agent has. Similarly, halving the the cost of\nfulfilling a request is equivalent to doubling the amount of money\nthat everyone has. With a fixed amount of money M, there\nis an optimal product nc of the number of agents and the\ncost c of fulfilling a request.\nTheorem 5.1 also tells us how to deal with a dynamic pool\nof agents. Our system can handle newcomers relatively\neasily: simply allow them to join with no money. This gives\nexisting agents no incentive to leave and rejoin as\nnewcomers. We then change the price of fulfilling a request so that\nthe optimal ratio is maintained. This method has the nice\nfeature that it can be implemented in a distributed fashion;\nif all nodes in the system have a good estimate of n then\nthey can all adjust prices automatically. (Alternatively, the\nnumber of agents in the system can be posted in a\npublic place.) Approaches that rely on adjusting the amount\nof money may require expensive system-wide computations\n(see [26] for an example), and must be carefully tuned to\navoid creating incentives for agents to manipulate the\nsystem by which this is done.\nNote that, in principle, the realization that the cost of\nfulfilling a request can change can affect an agent\"s\nstrategy. For example, if an agent expects the cost to increase,\nthen he may want to defer volunteering to fulfill a request.\nHowever, if the number of agents in the system is always\nincreasing, then the cost always decreases, so there is never\nany advantage in waiting.\nThere may be an advantage in delaying a request, but it\nis far more costly, in terms of waiting costs than in\nproviding service, since we assume the need for a service is often\nsubject to real waiting costs, while the need to supply the\nservice is merely to augment a money supply. (Related\nissues are discussed in [10].)\nWe ultimately hope to modify the mechanism so that the\nprice of a job can be set endogenously within the system\n(as in real-world economies), with agents bidding for jobs\nrather than there being a fixed cost set externally. However,\nwe have not yet explored the changes required to implement\nthis change. Thus, for now, we assume that the cost is set\nas a function of the number of agents in the system (and\nthat there is no possibility for agents to satisfy a request for\nless than the official cost or for requesters to offer to pay\nmore than it).\n6. SYBILS AND COLLUSION\nIn a naive sense, our system is essentially sybil-proof. To\nget d dollars, his sybils together still have to perform d units\nof work. Moreover, since newcomers enter the system with\n$0, there is no benefit to creating new agents simply to take\nadvantage of an initial endowment. Nevertheless, there are\nsome less direct ways that an agent could take advantage\nof sybils. First, by having more identities he will have a\ngreater probability of getting chosen to make a request. It\nis easy to see that this will lead to the agent having higher\ntotal utility. However, this is just an artifact of our model.\nTo make our system simple to analyze, we have assumed\nthat request opportunities came uniformly at random. In\npractice, requests are made to satisfy a desire. Our model\nimplicitly assumed that all agents are equally likely to have\na desire at any particular time. Having sybils should not\nincrease the need to have a request satisfied. Indeed, it would\nbe reasonable to assume that sybils do not make requests at\nall.\nSecond, having sybils makes it more likely that one of the\nsybils will be chosen to fulfill a request. This can allow a\nuser to increase his utility by setting a lower threshold; that\nis, to use a strategy Sk where k is smaller than the k used\nby the Nash equilibrium strategy. Intuitively, the need for\nmoney is not as critical if money is easier to obtain.\nUnlike the first concern, this seems like a real issue. It seems\nreasonable to believe that when people make a decision\nbetween a number of nodes to satisfy a request they do so\nat random, at least to some extent. Even if they look for\nadvertised node features to help make this decision, sybils\nwould allow a user to advertise a wide range of features.\nThird, an agent can drive down the cost of fulfilling a\nrequest by introducing many sybils. Similarly, he could\nincrease the cost (and thus the value of his money) by making\na number of sybils leave the system. Concievably he could\nalternate between these techniques to magnify the effects of\nwork he does. We have not yet calculated the exact effect of\nthis change (it interacts with the other two effects of having\nsybils that we have already noted). Given the number of\nsybils that would be needed to cause a real change in the\nperceived size of a large P2P network, the practicality of this\nattack depends heavily on how much sybils cost an attacker\nand what resources he has available.\nThe second point raised regarding sybils also applies to\ncollusion if we allow money to be loaned. If k agents\ncollude, they can agree that, if one runs out of money, another\nin the group will loan him money. By pooling their money\nin this way, the k agents can again do better by setting a\nhigher threshold. Note that the loan mechanism doesn\"t\nneed to be built into the system; the agents can simply use\na fake transaction to transfer the money. These appear\nto be the main avenues for collusive attacks, but we are still\nexploring this issue.\n7. CONCLUSION\nWe have given a formal analysis of a scrip system and\nhave shown that the existence of a Nash equilibrium where\nall agents use a threshold strategy. Moreover, we can\ncompute efficiency of equilibrium strategy and optimize the price\n(or money supply) to maximize efficiency. Thus, our\nanalysis provides a formal mechanisms for solving some important\nproblems in implementing scrip systems. It tells us that with\na fixed population of rational users, such systems are very\nunlikely to become unstable. Thus if this stability is\ncommon belief among the agents we would not expect inflation,\nbubbles, or crashes because of agent speculation. However,\nwe cannot rule out the possibility that that agents may have\nother beliefs that will cause them to speculate. Our\nanalysis also tells us how to scale the system to handle an influx\nof new users without introducing these problems: scale the\nmoney supply to keep the average amount of money constant\n(or equivalently adjust prices to achieve the same goal).\nThere are a number of theoretical issues that are still open,\nincluding a characterization of the multiplicity of\nequilibria - are there usually 2? In addition, we expect that one\nshould be able to compute analytic estimates for the best\nresponse function and optimal pricing which would allow us\nto understand the relationship between pricing and various\nparameters in the model.\n147\nIt would also be of great interest to extend our analysis\nto handle more realistic settings. We mention a few possible\nextensions here:\n\u2022 We have assumed that the world is homogeneous in a\nnumber of ways, including request frequency, utility,\nand ability to satisfy requests. It would be\ninteresting to examine how relaxing any of these assumptions\nwould alter our results.\n\u2022 We have assumed that there is no cost to an agent\nto be a member of the system. Suppose instead that\nwe imposed a small cost simply for being present in\nthe system to reflect the costs of routing messages and\noverlay maintainance. This modification could have a\nsignificant impact on sybil attacks.\n\u2022 We have described a scrip system that works when\nthere are no altruists and have shown that no system\ncan work once there there are sufficiently many\naltruists. What happens between these extremes?\n\u2022 One type of irrational behavior encountered with\nscrip systems is hoarding. There are some similarities\nbetween hoarding and altruistic behavior. While an\naltruist provide service for everyone, a hoarder will\nvolunteer for all jobs (in order to get more money) and\nrarely request service (so as not to spend money). It\nwould be interesting to investigate the extent to which\nour system is robust against hoarders. Clearly with\ntoo many hoarders, there may not be enough money\nremaining among the non-hoarders to guarantee that,\ntypically, a non-hoarder would have enough money to\nsatisfy a request.\n\u2022 Finally, in P2P filesharing systems, there are\noverlapping communities of various sizes that are significantly\nmore likely to be able to satisfy each other\"s requests.\nIt would be interesting to investigate the effect of such\ncommunities on the equilibrium of our system.\nThere are also a number of implementation issues that\nwould have to be resolved in a real system. For example, we\nneed to worry about the possibility of agents counterfeiting\nmoney or lying about whether service was actually provided.\nKarma [26] provdes techniques for dealing with both of these\nissues and a number of others, but some of Karma\"s\nimplementation decisions point to problems for our model. For\nexample, it is prohibitively expensive to ensure that bank\naccount balances can never go negative, a fact that our model\ndoes not capture. Another example is that Karma has nodes\nserve as bookkeepers for other nodes account balances. Like\nmaintaining a presence in the network, this imposes a cost\non the node, but unlike that, responsibility it can be easily\nshirked. Karma suggests several ways to incentivize nodes\nto perform these duties. We have not investigated whether\nthese mechanisms be incorporated without disturbing our\nequilibrium.\n8. ACKNOWLEDGEMENTS\nWe would like to thank Emin Gun Sirer, Shane\nHenderson, Jon Kleinberg, and 3 anonymous referees for helpful\nsuggestions. EF, IK and JH are supported in part by NSF\nunder grant ITR-0325453. JH is also supported in part\nby NSF under grants CTC-0208535 and IIS-0534064, by\nONR under grant N00014-01-10-511, by the DoD\nMultidisciplinary University Research Initiative (MURI) program\nadministered by the ONR under grants N00014-01-1-0795 and\nN00014-04-1-0725, and by AFOSR under grant\nF49620-021-0101.\n9. REFERENCES\n[1] E. Adar and B. A. Huberman. Free riding on\nGnutella. First Monday, 5(10), 2000.\n[2] K. G. Anagnostakis and M. Greenwald.\nExchange-based incentive mechanisms for peer-to-peer\nfile sharing. In International Conference on Distributed\nComputing Systems (ICDCS), pages 524-533, 2004.\n[3] BitTorrent Inc. BitTorrent web site.\nhttp://www.bittorent.com.\n[4] A. Cheng and E. Friedman. Sybilproof reputation\nmechanisms. In Workshop on Economics of\nPeer-to-Peer Systems (P2PECON), pages 128-132,\n2005.\n[5] Cornell Information Technologies. 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In Conference on the World Wide\nWeb (WWW), pages 640-651, 2003.\n[18] M. Kandori. Social norms and community\nenforcement. Review of Economic Studies, 59:63-80,\n1992.\n[19] LogiSense Corporation. LogiSense web site.\nhttp://www.logisense.com/tm p2p.html.\n[20] L. Lovasz and P. Winkler. Mixing of random walks\nand other diffusions on a graph. In Surveys in\nCombinatorics, 1993, Walker (Ed.), London\nMathematical Society Lecture Note Series 187,\nCambridge University Press. 1995.\n[21] Open Source Technology Group. Slashdot\nFAQcomments and moderation.\nhttp://slashdot.org/faq/com-mod.shtml#cm700.\n[22] OSMB LLC. Gnutella web site.\nhttp://www.gnutella.com/.\n[23] M. L. Puterman. Markov Decision Processes. Wiley,\n1994.\n[24] SETI@home. SETI@home web page.\nhttp://setiathome.ssl.berkeley.edu/.\n[25] Sharman Networks Ltd. Kazaa web site.\nhttp://www.kazaa.com/.\n[26] V. Vishnumurthy, S. Chandrakumar, and E. Sirer.\nKarma: A secure economic framework for peer-to-peer\nresource sharing. In Workshop on Economics of\nPeer-to-Peer Systems (P2PECON), 2003.\n[27] L. Xiong and L. Liu. Building trust in decentralized\npeer-to-peer electronic communities. In Internation\nConference on Electronic Commerce Research\n(ICECR), 2002.\n[28] H. Zhang, A. Goel, R. Govindan, K. Mason, and B. V.\nRoy. Making eigenvector-based reputation systems\nrobust to collusion. In Workshop on Algorithms and\nModels for the Web-Graph(WAW), pages 92-104,\n2004.\n149", "keywords": "nash equilibrium;game theory;gnutellum network;scrip system;agent;threshold strategy;reputation system;social welfare;game;online system;maximum entropy;p2p network;bittorrent;emule"}
{"name": "train_J-36", "title": "Playing Games in Many Possible Worlds", "abstract": "In traditional game theory, players are typically endowed with exogenously given knowledge of the structure of the game-either full omniscient knowledge or partial but fixed information. In real life, however, people are often unaware of the utility of taking a particular action until they perform research into its consequences. In this paper, we model this phenomenon. We imagine a player engaged in a questionand-answer session, asking questions both about his or her own preferences and about the state of reality; thus we call this setting Socratic game theory. In a Socratic game, players begin with an a priori probability distribution over many possible worlds, with a different utility function for each world. Players can make queries, at some cost, to learn partial information about which of the possible worlds is the actual world, before choosing an action. We consider two query models: (1) an unobservable-query model, in which players learn only the response to their own queries, and (2) an observable-query model, in which players also learn which queries their opponents made. The results in this paper consider cases in which the underlying worlds of a two-player Socratic game are either constant-sum games or strategically zero-sum games, a class that generalizes constant-sum games to include all games in which the sum of payoffs depends linearly on the interaction between the players. When the underlying worlds are constant sum, we give polynomial-time algorithms to find Nash equilibria in both the observable- and unobservable-query models. When the worlds are strategically zero sum, we give efficient algorithms to find Nash equilibria in unobservablequery Socratic games and correlated equilibria in observablequery Socratic games.", "fulltext": "1. INTRODUCTION\nLate October 1960. A smoky room. Democratic Party\nstrategists huddle around a map. How should the Kennedy\ncampaign allocate its remaining advertising budget? Should\nit focus on, say, California or New York? The Nixon\ncampaign faces the same dilemma. Of course, neither campaign\nknows the effectiveness of its advertising in each state.\nPerhaps Californians are susceptible to Nixon\"s advertising, but\nare unresponsive to Kennedy\"s. In light of this uncertainty,\nthe Kennedy campaign may conduct a survey, at some cost,\nto estimate the effectiveness of its advertising. Moreover, the\nlarger-and more expensive-the survey, the more accurate\nit will be. Is the cost of a survey worth the information that\nit provides? How should one balance the cost of acquiring\nmore information against the risk of playing a game with\nhigher uncertainty?\nIn this paper, we model situations of this type as Socratic\ngames. As in traditional game theory, the players in a\nSocratic game choose actions to maximize their payoffs, but we\nmodel players with incomplete information who can make\ncostly queries to reduce their uncertainty about the state of\nthe world before they choose their actions. This approach\ncontrasts with traditional game theory, in which players are\nusually modeled as having fixed, exogenously given\ninformation about the structure of the game and its payoffs. (In\ntraditional games of incomplete and imperfect information,\nthere is information that the players do not have; in Socratic\ngames, unlike in these games, the players have a chance to\nacquire the missing information, at some cost.) A number of\nrelated models have been explored by economists and\ncomputer scientists motivated by similar situations, often with\na focus on mechanism design and auctions; a sampling of\nthis research includes the work of Larson and Sandholm [41,\n42, 43, 44], Parkes [59], Fong [22], Compte and Jehiel [12],\nRezende [63], Persico and Matthews [48, 60], Cr\u00b4emer and\nKhalil [15], Rasmusen [62], and Bergemann and V\u00a8alim\u00a8aki [4,\n5]. The model of Bergemann and V\u00a8alim\u00a8aki is similar in\nmany regards to the one that we explore here; see Section 7\nfor some discussion.\nA Socratic game proceeds as follows. A real world is\ncho150\nsen randomly from a set of possible worlds according to a\ncommon prior distribution. Each player then selects an\narbitrary query from a set of available costly queries and\nreceives a corresponding piece of information about the real\nworld. Finally each player selects an action and receives a\npayoff-a function of the players\" selected actions and the\nidentity of the real world-less the cost of the query that\nhe or she made. Compared to traditional game theory, the\ndistinguishing feature of our model is the introduction of\nexplicit costs to the players for learning arbitrary partial\ninformation about which of the many possible worlds is the\nreal world.\nOur research was initially inspired by recent results in\npsychology on decision making, but it soon became clear that\nSocratic game theory is also a general tool for understanding\nthe exploitation versus exploration tradeoff, well studied\nin machine learning, in a strategic multiplayer environment.\nThis tension between the risk arising from uncertainty and\nthe cost of acquiring information is ubiquitous in economics,\npolitical science, and beyond.\nOur results. We consider Socratic games under two\nmodels: an unobservable-query model where players learn only\nthe response to their own queries and an observable-query\nmodel where players also learn which queries their opponents\nmade. We give efficient algorithms to find Nash\nequilibriai.e., tuples of strategies from which no player has unilateral\nincentive to deviate-in broad classes of two-player Socratic\ngames in both models. Our first result is an efficient\nalgorithm to find Nash equilibria in unobservable-query\nSocratic games with constant-sum worlds, in which the sum\nof the players\" payoffs is independent of their actions. Our\ntechniques also yield Nash equilibria in unobservable-query\nSocratic games with strategically zero-sum worlds.\nStrategically zero-sum games generalize constant-sum games by\nallowing the sum of the players\" payoffs to depend on\nindividual players\" choices of strategy, but not on any interaction\nof their choices. Our second result is an efficient algorithm\nto find Nash equilibria in observable-query Socratic games\nwith constant-sum worlds. Finally, we give an efficient\nalgorithm to find correlated equilibria-a weaker but\nincreasingly well-studied solution concept for games [2, 3, 32, 56,\n57]-in observable-query Socratic games with strategically\nzero-sum worlds.\nLike all games, Socratic games can be viewed as a\nspecial case of extensive-form games, which represent games\nby trees in which internal nodes represent choices made by\nchance or by the players, and the leaves represent outcomes\nthat correspond to a vector of payoffs to the players.\nAlgorithmically, the generality of extensive-form games makes\nthem difficult to solve efficiently, and the special cases that\nare known to be efficiently solvable do not include even\nsimple Socratic games. Every (complete-information) classical\ngame is a trivial Socratic game (with a single possible world\nand a single trivial query), and efficiently finding Nash\nequilibria in classical games has been shown to be hard [10, 11,\n13, 16, 17, 27, 54, 55]. Therefore we would not expect to\nfind a straightforward polynomial-time algorithm to\ncompute Nash equilibria in general Socratic games. However, it\nis well known that Nash equilibria can be found efficiently\nvia an LP for two-player constant-sum games [49, 71] (and\nstrategically zero-sum games [51]). A Socratic game is itself\na classical game, so one might hope that these results can\nbe applied to Socratic games with constant-sum (or\nstrategically zero-sum) worlds.\nWe face two major obstacles in extending these\nclassical results to Socratic games. First, a Socratic game with\nconstant-sum worlds is not itself a constant-sum classical\ngame-rather, the resulting classical game is only\nstrategically zero sum. Worse yet, a Socratic game with\nstrategically zero-sum worlds is not itself classically strategically\nzero sum-indeed, there are no known efficient\nalgorithmic techniques to compute Nash equilibria in the resulting\nclass of classical games. (Exponential-time algorithms like\nLemke/Howson, of course, can be used [45].) Thus even\nwhen it is easy to find Nash equilibria in each of the worlds\nof a Socratic game, we require new techniques to solve the\nSocratic game itself. Second, even when the Socratic game\nitself is strategically zero sum, the number of possible\nstrategies available to each player is exponential in the natural\nrepresentation of the game. As a result, the standard linear\nprograms for computing equilibria have an exponential\nnumber of variables and an exponential number of constraints.\nFor unobservable-query Socratic games with strategically\nzero-sum worlds, we address these obstacles by\nformulating a new LP that uses only polynomially many variables\n(though still an exponential number of constraints) and then\nuse ellipsoid-based techniques to solve it. For\nobservablequery Socratic games, we handle the exponentiality by\ndecomposing the game into stages, solving the stages\nseparately, and showing how to reassemble the solutions\nefficiently. To solve the stages, it is necessary to find Nash\nequilibria in Bayesian strategically zero-sum games, and we\ngive an explicit polynomial-time algorithm to do so.\n2. GAMES AND SOCRATIC GAMES\nIn this section, we review background on game theory and\nformally introduce Socratic games. We present these\nmodels in the context of two-player games, but the multiplayer\ncase is a natural extension. Throughout the paper,\nboldface variables will be used to denote a pair of variables (e.g.,\na = ai, aii ). Let Pr[x \u2190 \u03c0] denote the probability that a\nparticular value x is drawn from the distribution \u03c0, and let\nEx\u223c\u03c0[g(x)] denote the expectation of g(x) when x is drawn\nfrom \u03c0.\n2.1 Background on Game Theory\nConsider two players, Player I and Player II, each of whom\nis attempting to maximize his or her utility (or payoff). A\n(two-player) game is a pair A, u , where, for i \u2208 {i,ii},\n\u2022 Ai is the set of pure strategies for Player i, and A =\nAi, Aii ; and\n\u2022 ui : A \u2192 R is the utility function for Player i, and\nu = ui, uii .\nWe require that A and u be common knowledge. If each\nPlayer i chooses strategy ai \u2208 Ai, then the payoffs to\nPlayers I and II are ui(a) and uii(a), respectively. A game is\nconstant sum if, for all a \u2208 A, we have that ui(a) + uii(a) = c\nfor some fixed c independent of a.\nPlayer i can also play a mixed strategy \u03b1i \u2208 Ai, where Ai\ndenotes the space of probability measures over the set Ai.\nPayoff functions are generalized as ui (\u03b1) = ui (\u03b1i, \u03b1ii) :=\nEa\u223c\u03b1[ui (a)] =\nP\na\u2208A \u03b1(a)ui (a), where the quantity \u03b1(a) =\n151\n\u03b1i(ai) \u00b7 \u03b1ii(aii) denotes the joint probability of the\nindependent events that each Player i chooses action ai from the\ndistribution \u03b1i. This generalization to mixed strategies is\nknown as von Neumann/Morgenstern utility [70], in which\nplayers are indifferent between a guaranteed payoff x and an\nexpected payoff of x.\nA Nash equilibrium is a pair \u03b1 of mixed strategies so that\nneither player has an incentive to change his or her strategy\nunilaterally. Formally, the strategy pair \u03b1 is a Nash\nequilibrium if and only if both ui(\u03b1i, \u03b1ii) = max\u03b1i\u2208Ai ui(\u03b1i, \u03b1ii)\nand uii(\u03b1i, \u03b1ii) = max\u03b1ii\u2208Aii uii(\u03b1i, \u03b1ii); that is, the\nstrategies \u03b1i and \u03b1ii are mutual best responses.\nA correlated equilibrium is a distribution \u03c8 over A that\nobeys the following: if a \u2208 A is drawn randomly according\nto \u03c8 and Player i learns ai, then no Player i has incentive to\ndeviate unilaterally from playing ai. (A Nash equilibrium is\na correlated equilibrium in which \u03c8(a) = \u03b1i(ai) \u00b7 \u03b1ii(aii) is a\nproduct distribution.) Formally, in a correlated equilibrium,\nfor every a \u2208 A we must have that ai is a best response to\na randomly chosen \u02c6aii \u2208 Aii drawn according to \u03c8(ai, \u02c6aii),\nand the analogous condition must hold for Player II.\n2.2 Socratic Games\nIn this section, we formally define Socratic games. A\nSocratic game is a 7-tuple A, W, u, S, Q, p, \u03b4 , where, for\ni \u2208 {i,ii}:\n\u2022 Ai is, as before, the set of pure strategies for Player i.\n\u2022 W is a set of possible worlds, one of which is the real\nworld wreal.\n\u2022 ui = {uw\ni : A \u2192 R | w \u2208 W} is a set of payoff functions\nfor Player i, one for each possible world.\n\u2022 S is a set of signals.\n\u2022 Qi is a set of available queries for Player i. When\nPlayer i makes query qi : W \u2192 S, he or she receives the\nsignal qi(wreal). When Player i receives signal qi(wreal)\nin response to query qi, he or she can infer that wreal \u2208\n{w : qi(w) = qi(wreal)}, i.e., the set of possible worlds\nfrom which query qi cannot distinguish wreal.\n\u2022 p : W \u2192 [0, 1] is a probability distribution over the\npossible worlds.\n\u2022 \u03b4i : Qi \u2192 R\u22650\ngives the query cost for each available\nquery for Player i.\nInitially, the world wreal is chosen according to the\nprobability distribution p, but the identity of wreal remains\nunknown to the players. That is, it is as if the players are\nplaying the game A, uwreal but do not know wreal. The\nplayers make queries q \u2208 Q, and Player i receives the signal\nqi(wreal). We consider both observable queries and\nunobservable queries. When queries are observable, each player\nlearns which query was made by the other player, and the\nresults of his or her own query-that is, each Player i learns\nqi, qii, and qi(wreal). For unobservable queries, Player i learns\nonly qi and qi(wreal). After learning the results of the queries,\nthe players select strategies a \u2208 A and receive as payoffs\nu\nwreal\ni (a) \u2212 \u03b4i(qi).\nIn the Socratic game, a pure strategy for Player i consists\nof a query qi \u2208 Qi and a response function mapping any\nresult of the query qi to a strategy ai \u2208 Ai to play. A player\"s\nstate of knowledge after a query is a point in R := Q \u00d7 S\nor Ri := Qi \u00d7 S for observable or unobservable queries,\nrespectively. Thus Player i\"s response function maps R or\nRi to Ai. Note that the number of pure strategies is\nexponential, as there are exponentially many response\nfunctions. A mixed strategy involves both randomly choosing\na query qi \u2208 Qi and randomly choosing an action ai \u2208 Ai\nin response to the results of the query. Formally, we will\nconsider a mixed-strategy-function profile f = fquery\n, fresp\nto have two parts:\n\u2022 a function fquery\ni : Qi \u2192 [0, 1], where fquery\ni (qi) is the\nprobability that Player i makes query qi.\n\u2022 a function fresp\ni that maps R or Ri to a\nprobability distribution over actions. Player i chooses an\naction ai \u2208 Ai according to the probability distribution\nfresp\ni (q, qi(w)) for observable queries, and according to\nfresp\ni (qi, qi(w)) for unobservable queries. (With\nunobservable queries, for example, the probability that\nPlayer I plays action ai conditioned on making query\nqi in world w is given by Pr[ai \u2190 fresp\ni (qi, qi(w))].)\nMixed strategies are typically defined as probability\ndistributions over the pure strategies, but here we represent a\nmixed strategy by a pair fquery\n, fresp\n, which is commonly\nreferred to as a behavioral strategy in the game-theory\nliterature. As in any game with perfect recall, one can\neasily map a mixture of pure strategies to a behavioral strategy\nf = fquery\n, fresp\nthat induces the same probability of\nmaking a particular query qi or playing a particular action after\nmaking a query qi in a particular world. Thus it suffices to\nconsider only this representation of mixed strategies.\nFor a strategy-function profile f for observable queries, the\n(expected) payoff to Player i is given by\nX\nq\u2208Q,w\u2208W,a\u2208A\n2\n6\n6\n4\nfquery\ni (qi) \u00b7 fquery\nii (qii) \u00b7 p(w)\n\u00b7 Pr[ai \u2190 fresp\ni (q, qi(w))]\n\u00b7 Pr[aii \u2190 fresp\nii (q, qii(w))]\n\u00b7 (uw\ni (a) \u2212 \u03b4i(qi))\n3\n7\n7\n5 .\nThe payoffs for unobservable queries are analogous, with\nfresp\nj (qj, qj(w)) in place of fresp\nj (q, qj(w)).\n3. STRATEGICALLY ZERO-SUM GAMES\nWe can view a Socratic game G with constant-sum worlds\nas an exponentially large classical game, with pure\nstrategies make query qi and respond according to fi.\nHowever, this classical game is not constant sum. The sum of\nthe players\" payoffs varies depending upon their strategies,\nbecause different queries incur different costs. However, this\ngame still has significant structure: the sum of payoffs varies\nonly because of varying query costs. Thus the sum of\npayoffs does depend on players\" choice of strategies, but not on\nthe interaction of their choices-i.e., for fixed functions gi\nand gii, we have ui(q, f) + uii(q, f) = gi(qi, fi) + gii(qii, fii)\nfor all strategies q, f . Such games are called strategically\nzero sum and were introduced by Moulin and Vial [51], who\ndescribe a notion of strategic equivalence and define\nstrategically zero-sum games as those strategically equivalent to\nzero-sum games. It is interesting to note that two Socratic\ngames with the same queries and strategically equivalent\nworlds are not necessarily strategically equivalent.\nA game A, u is strategically zero sum if there exist labels\n(i, ai) for every Player i and every pure strategy ai \u2208 Ai\n152\nsuch that, for all mixed-strategy profiles \u03b1, we have that the\nsum of the utilities satisfies\nui(\u03b1)+uii(\u03b1) =\nX\nai\u2208Ai\n\u03b1i(ai)\u00b7 (i, ai)+\nX\naii\u2208Aii\n\u03b1ii(aii)\u00b7 (ii, aii).\nNote that any constant-sum game is strategically zero sum\nas well.\nIt is not immediately obvious that one can efficiently\ndecide if a given game is strategically zero sum. For\ncompleteness, we give a characterization of classical strategically\nzero-sum games in terms of the rank of a simple matrix\nderived from the game\"s payoffs, allowing us to efficiently\ndecide if a given game is strategically zero sum and, if it is, to\ncompute the labels (i, ai).\nTheorem 3.1. Consider a game G = A, u with Ai =\n{a1\ni , . . . , ani\ni }. Let MG\nbe the ni-by-nii matrix whose i, j th\nentry MG\n(i,j) satisfies log2 MG\n(i,j) = ui(ai\ni , aj\nii) + uii(ai\ni , aj\nii).\nThen the following are equivalent:\n(i) G is strategically zero sum;\n(ii) there exist labels (i, ai) for every player i \u2208 {i,ii} and\nevery pure strategy ai \u2208 Ai such that, for all pure\nstrategies a \u2208 A, we have ui(a) + uii(a) = (i, ai) +\n(ii, aii); and\n(iii) rank(MG\n) = 1.\nProof Sketch. (i \u21d2 ii) is immediate; every pure\nstrategy is a trivially mixed strategy. For (ii \u21d2 iii), let ci be the\nn-element column vector with jth component 2 (i,a\nj\ni )\n; then\nci \u00b7 cii\nT\n= MG\n. For (iii \u21d2 i), if rank(MG\n) = 1, then MG\n=\nu \u00b7 vT\n. We can prove that G is strategically zero sum by\nchoosing labels (i, aj\ni ) := log2 uj and (ii, aj\nii) := log2 vj.\n4. SOCRATIC GAMES WITH\nUNOBSERVABLE QUERIES\nWe begin with Socratic games with unobservable queries,\nwhere a player\"s choice of query is not revealed to her\nopponent. We give an efficient algorithm to solve\nunobservablequery Socratic games with strategically zero-sum worlds.\nOur algorithm is based upon the LP shown in Figure 1,\nwhose feasible points are Nash equilibria for the game. The\nLP has polynomially many variables but exponentially many\nconstraints. We give an efficient separation oracle for the LP,\nimplying that the ellipsoid method [28, 38] yields an efficient\nalgorithm. This approach extends the techniques of Koller\nand Megiddo [39] (see also [40]) to solve constant-sum games\nrepresented in extensive form. (Recall that their result does\nnot directly apply in our case; even a Socratic game with\nconstant-sum worlds is not a constant-sum classical game.)\nLemma 4.1. Let G = A, W, u, S, Q, p, \u03b4 be an arbitrary\nunobservable-query Socratic game with strategically zero-sum\nworlds. Any feasible point for the LP in Figure 1 can be\nefficiently mapped to a Nash equilibrium for G, and any Nash\nequilibrium for G can be mapped to a feasible point for the\nprogram.\nProof Sketch. We begin with a description of the\ncorrespondence between feasible points for the LP and Nash\nequilibria for G. First, suppose that strategy profile f =\nfquery\n, fresp\nforms a Nash equilibrium for G. Then the\nfollowing setting for the LP variables is feasible:\nyi\nqi\n= fquery\ni (qi)\nxi\nai,qi,w = Pr[ai \u2190 fresp\ni (qi, qi(w))] \u00b7 yi\nqi\n\u03c1i =\nP\nw,q\u2208Q,a\u2208A\np(w) \u00b7 xi\nai,qi,w \u00b7 xii\naii,qii,w \u00b7 [uw\ni (a) \u2212 \u03b4i(qi)].\n(We omit the straightforward calculations that verify\nfeasibility.) Next, suppose xi\nai,qi,w, yi\nqi\n, \u03c1i is feasible for the LP.\nLet f be the strategy-function profile defined as\nfquery\ni : qi \u2192 yi\nqi\nfresp\ni (qi, qi(w)) : ai \u2192 xi\nai,qi,w/yi\nqi\n.\nVerifying that this strategy profile is a Nash equilibrium\nrequires checking that fresp\ni (qi, qi(w)) is a well-defined\nfunction (from constraint VI), that fquery\ni and fresp\ni (qi, qi(w)) are\nprobability distributions (from constraints III and IV), and\nthat each player is playing a best response to his or her\nopponent\"s strategy (from constraints I and II). Finally, from\nconstraints I and II, the expected payoff to Player i is at most\n\u03c1i. Because the right-hand side of constraint VII is equal\nto the expected sum of the payoffs from f and is at most\n\u03c1i + \u03c1ii, the payoffs are correct and imply the lemma.\nWe now give an efficient separation oracle for the LP in\nFigure 1, thus allowing the ellipsoid method to solve the\nLP in polynomial time. Recall that a separation oracle is\na function that, given a setting for the variables in the LP,\neither returns feasible or returns a particular constraint\nof the LP that is violated by that setting of the variables.\nAn efficient, correct separation oracle allows us to solve the\nLP efficiently via the ellipsoid method.\nLemma 4.2. There exists a separation oracle for the LP\nin Figure 1 that is correct and runs in polynomial time.\nProof. Here is a description of the separation oracle SP.\nOn input xi\nai,qi,w, yi\nqi\n, \u03c1i :\n1. Check each of the constraints (III), (IV), (V), (VI),\nand (VII). If any one of these constraints is violated,\nthen return it.\n2. Define the strategy profile f as follows:\nfquery\ni : qi \u2192 yi\nqi\nfresp\ni (qi, qi(w)) : ai \u2192 xi\nai,qi,w/yi\nqi\nFor each query qi, we will compute a pure best-response\nfunction \u02c6f\nqi\ni for Player I to strategy fii after making\nquery qi.\nMore specifically, given fii and the result qi(wreal) of the\nquery qi, it is straightforward to compute the\nprobability that, conditioned on the fact that the result of\nquery qi is qi(w), the world is w and Player II will play\naction aii \u2208 Aii. Therefore, for each query qi and\nresponse qi(w), Player I can compute the expected utility\nof each pure response ai to the induced mixed strategy\nover Aii for Player II. Player I can then select the ai\nmaximizing this expected payoff.\nLet \u02c6fi be the response function such that \u02c6fi(qi, qi(w)) =\n\u02c6f\nqi\ni (qi(w)) for every qi \u2208 Qi. Similarly, compute \u02c6fii.\n153\nPlayer i does not prefer \u2018make query qi, then play according to the function fi\" :\n\u2200qi \u2208 Qi, fi : Ri \u2192 Ai : \u03c1i \u2265\nP\nw\u2208W,aii\u2208Aii,qii\u2208Qii,ai=fi(qi,qi(w))\n`\np(w) \u00b7 xii\naii,qii,w \u00b7 [uw\ni (a) \u2212 \u03b4i(qi)]\n\u00b4\n(I)\n\u2200qii \u2208 Qii, fii : Rii \u2192 Aii : \u03c1ii \u2265\nP\nw\u2208W,ai\u2208Ai,qi\u2208Qi,aii=fii(qii,qii(w))\n`\np(w) \u00b7 xi\nai,qi,w \u00b7 [uw\nii (a) \u2212 \u03b4ii(qii)]\n\u00b4\n(II)\nEvery player\"s choices form a probability distribution in every world:\n\u2200i \u2208 {i,ii}, w \u2208 W : 1 =\nP\nai\u2208Ai,qi\u2208Qi\nxi\nai,qi,w (III)\n\u2200i \u2208 {i,ii}, w \u2208 W : 0 \u2264 xi\nai,qi,w (IV)\nQueries are independent of the world, and actions depend only on query output:\n\u2200i \u2208 {i,ii}, qi \u2208 Qi, w \u2208 W, w \u2208 W such that qi(w) = qi(w ) :\nyi\nqi\n=\nP\nai\u2208Ai\nxi\nai,qi,w (V)\nxi\nai,qi,w = xi\nai,qi,w (VI)\nThe payoffs are consistent with the labels (i, ai, w):\n\u03c1i + \u03c1ii =\nP\ni\u2208{i,ii}\nP\nw\u2208W,qi\u2208Qi,ai\u2208Ai\n`\np(w) \u00b7 xi\nai,qi,w \u00b7 [ (i, ai, w) \u2212 \u03b4i(qi)]\n\u00b4\n(VII)\nFigure 1: An LP to find Nash equilibria in unobservable-query Socratic games with strategically zero-sum\nworlds. The input is a Socratic game A, W, u, S, Q, p, \u03b4 so that world w is strategically zero sum with labels\n(i, ai, w). Player i makes query qi \u2208 Qi with probability yi\nqi\nand, when the actual world is w \u2208 W, makes query\nqi and plays action ai with probability xi\nai,qi,w. The expected payoff to Player i is given by \u03c1i.\n3. Let \u02c6\u03c1\nqi\ni be the expected payoff to Player I using the\nstrategy make query qi and play response function\n\u02c6fi if Player II plays according to fii.\nLet \u02c6\u03c1i = maxqi\u2208Qq \u02c6\u03c1\nqi\ni and let \u02c6qi = arg maxqi\u2208Qq \u02c6\u03c1\nqi\ni .\nSimilarly, define \u02c6\u03c1\nqii\nii , \u02c6\u03c1ii, and \u02c6qii.\n4. For the \u02c6fi and \u02c6qi defined in Step 3, return constraint\n(I-\u02c6qi- \u02c6fi) or (II-\u02c6qii- \u02c6fii) if either is violated. If both are\nsatisfied, then return feasible.\nWe first note that the separation oracle runs in polynomial\ntime and then prove its correctness. Steps 1 and 4 are clearly\npolynomial. For Step 2, we have described how to compute\nthe relevant response functions by examining every action of\nPlayer I, every world, every query, and every action of Player\nII. There are only polynomially many queries, worlds, query\nresults, and pure actions, so the running time of Steps 2 and\n3 is thus polynomial.\nWe now sketch the proof that the separation oracle works\ncorrectly. The main challenge is to show that if any\nconstraint (I-qi-fi ) is violated then (I-\u02c6qi- \u02c6fi) is violated in Step 4.\nFirst, we observe that, by construction, the function \u02c6fi\ncomputed in Step 3 must be a best response to Player II playing\nfii, no matter what query Player I makes. Therefore the\nstrategy make query \u02c6qi, then play response function \u02c6fi\nmust be a best response to Player II playing fii, by definition\nof \u02c6qi. The right-hand side of each constraint (I-qi-fi ) is equal\nto the expected payoff that Player I receives when playing\nthe pure strategy make query qi and then play response\nfunction fi  against Player II\"s strategy of fii. Therefore,\nbecause the pure strategy make query \u02c6qi and then play\nresponse function \u02c6fi is a best response to Player II\nplaying fii, the right-hand side of constraint (I-\u02c6qi- \u02c6fi) is at least\nas large as the right hand side of any constraint (I-\u02c6qi-fi ).\nTherefore, if any constraint (I-qi-fi ) is violated, constraint\n(I-\u02c6qi- \u02c6fi) is also violated. An analogous argument holds for\nPlayer II.\nThese lemmas and the well-known fact that Nash\nequilibria always exist [52] imply the following theorem:\nTheorem 4.3. Nash equilibria can be found in\npolynomial time for any two-player unobservable-query Socratic\ngame with strategically zero-sum worlds.\n5. SOCRATIC GAMES WITH\nOBSERVABLE QUERIES\nIn this section, we give efficient algorithms to find (1) a\nNash equilibrium for observable-query Socratic games with\nconstant-sum worlds and (2) a correlated equilibrium in the\nbroader class of Socratic games with strategically zero-sum\nworlds. Recall that a Socratic game G = A, W, u, S, Q, p, \u03b4\nwith observable queries proceeds in two stages:\nStage 1: The players simultaneously choose queries q \u2208 Q.\nPlayer i receives as output qi, qii, and qi(wreal).\nStage 2: The players simultaneously choose strategies a \u2208\nA. The payoff to Player i is u\nwreal\ni (a) \u2212 \u03b4i(qi).\nUsing backward induction, we first solve Stage 2 and then\nproceed to the Stage-1 game.\nFor a query q \u2208 Q, we would like to analyze the Stage-2\ngame \u02c6Gq resulting from the players making queries q in\nStage 1. Technically, however, \u02c6Gq is not actually a game,\nbecause at the beginning of Stage 2 the players have different\ninformation about the world: Player I knows qi(wreal), and\n154\nPlayer II knows qii(wreal). Fortunately, the situation in which\nplayers have asymmetric private knowledge has been well\nstudied in the game-theory literature. A Bayesian game is\na quadruple A, T, r, u , where:\n\u2022 Ai is the set of pure strategies for Player i.\n\u2022 Ti is the set of types for Player i.\n\u2022 r is a probability distribution over T; r(t) denotes the\nprobability that Player i has type ti for all i.\n\u2022 ui : A \u00d7 T \u2192 R is the payoff function for Player i.\nIf the players have types t and play pure strategies a,\nthen ui(a, t) denotes the payoff for Player i.\nInitially, a type t is drawn randomly from T according to the\ndistribution r. Player i learns his type ti, but does not learn\nany other player\"s type. Player i then plays a mixed strategy\n\u03b1i \u2208 Ai-that is, a probability distribution over Ai-and\nreceives payoff ui(\u03b1, t). A strategy function is a function\nhi : Ti \u2192 Ai; Player i plays the mixed strategy hi(ti) \u2208 Ai\nwhen her type is ti. A strategy-function profile h is a\nBayesian Nash equilibrium if and only if no Player i has\nunilateral incentive to deviate from hi if the other players play\naccording to h. For a two-player Bayesian game, if \u03b1 = h(t),\nthen the profile h is a Bayesian Nash equilibrium exactly\nwhen the following condition and its analogue for Player II\nhold: Et\u223cr[ui(\u03b1, t)] = maxhi\nEt\u223cr[ui( hi(ti), \u03b1ii , t)]. These\nconditions hold if and only if, for all ti \u2208 Ti occurring with\npositive probability, Player i\"s expected utility conditioned\non his type being ti is maximized by hi(ti). A Bayesian\ngame is constant sum if for all a \u2208 A and all t \u2208 T, we\nhave ui(a, t) + uii(a, t) = ct, for some constant ct\nindependent of a. A Bayesian game is strategically zero sum if the\nclassical game A, u(\u00b7, t) is strategically zero sum for every\nt \u2208 T. Whether a Bayesian game is strategically zero sum\ncan be determined as in Theorem 3.1. (For further\ndiscussion of Bayesian games, see [25, 31].)\nWe now formally define the Stage-2 game as a Bayesian\ngame. Given a Socratic game G = A, W, u, S, Q, p, \u03b4 and\na query profile q \u2208 Q, we define the Stage-2 Bayesian game\nGstage2(q) := A, Tq\n, pstage2(q)\n, ustage2(q)\n, where:\n\u2022 Ai, the set of pure strategies for Player i, is the same\nas in the original Socratic game;\n\u2022 Tq\ni = {qi(w) : w \u2208 W}, the set of types for Player i, is\nthe set of signals that can result from query qi;\n\u2022 pstage2(q)\n(t) = Pr[q(w) = t | w \u2190 p]; and\n\u2022 u\nstage2(q)\ni (a, t) =\nP\nw\u2208W Pr[w \u2190 p | q(w) = t] \u00b7 uw\ni (a).\nWe now define the Stage-1 game in terms of the payoffs\nfor the Stage-2 games. Fix any algorithm alg that finds a\nBayesian Nash equilibrium hq,alg\n:= alg(Gstage2(q)) for each\nStage-2 game. Define valuealg\ni (Gstage2(q)) to be the expected\npayoff received by Player i in the Bayesian game Gstage2(q)\nif each player plays according to hq,alg\n, that is,\nvaluealg\ni (Gstage2(q))\n:=\nP\nw\u2208W p(w) \u00b7 u\nstage2(q)\ni (hq,alg\n(q(w)), q(w)).\nDefine the game Galg\nstage1 := Astage1\n, ustage1(alg)\n, where:\n\u2022 Astage1\n:= Q, the set of available queries in the Socratic\ngame; and\n\u2022 u\nstage1(alg)\ni (q) := valuealg\ni (Gstage2(q)) \u2212 \u03b4i(qi).\nI.e., players choose queries q and receive payoffs\ncorresponding to valuealg\n(Gstage2(q)), less query costs.\nLemma 5.1. Consider an observable-query Socratic game\nG = A, W, u, S, Q, p, \u03b4 . Let Gstage2(q) be the Stage-2 games\nfor all q \u2208 Q, let alg be an algorithm finding a Bayesian\nNash equilibrium in each Gstage2(q), and let Galg\nstage1 be the\nStage-1 game. Let \u03b1 be a Nash equilibrium for Galg\nstage1, and\nlet hq,alg\n:= alg(Gstage2(q)) be a Bayesian Nash equilibrium\nfor each Gstage2(q). Then the following strategy profile is a\nNash equilibrium for G:\n\u2022 In Stage 1, Player i makes query qi with probability\n\u03b1i(qi). (That is, set fquery\n(q) := \u03b1(q).)\n\u2022 In Stage 2, if q is the query in Stage 1 and qi(wreal)\ndenotes the response to Player i\"s query, then Player i\nchooses action ai with probability hq,alg\ni (qi(wreal)). (In\nother words, set fresp\ni (q, qi(w)) := hq,alg\ni (qi(w)).)\nWe now find equilibria in the stage games for Socratic games\nwith constant- or strategically zero-sum worlds. We first\nshow that the stage games are well structured in this setting:\nLemma 5.2. Consider an observable-query Socratic game\nG = A, W, u, S, Q, p, \u03b4 with constant-sum worlds. Then\nthe Stage-1 game Galg\nstage1 is strategically zero sum for every\nalgorithm alg, and every Stage-2 game Gstage2(q) is Bayesian\nconstant sum. If the worlds of G are strategically zero sum,\nthen every Gstage2(q) is Bayesian strategically zero sum.\nWe now show that we can efficiently compute equilibria for\nthese well-structured stage games.\nTheorem 5.3. There exists a polynomial-time algorithm\nBNE finding Bayesian Nash equilibria in strategically\nzerosum Bayesian (and thus classical strategically zero-sum or\nBayesian constant-sum) two-player games.\nProof Sketch. Let G = A, T, r, u be a strategically\nzero-sum Bayesian game. Define an unobservable-query\nSocratic game G\u2217\nwith one possible world for each t \u2208 T, one\navailable zero-cost query qi for each Player i so that qi\nreveals ti, and all else as in G. Bayesian Nash equilibria in G\ncorrespond directly to Nash equilibria in G\u2217\n, and the worlds\nof G\u2217\nare strategically zero sum. Thus by Theorem 4.3 we\ncan compute Nash equilibria for G\u2217\n, and thus we can\ncompute Bayesian Nash equilibria for G.\n(LP\"s for zero-sum two-player Bayesian games have been\npreviously developed and studied [61].)\nTheorem 5.4. We can compute a Nash equilibrium for\nan arbitrary two-player observable-query Socratic game G =\nA, W, u, S, Q, p, \u03b4 with constant-sum worlds in polynomial\ntime.\nProof. Because each world of G is constant sum, Lemma\n5.2 implies that the induced Stage-2 games Gstage2(q) are\nall Bayesian constant sum. Thus we can use algorithm\nBNE to compute a Bayesian Nash equilibrium hq,BNE\n:=\nBNE(Gstage2(q)) for each q \u2208 Q, by Theorem 5.3.\nFurthermore, again by Lemma 5.2, the induced Stage-1 game\nGBNE\nstage1 is classical strategically zero sum. Therefore we can\nagain use algorithm BNE to compute a Nash equilibrium\n\u03b1 := BNE(GBNE\nstage1), again by Theorem 5.3. Therefore, by\nLemma 5.1, we can assemble \u03b1 and the hq,BNE\n\"s into a Nash\nequilibrium for the Socratic game G.\n155\nWe would like to extend our results on observable-query\nSocratic games to Socratic games with strategically\nzerosum worlds. While we can still find Nash equilibria in the\nStage-2 games, the resulting Stage-1 game is not in\ngeneral strategically zero sum. Thus, finding Nash equilibria\nin observable-query Socratic games with strategically\nzerosum worlds seems to require substantially new techniques.\nHowever, our techniques for decomposing observable-query\nSocratic games do allow us to find correlated equilibria in\nthis case.\nLemma 5.5. Consider an observable-query Socratic game\nG = A, W, u, S, Q, p, \u03b4 . Let alg be an arbitrary algorithm\nthat finds a Bayesian Nash equilibrium in each of the derived\nStage-2 games Gstage2(q), and let Galg\nstage1 be the derived\nStage1 game. Let \u03c6 be a correlated equilibrium for Galg\nstage1, and let\nhq,alg\n:= alg(Gstage2(q)) be a Bayesian Nash equilibrium for\neach Gstage2(q). Then the following distribution over pure\nstrategies is a correlated equilibrium for G:\n\u03c8(q, f) := \u03c6(q)\nY\ni\u2208{i,ii}\nY\ns\u2208S\nPr\nh\nfi(q, s) \u2190 hq,alg\ni (s)\ni\n.\nThus to find a correlated equilibrium in an observable-query\nSocratic game with strategically zero-sum worlds, we need\nonly algorithm BNE from Theorem 5.3 along with an\nefficient algorithm for finding a correlated equilibrium in a\ngeneral game. Such an algorithm exists (the definition of\ncorrelated equilibria can be directly translated into an LP [3]),\nand therefore we have the following theorem:\nTheorem 5.6. We can provide both efficient oracle\naccess and efficient sampling access to a correlated\nequilibrium for any observable-query two-player Socratic game with\nstrategically zero-sum worlds.\nBecause the support of the correlated equilibrium may be\nexponentially large, providing oracle and sampling access is\nthe natural way to represent the correlated equilibrium.\nBy Lemma 5.5, we can also compute correlated equilibria\nin any observable-query Socratic game for which Nash\nequilibria are computable in the induced Gstage2(q) games (e.g.,\nwhen Gstage2(q) is of constant size).\nAnother potentially interesting model of queries in\nSocratic games is what one might call public queries, in which\nboth the choice and outcome of a player\"s query is\nobservable by all players in the game. (This model might be most\nappropriate in the presence of corporate espionage or media\nleaks, or in a setting in which the queries-and thus their\nresults-are done in plain view.) The techniques that we\nhave developed in this section also yield exactly the same\nresults as for observable queries. The proof is actually\nsimpler: with public queries, the players\" payoffs are common\nknowledge when Stage 2 begins, and thus Stage 2 really is a\ncomplete-information game. (There may still be uncertainty\nabout the real world, but all players use the observed\nsignals to infer exactly the same set of possible worlds in which\nwreal may lie; thus they are playing a complete-information\ngame against each other.) Thus we have the same results\nas in Theorems 5.4 and 5.6 more simply, by solving Stage 2\nusing a (non-Bayesian) Nash-equilibrium finder and solving\nStage 1 as before.\nOur results for observable queries are weaker than for\nunobservable: in Socratic games with worlds that are\nstrategically zero sum but not constant sum, we find only a\ncorrelated equilibrium in the observable case, whereas we find a\nNash equilibrium in the unobservable case. We might hope\nto extend our unobservable-query techniques to observable\nqueries, but there is no obvious way to do so. The\nfundamental obstacle is that the LP\"s payoff constraint becomes\nnonlinear if there is any dependence on the probability that\nthe other player made a particular query. This dependence\narises with observable queries, suggesting that observable\nSocratic games with strategically zero-sum worlds may be\nharder to solve.\n6. RELATED WORK\nOur work was initially motivated by research in the social\nsciences indicating that real people seem (irrationally)\nparalyzed when they are presented with additional options. In\nthis section, we briefly review some of these social-science\nexperiments and then discuss technical approaches related\nto Socratic game theory.\nPrima facie, a rational agent\"s happiness given an added\noption can only increase. However, recent research has found\nthat more choices tend to decrease happiness: for\nexample, students choosing among extra-credit options are more\nlikely to do extra credit if given a small subset of the choices\nand, moreover, produce higher-quality work [35]. (See also\n[19].) The psychology literature explores a number of\nexplanations: people may miscalculate their opportunity cost by\ncomparing their choice to a component-wise maximum of\nall other options instead of the single best alternative [65],\na new option may draw undue attention to aspects of the\nother options [67], and so on. The present work explores\nan economic explanation of this phenomenon: information\nis not free. When there are more options, a decision-maker\nmust spend more time to achieve a satisfactory outcome.\nSee, e.g., the work of Skyrms [68] for a philosophical\nperspective on the role of deliberation in strategic situations.\nFinally, we note the connection between Socratic games and\nmodal logic [34], a formalism for the logic of possibility and\nnecessity.\nThe observation that human players typically do not play\nrational strategies has inspired some attempts to model\npartially rational players. The typical model of this\nsocalled bounded rationality [36, 64, 66] is to postulate bounds\non computational power in computing the consequences of\na strategy. The work on bounded rationality [23, 24, 53, 58]\ndiffers from the models that we consider here in that instead\nof putting hard limitations on the computational power of\nthe agents, we instead restrict their a priori knowledge of\nthe state of the world, requiring them to spend time (and\ntherefore money/utility) to learn about it.\nPartially observable stochastic games (POSGs) are a\ngeneral framework used in AI to model situations of multi-agent\nplanning in an evolving, unknown environment, but the\ngenerality of POSGs seems to make them very difficult [6].\nRecent work has been done in developing algorithms for\nrestricted classes of POSGs, most notably classes of\ncooperative POSGs-e.g., [20, 30]-which are very different from\nthe competitive strategically zero-sum games we address in\nthis paper.\nThe fundamental question in Socratic games is deciding\non the comparative value of making a more costly but more\ninformative query, or concluding the data-gathering phase\nand picking the best option, given current information. This\ntradeoff has been explored in a variety of other contexts;\na sampling of these contexts includes aggregating results\n156\nfrom delay-prone information sources [8], doing approximate\nreasoning in intelligent systems [72], deciding when to take\nthe current best guess of disease diagnosis from a\nbeliefpropagation network and when to let it continue inference\n[33], among many others.\nThis issue can also be viewed as another perspective on\nthe general question of exploration versus exploitation that\narises often in AI: when is it better to actively seek\nadditional information instead of exploiting the knowledge one\nalready has? (See, e.g., [69].) Most of this work differs\nsignificantly from our own in that it considers single-agent\nplanning as opposed to the game-theoretic setting. A\nnotable exception is the work of Larson and Sandholm [41, 42,\n43, 44] on mechanism design for interacting agents whose\ncomputation is costly and limited. They present a model\nin which players must solve a computationally intractable\nvaluation problem, using costly computation to learn some\nhidden parameters, and results for auctions and bargaining\ngames in this model.\n7. FUTURE DIRECTIONS\nEfficiently finding Nash equilibria in Socratic games with\nnon-strategically zero-sum worlds is probably difficult\nbecause the existence of such an algorithm for classical games\nhas been shown to be unlikely [10, 11, 13, 16, 17, 27, 54,\n55]. There has, however, been some algorithmic success in\nfinding Nash equilibria in restricted classical settings (e.g.,\n[21, 46, 47, 57]); we might hope to extend our results to\nanalogous Socratic games.\nAn efficient algorithm to find correlated equilibria in\ngeneral Socratic games seems more attainable. Suppose the\nplayers receive recommended queries and responses. The\ndifficulty is that when a player considers a deviation from\nhis recommended query, he already knows his recommended\nresponse in each of the Stage-2 games. In a correlated\nequilibrium, a player\"s expected payoff generally depends on his\nrecommended strategy, and thus a player may deviate in\nStage 1 so as to land in a Stage-2 game where he has been\ngiven a better than average recommended response.\n(Socratic games are succinct games of superpolynomial type,\nso Papadimitriou\"s results [56] do not imply correlated\nequilibria for them.)\nSocratic games can be extended to allow players to make\nadaptive queries, choosing subsequent queries based on\nprevious results. Our techniques carry over to O(1) rounds of\nunobservable queries, but it would be interesting to\ncompute equilibria in Socratic games with adaptive observable\nqueries or with \u03c9(1) rounds of unobservable queries.\nSpecial cases of adaptive Socratic games are closely related to\nsingle-agent problems like minimum latency [1, 7, 26],\ndetermining strategies for using priced information [9, 29, 37],\nand an online version of minimum test cover [18, 50].\nAlthough there are important technical distinctions between\nadaptive Socratic games and these problems, approximation\ntechniques from this literature may apply to Socratic games.\nThe question of approximation raises interesting questions\neven in non-adaptive Socratic games. An -approximate\nNash equilibrium is a strategy profile \u03b1 so that no player\ncan increase her payoff by an additive by deviating from \u03b1.\nFinding approximate Nash equilibria in both adaptive and\nnon-adaptive Socratic games is an interesting direction to\npursue.\nAnother natural extension is the model where query\nresults are stochastic. In this paper, we model a query as\ndeterministically partitioning the possible worlds into\nsubsets that the query cannot distinguish. However, one could\ninstead model a query as probabilistically mapping the set\nof possible worlds into the set of signals. With this\nmodification, our unobservable-query model becomes equivalent\nto the model of Bergemann and V\u00a8alim\u00a8aki [4, 5], in which\nthe result of a query is a posterior distribution over the\nworlds. Our techniques allow us to compute equilibria in\nsuch a stochastic-query model provided that each query is\nrepresented as a table that, for each world/signal pair, lists\nthe probability that the query outputs that signal in that\nworld. It is also interesting to consider settings in which the\ngame\"s queries are specified by a compact representation of\nthe relevant probability distributions. (For example, one\nmight consider a setting in which the algorithm has only a\nsampling oracle for the posterior distributions envisioned by\nBergemann and V\u00a8alim\u00a8aki.) Efficiently finding equilibria in\nsuch settings remains an open problem.\nAnother interesting setting for Socratic games is when the\nset Q of available queries is given by Q = P(\u0393)-i.e., each\nplayer chooses to make a set q \u2208 P(\u0393) of queries from a\nspecified groundset \u0393 of queries. Here we take the query\ncost to be a linear function, so that \u03b4(q) =\nP\n\u03b3\u2208q \u03b4({\u03b3}).\nNatural groundsets include comparison queries (if my\nopponent is playing strategy aii, would I prefer to play ai or\n\u02c6ai?), strategy queries (what is my vector of payoffs if I\nplay strategy ai?), and world-identity queries (is the world\nw \u2208 W the real world?). When one can infer a polynomial\nbound on the number of queries made by a rational player,\nthen our results yield efficient solutions. (For example, we\ncan efficiently solve games in which every groundset element\n\u03b3 \u2208 \u0393 has \u03b4({\u03b3}) = \u03a9(M \u2212 M), where M and M denote\nthe maximum and minimum payoffs to any player in any\nworld.) Conversely, it is NP-hard to compute a Nash\nequilibrium for such a game when every \u03b4({\u03b3}) \u2264 1/|W|2\n, even\nwhen the worlds are constant sum and Player II has only\na single available strategy. Thus even computing a best\nresponse for Player I is hard. (This proof proceeds by\nreduction from set cover; intuitively, for sufficiently low query\ncosts, Player I must fully identify the actual world through\nhis queries. Selecting a minimum-sized set of these queries\nis hard.) Computing Player I\"s best response can be viewed\nas maximizing a submodular function, and thus a best\nresponse can be (1 \u2212 1/e) \u2248 0.63 approximated greedily [14].\nAn interesting open question is whether this approximate\nbest-response calculation can be leveraged to find an\napproximate Nash equilibrium.\n8. ACKNOWLEDGEMENTS\nPart of this work was done while all authors were at MIT\nCSAIL. We thank Erik Demaine, Natalia Hernandez\nGardiol, Claire Monteleoni, Jason Rennie, Madhu Sudan, and\nKatherine White for helpful comments and discussions.\n9. REFERENCES\n[1] Aaron Archer and David P. Williamson. Faster\napproximation algorithms for the minimum latency\nproblem. 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Kluwer,\n1995.\n159", "keywords": "algorithm;game theory;nash equilibrium;strategic multiplayer environment;constant-sum game;correlate equilibrium;auction;arbitrary partial information;questionand-answer session;information acquisition;socratic game;priori probability distribution;observable-query model;missing information;game-either full omniscient knowledge;unobservable-query model"}
{"name": "train_J-37", "title": "Finding Equilibria in Large Sequential Games of Imperfect Information", "abstract": "Finding an equilibrium of an extensive form game of imperfect information is a fundamental problem in computational game theory, but current techniques do not scale to large games. To address this, we introduce the ordered game isomorphism and the related ordered game isomorphic abstraction transformation. For a multi-player sequential game of imperfect information with observable actions and an ordered signal space, we prove that any Nash equilibrium in an abstracted smaller game, obtained by one or more applications of the transformation, can be easily converted into a Nash equilibrium in the original game. We present an algorithm, GameShrink, for abstracting the game using our isomorphism exhaustively. Its complexity is \u02dcO(n2 ), where n is the number of nodes in a structure we call the signal tree. It is no larger than the game tree, and on nontrivial games it is drastically smaller, so GameShrink has time and space complexity sublinear in the size of the game tree. Using GameShrink, we find an equilibrium to a poker game with 3.1 billion nodes-over four orders of magnitude more than in the largest poker game solved previously. We discuss several electronic commerce applications for GameShrink. To address even larger games, we introduce approximation methods that do not preserve equilibrium, but nevertheless yield (ex post) provably close-to-optimal strategies.", "fulltext": "1. INTRODUCTION\nIn environments with more than one agent, an agent\"s\noutcome is generally affected by the actions of the other\nagent(s). Consequently, the optimal action of one agent can\ndepend on the others. Game theory provides a normative\nframework for analyzing such strategic situations. In\nparticular, it provides solution concepts that define what rational\nbehavior is in such settings. The most famous and\nimportant solution concept is that of Nash equilibrium [36]. It is\na strategy profile (one strategy for each agent) in which no\nagent has incentive to deviate to a different strategy.\nHowever, for the concept to be operational, we need algorithmic\ntechniques for finding an equilibrium.\nGames can be classified as either games of perfect\ninformation or imperfect information. Chess and Go are examples\nof the former, and, until recently, most game playing work\nhas been on games of this type. To compute an optimal\nstrategy in a perfect information game, an agent traverses\nthe game tree and evaluates individual nodes. If the agent\nis able to traverse the entire game tree, she simply computes\nan optimal strategy from the bottom-up, using the principle\nof backward induction.1\nIn computer science terms, this is\ndone using minimax search (often in conjunction with\n\u03b1\u03b2-pruning to reduce the search tree size and thus enhance\nspeed). Minimax search runs in linear time in the size of the\ngame tree.2\nThe differentiating feature of games of imperfect\ninformation, such as poker, is that they are not fully observable:\nwhen it is an agent\"s turn to move, she does not have access\nto all of the information about the world. In such games,\nthe decision of what to do at a point in time cannot\ngenerally be optimally made without considering decisions at all\nother points in time (including ones on other paths of play)\nbecause those other decisions affect the probabilities of\nbeing at different states at the current point in time. Thus\nthe algorithms for perfect information games do not solve\ngames of imperfect information.\nFor sequential games with imperfect information, one could\ntry to find an equilibrium using the normal (matrix) form,\nwhere every contingency plan of the agent is a pure strategy\nfor the agent.3\nUnfortunately (even if equivalent strategies\n1\nThis actually yields a solution that satisfies not only the\nNash equilibrium solution concept, but a stronger solution\nconcept called subgame perfect Nash equilibrium [45].\n2\nThis type of algorithm still does not scale to huge\ntrees (such as in chess or Go), but effective game-playing\nagents can be developed even then by evaluating\nintermediate nodes using a heuristic evaluation and then treating\nthose nodes as leaves.\n3\nAn -equilibrium in a normal form game with any\n160\nare replaced by a single strategy [27]) this representation is\ngenerally exponential in the size of the game tree [52].\nBy observing that one needs to consider only sequences of\nmoves rather than pure strategies [41, 46, 22, 52], one arrives\nat a more compact representation, the sequence form, which\nis linear in the size of the game tree.4\nFor 2-player games,\nthere is a polynomial-sized (in the size of the game tree)\nlinear programming formulation (linear complementarity in\nthe non-zero-sum case) based on the sequence form such that\nstrategies for players 1 and 2 correspond to primal and dual\nvariables. Thus, the equilibria of reasonable-sized 2-player\ngames can be computed using this method [52, 24, 25].5\nHowever, this approach still yields enormous (unsolvable)\noptimization problems for many real-world games, such as\npoker.\n1.1 Our approach\nIn this paper, we take a different approach to tackling\nthe difficult problem of equilibrium computation. Instead\nof developing an equilibrium-finding method per se, we\ninstead develop a methodology for automatically abstracting\ngames in such a way that any equilibrium in the smaller\n(abstracted) game corresponds directly to an equilibrium in\nthe original game. Thus, by computing an equilibrium in\nthe smaller game (using any available equilibrium-finding\nalgorithm), we are able to construct an equilibrium in the\noriginal game. The motivation is that an equilibrium for\nthe smaller game can be computed drastically faster than\nfor the original game.\nTo this end, we introduce games with ordered signals\n(Section 2), a broad class of games that has enough structure\nwhich we can exploit for abstraction purposes. Instead of\noperating directly on the game tree (something we found\nto be technically challenging), we instead introduce the use\nof information filters (Section 2.1), which coarsen the\ninformation each player receives. They are used in our analysis\nand abstraction algorithm. By operating only in the space\nof filters, we are able to keep the strategic structure of the\ngame intact, while abstracting out details of the game in a\nway that is lossless from the perspective of equilibrium\nfinding. We introduce the ordered game isomorphism to describe\nstrategically symmetric situations and the ordered game\nisomorphic abstraction transformation to take advantange of\nsuch symmetries (Section 3). As our main equilibrium\nresult we have the following:\nconstant number of agents can be constructed in\nquasipolynomial time [31], but finding an exact equilibrium is\nPPAD-complete even in a 2-player game [8]. The most\nprevalent algorithm for finding an equilibrium in a 2-agent\ngame is Lemke-Howson [30], but it takes exponentially many\nsteps in the worst case [44]. For a survey of equilibrium\ncomputation in 2-player games, see [53]. Recently,\nequilibriumfinding algorithms that enumerate supports (i.e., sets of\npure strategies that are played with positive probability)\nhave been shown efficient on many games [40], and efficient\nmixed integer programming algorithms that search in the\nspace of supports have been developed [43]. For more than\ntwo players, many algorithms have been proposed, but they\ncurrently only scale to very small games [19, 34, 40].\n4\nThere were also early techniques that capitalized in\ndifferent ways on the fact that in many games the vast majority\nof pure strategies are not played in equilibrium [54, 23].\n5\nRecently this approach was extended to handle\ncomputing sequential equilibria [26] as well [35].\nTheorem 2 Let \u0393 be a game with ordered\nsignals, and let F be an information filter for \u0393. Let\nF be an information filter constructed from F by\none application of the ordered game isomorphic\nabstraction transformation, and let \u03c3 be a Nash\nequilibrium strategy profile of the induced game\n\u0393F (i.e., the game \u0393 using the filter F ). If \u03c3 is\nconstructed by using the corresponding strategies\nof \u03c3 , then \u03c3 is a Nash equilibrium of \u0393F .\nThe proof of the theorem uses an equivalent\ncharacterization of Nash equilibria: \u03c3 is a Nash equilibrium if and\nonly if there exist beliefs \u03bc (players\" beliefs about unknown\ninformation) at all points of the game reachable by \u03c3 such\nthat \u03c3 is sequentially rational (i.e., a best response) given \u03bc,\nwhere \u03bc is updated using Bayes\" rule. We can then use the\nfact that \u03c3 is a Nash equilibrium to show that \u03c3 is a Nash\nequilibrium considering only local properties of the game.\nWe also give an algorithm, GameShrink, for abstracting\nthe game using our isomorphism exhaustively (Section 4).\nIts complexity is \u02dcO(n2\n), where n is the number of nodes in\na structure we call the signal tree. It is no larger than the\ngame tree, and on nontrivial games it is drastically smaller,\nso GameShrink has time and space complexity sublinear in\nthe size of the game tree. We present several algorithmic and\ndata structure related speed improvements (Section 4.1),\nand we demonstrate how a simple modification to our\nalgorithm yields an approximation algorithm (Section 5).\n1.2 Electronic commerce applications\nSequential games of imperfect information are ubiquitous,\nfor example in negotiation and in auctions. Often aspects\nof a player\"s knowledge are not pertinent for deciding what\naction the player should take at a given point in the game.\nOn the trivial end, some aspects of a player\"s knowledge are\nnever pertinent (e.g., whether it is raining or not has no\nbearing on the bidding strategy in an art auction), and such\naspects can be completely left out of the model specification.\nHowever, some aspects can be pertinent in certain states\nof the game while they are not pertinent in other states,\nand thus cannot be left out of the model completely.\nFurthermore, it may be highly non-obvious which aspects are\npertinent in which states of the game. Our algorithm\nautomatically discovers which aspects are irrelevant in different\nstates, and eliminates those aspects of the game, resulting\nin a more compact, equivalent game representation.\nOne broad application area that has this property is\nsequential negotiation (potentially over multiple issues).\nAnother broad application area is sequential auctions\n(potentially over multiple goods). For example, in those states of\na 1-object auction where bidder A can infer that his\nvaluation is greater than that of bidder B, bidder A can ignore all\nhis other information about B\"s signals, although that\ninformation would be relevant for inferring B\"s exact valuation.\nFurthermore, in some states of the auction, a bidder might\nnot care which exact other bidders have which valuations,\nbut cares about which valuations are held by the other\nbidders in aggregate (ignoring their identities). Many open-cry\nsequential auction and negotiation mechanisms fall within\nthe game model studied in this paper (specified in detail\nlater), as do certain other games in electronic commerce,\nsuch as sequences of take-it-or-leave-it offers [42].\nOur techniques are in no way specific to an application.\nThe main experiment that we present in this paper is on\n161\na recreational game. We chose a particular poker game as\nthe benchmark problem because it yields an extremely\ncomplicated and enormous game tree, it is a game of imperfect\ninformation, it is fully specified as a game (and the data is\navailable), and it has been posted as a challenge problem\nby others [47] (to our knowledge no such challenge\nproblem instances have been proposed for electronic commerce\napplications that require solving sequential games).\n1.3 Rhode Island Hold\"em poker\nPoker is an enormously popular card game played around\nthe world. The 2005 World Series of Poker had over $103\nmillion dollars in total prize money, including $56 million\nfor the main event. Increasingly, poker players compete\nin online casinos, and television stations regularly\nbroadcast poker tournaments. Poker has been identified as an\nimportant research area in AI due to the uncertainty\nstemming from opponents\" cards, opponents\" future actions, and\nchance moves, among other reasons [5].\nAlmost since the field\"s founding, game theory has been\nused to analyze different aspects of poker [28; 37; 3; 51, pp.\n186-219]. However, this work was limited to tiny games that\ncould be solved by hand. More recently, AI researchers have\nbeen applying the computational power of modern hardware\nto computing game theory-based strategies for larger games.\nKoller and Pfeffer determined solutions to poker games with\nup to 140,000 nodes using the sequence form and linear\nprogramming [25]. Large-scale approximations have been\ndeveloped [4], but those methods do not provide any\nguarantees about the performance of the computed strategies.\nFurthermore, the approximations were designed manually\nby a human expert. Our approach yields an automated\nabstraction mechanism along with theoretical guarantees on\nthe strategies\" performance.\nRhode Island Hold\"em was invented as a testbed for\ncomputational game playing [47]. It was designed so that it was\nsimilar in style to Texas Hold\"em, yet not so large that\ndevising reasonably intelligent strategies would be impossible.\n(The rules of Rhode Island Hold\"em, as well as a discussion\nof how Rhode Island Hold\"em can be modeled as a game\nwith ordered signals, that is, it fits in our model, is available\nin an extended version of this paper [13].) We applied the\ntechniques developed in this paper to find an exact\n(minimax) solution to Rhode Island Hold\"em, which has a game\ntree exceeding 3.1 billion nodes.\nApplying the sequence form to Rhode Island Hold\"em\ndirectly without abstraction yields a linear program with\n91,224,226 rows, and the same number of columns. This is\nmuch too large for (current) linear programming algorithms\nto handle. We used our GameShrink algorithm to reduce\nthis with lossless abstraction, and it yielded a linear program\nwith 1,237,238 rows and columns-with 50,428,638 non-zero\ncoefficients. We then applied iterated elimination of\ndominated strategies, which further reduced this to 1,190,443\nrows and 1,181,084 columns. (Applying iterated\nelimination of dominated strategies without GameShrink yielded\n89,471,986 rows and 89,121,538 columns, which still would\nhave been prohibitively large to solve.) GameShrink\nrequired less than one second to perform the shrinking (i.e.,\nto compute all of the ordered game isomorphic abstraction\ntransformations). Using a 1.65GHz IBM eServer p5 570 with\n64 gigabytes of RAM (the linear program solver actually\nneeded 25 gigabytes), we solved it in 7 days and 17 hours\nusing the interior-point barrier method of CPLEX version\n9.1.2. We recently demonstrated our optimal Rhode Island\nHold\"em poker player at the AAAI-05 conference [14], and\nit is available for play on-line at http://www.cs.cmu.edu/\n~gilpin/gsi.html.\nWhile others have worked on computer programs for\nplaying Rhode Island Hold\"em [47], no optimal strategy has been\nfound before. This is the largest poker game solved to date\nby over four orders of magnitude.\n2. GAMES WITH ORDERED SIGNALS\nWe work with a slightly restricted class of games, as\ncompared to the full generality of the extensive form. This class,\nwhich we call games with ordered signals, is highly\nstructured, but still general enough to capture a wide range of\nstrategic situations. A game with ordered signals consists\nof a finite number of rounds. Within a round, the players\nplay a game on a directed tree (the tree can be different in\ndifferent rounds). The only uncertainty players face stems\nfrom private signals the other players have received and from\nthe unknown future signals. In other words, players observe\neach others\" actions, but potentially not nature\"s actions.\nIn each round, there can be public signals (announced to all\nplayers) and private signals (confidentially communicated\nto individual players). For simplicity, we assume-as is the\ncase in most recreational games-that within each round,\nthe number of private signals received is the same across\nplayers (this could quite likely be relaxed). We also assume\nthat the legal actions that a player has are independent of\nthe signals received. For example, in poker, the legal\nbetting actions are independent of the cards received. Finally,\nthe strongest assumption is that there is a partial ordering\nover sets of signals, and the payoffs are increasing (not\nnecessarily strictly) in these signals. For example, in poker, this\npartial ordering corresponds exactly to the ranking of card\nhands.\nDefinition 1. A game with ordered signals is a tuple\n\u0393 = I, G, L, \u0398, \u03ba, \u03b3, p, , \u03c9, u where:\n1. I = {1, . . . , n} is a finite set of players.\n2. G = G1\n, . . . , Gr\n, Gj\n=\n`\nV j\n, Ej\n\u00b4\n, is a finite collection\nof finite directed trees with nodes V j\nand edges Ej\n. Let\nZj\ndenote the leaf nodes of Gj\nand let Nj\n(v) denote\nthe outgoing neighbors of v \u2208 V j\n. Gj\nis the stage game\nfor round j.\n3. L = L1\n, . . . , Lr\n, Lj\n: V j\n\\ Zj\n\u2192 I indicates which\nplayer acts (chooses an outgoing edge) at each internal\nnode in round j.\n4. \u0398 is a finite set of signals.\n5. \u03ba = \u03ba1\n, . . . , \u03bar\nand \u03b3 = \u03b31\n, . . . , \u03b3r\nare vectors of\nnonnegative integers, where \u03baj\nand \u03b3j\ndenote the\nnumber of public and private signals (per player),\nrespectively, revealed in round j. Each signal \u03b8 \u2208 \u0398 may\nonly be revealed once, and in each round every player\nreceives the same number of private signals, so we\nrequire\nPr\nj=1 \u03baj\n+ n\u03b3j\n\u2264 |\u0398|. The public information\nrevealed in round j is \u03b1j\n\u2208 \u0398\u03baj\nand the public\ninformation revealed in all rounds up through round j\nis \u02dc\u03b1j\n=\n`\n\u03b11\n, . . . , \u03b1j\n\u00b4\n. The private information\nrevealed to player i \u2208 I in round j is \u03b2j\ni \u2208 \u0398\u03b3j\nand\nthe private information revaled to player i \u2208 I in all\nrounds up through round j is \u02dc\u03b2j\ni =\n`\n\u03b21\ni , . . . , \u03b2j\ni\n\u00b4\n. We\n162\nalso write \u02dc\u03b2j\n=\n\n\u02dc\u03b2j\n1, . . . , \u02dc\u03b2j\nn\n\nto represent all private\ninformation up through round j, and\n\n\u02dc\u03b2\nj\ni , \u02dc\u03b2j\n\u2212i\n\n=\n\n\u02dc\u03b2j\n1, . . . , \u02dc\u03b2j\ni\u22121, \u02dc\u03b2\nj\ni , \u02dc\u03b2j\ni+1, . . . , \u02dc\u03b2j\nn\n\nis \u02dc\u03b2j\nwith \u02dc\u03b2j\ni replaced\nwith \u02dc\u03b2\nj\ni . The total information revealed up through\nround j,\n\n\u02dc\u03b1j\n, \u02dc\u03b2j\n\n, is said to be legal if no signals are\nrepeated.\n6. p is a probability distribution over \u0398, with p(\u03b8) > 0\nfor all \u03b8 \u2208 \u0398. Signals are drawn from \u0398 according\nto p without replacement, so if X is the set of signals\nalready revealed, then\np(x | X) =\n(\np(x)P\ny /\u2208X p(y)\nif x /\u2208 X\n0 if x \u2208 X.\n7. is a partial ordering of subsets of \u0398 and is defined\nfor at least those pairs required by u.\n8. \u03c9 :\nrS\nj=1\nZj\n\u2192 {over, continue} is a mapping of\nterminal nodes within a stage game to one of two\nvalues: over, in which case the game ends, or continue,\nin which case the game continues to the next round.\nClearly, we require \u03c9(z) = over for all z \u2208 Zr\n. Note\nthat \u03c9 is independent of the signals. Let \u03c9j\nover = {z \u2208\nZj\n| \u03c9(z) = over} and \u03c9j\ncont = {z \u2208 Zj\n| \u03c9(z) =\ncontinue}.\n9. u = (u1\n, . . . , ur\n), uj\n:\nj\u22121\nk=1\n\u03c9k\ncont \u00d7 \u03c9j\nover \u00d7\nj\nk=1\n\u0398\u03bak\n\u00d7\nn\ni=1\nj\nk=1\n\u0398\u03b3k\n\u2192 Rn\nis a utility function such that for\nevery j, 1 \u2264 j \u2264 r, for every i \u2208 I, and for every\n\u02dcz \u2208\nj\u22121\nk=1\n\u03c9k\ncont \u00d7 \u03c9j\nover, at least one of the following two\nconditions holds:\n(a) Utility is signal independent: uj\ni (\u02dcz, \u03d1) = uj\ni (\u02dcz, \u03d1 )\nfor all legal \u03d1, \u03d1 \u2208\nj\nk=1\n\u0398\u03bak\n\u00d7\nn\ni=1\nj\nk=1\n\u0398\u03b3k\n.\n(b) is defined for all legal signals (\u02dc\u03b1j\n, \u02dc\u03b2j\ni ), (\u02dc\u03b1j\n, \u02dc\u03b2 j\ni )\nthrough round j and a player\"s utility is increasing\nin her private signals, everything else equal:\n\n\u02dc\u03b1j\n, \u02dc\u03b2j\ni\n\n\u02dc\u03b1j\n, \u02dc\u03b2 j\ni\n\n=\u21d2\nui\n\n\u02dcz, \u02dc\u03b1j\n,\n\n\u02dc\u03b2j\ni , \u02dc\u03b2j\n\u2212i\n\n\u2265 ui\n\n\u02dcz, \u02dc\u03b1j\n,\n\n\u02dc\u03b2\nj\ni , \u02dc\u03b2j\n\u2212i\n\n.\nWe will use the term game with ordered signals and the\nterm ordered game interchangeably.\n2.1 Information filters\nIn this subsection, we define an information filter for\nordered games. Instead of completely revealing a signal (either\npublic or private) to a player, the signal first passes through\nthis filter, which outputs a coarsened signal to the player. By\nvarying the filter applied to a game, we are able to obtain\na wide variety of games while keeping the underlying action\nspace of the game intact. We will use this when designing\nour abstraction techniques. Formally, an information filter\nis as follows.\nDefinition 2. Let \u0393 = I, G, L, \u0398, \u03ba, \u03b3, p, , \u03c9, u be an\nordered game. Let Sj\n\u2286\nj\nk=1\n\u0398\u03bak\n\u00d7\nj\nk=1\n\u0398\u03b3k\nbe the set of\nlegal signals (i.e., no repeated signals) for one player through\nround j. An information filter for \u0393 is a collection F =\nF1\n, . . . , Fr\nwhere each Fj\nis a function Fj\n: Sj\n\u2192 2Sj\nsuch that each of the following conditions hold:\n1. (Truthfulness) (\u02dc\u03b1j\n, \u02dc\u03b2j\ni ) \u2208 Fj\n(\u02dc\u03b1j\n, \u02dc\u03b2j\ni ) for all legal (\u02dc\u03b1j\n, \u02dc\u03b2j\ni ).\n2. (Independence) The range of Fj\nis a partition of Sj\n.\n3. (Information preservation) If two values of a signal are\ndistinguishable in round k, then they are\ndistinguishable fpr each round j > k. Let mj\n=\nPj\nl=1 \u03bal\n+\u03b3l\n. We\nrequire that for all legal (\u03b81, . . . , \u03b8mk , . . . , \u03b8mj ) \u2286 \u0398 and\n(\u03b81, . . . , \u03b8mk , . . . , \u03b8mj ) \u2286 \u0398:\n(\u03b81, . . . , \u03b8mk ) /\u2208 Fk\n(\u03b81, . . . , \u03b8mk ) =\u21d2\n(\u03b81, . . . , \u03b8mk , . . . , \u03b8mj ) /\u2208 Fj\n(\u03b81, . . . , \u03b8mk , . . . , \u03b8mj ).\nA game with ordered signals \u0393 and an information filter\nF for \u0393 defines a new game \u0393F . We refer to such games as\nfiltered ordered games. We are left with the original game\nif we use the identity filter Fj\n\n\u02dc\u03b1j\n, \u02dc\u03b2j\ni\n\n=\nn\n\u02dc\u03b1j\n, \u02dc\u03b2j\ni\no\n. We\nhave the following simple (but important) result:\nProposition 1. A filtered ordered game is an extensive\nform game satisfying perfect recall.\nA simple proof proceeds by constructing an extensive form\ngame directly from the ordered game, and showing that it\nsatisfies perfect recall. In determining the payoffs in a game\nwith filtered signals, we take the average over all real signals\nin the filtered class, weighted by the probability of each real\nsignal occurring.\n2.2 Strategies and Nash equilibrium\nWe are now ready to define behavior strategies in the\ncontext of filtered ordered games.\nDefinition 3. A behavior strategy for player i in round\nj of \u0393 = I, G, L, \u0398, \u03ba, \u03b3, p, , \u03c9, u with information filter\nF is a probability distribution over possible actions, and is\ndefined for each player i, each round j, and each v \u2208 V j\n\\Zj\nfor Lj\n(v) = i:\n\u03c3j\ni,v :\nj\u22121\nk=1\n\u03c9k\ncont\u00d7Range\n\nFj\n\n\u2192 \u0394\nn\nw \u2208 V j\n| (v, w) \u2208 Ej\no\n.\n(\u0394(X) is the set of probability distributions over a finite set\nX.) A behavior strategy for player i in round j is \u03c3j\ni =\n(\u03c3j\ni,v1\n, . . . , \u03c3j\ni,vm\n) for each vk \u2208 V j\n\\ Zj\nwhere Lj\n(vk) = i.\nA behavior strategy for player i in \u0393 is \u03c3i =\n`\n\u03c31\ni , . . . , \u03c3r\ni\n\u00b4\n.\nA strategy profile is \u03c3 = (\u03c31, . . . , \u03c3n). A strategy profile with\n\u03c3i replaced by \u03c3i is (\u03c3i, \u03c3\u2212i) = (\u03c31, . . . , \u03c3i\u22121, \u03c3i, \u03c3i+1, . . . , \u03c3n).\nBy an abuse of notation, we will say player i receives an\nexpected payoff of ui(\u03c3) when all players are playing the\nstrategy profile \u03c3. Strategy \u03c3i is said to be player i\"s best\nresponse to \u03c3\u2212i if for all other strategies \u03c3i for player i we\nhave ui(\u03c3i, \u03c3\u2212i) \u2265 ui(\u03c3i, \u03c3\u2212i). \u03c3 is a Nash equilibrium if,\nfor every player i, \u03c3i is a best response for \u03c3\u2212i. A Nash\nequilibrium always exists in finite extensive form games [36],\nand one exists in behavior strategies for games with perfect\nrecall [29]. Using these observations, we have the following\ncorollary to Proposition 1:\n163\nCorollary 1. For any filtered ordered game, a Nash\nequilibrium exists in behavior strateges.\n3. EQUILIBRIUM-PRESERVING\nABSTRACTIONS\nIn this section, we present our main technique for reducing\nthe size of games. We begin by defining a filtered signal tree\nwhich represents all of the chance moves in the game. The\nbold edges (i.e. the first two levels of the tree) in the game\ntrees in Figure 1 correspond to the filtered signal trees in\neach game.\nDefinition 4. Associated with every ordered game \u0393 =\nI, G, L, \u0398, \u03ba, \u03b3, p, , \u03c9, u and information filter F is a\nfiltered signal tree, a directed tree in which each node\ncorresponds to some revealed (filtered) signals and edges\ncorrespond to revealing specific (filtered) signals. The nodes in the\nfiltered signal tree represent the set of all possible revealed\nfiltered signals (public and private) at some point in time. The\nfiltered public signals revealed in round j correspond to the\nnodes in the \u03baj\nlevels beginning at level\nPj\u22121\nk=1\n`\n\u03bak\n+ n\u03b3k\n\u00b4\nand the private signals revealed in round j correspond to\nthe nodes in the n\u03b3j\nlevels beginning at level\nPj\nk=1 \u03bak\n+\nPj\u22121\nk=1 n\u03b3k\n. We denote children of a node x as N(x). In\naddition, we associate weights with the edges corresponding\nto the probability of the particular edge being chosen given\nthat its parent was reached.\nIn many games, there are certain situations in the game\nthat can be thought of as being strategically equivalent to\nother situations in the game. By melding these situations\ntogether, it is possible to arrive at a strategically\nequivalent smaller game. The next two definitions formalize this\nnotion via the introduction of the ordered game isomorphic\nrelation and the ordered game isomorphic abstraction\ntransformation.\nDefinition 5. Two subtrees beginning at internal nodes\nx and y of a filtered signal tree are ordered game\nisomorphic if x and y have the same parent and there is a\nbijection f : N(x) \u2192 N(y), such that for w \u2208 N(x) and\nv \u2208 N(y), v = f(w) implies the weights on the edges (x, w)\nand (y, v) are the same and the subtrees beginning at w and\nv are ordered game isomorphic. Two leaves\n(corresponding to filtered signals \u03d1 and \u03d1 up through round r) are\nordered game isomorphic if for all \u02dcz \u2208\nr\u22121\nj=1\n\u03c9j\ncont \u00d7 \u03c9r\nover,\nur\n(\u02dcz, \u03d1) = ur\n(\u02dcz, \u03d1 ).\nDefinition 6. Let \u0393 = I, G, L, \u0398, \u03ba, \u03b3, p, , \u03c9, u be an\nordered game and let F be an information filter for \u0393. Let\n\u03d1 and \u03d1 be two nodes where the subtrees in the induced\nfiltered signal tree corresponding to the nodes \u03d1 and \u03d1 are\nordered game isomorphic, and \u03d1 and \u03d1 are at either levelPj\u22121\nk=1\n`\n\u03bak\n+ n\u03b3k\n\u00b4\nor\nPj\nk=1 \u03bak\n+\nPj\u22121\nk=1 n\u03b3k\nfor some round\nj. The ordered game isomorphic abstraction transformation\nis given by creating a new information filter F :\nF j\n\n\u02dc\u03b1j\n, \u02dc\u03b2j\ni\n\n=\n8\n<\n:\nFj\n\n\u02dc\u03b1j\n, \u02dc\u03b2j\ni\n\nif\n\n\u02dc\u03b1j\n, \u02dc\u03b2j\ni\n\n/\u2208 \u03d1 \u222a \u03d1\n\u03d1 \u222a \u03d1 if\n\n\u02dc\u03b1j\n, \u02dc\u03b2j\ni\n\n\u2208 \u03d1 \u222a \u03d1 .\nFigure 1 shows the ordered game isomorphic abstraction\ntransformation applied twice to a tiny poker game.\nTheorem 2, our main equilibrium result, shows how the ordered\ngame isomorphic abstraction transformation can be used to\ncompute equilibria faster.\nTheorem 2. Let \u0393 = I, G, L, \u0398, \u03ba, \u03b3, p, , \u03c9, u be an\nordered game and F be an information filter for \u0393. Let F be\nan information filter constructed from F by one application\nof the ordered game isomorphic abstraction transformation.\nLet \u03c3 be a Nash equilibrium of the induced game \u0393F . If\nwe take \u03c3j\ni,v\n\n\u02dcz, Fj\n\n\u02dc\u03b1j\n, \u02dc\u03b2j\ni\n\n= \u03c3 j\ni,v\n\n\u02dcz, F j\n\n\u02dc\u03b1j\n, \u02dc\u03b2j\ni\n\n, \u03c3 is\na Nash equilibrium of \u0393F .\nProof. For an extensive form game, a belief system \u03bc\nassigns a probability to every decision node x such thatP\nx\u2208h \u03bc(x) = 1 for every information set h. A strategy\nprofile \u03c3 is sequentially rational at h given belief system \u03bc if\nui(\u03c3i, \u03c3\u2212i | h, \u03bc) \u2265 ui(\u03c4i, \u03c3\u2212i | h, \u03bc)\nfor all other strategies \u03c4i, where i is the player who controls\nh. A basic result [33, Proposition 9.C.1] characterizing Nash\nequilibria dictates that \u03c3 is a Nash equilibrium if and only\nif there is a belief system \u03bc such that for every information\nset h with Pr(h | \u03c3) > 0, the following two conditions hold:\n(C1) \u03c3 is sequentially rational at h given \u03bc; and (C2) \u03bc(x) =\nPr(x | \u03c3)\nPr(h | \u03c3)\nfor all x \u2208 h. Since \u03c3 is a Nash equilibrium of \u0393 ,\nthere exists such a belief system \u03bc for \u0393F . Using \u03bc , we will\nconstruct a belief system \u03bc for \u0393 and show that conditions\nC1 and C2 hold, thus supporting \u03c3 as a Nash equilibrium.\nFix some player i \u2208 I. Each of i\"s information sets in some\nround j corresponds to filtered signals Fj\n\n\u02dc\u03b1\u2217j\n, \u02dc\u03b2\u2217j\ni\n\n, history\nin the first j \u2212 1 rounds (z1, . . . , zj\u22121) \u2208\nj\u22121\nk=1\n\u03c9k\ncont, and\nhistory so far in round j, v \u2208 V j\n\\ Zj\n. Let \u02dcz = (z1, . . . , zj\u22121, v)\nrepresent all of the player actions leading to this\ninformation set. Thus, we can uniquely specify this information set\nusing the information\n\nFj\n\n\u02dc\u03b1\u2217j\n, \u02dc\u03b2\u2217j\ni\n\n, \u02dcz\n\n.\nEach node in an information set corresponds to the\npossible private signals the other players have received. Denote\nby \u02dc\u03b2 some legal\n(Fj\n(\u02dc\u03b1j\n, \u02dc\u03b2j\n1), . . . , Fj\n(\u02dc\u03b1j\n, \u02dc\u03b2j\ni\u22121), Fj\n(\u02dc\u03b1j\n, \u02dc\u03b2j\ni+1), . . . , Fj\n(\u02dc\u03b1j\n, \u02dc\u03b2j\nn)).\nIn other words, there exists (\u02dc\u03b1j\n, \u02dc\u03b2j\n1, . . . , \u02dc\u03b2j\nn) such that\n(\u02dc\u03b1j\n, \u02dc\u03b2j\ni ) \u2208 Fj\n(\u02dc\u03b1\u2217j\n, \u02dc\u03b2\u2217j\ni ), (\u02dc\u03b1j\n, \u02dc\u03b2j\nk) \u2208 Fj\n(\u02dc\u03b1j\n, \u02dc\u03b2j\nk)\nfor k = i, and no signals are repeated. Using such a set\nof signals (\u02dc\u03b1j\n, \u02dc\u03b2j\n1, . . . , \u02dc\u03b2j\nn), let \u02c6\u03b2 denote (F j\n(\u02dc\u03b1j\n, \u02dc\u03b2j\n1), . . . ,\nF j\n(\u02dc\u03b1j\n, \u02dc\u03b2j\ni\u22121), F j\n(\u02dc\u03b1j\n, \u02dc\u03b2j\ni+1), . . . , F j\n(\u02dc\u03b1j\n, \u02dc\u03b2j\nn). (We will abuse\nnotation and write F j\n\u2212i\n\n\u02c6\u03b2\n\n= \u02c6\u03b2 .) We can now compute \u03bc\ndirectly from \u03bc :\n\u03bc\n\n\u02c6\u03b2 | Fj\n\n\u02dc\u03b1j\n, \u02dc\u03b2j\ni\n\n, \u02dcz\n\n=\n8\n>>>>>><\n>>>>>>:\n\u03bc\n\n\u02c6\u03b2 | F j\n\n\u02dc\u03b1j\n, \u02dc\u03b2j\ni\n\n, \u02dcz\n\nif Fj\n\n\u02dc\u03b1j\n, \u02dc\u03b2j\ni\n\n= F j\n\n\u02dc\u03b1j\n, \u02dc\u03b2j\ni\n\nor \u02c6\u03b2 = \u02c6\u03b2\np\u2217\n\u03bc\n\n\u02c6\u03b2 | F j\n\n\u02dc\u03b1j\n, \u02dc\u03b2j\ni\n\n, \u02dcz\n\nif Fj\n\n\u02dc\u03b1j\n, \u02dc\u03b2j\ni\n\n= F j\n\n\u02dc\u03b1j\n, \u02dc\u03b2j\ni\n\nand \u02c6\u03b2 = \u02c6\u03b2\n164\nJ1\nJ2\nJ2 K1\nK1\nK2\nK2\nc b\nC B F B\nf b\nc b\nC B F B\nf b\nc b\nC\nf b\nB BF\nc b\nC\nf b\nB BF\nc b\nC B F B\nf b\nc b\nC BF B\nf b\nc b\nC\nf b\nB BF\nc b\nC\nf b\nB BF\nc b\nC\nf b\nB BF\nc b\nC\nf b\nB BF\nc b\nC B F B\nf b\nc b\nC B F B\nf b\n0 0\n0-1\n-1\n-1\n-1\n-1\n-1\n-1\n-1-1\n-1 -1\n-1\n-1\n-1\n-1\n-1\n-1\n-1-1\n-1 -1\n-1\n-1\n-10 0\n0\n0 0\n0\n0 0\n0\n-1\n-2\n-2 -1\n-2\n-2 -1\n-2\n-2 -1\n-2\n-2 1\n2\n2 1\n2\n2 1\n2\n2 1\n2\n2\nJ1 K1 K2 J1 J2 K2 J1 J2 K1\n1\n1\n1\n1 1\n1 1\n1\n2\n2\n2\n2\n2\n2\n2\n2\n{{J1}, {J2}, {K1}, {K2}}\n{{J1,J2}, {K1}, {K2}}\nc b\nC BF B\nf b\nc b\nC\nf b\nB BF\nc b\nC B F B\nf b\nJ1,J2 K1 K2\n1\n1\nc b\nC\nf b\nB BF\nc b\nC BF B\nf b\nc b\nC BF B\nf b\nc b\nC B F B\nf b\nJ1,J2\nK1\nK2\n1\n1\n1\n1\nJ1,J2 K2 J1,J2 K1\n0 0\n0-1\n-1\n-1\n-1 -1\n-1\n-1\n-2\n-2 -1\n-2\n-2\n2\n2\n2\n2\n2\n2\n-1\n-1-1\n-1\n0 0\n0\n1\n2\n2\n-1\n-1-1\n-1\n0 0\n0\n1\n2\n2\nc b\nC B F B\nf b\n-1\n-10 0\n0\nc b\nB F B\nf b\n-1\n-1-1\n-2\n-2\nc b\nC BF B\nf b\n0 0\n0-1\n-1\nc b\nC BF B\nf b\nJ1,J2\nJ1,J2 J1,J2K1,K2\nK1,K2\nK1,K2\n-1\n-1\n1\n2\n2\n2\n2\n2\n2\n{{J1,J2}, {K1,K2}}\n1\n1 1\n1\n1/4 1/4 1/4 1/4\n1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3\n1/4\n1/41/2\n1/3 1/3 1/3\n1/32/3 1/32/3\n1/2 1/2\n1/3 2/3 2/3 1/3\nFigure 1: GameShrink applied to a tiny two-person four-card (two Jacks and two Kings) poker game. Next\nto each game tree is the range of the information filter F. Dotted lines denote information sets, which are\nlabeled by the controlling player. Open circles are chance nodes with the indicated transition probabilities.\nThe root node is the chance node for player 1\"s card, and the next level is for player 2\"s card. The payment\nfrom player 2 to player 1 is given below each leaf. In this example, the algorithm reduces the game tree from\n53 nodes to 19 nodes.\nwhere p\u2217\n=\nPr(\u02c6\u03b2 | F j\n(\u02dc\u03b1j\n, \u02dc\u03b2\nj\ni ))\nPr(\u02c6\u03b2 | F j (\u02dc\u03b1j , \u02dc\u03b2\nj\ni ))\n. The following three claims\nshow that \u03bc as calculated above supports \u03c3 as a Nash\nequilibrium.\nClaim 1. \u03bc is a valid belief system for \u0393F .\nClaim 2. For all information sets h with Pr(h | \u03c3) > 0,\n\u03bc(x) = Pr(x | \u03c3)\nPr(h | \u03c3)\nfor all x \u2208 h.\nClaim 3. For all information sets h with Pr(h | \u03c3) > 0,\n\u03c3 is sequentially rational at h given \u03bc.\nThe proofs of Claims 1-3 are in an extended version of this\npaper [13]. By Claims 1 and 2, we know that condition C2\nholds. By Claim 3, we know that condition C1 holds. Thus,\n\u03c3 is a Nash equilibrium.\n3.1 Nontriviality of generalizing beyond this\nmodel\nOur model does not capture general sequential games of\nimperfect information because it is restricted in two ways\n(as discussed above): 1) there is a special structure\nconnecting the player actions and the chance actions (for one,\nthe players are assumed to observe each others\" actions, but\nnature\"s actions might not be publicly observable), and 2)\nthere is a common ordering of signals. In this subsection we\nshow that removing either of these conditions can make our\ntechnique invalid.\nFirst, we demonstrate a failure when removing the first\nassumption. Consider the game in Figure 2.6\nNodes a and\nb are in the same information set, have the same parent\n(chance) node, have isomorphic subtrees with the same\npayoffs, and nodes c and d also have similar structural\nproperties. By merging the subtrees beginning at a and b, we get\nthe game on the right in Figure 2. In this game, player\n1\"s only Nash equilibrium strategy is to play left. But in\nthe original game, player 1 knows that node c will never be\nreached, and so should play right in that information set.\n1/4\n1/4 1/4\n1/4\n2 2 2\n1\n1\n1 2 1 2 3 0 3 0\n-10 10\n1/2 1/4 1/4\n2 2 2\n1\n1 2 3 0 3 0\na b\n2 2 2 10-10\nc\nd\nFigure 2: Example illustrating difficulty in\ndeveloping a theory of equilibrium-preserving abstractions\nfor general extensive form games.\nRemoving the second assumption (that the utility\nfunctions are based on a common ordering of signals) can also\ncause failure. Consider a simple three-card game with a\ndeck containing two Jacks (J1 and J2) and a King (K),\nwhere player 1\"s utility function is based on the ordering\n6\nWe thank Albert Xin Jiang for providing this example.\n165\nK J1 \u223c J2 but player 2\"s utility function is based on the\nordering J2 K J1. It is easy to check that in the\nabstracted game (where Player 1 treats J1 and J2 as being\nequivalent) the Nash equilibrium does not correspond to\na Nash equilibrium in the original game.7\n4. GAMESHRINK: AN EFFICIENT\nALGORITHM FOR COMPUTING ORDERED\nGAME ISOMORPHIC ABSTRACTION\nTRANSFORMATIONS\nThis section presents an algorithm, GameShrink, for\nconducting the abstractions. It only needs to analyze the signal\ntree discussed above, rather than the entire game tree.\nWe first present a subroutine that GameShrink uses. It\nis a dynamic program for computing the ordered game\nisomorphic relation. Again, it operates on the signal tree.\nAlgorithm 1. OrderedGameIsomorphic? (\u0393, \u03d1, \u03d1 )\n1. If \u03d1 and \u03d1 have different parents, then return false.\n2. If \u03d1 and \u03d1 are both leaves of the signal tree:\n(a) If ur\n(\u03d1 | \u02dcz) = ur\n(\u03d1 | \u02dcz) for all \u02dcz \u2208\nr\u22121\nj=1\n\u03c9j\ncont \u00d7\n\u03c9r\nover, then return true.\n(b) Otherwise, return false.\n3. Create a bipartite graph G\u03d1,\u03d1 = (V1, V2, E) with V1 =\nN(\u03d1) and V2 = N(\u03d1 ).\n4. For each v1 \u2208 V1 and v2 \u2208 V2:\nIf OrderedGameIsomorphic? (\u0393, v1, v2)\nCreate edge (v1, v2)\n5. Return true if G\u03d1,\u03d1 has a perfect matching; otherwise,\nreturn false.\nBy evaluating this dynamic program from bottom to top,\nAlgorithm 1 determines, in time polynomial in the size of\nthe signal tree, whether or not any pair of equal depth\nnodes x and y are ordered game isomorphic. We can\nfurther speed up this computation by only examining nodes\nwith the same parent, since we know (from step 1) that\nno nodes with different parents are ordered game\nisomorphic. The test in step 2(a) can be computed in O(1) time\nby consulting the relation from the specification of the\ngame. Each call to OrderedGameIsomorphic? performs at\nmost one perfect matching computation on a bipartite graph\nwith O(|\u0398|) nodes and O(|\u0398|2\n) edges (recall that \u0398 is the\nset of signals). Using the Ford-Fulkerson algorithm [12] for\nfinding a maximal matching, this takes O(|\u0398|3\n) time. Let\nS be the maximum number of signals possibly revealed in\nthe game (e.g., in Rhode Island Hold\"em, S = 4 because\neach of the two players has one card in the hand plus there\nare two cards on the table). The number of nodes, n, in\nthe signal tree is O(|\u0398|S\n). The dynamic program visits each\nnode in the signal tree, with each visit requiring O(|\u0398|2\n)\ncalls to the OrderedGameIsomorphic? routine. So, it takes\nO(|\u0398|S\n|\u0398|3\n|\u0398|2\n) = O(|\u0398|S+5\n) time to compute the entire\nordered game isomorphic relation.\nWhile this is exponential in the number of revealed\nsignals, we now show that it is polynomial in the size of the\nsignal tree-and thus polynomial in the size of the game tree\n7\nWe thank an anonymous person for this example.\nbecause the signal tree is smaller than the game tree. The\nnumber of nodes in the signal tree is\nn = 1 +\nSX\ni=1\niY\nj=1\n(|\u0398| \u2212 j + 1)\n(Each term in the summation corresponds to the number of\nnodes at a specific depth of the tree.) The number of leaves\nis\nSY\nj=1\n(|\u0398| \u2212 j + 1) =\n|\u0398|\nS\n!\nS!\nwhich is a lower bound on the number of nodes. For large\n|\u0398| we can use the relation\n`n\nk\n\u00b4\n\u223c nk\nk!\nto get\n|\u0398|\nS\n!\nS! \u223c\n\u201e\n|\u0398|S\nS!\n\u00ab\nS! = |\u0398|S\nand thus the number of leaves in the signal tree is \u03a9(|\u0398|S\n).\nThus, O(|\u0398|S+5\n) = O(n|\u0398|5\n), which proves that we can\nindeed compute the ordered game isomorphic relation in time\npolynomial in the number of nodes, n, of the signal tree.\nThe algorithm often runs in sublinear time (and space) in\nthe size of the game tree because the signal tree is\nsignificantly smaller than the game tree in most nontrivial games.\n(Note that the input to the algorithm is not an explicit game\ntree, but a specification of the rules, so the algorithm does\nnot need to read in the game tree.) See Figure 1. In\ngeneral, if an ordered game has r rounds, and each round\"s stage\ngame has at least b nonterminal leaves, then the size of the\nsignal tree is at most 1\nbr of the size of the game tree. For\nexample, in Rhode Island Hold\"em, the game tree has 3.1\nbillion nodes while the signal tree only has 6,632,705.\nGiven the OrderedGameIsomorphic? routine for\ndetermining ordered game isomorphisms in an ordered game, we\nare ready to present the main algorithm, GameShrink.\nAlgorithm 2. GameShrink (\u0393)\n1. Initialize F to be the identity filter for \u0393.\n2. For j from 1 to r:\nFor each pair of sibling nodes \u03d1, \u03d1 at either levelPj\u22121\nk=1\n`\n\u03bak\n+ n\u03b3k\n\u00b4\nor\nPj\nk=1 \u03bak\n+\nPj\u22121\nk=1 n\u03b3k\nin the\nfiltered (according to F) signal tree:\nIf OrderedGameIsomorphic?(\u0393, \u03d1, \u03d1 ), then\nFj\n(\u03d1) \u2190 Fj\n(\u03d1 ) \u2190 Fj\n(\u03d1) \u222a Fj\n(\u03d1 ).\n3. Output F.\nGiven as input an ordered game \u0393, GameShrink applies\nthe shrinking ideas presented above as aggressively as\npossible. Once it finishes, there are no contractible nodes (since it\ncompares every pair of nodes at each level of the signal tree),\nand it outputs the corresponding information filter F. The\ncorrectness of GameShrink follows by a repeated application\nof Theorem 2. Thus, we have the following result:\nTheorem 3. GameShrink finds all ordered game\nisomorphisms and applies the associated ordered game isomorphic\nabstraction transformations. Furthermore, for any Nash\nequilibrium, \u03c3 , of the abstracted game, the strategy profile\nconstructed for the original game from \u03c3 is a Nash equilibrium.\nThe dominating factor in the run time of GameShrink is\nin the rth\niteration of the main for-loop. There are at most\n166\n`|\u0398|\nS\n\u00b4\nS! nodes at this level, where we again take S to be the\nmaximum number of signals possibly revealed in the game.\nThus, the inner for-loop executes O\n\u201e`|\u0398|\nS\n\u00b4\nS!\n2\n\u00ab\ntimes. As\ndiscussed in the next subsection, we use a union-find data\nstructure to represent the information filter F. Each\niteration of the inner for-loop possibly performs a union\noperation on the data structure; performing M operations on\na union-find data structure containing N elements takes\nO(\u03b1(M, N)) amortized time per operation, where \u03b1(M, N)\nis the inverse Ackermann\"s function [1, 49] (which grows\nextremely slowly). Thus, the total time for GameShrink is\nO\n\u201e`|\u0398|\nS\n\u00b4\nS!\n2\n\u03b1\n\u201e`|\u0398|\nS\n\u00b4\nS!\n2\n, |\u0398|S\n\u00ab\u00ab\n. By the inequality\n`n\nk\n\u00b4\n\u2264 nk\nk!\n, this is O\n`\n(|\u0398|S\n)2\n\u03b1\n`\n(|\u0398|S\n)2\n, |\u0398|S\n\u00b4\u00b4\n. Again,\nalthough this is exponential in S, it is \u02dcO(n2\n), where n is the\nnumber of nodes in the signal tree. Furthermore,\nGameShrink tends to actually run in sublinear time and space in\nthe size of the game tree because the signal tree is\nsignificantly smaller than the game tree in most nontrivial games,\nas discussed above.\n4.1 Efficiency enhancements\nWe designed several speed enhancement techniques for\nGameShrink, and all of them are incorporated into our\nimplementation. One technique is the use of the union-find\ndata structure for storing the information filter F. This\ndata structure uses time almost linear in the number of\noperations [49]. Initially each node in the signalling tree is\nits own set (this corresponds to the identity information\nfilter); when two nodes are contracted they are joined into\na new set. Upon termination, the filtered signals for the\nabstracted game correspond exactly to the disjoint sets in\nthe data structure. This is an efficient method of recording\ncontractions within the game tree, and the memory\nrequirements are only linear in the size of the signal tree.\nDetermining whether two nodes are ordered game\nisomorphic requires us to determine if a bipartite graph has a\nperfect matching. We can eliminate some of these computations\nby using easy-to-check necessary conditions for the ordered\ngame isomorphic relation to hold. One such condition is to\ncheck that the nodes have the same number of chances as\nbeing ranked (according to ) higher than, lower than, and\nthe same as the opponents. We can precompute these\nfrequencies for every game tree node. This substantially speeds\nup GameShrink, and we can leverage this database across\nmultiple runs of the algorithm (for example, when trying\ndifferent abstraction levels; see next section). The indices\nfor this database depend on the private and public signals,\nbut not the order in which they were revealed, and thus\ntwo nodes may have the same corresponding database\nentry. This makes the database significantly more compact.\n(For example in Texas Hold\"em, the database is reduced by\na factor\n`50\n3\n\u00b4`47\n1\n\u00b4`46\n1\n\u00b4\n/\n`50\n5\n\u00b4\n= 20.) We store the histograms\nin a 2-dimensional database. The first dimension is indexed\nby the private signals, the second by the public signals. The\nproblem of computing the index in (either) one of the\ndimensions is exactly the problem of computing a bijection\nbetween all subsets of size r from a set of size n and\nintegers in\n\u02c6\n0, . . . ,\n`n\nr\n\u00b4\n\u2212 1\n\u02dc\n. We efficiently compute this using\nthe subsets\" colexicographical ordering [6]. Let {c1, . . . , cr},\nci \u2208 {0, . . . , n \u2212 1}, denote the r signals and assume that\nci < ci+1. We compute a unique index for this set of signals\nas follows: index(c1, . . . , cr) =\nPr\ni=1\n`ci\ni\n\u00b4\n.\n5. APPROXIMATION METHODS\nSome games are too large to compute an exact\nequilibrium, even after using the presented abstraction technique.\nThis section discusses general techniques for computing\napproximately optimal strategy profiles. For a two-player game,\nwe can always evaluate the worst-case performance of a\nstrategy, thus providing some objective evaluation of the\nstrength of the strategy. To illustrate this, suppose we know\nplayer 2\"s planned strategy for some game. We can then fix\nthe probabilities of player 2\"s actions in the game tree as\nif they were chance moves. Then player 1 is faced with a\nsingle-agent decision problem, which can be solved\nbottomup, maximizing expected payoff at every node. Thus, we can\nobjectively determine the expected worst-case performance\nof player 2\"s strategy. This will be most useful when we\nwant to evaluate how well a given strategy performs when\nwe know that it is not an equilibrium strategy. (A\nvariation of this technique may also be applied in n-person games\nwhere only one player\"s strategies are held fixed.) This\ntechnique provides ex post guarantees about the worst-case\nperformance of a strategy, and can be used independently of\nthe method that is used to compute the strategies.\n5.1 State-space approximations\nBy slightly modifying GameShrink, we can obtain an\nalgorithm that yields even smaller game trees, at the expense\nof losing the equilibrium guarantees of Theorem 2. Instead\nof requiring the payoffs at terminal nodes to match exactly,\nwe can instead compute a penalty that increases as the\ndifference in utility between two nodes increases.\nThere are many ways in which the penalty function could\nbe defined and implemented. One possibility is to create\nedge weights in the bipartite graphs used in Algorithm 1,\nand then instead of requiring perfect matchings in the\nunweighted graph we would instead require perfect matchings\nwith low cost (i.e., only consider two nodes to be ordered\ngame isomorphic if the corresponding bipartite graph has a\nperfect matching with cost below some threshold). Thus,\nwith this threshold as a parameter, we have a knob to turn\nthat in one extreme (threshold = 0) yields an optimal\nabstraction and in the other extreme (threshold = \u221e) yields\na highly abstracted game (this would in effect restrict\nplayers to ignoring all signals, but still observing actions). This\nknob also begets an anytime algorithm. One can solve\nincreasingly less abstracted versions of the game, and evaluate\nthe quality of the solution at every iteration using the ex post\nmethod discussed above.\n5.2 Algorithmic approximations\nIn the case of two-player zero-sum games, the\nequilibrium computation can be modeled as a linear program (LP),\nwhich can in turn be solved using the simplex method. This\napproach has inherent features which we can leverage into\ndesirable properties in the context of solving games.\nIn the LP, primal solutions correspond to strategies of\nplayer 2, and dual solutions correspond to strategies of player\n1. There are two versions of the simplex method: the primal\nsimplex and the dual simplex. The primal simplex maintains\nprimal feasibility and proceeds by finding better and better\nprimal solutions until the dual solution vector is feasible,\n167\nat which point optimality has been reached. Analogously,\nthe dual simplex maintains dual feasibility and proceeds by\nfinding increasingly better dual solutions until the primal\nsolution vector is feasible. (The dual simplex method can\nbe thought of as running the primal simplex method on the\ndual problem.) Thus, the primal and dual simplex\nmethods serve as anytime algorithms (for a given abstraction)\nfor players 2 and 1, respectively. At any point in time, they\ncan output the best strategies found so far.\nAlso, for any feasible solution to the LP, we can get bounds\non the quality of the strategies by examining the primal and\ndual solutions. (When using the primal simplex method,\ndual solutions may be read off of the LP tableau.) Every\nfeasible solution of the dual yields an upper bound on the\noptimal value of the primal, and vice versa [9, p. 57]. Thus,\nwithout requiring further computation, we get lower bounds\non the expected utility of each agent\"s strategy against that\nagent\"s worst-case opponent.\nOne problem with the simplex method is that it is not a\nprimal-dual algorithm, that is, it does not maintain both\nprimal and dual feasibility throughout its execution. (In fact,\nit only obtains primal and dual feasibility at the very end of\nexecution.) In contrast, there are interior-point methods for\nlinear programming that maintain primal and dual\nfeasibility throughout the execution. For example, many\ninteriorpoint path-following algorithms have this property [55, Ch.\n5]. We observe that running such a linear programming\nmethod yields a method for finding -equilibria (i.e.,\nstrategy profiles in which no agent can increase her expected\nutility by more than by deviating). A threshold on can also\nbe used as a termination criterion for using the method as\nan anytime algorithm. Furthermore, interior-point methods\nin this class have polynomial-time worst-case run time, as\nopposed to the simplex algorithm, which takes exponentially\nmany steps in the worst case.\n6. RELATED RESEARCH\nFunctions that transform extensive form games have been\nintroduced [50, 11]. In contrast to our work, those\napproaches were not for making the game smaller and easier\nto solve. The main result is that a game can be derived\nfrom another by a sequence of those transformations if and\nonly if the games have the same pure reduced normal form.\nThe pure reduced normal form is the extensive form game\nrepresented as a game in normal form where duplicates of\npure strategies (i.e., ones with identical payoffs) are removed\nand players essentially select equivalence classes of\nstrategies [27]. An extension to that work shows a similar result,\nbut for slightly different transformations and mixed reduced\nnormal form games [21]. Modern treatments of this prior\nwork on game transformations exist [38, Ch. 6], [10].\nThe recent notion of weak isomorphism in extensive form\ngames [7] is related to our notion of restricted game\nisomorphism. The motivation of that work was to justify solution\nconcepts by arguing that they are invariant with respect\nto isomorphic transformations. Indeed, the author shows,\namong other things, that many solution concepts, including\nNash, perfect, subgame perfect, and sequential equilibrium,\nare invariant with respect to weak isomorphisms. However,\nthat definition requires that the games to be tested for weak\nisomorphism are of the same size. Our focus is totally\ndifferent: we find strategically equivalent smaller games. Also,\ntheir paper does not provide algorithms.\nAbstraction techniques have been used in artificial\nintelligence research before. In contrast to our work, most (but\nnot all) research involving abstraction has been for\nsingleagent problems (e.g. [20, 32]). Furthermore, the use of\nabstraction typically leads to sub-optimal solutions, unlike\nthe techniques presented in this paper, which yield\noptimal solutions. A notable exception is the use of abstraction\nto compute optimal strategies for the game of Sprouts [2].\nHowever, a significant difference to our work is that Sprouts\nis a game of perfect information.\nOne of the first pieces of research to use abstraction in\nmulti-agent settings was the development of partition search,\nwhich is the algorithm behind GIB, the world\"s first\nexpertlevel computer bridge player [17, 18]. In contrast to other\ngame tree search algorithms which store a particular game\nposition at each node of the search tree, partition search\nstores groups of positions that are similar. (Typically, the\nsimilarity of two game positions is computed by ignoring the\nless important components of each game position and then\nchecking whether the abstracted positions are similar-in\nsome domain-specific expert-defined sense-to each other.)\nPartition search can lead to substantial speed improvements\nover \u03b1-\u03b2-search. However, it is not game theory-based (it\ndoes not consider information sets in the game tree), and\nthus does not solve for the equilibrium of a game of\nimperfect information, such as poker.8\nAnother difference is that\nthe abstraction is defined by an expert human while our\nabstractions are determined automatically.\nThere has been some research on the use of abstraction\nfor imperfect information games. Most notably, Billings et\nal [4] describe a manually constructed abstraction for Texas\nHold\"em poker, and include promising results against expert\nplayers. However, this approach has significant drawbacks.\nFirst, it is highly specialized for Texas Hold\"em. Second,\na large amount of expert knowledge and effort was used in\nconstructing the abstraction. Third, the abstraction does\nnot preserve equilibrium: even if applied to a smaller game,\nit might not yield a game-theoretic equilibrium. Promising\nideas for abstraction in the context of general extensive form\ngames have been described in an extended abstract [39], but\nto our knowledge, have not been fully developed.\n7. CONCLUSIONS AND DISCUSSION\nWe introduced the ordered game isomorphic abstraction\ntransformation and gave an algorithm, GameShrink, for\nabstracting the game using the isomorphism exhaustively. We\nproved that in games with ordered signals, any Nash\nequilibrium in the smaller abstracted game maps directly to a\nNash equilibrium in the original game.\nThe complexity of GameShrink is \u02dcO(n2\n), where n is the\nnumber of nodes in the signal tree. It is no larger than the\ngame tree, and on nontrivial games it is drastically smaller,\nso GameShrink has time and space complexity sublinear in\n8\nBridge is also a game of imperfect information, and\npartition search does not find the equilibrium for that\ngame either. Instead, partition search is used in\nconjunction with statistical sampling to simulate the uncertainty\nin bridge. There are also other bridge programs that use\nsearch techniques for perfect information games in\nconjunction with statistical sampling and expert-defined\nabstraction [48]. Such (non-game-theoretic) techniques are unlikely\nto be competitive in poker because of the greater importance\nof information hiding and bluffing.\n168\nthe size of the game tree. Using GameShrink, we found\na minimax equilibrium to Rhode Island Hold\"em, a poker\ngame with 3.1 billion nodes in the game tree-over four\norders of magnitude more than in the largest poker game\nsolved previously.\nTo further improve scalability, we introduced an\napproximation variant of GameShrink, which can be used as an\nanytime algorithm by varying a parameter that controls\nthe coarseness of abstraction. We also discussed how (in\na two-player zero-sum game), linear programming can be\nused in an anytime manner to generate approximately\noptimal strategies of increasing quality. The method also yields\nbounds on the suboptimality of the resulting strategies. We\nare currently working on using these techniques for full-scale\n2-player limit Texas Hold\"em poker, a highly popular card\ngame whose game tree has about 1018\nnodes. That game\ntree size has required us to use the approximation version of\nGameShrink (as well as round-based abstraction) [16, 15].\n8. 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Spieltheoretische behandlung eines oligopolmodells\nmit nachfragetr\u00a8agheit. Zeitschrift f\u00a8ur die gesamte\nStaatswissenschaft, 12:301-324, 1965.\n[46] R. Selten. Evolutionary stability in extensive two-person games\n- correction and further development. Mathematical Social\nSciences, 16:223-266, 1988.\n[47] J. Shi and M. Littman. Abstraction methods for game theoretic\npoker. In Computers and Games, pages 333-345.\nSpringer-Verlag, 2001.\n[48] S. J. J. Smith, D. S. Nau, and T. Throop. Computer bridge: A\nbig win for AI planning. AI Magazine, 19(2):93-105, 1998.\n[49] R. E. Tarjan. Efficiency of a good but not linear set union\nalgorithm. Journal of the ACM, 22(2):215-225, 1975.\n[50] F. Thompson. Equivalence of games in extensive form. RAND\nMemo RM-759, The RAND Corporation, Jan. 1952.\n[51] J. von Neumann and O. Morgenstern. Theory of games and\neconomic behavior. Princeton University Press, 1947.\n[52] B. von Stengel. 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{"name": "train_J-38", "title": "Multi-Attribute Coalitional Games\u2217", "abstract": "We study coalitional games where the value of cooperation among the agents are solely determined by the attributes the agents possess, with no assumption as to how these attributes jointly determine this value. This framework allows us to model diverse economic interactions by picking the right attributes. We study the computational complexity of two coalitional solution concepts for these gamesthe Shapley value and the core. We show how the positive results obtained in this paper imply comparable results for other games studied in the literature.", "fulltext": "1. INTRODUCTION\nWhen agents interact with one another, the value of their\ncontribution is determined by what they can do with their\nskills and resources, rather than simply their identities.\nConsider the problem of forming a soccer team. For a team to\nbe successful, a team needs some forwards, midfielders,\ndefenders, and a goalkeeper. The relevant attributes of the\nplayers are their skills at playing each of the four positions.\nThe value of a team depends on how well its players can play\nthese positions. At a finer level, we can extend the model\nto consider a wider range of skills, such as passing,\nshooting, and tackling, but the value of a team remains solely a\nfunction of the attributes of its players.\nConsider an example from the business world.\nCompanies in the metals industry are usually vertically-integrated\nand diversified. They have mines for various types of ores,\nand also mills capable of processing and producing\ndifferent kinds of metal. They optimize their production profile\naccording to the market prices for their products. For\nexample, when the price of aluminum goes up, they will\nallocate more resources to producing aluminum. However, each\ncompany is limited by the amount of ores it has, and its\ncapacities in processing given kinds of ores. Two or more\ncompanies may benefit from trading ores and processing\ncapacities with one another. To model the metal industry, the\nrelevant attributes are the amount of ores and the\nprocessing capacities of the companies. Given the exogenous input\nof market prices, the value of a group of companies will be\ndetermined by these attributes.\nMany real-world problems can be likewise modeled by\npicking the right attributes. As attributes apply to both\nindividual agents and groups of agents, we propose the use\nof coalitional game theory to understand what groups may\nform and what payoffs the agents may expect in such models.\nCoalitional game theory focuses on what groups of agents\ncan achieve, and thus connects strongly with e-commerce,\nas the Internet economies have significantly enhanced the\nabilities of business to identify and capitalize on profitable\nopportunities of cooperation. Our goal is to understand\nthe computational aspects of computing the solution\nconcepts (stable and/or fair distribution of payoffs, formally\ndefined in Section 3) for coalitional games described using\nattributes. Our contributions can be summarized as follows:\n\u2022 We define a formal representation for coalitional games\nbased on attributes, and relate this representation to\nothers proposed in the literature. We show that when\ncompared to other representations, there exists games\nfor which a multi-attribute description can be\nexponentially more succinct, and for no game it is worse.\n\u2022 Given the generality of the model, positive results carry\nover to other representations. We discuss two positive\nresults in the paper, one for the Shapley value and one\nfor the core, and show how these imply related results\nin the literature.\n170\n\u2022 We study an approximation heuristic for the Shapley\nvalue when its exact values cannot be found efficiently.\nWe provide an explicit bound on the maximum error\nof the estimate, and show that the bound is\nasymptotically tight. We also carry out experiments to evaluate\nhow the heuristic performs on random instances.1\n2. RELATED WORK\nCoalitional game theory has been well studied in\neconomics [9, 10, 14]. A vast amount of literature have focused\non defining and comparing solution concepts, and\ndetermining their existence and properties. The first algorithmic\nstudy of coalitional games, as far as we know, is performed\nby Deng and Papadimitriou in [5]. They consider coalitional\ngames defined on graphs, where the players are the vertices\nand the value of coalition is determined by the sum of the\nweights of the edges spanned by these players. This can be\nefficiently modeled and generalized using attributes.\nAs a formal representation, multi-attribute coalitional games\nis closely related to the multi-issue representation of Conitzer\nand Sandholm [3] and our work on marginal contribution\nnetworks [7]. Both of these representations are based on\ndividing a coalitional game into subgames (termed issues\nin [3] and rules in [7]), and aggregating the subgames via\nlinear combination. The key difference in our work is the\nunrestricted aggregation of subgames: the aggregation could\nbe via a polynomial function of the attributes, or even by\ntreating the subgames as input to another computational\nproblem such as a min-cost flow problem. The relationship\nof these models will be made clear after we define the\nmultiattribute representation in Section 4.\nAnother representation proposed in the literature is one\nspecialized for superadditive games by Conitzer and\nSandholm [2]. This representation is succinct, but to find the\nvalues of some coalitions may require solving an NP-hard\nproblem. While it is possible for multi-attribute coalitional\ngames to efficiently represent these games, it necessarily\nrequires the solution to an NP-hard problem in order to find\nout the values of some coalitions. In this paper, we stay\nwithin the boundary of games that admits efficient\nalgorithm for determining the value of coalitions. We will\ntherefore not make further comparisons with [2].\nThe model of coalitional games with attributes has been\nconsidered in the works of Shehory and Kraus. They model\nthe agents as possessing capabilities that indicates their\nproficiencies in different areas, and consider how to efficiently\nallocate tasks [12] and the dynamics of coalition formation\n[13]. Our work differs significantly as our focus is on\nreasoning about solution concepts. Our model also covers a wider\nscope as attributes generalize the notion of capabilities.\nYokoo et al. have also considered a model of coalitional\ngames where agents are modeled by sets of skills, and these\nskills in turn determine the value of coalitions [15]. There are\ntwo major differences between their work and ours. Firstly,\nYokoo et al. assume that each skill is fundamentally different\nfrom another, hence no two agents may possess the same\nskill. Also, they focus on developing new solution concepts\nthat are robust with respect to manipulation by agents. Our\nfocus is on reasoning about traditional solution concepts.\n1\nWe acknowledge that random instances may not be typical\nof what happens in practice, but given the generality of our\nmodel, it provides the most unbiased view.\nOur work is also related to the study of cooperative games\nwith committee control [4]. In these games, there is usually\nan underlying set of resources each controlled by a\n(possibly overlapping) set of players known as the committee,\nengaged in a simple game (defined in Section 3).\nmultiattribute coalitional games generalize these by considering\nrelationship between the committee and the resources\nbeyond simple games. We note that when restricted to simple\ngames, we derive similar results to that in [4].\n3. PRELIMINARIES\nIn this section, we will review the relevant concepts of\ncoalitional game theory and its two most important solution\nconcepts - the Shapley value and the core. We will then\ndefine the computational questions that will be studied in\nthe second half of the paper.\n3.1 Coalitional Games\nThroughout this paper, we assume that payoffs to groups\nof agents can be freely distributed among its members. This\ntransferable utility assumption is commonly made in\ncoalitional game theory. The canonical representation of a\ncoalitional game with transferable utility is its characteristic form.\nDefinition 1. A coalition game with transferable utility in\ncharacteristic form is denoted by the pair N, v , where\n\u2022 N is the set of agents; and\n\u2022 v : 2N\n\u2192 R is a function that maps each group of\nagents S \u2286 N to a real-valued payoff.\nA group of agents in a game is known as a coalition, and the\nentire set of agents is known as the grand coalition.\nAn important class of coalitional games is the class of\nmonotonic games.\nDefinition 2. A coalitional game is monotonic if for all\nS \u2282 T \u2286 N, v(S) \u2264 v(T).\nAnother important class of coalitional games is the class\nof simple games. In a simple game, a coalition either wins,\nin which case it has a value of 1, or loses, in which case it\nhas a value of 0. It is often used to model voting situations.\nSimple games are often assumed to be monotonic, i.e., if S\nwins, then for all T \u2287 S, T also wins. This coincides with\nthe notion of using simple games as a model for voting. If a\nsimple game is monotonic, then it is fully described by the\nset of minimal winning coalitions, i.e., coalitions S for which\nv(S) = 1 but for all coalitions T \u2282 S, v(T) = 0.\nAn outcome in a coalitional game specifies the utilities\nthe agents receive. A solution concept assigns to each\ncoalitional game a set of reasonable outcomes. Different\nsolution concepts attempt to capture in some way outcomes\nthat are stable and/or fair. Two of the best known solution\nconcepts are the Shapley value and the core.\nThe Shapley value is a normative solution concept that\nprescribes a fair way to divide the gains from cooperation\nwhen the grand coalition is formed. The division of payoff\nto agent i is the average marginal contribution of agent i\nover all possible permutations of the agents. Formally,\nDefinition 3. The Shapley value of agent i, \u03c6i(v), in game\nN, v is given by the following formula\n\u03c6i(v) =\nS\u2286N\\{i}\n|S|!(|N| \u2212 |S| \u2212 1)!\n|N|!\n(v(S \u222a {i}) \u2212 v(S))\n171\nThe core is a descriptive solution concept that focuses on\noutcomes that are stable. Stability under core means that\nno set of players can jointly deviate to improve their payoffs.\nDefinition 4. An outcome x \u2208 R|N|\nis in the core of the\ngame N, v if for all S \u2286 N,\ni\u2208S\nxi \u2265 v(S)\nNote that the core of a game may be empty, i.e., there may\nnot exist any payoff vector that satisfies the stability\nrequirement for the given game.\n3.2 Computational Problems\nWe will study the following three problems related to\nsolution concepts in coalitional games.\nProblem 1. (Shapley Value) Given a description of the\ncoalitional game and an agent i, compute the Shapley value\nof agent i.\nProblem 2. (Core Membership) Given a description of\nthe coalitional game and a payoff vector x such that\n\u00c8\ni\u2208N xi =\nv(N), determine if\n\u00c8\ni\u2208S xi \u2265 v(S) for all S \u2286 N.\nProblem 3. (Core Non-emptiness) Given a description\nof the coalitional game, determine if there exists any payoff\nvector x such that\n\u00c8\ni\u2208S xi \u2265 V (S) for all S \u2286 N, and\u00c8\ni\u2208N xi = v(N).\nNote that the complexity of the above problems depends\non the how the game is described. All these problems will\nbe easy if the game is described by its characteristic form,\nbut only so because the description takes space\nexponential in the number of agents, and hence simple brute-force\napproach takes time polynomial to the input description.\nTo properly understand the computational complexity\nquestions, we have to look at compact representation.\n4. FORMAL MODEL\nIn this section, we will give a formal definition of\nmultiattribute coalitional games, and show how it is related to\nsome of the representations discussed in the literature. We\nwill also discuss some limitations to our proposed approach.\n4.1 Multi-Attribute Coalitional Games\nA multi-attribute coalitional game (MACG) consists of\ntwo parts: a description of the attributes of the agents,\nwhich we termed an attribute model, and a function that\nassigns values to combination of attributes. Together, they\ninduce a coalitional game over the agents. We first define\nthe attribute model.\nDefinition 5. An attribute model is a tuple N, M, A , where\n\u2022 N denotes the set of agents, of size n;\n\u2022 M denotes the set of attributes, of size m;\n\u2022 A \u2208 Rm\u00d7n\n, the attribute matrix, describes the values\nof the attributes of the agents, with Aij denoting the\nvalue of attribute i for agent j.\nWe can directly define a function that maps combinations\nof attributes to real values. However, for many problems,\nwe can describe the function more compactly by computing\nit in two steps: we first compute an aggregate value for\neach attribute, then compute the values of combination of\nattributes using only the aggregated information. Formally,\nDefinition 6. An aggregating function (or aggregator) takes\nas input a row of the attribute matrix and a coalition S, and\nsummarizes the attributes of the agents in S with a single\nnumber. We can treat it as a mapping from Rn\n\u00d7 2N\n\u2192 R.\nAggregators often perform basic arithmetic or logical\noperations. For example, it may compute the sum of the\nattributes, or evaluate a Boolean expression by treating the\nagents i \u2208 S as true and j /\u2208 S as false. Analogous to the\nnotion of simple games, we call an aggregator simple if its\nrange is {0, 1}. For any aggregator, there is a set of relevant\nagents, and a set of irrelevant agents. An agent i is\nirrelevant to aggregator aj\nif aj\n(S \u222a {i}) = aj\n(S) for all S \u2286 N.\nA relevant agent is one not irrelevant.\nGiven the attribute matrix, an aggregator assigns a value\nto each coalition S \u2286 N. Thus, each aggregator defines a\ngame over N. For aggregator aj\n, we refer to this induced\ngame as the game of attribute j, and denote it with aj\n(A).\nWhen the attribute matrix is clear from the context, we may\ndrop A and simply denote the game as aj\n. We may refer to\nthe game as the aggregator when no ambiguities arise.\nWe now define the second step of the computation with\nthe help of aggregators.\nDefinition 7. An aggregate value function takes as input\nthe values of the aggregators and maps these to a real value.\nIn this paper, we will focus on having one aggregator per\nattribute. Therefore, in what follows, we will refer to the\naggregate value function as a function over the attributes.\nNote that when all aggregators are simple, the aggregate\nvalue function implicitly defines a game over the attributes,\nas it assigns a value to each set of attributes T \u2286 M. We\nrefer to this as the game among attributes.\nWe now define multi-attribute coalitional game.\nDefinition 8. A multi-attribute coalitional game is defined\nby the tuple N, M, A, a, w , where\n\u2022 N, M, A is an attribute model;\n\u2022 a is a set of aggregators, one for each attribute; we can\ntreat the set together as a vector function, mapping\nRm\u00d7n\n\u00d7 2N\n\u2192 Rm\n\u2022 w : Rm\n\u2192 R is an aggregate value function.\nThis induces a coalitional game with transferable payoffs\nN, v with players N and the value function defined by\nv(S) = w(a(A, S))\nNote that MACG as defined is fully capable of\nrepresenting any coalitional game N, v . We can simply take the set\nof attributes as equal to the set of agents, i.e., M = N, an\nidentity matrix for A, aggregators of sums, and the\naggregate value function w to be v.\n172\n4.2 An Example\nLet us illustrate how MACG can be used to represent a\ngame with a simple example. Suppose there are four types\nof resources in the world: gold, silver, copper, and iron, that\neach agent is endowed with some amount of these resources,\nand there is a fixed price for each of the resources in the\nmarket. This game can be described using MACG with an\nattribute matrix A, where Aij denote the amount of resource\ni that agent j is endowed. For each resource, the\naggregator sums together the amount of resources the agents have.\nFinally, the aggregate value function takes the dot product\nbetween the market price vector and the aggregate vector.\nNote the inherent flexibility in the model: only limited\nwork would be required to update the game as the market\nprice changes, or when a new agent arrives.\n4.3 Relationship with Other Representations\nAs briefly discussed in Section 2, MACG is closely related\nto two other representations in the literature, the\nmultiissue representation of Conitzer and Sandholm [3], and our\nwork on marginal contribution nets [7]. To make their\nrelationships clear, we first review these two representations.\nWe have changed the notations from the original papers to\nhighlight their similarities.\nDefinition 9. A multi-issue representation is given as a\nvector of coalitional games, (v1, v2, . . . vm), each possibly\nwith a varying set of agents, say N1, . . . , Nm. The\ncoalitional game N, v induced by multi-issue representation has\nplayer set N =\n\u00cbm\ni=1 Ni, and for each coalition S \u2286 N,\nv(S) =\n\u00c8m\ni=1 v(S \u2229 Ni). The games vi are assumed to be\nrepresented in characteristic form.\nDefinition 10. A marginal contribution net is given as a\nset of rules (r1, r2, . . . , rm), where rule ri has a weight wi,\nand a pattern pi that is a conjunction over literals\n(positive or negative). The agents are represented as literals. A\ncoalition S is said to satisfy the pattern pi, if we treat the\nagents i \u2208 S as true, an agent j /\u2208 S as false, pi(S)\nevaluates to true. Denote the set of literals involved in rule i\nby Ni. The coalitional game N, v induced by a marginal\ncontribution net has player set N =\n\u00cbm\ni=1 Ni, and for each\ncoalition S \u2286 N, v(S) =\n\u00c8\ni:pi(S)=true wi.\nFrom these definitions, we can see the relationships among\nthese three representations clearly. An issue of a multi-issue\nrepresentation corresponds to an attribute in MACG.\nSimilarly, a rule of a marginal contribution net corresponds to\nan attribute in MACG. The aggregate value functions are\nsimple sums and weighted sums for the respective\nrepresentations. Therefore, it is clear that MACG will be no less\nsuccinct than either representation.\nHowever, MACG differs in two important way. Firstly,\nthere is no restriction on the operations performed by the\naggregate value function over the attributes. This is an\nimportant generalization over the linear combination of issues\nor rules in the other two approaches. In particular, there are\ngames for which MACG can be exponentially more compact.\nThe proof of the following proposition can be found in the\nAppendix.\nProposition 1. Consider the parity game N, v where\ncoalition S \u2286 N has value v(S) = 1 if |S| is odd, and v(S) =\n0 otherwise. MACG can represent the game in O(n) space.\nBoth multi-issue representation and marginal contribution\nnets requires O(2n\n) space.\nA second important difference of MACG is that the\nattribute model and the value function is cleanly separated.\nAs suggested in the example in Section 4.2, this often\nallows us more efficient update of the values of the game as it\nchanges. Also, the same attribute model can be evaluated\nusing different value functions, and the same value function\ncan be used to evaluate different attribute model. Therefore,\nMACG is very suitable for representing multiple games. We\nbelieve the problems of updating games and representing\nmultiple games are interesting future directions to explore.\n4.4 Limitation of One Aggregator per Attribute\nBefore focusing on one aggregator per attribute for the\nrest of the paper, it is natural to wonder if any is lost per\nsuch restriction. The unfortunate answer is yes, best\nillustrated by the following. Consider again the problem of\nforming a soccer team discussed in the introduction, where\nwe model the attributes of the agents as their ability to take\nthe four positions of the field, and the value of a team\ndepends on the positions covered. If we first aggregate each\nof the attribute individually, we will lose the distributional\ninformation of the attributes. In other words, we will not\nbe able to distinguish between two teams, one of which has\na player for each position, the other has one player who can\nplay all positions, but the rest can only play the same one\nposition.\nThis loss of distributional information can be recovered\nby using aggregators that take as input multiple rows of\nthe attribute matrix rather than just a single row.\nAlternatively, if we leave such attributes untouched, we can leave\nthe burden of correctly evaluating these attributes to the\naggregate value function. However, for many problems that we\nfound in the literature, such as the transportation domain\nof [12] and the flow game setting of [4], the distribution of\nattributes does not affect the value of the coalitions. In\naddition, the problem may become unmanageably complex as\nwe introduce more complicated aggregators. Therefore, we\nwill focus on the representation as defined in Definition 8.\n5. SHAPLEY VALUE\nIn this section, we focus on computational issues of\nfinding the Shapley value of a player in MACG. We first set\nup the problem with the use of oracles to avoid\ncomplexities arising from the aggregators. We then show that when\nattributes are linearly separable, the Shapley value can be\nefficiently computed. This generalizes the proofs of related\nresults in the literature. For the non-linearly separable case,\nwe consider a natural heuristic for estimating the Shapley\nvalue, and study the heuristic theoretically and empirically.\n5.1 Problem Setup\nWe start by noting that computing the Shapley value for\nsimple aggregators can be hard in general. In particular, we\ncan define aggregators to compute weighted majority over\nits input set of agents. As noted in [6], finding the Shapley\nvalue of a weighted majority game is #P-hard. Therefore,\ndiscussion of complexity of Shapley value for MACG with\nunrestricted aggregators is moot.\nInstead of placing explicit restriction on the aggregator,\nwe assume that the Shapley value of the aggregator can be\n173\nanswered by an oracle. For notation, let \u03c6i(u) denote the\nShapley value for some game u. We make the following\nassumption:\nAssumption 1. For each aggregator aj\nin a MACG, there\nis an associated oracle that answers the Shapley value of the\ngame of attribute j. In other words, \u03c6i(aj\n) is known.\nFor many aggregators that perform basic operations over\nits input, polynomial time oracle for Shapley value exists.\nThis include operations such as sum, and symmetric\nfunctions when the attributes are restricted to {0, 1}. Also, when\nonly few agents have an effect on the aggregator, brute-force\ncomputation for Shapley value is feasible. Therefore, the\nabove assumption is reasonable for many settings. In any\ncase, such abstraction allows us to focus on the aggregate\nvalue function.\n5.2 Linearly Separable Attributes\nWhen the aggregate value function can be written as a\nlinear function of the attributes, the Shapley value of the\ngame can be efficiently computed.\nTheorem 1. Given a game N, v represented as a MACG\nN, M, A, a, w , if the aggregate value function can be\nwritten as a linear function of its attributes, i.e.,\nw(a(A, S)) =\nm\nj=1\ncj aj\n(A, S)\nThe Shapley value of agent i in N, v is given by\n\u03c6i(v) =\nm\nj=1\ncj \u03c6i(aj\n) (1)\nProof. First, we note that Shapley value satisfies an\nadditivity axiom [11].\nThe Shapley value satisfies additivity, namely,\n\u03c6i(a + b) = \u03c6i(a) + \u03c6i(b), where N, a + b is\na game defined to be (a + b)(S) = a(S) + b(S)\nfor all S \u2286 N.\nIt is also clear that Shapley value satisfies scaling, namely\n\u03c6i(\u03b1v) = \u03b1\u03c6i(v)\nwhere (\u03b1v)(S) = \u03b1v(S) for all S \u2286 N.\nSince the aggregate value function can be expressed as a\nweighted sum of games of attributes,\n\u03c6i(v) = \u03c6i(w(a)) = \u03c6i(\nm\nj=1\ncjaj\n) =\nm\nj=1\ncj\u03c6i(aj\n)\nMany positive results regarding efficient computation of\nShapley value in the literature depends on some form of\nlinearity. Examples include the edge-spanning game on graphs\nby Deng and Papadimitriou [5], the multi-issue\nrepresentation of [3], and the marginal contribution nets of [7]. The\nkey to determine if the Shapley value can be efficiently\ncomputed depends on the linear separability of attributes. Once\nthis is satisfied, as long as the Shapley value of the game of\nattributes can be efficiently determined, the Shapley value\nof the entire game can be efficiently computed.\nCorollary 1. The Shapley value for the edge-spanning\ngame of [5], games in multi-issue representation [3], and\ngames in marginal contribution nets [7], can be computed in\npolynomial time.\n5.3 Polynomial Combination of Attributes\nWhen the aggregate value function cannot be expressed\nas a linear function of its attributes, computing the Shapley\nvalue exactly is difficult. Here, we will focus on aggregate\nvalue function that can be expressed as some polynomial\nof its attributes. If we do not place a limit on the degree\nof the polynomial, and the game N, v is not necessarily\nmonotonic, the problem is #P-hard.\nTheorem 2. Computing the Shapley value of a MACG\nN, M, A, a, w , when w can be an arbitrary polynomial of\nthe aggregates a, is #P-hard, even when the Shapley value\nof each aggregator can be efficiently computed.\nThe proof is via reduction from three-dimensional matching,\nand details can be found in the Appendix.\nEven if we restrict ourselves to monotonic games, and\nnon-negative coefficients for the polynomial aggregate value\nfunction, computing the exact Shapley value can still be\nhard. For example, suppose there are two attributes. All\nagents in some set B \u2286 N possess the first attribute, and all\nagents in some set C \u2286 N possess the second, and B and C\nare disjoint. For a coalition S \u2286 N, the aggregator for the\nfirst evaluates to 1 if and only if |S \u2229 B| \u2265 b , and similarly,\nthe aggregator for the second evaluates to 1 if and only if\n|S \u2229 C| \u2265 c . Let the cardinality of the sets B and C be b\nand c. We can verify that the Shapley value of an agent i in\nB equals\n\u03c6i =\n1\nb\nb \u22121\ni=0\nb\ni\n\u00a1\u00a0 c\nc \u22121\n\u00a1\nb+c\nc +i\u22121\n\u00a1\nc \u2212 c + 1\nb + c \u2212 c \u2212 i + 1\nThe equation corresponds to a weighted sum of probability\nvalues of hypergeometric random variables. The\ncorrespondence with hypergeometric distribution is due to sampling\nwithout replacement nature of Shapley value. As far as we\nknow, there is no close-form formula to evaluate the sum\nabove. In addition, as the number of attributes involved\nincreases, we move to multi-variate hypergeometric random\nvariables, and the number of summands grow exponentially\nin the number of attributes. Therefore, it is highly unlikely\nthat the exact Shapley value can be determined efficiently.\nTherefore, we look for approximation.\n5.3.1 Approximation\nFirst, we need a criteria for evaluating how well an\nestimate, \u02c6\u03c6, approximates the true Shapley value, \u03c6. We\nconsider the following three natural criteria:\n\u2022 Maximum underestimate: maxi \u03c6i/\u02c6\u03c6i\n\u2022 Maximum overestimate: maxi\n\u02c6\u03c6i/\u03c6i\n\u2022 Total variation: 1\n2\n\u00c8\ni |\u03c6i \u2212 \u02c6\u03c6i|, or alternatively\nmaxS |\n\u00c8\ni\u2208S \u03c6i \u2212\n\u00c8\ni\u2208S\n\u02c6\u03c6i|\nThe total variation criterion is more meaningful when we\nnormalize the game to having a value of 1 for the grand\ncoalition, i.e., v(N) = 1. We can also define additive\nanalogues of the under- and overestimates, especially when the\ngames are normalized.\n174\nWe will assume for now that the aggregate value\nfunction is a polynomial over the attributes with non-negative\ncoefficients. We will also assume that the aggregators are\nsimple. We will evaluate a specific heuristic that is\nanalogous to Equation (1). Suppose the aggregate function can\nbe written as a polynomial with p terms\nw(a(A, S)) =\np\nj=1\ncj aj(1)\n(A, S)aj(2)\n(A, S) \u00b7 \u00b7 \u00b7 aj(kj )\n(A, S)\n(2)\nFor term j, the coefficient of the term is cj , its degree kj ,\nand the attributes involved in the term are j(1), . . . , j(kj ).\nWe compute an estimate \u02c6\u03c6 to the Shapley value as\n\u02c6\u03c6i =\np\nj=1\nkj\nl=1\ncj\nkj\n\u03c6i(aj(l)\n) (3)\nThe idea behind the estimate is that for each term, we divide\nthe value of the term equally among all its attributes. This\nis represented by the factor\ncj\nkj\n. Then for for each attribute\nof an agent, we assign the player a share of value from the\nattribute. This share is determined by the Shapley value\nof the simple game of that attribute. Without considering\nthe details of the simple games, this constitutes a fair (but\nblind) rule of sharing.\n5.3.2 Theoretical analysis of heuristic\nWe can derive a simple and tight bound for the maximum\n(multiplicative) underestimate of the heuristic estimate.\nTheorem 3. Given a game N, v represented as a MACG\nN, M, A, a, w , suppose w can be expressed as a\npolynomial function of its attributes (cf Equation (2)). Let K =\nmaxjkj, i.e., the maximum degree of the polynomial. Let \u02c6\u03c6\ndenote the estimated Shapley value using Equation (3), and\n\u03c6 denote the true Shapley value. For all i \u2208 N, \u03c6i \u2265 K \u02c6\u03c6i.\nProof. We bound the maximum underestimate\nterm-byterm. Let tj be the j-th term of the polynomial. We note\nthat the term can be treated as a game among attributes,\nas it assigns a value to each coalition S \u2286 N. Without loss\nof generality, renumber attributes j(1) through j(kj ) as 1\nthrough kj.\ntj (S) = cj\nkj\nl=1\nal\n(A, S)\nTo make the equations less cluttered, let\nB(N, S) =\n|S|!(|N| \u2212 |S| \u2212 1)!\n|N|!\nand for a game a, contribution of agent i to group S : i /\u2208 S,\n\u2206i(a, S) = a(S \u222a {i}) \u2212 a(S)\nThe true Shapley value of the game tj is\n\u03c6i(tj) = cj\nS\u2286N\\{i}\nB(N, S)\u2206i(tj, S)\nFor each coalition S, i /\u2208 S, \u2206i(tj , S) = 1 if and only if for\nat least one attribute, say l\u2217\n, \u2206i(al\u2217\n, S) = 1. Therefore, if\nwe sum over all the attributes, we would have included l\u2217\nfor sure.\n\u03c6i(tj) \u2264 cj\nkj\nj=1 S\u2286N\\{i}\nB(N, S)\u2206i(aj\n, S)\n= kj\nkj\nj=1\ncj\nkj\n\u03c6i(aj\n)\n= kj\n\u02c6\u03c6i(T)\nSumming over the terms, we see that the worst case\nunderestimate is by the maximum degree.\nWithout loss of generality, since the bound is\nmultiplicative, we can normalize the game to having v(N) = 1. As a\ncorollary, because we cannot overestimate any set by more\nthan K times, we obtain a bound on the total variation:\nCorollary 2. The total variation between the estimated\nShapley value and the true Shapley value, for K-degree bounded\npolynomial aggregate value function, is K\u22121\nK\n.\nWe can show that this bound is tight.\nExample 1. Consider a game with n players and K\nattributes. Let the first (n\u22121) agents be a member of the first\n(K \u2212 1) attributes, and that the corresponding aggregator\nreturns 1 if any one of the first (K \u2212 1) agents is present.\nLet the n-th agent be the sole member of the K-th attribute.\nThe estimated Shapley will assign a value of K\u22121\nK\n1\nn\u22121\nto the\nfirst (n \u2212 1) agents and 1\nK\nto the n-th agent. However, the\ntrue Shapley value of the n-th agent tends to 1 as n \u2192 \u221e,\nand the total variation approaches K\u22121\nK\n.\nIn general, we cannot bound how much \u02c6\u03c6 may\noverestimate the true Shapley value. The problem is that \u02c6\u03c6i may\nbe non-zero for agent i even though may have no influence\nover the outcome of a game when attributes are multiplied\ntogether, as illustrated by the following example.\nExample 2. Consider a game with 2 players and 2\nattributes, and let the first agent be a member of both\nattributes, and the other agent a member of the second\nattribute. For a coalition S, the first aggregator evaluates to\n1 if agent 1 \u2208 S, and the second aggregator evaluates to 1 if\nboth agents are in S. While agent 2 is not a dummy with\nrespect to the second attribute, it is a dummy with respect\nto the product of the attributes. Agent 2 will be assigned a\nvalue of 1\n4\nby the estimate.\nAs mentioned, for simple monotonic games, a game is fully\ndescribed by its set of minimal winning coalitions. When\nthe simple aggregators are represented as such, it is possible\nto check, in polynomial time, for agents turning dummies\nafter attributes are multiplied together. Therefore, we can\nimprove the heuristic estimate in this special case.\n5.3.3 Empirical evaluation\nDue to a lack of benchmark problems for coalitional games,\nwe have tested the heuristic on random instances. We\nbelieve more meaningful results can be obtained when we have\nreal instances to test this heuristic on.\nOur experiment is set up as follows. We control three\nparameters of the experiment: the number of players (6 \u2212 10),\n175\n0\n0.025\n0.05\n0.075\n0.1\n0.125\n0.15\n0.175\n0.2\n6 7 8 9 10\nNo. of Players\nTotalVariationDistance\n2\n3\n4\n5\n(a) Effect of Max Degree\n0\n0.025\n0.05\n0.075\n0.1\n0.125\n0.15\n0.175\n0.2\n6 7 8 9 10\nNo. of Players\nTotalVariationDistance\n4\n5\n6\n(b) Effect of Number of Attributes\nFigure 1: Experimental results\nthe number of attributes (3 \u2212 8), and the maximum degree\nof the polynomial (2 \u2212 5). For each attribute, we randomly\nsample one to three minimal winning coalitions. We then\nrandomly generate a polynomial of the desired maximum\ndegree with a random number (3 \u2212 12) of terms, each with\na random positive weight. We normalize each game to have\nv(N) = 1. The results of the experiments are shown in\nFigure 1. The y-axis of the graphs shows the total variation,\nand the x-axis the number of players. Each datapoint is an\naverage of approximately 700 random samples.\nFigure 1(a) explores the effect of the maximum degree\nand the number of players when the number of attributes is\nfixed (at six). As expected, the total variation increases as\nthe maximum degree increases. On the other hand, there is\nonly a very small increase in error as the number of players\nincreases. The error is nowhere near the theoretical\nworstcase bound of 1\n2\nto 4\n5\nfor polynomials of degrees 2 to 5.\nFigure 1(b) explores the effect of the number of attributes\nand the number of players when the maximum degree of the\npolynomial is fixed (at three). We first note that these three\nlines are quite tightly clustered together, suggesting that the\nnumber of attributes has relatively little effect on the error\nof the estimate. As the number of attributes increases, the\ntotal variation decreases. We think this is an interesting\nphenomenon. This is probably due to the precise construct\nrequired for the worst-case bound, and so as more attributes\nare available, we have more diverse terms in the polynomial,\nand the diversity pushes away from the worst-case bound.\n6. CORE-RELATED QUESTIONS\nIn this section, we look at the complexity of the two\ncomputational problems related to the core: Core\nNonemptiness and Core Membership. We show that the\nnonemptiness of core of the game among attributes and the\ncores of the aggregators imply non-emptiness of the core of\nthe game induced by the MACG. We also show that there\nappears to be no such general relationship that relates the\ncore memberships of the game among attributes, games of\nattributes, and game induced by MACG.\n6.1 Problem Setup\nThere are many problems in the literature for which the\nquestions of Core Non-emptiness and Core\nMembership are known to be hard [1]. For example, for the\nedgespanning game that Deng and Papadimitriou studied [5],\nboth of these questions are coNP-complete. As MACG can\nmodel the edge-spanning game in the same amount of space,\nthese hardness results hold for MACG as well.\nAs in the case for computing Shapley value, we attempt\nto find a way around the hardness barrier by assuming the\nexistence of oracles, and try to build algorithms with these\noracles. First, we consider the aggregate value function.\nAssumption 2. For a MACG N, M, A, a, w , we assume\nthere are oracles that answers the questions of Core\nNonemptiness, and Core Membership for the aggregate value\nfunction w.\nWhen the aggregate value function is a non-negative linear\nfunction of its attributes, the core is always non-empty, and\ncore membership can be determined efficiently.\nThe concept of core for the game among attributes makes\nthe most sense when the aggregators are simple games. We\nwill further assume that these simple games are monotonic.\nAssumption 3. For a MACG N, M, A, a, w , we assume\nall aggregators are monotonic and simple. We also assume\nthere are oracles that answers the questions of Core\nNonemptiness, and Core Membership for the aggregators.\nWe consider this a mild assumption. Recall that monotonic\nsimple games are fully described by their set of minimal\nwinning coalitions (cf Section 3). If the aggregators are\nrepresented as such, Core Non-emptiness and Core\nMembership can be checked in polynomial time. This is due to the\nfollowing well-known result regarding simple games:\nLemma 1. A simple game N, v has a non-empty core\nif and only if it has a set of veto players, say V , such that\nv(S) = 0 for all S \u2287 V . Further, A payoff vector x is in the\ncore if and only if xi = 0 for all i /\u2208 V .\n6.2 Core Non-emptiness\nThere is a strong connection between the non-emptiness\nof the cores of the games among attributes, games of the\nattributes, and the game induced by a MACG.\nTheorem 4. Given a game N, v represented as a MACG\nN, M, A, a, w , if the core of the game among attributes,\n176\nM, w , is non-empty, and the cores of the games of\nattributes are non-empty, then the core of N, v is non-empty.\nProof. Let u be an arbitrary payoff vector in the core of\nthe game among attributes, M, w . For each attribute j,\nlet \u03b8j\nbe an arbitrary payoff vector in the core of the game\nof attribute j. By Lemma 1, each attribute j must have a\nset of veto players; let this set be denoted by Pj\n. For each\nagent i \u2208 N, let yi =\n\u00c8\nj uj\u03b8j\ni . We claim that this vector y\nis in the core of N, v . Consider any coalition S \u2286 N,\nv(S) = w(a(A, S)) \u2264\nj:S\u2287P j\nuj (4)\nThis is true because an aggregator cannot evaluate to 1\nwithout all members of the veto set. For any attribute j, by\nLemma 1,\n\u00c8\ni\u2208P j \u03b8j\ni = 1. Therefore,\nj:S\u2287P j\nuj =\nj:S\u2287P j\nuj\ni\u2208P j\n\u03b8j\ni\n=\ni\u2208S j:S\u2287P j\nuj\u03b8j\ni\n\u2264\ni\u2208S\nyi\nNote that the proof is constructive, and hence if we are\ngiven an element in the core of the game among attributes,\nwe can construct an element of the core of the coalitional\ngame. From Theorem 4, we can obtain the following\ncorollaries that have been previously shown in the literature.\nCorollary 3. The core of the edge-spanning game of [5]\nis non-empty when the edge weights are non-negative.\nProof. Let the players be the vertices, and their\nattributes the edges incident on them. For each attribute,\nthere is a veto set - namely, both endpoints of the edges.\nAs previously observed, an aggregate value function that is a\nnon-negative linear function of its aggregates has non-empty\ncore. Therefore, the precondition of Theorem 4 is satisfied,\nand the edge-spanning game with non-negative edge weights\nhas a non-empty core.\nCorollary 4 (Theorem 1 of [4]). The core of a flow\ngame with committee control, where each edge is controlled\nby a simple game with a veto set of players, is non-empty.\nProof. We treat each edge of the flow game as an\nattribute, and so each attribute has a veto set of players. The\ncore of a flow game (without committee) has been shown\nto be non-empty in [8]. We can again invoke Theorem 4 to\nshow the non-emptiness of core for flow games with\ncommittee control.\nHowever, the core of the game induced by a MACG may\nbe non-empty even when the core of the game among\nattributes is empty, as illustrated by the following example.\nExample 3. Suppose the minimal winning coalition of all\naggregators in a MACG N, M, A, a, w is N, then v(S) = 0\nfor all coalitions S \u2282 N. As long as v(N) \u2265 0, any\nnonnegative vector x that satisfies\n\u00c8\ni\u2208N xi = v(N) is in the\ncore of N, v .\nComplementary to the example above, when all the\naggregators have empty cores, the core of N, v is also empty.\nTheorem 5. Given a game N, v represented as a MACG\nN, M, A, a, w , if the cores of all aggregators are empty,\nv(N) > 0, and for each i \u2208 N, v({i}) \u2265 0, then the core of\nN, v is empty.\nProof. Suppose the core of N, v is non-empty. Let x\nbe a member of the core, and pick an agent i such that xi >\n0. However, for each attribute, since the core is empty, by\nLemma 1, there are at least two disjoint winning coalitions.\nPick the winning coalition Sj\nthat does not include i for\neach attribute j. Let S\u2217\n=\n\u00cb\nj Sj\n. Because S\u2217\nis winning\nfor all coalitions, v(S\u2217\n) = v(N). However,\nv(N) =\nj\u2208N\nxj = xi +\nj /\u2208N\nxj \u2265 xi +\nj\u2208S\u2217\nxj >\nj\u2208S\u2217\nxj\nTherefore, v(S\u2217\n) >\n\u00c8\nj\u2208S\u2217 xj, contradicting the fact that x\nis in the core of N, v .\nWe do not have general results regarding the problem of\nCore Non-emptiness when some of the aggregators have\nnon-empty cores while others have empty cores. We suspect\nknowledge about the status of the cores of the aggregators\nalone is insufficient to decide this problem.\n6.3 Core Membership\nSince it is possible for the game induced by the MACG\nto have a non-empty core when the core of the aggregate\nvalue function is empty (Example 3), we try to explore the\nproblem of Core Membership assuming that the core of\nboth the game among attributes, M, w , and the underlying\ngame, N, v , is known to be non-empty, and see if there\nis any relationship between their members. One reasonable\nrequirement is whether a payoff vector x in the core of N, v\ncan be decomposed and re-aggregated to a payoff vector y\nin the core of M, w . Formally,\nDefinition 11. We say that a vector x \u2208 Rn\n\u22650 can be\ndecomposed and re-aggregated into a vector y \u2208 Rm\n\u22650 if there\nexists Z \u2208 Rm\u00d7n\n\u22650 , such that\nyi =\nn\nj=1\nZij for all i\nxj =\nm\ni=1\nZij for all j\nWe may refer Z as shares.\nWhen there is no restriction on the entries of Z, it is\nalways possible to decompose a payoff vector x in the core of\nN, v to a payoff vector y in the core of M, w . However, it\nseems reasonable to restrict that if an agent j is irrelevant to\nthe aggregator i, i.e., i never changes the outcome of\naggregator j, then Zij should be restricted to be 0. Unfortunately,\nthis restriction is already too strong.\nExample 4. Consider a MACG N, M, A, a, w with two\nplayers and three attributes. Suppose agent 1 is irrelevant\nto attribute 1, and agent 2 is irrelevant to attributes 2 and\n3. For any set of attributes T \u2286 M, let w be defined as\nw(T) =\n0 if |T| = 0 or 1\n6 if |T| = 2\n10 if |T| = 3\n177\nSince the core of a game with a finite number of players forms\na polytope, we can verify that the set of vectors (4, 4, 2),\n(4, 2, 4), and (2, 4, 4), fully characterize the core C of M, w .\nOn the other hand, the vector (10, 0) is in the core of N, v .\nThis vector cannot be decomposed and re-aggregated to a\nvector in C under the stated restriction.\nBecause of the apparent lack of relationship among\nmembers of the core of N, v and that of M, w , we believe an\nalgorithm for testing Core Membership will require more\ninput than just the veto sets of the aggregators and the\noracle of Core Membership for the aggregate value function.\n7. CONCLUDING REMARKS\nMulti-attribute coalitional games constitute a very\nnatural way of modeling problems of interest. Its space\nrequirement compares favorably with other representations\ndiscussed in the literature, and hence it serves well as a\nprototype to study computational complexity of coalitional\ngame theory for a variety of problems. Positive results\nobtained under this representation can easily be translated to\nresults about other representations. Some of these corollary\nresults have been discussed in Sections 5 and 6.\nAn important direction to explore in the future is the\nquestion of efficiency in updating a game, and how to\nevaluate the solution concepts without starting from scratch. As\npointed out at the end of Section 4.3, MACG is very\nnaturally suited for updates. Representation results regarding\nefficiency of updates, and algorithmic results regarding how\nto compute the different solution concepts from updates, will\nboth be very interesting.\nOur work on approximating the Shapley value when the\naggregate value function is a non-linear function of the\nattributes suggests more work to be done there as well. Given\nthe natural probabilistic interpretation of the Shapley value,\nwe believe that a random sampling approach may have\nsignificantly better theoretical guarantees.\n8. REFERENCES\n[1] J. M. Bilbao, J. R. Fern\u00b4andez, and J. J. L\u00b4opez.\nComplexity in cooperative game theory.\nhttp://www.esi.us.es/~mbilbao.\n[2] V. Conitzer and T. Sandholm. Complexity of\ndetermining nonemptiness of the core. In Proc. 18th\nInt. Joint Conf. on Artificial Intelligence, pages\n613-618, 2003.\n[3] V. Conitzer and T. Sandholm. Computing Shapley\nvalues, manipulating value division schemes, and\nchecking core membership in multi-issue domains. In\nProc. 19th Nat. Conf. on Artificial Intelligence, pages\n219-225, 2004.\n[4] I. J. Curiel, J. J. Derks, and S. H. Tijs. On balanced\ngames and games with committee control. OR\nSpectrum, 11:83-88, 1989.\n[5] X. Deng and C. H. Papadimitriou. On the complexity\nof cooperative solution concepts. Math. Oper. Res.,\n19:257-266, May 1994.\n[6] M. R. Garey and D. S. Johnson. Computers and\nIntractability: A Guide to the Theory of\nNP-Completeness. W. H. Freeman, New York, 1979.\n[7] S. Ieong and Y. Shoham. Marginal contribution nets:\nA compact representation scheme for coalitional\ngames. In Proc. 6th ACM Conf. on Electronic\nCommerce, pages 193-202, 2005.\n[8] E. Kalai and E. Zemel. Totally balanced games and\ngames of flow. Math. Oper. Res., 7:476-478, 1982.\n[9] A. Mas-Colell, M. D. Whinston, and J. R. Green.\nMicroeconomic Theory. Oxford University Press, New\nYork, 1995.\n[10] M. J. Osborne and A. Rubinstein. A Course in Game\nTheory. The MIT Press, Cambridge, Massachusetts,\n1994.\n[11] L. S. Shapley. A value for n-person games. In H. W.\nKuhn and A. W. Tucker, editors, Contributions to the\nTheory of Games II, number 28 in Annals of\nMathematical Studies, pages 307-317. Princeton\nUniversity Press, 1953.\n[12] O. Shehory and S. Kraus. Task allocation via coalition\nformation among autonomous agents. In Proc. 14th\nInt. Joint Conf. on Artificial Intelligence, pages 31-45,\n1995.\n[13] O. Shehory and S. Kraus. A kernel-oriented model for\nautonomous-agent coalition-formation in general\nenvironments: Implentation and results. In Proc. 13th\nNat. Conf. on Artificial Intelligence, pages 134-140,\n1996.\n[14] J. von Neumann and O. Morgenstern. Theory of\nGames and Economic Behvaior. Princeton University\nPress, 1953.\n[15] M. Yokoo, V. Conitzer, T. Sandholm, N. Ohta, and\nA. Iwasaki. Coalitional games in open anonymous\nenvironments. In Proc. 20th Nat. Conf. on Artificial\nIntelligence, pages 509-515, 2005.\nAppendix\nWe complete the missing proofs from the main text here.\nTo prove Proposition 1, we need the following lemma.\nLemma 2. Marginal contribution nets when all coalitions\nare restricted to have values 0 or 1 have the same\nrepresentation power as an AND/OR circuit with negation at the\nliteral level (i.e., AC0\ncircuit) of depth two.\nProof. If a rule assigns a negative value in the marginal\ncontribution nets, we can write the rule by a corresponding\nset of at most n rules, where n is the number of agents, such\nthat each of which has positive values through application of\nDe Morgan\"s Law. With all values of the rules non-negative,\nwe can treat the weighted summation step of marginal\ncontribution nets can be viewed as an OR, and each rule as\na conjunction over literals, possibly negated. This exactly\nmatch up with an AND/OR circuit of depth two.\nProof (Proposition 1). The parity game can be\nrepresented with a MACG using a single attribute, aggregator\nof sum, and an aggregate value function that evaluates that\nsum modulus two.\nAs a Boolean function, parity is known to require an\nexponential number of prime implicants. By Lemma 2, a prime\nimplicant is the exact analogue of a pattern in a rule of\nmarginal contribution nets. Therefore, to represent the parity\nfunction, a marginal contribution nets must be an\nexponential number of rules.\nFinally, as shown in [7], a marginal contribution net is at\nworst a factor of O(n) less compact than multi-issue\nrepresentation. Therefore, multi-issue representation will also\n178\ntake exponential space to represent the parity game. This\nis assuming that each issue in the game is represented in\ncharacteristic form.\nProof (Theorem 2). An instance of three-dimensional\nmatching is as follows [6]: Given set P \u2286 W \u00d7 X \u00d7 Y ,\nwhere W , X, Y are disjoint sets having the same number q\nof elements, does there exist a matching P \u2286 P such that\n|P | = q and no two elements of P agree in any\ncoordinate. For notation, let P = {p1, p2, . . . , pK}. We construct\na MACG N, M, A, a, w as follows:\n\u2022 M: Let attributes 1 to q correspond to elements in W ,\n(q+1) to 2q correspond to elements in X, (2q+1) to 3q\ncorresponds to element in Y , and let there be a special\nattribute (3q + 1).\n\u2022 N: Let player i corresponds to pi, and let there be a\nspecial player .\n\u2022 A: Let Aji = 1 if the element corresponding to\nattribute j is in pi. Thus, for the first K columns, there\nare exactly three non-zero entries. We also set\nA(3q+1) = 1.\n\u2022 a: for each aggregator j, aj\n(A(S)) = 1 if and only if\nsum of row j of A(S) equals 1.\n\u2022 w: product over all aj\n.\nIn the game N, v that corresponds to this construction,\nv(S) = 1 if and only if all attributes are covered exactly\nonce. Therefore, for /\u2208 T \u2286 N, v(T \u222a { }) \u2212 v(T) = 1 if\nand only if T covers attributes 1 to 3q exactly once. Since\nall such T, if exists, must be of size q, the number of\nthreedimensional matchings is given by\n\u03c6 (v)\n(K + 1)!\nq!(K \u2212 q)!\n179", "keywords": "cooperation;polynomial function min-cost flow problem;diverse economic interaction;coalitional game theory;coalitional game;linear combination;min-cost flow problem;graph;agent;unrestricted aggregation of subgame;shapley value;multi-issue representation;superadditive game;compact representation;computational complexity;core;multi-attribute model;multi-attribute coalitional game"}
{"name": "train_J-39", "title": "The Sequential Auction Problem on eBay: An Empirical Analysis and a Solution", "abstract": "Bidders on eBay have no dominant bidding strategy when faced with multiple auctions each offering an item of interest. As seen through an analysis of 1,956 auctions on eBay for a Dell E193FP LCD monitor, some bidders win auctions at prices higher than those of other available auctions, while others never win an auction despite placing bids in losing efforts that are greater than the closing prices of other available auctions. These misqueues in strategic behavior hamper the efficiency of the system, and in so doing limit the revenue potential for sellers. This paper proposes a novel options-based extension to eBay\"s proxy-bidding system that resolves this strategic issue for buyers in commoditized markets. An empirical analysis of eBay provides a basis for computer simulations that investigate the market effects of the options-based scheme, and demonstrates that the options-based scheme provides greater efficiency than eBay, while also increasing seller revenue.", "fulltext": "1. INTRODUCTION\nElectronic markets represent an application of information\nsystems that has generated significant new trading\nopportunities while allowing for the dynamic pricing of goods. In\naddition to marketplaces such as eBay, electronic marketplaces\nare increasingly used for business-to-consumer auctions (e.g.\nto sell surplus inventory [19]).\nMany authors have written about a future in which\ncommerce is mediated by online, automated trading agents [10,\n25, 1]. There is still little evidence of automated trading\nin e-markets, though. We believe that one leading place of\nresistance is in the lack of provably optimal bidding\nstrategies for any but the simplest of market designs. Without\nthis, we do not expect individual consumers, or firms, to\nbe confident in placing their business in the hands of an\nautomated agent.\nOne of the most common examples today of an electronic\nmarketplace is eBay, where the gross merchandise volume\n(i.e., the sum of all successfully closed listings) during 2005\nwas $44B. Among items listed on eBay, many are essentially\nidentical. This is especially true in the Consumer\nElectronics category [9], which accounted for roughly $3.5B of eBay\"s\ngross merchandise volume in 2005. This presence of\nessentially identical items can expose bidders, and sellers, to risks\nbecause of the sequential auction problem.\nFor example, Alice may want an LCD monitor, and could\npotentially bid in either a 1 o\"clock or 3 o\"clock eBay\nauction. While Alice would prefer to participate in whichever\nauction will have the lower winning price, she cannot\ndetermine beforehand which auction that may be, and could\nend up winning the wrong auction. This is a problem of\nmultiple copies.\nAnother problem bidders may face is the exposure\nproblem. As investigated by Bykowsky et al. [6], exposure\nproblems exist when buyers desire a bundle of goods but may\nonly participate in single-item auctions.1\nFor example, if\nAlice values a video game console by itself for $200, a video\ngame by itself for $30, and both a console and game for $250,\nAlice must determine how much of the $20 of synergy value\nshe might include in her bid for the console alone. Both\nproblems arise in eBay as a result of sequential auctions of\nsingle items coupled with patient bidders with substitutes\nor complementary valuations.\nWhy might the sequential auction problem be bad?\nComplex games may lead to bidders employing costly strategies\nand making mistakes. Potential bidders who do not wish\nto bear such costs may choose not to participate in the\n1\nThe exposure problem has been primarily investigated by\nBykowsky et al. in the context of simultaneous single-item\nauctions. The problem is also a familiar one of online\ndecision making.\n180\nmarket, inhibiting seller revenue opportunities.\nAdditionally, among those bidders who do choose to participate, the\nmistakes made may lead to inefficient allocations, further\nlimiting revenue opportunities.\nWe are interested in creating modifications to eBay-style\nmarkets that simplify the bidder problem, leading to simple\nequilibrium strategies, and preferably better efficiency and\nrevenue properties.\n1.1 Options + Proxies: A Proposed Solution\nRetail stores have developed policies to assist their\ncustomers in addressing sequential purchasing problems.\nReturn policies alleviate the exposure problem by allowing\ncustomers to return goods at the purchase price. Price\nmatching alleviates the multiple copies problem by allowing buyers\nto receive from sellers after purchase the difference between\nthe price paid for a good and a lower price found elsewhere\nfor the same good [7, 15, 18]. Furthermore, price matching\ncan reduce the impact of exactly when a seller brings an\nitem to market, as the price will in part be set by others\nselling the same item. These two retail policies provide the\nbasis for the scheme proposed in this paper.2\nWe extend the proxy bidding technology currently\nemployed by eBay. Our super-proxy extension will take\nadvantage of a new, real options-based, market infrastructure\nthat enables simple, yet optimal, bidding strategies. The\nextensions are computationally simple, handle temporal\nissues, and retain seller autonomy in deciding when to enter\nthe market and conduct individual auctions.\nA seller sells an option for a good, which will ultimately\nlead to either a sale of the good or the return of the option.\nBuyers interact through a proxy agent, defining a value on\nall possible bundles of goods in which they have interest\ntogether with the latest time period in which they are\nwilling to wait to receive the good(s). The proxy agents use\nthis information to determine how much to bid for options,\nand follow a dominant bidding strategy across all relevant\nauctions. A proxy agent exercises options held when the\nbuyer\"s patience has expired, choosing options that\nmaximize a buyer\"s payoff given the reported valuation. All other\noptions are returned to the market and not exercised. The\noptions-based protocol makes truthful and immediate\nrevelation to a proxy a dominant strategy for buyers, whatever\nthe future auction dynamics.\nWe conduct an empirical analysis of eBay, collecting data\non over four months of bids for Dell LCD screens (model\nE193FP) starting in the Summer of 2005. LCD screens are\na high-ticket item, for which we demonstrate evidence of\nthe sequential bidding problem. We first infer a\nconservative model for the arrival time, departure time and value of\nbidders on eBay for LCD screens during this period. This\nmodel is used to simulate the performance of the\noptionsbased infrastructure, in order to make direct comparisons to\nthe actual performance of eBay in this market.\nWe also extend the work of Haile and Tamer [11] to\nestimate an upper bound on the distribution of value of eBay\nbidders, taking into account the sequential auction\nproblem when making the adjustments. Using this estimate, one\ncan approximate how much greater a bidder\"s true value is\n2\nPrior work has shown price matching as a potential\nmechanism for colluding firms to set monopoly prices. However,\nin our context, auction prices will be matched, which are\nnot explicitly set by sellers but rather by buyers\" bids.\nfrom the maximum bid they were observed to have placed\non eBay. Based on this approximation, revenue generated\nin a simulation of the options-based scheme exceeds\nrevenue on eBay for the comparable population and sequence of\nauctions by 14.8%, while the options-based scheme\ndemonstrates itself as being 7.5% more efficient.\n1.2 Related Work\nA number of authors [27, 13, 28, 29] have analyzed the\nmultiple copies problem, often times in the context of\ncategorizing or modeling sniping behavior for reasons other\nthan those first brought forward by Ockenfels and Roth\n[20]. These papers perform equilibrium analysis in simpler\nsettings, assuming bidders can participate in at most two\nauctions. Peters & Severinov [21] extend these models to\nallow buyers to consider an arbitrary number of auctions, and\ncharacterize a perfect Bayesian equilibrium. However, their\nmodel does not allow auctions to close at distinct times and\ndoes not consider the arrival and departure of bidders.\nPrevious work have developed a data-driven approach\ntoward developing a taxonomy of strategies employed by\nbidders in practice when facing multi-unit auctions, but have\nnot considered the sequential bidding problem [26, 2].\nPrevious work has also sought to provide agents with smarter\nbidding strategies [4, 3, 5, 1]. Unfortunately, it seems hard\nto design artificial agents with equilibrium bidding\nstrategies, even for a simple simultaneous ascending price auction.\nIwasaki et al. [14] have considered the role of options in\nthe context of a single, monolithic, auction design to help\nbidders with marginal-increasing values avoid exposure in\na multi-unit, homogeneous item auction problem. In other\ncontexts, options have been discussed for selling coal mine\nleases [23], or as leveled commitment contracts for use in a\ndecentralized market place [24]. Most similar to our work,\nGopal et al. [9] use options for reducing the risks of buyers\nand sellers in the sequential auction problem. However, their\nwork uses costly options and does not remove the sequential\nbidding problem completely.\nWork on online mechanisms and online auctions [17, 12,\n22] considers agents that can dynamically arrive and depart\nacross time. We leverage a recent price-based\ncharacterization by Hajiaghayi et al. [12] to provide a dominant strategy\nequilibrium for buyers within our options-based protocol.\nThe special case for single-unit buyers is equivalent to the\nprotocol of Hajiaghayi et al., albeit with an options-based\ninterpretation.\nJiang and Leyton-Brown [16] use machine learning\ntechniques for bid identification in online auctions.\n2. EBAY AND THE DELL E193FP\nThe most common type of auction held on eBay is a\nsingleitem proxy auction. Auctions open at a given time and\nremain open for a set period of time (usually one week).\nBidders bid for the item by giving a proxy a value ceiling. The\nproxy will bid on behalf of the bidder only as much as is\nnecessary to maintain a winning position in the auction, up to\nthe ceiling received from the bidder. Bidders may\ncommunicate with the proxy multiple times before an auction closes.\nIn the event that a bidder\"s proxy has been outbid, a bidder\nmay give the proxy a higher ceiling to use in the auction.\neBay\"s proxy auction implements an incremental version of\na Vickrey auction, with the item sold to the highest bidder\nfor the second-highest bid plus a small increment.\n181\n10\n0\n10\n1\n10\n2\n10\n3\n10\n4\n10\n0\n10\n1\n10\n2\n10\n3\n10\n4\nNumber of Auctions\nNumberofBidders\nAuctions Available\nAuctions in Which Bid\nFigure 1: Histogram of number of LCD auctions\navailable to each bidder and number of LCD auctions in which\na bidder participates.\nThe market analyzed in this paper is that of a specific\nmodel of an LCD monitor, a 19 Dell LCD model E193FP.\nThis market was selected for a variety of reasons including:\n\u2022 The mean price of the monitor was $240 (with\nstandard deviation $32), so we believe it reasonable to\nassume that bidders on the whole are only interested in\nacquiring one copy of the item on eBay.3\n\u2022 The volume transacted is fairly high, at approximately\n500 units sold per month.\n\u2022 The item is not usually bundled with other items.\n\u2022 The item is typically sold as new, and so suitable for\nthe price-matching of the options-based scheme.\nRaw auction information was acquired via a PERL script.\nThe script accesses the eBay search engine,4\nand returns all\nauctions containing the terms \u2018Dell\" and \u2018LCD\" that have\nclosed within the past month.5\nData was stored in a text\nfile for post-processing. To isolate the auctions in the\ndomain of interest, queries were made against the titles of eBay\nauctions that closed between 27 May, 2005 through 1\nOctober, 2005.6\nFigure 1 provides a general sense of how many LCD\nauctions occur while a bidder is interested in pursuing a\nmonitor.7\n8,746 bidders (86%) had more than one auction\navailable between when they first placed a bid on eBay and the\n3\nFor reference, Dell\"s October 2005 mail order catalogue\nquotes the price of the monitor as being $379 without a\ndesktop purchase, and $240 as part of a desktop purchase\nupgrade.\n4\nhttp://search.ebay.com\n5\nThe search is not case-sensitive.\n6\nSpecifically, the query found all auctions where the title\ncontained all of the following strings: \u2018Dell,\" \u2018LCD\" and\n\u2018E193FP,\" while excluding all auctions that contained any\nof the following strings: \u2018Dimension,\" \u2018GHZ,\" \u2018desktop,\" \u2018p4\"\nand \u2018GB.\" The exclusion terms were incorporated so that the\nonly auctions analyzed would be those selling exclusively the\nLCD of interest. For example, the few bundled auctions\nselling both a Dell Dimension desktop and the E193FP LCD\nare excluded.\n7\nAs a reference, most auctions close on eBay between noon\nand midnight EDT, with almost two auctions for the Dell\nLCD monitor closing each hour on average during peak time\nperiods. Bidders have an average observed patience of 3.9\ndays (with a standard deviation of 11.4 days).\nlatest closing time of an auction in which they bid (with an\naverage of 78 auctions available). Figure 1 also illustrates\nthe number of auctions in which each bidder participates.\nOnly 32.3% of bidders who had more than one auction\navailable are observed to bid in more than one auction (bidding\nin 3.6 auctions on average). A simple regression analysis\nshows that bidders tend to submit maximal bids to an\nauction that are $1.22 higher after spending twice as much time\nin the system, as well as bids that are $0.27 higher in each\nsubsequent auction.\nAmong the 508 bidders that won exactly one monitor and\nparticipated in multiple auctions, 201 (40%) paid more than\n$10 more than the closing price of another auction in which\nthey bid, paying on average $35 more (standard deviation\n$21) than the closing price of the cheapest auction in which\nthey bid but did not win. Furthermore, among the 2,216\nbidders that never won an item despite participating in\nmultiple auctions, 421 (19%) placed a losing bid in one auction\nthat was more than $10 higher than the closing price of\nanother auction in which they bid, submitting a losing bid on\naverage $34 more (standard deviation $23) than the\nclosing price of the cheapest auction in which they bid but did\nnot win. Although these measures do not say a bidder that\nlost could have definitively won (because we only consider\nthe final winning price and not the bid of the winner to her\nproxy), or a bidder that won could have secured a better\nprice, this is at least indicative of some bidder mistakes.\n3. MODELING THE SEQUENTIAL\nAUCTION PROBLEM\nWhile the eBay analysis was for simple bidders who\ndesire only a single item, let us now consider a more general\nscenario where people may desire multiple goods of different\ntypes, possessing general valuations over those goods.\nConsider a world with buyers (sometimes called bidders)\nB and K different types of goods G1...GK . Let T = {0, 1, ...}\ndenote time periods. Let L denote a bundle of goods,\nrepresented as a vector of size K, where Lk \u2208 {0, 1} denotes\nthe quantity of good type Gk in the bundle.8\nThe type of a\nbuyer i \u2208 B is (ai, di, vi), with arrival time ai \u2208 T, departure\ntime di \u2208 T, and private valuation vi(L) \u2265 0 for each bundle\nof goods L received between ai and di, and zero value\notherwise. The arrival time models the period in which a buyer\nfirst realizes her demand and enters the market, while the\ndeparture time models the period in which a buyer loses\ninterest in acquiring the good(s). In settings with general\nvaluations, we need an additional assumption: an upper bound\non the difference between a buyer\"s arrival and departure,\ndenoted \u0394Max. Buyers have quasi-linear utilities, so that\nthe utility of buyer i receiving bundle L and paying p, in\nsome period no later than di, is ui(L, p) = vi(L) \u2212 p. Each\nseller j \u2208 S brings a single item kj to the market, has no\nintrinsic value and wants to maximize revenue. Seller j has\nan arrival time, aj, which models the period in which she\nis first interested in listing the item, while the departure\ntime, dj, models the latest period in which she is willing to\nconsider having an auction for the item close. A seller will\nreceive payment by the end of the reported departure of the\nwinning buyer.\n8\nWe extend notation whereby a single item k of type Gk\nrefers to a vector L : Lk = 1.\n182\nWe say an individual auction in a sequence is locally\nstrategyproof (LSP) if truthful bidding is a dominant strategy\nfor a buyer that can only bid in that auction. Consider the\nfollowing example to see that LSP is insufficient for the\nexistence of a dominant bidding strategy for buyers facing a\nsequence of auctions.\nExample 1. Alice values one ton of Sand with one ton\nof Stone at $2, 000. Bob holds a Vickrey auction for one ton\nof Sand on Monday and a Vickrey auction for one ton of\nStone on Tuesday. Alice has no dominant bidding strategy\nbecause she needs to know the price for Stone on Tuesday to\nknow her maximum willingness to pay for Sand on Monday.\nDefinition 1. The sequential auction problem. Given\na sequence of auctions, despite each auction being locally\nstrategyproof, a bidder has no dominant bidding strategy.\nConsider a sequence of auctions. Generally, auctions\nselling the same item will be uncertainly-ordered, because a\nbuyer will not know the ordering of closing prices among\nthe auctions. Define the interesting bundles for a buyer as\nall bundles that could maximize the buyer\"s profit for some\ncombination of auctions and bids of other buyers.9\nWithin\nthe interesting bundles, say that an item has uncertain\nmarginal value if the marginal value of an item depends on the\nother goods held by the buyer.10\nSay that an item is\noversupplied if there is more than one auction offering an item\nof that type. Say two bundles are substitutes if one of those\nbundles has the same value as the union of both bundles.11\nProposition 1. Given locally strategyproof single-item\nauctions, the sequential auction problem exists for a bidder if\nand only if either of the following two conditions is true: (1)\nwithin the set of interesting bundles (a) there are two\nbundles that are substitutes, (b) there is an item with uncertain\nmarginal value, or (c) there is an item that is over-supplied;\n(2) a bidder faces competitors\" bids that are conditioned on\nthe bidder\"s past bids.\nProof. (Sketch.)(\u21d0) A bidder does not have a dominant\nstrategy when (a) she does not know which bundle among\nsubstitutes to pursue, (b) she faces the exposure problem,\nor (c) she faces the multiple copies problem. Additionally,\na bidder does not have a dominant strategy when she does\nnot how to optimally influence the bids of competitors.(\u21d2)\nBy contradiction. A bidder has a dominant strategy to bid\nits constant marginal value for a given item in each auction\navailable when conditions (1) and (2) are both false.\nFor example, the following buyers all face the sequential\nauction problem as a result of condition (a), (b) and (c)\nrespectively: a buyer who values one ton of Sand for $1,000,\nor one ton of Stone for $2,000, but not both Sand and Stone;\na buyer who values one ton of Sand for $1,000, one ton of\nStone for $300, and one ton of Sand and one ton of Stone for\n$1,500, and can participate in an auction for Sand before an\nauction for Stone; a buyer who values one ton of Sand for\n$1,000 and can participate in many auctions selling Sand.\n9\nAssume that the empty set is an interesting bundle.\n10\nFormally, an item k has uncertain marginal value if |{m :\nm = vi(Q) \u2212 vi(Q \u2212 k), \u2200Q \u2286 L \u2208 InterestingBundle, Q \u2287\nk}| > 1.\n11\nFormally, two bundles A and B are substitutes if vi(A \u222a\nB) = max(vi(A), vi(B)), where A \u222a B = L where Lk =\nmax(Ak, Bk).\n4. SUPER PROXIES AND OPTIONS\nThe novel solution proposed in this work to resolve the\nsequential auction problem consists of two primary\ncomponents: richer proxy agents, and options with price matching.\nIn finance, a real option is a right to acquire a real good at\na certain price, called the exercise price. For instance, Alice\nmay obtain from Bob the right to buy Sand from him at\nan exercise price of $1, 000. An option provides the right to\npurchase a good at an exercise price but not the obligation.\nThis flexibility allows buyers to put together a collection of\noptions on goods and then decide which to exercise.\nOptions are typically sold at a price called the option\nprice. However, options obtained at a non-zero option price\ncannot generally support a simple, dominant bidding\nstrategy, as a buyer must compute the expected value of an\noption to justify the cost [8]. This computation requires a\nmodel of the future, which in our setting requires a model\nof the bidding strategies and the values of other bidders.\nThis is the very kind of game-theoretic reasoning that we\nwant to avoid.\nInstead, we consider costless options with an option price\nof zero. This will require some care as buyers are weakly\nbetter off with a costless option than without one, whatever\nits exercise price. However, multiple bidders pursuing\noptions with no intention of exercising them would cause the\nefficiency of an auction for options to unravel. This is the\nrole of the mandatory proxy agents, which intermediate\nbetween buyers and the market. A proxy agent forces a link\nbetween the valuation function used to acquire options and\nthe valuation used to exercise options. If a buyer tells her\nproxy an inflated value for an item, she runs the risk of\nhaving the proxy exercise options at a price greater than her\nvalue.\n4.1 Buyer Proxies\n4.1.1 Acquiring Options\nAfter her arrival, a buyer submits her valuation \u02c6vi\n(perhaps untruthfully) to her proxy in some period \u02c6ai \u2265 ai,\nalong with a claim about her departure time \u02c6di \u2265 \u02c6ai. All\ntransactions are intermediated via proxy agents. Each\nauction is modified to sell an option on that good to the\nhighest bidding proxy, with an initial exercise price set to the\nsecond-highest bid received.12\nWhen an option in which a buyer is interested becomes\navailable for the first time, the proxy determines its bid\nby computing the buyer\"s maximum marginal value for the\nitem, and then submits a bid in this amount. A proxy does\nnot bid for an item when it already holds an option. The\nbid price is:\nbidt\ni(k) = max\nL\n[\u02c6vi(L + k) \u2212 \u02c6vi(L)] (1)\nBy having a proxy compute a buyer\"s maximum marginal\nvalue for an item and then bidding only that amount, a\nbuyer\"s proxy will win any auction that could possibly be of\nbenefit to the buyer and only lose those auctions that could\nnever be of value to the buyer.\n12\nThe system can set a reserve price for each good, provided\nthat the reserve is universal for all auctions selling the same\nitem. Without a universal reserve price, price matching is\nnot possible because of the additional restrictions on prices\nthat individual sellers will accept.\n183\nBuyer Type Monday Tuesday\nMolly (Mon, Tues, $8) 6Nancy 6Nancy \u2192 4Polly\nNancy (Mon, Tues, $6) - 4Polly\nPolly (Mon, Tues, $4)\n-Table 1: Three-buyer example with each wanting a\nsingle item and one auction occurring on Monday and\nTuesday. XY  implies an option with exercise price X and\nbookkeeping that a proxy has prevented Y from\ncurrently possessing an option. \u2192 is the updating of\nexercise price and bookkeeping.\nWhen a proxy wins an auction for an option, the proxy\nwill store in its local memory the identity (which may be\na pseudonym) of the proxy not holding an option because\nof the proxy\"s win (i.e., the proxy that it \u2018bumped\" from\nwinning, if any). This information will be used for price\nmatching.\n4.1.2 Pricing Options\nSellers agree by joining the market to allow the proxy\nrepresenting a buyer to adjust the exercise price of an option\nthat it holds downwards if the proxy discovers that it could\nhave achieved a better price by waiting to bid in a later\nauction for an option on the same good. To assist in the\nimplementation of the price matching scheme each proxy\ntracks future auctions for an option that it has already won\nand will determine who would be bidding in that auction\nhad the proxy delayed its entry into the market until this\nlater auction. The proxy will request price matching from\nthe seller that granted it an option if the proxy discovers that\nit could have secured a lower price by waiting. To reiterate,\nthe proxy does not acquire more than one option for any\ngood. Rather, it reduces the exercise price on its already\nissued option if a better deal is found.\nThe proxy is able to discover these deals by asking each\nfuture auction to report the identities of the bidders in that\nauction together with their bids. This needs to be enforced\nby eBay, as the central authority. The highest bidder in this\nlater auction, across those whose identity is not stored in\nthe proxy\"s memory for the given item, is exactly the bidder\nagainst whom the proxy would be competing had it delayed\nits entry until this auction. If this high bid is lower than the\ncurrent option price held, the proxy price matches down\nto this high bid price.\nAfter price matching, one of two adjustments will be made\nby the proxy for bookkeeping purposes. If the winner of\nthe auction is the bidder whose identity has been in the\nproxy\"s local memory, the proxy will replace that local\ninformation with the identity of the bidder whose bid it just\nprice matched, as that is now the bidder the proxy has\nprevented from obtaining an option. If the auction winner\"s\nidentity is not stored in the proxy\"s local memory the\nmemory may be cleared. In this case, the proxy will simply price\nmatch against the bids of future auction winners on this\nitem until the proxy departs.\nExample 2 (Table 1). Molly\"s proxy wins the\nMonday auction, submitting a bid of $8 and receiving an option\nfor $6. Molly\"s proxy adds Nancy to its local memory as\nNancy\"s proxy would have won had Molly\"s proxy not bid.\nOn Tuesday, only Nancy\"s and Polly\"s proxy bid (as Molly\"s\nproxy holds an option), with Nancy\"s proxy winning an\nopBuyer Type Monday Tuesday\nTruth:\nMolly (Mon, Mon, $8)\n6NancyNancy (Mon, Tues, $6) - 4Polly\nPolly (Mon, Tues, $4)\n-Misreport:\nMolly (Mon, Mon, $8)\n-Nancy (Mon, Tues, $10) 8Molly 8Molly \u2192 4\u03c6\nPolly (Mon, Tues, $4) - 0\u03c6\nMisreport &\nmatch low:\nMolly (Mon, Mon, $8)\n-Nancy (Mon, Tues, $10) 8 8 \u2192 0\nPolly (Mon, Tues, $4) - 0\nTable 2: Examples demonstrating why bookkeeping will\nlead to a truthful system whereas simply matching to the\nlowest winning price will not.\ntion for $4 and noting that it bumped Polly\"s proxy. At this\ntime, Molly\"s proxy will price match its option down to $4\nand replace Nancy with Polly in its local memory as per the\nprice match algorithm, as Polly would be holding an option\nhad Molly never bid.\n4.1.3 Exercising Options\nAt the reported departure time the proxy chooses which\noptions to exercise. Therefore, a seller of an option must\nwait until period \u02c6dw for the option to be exercised and\nreceive payment, where w was the winner of the option.13\nFor\nbidder i, in period \u02c6di, the proxy chooses the option(s) that\nmaximize the (reported) utility of the buyer:\n\u03b8\u2217\nt = argmax\n\u03b8\u2286\u0398\n(\u02c6vi(\u03b3(\u03b8)) \u2212 \u03c0(\u03b8)) (2)\nwhere \u0398 is the set of all options held, \u03b3(\u03b8) are the goods\ncorresponding to a set of options, and \u03c0(\u03b8) is the sum of\nexercise prices for a set of options. All other options are\nreturned.14\nNo options are exercised when no combination\nof options have positive utility.\n4.1.4 Why bookkeep and not match winning price?\nOne may believe that an alternative method for\nimplementing a price matching scheme could be to simply have\nproxies match the lowest winning price they observe after\nwinning an option. However, as demonstrated in Table 2,\nsuch a simple price matching scheme will not lead to a\ntruthful system.\nThe first scenario in Table 2 demonstrates the outcome\nif all agents were to truthfully report their types. Molly\n13\nWhile this appears restrictive on the seller, we believe it not\nsignificantly different than what sellers on eBay currently\nendure in practice. An auction on eBay closes at a specific\ntime, but a seller must wait until a buyer relinquishes\npayment before being able to realize the revenue, an amount of\ntime that could easily be days (if payment is via a money\norder sent through courier) to much longer (if a buyer is\nslow but not overtly delinquent in remitting her payment).\n14\nPresumably, an option returned will result in the seller\nholding a new auction for an option on the item it still\npossesses. However, the system will not allow a seller to\nre-auction an option until \u0394Max after the option had first\nbeen issued in order to maintain a truthful mechanism.\n184\nwould win the Monday auction and receive an option with\nan exercise price of $6 (subsequently exercising that option\nat the end of Monday), and Nancy would win the Tuesday\nauction and receive an option with an exercise price of $4\n(subsequently exercising that option at the end of Tuesday).\nThe second scenario in Table 2 demonstrates the outcome\nif Nancy were to misreport her value for the good by\nreporting an inflated value of $10, using the proposed bookkeeping\nmethod. Nancy would win the Monday auction and receive\nan option with an exercise price of $8. On Tuesday, Polly\nwould win the auction and receive an option with an exercise\nprice of $0. Nancy\"s proxy would observe that the highest\nbid submitted on Tuesday among those proxies not stored\nin local memory is Polly\"s bid of $4, and so Nancy\"s proxy\nwould price match the exercise price of its option down to\n$4. Note that the exercise price Nancy\"s proxy has obtained\nat the end of Tuesday is the same as when she truthfully\nrevealed her type to her proxy.\nThe third scenario in Table 2 demonstrates the outcome if\nNancy were to misreport her value for the good by reporting\nan inflated value of $10, if the price matching scheme were\nfor proxies to simply match their option price to the\nlowest winning price at any time while they are in the system.\nNancy would win the Monday auction and receive an option\nwith an exercise price of $8. On Tuesday, Polly would win\nthe auction and receive an option with an exercise price of\n$0. Nancy\"s proxy would observe that the lowest price on\nTuesday was $0, and so Nancy\"s proxy would price match\nthe exercise price of its option down to $0. Note that the\nexercise price Nancy\"s proxy has obtained at the end of\nTuesday is lower than when she truthfully revealed her type to\nthe proxy.\nTherefore, a price matching policy of simply matching the\nlowest price paid may not elicit truthful information from\nbuyers.\n4.2 Complexity of Algorithm\nAn XOR-valuation of size M for buyer i is a set of M\nterms, < L1\n, v1\ni > ...< LM\n, vM\ni >, that maps distinct\nbundles to values, where i is interested in acquiring at most one\nsuch bundle. For any bundle S, vi(S) = maxLm\u2286S(vm\ni ).\nTheorem 1. Given an XOR-valuation which possesses\nM terms, there is an O(KM2\n) algorithm for computing all\nmaximum marginal values, where K is the number of\ndifferent item types in which a buyer may be interested.\nProof. For each item type, recall Equation 1 which\ndefines the maximum marginal value of an item. For each\nbundle L in the M-term valuation, vi(L + k) may be found\nby iterating over the M terms. Therefore, the number of\nterms explored to determine the maximum marginal value\nfor any item is O(M2\n), and so the total number of\nbundle comparisons to be performed to calculate all maximum\nmarginal values is O(KM2\n).\nTheorem 2. The total memory required by a proxy for\nimplementing price matching is O(K), where K is the\nnumber of distinct item types. The total work performed by a\nproxy to conduct price matching in each auction is O(1).\nProof. By construction of the algorithm, the proxy stores\none maximum marginal value for each item for bidding, of\nwhich there are O(K); at most one buyer\"s identity for each\nitem, of which there are O(K); and one current option\nexercise price for each item, of which there are O(K). For\neach auction, the proxy either submits a precomputed bid\nor price matches, both of which take O(1) work.\n4.3 Truthful Bidding to the Proxy Agent\nProxies transform the market into a direct revelation\nmechanism, where each buyer i interacts with the proxy only\nonce,15\nand does so by declaring a bid, bi, which is\ndefined as an announcement of her type, (\u02c6ai, \u02c6di, \u02c6vi), where\nthe announcement may or may not be truthful. We\ndenote all received bids other than i\"s as b\u2212i. Given bids,\nb = (bi, b\u2212i), the market determines allocations, xi(b), and\npayments, pi(b) \u2265 0, to each buyer (using an online\nalgorithm).\nA dominant strategy equilibrium for buyers requires that\nvi(xi(bi, b\u2212i))\u2212pi(bi, b\u2212i) \u2265 vi(xi(bi, b\u2212i))\u2212pi(bi, b\u2212i), \u2200bi =\nbi, \u2200b\u2212i.\nWe now establish that it is a dominant strategy for a buyer\nto reveal her true valuation and true departure time to her\nproxy agent immediately upon arrival to the system. The\nproof builds on the price-based characterization of\nstrategyproof single-item online auctions in Hajiaghayi et al. [12].\nDefine a monotonic and value-independent price function\npsi(ai, di, L, v\u2212i) which can depend on the values of other\nagents v\u2212i. Price psi(ai, di, L, v\u2212i) will represent the price\navailable to agent i for bundle L in the mechanism if it\nannounces arrival time ai and departure time di. The price\nis independent of the value vi of agent i, but can depend on\nai, di and L as long as it satisfies a monotonicity condition.\nDefinition 2. Price function psi(ai, di, L, v\u2212i) is\nmonotonic if psi(ai, di, L , v\u2212i) \u2264 psi(ai, di, L, v\u2212i) for all ai \u2264\nai, all di \u2265 di, all bundles L \u2286 L and all v\u2212i.\nLemma 1. An online combinatorial auction will be\nstrategyproof (with truthful reports of arrival, departure and value\na dominant strategy) when there exists a monotonic and\nvalue-independent price function, psi(ai, di, L, v\u2212i), such that\nfor all i and all ai, di \u2208 T and all vi, agent i is allocated\nbundle L\u2217\n= argmaxL [vi(L) \u2212 psi(ai, di, L, v\u2212i)] in period di\nand makes payment psi(ai, di, L\u2217\n, v\u2212i).\nProof. Agent i cannot benefit from reporting a later\ndeparture \u02c6di because the allocation is made in period \u02c6di and\nthe agent would have no value for this allocation. Agent\ni cannot benefit from reporting a later arrival \u02c6ai \u2265 ai or\nearlier departure \u02c6di \u2264 di because of price monotonicity.\nFinally, the agent cannot benefit from reporting some \u02c6vi = vi\nbecause its reported valuation does not change the prices\nit faces and the mechanism maximizes its utility given its\nreported valuation and given the prices.\nLemma 2. At any given time, there is at most one buyer\nin the system whose proxy does not hold an option for a\ngiven item type because of buyer i\"s presence in the system,\nand the identity of that buyer will be stored in i\"s proxy\"s\nlocal memory at that time if such a buyer exists.\nProof. By induction. Consider the first proxy that a\nbuyer prevents from winning an option. Either (a) the\n15\nFor analysis purposes, we view the mechanism as an opaque\nmarket so that the buyer cannot condition her bid on bids\nplaced by others.\n185\nbumped proxy will leave the system having never won an\noption, or (b) the bumped proxy will win an auction in the\nfuture. If (a), the buyer\"s presence prevented exactly that\none buyer from winning an option, but will have not\nprevented any other proxies from winning an option (as the\nbuyer\"s proxy will not bid on additional options upon\nsecuring one), and will have had that bumped proxy\"s identity\nin its local memory by definition of the algorithm. If (b),\nthe buyer has not prevented the bumped proxy from\nwinning an option after all, but rather has prevented only the\nproxy that lost to the bumped proxy from winning (if any),\nwhose identity will now be stored in the proxy\"s local\nmemory by definition of the algorithm. For this new identity in\nthe buyer\"s proxy\"s local memory, either scenario (a) or (b)\nwill be true, ad infinitum.\nGiven this, we show that the options-based\ninfrastructure implements a price-based auction with a monotonic and\nvalue-independent price schedule to every agent.\nTheorem 3. Truthful revelation of valuation, arrival and\ndeparture is a dominant strategy for a buyer in the\noptionsbased market.\nProof. First, define a simple agent-independent price\nfunction pk\ni (t, v\u2212i) as the highest bid by the proxies not\nholding an option on an item of type Gk at time t, not\nincluding the proxy representing i herself and not\nincluding any proxies that would have already won an option had\ni never entered the system (i.e., whose identity is stored\nin i\"s proxy\"s local memory)(\u221e if no supply at t). This\nset of proxies is independent of any declaration i makes to\nits proxy (as the set explicitly excludes the at most one\nproxy (see Lemma 2) that i has prevented from holding\nan option), and each bid submitted by a proxy within this\nset is only a function of their own buyer\"s declared\nvaluation (see Equation 1). Furthermore, i cannot influence\nthe supply she faces as any options returned by bidders\ndue to a price set by i\"s proxy\"s bid will be re-auctioned\nafter i has departed the system. Therefore, pk\ni (t, v\u2212i) is\nindependent of i\"s declaration to its proxy. Next, define\npsk\ni (\u02c6ai, \u02c6di, v\u2212i) = min\u02c6ai\u2264\u03c4\u2264 \u02c6di\n[pk\ni (\u03c4, v\u2212i)] (possibly \u221e) as the\nminimum price over pk\ni (t, v\u2212i), which is clearly monotonic.\nBy construction of price matching, this is exactly the price\nobtained by a proxy on any option that it holds at\ndeparture. Define psi(\u02c6ai, \u02c6di, L, v\u2212i) =\n\u00c8k=K\nk=1 psk\ni (\u02c6ai, \u02c6di, v\u2212i)Lk,\nwhich is monotonic in \u02c6ai, \u02c6di and L since psk\ni (\u02c6ai, \u02c6di, v\u2212i) is\nmonotonic in \u02c6ai and \u02c6di and (weakly) greater than zero for\neach k. Given the set of options held at \u02c6di, which may be\na subset of those items with non-infinite prices, the proxy\nexercises options to maximize the reported utility. Left to\nshow is that all bundles that could not be obtained with\noptions held are priced sufficiently high as to not be\npreferred. For each such bundle, either there is an item priced\nat \u221e (in which case the bundle would not be desired) or\nthere must be an item in that bundle for which the proxy\ndoes not hold an option that was available. In all auctions\nfor such an item there must have been a distinct bidder\nwith a bid greater than bidt\ni(k), which subsequently results\nin psk\ni (\u02c6ai, \u02c6di, v\u2212i) > bidt\ni(k), and so the bundle without k\nwould be preferred to the bundle.\nTheorem 4. The super proxy, options-based scheme is\nindividually-rational for both buyers and sellers.\nPrice \u03c3(Price) Value Surplus\neBay $240.24 $32 $244 $4\nOptions $239.66 $12 $263 $23\nTable 3: Average price paid, standard deviation of\nprices paid, average bidder value among winners, and\naverage winning bidder surplus on eBay for Dell E193FP\nLCD screens as well as the simulated options-based\nmarket using worst-case estimates of bidders\" true value.\nProof. By construction, the proxy exercises the profit\nmaximizing set of options obtained, or no options if no set\nof options derives non-negative surplus. Therefore, buyers\nare guaranteed non-negative surplus by participating in the\nscheme. For sellers, the price of each option is based on a\nnon-negative bid or zero.\n5. EVALUATING THE OPTIONS / PROXY\nINFRASTRUCTURE\nA goal of the empirical benchmarking and a reason to\ncollect data from eBay is to try and build a realistic model\nof buyers from which to estimate seller revenue and other\nmarket effects under the options-based scheme.\nWe simulate a sequence of auctions that match the timing\nof the Dell LCD auctions on eBay.16\nWhen an auction\nsuccessfully closes on eBay, we simulate a Vickrey auction for\nan option on the item sold in that period. Auctions that do\nnot successfully close on eBay are not simulated. We\nestimate the arrival, departure and value of each bidder on eBay\nfrom their observed behavior.17\nArrival is estimated as the\nfirst time that a bidder interacts with the eBay proxy, while\ndeparture is estimated as the latest closing time among eBay\nauctions in which a bidder participates.\nWe initially adopt a particularly conservative estimate for\nbidder value, estimating it as the highest bid a bidder was\nobserved to make on eBay. Table 3 compares the\ndistribution of closing prices on eBay and in the simulated options\nscheme. While the average revenue in both schemes is\nvirtually the same ($239.66 in the options scheme vs. $240.24\non eBay), the winners in the options scheme tend to value\nthe item won 7% more than the winners on eBay ($263 in\nthe options scheme vs. $244 on eBay).\n5.1 Bid Identification\nWe extend the work of Haile and Tamer [11] to sequential\nauctions to get a better view of underlying bidder values.\nRather than assume for bidders an equilibrium behavior as\nin standard econometric techniques, Haile and Tamer do not\nattempt to model how bidders\" true values get mapped into a\nbid in any given auction. Rather, in the context of repeated\n16\nWhen running the simulations, the results of the first and\nfinal ten days of auctions are not recorded to reduce edge\neffects that come from viewing a discrete time window of a\ncontinuous process.\n17\nFor the 100 bidders that won multiple times on eBay, we\nhave each one bid a constant marginal value for each\nadditional item in each auction until the number of options\nheld equals the total number of LCDs won on eBay, with\neach option available for price matching independently. This\nbidding strategy is not a dominant strategy (falling outside\nthe type space possible for buyers on which the proof of\ntruthfulness has been built), but is believed to be the most\nappropriate first order action for simulation.\n186\n0 100 200 300 400 500\n0\n0.2\n0.4\n0.6\n0.8\n1\nValue ($)\nCDF Observed Max Bids Upper Bound of True Value\nFigure 2: CDF of maximum bids observed and upper\nbound estimate of the bidding population\"s distribution\nfor maximum willingness to pay. The true population\ndistribution lies below the estimated upper bound.\nsingle-item auctions with distinct bidder populations, Haile\nand Tamer make only the following two assumptions when\nestimating the distribution of true bidder values:\n1. Bidders do not bid more than they are willing to pay.\n2. Bidders do not allow an opponent to win at a price\nthey are willing to beat.\nFrom the first of their two assumptions, given the bids placed\nby each bidder in each auction, Haile and Tamer derive a\nmethod for estimating an upper bound of the bidding\npopulation\"s true value distribution (i.e., the bound that lies\nabove the true value distribution). From the second of their\ntwo assumptions, given the winning price of each auction,\nHaile and Tamer derive a method for estimating a lower\nbound of the bidding population\"s true value distribution.\nIt is only the upper-bound of the distribution that we\nutilize in our work.\nHaile and Tamer assume that bidders only participate in\na single auction, and require independence of the bidding\npopulation from auction to auction. Neither assumption is\nvalid here: the former because bidders are known to bid\nin more than one auction, and the latter because the set\nof bidders in an auction is in all likelihood not a true i.i.d.\nsampling of the overall bidding population. In particular,\nthose who win auctions are less likely to bid in successive\nauctions, while those who lose auctions are more likely to\nremain bidders in future auctions.\nIn applying their methods we make the following\nadjustments:\n\u2022 Within a given auction, each individual bidder\"s true\nwillingness to pay is assumed weakly greater than the\nmaximum bid that bidder submits across all auctions\nfor that item (either past or future).\n\u2022 When estimating the upper bound of the value\ndistribution, if a bidder bids in more than one auction,\nrandomly select one of the auctions in which the\nbidder bid, and only utilize that one observation during\nthe estimation.18\n18\nIn current work, we assume that removing duplicate\nbidders is sufficient to make the buying populations\nindependent i.i.d. draws from auction to auction. If one believes\nthat certain portions of the population are drawn to\ncerPrice \u03c3(Price) Value Surplus\neBay $240.24 $32 $281 $40\nOptions $275.80 $14 $302 $26\nTable 4: Average price paid, standard deviation of\nprices paid, average bidder value among winners, and\naverage winning bidder surplus on eBay for Dell E193FP\nLCD screens as well as in the simulated options-based\nmarket using an adjusted Haile and Tamer estimate of\nbidders\" true values being 15% higher than their\nmaximum observed bid.\nFigure 2 provides the distribution of maximum bids placed\nby bidders on eBay as well as the estimated upper bound of\nthe true value distribution of bidders based on the extended\nHaile and Tamer method.19\nAs can be seen, the smallest\nrelative gap between the two curves meaningfully occurs near\nthe 80th percentile, where the upper bound is 1.17 times\nthe maximum bid. Therefore, adopted as a less\nconservative model of bidder values is a uniform scaling factor of\n1.15.\nWe now present results from this less conservative\nanalysis. Table 4 shows the distribution of closing prices in\nauctions on eBay and in the simulated options scheme. The\nmean price in the options scheme is now significantly higher,\n15% greater, than the prices on eBay ($276 in the options\nscheme vs. $240 on eBay), while the standard deviation\nof closing prices is lower among the options scheme auctions\n($14 in the options scheme vs. $32 on eBay). Therefore, not\nonly is the expected revenue stream higher, but the lower\nvariance provides sellers a greater likelihood of realizing that\nhigher revenue.\nThe efficiency of the options scheme remains higher than\non eBay. The winners in the options scheme now have an\naverage estimated value 7.5% higher at $302.\nIn an effort to better understand this efficiency, we\nformulated a mixed integer program (MIP) to determine a\nsimple estimate of the allocative efficiency of eBay. The\nMIP computes the efficient value of the o\ufb04ine problem with\nfull hindsight on all bids and all supply.20\nUsing a scaling\nof 1.15, the total value allocated to eBay winners is\nestimated at $551,242, while the optimal value (from the MIP)\nis $593,301. This suggests an allocative efficiency of 92.9%:\nwhile the typical value of a winner on eBay is $281, an\naverage value of $303 was possible.21\nNote the options-based\ntain auctions, then further adjustments would be required\nin order to utilize these techniques.\n19\nThe estimation of the points in the curve is a\nminimization over many variables, many of which can have\nsmallnumbers bias. Consequently, Haile and Tamer suggest using\na weighted average over all terms yi of\n\u00c8\ni yi\nexp(yi\u03c1)\u00c8j exp(yj \u03c1)\nto\napproximate the minimum while reducing the small\nnumber effects. We used \u03c1 = \u22121000 and removed observations\nof auctions with 17 bidders or more as they occurred very\ninfrequently. However, some small numbers bias still\ndemonstrated itself with the plateau in our upper bound estimate\naround a value of $300.\n20\nBuyers who won more than one item on eBay are cloned\nso that they appear to be multiple bidders of identical type.\n21\nAs long as one believes that every bidder\"s true value is a\nconstant factor \u03b1 away from their observed maximum bid,\nthe 92.9% efficiency calculation holds for any value of \u03b1. In\npractice, this belief may not be reasonable. For example, if\nlosing bidders tend to have true values close to their observed\n187\nscheme comes very close to achieving this level of efficiency\n[at 99.7% efficient in this estimate] even though it operates\nwithout the benefit of hindsight.\nFinally, although the typical winning bidder surplus\ndecreases between eBay and the options-based scheme, some\nsurplus redistribution would be possible because the total\nmarket efficiency is improved.22\n6. DISCUSSION\nThe biggest concern with our scheme is that proxy agents\nwho may be interested in many different items may acquire\nmany more options than they finally exercise. This can lead\nto efficiency loss. Notice that this is not an issue when\nbidders are only interested in a single item (as in our empirical\nstudy), or have linear-additive values on items.\nTo fix this, we would prefer to have proxy agents use more\ncaution in acquiring options and use a more adaptive bidding\nstrategy than that in Equation 1. For instance, if a proxy\nis already holding an option with an exercise price of $3 on\nsome item for which it has value of $10, and it values some\nsubstitute item at $5, the proxy could reason that in no\ncircumstance will it be useful to acquire an option on the\nsecond item.\nWe formulate a more sophisticated bidding strategy along\nthese lines. Let \u0398t be the set of all options a proxy for bidder\ni already possesses at time t. Let \u03b8t \u2286 \u0398t, be a subset of\nthose options, the sum of whose exercise prices are \u03c0(\u03b8t),\nand the goods corresponding to those options being \u03b3(\u03b8t).\nLet \u03a0(\u03b8t) = \u02c6vi(\u03b3(\u03b8t)) \u2212 \u03c0(\u03b8t) be the (reported) available\nsurplus associated with a set of options. Let \u03b8\u2217\nt be the set\nof options currently held that would maximize the buyer\"s\nsurplus; i.e., \u03b8\u2217\nt = argmax\u03b8t\u2286\u0398t\n\u03a0(\u03b8t).\nLet the maximal willingness to pay for an item k represent\na price above which the agent knows it would never exercise\nan option on the item given the current options held. This\ncan be computed as follows:\nbidt\ni(k) = max\nL\n[0, min[\u02c6vi(L + k) \u2212 \u03a0(\u03b8\u2217\nt ), \u02c6vi(L + k) \u2212 \u02c6vi(L)]]\n(3)\nwhere \u02c6vi(L+k)\u2212\u03a0(\u03b8\u2217\nt ) considers surplus already held, \u02c6vi(L+\nk)\u2212\u02c6vi(L) considers the marginal value of a good, and taking\nthe max[0, .] considers the overall use of pursuing the good.\nHowever, and somewhat counter intuitively, we are not\nable to implement this bidding scheme without forfeiting\ntruthfulness. The \u03a0(\u03b8\u2217\nt ) term in Equation 3 (i.e., the amount\nof guaranteed surplus bidder i has already obtained) can be\ninfluenced by proxy j\"s bid. Therefore, bidder j may have\nthe incentive to misrepresent her valuation to her proxy if\nshe believes doing so will cause i to bid differently in the\nfuture in a manner beneficial to j. Consider the following\nexample where the proxy scheme is refined to bid the\nmaximum willingness to pay.\nExample 3. Alice values either one ton of Sand or one\nton of Stone for $2,000. Bob values either one ton of Sand\nor one ton of Stone for $1,500. All bidders have a patience\nmaximum bids while eBay winners have true values much\ngreater than their observed maximum bids then downward\nbias is introduced in the efficiency calculation at present.\n22\nThe increase in eBay winner surplus between Tables 3 and\n4 is to be expected as the \u03b1 scaling strictly increases the\nestimated value of the eBay winners while holding the prices\nat which they won constant.\nof 2 days. On day one, a Sand auction is held, where Alice\"s\nproxy bids $2,000 and Bob\"s bids $1,500. Alice\"s proxy wins\nan option to purchase Sand for $1,500. On day two, a Stone\nauction is held, where Alice\"s proxy bids $1,500 [as she has\nalready obtained a guaranteed $500 of surplus from winning\na Sand option, and so reduces her Stone bid by this amount],\nand Bob\"s bids $1,500. Either Alice\"s proxy or Bob\"s proxy\nwill win the Stone option. At the end of the second day,\nAlice\"s proxy holds an option with an exercise price of $1,500\nto obtain a good valued for $2,000, and so obtains $500 in\nsurplus.\nNow, consider what would have happened had Alice\ndeclared that she valued only Stone.\nExample 4. Alice declares valuing only Stone for $2,000.\nBob values either one ton of Sand or one ton of Stone for\n$1,500. All bidders have a patience of 2 days. On day one, a\nSand auction is held, where Bob\"s proxy bids $1,500. Bob\"s\nproxy wins an option to purchase Sand for $0. On day two,\na Stone auction is held, where Alice\"s proxy bids $2,000, and\nBob\"s bids $0 [as he has already obtained a guaranteed $1,500\nof surplus from winning a Sand option, and so reduces his\nStone bid by this amount]. Alice\"s proxy wins the Stone\noption for $0. At the end of the second day, Alice\"s proxy\nholds an option with an exercise price of $0 to obtain a good\nvalued for $2,000, and so obtains $2,000 in surplus.\nBy misrepresenting her valuation (i.e., excluding her value\nof Sand), Alice was able to secure higher surplus by guiding\nBob\"s bid for Stone to $0. An area of immediate further\nwork by the authors is to develop a more sophisticated proxy\nagent that can allow for bidding of maximum willingness to\npay (Equation 3) while maintaining truthfulness.\nAn additional, practical, concern with our proxy scheme\nis that we assume an available, trusted, and well understood\nmethod to characterize goods (and presumably the quality\nof goods). We envision this happening in practice by\nsellers defining a classification for their item upon entering the\nmarket, for instance via a UPC code. Just as in eBay, this\nwould allow an opportunity for sellers to improve revenue by\noverstating the quality of their item (new vs. like new),\nand raises the issue of how well a reputation scheme could\naddress this.\n7. CONCLUSIONS\nWe introduced a new sales channel, consisting of an\noptionsbased and proxied auction protocol, to address the\nsequential auction problem that exists when bidders face\nmultiple auctions for substitutes and complements goods. Our\nscheme provides bidders with a simple, dominant and\ntruthful bidding strategy even though the market remains open\nand dynamic.\nIn addition to exploring more sophisticated proxies that\nbid in terms of maximum willingness to pay, future work\nshould aim to better model seller incentives and resolve the\nstrategic problems facing sellers. For instance, does the\noptions scheme change seller incentives from what they\ncurrently are on eBay?\nAcknowledgments\nWe would like to thank Pai-Ling Yin. Helpful comments\nhave been received from William Simpson, attendees at\nHar188\nvard University\"s EconCS and ITM seminars, and\nanonymous reviewers. Thank you to Aaron L. Roth and\nKangXing Jin for technical support. All errors and omissions\nremain our own.\n8. REFERENCES\n[1] P. Anthony and N. R. Jennings. Developing a bidding\nagent for multiple heterogeneous auctions. ACM\nTrans. On Internet Technology, 2003.\n[2] R. Bapna, P. Goes, A. Gupta, and Y. Jin. User\nheterogeneity and its impact on electronic auction\nmarket design: An empirical exploration. MIS\nQuarterly, 28(1):21-43, 2004.\n[3] D. Bertsimas, J. Hawkins, and G. Perakis. Optimal\nbidding in on-line auctions. Working Paper, 2002.\n[4] C. Boutilier, M. Goldszmidt, and B. Sabata.\nSequential auctions for the allocation of resources with\ncomplementarities. In Proc. 16th International Joint\nConference on Artificial Intelligence (IJCAI-99),\npages 527-534, 1999.\n[5] A. Byde, C. Preist, and N. R. Jennings. 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Working Paper, University of\nChicago, 2005.\n189", "keywords": "business-to-consumer auction;empirical analysis;automated trading agent;electronic marketplace;computer simulation;market effect;option;trading opportunity;options-based extension;ebay;sequential auction problem;bidding strategy;strategic behavior;commoditized market;proxy-bidding system;multiple auction;proxy bid;online auction"}
{"name": "train_J-40", "title": "Networks Preserving Evolutionary Equilibria and the Power of Randomization", "abstract": "We study a natural extension of classical evolutionary game theory to a setting in which pairwise interactions are restricted to the edges of an undirected graph or network. We generalize the definition of an evolutionary stable strategy (ESS), and show a pair of complementary results that exhibit the power of randomization in our setting: subject to degree or edge density conditions, the classical ESS of any game are preserved when the graph is chosen randomly and the mutation set is chosen adversarially, or when the graph is chosen adversarially and the mutation set is chosen randomly. We examine natural strengthenings of our generalized ESS definition, and show that similarly strong results are not possible for them.", "fulltext": "1. INTRODUCTION\nIn this paper, we introduce and examine a natural\nextension of classical evolutionary game theory (EGT) to a setting\nin which pairwise interactions are restricted to the edges of\nan undirected graph or network. This extension generalizes\nthe classical setting, in which all pairs of organisms in an\ninfinite population are equally likely to interact. The\nclassical setting can be viewed as the special case in which the\nunderlying network is a clique.\nThere are many obvious reasons why one would like to\nexamine more general graphs, the primary one being in that\nmany scenarios considered in evolutionary game theory, all\ninteractions are in fact not possible. For example,\ngeographical restrictions may limit interactions to physically\nproximate pairs of organisms. More generally, as evolutionary\ngame theory has become a plausible model not only for\nbiological interaction, but also economic and other kinds of\ninteraction in which certain dynamics are more imitative than\noptimizing (see [2, 16] and chapter 4 of [19]), the network\nconstraints may come from similarly more general sources.\nEvolutionary game theory on networks has been considered\nbefore, but not in the generality we will do so here (see\nSection 4).\nWe generalize the definition of an evolutionary stable\nstrategy (ESS) to networks, and show a pair of complementary\nresults that exhibit the power of randomization in our\nsetting: subject to degree or edge density conditions, the\nclassical ESS of any game are preserved when the graph is\nchosen randomly and the mutation set is chosen adversarially,\nor when the graph is chosen adversarially and the mutation\nset is chosen randomly. We examine natural strengthenings\nof our generalized ESS definition, and show that similarly\nstrong results are not possible for them.\nThe work described here is part of recent efforts\nexamining the relationship between graph topology or structure\nand properties of equilibrium outcomes. Previous works in\nthis line include studies of the relationship of topology to\nproperties of correlated equilibria in graphical games [11],\nand studies of price variation in graph-theoretic market\nexchange models [12]. More generally, this work contributes\nto the line of graph-theoretic models for game theory\ninvestigated in both computer science [13] and economics [10].\n2. CLASSICAL EGT\nThe fundamental concept of evolutionary game theory is\nthe evolutionarily stable strategy (ESS). Intuitively, an ESS\nis a strategy such that if all the members of a population\nadopt it, then no mutant strategy could invade the\npopulation [17]. To make this more precise, we describe the basic\nmodel of evolutionary game theory, in which the notion of\nan ESS resides.\nThe standard model of evolutionary game theory\nconsiders an infinite population of organisms, each of which plays\na strategy in a fixed, 2-player, symmetric game. The game\nis defined by a fitness function F. All pairs of members of\nthe infinite population are equally likely to interact with one\nanother. If two organisms interact, one playing strategy s\n200\nand the other playing strategy t, the s-player earns a fitness\nof F(s|t) while the t-player earns a fitness of F(t|s).\nIn this infinite population of organisms, suppose there is a\n1 \u2212 fraction who play strategy s, and call these organisms\nincumbents; and suppose there is an fraction who play t,\nand call these organisms mutants. Assume two organisms\nare chosen uniformly at random to play each other. The\nstrategy s is an ESS if the expected fitness of an\norganism playing s is higher than that of an organism playing t,\nfor all t = s and all sufficiently small . Since an\nincumbent will meet another incumbent with probability 1 \u2212\nand it will meet a mutant with probability , we can\ncalculate the expected fitness of an incumbent, which is simply\n(1 \u2212 )F(s|s) + F(s|t). Similarly, the expected fitness of\na mutant is (1 \u2212 )F(t|s) + F(t|t). Thus we come to the\nformal definition of an ESS [19].\nDefinition 2.1. A strategy s is an evolutionarily stable\nstrategy (ESS) for the 2-player, symmetric game given by\nfitness function F, if for every strategy t = s, there exists\nan t such that for all 0 < < t, (1 \u2212 )F(s|s) + F(s|t) >\n(1 \u2212 )F(t|s) + F(t|t).\nA consequence of this definition is that for s to be an ESS,\nit must be the case that F(s|s) \u2265 F(t|s), for all strategies\nt. This inequality means that s must be a best response\nto itself, and thus any ESS strategy s must also be a Nash\nequilibrium. In general the notion of ESS is more\nrestrictive than Nash equilibrium, and not all 2-player, symmetric\ngames have an ESS.\nIn this paper our interest is to examine what kinds of\nnetwork structure preserve the ESS strategies for those games\nthat do have a standard ESS. First we must of course\ngeneralize the definition of ESS to a network setting.\n3. EGT ON GRAPHS\nIn our setting, we will no longer assume that two\norganisms are chosen uniformly at random to interact. Instead,\nwe assume that organisms interact only with those in their\nlocal neighborhood, as defined by an undirected graph or\nnetwork. As in the classical setting (which can be viewed\nas the special case of the complete network or clique), we\nshall assume an infinite population, by which we mean we\nexamine limiting behavior in a family of graphs of increasing\nsize.\nBefore giving formal definitions, some comments are in\norder on what to expect in moving from the classical to the\ngraph-theoretic setting. In the classical (complete graph)\nsetting, there exist many symmetries that may be broken in\nmoving to the the network setting, at both the group and\nindividual level. Indeed, such asymmetries are the primary\ninterest in examining a graph-theoretic generalization.\nFor example, at the group level, in the standard ESS\ndefinition, one need not discuss any particular set of mutants of\npopulation fraction . Since all organisms are equally likely\nto interact, the survival or fate of any specific mutant set is\nidentical to that of any other. In the network setting, this\nmay not be true: some mutant sets may be better able to\nsurvive than others due to the specific topologies of their\ninteractions in the network. For instance, foreshadowing some\nof our analysis, if s is an ESS but F(t|t) is much larger than\nF(s|s) and F(s|t), a mutant set with a great deal of\ninternal interaction (that is, edges between mutants) may be\nable to survive, whereas one without this may suffer. At\nthe level of individuals, in the classical setting, the assertion\nthat one mutant dies implies that all mutants die, again by\nsymmetry. In the network setting, individual fates may\ndiffer within a group all playing a common strategy. These\nobservations imply that in examining ESS on networks we\nface definitional choices that were obscured in the classical\nmodel.\nIf G is a graph representing the allowed pairwise\ninteractions between organisms (vertices), and u is a vertex of G\nplaying strategy su, then the fitness of u is given by\nF(u) =\nP\nv\u2208\u0393(u) F(su|sv)\n|\u0393(u)|\n.\nHere sv is the strategy being played by the neighbor v, and\n\u0393(u) = {v \u2208 V : (u, v) \u2208 E}. One can view the fitness of\nu as the average fitness u would obtain if it played each if\nits neighbors, or the expected fitness u would obtain if it\nwere assigned to play one of its neighbors chosen uniformly\nat random.\nClassical evolutionary game theory examines an infinite,\nsymmetric population. Graphs or networks are inherently\nfinite objects, and we are specifically interested in their\nasymmetries, as discussed above. Thus all of our definitions shall\nrevolve around an infinite family G = {Gn}\u221e\nn=0 of finite\ngraphs Gn over n vertices, but we shall examine asymptotic\n(large n) properties of such families.\nWe first give a definition for a family of mutant vertex\nsets in such an infinite graph family to contract.\nDefinition 3.1. Let G = {Gn}\u221e\nn=0 be an infinite family\nof graphs, where Gn has n vertices. Let M = {Mn}\u221e\nn=0\nbe any family of subsets of vertices of the Gn such that\n|Mn| \u2265 n for some constant > 0. Suppose all the vertices\nof Mn play a common (mutant) strategy t, and suppose the\nremaining vertices in Gn play a common (incumbent)\nstrategy s. We say that Mn contracts if for sufficiently large n,\nfor all but o(n) of the j \u2208 Mn, j has an incumbent neighbor\ni such that F(j) < F(i).\nA reasonable alternative would be to ask that the\ncondition above hold for all mutants rather than all but o(n).\nNote also that we only require that a mutant have one\nincumbent neighbor of higher fitness in order to die; one might\nconsidering requiring more. In Sections 6.1 and 6.2 we\nconsider these stronger conditions and demonstrate that our\nresults can no longer hold.\nIn order to properly define an ESS for an infinite family of\nfinite graphs in a way that recovers the classical definition\nasymptotically in the case of the family of complete graphs,\nwe first must give a definition that restricts attention to\nfamilies of mutant vertices that are smaller than some invasion\nthreshold n, yet remain some constant fraction of the\npopulation. This prevents invasions that survive merely by\nconstituting a vanishing fraction of the population.\nDefinition 3.2. Let > 0, and let G = {Gn}\u221e\nn=0 be\nan infinite family of graphs, where Gn has n vertices. Let\nM = {Mn}\u221e\nn=0 be any family of (mutant) vertices in Gn.\nWe say that M is -linear if there exists an , > > 0,\nsuch that for all sufficiently large n, n > |Mn| > n.\nWe can now give our definition for a strategy to be\nevolutionarily stable when employed by organisms interacting\nwith their neighborhood in a graph.\n201\nDefinition 3.3. Let G = {Gn}\u221e\nn=0 be an infinite family\nof graphs, where Gn has n vertices. Let F be any 2-player,\nsymmetric game for which s is a strategy. We say that s is\nan ESS with respect to F and G if for all mutant strategies\nt = s, there exists an t > 0 such that for any t-linear\nfamily of mutant vertices M = {Mn}\u221e\nn=0 all playing t, for n\nsufficiently large, Mn contracts.\nThus, to violate the ESS property for G, one must witness\na family of mutations M in which each Mn is an arbitrarily\nsmall but nonzero constant fraction of the population of Gn,\nbut does not contract (i.e. every mutant set has a subset of\nlinear size that survives all of its incumbent interactions).\nIn Section A.1 we show that the definition given coincides\nwith the classical one in the case where G is the family of\ncomplete graphs, in the limit of large n. We note that even\nin the classical model, small sets of mutants were allowed to\nhave greater fitness than the incumbents, as long as the size\nof the set was o(n) [18].\nIn the definition above there are three parameters: the\ngame F, the graph family G and the mutation family M.\nOur main results will hold for any 2-player, symmetric game\nF. We will also study two rather general settings for G and\nM: that in which G is a family of random graphs and M is\narbitrary, and that in which G is nearly arbitrary and M is\nrandomly chosen. In both cases, we will see that, subject to\nconditions on degree or edge density (essentially forcing\nconnectivity of G but not much more), for any 2-player,\nsymmetric game, the ESS of the classical settings, and only those\nstrategies, are always preserved. Thus a common theme of\nthese results is the power of randomization: as long as either\nthe network itself is chosen randomly, or the mutation set is\nchosen randomly, classical ESS are preserved.\n4. RELATED WORK\nThere has been previous work that analyzes which\nstrategies are resilient to mutant invasions with respect to various\ntypes of graphs. What sets our work apart is that the model\nwe consider encompasses a significantly more general class of\ngames and graph topologies. We will briefly survey this\nliterature and point out the differences in the previous models\nand ours.\nIn [8], [3], and [4], the authors consider specific families\nof graphs, such as cycles and lattices, where players play\nspecific games, such as 2 \u00d7 2-games or k \u00d7 k-coordination\ngames. In these papers the authors specify a simple, local\ndynamic for players to improve their payoffs by changing\nstrategies, and analyze what type of strategies will grow to\ndominate the population. The model we propose is more\ngeneral than both of these, as it encompasses a larger class\nof graphs as well as a richer set of games.\nAlso related to our work is that of [14], where the authors\npropose two models. The first assumes organisms interact\naccording to a weighted, undirected graph. However, the\nfitness of each organism is simply assigned and does not\ndepend on the actions of each organism\"s neighborhood. The\nsecond model has organisms arranged around a directed\ncycle, where neighbors play a 2 \u00d7 2-game. With probability\nproportional to its fitness, an organism is chosen to\nreproduce by placing a replica of itself in its neighbors position,\nthereby killing the neighbor. We consider more general\ngames than the first model and more general graphs than\nthe second.\nFinally, the works most closely related to ours are [7], [15],\nand [6]. The authors consider 2-action, coordination games\nplayed by players in a general undirected graph. In these\nthree works, the authors specify a dynamic for a strategy to\nreproduce, and analyze properties of the graph that allow a\nstrategy to overrun the population. Here again, one can see\nthat our model is more general than these, as it allows for\norganisms to play any 2-player, symmetric game.\n5. NETWORKS PRESERVING ESS\nWe now proceed to state and prove two complementary\nresults in the network ESS model defined in Section 3. First,\nwe consider a setting where the graphs are generated via the\nGn,p model of Erd\u02ddos and R\u00b4enyi [5]. In this model, every\npair of vertices are joined by an edge independently and\nwith probability p (where p may depend on n). The mutant\nset, however, will be constructed adversarially (subject to\nthe linear size constraint given by Definition 3.3). For these\nsettings, we show that for any 2-player, symmetric game, s\nis a classical ESS of that game, if and only if s is an ESS\nfor {Gn,p}\u221e\nn=0, where p = \u2126(1/nc\n) and 0 \u2264 c < 1, and any\nmutant family {Mn}\u221e\nn=0, where each Mn has linear size. We\nnote that under these settings, if we let c = 1 \u2212 \u03b3 for small\n\u03b3 > 0, the expected number of edges in Gn is n1+\u03b3\nor larger\n- that is, just superlinear in the number of vertices and\npotentially far smaller than O(n2\n). It is easy to convince\noneself that once the graphs have only a linear number of\nedges, we are flirting with disconnectedness, and there may\nsimply be large mutant sets that can survive in isolation due\nto the lack of any incumbent interactions in certain games.\nThus in some sense we examine the minimum plausible edge\ndensity.\nThe second result is a kind of dual to the first, considering\na setting where the graphs are chosen arbitrarily (subject to\nconditions) but the mutant sets are chosen randomly. It\nstates that for any 2-player, symmetric game, s is a\nclassical ESS for that game, if and only if s is an ESS for any\n{Gn = (Vn, En)}\u221e\nn=0 in which for all v \u2208 Vn, deg(v) = \u2126(n\u03b3\n)\n(for any constant \u03b3 > 0), and a family of mutant sets\n{Mn}\u221e\nn=0, that is chosen randomly (that is, in which each\norganism is labeled a mutant with constant probability > 0).\nThus, in this setting we again find that classical ESS are\npreserved subject to edge density restrictions. Since the degree\nassumption is somewhat strong, we also prove another result\nwhich only assumes that |En| \u2265 n1+\u03b3\n, and shows that there\nmust exist at least 1 mutant with an incumbent neighbor of\nhigher fitness (as opposed to showing that all but o(n)\nmutants have an incumbent neighbor of higher fitness). As will\nbe discussed, this rules out stationary mutant invasions.\n5.1 Random Graphs, Adversarial Mutations\nNow we state and prove a theorem which shows that if s\nis a classical ESS, then s will be an ESS for random graphs,\nwhere a linear sized set of mutants is chosen by an adversary.\nTheorem 5.1. Let F be any 2-player, symmetric game,\nand suppose s is a classical ESS of F. Let the infinite\ngraph family {Gn}\u221e\nn=0 be drawn according to Gn,p, where\np = \u2126(1/nc\n) and 0 \u2264 c < 1. Then with probability 1, s is\nan ESS.\nThe main idea of the proof is to divide mutants into 2\ncategories, those with normal fitness and those with\nab202\nnormal fitness. First, we show all but o(n) of the\npopulation (incumbent or mutant) have an incumbent neighbor of\nnormal fitness. This will imply that all but o(n) of the\nmutants of normal fitness have an incumbent neighbor of higher\nfitness. The vehicle for proving this is Theorem 2.15 of [5],\nwhich gives an upper bound on the number of vertices not\nconnected to a sufficiently large set. This theorem assumes\nthat the size of this large set is known with equality, which\nnecessitates the union bound argument below. Secondly, we\nshow that there can be at most o(n) mutants with abnormal\nfitness. Since there are so few of them, even if none of them\nhave an incumbent neighbor of higher fitness, s will still be\nan ESS with respect to F and G.\nProof. (Sketch) Let t = s be the mutant strategy. Since\ns is a classical ESS, there exists an t such that (1\u2212 )F(s|s)+\nF(s|t) > (1 \u2212 )F(t|s) + F(t|t), for all 0 < < t. Let M\nbe any mutant family that is t-linear. Thus for any fixed\nvalue of n that is sufficiently large, there exists an such\nthat |Mn| = n and t > > 0. Also, let In = Vn \\ Mn and\nlet I \u2286 In be the set of incumbents that have fitness in the\nrange (1 \u00b1 \u03c4)[(1 \u2212 )F(s|s) + F(s|t)] for some constant \u03c4,\n0 < \u03c4 < 1/6. Lemma 5.1 below shows (1 \u2212 )n \u2265 |I | \u2265\n(1 \u2212 )n \u2212 24 log n\n\u03c42p\n. Finally, let\nTI = {x \u2208 V \\ I : \u0393(x) \u2229 I = \u2205}.\n(For the sake of clarity we suppress the subscript n on the\nsets I and T.) The union bound gives us\nPr(|TI | \u2265 \u03b4n) \u2264\n(1\u2212 )n\nX\ni=(1\u2212 )n\u2212 24 log n\n\u03c42p\nPr(|TI | \u2265 \u03b4n and |I | = i) (1)\nLetting \u03b4 = n\u2212\u03b3\nfor some \u03b3 > 0 gives \u03b4n = o(n). We will\napply Theorem 2.15 of [5] to the summand on the right hand\nside of Equation 1. If we let \u03b3 = (1\u2212c)/2, and combine this\nwith the fact that 0 \u2264 c < 1, all of the requirements of this\ntheorem will be satisfied (details omitted). Now when we\napply this theorem to Equation 1, we get\nPr(|TI | \u2265 \u03b4n) \u2264\n(1\u2212 )n\nX\ni=(1\u2212 )n\u2212 24 log n\n\u03c42p\nexp\n\u201e\n\u2212\n1\n6\nC\u03b4n\n\u00ab\n(2)\n= o(1)\nThis is because equation 2 has only 24 log n\n\u03c42p\nterms, and\nTheorem 2.15 of [5] gives us that C \u2265 (1 \u2212 )n1\u2212c\n\u2212 24 log n\n\u03c42 .\nThus we have shown, with probability tending to 1 as n \u2192\n\u221e, at most o(n) individuals are not attached to an\nincumbent which has fitness in the range (1 \u00b1 \u03c4)[(1 \u2212 )F(s|s) +\nF(s|t)]. This implies that the number of mutants of\napproximately normal fitness, not attached to an incumbent\nof approximately normal fitness, is also o(n).\nNow those mutants of approximately normal fitness that\nare attached to an incumbent of approximately normal\nfitness have fitness in the range (1\u00b1\u03c4)[(1\u2212 )F(t|s)+ F(t|t)].\nThe incumbents that they are attached to have fitness in the\nrange (1\u00b1\u03c4)[(1\u2212 )F(s|s)+ F(s|t)]. Since s is an ESS of F,\nwe know (1\u2212 )F(s|s)+ F(s|t) > (1\u2212 )F(t|s)+ F(t|t), thus\nif we choose \u03c4 small enough, we can ensure that all but o(n)\nmutants of normal fitness have a neighboring incumbent of\nhigher fitness.\nFinally by Lemma 5.1, we know there are at most o(n)\nmutants of abnormal fitness. So even if all of them are more fit\nthan their respective incumbent neighbors, we have shown\nall but o(n) of the mutants have an incumbent neighbor of\nhigher fitness.\nWe now state and prove the lemma used in the proof\nabove.\nLemma 5.1. For almost every graph Gn,p with (1 \u2212 )n\nincumbents, all but 24 log n\n\u03b42p\nincumbents have fitness in the\nrange (1\u00b1\u03b4)[(1\u2212 )F(s|s)+ F(s|t)], where p = \u2126(1/nc\n) and\n, \u03b4 and c are constants satisfying 0 < < 1, 0 < \u03b4 < 1/6,\n0 \u2264 c < 1. Similarly, under the same assumptions, all\nbut 24 log n\n\u03b42p\nmutants have fitness in the range (1 \u00b1 \u03b4)[(1 \u2212\n)F(t|s) + F(t|t)].\nProof. We define the mutant degree of a vertex to be\nthe number of mutant neighbors of that vertex, and\nincumbent degree analogously. Observe that the only way for\nan incumbent to have fitness far from its expected value of\n(1\u2212 )F(s|s)+ F(s|t) is if it has a fraction of mutant\nneighbors either much higher or much lower than . Theorem\n2.14 of [5] gives us a bound on the number of such\nincumbents. It states that the number of incumbents with mutant\ndegree outside the range (1 \u00b1 \u03b4)p|M| is at most 12 log n\n\u03b42p\n. By\nthe same theorem, the number of incumbents with\nincumbent degree outside the range (1 \u00b1 \u03b4)p|I| is at most 12 log n\n\u03b42p\n.\nFrom the linearity of fitness as a function of the fraction\nof mutant or incumbent neighbors, one can show that for\nthose incumbents with mutant and incumbent degree in the\nexpected range, their fitness is within a constant factor of\n(1 \u2212 )F(s|s) + F(s|t), where that constant goes to 1 as n\ntends to infinity and \u03b4 tends to 0. The proof for the mutant\ncase is analogous.\nWe note that if in the statement of Theorem 5.1 we let\nc = 0, then p = 1. This, in turn, makes G = {Kn}\u221e\nn=0,\nwhere Kn is a clique of n vertices. Then for any Kn all\nof the incumbents will have identical fitness and all of the\nmutants will have identical fitness. Furthermore, since s was\nan ESS for G, the incumbent fitness will be higher than the\nmutant fitness. Finally, one can show that as n \u2192 \u221e, the\nincumbent fitness converges to (1 \u2212 )F(s|s) + F(s|t), and\nthe mutant fitness converges to (1 \u2212 )F(t|s) + F(t|t). In\nother words, s must be a classical ESS, providing a converse\nto Theorem 5.1. We rigorously present this argument in\nSection A.1.\n5.2 Adversarial Graphs, Random Mutations\nWe now move on to our second main result. Here we show\nthat if the graph family, rather than being chosen randomly,\nis arbitrary subject to a minimum degree requirement, and\nthe mutation sets are randomly chosen, classical ESS are\nagain preserved. A modified notion of ESS allows us to\nconsiderably weaken the degree requirement to a minimum\nedge density requirement.\nTheorem 5.2. Let G = {Gn = (Vn, En)}\u221e\nn=0 be an\ninfinite family of graphs in which for all v \u2208 Vn, deg(v) = \u2126(n\u03b3\n)\n(for any constant \u03b3 > 0). Let F be any 2-player, symmetric\ngame, and suppose s is a classical ESS of F. Let t be any\nmutant strategy, and let the mutant family M = {Mn}\u221e\nn=0 be\nchosen randomly by labeling each vertex a mutant with\nconstant probability , where t > > 0. Then with probability\n1, s is an ESS with respect to F, G and M.\n203\nProof. Let t = s be the mutant strategy and let X be\nthe event that every incumbent has fitness within the range\n(1 \u00b1 \u03c4)[(1 \u2212 )F(s|s) + F(s|t)], for some constant \u03c4 > 0 to\nbe specified later. Similarly, let Y be the event that every\nmutant has fitness within the range (1 \u00b1 \u03c4)[(1 \u2212 )F(t|s) +\nF(t|t)]. Since Pr(X \u2229 Y ) = 1 \u2212 Pr(\u00acX \u222a \u00acY ), we proceed\nby showing Pr(\u00acX \u222a \u00acY ) = o(1).\n\u00acX is the event that there exists an incumbent with fitness\noutside the range (1\u00b1\u03c4)[(1\u2212 )F(s|s)+ F(s|t)]. If degM (v)\ndenotes the number of mutant neighbors of v, similarly,\ndegI (v) denotes the number of incumbent neighbors of v,\nthen an incumbent i has fitness\ndegI (i)\ndeg(i)\nF(s|s)+\ndegM (i)\ndeg(i)\nF(s|t).\nSince F(s|s) and F(s|t) are fixed quantities, the only\nvariation in an incumbents fitness can come from variation in the\nterms degI (i)\ndeg(i)\nand degM (i)\ndeg(i)\n. One can use the Chernoff bound\nfollowed by the union bound to show that for any incumbent\ni,\nPr(F(i) /\u2208 (1 \u00b1 \u03c4)[(1 \u2212 )F(s|s) + F(s|t)])\n< 4 exp\n\u201e\n\u2212\ndeg(i)\u03c42\n3\n\u00ab\n.\nNext one can use the union bound again to bound the\nprobability of the event \u00acX,\nPr(\u00acX) \u2264 4n exp\n\u201e\n\u2212\ndi\u03c42\n3\n\u00ab\nwhere di = mini\u2208V \\M deg(i), 0 < \u2264 1/2. An analogous\nargument can be made to show Pr(\u00acY ) < 4n exp(\u2212\ndj \u03c42\n3\n),\nwhere dj = minj\u2208M deg(j) and 0 < \u2264 1/2. Thus, by the\nunion bound,\nPr(\u00acX \u222a \u00acY ) < 8n exp\n\u201e\n\u2212\nd\u03c42\n3\n\u00ab\nwhere d = minv\u2208V deg(v), 0 < \u2264 1/2. Since deg(v) =\n\u2126(n\u03b3\n), for all v \u2208 V , and , \u03c4 and \u03b3 are all constants greater\nthan 0,\nlim\nn\u2192\u221e\n8n\nexp ( d\u03c42/3)\n= 0,\nso Pr(\u00acX\u222a\u00acY ) = o(1). Thus, we can choose \u03c4 small enough\nsuch that (1 + \u03c4)[(1 \u2212 )F(t|s) + F(t|t)] < (1 \u2212 \u03c4)[(1 \u2212\n)F(s|s)+ F(s|t)], and then choose n large enough such that\nwith probability 1 \u2212 o(1), every incumbent will have fitness\nin the range (1\u00b1\u03c4)[(1\u2212 )F(s|s)+F(s|t)], and every mutant\nwill have fitness in the range (1 \u00b1 \u03c4)[(1 \u2212 )F(t|s) + F(t|t)].\nSo with high probability, every incumbent will have a higher\nfitness than every mutant.\nBy arguments similar to those following the proof of\nTheorem 5.1, if we let G = {Kn}\u221e\nn=0, each incumbent will have\nthe same fitness and each mutant will have the same fitness.\nFurthermore, since s is an ESS for G, the incumbent fitness\nmust be higher than the mutant fitness. Here again, one\nhas to show show that as n \u2192 \u221e, the incumbent fitness\nconverges to (1 \u2212 )F(s|s) + F(s|t), and the mutant fitness\nconverges to (1 \u2212 )F(t|s) + F(t|t). Observe that the exact\nfraction mutants of Vn is now a random variable. So to prove\nthis convergence we use an argument similar to one that is\nused to prove that sequence of random variables that\nconverges in probability also converges in distribution (details\nomitted). This in turn establishes that s must be a classical\nESS, and we thus obtain a converse to Theorem 5.2. This\nargument is made rigorous in Section A.2.\nThe assumption on the degree of each vertex of\nTheorem 5.2 is rather strong. The following theorem relaxes\nthis requirement and only necessitates that every graph have\nn1+\u03b3\nedges, for some constant \u03b3 > 0, in which case it shows\nthere will alway be at least 1 mutant with an incumbent\nneighbor of higher fitness. A strategy that is an ESS in\nthis weakened sense will essentially rule out stable, static\nsets of mutant invasions, but not more complex invasions.\nAn example of more complex invasions are mutant sets that\nsurvive, but only by perpetually migrating through the\ngraph under some natural evolutionary dynamics, akin to\ngliders in the well-known Game of Life [1].\nTheorem 5.3. Let F be any game, and let s be a classical\nESS of F, and let t = s be a mutant strategy. For any graph\nfamily G = {Gn = (Vn, En)}\u221e\nn=0 in which |En| \u2265 n1+\u03b3\n(for\nany constant \u03b3 > 0), and any mutant family M = {Mn}\u221e\nn=0\nwhich is determined by labeling each vertex a mutant with\nprobability , where t > > 0, the probability that there\nexists a mutant with an incumbent neighbor of higher fitness\napproaches 1 as n \u2192 \u221e.\nProof. (Sketch) The main idea behind the proof is to\nshow that with high probability, over only the choice of\nmutants, there will be an incumbent-mutant edge in which both\nvertices have high degree. If their degree is high enough, we\ncan show that close to an fraction of their neighbors are\nmutants, and thus their fitnesses are very close to what we\nexpect them to be in the classical case. Since s is an ESS,\nthe fitness of the incumbent will be higher than the mutant.\nWe call an edge (i, j) \u2208 En a g(n)-barbell if deg(i) \u2265 g(n)\nand deg(j) \u2265 g(n). Suppose Gn has at most h(n) edges that\nare g(n)-barbells. This means there are at least |En| \u2212 h(n)\nedges in which at least one vertex has degree at most g(n).\nWe call these vertices light vertices. Let (n) be the number\nof light vertices in Gn. Observe that |En|\u2212h(n) \u2264 (n)g(n).\nThis is because each light vertex is incident on at most g(n)\nedges. This gives us that\n|En| \u2264 h(n) + (n)g(n) \u2264 h(n) + ng(n).\nSo if we choose h(n) and g(n) such that h(n) + ng(n) =\no(n1+\u03b3\n), then |En| = o(n1+\u03b3\n). This contradicts the\nassumption that |En| = \u2126(n1+\u03b3\n). Thus, subject to the above\nconstraint on h(n) and g(n), Gn must contain at least h(n)\nedges that are g(n)-barbells.\nNow let Hn denote the subgraph induced by the barbell\nedges of Gn. Note that regardless of the structure of Gn,\nthere is no reason that Hn should be connected. Thus, let\nm be the number of connected components of Hn, and let\nc1, c2, . . . , cm be the number of vertices in each of these\nconnected components. Note that since Hn is an edge-induced\nsubgraph we have ck \u2265 2 for all components k. Let us choose\nthe mutant set by first flipping the vertices in Hn only. We\nnow show that the probability, with respect to the random\nmutant set, that none of the components of Hn have an\nincumbent-mutant edge is exponentially small in n. Let An\nbe the event that every component of Hn contains only\nmutants or only incumbents. Then algebraic manipulations can\nestablish that\nPr[An] = \u03a0m\nk=1( ck\n+ (1 \u2212 )ck\n)\n\u2264 (1 \u2212 )(1\u2212 \u03b22\n2\n)\nPm\nk=1 ck\n204\nwhere \u03b2 is a constant. Thus for sufficiently small the bound\ndecreases exponentially with\nPm\nk=1 ck. Furthermore, sincePm\nk=1\n`ck\n2\n\u00b4\n\u2265 h(n) (with equality achieved by making each\ncomponent a clique), one can show that\nPm\nk=1 ck \u2265\np\nh(n).\nThus, as long as h(n) \u2192 \u221e with n, the probability that all\ncomponents are uniformly labeled will go to 0.\nNow assuming that there exists a non-uniformly labeled\ncomponent, by construction that component contains an\nedge (i, j) where i is an incumbent and j is a mutant, that\nis a g(n)-barbell. We also assume that the h(n) vertices\nalready labeled have been done so arbitrarily, but that the\nremaining g(n) \u2212 h(n) vertices neighboring i and j are\nlabeled mutants independently with probability . Then via\na standard Chernoff bound argument, one can show that\nwith high probability, the fraction of mutants neighboring\ni and the fraction of mutants neighboring j is in the range\n(1 \u00b1 \u03c4)(g(n)\u2212h(n))\ng(n)\n. Similarly, one can show that the\nfraction of incumbents neighboring i and the fraction of mutants\nneighboring j is in the range 1 \u2212 (1 \u00b1 \u03c4)(g(n)\u2212h(n))\ng(n)\n.\nSince s is an ESS, there exists a \u03b6 > 0 such that (1 \u2212\n)F(s|s) + F(s|t) = (1 \u2212 )F(t|s) + F(t|t) + \u03b6. If we\nchoose g(n) = n\u03b3\n, and h(n) = o(g(n)), we can choose n\nlarge enough and \u03c4 small enough to force F(i) > F(j), as\ndesired.\n6. LIMITATIONS OF STRONGER MODELS\nIn this section we show that if one tried to strengthen\nthe model described in Section 3 in two natural ways, one\nwould not be able to prove results as strong as Theorems 5.1\nand 5.2, which hold for every 2-player, symmetric game.\n6.1 Stronger Contraction for the Mutant Set\nIn Section 3 we alluded to the fact that we made certain\ndesign decisions in arriving at Definitions 3.1, 3.2 and 3.3.\nOne such decision was to require that all but o(n) mutants\nhave incumbent neighbors of higher fitness. Instead, we\ncould have required that all mutants have an incumbent\nneighbor of higher fitness. The two theorems in this\nsubsection show that if one were to strengthen our notion of\ncontraction for the mutant set, given by Definition 3.1, in\nthis way, it would be impossible to prove theorems analogous\nto Theorems 5.1 and 5.3.\nRecall that Definition 3.1 gave the notion of contraction\nfor a linear sized subset of mutants. In what follows, we\nwill say an edge (i, j) contracts if i is an incumbent, j is a\nmutant, and F(i) > F(j). Also, recall that Theorem 5.1\nstated that if s is a classical ESS, then it is an ESS for\nrandom graphs with adversarial mutations. Next, we prove\nthat if we instead required every incumbent-mutant edge to\ncontract, this need not be the case.\nTheorem 6.1. Let F be a 2-player, symmetric game that\nhas a classical ESS s for which there exists a mutant\nstrategy t = s with F(t|t) > F(s|s) and F(t|t) > F(s|t). Let\nG = {Gn}\u221e\nn=0 be an infinite family of random graphs drawn\naccording to Gn,p, where p = \u2126(1/nc\n) for any constant\n0 \u2264 c < 1. Then with probability approaching 1 as n \u2192 \u221e,\nthere exists a mutant family M = {Mn}\u221e\nn=0, where tn >\n|Mn| > n and t, > 0, in which there is an edge that does\nnot contract.\nProof. (Sketch) With probability approaching 1 as n \u2192\n\u221e, there exists a vertex j where deg(j) is arbitrarily close\nto n. So label j mutant, label one of its neighbors\nincumbent, denoted i, and label the rest of j\"s neighborhood\nmutant. Also, label all of i\"s neighbors incumbent, with\nthe exception of j and j\"s neighbors (which were already\nlabeled mutant). In this setting, one can show that F(j)\nwill be arbitrarily close to F(t|t) and F(i) will be a convex\ncombination of F(s|s) and F(s|t), which are both strictly\nless than F(t|t).\nTheorem 5.3 stated that if s is a classical ESS, then for\ngraphs where |En| \u2265 n1+\u03b3\n, for some \u03b3 > 0, and where each\norganism is labeled a mutant with probability , one edge\nmust contract. Below we show that, for certain graphs and\ncertain games, there will always exist one edge that will not\ncontract.\nTheorem 6.2. Let F be a 2-player, symmetric game that\nhas a classical ESS s, such that there exists a mutant\nstrategy t = s where F(t|s) > F(s|t). There exists an infinite\nfamily of graphs {Gn = (Vn, En)}\u221e\nn=0, where |En| = \u0398(n2\n),\nsuch that for a mutant family M = {Mn}\u221e\nn=0, which is\ndetermined by labeling each vertex a mutant with probability\n> 0, the probability there exists an edge in En that does\nnot contract approaches 1 as n \u2192 \u221e.\nProof. (Sketch) Construct Gn as follows. Pick n/4\nvertices u1, u2, . . . , un/4 and add edges such that they from\na clique. Then, for each ui, i \u2208 [n/4] add edges (ui, vi),\n(vi, wi) and (wi, xi). With probability 1 as n \u2192 \u221e, there\nexists an i such that ui and wi are mutants and vi and xi\nare incumbents. Observe that F(vi) = F(xi) = F(s|t) and\nF(wi) = F(t|s).\n6.2 Stronger Contraction for Individuals\nThe model of Section 3 requires that for an edge (i, j) to\ncontract, the fitness of i must be greater than the fitness of j.\nOne way to strengthen this notion of contraction would be\nto require that the maximum fitness incumbent in the\nneighborhood of j be more fit than the maximum fitness mutant\nin the neighborhood of j. This models the idea that each\norganism is trying to take over each place in its\nneighborhood, but only the most fit organism in the neighborhood\nof a vertex gets the privilege of taking it. If we assume that\nwe adopt this notion of contraction for individual mutants,\nand require that all incumbent-mutant edges contract, we\nwill next show that Theorems 6.1 and 6.2 still hold, and\nthus it is still impossible to get results such as Theorems 5.1\nand 5.3 which hold for every 2-player, symmetric game.\nIn the proof of Theorem 6.1 we proved that F(i) is strictly\nless than F(j). Observe that maximum fitness mutant in\nthe neighborhood of j must have fitness at least F(j). Also\nobserve that there is only 1 incumbent in the neighborhood\nof j, namely i. So under this stronger notion of contraction,\nthe edge (i, j) will not contract.\nSimilarly, in the proof of Theorem 6.2, observe that the\nonly mutant in the neighborhood of wi is wi itself, which\nhas fitness F(t|s). Furthermore, the only incumbents in the\nneighborhood of wi are vi and xi, both of which have fitness\nF(s|t). By assumption, F(t|s) > F(s|t), thus, under this\nstronger notion of contraction, neither of the\nincumbentmutant edges, (vi, wi) and (xi, wi), will contract.\n7. REFERENCES\n[1] Elwyn R. Berlekamp, John Horton Conway, and\nRichard K. Guy. Winning Ways for Your\n205\nMathematical Plays, volume 4. AK Peters, Ltd, March\n2004.\n[2] Jonas Bj\u00a8ornerstedt and Karl H. Schlag. On the\nevolution of imitative behavior. Discussion Paper\nB-378, University of Bonn, 1996.\n[3] L. E. Blume. The statistical mechanics of strategic\ninteraction. Games and Economic Behavior,\n5:387-424, 1993.\n[4] L. E. Blume. The statistical mechanics of\nbest-response strategy revision. Games and Economic\nBehavior, 11(2):111-145, November 1995.\n[5] B. Bollob\u00b4as. Random Graphs. Cambridge University\nPress, 2001.\n[6] Michael Suk-Young Chwe. Communication and\ncoordination in social networks. Review of Economic\nStudies, 67:1-16, 2000.\n[7] Glenn Ellison. Learning, local interaction, and\ncoordination. Econometrica, 61(5):1047-1071, Sept.\n1993.\n[8] I. Eshel, L. Samuelson, and A. Shaked. Altruists,\negoists, and hooligans in a local interaction model.\nThe American Economic Review, 88(1), 1998.\n[9] Geoffrey R. Grimmett and David R. Stirzaker.\nProbability and Random Processes. Oxford University\nPress, 3rd edition, 2001.\n[10] M. Jackson. A survey of models of network formation:\nStability and efficiency. In Group Formation in\nEconomics; Networks, Clubs and Coalitions.\nCambridge University Press, 2004.\n[11] S. Kakade, M. Kearns, J. Langford, and L. Ortiz.\nCorrelated equilibria in graphical games. ACM\nConference on Electronic Commerce, 2003.\n[12] S. Kakade, M. Kearns, L. Ortiz, R. Pemantle, and\nS. Suri. Economic properties of social networks.\nNeural Information Processing Systems, 2004.\n[13] M. Kearns, M. Littman, and S. Singh. Graphical\nmodels for game theory. Conference on Uncertainty in\nArtificial Intelligence, pages 253-260, 2001.\n[14] E. Lieberman, C. Hauert, and M. A. Nowak.\nEvolutionary dynamics on graphs. Nature,\n433:312-316, 2005.\n[15] S. Morris. Contagion. Review of Economic Studies,\n67(1):57-78, 2000.\n[16] Karl H. Schlag. Why imitate and if so, how? Journal\nof Economic Theory, 78:130-156, 1998.\n[17] J. M. Smith. Evolution and the Theory of Games.\nCambridge University Press, 1982.\n[18] William L. Vickery. How to cheat against a simple\nmixed strategy ESS. Journal of Theoretical Biology,\n127:133-139, 1987.\n[19] J\u00a8orgen W. Weibull. Evolutionary Game Theory. The\nMIT Press, 1995.\nAPPENDIX\nA. GRAPHICAL AND CLASSICAL ESS\nIn this section we explore the conditions under which a\ngraphical ESS is also a classical ESS. To do so, we state and\nprove two theorems which provide converses to each of the\nmajor theorems in Section 3.\nA.1 Random Graphs, Adversarial Mutations\nTheorem 5.2 states that if s is a classical ESS and G =\n{Gn,p}, where p = \u2126(1/nc\n) and 0 \u2264 c < 1, then with\nprobability 1 as n \u2192 \u221e, s is an ESS with respect to G. Here we\nshow that if s is an ESS with respect to G, then s is a\nclassical ESS. In order to prove this theorem, we do not need the\nfull generality of s being an ESS for G when p = \u2126(1/nc\n)\nwhere 0 \u2264 c < 1. All we need is s to be an ESS for G when\np = 1. In this case there are no more probabilistic events\nin the theorem statement. Also, since p = 1 each graph in\nG is a clique, so if one incumbent has a higher fitness than\none mutant, then all incumbents have higher fitness than all\nmutants. This gives rise to the following theorem.\nTheorem A.1. Let F be any 2-player, symmetric game,\nand suppose s is a strategy for F and t = s is a mutant\nstrategy. Let G = {Kn}\u221e\nn=0. If, as n \u2192 \u221e, for any t-linear\nfamily of mutants M = {Mn}\u221e\nn=0, there exists an incumbent\ni and a mutant j such that F(i) > F(j), then s is a classical\nESS of F.\nThe proof of this theorem analyzes the limiting behavior\nof the mutant population as the size of the cliques in G tends\nto infinity. It also shows how the definition of ESS given in\nSection 5 recovers the classical definition of ESS.\nProof. Since each graph in G is a clique, every\nincumbent will have the same number of incumbent and mutant\nneighbors, and every mutant will have the same number of\nincumbent and mutant neighbors. Thus, all incumbents will\nhave identical fitness and all mutants will have identical\nfitness. Next, one can construct an t-linear mutant family\nM, where the fraction of mutants converges to for any ,\nwhere t > > 0. So for n large enough, the number of\nmutants in Kn will be arbitrarily close to n. Thus, any\nmutant subset of size n will result in all incumbents having\nfitness (1 \u2212 n\nn\u22121\n)F(s|s) + n\nn\u22121\nF(s|t), and all mutants\nhaving fitness (1 \u2212 n\u22121\nn\u22121\n)F(t|s) + n\u22121\nn\u22121\nF(t|t). Furthermore, by\nassumption the incumbent fitness must be higher than the\nmutant fitness. This implies,\nlim\nn\u2192\u221e\n\u201e\n(1 \u2212\nn\nn \u2212 1\n)F(s|s) +\nn\nn \u2212 1\nF(s|t) >\n(1 \u2212\nn \u2212 1\nn \u2212 1\n)F(t|s) +\nn \u2212 1\nn \u2212 1\nF(t|t)\n\u00ab\n= 1.\nThis implies, (1\u2212 )F(s|s)+ F(s|t) > (1\u2212 )F(t|s)+ F(t|t),\nfor all , where t > > 0.\nA.2 Adversarial Graphs, Random Mutations\nTheorem 5.2 states that if s is a classical ESS for a\n2player, symmetric game F, where G is chosen adversarially\nsubject to the constraint that the degree of each vertex is\n\u2126(n\u03b3\n) (for any constant \u03b3 > 0), and mutants are chosen\nwith probability , then s is an ESS with respect to F, G,\nand M. Here we show that if s is an ESS with respect to F,\nG, and M then s is a classical ESS.\nAll we will need to prove this is that s is an ESS with\nrespect to G = {Kn}\u221e\nn=0, that is when each vertex has degree\nn \u2212 1. As in Theorem A.1, since the graphs are cliques, if\none incumbent has higher fitness than one mutant, then all\nincumbents have higher fitness than all mutants. Thus, the\ntheorem below is also a converse to Theorem 5.3. (Recall\nthat Theorem 5.3 uses a weaker notion of contraction that\n206\nrequires only one incumbent to have higher fitness than one\nmutant.)\nTheorem A.2. Let F be any 2-player symmetric game,\nand suppose s is an incumbent strategy for F and t = s\nis a mutant strategy. Let G = {Kn}\u221e\nn=0. If with\nprobability 1 as n \u2192 \u221e, s is an ESS for G and a mutant family\nM = {Mn}\u221e\nn=0, which is determined by labeling each vertex\na mutant with probability , where t > > 0, then s is a\nclassical ESS of F.\nThis proof also analyzes the limiting behavior of the\nmutant population as the size of the cliques in G tends to\ninfinity. Since the mutants are chosen randomly we will use\nan argument similar to the proof that a sequence of random\nvariables that converges in probability, also converge in\ndistribution. In this case the sequence of random variables will\nbe actual fraction of mutants in each Kn.\nProof. Fix any value of , where n > > 0, and\nconstruct each Mn by labeling a vertex a mutant with\nprobability . By the same argument as in the proof of Theorem A.1,\nif the actual number of mutants in Kn is denoted by nn,\nany mutant subset of size nn will result in all incumbents\nhaving fitness (1 \u2212 nn\nn\u22121\n)F(s|s) + nn\nn\u22121\nF(s|t), and in all\nmutants having fitness (1 \u2212 nn\u22121\nn\u22121\n)F(t|s) + nn\u22121\nn\u22121\nF(t|t). This\nimplies\nlim\nn\u2192\u221e\nPr(s is an ESS for Gn w.r.t. nn mutants) = 1 \u21d2\nlim\nn\u2192\u221e\nPr\n\u201e\n(1 \u2212\nnn\nn \u2212 1\n)F(s|s) +\nnn\nn \u2212 1\nF(s|t) >\n(1 \u2212\nnn \u2212 1\nn \u2212 1\n)F(t|s) +\nnn \u2212 1\nn \u2212 1\nF(t|t)\n\u00ab\n= 1 \u21d4\nlim\nn\u2192\u221e\nPr\n\u201e\nn >\nF(t|s) \u2212 F(s|s)\nF(s|t) \u2212 F(s|s) \u2212 F(t|t) + F(t|s)\n+\nF(s|s) \u2212 F(t|t)\nn\n\u00ab\n= 1 (3)\nBy two simple applications of the Chernoff bound and an\napplication of the union bound, one can show the sequence\nof random variables { n}\u221e\nn=0 converges to in probability.\nNext, if we let Xn = \u2212 n, X = \u2212 , b = \u2212F(s|s) + F(t|t),\nand a = \u2212 F (t|s)\u2212F (s|s)\nF (s|t)\u2212F (s|s)\u2212F (t|t)+F (t|s)\n, by Theorem A.3\nbelow, we get that limn\u2192\u221e Pr(Xn < a + b/n) = Pr(X < a).\nCombining this with equation 3, Pr( > \u2212a) = 1.\nThe proof of the following theorem is very similar to the\nproof that a sequence of random variables that converges in\nprobability, also converge in distribution. A good\nexplanation of this can be found in [9], which is the basis for the\nargument below.\nTheorem A.3. If {Xn}\u221e\nn=0 is a sequence of random\nvariables that converge in probability to the random variable X,\nand a and b are constants, then limn\u2192\u221e Pr(Xn < a+b/n) =\nPr(X < a).\nProof. By Lemma A.1 (see below) we have the following\ntwo inequalities,\nPr(X < a + b/n \u2212 \u03c4)\n\u2264 Pr(Xn < a + b/n) + Pr(|X \u2212 Xn| > \u03c4),\nPr(Xn < a + b/n)\n\u2264 Pr(X < a + b/n + \u03c4) + Pr(|X \u2212 Xn| > \u03c4).\nCombining these gives,\nPr(X < a + b/n \u2212 \u03c4) \u2212 Pr(|X \u2212 Xn| > \u03c4)\n\u2264 Pr(Xn < a + b/n)\n\u2264 Pr(X < a + b/n + \u03c4) + Pr(|X \u2212 Xn| > \u03c4).\nThere exists an n0 such that for all n > n0, |b/n| < \u03c4, so\nthe following statement holds for all n > n0.\nPr(X < a \u2212 2\u03c4) \u2212 Pr(|X \u2212 Xn| > \u03c4)\n\u2264 Pr(Xn < a + b/n)\n\u2264 Pr(X < a + 2\u03c4) + Pr(|X \u2212 Xn| > \u03c4).\nTake the limn\u2192\u221e of both sides of both inequalities, and\nsince Xn converges in probability to X,\nPr(X < a \u2212 2\u03c4) \u2264 lim\nn\u2192\u221e\nPr(Xn < a + b/n) (4)\n\u2264 Pr(X < a + 2\u03c4). (5)\nRecall that X is a continuous random variable representing\nthe fraction of mutants in an infinite sized graph. So if we\nlet FX (a) = Pr(X < a), we see that FX (a) is a cumulative\ndistribution function of a continuous random variable, and\nis therefore continuous from the right. So\nlim\n\u03c4\u21930\nFX (a \u2212 \u03c4) = lim\n\u03c4\u21930\nFX (a + \u03c4) = FX (a).\nThus if we take the lim\u03c4\u21930 of inequalities 4 and 5 we get\nPr(X < a) = lim\nn\u2192\u221e\nPr(Xn < a + b/n).\nThe following lemma is quite useful, as it expresses the\ncumulative distribution of one random variable Y , in terms\nof the cumulative distribution of another random variable\nX and the difference between X and Y .\nLemma A.1. If X and Y are random variables, c \u2208\nand \u03c4 > 0, then\nPr(Y < c) \u2264 Pr(X < c + \u03c4) + Pr(|Y \u2212 X| > \u03c4).\nProof.\nPr(Y < c)\n= Pr(Y < c, X < c + \u03c4) + Pr(Y < c, X \u2265 c + \u03c4)\n\u2264 Pr(Y < c | X < c + \u03c4) Pr(X < c + \u03c4)\n+ Pr(|Y \u2212 X| > \u03c4)\n\u2264 Pr(X < c + \u03c4) + Pr(|Y \u2212 X| > \u03c4)\n207", "keywords": "nash equilibrium;game theory;randomization power;evolutionary stable strategy;natural strengthening;geographical restriction;equilibrium outcome;power of randomization;undirected graph;edge density condition;graph topology;mutation set;evolutionary game theory;graph-theoretic model;relationship of topology;network;topology relationship;pairwise interaction"}
{"name": "train_J-41", "title": "An Analysis of Alternative Slot Auction Designs for Sponsored Search", "abstract": "Billions of dollars are spent each year on sponsored search, a form of advertising where merchants pay for placement alongside web search results. Slots for ad listings are allocated via an auction-style mechanism where the higher a merchant bids, the more likely his ad is to appear above other ads on the page. In this paper we analyze the incentive, efficiency, and revenue properties of two slot auction designs: rank by bid (RBB) and rank by revenue (RBR), which correspond to stylized versions of the mechanisms currently used by Yahoo! and Google, respectively. We also consider first- and second-price payment rules together with each of these allocation rules, as both have been used historically. We consider both the short-run incomplete information setting and the long-run complete information setting. With incomplete information, neither RBB nor RBR are truthful with either first or second pricing. We find that the informational requirements of RBB are much weaker than those of RBR, but that RBR is efficient whereas RBB is not. We also show that no revenue ranking of RBB and RBR is possible given an arbitrary distribution over bidder values and relevance. With complete information, we find that no equilibrium exists with first pricing using either RBB or RBR. We show that there typically exists a multitude of equilibria with second pricing, and we bound the divergence of (economic) value in such equilibria from the value obtained assuming all merchants bid truthfully.", "fulltext": "1. INTRODUCTION\nToday, Internet giants Google and Yahoo! boast a\ncombined market capitalization of over $150 billion, largely on\nthe strength of sponsored search, the fastest growing\ncomponent of a resurgent online advertising industry.\nPricewaterhouseCoopers estimates that 2004 industry-wide sponsored\nsearch revenues were $3.9 billion, or 40% of total\nInternet advertising revenues.1\nIndustry watchers expect 2005\nrevenues to reach or exceed $7 billion.2\nRoughly 80% of\nGoogle\"s estimated $4 billion in 2005 revenue and roughly\n45% of Yahoo!\"s estimated $3.7 billion in 2005 revenue will\nlikely be attributable to sponsored search.3\nA number of\nother companies-including LookSmart, FindWhat,\nInterActiveCorp (Ask Jeeves), and eBay (Shopping.com)-earn\nhundreds of millions of dollars of sponsored search revenue\nannually.\nSponsored search is a form of advertising where merchants\npay to appear alongside web search results. For example,\nwhen a user searches for used honda accord san diego in\na web search engine, a variety of commercial entities (San\nDiego car dealers, Honda Corp, automobile information\nportals, classified ad aggregators, eBay, etc...) may bid to to\nhave their listings featured alongside the standard\nalgorithmic search listings. Advertisers bid for placement on the\npage in an auction-style format where the higher they bid\nthe more likely their listing will appear above other ads on\nthe page. By convention, sponsored search advertisers\ngenerally pay per click, meaning that they pay only when a user\nclicks on their ad, and do not pay if their ad is displayed but\nnot clicked. Though many people claim to systematically\nignore sponsored search ads, Majestic Research reports that\n1\nwww.iab.net/resources/adrevenue/pdf/IAB PwC 2004full.pdf\n2\nbattellemedia.com/archives/002032.php\n3\nThese are rough back of the envelope estimates. Google\nand Yahoo! 2005 revenue estimates were obtained from\nYahoo! Finance. We assumed $7 billion in 2005 industry-wide\nsponsored search revenues. We used Nielsen/NetRatings\nestimates of search engine market share in the US, the most\nmonetized market:\nwired-vig.wired.com/news/technology/0,1282,69291,00.html\nUsing comScore\"s international search engine market share\nestimates would yield different estimates:\nwww.comscore.com/press/release.asp?press=622\n218\nas many as 17% of Google searches result in a paid click, and\nthat Google earns roughly nine cents on average for every\nsearch query they process.4\nUsually, sponsored search results appear in a separate\nsection of the page designated as sponsored above or to the\nright of the algorithmic results. Sponsored search results\nare displayed in a format similar to algorithmic results: as\na list of items each containing a title, a text description,\nand a hyperlink to a corresponding web page. We call each\nposition in the list a slot. Generally, advertisements that\nappear in a higher ranked slot (higher on the page) garner\nmore attention and more clicks from users. Thus, all else\nbeing equal, merchants generally prefer higher ranked slots\nto lower ranked slots.\nMerchants bid for placement next to particular search\nqueries; for example, Orbitz and Travelocity may bid for\nlas vegas hotel while Dell and HP bid for laptop\ncomputer. As mentioned, bids are expressed as a maximum\nwillingness to pay per click. For example, a forty-cent bid\nby HostRocket for web hosting means HostRocket is\nwilling to pay up to forty cents every time a user clicks on their\nad.5\nThe auctioneer (the search engine6\n) evaluates the bids\nand allocates slots to advertisers. In principle, the\nallocation decision can be altered with each new incoming search\nquery, so in effect new auctions clear continuously over time\nas search queries arrive.\nMany allocation rules are plausible. In this paper, we\ninvestigate two allocation rules, roughly corresponding to the\ntwo allocation rules used by Yahoo! and Google. The rank\nby bid (RBB) allocation assigns slots in order of bids, with\nhigher ranked slots going to higher bidders. The rank by\nrevenue (RBR) allocation assigns slots in order of the\nproduct of bid times expected relevance, where relevance is the\nproportion of users that click on the merchant\"s ad after\nviewing it. In our model, we assume that an ad\"s expected\nrelevance is known to the auctioneer and the advertiser (but\nnot necessarily to other advertisers), and that clickthrough\nrate decays monotonically with lower ranked slots. In\npractice, the expected clickthrough rate depends on a number\nof factors, including the position on the page, the ad text\n(which in turn depends on the identity of the bidder), the\nnature and intent of the user, and the context of other ads\nand algorithmic results on the page, and must be learned\nover time by both the auctioneer and the bidder [13]. As of\nthis writing, to a rough first-order approximation, Yahoo!\nemploys a RBB allocation and Google employs a RBR\nallocation, though numerous caveats apply in both cases when\nit comes to the vagaries of real-world implementations.7\nEven when examining a one-shot version of a slot\nauction, the mechanism differs from a standard multi-item\nauc4\nbattellemedia.com/archives/001102.php\n5\nUsually advertisers also set daily or monthly budget caps;\nin this paper we do not model budget constraints.\n6\nIn the sponsored search industry, the auctioneer and search\nengine are not always the same entity. For example Google\nruns the sponsored search ads for AOL web search, with\nrevenue being shared. Similarly, Yahoo! currently runs the\nsponsored search ads for MSN web search, though Microsoft\nwill begin independent operations soon.\n7\nHere are two among many exceptions to the Yahoo! =\nRBB and Google = RBR assertion: (1) Yahoo! excludes\nads deemed insufficiently relevant either by a human editor\nor due to poor historical click rate; (2) Google sets differing\nreserve prices depending on Google\"s estimate of ad quality.\ntion in subtle ways. First, a single bid per merchant is used\nto allocate multiple non-identical slots. Second, the bid is\ncommunicated not as a direct preference over slots, but as\na preference for clicks that depend stochastically on slot\nallocation.\nWe investigate a number of economic properties of RBB\nand RBR slot auctions. We consider the short-run\nincomplete information case in Section 3, adapting and\nextending standard analyses of single-item auctions. In Section 4\nwe turn to the long-run complete information case; our\ncharacterization results here draw on techniques from\nlinear programming. Throughout, important observations are\nhighlighted as claims supported by examples. Our\ncontributions are as follows:\n\u2022 We show that with multiple slots, bidders do not reveal\ntheir true values with either RBB or RBR, and with\neither first- or second-pricing.\n\u2022 With incomplete information, we find that the\ninformational requirements of playing the equilibrium bid\nare much weaker for RBB than for RBR, because\nbidders need not know any information about each others\"\nrelevance (or even their own) with RBB.\n\u2022 With incomplete information, we prove that RBR is\nefficient but that RBB is not.\n\u2022 We show via a simple example that no general revenue\nranking of RBB and RBR is possible.\n\u2022 We prove that in a complete-information setting,\nfirstprice slot auctions have no pure strategy Nash\nequilibrium, but that there always exists a pure-strategy\nequilibrium with second pricing.\n\u2022 We provide a constant-factor bound on the deviation\nfrom efficiency that can occur in the equilibrium of a\nsecond-price slot auction.\nIn Section 2 we specify our model of bidders and the\nvarious slot auction formats.\nIn Section 3.1 we study the incentive properties of each\nformat, asking in which cases agents would bid truthfully.\nThere is possible confusion here because the second-price\ndesign for slot auctions is reminiscent of the Vickrey auction\nfor a single item; we note that for slot auctions the Vickrey\nmechanism is in fact very different from the second-price\nmechanism, and so they have different incentive properties.8\nIn Section 3.2 we derive the Bayes-Nash equilibrium bids\nfor the various auction formats. This is useful for the\nefficiency and revenue results in later sections. It should\nbecome clear in this section that slot auctions in our model\nare a straightforward generalization of single-item auctions.\nSections 3.3 and 3.4 address questions of efficiency and\nrevenue under incomplete information, respectively.\nIn Section 4.1 we determine whether pure-strategy\nequilibria exist for the various auction formats, under complete\ninformation. In Section 4.2 we derive bounds on the\ndeviation from efficiency in the pure-strategy equilibria of\nsecondprice slot auctions.\nOur approach is positive rather than normative. We aim\nto clarify the incentive, efficiency, and revenue properties of\ntwo slot auction designs currently in use, under settings of\n8\nOther authors have also made this observation [5, 6].\n219\nincomplete and complete information. We do not attempt\nto derive the optimal mechanism for a slot auction.\nRelated work. Feng et al. [7] compare the revenue\nperformance of various ranking mechanisms for slot auctions\nin a model with incomplete information, much as we do in\nSection 3.4, but they obtain their results via simulations\nwhereas we perform an equilibrium analysis.\nLiu and Chen [12] study properties of slot auctions under\nincomplete information. Their setting is essentially the same\nas ours, except they restrict their attention to a model with\na single slot and a binary type for bidder relevance (high or\nlow). They find that RBR is efficient, but that no general\nrevenue ranking of RBB and RBR is possible, which agrees\nwith our results. They also take a design approach and\nshow how the auctioneer should assign relevance scores to\noptimize its revenue.\nEdelman et al. [6] model the slot auction problem both as\na static game of complete information and a dynamic game\nof incomplete information. They study the locally\nenvyfree equilibria of the static game of complete information;\nthis is a solution concept motivated by certain bidding\nbehaviors that arise due to the presence of budget constraints.\nThey do not view slot auctions as static games of\nincomplete information as we do, but do study them as dynamic\ngames of incomplete information and derive results on the\nuniqueness and revenue properties of the resulting\nequilibria. They also provide a nice description of the evolution of\nthe market for sponsored search.\nVarian [18] also studies slot auctions under a setting of\ncomplete information. He focuses on symmetric\nequilibria, which are a refinement of Nash equilibria appropriate for\nslot auctions. He provides bounds on the revenue obtained\nin equilibrium. He also gives bounds that can be used to\ninfer bidder values given their bids, and performs some\nempirical analysis using these results. In contrast, we focus\ninstead on efficiency and provide bounds on the deviation\nfrom efficiency in complete-information equilibria.\n2. PRELIMINARIES\nWe focus on a slot auction for a single keyword. In a\nsetting of incomplete information, a bidder knows only\ndistributions over others\" private information (value per click\nand relevance). With complete information, a bidder knows\nothers\" private information, and so does not need to rely on\ndistributions to strategize. We first describe the model for\nthe case with incomplete information, and drop the\ndistributional information from the model when we come to the\ncomplete-information case in Section 4.\n2.1 The Model\nThere is a fixed number K of slots to be allocated among\nN bidders. We assume without loss of generality that K \u2264\nN, since superfluous slots can remain blank. Bidder i assigns\na value of Xi to each click received on its advertisement,\nregardless of this advertisement\"s rank.9\nThe probability\nthat i\"s advertisement will be clicked if viewed is Ai \u2208 [0, 1].\nWe refer to Ai as bidder i\"s relevance. We refer to Ri =\nAiXi as bidder i\"s revenue. The Xi, Ai, and Ri are random\n9\nIndeed Kitts et al. [10] find that in their sample of actual\nclick data, the correlation between rank and conversion rate\nis not statistically significant. However, for the purposes\nof our model it is also important that bidders believe that\nconversion rate does not vary with rank.\nvariables and we denote their realizations by xi, \u03b1i, and ri\nrespectively. The probability that an advertisement will be\nviewed if placed in slot j is \u03b3j \u2208 [0, 1]. We assume \u03b31 >\n\u03b32 > . . . > \u03b3K. Hence bidder i\"s advertisement will have a\nclickthrough rate of \u03b3j\u03b1i if placed in slot j. Of course, an\nadvertisement does not receive any clicks if it is not allocated\na slot.\nEach bidder\"s value and relevance pair (Xi, Ai) is\nindependently and identically distributed on [0, \u00afx] \u00d7 [0, 1] according\nto a continuous density function f that has full support on\nits domain. The density f and slot probabilities \u03b31, . . . , \u03b3K\nare common knowledge. Only bidder i knows the\nrealization xi of its value per click Xi. Both bidder i and the seller\nknow the realization \u03b1i of Ai, but this realization remains\nunobservable to the other bidders.\nWe assume that bidders have quasi-linear utility\nfunctions. That is, the expected utility to bidder i of obtaining\nthe slot of rank j at a price of b per click is\nui(j, b) = \u03b3j\u03b1i(xi \u2212 b)\nIf the advertising firms bidding in the slot auction are\nriskneutral and have ample liquidity, quasi-linearity is a\nreasonable assumption.\nThe assumptions of independence, symmetry, and\nriskneutrality made above are all quite standard in single-item\nauction theory [11, 19]. The assumption that clickthrough\nrate decays monotonically with lower slots-by the same\nfactors for each agent-is unique to the slot auction\nproblem. We view it as a main contribution of our work to\nshow that this assumption allows for tractable analysis of\nthe slot auction problem using standard tools from\nsingleitem auction theory. It also allows for interesting results in\nthe complete information case. A common model of\ndecaying clickthrough rate is the exponential decay model, where\n\u03b3k = 1\n\u03b4k\u22121 with decay \u03b4 > 1. Feng et al. [7] state that\ntheir actual clickthrough data is fitted extremely well by an\nexponential decay model with \u03b4 = 1.428.\nOur model lacks budget constraints, which are an\nimportant feature of real slot auctions. With budget constraints\nkeyword auctions cannot be considered independently of one\nanother, because the budget must be allocated across\nmultiple keywords-a single advertiser typically bids on multiple\nkeywords relevant to his business. Introducing this element\ninto the model is an important next step for future work.10\n2.2 Auction Formats\nIn a slot auction a bidder provides to the seller a declared\nvalue per click \u02dcxi(xi, \u03b1i) which depends on his true value\nand relevance. We often denote this declared value (bid)\nby \u02dcxi for short. Since a bidder\"s relevance \u03b1i is observable\nto the seller, the bidder cannot misrepresent it. We denote\nthe kth\nhighest of the N declared values by \u02dcx(k)\n, and the\nkth\nhighest of the N declared revenues by \u02dcr(k)\n, where the\ndeclared revenue of bidder i is \u02dcri = \u03b1i \u02dcxi. We consider two\ntypes of allocation rules, rank by bid (RBB) and rank\nby revenue (RBR):\n10\nModels with budget constraints have begun to appear in\nthis research area. Abrams [1] and Borgs et al. [3] design\nmulti-unit auctions for budget-constrained bidders, which\ncan be interpreted as slot auctions, with a focus on revenue\noptimization and truthfulness. Mehta et al. [14] address\nthe problem of matching user queries to budget-constrained\nadvertisers so as to maximize revenue.\n220\nRBB. Slot k goes to bidder i if and only if \u02dcxi = \u02dcx(k)\n.\nRBR. Slot k goes to bidder i if and only if \u02dcri = \u02dcr(k)\n.\nWe will commonly represent an allocation by a one-to-one\nfunction \u03c3 : [K] \u2192 [N], where [n] is the set of integers\n{1, 2, . . . , n}. Hence slot k goes to bidder \u03c3(k).\nWe also consider two different types of payment rules.\nNote that no matter what the payment rule, a bidder that\nis not allocated a slot will pay 0 since his listing cannot\nreceive any clicks.\nFirst-price. The bidder allocated slot k, namely \u03c3(k), pays\n\u02dcx\u03c3(k) per click under both the RBB and RBR\nallocation rules.\nSecond-price. If k < N, bidder \u03c3(k) pays \u02dcx\u03c3(k+1) per click\nunder the RBB rule, and pays \u02dcr\u03c3(k+1)/\u03b1\u03c3(k) per click\nunder the RBR rule. If k = N, bidder \u03c3(k) pays 0 per\nclick.11\nIntuitively, a second-price payment rule sets a bidder\"s\npayment to the lowest bid it could have declared while\nmaintaining the same ranking, given the allocation rule used.\nOverture introduced the first slot auction design in 1997,\nusing a first-price RBB scheme. Google then followed in\n2000 with a second-price RBR scheme. In 2002, Overture\n(at this point acquired by Yahoo!) then switched to second\npricing but still allocates using RBB. One possible reason\nfor the switch is given in Section 4.\nWe assume that ties are broken as follows in the event\nthat two agents make the exact same bid or declare the\nsame revenue. There is a permutation of the agents \u03ba :\n[N] \u2192 [N] that is fixed beforehand. If the bids of agents i\nand j are tied, then agent i obtains a higher slot if and only\nif \u03ba(i) < \u03ba(j). This is consistent with the practice in real\nslot auctions where ties are broken by the bidders\" order of\narrival.\n3. INCOMPLETE INFORMATION\n3.1 Incentives\nIt should be clear that with a first-price payment rule,\ntruthful bidding is neither a dominant strategy nor an ex\npost Nash equilibrium using either RBB or RBR, because\nthis guarantees a payoff of 0. There is always an incentive\nto shade true values with first pricing.\nThe second-price payment rule is reminiscent of the\nsecondprice (Vickrey) auction used for selling a single item, and in\na Vickrey auction it is a dominant strategy for a bidder to\nreveal his true value for the item [19]. However, using a\nsecond-price rule in a slot auction together with either\nallocation rule above does not yield an incentive-compatible\nmechanism, either in dominant strategies or ex post Nash\nequilibrium.12\nWith a second-price rule there is no\nincentive for a bidder to bid higher than his true value per click\nusing either RBB or RBR: this either leads to no change\n11\nWe are effectively assuming a reserve price of zero, but in\npractice search engines charge a non-zero reserve price per\nclick.\n12\nUnless of course there is only a single slot available, since\nthis is the single-item case. With a single slot both RBB\nand RBR with a second-price payment rule are\ndominantstrategy incentive-compatible.\nin the outcome, or a situation in which he will have to pay\nmore than his value per click for each click received,\nresulting in a negative payoff.13\nHowever, with either allocation\nrule there may be an incentive to shade true values with\nsecond pricing.\nClaim 1. With second pricing and K \u2265 2, truthful\nbidding is not a dominant strategy nor an ex post Nash\nequilibrium for either RBB or RBR.\nExample. There are two agents and two slots. The\nagents have relevance \u03b11 = \u03b12 = 1, whereas \u03b31 = 1 and\n\u03b32 = 1/2. Agent 1 has a value of x1 = 6 per click, and agent\n2 has a value of x2 = 4 per click. Let us first consider the\nRBB rule. Suppose agent 2 bids truthfully. If agent 1 also\nbids truthfully, he wins the first slot and obtains a payoff of\n2. However, if he shades his bid down below 4, he obtains\nthe second slot at a cost of 0 per click yielding a payoff of\n3. Since the agents have equal relevance, the exact same\nsituation holds with the RBR rule. Hence truthful bidding\nis not a dominant strategy in either format, and neither is\nit an ex post Nash equilibrium.\nTo find payments that make RBB and RBR\ndominantstrategy incentive-compatible, we can apply Holmstrom\"s\nlemma [9] (see also chapter 3 in Milgrom [15]). Under the\nrestriction that a bidder with value 0 per click does not pay\nanything (even if he obtains a slot, which can occur if there\nare as many slots as bidders), this lemma implies that there\nis a unique payment rule that achieves dominant-strategy\nincentive compatibility for either allocation rule. For RBB,\nthe bidder allocated slot k is charged per click\nKX\ni=k+1\n(\u03b3i\u22121 \u2212 \u03b3i)\u02dcx(i)\n+ \u03b3K \u02dcx(K+1)\n(1)\nNote that if K = N, \u02dcx(K+1)\n= 0 since there is no K + 1th\nbidder. For RBR, the bidder allocated slot k is charged per\nclick\n1\n\u03b1\u03c3(k)\nKX\ni=k+1\n(\u03b3i\u22121 \u2212 \u03b3i)\u02dcr(i)\n+ \u03b3K \u02dcr(K+1)\n!\n(2)\nUsing payment rule (2) and RBR, the auctioneer is aware\nof the true revenues of the bidders (since they reveal their\nvalues truthfully), and hence ranks them according to their\ntrue revenues. We show in Section 3.3 that this allocation\nis in fact efficient. Since the VCG mechanism is the unique\nmechanism that is efficient, truthful, and ensures bidders\nwith value 0 pay nothing (by the Green-Laffont theorem [8]),\nthe RBR rule and payment scheme (2) constitute exactly the\nVCG mechanism.\nIn the VCG mechanism an agent pays the externality he\nimposes on others. To understand payment (2) in this sense,\nnote that the first term is the added utility (due to an\nincreased clickthrough rate) agents in slots k + 1 to K would\nreceive if they were all to move up a slot; the last term is the\nutility that the agent with the K +1st\nrevenue would receive\nby obtaining the last slot as opposed to nothing. The\nleading coefficient simply reduces the agent\"s expected payment\nto a payment per click.\n13\nIn a dynamic setting with second pricing, there may be an\nincentive to bid higher than one\"s true value in order to\nexhaust competitors\" budgets. This phenomenon is commonly\ncalled bid jamming or antisocial bidding [4].\n221\n3.2 Equilibrium Analysis\nTo understand the efficiency and revenue properties of\nthe various auction formats, we must first understand which\nrankings of the bidders occur in equilibrium with different\nallocation and payment rule combinations. The following\nlemma essentially follows from the Monotonic Selection\nTheorem by Milgrom and Shannon [16].\nLemma 1. In a RBB (RBR) auction with either a\nfirstor second-price payment rule, the symmetric Bayes-Nash\nequilibrium bid is strictly increasing with value ( revenue).\nAs a consequence of this lemma, we find that RBB and\nRBR auctions allocate the slots greedily by the true values\nand revenues of the agents, respectively (whether using\nfirstor second-price payment rules). This will be relevant in\nSection 3.3 below. For a first-price payment rule, we can\nexplicitly derive the symmetric Bayes-Nash equilibrium bid\nfunctions for RBB and RBR auctions. The purpose of this\nexercise is to lend qualitative insights into the parameters\nthat influence an agent\"s bidding, and to derive formulae for\nthe expected revenue in RBB and RBR auctions in order\nto make a revenue ranking of these two allocation rules (in\nSection 3.4).\nLet G(y) be the expected resulting clickthrough rate, in\na symmetric equilibrium of the RBB auction (with either\npayment rule), to a bidder with value y and relevance \u03b1 =\n1. Let H(y) be the analogous quantity for a bidder with\nrevenue y and relevance 1 in a RBR auction. By Lemma 1,\na bidder with value y will obtain slot k in a RBB auction\nif y is the kth\nhighest of the true realized values. The same\napplies in a RBR auction when y is the kth\nhighest of the true\nrealized revenues. Let FX (y) be the distribution function for\nvalue, and let FR(y) be the distribution function for revenue.\nThe probability that y is the kth\nhighest out of N values is\nN \u2212 1\nk \u2212 1\n!\n(1 \u2212 FX (y))k\u22121\nFX (y)N\u2212k\nwhereas the probability that y is the kth\nhighest out of N\nrevenues is the same formula with FR replacing FX . Hence\nwe have\nG(y) =\nKX\nk=1\n\u03b3k\nN \u2212 1\nk \u2212 1\n!\n(1 \u2212 FX (y))k\u22121\nFX (y)N\u2212k\nThe H function is analogous to G with FR replacing FX .\nIn the two propositions that follow, g and h are the\nderivatives of G and H respectively. We omit the proof of the\nnext proposition, because it is almost identical to the\nderivation of the equilibrium bid in the single-item case (see\nKrishna [11], Proposition 2.2).\nProposition 1. The symmetric Bayes-Nash equilibrium\nstrategies in a first-price RBB auction are given by\n\u02dcxB\n(x, \u03b1) =\n1\nG(x)\nZ x\n0\ny g(y)dy\nThe first-price equilibrium above closely parallels the\nfirstprice equilibrium in the single-item model. With a single\nitem g is the density of the second highest value among all\nN agent values, whereas in a slot auction it is a weighted\ncombination of the densities for the second, third, etc.\nhighest values.\nNote that the symmetric Bayes-Nash equilibrium bid in\na first-price RBB auction does not depend on a bidder\"s\nrelevance \u03b1. To see clearly why, note that a bidder chooses\na bid b so as to maximize the objective\n\u03b1G(\u02dcx\u22121\n(b))(x \u2212 b)\nand here \u03b1 is just a leading constant factor. So dropping\nit does not change the set of optimal solutions. Hence the\nequilibrium bid depends only on the value x and function\nG, and G in turn depends only on the marginal cumulative\ndistribution of value FX . So really only the latter needs to\nbe common knowledge to the bidders. On the other hand,\nwe will now see that information about relevance is needed\nfor bidders to play the equilibrium in the first-price RBR\nauction. So the informational requirements for a first-price\nRBB auction are much weaker than for a first-price RBR\nauction: in the RBB auction a bidder need not know his own\nrelevance, and need not know any distributional information\nover others\" relevance in order to play the equilibrium.\nAgain we omit the next proposition\"s proof since it is so\nsimilar to the one above.\nProposition 2. The symmetric Bayes-Nash equilibrium\nstrategies in a first-price RBR auction are given by\n\u02dcxR\n(x, \u03b1) =\n1\n\u03b1H(\u03b1x)\nZ \u03b1x\n0\ny h(y) dy\nHere it can be seen that the equilibrium bid is increasing\nwith x, but not necessarily with \u03b1. This should not be much\nof a concern to the auctioneer, however, because in any case\nthe declared revenue in equilibrium is always increasing in\nthe true revenue.\nIt would be interesting to obtain the equilibrium bids\nwhen using a second-price payment rule, but it appears that\nthe resulting differential equations for this case do not have a\nneat analytical solution. Nonetheless, the same conclusions\nabout the informational requirements of the RBB and RBR\nrules still hold, as can be seen simply by inspecting the\nobjective function associated with an agent\"s bidding problem\nfor the second-price case.\n3.3 Efficiency\nA slot auction is efficient if in equilibrium the sum of the\nbidders\" revenues from their allocated slots is maximized.\nUsing symmetry as our equilibrium selection criterion, we\nfind that the RBB auction is not efficient with either\npayment rule.\nClaim 2. The RBB auction is not efficient with either\nfirst or second pricing.\nExample. There are two agents and one slot, with \u03b31 =\n1. Agent 1 has a value of x1 = 6 per click and relevance\n\u03b11 = 1/2. Agent 2 has a value of x2 = 4 per click and\nrelevance \u03b12 = 1. By Lemma 1, agents are ranked greedily\nby value. Hence agent 1 obtains the lone slot, for a total\nrevenue of 3 to the agents. However, it is most efficient to\nallocate the slot to agent 2, for a total revenue of 4.\nExamples with more agents or more slots are simple to\nconstruct along the same lines. On the other hand, under\nour assumptions on how clickthrough rate decreases with\nlower rank, the RBR auction is efficient with either payment\nrule.\n222\nTheorem 1. The RBR auction is efficient with either\nfirst- or second-price payments rules.\nProof. Since by Lemma 1 the agents\" equilibrium bids\nare increasing functions of their revenues in the RBR\nauction, slots are allocated greedily according to true revenues.\nLet \u03c3 be a non-greedy allocation. Then there are slots s, t\nwith s < t and r\u03c3(s) < r\u03c3(t). We can switch the agents in\nslots s and t to obtain a new allocation, and the difference\nbetween the total revenue in this new allocation and the\noriginal allocation\"s total revenue is\n`\n\u03b3tr\u03c3(s) + \u03b3sr\u03c3(t)\n\u00b4\n\u2212\n`\n\u03b3sr\u03c3(s) + \u03b3tr\u03c3(t)\n\u00b4\n= (\u03b3s \u2212 \u03b3t)\n`\nr\u03c3(t) \u2212 r\u03c3(s)\n\u00b4\nBoth parenthesized terms above are positive. Hence the\nswitch has increased the total revenue to the bidders. If we\ncontinue to perform such switches, we will eventually reach\na greedy allocation of greater revenue than the initial\nallocation. Since the initial allocation was arbitrary, it follows\nthat a greedy allocation is always efficient, and hence the\nRBR auction\"s allocation is efficient.\nNote that the assumption that clickthrough rate decays\nmontonically by the same factors \u03b31, . . . , \u03b3K for all agents is\ncrucial to this result. A greedy allocation scheme does not\nnecessarily find an efficient solution if the clickthrough rates\nare monotonically decreasing in an independent fashion for\neach agent.\n3.4 Revenue\nTo obtain possible revenue rankings for the different\nauction formats, we first note that when the allocation rule is\nfixed to RBB, then using either a first-price, second-price, or\ntruthful payment rule leads to the same expected revenue in\na symmetric, increasing Bayes-Nash equilibrium. Because\na RBB auction ranks agents by their true values in\nequilibrium for any of these payment rules (by Lemma 1), it\nfollows that expected revenue is the same for all these\npayment rules, following arguments that are virtually identical\nto those used to establish revenue equivalence in the\nsingleitem case (see e.g. Proposition 3.1 in Krishna [11]). The\nsame holds for RBR auctions; however, the revenue ranking\nof the RBB and RBR allocation rules is still unclear.\nBecause of this revenue equivalence principle, we can choose\nwhichever payment rule is most convenient for the purpose\nof making revenue comparisons.\nUsing Propositions 1 and 2, it is a simple matter to\nderive formulae for the expected revenue under both allocation\nrules. The payment of an agent in a RBB auction is\nmB\n(x, \u03b1) = \u03b1G(x)\u02dcxV\n(x, \u03b1)\nThe expected revenue is then N \u00b7 E\n\u02c6\nmV\n(X, A)\n\u02dc\n, where the\nexpectation is taken with respect to the joint density of value\nand relevance. The expected revenue formula for RBR\nauctions is entirely analogous using \u02dcxR\n(x, \u03b1) and the H\nfunction. With these in hand we can obtain revenue rankings\nfor specific numbers of bidders and slots, and specific\ndistributions over values and relevance.\nClaim 3. For fixed K, N, and fixed \u03b31, . . . , \u03b3K, no\nrevenue ranking of RBB and RBR is possible for an arbitrary\ndensity f.\nExample. Assume there are 2 bidders, 2 slots, and that\n\u03b31 = 1, \u03b32 = 1/2. Assume that value-relevance pairs are\nuniformly distributed over [0, 1]\u00d7 [0, 1]. For such a\ndistribution with a closed-form formula, it is most convenient to use\nthe revenue formulae just derived. RBB dominates RBR in\nterms of revenue for these parameters. The formula for the\nexpected revenue in a RBB auction yields 1/12, whereas for\nRBR auctions we have 7/108.\nAssume instead that with probability 1/2 an agent\"s\nvaluerelevance pair is (1, 1/2), and that with probability 1/2 it\nis (1/2, 1). In this scenario it is more convenient to appeal\nto formulae (1) and (2). In a truthful auction the second\nagent will always pay 0. According to (1), in a truthful\nRBB auction the first agent makes an expected payment of\nE\n\u02c6\n(\u03b31 \u2212 \u03b32)A\u03c3(1)X\u03c3(2)\n\u02dc\n=\n1\n2\nE\n\u02c6\nA\u03c3(1)\n\u02dc\nE\n\u02c6\nX\u03c3(2)\n\u02dc\nwhere we have used the fact that value and relevance are\nindependently distributed for different agents. The expected\nrelevance of the agent with the highest value is E\n\u02c6\nA\u03c3(1)\n\u02dc\n=\n5/8. The expected second highest value is also E\n\u02c6\nX\u03c3(2)\n\u02dc\n=\n5/8. The expected revenue for a RBB auction here is then\n25/128. According to (2), in a truthful RBR auction the\nfirst agent makes an expected payment of\nE\n\u02c6\n(\u03b31 \u2212 \u03b32)R\u03c3(2)\n\u02dc\n=\n1\n2\nE\n\u02c6\nR\u03c3(2)\n\u02dc\nIn expectation the second highest revenue is E\n\u02c6\nR\u03c3(2)\n\u02dc\n=\n1/2, so the expected revenue for a RBR auction is 1/4.\nHence in this case the RBR auction yields higher expected\nrevenue.1415\nThis example suggests the following conjecture: when\nvalue and relevance are either uncorrelated or positively\ncorrelated, RBB dominates RBR in terms of revenue. When\nvalue and relevance are negatively correlated, RBR\ndominates.\n4. COMPLETE INFORMATION\nIn typical slot auctions such as those run by Yahoo! and\nGoogle, bidders can adjust their bids up or down at any\ntime. As B\u00a8orgers et al. [2] and Edelman et al. [6] have\nnoted, this can be viewed as a continuous-time process in\nwhich bidders learn each other\"s bids. If the process\nstabilizes the result can then be modeled as a Nash equilibrium\nin pure strategies of the static one-shot game of complete\ninformation, since each bidder will be playing a best-response\nto the others\" bids.16\nThis argument seems especially\nappropriate for Yahoo!\"s slot auction design where all bids are\n14\nTo be entirely rigorous and consistent with our initial\nassumptions, we should have constructed a continuous\nprobability density with full support over an appropriate domain.\nTaking the domain to be e.g. [0, 1] \u00d7 [0, 1] and a continuous\ndensity with full support that is sufficiently concentrated\naround (1, 1/2) and (1/2, 1), with roughly equal mass around\nboth, would yield the same conclusion.\n15\nClaim 3 should serve as a word of caution, because Feng\net al. [7] find through their simulations that with a\nbivariate normal distribution over value-relevance pairs, and with\n5 slots, 15 bidders, and \u03b4 = 2, RBR dominates RBB in\nterms of revenue for any level of correlation between value\nand relevance. However, they assume that bidding behavior\nin a second-price slot auction can be well approximated by\ntruthful bidding.\n16\nWe do not claim that bidders will actually learn each\nothers\" private information (value and relevance), just that for\na stable set of bids there is a corresponding equilibrium of\nthe complete information game.\n223\nmade public. Google keeps bids private, but\nexperimentation can allow one to discover other bids, especially since\nsecond pricing automatically reveals to an agent the bid of\nthe agent ranked directly below him.\n4.1 Equilibrium Analysis\nIn this section we ask whether a pure-strategy Nash\nequilibrium exists in a RBB or RBR slot auction, with either\nfirst or second pricing.\nBefore dealing with the first-price case there is a technical\nissue involving ties. In our model we allow bids to be\nnonnegative real numbers for mathematical convenience, but\nthis can become problematic because there is then no bid\nthat is just higher than another. We brush over such\nissues by assuming that an agent can bid infinitesimally\nhigher than another. This is imprecise but allows us to\nfocus on the intuition behind the result that follows. See\nReny [17] for a full treatment of such issues.\nFor the remainder of the paper, we assume that there are\nas many slots as bidders. The following result shows that\nthere can be no pure-strategy Nash equilibrium with first\npricing.17\nNote that the argument holds for both RBB and\nRBR allocation rules. For RBB, bids should be interpreted\nas declared values, and for RBR as declared revenues.\nTheorem 2. There exists no complete information Nash\nequilibrium in pure strategies in the first-price slot auction,\nfor any possible values of the agents, whether using a RBB\nor RBR allocation rule.\nProof. Let \u03c3 : [K] \u2192 [N] be the allocation of slots to\nthe agents resulting from their bids. Let ri and bi be the\nrevenue and bid of the agent ranked ith\n, respectively. Note\nthat we cannot have bi > bi+1, or else the agent in slot\ni can make a profitable deviation by instead bidding bi \u2212\n> bi+1 for small enough > 0. This does not change\nits allocation, but increases its profit. Hence we must have\nbi = bi+1 (i.e. with one bidder bidding infinitesimally higher\nthan the other). Since this holds for any two consecutive\nbidders, it follows that in a Nash equilibrium all bidders\nmust be bidding 0 (since the bidder ranked last matches the\nbid directly below him, which is 0 by default because there\nis no such bid). But this is impossible: consider the bidder\nranked last. The identity of this bidder is always clear given\nthe deterministic tie-breaking rule. This bidder can obtain\nthe top spot and increase his revenue by (\u03b31 \u2212\u03b3K)rK > 0 by\nbidding some > 0, and for small enough this is necessarily\na profitable deviation. Hence there is no Nash equilibrium\nin pure strategies.\nOn the other hand, we find that in a second-price slot\nauction there can be a multitude of pure strategy Nash\nequilibria. The next two lemmas give conditions that characterize\nthe allocations that can occur as a result of an equilibrium\nprofile of bids, given fixed agent values and revenues. Then\nif we can exhibit an allocation that satisfies these conditions,\nthere must exist at least one equilibrium. We first consider\nthe RBR case.\n17\nB\u00a8orgers et al. [2] have proven this result in a model with\nthree bidders and three slots, and we generalize their\nargument. Edelman et al. [6] also point out this non-existence\nphenomenon. They only illustrate the fact with an example\nbecause the result is quite immediate.\nLemma 2. Given an allocation \u03c3, there exists a Nash\nequilibrium profile of bids b leading to \u03c3 in a second-price RBR\nslot auction if and only if\n\u201e\n1 \u2212\n\u03b3i\n\u03b3j+1\n\u00ab\nr\u03c3(i) \u2264 r\u03c3(j)\nfor 1 \u2264 j \u2264 N \u2212 2 and i \u2265 j + 2.\nProof. There exists a desired vector b which constitutes\na Nash equilibrium if and only if the following set of\ninequalities can be satisfied (the variables are the \u03c0i and bj):\n\u03c0i \u2265 \u03b3j(r\u03c3(i) \u2212 bj) \u2200i, \u2200j < i (3)\n\u03c0i \u2265 \u03b3j(r\u03c3(i) \u2212 bj+1) \u2200i, \u2200j > i (4)\n\u03c0i = \u03b3i(r\u03c3(i) \u2212 bi+1) \u2200i (5)\nbi \u2265 bi+1 1 \u2264 i \u2264 N \u2212 1 (6)\n\u03c0i \u2265 0, bi \u2265 0 \u2200i\nHere r\u03c3(i) is the revenue of the agent allocated slot i, and\n\u03c0i and bi may be interpreted as this agent\"s surplus and\ndeclared revenue, respectively. We first argue that\nconstraints (6) can be removed, because the inequalities above\ncan be satisfied if and only if the inequalities without (6) can\nbe satisfied. The necessary direction is immediate. Assume\nwe have a vector (\u03c0, b) which satisfies all inequalities above\nexcept (6). Then there is some i for which bi < bi+1.\nConstruct a new vector (\u03c0, b ) identical to the original except\nwith bi+1 = bi. We now have bi = bi+1. An agent in slot\nk < i sees the price of slot i decrease from bi+1 to bi+1 = bi,\nbut this does not make i more preferred than k to this agent\nbecause we have \u03c0k \u2265 \u03b3i\u22121(r\u03c3(k) \u2212 bi) \u2265 \u03b3i(r\u03c3(k) \u2212 bi) =\n\u03b3i(r\u03c3(k) \u2212bi+1) (i.e. because the agent in slot k did not\noriginally prefer slot i \u2212 1 at price bi, he will not prefer slot i\nat price bi). A similar argument applies for agents in slots\nk > i + 1. The agent in slot i sees the price of this slot\ngo down, which only makes it more preferred. Finally, the\nagent in slot i + 1 sees no change in the price of any slot, so\nhis slot remains most preferred. Hence inequalities (3)-(5)\nremain valid at (\u03c0, b ). We first make this change to the bi+1\nwhere bi < bi+1 and index i is smallest. We then recursively\napply the change until we eventually obtain a vector that\nsatisfies all inequalities.\nWe safely ignore inequalities (6) from now on. By the\nFarkas lemma, the remaining inequalities can be satisfied if\nand only if there is no vector z such that\nX\ni,j\n(\u03b3j r\u03c3(i)) z\u03c3(i)j > 0\nX\ni>j\n\u03b3jz\u03c3(i)j +\nX\ni<j\n\u03b3j\u22121z\u03c3(i)j\u22121 \u2264 0 \u2200j (7)\nX\nj\nz\u03c3(i)j \u2264 0 \u2200i (8)\nz\u03c3(i)j \u2265 0 \u2200i, \u2200j = i\nz\u03c3(i)i free \u2200i\nNote that a variable of the form z\u03c3(i)i appears at most once\nin a constraint of type (8), so such a variable can never be\npositive. Also, z\u03c3(i)1 = 0 for all i = 1 by constraint (7),\nsince such variables never appear with another of the form\nz\u03c3(i)i.\nNow if we wish to raise z\u03c3(i)j above 0 by one unit for j = i,\nwe must lower z\u03c3(i)i by one unit because of the constraint\nof type (8). Because \u03b3jr\u03c3(i) \u2264 \u03b3ir\u03c3(i) for i < j, raising\n224\nz\u03c3(i)j with i < j while adjusting other variables to maintain\nfeasibility cannot make the objective\nP\ni,j(\u03b3jr\u03c3(i))z\u03c3(i)j\npositive. If this objective is positive, then this is due to some\ncomponent z\u03c3(i)j with i > j being positive.\nNow for the constraints of type (7), if i > j then z\u03c3(i)j\nappears with z\u03c3(j\u22121)j\u22121 (for 1 < j < N). So to raise the\nformer variable \u03b3\u22121\nj units and maintain feasibility, we must\n(I) lower z\u03c3(i)i by \u03b3\u22121\nj units, and (II) lower z\u03c3(j\u22121)j\u22121 by\n\u03b3\u22121\nj\u22121 units. Hence if the following inequalities hold:\nr\u03c3(i) \u2264\n\u201e\n\u03b3i\n\u03b3j\n\u00ab\nr\u03c3(i) + r\u03c3(j\u22121) (9)\nfor 2 \u2264 j \u2264 N \u2212 1 and i > j, raising some z\u03c3(i)j with\ni > j cannot make the objective positive, and there is no\nz that satisfies all inequalities above. Conversely, if some\ninequality (9) does not hold, the objective can be made\npositive by raising the corresponding z\u03c3(i)j and adjusting other\nvariables so that feasibility is just maintained. By a slight\nreindexing, inequalities (9) yield the statement of the\ntheorem.\nThe RBB case is entirely analogous.\nLemma 3. Given an allocation \u03c3, there exists a Nash\nequilibrium profile of bids b leading to \u03c3 in a second-price RBB\nslot auction if and only if\n\u201e\n1 \u2212\n\u03b3i\n\u03b3j+1\n\u00ab\nx\u03c3(i) \u2264 x\u03c3(j)\nfor 1 \u2264 j \u2264 N \u2212 2 and i \u2265 j + 2.\nProof Sketch. The proof technique is the same as in the\nprevious lemma. The desired Nash equilibrium exists if and\nonly if a related set of inequalities can be satisfied; by the\nFarkas lemma, this occurs if and only if an alternate set of\ninequalities cannot be satisfied. The conditions that\ndetermine whether the latter holds are given in the statement of\nthe lemma.\nThe two lemmas above immediately lead to the following\nresult.\nTheorem 3. There always exists a complete information\nNash equilibrium in pure strategies in the second-price RBB\nslot auction. There always exists an efficient complete\ninformation Nash equilibrium in pure strategies in the\nsecondprice RBR slot auction.\nProof. First consider RBB. Suppose agents are ranked\naccording to their true values. Since x\u03c3(i) \u2264 x\u03c3(j) for i > j,\nthe system of inequalities in Lemma 3 is satisfied, and the\nallocation is the result of some Nash equilibrium bid profile.\nBy the same type of argument but appealing to Lemma 2\nfor RBR, there exists a Nash equilibrium bid profile such\nthat bidders are ranked according to their true revenues.\nBy Theorem 1, this latter allocation is efficient.\nThis theorem establishes existence but not uniqueness.\nIndeed we expect that in many cases there will be multiple\nallocations (and hence equilibria) which satisfy the\nconditions of Lemmas 2 and 3. In particular, not all equilibria of\na second-price RBR auction will be efficient. For instance,\naccording to Lemma 2, with two agents and two slots any\nallocation can arise in a RBR equilibrium because no\nconstraints apply.\nTheorems 2 and 3 taken together provide a possible\nexplanation for Yahoo!\"s switch from first to second pricing.\nWe saw in Section 3.1 that this does not induce truthfulness\nfrom bidders. With first pricing, there will always be some\nbidder that feels compelled to adjust his bid. Second pricing\nis more convenient because an equilibrium can be reached,\nand this reduces the cost of bid management.\n4.2 Efficiency\nFor a given allocation rule, we call the allocation that\nwould result if the bidders reported their values truthfully\nthe standard allocation. Hence in the standard RBB\nallocation bidders are ranked by true values, and in the standard\nRBR allocation they are ranked by true revenues.\nAccording to Lemmas 2 and 3, a ranking that results from a Nash\nequilibrium profile can only deviate from the standard\nallocation by having agents with relatively similar values or\nrevenues switch places. That is, if ri > rj then with RBR\nagent j can be ranked higher than i only if the ratio rj/ri is\nsufficiently large; similarly for RBB. This suggests that the\nvalue of an equilibrium allocation cannot differ too much\nfrom the value obtained in the standard allocation, and the\nfollowing theorems confirms this.\nFor an allocation \u03c3 of slots to agents, we denote its\ntotal value by f(\u03c3) =\nPN\ni=1 \u03b3ir\u03c3(i). We denote by g(\u03c3) =\nPN\ni=1 \u03b3ix\u03c3(i) allocation \u03c3\"s value when assuming all agents\nhave identical relevance, normalized to 1. Let\nL = min\ni=1,...,N\u22121\nmin\n\uf6be\n\u03b3i+1\n\u03b3i\n, 1 \u2212\n\u03b3i+2\n\u03b3i+1\nff\n(where by default \u03b3N+1 = 0). Let \u03b7x and \u03b7r be the standard\nallocations when using RBB and RBR, respectively.\nTheorem 4. For an allocation \u03c3 that results from a\npurestrategy Nash equilibrium of a second-price RBR slot\nauction, we have f(\u03c3) \u2265 Lf(\u03b7r).\nProof. We number the agents so that agent i has the\nith\nhighest revenue, so r1 \u2265 r2 \u2265 . . . \u2265 rN . Hence the\nstandard allocation has value f(\u03b7r) =\nPN\ni=1 \u03b3iri. To prove\nthe theorem, we will make repeated use of the fact thatP\nk akP\nk bk\n\u2265 mink\nak\nbk\nwhen the ak and bk are positive. Note\nthat according to Lemma 2, if agent i lies at least two slots\nbelow slot j, then r\u03c3(j) \u2265 ri\n\n1 \u2212\n\u03b3j+2\n\u03b3j+1\n\n.\nIt may be the case that for some slot i, we have \u03c3(i) > i\nand for slots k > i + 1 we have \u03c3(k) > i. We then say that\nslot i is inverted. Let S be the set of agents with indices at\nleast i + 1; there are N \u2212 i of these. If slot i is inverted, it is\noccupied by some agent from S. Also all slots strictly lower\nthan i + 1 must be occupied by the remaining agents from\nS, since \u03c3(k) > i for k \u2265 i + 2. The agent in slot i + 1 must\nthen have an index \u03c3(i + 1) \u2264 i (note this means slot i + 1\ncannot be inverted). Now there are two cases. In the first\ncase we have \u03c3(i) = i + 1. Then\n\u03b3ir\u03c3(i) + \u03b3i+1r\u03c3(i+1)\n\u03b3iri + \u03b3i+1ri+1\n\u2265\n\u03b3i+1ri + \u03b3iri+1\n\u03b3iri + \u03b3i+1ri+1\n\u2265 min\n\uf6be\n\u03b3i+1\n\u03b3i\n,\n\u03b3i\n\u03b3i+1\nff\n=\n\u03b3i+1\n\u03b3i\nIn the second case we have \u03c3(i) > i+1. Then since all agents\nin S except the one in slot i lie strictly below slot i + 1, and\n225\nthe agent in slot i is not agent i + 1, it must be that agent\ni+1 is in a slot strictly below slot i+1. This means that it is\nat least two slots below the agent that actually occupies slot\ni, and by Lemma 2 we then have r\u03c3(i) \u2265 ri+1\n\n1 \u2212\n\u03b3i+2\n\u03b3i+1\n\n.\nThus,\n\u03b3ir\u03c3(i) + \u03b3i+1r\u03c3(i+1)\n\u03b3iri + \u03b3i+1ri+1\n\u2265\n\u03b3i+1ri + \u03b3ir\u03c3(i)\n\u03b3iri + \u03b3i+1ri+1\n\u2265 min\n\uf6be\n\u03b3i+1\n\u03b3i\n, 1 \u2212\n\u03b3i+2\n\u03b3i+1\nff\nIf slot i is not inverted, then on one hand we may have\n\u03c3(i) \u2264 i, in which case r\u03c3(i)/ri \u2265 1. On the other hand we\nmay have \u03c3(i) > i but there is some agent with index j \u2264 i\nthat lies at least two slots below slot i. Then by Lemma 2,\nr\u03c3(i) \u2265 rj\n\n1 \u2212\n\u03b3i+2\n\u03b3i+1\n\n\u2265 ri\n\n1 \u2212\n\u03b3i+2\n\u03b3i+1\n\n.\nWe write i \u2208 I if slot i is inverted, and i \u2208 I if neither i nor\ni \u2212 1 are inverted. By our arguments above two consecutive\nslots cannot be inverted, so we can write\nf(\u03c3)\nf(\u03b3r)\n=\nP\ni\u2208I\n`\n\u03b3ir\u03c3(i) + \u03b3i+1r\u03c3(i+1)\n\u00b4\n+\nP\ni\u2208I \u03b3ir\u03c3(i)\nP\ni\u2208I (\u03b3iri + \u03b3i+1ri+1) +\nP\ni\u2208I \u03b3iri\n\u2265 min\n\uf6be\nmin\ni\u2208I\n\uf6be\n\u03b3ir\u03c3(i) + \u03b3i+1r\u03c3(i+1)\n\u03b3iri + \u03b3i+1ri+1\nff\n, min\ni\u2208I\n\uf6be\n\u03b3ir\u03c3(i)\n\u03b3iri\nffff\n\u2265 L\nand this completes the proof.\nNote that for RBR, the standard value is also the\nefficient value by Theorem 1. Also note that for an exponential\ndecay model, L = min\n\u02d81\n\u03b4\n, 1 \u2212 1\n\u03b4\n\u00af\n. With \u03b4 = 1.428 (see\nSection 2.1), the factor is L \u2248 1/3.34, so the total value in a\npure-strategy Nash equilibrium of a second-price RBR slot\nauction is always within a factor of 3.34 of the efficient value\nwith such a discount.\nAgain for RBB we have an analogous result.\nTheorem 5. For an allocation \u03c3 that results from a\npurestrategy Nash equilibrium of a second-price RBB slot\nauction, we have g(\u03c3) \u2265 Lg(\u03b7x).\nProof Sketch. Simply substitute bidder values for bidder\nrevenues in the proof of Theorem 4, and appeal to Lemma 3.\n5. CONCLUSIONS\nThis paper analyzed stylized versions of the slot auction\ndesigns currently used by Yahoo! and Google, namely rank\nby bid (RBB) and rank by revenue (RBR), respectively.\nWe also considered first and second pricing rules together\nwith each of these allocation rules, since both have been used\nhistorically. We first studied the short-run setting with\nincomplete information, corresponding to the case where\nagents have just approached the mechanism. Our\nequilibrium analysis revealed that RBB has much weaker\ninformational requirements than RBR, because bidders need not\nknow any information about relevance (even their own) to\nplay the Bayes-Nash equilibrium. However, RBR leads to\nan efficient allocation in equilibrium, whereas RBB does not.\nWe showed that for an arbitrary distribution over value and\nrelevance, no revenue ranking of RBB and RBR is possible.\nWe hope that the tools we used to establish these results\n(revenue equivalence, the form of first-price equilibria, the\ntruthful payments rules) will help others wanting to pursue\nfurther analyses of slot auctions.\nWe also studied the long-run case where agents have\nexperimented with their bids and each settled on one they\nfind optimal. We argued that a stable set of bids in this\nsetting can be modeled as a pure-strategy Nash equilibrium\nof the static game of complete information. We showed that\nno pure-strategy equilibrium exists with either RBB or RBR\nusing first pricing, but that with second pricing there always\nexists such an equilibrium (in the case of RBR, an efficient\nequilibrium). In general second pricing allows for multiple\npure-strategy equilibria, but we showed that the value of\nsuch equilibria diverges by only a constant factor from the\nvalue obtained if all agents bid truthfully (which in the case\nof RBR is the efficient value).\n6. FUTURE WORK\nIntroducing budget constraints into the model is a\nnatural next step for future work. The complication here lies\nin the fact that budgets are often set for entire campaigns\nrather than single keywords. Assuming that the optimal\nchoice of budget can be made independent of the choice\nof bid for a specific keyword, it can be shown that it is a\ndominant-strategy to report this optimal budget with one\"s\nbid. The problem is then to ascertain that bids and budgets\ncan indeed be optimized separately, or to find a plausible\nmodel where deriving equilibrium bids and budgets together\nis tractable.\nIdentifying a condition on the distribution over value and\nrelevance that actually does yield a revenue ranking of RBB\nand RBR (such as correlation between value and relevance,\nperhaps) would yield a more satisfactory characterization\nof their relative revenue properties. Placing bounds on the\nrevenue obtained in a complete information equilibrium is\nalso a relevant question.\nBecause the incomplete information case is such a close\ngeneralization of the most basic single-item auction model,\nit would be interesting to see which standard results from\nsingle-item auction theory (e.g. results with risk-averse\nbidders, an endogenous number of bidders, asymmetries, etc...)\nautomatically generalize and which do not, to fully\nunderstand the structural differences between single-item and slot\nauctions.\nAcknowledgements\nDavid Pennock provided valuable guidance throughout this\nproject. I would also like to thank David Parkes for helpful\ncomments.\n7. REFERENCES\n[1] Z. Abrams. Revenue maximization when bidders have\nbudgets. In Proc. the ACM-SIAM Symposium on\nDiscrete Algorithms, 2006.\n[2] T. B\u00a8orgers, I. Cox, and M. Pesendorfer. Personal\nCommunication.\n[3] C. Borgs, J. Chayes, N. Immorlica, M. Mahdian, and\nA. Saberi. Multi-unit auctions with\nbudget-constrained bidders. In Proc. the Sixth ACM\nConference on Electronic Commerce, Vancouver, BC,\n2005.\n[4] F. Brandt and G. Wei\u00df. Antisocial agents and Vickrey\nauctions. In J.-J. C. Meyer and M. Tambe, editors,\n226\nIntelligent Agents VIII, volume 2333 of Lecture Notes\nin Artificial Intelligence. Springer Verlag, 2001.\n[5] B. Edelman and M. Ostrovsky. Strategic bidder\nbehavior in sponsored search auctions. In Workshop\non Sponsored Search Auctions, ACM Electronic\nCommerce, 2005.\n[6] B. Edelman, M. Ostrovsky, and M. Schwarz. Internet\nadvertising and the generalized second price auction:\nSelling billions of dollars worth of keywords. NBER\nworking paper 11765, November 2005.\n[7] J. Feng, H. K. Bhargava, and D. M. Pennock.\nImplementing sponsored search in web search engines:\nComputational evaluation of alternative mechanisms.\nINFORMS Journal on Computing, 2005. Forthcoming.\n[8] J. Green and J.-J. Laffont. Characterization of\nsatisfactory mechanisms for the revelation of\npreferences for public goods. Econometrica,\n45:427-438, 1977.\n[9] B. Holmstrom. Groves schemes on restricted domains.\nEconometrica, 47(5):1137-1144, 1979.\n[10] B. Kitts, P. Laxminarayan, B. LeBlanc, and\nR. Meech. A formal analysis of search auctions\nincluding predictions on click fraud and bidding\ntactics. In Workshop on Sponsored Search Auctions,\nACM Electronic Commerce, 2005.\n[11] V. Krishna. Auction Theory. Academic Press, 2002.\n[12] D. Liu and J. Chen. Designing online auctions with\npast performance information. Decision Support\nSystems, 2005. Forthcoming.\n[13] C. Meek, D. M. Chickering, and D. B. Wilson.\nStochastic and contingent payment auctions. In\nWorkshop on Sponsored Search Auctions, ACM\nElectronic Commerce, 2005.\n[14] A. Mehta, A. Saberi, U. Vazirani, and V. Vazirani.\nAdwords and generalized on-line matching. In Proc.\n46th IEEE Symposium on Foundations of Computer\nScience, 2005.\n[15] P. Milgrom. Putting Auction Theory to Work.\nCambridge University Press, 2004.\n[16] P. Milgrom and C. Shannon. Monotone comparative\nstatics. Econometrica, 62(1):157-180, 1994.\n[17] P. J. Reny. On the existence of pure and mixed\nstrategy Nash equilibria in discontinuous games.\nEconometrica, 67(5):1029-1056, 1999.\n[18] H. R. Varian. Position auctions. Working Paper,\nFebruary 2006.\n[19] W. Vickrey. Counterspeculation, auctions and\ncompetitive sealed tenders. Journal of Finance,\n16:8-37, 1961.\n227", "keywords": "rank by bid;second pricing;incomplete information;web search engine;resurgent online advertising industry;second-price payment rule;alternative slot auction design;rank by revenue;pay per click;divergence of value;divergence of economic value;auction theory;combined market capitalization;multitude of equilibrium;sponsor search;sponsored search;slot allocation;auction-style mechanism;search engine;ad listing;equilibrium multitude"}
{"name": "train_J-42", "title": "The Dynamics of Viral Marketing \u2217", "abstract": "We present an analysis of a person-to-person recommendation network, consisting of 4 million people who made 16 million recommendations on half a million products. We observe the propagation of recommendations and the cascade sizes, which we explain by a simple stochastic model. We then establish how the recommendation network grows over time and how effective it is from the viewpoint of the sender and receiver of the recommendations. While on average recommendations are not very effective at inducing purchases and do not spread very far, we present a model that successfully identifies product and pricing categories for which viral marketing seems to be very effective.", "fulltext": "1. INTRODUCTION\nWith consumers showing increasing resistance to\ntraditional forms of advertising such as TV or newspaper ads,\nmarketers have turned to alternate strategies, including\nviral marketing. Viral marketing exploits existing social\nnetworks by encouraging customers to share product\ninformation with their friends. Previously, a few in depth\nstudies have shown that social networks affect the adoption of\nindividual innovations and products (for a review see [15]\nor [16]). But until recently it has been difficult to measure\nhow influential person-to-person recommendations actually\nare over a wide range of products. We were able to directly\nmeasure and model the effectiveness of recommendations by\nstudying one online retailer\"s incentivised viral marketing\nprogram. The website gave discounts to customers\nrecommending any of its products to others, and then tracked the\nresulting purchases and additional recommendations.\nAlthough word of mouth can be a powerful factor\ninfluencing purchasing decisions, it can be tricky for advertisers\nto tap into. Some services used by individuals to\ncommunicate are natural candidates for viral marketing, because the\nproduct can be observed or advertised as part of the\ncommunication. Email services such as Hotmail and Yahoo had\nvery fast adoption curves because every email sent through\nthem contained an advertisement for the service and because\nthey were free. Hotmail spent a mere $50,000 on traditional\nmarketing and still grew from zero to 12 million users in 18\nmonths [7]. Google\"s Gmail captured a significant part of\nmarket share in spite of the fact that the only way to sign\nup for the service was through a referral.\nMost products cannot be advertised in such a direct way.\nAt the same time the choice of products available to\nconsumers has increased manyfold thanks to online retailers\nwho can supply a much wider variety of products than\ntraditional brick-and-mortar stores. Not only is the variety\nof products larger, but one observes a \u2018fat tail\"\nphenomenon, where a large fraction of purchases are of relatively\nobscure items. On Amazon.com, somewhere between 20 to\n40 percent of unit sales fall outside of its top 100,000 ranked\nproducts [2]. Rhapsody, a streaming-music service, streams\nmore tracks outside than inside its top 10,000 tunes [1].\nEffectively advertising these niche products using traditional\nadvertising approaches is impractical. Therefore using more\ntargeted marketing approaches is advantageous both to the\nmerchant and the consumer, who would benefit from\nlearning about new products.\nThe problem is partly addressed by the advent of\nonline product and merchant reviews, both at retail sites such\nas EBay and Amazon, and specialized product comparison\nsites such as Epinions and CNET. Quantitative marketing\ntechniques have been proposed [12], and the rating of\nproducts and merchants has been shown to effect the likelihood\nof an item being bought [13, 4]. Of further help to the\nconsumer are collaborative filtering recommendations of the\nform people who bought x also bought y feature [11].\nThese refinements help consumers discover new products\n228\nand receive more accurate evaluations, but they cannot\ncompletely substitute personalized recommendations that one\nreceives from a friend or relative. It is human nature to be\nmore interested in what a friend buys than what an\nanonymous person buys, to be more likely to trust their opinion,\nand to be more influenced by their actions. Our friends are\nalso acquainted with our needs and tastes, and can make\nappropriate recommendations. A Lucid Marketing survey\nfound that 68% of individuals consulted friends and relatives\nbefore purchasing home electronics - more than the half who\nused search engines to find product information [3].\nSeveral studies have attempted to model just this kind\nof network influence. Richardson and Domingos [14] used\nEpinions\" trusted reviewer network to construct an\nalgorithm to maximize viral marketing efficiency assuming that\nindividuals\" probability of purchasing a product depends on\nthe opinions on the trusted peers in their network. Kempe,\nKleinberg and Tardos [8] evaluate the efficiency of several\nalgorithms for maximizing the size of influence set given\nvarious models of adoption. While these models address the\nquestion of maximizing the spread of influence in a network,\nthey are based on assumed rather than measured influence\neffects.\nIn contrast, in our study we are able to directly observe\nthe effectiveness of person to person word of mouth\nadvertising for hundreds of thousands of products for the first time.\nWe find that most recommendation chains do not grow very\nlarge, often terminating with the initial purchase of a\nproduct. However, occasionally a product will propagate through\na very active recommendation network. We propose a simple\nstochastic model that seems to explain the propagation of\nrecommendations. Moreover, the characteristics of\nrecommendation networks influence the purchase patterns of their\nmembers. For example, individuals\" likelihood of\npurchasing a product initially increases as they receive additional\nrecommendations for it, but a saturation point is quickly\nreached. Interestingly, as more recommendations are sent\nbetween the same two individuals, the likelihood that they\nwill be heeded decreases. We also propose models to identify\nproducts for which viral marketing is effective: We find that\nthe category and price of product plays a role, with\nrecommendations of expensive products of interest to small, well\nconnected communities resulting in a purchase more often.\nWe also observe patterns in the timing of recommendations\nand purchases corresponding to times of day when people\nare likely to be shopping online or reading email. We report\non these and other findings in the following sections.\n2. THE RECOMMENDATION NETWORK\n2.1 Dataset description\nOur analysis focuses on the recommendation referral\nprogram run by a large retailer. The program rules were as\nfollows. Each time a person purchases a book, music, or a\nmovie he or she is given the option of sending emails\nrecommending the item to friends. The first person to purchase\nthe same item through a referral link in the email gets a 10%\ndiscount. When this happens the sender of the\nrecommendation receives a 10% credit on their purchase.\nThe recommendation dataset consists of 15,646,121\nrecommendations made among 3,943,084 distinct users. The\ndata was collected from June 5 2001 to May 16 2003. In\ntotal, 548,523 products were recommended, 99% of them\nbelonging to 4 main product groups: Books, DVDs, Music\nand Videos. In addition to recommendation data, we also\ncrawled the retailer\"s website to obtain product categories,\nreviews and ratings for all products. Of the products in our\ndata set, 5813 (1%) were discontinued (the retailer no longer\nprovided any information about them).\nAlthough the data gives us a detailed and accurate view\nof recommendation dynamics, it does have its limitations.\nThe only indication of the success of a recommendation\nis the observation of the recipient purchasing the product\nthrough the same vendor. We have no way of knowing if\nthe person had decided instead to purchase elsewhere,\nborrow, or otherwise obtain the product. The delivery of the\nrecommendation is also somewhat different from one person\nsimply telling another about a product they enjoy, possibly\nin the context of a broader discussion of similar products.\nThe recommendation is received as a form email including\ninformation about the discount program. Someone reading\nthe email might consider it spam, or at least deem it less\nimportant than a recommendation given in the context of\na conversation. The recipient may also doubt whether the\nfriend is recommending the product because they think the\nrecipient might enjoy it, or are simply trying to get a\ndiscount for themselves. Finally, because the recommendation\ntakes place before the recommender receives the product,\nit might not be based on a direct observation of the\nproduct. Nevertheless, we believe that these recommendation\nnetworks are reflective of the nature of word of mouth\nadvertising, and give us key insights into the influence of social\nnetworks on purchasing decisions.\n2.2 Recommendation network statistics\nFor each recommendation, the dataset included the\nproduct and product price, sender ID, receiver ID, the sent date,\nand a buy-bit, indicating whether the recommendation\nresulted in a purchase and discount. The sender and receiver\nID\"s were shadowed. We represent this data set as a\ndirected multi graph. The nodes represent customers, and\na directed edge contains all the information about the\nrecommendation. The edge (i, j, p, t) indicates that i\nrecommended product p to customer j at time t.\nThe typical process generating edges in the\nrecommendation network is as follows: a node i first buys a product p at\ntime t and then it recommends it to nodes j1, . . . , jn. The\nj nodes can they buy the product and further recommend\nit. The only way for a node to recommend a product is to\nfirst buy it. Note that even if all nodes j buy a product,\nonly the edge to the node jk that first made the purchase\n(within a week after the recommendation) will be marked\nby a buy-bit. Because the buy-bit is set only for the first\nperson who acts on a recommendation, we identify additional\npurchases by the presence of outgoing recommendations for\na person, since all recommendations must be preceded by a\npurchase. We call this type of evidence of purchase a\nbuyedge. Note that buy-edges provide only a lower bound on the\ntotal number of purchases without discounts. It is possible\nfor a customer to not be the first to act on a\nrecommendation and also to not recommend the product to others.\nUnfortunately, this was not recorded in the data set. We\nconsider, however, the buy-bits and buy-edges as proxies for\nthe total number of purchases through recommendations.\nFor each product group we took recommendations on all\nproducts from the group and created a network. Table 1\n229\n0 1 2 3 4\nx 10\n6\n0\n2\n4\n6\n8\n10\n12\nx 10\n4\nnumber of nodes\nsizeofgiantcomponent\nby month\nquadratic fit\n0 10 20\n0\n2\n4\nx 10\n6\nm (month)\nn\n# nodes\n1.7*10\n6\nm\n10\n0\n10\n1\n10\n2\n10\n3\n10\n1\n10\n2\n10\n3\n10\n4\n10\n5\n10\n6\nkp\n(recommendations by a person for a product)\nN(x>=k\np\n)\nlevel 0\n\u03b3 = 2.6\nlevel 1\n\u03b3 = 2.0\nlevel 2\n\u03b3 = 1.5\nlevel 3\n\u03b3 = 1.2\nlevel 4\n\u03b3 = 1.2\n(a) Network growth (b) Recommending by level\nFigure 1: (a) The size of the largest connected\ncomponent of customers over time. The inset shows the\nlinear growth in the number of customers n over\ntime. (b) The number of recommendations sent by\na user with each curve representing a different depth\nof the user in the recommendation chain. A power\nlaw exponent \u03b3 is fitted to all but the tail.\n(first 7 columns) shows the sizes of various product group\nrecommendation networks with p being the total number\nof products in the product group, n the total number of\nnodes spanned by the group recommendation network and\ne the number of edges (recommendations). The column eu\nshows the number of unique edges - disregarding multiple\nrecommendations between the same source and recipient.\nIn terms of the number of different items, there are by far\nthe most music CDs, followed by books and videos. There\nis a surprisingly small number of DVD titles. On the other\nhand, DVDs account for more half of all recommendations in\nthe dataset. The DVD network is also the most dense,\nhaving about 10 recommendations per node, while books and\nmusic have about 2 recommendations per node and videos\nhave only a bit more than 1 recommendation per node.\nMusic recommendations reached about the same number\nof people as DVDs but used more than 5 times fewer\nrecommendations to achieve the same coverage of the nodes. Book\nrecommendations reached by far the most people - 2.8\nmillion. Notice that all networks have a very small number\nof unique edges. For books, videos and music the number\nof unique edges is smaller than the number of nodes - this\nsuggests that the networks are highly disconnected [5].\nFigure 1(a) shows the fraction of nodes in largest weakly\nconnected component over time. Notice the component is\nvery small. Even if we compose a network using all the\nrecommendations in the dataset, the largest connected\ncomponent contains less than 2.5% (100,420) of the nodes, and the\nsecond largest component has only 600 nodes. Still, some\nsmaller communities, numbering in the tens of thousands\nof purchasers of DVDs in categories such as westerns,\nclassics and Japanese animated films (anime), had connected\ncomponents spanning about 20% of their members.\nThe insert in figure 1(a) shows the growth of the\ncustomer base over time. Surprisingly it was linear, adding on\naverage 165,000 new users each month, which is an\nindication that the service itself was not spreading epidemically.\nFurther evidence of non-viral spread is provided by the\nrelatively high percentage (94%) of users who made their first\nrecommendation without having previously received one.\nBack to table 1: given the total number of\nrecommendations e and purchases (bb + be) influenced by\nrecommendations we can estimate how many recommendations need\nto be independently sent over the network to induce a new\npurchase. Using this metric books have the most influential\nrecommendations followed by DVDs and music. For books\none out of 69 recommendations resulted in a purchase. For\nDVDs it increases to 108 recommendations per purchase and\nfurther increases to 136 for music and 203 for video.\nEven with these simple counts we can make the first few\nobservations. It seems that some people got quite\nheavily involved in the recommendation program, and that they\ntended to recommend a large number of products to the\nsame set of friends (since the number of unique edges is so\nsmall). This shows that people tend to buy more DVDs and\nalso like to recommend them to their friends, while they\nseem to be more conservative with books. One possible\nreason is that a book is bigger time investment than a DVD:\none usually needs several days to read a book, while a DVD\ncan be viewed in a single evening.\nOne external factor which may be affecting the\nrecommendation patterns for DVDs is the existence of referral websites\n(www.dvdtalk.com). On these websites people, who want to\nbuy a DVD and get a discount, would ask for\nrecommendations. This way there would be recommendations made\nbetween people who don\"t really know each other but rather\nhave an economic incentive to cooperate. We were not able\nto find similar referral sharing sites for books or CDs.\n2.3 Forward recommendations\nNot all people who make a purchase also decide to give\nrecommendations. So we estimate what fraction of people\nthat purchase also decide to recommend forward. To obtain\nthis information we can only use the nodes with purchases\nthat resulted in a discount.\nThe last 3 columns of table 1 show that only about a\nthird of the people that purchase also recommend the\nproduct forward. The ratio of forward recommendations is much\nhigher for DVDs than for other kinds of products. Videos\nalso have a higher ratio of forward recommendations, while\nbooks have the lowest. This shows that people are most keen\non recommending movies, while more conservative when\nrecommending books and music.\nFigure 1(b) shows the cumulative out-degree distribution,\nthat is the number of people who sent out at least kp\nrecommendations, for a product. It shows that the deeper an\nindividual is in the cascade, if they choose to make\nrecommendations, they tend to recommend to a greater number\nof people on average (the distribution has a higher\nvariance). This effect is probably due to only very heavily\nrecommended products producing large enough cascades to\nreach a certain depth. We also observe that the probability\nof an individual making a recommendation at all (which can\nonly occur if they make a purchase), declines after an initial\nincrease as one gets deeper into the cascade.\n2.4 Identifying cascades\nAs customers continue forwarding recommendations, they\ncontribute to the formation of cascades. In order to\nidentify cascades, i.e. the causal propagation of\nrecommendations, we track successful recommendations as they influence\npurchases and further recommendations. We define a\nrecommendation to be successful if it reached a node before its first\npurchase. We consider only the first purchase of an item,\nbecause there are many cases when a person made multiple\n230\nGroup p n e eu bb be Purchases Forward Percent\nBook 103,161 2,863,977 5,741,611 2,097,809 65,344 17,769 65,391 15,769 24.2\nDVD 19,829 805,285 8,180,393 962,341 17,232 58,189 16,459 7,336 44.6\nMusic 393,598 794,148 1,443,847 585,738 7,837 2,739 7,843 1,824 23.3\nVideo 26,131 239,583 280,270 160,683 909 467 909 250 27.6\nTotal 542,719 3,943,084 15,646,121 3,153,676 91,322 79,164 90,602 25,179 27.8\nTable 1: Product group recommendation statistics. p: number of products, n: number of nodes, e: number of\nedges (recommendations), eu: number of unique edges, bb: number of buy bits, be: number of buy edges. Last\n3 columns of the table: Fraction of people that purchase and also recommend forward. Purchases: number\nof nodes that purchased. Forward: nodes that purchased and then also recommended the product.\n973\n938\n(a) Medical book (b) Japanese graphic novel\nFigure 2: Examples of two product recommendation networks: (a) First aid study guide First Aid for the\nUSMLE Step, (b) Japanese graphic novel (manga) Oh My Goddess!: Mara Strikes Back.\n10\n0\n10\n5\n10\n0\n10\n2\n10\n4\n10\n6\n10\n8\nNumber of recommendations\nCount\n= 3.4e6 x\u22122.30\nR2\n=0.96\n10\n0\n10\n1\n10\n2\n10\n3\n10\n4\n10\n0\n10\n2\n10\n4\n10\n6\n10\n8\nNumber of purchases\nCount\n= 4.1e6 x\u22122.49\nR2\n=0.99\n(a) Recommendations (b) Purchases\nFigure 3: Distribution of the number of\nrecommendations and number of purchases made by a node.\npurchases of the same product, and in between those\npurchases she may have received new recommendations. In this\ncase one cannot conclude that recommendations following\nthe first purchase influenced the later purchases.\nEach cascade is a network consisting of customers (nodes)\nwho purchased the same product as a result of each other\"s\nrecommendations (edges). We delete late recommendations\n- all incoming recommendations that happened after the\nfirst purchase of the product. This way we make the\nnetwork time increasing or causal - for each node all incoming\nedges (recommendations) occurred before all outgoing edges.\nNow each connected component represents a time obeying\npropagation of recommendations.\nFigure 2 shows two typical product recommendation\nnetworks: (a) a medical study guide and (b) a Japanese graphic\nnovel. Throughout the dataset we observe very similar\npatters. Most product recommendation networks consist of a\nlarge number of small disconnected components where we\ndo not observe cascades. Then there is usually a small\nnumber of relatively small components with recommendations\nsuccessfully propagating.\nThis observation is reflected in the heavy tailed\ndistribution of cascade sizes (see figure 4), having a power-law\nexponent close to 1 for DVDs in particular.\nWe also notice bursts of recommendations (figure 2(b)).\nSome nodes recommend to many friends, forming a star like\npattern. Figure 3 shows the distribution of the\nrecommendations and purchases made by a single node in the\nrecommendation network. Notice the power-law distributions and\nlong flat tails. The most active person made 83,729\nrecommendations and purchased 4,416 different items. Finally,\nwe also sometimes observe \u2018collisions\", where nodes receive\nrecommendations from two or more sources. A detailed\nenumeration and analysis of observed topological cascade\npatterns for this dataset is made in [10].\n2.5 The recommendation propagation model\nA simple model can help explain how the wide variance we\nobserve in the number of recommendations made by\nindividuals can lead to power-laws in cascade sizes (figure 4). The\nmodel assumes that each recipient of a recommendation will\nforward it to others if its value exceeds an arbitrary\nthreshold that the individual sets for herself. Since exceeding this\nvalue is a probabilistic event, let\"s call pt the probability\nthat at time step t the recommendation exceeds the\nthresh231\n10\n0\n10\n1\n10\n2\n10\n0\n10\n2\n10\n4\n10\n6\n= 1.8e6 x\u22124.98\nR2\n=0.99\n10\n0\n10\n1\n10\n2\n10\n3\n10\n0\n10\n2\n10\n4\n= 3.4e3 x\u22121.56\nR2\n=0.83\n10\n0\n10\n1\n10\n2\n10\n0\n10\n2\n10\n4\n= 4.9e5 x\u22126.27\nR2\n=0.97\n10\n0\n10\n1\n10\n2\n10\n0\n10\n2\n10\n4\n= 7.8e4 x\u22125.87\nR2\n=0.97\n(a) Book (b) DVD (c) Music (d) Video\nFigure 4: Size distribution of cascades (size of cascade vs. count). Bold line presents a power-fit.\nold. In that case the number of recommendations Nt+1 at\ntime (t + 1) is given in terms of the number of\nrecommendations at an earlier time by\nNt+1 = ptNt (1)\nwhere the probability pt is defined over the unit interval.\nNotice that, because of the probabilistic nature of the\nthreshold being exceeded, one can only compute the final\ndistribution of recommendation chain lengths, which we now\nproceed to do.\nSubtracting from both sides of this equation the term Nt\nand diving by it we obtain\nN(t+1) \u2212 Nt\nNt\n= pt \u2212 1 (2)\nSumming both sides from the initial time to some very\nlarge time T and assuming that for long times the numerator\nis smaller than the denominator (a reasonable assumption)\nwe get\ndN\nN\n= pt (3)\nThe left hand integral is just ln(N), and the right hand\nside is a sum of random variables, which in the limit of a very\nlarge uncorrelated number of recommendations is normally\ndistributed (central limit theorem).\nThis means that the logarithm of the number of messages\nis normally distributed, or equivalently, that the number of\nmessages passed is log-normally distributed. In other words\nthe probability density for N is given by\nP(N) =\n1\nN\n\u221a\n2\u03c0\u03c32\nexp\n\u2212(ln(N) \u2212 \u03bc)2\n2\u03c32\n(4)\nwhich, for large variances describes a behavior whereby\nthe typical number of recommendations is small (the mode\nof the distribution) but there are unlikely events of large\nchains of recommendations which are also observable.\nFurthermore, for large variances, the lognormal\ndistribution can behave like a power law for a range of values. In\norder to see this, take the logarithms on both sides of the\nequation (equivalent to a log-log plot) and one obtains\nln(P(N)) = \u2212 ln(N) \u2212 ln(\n\u221a\n2\u03c0\u03c32) \u2212\n(ln (N) \u2212 \u03bc)2\n2\u03c32\n(5)\nSo, for large \u03c3, the last term of the right hand side goes\nto zero, and since the the second term is a constant one\nobtains a power law behavior with exponent value of\nminus one. There are other models which produce power-law\ndistributions of cascade sizes, but we present ours for its\nsimplicity, since it does not depend on network topology [6]\nor critical thresholds in the probability of a recommendation\nbeing accepted [18].\n3. SUCCESS OF RECOMMENDATIONS\nSo far we only looked into the aggregate statistics of the\nrecommendation network. Next, we ask questions about\nthe effectiveness of recommendations in the\nrecommendation network itself. First, we analyze the probability of\npurchasing as one gets more and more recommendations. Next,\nwe measure recommendation effectiveness as two people\nexchange more and more recommendations. Lastly, we\nobserve the recommendation network from the perspective of\nthe sender of the recommendation. Does a node that makes\nmore recommendations also influence more purchases?\n3.1 Probability of buying versus number of\nincoming recommendations\nFirst, we examine how the probability of purchasing changes\nas one gets more and more recommendations. One would\nexpect that a person is more likely to buy a product if she gets\nmore recommendations. On the other had one would also\nthink that there is a saturation point - if a person hasn\"t\nbought a product after a number of recommendations, they\nare not likely to change their minds after receiving even more\nof them. So, how many recommendations are too many?\nFigure 5 shows the probability of purchasing a product\nas a function of the number of incoming recommendations\non the product. As we move to higher numbers of incoming\nrecommendations, the number of observations drops rapidly.\nFor example, there were 5 million cases with 1 incoming\nrecommendation on a book, and only 58 cases where a\nperson got 20 incoming recommendations on a particular book.\nThe maximum was 30 incoming recommendations. For these\nreasons we cut-off the plot when the number of observations\nbecomes too small and the error bars too large.\nFigure 5(a) shows that, overall, book recommendations\nare rarely followed. Even more surprisingly, as more and\nmore recommendations are received, their success decreases.\nWe observe a peak in probability of buying at 2 incoming\nrecommendations and then a slow drop.\nFor DVDs (figure 5(b)) we observe a saturation around 10\nincoming recommendations. This means that after a person\ngets 10 recommendations on a particular DVD, they\nbecome immune to them - their probability of buying does\nnot increase anymore. The number of observations is 2.5\nmillion at 1 incoming recommendation and 100 at 60\nincoming recommendations. The maximal number of received\nrecommendations is 172 (and that person did not buy)\n232\n2 4 6 8 10\n0\n0.01\n0.02\n0.03\n0.04\n0.05\n0.06\nIncoming Recommendations\nProbabilityofBuying\n10 20 30 40 50 60\n0\n0.02\n0.04\n0.06\n0.08\nIncoming Recommendations\nProbabilityofBuying\n(a) Books (b) DVD\nFigure 5: Probability of buying a book (DVD) given a number of incoming recommendations.\n5 10 15 20 25 30 35 40\n4\n6\n8\n10\n12\nx 10\n\u22123\nExchanged recommendations\nProbabilityofbuying\n5 10 15 20 25 30 35 40\n0.02\n0.03\n0.04\n0.05\n0.06\n0.07\nExchanged recommendations\nProbabilityofbuying\n(a) Books (b) DVD\nFigure 6: The effectiveness of recommendations\nwith the total number of exchanged\nrecommendations.\n3.2 Success of subsequent recommendations\nNext, we analyze how the effectiveness of\nrecommendations changes as two persons exchange more and more\nrecommendations. A large number of exchanged\nrecommendations can be a sign of trust and influence, but a sender of too\nmany recommendations can be perceived as a spammer. A\nperson who recommends only a few products will have her\nfriends\" attention, but one who floods her friends with all\nsorts of recommendations will start to loose her influence.\nWe measure the effectiveness of recommendations as a\nfunction of the total number of previously exchanged\nrecommendations between the two nodes. We construct the\nexperiment in the following way. For every recommendation\nr on some product p between nodes u and v, we first\ndetermine how many recommendations were exchanged between\nu and v before recommendation r. Then we check whether v,\nthe recipient of recommendation, purchased p after\nrecommendation r arrived. For the experiment we consider only\nnode pairs (u, v), where there were at least a total of 10\nrecommendations sent from u to v. We perform the experiment\nusing only recommendations from the same product group.\nFigure 6 shows the probability of buying as a function of\nthe total number of exchanged recommendations between\ntwo persons up to that point. For books we observe that\nthe effectiveness of recommendation remains about constant\nup to 3 exchanged recommendations. As the number of\nexchanged recommendations increases, the probability of\nbuying starts to decrease to about half of the original value and\nthen levels off. For DVDs we observe an immediate and\nconsistent drop. This experiment shows that recommendations\nstart to lose effect after more than two or three are passed\nbetween two people. We performed the experiment also for\nvideo and music, but the number of observations was too\nlow and the measurements were noisy.\n3.3 Success of outgoing recommendations\nIn previous sections we examined the data from the\nviewpoint of the receiver of the recommendation. Now we look\nfrom the viewpoint of the sender. The two interesting\nquestions are: how does the probability of getting a 10% credit\nchange with the number of outgoing recommendations; and\ngiven a number of outgoing recommendations, how many\npurchases will they influence?\nOne would expect that recommendations would be the\nmost effective when recommended to the right subset of\nfriends. If one is very selective and recommends to too few\nfriends, then the chances of success are slim. One the other\nhand, recommending to everyone and spamming them with\nrecommendations may have limited returns as well.\nThe top row of figure 7 shows how the average number\nof purchases changes with the number of outgoing\nrecommendations. For books, music, and videos the number of\npurchases soon saturates: it grows fast up to around 10\noutgoing recommendations and then the trend either slows or\nstarts to drop. DVDs exhibit different behavior, with the\nexpected number of purchases increasing throughout. But\nif we plot the probability of getting a 10% credit as a\nfunction of the number of outgoing recommendations, as in the\nbottom row of figure 7, we see that the success of DVD\nrecommendations saturates as well, while books, videos and\nmusic have qualitatively similar trends. The difference in\nthe curves for DVD recommendations points to the presence\nof collisions in the dense DVD network, which has 10\nrecommendations per node and around 400 per product - an\norder of magnitude more than other product groups. This\nmeans that many different individuals are recommending to\nthe same person, and after that person makes a purchase,\neven though all of them made a \u2018successful recommendation\"\n233\n10 20 30 40 50 60\n0\n0.1\n0.2\n0.3\n0.4\n0.5\nOutgoing Recommendations\nNumberofPurchases\n20 40 60 80 100 120 140\n0\n1\n2\n3\n4\n5\n6\n7\nOutgoing Recommendations\nNumberofPurchases\n5 10 15 20\n0\n0.05\n0.1\n0.15\n0.2\nOutgoing Recommendations\nNumberofPurchases\n2 4 6 8 10 12\n0\n0.05\n0.1\n0.15\n0.2\n0.25\nOutgoing Recommendations\nNumberofPurchases\n10 20 30 40 50 60 70 80\n0\n0.05\n0.1\n0.15\n0.2\n0.25\nOutgoing Recommendations\nProbabilityofCredit\n10 20 30 40 50 60 70 80\n0\n0.02\n0.04\n0.06\n0.08\n0.1\n0.12\nOutgoing Recommendations\nProbabilityofCredit\n5 10 15 20\n0\n0.02\n0.04\n0.06\n0.08\n0.1\nOutgoing Recommendations\nProbabilityofCredit\n2 4 6 8 10 12 14\n0\n0.02\n0.04\n0.06\n0.08\nOutgoing Recommendations\nProbabilityofCredit\n(a) Books (b) DVD (c) Music (d) Video\nFigure 7: Top row: Number of resulting purchases given a number of outgoing recommendations. Bottom\nrow: Probability of getting a credit given a number of outgoing recommendations.\n1 2 3 4 5 6 7 > 7\n0\n0.05\n0.1\n0.15\n0.2\n0.25\n0.3\n0.35\nLag [day]\nProportionofPurchases\n1 2 3 4 5 6 7 > 7\n0\n0.1\n0.2\n0.3\n0.4\n0.5\nLag [day]\nProportionofPurchases\n(a) Books (b) DVD\nFigure 8: The time between the recommendation\nand the actual purchase. We use all purchases.\nby our definition, only one of them receives a credit.\n4. TIMING OF RECOMMENDATIONS AND\nPURCHASES\nThe recommendation referral program encourages people\nto purchase as soon as possible after they get a\nrecommendation, since this maximizes the probability of getting a\ndiscount. We study the time lag between the recommendation\nand the purchase of different product groups, effectively how\nlong it takes a person to both receive a recommendation,\nconsider it, and act on it.\nWe present the histograms of the thinking time, i.e. the\ndifference between the time of purchase and the time the last\nrecommendation was received for the product prior to the\npurchase (figure 8). We use a bin size of 1 day. Around\n35%40% of book and DVD purchases occurred within a day after\nthe last recommendation was received. For DVDs 16%\npurchases occur more than a week after last recommendation,\nwhile this drops to 10% for books. In contrast, if we consider\nthe lag between the purchase and the first recommendation,\nonly 23% of DVD purchases are made within a day, while the\nproportion stays the same for books. This reflects a greater\nlikelihood for a person to receive multiple recommendations\nfor a DVD than for a book. At the same time, DVD\nrecommenders tend to send out many more recommendations,\nonly one of which can result in a discount. Individuals then\noften miss their chance of a discount, which is reflected in\nthe high ratio (78%) of recommended DVD purchases that\ndid not a get discount (see table 1, columns bb and be). In\ncontrast, for books, only 21% of purchases through\nrecommendations did not receive a discount.\nWe also measure the variation in intensity by time of day\nfor three different activities in the recommendation system:\nrecommendations (figure 9(a)), all purchases (figure 9(b)),\nand finally just the purchases which resulted in a discount\n(figure 9(c)). Each is given as a total count by hour of day.\nThe recommendations and purchases follow the same\npattern. The only small difference is that purchases reach a\nsharper peak in the afternoon (after 3pm Pacific Time, 6pm\nEastern time). The purchases that resulted in a discount\nlook like a negative image of the first two figures. This means\nthat most of discounted purchases happened in the morning\nwhen the traffic (number of purchases/recommendations) on\nthe retailer\"s website was low. This makes a lot of sense since\nmost of the recommendations happened during the day, and\nif the person wanted to get the discount by being the first\none to purchase, she had the highest chances when the traffic\non the website was the lowest.\n5. RECOMMENDATION EFFECTIVENESS\nBY BOOK CATEGORY\nSocial networks are a product of the contexts that bring\npeople together. Some contexts result in social ties that\nare more effective at conducting an action. For example,\nin small world experiments, where participants attempt to\nreach a target individual through their chain of\nacquaintances, profession trumped geography, which in turn was\nmore useful in locating a target than attributes such as\nreligion or hobbies [9, 17]. In the context of product\nrecommendations, we can ask whether a recommendation for a work\nof fiction, which may be made by any friend or neighbor, is\n234\n0 5 10 15 20 25\n0\n2\n4\n6\n8\n10\nx 10\n5\nHour of the Day\nRecommendtions\n0 5 10 15 20 25\n0\n0.5\n1\n1.5\n2\nx 10\n4\nHour of the Day\nAllPurchases\n0 5 10 15 20 25\n0\n1000\n2000\n3000\n4000\n5000\n6000\n7000\nHour of the Day\nDiscountedPurchases\n(a) Recommendations (b) Purchases (c) Purchases with Discount\nFigure 9: Time of day for purchases and recommendations. (a) shows the distribution of recommendations\nover the day, (b) shows all purchases and (c) shows only purchases that resulted in getting discount.\nmore or less influential than a recommendation for a\ntechnical book, which may be made by a colleague at work or\nschool.\nTable 2 shows recommendation trends for all top level\nbook categories by subject. An analysis of other product\ntypes can be found in the extended version of the paper. For\nclarity, we group the results by 4 different category types:\nfiction, personal/leisure, professional/technical, and\nnonfiction/other. Fiction encompasses categories such as Sci-Fi\nand Romance, as well as children\"s and young adult books.\nPersonal/Leisure encompasses everything from gardening,\nphotography and cooking to health and religion.\nFirst, we compare the relative number of\nrecommendations to reviews posted on the site (column cav/rp1 of\ntable 2). Surprisingly, we find that the number of people\nmaking personal recommendations was only a few times greater\nthan the number of people posting a public review on the\nwebsite. We observe that fiction books have relatively few\nrecommendations compared to the number of reviews, while\nprofessional and technical books have more\nrecommendations than reviews. This could reflect several factors. One is\nthat people feel more confident reviewing fiction than\ntechnical books. Another is that they hesitate to recommend a\nwork of fiction before reading it themselves, since the\nrecommendation must be made at the point of purchase. Yet\nanother explanation is that the median price of a work of\nfiction is lower than that of a technical book. This means\nthat the discount received for successfully recommending a\nmystery novel or thriller is lower and hence people have less\nincentive to send recommendations.\nNext, we measure the per category efficacy of\nrecommendations by observing the ratio of the number of purchases\noccurring within a week following a recommendation to the\nnumber of recommenders for each book subject category\n(column b of table 2). On average, only 2% of the\nrecommenders of a book received a discount because their\nrecommendation was accepted, and another 1% made a\nrecommendation that resulted in a purchase, but not a discount.\nWe observe marked differences in the response to\nrecommendation for different categories of books. Fiction in general\nis not very effectively recommended, with only around 2%\nof recommenders succeeding. The efficacy was a bit higher\n(around 3%) for non-fiction books dealing with personal and\nleisure pursuits, but is significantly higher in the professional\nand technical category. Medical books have nearly double\nthe average rate of recommendation acceptance. This could\nbe in part attributed to the higher median price of medical\nbooks and technical books in general. As we will see in\nSection 6, a higher product price increases the chance that a\nrecommendation will be accepted.\nRecommendations are also more likely to be accepted for\ncertain religious categories: 4.3% for Christian living and\ntheology and 4.8% for Bibles. In contrast, books not tied\nto organized religions, such as ones on the subject of new\nage (2.5%) and occult (2.2%) spirituality, have lower\nrecommendation effectiveness. These results raise the interesting\npossibility that individuals have greater influence over one\nanother in an organized context, for example through a\nprofessional contact or a religious one. There are exceptions of\ncourse. For example, Japanese anime DVDs have a strong\nfollowing in the US, and this is reflected in their frequency\nand success in recommendations. Another example is that of\ngardening. In general, recommendations for books relating\nto gardening have only a modest chance of being accepted,\nwhich agrees with the individual prerogative that\naccompanies this hobby. At the same time, orchid cultivation can be\na highly organized and social activity, with frequent \u2018shows\"\nand online communities devoted entirely to orchids. Perhaps\nbecause of this, the rate of acceptance of orchid book\nrecommendations is twice as high as those for books on vegetable\nor tomato growing.\n6. MODELING THE RECOMMENDATION\nSUCCESS\nWe have examined the properties of recommendation\nnetwork in relation to viral marketing, but one question still\nremains: what determines the product\"s viral marketing\nsuccess? We present a model which characterizes product\ncategories for which recommendations are more likely to be\naccepted. We use a regression of the following product\nattributes to correlate them with recommendation success:\n\u2022 r: number of recommendations\n\u2022 ns: number of senders of recommendations\n\u2022 nr: number of recipients of recommendations\n\u2022 p: price of the product\n\u2022 v: number of reviews of the product\n\u2022 t: average product rating\n235\ncategory np n cc rp1 vav cav/ pm b \u2217 100\nrp1\nBooks general 370230 2,860,714 1.87 5.28 4.32 1.41 14.95 3.12\nFiction\nChildren\"s Books 46,451 390,283 2.82 6.44 4.52 1.12 8.76 2.06**\nLiterature & Fiction 41,682 502,179 3.06 13.09 4.30 0.57 11.87 2.82*\nMystery and Thrillers 10,734 123,392 6.03 20.14 4.08 0.36 9.60 2.40**\nScience Fiction & Fantasy 10,008 175,168 6.17 19.90 4.15 0.64 10.39 2.34**\nRomance 6,317 60,902 5.65 12.81 4.17 0.52 6.99 1.78**\nTeens 5,857 81,260 5.72 20.52 4.36 0.41 9.56 1.94**\nComics & Graphic Novels 3,565 46,564 11.70 4.76 4.36 2.03 10.47 2.30*\nHorror 2,773 48,321 9.35 21.26 4.16 0.44 9.60 1.81**\nPersonal/Leisure\nReligion and Spirituality 43,423 441,263 1.89 3.87 4.45 1.73 9.99 3.13\nHealth Mind and Body 33,751 572,704 1.54 4.34 4.41 2.39 13.96 3.04\nHistory 28,458 28,3406 2.74 4.34 4.30 1.27 18.00 2.84\nHome and Garden 19,024 180,009 2.91 1.78 4.31 3.48 15.37 2.26**\nEntertainment 18,724 258,142 3.65 3.48 4.29 2.26 13.97 2.66*\nArts and Photography 17,153 179,074 3.49 1.56 4.42 3.85 20.95 2.87\nTravel 12,670 113,939 3.91 2.74 4.26 1.87 13.27 2.39**\nSports 10,183 120,103 1.74 3.36 4.34 1.99 13.97 2.26**\nParenting and Families 8,324 182,792 0.73 4.71 4.42 2.57 11.87 2.81\nCooking Food and Wine 7,655 146,522 3.02 3.14 4.45 3.49 13.97 2.38*\nOutdoors & Nature 6,413 59,764 2.23 1.93 4.42 2.50 15.00 3.05\nProfessional/Technical\nProfessional & Technical 41,794 459,889 1.72 1.91 4.30 3.22 32.50 4.54**\nBusiness and Investing 29,002 476,542 1.55 3.61 4.22 2.94 20.99 3.62**\nScience 25,697 271,391 2.64 2.41 4.30 2.42 28.00 3.90**\nComputers and Internet 18,941 375,712 2.22 4.51 3.98 3.10 34.95 3.61**\nMedicine 16,047 175,520 1.08 1.41 4.40 4.19 39.95 5.68**\nEngineering 10,312 107,255 1.30 1.43 4.14 3.85 59.95 4.10**\nLaw 5,176 53,182 2.64 1.89 4.25 2.67 24.95 3.66*\nNonfiction-other\nNonfiction 55,868 560,552 2.03 3.13 4.29 1.89 18.95 3.28**\nReference 26,834 371,959 1.94 2.49 4.19 3.04 17.47 3.21\nBiographies and Memoirs 18,233 277,356 2.80 7.65 4.34 0.90 14.00 2.96\nTable 2: Statistics by book category: np:number of products in category, n number of customers, cc percentage\nof customers in the largest connected component, rp1 av. # reviews in 2001 - 2003, rp2 av. # reviews\n1st 6 months 2005, vav average star rating, cav average number of people recommending product, cav/rp1\nratio of recommenders to reviewers, pm median price, b ratio of the number of purchases resulting from a\nrecommendation to the number of recommenders. The symbol ** denotes statistical significance at the 0.01\nlevel, * at the 0.05 level.\nFrom the original set of half a million products, we\ncompute a success rate s for the 48,218 products that had at\nleast one purchase made through a recommendation and for\nwhich a price was given. In section 5 we defined\nrecommendation success rate s as the ratio of the total number\npurchases made through recommendations and the number\nof senders of the recommendations. We decided to use this\nkind of normalization, rather than normalizing by the total\nnumber of recommendations sent, in order not to penalize\ncommunities where a few individuals send out many\nrecommendations (figure 2(b)). Since the variables follow a heavy\ntailed distribution, we use the following model:\ns = exp(\ni\n\u03b2i log(xi) + i)\nwhere xi are the product attributes (as described on\nprevious page), and i is random error.\nWe fit the model using least squares and obtain the\ncoefficients \u03b2i shown on table 3. With the exception of the\naverage rating, they are all significant. The only two\nattributes with a positive coefficient are the number of\nrecommendations and price. This shows that more expensive\nand more recommended products have a higher success rate.\nThe number of senders and receivers have large negative\ncoefficients, showing that successfully recommended products\nare more likely to be not so widely popular. They have\nrelatively many recommendations with a small number of\nsenders and receivers, which suggests a very dense\nrecommendation network where lots of recommendations were\nexchanged between a small community of people.\nThese insights could be to marketers - personal\nrecommendations are most effective in small, densely connected\ncommunities enjoying expensive products.\n236\nVariable Coefficient \u03b2i\nconst -0.940 (0.025)**\nr 0.426 (0.013)**\nns -0.782 (0.004)**\nnr -1.307 (0.015)**\np 0.128 (0.004)**\nv -0.011 (0.002)**\nt -0.027 (0.014)*\nR2\n0.74\nTable 3: Regression using the log of the\nrecommendation success rate, ln(s), as the dependent variable.\nFor each coefficient we provide the standard error\nand the statistical significance level (**:0.01, *:0.1).\n7. DISCUSSION AND CONCLUSION\nAlthough the retailer may have hoped to boost its\nrevenues through viral marketing, the additional purchases that\nresulted from recommendations are just a drop in the bucket\nof sales that occur through the website. Nevertheless, we\nwere able to obtain a number of interesting insights into how\nviral marketing works that challenge common assumptions\nmade in epidemic and rumor propagation modeling.\nFirstly, it is frequently assumed in epidemic models that\nindividuals have equal probability of being infected every\ntime they interact. Contrary to this we observe that the\nprobability of infection decreases with repeated interaction.\nMarketers should take heed that providing excessive\nincentives for customers to recommend products could backfire\nby weakening the credibility of the very same links they are\ntrying to take advantage of.\nTraditional epidemic and innovation diffusion models also\noften assume that individuals either have a constant\nprobability of \u2018converting\" every time they interact with an\ninfected individual or that they convert once the fraction of\ntheir contacts who are infected exceeds a threshold. In both\ncases, an increasing number of infected contacts results in\nan increased likelihood of infection. Instead, we find that\nthe probability of purchasing a product increases with the\nnumber of recommendations received, but quickly saturates\nto a constant and relatively low probability. This means\nindividuals are often impervious to the recommendations of\ntheir friends, and resist buying items that they do not want.\nIn network-based epidemic models, extremely highly\nconnected individuals play a very important role. For example,\nin needle sharing and sexual contact networks these nodes\nbecome the super-spreaders by infecting a large number\nof people. But these models assume that a high degree node\nhas as much of a probability of infecting each of its neighbors\nas a low degree node does. In contrast, we find that there\nare limits to how influential high degree nodes are in the\nrecommendation network. As a person sends out more and\nmore recommendations past a certain number for a product,\nthe success per recommendation declines. This would seem\nto indicate that individuals have influence over a few of their\nfriends, but not everybody they know.\nWe also presented a simple stochastic model that allows\nfor the presence of relatively large cascades for a few\nproducts, but reflects well the general tendency of\nrecommendation chains to terminate after just a short number of steps.\nWe saw that the characteristics of product reviews and\neffectiveness of recommendations vary by category and price,\nwith more successful recommendations being made on\ntechnical or religious books, which presumably are placed in the\nsocial context of a school, workplace or place of worship.\nFinally, we presented a model which shows that smaller\nand more tightly knit groups tend to be more conducive to\nviral marketing. So despite the relative ineffectiveness of the\nviral marketing program in general, we found a number of\nnew insights which we hope will have general applicability\nto marketing strategies and to future models of viral\ninformation spread.\n8. REFERENCES\n[1] Anonymous. Profiting from obscurity: What the long\ntail means for the economics of e-commerce.\nEconomist, 2005.\n[2] E. Brynjolfsson, Y. Hu, and M. D. Smith. Consumer\nsurplus in the digital economy: Estimating the value\nof increased product variety at online booksellers.\nManagement Science, 49(11), 2003.\n[3] K. Burke. As consumer attitudes shift, so must\nmarketing strategies. 2003.\n[4] J. Chevalier and D. Mayzlin. The effect of word of\nmouth on sales: Online book reviews. 2004.\n[5] P. Erd\u00a8os and A. R\u00b4enyi. On the evolution of random\ngraphs. Publ. Math. Inst. Hung. Acad. Sci., 1960.\n[6] D. Gruhl, R. Guha, D. Liben-Nowell, and A. Tomkins.\nInformation diffusion through blogspace. In WWW\n\"04, 2004.\n[7] S. 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Elsevier Science, 2002.\n[14] M. Richardson and P. Domingos. Mining\nknowledge-sharing sites for viral marketing. In ACM\nSIGKDD International Conference on Knowledge\nDiscovery and Data Mining (KDD), 2002.\n[15] E. M. Rogers. Diffusion of Innovations. Free Press,\nNew York, fourth edition, 1995.\n[16] D. Strang and S. A. Soule. Diffusion in organizations\nand social movements: From hybrid corn to poison\npills. Annual Review of Sociology, 24:265-290, 1998.\n[17] J. Travers and S. Milgram. An experimental study of\nthe small world problem. Sociometry, 1969.\n[18] D. Watts. A simple model of global cascades on\nrandom networks. PNAS, 99(9):4766-5771, Apr 2002.\n237", "keywords": "directed multi graph;product;consumer;recommender system;viral market;recommendation network;viral marketing;advertisement;pricing category;probability;e-commerce;purchase;stochastic model;connected individual"}
{"name": "train_J-44", "title": "Scouts, Promoters, and Connectors: The Roles of Ratings in Nearest Neighbor Collaborative Filtering", "abstract": "Recommender systems aggregate individual user ratings into predictions of products or services that might interest visitors. The quality of this aggregation process crucially affects the user experience and hence the effectiveness of recommenders in e-commerce. We present a novel study that disaggregates global recommender performance metrics into contributions made by each individual rating, allowing us to characterize the many roles played by ratings in nearestneighbor collaborative filtering. In particular, we formulate three roles-scouts, promoters, and connectors-that capture how users receive recommendations, how items get recommended, and how ratings of these two types are themselves connected (resp.). These roles find direct uses in improving recommendations for users, in better targeting of items and, most importantly, in helping monitor the health of the system as a whole. For instance, they can be used to track the evolution of neighborhoods, to identify rating subspaces that do not contribute (or contribute negatively) to system performance, to enumerate users who are in danger of leaving, and to assess the susceptibility of the system to attacks such as shilling. We argue that the three rating roles presented here provide broad primitives to manage a recommender system and its community.", "fulltext": "1. INTRODUCTION\nRecommender systems have become integral to e-commerce,\nproviding technology that suggests products to a visitor\nbased on previous purchases or rating history.\nCollaborative filtering, a common form of recommendation, predicts\na user\"s rating for an item by combining (other) ratings of\nthat user with other users\" ratings. Significant research has\nbeen conducted in implementing fast and accurate\ncollaborative filtering algorithms [2, 7], designing interfaces for\npresenting recommendations to users [1], and studying the\nrobustness of these algorithms [8]. However, with the\nexception of a few studies on the influence of users [10], little\nattention has been paid to unraveling the inner workings\nof a recommender in terms of the individual ratings and the\nroles they play in making (good) recommendations. Such an\nunderstanding will give an important handle to monitoring\nand managing a recommender system, to engineer\nmechanisms to sustain the recommender, and thereby ensure its\ncontinued success.\nOur motivation here is to disaggregate global recommender\nperformance metrics into contributions made by each\nindividual rating, allowing us to characterize the many roles\nplayed by ratings in nearest-neighbor collaborative filtering.\nWe identify three possible roles: (scouts) to connect the user\ninto the system to receive recommendations, (promoters) to\nconnect an item into the system to be recommended, and\n(connectors) to connect ratings of these two kinds. Viewing\nratings in this way, we can define the contribution of a\nrating in each role, both in terms of allowing recommendations\nto occur, and in terms of influence on the quality of\nrecommendations. In turn, this capability helps support scenarios\nsuch as:\n1. Situating users in better neighborhoods: A user\"s\nratings may inadvertently connect the user to a\nneighborhood for which the user\"s tastes may not be a perfect\nmatch. Identifying ratings responsible for such bad\nrecommendations and suggesting new items to rate can\nhelp situate the user in a better neighborhood.\n2. Targeting items: Recommender systems suffer from\nlack of user participation, especially in cold-start\nscenarios [13] involving newly arrived items. Identifying\nusers who can be encouraged to rate specific items\nhelps ensure coverage of the recommender system.\n3. Monitoring the evolution of the recommender system\nand its stakeholders: A recommender system is\nconstantly under change: growing with new users and\n250\nitems, shrinking with users leaving the system, items\nbecoming irrelevant, and parts of the system under\nattack. Tracking the roles of a rating and its evolution\nover time provides many insights into the health of the\nsystem, and how it could be managed and improved.\nThese include being able to identify rating subspaces\nthat do not contribute (or contribute negatively) to\nsystem performance, and could be removed; to\nenumerate users who are in danger of leaving, or have left\nthe system; and to assess the susceptibility of the\nsystem to attacks such as shilling [5].\nAs we show, the characterization of rating roles presented\nhere provides broad primitives to manage a recommender\nsystem and its community. The rest of the paper is\norganized as follows. Background on nearest-neighbor\ncollaborative filtering and algorithm evaluation is discussed in\nSection 2. Section 3 defines and discusses the roles of a rating,\nand Section 4 defines measures of the contribution of a\nrating in each of these roles. In Section 5, we illustrate the use\nof these roles to address the goals outlined above.\n2. BACKGROUND\n2.1 Algorithms\nNearest-neighbor collaborative filtering algorithms either\nuse neighborhoods of users or neighborhoods of items to\ncompute a prediction. An algorithm of the first kind is\ncalled user-based, and one of the second kind is called\nitembased [12]. In both families of algorithms, neighborhoods are\nformed by first computing the similarity between all pairs\nof users (for user-based) or items (for item-based).\nPredictions are then computed by aggregating ratings, which in a\nuser-based algorithm involves aggregating the ratings of the\ntarget item by the user\"s neighbors and, in an item-based\nalgorithm, involves aggregating the user\"s ratings of items\nthat are neighbors of the target item. Algorithms within\nthese families differ in the definition of similarity,\nformation of neighborhoods, and the computation of predictions.\nWe consider a user-based algorithm based on that defined\nfor GroupLens [11] with variations from Herlocker et al. [2],\nand an item-based algorithm similar to that of Sarwar et\nal. [12].\nThe algorithm used by Resnick et al. [11] defines the\nsimilarity of two users u and v as the Pearson correlation of\ntheir common ratings:\nsim(u, v) =\nP\ni\u2208Iu\u2229Iv\n(ru,i \u2212 \u00afru)(rv,i \u2212 \u00afrv)\nqP\ni\u2208Iu\n(ru,i \u2212 \u00afru)2\nqP\ni\u2208Iv\n(rv,i \u2212 \u00afrv)2\n,\nwhere Iu is the set of items rated by user u, ru,i is user u\"s\nrating for item i, and \u00afru is the average rating of user u\n(similarly for v). Similarity computed in this manner is typically\nscaled by a factor proportional to the number of common\nratings, to reduce the chance of making a recommendation\nmade on weak connections:\nsim (u, v) =\nmax(|Iu \u2229 Iv|, \u03b3)\n\u03b3\n\u00b7 sim(u, v),\nwhere \u03b3 \u2248 5 is a constant used as a lower limit in scaling [2].\nThese new similarities are then used to define a static\nneighborhood Nu for each user u consisting of the top K users\nmost similar to user u. A prediction for user u and item\ni is computed by a weighted average of the ratings by the\nneighbors\npu,i = \u00afru +\nP\nv\u2208V sim (u, v)(rv,i \u2212 \u00afrv)\nP\nv\u2208V sim (u, v)\n(1)\nwhere V = Nu \u2229 Ui is the set of users most similar to u who\nhave rated i.\nThe item-based algorithm we use is the one defined by\nSarwar et al. [12]. In this algorithm, similarity is defined as\nthe adjusted cosine measure\nsim(i, j) =\nP\nu\u2208Ui\u2229Uj\n(ru,i \u2212 \u00afru)(ru,j \u2212 \u00afru)\nqP\nu\u2208Ui\n(ru,i \u2212 \u00afru)2\nqP\nu\u2208Uj\n(ru,j \u2212 \u00afru)2\n(2)\nwhere Ui is the set of users who have rated item i. As for\nthe user-based algorithm, the similarity weights are adjusted\nproportionally to the number of users that have rated the\nitems in common\nsim (i, j) =\nmax(|Ui \u2229 Uj|, \u03b3)\n\u03b3\n\u00b7 sim(i, j). (3)\nGiven the similarities, the neighborhood Ni of an item i is\ndefined as the top K most similar items for that item. A\nprediction for user u and item i is computed as the weighted\naverage\npu,i = \u00afri +\nP\nj\u2208J sim (i, j)(ru,j \u2212 \u00afrj)\nP\nj\u2208J sim (i, j)\n(4)\nwhere J = Ni \u2229 Iu is the set of items rated by u that are\nmost similar to i.\n2.2 Evaluation\nRecommender algorithms have typically been evaluated\nusing measures of predictive accuracy and coverage [3].\nStudies on recommender algorithms, notably Herlocker et al. [2]\nand Sarwar et al. [12], typically compute predictive accuracy\nby dividing a set of ratings into training and test sets, and\ncompute the prediction for an item in the test set using the\nratings in the training set. A standard measure of predictive\naccuracy is mean absolute error (MAE), which for a test set\nT = {(u, i)} is defined as,\nMAE =\nP\n(u,i)\u2208T |pu,i \u2212 ru,i|\n|T |\n. (5)\nCoverage has a number of definitions, but generally refers\nto the proportion of items that can be predicted by the\nalgorithm [3].\nA practical issue with predictive accuracy is that users\ntypically are presented with recommendation lists, and not\nindividual numeric predictions. Recommendation lists are\nlists of items in decreasing order of prediction (sometimes\nstated in terms of star-ratings), and so predictive accuracy\nmay not be reflective of the accuracy of the list. So, instead\nwe can measure recommendation or rank accuracy, which\nindicates the extent to which the list is in the correct\norder. Herlocker et al. [3] discuss a number of rank accuracy\nmeasures, which range from Kendall\"s Tau to measures that\nconsider the fact that users tend to only look at a prefix of\nthe list [5]. Kendall\"s Tau measures the number of inversions\nwhen comparing ordered pairs in the true user ordering of\n251\nJim\nTom\nJeff\nMy Cousin Vinny\nThe Matrix\nStar Wars\nThe Mask\nFigure 1: Ratings in simple movie recommender.\nitems and the recommended order, and is defined as\n\u03c4 =\nC \u2212 D\np\n(C + D + TR)(C + D + TP)\n(6)\nwhere C is the number of pairs that the system predicts in\nthe correct order, D the number of pairs the system\npredicts in the wrong order, TR the number of pairs in the true\nordering that have the same ratings, and TP is the\nnumber of pairs in the predicted ordering that have the same\nratings [3]. A shortcoming of the Tau metric is that it is\noblivious to the position in the ordered list where the\ninversion occurs [3]. For instance, an inversion toward the end\nof the list is given the same weight as one in the beginning.\nOne solution is to consider inversions only in the top few\nitems in the recommended list or to weight inversions based\non their position in the list.\n3. ROLES OF A RATING\nOur basic observation is that each rating plays a\ndifferent role in each prediction in which it is used. Consider a\nsimplified movie recommender system with three users Jim,\nJeff, and Tom and their ratings for a few movies, as shown\nin Fig. 1. (For this initial discussion we will not consider the\nrating values involved.) The recommender predicts whether\nTom will like The Mask using the other already available\nratings. How this is done depends on the algorithm:\n1. An item-based collaborative filtering algorithm\nconstructs a neighborhood of movies around The Mask by\nusing the ratings of users who rated The Mask and\nother movies similarly (e.g., Jim\"s ratings of The Matrix\nand The Mask; and Jeff\"s ratings of Star Wars and The\nMask). Tom\"s ratings of those movies are then used to\nmake a prediction for The Mask.\n2. A user-based collaborative filtering algorithm would\nconstruct a neighborhood around Tom by tracking other\nusers whose rating behaviors are similar to Tom\"s (e.g.,\nTom and Jeff have rated Star Wars; Tom and Jim have\nrated The Matrix). The prediction of Tom\"s rating for\nThe Mask is then based on the ratings of Jeff and Tim.\nAlthough the nearest-neighbor algorithms aggregate the\nratings to form neighborhoods used to compute predictions, we\ncan disaggregate the similarities to view the computation of\na prediction as simultaneously following parallel paths of\nratings. So, irrespective of the collaborative filtering\nalgorithm used, we can visualize the prediction of Tom\"s rating\nof The Mask as walking through a sequence of ratings. In\nJim\nTom\nJeff\nThe Matrix\nStar Wars\nThe Mask\nq1\nq2 q3\np1\np2\np3\nFigure 2: Ratings used to predict The Mask for Tom.\nJim\nTom\nJeff\nThe Matrix\nStar Wars\nThe Mask\nq1\nq2\nq3\np1 p2\np3\nJerry\nr2\nr3\nFigure 3: Prediction of The Mask for Tom in which a\nrating is used more than once.\nthis example, two paths were used for this prediction as\ndepicted in Fig. 2: (p1, p2, p3) and (q1, q2, q3). Note that these\npaths are undirected, and are all of length 3. Only the order\nin which the ratings are traversed is different between the\nitem-based algorithm (e.g., (p3, p2, p1), (q3, q2, q1)) and the\nuser-based algorithm (e.g., (p1, p2, p3), (q1, q2, q3).) A rating\ncan be part of many paths for a single prediction as shown\nin Fig. 3, where three paths are used for a prediction, two\nof which follow p1: (p1, p2, p3) and (p1, r2, r3).\nPredictions in a collaborative filtering algorithms may\ninvolve thousands of such walks in parallel, each playing a part\nin influencing the predicted value. Each prediction path\nconsists of three ratings, playing roles that we call scouts,\npromoters, and connectors. To illustrate these roles, consider\nthe path (p1, p2, p3) in Fig. 2 used to make a prediction of\nThe Mask for Tom:\n1. The rating p1 (Tom \u2192 Star Wars) makes a connection\nfrom Tom to other ratings that can be used to predict\nTom\"s rating for The Mask. This rating serves as a\nscout in the bipartite graph of ratings to find a path\nthat leads to The Mask.\n2. The rating p2 (Jeff \u2192 Star Wars) helps the system\nrecommend The Mask to Tom by connecting the scout to\nthe promoter.\n3. The rating p3 (Jeff \u2192 The Mask) allows connections to\nThe Mask, and, therefore, promotes this movie to Tom.\nFormally, given a prediction pu,a of a target item a for user\nu, a scout for pu,a is a rating ru,i such that there exists a\nuser v with ratings rv,a and rv,i for some item i; a promoter\nfor pu,a is a rating rv,a for some user v, such that there exist\nratings rv,i and ru,i for an item i, and; a connector for pu,a\n252\nJim\nTom\nJeff\nJerry\nMy Cousin Vinny\nThe Matrix\nStar Wars\nThe Mask\nJurasic Park\nFigure 4: Scouts, promoters, and connectors.\nis a rating rv,i by some user v and rating i, such that there\nexists ratings ru,i and rv,a. The scouts, connectors, and\npromoters for the prediction of Tom\"s rating of The Mask\nare p1 and q1, p2 and q2, and p3 and q3 (respectively). Each\nof these roles has a value in the recommender to the user,\nthe user\"s neighborhood, and the system in terms of allowing\nrecommendations to be made.\n3.1 Roles in Detail\nRatings that act as scouts tend to help the recommender\nsystem suggest more movies to the user, though the extent\nto which this is true depends on the rating behavior of other\nusers. For example, in Fig. 4 the rating Tom \u2192 Star Wars\nhelps the system recommend only The Mask to him, while\nTom \u2192 The Matrix helps recommend The Mask, Jurassic\nPark, and My Cousin Vinny. Tom makes a connection to\nJim who is a prolific user of the system, by rating The\nMatrix. However, this does not make The Matrix the best\nmovie to rate for everyone. For example, Jim is benefited\nequally by both The Mask and The Matrix, which allow the\nsystem to recommend Star Wars to him. His rating of The\nMask is the best scout for Jeff, and Jerry\"s only scout is his\nrating of Star Wars. This suggests that good scouts allow\na user to build similarity with prolific users, and thereby\nensure they get more from the system.\nWhile scouts represent beneficial ratings from the\nperspective of a user, promoters are their duals, and are of benefit\nto items. In Fig. 4, My Cousin Vinny benefits from Jim\"s\nrating, since it allows recommendations to Jeff and Tom.\nThe Mask is not so dependent on just one rating, since the\nratings by Jim and Jeff help it. On the other hand, Jerry\"s\nrating of Star Wars does not help promote it to any other\nuser. We conclude that a good promoter connects an item to\na broader neighborhood of other items, and thereby ensures\nthat it is recommended to more users.\nConnectors serve a crucial role in a recommender system\nthat is not as obvious. The movies My Cousin Vinny and\nJurassic Park have the highest recommendation potential\nsince they can be recommended to Jeff, Jerry and Tom based\non the linkage structure illustrated in Fig. 4. Beside the\nfact that Jim rated these movies, these recommendations are\npossible only because of the ratings Jim \u2192 The Matrix and\nJim \u2192 The Mask, which are the best connectors. A\nconnector improves the system\"s ability to make recommendations\nwith no explicit gain for the user.\nNote that every rating can be of varied benefit in each of\nthese roles. The rating Jim \u2192 My Cousin Vinny is a poor\nscout and connector, but is a very good promoter. The\nrating Jim \u2192 The Mask is a reasonably good scout, a very\ngood connector, and a good promoter. Finally, the rating\nJerry \u2192 Star Wars is a very good scout, but is of no value\nas a connector or promoter. As illustrated here, a rating\ncan have different value in each of the three roles in terms of\nwhether a recommendation can be made or not. We could\nmeasure this value by simply counting the number of times\na rating is used in each role, which alone would be\nhelpful in characterizing the behavior of a system. But we can\nalso measure the contribution of each rating to the quality\nof recommendations or health of the system. Since every\nprediction is a combined effort of several recommendation\npaths, we are interested in discerning the influence of each\nrating (and, hence, each path) in the system towards the\nsystem\"s overall error. We can understand the dynamics of\nthe system at a finer granularity by tracking the influence\nof a rating according to the role played. The next section\ndescribes the approach to measuring the values of a rating\nin each role.\n4. CONTRIBUTIONS OF RATINGS\nAs we\"ve seen, a rating may play different roles in different\npredictions and, in each prediction, contribute to the quality\nof a prediction in different ways. Our approach can use any\nnumeric measure of a property of system health, and assigns\ncredit (or blame) to each rating proportional to its influence\nin the prediction. By tracking the role of each rating in a\nprediction, we can accumulate the credit for a rating in each\nof the three roles, and also track the evolution of the roles\nof rating over time in the system.\nThis section defines the methodology for computing the\ncontribution of ratings by first defining the influence of a\nrating, and then instantiating the approach for predictive\naccuracy, and then rank accuracy. We also demonstrate how\nthese contributions can be aggregated to study the\nneighborhood of ratings involved in computing a user\"s\nrecommendations. Note that although our general formulation for rating\ninfluence is algorithm independent, due to space\nconsiderations, we present the approach for only item-based\ncollaborative filtering. The definition for user-based algorithms is\nsimilar and will be presented in an expanded version of this\npaper.\n4.1 Influence of Ratings\nRecall that an item-based approach to collaborative\nfiltering relies on building item neighborhoods using the\nsimilarity of ratings by the same user. As described earlier,\nsimilarity is defined by the adjusted cosine measure (Equations (2)\nand (3)). A set of the top K neighbors is maintained for all\nitems for space and computational efficiency. A prediction\nof item i for a user u is computed as the weighted deviation\nfrom the item\"s mean rating as shown in Equation (4). The\nlist of recommendations for a user is then the list of items\nsorted in descending order of their predicted values.\nWe first define impact(a, i, j), the impact a user a has in\ndetermining the similarity between two items i and j. This\nis the change in the similarity between i and j when a\"s\nrating is removed, and is defined as\nimpact(a, i, j) =\n|sim (i, j) \u2212 sim\u00afa(i, j)|\nP\nw\u2208Cij\n|sim (i, j) \u2212 sim \u00afw(i, j)|\nwhere Cij = {u \u2208 U | \u2203 ru,i, ru,j \u2208 R(u)} is the set of coraters\n253\nof items i and j (users who rate both i and j), R(u) is the set\nof ratings provided by user u, and sim\u00afa(i, j) is the similarity\nof i and j when the ratings of user a are removed\nsim\u00afa(i, j) =\nP\nv\u2208U\\{a} (ru,i \u2212 \u00afru)(ru,j \u2212 \u00afru)\nqP\nu\u2208U\\{a}(ru,i \u2212 \u00afru)2\nqP\nu\u2208U\\{a}(ru,j \u2212 \u00afru)2\n,\nand adjusted for the number of raters\nsim\u00afa(i, j) =\nmax(|Ui \u2229 Uj| \u2212 1, \u03b3)\n\u03b3\n\u00b7 sim(i, j).\nIf all coraters of i and j rate them identically, we define the\nimpact as\nimpact(a, i, j) =\n1\n|Cij|\nsince\nP\nw\u2208Cij\n|sim (i, j) \u2212 sim \u00afw(i, j)| = 0.\nThe influence of each path (u, j, v, i) = [ru,j, rv,j, rv,i] in\nthe prediction of pu,i is given by\ninfluence(u, j, v, i) =\nsim (i, j)\nP\nl\u2208Ni\u2229Iu\nsim (i, l)\n\u00b7 impact(v, i, j)\nIt follows that the sum of influences over all such paths, for\na given set of endpoints, is 1.\n4.2 Role Values for Predictive Accuracy\nThe value of a rating in each role is computed from the\ninfluence depending on the evaluation measure employed.\nHere we illustrate the approach using predictive accuracy as\nthe evaluation metric.\nIn general, the goodness of a prediction decides whether\nthe ratings involved must be credited or discredited for their\nrole. For predictive accuracy, the error in prediction e =\n|pu,i \u2212 ru,i| is mapped to a comfort level using a mapping\nfunction M(e). Anecdotal evidence suggests that users are\nunable to discern errors less than 1.0 (for a rating scale of 1\nto 5) [4], and so an error less than 1.0 is considered\nacceptable, but anything larger is not. We hence define M(e) as\n(1 \u2212 e) binned to an appropriate value in [\u22121, \u22120.5, 0.5, 1].\nFor each prediction pu,i, M(e) is attributed to all the paths\nthat assisted the computation of pu,i, proportional to their\ninfluences. This tribute, M(e)\u2217influence(u, j, v, i), is in turn\ninherited by each of the ratings in the path [ru,j, rv,j, rv,i],\nwith the credit/blame accumulating to the respective roles\nof ru,j as a scout, rv,j as a connector, and rv,i as a\npromoter. In other words, the scout value SF(ru,j), the\nconnector value CF(rv,j) and the promoter value PF(rv,i) are\nall incremented by the tribute amount. Over a large\nnumber of predictions, scouts that have repeatedly resulted in\nbig error rates have a big negative scout value, and vice\nversa (similarly with the other roles). Every rating is thus\nsummarized by its triple [SF, CF, PF].\n4.3 Role Values for Rank Accuracy\nWe now define the computation of the contribution of\nratings to observed rank accuracy. For this computation, we\nmust know the user\"s preference order for a set of items for\nwhich predictions can be computed. We assume that we\nhave a test set of the users\" ratings of the items presented\nin the recommendation list. For every pair of items rated\nby a user in the test data, we check whether the predicted\norder is concordant with his preference. We say a pair (i, j)\nis concordant (with error ) whenever one of the following\nholds:\n\u2022 if (ru,i < ru,j) then (pu,i \u2212 pu,j < );\n\u2022 if (ru,i > ru,j) then (pu,i \u2212 pu,j > ); or\n\u2022 if (ru,i = ru,j) then (|pu,i \u2212 pu,j| \u2264 ).\nSimilarly, a pair (i, j) is discordant (with error ) if it is not\nconcordant. Our experiments described below use an error\ntolerance of = 0.1.\nAll paths involved in the prediction of the two items in\na concordant pair are credited, and the paths involved in\na discordant pair are discredited. The credit assigned to a\npair of items (i, j) in the recommendation list for user u is\ncomputed as\nc(i, j) =\n(\nt\nT\n\u00b7 1\nC+D\nif (i, j) are concordant\n\u2212 t\nT\n\u00b7 1\nC+D\nif (i, j) are discordant\n(7)\nwhere t is the number of items in the user\"s test set whose\nratings could be predicted, T is the number of items rated\nby user u in the test set, C is the number of concordances\nand D is the number of discordances. The credit c is then\ndivided among all paths responsible for predicting pu,i and\npu,j proportional to their influences. We again add the role\nvalues obtained from all the experiments to form a triple\n[SF, CF, PF] for each rating.\n4.4 Aggregating rating roles\nAfter calculating the role values for individual ratings, we\ncan also use these values to study neighborhoods and the\nsystem. Here we consider how we can use the role values\nto characterize the health of a neighborhood. Consider the\nlist of top recommendations presented to a user at a\nspecific point in time. The collaborative filtering algorithm\ntraversed many paths in his neighborhood through his scouts\nand other connectors and promoters to make these\nrecommendations. We call these ratings the recommender\nneighborhood of the user. The user implicitly chooses this\nneighborhood of ratings through the items he rates. Apart from\nthe collaborative filtering algorithm, the health of this\nneighborhood completely influences a user\"s satisfaction with the\nsystem. We can characterize a user\"s recommender\nneighborhood by aggregating the individual role values of the\nratings involved, weighted by the influence of individual ratings\nin determining his recommended list. Different sections of\nthe user\"s neighborhood wield varied influence on his\nrecommendation list. For instance, ratings reachable through\nhighly rated items have a bigger say in the recommended\nitems.\nOur aim is to study the system and classify users with\nrespect to their positioning in a healthy or unhealthy\nneighborhood. A user can have a good set of scouts, but may\nbe exposed to a neighborhood with bad connectors and\npromoters. He can have a good neighborhood, but his bad\nscouts may ensure the neighborhood\"s potential is rendered\nuseless. We expect that users with good scouts and good\nneighborhoods will be most satisfied with the system in the\nfuture.\nA user\"s neighborhood is characterized by a triple that\nrepresents the weighted sum of the role values of individual\nratings involved in making recommendations. Consider a\nuser u and his ordered list of recommendations L. An item i\n254\nin the list is weighted inversely, as K(i), depending on its\nposition in the list. In our studies we use K(i) =\np\nposition(i).\nSeveral paths of ratings [ru,j, rv,j, rv,i] are involved in\npredicting pu,i which ultimately decides its position in L, each\nwith influence(u, j, v, i).\nThe recommender neighborhood of a user u is\ncharacterized by the triple, [SFN(u), CFN(u), PFN(u)] where\nSFN(u) =\nX\ni\u2208L\nP\n[ru,j ,rv,j ,rv,i] SF(ru,j)influence(u, j, v, i)\nK(i)\n!\nCFN(u) and PFN(u) are defined similarly. This triple\nestimates the quality of u\"s recommendations based on the past\ntrack record of the ratings involved in their respective roles.\n5. EXPERIMENTATION\nAs we have seen, we can assign role values to each rating\nwhen evaluating a collaborative filtering system. In this\nsection, we demonstrate the use of this approach to our overall\ngoal of defining an approach to monitor and manage the\nhealth of a recommender system through experiments done\non the MovieLens million rating dataset. In particular, we\ndiscuss results relating to identifying good scouts,\npromoters, and connectors; the evolution of rating roles; and the\ncharacterization of user neighborhoods.\n5.1 Methodology\nOur experiments use the MovieLens million rating dataset,\nwhich consists of ratings by 6040 users of 3952 movies. The\nratings are in the range 1 to 5, and are labeled with the time\nthe rating was given. As discussed before, we consider only\nthe item-based algorithm here (with item neighborhoods of\nsize 30) and, due to space considerations, only present role\nvalue results for rank accuracy.\nSince we are interested in the evolution of the rating role\nvalues over time, the model of the recommender system is\nbuilt by processing ratings in their arrival order. The\ntimestamping provided by MovieLens is hence crucial for the\nanalyses presented here. We make assessments of rating roles at\nintervals of 10,000 ratings and processed the first 200,000\nratings in the dataset (giving rise to 20 snapshots). We\nincrementally update the role values as the time ordered\nratings are merged into the model. To keep the experiment\ncomputationally manageable, we define a test dataset for\neach user. As the time ordered ratings are merged into the\nmodel, we label a small randomly selected percentage (20%)\nas test data. At discrete epochs, i.e., after processing every\n10,000 ratings, we compute the predictions for the ratings\nin the test data, and then compute the role values for the\nratings used in the predictions. One potential criticism of\nthis methodology is that the ratings in the test set are never\nevaluated for their roles. We overcome this concern by\nrepeating the experiment, using different random seeds. The\nprobability that every rating is considered for evaluation is\nthen considerably high: 1 \u2212 0.2n\n, where n is the number\nof times the experiment is repeated with different random\nseeds. The results here are based on n = 4 repetitions.\nThe item-based collaborative filtering algorithm\"s\nperformance was ordinary with respect to rank accuracy. Fig. 5\nshows a plot of the precision and recall as ratings were\nmerged in time order into the model. The recall was always\nhigh, but the average precision was just about 53%.\n0\n0.2\n0.4\n0.6\n0.8\n1\n1.2\n10000\n30000\n50000\n70000\n90000110000130000150000\nRatings merged into model\nValue\nPrecision\nRecall\nFigure 5: Precision and recall for the item-based\ncollaborative filtering algorithm.\n5.2 Inducing good scouts\nThe ratings of a user that serve as scouts are those that\nallow the user to receive recommendations. We claim that\nusers with ratings that have respectable scout values will\nbe happier with the system than those with ratings with\nlow scout values. Note that the item-based algorithm\ndiscussed here produces recommendation lists with nearly half\nof the pairs in the list discordant from the user\"s preference.\nWhether all of these discordant pairs are observable by the\nuser is unclear, however, certainly this suggests that there\nis a need to be able to direct users to items whose ratings\nwould improve the lists.\nThe distribution of the scout values for most users\"\nratings are Gaussian with mean zero. Fig. 6 shows the\nfrequency distribution of scout values for a sample user at a\ngiven snapshot. We observe that a large number of ratings\nnever serve as scouts for their users. A relatable scenario\nis when Amazon\"s recommender makes suggestions of books\nor items based on other items that were purchased as gifts.\nWith simple relevance feedback from the user, such ratings\ncan be isolated as bad scouts and discounted from future\npredictions. Removing bad scouts was found to be\nworthwhile for individual users but the overall performance\nimprovement was only marginal.\nAn obvious question is whether good scouts can be formed\nby merely rating popular movies as suggested by Rashid et\nal. [9]. They show that a mix of popularity and rating\nentropy identifies the best items to suggest to new users\nwhen evaluated using MAE. Following their intuition, we\nwould expect to see a higher correlation between\npopularityentropy and good scouts. We measured the Pearson\ncorrelation coefficient between aggregated scout values for a movie\nwith the popularity of a movie (number of times it is rated);\nand with its popularity*variance measure at different\nsnapshots of the system. Note that the scout values were initially\nanti-correlated with popularity (Fig. 7), but became\nmoderately correlated as the system evolved. Both popularity and\npopularity*variance performed similarly. A possible\nexplanation is that there has been insufficient time for the popular\nmovies to accumulate ratings.\n255\n-10\n0\n10\n20\n30\n40\n50\n60\n-0.08 -0.06 -0.04 -0.02 0 0.02 0.04\nScout Value\nFrequency\nFigure 6: Distribution of scout values for a sample\nuser.\n-0.4\n-0.2\n0\n0.2\n0.4\n0.6\n0.8\n30000 60000 90000 120000 150000 180000\nPopularity\nPop*Var\nFigure 7: Correlation between aggregated scout\nvalue and item popularity (computed at different\nintervals).\n-0.6\n-0.4\n-0.2\n0\n0.2\n0.4\n0.6\n0.8\n1\n30000 60000 90000 120000 150000 180000\nFigure 8: Correlation between aggregated promoter\nvalue and user prolificity (computed at different\nintervals).\nTable 1: Movies forming the best scouts.\nBest Scouts Conf. Pop.\nBeing John Malkovich (1999) 1.00 445\nStar Wars: Episode IV - A New Hope (1977) 0.92 623\nPrincess Bride, The (1987) 0.85 477\nSixth Sense, The (1999) 0.85 617\nMatrix, The (1999) 0.77 522\nGhostbusters (1984) 0.77 441\nCasablanca (1942) 0.77 384\nInsider, The (1999) 0.77 235\nAmerican Beauty (1999) 0.69 624\nTerminator 2: Judgment Day (1991) 0.69 503\nFight Club (1999) 0.69 235\nShawshank Redemption, The (1994) 0.69 445\nRun Lola Run (Lola rennt) (1998) 0.69 220\nTerminator, The (1984) 0.62 450\nUsual Suspects, The (1995) 0.62 326\nAliens (1986) 0.62 385\nNorth by Northwest (1959) 0.62 245\nFugitive, The (1993) 0.62 402\nEnd of Days (1999) 0.62 132\nRaiders of the Lost Ark (1981) 0.54 540\nSchindler\"s List (1993) 0.54 453\nBack to the Future (1985) 0.54 543\nToy Story (1995) 0.54 419\nAlien (1979) 0.54 415\nAbyss, The (1989) 0.54 345\n2001: A Space Odyssey (1968) 0.54 358\nDogma (1999) 0.54 228\nLittle Mermaid, The (1989) 0.54 203\nTable 2: Movies forming the worst scouts.\nWorst scouts Conf. Pop.\nHarold and Maude (1971) 0.46 141\nGrifters, The (1990) 0.46 180\nSting, The (1973) 0.38 244\nGodfather: Part III, The (1990) 0.38 154\nLawrence of Arabia (1962) 0.38 167\nHigh Noon (1952) 0.38 84\nWomen on the Verge of a... (1988) 0.38 113\nGrapes of Wrath, The (1940) 0.38 115\nDuck Soup (1933) 0.38 131\nArsenic and Old Lace (1944) 0.38 138\nMidnight Cowboy (1969) 0.38 137\nTo Kill a Mockingbird (1962) 0.31 195\nFour Weddings and a Funeral (1994) 0.31 271\nGood, The Bad and The Ugly, The (1966) 0.31 156\nIt\"s a Wonderful Life (1946) 0.31 146\nPlayer, The (1992) 0.31 220\nJackie Brown (1997) 0.31 118\nBoat, The (Das Boot) (1981) 0.31 210\nManhattan (1979) 0.31 158\nTruth About Cats & Dogs, The (1996) 0.31 143\nGhost (1990) 0.31 227\nLone Star (1996) 0.31 125\nBig Chill, The (1983) 0.31 184\n256\nBy studying the evolution of scout values, we can identify\nmovies that consistently feature in good scouts over time.\nWe claim these movies will make viable scouts for other\nusers. We found the aggregated scout values for all movies\nin intervals of 10,000 ratings each. A movie is said to induce\na good scout if the movie was in the top 100 of the sorted\nlist, and to induce a bad scout if it was in bottom 100 of\nthe same list. Movies appearing consistently high over time\nare expected to remain up there in the future. The effective\nconfidence in a movie m is\nCm =\nTm \u2212 Bm\nN\n(8)\nwhere Tm is the number of times it appeared in the top\n100, Bm the number of times it appeared in the bottom\n100, and N is the number of intervals considered. Using\nthis measure, the top few movies expected to induce the\nbest scouts are shown in Table 1. Movies that would be bad\nscout choices are shown in Table 2 with their associated\nconfidences. The popularities of the movies are also displayed.\nAlthough more popular movies appear in the list of good\nscouts, these tables show that a blind choice of scout based\non popularity alone can be potentially dangerous.\nInterestingly, the best scout-\u2018Being John Malkovich\"-is about a\npuppeteer who discovers a portal into a movie star, a movie\nthat has been described variously on amazon.com as \u2018makes\nyou feel giddy,\" \u2018seriously weird,\" \u2018comedy with depth,\" \u2018silly,\"\n\u2018strange,\" and \u2018inventive.\" Indicating whether someone likes\nthis movie or not goes a long way toward situating the user\nin a suitable neighborhood, with similar preferences.\nOn the other hand, several factors may have made a movie\na bad scout, like the sharp variance in user preferences in\nthe neighborhood of a movie. Two users may have the\nsame opinion about Lawrence of Arabia, but they may\ndiffer sharply about how they felt about the other movies they\nsaw. Bad scouts ensue when there is deviation in behavior\naround a common synchronization point.\n5.3 Inducing good promoters\nRatings that serve to promote items in a collaborative\nfiltering system are critical to allowing a new item be\nrecommended to users. So, inducing good promoters is important\nfor cold-start recommendation. We note that the frequency\ndistribution of promoter values for a sample movie\"s ratings\nis also Gaussian (similar to Fig. 6). This indicates that the\npromotion of a movie is benefited most by the ratings of a\nfew users, and are unaffected by the ratings of most users.\nWe find a strong correlation between a user\"s number of\nratings and his aggregated promoter value. Fig. 8 depicts the\nevolution of the Pearson correlation co-efficient between the\nprolificity of a user (number of ratings) versus his\naggregated promoter value. We expect that conspicuous shills,\nby recommending wrong movies to users, will be\ndiscredited with negative aggregate promoter values and should be\nidentifiable easily.\nGiven this observation, the obvious rule to follow when\nintroducing a new movie is to have it rated directly by\nprolific users who posses high aggregated promoter values. A\nnew movie is thus cast into the neighborhood of many other\nmovies improving its visibility. Note, though, that a user\nmay have long stopped using the system. Tracking\npromoter values consistently allows only the most active recent\nusers to be considered.\n5.4 Inducing good connectors\nGiven the way scouts, connectors, and promoters are\ncharacterized, it follows that the movies that are part of the best\nscouts are also part of the best connectors. Similarly, the\nusers that constitute the best promoters are also part of the\nbest connectors. Good connectors are induced by\nensuring a user with a high promoter value rates a movie with a\nhigh scout value. In our experiments, we find that a rating\"s\nlongest standing role is often as a connector. A rating with a\npoor connector value is often seen due to its user being a bad\npromoter, or its movie being a bad scout. Such ratings can\nbe removed from the prediction process to bring marginal\nimprovements to recommendations. In some selected\nexperiments, we observed that removing a set of badly behaving\nconnectors helped improve the system\"s overall performance\nby 1.5%. The effect was even higher on a few select users\nwho observed an improvement of above 10% in precision\nwithout much loss in recall.\n5.5 Monitoring the evolution of rating roles\nOne of the more significant contributions of our work is\nthe ability to model the evolution of recommender systems,\nby studying the changing roles of ratings over time. The role\nand value of a rating can change depending on many factors\nlike user behavior, redundancy, shilling effects or\nproperties of the collaborative filtering algorithm used. Studying\nthe dynamics of rating roles in terms of transitions between\ngood, bad, and negligible values can provide insights into the\nfunctioning of the recommender system. We believe that a\ncontinuous visualization of these transitions will improve the\nability to manage a recommender system.\nWe classify different rating states as good, bad, or\nnegligible. Consider a user who has rated 100 movies in a\nparticular interval, of which 20 are part of the test set. If a\nscout has a value greater than 0.005, it indicates that it is\nuniquely involved in at least 2 concordant predictions, which\nwe will say is good. Thus, a threshold of 0.005 is chosen to\nbin a rating as good, bad or negligible in terms of its scout,\nconnector and promoter value. For instance, a rating r, at\ntime t with role value triple [0.1, 0.001, \u22120.01] is classified as\n[scout +, connector 0, promoter \u2212], where + indicates good,\n0 indicates negligible, and \u2212 indicates bad.\nThe positive credit held by a rating is a measure of its\ncontribution to the betterment of the system, and the discredit\nis a measure of its contribution to the detriment of the\nsystem. Even though the positive roles (and the negative roles)\nmake up a very small percentage of all ratings, their\ncontribution supersedes their size. For example, even though only\n1.7% of all ratings were classified as good scouts, they hold\n79% of all positive credit in the system! Similarly, the bad\nscouts were just 1.4% of all ratings but hold 82% of all\ndiscredit. Note that good and bad scouts, together, comprise\nonly 1.4% + 1.7% = 3.1% of the ratings, implying that the\nmajority of the ratings are negligible role players as scouts\n(more on this later). Likewise, good connectors were 1.2%\nof the system, and hold 30% of all positive credit. The bad\nconnectors (0.8% of the system) hold 36% of all discredit.\nGood promoters (3% of the system) hold 46% of all credit,\nwhile bad promoters (2%) hold 50% of all discredit. This\nreiterates that a few ratings influence most of the system\"s\nperformance. Hence it is important to track transitions\nbetween them regardless of their small numbers.\n257\nAcross different snapshots, a rating can remain in the\nsame state or change. A good scout can become a bad scout,\na good promoter can become a good connector, good and\nbad scouts can become vestigial, and so on. It is not\npractical to expect a recommender system to have no ratings in\nbad roles. However, it suffices to see ratings in bad roles\neither convert to good or vestigial roles. Similarly, observing\na large number of good roles become bad ones is a sign of\nimminent failure of the system.\nWe employ the principle of non-overlapping episodes [6]\nto count such transitions. A sequence such as:\n[+, 0, 0] \u2192 [+, 0, 0] \u2192 [0, +, 0] \u2192 [0, 0, 0]\nis interpreted as the transitions\n[+, 0, 0] ; [0, +, 0] : 1\n[+, 0, 0] ; [0, 0, 0] : 1\n[0, +, 0] ; [0, 0, 0] : 1\ninstead of\n[+, 0, 0] ; [0, +, 0] : 2\n[+, 0, 0] ; [0, 0, 0] : 2\n[0, +, 0] ; [0, 0, 0] : 1.\nSee [6] for further details about this counting procedure.\nThus, a rating can be in one of 27 possible states, and there\nare about 272\npossible transitions. We make a further\nsimplification and utilize only 9 states, indicating whether the\nrating is a scout, promoter, or connector, and whether it\nhas a positive, negative, or negligible role. Ratings that\nserve multiple purposes are counted using multiple episode\ninstantiations but the states themselves are not duplicated\nbeyond the 9 restricted states. In this model, a transition\nsuch as [+, 0, +] ; [0, +, 0] : 1 is counted as\n[scout+] ; [scout0] : 1\n[scout+] ; [connector+] : 1\n[scout+] ; [promoter0] : 1\n[connector0] ; [scout0] : 1\n[connector0] ; [scout+] : 1\n[connector0] ; [promoter0] : 1\n[promoter+] ; [scout0] : 1\n[promoter+] ; [connector+] : 1\n[promoter+] ; [promoter0] : 1\nOf these, transitions like [pX] ; [q0] where p = q, X \u2208\n{+, 0, \u2212} are considered uninteresting, and only the rest are\ncounted.\nFig. 9 depicts the major transitions counted while\nprocessing the first 200,000 ratings from the MovieLens dataset.\nOnly transitions with frequency greater than or equal to 3%\nare shown. The percentages for each state indicates the\nnumber of ratings that were found to be in those states.\nWe consider transitions from any state to a good state as\nhealthy, from any state to a bad state as unhealthy, and\nfrom any state to a vestigial state as decaying.\nFrom Fig. 9, we can observe:\n\u2022 The bulk of the ratings have negligible values,\nirrespective of their role. The majority of the transitions\ninvolve both good and bad ratings becoming\nnegligible.\nScout +\n(2%)\n\nScout(1.5%)\nScout 0\n(96.5%)\nConnector +\n(1.2%)\n\nConnector(0.8%)\nConnector 0\n(98%)\nPromoter +\n(3%)\n\nPromoter(2%)\nPromoter 0\n(95%)\n84%\n84%\n81%\n74%\n10%\n6%\n11%\n77%\n8%\n7%\n8%\n82%\n4%\n86%\n4%\n68%\n15%\n13%\n5%\n5%\n77%\n11%\n7%\n5%\n4%\n3%\n3%\n3%\nHealthy\nUnhealthy\nDecaying\nFigure 9: Transitions among rating roles.\n\u2022 The number of good ratings is comparable to the bad\nratings, and ratings are seen to switch states often,\nexcept in the case of scouts (see below).\n\u2022 The negative and positive scout states are not\nreachable through any transition, indicating that these\nratings must begin as such, and cannot be coerced into\nthese roles.\n\u2022 Good promoters and good connectors have a much\nlonger survival period than scouts. Transitions that\nrecur to these states have frequencies of 10% and 15%\nwhen compared to just 4% for scouts. Good\nconnectors are the slowest to decay whereas (good) scouts\ndecay the fastest.\n\u2022 Healthy percentages are seen on transitions between\npromoters and connectors. As indicated earlier, there\nare hardly any transitions from promoters/connectors\nto scouts. This indicates that, over the long run, a\nuser\"s rating is more useful to others (movies or other\nusers) than to the user himself.\n\u2022 The percentages of healthy transitions outweigh the\nunhealthy ones - this hints that the system is healthy,\nalbeit only marginally.\nNote that these results are conditioned by the static nature\nof the dataset, which is a set of ratings over a fixed window\nof time. However a diagram such as Fig. 9 is clearly useful\nfor monitoring the health of a recommender system. For\ninstance, acceptable limits can be imposed on different types\nof transitions and, if a transition fails to meet the\nthreshold, the recommender system or a part of it can be brought\nunder closer scrutiny. Furthermore, the role state transition\ndiagram would also be the ideal place to study the effects of\nshilling, a topic we will consider in future research.\n5.6 Characterizing neighborhoods\nEarlier we saw that we can characterize the neighborhood\nof ratings involved in creating a recommendation list L for\n258\na user. In our experiment, we consider lists of length 30,\nand sample the lists of about 5% of users through the\nevolution of the model (at intervals of 10,000 ratings each) and\ncompute their neighborhood characteristics. To simplify our\npresentation, we consider the percentage of the sample that\nfall into one of the following categories:\n1. Inactive user: (SFN(u) = 0)\n2. Good scouts, Good neighborhood:\n(SFN(u) > 0) \u2227 (CFN(u) > 0 \u2227 PFN(u) > 0)\n3. Good scouts, Bad neighborhood:\n(SFN(u) > 0) \u2227 (CFN(u) < 0 \u2228 PFN(u) < 0)\n4. Bad scouts, Good neighborhood:\n(SFN(u) < 0) \u2227 (CFN(u) > 0 \u2227 PFN(u) > 0)\n5. Bad scouts, Bad neighborhood:\n(SFN(u) < 0) \u2227 (CFN(u) < 0 \u2228 PFN(u) < 0)\nFrom our sample set of 561 users, we found that 476 users\nwere inactive. Of the remaining 85 users, we found 26 users\nhad good scouts and a good neighborhood, 6 had bad scouts\nand a good neighborhood, 29 had good scouts and a bad\nneighborhood, and 24 had bad scouts and a bad\nneighborhood. Thus, we conjecture that 59 users (29+24+6) are in\ndanger of leaving the system.\nAs a remedy, users with bad scouts and a good\nneighborhood can be asked to reconsider rating of some movies\nhoping to improve the system\"s recommendations. The\nsystem can be expected to deliver more if they engineer some\ngood scouts. Users with good scouts and a bad\nneighborhood are harder to address; this situation might entail\nselectively removing some connector-promoter pairs that are\ncausing the damage. Handling users with bad scouts and\nbad neighborhoods is a more difficult challenge.\nSuch a classification allows the use of different strategies\nto better a user\"s experience with the system depending on\nhis context. In future work, we intend to conduct field\nstudies and study the improvement in performance of different\nstrategies for different contexts.\n6. CONCLUSIONS\nTo further recommender system acceptance and\ndeployment, we require new tools and methodologies to manage\nan installed recommender and develop insights into the roles\nplayed by ratings. A fine-grained characterization in terms\nof rating roles such as scouts, promoters, and connectors,\nas done here, helps such an endeavor. Although we have\npresented results on only the item-based algorithm with list\nrank accuracy as the metric, the same approach outlined\nhere applies to user-based algorithms and other metrics.\nIn future research, we plan to systematically study the\nmany algorithmic parameters, tolerances, and cutoff\nthresholds employed here and reason about their effects on the\ndownstream conclusions. We also aim to extend our\nformulation to other collaborative filtering algorithms, study\nthe effect of shilling in altering rating roles, conduct field\nstudies, and evaluate improvements in user experience by\ntweaking ratings based on their role values. Finally, we plan\nto develop the idea of mining the evolution of rating role\npatterns into a reporting and tracking system for all aspects\nof recommender system health.\n7. REFERENCES\n[1] Cosley, D., Lam, S., Albert, I., Konstan, J., and\nRiedl, J. Is Seeing Believing?: How Recommender\nSystem Interfaces Affect User\"s Opinions. In Proc.\nCHI (2001), pp. 585-592.\n[2] Herlocker, J. L., Konstan, J. A., Borchers, A.,\nand Riedl, J. An Algorithmic Framework for\nPerforming Collaborative Filtering. In Proc. SIGIR\n(1999), pp. 230-237.\n[3] Herlocker, J. L., Konstan, J. A., Terveen,\nL. G., and Riedl, J. T. Evaluating Collaborative\nFiltering Recommender Systems. ACM Transactions\non Information Systems Vol. 22, 1 (2004), pp. 5-53.\n[4] Konstan, J. A. Personal communication. 2003.\n[5] Lam, S. K., and Riedl, J. Shilling Recommender\nSystems for Fun and Profit. In Proceedings of the 13th\nInternational World Wide Web Conference (2004),\nACM Press, pp. 393-402.\n[6] Laxman, S., Sastry, P. S., and Unnikrishnan,\nK. P. Discovering Frequent Episodes and Learning\nHidden Markov Models: A Formal Connection. IEEE\nTransactions on Knowledge and Data Engineering\nVol. 17, 11 (2005), 1505-1517.\n[7] McLaughlin, M. R., and Herlocker, J. L. A\nCollaborative Filtering Algorithm and Evaluation\nMetric that Accurately Model the User Experience. In\nProceedings of the 27th Annual International ACM\nSIGIR Conference on Research and Development in\nInformation Retrieval (2004), pp. 329 - 336.\n[8] O\"Mahony, M., Hurley, N. J., Kushmerick, N.,\nand Silvestre, G. Collaborative Recommendation:\nA Robustness Analysis. ACM Transactions on\nInternet Technology Vol. 4, 4 (Nov 2004), pp. 344-377.\n[9] Rashid, A. M., Albert, I., Cosley, D., Lam, S.,\nMcNee, S., Konstan, J. A., and Riedl, J. Getting\nto Know You: Learning New User Preferences in\nRecommender Systems. In Proceedings of the 2002\nConference on Intelligent User Interfaces (IUI 2002)\n(2002), pp. 127-134.\n[10] Rashid, A. M., Karypis, G., and Riedl, J.\nInfluence in Ratings-Based Recommender Systems:\nAn Algorithm-Independent Approach. In Proc. of the\nSIAM International Conference on Data Mining\n(2005).\n[11] Resnick, P., Iacovou, N., Sushak, M.,\nBergstrom, P., and Riedl, J. GroupLens: An\nOpen Architecture for Collaborative Filtering of\nNetnews. In Proceedings of the Conference on\nComputer Supported Collaborative Work (CSCW\"94)\n(1994), ACM Press, pp. 175-186.\n[12] Sarwar, B., Karypis, G., Konstan, J., and Reidl,\nJ. Item-Based Collaborative Filtering\nRecommendation Algorithms. In Proceedings of the\nTenth International World Wide Web Conference\n(WWW\"10) (2001), pp. 285-295.\n[13] Schein, A., Popescu, A., Ungar, L., and\nPennock, D. Methods and Metrics for Cold-Start\nRecommendation. In Proc. SIGIR (2002),\npp. 253-260.\n259", "keywords": "opinion;list rank accuracy;recommender system;neighborhood;nearest neighbor;rating;recommender;promoter;aggregation process;scout;purchase;collaborative filtering algorithm;collaborative filter;user-base and item-base algorithm;connector"}
{"name": "train_J-45", "title": "Empirical Mechanism Design: Methods, with Application to a Supply-Chain Scenario", "abstract": "Our proposed methods employ learning and search techniques to estimate outcome features of interest as a function of mechanism parameter settings. We illustrate our approach with a design task from a supply-chain trading competition. Designers adopted several rule changes in order to deter particular procurement behavior, but the measures proved insufficient. Our empirical mechanism analysis models the relation between a key design parameter and outcomes, confirming the observed behavior and indicating that no reasonable parameter settings would have been likely to achieve the desired effect. More generally, we show that under certain conditions, the estimator of optimal mechanism parameter setting based on empirical data is consistent.", "fulltext": "1. MOTIVATION\nWe illustrate our problem with an anecdote from a supply chain\nresearch exercise: the 2003 and 2004 Trading Agent Competition\n(TAC) Supply Chain Management (SCM) game. TAC/SCM [1]\ndefines a scenario where agents compete to maximize their profits\nas manufacturers in a supply chain. The agents procure components\nfrom the various suppliers and assemble finished goods for sale to\ncustomers, repeatedly over a simulated year.\nAs it happened, the specified negotiation behavior of suppliers\nprovided a great incentive for agents to procure large quantities of\ncomponents on day 0: the very beginning of the simulation. During\nthe early rounds of the 2003 SCM competition, several agent\ndevelopers discovered this, and the apparent success led to most agents\nperforming the majority of their purchasing on day 0. Although\njockeying for day-0 procurement turned out to be an interesting\nstrategic issue in itself [19], the phenomenon detracted from other\ninteresting problems, such as adapting production levels to varying\ndemand (since component costs were already sunk), and dynamic\nmanagement of production, sales, and inventory. Several\nparticipants noted that the predominance of day-0 procurement\novershadowed other key research issues, such as factory scheduling [2] and\noptimizing bids for customer orders [13]. After the 2003\ntournament, there was a general consensus in the TAC community that\nthe rules should be changed to deter large day-0 procurement.\nThe task facing game organizers can be viewed as a problem in\nmechanism design. The designers have certain game features\nunder their control, and a set of objectives regarding game outcomes.\nUnlike most academic treatments of mechanism design, the\nobjective is a behavioral feature (moderate day-0 procurement) rather\nthan an allocation feature like economic efficiency, and the allowed\nmechanisms are restricted to those judged to require only an\nincremental modification of the current game. Replacing the\nsupplychain negotiation procedures with a one-shot direct mechanism, for\nexample, was not an option. We believe that such operational\nrestrictions and idiosyncratic objectives are actually quite typical of\npractical mechanism design settings, where they are perhaps more\ncommonly characterized as incentive engineering problems.\nIn response to the problem, the TAC/SCM designers adopted\nseveral rule changes intended to penalize large day-0 orders. These\nincluded modifications to supplier pricing policies and introduction\nof storage costs assessed on inventories of components and finished\ngoods. Despite the changes, day-0 procurement was very high in\nthe early rounds of the 2004 competition. In a drastic measure, the\nGameMaster imposed a fivefold increase of storage costs midway\nthrough the tournament. Even this did not stem the tide, and day-0\nprocurement in the final rounds actually increased (by some\nmeasures) from 2003 [9].\nThe apparent difficulty in identifying rule modifications that\neffect moderation in day-0 procurement is quite striking. Although\nthe designs were widely discussed, predictions for the effects of\nvarious proposals were supported primarily by intuitive arguments\nor at best by back-of-the-envelope calculations. Much of the\ndifficulty, of course, is anticipating the agents\" (and their\ndevelopers\") responses without essentially running a gaming exercise for\nthis purpose. The episode caused us to consider whether new\nap306\nproaches or tools could enable more systematic analysis of design\noptions. Standard game-theoretic and mechanism design methods\nare clearly relevant, although the lack of an analytic description of\nthe game seems to be an impediment. Under the assumption that\nthe simulator itself is the only reliable source of outcome\ncomputation, we refer to our task as empirical mechanism design.\nIn the sequel, we develop some general methods for empirical\nmechanism design and apply them to the TAC/SCM redesign\nproblem. Our analysis focuses on the setting of storage costs (taking\nother game modifications as fixed), since this is the most direct\ndeterrent to early procurement adopted. Our results confirm the basic\nintuition that incentives for day-0 purchasing decrease as storage\ncosts rise. We also confirm that the high day-0 procurement\nobserved in the 2004 tournament is a rational response to the setting\nof storage costs used. Finally, we conclude from our data that it is\nvery unlikely that any reasonable setting of storage costs would\nresult in acceptable levels of day-0 procurement, so a different design\napproach would have been required to eliminate this problem.\nOverall, we contribute a formal framework and a set of methods\nfor tackling indirect mechanism design problems in settings where\nonly a black-box description of players\" utilities is available. Our\nmethods incorporate estimation of sets of Nash equilibria and\nsample Nash equilibria, used in conjuction to support general claims\nabout the structure of the mechanism designer\"s utility, as well as a\nrestricted probabilistic analysis to assess the likelihood of\nconclusions. We believe that most realistic problems are too complex to\nbe amenable to exact analysis. Consequently, we advocate the\napproach of gathering evidence to provide indirect support of specific\nhypotheses.\n2. PRELIMINARIES\nA normal form game2\nis denoted by [I, {Ri}, {ui(r)}], where I\nrefers to the set of players and m = |I| is the number of players.\nRi is the set of strategies available to player i \u2208 I, with R =\nR1 \u00d7. . .\u00d7Rm representing the set of joint strategies of all players.\nWe designate the set of pure strategies available to player i by Ai,\nand denote the joint set of pure strategies of all players by A =\nA1 \u00d7. . .\u00d7Am. It is often convenient to refer to a strategy of player\ni separately from that of the remaining players. To accommodate\nthis, we use a\u2212i to denote the joint strategy of all players other than\nplayer i.\nLet Si be the set of all probability distributions (mixtures) over\nAi and, similarly, S be the set of all distributions over A. An s \u2208 S\nis called a mixed strategy profile. When the game is finite (i.e., A\nand I are both finite), the probability that a \u2208 A is played under\ns is written s(a) = s(ai, a\u2212i). When the distribution s is not\ncorrelated, we can simply say si(ai) when referring to the probability\nplayer i plays ai under s.\nNext, we define the payoff (utility) function of each player i by\nui : A1 \u00d7\u00b7 \u00b7 \u00b7\u00d7Am \u2192 R, where ui(ai, a\u2212i) indicates the payoff to\nplayer i to playing pure strategy ai when the remaining players play\na\u2212i. We can extend this definition to mixed strategies by assuming\nthat ui are von Neumann-Morgenstern (vNM) utilities as follows:\nui(s) = Es[ui], where Es is the expectation taken with respect to\nthe probability distribution of play induced by the players\" mixed\nstrategy s.\n2\nBy employing the normal form, we model agents as playing a\nsingle action, with decisions taken simultaneously. This is appropriate\nfor our current study, which treats strategies (agent programs) as\natomic actions. We could capture finer-grained decisions about\naction over time in the extensive form. Although any extensive game\ncan be recast in normal form, doing so may sacrifice compactness\nand blur relevant distinctions (e.g., subgame perfection).\nOccasionally, we write ui(x, y) to mean that x \u2208 Ai or Si and\ny \u2208 A\u2212i or S\u2212i depending on context. We also express the set of\nutility functions of all players as u(\u00b7) = {u1(\u00b7), . . . , um(\u00b7)}.\nWe define a function, : R \u2192 R, interpreted as the maximum\nbenefit any player can obtain by deviating from its strategy in the\nspecified profile.\n(r) = max\ni\u2208I\nmax\nai\u2208Ai\n[ui(ai, r\u2212i) \u2212 ui(r)], (1)\nwhere r belongs to some strategy set, R, of either pure or mixed\nstrategies.\nFaced with a game, an agent would ideally play its best strategy\ngiven those played by the other agents. A configuration where all\nagents play strategies that are best responses to the others\nconstitutes a Nash equilibrium.\nDEFINITION 1. A strategy profile r = (r1, . . . , rm) constitutes\na Nash equilibrium of game [I, {Ri}, {ui(r)}] if for every i \u2208 I,\nri \u2208 Ri, ui(ri, r\u2212i) \u2265 ui(ri, r\u2212i).\nWhen r \u2208 A, the above defines a pure strategy Nash equilibrium;\notherwise the definition describes a mixed strategy Nash\nequilibrium. We often appeal to the concept of an approximate, or -Nash\nequilibrium, where is the maximum benefit to any agent for\ndeviating from the prescribed strategy. Thus, (r) as defined above (1)\nis such that profile r is an -Nash equilibrium iff (r) \u2264 .\nIn this study we devote particular attention to games that exhibit\nsymmetry with respect to payoffs, rendering agents strategically\nidentical.\nDEFINITION 2. A game [I, {Ri}, {ui(r)}] is symmetric if for\nall i, j \u2208 I, (a) Ri = Rj and (b) ui(ri, r\u2212i) = uj (rj, r\u2212j)\nwhenever ri = rj and r\u2212i = r\u2212j\n3. THE MODEL\nWe model the strategic interactions between the designer of the\nmechanism and its participants as a two-stage game. The designer\nmoves first by selecting a value, \u03b8, from a set of allowable\nmechanism settings, \u0398. All the participant agents observe the mechanism\nparameter \u03b8 and move simultaneously thereafter. For example, the\ndesigner could be deciding between a first-price and second-price\nsealed-bid auction mechanisms, with the presumption that after the\nchoice has been made, the bidders will participate with full\nawareness of the auction rules.\nSince the participants play with full knowledge of the\nmechanism parameter, we define a game between them in the second stage\nas \u0393\u03b8 = [I, {Ri}, {ui(r, \u03b8)}]. We refer to \u0393\u03b8 as a game induced\nby \u03b8. Let N(\u03b8) be the set of strategy profiles considered solutions\nof the game \u0393\u03b8.3\nSuppose that the goal of the designer is to optimize the value\nof some welfare function, W (r, \u03b8), dependent on the mechanism\nparameter and resulting play, r. We define a pessimistic measure,\nW ( \u02c6R, \u03b8) = inf{W (r, \u03b8) : r \u2208 \u02c6R}, representing the worst-case\nwelfare of the game induced by \u03b8, assuming that agents play some\njoint strategy in \u02c6R. Typically we care about W (N(\u03b8), \u03b8), the\nworst-case outcome of playing some solution.4\nOn some problems we can gain considerable advantage by\nusing an aggregation function to map the welfare outcome of a game\n3\nWe generally adopt Nash equilibrium as the solution concept, and\nthus take N(\u03b8) to be the set of equilibria. However, much of the\nmethodology developed here could be employed with alternative\ncriteria for deriving agent behavior from a game definition.\n4\nAgain, alternatives are available. For example, if one has a\nprobability distribution over the solution set N(\u03b8), it would be natural\nto take the expectation of W (r, \u03b8) instead.\n307\nspecified in terms of agent strategies to an equivalent welfare\noutcome specified in terms of a lower-dimensional summary.\nDEFINITION 3. A function \u03c6 : R1 \u00d7 \u00b7 \u00b7 \u00b7 \u00d7 Rm \u2192 Rq\nis an\naggregation function if m \u2265 q and W (r, \u03b8) = V (\u03c6(r), \u03b8) for\nsome function V .\nWe overload the function symbol to apply to sets of strategy\nprofiles: \u03c6( \u02c6R) = {\u03c6(r) : r \u2208 \u02c6R}. For convenience of exposition, we\nwrite \u03c6\u2217\n(\u03b8) to mean \u03c6(N(\u03b8)).\nUsing an aggregation function yields a more compact\nrepresentation of strategy profiles. For example, suppose-as in our\napplication below-that an agent\"s strategy is defined by a numeric\nparameter. If all we care about is the total value played, we may\ntake \u03c6(a) =\nPm\ni=1 ai. If we have chosen our aggregator carefully,\nwe may also capture structure not obvious otherwise. For example,\n\u03c6\u2217\n(\u03b8) could be decreasing in \u03b8, whereas N(\u03b8) might have a more\ncomplex structure.\nGiven a description of the solution correspondence N(\u03b8)\n(equivalently, \u03c6\u2217\n(\u03b8)), the designer faces a standard optimization\nproblem. Alternatively, given a simulator that could produce an\nunbiased sample from the distribution of W (N(\u03b8), \u03b8) for any \u03b8, the\ndesigner would be faced with another much appreciated problem\nin the literature: simulation optimization [12].\nHowever, even for a game \u0393\u03b8 with known payoffs it may be\ncomputationally intractable to solve for Nash equilibria, particularly if\nthe game has large or infinite strategy sets. Additionally, we wish\nto study games where the payoffs are not explicitly given, but must\nbe determined from simulation or other experience with the game.5\nAccordingly, we assume that we are given a (possibly noisy) data\nset of payoff realizations: Do = {(\u03b81\n, a1\n, U1\n), . . . , (\u03b8k\n, ak\n, Uk\n)},\nwhere for every data point \u03b8i\nis the observed mechanism parameter\nsetting, ai\nis the observed pure strategy profile of the participants,\nand Ui\nis the corresponding realization of agent payoffs. We may\nalso have additional data generated by a (possibly noisy) simulator:\nDs = {(\u03b8k+1\n, ak+1\n, Uk+1\n), . . . , (\u03b8k+l\n, ak+l\n, Uk+l\n)}. Let D =\n{Do, Ds} be the combined data set. (Either Do or Ds may be null\nfor a particular problem.)\nIn the remainder of this paper, we apply our modeling approach,\ntogether with several empirical game-theoretic methods, in order to\nanswer questions regarding the design of the TAC/SCM scenario.\n4. EMPIRICAL DESIGN ANALYSIS\nSince our data comes in the form of payoff experience and not as\nthe value of an objective function for given settings of the control\nvariable, we can no longer rely on the methods for optimizing\nfunctions using simulations. Indeed, a fundamental aspect of our design\nproblem involves estimating the Nash equilibrium correspondence.\nFurthermore, we cannot rely directly on the convergence results\nthat abound in the simulation optimization literature, and must\nestablish probabilistic analysis methods tailored for our problem\nsetting.\n4.1 TAC/SCM Design Problem\nWe describe our empirical design analysis methods by presenting\na detailed application to the TAC/SCM scenario introduced above.\nRecall that during the 2004 tournament, the designers of the\nsupplychain game chose to dramatically increase storage costs as a\nmeasure aimed at curbing day-0 procurement, to little avail. Here we\nsystematically explore the relationship between storage costs and\n5\nThis is often the case for real games of interest, where natural\nlanguage or algorithmic descriptions may substitute for a formal\nspecification of strategy and payoff functions.\nthe aggregate quantity of components procured on day 0 in\nequilibrium. In doing so, we consider several questions raised during and\nafter the tournament. First, does increasing storage costs actually\nreduce day-0 procurement? Second, was the excessive day-0\nprocurement that was observed during the 2004 tournament rational?\nAnd third, could increasing storage costs sufficiently have reduced\nday-0 procurement to an acceptable level, and if so, what should\nthe setting of storage costs have been? It is this third question that\ndefines the mechanism design aspect of our analysis.6\nTo apply our methods, we must specify the agent strategy sets,\nthe designer\"s welfare function, the mechanism parameter space,\nand the source of data. We restrict the agent strategies to be a\nmultiplier on the quantity of the day-0 requests by one of the\nfinalists, Deep Maize, in the 2004 TAC/SCM tournament. We further\nrestrict it to the set [0,1.5], since any strategy below 0 is illegal\nand strategies above 1.5 are extremely aggressive (thus unlikely to\nprovide refuting deviations beyond those available from included\nstrategies, and certainly not part of any desirable equilibrium). All\nother behavior is based on the behavior of Deep Maize and is\nidentical for all agents. This choice can provide only an estimate of the\nactual tournament behavior of a typical agent. However, we\nbelieve that the general form of the results should be robust to changes\nin the full agent behavior.\nWe model the designer\"s welfare function as a threshold on the\nsum of day-0 purchases. Let \u03c6(a) =\nP6\ni=1 ai be the\naggregation function representing the sum of day-0 procurement of the six\nagents participating in a particular supply-chain game (for mixed\nstrategy profiles s, we take expectation of \u03c6 with respect to the\nmixture). The designer\"s welfare function W (N(\u03b8), \u03b8) is then given by\nI{sup{\u03c6\u2217\n(\u03b8)} \u2264 \u03b1}, where \u03b1 is the maximum acceptable level of\nday-0 procurement and I is the indicator function. The designer\nselects a value \u03b8 of storage costs, expressed as an annual\npercentage of the baseline value of components in the inventory (charged\ndaily), from the set \u0398 = R+\n. Since the designer\"s decision\ndepends only on \u03c6\u2217\n(\u03b8), we present all of our results in terms of the\nvalue of the aggregation function.\n4.2 Estimating Nash Equilibria\nThe objective of TAC/SCM agents is to maximize profits\nrealized over a game instance. Thus, if we fix a strategy for each agent\nat the beginning of the simulation and record the corresponding\nprofits at the end, we will have obtained a data point in the form\n(a, U(a)). If we also have fixed the parameter \u03b8 of the simulator,\nthe resulting data point becomes part of our data set D. This data\nset, then, contains data only in the form of pure strategies of\nplayers and their corresponding payoffs, and, consequently, in order to\nformulate the designer\"s problem as optimization, we must first\ndetermine or approximate the set of Nash equilibria of each game \u0393\u03b8.\nThus, we need methods for approximating Nash equilibria for\ninfinite games. Below, we describe the two methods we used in our\nstudy. The first has been explored empirically before, whereas the\nsecond is introduced here as the method specifically designed to\napproximate a set of Nash equilibria.\n4.2.1 Payoff Function Approximation\nThe first method for estimating Nash equilibria based on data\nuses supervised learning to approximate payoff functions of\nmech6\nWe do not address whether and how other measures (e.g.,\nconstraining procurement directly) could have achieved design\nobjectives. Our approach takes as given some set of design options, in\nthis case defined by the storage cost parameter. In principle our\nmethods could be applied to a different or larger design space,\nthough with corresponding complexity growth.\n308\nanism participants from a data set of game experience [17]. Once\napproximate payoff functions are available for all players, the Nash\nequilibria may be either found analytically or approximated using\nnumerical techniques, depending on the learning model. In what\nfollows, we estimate only a sample Nash equilibrium using this\ntechnique, although this restriction can be removed at the expense\nof additional computation time.\nOne advantage of this method is that it can be applied to any\ndata set and does not require the use of a simulator. Thus, we can\napply it when Ds = \u2205. If a simulator is available, we can generate\nadditional data to build confidence in our initial estimates.7\nWe tried the following methods for approximating payoff\nfunctions: quadratic regression (QR), locally weighted average (LWA),\nand locally weighted linear regression (LWLR). We also used\ncontrol variates to reduce the variance of payoff estimates, as in our\nprevious empirical game-theoretic analysis of TAC/SCM-03 [19].\nThe quadratic regression model makes it possible to compute\nequilibria of the learned game analytically. For the other methods\nwe applied replicator dynamics [7] to a discrete approximation of\nthe learned game. The expected total day-0 procurement in\nequilibrium was taken as the estimate of an outcome.\n4.2.2 Search in Strategy Profile Space\nWhen we have access to a simulator, we can also use directed\nsearch through profile space to estimate the set of Nash equilibria,\nwhich we describe here after presenting some additional notation.\nDEFINITION 4. A strategic neighbor of a pure strategy profile\na is a profile that is identical to a in all but one strategy. We define\nSnb(a, D) as the set of all strategic neighbors of a available in\nthe data set D. Similarly, we define Snb(a, \u02dcD) to be all strategic\nneighbors of a not in D. Finally, for any a \u2208 Snb(a, D) we define\nthe deviating agent as i(a, a ).\nDEFINITION 5. The -bound, \u02c6, of a pure strategy profile a is\ndefined as maxa \u2208Snb(a,D) max{ui(a,a )(a )\u2212ui(a,a )(a), 0}. We\nsay that a is a candidate \u03b4-equilibrium for \u03b4 \u2265 \u02c6.\nWhen Snb(a, \u02dcD) = \u2205 (i.e., all strategic neighbors are represented\nin the data), a is confirmed as an \u02c6-Nash equilibrium.\nOur search method operates by exploring deviations from\ncandidate equilibria. We refer to it as BestFirstSearch, as it selects\nwith probability one a strategy profile a \u2208 Snb(a, \u02dcD) that has the\nsmallest \u02c6in D.\nFinally we define an estimator for a set of Nash equilibria.\nDEFINITION 6. For a set K, define Co(K) to be the convex\nhull of K. Let B\u03b4 be the set of candidates at level \u03b4. We define\n\u02c6\u03c6\u2217\n(\u03b8) = Co({\u03c6(a) : a \u2208 B\u03b4}) for a fixed \u03b4 to be an estimator of\n\u03c6\u2217\n(\u03b8).\nIn words, the estimate of a set of equilibrium outcomes is the\nconvex hull of all aggregated strategy profiles with -bound below\nsome fixed \u03b4. This definition allows us to exploit structure\narising from the aggregation function. If two profiles are close in terms\nof aggregation values, they may be likely to have similar -bounds.\nIn particular, if one is an equilibrium, the other may be as well. We\npresent some theoretical support for this method of estimating the\nset of Nash equilibria below.\nSince the game we are interested in is infinite, it is necessary to\nterminate BestFirstSearch before exploring the entire space of\nstrat7\nFor example, we can use active learning techniques [5] to improve\nthe quality of payoff function approximation. In this work, we\ninstead concentrate on search in strategy profile space.\negy profiles. We currently determine termination time in a\nsomewhat ad-hoc manner, based on observations about the current set of\ncandidate equilibria.8\n4.3 Data Generation\nOur data was collected by simulating TAC/SCM games on a\nlocal version of the 2004 TAC/SCM server, which has a configuration\nsetting for the storage cost. Agent strategies in simulated games\nwere selected from the set {0, 0.3, 0.6, . . . , 1.5} in order to have\npositive probability of generating strategic neighbors.9\nA\nbaseline data set Do was generated by sampling 10 randomly generated\nstrategy profiles for each \u03b8 \u2208 {0, 50, 100, 150, 200}. Between 5\nand 10 games were run for each profile after discarding games that\nhad various flaws.10\nWe used search to generate a simulated data\nset Ds, performing between 12 and 32 iterations of BestFirstSearch\nfor each of the above settings of \u03b8. Since simulation cost is\nextremely high (a game takes nearly 1 hour to run), we were able to\nrun a total of 2670 games over the span of more than six months.\nFor comparison, to get the entire description of an empirical game\ndefined by the restricted finite joint strategy space for each value\nof \u03b8 \u2208 {0, 50, 100, 150, 200} would have required at least 23100\ngames (sampling each profile 10 times).\n4.4 Results\n4.4.1 Analysis of the Baseline Data Set\nWe applied the three learning methods described above to the\nbaseline data set Do. Additionally, we generated an estimate of the\nNash equilibrium correspondence, \u02c6\u03c6\u2217\n(\u03b8), by applying Definition 6\nwith \u03b4 =2.5E6. The results are shown in Figure 1. As we can see,\nthe correspondence \u02c6\u03c6\u2217\n(\u03b8) has little predictive power based on Do,\nand reveals no interesting structure about the game. In contrast, all\nthree learning methods suggest that total day-0 procurement is a\ndecreasing function of storage costs.\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n0 50 100 150 200\nStorage Cost\nTotalDay-0Procurement\nLWA\nLWLR\nQR\nBaselineMin\nBaselineMax\nFigure 1: Aggregate day-0 procurement estimates based on Do.\nThe correspondence \u02c6\u03c6\u2217\n(\u03b8) is the interval between\nBaselineMin and BaselineMax.\n8\nGenerally, search is terminated once the set of candidate equilibria\nis small enough to draw useful conclusions about the likely range\nof equilibrium strategies in the game.\n9\nOf course, we do not restrict our Nash equilibrium estimates to\nstay in this discrete subset of [0,1.5].\n10\nFor example, if we detected that any agent failed during the\ngame (failures included crashes, network connectivity problems,\nand other obvious anomalies), the game would be thrown out.\n309\n4.4.2 Analysis of Search Data\nTo corroborate the initial evidence from the learning methods,\nwe estimated \u02c6\u03c6\u2217\n(\u03b8) (again, using \u03b4 =2.5E6) on the data set D =\n{Do, Ds}, where Ds is data generated through the application of\nBestFirstSearch. The results of this estimate are plotted against the\nresults of the learning methods trained on Do\n11\nin Figure 2. First,\nwe note that the addition of the search data narrows the range of\npotential equilibria substantially. Furthermore, the actual point\npredictions of the learning methods and those based on -bounds\nafter search are reasonably close. Combining the evidence gathered\nfrom these two very different approaches to estimating the outcome\ncorrespondence yields a much more compelling picture of the\nrelationship between storage costs and day-0 procurement than either\nmethod used in isolation.\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n0 50 100 150 200\nStorage Cost\nTotayDay-0Procurement\nLWA\nLWLR\nQR\nSearchMin\nSearchMax\nFigure 2: Aggregate day-0 procurement estimates based on\nsearch in strategy profile space compared to function\napproximation techniques trained on Do. The correspondence \u02c6\u03c6\u2217\n(\u03b8)\nfor D = {Do, Ds} is the interval between SearchMin and\nSearchMax.\nThis evidence supports the initial intuition that day-0\nprocurement should be decreasing with storage costs. It also confirms that\nhigh levels of day-0 procurement are a rational response to the 2004\ntournament setting of average storage cost, which corresponds to\n\u03b8 = 100. The minimum prediction for aggregate procurement at\nthis level of storage costs given by any experimental methods is\napproximately 3. This is quite high, as it corresponds to an\nexpected commitment of 1/3 of the total supplier capacity for the\nentire game. The maximum prediction is considerably higher at 4.5.\nIn the actual 2004 competition, aggregate day-0 procurement was\nequivalent to 5.71 on the scale used here [9]. Our predictions\nunderestimate this outcome to some degree, but show that any rational\noutcome was likely to have high day-0 procurement.\n4.4.3 Extrapolating the Solution Correspondence\nWe have reasonably strong evidence that the outcome\ncorrespondence is decreasing. However, the ultimate goal is to be able to\neither set the storage cost parameter to a value that would curb day-0\nprocurement in equilibrium or conclude that this is not possible.\nTo answer this question directly, suppose that we set a\nconservative threshold \u03b1 = 2 on aggregate day-0 procurement.12\nLinear\n11\nIt is unclear how meaningful the results of learning would be if\nDs were added to the training data set. Indeed, the additional data\nmay actually increase the learning variance.\n12\nRecall that designer\"s objective is to incentivize aggergate day-0\nprocurement that is below the threshold \u03b1. Our threshold here still\nrepresents a commitment of over 20% of the suppliers\" capacity for\nextrapolation of the maximum of the outcome correspondence\nestimated from D yields \u03b8 = 320.\nThe data for \u03b8 = 320 were collected in the same way as for other\nstorage cost settings, with 10 randomly generated profiles followed\nby 33 iterations of BestFirstSearch. Figure 3 shows the detailed\n-bounds for all profiles in terms of their corresponding values of\n\u03c6.\n0.00E+00\n5.00E+06\n1.00E+07\n1.50E+07\n2.00E+07\n2.50E+07\n3.00E+07\n3.50E+07\n4.00E+07\n4.50E+07\n5.00E+07\n2.1 2.4 2.7 3 3.3 3.6 3.9 4.2 4.5 4.8 5.1 5.4 5.7 6 6.3 6.6 6.9 7.2\nTotal Day-0 Procurement\n\u03b5\u2212boundFigure 3: Values of \u02c6 for profiles explored using search when\n\u03b8 = 320. Strategy profiles explored are presented in terms of\nthe corresponding values of \u03c6(a). The gray region corresponds\nto \u02c6\u03c6\u2217\n(320) with \u03b4 =2.5M.\nThe estimated set of aggregate day-0 outcomes is very close to\nthat for \u03b8 = 200, indicating that there is little additional benefit\nto raising storage costs above 200. Observe, that even the lower\nbound of our estimated set of Nash equilibria is well above the\ntarget day-0 procurement of 2. Furthermore, payoffs to agents are\nalmost always negative at \u03b8 = 320. Consequently, increasing the\ncosts further would be undesirable even if day-0 procurement could\neventually be curbed. Since we are reasonably confident that \u03c6\u2217\n(\u03b8)\nis decreasing in \u03b8, we also do not expect that setting \u03b8 somewhere\nbetween 200 and 320 will achieve the desired result.\nWe conclude that it is unlikely that day-0 procurement could ever\nbe reduced to a desirable level using any reasonable setting of the\nstorage cost parameter. That our predictions tend to underestimate\ntournament outcomes reinforces this conclusion. To achieve the\ndesired reduction in day-0 procurement requires redesigning other\naspects of the mechanism.\n4.5 Probabilistic Analysis\nOur empirical analysis has produced evidence in support of the\nconclusion that no reasonable setting of storage cost was likely to\nsufficiently curb excessive day-0 procurement in TAC/SCM \"04.\nAll of this evidence has been in the form of simple interpolation and\nextrapolation of estimates of the Nash equilibrium correspondence.\nThese estimates are based on simulating game instances, and are\nsubject to sampling noise contributed by the various stochastic\nelements of the game. In this section, we develop and apply methods\nfor evaluating the sensitivity of our -bound calculations to such\nstochastic effects.\nSuppose that all agents have finite (and small) pure strategy sets,\nA. Thus, it is feasible to sample the entire payoff matrix of the\ngame. Additionally, suppose that noise is additive with zero-mean\nthe entire game on average, so in practice we would probably want\nthe threshold to be even lower.\n310\nand finite variance, that is, Ui(a) = ui(a) + \u02dc\u03bei(a), where Ui(a) is\nthe observed payoff to i when a was played, ui(a) is the actual\ncorresponding payoff, and \u02dc\u03bei(a) is a mean-zero normal random\nvariable. We designate the known variance of \u02dc\u03bei(a) by \u03c32\ni (a). Thus,\nwe assume that \u02dc\u03bei(a) is normal with distribution N(0, \u03c32\ni (a)).\nWe take \u00afui(a) to be the sample mean over all Ui(a) in D, and\nfollow Chang and Huang [3] to assume that we have an improper\nprior over the actual payoffs ui(a) and sampling was independent\nfor all i and a. We also rely on their result that ui(a)|\u00afui(a) =\n\u00afui(a)\u2212Zi(a)/[\u03c3i(a)/\np\nni(a)] are independent with posterior\ndistributions N(\u00afui(a), \u03c32\ni (a)/ni(a)), where ni(a) is the number of\nsamples taken of payoffs to i for pure profile a, and Zi(a) \u223c\nN(0, 1).\nWe now derive a generic probabilistic bound that a profile a \u2208\nA is an -Nash equilibrium. If ui(\u00b7)|\u00afui(\u00b7) are independent for all\ni \u2208 I and a \u2208 A, we have the following result (from this point on\nwe omit conditioning on \u00afui(\u00b7) for brevity):\nPROPOSITION 1.\nPr\n\u201e\nmax\ni\u2208I\nmax\nb\u2208Ai\nui(b, a\u2212i) \u2212 ui(a) \u2264\n\u00ab\n=\n=\nY\ni\u2208I\nZ\nR\nY\nb\u2208Ai\\ai\nPr(ui(b, a\u2212i) \u2264 u + )fui(a)(u)du,\n(2)\nwhere fui(a)(u) is the pdf of N(\u00afui(a), \u03c3i(a)).\nThe proofs of this and all subsequent results are in the Appendix.\nThe posterior distribution of the optimum mean of n samples,\nderived by Chang and Huang [3], is\nPr (ui(a) \u2264 c) = 1 \u2212 \u03a6\n\"p\nni(a)(\u00afui(a) \u2212 c)\n\u03c3i(a)\n#\n, (3)\nwhere a \u2208 A and \u03a6(\u00b7) is the N(0, 1) distribution function.\nCombining the results (2) and (3), we obtain a probabilistic\nconfidence bound that (a) \u2264 \u03b3 for a given \u03b3.\nNow, we consider cases of incomplete data and use the results\nwe have just obtained to construct an upper bound (restricted to\nprofiles represented in data) on the distribution of sup{\u03c6\u2217\n(\u03b8)} and\ninf{\u03c6\u2217\n(\u03b8)} (assuming that both are attainable):\nPr{sup{\u03c6\u2217\n(\u03b8)} \u2264 x} \u2264D\nPr{\u2203a \u2208 D : \u03c6(a) \u2264 x \u2227 a \u2208 N(\u03b8)} \u2264\nX\na\u2208D:\u03c6(a)\u2264x\nPr{a \u2208 N(\u03b8)} =\nX\na\u2208D:\u03c6(a)\u2264x\nPr{ (a) = 0},\nwhere x is a real number and \u2264D indicates that the upper bound\naccounts only for strategies that appear in the data set D. Since the\nevents {\u2203a \u2208 D : \u03c6(a) \u2264 x \u2227 a \u2208 N(\u03b8)} and {inf{\u03c6\u2217\n(\u03b8)} \u2264 x}\nare equivalent, this also defines an upper bound on the\nprobability of {inf{\u03c6\u2217\n(\u03b8)} \u2264 x}. The values thus derived comprise the\nTables 1 and 2.\n\u03c6\u2217\n(\u03b8) \u03b8 = 0 \u03b8 = 50 \u03b8 = 100\n<2.7 0.000098 0 0.146\n<3 0.158 0.0511 0.146\n<3.9 0.536 0.163 1\n<4.5 1 1 1\nTable 1: Upper bounds on the distribution of inf{\u03c6\u2217\n(\u03b8)}\nrestricted to D for \u03b8 \u2208 {0, 50, 100} when N(\u03b8) is a set of Nash\nequilibria.\n\u03c6\u2217\n(\u03b8) \u03b8 = 150 \u03b8 = 200 \u03b8 = 320\n<2.7 0 0 0.00132\n<3 0.0363 0.141 1\n<3.9 1 1 1\n<4.5 1 1 1\nTable 2: Upper bounds on the distribution of inf{\u03c6\u2217\n(\u03b8)}\nrestricted to D for \u03b8 \u2208 {150, 200, 320} when N(\u03b8) is a set of\nNash equilibria.\nTables 1 and 2 suggest that the existence of any equilibrium with\n\u03c6(a) < 2.7 is unlikely for any \u03b8 that we have data for, although\nthis judgment, as we mentioned, is only with respect to the profiles\nwe have actually sampled. We can then accept this as another piece\nof evidence that the designer could not find a suitable setting of \u03b8\nto achieve his objectives-indeed, the designer seems unlikely to\nachieve his objective even if he could persuade participants to play\na desirable equilibrium!\nTable 1 also provides additional evidence that the agents in the\n2004 TAC/SCM tournament were indeed rational in procuring large\nnumbers of components at the beginning fo the game. If we look at\nthe third column of this table, which corresponds to \u03b8 = 100, we\ncan gather that no profile a in our data with \u03c6(a) < 3 is very likely\nto be played in equilibrium.\nThe bounds above provide some general evidence, but ultimately\nwe are interested in a concrete probabilistic assessment of our\nconclusion with respect to the data we have sampled. Particularly, we\nwould like to say something about what happens for the settings of\n\u03b8 for which we have no data. To derive an approximate\nprobabilistic bound on the probability that no \u03b8 \u2208 \u0398 could have achieved the\ndesigner\"s objective, let \u222aJ\nj=1\u0398j, be a partition of \u0398, and assume\nthat the function sup{\u03c6\u2217\n(\u03b8)} satisfies the Lipschitz condition with\nLipschitz constant Aj on each subset \u0398j.13\nSince we have\ndetermined that raising the storage cost above 320 is undesirable due to\nsecondary considerations, we restrict attention to \u0398 = [0, 320]. We\nnow define each subset j to be the interval between two points for\nwhich we have produced data. Thus,\n\u0398 = [0, 50]\n[\n(50, 100]\n[\n(100, 150]\n[\n(150, 200]\n[\n(200, 320],\nwith j running between 1 and 5, corresponding to subintervals\nabove. We will further denote each \u0398j by (aj , bj].14\nThen, the\nfollowing Proposition gives us an approximate upper bound15\non\nthe probability that sup{\u03c6\u2217\n(\u03b8)} \u2264 \u03b1.\nPROPOSITION 2.\nPr{\n_\n\u03b8\u2208\u0398\nsup{\u03c6(\u03b8)} \u2264 \u03b1} \u2264D\n5X\nj=1\nX\ny,z\u2208D:y+z\u2264cj\n0\n@\nX\na:\u03c6(a)=z\nPr{ (a) = 0}\n1\nA \u00d7\n\u00d7\n0\n@\nX\na:\u03c6(a)=y\nPr{ (a) = 0}\n1\nA ,\nwhere cj = 2\u03b1 + Aj(bj \u2212 aj) and \u2264D indicates that the upper\nbound only accounts for strategies that appear in the data set D.\n13\nA function that satisfies the Lipschitz condition is called Lipschitz\ncontinuous.\n14\nThe treatment for the interval [0,50] is identical.\n15\nIt is approximate in a sense that we only take into account\nstrategies that are present in the data.\n311\nDue to the fact that our bounds are approximate, we cannot use\nthem as a conclusive probabilistic assessment. Instead, we take this\nas another piece of evidence to complement our findings.\nEven if we can assume that a function that we approximate from\ndata is Lipschitz continuous, we rarely actually know the Lipschitz\nconstant for any subset of \u0398. Thus, we are faced with a task of\nestimating it from data. Here, we tried three methods of doing\nthis. The first one simply takes the highest slope that the function\nattains within the available data and uses this constant value for\nevery subinterval. This produces the most conservative bound, and\nin many situations it is unlikely to be informative.\nAn alternative method is to take an upper bound on slope\nobtained within each subinterval using the available data. This\nproduces a much less conservative upper bound on probabilities.\nHowever, since the actual upper bound is generally greater for each\nsubinterval, the resulting probabilistic bound may be deceiving.\nA final method that we tried is a compromise between the two\nabove. Instead of taking the conservative upper bound based on\ndata over the entire function domain \u0398, we take the average of\nupper bounds obtained at each \u0398j. The bound at an interval is then\ntaken to be the maximum of the upper bound for this interval and\nthe average upper bound for all intervals.\nThe results of evaluating the expression for\nPr{\n_\n\u03b8\u2208\u0398\nsup{\u03c6\u2217\n(\u03b8)} \u2264 \u03b1}\nwhen \u03b1 = 2 are presented in Table 3. In terms of our claims in\nmaxj Aj Aj max{Aj ,ave(Aj)}\n1 0.00772 0.00791\nTable 3: Approximate upper bound on probability that some\nsetting of \u03b8 \u2208 [0, 320] will satisfy the designer objective with\ntarget \u03b1 = 2. Different methods of approximating the upper\nbound on slope in each subinterval j are used.\nthis work, the expression gives an upper bound on the probability\nthat some setting of \u03b8 (i.e., storage cost) in the interval [0,320] will\nresult in total day-0 procurement that is no greater in any\nequilibrium than the target specified by \u03b1 and taken here to be 2. As we\nhad suspected, the most conservative approach to estimating the\nupper bound on slope, presented in the first column of the table,\nprovides us little information here. However, the other two\nestimation approaches, found in columns two and three of Table 3,\nsuggest that we are indeed quite confident that no reasonable setting of\n\u03b8 \u2208 [0, 320] would have done the job. Given the tremendous\ndifficulty of the problem, this result is very strong.16\nStill, we must be\nvery cautious in drawing too heroic a conclusion based on this\nevidence. Certainly, we have not checked all the profiles but only\na small proportion of them (infinitesimal, if we consider the\nentire continuous domain of \u03b8 and strategy sets). Nor can we expect\never to obtain enough evidence to make completely objective\nconclusions. Instead, the approach we advocate here is to collect as\nmuch evidence as is feasible given resource constraints, and make\nthe most compelling judgment based on this evidence, if at all\npossible.\n5. CONVERGENCE RESULTS\nAt this point, we explore abstractly whether a design parameter\nchoice based on payoff data can be asymptotically reliable.\n16\nSince we did not have all the possible deviations for any profile\navailable in the data, the true upper bounds may be even lower.\nAs a matter of convenience, we will use notation un,i(a) to\nrefer to a payoff function of player i based on an average over n\ni.i.d. samples from the distribution of payoffs. We also assume that\nun,i(a) are independent for all a \u2208 A and i \u2208 I. We will use\nthe notation \u0393n to refer to the game [I, R, {ui,n(\u00b7)}], whereas \u0393\nwill denote the underlying game, [I, R, {ui(\u00b7)}]. Similarly, we\ndefine n(r) to be (r) with respect to the game \u0393n.\nIn this section, we show that n(s) \u2192 (s) a.s. uniformly on\nthe mixed strategy space for any finite game, and, furthermore, that\nall mixed strategy Nash equilibria in empirical games eventually\nbecome arbitrarily close to some Nash equilibrium strategies in the\nunderlying game. We use these results to show that under certain\nconditions, the optimal choice of the design parameter based on\nempirical data converges almost surely to the actual optimum.\nTHEOREM 3. Suppose that |I| < \u221e, |A| < \u221e. Then n(s) \u2192\n(s) a.s. uniformly on S.\nRecall that N is a set of all Nash equilibria of \u0393. If we define\nNn,\u03b3 = {s \u2208 S : n(s) \u2264 \u03b3}, we have the following corollary to\nTheorem 3:\nCOROLLARY 4. For every \u03b3 > 0, there is M such that \u2200n \u2265\nM, N \u2282 Nn,\u03b3 a.s.\nPROOF. Since (s) = 0 for every s \u2208 N, we can find M large\nenough such that Pr{supn\u2265M sups\u2208N n(s) < \u03b3} = 1.\nBy the Corollary, for any game with a finite set of pure strategies\nand for any > 0, all Nash equilibria lie in the set of empirical\n-Nash equilibria if enough samples have been taken. As we now\nshow, this provides some justification for our use of a set of profiles\nwith a non-zero -bound as an estimate of the set of Nash equilibria.\nFirst, suppose we conclude that for a particular setting of \u03b8,\nsup{\u02c6\u03c6\u2217\n(\u03b8)} \u2264 \u03b1. Then, since for any fixed > 0, N(\u03b8) \u2282\nNn, (\u03b8) when n is large enough,\nsup{\u03c6\u2217\n(\u03b8)} = sup\ns\u2208N (\u03b8)\n\u03c6(s) \u2264\nsup\ns\u2208Nn, (\u03b8)\n\u03c6(s) = sup{\u02c6\u03c6\u2217\n(\u03b8)} \u2264 \u03b1\nfor any such n. Thus, since we defined the welfare function of\nthe designer to be I{sup{\u03c6\u2217\n(\u03b8)} \u2264 \u03b1} in our domain of interest,\nthe empirical choice of \u03b8 satisfies the designer\"s objective, thereby\nmaximizing his welfare function.\nAlternatively, suppose we conclude that inf{\u02c6\u03c6\u2217\n(\u03b8)} > \u03b1 for\nevery \u03b8 in the domain. Then,\n\u03b1 < inf{\u02c6\u03c6\u2217\n(\u03b8)} = inf\ns\u2208Nn, (\u03b8)\n\u03c6(s) \u2264 inf\ns\u2208N (\u03b8)\n\u03c6(s) \u2264\n\u2264 sup\ns\u2208N (\u03b8)\n\u03c6(s) = sup{\u03c6\u2217\n(\u03b8)},\nfor every \u03b8, and we can conclude that no setting of \u03b8 will satisfy\nthe designer\"s objective.\nNow, we will show that when the number of samples is large\nenough, every Nash equilibrium of \u0393n is close to some Nash\nequilibrium of the underlying game. This result will lead us to consider\nconvergence of optimizers based on empirical data to actual\noptimal mechanism parameter settings.\nWe first note that the function (s) is continuous in a finite game.\nLEMMA 5. Let S be a mixed strategy set defined on a finite\ngame. Then : S \u2192 R is continuous.\n312\nFor the exposition that follows, we need a bit of additional\nnotation. First, let (Z, d) be a metric space, and X, Y \u2282 Z and define\ndirected Hausdorff distance from X to Y to be\nh(X, Y ) = sup\nx\u2208X\ninf\ny\u2208Y\nd(x, y).\nObserve that U \u2282 X \u21d2 h(U, Y ) \u2264 h(X, Y ). Further, define\nBS(x, \u03b4) to be an open ball in S \u2282 Z with center x \u2208 S and\nradius \u03b4. Now, let Nn denote all Nash equilibria of the game \u0393n\nand let\nN\u03b4 =\n[\nx\u2208N\nBS(x, \u03b4),\nthat is, the union of open balls of radius \u03b4 with centers at Nash\nequilibria of \u0393. Note that h(N\u03b4, N) = \u03b4.\nWe can then prove the following general result.\nTHEOREM 6. Suppose |I| < \u221e and |A| < \u221e. Then almost\nsurely h(Nn, N) converges to 0.\nWe will now show that in the special case when \u0398 and A are\nfinite and each \u0393\u03b8 has a unique Nash equilibrium, the estimates\n\u02c6\u03b8 of optimal designer parameter converge to an actual optimizer\nalmost surely.\nLet \u02c6\u03b8 = arg max\u03b8\u2208\u0398 W (Nn(\u03b8), \u03b8), where n is the number of\ntimes each pure profile was sampled in \u0393\u03b8 for every \u03b8, and let \u03b8\u2217\n=\narg max\u03b8\u2208\u0398 W (N(\u03b8), \u03b8).\nTHEOREM 7. Suppose |N(\u03b8)| = 1 for all \u03b8 \u2208 \u0398 and suppose\nthat \u0398 and A are finite. Let W (s, \u03b8) be continuous at the unique\ns\u2217\n(\u03b8) \u2208 N(\u03b8) for each \u03b8 \u2208 \u0398. Then \u02c6\u03b8 is a consistent estimator of\n\u03b8\u2217\nif W (N(\u03b8), \u03b8) is defined as a supremum, infimum, or\nexpectation over the set of Nash equilibria. In fact, \u02c6\u03b8 \u2192 \u03b8\u2217\na.s. in each of\nthese cases.\nThe shortcoming of the above result is that, within our\nframework, the designer has no way of knowing or ensuring that \u0393\u03b8 do,\nindeed, have unique equilibria. However, it does lend some\ntheoretical justification for pursuing design in this manner, and, perhaps,\nwill serve as a guide for more general results in the future.\n6. RELATED WORK\nThe mechanism design literature in Economics has typically\nexplored existence of a mechanism that implements a social choice\nfunction in equilibrium [10]. Additionally, there is an extensive\nliterature on optimal auction design [10], of which the work by Roger\nMyerson [11] is, perhaps, the most relevant. In much of this work,\nanalytical results are presented with respect to specific utility\nfunctions and accounting for constraints such as incentive compatibility\nand individual rationality.\nSeveral related approaches to search for the best mechanism\nexist in the Computer Science literature. Conitzer and Sandholm [6]\ndeveloped a search algorithm when all the relevant game\nparameters are common knowledge. When payoff functions of players\nare unknown, a search using simulations has been explored as an\nalternative. One approach in that direction, taken in [4] and [15],\nis to co-evolve the mechanism parameter and agent strategies,\nusing some notion of social utility and agent payoffs as fitness\ncriteria. An alternative to co-evolution explored in [16] was to\noptimize a well-defined welfare function of the designer using genetic\nprogramming. In this work the authors used a common learning\nstrategy for all agents and defined an outcome of a game induced\nby a mechanism parameter as the outcome of joint agent learning.\nMost recently, Phelps et al. [14] compared two mechanisms based\non expected social utility with expectation taken over an empirical\ndistribution of equilibria in games defined by heuristic strategies,\nas in [18].\n7. CONCLUSION\nIn this work we spent considerable effort developing general\ntactics for empirical mechanism design. We defined a formal\ngametheoretic model of interaction between the designer and the\nparticipants of the mechanism as a two-stage game. We also described in\nsome generality the methods for estimating a sample Nash\nequilibrium function when the data is extremely scarce, or a Nash\nequilibrium correspondence when more data is available. Our techniques\nare designed specifically to deal with problems in which both the\nmechanism parameter space and the agent strategy sets are infinite\nand only a relatively small data set can be acquired.\nA difficult design issue in the TAC/SCM game which the TAC\ncommunity has been eager to address provides us with a setting\nto test our methods. In applying empirical game analysis to the\nproblem at hand, we are fully aware that our results are inherently\ninexact. Thus, we concentrate on collecting evidence about the\nstructure of the Nash equilibrium correspondence. In the end, we\ncan try to provide enough evidence to either prescribe a parameter\nsetting, or suggest that no setting is possible that will satisfy the\ndesigner. In the case of TAC/SCM, our evidence suggests quite\nstrongly that storage cost could not have been effectively adjusted\nin the 2004 tournament to curb excessive day-0 procurement\nwithout detrimental effects on overall profitability. The success of our\nanalysis in this extremely complex environment with high\nsimulation costs makes us optimistic that our methods can provide\nguidance in making mechanism design decisions in other challenging\ndomains. The theoretical results confirm some intuitions behind\nthe empirical mechanism design methods we have introduced, and\nincreases our confidence that our framework can be effective in\nestimating the best mechanism parameter choice in relatively general\nsettings.\nAcknowledgments\nWe thank Terence Kelly, Matthew Rudary, and Satinder Singh for\nhelpful comments on earlier drafts of this work. This work was\nsupported in part by NSF grant IIS-0205435 and the DARPA REAL\nstrategic reasoning program.\n8. REFERENCES\n[1] R. Arunachalam and N. M. Sadeh. The supply chain trading\nagent competition. Electronic Commerce Research and\nApplications, 4:63-81, 2005.\n[2] M. Benisch, A. Greenwald, V. Naroditskiy, and M. 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In\nWorkshop on Agent Mediated Electronic Commerce VI,\n2004.\n[15] S. Phelps, S. Parsons, P. McBurney, and E. Sklar.\nCo-evolution of auction mechanisms and trading strategies:\ntowards a novel approach to microeconomic design. In\nECOMAS 2002 Workshop, 2002.\n[16] S. Phelps, S. Parsons, E. Sklar, and P. McBurney. Using\ngenetic programming to optimise pricing rules for a\ndouble-auction market. In Workshop on Agents for Electronic\nCommerce, 2003.\n[17] Y. Vorobeychik, M. P. Wellman, and S. Singh. Learning\npayoff functions in infinite games. In Nineteenth\nInternational Joint Conference on Artificial Intelligence,\npages 977-982, 2005.\n[18] W. E. Walsh, R. Das, G. Tesauro, and J. O. Kephart.\nAnalyzing complex strategic interactions in multi-agent\nsystems. In AAAI-02 Workshop on Game Theoretic and\nDecision Theoretic Agents, 2002.\n[19] M. P. Wellman, J. J. Estelle, S. Singh, Y. Vorobeychik,\nC. Kiekintveld, and V. Soni. Strategic interactions in a supply\nchain game. Computational Intelligence, 21(1):1-26,\nFebruary 2005.\nAPPENDIX\nA. PROOFS\nA.1 Proof of Proposition 1\nPr\n\u201e\nmax\ni\u2208I\nmax\nb\u2208Ai\\ai\nui(b, a\u2212i) \u2212 ui(a) \u2264\n\u00ab\n=\n=\nY\ni\u2208I\nEui(a)\n\u00bb\nPr( max\nb\u2208Ai\\ai\nui(b, a\u2212i) \u2212 ui(a) \u2264 |ui(a))\n\n=\n=\nY\ni\u2208I\nZ\nR\nY\nb\u2208Ai\\ai\nPr(ui(b, a\u2212i) \u2264 u + )fui(a)(u)du.\nA.2 Proof of Proposition 2\nFirst, let us suppose that some function, f(x) defined on [ai, bi],\nsatisfy Lipschitz condition on (ai, bi] with Lipschitz constant Ai.\nThen the following claim holds:\nClaim: infx\u2208(ai,bi] f(x) \u2265 0.5(f(ai) + f(bi) \u2212 Ai(bi \u2212 ai).\nTo prove this claim, note that the intersection of lines at f(ai)\nand f(bi) with slopes \u2212Ai and Ai respectively will determine the\nlower bound on the minimum of f(x) on [ai, bi] (which is a lower\nbound on infimum of f(x) on (ai, bj ]). The line at f(ai) is\ndetermined by f(ai) = \u2212Aiai + cL and the line at f(bi) is determined\nby f(bi) = Aibi +cR. Thus, the intercepts are cL = f(ai)+Aiai\nand cR = f(bi) + Aibi respectively. Let x\u2217\nbe the point at which\nthese lines intersect. Then,\nx\u2217\n= \u2212\nf(x\u2217\n) \u2212 cR\nA\n=\nf(x\u2217\n) \u2212 cL\nA\n.\nBy substituting the expressions for cR and cL, we get the desired\nresult.\nNow, subadditivity gives us\nPr{\n_\n\u03b8\u2208\u0398\nsup{\u03c6\u2217\n(\u03b8)} \u2264 \u03b1} \u2264\n5X\nj=1\nPr{\n_\n\u03b8\u2208\u0398j\nsup{\u03c6\u2217\n(\u03b8)} \u2264 \u03b1},\nand, by the claim,\nPr{\n_\n\u03b8\u2208\u0398j\nsup{\u03c6\u2217\n(\u03b8)} \u2264 \u03b1} =\n1 \u2212 Pr{ inf\n\u03b8\u2208\u0398j\nsup{\u03c6\u2217\n(\u03b8)} > \u03b1} \u2264\nPr{sup{\u03c6\u2217\n(aj)} + sup{\u03c6\u2217\n(bj)} \u2264 2\u03b1 + Aj(bj \u2212 aj )}.\nSince we have a finite number of points in the data set for each\n\u03b8, we can obtain the following expression:\nPr{sup{\u03c6\u2217\n(aj)} + sup{\u03c6\u2217\n(bj)} \u2264 cj } =D\nX\ny,z\u2208D:y+z\u2264cj\nPr{sup{\u03c6\u2217\n(bj )} = y} Pr{sup{\u03c6\u2217\n(aj)} = z}.\nWe can now restrict attention to deriving an upper bound on\nPr{sup{\u03c6\u2217\n(\u03b8)} = y} for a fixed \u03b8. To do this, observe that\nPr{sup{\u03c6\u2217\n(\u03b8)} = y} \u2264D Pr{\n_\na\u2208D:\u03c6(a)=y\n(a) = 0} \u2264\nX\na\u2208D:\u03c6(a)=y\nPr{ (a) = 0}\nby subadditivity and the fact that a profile a is a Nash equilibrium\nif and only if (a) = 0.\nPutting everything together yields the desired result.\nA.3 Proof of Theorem 3\nFirst, we will need the following fact:\nClaim: Given a function fi(x) and a set X, | maxx\u2208X f1(x) \u2212\nmaxx\u2208X f2(x)| \u2264 maxx\u2208X |f1(x) \u2212 f2(x)|.\nTo prove this claim, observe that\n| max\nx\u2208X\nf1(x) \u2212 max\nx\u2208X\nf2(x)| =\n\uf6be\nmaxx f1(x) \u2212 maxx f2(x) if maxx f1(x) \u2265 maxx f2(x)\nmaxx f2(x) \u2212 maxx f1(x) if maxx f2(x) \u2265 maxx f1(x)\nIn the first case,\nmax\nx\u2208X\nf1(x) \u2212 max\nx\u2208X\nf2(x) \u2264 max\nx\u2208X\n(f1(x) \u2212 f2(x)) \u2264\n\u2264 max\nx\u2208X\n|f1(x) \u2212 f2(x)|.\n314\nSimilarly, in the second case,\nmax\nx\u2208X\nf2(x) \u2212 max\nx\u2208X\nf1(x) \u2264 max\nx\u2208X\n(f2(x) \u2212 f1(x)) \u2264\n\u2264 max\nx\u2208X\n|f2(x) \u2212 f1(x)| = max\nx\u2208X\n|f1(x) \u2212 f2(x)|.\nThus, the claim holds.\nBy the Strong Law of Large Numbers, un,i(a) \u2192 ui(a) a.s. for\nall i \u2208 I, a \u2208 A. That is,\nPr{ lim\nn\u2192\u221e\nun,i(a) = ui(a)} = 1,\nor, equivalently [8], for any \u03b1 > 0 and \u03b4 > 0, there is M(i, a) > 0\nsuch that\nPr{ sup\nn\u2265M(i,a)\n|un,i(a) \u2212 ui(a)| <\n\u03b4\n2|A|\n} \u2265 1 \u2212 \u03b1.\nBy taking M = maxi\u2208I maxa\u2208A M(i, a), we have\nPr{max\ni\u2208I\nmax\na\u2208A\nsup\nn\u2265M\n|un,i(a) \u2212 ui(a)| <\n\u03b4\n2|A|\n} \u2265 1 \u2212 \u03b1.\nThus, by the claim, for any n \u2265 M,\nsup\nn\u2265M\n| n(s) \u2212 (s)| \u2264\nmax\ni\u2208I\nmax\nai\u2208Ai\nsup\nn\u2265M\n|un,i(ai, s\u2212i) \u2212 ui(ai, s\u2212i)|+\n+ sup\nn\u2265M\nmax\ni\u2208I\n|un,i(s) \u2212 ui(s)| \u2264\nmax\ni\u2208I\nmax\nai\u2208Ai\nX\nb\u2208A\u2212i\nsup\nn\u2265M\n|un,i(ai, b) \u2212 ui(ai, b)|s\u2212i(b)+\n+ max\ni\u2208I\nX\nb\u2208A\nsup\nn\u2265M\n|un,i(b) \u2212 ui(b)|s(b) \u2264\nmax\ni\u2208I\nmax\nai\u2208Ai\nX\nb\u2208A\u2212i\nsup\nn\u2265M\n|un,i(ai, b) \u2212 ui(ai, b)|+\n+ max\ni\u2208I\nX\nb\u2208A\nsup\nn\u2265M\n|un,i(b) \u2212 ui(b)| <\nmax\ni\u2208I\nmax\nai\u2208Ai\nX\nb\u2208A\u2212i\n(\n\u03b4\n2|A|\n) + max\ni\u2208I\nX\nb\u2208A\n(\n\u03b4\n2|A|\n) \u2264 \u03b4\nwith probability at least 1 \u2212 \u03b1. Note that since s\u2212i(a) and s(a)\nare bounded between 0 and 1, we were able to drop them from\nthe expressions above to obtain a bound that will be valid\nindependent of the particular choice of s. Furthermore, since the above\nresult can be obtained for an arbitrary \u03b1 > 0 and \u03b4 > 0, we have\nPr{limn\u2192\u221e n(s) = (s)} = 1 uniformly on S.\nA.4 Proof of Lemma 5\nWe prove the result using uniform continuity of ui(s) and\npreservation of continuity under maximum.\nClaim: A function f : Rk\n\u2192 R defined by f(t) =\nPk\ni=1 ziti,\nwhere zi are constants in R, is uniformly continuous in t.\nThe claim follows because |f(t)\u2212f(t )| = |\nPk\ni=1 zi(ti\u2212ti)| \u2264\nPk\ni=1 |zi||ti \u2212 ti|. An immediate result of this for our purposes is\nthat ui(s) is uniformly continuous in s and ui(ai, s\u2212i) is uniformly\ncontinuous in s\u2212i.\nClaim: Let f(a, b) be uniformly continuous in b \u2208 B for every\na \u2208 A, with |A| < \u221e. Then V (b) = maxa\u2208A f(a, b) is uniformly\ncontinuous in b.\nTo show this, take \u03b3 > 0 and let b, b \u2208 B such that b \u2212 b <\n\u03b4(a) \u21d2 |f(a, b) \u2212 f(a, b )| < \u03b3. Now take \u03b4 = mina\u2208A \u03b4(a).\nThen, whenever b \u2212 b < \u03b4,\n|V (b) \u2212 V (b )| = | max\na\u2208A\nf(a, b) \u2212 max\na\u2208A\nf(a, b )| \u2264\nmax\na\u2208A\n|f(a, b) \u2212 f(a, b )| < \u03b3.\nNow, recall that (s) = maxi[maxai\u2208Ai ui(ai, s\u2212i) \u2212 ui(s)]. By\nthe claims above, maxai\u2208Ai ui(ai, s\u2212i) is uniformly continuous in\ns\u2212i and ui(s) is uniformly continuous in s. Since the difference of\ntwo uniformly continuous functions is uniformly continuous, and\nsince this continuity is preserved under maximum by our second\nclaim, we have the desired result.\nA.5 Proof of Theorem 6\nChoose \u03b4 > 0. First, we need to ascertain that the following\nclaim holds:\nClaim: \u00af = mins\u2208S\\N\u03b4\n(s) exists and \u00af > 0.\nSince N\u03b4 is an open subset of compact S, it follows that S \\\nN\u03b4 is compact. As we had also proved in Lemma 5 that (s) is\ncontinuous, existence follows from the Weierstrass theorem. That\n\u00af > 0 is clear since (s) = 0 if and only if s is a Nash equilibrium\nof \u0393.\nNow, by Theorem 3, for any \u03b1 > 0 there is M such that\nPr{ sup\nn\u2265M\nsup\ns\u2208S\n| n(s) \u2212 (s)| < \u00af} \u2265 1 \u2212 \u03b1.\nConsequently, for any \u03b4 > 0,\nPr{ sup\nn\u2265M\nh(Nn, N\u03b4) < \u03b4} \u2265 Pr{\u2200n \u2265 M Nn \u2282 N\u03b4} \u2265\nPr{ sup\nn\u2265M\nsup\ns\u2208N\n(s) < \u00af} \u2265\nPr{ sup\nn\u2265M\nsup\ns\u2208S\n| n(s) \u2212 (s)| < \u00af} \u2265 1 \u2212 \u03b1.\nSince this holds for an arbitrary \u03b1 > 0 and \u03b4 > 0, the desired result\nfollows.\nA.6 Proof of Theorem 7\nFix \u03b8 and choose \u03b4 > 0. Since W (s, \u03b8) is continuous at s\u2217\n(\u03b8),\ngiven > 0 there is \u03b4 > 0 such that for every s that is within \u03b4 of\ns\u2217\n(\u03b8), |W (s , \u03b8) \u2212 W (s\u2217\n(\u03b8), \u03b8)| < . By Theorem 6, we can find\nM(\u03b8) large enough such that all s \u2208 Nn are within \u03b4 of s\u2217\n(\u03b8) for\nall n \u2265 M(\u03b8) with probability 1. Consequently, for any > 0 we\ncan find M(\u03b8) large enough such that with probability 1 we have\nsupn\u2265M(\u03b8) sups \u2208Nn\n|W (s , \u03b8) \u2212 W (s\u2217\n(\u03b8), \u03b8)| < .\nLet us assume without loss of generality that there is a unique\noptimal choice of \u03b8. Now, since the set \u0398 is finite, there is also the\nsecond-best choice of \u03b8 (if there is only one \u03b8 \u2208 \u0398 this discussion\nis moot anyway):\n\u03b8\u2217\u2217\n= arg max\n\u0398\\\u03b8\u2217\nW (s\u2217\n(\u03b8), \u03b8).\nSuppose w.l.o.g. that \u03b8\u2217\u2217\nis also unique and let\n\u2206 = W (s\u2217\n(\u03b8\u2217\n), \u03b8\u2217\n) \u2212 W (s\u2217\n(\u03b8\u2217\u2217\n), \u03b8\u2217\u2217\n).\nThen if we let < \u2206/2 and let M = max\u03b8\u2208\u0398 M(\u03b8), where each\nM(\u03b8) is large enough such that supn\u2265M(\u03b8) sups \u2208Nn\n|W (s , \u03b8)\u2212\nW (s\u2217\n(\u03b8), \u03b8)| < a.s., the optimal choice of \u03b8 based on any\nempirical equilibrium will be \u03b8\u2217\nwith probability 1. Thus, in\nparticular, given any probability distribution over empirical equilibria, the\nbest choice of \u03b8 will be \u03b8\u2217\nwith probability 1 (similarly, if we take\nsupremum or infimum of W (Nn(\u03b8), \u03b8) over the set of empirical\nequilibria in constructing the objective function).\n315", "keywords": "analysis;nash equilibrium;participant;game theory;observed behavior;outcome feature of interest;parameter setting;player;gametheoretic model;supply-chain trading;two-stage game;empirical mechanism design;interest outcome feature;empirical mechanism"}
{"name": "train_J-47", "title": "On the Computational Power of Iterative Auctions\u2217", "abstract": "We embark on a systematic analysis of the power and limitations of iterative combinatorial auctions. Most existing iterative combinatorial auctions are based on repeatedly suggesting prices for bundles of items, and querying the bidders for their demand under these prices. We prove a large number of results showing the boundaries of what can be achieved by auctions of this kind. We first focus on auctions that use a polynomial number of demand queries, and then we analyze the power of different kinds of ascending-price auctions.", "fulltext": "1. INTRODUCTION\nCombinatorial auctions have recently received a lot of\nattention. In a combinatorial auction, a set M of m\nnonidentical items are sold in a single auction to n competing\nbidders. The bidders have preferences regarding the bundles\nof items that they may receive. The preferences of bidder i\nare specified by a valuation function vi : 2M\n\u2192 R+\n, where\nvi(S) denotes the value that bidder i attaches to winning the\nbundle of items S. We assume free disposal, i.e., that the\nvi\"s are monotone non-decreasing. The usual goal of the\nauctioneer is to optimize the social welfare\nP\ni vi(Si), where the\nallocation S1...Sn must be a partition of the items.\nApplications include many complex resource allocation problems\nand, in fact, combinatorial auctions may be viewed as the\ncommon abstraction of many complex resource allocation\nproblems. Combinatorial auctions face both economic and\ncomputational difficulties and are a central problem in the\nrecently active border of economic theory and computer\nscience. A forthcoming book [11] addresses many of the issues\ninvolved in the design and implementation of combinatorial\nauctions.\nThe design of a combinatorial auction involves many\nconsiderations. In this paper we focus on just one central\nissue: the communication between bidders and the allocation\nmechanism - preference elicitation. Transferring all\ninformation about bidders\" preferences requires an infeasible\n(exponential in m) amount of communication. Thus,\ndirect revelation auctions in which bidders simply declare\ntheir preferences to the mechanism are only practical for\nvery small auction sizes or for very limited families of bidder\npreferences. We have therefore seen a multitude of suggested\niterative auctions in which the auction protocol repeatedly\ninteracts with the different bidders, aiming to adaptively\nelicit enough information about the bidders\" preferences as\nto be able to find a good (optimal or close to optimal)\nallocation.\nMost of the suggested iterative auctions proceed by\nmaintaining temporary prices for the bundles of items and\nrepeatedly querying the bidders as to their preferences between the\nbundles under the current set of prices, and then updating\nthe set of bundle prices according to the replies received\n(e.g., [22, 12, 17, 37, 3]). Effectively, such an iterative\nauction accesses the bidders\" preferences by repeatedly making\nthe following type of demand query to bidders: Query to\nbidder i: a vector of bundle prices p = {p(S)}S\u2286M ; Answer:\na bundle of items S \u2286 M that maximizes vi(S) \u2212 p(S)..\nThese types of queries are very natural in an economic\nsetting as they capture the revealed preferences of the\nbidders. Some auctions, called item-price or linear-price\nauctions, specify a price pi for each item, and the price of any\ngiven bundle S is always linear, p(S) =\nP\ni\u2208S pi. Other\nauctions, called bundle-price auctions, allow specifying\narbitrary (non-linear) prices p(S) for bundles. Another\nimportant differentiation between models of iterative auctions is\n29\nbased on whether they use anonymous or non-anonymous\nprices: In some auctions the prices that are presented to the\nbidders are always the same (anonymous prices). In other\nauctions (non-anonymous), different bidders may face\ndifferent (discriminatory) vectors of prices. In ascending-price\nauctions, forcing prices to be anonymous may be a\nsignificant restriction.\nIn this paper, we embark on a systematic analysis of the\ncomputational power of iterative auctions that are based\non demand queries. We do not aim to present auctions for\npractical use but rather to understand the limitations and\npossibilities of these kinds of auctions. In the first part of\nthis paper, our main question is what can be done using a\npolynomial number of these types of queries? That is,\npolynomial in the main parameters of the problem: n, m and the\nnumber of bits t needed for representing a single value vi(S).\nNote that from an algorithmic point of view we are talking\nabout sub-linear time algorithms: the input size here is\nreally n(2m\n\u2212 1) numbers - the descriptions of the valuation\nfunctions of all bidders. There are two aspects to\ncomputational efficiency in these settings: the first is the\ncommunication with the bidders, i.e., the number of queries made, and\nthe second is the usual computational tractability. Our\nlower bounds will depend only on the number of\nqueriesand hold independently of any computational assumptions\nlike P = NP. Our upper bounds will always be\ncomputationally efficient both in terms of the number of queries\nand in terms of regular computation. As mentioned, this\npaper concentrates on the single aspect of preference elicitation\nand on its computational consequences and does not address\nissues of incentives. This strengthens our lower bounds, but\nmeans that the upper bounds require evaluation from this\nperspective also before being used in any real combinatorial\nauction.1\nThe second part of this paper studies the power of\nascending -price auctions. Ascending auctions are iterative\nauctions where the published prices cannot decrease in time. In\nthis work, we try to systematically analyze what do the\ndifferences between various models of ascending auctions mean.\nWe try to answer the following questions: (i) Which models\nof ascending auctions can find the optimal allocation, and for\nwhich classes of valuations? (ii) In cases where the optimal\nallocation cannot be determined by ascending auctions, how\nwell can such auctions approximate the social welfare? (iii)\nHow do the different models for ascending auctions compare?\nAre some models computationally stronger than others?\nAscending auctions have been extensively studied in the\nliterature (see the recent survey by Parkes [35]). Most of this\nwork presented \"upper bounds\", i.e., proposed mechanisms\nwith ascending prices and analyzed their properties. A\nresult which is closer in spirit to ours, is by Gul and Stacchetti\n[17], who showed that no item-price ascending auction can\nalways determine the VCG prices, even for substitutes\nvaluations.2\nOur framework is more general than the traditional\nline of research that concentrates on the final allocation and\n1\nWe do observe however that some weak incentive\nproperty comes for free in demand-query auctions since myopic\nplayers will answer all demand queries truthfully. We also\nnote that in some cases (but not always!) the incentives\nissues can be handled orthogonally to the preference\nelicitation issues, e.g., by using Vickrey-Clarke-Groves (VCG)\nprices (e.g., [4, 34]).\n2\nWe further discuss this result in Section 5.3.\nIterative auctions\nDemand auctions\nItem-price\nauctions\nAnonymous\nprice auctions\nAscending\nauctions\n1\n2\n3\n4\n5\n6\n97\n8\n10\nFigure 1: The diagram classifies the following auctions\naccording to their properties:\n(1) The adaptation [12] for Kelso & Crawford\"s [22]\nauction.\n(2) The Proxy Auction [3] by Ausubel & Milgrom.\n(3) iBundle(3) by Parkes & Ungar [34].\n(4) iBundle(2) by Parkes & Ungar [37].\n(5) Our descending adaptation for the 2-approximation\nfor submodular valuations by [25] (see Subsection 5.4).\n(6) Ausubel\"s [4] auction for substitutes valuations.\n(7) The adaptation by Nisan & Segal [32] of the O(\n\u221a\nm)\napproximation by [26].\n(8) The duplicate-item auction by [5].\n(9) Auction for Read-Once formulae by [43].\n(10) The AkBA Auction by Wurman & Wellman [42].\npayments and in particular, on reaching \"Walrasian\nequilibria\" or \"Competitive equilibria\". A Walrasian equilibrium3\nis known to exist in the case of Substitutes valuations, and\nis known to be impossible for any wider class of valuations\n[16]. This does not rule out other allocations by ascending\nauctions: in this paper we view the auctions as a\ncomputational process where the outcome - both the allocation\nand the payments - can be determined according to all the\ndata elicited throughout the auction; This general\nframework strengthens our negative results.4\nWe find the study of ascending auctions appealing for\nvarious reasons. First, ascending auctions are widely used in\nmany real-life settings from the FCC spectrum auctions [15]\nto almost any e-commerce website (e.g., [2, 1]). Actually,\nthis is maybe the most straightforward way to sell items: ask\nthe bidders what would they like to buy under certain prices,\nand increase the prices of over-demanded goods. Ascending\nauctions are also considered more intuitive for many bidders,\nand are believed to increase the trust of the bidders in the\nauctioneer, as they see the result gradually emerging from\nthe bidders\" responses. Ascending auctions also have other\ndesired economic properties, e.g., they incur smaller\ninformation revelation (consider, for example, English auctions\nvs. second-price sealed bid auctions).\n1.1 Extant Work\nMany iterative combinatorial auction mechanisms rely on\ndemand queries (see the survey in [35]). Figure 1\nsumma3\nA Walrasian equilibrium is vector of item prices for which\nall the items are sold when each bidder receives a bundle in\nhis demand set.\n4\nIn few recent auction designs (e.g., [4, 28]) the payments\nare not necessarily the final prices of the auctions.\n30\nValuation family Upper bound Reference Lower bound Reference\nGeneral min(n, O(\n\u221a\nm)) [26], Section 4.2 min(n, m1/2\u2212\n) [32]\nSubstitutes 1 [32]\nSubmodular 2 [25], 1+ 1\n2m\n, 1-1\ne\n(*) [32],[23]\nSubadditive O(logm) [13] 2 [13]\nk-duplicates O(m1/k+1\n) [14] O(m1/k+1\n) [14]\nProcurement ln m [32] (log m)/2 [29, 32]\nFigure 2: The best approximation factors currently achievable by computationally-efficient combinatorial auctions,\nfor several classes of valuations. All lower bounds in the table apply to all iterative auctions (except the one marked\nby *); all upper bounds in the table are achieved with item-price demand queries.\nrizes the basic classes of auctions implied by combinations\nof the above properties and classifies some of the auctions\nproposed in the literature according to this classification.\nFor our purposes, two families of these auctions serve as\nthe main motivating starting points: the first is the\nascending item-price auctions of [22, 17] that with computational\nefficiency find an optimal allocation among (gross)\nsubstitutes valuations, and the second is the ascending\nbundleprice auctions of [37, 3] that find an optimal allocation\namong general valuations - but not necessarily with\ncomputational efficiency. The main lower bound in this area,\ndue to [32], states that indeed, due to inherent\ncommunication requirements, it is not possible for any iterative auction\nto find the optimal allocation among general valuations with\nsub-exponentially many queries. A similar exponential lower\nbound was shown in [32] also for even approximating the\noptimal allocation to within a factor of m1/2\u2212\n. Several lower\nbounds and upper bounds for approximation are known for\nsome natural classes of valuations - these are summarized\nin Figure 2.\nIn [32], the universal generality of demand queries is also\nshown: any non-deterministic communication protocol for\nfinding an allocation that optimizes the social welfare can\nbe converted into one that only uses demand queries (with\nbundle prices). In [41] this was generalized also to\nnondeterministic protocols for finding allocations that satisfy\nother natural types of economic requirements (e.g.,\napproximate social efficiency, envy-freeness). However, in [33] it was\ndemonstrated that this completeness of demand queries\nholds only in the nondeterministic setting, while in the usual\ndeterministic setting, demand queries (even with bundle\nprices) may be exponentially weaker than general\ncommunication.\nBundle-price auctions are a generalization of (the more\nnatural and intuitive) item-price auctions. It is known that\nindeed item-price auctions may be exponentially weaker: a\nnice example is the case of valuations that are a XOR of k\nbundles5\n, where k is small (say, polynomial). Lahaie and\nParkes [24] show an economically-efficient bundle-price\nauction that uses a polynomial number of queries whenever k is\npolynomial. In contrast, [7] show that there exist valuations\nthat are XORs of k =\n\u221a\nm bundles such that any item-price\nauction that finds an optimal allocation between them\nrequires exponentially many queries. These results are part\nof a recent line of research ([7, 43, 24, 40]) that study the\npreference elicitation problem in combinatorial auctions\nand its relation to the full elicitation problem (i.e.,\nlearn5\nThese are valuations where bidders have values for k\nspecific packages, and the value of each bundle is the maximal\nvalue of one of these packages that it contains.\ning the exact valuations of the bidders). These papers adapt\nmethods from machine-learning theory to the\ncombinatorialauction setting. The preference elicitation problem and the\nfull elicitation problem relate to a well studied problem in\nmicroeconomics known as the integrability problem (see, e.g.,\n[27]). This problem studies if and when one can derive the\nutility function of a consumer from her demand function.\nPaper organization: Due to the relatively large\nnumber of results we present, we start with a survey of our new\nresults in Section 2. After describing our formal model in\nSection 3, we present our results concerning the power of\ndemand queries in Section 4. Then, we describe the power of\nitem-price ascending auctions (Section 5) and bundle-price\nascending auctions (Section 6). Readers who are mainly\ninterested in the self-contained discussion of ascending\nauctions can skip Section 4.\nMissing proofs from Section 4 can be found in part I of\nthe full paper ([8]). Missing proofs from Sections 5 and 6\ncan be found in part II of the full paper ([9]).\n2. A SURVEY OF OUR RESULTS\nOur systematic analysis is composed of the combination\nof a rather large number of results characterizing the power\nand limitations of various classes of auctions. In this section,\nwe will present an exposition describing our new results. We\nfirst discuss the power of demand-query iterative auctions,\nand then we turn our attention to ascending auctions.\nFigure 3 summarizes some of our main results.\n2.1 Demand Queries\nComparison of query types\nWe first ask what other natural types of queries could\nwe imagine iterative auctions using? Here is a list of such\nqueries that are either natural, have been used in the\nliterature, or that we found useful.\n1. Value query: The auctioneer presents a bundle S, the\nbidder reports his value v(S) for this bundle.\n2. Marginal-value query: The auctioneer presents a\nbundle A and an item j, the bidder reports how much he\nis willing to pay for j, given that he already owns A,\ni.e., v(j|A) = v(A \u222a {j}) \u2212 v(A).\n3. Demand query (with item prices): The auctioneer\npresents a vector of item prices p1...pm; the bidder reports\nhis demand under these prices, i.e., some set S that\nmaximizes v(S) \u2212\nP\ni\u2208S pi.6\n6\nA tie breaking rule should be specified. All of our results\n31\nCommunication Constraint\nCan find an\noptimal allocation?\nUpper bound for\nwelfare approx.\nLower bound for\nwelfare approx.\nItem-Price Demand Queries Yes 1 1\nPoly. Communication No [32] min(n, O(m1/2\n)) [26] min(n, m1/2\u2212\n) [32]\nPoly. Item-Price Demand Queries No [32] min(n, O(m1/2\n)) min(n, m1/2\u2212\n) [32]\nPoly. Value Queries No [32] O( m\u221a\nlog m\n) [19] O( m\nlog m\n)\nAnonymous Item-Price AA No - min(O(n), O(m1/2\u2212\n))\nNon-anonymous Item-Price AA No\n-Anonymous Bundle-Price AA No - min(O(n), O(m1/2\u2212\n))\nNon-anonymous Bundle-Price AA Yes [37] 1 1\nPoly Number of Item-Price AA No min(n, O(m1/2\n\n))Figure 3: This paper studies the economic efficiency of auctions that follow certain communication constraints. For\neach class of auctions, the table shows whether the optimal allocation can be achieved, or else, how well can it be\napproximated (both upper bounds and lower bounds). New results are highlighted.\nAbbreviations: Poly. (Polynomial number/size), AA (ascending auctions). - means that nothing is currently\nknown except trivial solutions.\n4. Indirect-utility query: The auctioneer presents a set of\nitem prices p1...pm, and the bidder responds with his\nindirect-utility under these prices, that is, the\nhighest utility he can achieve from a bundle under these\nprices: maxS\u2286M (v(S) \u2212\nP\ni\u2208S pi).7\n5. Relative-demand query: the auctioneer presents a set\nof non-zero prices p1...pm, and the bidder reports the\nbundle that maximizes his value per unit of money,\ni.e., some set that maximizes v(S)P\ni\u2208S pi\n.8\nTheorem: Each of these queries can be efficiently (i.e., in\ntime polynomial in n, m, and the number of bits of precision\nt needed to represent a single value vi(S)) simulated by a\nsequence of demand queries with item prices.\nIn particular this shows that demand queries can elicit all\ninformation about a valuation by simulating all 2m\n\u22121 value\nqueries. We also observe that value queries and\nmarginalvalue queries can simulate each other in polynomial time\nand that demand queries and indirect-utility queries can also\nsimulate each other in polynomial time. We prove that\nexponentially many value queries may be needed in order to\nsimulate a single demand query. It is interesting to note\nthat for the restricted class of substitutes valuations,\ndemand queries may be simulated by polynomial number of\nvalue queries [6].\nWelfare approximation\nThe next question that we ask is how well can a\ncomputationally-efficient auction that uses only demand queries\napproximate the optimal allocation? Two separate\nobstacles are known: In [32], a lower bound of min(n, m1/2\u2212\n),\nfor any fixed > 0, was shown for the approximation factor\napply for any fixed tie breaking rule.\n7\nThis is exactly the utility achieved by the bundle which\nwould be returned in a demand query with the same prices.\nThis notion relates to the Indirect-utility function studied\nin the Microeconomic literature (see, e.g., [27]).\n8\nNote that when all the prices are 1, the bidder actually\nreports the bundle with the highest per-item price. We found\nthis type of query useful, for example, in the design of the\napproximation algorithm described in Figure 5 in Section\n4.2.\nobtained using any polynomial amount of communication.\nA computational bound with the same value applies even for\nthe case of single-minded bidders, but under the assumption\nof NP = ZPP [39]. As noted in [32], the\ncomputationallyefficient greedy algorithm of [26] can be adapted to become\na polynomial-time iterative auction that achieves a nearly\nmatching approximation factor of min(n, O(\n\u221a\nm)). This\niterative auction may be implemented with bundle-price\ndemand queries but, as far as we see, not as one with item\nprices. Since in a single bundle-price demand query an\nexponential number of prices can be presented, this algorithm\ncan have an exponential communication cost. In Section\n4.2, we describe a different item-price auction that achieves\nthe same approximation factor with a polynomial number\nof queries (and thus with a polynomial communication).\nTheorem: There exists a computationally-efficient\niterative auction with item-price demand queries that finds an\nallocation that approximates the optimal welfare between\narbitrary valuations to within a factor of min(n, O(\n\u221a\nm)).\nOne may then attempt obtaining such an approximation\nfactor using iterative auctions that use only the weaker value\nqueries. However, we show that this is impossible:\nTheorem: Any iterative auction that uses a polynomial\n(in n and m) number of value queries can not achieve an\napproximation factor that is better than O( m\nlog m\n).9\nNote however that auctions with only value queries are not\ncompletely trivial in power: the bundling auctions of\nHolzman et al. [19] can easily be implemented by a polynomial\nnumber of value queries and can achieve an approximation\nfactor of O( m\u221a\nlog m\n) by using O(log m) equi-sized bundles.\nWe do not know how to close the (tiny) gap between this\nupper bound and our lower bound.\nRepresenting bundle-prices\nWe then deal with a critical issue with bundle-price\nauctions that was side-stepped by our model, as well as by all\nprevious works that used bundle-price auctions: how are\n9\nThis was also proven independently by Shahar Dobzinski\nand Michael Schapira.\n32\nthe bundle prices represented? For item-price auctions this\nis not an issue since a query needs only to specify a small\nnumber, m, of prices. In bundle-price auctions that\nsituation is more difficult since there are exponentially many\nbundles that require pricing. Our basic model (like all\nprevious work that used bundle prices, e.g., [37, 34, 3]), ignores\nthis issue, and only requires that the prices be determined,\nsomehow, by the protocol. A finer model would fix a\nspecific language for denoting bundle prices, force the protocol\nto represent the bundle-prices in this language, and require\nthat the representations of the bundle-prices also be\npolynomial.\nWhat could such a language for denoting prices for all\nbundles look like? First note that specifying a price for\neach bundle is equivalent to specifying a valuation. Second,\nas noted in [31], most of the proposed bidding languages\nare really just languages for representing valuations, i.e., a\nsyntactic representation of valuations - thus we could use\nany of them. This point of view opens up the general issue\nof which language should be used in bundle-price auctions\nand what are the implications of this choice.\nHere we initiate this line of investigation. We consider\nbundle-price auctions where the prices must be given as a\nXOR-bid, i.e., the protocol must explicitly indicate the price\nof every bundle whose value is different than that of all of\nits proper subsets. Note that all bundle-price auctions that\ndo not explicitly specify a bidding language must implicitly\nuse this language or a weaker one, since without a specific\nlanguage one would need to list prices for all bundles,\nperhaps except for trivial ones (those with value 0, or more\ngenerally, those with a value that is determined by one of\ntheir proper subsets.) We show that once the\nrepresentation length of bundle prices is taken into account (using the\nXOR-language), bundle-price auctions are no more strictly\nstronger than item-price auctions. Define the cost of an\niterative auction as the total length of the queries and answers\nused throughout the auction (in the worst case).\nTheorem: For some class of valuations, bundle price\nauctions that use the XOR-language require an exponential cost\nfor finding the optimal allocation. In contrast, item-price\nauctions can find the optimal allocation for this class within\npolynomial cost.10\nThis put doubts on the applicability of bundle-price\nauctions like [3, 37], and it may justify the use of hybrid\npricing methods such as Ausubel, Cramton and Milgrom\"s\nClock-Proxy auction ([10]).\nDemand queries and linear programs\nThe winner determination problem in combinatorial\nauctions may be formulated as an integer program. In many\ncases solving the linear-program relaxation of this integer\nprogram is useful: for some restricted classes of valuations\nit finds the optimum of the integer program (e.g., substitute\nvaluations [22, 17]) or helps approximating the optimum\n(e.g., by randomized rounding [13, 14]). However, the linear\nprogram has an exponential number of variables. Nisan and\nSegal [32] observed the surprising fact that despite the\nex10\nOur proof relies on the sophisticated known lower bounds\nfor constant depth circuits. We were not able to find an\nelementary proof.\nponential number of variables, this linear program may be\nsolved within polynomial communication. The basic idea is\nto solve the dual program using the Ellipsoid method (see,\ne.g., [20]). The dual program has a polynomial number of\nvariables, but an exponential number of constraints. The\nEllipsoid algorithm runs in polynomial time even on such\nprograms, provided that a separation oracle is given for\nthe set of constraints. Surprisingly, such a separation oracle\ncan be implemented using a single demand query (with item\nprices) to each of the bidders.\nThe treatment of [32] was somewhat ad-hoc to the\nproblem at hand (the case of substitute valuations). Here we\ngive a somewhat more general form of this important\nobservation. Let us call the following class of linear programs\ngeneralized-winner-determination-relaxation (GWDR)\nLPs:\nMaximize\nX\ni\u2208N,S\u2286M\nwi xi,S vi(S)\ns.t.\nX\ni\u2208N, S|j\u2208S\nxi,S \u2264 qj \u2200j \u2208 M\nX\nS\u2286M\nxi,S \u2264 di \u2200i \u2208 N\nxi,S \u2265 0 \u2200i \u2208 N, S \u2286 M\nThe case where wi = 1, di = 1, qj = 1 (for every i, j)\nis the usual linear relaxation of the winner determination\nproblem. More generally, wi may be viewed as the weight\ngiven to bidder i\"s welfare, qj may be viewed as the quantity\nof units of good j, and di may be viewed as duplicity of the\nnumber of bidders of type i.\nTheorem: Any GWDR linear program may be solved in\npolynomial time (in n, m, and the number of bits of precision\nt) using only demand queries with item prices.11\n2.2 Ascending Auctions\nAscending item-price auctions:\nIt is well known that the item-price ascending auctions\nof Kelso and Crawford [22] and its variants [12, 16] find\nthe optimal allocation as long as all players\" valuations have\nthe substitutes property. The obvious question is whether\nthe optimal allocation can be found for a larger class of\nvaluations.\nOur main result here is a strong negative result:\nTheorem: There is a 2-item 2-player problem where no\nascending item-price auction can find the optimal allocation.\nThis is in contrast to both the power of bundle-price\nascending auctions and to the power of general item-price\ndemand queries (see above), both of which can always find the\noptimal allocation and in fact even provide full preference\nelicitation. The same proof proves a similar impossibility\nresult for other types of auctions (e.g., descending auctions,\nnon-anonymous auctions). More extension of this result:\n\u2022 Eliciting some classes of valuations requires an\nexponential number of ascending item-price trajectories.\n11\nThe produced optimal solution will have polynomial\nsupport and thus can be listed fully.\n33\n\u2022 At least k \u2212 1 ascending item-price trajectories are\nneeded to elicit XOR formulae with k terms. This\nresult is in some sense tight, since we show that any\nk-term XOR formula can be fully elicited by k\u22121\nnondeterministic (i.e., when some exogenous teacher\ninstructs the auctioneer on how to increase the prices)\nascending auctions.12\nWe also show that item-price ascending auctions and\niterative auctions that are limited to a polynomial number\nof queries (of any kind, not necessarily ascending) are\nincomparable in their power: ascending auctions, with small\nenough increments, can elicit the preferences in cases where\nany polynomial number of queries cannot.\nMotivated by several recent papers that studied the\nrelation between eliciting and fully-eliciting the preferences in\ncombinatorial auctions (e.g., [7, 24]), we explore the\ndifference between these problems in the context of ascending\nauctions. We show that although a single ascending auction can\ndetermine the optimal allocation among any number of\nbidders with substitutes valuations, it cannot fully-elicit such a\nvaluation even for a single bidder. While it was shown in [25]\nthat the set of substitutes valuations has measure zero in the\nspace of general valuations, its dimension is not known, and\nin particular it is still open whether a polynomial amount\nof information suffices to describe a substitutes valuation.\nWhile our result may be a small step in that direction (a\npolynomial full elicitation may still be possible with other\ncommunication protocols), we note that our impossibility\nresult also holds for valuations in the class OXS defined by\n[25], valuations that we are able to show have a compact\nrepresentation.\nWe also give several results separating the power of\ndifferent models for ascending combinatorial auctions that use\nitem-prices: we prove, not surprisingly, that adaptive\nascending auctions are more powerful than oblivious\nascending auctions and that non-deterministic ascending auctions\nare more powerful than deterministic ascending auctions.\nWe also compare different kinds of non-anonymous auctions\n(e.g., simultaneous or sequential), and observe that\nanonymous bundle-price auctions and non-anonymous item-price\nauctions are incomparable in their power. Finally,\nmotivated by Dutch auctions, we consider descending auctions,\nand how they compare to ascending ones; we show classes of\nvaluations that can be elicited by ascending item-price\nauctions but not by descending item-price auctions, and vice\nversa.\nAscending bundle-price auctions:\nAll known ascending bundle-price auctions that are able\nto find the optimal allocation between general valuations\n(with free disposal) use non-anonymous prices.\nAnonymous ascending-price auctions (e.g., [42, 21, 37]) are only\nknown to be able to find the optimal allocation among\nsuperadditive valuations or few other simple classes ([36]). We\nshow that this is no mistake:\nTheorem: No ascending auction with anonymous prices\ncan find the optimal allocation between general valuations.\n12\nNon-deterministic computation is widely used in CS and\nalso in economics (e.g, a Walrasian equilibrium or [38]). In\nsome settings, deterministic and non-deterministic models\nhave equal power (e.g., computation with finite automata).\nThis bound is regardless of the running time, and it also\nholds for descending auctions and non-deterministic\nauctions.\nWe strengthen this result significantly by showing that\nanonymous ascending auctions cannot produce a better than\nO(\n\u221a\nm) approximation - the approximation ratio that can\nbe achieved with a polynomial number of queries ([26, 32])\nand, as mentioned, with a polynomial number of item-price\ndemand queries. The same lower bound clearly holds for\nanonymous item-price ascending auctions since such\nauctions can be simulated by anonymous bundle-price\nascending auctions. We currently do not have any lower bound on\nthe approximation achievable by non-anonymous item-price\nascending auctions.\nFinally, we study the performance of the existing\ncomputationally-efficient ascending auctions. These protocols ([37,\n3]) require exponential time in the worst case, and this is\nunavoidable as shown by [32]. However, we also observe that\nthese auctions, as well as the whole class of similar\nascending bundle-price auctions, require an exponential time even\nfor simple additive valuations. This is avoidable and indeed\nthe ascending item-price auctions of [22] can find the\noptimal allocation for these simple valuations with polynomial\ncommunication.\n3. THE MODEL\n3.1 Discrete Auctions for Continuous Values\nOur model aims to capture iterative auctions that operate\non real-valued valuations. There is a slight technical\ndifficulty here in bridging the gap between the discrete nature\nof an iterative auction, and the continuous nature of the\nvaluations. This is exactly the same problem as in modeling\na simple English auction. There are three standard formal\nways to model it:\n1. Model the auction as a continuous process and study\nits trajectory in time. For example, the so-called Japanese\nauction is basically a continuous model of an English\nmodel.13\n2. Model the auction as discrete and the valuations as\ncontinuously valued. In this case we introduce a\nparameter and usually require the auction to produce\nresults that are -close to optimal.\n3. Model the valuations as discrete. In this case we will\nassume that all valuations are integer multiples of some\nsmall fixed quantity \u03b4, e.g., 1 penny. All\ncommunication in this case is then naturally finite.\nIn this paper we use the latter formulation and assume\nthat all values are multiples of some \u03b4. Thus, in some parts\nof the paper we assume without loss of generality that \u03b4 = 1,\nhence all valuations are integral. Almost all (if not all) of\nour results can be translated to the other two models with\nlittle effort.\n3.2 Valuations\nA single auctioneer is selling m indivisible\nnon-homogeneous items in a single auction, and let M be the set of these\n13\nAnother similar model is the moving knives model in the\ncake-cutting literature.\n34\nitems and N be the set of bidders. Each one of the n\nbidders in the auction has a valuation function vi : 2m\n\u2192\n{0, \u03b4, 2\u03b4, ..., L}, where for every bundle of items S \u2286 M,\nvi(S) denotes the value of bidder i for the bundle S and is\na multiple of \u03b4 in the range 0...L. We will sometimes\ndenote the number of bits needed to represent such values in\nthe range 0...L by t = log L. We assume free disposal, i.e.,\nS \u2286 T implies vi(S) \u2264 vi(T) and that vi(\u2205) = 0 for all\nbidders.\nWe will mention the following classes of valuations:\n\u2022 A valuation is called sub-modular if for all sets of items\nA and B we have that v(A \u222a B) + v(A \u2229 B) \u2264 v(A) +\nv(B).\n\u2022 A valuation is called super-additive if for all disjoint\nsets of items A and B we have that v(A\u222aB) \u2265 v(A)+\nv(B).\n\u2022 A valuation is called a k-bundle XOR if it can be\nrepresented as a XOR combination of at most k atomic\nbids [30], i.e., if there are at most k bundles Si and\nprices pi such that for all S, v(S) = maxi|S\u2287Si\npi. Such\nvaluations will be denoted by v = (S1 : p1) \u2295 (S2 :\np2) \u2295 . . . \u2295 (Sk : pk).14\n3.3 Iterative Auctions\nThe auctioneer sets up a protocol (equivalently an\nalgorithm), where at each stage of the protocol some\ninformation q - termed the query - is sent to some bidder i,\nand then bidder i replies with some reply that depends on\nthe query as well as on his own valuation. In this paper,\nwe assume that we have complete control over the bidders\"\nbehavior, and thus the protocol also defines a reply function\nri(q, vi) that specifies bidder i\"s reply to query q. The\nprotocol may be adaptive: the query value as well as the queried\nbidder may depend on the replies received for past queries.\nAt the end of the protocol, an allocation S1...Sn must be\ndeclared, where Si \u2229 Sj = \u2205 for i = j.\nWe say that the auction finds an optimal allocation if\nit finds the allocation that maximizes the social welfareP\ni vi(Si). We say that it finds a c-approximation if\nP\ni vi(Si)\n\u2265\nP\ni vi(Ti)/c where T1...Tn is an optimal allocation. The\nrunning time of the auction on a given instance of the\nbidders\" valuations is the total number of queries made on this\ninstance. The running time of a protocol is the worst case\ncost over all instances. Note that we impose no\ncomputational limitations on the protocol or on the players.15\nThis\nof course only strengthens our hardness results. Yet, our\npositive results will not use this power and will be efficient\nalso in the usual computational sense.\nOur goal will be to design computationally-efficient\nprotocols. We will deem a protocol computationally-efficient if\nits cost is polynomial in the relevant parameters: the\nnumber of bidders n, the number of items m, and t = log L,\nwhere L is the largest possible value of a bundle. However,\nwhen we discuss ascending-price auctions and their variants,\na computationally-efficient protocol will be required to be\n14\nFor example, v = (abcd : 5) \u2295 (ab : 3) \u2295 (c : 4) denotes the\nXOR valuation with the terms abcd, ab, c and prices 5, 3, 4\nrespectively. For this valuation, v(abcd) = 5, v(abd) = 3,\nv(abc) = 4.\n15\nThe running time really measures communication costs and\nnot computational running time.\npseudo-polynomial, i.e., it should ask a number of queries\nwhich is polynomial in m, n and L\n\u03b4\n. This is because that\nascending auctions can usually not achieve such running times\n(consider even the English auction on a single item).16\nNote\nthat all of our results give concrete bounds, where the\ndependence on the parameters is given explicitly; we use the\nstandard big-Oh notation just as a shorthand.\nWe say than an auction elicits some class V of valuations,\nif it determines the optimal allocation for any profile of\nvaluations drawn from V ; We say that an auction fully elicits\nsome class of valuations V , if it can fully learn any single\nvaluation v \u2208 V (i.e., learn v(S) for every S).\n3.4 Demand Queries and Ascending Auctions\nMost of the paper will be concerned with a common\nspecial case of iterative auctions that we term demand\nauctions. In such auctions, the queries that are sent to bidders\nare demand queries: the query specifies a price p(S) \u2208 +\nfor each bundle S. The reply of bidder i is simply the set\nmost desired - demanded - under these prices. Formally,\na set S that maximizes vi(S) \u2212 p(S). It may happen that\nmore than one set S maximizes this value. In which case,\nties are broken according to some fixed tie-breaking rule,\ne.g., the lexicographically first such set is returned. All of\nour results hold for any fixed tie-breaking rule.\nAscending auctions are iterative auctions with\nnon-decreasing prices:\nDefinition 1. In an ascending auction, the prices in the\nqueries to the same bidder can only increase in time.\nFormally, let p be a query made for bidder i, and q be a query\nmade for bidder i at a later stage in the protocol. Then for\nall sets S, q(S) \u2265 p(S). A similar variant, which we also\nstudy and that is also common in real life, is descending\nauctions, in which prices can only decrease in time.\nNote that the term ascending auction refers to an\nauction with a single ascending trajectory of prices. It may\nbe useful to define multi-trajectory ascending auctions, in\nwhich the prices maybe reset to zero a number of times (see,\ne.g., [4]).\nWe consider two main restrictions on the types of allowed\ndemand queries:\nDefinition 2. Item Prices: The prices in each query\nare given by prices pj for each item j. The price of a set S\nis additive: p(S) =\nP\nj\u2208S pj.\nDefinition 3. Anonymous prices: The prices seen by\nthe bidders at any stage in the auction are the same, i.e.\nwhenever a query is made to some bidder, the same query is\nalso made to all other bidders (with the prices unchanged).\nIn auctions with non-anonymous (discriminatory) prices,\neach bidder i has personalized prices denoted by pi\n(S).17\nIn this paper, all auctions are anonymous unless otherwise\nspecified.\nNote that even though in our model valuations are integral\n(or multiples of some \u03b4), we allow the demand query to\n16\nMost of the auctions we present may be adapted to run in\ntime polynomial in log L, using a binary-search-like\nprocedure, losing their ascending nature.\n17\nNote that a non-anonymous auction can clearly be\nsimulated by n parallel anonymous auctions.\n35\nuse arbitrary real numbers in +. That is, we assume that\nthe increment we use in the ascending auctions may be\nsignificantly smaller than \u03b4. All our hardness results hold\nfor any , even for continuous price increments. A practical\nissue here is how will the query be specified: in the general\ncase, an exponential number of prices needs to be sent in a\nsingle query. Formally, this is not a problem as the model\ndoes not limit the length of queries in any way - the protocol\nmust simply define what the prices are in terms of the replies\nreceived for previous queries. We look into this issue further\nin Section 4.3.\n4. THE POWER OF DEMAND QUERIES\nIn this section, we study the power of iterative auctions\nthat use demand queries (not necessarily ascending). We\nstart by comapring demand queries to other types of queries.\nThen, we discuss how well can one approximate the optimal\nwelfare using a polynomial number of demand queries. We\nalso initiate the study of the representation of bundle-price\ndemand queries, and finally, we show how demand queries\nhelp solving the linear-programming relaxation of\ncombinatorial auctions in polynomial time.\n4.1 The Power of Different Types of Queries\nIn this section we compare the power of the various types\nof queries defined in Section 2. We will present\ncomputationally -efficient simulations of these query types using\nitem-price demand queries. In Section 5.1 we show that\nthese simulations can also be done using item-price\nascending auctions.\nLemma 4.1. A value query can be simulated by m\nmarginalvalue queries. A marginal-value query can be simulated by\ntwo value queries.\nLemma 4.2. A value query can be simulated by mt\ndemand queries (where t = log L is the number of bits needed\nto represent a single bundle value).18\nAs a direct corollary we get that demand auctions can\nalways fully elicit the bidders\" valuations by simulating all\npossible 2m\n\u2212 1 queries and thus elicit enough information\nfor determining the optimal allocation. Note, however, that\nthis elicitation may be computationally inefficient.\nThe next lemma shows that demand queries can be\nexponentially more powerful than value queries.\nLemma 4.3. An exponential number of value queries may\nbe required for simulating a single demand query.\nIndirect utility queries are, however, equivalent in power\nto demand queries:\nLemma 4.4. An indirect-utility query can be simulated by\nmt + 1 demand queries. A demand query can be simulated\nby m + 1 indirect-utility queries.\nDemand queries can also simulate relative-demand queries:19\n18\nNote that t bundle-price demand queries can easily\nsimulate a value query by setting the prices of all the bundles\nexcept S (the bundle with the unknown value) to be L, and\nperforming a binary search on the price of S.\n19\nNote: although in our model values are integral (our\nmultiples of \u03b4), we allow the query prices to be arbitrary real\nnumV MV D IU RD\nV 1 2 exp exp exp\nMV m 1 exp exp exp\nD mt poly 1 mt+1 poly\nIU 1 2 m+1 1 poly\nRD - - - - 1\nFigure 4: Each entry in the table specifies how many\nqueries of this row are needed to simulate a query from\nthe relevant column.\nAbbreviations: V (value query), MV (marginal-value\nquery), D (demand query), IU (Indirect-utility query),\nRD (relative demand query).\nLemma 4.5. Relative-demand queries can be simulated by\na polynomial number of demand queries.\nAccording to our definition of relative-demand queries,\nthey clearly cannot simulate even value queries. Figure 4\nsummarizes the relations between these query types.\n4.2 Approximating the Social Welfare with\nValue and Demand Queries\nWe know from [32] that iterative combinatorial auctions\nthat only use a polynomial number of queries can not find\nan optimal allocation among general valuations and in fact\ncan not even approximate it to within a factor better than\nmin{n, m1/2\u2212\n}. In this section we ask how well can this\napproximation be done using demand queries with item prices,\nor using the weaker value queries. We show that, using\ndemand queries, the lower bound can be matched, while value\nqueries can only do much worse.\nFigure 5 describes a polynomial-time algorithm that achieves\na min(n, O(\n\u221a\nm)) approximation ratio. This algorithm\ngreedily picks the bundles that maximize the bidders\" per-item\nvalue (using relative-demand queries, see Section 4.1). As\na final step, it allocates all the items to a single bidder if\nit improves the social welfare (this can be checked using\nvalue queries). Since both value queries and relative-demand\nqueries can be simulated by a polynomial number of\ndemand queries with item prices (Lemmas 4.2 and 4.5), this\nalgorithm can be implemented by a polynomial number of\ndemand queries with item prices.20\nTheorem 4.6. The auction described in Figure 5 can be\nimplemented by a polynomial number of demand queries and\nachieves a min{n, 4\n\u221a\nm}-approximation for the social\nwelfare.\nWe now ask how well can the optimal welfare be\napproximated by a polynomial number of value queries. First we\nnote that value queries are not completely powerless: In\n[19] it is shown that if the m items are split into k fixed\nbundles of size m/k each, and these fixed bundles are\nauctioned as though each was indivisible, then the social welfare\nbers, thus we may have bundles with arbitrarily close\nrelative demands. In this sense the simulation above is only up\nto any given (and the number of queries is O(log L+log 1\n)).\nWhen the relative-demand query prices are given as rational\nnumbers, exact simulation is implied when log is linear in\nthe input length.\n20\nIn the full paper [8], we observe that this algorithm can be\nimplemented by two descending item-price auctions (where\nwe allow removing items along the auction).\n36\ngenerated by such an auction is at least m\u221a\nk\n-approximation\nof that possible in the original auction. Notice that such\nan auction can be implemented by 2k\n\u2212 1 value queries to\neach bidder - querying the value of each bundle of the fixed\nbundles. Thus, if we choose k = log m bundles we get an\nm\u221a\nlog m\n-approximation while still using a polynomial number\nof queries.\nThe following lemma shows that not much more is possible\nusing value queries:\nLemma 4.7. Any iterative auction that uses only value\nqueries and distinguishes between k-tuples of 0/1 valuations\nwhere the optimal allocation has value 1, and those where the\noptimal allocation has value k requires at least 2\nm\nk queries.\nProof. Consider the following family of valuations: for\nevery S, such that |S| > m/2, v(S) = 1, and there exists a\nsingle set T, such that for |S| \u2264 m/2, v(S) = 1 iff T \u2286 S\nand v(S) = 0 otherwise. Now look at the behavior of the\nprotocol when all valuations vi have T = {1...m}. Clearly\nin this case the value of the best allocation is 1 since no set\nof size m\n2\nor lower has non-zero value for any player. Fix the\nsequence of queries and answers received on this k-tuple of\nvaluations.\nNow consider the k-tuple of valuations chosen at random\nas follows: a partition of the m items into k sets T1...Tk\neach of size m\nk\neach is chosen uniformly at random among\nall such partitions. Now consider the k-tuple of valuations\nfrom our family that correspond to this partition - clearly\nTi can be allocated to i, for each i, getting a total value of k.\nNow look at the protocol when running on these valuations\nand compare its behavior to the original case. Note that the\nanswer to a query S to player i differs between the case of\nTi and the original case of T = {1...m} only if |S| \u2264 m\n2\nand\nTi \u2286 S. Since Ti is distributed uniformly among all sets of\nsize exactly m\nk\n, we have that for any fixed query S to player\ni, where |S| \u2264 m\n2\n,\nPr[Ti \u2286 S] \u2264\n\u201e\n|S|\nm\n\u00ab|Ti|\n\u2264 2\u2212 m\nk\nUsing the union-bound, if the original sequence of queries\nwas of length less than 2\nm\nk , then with positive probability\nnone of the queries in the sequence would receive a different\nanswer than for the original input tuple. This is forbidden\nsince the protocol must distinguish between this case and\nthe original case - which cannot happen if all queries receive\nthe same answer. Hence there must have been at least 2\nm\nk\nqueries for the original tuple of valuations.\nWe conclude that a polynomial time protocol that uses\nonly value queries cannot obtain a better than O( m\nlog m\n)\napproximation of the welfare:\nTheorem 4.8. An iterative auction that uses a\npolynomial number of value queries cannot achieve better than\nO( m\nlog m\n)-approximation for the social welfare.\nProof. Immediate from Lemma 4.7: achieving any\napproximation ratio k which is asymptotically greater than\nm\nlog m\nneeds an exponential number of value queries.\nAn Approximation Algorithm:\nInitialization: Let T \u2190 M be the current items for sale.\nLet K \u2190 N be the currently participating bidders.\nLet S\u2217\n1 \u2190 \u2205, ..., S\u2217\nn \u2190 \u2205 be the provisional allocation.\nRepeat until T = \u2205 or K = \u2205:\nAsk each bidder i in K for the bundle Si that maximizes\nher per-item value, i.e., Si \u2208 argmaxS\u2286T\nvi(S)\n|S|\n.\nLet i be the bidder with the maximal per-item value,\ni.e., i \u2208 argmaxi\u2208K\nvi(Si)\n|Si|\n.\nSet: s\u2217\ni = si, K = K \\ i, M = M \\ Si\nFinally: Ask the bidders for their values vi(M) for the\ngrand bundle. If allocating all the items to some bidder i\nimproves the social welfare achieved so far\n(i.e., \u2203i \u2208 N such that vi(M) >\nP\ni\u2208N vi(S\u2217\ni )),\nthen allocate all items to this bidder i.\nFigure 5: This algorithm achieves a min{n, 4\n\u221a\n\nm}approximation for the social welfare, which is\nasymptotically the best worst-case approximation possible with\npolynomial communication. This algorithm can be\nimplemented with a polynomial number of demand queries.\n4.3 The Representation of Bundle Prices\nIn this section we explicitly fix the language in which\nbundle prices are presented to the bidders in bundle-price\nauctions. This language requires the algorithm to explicitly list\nthe price of every bundle with a non-trivial price.\nTrivial in this context is a price that is equal to that of one of\nits proper subsets (which was listed explicitly). This\nrepresentation is equivalent to the XOR-language for expressing\nvaluations. Formally, each query q is given by an\nexpression: q = (S1 : p1) \u2295 (S2 : p2) \u2295 ... \u2295 (Sl : pl). In this\nrepresentation, the price demanded for every set S is simply\np(S) = max{k=1...l|Sk\u2286S}pk.\nDefinition 4. The length of the query q = (S1 : p1) \u2295\n(S2 : p2) \u2295 ... \u2295 (Sl : pl) is l. The cost of an algorithm is the\nsum of the lengths of the queries asked during the operation\nof the algorithm on the worst case input.\nNote that under this definition, bundle-price auctions are\nnot necessarily stronger than item-price auctions. An\nitemprice query that prices each item for 1, is translated to an\nexponentially long bundle-price query that needs to specify\nthe price |S| for each bundle S. But perhaps bundle-price\nauctions can still find optimal allocations whenever\nitemprice auction can, without directly simulating such queries?\nWe show that this is not the case: indeed, when the\nrepresentation length is taken into account, bundle price auctions\nare sometimes seriously inferior to item price auctions.\nConsider the following family of valuations: Each item is\nvalued at 3, except that for some single set S, its value is a\nbit more: 3|S| + b, where b \u2208 {0, 1, 2}. Note that an item\nprice auction can easily find the optimal allocation between\nany two such valuations: Set the prices of each item to 3+ ;\nif the demand sets of the two players are both empty, then\nb = 0 for both valuations, and an arbitrary allocation is fine.\nIf one of them is empty and the other non-empty, allocate\nthe non-empty demand set to its bidder, and the rest to the\nother. If both demand sets are non-empty then, unless they\nform an exact partition, we need to see which b is larger,\nwhich we can do by increasing the price of a single item in\neach demand set.\n37\nWe will show that any bundle-price auction that uses only\nthe XOR-language to describe bundle prices requires an\nexponential cost (which includes the sum of all description\nlengths of prices) to find an optimal allocation between any\ntwo such valuations.\nLemma 4.9. Every bundle-price auction that uses\nXORexpressions to denote bundle prices requires 2\u2126(\n\u221a\nm)\ncost in\norder to find the optimal allocation among two valuations\nfrom the above family.\nThe complication in the proof stems from the fact that\nusing XOR-expressions, the length of the price description\ndepends on the number of bundles whose price is strictly\nlarger than each of their subsets - this may be significantly\nsmaller than the number of bundles that have a non-zero\nprice. (The proof becomes easy if we require the protocol\nto explicitly name every bundle with non-zero price.) We\ndo not know of any elementary proof for this lemma\n(although we believe that one can be found). Instead we\nreduce the problem to a well known lower bound in boolean\ncircuit complexity [18] stating that boolean circuits of depth\n3 that compute the majority function on m variables require\n2\u2126(\n\u221a\nm)\nsize.\n4.4 Demand Queries and Linear Programming\nConsider the following linear-programming relaxation for\nthe generalized winner-determination problem in\ncombinatorial auctions (the primal program):\nMaximize\nX\ni\u2208N,S\u2286M\nwi xi,S vi(S)\ns.t.\nX\ni\u2208N, S|j\u2208S\nxi,S \u2264 qj \u2200j \u2208 M\nX\nS\u2286M\nxi,S \u2264 di \u2200i \u2208 N\nxi,S \u2265 0 \u2200i \u2208 N, S \u2286 M\nNote that the primal program has an exponential number\nof variables. Yet, we will be able to solve it in polynomial\ntime using demand queries to the bidders. The solution will\nhave a polynomial size support (non-zero values for xi,S),\nand thus we will be able to describe it in polynomial time.\nHere is its dual:\nMinimize\nX\nj\u2208M\nqjpj +\nX\ni\u2208N\ndiui\ns.t. ui +\nX\nj\u2208S\npj \u2265 wivi(S) \u2200i \u2208 N, S \u2286 M\npi \u2265 0, uj \u2265 0 \u2200i \u2208 M, j \u2208 N\nNotice that the dual problem has exactly n + m variables\nbut an exponential number of constraints. Thus, the dual\ncan be solved using the Ellipsoid method in polynomial time\n- if a separation oracle can be implemented in polynomial\ntime. Recall that a separation oracle, when given a possible\nsolution, either confirms that it is a feasible solution, or\nresponds with a constraint that is violated by the possible\nsolution.\nWe construct a separation oracle for solving the dual\nprogram, using a single demand query to each of the bidders.\nConsider a possible solution (u, p) for the dual program. We\ncan re-write the constraints of the dual program as:\nui/wi \u2265 vi(S) \u2212\nX\nj\u2208S\npj/wi\nNow a demand query to bidder i with prices pj/wi reveals\nexactly the set S that maximizes the RHS of the previous\ninequality. Thus, in order to check whether (u, p) is\nfeasible it suffices to (1) query each bidder i for his demand\nDi under the prices pj/wi; (2) check only the n constraints\nui +\nP\nj\u2208Di\npj \u2265 wivi(Di) (where vi(Di) can be simulated\nusing a polynomial sequence of demand queries as shown in\nLemma 4.2). If none of these is violated then we are assured\nthat (u, p) is feasible; otherwise we get a violated constraint.\nWhat is left to be shown is how the primal program can\nbe solved. (Recall that the primal program has an\nexponential number of variables.) Since the Ellipsoid algorithm\nruns in polynomial time, it encounters only a polynomial\nnumber of constraints during its operation. Clearly, if all\nother constraints were removed from the dual program, it\nwould still have the same solution (adding constraints can\nonly decrease the space of feasible solutions). Now take the\nreduced dual where only the constraints encountered\nexist, and look at its dual. It will have the same solution as the\noriginal dual and hence of the original primal. However, look\nat the form of this dual of the reduced dual. It is just a\nversion of the primal program with a polynomial number of\nvariables - those corresponding to constraints that remained\nin the reduced dual. Thus, it can be solved in polynomial\ntime, and this solution clearly solves the original primal\nprogram, setting all other variables to zero.\n5. ITEM-PRICE ASCENDING AUCTIONS\nIn this section we characterize the power of ascending\nitem-price auctions. We first show that this power is not\ntrivial: such auctions can in general elicit an exponential\namount of information. On the other hand, we show that\nthe optimal allocation cannot always be determined by a\nsingle ascending auction, and in some cases, nor by an\nexponential number of ascending-price trajectories. Finally,\nwe separate the power of different models of ascending\nauctions.\n5.1 The Power of Item-Price Ascending\nAuctions\nWe first show that if small enough increments are allowed,\na single ascending trajectory of item-prices can elicit\npreferences that cannot be elicited with polynomial\ncommunication. As mentioned, all our hardness results hold for any\nincrement, even infinitesimal.\nTheorem 5.1. Some classes of valuations can be elicited\nby item-price ascending auctions, but cannot be elicited by a\npolynomial number of queries of any kind.\nProof. (sketch) Consider two bidders with v(S) = 1 if\n|S| > n\n2\n, v(S) = 0 if |S| < n\n2\nand every S such that |S| = n\n2\nhas an unknown value from {0, 1}. Due to [32], determining\nthe optimal allocation here requires exponential\ncommunication in the worst case. Nevertheless, we show (see [9]) that\nan item-price ascending auction can do it, as long as it can\nuse exponentially small increments.\nWe now describe another positive result for the power of\nitem-price ascending auctions. In section 4.1, we showed\n38\nv(ab) v(a) v(b)\nBidder 1 2 \u03b1 \u2208 (0, 1) \u03b2 \u2208 (0, 1)\nBidder 2 2 2 2\nFigure 6: No item-price ascending auctions can\ndetermine the optimal allocation for this class of valuations.\nthat a value query can be simulated with a (truly)\npolynomial number of item-price demand queries. Here, we show\nthat every value query can be simulated by a (pseudo)\npolynomial number of ascending item-price demand queries. (In\nthe next subsection, we show that we cannot always\nsimulate even a pair of value queries using a single item-price\nascending auction.) In the full paper (part II,[9]), we show\nthat we can simulate other types of queries using item-price\nascending auctions.\nProposition 5.2. A value query can be simulated by an\nitem-price ascending auction. This simulation requires a\npolynomial number of queries.\nActually, the proof for Proposition 5.2 proves a stronger\nuseful result regarding the information elicited by iterative\nauctions. It says that in any iterative auction in which the\nchanges of prices are small enough in each stage\n(pseudocontinuous auctions), the value of all bundles demanded\nduring the auction can be computed. The basic idea is that\nwhen the bidder moves from demanding some bundle Ti to\ndemanding another bundle Ti+1, there is a point in which she\nis indifferent between these two bundles. Thus, knowing the\nvalue of some demanded bundle (e.g., the empty set) enables\ncomputing the values of all other demanded bundles.\nWe say that an auction is pseudo-continuous, if it only\nuses demand queries, and in each step, the price of at most\none item is changed by (for some \u2208 (0, \u03b4]) with respect\nto the previous query.\nProposition 5.3. Consider any pseudo-continuous\nauction (not necessarily ascending), in which bidder i demands\nthe empty set at least once along the auction. Then, the\nvalue of every bundle demanded by bidder i throughout the\nauction can be calculated at the end of the auction.\n5.2 Limitations of Item-Price Ascending\nAuctions\nAlthough we observed that demand queries can solve any\ncombinatorial auction problem, when the queries are\nrestricted to be ascending, some classes of valuations cannot\nbe elicited nor fully-elicited. An example for such class of\nvaluations is given in Figure 6.\nTheorem 5.4. There are classes of valuations that\ncannot be elicited nor fully elicited by any item-price ascending\nauction.\nProof. Let bidder 1 have the valuation described in the\nfirst row of Figure 6, where \u03b1 and \u03b2 are unknown values in\n(0, 1). First, we prove that this class cannot be fully elicited\nby a single ascending auction. Specifically, an ascending\nauction cannot reveal the values of both \u03b1 and \u03b2.\nAs long as pa and pb are both below 1, the bidder will\nalways demand the whole bundle ab: her utility from ab is\nstrictly greater than the utility from either a or b separately.\nFor example, we show that u1(ab) > u1(a):\nu1(ab) = 2 \u2212 (pa + pb) = 1 \u2212 pa + 1 \u2212 pb\n> vA(a) \u2212 pa + 1 \u2212 pb > u1(a)\nThus, in order to gain any information about \u03b1 or \u03b2, the\nprice of one of the items should become at least 1, w.l.o.g.\npa \u2265 1. But then, the bundle a will not be demanded by\nbidder 1 throughout the auction, thus no information at all\nwill be gained about \u03b1.\nNow, assume that bidder 2 is known to have the valuation\ndescribed in the second row of Figure 6. The optimal\nallocation depends on whether \u03b1 is greater than \u03b2 (in bidder 1\"s\nvaluation), and we proved that an ascending auction cannot\ndetermine this.\nThe proof of the theorem above shows that for an\nunknown value to be revealed, the price of one item should be\ngreater than 1, and the other price should be smaller than\n1. Therefore, in a price-monotonic trajectory of prices, only\none of these values can be revealed. An immediate\nconclusion is that this impossibility result also holds for item-price\ndescending auctions. Since no such trajectory exists, then\nthe same conclusion even holds for non-deterministic\nitemprice auctions (in which exogenous data tells us how to\nincrease the prices). Also note that since the hardness stems\nfrom the impossibility to fully-elicit a valuation of a single\nbidder, this result also holds for non-anonymous ascending\nitem-price auctions.\n5.3 Limitations of Multi-Trajectory\nAscending Auctions\nAccording to Theorem 5.4, no ascending item-price\nauction can always elicit the preferences (we prove a similar\nresult for bundle prices in section 6). But can two\nascending trajectories do the job? Or a polynomial number of\nascending trajectories? We give negative answers for such\nsuggestions.\nWe define a k-trajectory ascending auction as a\ndemandquery iterative auction in which the demand queries can be\npartitioned to k sets of queries, where the prices published\nin each set only increase in time. Note that we use a general\ndefinition; It allows the trajectories to run in parallel or\nsequentially, and to use information elicited in some\ntrajectories for determining the future queries in other trajectories.\nThe power of multiple-trajectory auctions can be\ndemonstrated by the negative result of Gul and Stacchetti [17] who\nshowed that even for an auction among substitutes\nvaluations, an anonymous ascending item-price auction cannot\ncompute VCG prices for all players.21\nAusubel [4] overcame\nthis impossibility result and designed auctions that do\ncompute VCG prices by organizing the auction as a sequence of\nn + 1 ascending auctions. Here, we prove that one cannot\nelicit XOR valuations with k terms by less than k \u2212 1\nascending trajectories. On the other hand, we show that an\nXOR formula can be fully elicited by k\u22121 non-deterministic\nascending auctions (or by k\u22121 deterministic ascending\nauctions if the auctioneer knows the atomic bundles).22\n21\nA recent unpublished paper by Mishra and Parkes\nextends this result, and shows that non-anonymous prices with\nbundle-prices are necessary in order that an ascending\nauction will end up with a universal-competitive-equilibrium\n(that leads to VCG payments).\n22\nThis result actually separates the power of deterministic\n39\nProposition 5.5. XOR valuations with k terms cannot\nbe elicited (or fully elicited) by any (k-2)-trajectory\nitemprice ascending auction, even when the atomic bundles are\nknown to the elicitor. However, these valuations can be\nelicited (and fully elicited) by (k-1)-trajectory\nnon-deterministic non-anonymous item-price ascending auctions.\nMoreover, an exponential number of trajectories is\nrequired for eliciting some classes of valuations:\nProposition 5.6. Elicitation and full-elicitation of some\nclasses of valuations cannot be done by any k-trajectory\nitemprice ascending auction, where k = o(2m\n).\nProof. (sketch) Consider the following class of\nvaluations: For |S| < m\n2\n, v(S) = 0 and for |S| > m\n2\n, v(S) = 2;\nevery bundle S of size m\n2\nhas some unknown value in (0, 1).\nWe show ([9]) that a single item-price ascending auction\ncan reveal the value of at most one bundle of size n\n2\n, and\ntherefore an exponential number of ascending trajectories is\nneeded in order to elicit such valuations.\nWe observe that the algorithm we presented in Section\n4.2 can be implemented by a polynomial number of\nascending auctions (each item-price demand query can be\nconsidered as a separate ascending auction), and therefore a\nmin(n, 4\n\u221a\nm)-approximation can be achieved by a\npolynomial number of ascending auctions. We do not currently\nhave a better upper bound or any lower bound.\n5.4 Separating the Various Models of\nAscending Auctions\nVarious models for ascending auctions have been suggested\nin the literature. In this section, we compare the power of\nthe different models. As mentioned, all auctions are\nconsidered anonymous and deterministic, unless specified\notherwise.\nAscending vs. Descending Auctions: We begin the\ndiscussion of the relation between ascending auctions and\ndescending auctions with an example. The algorithm by\nLehmann, Lehmann and Nisan [25] can be implemented by\na simple item-price descending auction (see the full paper for\ndetails [9]). This algorithm guarantees at least half of the\noptimal efficiency for submodular valuations. However, we are\nnot familiar with any ascending auction that guarantees a\nsimilar fraction of the efficiency. This raises a more general\nquestion: can ascending auctions solve any\ncombinatorialauction problem that is solvable using a descending auction\n(and vice versa)? We give negative answers to these\nquestions. The idea behind the proofs is that the information\nthat the auctioneer can get for free at the beginning of\neach type of auction is different.23\nand non-deterministic iterative auctions: our proof shows\nthat a non-deterministic iterative auction can elicit the\nkterm XOR valuations with a polynomial number of demand\nqueries, and [7] show that this elicitation must take an\nexponential number of demand queries.\n23\nIn ascending auctions, the auctioneer can reveal the most\nvaluable bundle (besides M) before she starts raising the\nprices, thus she can use this information for adaptively\nchoose the subsequent queries. In descending auctions, one\ncan easily find the bundle with the highest average per-item\nprice, keeping all other bundles with non-positive utilities,\nand use this information in the adaptive price change.\nProposition 5.7. There are classes that cannot be\nelicited (fully elicited) by ascending item-price auctions, but can\nbe elicited (resp. fully elicited) with a descending item-price\nauction.\nProposition 5.8. There are classes that cannot be\nelicited (fully elicited) by item-price descending auctions, but can\nbe elicited (resp. fully elicited) by item-price ascending\nauctions.\nDeterministic vs. Non-Deterministic Auctions:\nNondeterministic ascending auctions can be viewed as auctions\nwhere some benevolent teacher that has complete\ninformation guides the auctioneer on how she should raise the prices.\nThat is, preference elicitation can be done by a\nnon-deterministic ascending auction, if there is some ascending trajectory\nthat elicits enough information for determining the optimal\nallocation (and verifying that it is indeed optimal). We show\nthat non-deterministic ascending auctions are more powerful\nthan deterministic ascending auctions:\nProposition 5.9. Some classes can be elicited (fully\nelicited) by an item-price non-deterministic ascending\nauction, but cannot be elicited (resp. fully elicited) by item-price\ndeterministic ascending auctions.\nAnonymous vs. Non-Anonymous Auctions: As will\nbe shown in Section 6, the power of anonymous and\nnonanonymous bundle-price ascending auctions differs\nsignificantly. Here, we show that a difference also exists for\nitemprice ascending auctions.\nProposition 5.10. Some classes cannot be elicited by\nanonymous item-price ascending auctions, but can be elicited\nby a non-anonymous item-price ascending auction.\nSequential vs. Simultaneous Auctions: A\nnon-anonymous auction is called simultaneous if at each stage, the price\nof some item is raised by for every bidder. The auctioneer\ncan use the information gathered until each stage, in all the\npersonalized trajectories, to determine the next queries.\nA non-anonymous auction is called sequential if the\nauctioneer performs an auction for each bidder separately, in\nsequential order. The auctioneer can determine the next\nquery based on the information gathered in the trajectories\ncompleted so far and on the history of the current trajectory.\nProposition 5.11. There are classes that cannot be\nelicited by simultaneous non-anonymous item-price ascending\nauctions, but can be elicited by a sequential non-anonymous\nitem-price ascending auction.\nAdaptive vs. Oblivious Auctions: If the auctioneer\ndetermines the queries regardless of the bidders\" responses (i.e.,\nthe queries are predefined) we say that the auction is\noblivious. Otherwise, the auction is adaptive. We prove that an\nadaptive behaviour of the auctioneer may be beneficial.\nProposition 5.12. There are classes that cannot be\nelicited (fully elicited) using oblivious item-price ascending\nauctions, but can be elicited (resp. fully elicited) by an adaptive\nitem-price ascending auction.\n40\n5.5 Preference Elicitation vs. Full Elicitation\nPreference elicitation and full elicitation are closely\nrelated problems. If full elicitation is easy (e.g., in\npolynomial time) then clearly elicitation is also easy (by a\nnonanonymous auction, simply by learning all the valuations\nseparately24\n). On the other hand, there are examples where\npreference elicitation is considered easy but learning is\nhard (typically, elicitation requires smaller amount of\ninformation; some examples can be found in [7]).\nThe tatonnement algorithms by [22, 12, 16] end up with\nthe optimal allocation for substitutes valuations.25\nWe prove\nthat we cannot fully elicit substitutes valuations (or even\ntheir sub-class of OXS valuations defined in [25]), even for a\nsingle bidder, by an item-price ascending auction (although\nthe optimal allocation can be found by an ascending auction\nfor any number of bidders!).\nTheorem 5.13. Substitute valuations cannot be fully\nelicited by ascending item-price auctions. Moreover, they\ncannot be fully elicited by any m\n2\nascending trajectories (m > 3).\nWhether substitutes valuations have a compact\nrepresentation (i.e., polynomial in the number of goods) is an\nimportant open question. As a step in this direction, we show\nthat its sub-class of OXS valuations does have a compact\nrepresentation: every OXS valuation can be represented by\nat most m2\nvalues.26\nLemma 5.14. Any OXS valuation can be represented by\nno more than m2\nvalues.\n6. BUNDLE-PRICE ASCENDING\nAUCTIONS\nAll the ascending auctions in the literature that are proved\nto find the optimal allocation for unrestricted valuations are\nnon-anonymous bundle-price auctions (iBundle(3) by Parkes\nand Ungar [37] and the Proxy Auction by Ausubel and\nMilgrom [3]). Yet, several anonymous ascending auctions\nhave been suggested (e.g., AkBA [42], [21] and iBundle(2)\n[37]). In this section, we prove that anonymous bundle-price\nascending auctions achieve poor results in the worst-case.\nWe also show that the family of non-anonymous\nbundleprice ascending auctions can run exponentially slower than\nsimple item-price ascending auctions.\n6.1 Limitations of Anonymous Bundle-Price\nAscending Auctions\nWe present a class of valuations that cannot be elicited\nby anonymous bundle-price ascending auctions. These\nvaluations are described in Figure 7. The basic idea: for\ndetermining some unknown value of one bidder we must raise\n24\nNote that an anonymous ascending auction cannot\nnecessarily elicit a class that can be fully elicited by an ascending\nauction.\n25\nSubstitute valuations are defined, e.g., in [16]. Roughly\nspeaking, a bidder with a substitute valuation will continue\ndemand a certain item after the price of some other items\nwas increased. For completeness, we present in the full paper\n[9] a proof for the efficiency of such auctions for substitutes\nvaluations.\n26\nA unit-demand valuation is an XOR valuation in which\nall the atomic bundles are singletons. OXS valuations can\nbe interpreted as an aggregation (OR) of any number of\nunit-demand bidders.\nBid. 1 v1(ac) = 2 v1(bd) = 2 v1(cd) = \u03b1 \u2208 (0, 1)\nBid. 2 v2(ab) = 2 v2(cd) = 2 v2(bd) = \u03b2 \u2208 (0, 1)\nFigure 7: Anonymous ascending bundle-price auctions\ncannot determine the optimal allocation for this class of\nvaluations.\na price of a bundle that should be demanded by the other\nbidder in the future.\nTheorem 6.1. Some classes of valuations cannot be\nelicited by anonymous bundle-price ascending auctions.\nProof. Consider a pair of XOR valuations as described\nin Figure 7. For finding the optimal allocation we must know\nwhich value is greater between \u03b1 and \u03b2.27\nHowever, we\ncannot learn the value of both \u03b1 and \u03b2 by a single ascending\ntrajectory: assume w.l.o.g. that bidder 1 demands cd before\nbidder 2 demands bd (no information will be elicited if none\nof these happens). In this case, the price for bd must be\ngreater than 1 (otherwise, bidder 1 prefers bd to cd). Thus,\nbidder 2 will never demand the bundle bd, and no\ninformation will be elicited about \u03b2.\nThe valuations described in the proof of Theorem 6.1 can\nbe easily elicited by a non-anonymous item-price ascending\nauction. On the other hand, the valuations in Figure 6 can\nbe easily elicited by an anonymous bundle-price ascending\nauction. We conclude that the power of these two families\nof ascending auctions is incomparable.\nWe strengthen the impossibility result above by showing\nthat anonymous bundle-price auctions cannot even achieve\nbetter than a min{O(n), O(\n\u221a\nm)}-approximation for the\nsocial welfare. This approximation ratio can be achieved with\npolynomial communication, and specifically with a\npolynomial number of item-price demand queries.28\nTheorem 6.2. An anonymous bundle-price ascending\nauction cannot guarantee better than a min{ n\n2\n,\n\u221a\nm\n2\n}\napproximation for the optimal welfare.\nProof. (Sketch) Assume we have n bidders and n2\nitems\nfor sale, and that n is prime. We construct n2\ndistinct\nbundles with the following properties: for each bidder, we define\na partition Si\n= (Si\n1, ..., Si\nn) of the n2\nitems to n bundles,\nsuch that any two bundles from different partitions intersect.\nIn the full paper, part II [9] we show an explicit construction\nusing the properties of linear functions over finite fields. The\nrest of the proof is independent of the specific construction.\nUsing these n2\nbundles we construct a hard-to-elicit\nclass. Every bidder has an atomic bid, in his XOR valuation,\nfor each of these n2\nbundles. A bidder i has a value of 2 for\nany bundle Si\nj in his partition. For all bundles in the other\npartitions, he has a value of either 0 or of 1 \u2212 \u03b4, and these\nvalues are unknown to the auctioneer. Since every pair of\nbundles from different partitions intersect, only one bidder\ncan receive a bundle with a value of 2.\n27\nIf \u03b1 > \u03b2, the optimal allocation will allocate cd to bidder\n1 and ab to bidder 2. Otherwise, we give bd to bidder 2 and\nac to bidder 1. Note that both bidders cannot gain a value\nof 2 in the same allocation, due to the intersections of the\nhigh-valued bundles.\n28\nNote that bundle-price queries may use exponential\ncommunication, thus the lower bound of [32] does not hold.\n41\nNon-anonymous Bundle-Price Economically-Efficient\nAscending Auctions:\nInitialization: All prices are initialized to zero\n(non-anonymous bundle prices).\nRepeat: - Each bidder submits a bundle that maximizes his\nutility under his current personalized prices.\n- The auctioneer calculates a provisional allocation that\nmaximizes his revenue under the current prices.\n- The prices of bundles that were demanded by losing\nbidders are increased by .\nFinally: Terminate when the provisional allocation assigns\nto each bidder the bundle he demanded.\nFigure 8: Auctions from this family (denoted by NBEA\nauctions) are known to achieve the optimal welfare.\nNo bidder will demand a low-valued bundle, as long as the\nprice of one of his high-valued bundles is below 1 (and thus\ngain him a utility greater than 1). Therefore, for eliciting\nany information about the low-valued bundles, the\nauctioneer should first arbitrarily choose a bidder (w.l.o.g bidder\n1) and raise the prices of all the bundles (S1\n1 , ..., S1\nn) to be\ngreater than 1. Since the prices cannot decrease, the other\nbidders will clearly never demand these bundles in future\nstages. An adversary may choose the values such that the\nlow values of all the bidders for the bundles not in bidder 1\"s\npartition are zero (i.e., vi(S1\nj ) = 0 for every i = 1 and every\nj), however, allocating each bidder a different bundle from\nbidder 1\"s partition, might achieve a welfare of n+1\u2212(n\u22121)\u03b4\n(bidder 1\"s valuation is 2, and 1 \u2212 \u03b4 for all other bidders);\nIf these bundles were wrongly allocated, only a welfare of\n2 might be achieved (2 for bidder 1\"s high-valued bundle, 0\nfor all other bidders). At this point, the auctioneer cannot\nhave any information about the identity of the bundles with\nthe non-zero values. Therefore, an adversary can choose the\nvalues of the bundles received by bidders 2, ..., n in the final\nallocation to be zero. We conclude that anonymous\nbundleprice auctions cannot guarantee a welfare greater than 2 for\nthis class, where the optimal welfare can be arbitrarily close\nto n + 1.\n6.2 Bundle Prices vs. Item Prices\nThe core of the auctions in [37, 3] is the scheme described\nin Figure 8 (in the spirit of [35]) for auctions with\nnonanonymous bundle prices. Auctions from this scheme end\nup with the optimal allocation for any class of valuations.\nWe denote this family of ascending auctions as NBEA\nauctions29\n.\nNBEA auctions can elicit k-term XOR valuations by a\npolynomial (in k) number of steps , although the elicitation\nof such valuations may require an exponential number of\nitem-price queries ([7]), and item-price ascending auctions\ncannot do it at all (Theorem 5.4). Nevertheless, we show\nthat NBEA auctions (and in particular, iBundle(3) and the\nproxy auction) are sometimes inferior to simple item-price\ndemand auctions. This may justify the use of hybrid\nauctions that use both linear and non-linear prices (e.g., the\nclock-proxy auction [10]). We show that auctions from this\n29\nNon-anonymous Bundle-price economically Efficient\nAscending auctions. For completeness, we give in the full\npaper [9] a simple proof for the efficiency (up to an ) of\nauctions of this scheme .\nfamily may use an exponential number of queries even for\ndetermining the optimal allocation among two bidders with\nadditive valuations30\n, where such valuations can be elicited\nby a simple item-price ascending auction. We actually prove\nthis property for a wider class of auctions we call\nconservative auctions. We also observe that in conservative auctions,\nallowing the bidders to submit all the bundles in their\ndemand sets ensures that the auction runs a polynomial\nnumber of steps - if L is not too high (but with exponential\ncommunication, of course).\nAn ascending auction is called conservative if it is\nnonanonymous, uses bundle prices initialized to zero and at\nevery stage the auctioneer can only raise prices of bundles\ndemanded by the bidders until this stage. In addition, each\nbidder can only receive bundles he demanded during the\nauction. Note that NBEA auctions are by definition\nconservative.\nProposition 6.3. If every bidder demands a single\nbundle in each step of the auction, conservative auctions may\nrun for an exponential number of steps even for additive\nvaluations. If the bidders are allowed to submit all the bundles\nin their demand sets in each step, then conservative auctions\ncan run in a polynomial number of steps for any profile of\nvaluations, as long as the maximal valuation L is polynomial\nin m, n and 1\n\u03b4\n.\nAcknowledgments:\nThe authors thank Moshe Babaioff, Shahar Dobzinski, Ron\nLavi, Daniel Lehmann, Ahuva Mu\"alem, David Parkes, Michael\nSchapira and Ilya Segal for helpful discussions. Supported\nby grants from the Israeli Academy of Sciences and the\nUSAIsrael Binational Science Foundation.\n7. REFERENCES\n[1] amazon. Web Page: http://www.amazon.com.\n[2] ebay. Web Page: http://www.ebay.com.\n[3] L. M. Ausubel and P. R. Milgrom. Ascending auctions\nwith package bidding. 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{"name": "train_J-49", "title": "Information Markets vs. Opinion Pools: An Empirical Comparison", "abstract": "In this paper, we examine the relative forecast accuracy of information markets versus expert aggregation. We leverage a unique data source of almost 2000 people\"s subjective probability judgments on 2003 US National Football League games and compare with the market probabilities given by two different information markets on exactly the same events. We combine assessments of multiple experts via linear and logarithmic aggregation functions to form pooled predictions. Prices in information markets are used to derive market predictions. Our results show that, at the same time point ahead of the game, information markets provide as accurate predictions as pooled expert assessments. In screening pooled expert predictions, we find that arithmetic average is a robust and efficient pooling function; weighting expert assessments according to their past performance does not improve accuracy of pooled predictions; and logarithmic aggregation functions offer bolder predictions than linear aggregation functions. The results provide insights into the predictive performance of information markets, and the relative merits of selecting among various opinion pooling methods.", "fulltext": "1. INTRODUCTION\nForecasting is a ubiquitous endeavor in human societies.\nFor decades, scientists have been developing and exploring\nvarious forecasting methods, which can be roughly divided\ninto statistical and non-statistical approaches. Statistical\napproaches require not only the existence of enough\nhistorical data but also that past data contains valuable\ninformation about the future event. When these conditions can\nnot be met, non-statistical approaches that rely on\njudgmental information about the future event could be better\nchoices. One widely used non-statistical method is to elicit\nopinions from experts. Since experts are not generally in\nagreement, many belief aggregation methods have been\nproposed to combine expert opinions together and form a\nsingle prediction. These belief aggregation methods are called\nopinion pools, which have been extensively studied in\nstatistics [20, 24, 38], and management sciences [8, 9, 30, 31], and\napplied in many domains such as group decision making [29]\nand risk analysis [12].\nWith the fast growth of the Internet, information markets\nhave recently emerged as a promising non-statistical\nforecasting tool. Information markets (sometimes called\nprediction markets, idea markets, or event markets) are\nmarkets designed for aggregating information and making\npredictions about future events. To form the predictions,\ninformation markets tie payoffs of securities to outcomes of\nevents. For example, in an information market to predict\nthe result of a US professional National Football League\n(NFL) game, say New England vs Carolina, the security\npays a certain amount of money per share to its holders if\nand only if New England wins the game. Otherwise, it pays\noff nothing. The security price before the game reflects the\nconsensus expectation of market traders about the\nprobability of New England winning the game. Such markets\nare becoming very popular. The Iowa Electronic Markets\n(IEM) [2] are real-money futures markets to predict\neconomic and political events such as elections. The\nHollywood Stock Exchange (HSX) [3] is a virtual (play-money)\nexchange for trading securities to forecast future box office\nproceeds of new movies, and the outcomes of entertainment\nawards, etc. TradeSports.com [7], a real-money betting\nexchange registered in Ireland, hosts markets for sports,\npolitical, entertainment, and financial events. The Foresight\nExchange (FX) [4] allows traders to wager play money on\nunresolved scientific questions or other claims of public\ninterest, and NewsFutures.com\"s World News Exchange [1] has\n58\npopular sports and financial betting markets, also grounded\nin a play-money currency.\nDespite the popularity of information markets, one of the\nmost important questions to ask is: how accurately can\ninformation markets predict? Previous research in general\nshows that information markets are remarkably accurate.\nThe political election markets at IEM predict the election\noutcomes better than polls [16, 17, 18, 19]. Prices in HSX\nand FX have been found to give as accurate or more\naccurate predictions than judgment of individual experts [33,\n34, 37]. However, information markets have not been\ncalibrated against opinion pools, except for Servan-Schreiber\net. al [36], in which the authors compare two information\nmarkets against arithmetic average of expert opinions. Since\ninformation markets, in nature, offer an adaptive and\nselforganized mechanism to aggregate opinions of market\nparticipants, it is interesting to compare them with existing\nopinion pooling methods, to evaluate the performance of\ninformation markets from another perspective. The\ncomparison will provide beneficial guidance for practitioners to\nchoose the most appropriate method for their needs.\nThis paper contributes to the literature in two ways: (1)\nAs an initial attempt to compare information markets with\nopinion pools of multiple experts, it leads to a better\nunderstanding of information markets and their promise as an\nalternative institution for obtaining accurate forecasts; (2)\nIn screening opinion pools to be used in the comparison, we\ncast insights into relative performances of different opinion\npools. In terms of prediction accuracy, we compare two\ninformation markets with several linear and logarithmic\nopinion pools (LinOP and LogOP) at predicting the results of\nNFL games. Our results show that at the same time point\nahead of the game, information markets provide as accurate\npredictions as our carefully selected opinion pools. In\nselecting the opinion pools to be used in our comparison, we\nfind that arithmetic average is a robust and efficient pooling\nfunction; weighting expert assessments according to their\npast performances does not improve the prediction accuracy\nof opinion pools; and LogOP offers bolder predictions than\nLinOP. The remainder of the paper is organized as follows.\nSection 2 reviews popular opinion pooling methods.\nSection 3 introduces the basics of information markets. Data\nsets and our analysis methods are described in Section 4.\nWe present results and analysis in Section 5, followed by\nconclusions in Section 6.\n2. REVIEW OF OPINION POOLS\nClemen and Winkler [12] classify opinion pooling\nmethods into two broad categories: mathematical approaches\nand behavioral approaches. In mathematical approaches,\nthe opinions of individual experts are expressed as\nsubjective probability distributions over outcomes of an\nuncertain event. They are combined through various\nmathematical methods to form an aggregated probability\ndistribution. Genest and Zidek [24] and French [20] provide\ncomprehensive reviews of mathematical approaches. Mathematical\napproaches can be further distinguished into axiomatic\napproaches and Bayesian approaches. Axiomatic approaches\napply prespecified functions that map expert opinions,\nexpressed as a set of individual probability distributions, to\na single aggregated probability distribution. These\npooling functions are justified using axioms or certain desirable\nproperties. Two of the most common pooling functions are\nthe linear opinion pool (LinOP) and the logarithmic opinion\npool (LogOP). Using LinOP, the aggregate probability\ndistribution is a weighted arithmetic mean of individual\nprobability distributions:\np(\u03b8) =\nn\ni=1\nwipi(\u03b8), (1)\nwhere pi(\u03b8) is expert i\"s probability distribution of uncertain\nevent \u03b8, p(\u03b8) represents the aggregate probability\ndistribution, wi\"s are weights for experts, which are usually\nnonnegative and sum to 1, and n is the number of experts. Using\nLogOP, the aggregate probability distribution is a weighted\ngeometric mean of individual probability distributions:\np(\u03b8) = k\nn\ni=1\npi(\u03b8)wi\n, (2)\nwhere k is a normalization constant to ensure that the pooled\nopinion is a probability distribution. Other axiomatic\npooling methods often are extensions of LinOP [22], LogOP [23],\nor both [13]. Winkler [39] and Morris [29, 30] establish the\nearly framework of Bayesian aggregation methods. Bayesian\napproaches assume as if there is a decision maker who has a\nprior probability distribution over event \u03b8 and a likelihood\nfunction over expert opinions given the event. This decision\nmaker takes expert opinions as evidence and updates its\npriors over the event and opinions according to Bayes rule. The\nresulted posterior probability distribution of \u03b8 is the pooled\nopinion.\nBehavioral approaches have been widely studied in the\nfield of group decision making and organizational\nbehavior. The important assumption of behavioral approaches is\nthat, through exchanging opinions or information, experts\ncan eventually reach an equilibrium where further\ninteraction won\"t change their opinions. One of the best known\nbehavioral approaches is the Delphi technique [28].\nTypically, this method and its variants do not allow open\ndiscussion, but each expert has chance to judge opinions of other\nexperts, and is given feedback. Experts then can reassess\ntheir opinions and repeat the process until a consensus or a\nsmaller spread of opinions is achieved. Some other\nbehavioral methods, such as the Nominal Group technique [14],\npromote open discussions in controlled environments.\nEach approach has its pros and cons. Axiomatic\napproaches are easy to use. But they don\"t have a normative\nbasis to choose weights. In addition, several impossibility\nresults (e.g., Genest [21]) show that no aggregation\nfunction can satisfy all desired properties of an opinion pool,\nunless the pooled opinion degenerates to a single individual\nopinion, which effectively implies a dictator. Bayesian\napproaches are nicely based on the normative Bayesian\nframework. However, it is sometimes frustratingly difficult to\napply because it requires either (1) constructing an obscenely\ncomplex joint prior over the event and opinions (often\nimpractical even in terms of storage / space complexity, not\nto mention from an elicitation standpoint) or (2) making\nstrong assumptions about the prior, like conditional\nindependence of experts. Behavior approaches allow experts to\ndynamically improve their information and revise their\nopinions during interactions, but many of them are not fixed or\ncompletely specified, and can\"t guarantee convergence or\nrepeatability.\n59\n3. HOW INFORMATION MARKETS WORK\nMuch of the enthusiasm for information markets stems\nfrom Hayek hypothesis [26] and efficient market\nhypothesis [15]. Hayek, in his classic critique of central planning in\n1940\"s, claims that the price system in a competitive market\nis a very efficient mechanism to aggregate dispersed\ninformation among market participants. The efficient market\nhypothesis further states that, in an efficient market, the\nprice of a security almost instantly incorporates all\navailable information. The market price summarizes all relevant\ninformation across traders, hence is the market participants\"\nconsensus expectation about the future value of the security.\nEmpirical evidence supports both hypotheses to a large\nextent [25, 27, 35]. Thus, when associating the value of a\nsecurity with the outcome of an uncertain future event, market\nprice, by revealing the consensus expectation of the security\nvalue, can indirectly predict the outcome of the event. This\nidea gives rise to information markets.\nFor example, if we want to predict which team will win\nthe NFL game between New England and Carolina, an\ninformation market can trade a security $100 if New England\ndefeats Carolina, whose payoff per share at the end of the\ngame is specified as follow:\n$100 if New England wins the game;\n$0 otherwise.\nThe security price should roughly equal the expected payoff\nof the security in an efficient market. The time value of\nmoney usually can be ignored because durations of most\ninformation markets are short. Assuming exposure to risk is\nroughly equal for both outcomes, or that there are sufficient\neffectively risk-neutral speculators in the market, the price\nshould not be biased by the risk attitudes of various players\nin the market. Thus,\np = Pr(Patriots win) \u00d7 100 + [1 \u2212 Pr(Patriots win)] \u00d7 0,\nwhere p is the price of the security $100 if New England\ndefeats Carolina and Pr(Patriots win) is the probability\nthat New England will win the game. Observing the security\nprice p before the game, we can derive Pr(Patriots win),\nwhich is the market participants\" collective prediction about\nhow likely it is that New England will win the game.\nThe above security is a winner-takes-all contract. It is\nused when the event to be predicted is a discrete random\nvariable with disjoint outcomes (in this case binary). Its\nprice predicts the probability that a specific outcome will be\nrealized. When the outcome of a prediction problem can be\nany value in a continuous interval, we can design a security\nthat pays its holder proportional to the realized value. This\nkind of security is what Wolfers and Zitzewitz [40] called\nan index contract. It predicts the expected value of a\nfuture outcome. Many other aspects of a future event such as\nmedian value of outcome can also be predicted in\ninformation markets by designing and trading different securities.\nWolfers and Zitzewitz [40] provide a summary of the main\ntypes of securities traded in information markets and what\nstatistical properties they can predict. In practice,\nconceiving a security for a prediction problem is only one of the\nmany decisions in designing an effective information\nmarket. Spann and Skiera [37] propose an initial framework for\ndesigning information markets.\n4. DESIGN OF ANALYSIS\n4.1 Data Sets\nOur data sets cover 210 NFL games held between\nSeptember 28th, 2003 and December 28th, 2003. NFL games are\nvery suitable for our purposes because: (1) two online\nexchanges and one online prediction contest already exist that\nprovide data on both information markets and the\nopinions of self-identified experts for the same set of games; (2)\nthe popularity of NFL games in the United States provides\nnatural incentives for people to participate in information\nmarkets and/or the contest, which increases liquidity of\ninformation markets and improves the quality and number\nof opinions in the contest; (3) intense media coverage and\nanalysis of the profiles and strengths of teams and\nindividual players provide the public with much information so that\nparticipants of information markets and the contest can be\nviewed as knowledgeable regarding to the forecasting goal.\nInformation market data was acquired, by using a\nspecially designed crawler program, from TradeSports.com\"s\nFootball-NFL markets [7] and NewsFutures.com\"s Sports\nExchange [1]. For each NFL game, both TradeSports and\nNewsFutures have a winner-takes-all information market to\npredict the game outcome. We introduce the design of the\ntwo markets according to Spann and Skiera\"s three steps for\ndesigning an information market [37] as below.\n\u2022 Choice of forecasting goal: Markets at both\nTradeSports and NewsFutures aim at predicting which one\nof the two teams will win a NFL football game. They\ntrade similar winner-takes-all securities that pay off\n100 if a team wins the game and 0 if it loses the game.\nSmall differences exist in how they deal with ties. In\nthe case of a tie, TradeSports will unwind all trades\nthat occurred and refund all exchange fees, but the\nsecurity is worth 50 in NewsFutures. Since the\nprobability of a tie is usually very low (much less the 1%),\nprices at both markets effectively represent the market\nparticipants\" consensus assessment of the probability\nthat the team will win.\n\u2022 Incentive for participation and information\nrevelation: TradeSports and NewsFutures use different\nincentives for participation and information revelation.\nTradeSports is a real-money exchange. A trader needs\nto open and fund an account with a minimum of $100\nto participate in the market. Both profits and losses\ncan occur as a result of trading activity. On the\ncontrary, a trader can register at NewsFutures for free and\nget 2000 units of Sport Exchange virtual money at the\ntime of registration. Traders at NewsFutures will not\nincur any real financial loss. They can accumulate\nvirtual money by trading securities. The virtual money\ncan then be used to bid for a few real prizes at\nNewsFutures\" online shop.\n\u2022 Financial market design: Both markets at\nTradeSports and NewsFutures use the continuous double\nauction as their trading mechanism. TradeSports charges\na small fee on each security transaction and expiry,\nwhile NewsFutures does not.\nWe can see that the main difference between two information\nmarkets is real money vs. virtual money. Servan-Schreiber\n60\net. al [36] have compared the effect of money on the\nperformance of the two information markets and concluded that\nthe prediction accuracy of the two markets are at about the\nsame level. Not intending to compare these two markets,\nwe still use both markets in our analysis to ensure that our\nfindings are not accidental.\nWe obtain the opinions of 1966 self-identified experts for\nNFL games from the ProbabilityFootball online contest [5],\none of several ProbabilitySports contests [6]. The contest is\nfree to enter. Participants of the contest are asked to enter\ntheir subjective probability that a team will win a game\nby noon on the day of the game. Importantly, the contest\nevaluates the participants\" performance via the quadratic\nscoring rule:\ns = 100 \u2212 400 \u00d7 Prob Lose2\n, (3)\nwhere s represents the score that a participant earns for the\ngame, and Prob Lose is the probability that the participant\nassigns to the actual losing team. The quadratic score is\none of a family of so-called proper scoring rules that have\nthe property that an expert\"s expected score is maximized\nwhen the expert reports probabilities truthfully. For\nexample, for a game team A vs. team B, if a player assigns 0.5 to\nboth team A and B, his/her score for the game is 0 no matter\nwhich team wins. If he/she assigns 0.8 to team A and 0.2 to\nteam B, showing that he is confident in team A\"s winning,\nhe/she will score 84 points for the game if team A wins, and\nlose 156 points if team B wins. This quadratic scoring rule\nrewards bold predictions that are right, but penalizes bold\npredictions that turn out to be wrong. The top players,\nmeasured by accumulated scores over all games, win the prizes\nof the contest. The suggested strategy at the contest\nwebsite is to make picks for each game that match, as closely\nas possible, the probabilities that each team will win. This\nstrategy is correct if the participant seeks to maximize\nexpected score. However, as prizes are awarded only to the top\nfew winners, participants\" goals are to maximize the\nprobability of winning, not maximize expected score, resulting in a\nslightly different and more risk-seeking optimization.1\nStill,\nas far as we are aware, this data offer the closest thing\navailable to true subjective probability judgments from so many\npeople over so many public events that have corresponding\ninformation markets.\n4.2 Methods of Analysis\nIn order to compare the prediction accuracy of\ninformation markets and that of opinion pools, we proceed to derive\npredictions from market data of TradeSports and\nNewsFutures, form pooled opinions using expert data from\nProbabilityFootball contest, and specify the performance measures\nto be used.\n4.2.1 Deriving Predictions\nFor information markets, deriving predictions is\nstraightforward. We can take the security price and divide it by\n100 to get the market\"s prediction of the probability that\na team will win. To match the time when participants at\nthe ProbabilityFootball contest are required to report their\nprobability assessments, we derive predictions using the last\ntrade price before noon on the day of the game. For more\n1\nIdeally, prizes would be awarded by lottery in proportion\nto accumulated score.\nthan half of the games, this time is only about an hour\nearlier than the game starting time, while it is several hours\nearlier for other games. Two sets of market predictions are\nderived:\n\u2022 NF: Prediction equals NewsFutures\" last trade price\nbefore noon of the game day divided by 100.\n\u2022 TS: Prediction equals TradeSports\" last trade price\nbefore noon of the game day divided by 100.\nWe apply LinOP and LogOP to ProbabilityFootball data\nto obtain aggregate expert predictions. The reason that we\ndo not consider other aggregation methods include: (1) data\nfrom ProbabilityFootball is only suitable for mathematical\npooling methods-we can rule out behavioral approaches,\n(2) Bayesian aggregation requires us to make assumptions\nabout the prior probability distribution of game outcomes\nand the likelihood function of expert opinions: given the\nlarge number of games and participants, making reasonable\nassumptions is difficult, and (3) for axiomatic approaches,\nprevious research has shown that simpler aggregation\nmethods often perform better than more complex methods [12].\nBecause the output of LogOP is indeterminate if there are\nprobability assessments of both 0 and 1 (and because\nassessments of 0 and 1 are dictatorial using LogOP), we add\na small number 0.01 to an expert opinion if it is 0, and\nsubtract 0.01 from it if it is 1.\nIn pooling opinions, we consider two influencing factors:\nweights of experts and number of expert opinions to be\npooled. For weights of experts, we experiment with equal\nweights and performance-based weights. The\nperformancebased weights are determined according to previous\naccumulated score in the contest. The score for each game is\ncalculated according to equation 3, the scoring rule used in\nthe ProbabilityFootball contest. For the first week, since no\nprevious scores are available, we choose equal weights. For\nlater weeks, we calculate accumulated past scores for each\nplayer. Because the cumulative scores can be negative, we\nshift everyone\"s score if needed to ensure the weights are\nnon-negative. Thus,\nwi =\ncumulative scorei + shift\nn\nj=1(cumulative scorej + shift)\n. (4)\nwhere shift equals 0 if the smallest cumulative scorej is\nnon-negative, and equals the absolute value of the\nsmallest cumulative scorej otherwise. For simplicity, we call\nperformance-weighted opinion pool as weighted, and equally\nweighted opinion pool as unweighted. We will use them\ninterchangeably in the remaining of the paper.\nAs for the number of opinions used in an opinion pool,\nwe form different opinion pools with different number of\nexperts. Only the best performing experts are selected. For\nexample, to form an opinion pool with 20 expert opinions,\nwe choose the top 20 participants. Since there is no\nperformance record for the first week, we use opinions of all\nparticipants in the first week. For week 2, we select opinions of\n20 individuals whose scores in the first week are among the\ntop 20. For week 3, 20 individuals whose cumulative scores\nof week 1 and 2 are among the top 20s are selected. Experts\nare chosen in a similar way for later weeks. Thus, the top\n20 participants can change from week to week.\nThe possible opinion pools, varied in pooling functions,\nweighting methods, and number of expert opinions, are shown\n61\nTable 1: Pooled Expert Predictions\n# Symbol Description\n1 Lin-All-u Unweighted (equally weighted) LinOP\nof all experts.\n2 Lin-All-w Weighted (performance-weighted)\nLinOP of all experts.\n3 Lin-n-u Unweighted (equally weighted) LinOP\nwith n experts.\n4 Lin-n-w Weighted (performance-weighted)\nLinOP with n experts.\n5 Log-All-u Unweighted (equally weighted) LogOP\nof all experts.\n6 Log-All-w Weighted (performance-weighted)\nLogOP of all experts.\n7 Log-n-u Unweighted (equally weighted) LogOP\nwith n experts.\n8 Log-n-w Weighted (performance-weighted)\nLogOP with n experts.\nin Table 1. Lin represents linear, and Log represents\nLogarithmic. n is the number of expert opinions that are\npooled, and All indicates that all opinions are combined.\nWe use u to symbolize unweighted (equally weighted)\nopinion pools. w is used for weighted (performance-weighted)\nopinion pools. Lin-All-u, the equally weighted LinOP with\nall participants, is basically the arithmetic mean of all\nparticipants\" opinions. Log-All-u is simply the geometric mean\nof all opinions.\nWhen a participant did not enter a prediction for a\nparticular game, that participant was removed from the opinion\npool for that game. This contrasts with the\nProbabilityFootball average reported on the contest website and used\nby Servan-Schreiber et. al [36], where unreported\npredictions were converted to 0.5 probability predictions.\n4.2.2 Performance Measures\nWe use three common metrics to assess prediction\naccuracy of information markets and opinion pools. These\nmeasures have been used by Servan-Schreiber et. al [36] in\nevaluating the prediction accuracy of information markets.\n1. Absolute Error = Prob Lose,\nwhere Prob Lose is the probability assigned to the\neventual losing team. Absolute error simply measures\nthe difference between a perfect prediction (1 for\nwinning team) and the actual prediction. A prediction\nwith lower absolute error is more accurate.\n2. Quadratic Score = 100 \u2212 400 \u00d7 (Prob Lose2\n).\nQuadratic score is the scoring function that is used in\nthe ProbabilityFootball contest. It is a linear\ntransformation of squared error, Prob Lose2\n, which is one of\nthe mostly used metrics in evaluating forecasting\naccuracy. Quadratic score can be negative. A prediction\nwith higher quadratic score is more accurate.\n3. Logarithmic Score = log(Prob W in),\nwhere Prob W in is the probability assigned to the\neventual winning team. The logarithmic score, like\nthe quadratic score, is a proper scoring rule. A\nprediction with higher (less negative) logarithmic score is\nmore accurate.\n5. EMPIRICAL RESULTS\n5.1 Performance of Opinion Pools\nDepending on how many opinions are used, there can be\nnumerous different opinion pools. We first examine the\neffect of number of opinions on prediction accuracy by forming\nopinion pools with the number of expert opinions varying\nfrom 1 to 960. In the ProbabilityFootball Competition, not\nall 1966 registered participants provide their probability\nassessments for every game. 960 is the smallest number of\nparticipants for all games. For each game, we sort experts\naccording to their accumulated quadratic score in previous\nweeks. Predictions of the best performing n participants are\npicked to form an opinion pool with n experts.\nFigure 1 shows the prediction accuracy of LinOP and\nLogOP in terms of mean values of the three performance\nmeasures across all 210 games. We can see the following trends\nin the figure.\n1. Unweighted opinion pools and performance-weighted\nopinion pools have similar levels of prediction\naccuracy, especially for LinOP.\n2. For LinOP, increasing the number of experts in\ngeneral increases or keeps the same the level of prediction\naccuracy. When there are more than 200 experts, the\nprediction accuracy of LinOP is stable regarding the\nnumber of experts.\n3. LogOP seems more accurate than LinOP in terms of\nmean absolute error. But, using all other performance\nmeasures, LinOP outperforms LogOP.\n4. For LogOP, increasing the number of experts increases\nthe prediction accuracy at the beginning. But the\ncurves (including the points with all experts) for mean\nquadratic score, and mean logarithmic score have slight\nbell-shapes, which represent a decrease in prediction\naccuracy when the number of experts is very large.\nThe curves for mean absolute error, on the other hand,\nshow a consistent increase of accuracy.\nThe first and second trend above imply that when using\nLinOP, the simplest way, which has good prediction\naccuracy, is to average the opinions of all experts. Weighting\ndoes not seem to improve performance. Selecting experts\naccording to past performance also does not help. It is a\nvery interesting observation that even if many participants\nof the ProbabilityFootball contest do not provide accurate\nindividual predictions (they have negative quadratic scores\nin the contest), including their opinions into the opinion pool\nstill increases the prediction accuracy. One explanation of\nthis phenomena could be that biases of individual judgment\ncan offset with each other when opinions are diverse, which\nmakes the pooled prediction more accurate.\nThe third trend presents a controversy. The relative\nprediction accuracy of LogOP and LinOP flips when using\ndifferent accuracy measures. To investigate this disagreement,\nwe plot the absolute error of Log-All-u and Lin-All-u for each\ngame in Figure 2. When the absolute error of an opinion\n62\n0 100 200 300 400 500 600 700 800 900 All\n0.4\n0.405\n0.41\n0.415\n0.42\n0.425\n0.43\n0.435\n0.44\n0.445\n0.45\nNumber of Expert Opinions\nMeanAbsoluteError\nUnweighted Linear\nWeighted Linear\nUnweighted Logarithmic\nWeighted Logarithmic\nLin\u2212All\u2212u\nLin\u2212All\u2212w\nLog\u2212All\u2212u\nLog\u2212All\u2212w\n(a) Mean Absolute Error\n0 100 200 300 400 500 600 700 800 900 All\n4\n5\n6\n7\n8\n9\n10\n11\n12\n13\n14\nNumber of Expert Opinions\nMeanQuadraticScore\nUnweighted Linear\nWeighted Linear\nUnweighted Logarithmic\nWeighted Logarithmic\nLin\u2212All\u2212u\nLin\u2212All\u2212w\nLog\u2212All\u2212u\nLog\u2212All\u2212w\n0 100 200 300 400 500 600 700 800 900 All\n\u22120.71\n\u22120.7\n\u22120.69\n\u22120.68\n\u22120.67\n\u22120.66\n\u22120.65\n\u22120.64\n\u22120.63\n\u22120.62\nNumber of Expert Opinions\nMeanLogarithmicScore\nUnweighted Linear\nWeighted Linear\nUnweighted Logarithmic\nWeighted Logarithmic\nLin\u2212All\u2212u\nLin\u2212All\u2212w\nLog\u2212All\u2212u\nLog\u2212All\u2212w\n(b) Mean Quadratic Score (c) Mean Logarithmic Score\nFigure 1: Prediction Accuracy of Opinion Pools\npool for a game is less than 0.5, it means that the team\nfavored by the opinion pool wins the game. If it is greater than\n0.5, the underdog wins. Compared with Lin-All-u, Log-All-u\nhas lower absolute error when it is less than 0.5, and greater\nabsoluter error when it is greater than 0.5, which indicates\nthat predictions of Log-All-u are bolder, more close to 0 or 1,\nthan those of Lin-All-u. This is due to the nature of linear\nand logarithmic aggregating functions. Because quadratic\nscore and logarithmic score penalize bold predictions that\nare wrong, LogOP is less accurate when measured in these\nterms.\nSimilar reasoning accounts for the fourth trend. When\nthere are more than 500 experts, increasing number of\nexperts used in LogOP improves the prediction accuracy\nmeasured by absolute error, but worsens the accuracy measured\nby the other two metrics. Examining expert opinions, we\nfind that participants who rank lower are more frequent in\noffering extreme predictions (0 or 1) than those ranking high\nin the list. When we increase the number of experts in an\nopinion pool, we are incorporating more extreme predictions\ninto it. The resulting LogOP is bolder, and hence has lower\nmean quadratic score and mean logarithmic score.\n5.2 Comparison of Information Markets and\nOpinion Pools\nThrough the first screening of various opinion pools, we\nselect Lin-All-u, Log-All-u, Log-All-w, and Log-200-u to\ncompare with predictions from information markets. Lin-All-u\nas shown in Figure 1 can represent what LinOP can achieve.\nHowever, the performance of LogOP is not consistent when\nevaluated using different metrics. Log-All-u and Log-All-w\noffer either the best or the worst predictions. Log-200-u, the\nLogOP with the 200 top performing experts, provides more\nstable predictions. We use all of the three to stand for the\nperformance of LogOP in our later comparison.\nIf a prediction of the probability that a team will win a\ngame, either from an opinion pool or an information\nmarket, is higher than 0.5, we say that the team is the predicted\nfavorite for the game. Table 2 presents the number and\npercentage of games that predicted favorites actually win, out\nof a total of 210 games. All four opinion pools correctly\npredict a similar number and percentage of games as NF and\nTS. Since NF, TS, and the four opinion pools form their\npredictions using information available at noon of the game\n63\nTable 2: Number and Percentage of Games that Predicted Favorites Win\nNF TS Lin-All-u Log-All-u Log-All-w Log-200-u\nNumber 142 137 144 144 143 141\nPercentage 67.62% 65.24% 68.57% 68.57% 68.10% 67.14%\nTable 3: Mean of Prediction Accuracy Measures\nAbsolute Error Quadratic Score Logarithmic Score\nNF\n0.4253 15.4352 -0.6136\n(0.0121) (4.6072) (0.0258)\nTS\n0.4275 15.2739 -0.6121\n(0.0118) (4.3982) (0.0241)\nLin-All-u\n0.4292 13.0525 -0.6260\n(0.0126) (4.8088) (0.0268)\nLog-All-u\n0.4024 10.0099 -0.6546\n(0.0173) (6.6594) (0.0418)\nLog-All-w\n0.4059 10.4491 -0.6497\n(0.0168) (6.4440) (0.0398)\nLog-200-u\n0.4266 12.3868 -0.6319\n(0.0133) (5.0764) (0.0295)\n*Numbers in parentheses are standard errors.\n*Best value for each metric is shown in bold.\n0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\nAbsolute Error of Lin\u2212All\u2212u\nAbsoluteErrorofLog\u2212All\u2212u\n45 Degree Line\nAbsolute Error\nFigure 2: Absolute Error: Lin-All-u vs. Log-All-u\nday, information markets and opinion pools have\ncomparable potential at the same time point.\nWe then take a closer look at prediction accuracy of\ninformation markets and opinion pools using the three\nperformance measures. Table 3 displays mean values of these\nmeasures over 210 games. Numbers in parentheses are\nstandard errors, which estimate the standard deviation of the\nmean. To take into consideration of skewness of\ndistributions, we also report median values of accuracy measures in\nTable 4. Judged by the mean values of accuracy measures\nin Table 3, all methods have similar accuracy levels, with\nNF and TS slightly better than the opinion pools. However,\nthe median values of accuracy measures indicate that\nLogAll-u and Log-All-w opinion pools are more accurate than\nall other predictions.\nWe employ the randomization test [32] to study whether\nthe differences in prediction accuracy presented in Table 3\nand Table 4 are statistically significant. The basic idea of\nrandomization test is that, by randomly swapping\npredictions of two methods numerous times, an empirical\ndistribution for the difference of prediction accuracy can be\nconstructed. Using this empirical distribution, we are then able\nto evaluate that at what confidence level the observed\ndifference reflects a real difference. For example, the mean\nabsolute error of NF is higher than that of Log-All-u by\n0.0229, as shown in Table 3. To test whether this\ndifference is statistically significant, we shu\ufb04e predictions from\ntwo methods, randomly label half of predictions as NF and\nthe other half as Log-All-u, and compute the difference of\nmean absolute error of the newly formed NF and Log-All-u\ndata. The above procedure is repeated 10,000 times. The\n10,000 differences of mean absolute error results in an\nempirical distribution of the difference. Comparing our observed\ndifference, 0.0229, with this distribution, we find that the\nobserved difference is greater than 75.37% of the empirical\ndifferences. This leads us to conclude that the difference of\nmean absolute error between NF and Log-All-u is not\nstatistically significant, if we choose the level of significance to\nbe 0.05.\nTable 5 and Table 6 are results of randomization test for\nmean and median differences respectively. Each cell of the\ntable is for two different prediction methods, represented by\nname of the row and name of the column. The first lines\nof table cells are results for absolute error. The second and\nthird lines are dedicated to quadratic score and logarithmic\nscore respectively. We can see that, in terms of mean values\nof accuracy measures, the differences of all methods are not\nstatistically significant to any reasonable degree. When it\n64\nTable 4: Median of Prediction Accuracy Measures\nAbsolute Error Quadratic Score Logarithmic Score\nNF 0.3800 42.2400 -0.4780\nTS 0.4000 36.0000 -0.5108\nLin-All-u 0.3639 36.9755 -0.5057\nLog-All-u 0.3417 53.2894 -0.4181\nLog-All-w 0.3498 51.0486 -0.4305\nLog-200-u 0.3996 36.1300 -0.5101\n*Best value for each metric is shown in bold.\nTable 5: Statistical Confidence of Mean Differences in Prediction Accuracy\nTS Lin-All-u Log-All-u Log-All-w Log-200-u\nNF\n8.92% 22.07% 75.37% 66.47% 7.76%\n2.38% 26.60% 50.74% 44.26% 32.24%\n2.99% 22.81% 59.35% 56.21% 33.26%\nTS\n10.13% 77.79% 68.15% 4.35%\n27.25% 53.65% 44.90% 28.30%\n32.35% 57.89% 60.69% 38.84%\nLin-All-u\n82.19% 68.86% 9.75%\n28.91% 23.92% 6.81%\n44.17% 43.01% 17.36%\nLog-All-u\n11.14% 72.49%\n3.32% 18.89%\n5.25% 39.06%\nLog-All-w\n69.89%\n18.30%\n30.23%\n*In each table cell, row 1 accounts for absolute error, row 2 for quadratic score,\nand row 3 for logarithmic score.\ncomes to median values of prediction accuracy, Log-All-u\noutperforms Lin-All-u at a high confidence level.\nThese results indicate that differences in prediction\naccuracy between information markets and opinion pools are not\nstatistically significant. This may seem to contradict the\nresult of Servan-Schreiber et. al [36], in which NewsFutures\"s\ninformation markets have been shown to provide\nstatistically significantly more accurate predictions than the\n(unweighted) average of all ProbabilityFootball opinions. The\ndiscrepancy emerges in dealing with missing data. Not all\n1966 registered ProbabilityFootball participants offer\nprobability assessments for each game. When a participant does\nnot provide a probability assessment for a game, the\ncontest considers their prediction as 0.5.. This makes sense in\nthe context of the contest, since 0.5 always yields 0 quadratic\nscore. The ProbabilityFootball average reported on the\ncontest website and used by Servan-Schreiber et. al includes\nthese 0.5 estimates. Instead, we remove participants from\ngames that they do not provide assessments, pooling only\nthe available opinions together. Our treatment increases the\nprediction accuracy of Lin-All-u significantly.\n6. CONCLUSIONS\nWith the fast growth of the Internet, information markets\nhave recently emerged as an alternative tool for predicting\nfuture events. Previous research has shown that information\nmarkets give as accurate or more accurate predictions than\nindividual experts and polls. However, information\nmarkets, as an adaptive mechanism to aggregate different\nopinions of market participants, have not been calibrated against\nmany belief aggregation methods. In this paper, we compare\nprediction accuracy of information markets with linear and\nlogarithmic opinion pools (LinOP and LogOP) using\npredictions from two markets and 1966 individuals regarding the\noutcomes of 210 American football games during the 2003\nNFL season. In screening for representative opinion pools to\ncompare with information markets, we investigate the effect\nof weights and number of experts on prediction accuracy.\nOur results on both the comparison of information markets\nand opinion pools and the relative performance of different\nopinion pools are summarized as below.\n1. At the same time point ahead of the events,\ninformation markets offer as accurate predictions as our\nselected opinion pools.\nWe have selected four opinion pools to represent the\nprediction accuracy level that LinOP and LogOP can\nachieve. With all four performance metrics, our two\ninformation markets obtain similar prediction accuracy\nas the four opinion pools.\n65\nTable 6: Statistical Confidence of Median Differences in Prediction Accuracy\nTS Lin-All-u Log-All-u Log-All-w Log-200-u\nNF\n48.85% 47.3% 84.8% 77.9% 65.36%\n45.26% 44.55% 85.27% 75.65% 66.75%\n44.89% 46.04% 84.43% 77.16% 64.78%\nTS\n5.18% 94.83% 94.31% 0%\n5.37% 92.08% 92.53% 0%\n7.41% 95.62% 91.09% 0%\nLin-All-u\n95.11% 91.37% 7.31%\n96.10% 92.69% 9.84%\n95.45% 95.12% 7.79%\nLog-All-u\n23.47% 95.89%\n26.68% 93.85%\n22.47% 96.42%\nLog-All-w\n91.3%\n91.4%\n90.37%\n*In each table cell, row 1 accounts for absolute error, row 2 for quadratic score,\nand row 3 for logarithmic score.\n*Confidence above 95% is shown in bold.\n2. The arithmetic average of all opinions (Lin-All-u) is a\nsimple, robust, and efficient opinion pool.\nSimply averaging across all experts seems resulting in\nbetter predictions than individual opinions and\nopinion pools with a few experts. It is quite robust in the\nsense that even if the included individual predictions\nare less accurate, averaging over all opinions still gives\nbetter (or equally good) predictions.\n3. Weighting expert opinions according to past\nperformance does not seem to significantly improve\nprediction accuracy of either LinOP or LogOP.\nComparing performance-weighted opinion pools with\nequally weighted opinion pools, we do not observe much\ndifference in terms of prediction accuracy. Since we\nonly use one performance-weighting method,\ncalculating the weights according to past accumulated quadratic\nscore that participants earned, this might due to the\nweighting method we chose.\n4. LogOP yields bolder predictions than LinOP.\nLogOP yields predictions that are closer to the\nextremes, 0 or 1.\nAn information markets is a self-organizing mechanism\nfor aggregating information and making predictions.\nCompared with opinion pools, it is less constrained by space\nand time, and can eliminate the efforts to identify experts\nand decide belief aggregation methods. But the advantages\ndo not compromise their prediction accuracy to any extent.\nOn the contrary, information markets can provide real-time\npredictions, which are hardly achievable through resorting\nto experts. In the future, we are interested in further\nexploring:\n\u2022 Performance comparison of information markets with\nother opinion pools and mathematical aggregation\nprocedures.\nIn this paper, we only compare information markets\nwith two simple opinion pools, linear and logarithmic.\nIt will be meaningful to investigate their relative\nprediction accuracy with other belief aggregation methods\nsuch as Bayesian approaches. There are also a number\nof theoretical expert algorithms with proven worst-case\nperformance bounds [10] whose average-case or\npractical performance would be instructive to investigate.\n\u2022 Whether defining expertise more narrowly can improve\npredictions of opinion pools.\nIn our analysis, we broadly treat participants of the\nProbabilityFootball contest as experts in all games. If\nwe define expertise more narrowly, selecting experts\nin certain football teams to predict games involving\nthese teams, will the predictions of opinion pools be\nmore accurate?\n\u2022 The possibility of combining information markets with\nother forecasting methods to achieve better prediction\naccuracy.\nChen, Fine, and Huberman [11] use an information\nmarket to determine the risk attitude of participants,\nand then perform a nonlinear aggregation of their\npredictions based on their risk attitudes. The nonlinear\naggregation mechanism is shown to outperform both\nthe market and the best individual participants. It\nis worthy of more attention whether information\nmarkets, as an alternative forecasting method, can be used\ntogether with other methods to improve our\npredictions.\n7. ACKNOWLEDGMENTS\nWe thank Brian Galebach, the owner and operator of the\nProbabilitySports and ProbabilityFootball websites, for\nproviding us with such unique and valuable data. We thank\nVarsha Dani, Lance Fortnow, Omid Madani, Sumit\nSang66\nhai, and the anonymous reviewers for useful insights and\npointers.\nThe authors acknowledge the support of The Penn State\neBusiness Research Center.\n8. REFERENCES\n[1] http://us.newsfutures.com\n[2] http://www.biz.uiowa.edu/iem/\n[3] http://www.hsx.com/\n[4] http://www.ideosphere.com/fx/\n[5] http://www.probabilityfootball.com/\n[6] http://www.probabilitysports.com/\n[7] http://www.tradesports.com/\n[8] A. H. Ashton and R. H. Ashton. Aggregating\nsubjective forecasts: Some empirical results.\nManagement Science, 31:1499-1508, 1985.\n[9] R. P. Batchelor and P. Dua. Forecaster diversity and\nthe benefits of combining forecasts. Management\nScience, 41:68-75, 1995.\n[10] N. Cesa-Bianchi, Y. Freund, D. Haussler, D. P.\nHelmbold, R. E. Schapire, and M. K. Warmuth. How\nto use expert advice. Journal of the ACM,\n44(3):427-485, 1997.\n[11] K. Chen, L. Fine, and B. Huberman. Predicting the\nfuture. 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Computer-Intensive Methods for\nTesting Hypotheses: An Introduction. Wiley and Sons,\nInc., New York, 1989.\n[33] D. M. Pennock, S. Lawrence, C. L. Giles, and F. A.\nNielsen. The real power of artificial markets. Science,\n291:987-988, February 2002.\n[34] D. M. Pennock, S. Lawrence, F. A. Nielsen, and C. L.\nGiles. Extracting collective probabilistic forecasts from\nweb games. In Proceedings of the 7th ACM SIGKDD\nInternational Conference on Knowledge Discovery and\nData Mining, pages 174-183, San Francisco, CA, 2001.\n[35] C. Plott and S. Sunder. Rational expectations and the\naggregation of diverse information in laboratory\nsecurity markets. Econometrica, 56:1085-118, 1988.\n[36] E. Servan-Schreiber, J. Wolfers, D. M. Pennock, and\nB. Galebach. Prediction markets: Does money\nmatter? Electronic Markets, 14(3):243-251, 2004.\n[37] M. Spann and B. Skiera. Internet-based virtual stock\nmarkets for business forecasting. Management Science,\n49(10):1310-1326, 2003.\n[38] M. West. 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{"name": "train_J-50", "title": "Communication Complexity of Common Voting Rules\u2217", "abstract": "We determine the communication complexity of the common voting rules. The rules (sorted by their communication complexity from low to high) are plurality, plurality with runoff, single transferable vote (STV), Condorcet, approval, Bucklin, cup, maximin, Borda, Copeland, and ranked pairs. For each rule, we first give a deterministic communication protocol and an upper bound on the number of bits communicated in it; then, we give a lower bound on (even the nondeterministic) communication requirements of the voting rule. The bounds match for all voting rules except STV and maximin.", "fulltext": "1. INTRODUCTION\nOne key factor in the practicality of any preference\naggregation rule is its communication burden. To successfully\naggregate the agents\" preferences, it is usually not necessary\nfor all the agents to report all of their preference information.\nClever protocols that elicit the agents\" preferences partially\nand sequentially have the potential to dramatically reduce\nthe required communication. This has at least the following\nadvantages:\n\u2022 It can make preference aggregation feasible in settings\nwhere the total amount of preference information is\ntoo large to communicate.\n\u2022 Even when communicating all the preference\ninformation is feasible, reducing the communication\nrequirements lessens the burden placed on the agents. This is\nespecially true when the agents, rather than knowing\nall their preferences in advance, need to invest effort\n(such as computation or information gathering) to\ndetermine their preferences [16].\n\u2022 It preserves (some of) the agents\" privacy.\nMost of the work on reducing the communication burden\nin preference aggregation has focused on resource allocation\nsettings such as combinatorial auctions, in which an\nauctioneer auctions off a number of (possibly distinct) items\nin a single event. Because in a combinatorial auction,\nbidders can have separate valuations for each of an\nexponential number of possible bundles of items, this is a setting\nin which reducing the communication burden is especially\ncrucial. This can be accomplished by supplementing the\nauctioneer with an elicitor that incrementally elicits parts\nof the bidders\" preferences on an as-needed basis, based on\nwhat the bidders have revealed about their preferences so\nfar, as suggested by Conen and Sandholm [5]. For example,\nthe elicitor can ask for a bidder\"s value for a specific bundle\n(value queries), which of two bundles the bidder prefers\n(order queries), which bundle he ranks kth or what the rank of\na given bundle is (rank queries), which bundle he would\npurchase given a particular vector of prices (demand queries),\netc.-until (at least) the final allocation can be determined.\nExperimentally, this yields drastic savings in preference\nrevelation [11]. Furthermore, if the agents\" valuation functions\nare drawn from certain natural subclasses, the elicitation\nproblem can be solved using only polynomially many queries\neven in the worst case [23, 4, 13, 18, 14]. For a review\nof preference elicitation in combinatorial auctions, see [17].\nAscending combinatorial auctions are a well-known special\nform of preference elicitation, where the elicitor asks demand\nqueries with increasing prices [15, 21, 1, 9]. Finally, resource\n78\nallocation problems have also been studied from a\ncommunication complexity viewpoint, thereby deriving lower bounds\non the required communication. For example, Nisan and\nSegal show that exponential communication is required even\nto obtain a surplus greater than that obtained by\nauctioning off all objects as a single bundle [14]. Segal also studies\nsocial choice rules in general, and shows that for a large\nclass of social choice rules, supporting budget sets must be\nrevealed such that if every agent prefers the same outcome\nin her budget set, this proves the optimality of that\noutcome. Segal then uses this characterization to prove bounds\non the communication required in resource allocation as well\nas matching settings [20].\nIn this paper, we will focus on the communication\nrequirements of a generally applicable subclass of social choice\nrules, commonly known as voting rules. In a voting setting,\nthere is a set of candidate outcomes over which the voters\nexpress their preferences by submitting a vote (typically,\na ranking of the candidates), and the winner (that is, the\nchosen outcome) is determined based on these votes. The\ncommunication required by voting rules can be large either\nbecause the number of voters is large (such as, for example,\nin national elections), or because the number of candidates\nis large (for example, the agents can vote over allocations of\na number of resources), or both. Prior work [8] has studied\nelicitation in voting, studying how computationally hard it\nis to decide whether a winner can be determined with the\ninformation elicited so far, as well as how hard it is to find the\noptimal sequence of queries given perfect suspicions about\nthe voters\" preferences. In addition, that paper discusses\nstrategic (game-theoretic) issues introduced by elicitation.\nIn contrast, in this paper, we are concerned with the\nworst-case number of bits that must be communicated to\nexecute a given voting rule, when nothing is known in advance\nabout the voters\" preferences. We determine the\ncommunication complexity of the common voting rules. For each rule,\nwe first give an upper bound on the (deterministic)\ncommunication complexity by providing a communication protocol\nfor it and analyzing how many bits need to be transmitted\nin this protocol. (Segal\"s results [20] do not apply to most\nvoting rules because most voting rules are not\nintersectionmonotonic (or even monotonic).1\n) For many of the voting\nrules under study, it turns out that one cannot do better\nthan simply letting each voter immediately communicate all\nher (potentially relevant) information. However, for some\nrules (such as plurality with runoff, STV and cup) there is\na straightforward multistage communication protocol that,\nwith some analysis, can be shown to significantly outperform\nthe immediate communication of all (potentially relevant)\ninformation. Finally, for some rules (such as the Condorcet\nand Bucklin rules), we need to introduce a more complex\ncommunication protocol to achieve the best possible upper\n1\nFor two of the rules that we study that are\nintersectionmonotonic, namely the approval and Condorcet rules,\nSegal\"s results can in fact be used to give alternative proofs\nof our lower bounds. We only give direct proofs for these\nrules here because 1) these direct proofs are among the\neasier ones in this paper, 2) the alternative proofs are nontrivial\neven given Segal\"s results, and 3) a space constraint applies.\nHowever, we hope to also include the alternative proofs in a\nlater version.\nbound. After obtaining the upper bounds, we show that\nthey are tight by giving matching lower bounds on (even the\nnondeterministic) communication complexity of each voting\nrule. There are two exceptions: STV, for which our upper\nand lower bounds are apart by a factor log m; and maximin,\nfor which our best deterministic upper bound is also a factor\nlog m above the (nondeterministic) lower bound, although\nwe give a nondeterministic upper bound that matches the\nlower bound.\n2. REVIEW OF VOTING RULES\nIn this section, we review the common voting rules that\nwe study in this paper. A voting rule2\nis a function\nmapping a vector of the n voters\" votes (i.e. preferences over\ncandidates) to one of the m candidates (the winner) in the\ncandidate set C. In some cases (such as the Condorcet rule),\nthe rule may also declare that no winner exists. We do not\nconcern ourselves with what happens in case of a tie\nbetween candidates (our lower bounds hold regardless of how\nties are broken, and the communication protocols used for\nour upper bounds do not attempt to break the ties). All of\nthe rules that we study are rank-based rules, which means\nthat a vote is defined as an ordering of the candidates (with\nthe exception of the plurality rule, for which a vote is a\nsingle candidate, and the approval rule, for which a vote is a\nsubset of the candidates).\nWe will consider the following voting rules. (For rules that\ndefine a score, the candidate with the highest score wins.)\n\u2022 scoring rules. Let \u03b1 = \u03b11, . . . , \u03b1m be a vector of\nintegers such that \u03b11 \u2265 \u03b12 . . . \u2265 \u03b1m. For each voter, a\ncandidate receives \u03b11 points if it is ranked first by the voter,\n\u03b12 if it is ranked second etc. The score s\u03b1 of a candidate\nis the total number of points the candidate receives. The\nBorda rule is the scoring rule with \u03b1 = m\u22121, m\u22122, . . . , 0 .\nThe plurality rule is the scoring rule with \u03b1 = 1, 0, . . . , 0 .\n\u2022 single transferable vote (STV). The rule proceeds through\na series of m \u2212 1 rounds. In each round, the candidate with\nthe lowest plurality score (that is, the least number of voters\nranking it first among the remaining candidates) is\neliminated (and each of the votes for that candidate transfer\nto the next remaining candidate in the order given in that\nvote). The winner is the last remaining candidate.\n\u2022 plurality with run-off. In this rule, a first round\neliminates all candidates except the two with the highest plurality\nscores. Votes are transferred to these as in the STV rule,\nand a second round determines the winner from these two.\n\u2022 approval. Each voter labels each candidate as either\napproved or disapproved. The candidate approved by the\ngreatest number of voters wins.\n\u2022 Condorcet. For any two candidates i and j, let N(i, j) be\nthe number of voters who prefer i to j. If there is a candidate\ni that is preferred to any other candidate by a majority of\nthe voters (that is, N(i, j) > N(j, i) for all j = i-that is, i\nwins every pairwise election), then candidate i wins.\n2\nThe term voting protocol is often used to describe the same\nconcept, but we seek to draw a sharp distinction between\nthe rule mapping preferences to outcomes, and the\ncommunication/elicitation protocol used to implement this rule.\n79\n\u2022 maximin (aka. Simpson). The maximin score of i is\ns(i) = minj=i N(i, j)-that is, i\"s worst performance in a\npairwise election. The candidate with the highest maximin\nscore wins.\n\u2022 Copeland. For any two distinct candidates i and j, let\nC(i, j) = 1 if N(i, j) > N(j, i), C(i, j) = 1/2 if N(i, j) =\nN(j, i) and C(i, j) = 0 if N(i, j) < N(j, i). The Copeland\nscore of candidate i is s(i) = j=i C(i, j).\n\u2022 cup (sequential binary comparisons). The cup rule is\ndefined by a balanced3\nbinary tree T with one leaf per\ncandidate, and an assignment of candidates to leaves (each leaf\ngets one candidate). Each non-leaf node is assigned the\nwinner of the pairwise election of the node\"s children; the\ncandidate assigned to the root wins.\n\u2022 Bucklin. For any candidate i and integer l, let B(i, l)\nbe the number of voters that rank candidate i among the\ntop l candidates. The winner is arg mini(min{l : B(i, l) >\nn/2}). That is, if we say that a voter approves her top\nl candidates, then we repeatedly increase l by 1 until some\ncandidate is approved by more than half the voters, and this\ncandidate is the winner.\n\u2022 ranked pairs. This rule determines an order on all\nthe candidates, and the winner is the candidate at the top\nof this order. Sort all ordered pairs of candidates (i, j) by\nN(i, j), the number of voters who prefer i to j. Starting\nwith the pair (i, j) with the highest N(i, j), we lock in\nthe result of their pairwise election (i j). Then, we move\nto the next pair, and we lock the result of their pairwise\nelection. We continue to lock every pairwise result that does\nnot contradict the ordering established so far.\nWe emphasize that these definitions of voting rules do not\nconcern themselves with how the votes are elicited from the\nvoters; all the voting rules, including those that are\nsuggestively defined in terms of rounds, are in actuality just\nfunctions mapping the vector of all the voters\" votes to a\nwinner. Nevertheless, there are always many different ways\nof eliciting the votes (or the relevant parts thereof) from the\nvoters. For example, in the plurality with runoff rule, one\nway of eliciting the votes is to ask every voter to declare her\nentire ordering of the candidates up front. Alternatively, we\ncan first ask every voter to declare only her most preferred\ncandidate; then, we will know the two candidates in the\nrunoff, and we can ask every voter which of these two\ncandidates she prefers. Thus, we distinguish between the voting\nrule (the mapping from vectors of votes to outcomes) and the\ncommunication protocol (which determines how the relevant\nparts of the votes are actually elicited from the voters). The\ngoal of this paper is to give efficient communication\nprotocols for the voting rules just defined, and to prove that there\ndo not exist any more efficient communication protocols.\nIt is interesting to note that the choice of the\ncommunication protocol may affect the strategic behavior of the voters.\nMultistage communication protocols may reveal to the\nvoters some information about how the other voters are voting\n(for example, in the two-stage communication protocol just\ngiven for plurality with runoff, in the second stage voters\n3\nBalanced means that the difference in depth between two\nleaves can be at most one.\nwill know which two candidates have the highest plurality\nscores). In general, when the voters receive such\ninformation, it may give them incentives to vote differently than\nthey would have in a single-stage communication protocol\nin which all voters declare their entire votes simultaneously.\nOf course, even the single-stage communication protocol is\nnot strategy-proof4\nfor any reasonable voting rule, by the\nGibbard-Satterthwaite theorem [10, 19]. However, this does\nnot mean that we should not be concerned about adding\neven more opportunities for strategic voting. In fact, many\nof the communication protocols introduced in this paper do\nintroduce additional opportunities for strategic voting, but\nwe do not have the space to discuss this here. (In prior\nwork [8], we do give an example where an elicitation\nprotocol for the approval voting rule introduces strategic voting,\nand give principles for designing elicitation protocols that\ndo not introduce strategic problems.)\nNow that we have reviewed voting rules, we move on to a\nbrief review of communication complexity theory.\n3. REVIEW OF SOME COMMUNICATION\nCOMPLEXITY THEORY\nIn this section, we review the basic model of a\ncommunication problem and the lower-bounding technique of\nconstructing a fooling set. (The basic model of a communication\nproblem is due to Yao [22]; for an overview see Kushilevitz\nand Nisan [12].)\nEach player 1 \u2264 i \u2264 n knows (only) input xi. Together,\nthey seek to compute f(x1, x2, . . . , xn). In a deterministic\nprotocol for computing f, in each stage, one of the players\nannounces (to all other players) a bit of information based\non her own input and the bits announced so far.\nEventually, the communication terminates and all players know\nf(x1, x2, . . . , xn). The goal is to minimize the worst-case\n(over all input vectors) number of bits sent. The\ndeterministic communication complexity of a problem is the\nworstcase number of bits sent in the best (correct) deterministic\nprotocol for it. In a nondeterministic protocol, the next\nbit to be sent can be chosen nondeterministically. For the\npurposes of this paper, we will consider a nondeterministic\nprotocol correct if for every input vector, there is some\nsequence of nondeterministic choices the players can make so\nthat the players know the value of f when the protocol\nterminates. The nondeterministic communication complexity\nof a problem is the worst-case number of bits sent in the\nbest (correct) nondeterministic protocol for it.\nWe are now ready to give the definition of a fooling set.\nDefinition 1. A fooling set is a set of input vectors\n{(x1\n1, x1\n2, . . . , x1\nn), (x2\n1, x2\n2, . . . , x2\nn), . . . , (xk\n1 , xk\n2 , . . . , xk\nn) such\nthat for any i, f(xi\n1, xi\n2, . . . , xi\nn) = f0 for some constant f0,\nbut for any i = j, there exists some vector (r1, r2, . . . , rn) \u2208\n{i, j}n\nsuch that f(xr1\n1 , xr2\n2 , . . . , xrn\nn ) = f0. (That is, we can\nmix the inputs from the two input vectors to obtain a vector\nwith a different function value.)\nIt is known that if a fooling set of size k exists, then log k\nis a lower bound on the communication complexity (even\nthe nondeterministic communication complexity) [12].\n4\nA strategy-proof protocol is one in which it is in the players\"\nbest interest to report their preferences truthfully.\n80\nFor the purposes of this paper, f is the voting rule that\nmaps the votes to the winning candidate, and xi is voter\ni\"s vote (the information that the voting rule would require\nfrom the voter if there were no possibility of multistage\ncommunication-i.e. the most preferred candidate\n(plurality), the approved candidates (approval), or the ranking of\nall the candidates (all other protocols)). However, when we\nderive our lower bounds, f will only signify whether a\ndistinguished candidate a wins. (That is, f is 1 if a wins, and\n0 otherwise.) This will strengthen our lower bound results\n(because it implies that even finding out whether one given\ncandidate wins is hard).5\nThus, a fooling set in our\ncontext is a set of vectors of votes so that a wins (does not win)\nwith each of them; but for any two different vote vectors in\nthe set, there is a way of taking some voters\" votes from the\nfirst vector and the others\" votes from the second vector, so\nthat a does not win (wins).\nTo simplify the proofs of our lower bounds, we make\nassumptions such as the number of voters n is odd in many\nof these proofs. Therefore, technically, we do not prove the\nlower bound for (number of candidates, number of voters)\npairs (m, n) that do not satisfy these assumptions (for\nexample, if we make the above assumption, then we technically\ndo not prove the lower bound for any pair (m, n) in which\nn is even). Nevertheless, we always prove the lower bound\nfor a representative set of (m, n) pairs. For example, for\nevery one of our lower bounds it is the case that for infinitely\nmany values of m, there are infinitely many values of n such\nthat the lower bound is proved for the pair (m, n).\n4. RESULTS\nWe are now ready to present our results. For each voting\nrule, we first give a deterministic communication protocol\nfor determining the winner to establish an upper bound.\nThen, we give a lower bound on the nondeterministic\ncommunication complexity (even on the complexity of deciding\nwhether a given candidate wins, which is an easier\nquestion). The lower bounds match the upper bounds in all but\ntwo cases: the STV rule (upper bound O(n(log m)2\n); lower\nbound \u2126(n log m)) and the maximin rule (upper bound\nO(nm log m), although we do give a nondeterministic\nprotocol that is O(nm); lower bound \u2126(nm)).\nWhen we discuss a voting rule in which the voters rank the\ncandidates, we will represent a ranking in which candidate c1\nis ranked first, c2 is ranked second, etc. as c1 c2 . . . cm.\n5\nOne possible concern is that in the case where ties are\npossible, it may require much communication to verify whether\na specific candidate a is among the winners, but little\ncommunication to produce one of the winners. However, all the\nfooling sets we use in the proofs have the property that if\na wins, then a is the unique winner. Therefore, in these\nfooling sets, if one knows any one of the winners, then one\nknows whether a is a winner. Thus, computing one of the\nwinners requires at least as much communication as\nverifying whether a is among the winners. In general, when a\ncommunication problem allows multiple correct answers for\na given vector of inputs, this is known as computing a\nrelation rather than a function [12]. However, as per the above,\nwe can restrict our attention to a subset of the domain where\nthe voting rule truly is a (single-valued) function, and hence\nlower bounding techniques for functions rather than\nrelations will suffice.\nSometimes for the purposes of a proof the internal ranking\nof a subset of the candidates does not matter, and in this\ncase we will not specify it. For example, if S = {c2, c3},\nthen c1 S c4 indicates that either the ranking c1\nc2 c3 c4 or the ranking c1 c3 c2 c4 can be used\nfor the proof.\nWe first give a universal upper bound.\nTheorem 1. The deterministic communication\ncomplexity of any rank-based voting rule is O(nm log m).\nProof. This bound is achieved by simply having\neveryone communicate their entire ordering of the candidates\n(indicating the rank of an individual candidate requires only\nO(log m) bits, so each of the n voters can simply indicate\nthe rank of each of the m candidates).\nThe next lemma will be useful in a few of our proofs.\nLemma 1. If m divides n, then log(n!)\u2212m log((n/m)!) \u2265\nn(log m \u2212 1)/2.\nProof. If n/m = 1 (that is, n = m), then this\nexpression simplifies to log(n!). We have log(n!) =\nn\ni=1\nlog i \u2265\nn\nx=1\nlog(i)dx, which, using integration by parts, is equal to\nn log n \u2212 (n \u2212 1) > n(log n \u2212 1) = n(log m \u2212 1) > n(log m \u2212\n1)/2. So, we can assume that n/m \u2265 2. We observe that\nlog(n!) =\nn\ni=1\nlog i =\nn/m\u22121\ni=0\nm\nj=1\nlog(im+j) \u2265\nn/m\u22121\ni=1\nm\nj=1\nlog(im)\n= m\nn/m\u22121\ni=1\nlog(im), and that m log((n/m)!) = m\nn/m\ni=1\nlog(i).\nTherefore, log(n!) \u2212 m log((n/m)!) \u2265 m\nn/m\u22121\ni=1\nlog(im) \u2212\nm\nn/m\ni=1\nlog(i) = m((\nn/m\u22121\ni=1\nlog(im/i))\u2212log(n/m)) = m((n/m\u2212\n1) log m\u2212log n+log m) = n log m\u2212m log n. Now, using the\nfact that n/m \u2265 2, we have m log n = n(m/n) log m(n/m) =\nn(m/n)(log m + log(n/m)) \u2264 n(1/2)(log m + log 2). Thus,\nlog(n!) \u2212 m log((n/m)!) \u2265 n log m \u2212 m log n \u2265 n log m \u2212\nn(1/2)(log m + log 2) = n(log m \u2212 1)/2.\nTheorem 2. The deterministic communication\ncomplexity of the plurality rule is O(n log m).\nProof. Indicating one of the candidates requires only\nO(log m) bits, so each voter can simply indicate her most\npreferred candidate.\nTheorem 3. The nondeterministic communication\ncomplexity of the plurality rule is \u2126(n log m) (even to decide\nwhether a given candidate a wins).\nProof. We will exhibit a fooling set of size n !\n(( n\nm\n)!)m\nwhere\nn = (n\u22121)/2. Taking the logarithm of this gives log(n !)\u2212\nm log((n /m)!), so the result follows from Lemma 1. The\nfooling set will consist of all vectors of votes satisfying the\nfollowing constraints:\n\u2022 For any 1 \u2264 i \u2264 n , voters 2i\u22121 and 2i vote the same.\n81\n\u2022 Every candidate receives equally many votes from the\nfirst 2n = n \u2212 1 voters.\n\u2022 The last voter (voter n) votes for a.\nCandidate a wins with each one of these vote vectors\nbecause of the extra vote for a from the last voter. Given that\nm divides n , let us see how many vote vectors there are in\nthe fooling set. We need to distribute n voter pairs evenly\nover m candidates, for a total of n /m voter pairs per\ncandidate; and there are precisely n !\n(( n\nm\n)!)m\nways of doing this.6\nAll that remains to show is that for any two distinct vectors\nof votes in the fooling set, we can let each of the voters vote\naccording to one of these two vectors in such a way that a\nloses. Let i be a number such that the two vote vectors\ndisagree on the candidate for which voters 2i \u2212 1 and 2i vote.\nWithout loss of generality, suppose that in the first vote\nvector, these voters do not vote for a (but for some other\ncandidate, b, instead). Now, construct a new vote vector by\ntaking votes 2i \u2212 1 and 2i from the first vote vector, and\nthe remaining votes from the second vote vector. Then, b\nreceives 2n /m + 2 votes in this newly constructed vote\nvector, whereas a receives at most 2n /m+1 votes. So, a is not\nthe winner in the newly constructed vote vector, and hence\nwe have a correct fooling set.\nTheorem 4. The deterministic communication\ncomplexity of the plurality with runoff rule is O(n log m).\nProof. First, let every voter indicate her most preferred\ncandidate using log m bits. After this, the two candidates\nin the runoff are known, and each voter can indicate which\none she prefers using a single additional bit.\nTheorem 5. The nondeterministic communication\ncomplexity of the plurality with runoff rule is \u2126(n log m) (even\nto decide whether a given candidate a wins).\nProof. We will exhibit a fooling set of size n !\n(( n\nm\n)!)m\nwhere m = m/2 and n = (n \u2212 2)/4. Taking the\nlogarithm of this gives log(n !) \u2212 m log((n /m )!), so the result\nfollows from Lemma 1. Divide the candidates into m pairs:\n(c1, d1), (c2, d2), . . . , (cm , dm ) where c1 = a and d1 = b.\nThe fooling set will consist of all vectors of votes satisfying\nthe following constraints:\n\u2022 For any 1 \u2264 i \u2264 n , voters 4i \u2212 3 and 4i \u2212 2 rank\nthe candidates ck(i) a C \u2212 {a, ck(i)}, for some\ncandidate ck(i). (If ck(i) = a then the vote is simply\na C \u2212 {a}.)\n\u2022 For any 1 \u2264 i \u2264 n , voters 4i \u2212 1 and 4i rank the\ncandidates dk(i) a C \u2212 {a, dk(i)} (that is, their most\npreferred candidate is the candidate that is paired with\nthe candidate that the previous two voters vote for).\n6\nAn intuitive proof of this is the following. We can count\nthe number of permutations of n elements as follows. First,\ndivide the elements into m buckets of size n /m, so that if\nx is placed in a lower-indexed bucket than y, then x will\nbe indexed lower in the eventual permutation. Then, decide\non the permutation within each bucket (for which there are\n(n /m)! choices per bucket). It follows that n ! equals the\nnumber of ways to divide n elements into m buckets of size\nn /m, times ((n /m)!)m\n.\n\u2022 Every candidate is ranked at the top of equally many\nof the first 4n = n \u2212 2 votes.\n\u2022 Voter 4n +1 = n\u22121 ranks the candidates a C\u2212{a}.\n\u2022 Voter 4n + 2 = n ranks the candidates b C \u2212 {b}.\nCandidate a wins with each one of these vote vectors:\nbecause of the last two votes, candidates a and b are one vote\nahead of all the other candidates and continue to the runoff,\nand at this point all the votes that had another candidate\nranked at the top transfer to a, so that a wins the runoff.\nGiven that m divides n , let us see how many vote vectors\nthere are in the fooling set. We need to distribute n groups\nof four voters evenly over the m pairs of candidates, and\n(as in the proof of Theorem 3) there are n !\n(( n\nm\n)!)m\nways of\ndoing this. All that remains to show is that for any two\ndistinct vectors of votes in the fooling set, we can let each\nof the voters vote according to one of these two vectors in\nsuch a way that a loses. Let i be a number such that ck(i) is\nnot the same in both of these two vote vectors, that is, c1\nk(i)\n(ck(i) in the first vote vector) is not equal to c2\nk(i) (ck(i) in\nthe second vote vector). Without loss of generality, suppose\nc1\nk(i) = a. Now, construct a new vote vector by taking votes\n4i \u2212 3, 4i \u2212 2, 4i \u2212 1, 4i from the first vote vector, and the\nremaining votes from the second vote vector. In this newly\nconstructed vote vector, c1\nk(i) and d1\nk(i) each receive 4n /m+2\nvotes in the first round, whereas a receives at most 4n /m+1\nvotes. So, a does not continue to the runoff in the newly\nconstructed vote vector, and hence we have a correct fooling\nset.\nTheorem 6. The nondeterministic communication\ncomplexity of the Borda rule is \u2126(nm log m) (even to decide\nwhether a given candidate a wins).\nProof. We will exhibit a fooling set of size (m !)n\nwhere\nm = m\u22122 and n = (n\u22122)/4. This will prove the theorem\nbecause m ! is \u2126(m log m), so that log((m !)n\n) = n log(m !)\nis \u2126(nm log m). For every vector (\u03c01, \u03c02, . . . , \u03c0n ) consisting\nof n orderings of all candidates other than a and another\nfixed candidate b (technically, the orderings take the form of\na one-to-one function \u03c0i : {1, 2, . . . , m } \u2192 C \u2212 {a, b} with\n\u03c0i(j) = c indicating that candidate c is the jth in the order\nrepresented by \u03c0i), let the following vector of votes be an\nelement of the fooling set:\n\u2022 For 1 \u2264 i \u2264 n , let voters 4i \u2212 3 and 4i \u2212 2 rank the\ncandidates a b \u03c0i(1) \u03c0i(2) . . . \u03c0i(m ).\n\u2022 For 1 \u2264 i \u2264 n , let voters 4i \u2212 1 and 4i rank the\ncandidates \u03c0i(m ) \u03c0i(m \u2212 1) . . . \u03c0i(1) b a.\n\u2022 Let voter 4n + 1 = n \u2212 1 rank the candidates a\nb \u03c00(1) \u03c00(2) . . . \u03c00(m ) (where \u03c00 is an\narbitrary order of the candidates other than a and b\nwhich is the same for every element of the fooling set).\n\u2022 Let voter 4n + 2 = n rank the candidates \u03c00(m )\n\u03c00(m \u2212 1) . . . \u03c00(1) a b.\nWe observe that this fooling set has size (m !)n\n, and that\ncandidate a wins in each vector of votes in the fooling set (to\n82\nsee why, we observe that for any 1 \u2264 i \u2264 n , votes 4i\u22123 and\n4i \u2212 2 rank the candidates in the exact opposite way from\nvotes 4i \u2212 1 and 4i, which under the Borda rule means they\ncancel out; and the last two votes give one more point to a\nthan to any other candidate-besides b who gets two fewer\npoints than a). All that remains to show is that for any two\ndistinct vectors of votes in the fooling set, we can let each of\nthe voters vote according to one of these two vectors in such\na way that a loses. Let the first vote vector correspond to\nthe vector (\u03c01\n1, \u03c01\n2, . . . , \u03c01\nn ), and let the second vote vector\ncorrespond to the vector (\u03c02\n1, \u03c02\n2, . . . , \u03c02\nn ). For some i, we\nmust have \u03c01\ni = \u03c02\ni , so that for some candidate c /\u2208 {a, b},\n(\u03c01\ni )\u22121\n(c) < (\u03c02\ni )\u22121\n(c) (that is, c is ranked higher in \u03c01\ni than\nin \u03c02\ni ). Now, construct a new vote vector by taking votes\n4i\u22123 and 4i\u22122 from the first vote vector, and the remaining\nvotes from the second vote vector. a\"s Borda score remains\nunchanged. However, because c is ranked higher in \u03c01\ni than\nin \u03c02\ni , c receives at least 2 more points from votes 4i\u22123 and\n4i \u2212 2 in the newly constructed vote vector than it did in\nthe second vote vector. It follows that c has a higher Borda\nscore than a in the newly constructed vote vector. So, a is\nnot the winner in the newly constructed vote vector, and\nhence we have a correct fooling set.\nTheorem 7. The nondeterministic communication\ncomplexity of the Copeland rule is \u2126(nm log m) (even to decide\nwhether a given candidate a wins).\nProof. We will exhibit a fooling set of size (m !)n\nwhere\nm = (m \u2212 2)/2 and n = (n \u2212 2)/2. This will prove the\ntheorem because m ! is \u2126(m log m), so that log((m !)n\n) =\nn log(m !) is \u2126(nm log m). We write the set of candidates\nas the following disjoint union: C = {a, b} \u222a L \u222a R where\nL = {l1, l2, . . . , lm } and R = {r1, r2, . . . , rm }. For every\nvector (\u03c01, \u03c02, . . . , \u03c0n ) consisting of n permutations of the\nintegers 1 through m (\u03c0i : {1, 2, . . . , m } \u2192 {1, 2, . . . , m }),\nlet the following vector of votes be an element of the fooling\nset:\n\u2022 For 1 \u2264 i \u2264 n , let voter 2i \u2212 1 rank the candidates\na b l\u03c0i(1) r\u03c0i(1) l\u03c0i(2) r\u03c0i(2) . . .\nl\u03c0i(m ) r\u03c0i(m ).\n\u2022 For 1 \u2264 i \u2264 n , let voter 2i rank the candidates\nr\u03c0i(m ) l\u03c0i(m ) r\u03c0i(m \u22121) l\u03c0i(m \u22121) . . .\nr\u03c0i(1) l\u03c0i(1) b a.\n\u2022 Let voter n \u2212 1 = 2n + 1 rank the candidates a b\nl1 r1 l2 r2 . . . lm rm .\n\u2022 Let voter n = 2n +2 rank the candidates rm lm\nrm \u22121 lm \u22121 . . . r1 l1 a b.\nWe observe that this fooling set has size (m !)n\n, and\nthat candidate a wins in each vector of votes in the\nfooling set (every pair of candidates is tied in their pairwise\nelection, with the exception that a defeats b, so that a wins\nthe election by half a point). All that remains to show is\nthat for any two distinct vectors of votes in the fooling\nset, we can let each of the voters vote according to one\nof these two vectors in such a way that a loses. Let the\nfirst vote vector correspond to the vector (\u03c01\n1, \u03c01\n2, . . . , \u03c01\nn ),\nand let the second vote vector correspond to the vector\n(\u03c02\n1, \u03c02\n2, . . . , \u03c02\nn ). For some i, we must have \u03c01\ni = \u03c02\ni , so that\nfor some j \u2208 {1, 2, . . . , m }, we have (\u03c01\ni )\u22121\n(j) < (\u03c02\ni )\u22121\n(j).\nNow, construct a new vote vector by taking vote 2i\u22121 from\nthe first vote vector, and the remaining votes from the\nsecond vote vector. a\"s Copeland score remains unchanged. Let\nus consider the score of lj. We first observe that the rank of\nlj in vote 2i \u2212 1 in the newly constructed vote vector is at\nleast 2 higher than it was in the second vote vector, because\n(\u03c01\ni )\u22121\n(j) < (\u03c02\ni )\u22121\n(j). Let D1\n(lj) be the set of candidates\nin L \u222a R that voter 2i \u2212 1 ranked lower than lj in the first\nvote vector (D1\n(lj) = {c \u2208 L \u222a R : lj\n1\n2i\u22121 c}), and let\nD2\n(lj) be the set of candidates in L \u222a R that voter 2i \u2212 1\nranked lower than lj in the second vote vector (D2\n(lj) =\n{c \u2208 L \u222a R : lj\n2\n2i\u22121 c}). Then, it follows that in the\nnewly constructed vote vector, lj defeats all the candidates\nin D1\n(lj) \u2212 D2\n(lj) in their pairwise elections (because lj\nreceives an extra vote in each one of these pairwise elections\nrelative to the second vote vector), and loses to all the\ncandidates in D2\n(lj) \u2212 D1\n(lj) (because lj loses a vote in each one\nof these pairwise elections relative to the second vote\nvector), and ties with everyone else. But |D1\n(lj)|\u2212|D2\n(lj)| \u2265 2,\nand hence |D1\n(lj) \u2212 D2\n(lj)| \u2212 |D2\n(lj) \u2212 D1\n(lj)| \u2265 2. Hence,\nin the newly constructed vote vector, lj has at least two\nmore pairwise wins than pairwise losses, and therefore has\nat least 1 more point than if lj had tied all its pairwise\nelections. Thus, lj has a higher Copeland score than a in the\nnewly constructed vote vector. So, a is not the winner in the\nnewly constructed vote vector, and hence we have a correct\nfooling set.\nTheorem 8. The nondeterministic communication\ncomplexity of the maximin rule is O(nm).\nProof. The nondeterministic protocol will guess which\ncandidate w is the winner, and, for each other candidate\nc, which candidate o(c) is the candidate against whom c\nreceives its lowest score in a pairwise election. Then, let\nevery voter communicate the following:\n\u2022 for each candidate c = w, whether she prefers c to w;\n\u2022 for each candidate c = w, whether she prefers c to o(c).\nWe observe that this requires the communication of 2n(m\u2212\n1) bits. If the guesses were correct, then, letting N(d, e) be\nthe number of voters preferring candidate d to candidate e,\nwe should have N(c, o(c)) < N(w, c ) for any c = w, c = w,\nwhich will prove that w wins the election.\nTheorem 9. The nondeterministic communication\ncomplexity of the maximin rule is \u2126(nm) (even to decide whether\na given candidate a wins).\nProof. We will exhibit a fooling set of size 2n m\nwhere\nm = m \u2212 2 and n = (n \u2212 1)/4. Let b be a candidate other\nthan a. For every vector (S1, S2, . . . , Sn ) consisting of n\nsubsets Si \u2286 C \u2212 {a, b}, let the following vector of votes be\nan element of the fooling set:\n\u2022 For 1 \u2264 i \u2264 n , let voters 4i \u2212 3 and 4i \u2212 2 rank the\ncandidates Si a C \u2212 (Si \u222a {a, b}) b.\n\u2022 For 1 \u2264 i \u2264 n , let voters 4i \u2212 1 and 4i rank the\ncandidates b C \u2212 (Si \u222a {a, b}) a Si.\n83\n\u2022 Let voter 4n + 1 = n rank the candidates a b\nC \u2212 {a, b}.\nWe observe that this fooling set has size (2m\n)n\n= 2n m\n,\nand that candidate a wins in each vector of votes in the\nfooling set (in every one of a\"s pairwise elections, a is ranked\nhigher than its opponent by 2n +1 = (n+1)/2 > n/2 votes).\nAll that remains to show is that for any two distinct vectors\nof votes in the fooling set, we can let each of the voters vote\naccording to one of these two vectors in such a way that\na loses. Let the first vote vector correspond to the vector\n(S1\n1 , S1\n2 , . . . , S1\nn ), and let the second vote vector correspond\nto the vector (S2\n1 , S2\n2 , . . . , S2\nn ). For some i, we must have\nS1\ni = S2\ni , so that either S1\ni S2\ni or S2\ni S1\ni . Without loss\nof generality, suppose S1\ni S2\ni , and let c be some candidate\nin S1\ni \u2212 S2\ni . Now, construct a new vote vector by taking\nvotes 4i \u2212 3 and 4i \u2212 2 from the first vote vector, and the\nremaining votes from the second vote vector. In this newly\nconstructed vote vector, a is ranked higher than c by only\n2n \u22121 voters, for the following reason. Whereas voters 4i\u22123\nand 4i \u2212 2 do not rank c higher than a in the second vote\nvector (because c /\u2208 S2\ni ), voters 4i \u2212 3 and 4i \u2212 2 do rank\nc higher than a in the first vote vector (because c \u2208 S1\ni ).\nMoreover, in every one of b\"s pairwise elections, b is ranked\nhigher than its opponent by at least 2n voters. So, a has\na lower maximin score than b, therefore a is not the winner\nin the newly constructed vote vector, and hence we have a\ncorrect fooling set.\nTheorem 10. The deterministic communication\ncomplexity of the STV rule is O(n(log m)2\n).\nProof. Consider the following communication protocol.\nLet each voter first announce her most preferred candidate\n(O(n log m) communication). In the remaining rounds, we\nwill keep track of each voter\"s most preferred candidate\namong the remaining candidates, which will be enough to\nimplement the rule. When candidate c is eliminated, let\neach of the voters whose most preferred candidate among the\nremaining candidates was c announce their most preferred\ncandidate among the candidates remaining after c\"s\nelimination. If candidate c was the ith candidate to be eliminated\n(that is, there were m \u2212 i + 1 candidates remaining before\nc\"s elimination), it follows that at most n/(m \u2212 i + 1) voters\nhad candidate c as their most preferred candidate among\nthe remaining candidates, and thus the number of bits to be\ncommunicated after the elimination of the ith candidate is\nO((n/(m\u2212i+1)) log m).7\nThus, the total communication in\nthis communication protocol is O(n log m +\nm\u22121\ni=1\n(n/(m \u2212 i +\n1)) log m). Of course,\nm\u22121\ni=1\n1/(m \u2212 i + 1) =\nm\ni=2\n1/i, which is\nO(log m). Substituting into the previous expression, we find\nthat the communication complexity is O(n(log m)2\n).\nTheorem 11. The nondeterministic communication\ncomplexity of the STV rule is \u2126(n log m) (even to decide whether\na given candidate a wins).\nProof. We omit this proof because of space constraint.\n7\nActually, O((n/(m \u2212 i + 1)) log(m \u2212 i + 1)) is also correct,\nbut it will not improve the bound.\nTheorem 12. The deterministic communication\ncomplexity of the approval rule is O(nm).\nProof. Approving or disapproving of a candidate requires\nonly one bit of information, so every voter can simply\napprove or disapprove of every candidate for a total\ncommunication of nm bits.\nTheorem 13. The nondeterministic communication\ncomplexity of the approval rule is \u2126(nm) (even to decide whether\na given candidate a wins).\nProof. We will exhibit a fooling set of size 2n m\nwhere\nm = m \u2212 1 and n = (n \u2212 1)/4. For every vector\n(S1, S2, . . . , Sn ) consisting of n subsets Si \u2286 C \u2212 {a}, let\nthe following vector of votes be an element of the fooling\nset:\n\u2022 For 1 \u2264 i \u2264 n , let voters 4i \u2212 3 and 4i \u2212 2 approve\nSi \u222a {a}.\n\u2022 For 1 \u2264 i \u2264 n , let voters 4i \u2212 1 and 4i approve C \u2212\n(Si \u222a {a}).\n\u2022 Let voter 4n + 1 = n approve {a}.\nWe observe that this fooling set has size (2m\n)n\n= 2n m\n,\nand that candidate a wins in each vector of votes in the\nfooling set (a is approved by 2n + 1 voters, whereas each\nother candidate is approved by only 2n voters). All that\nremains to show is that for any two distinct vectors of votes\nin the fooling set, we can let each of the voters vote\naccording to one of these two vectors in such a way that a\nloses. Let the first vote vector correspond to the vector\n(S1\n1 , S1\n2 , . . . , S1\nn ), and let the second vote vector correspond\nto the vector (S2\n1 , S2\n2 , . . . , S2\nn ). For some i, we must have\nS1\ni = S2\ni , so that either S1\ni S2\ni or S2\ni S1\ni . Without loss\nof generality, suppose S1\ni S2\ni , and let b be some candidate\nin S1\ni \u2212 S2\ni . Now, construct a new vote vector by taking\nvotes 4i \u2212 3 and 4i \u2212 2 from the first vote vector, and the\nremaining votes from the second vote vector. In this newly\nconstructed vote vector, a is still approved by 2n + 1 votes.\nHowever, b is approved by 2n + 2 votes, for the following\nreason. Whereas voters 4i\u22123 and 4i\u22122 do not approve b in\nthe second vote vector (because b /\u2208 S2\ni ), voters 4i \u2212 3 and\n4i \u2212 2 do approve b in the first vote vector (because b \u2208 S1\ni ).\nIt follows that b\"s score in the newly constructed vote vector\nis b\"s score in the second vote vector (2n ), plus two. So, a\nis not the winner in the newly constructed vote vector, and\nhence we have a correct fooling set.\nInterestingly, an \u2126(m) lower bound can be obtained even\nfor the problem of finding a candidate that is approved by\nmore than one voter [20].\nTheorem 14. The deterministic communication\ncomplexity of the Condorcet rule is O(nm).\nProof. We maintain a set of active candidates S which\nis initialized to C. At each stage, we choose two of the active\ncandidates (say, the two candidates with the lowest indices),\nand we let each voter communicate which of the two\ncandidates she prefers. (Such a stage requires the communication\nof n bits, one per voter.) The candidate preferred by fewer\n84\nvoters (the loser of the pairwise election) is removed from\nS. (If the pairwise election is tied, both candidates are\nremoved.) After at most m \u2212 1 iterations, only one candidate\nis left (or zero candidates are left, in which case there is no\nCondorcet winner). Let a be the remaining candidate. To\nfind out whether candidate a is the Condorcet winner, let\neach voter communicate, for every candidate c = a, whether\nshe prefers a to c. (This requires the communication of at\nmost n(m \u2212 1) bits.) This is enough to establish whether\na won each of its pairwise elections (and thus, whether a is\nthe Condorcet winner).\nTheorem 15. The nondeterministic communication\ncomplexity of the Condorcet rule is \u2126(nm) (even to decide whether\na given candidate a wins).\nProof. We will exhibit a fooling set of size 2n m\nwhere\nm = m \u2212 1 and n = (n \u2212 1)/2. For every vector\n(S1, S2, . . . , Sn ) consisting of n subsets Si \u2286 C \u2212 {a}, let\nthe following vector of votes be an element of the fooling\nset:\n\u2022 For 1 \u2264 i \u2264 n , let voter 2i \u2212 1 rank the candidates\nSi a C \u2212 Si.\n\u2022 For 1 \u2264 i \u2264 n , let voter 2i rank the candidates C \u2212\nSi a Si.\n\u2022 Let voter 2n +1 = n rank the candidates a C \u2212{a}.\nWe observe that this fooling set has size (2m\n)n\n= 2n m\n,\nand that candidate a wins in each vector of votes in the\nfooling set (a wins each of its pairwise elections by a single\nvote). All that remains to show is that for any two distinct\nvectors of votes in the fooling set, we can let each of the\nvoters vote according to one of these two vectors in such a\nway that a loses. Let the first vote vector correspond to\nthe vector (S1\n1 , S1\n2 , . . . , S1\nn ), and let the second vote vector\ncorrespond to the vector (S2\n1 , S2\n2 , . . . , S2\nn ). For some i, we\nmust have S1\ni = S2\ni , so that either S1\ni S2\ni or S2\ni S1\ni .\nWithout loss of generality, suppose S1\ni S2\ni , and let b be\nsome candidate in S1\ni \u2212 S2\ni . Now, construct a new vote\nvector by taking vote 2i \u2212 1 from the first vote vector, and\nthe remaining votes from the second vote vector. In this\nnewly constructed vote vector, b wins its pairwise election\nagainst a by one vote (vote 2i \u2212 1 ranks b above a in the\nnewly constructed vote vector because b \u2208 S1\ni , whereas in\nthe second vote vector vote 2i \u2212 1 ranked a above b because\nb /\u2208 S2\ni ). So, a is not the Condorcet winner in the newly\nconstructed vote vector, and hence we have a correct fooling\nset.\nTheorem 16. The deterministic communication\ncomplexity of the cup rule is O(nm).\nProof. Consider the following simple communication\nprotocol. First, let all the voters communicate, for every one of\nthe matchups in the first round, which of its two candidates\nthey prefer. After this, the matchups for the second round\nare known, so let all the voters communicate which\ncandidate they prefer in each matchup in the second round-etc.\nBecause communicating which of two candidates is preferred\nrequires only one bit per voter, and because there are only\nm \u2212 1 matchups in total, this communication protocol\nrequires O(nm) communication.\nTheorem 17. The nondeterministic communication\ncomplexity of the cup rule is \u2126(nm) (even to decide whether a\ngiven candidate a wins).\nProof. We will exhibit a fooling set of size 2n m\nwhere\nm = (m \u2212 1)/2 and n = (n \u2212 7)/2. Given that m + 1 is a\npower of 2, so that one candidate gets a bye (that is, does not\nface an opponent) in the first round, let a be the candidate\nwith the bye. Of the m first-round matchups, let lj denote\nthe one (left) candidate in the jth matchup, and let rj be\nthe other (right) candidate. Let L = {lj : 1 \u2264 j \u2264 m }\nand R = {rj : 1 \u2264 j \u2264 m }, so that C = L \u222a R \u222a {a}.\n.\n.\n.\n.\n.\n.\n. . .\nl r l r l r\na\nm\"1 1 2 2 m\"\nFigure 1: The schedule for the cup rule used in the\nproof of Theorem 17.\nFor every vector (S1, S2, . . . , Sn ) consisting of n subsets\nSi \u2286 R, let the following vector of votes be an element of\nthe fooling set:\n\u2022 For 1 \u2264 i \u2264 n , let voter 2i \u2212 1 rank the candidates\nSi L a R \u2212 Si.\n\u2022 For 1 \u2264 i \u2264 n , let voter 2i rank the candidates R \u2212\nSi L a Si.\n\u2022 Let voters 2n +1 = n\u22126, 2n +2 = n\u22125, 2n +3 = n\u22124\nrank the candidates L a R.\n\u2022 Let voters 2n + 4 = n \u2212 3, 2n + 5 = n \u2212 2 rank the\ncandidates a r1 l1 r2 l2 . . . rm lm .\n\u2022 Let voters 2n + 6 = n \u2212 1, 2n + 7 = n rank the\ncandidates rm lm rm \u22121 lm \u22121 . . . r1 l1 a.\nWe observe that this fooling set has size (2m\n)n\n= 2n m\n.\nAlso, candidate a wins in each vector of votes in the fooling\nset, for the following reasons. Each candidate rj defeats its\nopponent lj in the first round. (For any 1 \u2264 i \u2264 n , the\nnet effect of votes 2i \u2212 1 and 2i on the pairwise election\nbetween rj and lj is zero; votes n \u2212 6, n \u2212 5, n \u2212 4 prefer\nlj to rj, but votes n \u2212 3, n \u2212 2, n \u2212 1, n all prefer rj to lj.)\nMoreover, a defeats every rj in their pairwise election. (For\nany 1 \u2264 i \u2264 n , the net effect of votes 2i \u2212 1 and 2i on the\npairwise election between a and rj is zero; votes n \u2212 1, n\nprefer rj to a, but votes n \u2212 6, n \u2212 5, n \u2212 4, n \u2212 3, n \u2212 2 all\nprefer a to rj.) It follows that a will defeat all the candidates\nthat it faces.\nAll that remains to show is that for any two distinct\nvectors of votes in the fooling set, we can let each of the voters\nvote according to one of these two vectors in such a way that\na loses. Let the first vote vector correspond to the vector\n85\n(S1\n1 , S1\n2 , . . . , S1\nn ), and let the second vote vector correspond\nto the vector (S2\n1 , S2\n2 , . . . , S2\nn ). For some i, we must have\nS1\ni = S2\ni , so that either S1\ni S2\ni or S2\ni S1\ni . Without\nloss of generality, suppose S1\ni S2\ni , and let rj be some\ncandidate in S1\ni \u2212 S2\ni . Now, construct a new vote vector by\ntaking vote 2i from the first vote vector, and the remaining\nvotes from the second vote vector. We note that, whereas\nin the second vote vector vote 2i preferred rj to lj (because\nrj \u2208 R\u2212S2\ni ), in the newly constructed vote vector this is no\nlonger the case (because rj \u2208 S1\ni ). It follows that, whereas\nin the second vote vector, rj defeated lj in the first round\nby one vote, in the newly constructed vote vector, lj\ndefeats rj in the first round. Thus, at least one lj advances\nto the second round after defeating its opponent rj. Now,\nwe observe that in the newly constructed vote vector, any\nlk wins its pairwise election against any rq with q = k. This\nis because among the first 2n votes, at least n \u2212 1 prefer lk\nto rq; votes n \u2212 6, n \u2212 5, n \u2212 4 prefer lk to rq; and, because\nq = k, either votes n \u2212 3, n \u2212 2 prefer lk to rq (if k < q),\nor votes n \u2212 1, n prefer lk to rq (if k > q). Thus, at least\nn + 4 = (n + 1)/2 > n/2 votes prefer lk to rq. Moreover,\nany lk wins its pairwise election against a. This is because\nonly votes n \u2212 3 and n \u2212 2 prefer a to lk. It follows that,\nafter the first round, any surviving candidate lk can only\nlose a matchup against another surviving lk , so that one of\nthe lk must win the election. So, a is not the winner in the\nnewly constructed vote vector, and hence we have a correct\nfooling set.\nTheorem 18. The deterministic communication\ncomplexity of the Bucklin rule is O(nm).\nProof. Let l be the minimum integer for which there is\na candidate who is ranked among the top l candidates by\nmore than half the votes. We will do a binary search for l.\nAt each point, we will have a lower bound lL which is smaller\nthan l (initialized to 0), and an upper bound lH which is at\nleast l (initialized to m). While lH \u2212 lL > 1, we continue\nby finding out whether (lH \u2212 l)/2 is smaller than l, after\nwhich we can update the bounds.\nTo find out whether a number k is smaller than l, we\ndetermine every voter\"s k most preferred candidates.\nEvery voter can communicate which candidates are among her\nk most preferred candidates using m bits (for each\ncandidate, indicate whether the candidate is among the top k or\nnot), but because the binary search requires log m iterations,\nthis gives us an upper bound of O((log m)nm), which is not\nstrong enough. However, if lL < k < lH , and we already\nknow a voter\"s lL most preferred candidates, as well as her lH\nmost preferred candidates, then the voter no longer needs to\ncommunicate whether the lL most preferred candidates are\namong her k most preferred candidates (because they must\nbe), and she no longer needs to communicate whether the\nm\u2212lH least preferred candidates are among her k most\npreferred candidates (because they cannot be). Thus the voter\nneeds to communicate only m\u2212lL \u2212(m\u2212lH ) = lH \u2212lL bits\nin any given stage. Because each stage, lH \u2212 lL is (roughly)\nhalved, each voter in total communicates only (roughly)\nm + m/2 + m/4 + . . . \u2264 2m bits.\nTheorem 19. The nondeterministic communication\ncomplexity of the Bucklin rule is \u2126(nm) (even to decide whether\na given candidate a wins).\nProof. We will exhibit a fooling set of size 2n m\nwhere\nm = (m\u22121)/2 and n = n/2. We write the set of candidates\nas the following disjoint union: C = {a} \u222a L \u222a R where\nL = {l1, l2, . . . , lm } and R = {r1, r2, . . . , rm }. For any\nsubset S \u2286 {1, 2, . . . , m }, let L(S) = {li : i \u2208 S} and let\nR(S) = {ri : i \u2208 S}. For every vector (S1, S2, . . . , Sn )\nconsisting of n sets Si \u2286 {1, 2, . . . , m }, let the following\nvector of votes be an element of the fooling set:\n\u2022 For 1 \u2264 i \u2264 n , let voter 2i \u2212 1 rank the candidates\nL(Si) R \u2212 R(Si) a L \u2212 L(Si) R(Si).\n\u2022 For 1 \u2264 i \u2264 n , let voter 2i rank the candidates L \u2212\nL(Si) R(Si) a L(Si) R \u2212 R(Si).\nWe observe that this fooling set has size (2m\n)n\n= 2n m\n,\nand that candidate a wins in each vector of votes in the\nfooling set, for the following reason. Each candidate in C \u2212 {a}\nis ranked among the top m candidates by exactly half the\nvoters (which is not enough to win). Thus, we need to look\nat the voters\" top m +1 candidates, and a is ranked m +1th\nby all voters. All that remains to show is that for any two\ndistinct vectors of votes in the fooling set, we can let each of\nthe voters vote according to one of these two vectors in such\na way that a loses. Let the first vote vector correspond to\nthe vector (S1\n1 , S1\n2 , . . . , S1\nn ), and let the second vote vector\ncorrespond to the vector (S2\n1 , S2\n2 , . . . , S2\nn ). For some i, we\nmust have S1\ni = S2\ni , so that either S1\ni S2\ni or S2\ni S1\ni .\nWithout loss of generality, suppose S1\ni S2\ni , and let j be\nsome integer in S1\ni \u2212 S2\ni . Now, construct a new vote vector\nby taking vote 2i \u2212 1 from the first vote vector, and the\nremaining votes from the second vote vector. In this newly\nconstructed vote vector, a is still ranked m + 1th by all\nvotes. However, lj is ranked among the top m candidates\nby n + 1 = n/2 + 1 votes. This is because whereas vote\n2i \u2212 1 does not rank lj among the top m candidates in the\nsecond vote vector (because j /\u2208 S2\ni , we have lj /\u2208 L(S2\ni )),\nvote 2i \u2212 1 does rank lj among the top m candidates in the\nfirst vote vector (because j \u2208 S1\ni , we have lj \u2208 L(S1\ni )). So, a\nis not the winner in the newly constructed vote vector, and\nhence we have a correct fooling set.\nTheorem 20. The nondeterministic communication\ncomplexity of the ranked pairs rule is \u2126(nm log m) (even to\ndecide whether a given candidate a wins).\nProof. We omit this proof because of space constraint.\n5. DISCUSSION\nOne key obstacle to using voting for preference\naggregation is the communication burden that an election places\non the voters. By lowering this burden, it may become\nfeasible to conduct more elections over more issues. In the\nlimit, this could lead to a shift from representational\ngovernment to a system in which most issues are decided by\nreferenda-a veritable e-democracy. In this paper, we\nanalyzed the communication complexity of the common voting\nrules. Knowing which voting rules require little\ncommunication is especially important when the issue to be voted\non is of low enough importance that the following is true:\nthe parties involved are willing to accept a rule that tends\n86\nto produce outcomes that are slightly less representative of\nthe voters\" preferences, if this rule reduces the\ncommunication burden on the voters significantly. The following table\nsummarizes the results we obtained.\nRule Lower bound Upper bound\nplurality \u2126(n log m) O(n log m)\nplurality w/ runoff \u2126(n log m) O(n log m)\nSTV \u2126(n log m) O(n(log m)2)\nCondorcet \u2126(nm) O(nm)\napproval \u2126(nm) O(nm)\nBucklin \u2126(nm) O(nm)\ncup \u2126(nm) O(nm)\nmaximin \u2126(nm) O(nm)\nBorda \u2126(nm log m) O(nm log m)\nCopeland \u2126(nm log m) O(nm log m)\nranked pairs \u2126(nm log m) O(nm log m)\nCommunication complexity of voting rules, sorted from low\nto high. All of the upper bounds are deterministic (with\nthe exception of maximin, for which the best deterministic\nupper bound we proved is O(nm log m)). All of the lower\nbounds hold even for nondeterministic communication and\neven just for determining whether a given candidate a is\nthe winner.\nOne area of future research is to study what happens when\nwe restrict our attention to communication protocols that\ndo not reveal any strategically useful information. This\nrestriction may invalidate some of the upper bounds that we\nderived using multistage communication protocols. Also, all\nof our bounds are worst-case bounds. It may be possible to\noutperform these bounds when the distribution of votes has\nadditional structure.\nWhen deciding which voting rule to use for an election,\nthere are many considerations to take into account. The\nvoting rules that we studied in this paper are the most\ncommon ones that have survived the test of time. One way to\nselect among these rules is to consider recent results on\ncomplexity. The table above shows that from a communication\ncomplexity perspective, plurality, plurality with runoff, and\nSTV are preferable. However, plurality has the undesirable\nproperty that it is computationally easy to manipulate by\nvoting strategically [3, 7]. Plurality with runoff is NP-hard\nto manipulate by a coalition of weighted voters, or by an\nindividual that faces correlated uncertainty about the\nothers\" votes [7, 6]. STV is NP-hard to manipulate in those\nsettings as well [7], but also by an individual with perfect\nknowledge of the others\" votes (when the number of\ncandidates is unbounded) [2]. Therefore, STV is more robust,\nalthough it may require slightly more worst-case\ncommunication as per the table above. Yet other selection criteria\nare the computational complexity of determining whether\nenough information has been elicited to declare a winner,\nand that of determining the optimal sequence of queries [8].\n6. REFERENCES\n[1] Lawrence Ausubel and Paul Milgrom. Ascending auctions\nwith package bidding. Frontiers of Theoretical Economics,\n1, 2002. No. 1, Article 1.\n[2] John Bartholdi, III and James Orlin. Single transferable\nvote resists strategic voting. 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In Proceedings\nof the National Conference on Artificial Intelligence\n(AAAI), pages 314-319, 2002.\n[8] Vincent Conitzer and Tuomas Sandholm. Vote elicitation:\nComplexity and strategy-proofness. In Proceedings of the\nNational Conference on Artificial Intelligence (AAAI),\npages 392-397, 2002.\n[9] Sven de Vries, James Schummer, and Rakesh V. Vohra. On\nascending auctions for heterogeneous objects, 2003. Draft.\n[10] Allan Gibbard. Manipulation of voting schemes.\nEconometrica, 41:587-602, 1973.\n[11] Benoit Hudson and Tuomas Sandholm. Effectiveness of\nquery types and policies for preference elicitation in\ncombinatorial auctions. In International Conference on\nAutonomous Agents and Multi-Agent Systems (AAMAS),\npages 386-393, 2004.\n[12] E Kushilevitz and N Nisan. Communication Complexity.\nCambridge University Press, 1997.\n[13] Sebasti\u00b4en Lahaie and David Parkes. Applying learning\nalgorithms to preference elicitation. In Proceedings of the\nACM Conference on Electronic Commerce, 2004.\n[14] Noam Nisan and Ilya Segal. The communication\nrequirements of efficient allocations and supporting prices.\nJournal of Economic Theory, 2005. Forthcoming.\n[15] David Parkes. iBundle: An efficient ascending price bundle\nauction. In Proceedings of the ACM Conference on\nElectronic Commerce (ACM-EC), pages 148-157, 1999.\n[16] Tuomas Sandholm. An implementation of the contract net\nprotocol based on marginal cost calculations. In\nProceedings of the National Conference on Artificial\nIntelligence (AAAI), pages 256-262, 1993.\n[17] Tuomas Sandholm and Craig Boutilier. Preference\nelicitation in combinatorial auctions. In Peter Cramton,\nYoav Shoham, and Richard Steinberg, editors,\nCombinatorial Auctions, chapter 10. MIT Press, 2005.\n[18] Paolo Santi, Vincent Conitzer, and Tuomas Sandholm.\nTowards a characterization of polynomial preference\nelicitation with value queries in combinatorial auctions. In\nConference on Learning Theory (COLT), pages 1-16, 2004.\n[19] Mark Satterthwaite. Strategy-proofness and Arrow\"s\nconditions: existence and correspondence theorems for\nvoting procedures and social welfare functions. Journal of\nEconomic Theory, 10:187-217, 1975.\n[20] Ilya Segal. The communication requirements of social choice\nrules and supporting budget sets, 2004. Draft. Presented at\nthe DIMACS Workshop on Computational Issues in\nAuction Design, Rutgers University, New Jersey, USA.\n[21] Peter Wurman and Michael Wellman. AkBA: A\nprogressive, anonymous-price combinatorial auction. In\nProceedings of the ACM Conference on Electronic\nCommerce (ACM-EC), pages 21-29, 2000.\n[22] A. C. Yao. Some complexity questions related to distributed\ncomputing. In Proceedings of the 11th ACM symposium on\ntheory of computing (STOC), pages 209-213, 1979.\n[23] Martin Zinkevich, Avrim Blum, and Tuomas Sandholm. On\npolynomial-time preference elicitation with value queries.\nIn Proceedings of the ACM Conference on Electronic\nCommerce (ACM-EC), pages 176-185, 2003.\n87", "keywords": "communication;protocol;preference aggregation;maximin;voting rule;complexity;preference;stv;vote;resource allocation;communication complexity;elicitation problem"}
{"name": "train_J-51", "title": "Complexity of (Iterated) Dominance\u2217", "abstract": "We study various computational aspects of solving games using dominance and iterated dominance. We first study both strict and weak dominance (not iterated), and show that checking whether a given strategy is dominated by some mixed strategy can be done in polynomial time using a single linear program solve. We then move on to iterated dominance. We show that determining whether there is some path that eliminates a given strategy is NP-complete with iterated weak dominance. This allows us to also show that determining whether there is a path that leads to a unique solution is NP-complete. Both of these results hold both with and without dominance by mixed strategies. (A weaker version of the second result (only without dominance by mixed strategies) was already known [7].) Iterated strict dominance, on the other hand, is path-independent (both with and without dominance by mixed strategies) and can therefore be done in polynomial time. We then study what happens when the dominating strategy is allowed to place positive probability on only a few pure strategies. First, we show that finding the dominating strategy with minimum support size is NP-complete (both for strict and weak dominance). Then, we show that iterated strict dominance becomes path-dependent when there is a limit on the support size of the dominating strategies, and that deciding whether a given strategy can be eliminated by iterated strict dominance under this restriction is NP-complete (even when the limit on the support size is 3). Finally, we study Bayesian games. We show that, unlike in normal form games, deciding whether a given pure strategy is dominated by another pure strategy in a Bayesian game is NP-complete (both with strict and weak dominance); however, deciding whether a strategy is dominated by some mixed strategy can still be done in polynomial time with a single linear program solve (both with strict and weak \u2217 This material is based upon work supported by the National Science Foundation under ITR grants IIS-0121678 and IIS-0427858, and a Sloan Fellowship. dominance). Finally, we show that iterated dominance using pure strategies can require an exponential number of iterations in a Bayesian game (both with strict and weak dominance).", "fulltext": "1. INTRODUCTION\nIn multiagent systems with self-interested agents, the\noptimal action for one agent may depend on the actions taken\nby other agents. In such settings, the agents require tools\nfrom game theory to rationally decide on an action. Game\ntheory offers various formal models of strategic settings-the\nbest-known of which is a game in normal (or matrix) form,\nspecifying a utility (payoff) for each agent for each\ncombination of strategies that the agents choose-as well as\nsolution concepts, which, given a game, specify which outcomes\nare reasonable (under various assumptions of rationality and\ncommon knowledge).\nProbably the best-known (and certainly the most-studied)\nsolution concept is that of Nash equilibrium. A Nash\nequilibrium specifies a strategy for each player, in such a way that\nno player has an incentive to (unilaterally) deviate from the\nprescribed strategy. Recently, numerous papers have\nstudied computing Nash equilibria in various settings [9, 4, 12,\n3, 13, 14], and the complexity of constructing a Nash\nequilibrium in normal form games has been labeled one of the\ntwo most important open problems on the boundary of P\ntoday [20].\nThe problem of computing solutions according to the\nperhaps more elementary solution concepts of dominance and\niterated dominance has received much less attention. (After\nan early short paper on an easy case [11], the main\ncomputational study of these concepts has actually taken place\nin a paper in the game theory community [7].1\n) A strategy\nstrictly dominates another strategy if it performs strictly\n1\nThis is not to say that computer scientists have ignored\n88\nbetter against all vectors of opponent strategies, and weakly\ndominates it if it performs at least as well against all vectors\nof opponent strategies, and strictly better against at least\none. The idea is that dominated strategies can be eliminated\nfrom consideration. In iterated dominance, the elimination\nproceeds in rounds, and becomes easier as more strategies\nare eliminated: in any given round, the dominating\nstrategy no longer needs to perform better than or as well as the\ndominated strategy against opponent strategies that were\neliminated in earlier rounds. Computing solutions\naccording to (iterated) dominance is important for at least the\nfollowing reasons: 1) it can be computationally easier than\ncomputing (for instance) a Nash equilibrium (and therefore\nit can be useful as a preprocessing step in computing a Nash\nequilibrium), and 2) (iterated) dominance requires a weaker\nrationality assumption on the players than (for instance)\nNash equilibrium, and therefore solutions derived according\nto it are more likely to occur.\nIn this paper, we study some fundamental computational\nquestions concerning dominance and iterated dominance,\nincluding how hard it is to check whether a given strategy can\nbe eliminated by each of the variants of these notions. The\nrest of the paper is organized as follows. In Section 2, we\nbriefly review definitions and basic properties of normal form\ngames, strict and weak dominance, and iterated strict and\nweak dominance. In the remaining sections, we study\ncomputational aspects of dominance and iterated dominance. In\nSection 3, we study one-shot (not iterated) dominance. In\nSection 4, we study iterated dominance. In Section 5, we\nstudy dominance and iterated dominance when the\ndominating strategy can only place probability on a few pure\nstrategies. Finally, in Section 6, we study dominance and\niterated dominance in Bayesian games.\n2. DEFINITIONS AND BASIC PROPERTIES\nIn this section, we briefly review normal form games, as\nwell as dominance and iterated dominance (both strict and\nweak). An n-player normal form game is defined as follows.\nDefinition 1. A normal form game is given by a set of\nplayers {1, 2, . . . , n}; and, for each player i, a (finite) set of\npure strategies \u03a3i and a utility function ui : \u03a31 \u00d7 \u03a32 \u00d7 . . . \u00d7\n\u03a3n \u2192 R (where ui(\u03c31, \u03c32, . . . , \u03c3n) denotes player i\"s utility\nwhen each player j plays action \u03c3j).\nThe two main notions of dominance are defined as follows.\nDefinition 2. Player i\"s strategy \u03c3i is said to be strictly\ndominated by player i\"s strategy \u03c3i if for any vector of\nstrategies \u03c3\u2212i for the other players, ui(\u03c3i, \u03c3\u2212i) > ui(\u03c3i, \u03c3\u2212i).\nPlayer i\"s strategy \u03c3i is said to be weakly dominated by\nplayer i\"s strategy \u03c3i if for any vector of strategies \u03c3\u2212i for the\nother players, ui(\u03c3i, \u03c3\u2212i) \u2265 ui(\u03c3i, \u03c3\u2212i), and for at least one\nvector of strategies \u03c3\u2212i for the other players, ui(\u03c3i, \u03c3\u2212i) >\nui(\u03c3i, \u03c3\u2212i).\nIn this definition, it is sometimes allowed for the\ndominating strategy \u03c3i to be a mixed strategy, that is, a probability\ndistribution over pure strategies. In this case, the utilities in\ndominance altogether. For example, simple dominance\nchecks are sometimes used as a subroutine in searching for\nNash equilibria [21].\nthe definition are the expected utilities.2\nThere are other\nnotions of dominance, such as very weak dominance (in which\nno strict inequality is required, so two strategies can\ndominate each other), but we will not study them here. When we\nare looking at the dominance relations for player i, the other\nplayers (\u2212i) can be thought of as a single player.3\n\nTherefore, in the rest of the paper, when we study one-shot (not\niterated) dominance, we will focus without loss of generality\non two-player games.4\nIn two-player games, we will\ngenerally refer to the players as r (row) and c (column) rather\nthan 1 and 2.\nIn iterated dominance, dominated strategies are removed\nfrom the game, and no longer have any effect on future\ndominance relations. Iterated dominance can eliminate more\nstrategies than dominance, as follows. \u03c3r may originally\nnot dominate \u03c3r because the latter performs better against\n\u03c3c; but then, once \u03c3c is removed because it is dominated by\n\u03c3c, \u03c3r dominates \u03c3r, and the latter can be removed. For\nexample, in the following game, R can be removed first, after\nwhich D is dominated.\nL R\nU 1, 1 0, 0\nD 0, 1 1, 0\nEither strict or weak dominance can be used in the\ndefinition of iterated dominance. We note that the process of\niterated dominance is never helped by removing a dominated\nmixed strategy, for the following reason. If \u03c3i gives player i\na higher utility than \u03c3i against mixed strategy \u03c3j for player\nj = i (and strategies \u03c3\u2212{i,j} for the other players), then for\nat least one pure strategy \u03c3j that \u03c3j places positive\nprobability on, \u03c3i must perform better than \u03c3i against \u03c3j (and\nstrategies \u03c3\u2212{i,j} for the other players). Thus, removing the\nmixed strategy \u03c3j does not introduce any new dominances.\nMore detailed discussions and examples can be found in\nstandard texts on microeconomics or game theory [17, 5].\nWe are now ready to move on to the core of this paper.\n3. DOMINANCE (NOT ITERATED)\nIn this section, we study the notion of one-shot (not\niterated) dominance. As a first observation, checking whether a\ngiven strategy is strictly (weakly) dominated by some pure\nstrategy is straightforward, by checking, for every pure\nstrategy for that player, whether the latter strategy performs\nstrictly better against all the opponent\"s strategies (at least\nas well against all the opponent\"s strategies, and strictly\n2\nThe dominated strategy \u03c3i is, of course, also allowed to be\nmixed, but this has no technical implications for the paper:\nwhen we study one-shot dominance, we ask whether a given\nstrategy is dominated, and it does not matter whether the\ngiven strategy is pure or mixed; when we study iterated\ndominance, there is no use in eliminating mixed strategies,\nas we will see shortly.\n3\nThis player may have a very large strategy space (one pure\nstrategy for every vector of pure strategies for the players\nthat are being replaced). Nevertheless, this will not result in\nan increase in our representation size, because the original\nrepresentation already had to specify utilities for each of\nthese vectors.\n4\nWe note that a restriction to two-player games would not\nbe without loss of generality for iterated dominance. This\nis because for iterated dominance, we need to look at the\ndominated strategies of each individual player, so we cannot\nmerge any players.\n89\nbetter against at least one).5\nNext, we show that\nchecking whether a given strategy is dominated by some mixed\nstrategy can be done in polynomial time by solving a single\nlinear program. (Similar linear programs have been given\nbefore [18]; we present the result here for completeness, and\nbecause we will build on the linear programs given below in\nTheorem 6.)\nProposition 1. Given the row player\"s utilities, a\nsubset Dr of the row player\"s pure strategies \u03a3r, and a\ndistinguished strategy \u03c3\u2217\nr for the row player, we can check in time\npolynomial in the size of the game (by solving a single linear\nprogram of polynomial size) whether there exists some mixed\nstrategy \u03c3r, that places positive probability only on strategies\nin Dr and dominates \u03c3\u2217\nr , both for strict and for weak\ndominance.\nProof. Let pdr be the probability that \u03c3r places on dr \u2208\nDr. We will solve a single linear program in each of our\nalgorithms; linear programs can be solved in polynomial\ntime [10]. For strict dominance, the question is whether the\npdr can be set so that for every pure strategy for the column\nplayer \u03c3c \u2208 \u03a3c,\ndr\u2208Dr\npdr ur(dr, \u03c3c) > ur(\u03c3\u2217\nr , \u03c3c). Because\nthe inequality must be strict, we cannot solve this directly\nby linear programming. We proceed as follows. Because the\ngame is finite, we may assume without loss of generality that\nall utilities are positive (if not, simply add a constant to all\nutilities.) Solve the following linear program:\nminimize\ndr\u2208Dr\npdr\nsuch that\nfor any \u03c3c \u2208 \u03a3c,\ndr\u2208Dr\npdr ur(dr, \u03c3c) \u2265 ur(\u03c3\u2217\nr , \u03c3c).\nIf \u03c3\u2217\nr is strictly dominated by some mixed strategy, this\nlinear program has a solution with objective value < 1.\n(The dominating strategy is a feasible solution with\nobjective value exactly 1. Because no constraint is binding for this\nsolution, we can reduce one of the probabilities slightly\nwithout affecting feasibility, thereby obtaining a solution with\nobjective value < 1.) Moreover, if this linear program has a\nsolution with objective value < 1, there is a mixed strategy\nstrictly dominating \u03c3\u2217\nr , which can be obtained by taking the\nLP solution and adding the remaining probability to any\nstrategy (because all the utilities are positive, this will add\nto the left side of any inequality, so all inequalities will\nbecome strict).\nFor weak dominance, we can solve the following linear\nprogram:\nmaximize\n\u03c3c\u2208\u03a3c\n((\ndr\u2208Dr\npdr ur(dr, \u03c3c)) \u2212 ur(\u03c3\u2217\nr , \u03c3c))\nsuch that\nfor any \u03c3c \u2208 \u03a3c,\ndr\u2208Dr\npdr ur(dr, \u03c3c) \u2265 ur(\u03c3\u2217\nr , \u03c3c);\ndr\u2208Dr\npdr = 1.\nIf \u03c3\u2217\nr is weakly dominated by some mixed strategy, then\nthat mixed strategy is a feasible solution to this program\nwith objective value > 0, because for at least one strategy\n\u03c3c \u2208 \u03a3c we have (\ndr\u2208Dr\npdr ur(dr, \u03c3c)) \u2212 ur(\u03c3\u2217\nr , \u03c3c) > 0. On\nthe other hand, if this program has a solution with\nobjective value > 0, then for at least one strategy \u03c3c \u2208 \u03a3c we\n5\nRecall that the assumption of a single opponent (that is,\nthe assumption of two players) is without loss of generality\nfor one-shot dominance.\nmust have (\ndr\u2208Dr\npdr ur(dr, \u03c3c)) \u2212 ur(\u03c3\u2217\nr , \u03c3c) > 0, and thus\nthe linear program\"s solution is a weakly dominating mixed\nstrategy.\n4. ITERATED DOMINANCE\nWe now move on to iterated dominance. It is well-known\nthat iterated strict dominance is path-independent [6,\n19]that is, if we remove dominated strategies until no more\ndominated strategies remain, in the end the remaining\nstrategies for each player will be the same, regardless of the\norder in which strategies are removed. Because of this, to\nsee whether a given strategy can be eliminated by iterated\nstrict dominance, all that needs to be done is to\nrepeatedly remove strategies that are strictly dominated, until no\nmore dominated strategies remain. Because we can check in\npolynomial time whether any given strategy is dominated\n(whether or not dominance by mixed strategies is allowed,\nas described in Section 3), this whole procedure takes only\npolynomial time. In the case of iterated dominance by pure\nstrategies with two players, Knuth et al. [11] slightly\nimprove on (speed up) the straightforward implementation of\nthis procedure by keeping track of, for each ordered pair of\nstrategies for a player, the number of opponent strategies\nthat prevent the first strategy from dominating the second.\nHereby the runtime for an m \u00d7 n game is reduced from\nO((m + n)4\n) to O((m + n)3\n). (Actually, they only study\nvery weak dominance (for which no strict inequalities are\nrequired), but the approach is easily extended.)\nIn contrast, iterated weak dominance is known to be\npathdependent.6\nFor example, in the following game, using\niterated weak dominance we can eliminate M first, and then\nD, or R first, and then U.\nL M R\nU 1, 1 0, 0 1, 0\nD 1, 1 1, 0 0, 0\nTherefore, while the procedure of removing weakly\ndominated strategies until no more weakly dominated strategies\nremain can certainly be executed in polynomial time, which\nstrategies survive in the end depends on the order in which\nwe remove the dominated strategies. We will investigate\ntwo questions for iterated weak dominance: whether a given\nstrategy is eliminated in some path, and whether there is a\npath to a unique solution (one pure strategy left per player).\nWe will show that both of these problems are\ncomputationally hard.\nDefinition 3. Given a game in normal form and a\ndistinguished strategy \u03c3\u2217\n, IWD-STRATEGY-ELIMINATION\nasks whether there is some path of iterated weak dominance\nthat eliminates \u03c3\u2217\n. Given a game in normal form,\nIWDUNIQUE-SOLUTION asks whether there is some path of\niterated weak dominance that leads to a unique solution (one\nstrategy left per player).\nThe following lemma shows a special case of normal form\ngames in which allowing for weak dominance by mixed\nstrategies (in addition to weak dominance by pure strategies) does\n6\nThere is, however, a restriction of weak dominance called\nnice weak dominance which is path-independent [15, 16]. For\nan overview of path-independence results, see Apt [1].\n90\nnot help. We will prove the hardness results in this setting,\nso that they will hold whether or not dominance by mixed\nstrategies is allowed.\nLemma 1. Suppose that all the utilities in a game are in\n{0, 1}. Then every pure strategy that is weakly dominated by\na mixed strategy is also weakly dominated by a pure strategy.\nProof. Suppose pure strategy \u03c3 is weakly dominated by\nmixed strategy \u03c3\u2217\n. If \u03c3 gets a utility of 1 against some\nopponent strategy (or vector of opponent strategies if there\nare more than 2 players), then all the pure strategies that\n\u03c3\u2217\nplaces positive probability on must also get a utility of 1\nagainst that opponent strategy (or else the expected utility\nwould be smaller than 1). Moreover, at least one of the\npure strategies that \u03c3\u2217\nplaces positive probability on must\nget a utility of 1 against an opponent strategy that \u03c3 gets\n0 against (or else the inequality would never be strict). It\nfollows that this pure strategy weakly dominates \u03c3.\nWe are now ready to prove the main results of this section.\nTheorem 1. IWD-STRATEGY-ELIMINATION is\nNPcomplete, even with 2 players, and with 0 and 1 being the\nonly utilities occurring in the matrix-whether or not\ndominance by mixed strategies is allowed.\nProof. The problem is in NP because given a sequence\nof strategies to be eliminated, we can easily check whether\nthis is a valid sequence of eliminations (even when\ndominance by mixed strategies is allowed, using Proposition 1).\nTo show that the problem is NP-hard, we reduce an\narbitrary satisfiability instance (given by a nonempty set of\nclauses C over a nonempty set of variables V , with\ncorresponding literals L = {+v : v \u2208 V } \u222a {\u2212v : v \u2208 V }) to the\nfollowing IWD-STRATEGY-ELIMINATION instance. (In\nthis instance, we will specify that certain strategies are\nuneliminable. A strategy \u03c3r can be made uneliminable, even\nwhen 0 and 1 are the only allowed utilities, by adding\nanother strategy \u03c3r and another opponent strategy \u03c3c, so that:\n1. \u03c3r and \u03c3r are the only strategies that give the row player\na utility of 1 against \u03c3c. 2. \u03c3r and \u03c3r always give the row\nplayer the same utility. 3. \u03c3c is the only strategy that gives\nthe column player a utility of 1 against \u03c3r, but otherwise\n\u03c3c always gives the column player utility 0. This makes it\nimpossible to eliminate any of these three strategies. We\nwill not explicitly specify the additional strategies to make\nthe proof more legible.)\nIn this proof, we will denote row player strategies by s, and\ncolumn player strategies by t, to improve legibility. Let the\nrow player\"s pure strategy set be given as follows. For every\nvariable v \u2208 V , the row player has corresponding strategies\ns1\n+v, s2\n+v, s1\n\u2212v, s2\n\u2212v. Additionally, the row player has the\nfollowing 2 strategies: s1\n0 and s2\n0, where s2\n0 = \u03c3\u2217\nr (that is, it is\nthe strategy we seek to eliminate). Finally, for every clause\nc \u2208 C, the row player has corresponding strategies s1\nc\n(uneliminable) and s2\nc. Let the column player\"s pure strategy set\nbe given as follows. For every variable v \u2208 V , the column\nplayer has a corresponding strategy tv. For every clause\nc \u2208 C, the column player has a corresponding strategy tc,\nand additionally, for every literal l \u2208 L that occurs in c, a\nstrategy tc,l. For every variable v \u2208 V , the column player\nhas corresponding strategies t+v, t\u2212v (both uneliminable).\nFinally, the column player has three additional strategies:\nt1\n0 (uneliminable), t2\n0, and t1.\nThe utility function for the row player is given as follows:\n\u2022 ur(s1\n+v, tv) = 0 for all v \u2208 V ;\n\u2022 ur(s2\n+v, tv) = 1 for all v \u2208 V ;\n\u2022 ur(s1\n\u2212v, tv) = 1 for all v \u2208 V ;\n\u2022 ur(s2\n\u2212v, tv) = 0 for all v \u2208 V ;\n\u2022 ur(s1\n+v, t1) = 1 for all v \u2208 V ;\n\u2022 ur(s2\n+v, t1) = 0 for all v \u2208 V ;\n\u2022 ur(s1\n\u2212v, t1) = 0 for all v \u2208 V ;\n\u2022 ur(s2\n\u2212v, t1) = 1 for all v \u2208 V ;\n\u2022 ur(sb\n+v, t+v) = 1 for all v \u2208 V and b \u2208 {1, 2};\n\u2022 ur(sb\n\u2212v, t\u2212v) = 1 for all v \u2208 V and b \u2208 {1, 2};\n\u2022 ur(sl, t) = 0 otherwise for all l \u2208 L and t \u2208 S2;\n\u2022 ur(s1\n0, tc) = 0 for all c \u2208 C;\n\u2022 ur(s2\n0, tc) = 1 for all c \u2208 C;\n\u2022 ur(sb\n0, t1\n0) = 1 for all b \u2208 {1, 2};\n\u2022 ur(s1\n0, t2\n0) = 1;\n\u2022 ur(s2\n0, t2\n0) = 0;\n\u2022 ur(sb\n0, t) = 0 otherwise for all b \u2208 {1, 2} and t \u2208 S2;\n\u2022 ur(sb\nc, t) = 0 otherwise for all c \u2208 C and b \u2208 {1, 2};\nand the row player\"s utility is 0 in every other case. The\nutility function for the column player is given as follows:\n\u2022 uc(s, tv) = 0 for all v \u2208 V and s \u2208 S1;\n\u2022 uc(s, t1) = 0 for all s \u2208 S1;\n\u2022 uc(s2\nl , tc) = 1 for all c \u2208 C and l \u2208 L where l \u2208 c\n(literal l occurs in clause c);\n\u2022 uc(s2\nl2\n, tc,l1 ) = 1 for all c \u2208 C and l1, l2 \u2208 L, l1 = l2\nwhere l2 \u2208 c;\n\u2022 uc(s1\nc, tc) = 1 for all c \u2208 C;\n\u2022 uc(s2\nc, tc) = 0 for all c \u2208 C;\n\u2022 uc(sb\nc, tc,l) = 1 for all c \u2208 C, l \u2208 L, and b \u2208 {1, 2};\n\u2022 uc(s2, tc) = uc(s2, tc,l) = 0 otherwise for all c \u2208 C and\nl \u2208 L;\nand the column player\"s utility is 0 in every other case. We\nnow show that the two instances are equivalent.\nFirst, suppose there is a solution to the satisfiability\ninstance: that is, a truth-value assignment to the variables in\nV such that all clauses are satisfied. Then, consider the\nfollowing sequence of eliminations in our game: 1. For every\nvariable v that is set to true in the assignment, eliminate\ntv (which gives the column player utility 0 everywhere). 2.\nThen, for every variable v that is set to true in the\nassignment, eliminate s2\n+v using s1\n+v (which is possible because tv\nhas been eliminated, and because t1 has not been eliminated\n(yet)). 3. Now eliminate t1 (which gives the column player\nutility 0 everywhere). 4. Next, for every variable v that is set\nto false in the assignment, eliminate s2\n\u2212v using s1\n\u2212v (which\nis possible because t1 has been eliminated, and because tv\nhas not been eliminated (yet)). 5. For every clause c which\nhas the variable corresponding to one of its positive literals\nl = +v set to true in the assignment, eliminate tc using tc,l\n(which is possible because s2\nl has been eliminated, and s2\nc\nhas not been eliminated (yet)). 6. For every clause c which\nhas the variable corresponding to one of its negative literals\nl = \u2212v set to false in the assignment, eliminate tc using tc,l\n91\n(which is possible because s2\nl has been eliminated, and s2\nc has\nnot been eliminated (yet)). 7. Because the assignment\nsatisfied the formula, all the tc have now been eliminated. Thus,\nwe can eliminate s2\n0 = \u03c3\u2217\nr using s1\n0. It follows that there is a\nsolution to the IWD-STRATEGY-ELIMINATION instance.\nNow suppose there is a solution to the\nIWD-STRATEGYELIMINATION instance. By Lemma 1, we can assume that\nall the dominances are by pure strategies. We first observe\nthat only s1\n0 can eliminate s2\n0 = \u03c3\u2217\nr , because it is the only\nother strategy that gets the row player a utility of 1 against\nt1\n0, and t1\n0 is uneliminable. However, because s2\n0 performs\nbetter than s1\n0 against the tc strategies, it follows that all of\nthe tc strategies must be eliminated. For each c \u2208 C, the\nstrategy tc can only be eliminated by one of the strategies tc,l\n(with the same c), because these are the only other strategies\nthat get the column player a utility of 1 against s1\nc, and s1\nc is\nuneliminable. But, in order for some tc,l to eliminate tc, s2\nl\nmust be eliminated first. Only s1\nl can eliminate s2\nl , because\nit is the only other strategy that gets the row player a utility\nof 1 against tl, and tl is uneliminable. We next show that for\nevery v \u2208 V only one of s2\n+v, s2\n\u2212v can be eliminated. This\nis because in order for s1\n+v to eliminate s2\n+v, tv needs to\nhave been eliminated and t1, not (so tv must be eliminated\nbefore t1); but in order for s1\n\u2212v to eliminate s2\n\u2212v, t1 needs to\nhave been eliminated and tv, not (so t1 must be eliminated\nbefore tv). So, set v to true if s2\n+v is eliminated, and to false\notherwise Because by the above, for every clause c, one of\nthe s2\nl with l \u2208 c must be eliminated, it follows that this is\na satisfying assignment to the satisfiability instance.\nUsing Theorem 1, it is now (relatively) easy to show that\nIWD-UNIQUE-SOLUTION is also NP-complete under the\nsame restrictions.\nTheorem 2. IWD-UNIQUE-SOLUTION is NP-complete,\neven with 2 players, and with 0 and 1 being the only\nutilities occurring in the matrix-whether or not dominance by\nmixed strategies is allowed.\nProof. Again, the problem is in NP because we can\nnondeterministically choose the sequence of eliminations and\nverify whether it is correct. To show NP-hardness, we reduce\nan arbitrary IWD-STRATEGY-ELIMINATION instance to\nthe following IWD-UNIQUE-SOLUTION instance. Let all\nthe strategies for each player from the original instance\nremain part of the new instance, and let the utilities resulting\nfrom the players playing a pair of these strategies be the\nsame. We add three additional strategies \u03c31\nr , \u03c32\nr , \u03c33\nr for the\nrow player, and three additional strategies \u03c31\nc , \u03c32\nc , \u03c33\nc for the\ncolumn player. Let the additional utilities be as follows:\n\u2022 ur(\u03c3r, \u03c3j\nc) = 1 for all \u03c3r /\u2208 {\u03c31\nr , \u03c32\nr , \u03c33\nr } and j \u2208 {2, 3};\n\u2022 ur(\u03c3i\nr, \u03c3c) = 1 for all i \u2208 {1, 2, 3} and \u03c3c /\u2208 {\u03c32\nc , \u03c33\nc };\n\u2022 ur(\u03c3i\nr, \u03c32\nc ) = 1 for all i \u2208 {2, 3};\n\u2022 ur(\u03c31\nr , \u03c33\nc ) = 1;\n\u2022 and the row player\"s utility is 0 in all other cases\ninvolving a new strategy.\n\u2022 uc(\u03c33\nr , \u03c3c) = 1 for all \u03c3c /\u2208 {\u03c31\nc , \u03c32\nc , \u03c33\nc };\n\u2022 uc(\u03c3\u2217\nr , \u03c3j\nc) = 1 for all j \u2208 {2, 3} (\u03c3\u2217\nr is the strategy to\nbe eliminated in the original instance);\n\u2022 uc(\u03c3i\nr, \u03c31\nc ) = 1 for all i \u2208 {1, 2};\n\u2022 ur(\u03c31\nr , \u03c32\nc ) = 1;\n\u2022 ur(\u03c32\nr , \u03c33\nc ) = 1;\n\u2022 and the column player\"s utility is 0 in all other cases\ninvolving a new strategy.\nWe proceed to show that the two instances are equivalent.\nFirst suppose there exists a solution to the original\nIWDSTRATEGY-ELIMINATION instance. Then, perform the\nsame sequence of eliminations to eliminate \u03c3\u2217\nr in the new\nIWD-UNIQUE-SOLUTION instance. (This is possible\nbecause at any stage, any weak dominance for the row player\nin the original instance is still a weak dominance in the new\ninstance, because the two strategies\" utilities for the row\nplayer are the same when the column player plays one of the\nnew strategies; and the same is true for the column player.)\nOnce \u03c3\u2217\nr is eliminated, let \u03c31\nc eliminate \u03c32\nc . (It performs\nbetter against \u03c32\nr .) Then, let \u03c31\nr eliminate all the other\nremaining strategies for the row player. (It always performs\nbetter against either \u03c31\nc or \u03c33\nc .) Finally, \u03c31\nc is the unique best\nresponse against \u03c31\nr among the column player\"s remaining\nstrategies, so let it eliminate all the other remaining\nstrategies for the column player. Thus, there exists a solution to\nthe IWD-UNIQUE-SOLUTION instance.\nNow suppose there exists a solution to the\nIWD-UNIQUESOLUTION instance. By Lemma 1, we can assume that all\nthe dominances are by pure strategies. We will show that\nnone of the new strategies (\u03c31\nr , \u03c32\nr , \u03c33\nr , \u03c31\nc , \u03c32\nc , \u03c33\nc ) can either\neliminate another strategy, or be eliminated before \u03c3\u2217\nr is\neliminated. Thus, there must be a sequence of eliminations\nending in the elimination of \u03c3\u2217\nr , which does not involve any of\nthe new strategies, and is therefore a valid sequence of\neliminations in the original game (because all original strategies\nperform the same against each new strategy). We now show\nthat this is true by exhausting all possibilities for the first\nelimination before \u03c3\u2217\nr is eliminated that involves a new\nstrategy. None of the \u03c3i\nr can be eliminated by a \u03c3r /\u2208 {\u03c31\nr , \u03c32\nr , \u03c33\nr },\nbecause the \u03c3i\nr perform better against \u03c31\nc . \u03c31\nr cannot\neliminate any other strategy, because it always performs poorer\nagainst \u03c32\nc . \u03c32\nr and \u03c33\nr are equivalent from the row player\"s\nperspective (and thus cannot eliminate each other), and\ncannot eliminate any other strategy because they always\nperform poorer against \u03c33\nc . None of the \u03c3j\nc can be eliminated\nby a \u03c3c /\u2208 {\u03c31\nc , \u03c32\nc , \u03c33\nc }, because the \u03c3j\nc always perform\nbetter against either \u03c31\nr or \u03c32\nr . \u03c31\nc cannot eliminate any other\nstrategy, because it always performs poorer against either\n\u03c3\u2217\nr or \u03c33\nr . \u03c32\nc cannot eliminate any other strategy, because\nit always performs poorer against \u03c32\nr or \u03c33\nr . \u03c33\nc cannot\neliminate any other strategy, because it always performs poorer\nagainst \u03c31\nr or \u03c33\nr . Thus, there exists a solution to the\nIWDSTRATEGY-ELIMINATION instance.\nA slightly weaker version of the part of Theorem 2\nconcerning dominance by pure strategies only is the main result\nof Gilboa et al. [7]. (Besides not proving the result for\ndominance by mixed strategies, the original result was weaker\nbecause it required utilities {0, 1, 2, 3, 4, 5, 6, 7, 8} rather than\njust {0, 1} (and because of this, our Lemma 1 cannot be\napplied to it to get the result for mixed strategies).)\n5. (ITERATED) DOMINANCE USING\nMIXED STRATEGIES WITH SMALL\nSUPPORTS\nWhen showing that a strategy is dominated by a mixed\nstrategy, there are several reasons to prefer exhibiting a\n92\ndominating strategy that places positive probability on as\nfew pure strategies as possible. First, this will reduce the\nnumber of bits required to specify the dominating\nstrategy (and thus the proof of dominance can be communicated\nquicker): if the dominating mixed strategy places positive\nprobability on only k strategies, then it can be specified\nusing k real numbers for the probabilities, plus k log m (where\nm is the number of strategies for the player under\nconsideration) bits to indicate which strategies are used. Second,\nthe proof of dominance will be cleaner: for a dominating\nmixed strategy, it is typically (always in the case of strict\ndominance) possible to spread some of the probability onto\nany unused pure strategy and still have a dominating\nstrategy, but this obscures which pure strategies are the ones that\nare key in making the mixed strategy dominating. Third,\nbecause (by the previous) the argument for eliminating the\ndominated strategy is simpler and easier to understand, it is\nmore likely to be accepted. Fourth, the level of risk\nneutrality required for the argument to work is reduced, at least in\nthe extreme case where dominance by a single pure strategy\ncan be exhibited (no risk neutrality is required here).\nThis motivates the following problem.\nDefinition 4 (MINIMUM-DOMINATING-SET). We\nare given the row player\"s utilities of a game in normal form,\na distinguished strategy \u03c3\u2217\nfor the row player, a specification\nof whether the dominance should be strict or weak, and a\nnumber k. We are asked whether there exists a mixed\nstrategy \u03c3 for the row player that places positive probability on\nat most k pure strategies, and dominates \u03c3\u2217\nin the required\nsense.\nUnfortunately, this problem is NP-complete.\nTheorem 3. MINIMUM-DOMINATING-SET is\nNPcomplete, both for strict and for weak dominance.\nProof. The problem is in NP because we can\nnondeterministically choose a set of at most k strategies to give\npositive probability, and decide whether we can dominate\n\u03c3\u2217\nwith these k strategies as described in Proposition 1. To\nshow NP-hardness, we reduce an arbitrary SET-COVER\ninstance (given a set S, subsets S1, S2, . . . , Sr, and a number\nt, can all of S be covered by at most t of the subsets?)\nto the following MINIMUM-DOMINATING-SET instance.\nFor every element s \u2208 S, there is a pure strategy \u03c3s for\nthe column player. For every subset Si, there is a pure\nstrategy \u03c3Si for the row player. Finally, there is the\ndistinguished pure strategy \u03c3\u2217\nfor the row player. The row\nplayer\"s utilities are as follows: ur(\u03c3Si , \u03c3s) = t + 1 if s \u2208 Si;\nur(\u03c3Si , \u03c3s) = 0 if s /\u2208 Si; ur(\u03c3\u2217\n, \u03c3s) = 1 for all s \u2208 S.\nFinally, we let k = t. We now proceed to show that the two\ninstances are equivalent.\nFirst suppose there exists a solution to the SET-COVER\ninstance. Without loss of generality, we can assume that\nthere are exactly k subsets in the cover. Then, for every\nSi that is in the cover, let the dominating strategy \u03c3 place\nexactly 1\nk\nprobability on the corresponding pure strategy\n\u03c3Si . Now, if we let n(s) be the number of subsets in the cover\ncontaining s (we observe that that n(s) \u2265 1), then for every\nstrategy \u03c3s for the column player, the row player\"s expected\nutility for playing \u03c3 when the column player is playing \u03c3s is\nu(\u03c3, \u03c3s) = n(s)\nk\n(k + 1) \u2265 k+1\nk\n> 1 = u(\u03c3\u2217\n, \u03c3s). So \u03c3 strictly\n(and thus also weakly) dominates \u03c3\u2217\n, and there exists a\nsolution to the MINIMUM-DOMINATING-SET instance.\nNow suppose there exists a solution to the\nMINIMUMDOMINATING-SET instance. Consider the (at most k)\npure strategies of the form \u03c3Si on which the dominating\nmixed strategy \u03c3 places positive probability, and let T be\nthe collection of the corresponding subsets Si. We claim that\nT is a cover. For suppose there is some s \u2208 S that is not in\nany of the subsets in T . Then, if the column player plays \u03c3s,\nthe row player (when playing \u03c3) will always receive utility\n0-as opposed to the utility of 1 the row player would receive\nfor playing \u03c3\u2217\n, contradicting the fact that \u03c3 dominates \u03c3\u2217\n(whether this dominance is weak or strict). It follows that\nthere exists a solution to the SET-COVER instance.\nOn the other hand, if we require that the dominating\nstrategy only places positive probability on a very small\nnumber of pure strategies, then it once again becomes easy\nto check whether a strategy is dominated. Specifically, to\nfind out whether player i\"s strategy \u03c3\u2217\nis dominated by\na strategy that places positive probability on only k pure\nstrategies, we can simply check, for every subset of k of\nplayer i\"s pure strategies, whether there is a strategy that\nplaces positive probability only on these k strategies and\ndominates \u03c3\u2217\n, using Proposition 1. This requires only\nO(|\u03a3i|k\n) such checks. Thus, if k is a constant, this\nconstitutes a polynomial-time algorithm.\nA natural question to ask next is whether iterated strict\ndominance remains computationally easy when dominating\nstrategies are required to place positive probability on at\nmost k pure strategies, where k is a small constant. (We\nhave already shown in Section 4 that iterated weak\ndominance is hard even when k = 1, that is, only dominance by\npure strategies is allowed.) Of course, if iterated strict\ndominance were path-independent under this restriction,\ncomputational easiness would follow as it did in Section 4.\nHowever, it turns out that this is not the case.\nObservation 1. If we restrict the dominating strategies\nto place positive probability on at most two pure strategies,\niterated strict dominance becomes path-dependent.\nProof. Consider the following game:\n7, 1 0, 0 0, 0\n0, 0 7, 1 0, 0\n3, 0 3, 0 0, 0\n0, 0 0, 0 3, 1\n1, 0 1, 0 1, 0\nLet (i, j) denote the outcome in which the row player plays\nthe ith row and the column player plays the jth column.\nBecause (1, 1), (2, 2), and (4, 3) are all Nash equilibria, none\nof the column player\"s pure strategies will ever be eliminated,\nand neither will rows 1, 2, and 4. We now observe that\nrandomizing uniformly over rows 1 and 2 dominates row 3,\nand randomizing uniformly over rows 3 and 4 dominates row\n5. However, if we eliminate row 3 first, it becomes impossible\nto dominate row 5 without randomizing over at least 3 pure\nstrategies.\nIndeed, iterated strict dominance turns out to be hard\neven when k = 3.\nTheorem 4. If we restrict the dominating strategies to\nplace positive probability on at most three pure strategies, it\nbecomes NP-complete to decide whether a given strategy can\nbe eliminated using iterated strict dominance.\n93\nProof. The problem is in NP because given a sequence\nof strategies to be eliminated, we can check in polynomial\ntime whether this is a valid sequence of eliminations (for any\nstrategy to be eliminated, we can check, for every subset of\nthree other strategies, whether there is a strategy placing\npositive probability on only these three strategies that\ndominates the strategy to be eliminated, using Proposition 1).\nTo show that the problem is NP-hard, we reduce an\narbitrary satisfiability instance (given by a nonempty set of\nclauses C over a nonempty set of variables V , with\ncorresponding literals L = {+v : v \u2208 V } \u222a {\u2212v : v \u2208 V }) to the\nfollowing two-player game.\nFor every variable v \u2208 V , the row player has strategies\ns+v, s\u2212v, s1\nv, s2\nv, s3\nv, s4\nv, and the column player has strategies\nt1\nv, t2\nv, t3\nv, t4\nv. For every clause c \u2208 C, the row player has a\nstrategy sc, and the column player has a strategy tc, as well\nas, for every literal l occurring in c, an additional strategy\ntl\nc. The row player has two additional strategies s1 and s2.\n(s2 is the strategy that we are seeking to eliminate.) Finally,\nthe column player has one additional strategy t1.\nThe utility function for the row player is given as follows\n(where is some sufficiently small number):\n\u2022 ur(s+v, tj\nv) = 4 if j \u2208 {1, 2}, for all v \u2208 V ;\n\u2022 ur(s+v, tj\nv) = 1 if j \u2208 {3, 4}, for all v \u2208 V ;\n\u2022 ur(s\u2212v, tj\nv) = 1 if j \u2208 {1, 2}, for all v \u2208 V ;\n\u2022 ur(s\u2212v, tj\nv) = 4 if j \u2208 {3, 4}, for all v \u2208 V ;\n\u2022 ur(s+v, t) = ur(s\u2212v, t) = 0 for all v \u2208 V and t /\u2208\n{t1\nv, t2\nv, t3\nv, t4\nv};\n\u2022 ur(si\nv, ti\nv) = 13 for all v \u2208 V and i \u2208 {1, 2, 3, 4};\n\u2022 ur(si\nv, t) = for all v \u2208 V , i \u2208 {1, 2, 3, 4}, and t = ti\nv;\n\u2022 ur(sc, tc) = 2 for all c \u2208 C;\n\u2022 ur(sc, t) = 0 for all c \u2208 C and t = tc;\n\u2022 ur(s1, t1) = 1 + ;\n\u2022 ur(s1, t) = for all t = t1;\n\u2022 ur(s2, t1) = 1;\n\u2022 ur(s2, tc) = 1 for all c \u2208 C;\n\u2022 ur(s2, t) = 0 for all t /\u2208 {t1} \u222a {tc : c \u2208 C}.\nThe utility function for the column player is given as\nfollows:\n\u2022 uc(si\nv, ti\nv) = 1 for all v \u2208 V and i \u2208 {1, 2, 3, 4};\n\u2022 uc(s, ti\nv) = 0 for all v \u2208 V , i \u2208 {1, 2, 3, 4}, and s = si\nv;\n\u2022 uc(sc, tc) = 1 for all c \u2208 C;\n\u2022 uc(sl, tc) = 1 for all c \u2208 C and l \u2208 L occurring in c;\n\u2022 uc(s, tc) = 0 for all c \u2208 C and s /\u2208 {sc} \u222a {sl : l \u2208 c};\n\u2022 uc(sc, tl\nc) = 1 + for all c \u2208 C;\n\u2022 uc(sl , tl\nc) = 1 + for all c \u2208 C and l = l occurring in\nc;\n\u2022 uc(s, tl\nc) = for all c \u2208 C and s /\u2208 {sc} \u222a {sl : l \u2208\nc, l = l };\n\u2022 uc(s2, t1) = 1;\n\u2022 uc(s, t1) = 0 for all s = s2.\nWe now show that the two instances are equivalent. First,\nsuppose that there is a solution to the satisfiability instance.\nThen, consider the following sequence of eliminations in our\ngame: 1. For every variable v that is set to true in the\nsatisfying assignment, eliminate s+v with the mixed strategy \u03c3r\nthat places probability 1/3 on s\u2212v, probability 1/3 on s1\nv,\nand probability 1/3 on s2\nv. (The expected utility of\nplaying \u03c3r against t1\nv or t2\nv is 14/3 > 4; against t3\nv or t4\nv, it is\n4/3 > 1; and against anything else it is 2 /3 > 0. Hence the\ndominance is valid.) 2. Similarly, for every variable v that\nis set to false in the satisfying assignment, eliminate s\u2212v\nwith the mixed strategy \u03c3r that places probability 1/3 on\ns+v, probability 1/3 on s3\nv, and probability 1/3 on s4\nv. (The\nexpected utility of playing \u03c3r against t1\nv or t2\nv is 4/3 > 1;\nagainst t3\nv or t4\nv, it is 14/3 > 4; and against anything else it\nis 2 /3 > 0. Hence the dominance is valid.) 3. For every\nc \u2208 C, eliminate tc with any tl\nc for which l was set to true\nin the satisfying assignment. (This is a valid dominance\nbecause tl\nc performs better than tc against any strategy other\nthan sl, and we eliminated sl in step 1 or in step 2.) 4.\nFinally, eliminate s2 with s1. (This is a valid dominance\nbecause s1 performs better than s2 against any strategy other\nthan those in {tc : c \u2208 C}, which we eliminated in step 3.)\nHence, there is an elimination path that eliminates s2.\nNow, suppose that there is an elimination path that\neliminates s2. The strategy that eventually dominates s2 must\nplace most of its probability on s1, because s1 is the only\nother strategy that performs well against t1, which cannot\nbe eliminated before s2. But, s1 performs significantly worse\nthan s2 against any strategy tc with c \u2208 C, so it follows that\nall these strategies must be eliminated first. Each strategy\ntc can only be eliminated by a strategy that places most\nof its weight on the corresponding strategies tl\nc with l \u2208 c,\nbecause they are the only other strategies that perform well\nagainst sc, which cannot be eliminated before tc. But, each\nstrategy tl\nc performs significantly worse than tc against sl,\nso it follows that for every clause c, for one of the literals\nl occurring in it, sl must be eliminated first. Now,\nstrategies of the form tj\nv will never be eliminated because they are\nthe unique best responses to the corresponding strategies sj\nv\n(which are, in turn, the best responses to the corresponding\ntj\nv). As a result, if strategy s+v (respectively, s\u2212v) is\neliminated, then its opposite strategy s\u2212v (respectively, s+v) can\nno longer be eliminated, for the following reason. There is no\nother pure strategy remaining that gets a significant utility\nagainst more than one of the strategies t1\nv, t2\nv, t3\nv, t4\nv, but s\u2212v\n(respectively, s+v) gets significant utility against all 4, and\ntherefore cannot be dominated by a mixed strategy placing\npositive probability on at most 3 strategies. It follows that\nfor each v \u2208 V , at most one of the strategies s+v, s\u2212v is\neliminated, in such a way that for every clause c, for one\nof the literals l occurring in it, sl must be eliminated. But\nthen setting all the literals l such that sl is eliminated to\ntrue constitutes a solution to the satisfiability instance.\nIn the next section, we return to the setting where there\nis no restriction on the number of pure strategies on which\na dominating mixed strategy can place positive probability.\n6. (ITERATED) DOMINANCE IN\nBAYESIAN GAMES\nSo far, we have focused on normal form games that are\nflatly represented (that is, every matrix entry is given\nex94\nplicitly). However, for many games, the flat representation\nis too large to write down explicitly, and instead, some\nrepresentation that exploits the structure of the game needs to\nbe used. Bayesian games, besides being of interest in their\nown right, can be thought of as a useful structured\nrepresentation of normal form games, and we will study them in\nthis section.\nIn a Bayesian game, each player first receives privately\nheld preference information (the player\"s type) from a\ndistribution, which determines the utility that that player receives\nfor every outcome of (that is, vector of actions played in) the\ngame. After receiving this type, the player plays an action\nbased on it.7\nDefinition 5. A Bayesian game is given by a set of\nplayers {1, 2, . . . , n}; and, for each player i, a (finite) set of\nactions Ai, a (finite) type space \u0398i with a probability\ndistribution \u03c0i over it, and a utility function ui : \u0398i \u00d7 A1 \u00d7 A2 \u00d7\n. . . \u00d7 An \u2192 R (where ui(\u03b8i, a1, a2, . . . , an) denotes player\ni\"s utility when i\"s type is \u03b8i and each player j plays action\naj). A pure strategy in a Bayesian game is a mapping from\ntypes to actions, \u03c3i : \u0398i \u2192 Ai, where \u03c3i(\u03b8i) denotes the\naction that player i plays for type \u03b8i.\nAny vector of pure strategies in a Bayesian game defines\nan (expected) utility for each player, and therefore we can\ntranslate a Bayesian game into a normal form game. In this\nnormal form game, the notions of dominance and iterated\ndominance are defined as before. However, the normal form\nrepresentation of the game is exponentially larger than the\nBayesian representation, because each player i has |Ai||\u0398i|\ndistinct pure strategies. Thus, any algorithm for Bayesian\ngames that relies on expanding the game to its normal form\nwill require exponential time. Specifically, our easiness\nresults for normal form games do not directly transfer to this\nsetting. In fact, it turns out that checking whether a\nstrategy is dominated by a pure strategy is hard in Bayesian\ngames.\nTheorem 5. In a Bayesian game, it is NP-complete to\ndecide whether a given pure strategy \u03c3r : \u0398r \u2192 Ar is\ndominated by some other pure strategy (both for strict and weak\ndominance), even when the row player\"s distribution over\ntypes is uniform.\nProof. The problem is in NP because it is easy to verify\nwhether a candidate dominating strategy is indeed a\ndominating strategy. To show that the problem is NP-hard, we\nreduce an arbitrary satisfiability instance (given by a set of\nclauses C using variables from V ) to the following Bayesian\ngame. Let the row player\"s action set be Ar = {t, f, 0} and\nlet the column player\"s action set be Ac = {ac : c \u2208 C}.\nLet the row player\"s type set be \u0398r = {\u03b8v : v \u2208 V }, with a\ndistribution \u03c0r that is uniform. Let the row player\"s utility\nfunction be as follows:\n\u2022 ur(\u03b8v, 0, ac) = 0 for all v \u2208 V and c \u2208 C;\n\u2022 ur(\u03b8v, b, ac) = |V | for all v \u2208 V , c \u2208 C, and b \u2208 {t, f}\nsuch that setting v to b satisfies c;\n\u2022 ur(\u03b8v, b, ac) = \u22121 for all v \u2208 V , c \u2208 C, and b \u2208 {t, f}\nsuch that setting v to b does not satisfy c.\n7\nIn general, a player can also receive a signal about the other\nplayers\" preferences, but we will not concern ourselves with\nthat here.\nLet the pure strategy to be dominated be the one that\nplays 0 for every type. We show that the strategy is\ndominated by a pure strategy if and only if there is a solution to\nthe satisfiability instance.\nFirst, suppose there is a solution to the satisfiability\ninstance. Then, let \u03c3d\nr be given by: \u03c3d\nr (\u03b8v) = t if v is set\nto true in the solution to the satisfiability instance, and\n\u03c3d\nr (\u03b8v) = f otherwise. Then, against any action ac by the\ncolumn player, there is at least one type \u03b8v such that either\n+v \u2208 c and \u03c3d\nr (\u03b8v) = t, or \u2212v \u2208 c and \u03c3d\nr (\u03b8v) = f. Thus,\nthe row player\"s expected utility against action ac is at least\n|V |\n|V |\n\u2212 |V |\u22121\n|V |\n= 1\n|V |\n> 0. So, \u03c3d\nr is a dominating strategy.\nNow, suppose there is a dominating pure strategy \u03c3d\nr .\nThis dominating strategy must play t or f for at least one\ntype. Thus, against any ac by the column player, there must\nat least be some type \u03b8v for which ur(\u03b8v, \u03c3d\nr (\u03b8v), ac) > 0.\nThat is, there must be at least one variable v such that\nsetting v to \u03c3d\nr (\u03b8v) satifies c. But then, setting each v to \u03c3d\nr (\u03b8v)\nmust satisfy all the clauses. So a satisfying assignment\nexists.\nHowever, it turns out that we can modify the linear\nprograms from Proposition 1 to obtain a polynomial time\nalgorithm for checking whether a strategy is dominated by a\nmixed strategy in Bayesian games.\nTheorem 6. In a Bayesian game, it can be decided in\npolynomial time whether a given (possibly mixed) strategy\n\u03c3r is dominated by some other mixed strategy, using linear\nprogramming (both for strict and weak dominance).\nProof. We can modify the linear programs presented in\nProposition 1 as follows. For strict dominance, again\nassuming without loss of generality that all the utilities in\nthe game are positive, use the following linear program (in\nwhich p\u03c3r\nr (\u03b8r, ar) is the probability that \u03c3r, the strategy to\nbe dominated, places on ar for type \u03b8r):\nminimize\n\u03b8r\u2208\u0398r ar\u2208Ar\npr(ar)\nsuch that\nfor any ac \u2208 Ac,\n\u03b8r\u2208\u0398r ar\u2208Ar\n\u03c0(\u03b8r)ur(\u03b8r, ar, ac)pr(\u03b8r, ar) \u2265\n\u03b8r\u2208\u0398r ar\u2208Ar\n\u03c0(\u03b8r)ur(\u03b8r, ar, ac)p\u03c3r\nr (\u03b8r, ar);\nfor any \u03b8r \u2208 \u0398r,\nar\u2208Ar\npr(\u03b8r, ar) \u2264 1.\nAssuming that \u03c0(\u03b8r) > 0 for all \u03b8r \u2208 \u0398r, this program\nwill return an objective value smaller than |\u0398r| if and only\nif \u03c3r is strictly dominated, by reasoning similar to that done\nin Proposition 1.\nFor weak dominance, use the following linear program:\nmaximize\nac\u2208Ac\n(\n\u03b8r\u2208\u0398r ar\u2208Ar\n\u03c0(\u03b8r)ur(\u03b8r, ar, ac)pr(\u03b8r, ar)\u2212\n\u03b8r\u2208\u0398r ar\u2208Ar\n\u03c0(\u03b8r)ur(\u03b8r, ar, ac)p\u03c3r\nr (\u03b8r, ar))\nsuch that\nfor any ac \u2208 Ac,\n\u03b8r\u2208\u0398r ar\u2208Ar\n\u03c0(\u03b8r)ur(\u03b8r, ar, ac)pr(\u03b8r, ar) \u2265\n\u03b8r\u2208\u0398r ar\u2208Ar\n\u03c0(\u03b8r)ur(\u03b8r, ar, ac)p\u03c3r\nr (\u03b8r, ar);\nfor any \u03b8r \u2208 \u0398r,\nar\u2208Ar\npr(\u03b8r, ar) = 1.\nThis program will return an objective value greater than\n0 if and only if \u03c3r is weakly dominated, by reasoning similar\nto that done in Proposition 1.\nWe now turn to iterated dominance in Bayesian games.\nNa\u00a8\u0131vely, one might argue that iterated dominance in Bayesian\n95\ngames always requires an exponential number of steps when\na significant fraction of the game\"s pure strategies can be\neliminated, because there are exponentially many pure\nstrategies. However, this is not a very strong argument because\noftentimes we can eliminate exponentially many pure\nstrategies in one step. For example, if for some type \u03b8r \u2208 \u0398r we\nhave, for all ac \u2208 Ac, that u(\u03b8r, a1\nr, ac) > u(\u03b8r, a2\nr, ac), then\nany pure strategy for the row player which plays action a2\nr\nfor type \u03b8r is dominated (by the strategy that plays\naction a1\nr for type \u03b8r instead)-and there are exponentially\nmany (|Ar||\u0398r|\u22121\n) such strategies. It is therefore\nconceivable that we need only polynomially many eliminations of\ncollections of a player\"s strategies. However, the following\ntheorem shows that this is not the case, by giving an\nexample where an exponential number of iterations (that is,\nalternations between the players in eliminating strategies)\nis required. (We emphasize that this is not a result about\ncomputational complexity.)\nTheorem 7. Even in symmetric 3-player Bayesian games,\niterated dominance by pure strategies can require an\nexponential number of iterations (both for strict and weak\ndominance), even with only three actions per player.\nProof. Let each player i \u2208 {1, 2, 3} have n + 1 types\n\u03b81\ni , \u03b82\ni , . . . , \u03b8n+1\ni . Let each player i have 3 actions ai, bi, ci,\nand let the utility function of each player be defined as\nfollows. (In the below, i + 1 and i + 2 are shorthand for\ni + 1(mod 3) and i + 2(mod 3) when used as player indices.\nAlso, \u2212\u221e can be replaced by a sufficiently negative\nnumber. Finally, \u03b4 and should be chosen to be very small (even\ncompared to 2\u2212(n+1)\n), and should be more than twice as\nlarge as \u03b4.)\n\u2022 ui(\u03b81\ni ; ai, ci+1, ci+2) = \u22121;\n\u2022 ui(\u03b81\ni ; ai, si+1, si+2) = 0 for si+1 = ci+1 or si+2 = ci+2;\n\u2022 ui(\u03b81\ni ; bi, si+1, si+2) = \u2212 for si+1 = ai+1 and si+2 =\nai+2;\n\u2022 ui(\u03b81\ni ; bi, si+1, si+2) = \u2212\u221e for si+1 = ai+1 or si+2 =\nai+2;\n\u2022 ui(\u03b81\ni ; ci, si+1, si+2) = \u2212\u221e for all si+1, si+2;\n\u2022 ui(\u03b8j\ni ; ai, si+1, si+2) = \u2212\u221e for all si+1, si+2 when j >\n1;\n\u2022 ui(\u03b8j\ni ; bi, si+1, si+2) = \u2212 for all si+1, si+2 when j > 1;\n\u2022 ui(\u03b8j\ni ; ci, si+1, ci+2) = \u03b4 \u2212 \u2212 1/2 for all si+1 when\nj > 1;\n\u2022 ui(\u03b8j\ni ; ci, si+1, si+2) = \u03b4\u2212 for all si+1 and si+2 = ci+2\nwhen j > 1.\nLet the distribution over each player\"s types be given by\np(\u03b8j\ni ) = 2\u2212j\n(with the exception that p(\u03b82\ni ) = 2\u22122\n+2\u2212(n+1)\n).\nWe will be interested in eliminating strategies of the\nfollowing form: play bi for type \u03b81\ni , and play one of bi or ci\notherwise. Because the utility function is the same for any\ntype \u03b8j\ni with j > 1, these strategies are effectively defined\nby the total probability that they place on ci,8\nwhich is\nt2\ni (2\u22122\n+ 2\u2212(n+1)\n) + n+1\nj=3 tj\ni 2\u2212j\nwhere tj\ni = 1 if player i\n8\nNote that the strategies are still pure strategies; the\nprobability placed on an action by a strategy here is simply the\nsum of the probabilities of the types for which the strategy\nchooses that action.\nplays ci for type \u03b8j\ni , and 0 otherwise. This probability is\ndifferent for any two different strategies of the given form,\nand we have exponentially many different strategies of the\ngiven form. For any probability q which can be expressed\nas t2(2\u22122\n+ 2\u2212(n+1)\n) + n+1\nj=3 tj2\u2212j\n(with all tj \u2208 {0, 1}),\nlet \u03c3i(q) denote the (unique) strategy of the given form for\nplayer i which places a total probability of q on ci. Any\nstrategy that plays ci for type \u03b81\ni or ai for some type \u03b8j\ni\nwith j > 1 can immediately be eliminated. We will show\nthat, after that, we must eliminate the strategies \u03c3i(q) with\nhigh q first, slowly working down to those with lower q.\nClaim 1: If \u03c3i+1(q ) and \u03c3i+2(q ) have not yet been\neliminated, and q < q , then \u03c3i(q) cannot yet be eliminated.\nProof: First, we show that no strategy \u03c3i(q ) can\neliminate \u03c3i(q). Against \u03c3i+1(q ), \u03c3i+2(q ), the utility of\nplaying \u03c3i(p) is \u2212 + p \u00b7 \u03b4 \u2212 p \u00b7 q /2. Thus, when q = 0, it is\nbest to set p as high as possible (and we note that \u03c3i+1(0)\nand \u03c3i+2(0) have not been eliminated), but when q > 0, it\nis best to set p as low as possible because \u03b4 < q /2. Thus,\nwhether q > q or q < q , \u03c3i(q) will always do strictly\nbetter than \u03c3i(q ) against some remaining opponent\nstrategies. Hence, no strategy \u03c3i(q ) can eliminate \u03c3i(q). The\nonly other pure strategies that could dominate \u03c3i(q) are\nstrategies that play ai for type \u03b81\ni , and bi or ci for all other\ntypes. Let us take such a strategy and suppose that it plays\nc with probability p. Against \u03c3i+1(q ), \u03c3i+2(q ) (which have\nnot yet been eliminated), the utility of playing this\nstrategy is \u2212(q )2\n/2 \u2212 /2 + p \u00b7 \u03b4 \u2212 p \u00b7 q /2. On the other hand,\nplaying \u03c3i(q) gives \u2212 + q \u00b7 \u03b4 \u2212 q \u00b7 q /2. Because q > q, we\nhave \u2212(q )2\n/2 < \u2212q \u00b7 q /2, and because \u03b4 and are small,\nit follows that \u03c3i(q) receives a higher utility. Therefore, no\nstrategy dominates \u03c3i(q), proving the claim.\nClaim 2: If for all q > q, \u03c3i+1(q ) and \u03c3i+2(q ) have been\neliminated, then \u03c3i(q) can be eliminated. Proof: Consider\nthe strategy for player i that plays ai for type \u03b81\ni , and bi for\nall other types (call this strategy \u03c3i); we claim \u03c3i dominates\n\u03c3i(q). First, if either of the other players k plays ak for \u03b81\nk,\nthen \u03c3i performs better than \u03c3i(q) (which receives \u2212\u221e in\nsome cases). Because the strategies for player k that play\nck for type \u03b81\nk, or ak for some type \u03b8j\nk with j > 1, have\nalready been eliminated, all that remains to check is that \u03c3i\nperforms better than \u03c3i(q) whenever both of the other two\nplayers play strategies of the following form: play bk for type\n\u03b81\nk, and play one of bk or ck otherwise. We note that among\nthese strategies, there are none left that place probability\ngreater than q on ck. Letting qk denote the probability with\nwhich player k plays ck, the expected utility of playing \u03c3i\nis \u2212qi+1 \u00b7 qi+2/2 \u2212 /2. On the other hand, the utility of\nplaying \u03c3i(q) is \u2212 + q \u00b7 \u03b4 \u2212 q \u00b7 qi+2/2. Because qi+1 \u2264 q, the\ndifference between these two expressions is at least /2 \u2212 \u03b4,\nwhich is positive. It follows that \u03c3i dominates \u03c3i(q).\nFrom Claim 2, it follows that all strategies of the form\n\u03c3i(q) will eventually be eliminated. However, Claim 1 shows\nthat we cannot go ahead and eliminate multiple such\nstrategies for one player, unless at least one other player\nsimultaneously keeps up in the eliminated strategies: every time\na \u03c3i(q) is eliminated such that \u03c3i+1(q) and \u03c3i+2(q) have\nnot yet been eliminated, we need to eliminate one of the\nlatter two strategies before any \u03c3i(q ) with q > q can be\neliminated-that is, we need to alternate between players.\nBecause there are exponentially many strategies of the form\n\u03c3i(q), it follows that iterated elimination will require\nexponentially many iterations to complete.\n96\nIt follows that an efficient algorithm for iterated\ndominance (strict or weak) by pure strategies in Bayesian games,\nif it exists, must somehow be able to perform (at least part\nof) many iterations in a single step of the algorithm (because\nif each step only performed a single iteration, we would need\nexponentially many steps). Interestingly, Knuth et al. [11]\nargue that iterated dominance appears to be an inherently\nsequential problem (in light of their result that iterated very\nweak dominance is P-complete, that is, apparently not\nefficiently parallelizable), suggesting that aggregating many\niterations may be difficult.\n7. CONCLUSIONS\nWhile the Nash equilibrium solution concept is studied\nmore and more intensely in our community, the perhaps\nmore elementary concept of (iterated) dominance has\nreceived much less attention. In this paper we studied various\ncomputational aspects of this concept.\nWe first studied both strict and weak dominance (not\niterated), and showed that checking whether a given strategy\nis dominated by some mixed strategy can be done in\npolynomial time using a single linear program solve. We then\nmoved on to iterated dominance. We showed that\ndetermining whether there is some path that eliminates a given\nstrategy is NP-complete with iterated weak dominance. This\nallowed us to also show that determining whether there is a\npath that leads to a unique solution is NP-complete. Both\nof these results hold both with and without dominance by\nmixed strategies. (A weaker version of the second result\n(only without dominance by mixed strategies) was already\nknown [7].) Iterated strict dominance, on the other hand,\nis path-independent (both with and without dominance by\nmixed strategies) and can therefore be done in polynomial\ntime.\nWe then studied what happens when the dominating\nstrategy is allowed to place positive probability on only a few pure\nstrategies. First, we showed that finding the dominating\nstrategy with minimum support size is NP-complete (both\nfor strict and weak dominance). Then, we showed that\niterated strict dominance becomes path-dependent when there\nis a limit on the support size of the dominating strategies,\nand that deciding whether a given strategy can be\neliminated by iterated strict dominance under this restriction is\nNP-complete (even when the limit on the support size is 3).\nFinally, we studied dominance and iterated dominance in\nBayesian games, as an example of a concise representation\nlanguage for normal form games that is interesting in its own\nright. We showed that, unlike in normal form games,\ndeciding whether a given pure strategy is dominated by another\npure strategy in a Bayesian game is NP-complete (both with\nstrict and weak dominance); however, deciding whether a\nstrategy is dominated by some mixed strategy can still be\ndone in polynomial time with a single linear program solve\n(both with strict and weak dominance). Finally, we showed\nthat iterated dominance using pure strategies can require an\nexponential number of iterations in a Bayesian game (both\nwith strict and weak dominance).\nThere are various avenues for future research. First, there\nis the open question of whether it is possible to complete\niterated dominance in Bayesian games in polynomial time\n(even though we showed that an exponential number of\nalternations between the players in eliminating strategies is\nsometimes required). Second, we can study computational\naspects of (iterated) dominance in concise representations\nof normal form games other than Bayesian games-for\nexample, in graphical games [9] or local-effect/action graph\ngames [12, 2]. (How to efficiently perform iterated very weak\ndominance has already been studied for partially observable\nstochastic games [8].) Finally, we can ask whether some of\nthe algorithms we described (such as the one for iterated\nstrict dominance with mixed strategies) can be made faster.\n8. REFERENCES\n[1] Krzysztof R. Apt. Uniform proofs of order independence for\nvarious strategy elimination procedures. Contributions to\nTheoretical Economics, 4(1), 2004.\n[2] Nivan A. R. Bhat and Kevin Leyton-Brown. Computing\nNash equilibria of action-graph games. In UAI, 2004.\n[3] Ben Blum, Christian R. Shelton, and Daphne Koller. A\ncontinuation method for Nash equilibria in structured\ngames. In IJCAI, 2003.\n[4] Vincent Conitzer and Tuomas Sandholm. Complexity\nresults about Nash equilibria. In IJCAI, pages 765-771,\n2003.\n[5] Drew Fudenberg and Jean Tirole. Game Theory. MIT\nPress, 1991.\n[6] Itzhak Gilboa, Ehud Kalai, and Eitan Zemel. On the order\nof eliminating dominated strategies. Operations Research\nLetters, 9:85-89, 1990.\n[7] Itzhak Gilboa, Ehud Kalai, and Eitan Zemel. The\ncomplexity of eliminating dominated strategies.\nMathematics of Operation Research, 18:553-565, 1993.\n[8] Eric A. Hansen, Daniel S. Bernstein, and Shlomo\nZilberstein. Dynamic programming for partially observable\nstochastic games. In AAAI, pages 709-715, 2004.\n[9] Michael Kearns, Michael Littman, and Satinder Singh.\nGraphical models for game theory. In UAI, 2001.\n[10] Leonid Khachiyan. A polynomial algorithm in linear\nprogramming. Soviet Math. Doklady, 20:191-194, 1979.\n[11] Donald E. Knuth, Christos H. Papadimitriou, and John N\nTsitsiklis. A note on strategy elimination in bimatrix\ngames. Operations Research Letters, 7(3):103-107, 1988.\n[12] Kevin Leyton-Brown and Moshe Tennenholtz. Local-effect\ngames. In IJCAI, 2003.\n[13] Richard Lipton, Evangelos Markakis, and Aranyak Mehta.\nPlaying large games using simple strategies. In ACM-EC,\npages 36-41, 2003.\n[14] Michael Littman and Peter Stone. A polynomial-time Nash\nequilibrium algorithm for repeated games. In ACM-EC,\npages 48-54, 2003.\n[15] Leslie M. Marx and Jeroen M. Swinkels. Order\nindependence for iterated weak dominance. Games and\nEconomic Behavior, 18:219-245, 1997.\n[16] Leslie M. Marx and Jeroen M. Swinkels. Corrigendum,\norder independence for iterated weak dominance. Games\nand Economic Behavior, 31:324-329, 2000.\n[17] Andreu Mas-Colell, Michael Whinston, and Jerry R. Green.\nMicroeconomic Theory. Oxford University Press, 1995.\n[18] Roger Myerson. Game Theory: Analysis of Conflict.\nHarvard University Press, Cambridge, 1991.\n[19] Martin J Osborne and Ariel Rubinstein. A Course in\nGame Theory. MIT Press, 1994.\n[20] Christos Papadimitriou. Algorithms, games and the\nInternet. In STOC, pages 749-753, 2001.\n[21] Ryan Porter, Eugene Nudelman, and Yoav Shoham. Simple\nsearch methods for finding a Nash equilibrium. In AAAI,\npages 664-669, 2004.\n97", "keywords": "game theory;nash equilibrium;bayesian game;dominance;normal form game;elimination;iterated dominance;self-interested agent;strategy;optimal action;multiagent system"}
{"name": "train_J-52", "title": "Hidden-Action in Multi-Hop Routing", "abstract": "In multi-hop networks, the actions taken by individual intermediate nodes are typically hidden from the communicating endpoints; all the endpoints can observe is whether or not the end-to-end transmission was successful. Therefore, in the absence of incentives to the contrary, rational (i.e., selfish) intermediate nodes may choose to forward packets at a low priority or simply not forward packets at all. Using a principal-agent model, we show how the hidden-action problem can be overcome through appropriate design of contracts, in both the direct (the endpoints contract with each individual router) and recursive (each router contracts with the next downstream router) cases. We further demonstrate that per-hop monitoring does not necessarily improve the utility of the principal or the social welfare in the system. In addition, we generalize existing mechanisms that deal with hidden-information to handle scenarios involving both hidden-information and hidden-action.", "fulltext": "1. INTRODUCTION\nEndpoints wishing to communicate over a multi-hop network\nrely on intermediate nodes to forward packets from the sender to\nthe receiver. In settings where the intermediate nodes are\nindependent agents (such as individual nodes in ad-hoc and\npeer-topeer networks or autonomous systems on the Internet), this poses\nan incentive problem; the intermediate nodes may incur significant\ncommunication and computation costs in the forwarding of packets\nwithout deriving any direct benefit from doing so. Consequently, a\nrational (i.e., utility maximizing) intermediate node may choose to\nforward packets at a low priority or not forward the packets at all.\nThis rational behavior may lead to suboptimal system performance.\nThe endpoints can provide incentives, e.g., in the form of\npayments, to encourage the intermediate nodes to forward their\npackets. However, the actions of the intermediate nodes are often hidden\nfrom the endpoints. In many cases, the endpoints can only observe\nwhether or not the packet has reached the destination, and cannot\nattribute failure to a specific node on the path. Even if some form\nof monitoring mechanism allows them to pinpoint the location of\nthe failure, they may still be unable to attribute the cause of failure\nto either the deliberate action of the intermediate node, or to some\nexternal factors beyond the control of the intermediate node, such\nas network congestion, channel interference, or data corruption.\nThe problem of hidden action is hardly unique to networks. Also\nknown as moral hazard, this problem has long been of interest in\nthe economics literature concerning information asymmetry,\nincentive and contract theory, and agency theory. We follow this\nliterature by formalizing the problem as a principal-agent model, where\nmultiple agents making sequential hidden actions [17, 27].\nOur results are threefold. First, we show that it is possible to\ndesign contracts to induce cooperation when intermediate nodes\ncan choose to forward or drop packets, as well as when the nodes\ncan choose to forward packets with different levels of quality of\nservice. If the path and transit costs are known prior to\ntransmission, the principal achieves first best solution, and can implement\nthe contracts either directly with each intermediate node or\nrecursively through the network (each node making a contract with the\nfollowing node) without any loss in utility. Second, we find that\nintroducing per-hop monitoring has no impact on the principal\"s\nexpected utility in equilibrium. For a principal who wishes to induce\nan equilibrium in which all intermediate nodes cooperate, its\nexpected total payment is the same with or without monitoring.\nHowever, monitoring provides a dominant strategy equilibrium, which\nis a stronger solution concept than the Nash equilibrium achievable\nin the absence of monitoring. Third, we show that in the absence\nof a priori information about transit costs on the packet forwarding\npath, it is possible to generalize existing mechanisms to overcome\nscenarios that involve both hidden-information and hidden-action.\nIn these scenarios, the principal pays a premium compared to\nscenarios with known transit costs.\n2. BASELINE MODEL\nWe consider a principal-agent model, where the principal is a\npair of communication endpoints who wish to communicate over\na multi-hop network, and the agents are the intermediate nodes\ncapable of forwarding packets between the endpoints. The\nprincipal (who in practice can be either the sender, the receiver, or\n117\nboth) makes individual take-it-or-leave-it offers (contracts) to the\nagents. If the contracts are accepted, the agents choose their\nactions sequentially to maximize their expected payoffs based on the\npayment schedule of the contract. When necessary, agents can in\nturn make subsequent take-it-or-leave-it offers to their downstream\nagents.\nWe assume that all participants are risk neutral and that standard\nassumptions about the global observability of the final outcome and\nthe enforceability of payments by guaranteeing parties hold.\nFor simplicity, we assume that each agent has only two possible\nactions; one involving significant effort and one involving little\neffort. We denote the action choice of agent i by ai \u2208 {0, 1}, where\nai = 0 and ai = 1 stand for the low-effort and high-effort actions,\nrespectively. Each action is associated with a cost (to the agent)\nC(ai), and we assume:\nC(ai = 1) > C(ai = 0)\nAt this stage, we assume that all nodes have the same C(ai) for\npresentation clarity, but we relax this assumption later. Without loss\nof generality we normalize the C(ai = 0) to be zero, and denote\nthe high-effort cost by c, so C(ai = 0) = 0 and C(ai = 1) = c.\nThe utility of agent i, denoted by ui, is a function of the payment\nit receives from the principal (si), the action it takes (ai), and the\ncost it incurs (ci), as follows:\nui(si, ci, ai) = si \u2212 aici\nThe outcome is denoted by x \u2208 {xG\n, xB\n}, where xG\nstands\nfor the Good outcome in which the packet reaches the\ndestination, and xB\nstands for the Bad outcome in which the packet\nis dropped before it reaches the destination. The outcome is a\nfunction of the vector of actions taken by the agents on the path,\na = (a1, ..., an) \u2208 {0, 1}n\n, and the loss rate on the channels, k.\nThe benefit of the sender from the outcome is denoted by w(x),\nwhere:\nw(xG\n) = wG\n; and w(xB\n) = wB\n= 0\nThe utility of the sender is consequently:\nu(x, S) = w(x) \u2212 S\nwhere: S =\nPn\ni=1 si\nA sender who wishes to induce an equilibrium in which all nodes\nengage in the high-effort action needs to satisfy two constraints for\neach agent i:\n(IR) Individual rationality (participation constraint)1\n: the\nexpected utility from participation should (weakly) exceed its\nreservation utility (which we normalize to 0).\n(IC) Incentive compatibility: the expected utility from exerting\nhigh-effort should (weakly) exceed its expected utility from\nexerting low-effort.\nIn some network scenarios, the topology and costs are common\nknowledge. That is, the sender knows in advance the path that its\npacket will take and the costs on that path. In other routing\nscenarios, the sender does not have this a priori information. We show\nthat our model can be applied to both scenarios with known and\nunknown topologies and costs, and highlight the implications of each\nscenario in the context of contracts. We also distinguish between\ndirect contracts, where the principal signs an individual contract\n1We use the notion of ex ante individual rationality, in which the agents\nchoose to participate before they know the state of the system.\nS Dn1\nSource Destination\nn intermediate nodes\nFigure 1: Multi-hop path from sender to destination.\nFigure 2: Structure of the multihop routing game under known\ntopology and transit costs.\nwith each node, and recursive contracts, where each node enters a\ncontractual relationship with its downstream node.\nThe remainder of this paper is organized as follows. In Section 3\nwe consider agents who decide whether to drop or forward\npackets with and without monitoring when the transit costs are common\nknowledge. In Section 4, we extend the model to scenarios with\nunknown transit costs. In Section 5, we distinguish between recursive\nand direct contracts and discuss their relationship. In Section 6, we\nshow that the model applies to scenarios in which agents choose\nbetween different levels of quality of service. We consider Internet\nrouting as a case study in Section 7. In Section 8 we present related\nwork, and Section 9 concludes the paper.\n3. KNOWN TRANSIT COSTS\nIn this section we analyze scenarios in which the principal knows\nin advance the nodes on the path to the destination and their costs,\nas shown in figure 1. We consider agents who decide whether to\ndrop or forward packets, and distinguish between scenarios with\nand without monitoring.\n3.1 Drop versus Forward without Monitoring\nIn this scenario, the agents decide whether to drop (a = 0) or\nforward (a = 1) packets. The principal uses no monitoring to\nobserve per-hop outcomes. Consequently, the principal makes the\npayment schedule to each agent contingent on the final outcome, x,\nas follows:\nsi(x) = (sB\ni , sG\ni )\nwhere:\nsB\ni = si(x = xB\n)\nsG\ni = si(x = xG\n)\nThe timeline of this scenario is shown in figure 2. Given a\nperhop loss rate of k, we can express the probability that a packet is\nsuccessfully delivered from node i to its successor i + 1 as:\nPr(xG\ni\u2192i+1|ai) = (1 \u2212 k)ai (1)\nwhere xG\ni\u2192j denotes a successful transmission from node i to j.\nPROPOSITION 3.1. Under the optimal contract that induces\nhigh-effort behavior from all intermediate nodes in the Nash\nEqui118\nlibrium2\n, the expected payment to each node is the same as its\nexpected cost, with the following payment schedule:\nsB\ni = si(x = xB\n) = 0 (2)\nsG\ni = si(x = xG\n) =\nc\n(1 \u2212 k)n\u2212i+1\n(3)\nPROOF. The principal needs to satisfy the IC and IR\nconstraints for each agent i, which can be expressed as follows:\n(IC)Pr(xG\n|aj\u2265i = 1)sG\ni + Pr(xB\n|aj\u2265i = 1)sB\ni \u2212 c \u2265\nPr(xG\n|ai = 0, aj>i = 1)sG\ni + Pr(xB\n|ai = 0, aj>i = 1)sB\ni\n(4)\nThis constraint says that the expected utility from forwarding is\ngreater than or equal to its expected utility from dropping, if all\nsubsequent nodes forward as well.\n(IR)Pr(xG\nS\u2192i|aj<i = 1)(Pr(xG\n|aj\u2265i = 1)sG\ni +\nPr(xB\n|aj\u2265i = 1)sB\ni \u2212 c) + Pr(xB\nS\u2192i|aj<i = 1)sB\ni \u2265 0\n(5)\nThis constraint says that the expected utility from participating is\ngreater than or equal to zero (reservation utility), if all other nodes\nforward.\nThe above constraints can be expressed as follows, based on\nEq. 1:\n(IC) : (1 \u2212 k)n\u2212i+1\nsG\ni + (1 \u2212 (1 \u2212 k)n\u2212i+1\n)sB\ni \u2212 c \u2265 sB\ni\n(IR) : (1\u2212k)i\n((1\u2212k)n\u2212i+1\nsG\ni +(1\u2212(1\u2212k)n\u2212i+1\n)sB\ni \u2212c)+\n(1 \u2212 (1 \u2212 k)i\n)sB\ni \u2265 0\nIt is a standard result that both constraints bind at the optimal\ncontract (see [23]). Solving the two equations, we obtain the\nsolution that is presented in Eqs. 2 and 3.\nWe next prove that the expected payment to a node equals its\nexpected cost in equilibrium. The expected cost of node i is its\ntransit cost multiplied by the probability that it faces this cost (i.e.,\nthe probability that the packet reaches node i), which is: (1 \u2212 k)i\nc.\nThe expected payment that node i receives is:\nPr(xG\n)sG\ni + Pr(xB\n)sB\ni = (1 \u2212 k)n+1 c\n(1 \u2212 k)n\u2212i+1\n= (1 \u2212 k)i\nc\nNote that the expected payment to a node decreases as the node\ngets closer to the destination due to the asymmetric distribution\nof risk. The closer the node is to the destination, the lower the\nprobability that a packet will fail to reach the destination, resulting\nin the low payment being made to the node.\nThe expected payment by the principal is:\nE[S] = (1 \u2212 k)n+1\nnX\ni=1\nsG\ni + (1 \u2212 (1 \u2212 k)n+1\n)\nnX\ni=1\nsB\ni\n= (1 \u2212 k)n+1\nnX\ni=1\nci\n(1 \u2212 k)n\u2212i+1\n(6)\nThe expected payment made by the principal depends not only\non the total cost, but also the number of nodes on the path.\nPROPOSITION 3.2. Given two paths with respective lengths of\nn1 and n2 hops, per-hop transit costs of c1 and c2, and per-hop\nloss rates of k1 and k2, such that:\n2Since transit nodes perform actions sequentially, this is really a\nsubgameperfect equilibrium (SPE), but we will refer to it as Nash equilibrium in the\nremainder of the paper.\nFigure 3: Two paths of equal total costs but different lengths and\nindividual costs.\n\u2022 c1n1 = c2n2 (equal total cost)\n\u2022 (1 \u2212 k1)n1+1\n= (1 \u2212 k2)n2+1\n(equal expected benefit)\n\u2022 n1 < n2 (path 1 is shorter than path 2)\nthe expected total payment made by the principal is lower on the\nshorter path.\nPROOF. The expected payment in path j is\nE[S]j =\nnj\nX\ni=1\ncj (1 \u2212 kj )i\n= cj (1 \u2212 kj )\n1 \u2212 (1 \u2212 kj)nj\nkj\nSo, we have to show that:\nc1(1 \u2212 k1)\n1 \u2212 (1 \u2212 k1)n1\nk1\n> c2(1 \u2212 k2)\n1 \u2212 (1 \u2212 k2)n2\nk2\nLet M = c1n1 = c2n2 and N = (1 \u2212 k1)n1+1\n= (1 \u2212 k2)n2+1\n.\nWe have to show that\nMN\n1\nn1+1 (1 \u2212 N\nn1\nn1+1 )\nn1(1 \u2212 N\n1\nn1+1 )\n<\nMN\n1\nn2+1 (1 \u2212 N\nn2\nn2+1 )\nn2(1 \u2212 N\n1\nn2+1 )\n(7)\nLet\nf =\nN\n1\nn+1 (1 \u2212 N\nn\nn+1 )\nn(1 \u2212 N\n1\nn+1 )\nThen, it is enough to show that f is monotonically increasing in n\n\u2202f\n\u2202n\n=\ng(N, n)\nh(N, n)\nwhere:\ng(N, n) = \u2212((ln(N)n \u2212 (n + 1)2\n)(N\n1\nn+1\n\u2212 N\nn+2\nn+1 ) \u2212 (n + 1)2\n(N + N\n2\nn+1 ))\nand\nh(N, n) = (n + 1)2\nn2\n(\u22121 + N\n1\nn+1 )2\nbut h(N, n) > 0 \u2200N, n, therefore, it is enough to show that\ng(N, n) > 0. Because N \u2208 (0, 1): (i) ln(N) < 0, and (ii)\nN\n1\nn+1 > N\nn+2\nn+1 . Therefore, g(N, n) > 0 \u2200N, n.\nThis means that, ceteris paribus, shorter paths should always be\npreferred over longer ones.\nFor example, consider the two topologies presented in Figure 3.\nWhile the paths are of equal total cost, the total expected payment\nby the principal is different. Based on Eqs. 2 and 3, the expected\ntotal payment for the top path is:\nE[S] = Pr(xG\n)(sG\nA + sG\nB)\n=\n\u201e\nc1\n(1 \u2212 k1)2\n+\nc1\n1 \u2212 k1\n\u00ab\n(1 \u2212 k1)3\n(8)\n119\nwhile the expect total payment for the bottom path is:\nE[S] = Pr(xG\n)(sG\nA + sG\nB + sG\nC )\n= (\nc2\n(1 \u2212 k2)3\n+\nc2\n(1 \u2212 k2)2\n+\nc2\n1 \u2212 k2\n)(1 \u2212 k2)4\nFor n1 = 2, c1 = 1.5, k1 = 0.5, n2 = 3, c2 = 1, k2 = 0.405,\nwe have equal total cost and equal expected benefit, but E[S]1 =\n0.948 and E[S]2 = 1.313.\n3.2 Drop versus Forward with Monitoring\nSuppose the principal obtains per-hop monitoring information.3\nPer-hop information broadens the set of mechanisms the principal\ncan use. For example, the principal can make the payment schedule\ncontingent on arrival to the next hop instead of arrival to the final\ndestination. Can such information be of use to a principal wishing\nto induce an equilibrium in which all intermediate nodes forward\nthe packet?\nPROPOSITION 3.3. In the drop versus forward model, the\nprincipal derives the same expected utility whether it obtains per-hop\nmonitoring information or not.\nPROOF. The proof to this proposition is already implied in the\nfindings of the previous section. We found that in the absence of\nper-hop information, the expected cost of each intermediate node\nequals its expected payment. In order to satisfy the IR constraint, it\nis essential to pay each intermediate node an expected amount of at\nleast its expected cost; otherwise, the node would be better-off not\nparticipating. Therefore, no other payment scheme can reduce the\nexpected payment from the principal to the intermediate nodes. In\naddition, if all nodes are incentivized to forward packets, the\nprobability that the packet reaches the destination is the same in both\nscenarios, thus the expected benefit of the principal is the same.\nIndeed, we have found that even in the absence of per-hop monitoring\ninformation, the principal achieves first-best solution.\nTo convince the reader that this is indeed the case, we provide an\nexample of a mechanism that conditions payments on arrival to the\nnext hop. This is possible only if per-hop monitoring information\nis provided. In the new mechanism, the principal makes the\npayment schedule contingent on whether the packet has reached the\nnext hop or not. That is, the payment to node i is sG\ni if the packet\nhas reached node i + 1, and sB\ni otherwise. We assume costless\nmonitoring, giving us the best case scenario for the use of\nmonitoring. As before, we consider a principal who wishes to induce an\nequilibrium in which all intermediate nodes forward the packet.\nThe expected utility of the principal is the difference between its\nexpected benefit and its expected payment. Because the expected\nbenefit when all nodes forward is the same under both scenarios,\nwe only need to show that the expected total payment is identical as\nwell. Under the monitoring mechanism, the principal has to satisfy\nthe following constraints:\n(IC)Pr(xG\ni\u2192i+1|ai = 1)sG\n+ Pr(xB\ni\u2192i+1|ai = 1)sB\n\u2212 c \u2265\nPr(xG\ni\u2192i+1|ai = 0)sG\n+ Pr(xB\ni\u2192i+1|ai = 0)sB\n(9)\n(IR)Pr(xG\nS\u2192i|aj<i = 1)(Pr(xG\ni\u2192i+1|ai = 1)sG\n+ Pr(xB\ni\u2192i+1|ai = 1)sB\n\u2212 c) \u2265 0\n(10)\n3For a recent proposal of an accountability framework that provides such\nmonitoring information see [4].\nThese constraints can be expressed as follows:\n(IC) : (1 \u2212 k)sG\n+ ksB\n\u2212 c \u2265 s0\n(IR) : (1 \u2212 k)i\n((1 \u2212 k)sG\n+ ksB\n\u2212 c) \u2265 0\nThe two constraints bind at the optimal contract as before, and\nwe get the following payment schedule:\nsB\n= 0\nsG\n=\nc\n1 \u2212 k\nThe expected total payment under this scenario is:\nE[S] =\nnX\ni=1\n((1 \u2212 k)i\n(sB\n+ (i \u2212 1)sG\n)) + (1 \u2212 k)n+1\nnsG\n= (1 \u2212 k)n+1\nnX\ni=1\nci\n(1 \u2212 k)n\u2212i+1\nas in the scenario without monitoring (see Equation 6.)\nWhile the expected total payment is the same with or without\nmonitoring, there are some differences between the two scenarios.\nFirst, the payment structure is different. If no per-hop monitoring\nis used, the payment to each node depends on its location (i). In\ncontrast, monitoring provides us with n identical contracts.\nSecond, the solution concept used is different. If no monitoring\nis used, the strategy profile of ai = 1 \u2200i is a Nash equilibrium,\nwhich means that no agent has an incentive to deviate unilaterally\nfrom the strategy profile. In contrast, with the use of monitoring,\nthe action chosen by node i is independent of the other agents\"\nforwarding behavior. Therefore, monitoring provides us with\ndominant strategy equilibrium, which is a stronger solution concept than\nNash equilibrium. [15], [16] discuss the appropriateness of\ndifferent solution concepts in the context of online environments.\n4. UNKNOWN TRANSIT COSTS\nIn certain network settings, the transit costs of nodes along the\nforwarding path may not be common knowledge, i.e., there exists\nthe problem of hidden information. In this section, we address the\nfollowing questions:\n1. Is it possible to design contracts that induce cooperative\nbehavior in the presence of both hidden-action and\nhiddeninformation?\n2. What is the principal\"s loss due to the lack of knowledge of\nthe transit costs?\nIn hidden-information problems, the principal employs\nmechanisms to induce truthful revelation of private information from the\nagents. In the routing game, the principal wishes to extract transit\ncost information from the network routers in order to determine the\nlowest cost path (LCP) for a given source-destination pair. The\nnetwork routers act strategically and declare transit costs to maximize\ntheir profit. Mechanisms that have been proposed in the literature\nfor the routing game [24, 13] assume that once the transit costs\nhave been obtained, and the LCP has been determined, the nodes\non the LCP obediently forward all packets, and that there is no loss\nin the network, i.e., k = 0. In this section, we consider both hidden\ninformation and hidden action, and generalize these mechanisms\nto induce both truth revelation and high-effort action in\nequilibrium, where nodes transmit over a lossy communication channel,\ni.e., k \u2265 0.\n4.1 V CG Mechanism\nIn their seminal paper [24], Nisan and Ronen present a VCG\nmechanism that induces truthful revelation of transit costs by edges\n120\nFigure 4: Game structure for F P SS, where only hidden-information\nis considered.\nFigure 5: Game structure for F P SS , where both\nhiddeninformation and hidden-action are considered.\nin a biconnected network, such that lowest cost paths can be\nchosen. Like all VCG mechanisms, it is a strategyproof mechanism,\nmeaning that it induces truthful revelation in a dominant strategy\nequilibrium. In [13] (FPSS), Feigenbaum et al. slightly modify\nthe model to have the routers as the selfish agents instead of the\nedges, and present a distributed algorithm that computes the VCG\npayments. The timeline of the FPSS game is presented in\nfigure 4. Under FPSS, transit nodes keep track of the amount of\ntraffic routed through them via counters, and payments are\nperiodically transferred from the principals to the transit nodes based on\nthe counter values. FPSS assumes that transit nodes are\nobedient in packet forwarding behavior, and will not update the counters\nwithout exerting high effort in packet forwarding.\nIn this section, we present FPSS , which generalizes FPSS to\noperate in an environment with lossy communication channels (i.e.,\nk \u2265 0) and strategic behavior in terms of packet forwarding. We\nwill show that FPSS induces an equilibrium in which all nodes\ntruthfully reveal their transit costs and forward packets if they are\non the LCP. Figure 5 presents the timeline of FPSS . In the first\nstage, the sender declares two payment functions, (sG\ni , sB\ni ), that\nwill be paid upon success or failure of packet delivery. Given these\npayments, nodes have incentive to reveal their costs truthfully, and\nlater to forward packets. Payments are transferred based on the\nfinal outcome.\nIn FPSS , each node i submits a bid bi, which is its reported\ntransit cost. Node i is said to be truthful if bi = ci. We write b for\nthe vector (b1, . . . , bn) of bids submitted by all transit nodes. Let\nIi(b) be the indicator function for the LCP given the bid vector b\nsuch that\nIi(b) =\n\uf6be\n1 if i is on the LCP;\n0 otherwise.\nFollowing FPSS [13], the payment received by node i at\nequilibrium is:\npi = biIi(b) + [\nX\nr\nIr(b|i\n\u221e)br \u2212\nX\nr\nIr(b)br]\n=\nX\nr\nIr(b|i\n\u221e)br \u2212\nX\nr=i\nIr(b)br\n(11)\nwhere the expression b|i\nx means that (b|i\nx)j = cj for all j = i,\nand (b|i\nx)i = x.\nIn FPSS , we compute sB\ni and sG\ni as a function of pi, k, and\nn. First, we recognize that sB\ni must be less than or equal to zero\nin order for the true LCP to be chosen. Otherwise, strategic nodes\nmay have an incentive to report extremely small costs to mislead\nthe principal into believing that they are on the LCP. Then, these\nnodes can drop any packets they receive, incur zero transit cost,\ncollect a payment of sB\ni > 0, and earn positive profit.\nPROPOSITION 4.1. Let the payments of FPSS be:\nsB\ni = 0\nsG\ni =\npi\n(1 \u2212 k)n\u2212i+1\nThen, FPSS has a Nash equilibrium in which all nodes truthfully\nreveal their transit costs and all nodes on the LCP forward packets.\nPROOF. In order to prove the proposition above, we have to\nshow that nodes have no incentive to engage in the following\nmisbehaviors:\n1. truthfully reveal cost but drop packet,\n2. lie about cost and forward packet,\n3. lie about cost and drop packet.\nIf all nodes truthfully reveal their costs and forward packets, the\nexpected utility of node i on the LCP is:\nE[u]i = Pr(xG\nS\u2192i)(E[si] \u2212 ci) + Pr(xB\nS\u2192i)sB\ni\n= (1 \u2212 k)i\n\n(1 \u2212 k)n\u2212i+1\nsG\ni + (1 \u2212 (1 \u2212 k)n\u2212i+1\n)sB\ni \u2212 ci\n\n+ (1 \u2212 (1 \u2212 k)i\n)sB\ni\n= (1 \u2212 k)i\n(1 \u2212 k)n\u2212i+1 pi\n(1 \u2212 k)n\u2212i+1\n\u2212 (1 \u2212 k)i\nci\n= (1 \u2212 k)i\n(pi \u2212 ci)\n\u2265 0\n(12)\nThe last inequality is derived from the fact that FPSS is a truthful\nmechanism, thus pi \u2265 ci. The expected utility of a node not on the\nLCP is 0.\nA node that drops a packet receives sB\ni = 0, which is smaller\nthan or equal to E[u]i for i \u2208 LCP and equals E[u]i for i /\u2208 LCP.\nTherefore, nodes cannot gain utility from misbehaviors (1) or (3).\nWe next show that nodes cannot gain utility from misbehavior (2).\n1. if i \u2208 LCP, E[u]i > 0.\n(a) if it reports bi > ci:\ni. if bi <\nP\nr Ir(b|i\n\u221e)br \u2212\nP\nr=i Ir(b)br, it is still\non the LCP, and since the payment is independent\nof bi, its utility does not change.\nii. if bi >\nP\nr Ir(b|i\n\u221e)br \u2212\nP\nr=i Ir(b)br, it will\nnot be on the LCP and obtain E[u]i = 0, which is\nless than its expected utility if truthfully revealing\nits cost.\n121\n(b) if it reports bi < ci, it is still on the LCP, and since\nthe payment is independent of bi, its utility does not\nchange.\n2. if i /\u2208 LCP, E[u]i = 0.\n(a) if it reports bi > ci, it remains out of the LCP, so its\nutility does not change.\n(b) if it reports bi < ci:\ni. if bi <\nP\nr Ir(b|i\n\u221e)br \u2212\nP\nr=i Ir(b)br, it joins\nthe LCP, and gains an expected utility of\nE[u]i = (1 \u2212 k)i\n(pi \u2212 ct)\nHowever, if i /\u2208 LCP, it means that\nci >\nX\nr\nIr(c|i\n\u221e)cr \u2212\nX\nr=i\nIr(c)cr\nBut if all nodes truthfully reveal their costs,\npi =\nX\nr\nIr(c|i\n\u221e)cr \u2212\nX\nr=i\nIr(c)cr < ci\ntherefore, E[u]i < 0\nii. if bi >\nP\nr Ir(b|i\n\u221e)br \u2212\nP\nr=i Ir(b)br, it\nremains out of the LCP, so its utility does not change.\nTherefore, there exists an equilibrium in which all nodes truthfully\nreveal their transit costs and forward the received packets.\nWe note that in the hidden information only context, FPSS\ninduces truthful revelation as a dominant strategy equilibrium. In\nthe current setting with both hidden information and hidden action,\nFPSS achieves a Nash equilibrium in the absence of per-hop\nmonitoring, and a dominant strategy equilibrium in the presence of\nper-hop monitoring, consistent with the results in section 3 where\nthere is hidden action only. In particular, with per-hop monitoring,\nthe principal declares the payments sB\ni and sG\ni to each node upon\nfailure or success of delivery to the next node. Given the payments\nsB\ni = 0 and sG\ni = pi/(1 \u2212 k), it is a dominant strategy for the\nnodes to reveal costs truthfully and forward packets.\n4.2 Discussion\nMore generally, for any mechanism M that induces a bid vector b\nin equilibrium by making a payment of pi(b) to node i on the LCP,\nthere exists a mechanism M that induces an equilibrium with the\nsame bid vector and packet forwarding by making a payment of:\nsB\ni = 0\nsG\ni =\npi(b)\n(1 \u2212 k)n\u2212i+1\n.\nA sketch of the proof would be as follows:\n1. IM\ni (b) = IM\ni (b)\u2200i, since M uses the same choice metric.\n2. The expected utility of a LCP node is E[u]i = (1 \u2212\nk)i\n(pi(b) \u2212 ci) \u2265 0 if it forwards and 0 if it drops, and\nthe expected utility of a non-LCP node is 0.\n3. From 1 and 2, we get that if a node i can increase its expected\nutility by deviating from bi under M , it can also increase its\nutility by deviating from bi in M, but this is in contradiction\nto bi being an equilibrium in M.\n4. Nodes have no incentive to drop packets since they derive an\nexpected utility of 0 if they do.\nIn addition to the generalization of FPSS into FPSS , we\ncan also consider the generalization of the first-price auction (FPA)\nmechanism, where the principal determines the LCP and pays each\nnode on the LCP its bid, pi(b) = bi. First-price auctions achieve\nNash equilibrium as opposed to dominant strategy equilibrium.\nTherefore, we should expect the generalization of FPA to achieve\nNash equilibrium with or without monitoring.\nWe make two additional comments concerning this class of\nmechanisms. First, we find that the expected total payment made\nby the principal under the proposed mechanisms is\nE[S] =\nnX\ni=1\n(1 \u2212 k)i\npi(b)\nand the expected benefit realized by the principal is\nE[w] = (1 \u2212 k)n+1\nwG\nwhere\nPn\ni=1 pi and wG\nare the expected payment and expected\nbenefit, respectively, when only the hidden-information problem is\nconsidered. When hidden action is also taken into consideration,\nthe generalized mechanism handles strategic forwarding behavior\nby conditioning payments upon the final outcome, and accounts for\nlossy communication channels by designing payments that reflect\nthe distribution of risk. The difference between expected payment\nand benefit is not due to strategic forwarding behavior, but to lossy\ncommunications. Therefore, in a lossless network, we should not\nsee any gap between expected benefits and payments, independent\nof strategic or non-strategic forwarding behavior.\nSecond, the loss to the principal due to unknown transit costs is\nalso known as the price of frugality, and is an active field of\nresearch [2, 12]. This price greatly depends on the network topology\nand on the mechanism employed. While it is simple to characterize\nthe principal\"s loss in some special cases, it is not a trivial problem\nin general. For example, in topologies with parallel disjoint paths\nfrom source to destination, we can prove that under first-price\nauctions, the loss to the principal is the difference between the cost of\nthe shortest path and the second-shortest path, and the loss is higher\nunder the FPSS mechanism.\n5. RECURSIVE CONTRACTS\nIn this section, we distinguish between direct and recursive\ncontracts. In direct contracts, the principal contracts directly with each\nnode on the path and pays it directly. In recursive payment, the\nprincipal contracts with the first node on the path, which in turn\ncontracts with the second, and so on, such that each node contracts\nwith its downstream node and makes the payment based on the final\nresult, as demonstrated in figure 6.\nWith direct payments, the principal needs to know the identity\nand cost of each node on the path and to have some communication\nchannel with the node. With recursive payments, every node needs\nto communicate only with its downstream node. Several questions\narise in this context:\n\u2022 What knowledge should the principal have in order to induce\ncooperative behavior through recursive contracts?\n\u2022 What should be the structure of recursive contracts that\ninduce cooperative behavior?\n\u2022 What is the relation between the total expected payment\nunder direct and recursive contracts?\n\u2022 Is it possible to design recursive contracts in scenarios of\nunknown transit costs?\n122\nFigure 6: Structure of the multihop routing game under known\ntopology and recursive contracts.\nIn order to answer the questions outlined above, we look at the\nIR and IC constraints that the principal needs to satisfy when\ncontracting with the first node on the path. When the principal designs\na contract with the first node, he should take into account the\nincentives that the first node should provide to the second node, and\nso on all the way to the destination.\nFor example, consider the topology given in figure 3 (a). When\nthe principal comes to design a contract with node A, he needs to\nconsider the subsequent contract that A should sign with B, which\nshould satisfy the following constrints.\n(IR) :Pr(xG\nA\u2192B|aA = 1)(E[s|aB = 1] \u2212 c)+\nPr(xB\nA\u2192B|aA = 1)sB\nA\u2192B \u2265 0\n(IC) :E[s|aB = 1] \u2212 c \u2265 E[s|aB = 0]\nwhere:\nE[s|aB = 1] = Pr(xG\nB\u2192D|aB = 1)sG\nA\u2192B\n+ Pr(xB\nB\u2192D|aB = 1)sB\nA\u2192B\nand\nE[s|aB = 0] = Pr(xG\nB\u2192D|aB = 0)sG\nA\u2192B\n+ Pr(xB\nB\u2192D|aB = 0)sB\nA\u2192B\nThese (binding) constraints yield the values of sB\nA\u2192B and sG\nA\u2192B:\nsB\nA\u2192B = 0\nsG\nA\u2192B = c/(1 \u2212 k)\nBased on these values, S can express the constraints it should\nsatisfy in a contract with A.\n(IR) :Pr(xG\nS\u2192A|aS = 1)(E[sS\u2192A \u2212 sA\u2192B|ai = 1\u2200i] \u2212 c)\n+ Pr(xB\nS\u2192A|aS = 1)sB\nS\u2192A \u2265 0\n(IC) : E[sS\u2192A \u2212 sA\u2192B|ai = 1\u2200i] \u2212 c\n\u2265 E[sS\u2192A \u2212 sA\u2192B|aA = 0, aB = 1]\nwhere:\nE[sS\u2192A \u2212 sA\u2192B|ai = 1\u2200i] =\nPr(xG\nA\u2192D|ai = 1\u2200i)(sG\nS\u2192A \u2212 sG\nA\u2192B)\n+Pr(xB\nA\u2192D|ai = 1\u2200i)(sB\nS\u2192A \u2212 sB\nA\u2192B)\nand\nE[sS\u2192A \u2212 sA\u2192B|aA = 0, aB = 1] =\nPr(xG\nA\u2192D|aA = 0, aB = 1)(sG\nS\u2192A \u2212 sG\nA\u2192B)\n+Pr(xB\nA\u2192D|aA = 0, aB = 1)(sB\nS\u2192A \u2212 sB\nA\u2192B)\nSolving for sB\nS\u2192A and sG\nS\u2192A, we get:\nsB\nS\u2192A = 0\nsG\nS\u2192A =\nc(2 \u2212 k)\n1 \u2212 2k + k2\nThe expected total payment is\nE[S] = sG\nS\u2192APr(xG\nS\u2192D) + sB\nS\u2192APr(xB\nS\u2192D)\n= c(2 \u2212 k)(1 \u2212 k)\n(13)\nwhich is equal to the expected total payment under direct contracts\n(see Eq. 8).\nPROPOSITION 5.1. The expected total payments by the\nprincipal under direct and recursive contracts are equal.\nPROOF. In order to calculate the expected total payment, we\nhave to find the payment to the first node on the path that will\ninduce appropriate behavior. Because sB\ni = 0 in the drop / forward\nmodel, both constraints can be reduced to:\nPr(xG\ni\u2192R|aj = 1\u2200j)(sG\ni \u2212 sG\ni+1) \u2212 ci = 0\n\u21d4 (1 \u2212 k)n\u2212i+1\n(sG\ni \u2212 sG\ni+1) \u2212 ci = 0\nwhich yields, for all 1 \u2264 i \u2264 n:\nsG\ni =\nci\n(1 \u2212 k)n\u2212i+1\n+ sG\ni+1\nThus,\nsG\nn =\ncn\n1 \u2212 k\nsG\nn\u22121 =\ncn\u22121\n(1 \u2212 k)2\n+ sG\nn =\ncn\u22121\n(1 \u2212 k)2\n+\ncn\n1 \u2212 k\n\u00b7 \u00b7 \u00b7\nsG\n1 =\nc1\n(1 \u2212 k)n\n+ sG\n2 = . . . =\nnX\ni=1\nci\n(1 \u2212 k)i\nand the expected total payment is\nE[S] = (1 \u2212 k)n+1\nsG\n1 = (1 \u2212 k)n+1\nnX\ni=1\nci\n(1 \u2212 k)n\u2212i+1\nwhich equals the total expected payment in direct payments, as\nexpressed in Eq. 6.\nBecause the payment is contingent on the final outcome, and the\nexpected payment to a node equals its expected cost, nodes have\nno incentive to offer their downstream nodes lower payment than\nnecessary, since if they do, their downstream nodes will not forward\nthe packet.\nWhat information should the principal posess in order to\nimplement recursive contracts? Like in direct payments, the expected\npayment is not affected solely by the total payment on the path, but\nalso by the topology. Therefore, while the principal only needs to\ncommunicate with the first node on the forwarding path and does\nnot have to know the identities of the other nodes, it still needs to\nknow the number of nodes on the path and their individual transit\ncosts.\nFinally, is it possible to design recursive contracts under\nunknown transit costs, and, if so, what should be the structure of such\ncontracts? Suppose the principal has implemented the distributed\nalgorithm that calculates the necessary payments, pi for truthful\n123\nrevelation, would the following payment schedule to the first node\ninduce cooperative behavior?\nsB\n1 = 0\nsG\n1 =\nnX\ni=1\npi\n(1 \u2212 k)i\nThe answer is not clear. Unlike contracts in known transit costs,\nthe expected payment to a node usually exceeds its expected cost.\nTherefore, transit nodes may not have the appropriate incentive to\nfollow the principal\"s guarantee during the payment phase. For\nexample, in FPSS , the principal guarantees to pay each node an\nexpected payment of pi > ci. We assume that payments are\nenforceable if made by the same entity that pledge to pay. However, in the\ncase of recursive contracts, the entity that pledges to pay in the cost\ndiscovery stage (the principal) is not the same as the entity that\ndefines and executes the payments in the forwarding stage (the transit\nnodes). Transit nodes, who design the contracts in the second stage,\nknow that their downstream nodes will forward the packet as long\nas the expected payment exceeds the expected cost, even if it is less\nthan the promised amount. Thus, every node has incentive to offer\nlower payments than promised and keep the profit. Transit nodes,\nwho know this is a plausible scenario, may no longer truthfully\nreveal their cost. Therefore, while recursive contracts under known\ntransit costs are strategically equivalent to direct contracts, it is not\nclear whether this is the case under unknown transit costs.\n6. HIGH-QUALITY VERSUS\nLOW-QUALITY FORWARDING\nSo far, we have considered the agents\" strategy space to be\nlimited to the drop (a = 0) and forward (a = 1) actions. In this\nsection, we consider a variation of the model where the agents choose\nbetween providing a low-quality service (a = 0) and a high-quality\nservice (a = 1).\nThis may correspond to a service-differentiated service model\nwhere packets are forwarded on a best-effort or a priority basis [6].\nIn contrast to drop versus forward, a packet may still reach the next\nhop (albeit with a lower probability) even if the low-effort action is\ntaken.\nAs a second example, consider the practice of hot-potato routing\nin inter-domain routing of today\"s Internet. Individual autonomous\nsystems (AS\"s) can either adopt hot-potato routing or early exit\nrouting (a = 0), where a packet is handed off to the downstream\nAS at the first possible exit, or late exit routing (a = 1), where an\nAS carries the packet longer than it needs to, handing off the packet\nat an exit closer to the destination. In the absence of explicit\nincentives, it is not surprising that AS\"s choose hot-potato routing to\nminimize their costs, even though it leads to suboptimal routes [28,\n29].\nIn both examples, in the absence of contracts, a rational node\nwould exert low-effort, resulting in lower performance.\nNevertheless, this behavior can be avoided with an appropriate design of\ncontracts.\nFormally, the probability that a packet successfully gets from\nnode i to node i + 1 is:\nPr(xG\ni\u2192i+1|ai) = 1 \u2212 (k \u2212 qai) (14)\nwhere: q \u2208 (0, 1] and k \u2208 (q, 1]\nIn the drop versus forward model, a low-effort action by any node\nresults in a delivery failure. In contrast, a node in the high/low\nscenario may exert low-effort and hope to free-ride on the\nhigheffort level exerted by the other agents.\nPROPOSITION 6.1. In the high-quality versus low-quality\nforwarding model, where transit costs are common knowledge, the\nprincipal derives the same expected utility whether it obtains\nperhop monitoring information or not.\nPROOF. The IC and IR constraints are the same as specified\nin the proof of proposition 3.1, but their values change, based on\nEq. 14 to reflect the different model:\n(IC) : (1\u2212k +q)n\u2212i+1\nsG\ni +(1\u2212(1\u2212k +q)n\u2212i+1\n)sB\ni \u2212c \u2265\n(1 \u2212 k)(1 \u2212 k + q)n\u2212i\nsG\ni + (1 \u2212 (1 \u2212 k)(1 \u2212 k + q)n\u2212i\n)sB\ni\n(IR) : (1 \u2212 k + q)i\n((1 \u2212 k + q)n\u2212i+1\nsG\ni\n+(1 \u2212 (1 \u2212 k + q)n\u2212i+1\n)sB\ni \u2212 c) + (1 \u2212 (1 \u2212 k + q)i\n)sB\ni \u2265 0\nFor this set of constraints, we obtain the following solution:\nsB\ni =\n(1 \u2212 k + q)i\nc(k \u2212 1)\nq\n(15)\nsG\ni =\n(1 \u2212 k + q)i\nc(k \u2212 1 + (1 \u2212 k + q)\u2212n\n)\nq\n(16)\nWe observe that in this version, both the high and the low payments\ndepend on i. If monitoring is used, we obtain the following\nconstraints:\n(IC) : (1 \u2212 k + q)sG\ni + (k \u2212 q)sB\ni \u2212 c \u2265 (1 \u2212 k)sG\ni + (k)sB\ni\n(IR) : (1 \u2212 k + q)i\n((1 \u2212 k + q)sG\ni + (k \u2212 q)sB\ni \u2212 c) \u2265 0\nand we get the solution:\nsB\ni =\nc(k \u2212 1)\nq\nsG\ni =\nck\nq\nThe expected payment by the principal with or without forwarding\nis the same, and equals:\nE[S] =\nc(1 \u2212 k + q)(1 \u2212 (1 \u2212 k + q)n\n)\nk \u2212 q\n(17)\nand this concludes the proof.\nThe payment structure in the high-quality versus low-quality\nforwarding model is different from that in the drop versus forward\nmodel. In particular, at the optimal contract, the low-outcome\npayment sB\ni is now less than zero. A negative payment means that\nthe agent must pay the principal in the event that the packet fails\nto reach the destination. In some settings, it may be necessary to\nimpose a limited liability constraint, i.e., si \u2265 0. This prevents the\nfirst-best solution from being achieved.\nPROPOSITION 6.2. In the high-quality versus low-quality\nforwarding model, if negative payments are disallowed, the expected\npayment to each node exceeds its expected cost under the optimal\ncontract.\nPROOF. The proof is a direct outcome of the following\nstatements, which are proved above:\n1. The optimal contract is the contract specified in equations 15\nand 16\n2. Under the optimal contract, E[si] equals node i s expected\ncost\n3. Under the optimal contract, sB\ni = (1\u2212k+q)i\nc(k\u22121)\nq\n< 0\nTherefore, under any other contract the sender will have to\ncompensate each node with an expected payment that is higher than its\nexpected transit cost.\n124\nThere is an additional difference between the two models. In\ndrop versus forward, a principal either signs a contract with all n\nnodes along the path or with none. This is because a single node\ndropping the packet determines a failure. In contrast, in high versus\nlow-quality forwarding, a success may occur under the low effort\nactions as well, and payments are used to increase the probability\nof success. Therefore, it may be possible for the principal to\nmaximize its utility by contracting with only m of the n nodes along the\npath. While the expected outcome depends on m, it is independent\nof which specific m nodes are induced. At the same time, the\nindividual expected payments decrease in i (see Eq. 16). Therefore,\na principal who wishes to sign a contract with only m out of the n\nnodes should do so with the nodes that are closest to the destination;\nnamely, nodes (n \u2212 m + 1, ..., n \u2212 1, n).\nSolving for the high-quality versus low-quality forwarding\nmodel with unknown transit costs is left for future work.\n7. CASE STUDY: INTERNET ROUTING\nWe can map different deployed and proposed Internet routing\nschemes to the various models we have considered in this work.\nBorder Gateway Protocol (BGP), the current inter-domain\nrouting protocol in the Internet, computes routes based on path vectors.\nSince the protocol reveals only the autonomous systems (AS\"s)\nalong a route but not the cost associated to them, the current BGP\nrouting is best characterized by lack of a priori information about\ntransit costs. In this case, the principal (e.g., a multi-homed site\nor a tier-1 AS) can implement one of the mechanisms proposed in\nSection 4 by contracting with individual nodes on the path. Such\ncontracts involve paying some premium over the real cost, and it\nis not clear whether recursive contacts can be implemented in this\nscenario. In addition, the current protocol does not have the\ninfrastructure to support implementation of direct contracts between\nendpoints and the network.\nRecently, several new architectures have been proposed in the\ncontext of the Internet to provide the principal not only with a set\nof paths from which it can chose (like BGP does) but also with\nthe performance along those paths and the network topology. One\napproach to obtain such information is through end-to-end\nprobing [1]. Another approach is to have the edge networks perform\nmeasurements and discover the network topology [32]. Yet another\napproach is to delegate the task of obtaining topology and\nperformance information to a third-party, like in the routing-as-a-service\nproposal [21]. These proposals are quite different in nature, but\nthey are common in their attempt to provide more visibility and\ntransparency into the network. If information about topology and\ntransit costs is obtained, the scenario is mapped to the known\ntransit costs model (Section 3). In this case, first-best contracts can be\nachieved through individual contracts with nodes along the path.\nHowever, as we have shown in Section 5, as long as each agent can\nchose the next hop, the principal can gain full benefit by\ncontracting with only the first hop (through the implementation of recursive\ncontracts).\nHowever, the various proposals for acquiring network topology\nand performance information do not deal with strategic behavior\nby the intermediate nodes. With the realization that the\ninformation collected may be used by the principal in subsequent\ncontractual relationships, the intermediate nodes may behave strategically,\nmisrepresenting their true costs to the entities that collect and\naggregate such information. One recent approach that can alleviate\nthis problem is to provide packet obituaries by having each packet\nto confirm its delivery or report its last successful AS hop [4].\nAnother approach is to have third parties like Keynote independently\nmonitor the network performance.\n8. RELATED WORK\nThe study of non-cooperative behavior in communication\nnetworks, and the design of incentives, has received significant\nattention in the context of wireless ad-hoc routing. [22] considers the\nproblem of malicious behavior, where nodes respond positively to\nroute requests but then fail to forward the actual packets. It\nproposes to mitigate it by detection and report mechanisms that will\nessentially help to route around the malicious nodes. However,\nrather than penalizing nodes that do not forward traffic, it bypasses\nthe misbehaving nodes, thereby relieving their burden. Therefore,\nsuch a mechanism is not effective against selfish behavior.\nIn order to mitigate selfish behavior, some approaches [7, 8, 9]\nrequire reputation exchange between nodes, or simply first-hand\nobservations [5]. Other approaches propose payment schemes [10,\n20, 31] to encourage cooperation. [31] is the closest to our work in\nthat it designs payment schemes in which the sender pays the\nintermediate nodes in order to prevent several types of selfish behavior.\nIn their approach, nodes are supposed to send receipts to a\nthirdparty entity. We show that this type of per-hop monitoring may not\nbe needed.\nIn the context of Internet routing, [4] proposes an accountability\nframework that provide end hosts and service providers\nafter-thefact audits on the fate of their packets. This proposal is part of a\nbroader approach to provide end hosts with greater control over the\npath of their packets [3, 30]. If senders have transit cost\ninformation and can fully control the path of their packets, they can design\ncontracts that yield them with first-best utility. The accountability\nframework proposed in [4] can serve two main goals: informing\nnodes of network conditions to help them make informed decision,\nand helping entities to establish whether individual ASs have\nperformed their duties adequately. While such a framework can be\nused for the first task, we propose a different approach to the\nsecond problem without the need of per-hop auditing information.\nResearch in distributed algorithmic mechanism design (DAMD)\nhas been applied to BGP routing [13, 14]. These works propose\nmechanisms to tackle the hidden-information problem, but ignore\nthe problem of forwarding enforcement. Inducing desired behavior\nis also the objective in [26], which attempts to respond to the\nchallenge of distributed AMD raised in [15]: if the same agents that\nseek to manipulate the system also run the mechanism, what\nprevents them from deviating from the mechanism\"s proposed rules to\nmaximize their own welfare? They start with the proposed\nmechanism presented in [13] and use mostly auditing mechanisms to\nprevent deviation from the algorithm.\nThe focus of this work is the design of a payment scheme that\nprovides the appropriate incentives within the context of multi-hop\nrouting. Like other works in this field, we assume that all the\naccounting services are done using out-of-band mechanisms.\nSecurity issues within this context, such as node authentication or\nmessage encryption, are orthogonal to the problem presented in this\npaper, and can be found, for example, in [18, 19, 25].\nThe problem of information asymmetry and hidden-action (also\nknown as moral hazard) is well studied in the economics\nliterature [11, 17, 23, 27]. [17] identifies the problem of moral hazard in\nproduction teams, and shows that it is impossible to design a\nsharing rule which is efficient and budget-balanced. [27] shows that this\ntask is made possible when production takes place sequentially.\n9. CONCLUSIONS AND FUTURE\nDIRECTIONS\nIn this paper we show that in a multi-hop routing setting, where\nthe actions of the intermediate nodes are hidden from the source\n125\nand/or destination, it is possible to design payment schemes to\ninduce cooperative behavior from the intermediate nodes. We\nconclude that monitoring per-hop outcomes may not improve the\nutility of the participants or the network performace. In addition, in\nscenarios of unknown transit costs, it is also possible to design\nmechanisms that induce cooperative behavior in equilibrium, but\nthe sender pays a premium for extracting information from the\ntransit nodes.\nOur model and results suggest several natural and intriguing\nresearch avenues:\n\u2022 Consider manipulative or collusive behaviors which may\narise under the proposed payment schemes.\n\u2022 Analyze the feasibility of recursive contracts under\nhiddeninformation of transit costs.\n\u2022 While the proposed payment schemes sustain cooperation in\nequilibrium, it is not a unique equilibrium. We plan to study\nunder what mechanisms this strategy profile may emerge as\na unique equilibrium (e.g., penalty by successor nodes).\n\u2022 Consider the effect of congestion and capacity constraints on\nthe proposed mechanisms. Our preliminary results show that\nwhen several senders compete for a single transit node\"s\ncapacity, the sender with the highest demand pays a premium\neven if transit costs are common knowledge. The premium\ncan be expressed as a function of the second-highest demand.\nIn addition, if congestion affects the probability of\nsuccessful delivery, a sender with a lower cost alternate path may\nend up with a lower utility level than his rival with a higher\ncost alternate path.\n\u2022 Fully characterize the full-information Nash equilibrium in\nfirst price auctions, and use this characterization to derive its\novercharging compared to truthful mechaisms.\n10. ACKNOWLEDGEMENTS\nWe thank Hal Varian for his useful comments. This work is\nsupported in part by the National Science Foundation under ITR\nawards ANI-0085879 and ANI-0331659, and Career award\nANI0133811.\n11. REFERENCES\n[1] ANDERSEN, D. G., BALAKRISHNAN, H., KAASHOEK, M. F., AND\nMORRIS, R. Resilient Overlay Networks. 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In Proc Hotnets-I (2002).\n126", "keywords": "mechanism;moralhazard;route;multi-hop;endpoint;hidden action;contract;hidden-action;failure cause;cost;multi-hop network;principal-agent model;intermediate node;moral hazard;cause of failure;priority;incentive;mechanism design"}
{"name": "train_J-53", "title": "A Price-Anticipating Resource Allocation Mechanism for Distributed Shared Clusters", "abstract": "In this paper we formulate the fixed budget resource allocation game to understand the performance of a distributed marketbased resource allocation system. Multiple users decide how to distribute their budget (bids) among multiple machines according to their individual preferences to maximize their individual utility. We look at both the efficiency and the fairness of the allocation at the equilibrium, where fairness is evaluated through the measures of utility uniformity and envy-freeness. We show analytically and through simulations that despite being highly decentralized, such a system converges quickly to an equilibrium and unlike the social optimum that achieves high efficiency but poor fairness, the proposed allocation scheme achieves a nice balance of high degrees of efficiency and fairness at the equilibrium.", "fulltext": "1. INTRODUCTION\nThe primary advantage of distributed shared clusters like\nthe Grid [7] and PlanetLab [1] is their ability to pool\ntogether shared computational resources. This allows increased\nthroughput because of statistical multiplexing and the bursty\nutilization pattern of typical users. Sharing nodes that are\ndispersed in the network allows lower delay because\napplications can store data close to users. Finally, sharing allows\ngreater reliability because of redundancy in hosts and\nnetwork connections.\nHowever, resource allocation in these systems remains the\nmajor challenge. The problem is how to allocate a shared\nresource both fairly and efficiently (where efficiency is the\nratio of the achieved social welfare to the social optimal)\nwith the presence of strategic users who act in their own\ninterests.\nSeveral non-economic allocation algorithms have been\nproposed, but these typically assume that task values (i.e., their\nimportance) are the same, or are inversely proportional to\nthe resources required, or are set by an omniscient\nadministrator. However, in many cases, task values vary\nsignificantly, are not correlated to resource requirements, and are\ndifficult and time-consuming for an administrator to set.\nInstead, we examine a market-based resource allocation\nsystem (others are described in [2, 4, 6, 21, 26, 27]) that allows\nusers to express their preferences for resources through a\nbidding mechanism.\nIn particular, we consider a price-anticipating [12] scheme\nin which a user bids for a resource and receives the ratio of\nhis bid to the sum of bids for that resource. This\nproportional scheme is simpler, more scalable, and more\nresponsive [15] than auction-based schemes [6, 21, 26]. Previous\nwork has analyzed price-anticipating schemes in the context\nof allocating network capacity for flows for users with\nunlimited budgets. In this work, we examine a price-anticipating\nscheme in the context of allocating computational\ncapacity for users with private preferences and limited budgets,\nresulting in a qualitatively different game (as discussed in\nSection 6).\nIn this paper, we formulate the fixed budget resource\nallocation game and study the existence and performance of\nthe Nash equilibria of this game. For evaluating the Nash\nequilibria, we consider both their efficiency, measuring how\nclose the social welfare at equilibrium is to the social\noptimum, and fairness, measuring how different the users\"\nutilities are. Although rarely considered in previous game\ntheoretical study, we believe fairness is a critical metric for a\nresource allocation schemes because the perception of\nunfairness will cause some users to reject a system with more\nefficient, but less fair resource allocation in favor of one with\nless efficient, more fair resource allocation. We use both\nutility uniformity and envy-freeness to measure fairness.\nUtility uniformity, which is common in Computer Science work,\nmeasures the closeness of utilities of different users.\nEnvyfreeness, which is more from the Economic perspective,\nmeasures the happiness of users with their own resources\ncompared to the resources of others.\nOur contributions are as follows:\n\u2022 We analyze the existence and performance of\n127\nNash equilibria. Using analysis, we show that there is\nalways a Nash equilibrium in the fixed budget game if the\nutility functions satisfy a fairly weak and natural condition\nof strong competitiveness. We also show the worst case\nperformance bounds: for m players the efficiency at equilibrium\nis \u2126(1/\n\u221a\nm), the utility uniformity is \u2265 1/m, and the\nenvyfreeness \u2265 2\n\u221a\n2\u22122 \u2248 0.83. Although these bounds are quite\nlow, the simulations described below indicate these bounds\nare overly pessimistic.\n\u2022 We describe algorithms that allow strategic users\nto optimize their utility. As part of the fixed budget\ngame analysis, we show that strategic users with linear\nutility functions can calculate their bids using a best response\nalgorithm that quickly results in an allocation with high\nefficiency with little computational and communication\noverhead. We present variations of the best response algorithm\nfor both finite and infinite parallelism tasks. In addition, we\npresent a local greedy adjustment algorithm that converges\nmore slowly than best response, but allows for non-linear or\nunformulatable utility functions.\n\u2022 We show that the price-anticipating resource\nallocation mechanism achieves a high degree of\nefficiency and fairness. Using simulation, we find that\nalthough the socially optimal allocation results in perfect\nefficiency, it also results in very poor fairness. Likewise,\nallocating according to only users\" preference weights results in a\nhigh fairness, but a mediocre efficiency. Intuition would\nsuggest that efficiency and fairness are exclusive. Surprisingly,\nthe Nash equilibrium, reached by each user iteratively\napplying the best response algorithm to adapt his bids, achieves\nnearly the efficiency of the social optimum and nearly the\nfairness of the weight-proportional allocation: the efficiency\nis \u2265 0.90, the utility uniformity is \u2265 0.65, and the\nenvyfreeness is \u2265 0.97, independent of the number of users in\nthe system. In addition, the time to converge to the\nequilibrium is \u2264 5 iterations when all users use the best response\nstrategy. The local adjustment algorithm performs similarly\nwhen there is sufficient competitiveness, but takes 25 to 90\niterations to stabilize.\nAs a result, we believe that shared distributed systems\nbased on the fixed budget game can be highly decentralized,\nyet achieve a high degree of efficiency and fairness.\nThe rest of the paper is organized as follows. We\ndescribe the model in Section 2 and derive the performance\nat the Nash equilibria for the infinite parallelism model in\nSection 3. In Section 4, we describe algorithms for users\nto optimize their own utility in the fixed budget game. In\nSection 5, we describe our simulator and simulation results.\nWe describe related work in Section 6. We conclude by\ndiscussing some limit of our model and future work in Section 7.\n2. THE MODEL\nPrice-Anticipating Resource Allocation. We study\nthe problem of allocating a set of divisible resources (or\nmachines). Suppose that there are m users and n machines.\nEach machine can be continuously divided for allocation\nto multiple users. An allocation scheme \u03c9 = (r1, . . . , rm),\nwhere ri = (ri1, \u00b7 \u00b7 \u00b7 , rin) with rij representing the share of\nmachine j allocated to user i, satisfies that for any 1 \u2264 i \u2264 m\nand 1 \u2264 j \u2264 n, rij \u2265 0 and\nPm\ni=1 rij \u2264 1. Let \u2126 denote the\nset of all the allocation schemes.\nWe consider the price anticipating mechanism in which\neach user places a bid to each machine, and the price of the\nmachine is determined by the total bids placed. Formally,\nsuppose that user i submits a non-negative bid xij to\nmachine j. The price of machine j is then set to Yj =\nPn\ni=1 xij,\nthe total bids placed on the machine j. Consequently, user i\nreceives a fraction of rij =\nxij\nYj\nof j. When Yj = 0, i.e. when\nthere is no bid on a machine, the machine is not allocated\nto anyone. We call xi = (xi1, . . . , xin) the bidding vector of\nuser i.\nThe additional consideration we have is that each user i\nhas a budget constraint Xi. Therefore, user i\"s total bids\nhave to sum up to his budget, i.e.\nPn\nj=1 xij = Xi. The\nbudget constraints come from the fact that the users do not\nhave infinite budget.\nUtility Functions. Each user i\"s utility is represented\nby a function Ui of the fraction (ri1, . . . , rin) the user receives\nfrom each machine. Given the problem domain we consider,\nwe assume that each user has different and relatively\nindependent preferences for different machines. Therefore, the\nbasic utility function we consider is the linear utility\nfunction: Ui(ri1, \u00b7 \u00b7 \u00b7 , rin) = wi1ri1 +\u00b7 \u00b7 \u00b7+winrin, where wij \u2265 0\nis user i\"s private preference, also called his weight, on\nmachine j. For example, suppose machine 1 has a faster CPU\nbut less memory than machine 2, and user 1 runs CPU\nbounded applications, while user 2 runs memory bounded\napplications. As a result, w11 > w12 and w21 < w22.\nOur definition of utility functions corresponds to the user\nhaving enough jobs or enough parallelism within jobs to\nutilize all the machines. Consequently, the user\"s goal is to grab\nas much of a resource as possible. We call this the infinite\nparallelism model. In practice, a user\"s application may have\nan inherent limit on parallelization (e.g., some computations\nmust be done sequentially) or there may be a system limit\n(e.g., the application\"s data is being served from a file server\nwith limited capacity). To model this, we also consider the\nmore realistic finite parallelism model, where the user\"s\nparallelism is bounded by ki, and the user\"s utility Ui is the\nsum of the ki largest wijrij. In this model, the user only\nsubmits bids to up to ki machines. Our abstraction is to\ncapture the essense of the problem and facilitate our\nanalysis. In Section 7, we discuss the limit of the above definition\nof utility functions.\nBest Response. As typically, we assume the users are\nselfish and strategic - they all act to maximize their own\nutility, defined by their utility functions. From the\nperspective of user i, if the total bids of the other users placed on\neach machine j is yj, then the best response of user i to the\nsystem is the solution of the following optimization problem:\nmaximize Ui(\nxij\nxij +yj\n) subject to\nPn\nj=1 xij = Xi, and xij \u2265 0.\nThe difficulty of the above optimization problem depends\non the formulation of Ui. We will show later how to solve\nit for the infinite parallelism model and provide a heuristic\nfor finite parallelism model.\nNash Equilibrium. By the assumption that the user is\nselfish, each user\"s bidding vector is the best response to the\nsystem. The question we are most interested in is whether\nthere exists a collection of bidding vectors, one for each user,\nsuch that each user\"s bidding vector is the best response to\nthose of the other users. Such a state is known as the Nash\nequilibrium, a central concept in Game Theory. Formally,\nthe bidding vectors x1, . . . , xm is a Nash equilibrium if for\n128\nany 1 \u2264 i \u2264 m, xi is the best response to the system, or, for\nany other bidding vector xi,\nUi(x1, . . . , xi, . . . , xm) \u2265 Ui(x1, . . . , xi, . . . , xm) .\nThe Nash equilibrium is desirable because it is a stable\nstate at which no one has incentive to change his strategy.\nBut a game may not have an equilibrium. Indeed, a Nash\nequilibrium may not exist in the price anticipating scheme\nwe define above. This can be shown by a simple example of\ntwo players and two machines. For example, let U1(r1, r2) =\nr1 and U2(r1, r2) = r1 + r2. Then player 1 should never bid\non machine 2 because it has no value to him. Now, player 2\nhas to put a positive bid on machine 2 to claim the machine,\nbut there is no lower limit, resulting in the non-existence of\nthe Nash equilibrium. We should note that even the mixed\nstrategy equilibrium does not exist in this example. Clearly,\nthis happens whenever there is a resource that is wanted\nby only one player. To rule out this case, we consider those\nstrongly competitive games.1\nUnder the infinite parallelism\nmodel, a game is called strongly competitive if for any 1 \u2264\nj \u2264 n, there exists an i = k such that wij, wkj > 0. Under\nsuch a condition, we have that (see [5] for a proof),\nTheorem 1. There always exists a pure strategy Nash\nequilibrium in a strongly competitive game.\nGiven the existence of the Nash equilibrium, the next\nimportant question is the performance at the Nash equilibrium,\nwhich is often measured by its efficiency and fairness.\nEfficiency (Price of Anarchy). For an allocation scheme\n\u03c9 \u2208 \u2126, denote by U(\u03c9) =\nP\ni Ui(ri) the social welfare under\n\u03c9. Let U\u2217\n= max\u03c9\u2208\u2126 U(\u03c9) denote the optimal social welfare\n- the maximum possible aggregated user utilities. The\nefficiency at an allocation scheme \u03c9 is defined as \u03c0(\u03c9) = U(\u03c9)\nU\u2217 .\nLet \u21260 denote the set of the allocation at the Nash\nequilibrium. When there exists Nash equilibrium, i.e. \u21260 = \u2205,\ndefine the efficiency of a game Q to be \u03c0(Q) = min\u03c9\u2208\u21260 \u03c0(\u03c9).\nIt is usually the case that \u03c0 < 1, i.e. there is an efficiency\nloss at a Nash equilibrium. This is the price of anarchy [18]\npaid for not having central enforcement of the user\"s good\nbehavior. This price is interesting because central control\nresults in the best possible outcome, but is not possible in\nmost cases.\nFairness. While the definition of efficiency is standard,\nthere are multiple ways to define fairness. We consider two\nmetrics. One is by comparing the users\" utilities. The utility\nuniformity \u03c4(\u03c9) of an allocation scheme \u03c9 is defined to be\nmini Ui(\u03c9)\nmaxi Ui(\u03c9)\n, the ratio of the minimum utility and the\nmaximum utility among the users. Such definition (or utility\ndiscrepancy defined similarly as maxi Ui(\u03c9)\nmini Ui(\u03c9)\n) is used\nextensively in Computer Science literature. Under this\ndefinition, the utility uniformity \u03c4(Q) of a game Q is defined to\nbe \u03c4(Q) = min\u03c9\u2208\u21260 \u03c4(\u03c9).\nThe other metric extensively studied in Economics is the\nconcept of envy-freeness [25]. Unlike the utility uniformity\nmetric, the enviness concerns how the user perceives the\nvalue of the share assigned to him, compared to the shares\nother users receive. Within such a framework, define the\nenvy-freeness of an allocation scheme \u03c9 by \u03c1(\u03c9) = mini,j\nUi(ri)\nUi(rj )\n.\n1Alternatives include adding a reservation price or limiting the\nlowest allowable bid to each machine. These alternatives,\nhowever, introduce the problem of coming up with the right price\nor limit.\nWhen \u03c1(\u03c9) \u2265 1, the scheme is known as an envy-free\nallocation scheme. Likewise, the envy-freeness \u03c1(Q) of a game\nQ is defined to be \u03c1(Q) = min\u03c9\u2208\u21260 \u03c1(\u03c9).\n3. NASH EQUILIBRIUM\nIn this section, we present some theoretical results\nregarding the performance at Nash equilibrium under the infinite\nparallelism model. We assume that the game is strongly\ncompetitive to guarantee the existence of equilibria. For a\nmeaningful discussion of efficiency and fairness, we assume\nthat the users are symmetric by requiring that Xi = 1 andPn\nj=1 wij = 1 for all the 1 \u2264 i \u2264 m. Or informally, we\nrequire all the users have the same budget, and they have\nthe same utility when they own all the resources. This\nprecludes the case when a user has an extremely high budget,\nresulting in very low efficiency or low fairness at equilibrium.\nWe first provide a characterization of the equilibria. By\ndefinition, the bidding vectors x1, . . . , xm is a Nash\nequilibrium if and only if each player\"s strategy is the best\nresponse to the group\"s bids. Since Ui is a linear function\nand the domain of each users bids {(xi1, . . . , xin)|\nP\nj xij =\nXi , and xij \u2265 0} is a convex set, the optimality condition is\nthat there exists \u03bbi > 0 such that\n\u2202Ui\n\u2202xij\n= wij\nYj \u2212 xij\nY 2\nj\n\uf6be\n= \u03bbi if xij > 0, and\n< \u03bbi if xij = 0.\n(1)\nOr intuitively, at an equilibrium, each user has the same\nmarginal value on machines where they place positive bids\nand has lower marginal values on those machines where they\ndo not bid.\nUnder the infinite parallelism model, it is easy to compute\nthe social optimum U\u2217\nas it is achieved when we allocate\neach machine wholly to the person who has the maximum\nweight on the machine, i.e. U\u2217\n=\nPn\nj=1 max1\u2264i\u2264m wij.\n3.1 Two-player Games\nWe first show that even in the simplest nontrivial case\nwhen there are two users and two machines, the game has\ninteresting properties. We start with two special cases to\nprovide some intuition about the game. The weight\nmatrices are shown in figure 1(a) and (b), which correspond\nrespectively to the equal-weight and opposite-weight games.\nLet x and y denote the respective bids of users 1 and 2 on\nmachine 1. Denote by s = x + y and \u03b4 = (2 \u2212 s)/s.\nEqual-weight game. In Figure 1, both users have equal\nvaluations for the two machines. By the optimality\ncondition, for the bid vectors to be in equilibrium, they need to\nsatisfy the following equations according to (1)\n\u03b1\ny\n(x + y)2\n= (1 \u2212 \u03b1)\n1 \u2212 y\n(2 \u2212 x \u2212 y)2\n\u03b1\nx\n(x + y)2\n= (1 \u2212 \u03b1)\n1 \u2212 x\n(2 \u2212 x \u2212 y)2\nBy simplifying the above equations, we obtain that \u03b4 =\n1 \u2212 1/\u03b1 and x = y = \u03b1. Thus, there exists a unique Nash\nequilibrium of the game where the two users have the same\nbidding vector. At the equilibrium, the utility of each user\nis 1/2, and the social welfare is 1. On the other hand, the\nsocial optimum is clearly 1. Thus, the equal-weight game\nis ideal as the efficiency, utility uniformity, and the\nenvyfreeness are all 1.\n129\nm1 m2\nu1 \u03b1 1 \u2212 \u03b1\nu2 \u03b1 1 \u2212 \u03b1\nm1 m2\nu1 \u03b1 1 \u2212 \u03b1\nu2 1 \u2212 \u03b1 \u03b1\n(a) equal weight game (b) opposite weight game\nFigure 1: Two special cases of two-player games.\nOpposite-weight game. The situation is different for\nthe opposite game in which the two users put the exact\nopposite weights on the two machines. Assume that \u03b1 \u2265\n1/2. Similarly, for the bid vectors to be at the equilibrium,\nthey need to satisfy\n\u03b1\ny\n(x + y)2\n= (1 \u2212 \u03b1)\n1 \u2212 y\n(2 \u2212 x \u2212 y)2\n(1 \u2212 \u03b1)\nx\n(x + y)2\n= \u03b1\n1 \u2212 x\n(2 \u2212 x \u2212 y)2\nBy simplifying the above equations, we have that each\nNash equilibrium corresponds to a nonnegative root of the\ncubic equation f(\u03b4) = \u03b43\n\u2212 c\u03b42\n+ c\u03b4 \u2212 1 = 0, where c =\n1\n2\u03b1(1\u2212\u03b1)\n\u2212 1.\nClearly, \u03b4 = 1 is a root of f(\u03b4). When \u03b4 = 1, we have\nthat x = \u03b1, y = 1 \u2212 \u03b1, which is the symmetric equilibrium\nthat is consistent with our intuition - each user puts a\nbid proportional to his preference of the machine. At this\nequilibrium, U = 2 \u2212 4\u03b1(1 \u2212 \u03b1), U\u2217\n= 2\u03b1, and U/U\u2217\n=\n(2\u03b1 + 1\n\u03b1\n) \u2212 2, which is minimized when \u03b1 =\n\u221a\n2\n2\nwith the\nminimum value of 2\n\u221a\n2 \u2212 2 \u2248 0.828. However, when \u03b1 is\nlarge enough, there exist two other roots, corresponding to\nless intuitive asymmetric equilibria.\nIntuitively, the asymmetric equilibrium arises when user 1\nvalues machine 1 a lot, but by placing even a relatively small\nbid on machine 1, he can get most of the machine because\nuser 2 values machine 1 very little, and thus places an even\nsmaller bid. In this case, user 1 gets most of machine 1 and\nalmost half of machine 2.\nThe threshold is at when f (1) = 0, i.e. when c = 1\n2\u03b1(1\u2212\u03b1)\n=\n4. This solves to \u03b10 = 2+\n\u221a\n2\n4\n\u2248 0.854. Those asymmetric\nequilibria at \u03b4 = 1 are bad as they yield lower efficiency\nthan the symmetric equilibrium. Let \u03b40 be the minimum\nroot. When \u03b1 \u2192 0, c \u2192 +\u221e, and \u03b40 = 1/c + o(1/c) \u2192 0.\nThen, x, y \u2192 1. Thus, U \u2192 3/2, U\u2217\n\u2192 2, and U/U\u2217\n\u2192 0.75.\nFrom the above simple game, we already observe that the\nNash equilibrium may not be unique, which is different from\nmany congestion games in which the Nash equilibrium is\nunique.\nFor the general two player game, we can show that 0.75\nis actually the worst efficiency bound with a proof in [5].\nFurther, at the asymmetric equilibrium, the utility\nuniformity approaches 1/2 when \u03b1 \u2192 1. This is the worst possible\nfor two player games because as we show in Section 3.2, a\nuser\"s utility at any Nash equilibrium is at least 1/m in the\nm-player game.\nAnother consequence is that the two player game is\nalways envy-free. Suppose that the two user\"s shares are r1 =\n(r11, . . . , r1n) and r2 = (r21, . . . , r2n) respectively. Then\nU1(r1) + U1(r2) = U1(r1 + r2) = U1(1, . . . , 1) = 1 because\nri1 + ri2 = 1 for all 1 \u2264 i \u2264 n. Again by that U1(r1) \u2265 1/2,\nwe have that U1(r1) \u2265 U1(r2), i.e. any equilibrium\nallocation is envy-free.\nTheorem 2. For a two player game, \u03c0(Q) \u2265 3/4, \u03c4(Q) \u2265\n0.5, and \u03c1(Q) = 1. All the bounds are tight in the worst case.\n3.2 Multi-player Game\nFor large numbers of players, the loss in social welfare\ncan be unfortunately large. The following example shows\nthe worst case bound. Consider a system with m = n2\n+ n\nplayers and n machines. Of the players, there are n2\nwho\nhave the same weights on all the machines, i.e. 1/n on each\nmachine. The other n players have weight 1, each on a\ndifferent machine and 0 (or a sufficiently small ) on all the\nother machines. Clearly, U\u2217\n= n. The following allocation\nis an equilibrium: the first n2\nplayers evenly distribute their\nmoney among all the machines, the other n player invest all\nof their money on their respective favorite machine. Hence,\nthe total money on each machine is n + 1. At this\nequilibrium, each of the first n2\nplayers receives 1\nn\n1/n\nn+1\n= 1\nn2(n+1)\non\neach machine, resulting in a total utility of n3\n\u00b7 1\nn2(n+1)\n< 1.\nThe other n players each receives 1\nn+1\non their favorite\nmachine, resulting in a total utility of n \u00b7 1\nn+1\n< 1. Therefore,\nthe total utility of the equilibrium is < 2, while the social\noptimum is n = \u0398(\n\u221a\nm). This bound is the worst possible.\nWhat about the utility uniformity of the multi-player\nallocation game? We next show that the utility uniformity of\nthe m-player allocation game cannot exceed m.\nLet (S1, . . . , Sn) be the current total bids on the n\nmachines, excluding user i. User i can ensure a utility of 1/m\nby distributing his budget proportionally to the current bids.\nThat is, user i, by bidding sij = Xi/\nPn\ni=1 Si on machine j,\nobtains a resource level of:\nrij =\nsij\nsij + Sj\n=\nSj/\nPn\ni=1 Si\nSj/\nPn\ni=1 Si + Sj\n=\n1\n1 +\nPn\ni=1 Si\n,\nwhere\nPn\nj=1 Sj =\nPm\nj=1 Xj \u2212 Xi = m \u2212 1.\nTherefore, rij = 1\n1+m\u22121\n= 1\nm\n. The total utility of user i\nis\nnX\nj=1\nrijwij = (1/m)\nnX\nj=1\nwij = 1/m .\nSince each user\"s utility cannot exceed 1, the minimal\npossible uniformity is 1/m.\nWhile the utility uniformity can be small, the envy-freeness,\non the other hand, is bounded by a constant of 2\n\u221a\n2 \u2212 2 \u2248\n0.828, as shown in [29]. To summarize, we have that\nTheorem 3. For the m-player game Q, \u03c0(Q) = \u2126(1/\n\u221a\nm),\n\u03c4(Q) \u2265 1/m, and \u03c1(Q) \u2265 2\n\u221a\n2 \u2212 2. All of these bounds are\ntight in the worst case.\n4. ALGORITHMS\nIn the previous section, we present the performance bounds\nof the game under the infinite parallelism model. However,\nthe more interesting questions in practice are how the\nequilibrium can be reached and what is the performance at the\nNash equilibrium for the typical distribution of utility\nfunctions. In particular, we would like to know if the intuitive\nstrategy of each player constantly re-adjusting his bids\naccording to the best response algorithm leads to the\nequilibrium. To answer these questions, we resort to simulations.\nIn this section, we present the algorithms that we use to\ncompute or approximate the best response and the social\noptimum in our experiments. We consider both the infinite\nparallelism and finite parallelism model.\n130\n4.1 Infinite Parallelism Model\nAs we mentioned before, it is easy to compute the social\noptimum under the infinite parallelism model - we simply\nassign each machine to the user who likes it the most. We\nnow present the algorithm for computing the best response.\nRecall that for weights w1, . . . , wn, total bids y1, . . . , yn, and\nthe budget X, the best response is to solve the following\noptimization problem\nmaximize U =\nPn\nj=1 wj\nxj\nxj +yj\nsubject to\nPn\nj=1 xj = X, and xj \u2265 0.\nTo compute the best response, we first sort\nwj\nyj\nin\ndecreasing order. Without loss of generality, suppose that\nw1\ny1\n\u2265\nw2\ny2\n\u2265 . . .\nwn\nyn\n.\nSuppose that x\u2217\n= (x\u2217\n1, . . . , x\u2217\nn) is the optimum solution.\nWe show that if x\u2217\ni = 0, then for any j > i, x\u2217\nj = 0 too.\nSuppose this were not true. Then\n\u2202U\n\u2202xj\n(x\u2217\n) = wj\nyj\n(x\u2217\nj + yj)2\n< wj\nyj\ny2\nj\n=\nwj\nyj\n\u2264\nwi\nyi\n=\n\u2202U\n\u2202xi\n(x\u2217\n) .\nThus it contradicts with the optimality condition (1).\nSuppose that k = max{i|x\u2217\ni > 0}. Again, by the optimality\ncondition, there exists \u03bb such that wi\nyi\n(x\u2217\ni +yi)2 = \u03bb for 1 \u2264 i \u2264 k,\nand x\u2217\ni = 0 for i > k. Equivalently, we have that:\nx\u2217\ni =\nr\nwiyi\n\u03bb\n\u2212 yi , for 1 \u2264 i \u2264 k, and x\u2217\ni = 0 for i > k.\nReplacing them in the equation\nPn\ni=1 x\u2217\ni = X, we can\nsolve for \u03bb =\n(\nPk\ni=1\n\u221a\nwiyi)2\n(X+\nPk\ni=1 yi)2 . Thus,\nx\u2217\ni =\n\u221a\nwiyi\nPk\ni=1\n\u221a\nwiyi\n(X +\nkX\ni=1\nyi) \u2212 yi .\nThe remaining question is how to determine k. It is the\nlargest value such that x\u2217\nk > 0. Thus, we obtain the\nfollowing algorithm to compute the best response of a user:\n1. Sort the machines according to wi\nyi\nin decreasing order.\n2. Compute the largest k such that\n\u221a\nwkyk\nPk\ni=1\n\u221a\nwiyi\n(X +\nkX\ni=1\nyi) \u2212 yk \u2265 0.\n3. Set xj = 0 for j > k, and for 1 \u2264 j \u2264 k, set:\nxj =\n\u221a\nwjyj\nPk\ni=1\n\u221a\nwiyi\n(X +\nkX\ni=1\nyi) \u2212 yj.\nThe computational complexity of this algorithm is O(n log n),\ndominated by the sorting. In practice, the best response can\nbe computed infrequently (e.g. once a minute), so for a\ntypically powerful modern host, this cost is negligible.\nThe best response algorithm must send and receive O(n)\nmessages because each user must obtain the total bids from\neach host. In practice, this is more significant than the\ncomputational cost. Note that hosts only reveal to users the sum\nof the bids on them. As a result, hosts do not reveal the\nprivate preferences and even the individual bids of one user to\nanother.\n4.2 Finite Parallelism Model\nRecall that in the finite parallelism model, each user i only\nplaces bids on at most ki machines. Of course, the infinite\nparallelism model is just a special case of finite parallelism\nmodel in which ki = n for all the i\"s. In the finite parallelism\nmodel, computing the social optimum is no longer trivial\ndue to bounded parallelism. It can instead be computed by\nusing the maximum matching algorithm.\nConsider the weighted complete bipartite graph G = U \u00d7\nV , where U = {ui |1 \u2264 i \u2264 m , and 1 \u2264 \u2264 ki}, V =\n{1, 2, . . . , n} with edge weight wij assigned to the edge (ui , vj).\nA matching of G is a set of edges with disjoint nodes, and\nthe weight of a matching is the total weights of the edges in\nthe matching. As a result, the following lemma holds.\nLemma 1. The social optimum is the same as the\nmaximum weight matching of G.\nThus, we can use the maximum weight matching\nalgorithm to compute the social optimum. The maximum weight\nmatching is a classical network problem and can be solved\nin polynomial time [8, 9, 14]. We choose to implement the\nHungarian algorithm [14, 19] because of its simplicity. There\nmay exist a more efficient algorithm for computing the\nmaximum matching by exploiting the special structure of G. This\nremains an interesting open question.\nHowever, we do not know an efficient algorithm to\ncompute the best response under the finite parallelism model.\nInstead, we provide the following local search heuristic.\nSuppose we again have n machines with weights w1, . . . , wn\nand total bids y1, . . . , yn. Let the user\"s budget be X and\nthe parallelism bound be k. Our goal is to compute an\nallocation of X to up to k machines to maximize the user\"s\nutility.\nFor a subset of machines A, denote by x(A) the best\nresponse on A without parallelism bound and by U(A) the\nutility obtained by the best response algorithm. The local\nsearch works as follows:\n1. Set A to be the k machines with the highest wi/yi.\n2. Compute U(A) by the infinite parallelism best response\nalgorithm (Sec 4.1) on A.\n3. For each i \u2208 A and each j /\u2208 A, repeat\n4. Let B = A \u2212 {i} + {j}, compute U(B).\n5. If(U(B) > U(A)), let A \u2190 B, and goto 2.\n6. Output x(A).\nIntuitively, by the local search heuristic, we test if we can\nswap a machine in A for one not in A to improve the best\nresponse utility. If yes, we swap the machines and repeat the\nprocess. Otherwise, we have reached a local maxima and\noutput that value. We suspect that the local maxima that\nthis algorithm finds is also the global maximum (with\nrespect to an individual user) and that this process stop after\na few number of iterations, but we are unable to establish\nit. However, in our simulations, this algorithm quickly\nconverges to a high (\u2265 .7) efficiency.\n131\n4.3 Local Greedy Adjustment\nThe above best response algorithms only work for the\nlinear utility functions described earlier. In practice,\nutility functions may have more a complicated form, or even\nworse, a user may not have a formulation of his utility\nfunction. We do assume that the user still has a way to measure\nhis utility, which is the minimum assumption necessary for\nany market-based resource allocation mechanism. In these\nsituations, users can use a more general strategy, the local\ngreedy adjustment method, which works as follows. A user\nfinds the two machines that provide him with the highest\nand lowest marginal utility. He then moves a fixed small\namount of money from the machine with low marginal\nutility to the machine with the higher one. This strategy aims\nto adjust the bids so that the marginal values at each\nmachine being bid on are the same. This condition guarantees\nthe allocation is the optimum when the utility function is\nconcave. The tradeoff for local greedy adjustment is that it\ntakes longer to stabilize than best-response.\n5. SIMULATION RESULTS\nWhile the analytic results provide us with worst-case\nanalysis for the infinite parallelism model, in this section we\nemploy simulations to study the properties of the Nash\nequilibria in more realistic scenarios and for the finite parallelism\nmodel. First, we determine whether the user bidding process\nconverges, and if so, what the rate of convergence is.\nSecond, in cases of convergence, we look at the performance at\nequilibrium, using the efficiency and fairness metrics defined\nabove.\nIterative Method. In our simulations, each user starts\nwith an initial bid vector and then iteratively updates his\nbids until a convergence criterion (described below) is met.\nThe initial bid is set proportional to the user\"s weights on\nthe machines. We experiment with two update methods, the\nbest response methods, as described in Section 4.1 and 4.2,\nand the local greedy adjustment method, as described in\nSection 4.3.\nConvergence Criteria. Convergence time measures how\nquickly the system reaches equilibrium. It is particularly\nimportant in the highly dynamic environment of distributed\nshared clusters, in which the system\"s conditions may change\nbefore reaching the equilibrium. Thus, a high convergence\nrate may be more significant than the efficiency at the\nequilibrium.\nThere are several different criteria for convergence. The\nstrongest criterion is to require that there is only negligible\nchange in the bids of each user. The problem with this\ncriterion is that it is too strict: users may see negligible change\nin their utilities, but according to this definition the\nsystem has not converged. The less strict utility gap criterion\nrequires there to be only negligible change in the users\"\nutility. Given users\" concern for utility, this is a more natural\ndefinition. Indeed, in practice, the user is probably not\nwilling to re-allocate their bids dramatically for a small utility\ngain. Therefore, we use the utility gap criterion to measure\nconvergence time for the best response update method, i.e.\nwe consider that the system has converged if the utility gap\nof each user is smaller than (0.001 in our experiments).\nHowever, this criterion does not work for the local greedy\nadjustment method because users of that method will\nexperience constant fluctuations in utility as they move money\naround. For this method, we use the marginal utility gap\ncriterion. We compare the highest and lowest utility\nmargins on the machines. If the difference is negligible, then we\nconsider the system to be converged.\nIn addition to convergence to the equilibrium, we also\nconsider the criterion from the system provider\"s view, the\nsocial welfare stabilization criterion. Under this criterion,\na system has stabilized if the change in social welfare is\n\u2264 . Individual users\" utility may not have converged. This\ncriterion is useful to evaluate how quickly the system as a\nwhole reaches a particular efficiency level.\nUser preferences. We experiment with two models of\nuser preferences, random distribution and correlated\ndistribution. With random distribution, users\" weights on the\ndifferent machines are independently and identically\ndistributed, according the uniform distribution. In practice,\nusers\" preferences are probably correlated based on factors\nlike the hosts\" location and the types of applications that\nusers run. To capture these correlations, we associate with\neach user and machine a resource profile vector where each\ndimension of the vector represents one resource (e.g., CPU,\nmemory, and network bandwidth). For a user i with a\nprofile pi = (pi1, . . . , pi ), pik represents user i\"s need for\nresource k. For machine j with profile qj = (qj1, . . . , qj ),\nqjk represents machine j\"s strength with respect to resource\nk. Then, wij is the dot product of user i\"s and machine\nj\"s resource profiles, i.e. wij = pi \u00b7 qj =\nP\nk=1 pikqjk. By\nusing these profiles, we compress the parameter space and\nintroduce correlations between users and machines.\nIn the following simulations, we fix the number of\nmachines to 100 and vary the number of users from 5 to 250\n(but we only report the results for the range of 5 \u2212 150\nusers since the results remain similar for a larger number of\nusers). Sections 5.1 and 5.2 present the simulation results\nwhen we apply the infinite parallelism and finite parallelism\nmodels, respectively. If the system converges, we report the\nnumber of iterations until convergence. A convergence time\nof 200 iterations indicates non-convergence, in which case\nwe report the efficiency and fairness values at the point we\nterminate the simulation.\n5.1 Infinite parallelism\nIn this section, we apply the infinite parallelism model,\nwhich assumes that users can use an unlimited number of\nmachines. We present the efficiency and fairness at the\nequilibrium, compared to two baseline allocation methods:\nsocial optimum and weight-proportional, in which users\ndistribute their bids proportionally to their weights on the\nmachines (which may seem a reasonable distribution method\nintuitively).\nWe present results for the two user preference models.\nWith uniform preferences, users\" weights for the different\nmachines are independently and identically distributed\naccording to the uniform distribution, U \u223c (0, 1) (and are\nnormalized thereafter). In correlated preferences, each user\"s\nand each machine\"s resource profile vector has three\ndimensions, and their values are also taken from the uniform\ndistribution, U \u223c (0, 1).\nConvergence Time. Figure 2 shows the convergence\ntime, efficiency and fairness of the infinite parallelism model\nunder uniform (left) and correlated (right) preferences. Plots\n(a) and (b) show the convergence and stabilization time\nof the best-response and local greedy adjustment methods.\n132\n0\n50\n100\n150\n200\n0 20 40 60 80 100 120 140 160\nConvergencetime(#iterations)\nNumber of Users\nUniform preferences\n(a)\nBest-Response\nGreedy (convergence)\nGreedy (stabilization)\n0\n50\n100\n150\n200\n0 20 40 60 80 100 120 140 160\nNumber of Users\nCorrelated preferences\n(b)\nBest-response\nGreedy (convergence)\nGreedy (stabilization)\n0\n0.2\n0.4\n0.6\n0.8\n1\n0 20 40 60 80 100 120 140 160\nEfficiency\nNumber of Users\n(c)\nNash equilibrium\nWeight-proportional\nSocial Optimum\n0\n0.2\n0.4\n0.6\n0.8\n1\n0 20 40 60 80 100 120 140 160\nNumber of Users\n(d)\nNash equilibrium\nWeight-proportional\nSocial optimum\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n0 20 40 60 80 100 120 140 160\nUtilityuniformity\nNumber of Users\n(e)\nNash equilibrium\nWeight-proportional\nSocial optimum\n0\n0.1\n0.2\n0.3\n0.4\n0.5\n0.6\n0.7\n0.8\n0.9\n1\n0 20 40 60 80 100 120 140 160\nNumber of Users\n(f)\nNash equilibrium\nWeight proportional\nSocial optimum\n0\n0.2\n0.4\n0.6\n0.8\n1\n0 20 40 60 80 100 120 140 160\nEnvy-freeness\nNumber of Users\n(g)\nNash equilibrium\nWeight proportional\nSocial optimum\n0\n0.2\n0.4\n0.6\n0.8\n1\n0 20 40 60 80 100 120 140 160\nNumber of Users\n(h)\nNash equilibrium\nWeight proportional\nSocial optimum\nFigure 2: Efficiency, utility uniformity, enviness and convergence time as a function of the number of users under the\ninfinite parallelism model, with uniform and correlated preferences. n = 100.\n133\n0\n0.2\n0.4\n0.6\n0.8\n1\n0 20 40 60 80 100\nEfficiency\nIteration number\nBest-Response\nGreedy\nFigure 3: Efficiency level over time under the infinite\nparallelism model. number of users = 40. n = 100.\nThe best-response algorithm converges within a few number\nof iterations for any number of users. In contrast, the local\ngreedy adjustment algorithm does not converge even within\n500 iterations when the number of users is smaller than 60,\nbut does converge for a larger number of users. We believe\nthat for small numbers of users, there are dependency cycles\namong the users that prevent the system from converging\nbecause one user\"s decisions affects another user, whose\ndecisions affect another user, etc. Regardless, the local greedy\nadjustment method stabilizes within 100 iterations.\nFigure 3 presents the efficiency over time for a system\nwith 40 users. It demonstrates that while both adjustment\nmethods reach the same social welfare, the best-response\nalgorithm is faster.\nIn the remainder of this paper, we will refer to the (Nash)\nequilibrium, independent of the adjustment method used to\nreach it.\nEfficiency. Figure 2 (c) and (d) present the efficiency as\na function of the number of users. We present the efficiency\nat equilibrium, and use the social optimum and the\nweightproportional static allocation methods for comparison.\nSocial optimum provides an efficient allocation by definition.\nFor both user preference models, the efficiency at the\nequilibrium is approximately 0.9, independent of the number of\nusers, which is only slightly worse than the social optimum.\nThe efficiency at the equilibrium is \u2248 50% improvement over\nthe weight-proportional allocation method for uniform\npreferences, and \u2248 30% improvement for correlated preferences.\nFairness. Figure 2(e) and (f) present the utility\nuniformity as a function of the number of users, and figures (g)\nand (h) present the envy-freeness. While the social optimum\nyields perfect efficiency, it has poor fairness. The\nweightproportional method achieves the highest fairness among the\nthree allocation methods, but the fairness at the equilibrium\nis close.\nThe utility uniformity is slightly better at the equilibrium\nunder uniform preferences (> 0.7) than under correlated\npreferences (> 0.6), since when users\" preferences are more\naligned, users\" happiness is more likely going to be at the\nexpense of each other. Although utility uniformity decreases\nin the number of users, it remains reasonable even for a large\nnumber of users, and flattens out at some point. At the\nsocial optimum, utility uniformity can be infinitely poor, as\nsome users may be allocated no resources at all. The same is\ntrue with respect to envy-freeness. The difference between\nuniform and correlated preferences is best demonstrated in\nthe social optimum results. When the number of users is\nsmall, it may be possible to satisfy all users to some extent\nif their preferences are not aligned, but if they are aligned,\neven with a very small number of users, some users get no\nresources, thus both utility uniformity and envy-freeness go\nto zero. As the number of users increases, it becomes almost\nimpossible to satisfy all users independent of the existence\nof correlation.\nThese results demonstrate the tradeoff between the\ndifferent allocation methods. The efficiency at the equilibrium is\nlower than the social optimum, but it performs much\nbetter with respect to fairness. The equilibrium allocation is\ncompletely envy-free under uniform preferences and almost\nenvy-free under correlated preferences.\n5.2 Finite parallelism\n0\n50\n100\n150\n200\n0 10 20 30 40 50 60 70 80 90\nConvergencetime(#iterations)\nNumber of Users\n5 machines/user\n20 machines/user\nFigure 4: Convergence time under the finite parallelism\nmodel. n = 100.\n0.6\n0.7\n0.8\n0.9\n1\n0 20 40 60 80 100\nEfficiency\nIteration number\n5-machines/user (40 users)\n20-machines/user (10 users)\nFigure 5: Efficiency level over time under the finite\nparallelism model with local search algorithm. n = 100.\nWe also consider the finite parallelism model and use the\nlocal search algorithm, as described in Section 4.2, to\nadjust user\"s bids. We again experimented with both the\nuniform and correlated preferences distributions and did not\nfind significant differences in the results so we present the\nsimulation results for only the uniform distribution.\nIn our experiments, the local search algorithm stops quickly\n- it usually discovers a local maximum within two\niterations. As mentioned before, we cannot prove that a local\nmaximum is the global maximum, but our experiments\nindicate that the local search heuristic leads to high efficiency.\n134\nConvergence time. Let \u2206 denote the parallelism bound\nthat limits the maximum number of machines each user can\nbid on. We experiment with \u2206 = 5 and \u2206 = 20. In both\ncases, we use 100 machines and vary the number of users.\nFigure 4 shows that the system does not always converge,\nbut if it does, the convergence happens quickly. The\nnonconvergence occurs when the number of users is between 20\nand 40 for \u2206 = 5, between 5 and 10 for \u2206 = 20. We\nbelieve that the non-convergence is caused by moderate\ncompetition. No competition allows the system to equilibrate\nquickly because users do not have to change their bids in\nreaction to changes in others\" bids. High competition also\nallows convergence because each user\"s decision has only a\nsmall impact on other users, so the system is more stable\nand can gradually reach convergence. However, when there\nis moderate competition, one user\"s decisions may cause\ndramatic changes in another\"s decisions and cause large\nfluctuations in bids. In both cases of non-convergence, the ratio of\ncompetitors per machine, \u03b4 = m\u00d7\u2206/n for m users and n\nmachines, is in the interval [1, 2]. Although the system does\nnot converge in these bad ranges, the system nontheless\nachieves and maintains a high level of overall efficiency after\na few iterations (as shown in Figure 5).\nPerformance. In Figure 6, we present the efficiency,\nutility uniformity, and envy-freeness at the Nash\nequilibrium for the finite parallelism model. When the system does\nnot converge, we measure performance by taking the\nminimum value we observe after running for many iterations.\nWhen \u2206 = 5, there is a performance drop, in particular\nwith respect to the fairness metrics, in the range between\n20 and 40 users (where it does not converge). For a larger\nnumber of users, the system converges and achieves a lower\nlevel of utility uniformity, but a high degree of efficiency and\nenvy-freeness, similar to those under the infinite parallelism\nmodel. As described above, this is due the competition ratio\nfalling into the head-to-head range. When the parallelism\nbound is large (\u2206 = 20), the performance is closer to the\ninfinite parallelism model, and we do not observe this drop\nin performance.\n6. RELATED WORK\nThere are two main groups of related work in resource\nallocation: those that incorporate an economic mechanism,\nand those that do not.\nOne non-economic approach is scheduling (surveyed by\nPinedo [20]). Examples of this approach are queuing in\nfirst-come, first-served (FCFS) order, queueing using the\nresource consumption of tasks (e.g., [28]), and scheduling\nusing combinatorial optimization [19]. These all assume that\nthe values and resource consumption of tasks are reported\naccurately, which does not apply in the presence of strategic\nusers. We view scheduling and resource allocation as two\nseparate functions. Resource allocation divides a resource\namong different users while scheduling takes a given\nallocation and orders a user\"s jobs.\nExamples of the economic approach are Spawn [26]), work\nby Stoica, et al. [24]., the Millennium resource allocator [4],\nwork by Wellman, et al. [27], Bellagio [2]), and Tycoon [15]).\nSpawn and the work by Wellman, et al. uses a reservation\nabstraction similar to the way airline seats are allocated.\nUnfortunately, reservations have a high latency to acquire\nresources, unlike the price-anticipating scheme we consider.\nThe tradeoff of the price-anticipating schemes is that users\nhave uncertainty about exactly how much of the resources\nthey will receive.\nBellagio[3] uses the SHARE centralized allocator. SHARE\nallocates resources using a centralized combinatorial auction\nthat allows users to express preferences with\ncomplementarities. Solving the NP-complete combinatorial auction\nproblem provides an optimally efficient allocation. The\npriceanticipating scheme that we consider does not explicitly\noperate on complementarities, thereby possibly losing some\nefficiency, but it also avoids the complexity and overhead of\ncombinatorial auctions.\nThere have been several analyses [10, 11, 12, 13, 23] of\nvariations of price-anticipating allocation schemes in the\ncontext of allocation of network capacity for flows. Their\nmethodology follows the study of congestion (potential) games [17,\n22] by relating the Nash equilibrium to the solution of a\n(usually convex) global optimization problem. But those\ntechniques no longer apply to our game because we model\nusers as having fixed budgets and private preferences for\nmachines. For example, unlike those games, there may\nexist multiple Nash equilibria in our game. Milchtaich [16]\nstudied congestion games with private preferences but the\ntechnique in [16] is specific to the congestion game.\n7. CONCLUSIONS\nThis work studies the performance of a market-based\nmechanism for distributed shared clusters using both analyatical\nand simulation methods. We show that despite the worst\ncase bounds, the system can reach a high performance level\nat the Nash equilibrium in terms of both efficiency and\nfairness metrics. In addition, with a few exceptions under\nthe finite parallelism model, the system reaches equilibrium\nquickly by using the best response algorithm and, when the\nnumber of users is not too small, by the greedy local\nadjustment method.\nWhile our work indicates that the price-anticipating scheme\nmay work well for resource allocation for shared clusters,\nthere are many interesting directions for future work. One\ndirection is to consider more realistic utility functions. For\nexample, we assume that there is no parallelization cost, and\nthere is no performance degradation when multiple users\nshare the same machine. In practice, both assumptions may\nnot be correct. For examples, the user must copy code and\ndata to a machine before running his application there, and\nthere is overhead for multiplexing resources on a single\nmachine. When the job size is large enough and the degree\nof multiplexing is sufficiently low, we can probably ignore\nthose effects, but those costs should be taken into account\nfor a more realistic modeling. Another assumption is that\nusers have infinite work, so the more resources they can\nacquire, the better. In practice, users have finite work. One\napproach to address this is to model the user\"s utility\naccording to the time to finish a task rather than the amount\nof resources he receives.\nAnother direction is to study the dynamic properties of\nthe system when the users\" needs change over time,\naccording to some statistical model. In addition to the usual\nquestions concerning repeated games, it would also be important\nto understand how users should allocate their budgets wisely\nover time to accomodate future needs.\n135\n0\n0.2\n0.4\n0.6\n0.8\n1\n0 20 40 60 80 100 120 140 160\nNumber of Users\n(a) Limit: 5 machines/user\nEfficiency\nUtility uniformity\nEnvy-freeness\n0\n0.2\n0.4\n0.6\n0.8\n1\n0 10 20 30 40 50 60 70 80 90\nNumber of Users\n(b) Limit: 20 machines/user\nEfficiency\nUtility uniformity\nEnvy-freeness\nFigure 6: Efficiency, utility uniformity and envy-freeness under the finite parallelism model. n = 100.\n8. ACKNOWLEDGEMENTS\nWe thank Bernardo Huberman, Lars Rasmusson, Eytan\nAdar and Moshe Babaioff for fruitful discussions. We also\nthank the anonymous reviewers for their useful comments.\n9. REFERENCES\n[1] http://planet-lab.org.\n[2] A. AuYoung, B. N. Chun, A. C. Snoeren, and A. Vahdat.\nResource Allocation in Federated Distributed Computing\nInfrastructures. 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{"name": "train_J-55", "title": "From Optimal Limited To Unlimited Supply Auctions", "abstract": "We investigate the class of single-round, sealed-bid auctions for a set of identical items to bidders who each desire one unit. We adopt the worst-case competitive framework defined by [9, 5] that compares the profit of an auction to that of an optimal single-price sale of least two items. In this paper, we first derive an optimal auction for three items, answering an open question from [8]. Second, we show that the form of this auction is independent of the competitive framework used. Third, we propose a schema for converting a given limited-supply auction into an unlimited supply auction. Applying this technique to our optimal auction for three items, we achieve an auction with a competitive ratio of 3.25, which improves upon the previously best-known competitive ratio of 3.39 from [7]. Finally, we generalize a result from [8] and extend our understanding of the nature of the optimal competitive auction by showing that the optimal competitive auction occasionally offers prices that are higher than all bid values.", "fulltext": "1. INTRODUCTION\nThe research area of optimal mechanism design looks at\ndesigning a mechanism to produce the most desirable outcome for the\nentity running the mechanism. This problem is well studied for the\nauction design problem where the optimal mechanism is the one\nthat brings the seller the most profit. Here, the classical approach\nis to design such a mechanism given the prior distribution from\nwhich the bidders\" preferences are drawn (See e.g., [12, 4]).\nRecently Goldberg et al. [9] introduced the use of worst-case\ncompetitive analysis (See e.g., [3]) to analyze the performance of auctions\nthat have no knowledge of the prior distribution. The goal of such\nwork is to design an auction that achieves a large constant fraction\nof the profit attainable by an optimal mechanism that knows the\nprior distribution in advance. Positive results in this direction are\nfueled by the observation that in auctions for a number of identical\nunits, much of the distribution from which the bidders are drawn\ncan be deduced on the fly by the auction as it is being run [9, 14,\n2].\nThe performance of an auction in such a worst-case competitive\nanalysis is measured by its competitive ratio, the ratio between a\nbenchmark performance and the auction\"s performance on the input\ndistribution that maximizes this ratio. The holy grail of the\nworstcase competitive analysis of auctions is the auction that achieves\nthe optimal competitive ratio (as small as possible). Since [9] this\nsearch has led to improved understanding of the nature of the\noptimal auction, the techniques for on-the-fly pricing in these\nscenarios, and the competitive ratio of the optimal auction [5, 7, 8]. In this\npaper we continue this line of research by improving in all of these\ndirections. Furthermore, we give evidence corroborating the\nconjecture that the form of the optimal auction is independent of the\nbenchmark used in the auction\"s competitive analysis. This result\nfurther validates the use of competitive analysis in gauging auction\nperformance.\nWe consider the single item, multi-unit, unit-demand auction\nproblem. In such an auction there are many units of a single item\navailable for sale to bidders who each desire only one unit. Each bidder\nhas a valuation representing how much the item is worth to him.\nThe auction is performed by soliciting a sealed bid from each of\nthe bidders and deciding on the allocation of units to bidders and\nthe prices to be paid by the bidders. The bidders are assumed to bid\nso as to maximize their personal utility, the difference between their\nvaluation and the price they pay. To handle the problem of\ndesigning and analyzing auctions where bidders may falsely declare their\nvaluations to get a better deal, we will adopt the solution concept\nof truthful mechanism design (see, e.g., [9, 15, 13]). In a truthful\nauction, revealing one\"s true valuation as one\"s bid is an optimal\nstrategy for each bidder regardless of the bids of the other bidders.\nIn this paper, we will restrict our attention to truthful (a.k.a.,\nincentive compatible or strategyproof) auctions.\nA particularly interesting special case of the auction problem is\nthe unlimited supply case. In this case the number of units for sale is\nat least the number of bidders in the auction. This is natural for the\nsale of digital goods where there is negligible cost for duplicating\n175\nand distributing the good. Pay-per-view television and\ndownloadable audio files are examples of such goods.\nThe competitive framework introduced in [9] and further refined\nin [5] uses the profit of the optimal omniscient single priced\nmechanism that sells at least two units as the benchmark for competitive\nanalysis. The assumption that two or more units are sold is\nnecessary because in the worst case it is impossible to obtain a constant\nfraction of the profit of the optimal mechanism when it sells only\none unit [9]. In this framework for competitive analysis, an auction\nis said to be \u03b2-competitive if it achieves a profit that is within a\nfactor of \u03b2 \u2265 1 of the benchmark profit on every input. The optimal\nauction is the one which is \u03b2-competitive with the minimum value\nof \u03b2.\nPrevious to this work, the best known auction for the unlimited\nsupply case had a competitive ratio of 3.39 [7] and the best lower\nbound known was 2.42 [8]. For the limited supply case, auctions\ncan achieve substantially better competitive ratios. When there are\nonly two units for sale, the optimal auction gives a competitive ratio\nof 2, which matches the lower bound for two units. When there\nare three units for sale, the best previously known auction had a\ncompetitive ratio of 2.3, compared with a lower bound of 13/6 \u2248\n2.17 [8].\nThe results of this paper are as follows:\n\u2022 We give the auction for three units that is optimally\ncompetitive against the profit of the omniscient single priced\nmechanism that sells at least two units. This auction achieves a\ncompetitive ratio of 13/6, matching the lower bound from\n[8] (Section 3).\n\u2022 We show that the form of the optimal auction is\nindependent of the benchmark used in competitive analysis. In doing\nso, we give an optimal three bidder auction for generalized\nbenchmarks (Section 4).\n\u2022 We give a general technique for converting a limited supply\nauction into an unlimited supply auction where it is possible\nto use the competitive ratio of the limited supply auction to\nobtain a bound on the competitive ratio of the unlimited\nsupply auction. We refer to auctions derived from this\nframework as aggregation auctions (Section 5).\n\u2022 We improve on the best known competitive ratio by\nproving that the aggregation auction constructed from our optimal\nthree-unit auction is 3.25-competitive (Section 5.1).\n\u2022 Assuming that the conjecture that the optimal -unit auction\nhas a competitive ratio that matches the lower bound proved\nin [8], we show that this optimal auction for \u2265 3 on some\ninputs will occasionally offer prices that are higher than any\nbid in that input (Section 6). For the three-unit case where we\nhave shown that the lower bound of [8] is tight, this\nobservation led to our construction of the optimal three-unit auction.\n2. DEFINITIONS AND BACKGROUND\nWe consider single-round, sealed-bid auctions for a set of\nidentical units of an item to bidders who each desire one unit. As\nmentioned in the introduction, we adopt the game-theoretic solution\nconcept of truthful mechanism design. A useful simplification of\nthe problem of designing truthful auctions is obtained through the\nfollowing algorithmic characterization [9]. Related formulations to\nthis one have appeared in numerous places in recent literature (e.g.,\n[1, 14, 5, 10]).\nDEFINITION 1. Given a bid vector of n bids, b = (b1, . . . , bn),\nlet b-i denote the vector of with bi replaced with a \u2018?\", i.e.,\nb-i = (b1, . . . , bi\u22121, ?, bi+1, . . . , bn).\nDEFINITION 2. Let f be a function from bid vectors (with a\n\u2018?\") to prices (non-negative real numbers). The deterministic\nbidindependent auction defined by f, BIf , works as follows. For each\nbidder i:\n1. Set ti = f(b-i).\n2. If ti < bi, bidder i wins at price ti.\n3. If ti > bi, bidder i loses.\n4. Otherwise, (ti = bi) the auction can either accept the bid at\nprice ti or reject it.\nA randomized bid-independent auction is a distribution over\ndeterministic bid-independent auctions.\nThe proof of the following theorem can be found, for example,\nin [5].\nTHEOREM 1. An auction is truthful if and only if it is equivalent\nto a bid-independent auction.\nGiven this equivalence, we will use the the terminology\nbidindependent and truthful interchangeably.\nFor a randomized bid-independent auction, f(b-i) is a random\nvariable. We denote the probability density of f(b-i) at z by \u03c1b-i (z).\nWe denote the profit of a truthful auction A on input b as A(b).\nThe expected profit of the auction, E[A(b)], is the sum of the\nexpected payments made by each bidder, which we denote by pi(b)\nfor bidder i. Clearly, the expected payment of each bid satisfies\npi(b) =\nbi\n0\nx\u03c1b-i (x)dx.\n2.1 Competitive Framework\nWe now review the competitive framework from [5]. In order\nto evaluate the performance of auctions with respect to the goal of\nprofit maximization, we introduce the optimal single price\nomniscient auction F and the related omniscient auction F(2)\n.\nDEFINITION 3. Give a vector b = (b1, . . . , bn), let b(i)\nrepresent the i-th largest value in b.\nThe optimal single price omniscient auction, F, is defined as\nfollows. Auction F on input b determines the value k such that\nkb(k) is maximized. All bidders with bi \u2265 b(k) win at price b(k); all\nremaining bidders lose. The profit of F on input b is thus F(b) =\nmax1\u2264k\u2264n kb(k).\nIn the competitive framework of [5] and subsequent papers, the\nperformance of a truthful auction is gauged in comparison to F(2)\n,\nthe optimal singled priced auction that sells at least two units. The\nprofit of F(2)\nis max2\u2264k\u2264n kb(k) There are a number of reasons\nto choose this benchmark for comparison, interested readers should\nsee [5] or [6] for a more detailed discussion.\nLet A be a truthful auction. We say that A is \u03b2-competitive\nagainst F(2)\n(or just \u03b2-competitive) if for all bid vectors b, the\nexpected profit of A on b satisfies\nE[A(b)] \u2265\nF(2)\n(b)\n\u03b2\n.\nIn Section 4 we generalize this framework to other profit\nbenchmarks.\n176\n2.2 Scale Invariant and Symmetric Auctions\nA symmetric auction is one where the auction outcome is\nunchanged when the input bids arrive in a different permutation.\nGoldberg et al. [8] show that a symmetric auction achieves the optimal\ncompetitive ratio. This is natural as the profit benchmark we\nconsider is symmetric, and it allows us to consider only symmetric\nauctions when looking for the one with the optimal competitive\nratio.\nAn auction defined by bid-independent function f is scale\ninvariant if, for all i and all z, Pr[f(b-i) \u2265 z] = Pr[f(cb-i) \u2265 cz].\nIt is conjectured that the assumption of scale invariance is without\nloss of generality. Thus, we are motivated to consider\nsymmetric scale-invariant auctions. When specifying a symmetric\nscaleinvariant auction we can assume that f is only a function of the\nrelative magnitudes of the n \u2212 1 bids in b-i and that one of the\nbids, bj = 1. It will be convenient to specify such auctions via the\ndensity function of f(b-i), \u03c1b-i (z). It is enough to specify such a\ndensity function of the form \u03c11,z1,...,zn\u22121 (z) with 1 \u2264 zi \u2264 zi+1.\n2.3 Limited Supply Versus Unlimited Supply\nFollowing [8], throughout the remainder of this paper we will\nbe making the assumption that n = , i.e., the number of bidders\nis equal to the number of units for sale. This is without loss of\ngenerality as (a) any lower bound that applies to the n = case\nalso extends to the case where n \u2265 [8], and (b) there is a\nreduction from the unlimited supply auction problem to the limited\nsupply auction problem that takes an unlimited supply auction that\nis \u03b2-competitive with F(2)\nand constructs a limited supply auction\nparameterized by that is \u03b2-competitive with F(2, )\n, the optimal\nomniscient auction that sells between 2 and units [6].\nHenceforth, we will assume that we are in the unlimited supply\ncase, and we will examine lower bounds for limited supply\nproblems by placing a restriction on the number of bidders in the\nauction.\n2.4 Lower Bounds and Optimal Auctions\nFrequently in this paper, we will refer to the best known lower\nbound on the competitive ratio of truthful auctions:\nTHEOREM 2. [8] The competitive ratio of any auction on n\nbidders is at least\n1 \u2212\nn\ni=2\n\u22121\nn\ni\u22121\ni\ni \u2212 1\nn \u2212 1\ni \u2212 1\n.\nDEFINITION 4. Let \u03a5n denote the n-bidder auction that achieves\nthe optimal competitive ratio.\nThis bound is derived by analyzing the performance of any\nauction on the following distribution B. In each random bid\nvector B, each bid Bi is drawn i.i.d. from the distribution such that\nPr[Bi \u2265 s] \u2264 1/s for all s \u2208 S.\nIn the two-bidder case, this lower bound is 2. This is achieved by\n\u03a52 which is the 1-unit Vickrey auction.1\nIn the three-bidder case,\nthis lower bound is 13/6. In the next section, we define the\nauction \u03a53 which matches this lower bound. In the four-bidder case,\nthis lower bound is 96/215. In the limit as the number of bidders\ngrows, this lower bound approaches a number which is\napproximately 2.42.\nIt is conjectured that this lower bound is tight for any number of\nbidders and the optimal auction, \u03a5n, matches it.\n1\nThe 1-unit Vickrey auction sells to the highest bidder at the second\nhighest bid value.\n2.5 Profit Extraction\nIn this section we review the truthful profit extraction mechanism\nProfitExtractR. This mechanism is a special case of a general\ncost-sharing schema due to Moulin and Shenker [11].\nThe goal of profit extraction is, given bids b, to extract a target\nvalue R of profit from some subset of the bidders.\nProfitExtractR: Given bids b, find the largest k such\nthat the highest k bidders can equally share the cost\nR. Charge each of these bidders R/k. If no subset\nof bidders can cover the cost, the mechanism has no\nwinners.\nImportant properties of this auction are as follows:\n\u2022 ProfitExtractR is truthful.\n\u2022 If R \u2264 F(b), ProfitExtractR(b) = R; otherwise it has no\nwinners and no revenue.\nWe will use this profit extraction mechanism in Section 5 with\nthe following intuition. Such a profit extractor makes it possible to\ntreat this subset of bidders as a single bid with value F(S). Note\nthat given a single bid, b, a truthful mechanism might offer it price\nt and if t \u2264 b then the bidder wins and pays t; otherwise the\nbidder pays nothing (and loses). Likewise, a mechanism can offer\nthe set of bidders S a target revenue R. If R \u2264 F(2)\n(S), then\nProfitExtractR raises R from S; otherwise, the it raises no\nrevenue from S.\n3. AN OPTIMAL AUCTION FOR THREE\nBIDDERS\nIn this section we define the optimal auction for three bidders,\n\u03a53, and prove that it indeed matches the known lower bound of\n13/6. We follow the definition and proof with a discussion of how\nthis auction was derived.\nDEFINITION 5. \u03a53 is scale-invariant and symmetric and given\nby the bid-independent function with density function\n\u03c11,x(z) =\n\u23a7\n\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a8\n\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a9\nFor x \u2264 3/2\n1 with probability 9/13\nz with probability density g(z) for z > 3/2\nFor x > 3/2\u23a7\n\u23aa\u23a8\n\u23aa\u23a9\n1 with probability 9/13 \u2212\nx\n3/2\nzg(z)dz\nx with probability\nx\n3/2\n(z + 1)g(z)dz\nz with probability density g(z) for z > x\nwhere g(x) = 2/13\n(x\u22121)3 .\nTHEOREM 3. The \u03a53 auction has a competitive ratio of 13/6 \u2248\n2.17, which is optimal. Furthermore, the auction raises exactly\n6\n13\nF(2)\non every input with non-identical bids.\nPROOF. Consider the bids 1, x, y, with 1 < x < y. There are\nthree cases.\nCASE 1 (x < y \u2264 3/2): F(2)\n= 3. The auction must raise\nexpected revenue of at least 18/13 on these bids. The bidder with\nvaluation x will pay 1 with 9/13, and the bidder with valuation y\nwill pay 1 with probability 9/13. Therefore \u03a53 raises 18/13 on\nthese bids.\nCASE 2 (x \u2264 3/2 < y): F(2)\n= 3. The auction must raise\nexpected revenue of at least 18/13 on these bids. The bidder with\n177\nvaluation x will pay 9/13 \u2212\ny\n3/2\nzg(z)dz in expectation. The\nbidder with valuation y will pay 9/13 +\ny\n3/2\nzg(z)dz in expectation.\nTherefore \u03a53 raises 18/13 on these bids.\nCASE 3 (3/2 < x \u2264 y): F(2)\n= 2x. The auction must raise\nexpected revenue of at least 12x/13 on these bids. Consider the\nrevenue raised from all three bidders:\nE[\u03a53(b)] = p(1, x, y) + p(x, 1, y) + p(y, 1, x)\n= 0 + 9/13 \u2212\ny\n3/2\nzg(z)dz + 9/13 \u2212\nx\n3/2\nzg(z)dz\n+ x\nx\n3/2\n(z + 1)g(z)dz +\ny\nx\nzg(z)dz\n= 18/13 + (x \u2212 2)\nx\n3/2\nzg(z)dz + x\nx\n3/2\ng(z)dz\n= 12x/13.\nThe final equation comes from substituting in g(x) = 2/13\n(x\u22121)3 and\nexpanding the integrals. Note that the fraction of F(2)\nraised on\nevery input is identical. If any of the inequalities 1 \u2264 x \u2264 y\nare not strict, the same proof applies giving a lower bound on the\nauction\"s profit; however, this bound may no longer be tight.\nMotivation for \u03a53\nIn this section, we will conjecture that a particular input distribution\nis worst-case, and show, as a consequence, that all inputs are\nworstcase in the optimal auction. By applying this consequence, we will\nderive an optimal auction for three bidders.\nA truthful, randomized auction on n bidders can be represented\nby a randomized function f : Rn\u22121\n\u00d7 n \u2192 R that maps masked\nbid vectors to prices in R. By normalization, we can assume that\nthe lowest possible bid is 1. Recall that \u03c1b-i (z) = Pr[f(b-i) = z].\nThe optimal auction for the finite auction problem can be found\nby the following optimization problem in which the variables are\n\u03c1b-i (z):\nmaximize r\nsubject to\nn\ni=1\nbi\nz=1\nz\u03c1b-i (z)dz \u2265 rF(2)\n(b)\n\u221e\nz=1\n\u03c1b-i (z)dz = 1\n\u03c1b-i (z) \u2265 0\nThis set of integral inequalities is difficult to maximize over.\nHowever, by guessing which constraints are tight and which are\nslack at the optimum, we will be able to derive a set of differential\nequations for which any feasible solution is an optimal auction.\nAs we discuss in Section 2.4, in [8], the authors define a\ndistribution and use it to find a lower bound on the competitive ratio of\nthe optimal auction. For two bidders, this bid distribution is the\nworst-case input distribution. We guess (and later verify) that this\ndistribution is the worst-case input distribution for three bidders as\nwell. Since this distribution has full support over the set of all bid\nvectors and a worst-case distribution puts positive probability only\non worst-case inputs, we can therefore assume that all but a\nmeasure zero set of inputs is worst-case for the optimal auction. In the\noptimal two-bidder auction, all inputs with non-identical bids are\nworst-case, so we will assume the same for three bidders.\nThe guess that these constraints are tight allows us to transform\nthe optimization problem into a feasibility problem constrained by\ndifferential equations. If the solution to these equations has value\nmatching the lower bound obtained from the worst-case\ndistribution, then this solution is the optimal auction and that our\nconjectured choice of worst-case distribution is correct.\nIn Section 6 we show that the optimal auction must sometimes\nplace probability mass on sale prices above the highest bid. This\nmotivates considering symmetric scale-invariant auctions for three\nbidders with probability density function, \u03c11,x(z), of the following\nform:\n\u03c11,x(z) =\n\u23a7\n\u23aa\u23a8\n\u23aa\u23a9\n1 with discrete probability a(x)\nx with discrete probability b(x)\nz with probability density g(z) for z > x\nIn this auction, the sale price for the first bidder is either one\nof the latter two bids, or higher than either bid with a probability\ndensity which is independent of the input.\nThe feasibility problem which arises from the linear optimization\nproblem by assuming the constraints are tight is as follows:\na(y) + a(x) + xb(x) +\ny\nx\nzg(z)dz = r max(3, 2x) \u2200x < y\na(x) + b(x) +\n\u221e\nx\ng(z)dz = 1\na(x) \u2265 0\nb(x) \u2265 0\ng(z) \u2265 0\nSolving this feasibility problem gives the auction \u03a53 proposed\nabove. The proof of its optimality validates its proposed form.\nFinding a simple restriction on the form of n-bidder auctions for\nn > 3 under which the optimal auction can be found analytically\nas above remains an open problem.\n4. GENERALIZED PROFIT BENCHMARKS\nIn this section, we widen our focus beyond auctions that compete\nwith F(2)\nto consider other benchmarks for an auction\"s profit. We\nwill show that, for three bidders, the form of the optimal auction\nis essentially independent of the benchmark profit used. This\nresults strongly corroborates the worst-case competitive analysis of\nauctions by showing that our techniques allow us to derive auctions\nwhich are competitive against a broad variety of reasonable\nbenchmarks rather than simply against F(2)\n.\nPrevious work in competitive analysis of auctions has focused on\nthe question of designing the auction with the best competitive\nratio against F(2)\n, the profit of the optimal omniscient single-priced\nmechanism that sells at least two items. However, it is reasonable to\nconsider other benchmarks. For instance, one might wish to\ncompete against V\u2217\n, the profit of the k-Vickrey auction with\noptimal-inhindsight choice of k.2\nAlternatively, if an auction is being used as\na subroutine in a larger mechanism, one might wish to choose the\nauction which is optimally competitive with a benchmark specific\nto that purpose.\nRecall that F(2)\n(b) = max2\u2265k\u2265n kb(k). We can generalize this\ndefinition to Gs, parameterized by s = (s2, . . . , sn) and defined as:\nGs(b) = max\n2\u2264k\u2264n\nskb(k).\nWhen considering Gs we assume without loss of generality that\nsi < si+1 as otherwise the constraint imposed by si+1 is irrelevant.\nNote that F(2)\nis the special case of Gs with si = i, and that V\u2217\n=\nGs with si = i \u2212 1.\n2\nRecall that the k-Vickrey auction sells a unit to each of the\nhighest k bidders at a price equal to the k + 1st highest bid, b(k+1),\nachieving a profit of kb(k+1).\n178\nCompeting with Gs\nWe will now design a three-bidder auction \u03a5s,t\n3 that achieves the\noptimal competitive ratio against Gs,t. As before, we will first find\na lower bound on the competitive ratio and then design an auction\nto meet that bound.\nWe can lower bound the competitive ratio of \u03a5s,t\n3 using the same\nworst-case distribution from [8] that we used against F(2)\n.\nEvaluating the performance of any auction competing against Gs,t on\nthis distribution will yield the following theorem. We denote the\noptimal auction for three bidders against Gs,t as \u03a5s,t\n3 .\nTHEOREM 4. The optimal three-bidder auction, \u03a5s,t\n3 ,\ncompeting against Gs,t(b) = max(sb(2), tb(3)) has a competitive ratio of\nat least s2\n+t2\n2t\n.\nThe proof can be found in the appendix.\nSimilarly, we can find the optimal auction against Gs,t using the\nsame technique we used to solve for the three bidder auction with\nthe best competitive ratio against F(2)\n.\nDEFINITION 6. \u03a5s,t\n3 is scale-invariant and symmetric and given\nby the bid-independent function with density function\n\u03c11,x(z) =\n\u23a7\n\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a8\n\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a9\nFor x \u2264 t\ns\n1 with probability t2\ns2+t2\nz with probability density g(z) for z > t\ns\nFor x > t\ns\u23a7\n\u23aa\u23aa\u23a8\n\u23aa\u23aa\u23a9\n1 with probability t2\ns2+t2 \u2212\nx\nt\ns\nzg(z)dz\nx with probability\nx\nt\ns\n(z + 1)g(z)dz\nz with probability density g(z) for z > x\nwhere g(x) = 2(t\u2212s)2\n/(s2\n+t2\n)\n(x\u22121)3 .\nTHEOREM 5. \u03a5s,t\n3 is s2\n+t2\n2t\n-competitive with Gs,t.\nThis auction, like \u03a53, can be derived by reducing the optimization\nproblem to a feasibility problem, guessing that the optimal solution\nhas the same form as \u03a5s,t\n3 , and solving. The auction is optimal\nbecause it matches the lower bound found above. Note that the form\nof \u03a5s,t\n3 is essentially the same as for \u03a53, but that the probability of\neach price is scaled depending on the values of s and t.\nThat our auction for three bidders matches the lower bound\ncomputed by the input distribution used in [8] is strong evidence that\nthis input distribution is the worst-case input distribution for any\nnumber of bidders and any generalized profit benchmark.\nFurthermore, we strongly suspect that for any number of bidders, the form\nof the optimal auction will be independent of the benchmark used.\n5. AGGREGATION AUCTIONS\nWe have seen that optimal auctions for small cases of the\nlimitedsupply model can be found analytically. In this section, we will\nconstruct a schema for turning limited supply auctions into\nunlimited supply auctions with a good competitive ratio.\nAs discussed in Section 2.5, the existence of a profit\nextractor, ProfitExtractR, allows an auction to treat a set of bids S\nas a single bid with value F(S). Given n bidders and an\nauction, Am, for m < n bidders, we can convert the m-bidder\nauction into an n-bidder auction by randomly partitioning the bidders\ninto m subsets and then treating each subset as a single bidder (via\nProfitExtractR) and running the m-bidder auction.\nDEFINITION 7. Given a truthful m-bidder auction, Am, the\nm-aggregation auction for Am, AggAm\n, works as follows:\n1. Cast each bid uniformly at random into one of m bins,\nresulting in bid vectors b(1)\n, . . . , b(m)\n.\n2. For each bin j, compute the aggregate bid Bj = F(b(j)\n).\nLet B be the vector of aggregate bids, and B\u2212j be the\naggregate bids for all bins other than j.\n3. Compute the aggregate price Tj = f(B\u2212j), where f is the\nbid-independent function for Am.\n4. For each bin j, run ProfitExtractTj on b(j)\n.\nSince Am and ProfitExtractR are truthful, Tj is computed\nindependently of any bid in bin j and thus the price offered any bidder\nin b(j)\nis independent of his bid; therefore,\nTHEOREM 6. If Am is truthful, the m-aggregation auction for\nAm, AggAm\n, is truthful.\nNote that this schema yields a new way of understanding the\nRandom Sampling Profit Extraction (RSPE) auction [5] as the\nsimplest case of an aggregation auction. It is the 2-aggregation auction\nfor \u03a52, the 1-unit Vickrey auction.\nTo analyze AggAm\n, consider throwing k balls into m labeled\nbins. Let k represent a configuration of balls in bins, so that ki is\nequal to the number of balls in bin i, and k(i) is equal to the number\nof balls in the ith largest bin. Let Km,k represent the set of all\npossible configurations of k balls in m bins. We write the multinomial\ncoefficient of k as k\nk\n. The probability that a particular\nconfiguration k arises by throwing balls into bins uniformly at random is\nk\nk\nm\u2212k\n.\nTHEOREM 7. Let Am be an auction with competitive ratio \u03b2.\nThen the m-aggregation auction for Am, AggAm\n, raises the\nfollowing fraction of the optimal revenue F(2)\n(b):\nE AggAm\n(b)\nF(2)\n\u2265 min\nk\u22652\nk\u2208Km,k\nF(2)\n(k) k\nk\n\u03b2kmk\nPROOF. By definition, F(2)\nsells to k \u2265 2 bidders at a single\nprice p. Let kj be the number of such bidders in b(j)\n. Clearly,\nF(b(j)\n) \u2265 pkj. Therefore,\nF(2)\n(F(b(1)\n), . . . , F(b(n)\n))\nF(2)(b)\n\u2265\nF(2)\n(pk1, . . . , pkn)\npk\n=\nF(2)\n(k1, . . . , kn)\nk\nThe inequality follows from the monotonicity of F(2)\n, and the\nequality from the homogeneity of F(2)\n.\nProfitExtractTj will raise Tj if Tj \u2264 Bj , and no profit\notherwise. Thus, E AggAm\n(b) \u2265 E F(2)\n(B)/\u03b2 . The theorem\nfollows by rewriting this expectation as a sum over all k in Km,k.\n5.1 A 3.25 Competitive Auction\nWe apply the aggregation auction schema to \u03a53, our optimal\nauction for three bidders, to achieve an auction with competitive\nratio 3.25. This improves on the previously best known auction\nwhich is 3.39-competitive [7].\nTHEOREM 8. The aggregation auction for \u03a53 has competitive\nratio 3.25.\n179\nPROOF. By theorem 7,\nE Agg\u03a53\n(b)\nF(2)(b)\n\u2265 min\nk\u22652\nk\ni=1\nk\u2212i\nj=1\nF(2)\n(i, j, k \u2212 i \u2212 j) k\ni,j,k\u2212i\u2212j\n\u03b2k3k\nFor k = 2 and k = 3, E Agg\u03a53\n(b) = 2\n3\nk/\u03b2. As k increases,\nE Agg\u03a53\n(b) /F(2)\nincreases as well. Since we do not expect\nto find a closed-form formula for the revenue, we lower bound\nF(2)\n(b) by 3b(3). Using large deviation bounds, one can show\nthat this lower bound is greater than 2\n3\nk/\u03b2 for large-enough k, and\nthe remainder can be shown by explicit calculation.\nPlugging in \u03b2 = 13/6, the competitive ratio is 13/4. As k\nincreases, the competitive ratio approaches 13/6.\nNote that the above bound on the competitive ratio of Agg\u03a53\nis tight. To see this, consider the bid vector with two very large\nand non-identical bids of h and h + with the remaining bids 1.\nGiven that the competitive ratio of \u03a53 is tight on this example,\nthe expected revenue of this auction on this input will be exactly\n13/4.\n5.2 A Gs,t-based Aggregation Auction\nIn this section we show that \u03a53 is not the optimal auction to\nuse in an aggregation auction. One can do better by choosing the\nauction that is optimally competitive against a specially tailored\nbenchmark.\nTo see why this might be the case, notice (Table 1) that the\nfraction of F(2)\n(b) raised for when there are k = 2 and k = 3\nwinning bidders in F(2)\n(b) is substantially smaller than the fraction of\nF(2)\n(b) raised when there are more winners. This occurs because\nthe expected ratio between F(2)\n(B) and F(2)\n(b) is lower in this\ncase while the competitive ratio of \u03a53 is constant. If we chose a\nthree bidder auction that performed better when F(2)\nhas smaller\nnumbers of winners, our aggregation auction would perform better\nin the worst case.\nOne approach is to compete against a different benchmark that\nputs more weight than F(2)\non solutions with a small number of\nwinners. Recall that F(2)\nis the instance of Gs,t with s = 2 and\nt = 3. By using the auction that competes optimally against Gs,t\nwith s > 2, while holding t = 3, we will raise a higher\nfraction of revenue on smaller numbers of winning bidders and a lower\nfraction of revenue on large numbers of winning bidders. We can\nnumerically optimize the values of s and t in Gs,t(b) in order to\nachieve the best competitive ratio for the aggregation auction. In\nfact, this will allow us to improve our competitive ratio slightly.\nTHEOREM 9. For an optimal choice of s and t, the aggregation\nauction for \u03a5s,t\n3 is 3.243-competitive.\nThe proof follows the outline of Theorem 7 and 8 with the\noptimal choice of s = 2.162 (while t is held constant at 3).\n5.3 Further Reducing the Competitive Ratio\nThere are a number of ways we might attempt to use this\naggregation auction schema to continue to push the competitive ratio\ndown. In this section, we give a brief discussion of several attempts.\n5.3.1 Agg\u03a5m\nfor m > 3\nIf the aggregation auction for \u03a52 has a competitive ratio of 4\nand the aggregation auction for \u03a53 has a competitive ratio of 3.25,\ncan we improve the competitive ratio by aggregating \u03a54 or \u03a5m\nfor larger m? We conjecture in the negative: for m > 3, the\naggregation auction for \u03a5m has a larger competitive ratio than the\naggregation auction for \u03a53. The primary difficulty in proving this\nk m = 2 m = 3 m = 4 m = 5 m = 6 m = 7\n2 0.25 0.3077 0.3349 0.3508 0.3612 0.3686\n3 0.25 0.3077 0.3349 0.3508 0.3612 0.3686\n4 0.3125 0.3248 0.3349 0.3438 0.3512 0.3573\n5 0.3125 0.3191 0.3244 0.3311 0.3378 0.3439\n6 0.3438 0.321 0.3057 0.3056 0.311 0.318\n7 0.3438 0.333 0.3081 0.3009 0.3025 0.3074\n8 0.3633 0.3229 0.3109 0.3022 0.3002 0.3024\n9 0.3633 0.3233 0.3057 0.2977 0.2927 0.292\n10 0.377 0.3328 0.308 0.2952 0.2866 0.2837\n11 0.377 0.3319 0.3128 0.298 0.2865 0.2813\n12 0.3872 0.3358 0.3105 0.3001 0.2894 0.2827\n13 0.3872 0.3395 0.3092 0.2976 0.2905 0.2841\n14 0.3953 0.3391 0.312 0.2961 0.2888 0.2835\n15 0.3953 0.3427 0.3135 0.2973 0.2882 0.2825\n16 0.4018 0.3433 0.3128 0.298 0.2884 0.2823\n17 0.4018 0.3428 0.3129 0.2967 0.2878 0.282\n18 0.4073 0.3461 0.3133 0.2959 0.2859 0.2808\n19 0.4073 0.3477 0.3137 0.2962 0.2844 0.2789\n20 0.4119 0.3486 0.3148 0.2973 0.2843 0.2777\n21 0.4119 0.3506 0.3171 0.298 0.2851 0.2775\n22 0.4159 0.3519 0.3189 0.2986 0.2863 0.2781\n23 0.4159 0.3531 0.3202 0.2995 0.2872 0.2791\n24 0.4194 0.3539 0.3209 0.3003 0.2878 0.2797\n25 0.4194 0.3548 0.3218 0.3012 0.2886 0.2801\nTable 1: E A(b)/F(2)\n(b) for Agg\u03a5m\nas a function of k, the\noptimal number of winners in F(2)\n(b). The lowest value for\neach column is printed in bold.\nconjecture lies in the difficulty of finding a closed-form solution\nfor the formula of Theorem 7. We can, however, evaluate this\nformula numerically for different values of m and k, assuming that the\ncompetitive ratio for \u03a5m matches the lower bound for m given by\nTheorem 2. Table 1 shows, for each value of m and k, the fraction\nof F(2)\nraised by the aggregation auction for Agg\u03a5m\nwhen there\nare k winning bidders, assuming the lower bound of Theorem 2 is\ntight.\n5.3.2 Convex combinations of Agg\u03a5m\nAs can be seen in Table 1, when m > 3, the worst-case value\nof k is no longer 2 and 3, but instead an increasing function of\nm. An aggregation auction for \u03a5m outperforms the aggregation\nauction for \u03a53 when there are two or three winning bidders, while\nthe aggregation auction for \u03a53 outperforms the other when there\nare at least six winning bidders. Thus, for instance, an auction\nwhich randomizes between aggregation auctions for \u03a53 and \u03a54\nwill have a worst-case which is better than that of either auction\nalone. Larger combinations of auctions will allow more room to\noptimize the worst-case. However, we suspect that no convex\ncombination of aggregation auctions will have a competitive ratio lower\nthan 3. Furthermore, note that we cannot yet claim the existence of\na good auction via this technique as the optimal auction \u03a5n for\nn > 3 is not known and it is only conjectured that the bound given\nby Theorem 2 and represented in Table 1 is correct for \u03a5n.\n6. A LOWER BOUND FOR CONSERVATIVE\nAUCTIONS\nIn this section, we define a class of auctions that never offer a\nsale price which is higher than any bid in the input and prove a\nlower bound on the competitive ratio of these auctions. As this\n180\nlower bound is stronger than the lower bound of Theorem 2 for\nn \u2265 3, it shows that the optimal auction must occasionally charge\na sales price higher than any bid in the input. Specifically, this result\npartially explains the form of the optimal three bidder auction.\nDEFINITION 8. We say an auction BIf is conservative if its\nbidindependent function f satisfies f(b-i) \u2264 max(b-i).\nWe can now state our lower bound for conservative auctions.\nTHEOREM 10. Let A be a conservative auction for n bidders.\nThen the competitive ratio of A is at least 3n\u22122\nn\n.\nCOROLLARY 1. The competitive ratio of any conservative\nauction for an arbitrary number of bidders is at least three.\nFor a two-bidder auction, this restriction does not prevent\noptimality. \u03a52, the 1-unit Vickrey auction, is conservative. For larger\nnumbers of bidders, however, the restriction to conservative\nauctions does affect the competitive ratio. For the three-bidder case,\n\u03a53 has competitive ratio 2.17, while the best conservative auction\nis no better than 2.33-competitive.\nThe k-Vickrey auction and the Random Sampling Optimal Price\nauction [9] are conservative auctions. The Random Sampling Profit\nExtraction auction [5] and the CORE auction [7], on the other hand,\nuse the ProfitExtractR mechanism as a subroutine and thus\nsometimes offer a sale price which is higher than the highest input bid\nvalue.\nIn [8], the authors define a restricted auction as one on which,\nfor any input, the sale prices are drawn from the set of input bid\nvalues. The class of conservative auctions can be viewed as a\ngeneralization of the class of restricted auctions and therefore our result\nbelow gives lower bounds on the performance of a broader class of\nauctions.\nWe will prove Theorem 10 with the aid of the following lemma:\nLEMMA 1. Let A be a conservative auction with competitive\nratio 1/r for n bidders. Let h n. Let h0 = 1 and hk = kh\notherwise. Then, for all k and H \u2265 kh, Pr[f(1, 1, . . . , 1, H) \u2264 hk] \u2265\nnr\u22121\nn\u22121\n+ k(3nr\u22122r\u2212n\nn\u22121\n).\nPROOF. The lemma is proved by strong induction on k. First\nsome notation that will be convenient. For any particular k and\nH we will be considering the bid vector b = (1, . . . , 1, hk, H)\nand placing bounds on \u03c1b-i (z). Since we can assume without loss\nof generality that the auction is symmetric, we will notate b-1 as\nb with any one of the 1-valued bids masked. Similarly we notate\nb-hk\n(resp. b-H ) as b with the hk-valued bid (resp. H-valued bid)\nmasked. We will also let p1(b), phk\n(b), and pH (b) represent the\nexpected payment of a 1-valued, hk-valued, and H-valued bidder\nin A on b, respectively (note by symmetry the expected payment\nfor all 1-valued bidders is the same).\nBase case (k = 0, hk = 1): A must raise revenue of at least rn\non b = (1, . . . , 1, 1, H):\nrn \u2264 pH (b) + (n \u2212 1)p1(b)\n= 1 + (n \u2212 1)\n1\n0\nx\u03c1b-1 (x)dx\n\u2264 1 + (n \u2212 1)\n1\n0\n\u03c1b-1 (x)dx\nThe second inequality follows from the conservatism of the\nunderlying auction. The base case follows trivially from the final\ninequality.\nInductive case (k > 0, hk = kh): Let b = (1, . . . , 1, hk, H).\nFirst, we will find an upper bound on pH(b)\npH (b) =\n1\n0\nx\u03c1b-H (x)dx +\nk\ni=1\nhi\nhi\u22121\nx\u03c1b-H (x)dx (1)\n\u2264 1 +\nk\ni=1\nhi\nhi\nhi\u22121\n\u03c1b-H (x)dx\n\u2264 1 +\n3nr \u2212 2r \u2212 n\nn \u2212 1\nk\u22121\ni=1\nih\n+ kh 1 \u2212\nnr \u2212 1\nn \u2212 1\n\u2212 (k \u2212 1)\n3nr \u2212 2r \u2212 n\nn \u2212 1\n(2)\n= kh\nn(1 \u2212 r)\nn \u2212 1\n+\n(k \u2212 1)\n2\n3nr \u2212 2r \u2212 n\nn \u2212 1\n+ 1. (3)\nEquation (1) follows from the conservatism of A and (2) is from\ninvoking the strong inductive hypothesis with H = kh and the\nobservation that the maximum possible revenue will be found by\nplacing exactly enough probability at each multiple of h to satisfy\nthe constraints of the inductive hypothesis and placing the\nremaining probability at kh. Next, we will find a lower bound on phk\n(b)\nby considering the revenue raised by the bids b. Recall that A must\nobtain a profit of at least rF(2)\n(b) = 2rkh. Given upper-bounds\non the profit from the H-valued, equation bid (3), and the 1-valued\nbids, the profit from the hk-valued bid must be at least:\nphk\n(b) \u2265 2rkh \u2212 (n \u2212 2)p1(b) \u2212 pH(b)\n\u2265 kh 2r \u2212\nn(1 \u2212 r)\nn \u2212 1\n+\n(k \u2212 1)\n2\n3nr \u2212 2r \u2212 n\nn \u2212 1\n\u2212 O(n).\n(4)\nIn order to lower bound Pr[f(b-hk\n) \u2264 kh], consider the auction\nthat minimizes it and is consistent with the lower bounds obtained\nby the strong inductive hypothesis on Pr[f(b-hk\n) \u2264 ih]. To\nminimize the constraints implied by the strong inductive hypothesis, we\nplace the minimal amount of probability mass required each price\nlevel. This gives \u03c1hk\n(b) with nr\u22121\nn\u22121\nprobability at 1 and exactly\n3nr\u22122r\u2212n\nn\u22121\nat each hi for 1 \u2264 i < k. Thus, the profit from offering\nprices at most hk\u22121 is nr\u22121\nn\u22121\n\u2212kh(k\u22121)3nr\u22122r\u2212n\nn\u22121\n. In order to\nsatisfy our lower bound, (4), on phk\n(b), it must put at least 3nr\u22122r\u2212n\nn\u22121\non hk.\nTherefore, the probability that the sale price will be no more than\nkh on masked bid vector on bid vector b = (1, . . . , 1, kh, H) must\nbe at least nr\u22121\nn\u22121\n+ k(3nr\u22122r\u2212n\nn\u22121\n).\nGiven Lemma 1, Theorem 10 is simple to prove.\nPROOF. Let A be a conservative auction. Suppose 3nr\u22122r\u2212n\nn\u22121\n=\n> 0. Let k = 1/ , H \u2265 kh, and h n. By Lemma 1,\nPr[f(1, . . . , 1, kh, H) \u2264 hk] \u2265 nr\u22121\nn\u22121\n+ k > 1. But this is a\ncontradiction, so 3nr\u22122r\u2212n\nn\u22121\n\u2264 0. Thus, r \u2264 n\n3n\u22122\n. The theorem\nfollows.\n7. CONCLUSIONS AND FUTURE WORK\nWe have found the optimal auction for the three-unit\nlimitedsupply case, and shown that its structure is essentially independent\nof the benchmark used in its competitive analysis. We have then\nused this auction to derive the best known auction for the unlimited\nsupply case.\nOur work leaves many interesting open questions. We found that\nthe lower bound of [8] is matched by an auction for three bidders,\n181\neven when competing against generalized benchmarks. The most\ninteresting open question from our work is whether the lower bound\nfrom Theorem 2 can be matched by an auction for more than three\nbidders. We conjecture that it can.\nSecond, we consider whether our techniques can be extended\nto find optimal auctions for greater numbers of bidders. The use\nof our analytic solution method requires knowledge of a restricted\nclass of auctions which is large enough to contain an optimal\nauction but small enough that the optimal auction in this class can be\nfound explicitly through analytic methods. No class of auctions\nwhich meets these criteria is known even for the four bidder case.\nAlso, when the number of bidders is greater than three, it might\nbe the case that the optimal auction is not expressible in terms of\nelementary functions.\nAnother interesting set of open questions concerns aggregation\nauctions. As we show, the aggregation auction for \u03a53 outperforms\nthe aggregation auction for \u03a52 and it appears that the aggregation\nauction for \u03a53 is better than \u03a5m for m > 3. We leave\nverification of this conjecture for future work. We also show that \u03a53 is\nnot the best three-bidder auction for use in an aggregation auction,\nbut the auction that beats it is able to reduce the competitive\nratio of the overall auction only a little bit. It would be interesting\nto know whether for any m there is an m-aggregation auction that\nsubstantially improves on the competitive ratio of Agg\u03a5m\n.\nFinally, we remark that very little is known about the structure\nof the optimal competitive auction. In our auction \u03a53, the sales\nprice for a given bidder is restricted either to be one of the other bid\nvalues or to be higher than all other bid values. The optimal\nauction for two bidders, the 1-unit Vickrey auction, also falls within\nthis class of auctions, as its sales prices are restricted to bid values.\nWe conjecture that an optimal auction for any number of bidders\nlies within this class. Our paper provides partial evidence for this\nconjecture: the lower bound of Section 6 on conservative auctions\nshows that the optimal auction must offer sales prices higher than\nany bid value if the lower bound of Theorem 2 is tight, as is\nconjectured. It remains to show that optimal auctions otherwise only\noffer sales prices at bid values.\n8. ACKNOWLEDGEMENTS\nThe authors wish to thank Yoav Shoham and Noga Alon for\nhelpful discussions.\n9. REFERENCES\n[1] A. Archer and E. Tardos. Truthful mechanisms for\none-parameter agents. In Proc. of the 42nd IEEE Symposium\non Foundations of Computer Science, 2001.\n[2] S. Baliga and R. Vohra. Market research and market design.\nAdvances in Theoretical Economics, 3, 2003.\n[3] A. Borodin and R. El-Yaniv. Online Computation and\nCompetitive Analysis. Cambridge University Press, 1998.\n[4] J. Bulow and J. Roberts. The Simple Economics of Optimal\nAuctions. The Journal of Political Economy, 97:1060-90,\n1989.\n[5] A. Fiat, A. V. Goldberg, J. D. Hartline, and A. R. Karlin.\nCompetitive generalized auctions. In Proc. 34th ACM\nSymposium on the Theory of Computing, pages 72-81.\nACM, 2002.\n[6] A. Goldberg, J. Hartline, A. Karlin, M. Saks, and A. Wright.\nCompetitive auctions and digital goods. Games and\nEconomic Behavior, 2002. Submitted for publication. An\nearlier version available as InterTrust Technical Report at\nURL http://www.star-lab.com/tr/tr-99-01.html.\n[7] A. V. Goldberg and J. D. Hartline. Competitiveness via\nconsensus. In Proc. 14th Symposium on Discrete Algorithms,\npages 215-222. ACM/SIAM, 2003.\n[8] A. V. Goldberg, J. D. Hartline, A. R. Karlin, and M. E. Saks.\nA lower bound on the competitive ratio of truthful auctions.\nIn Proc. 21st Symposium on Theoretical Aspects of\nComputer Science, pages 644-655. Springer, 2004.\n[9] A. V. Goldberg, J. D. Hartline, and A. Wright. Competitive\nauctions and digital goods. In Proc. 12th Symposium on\nDiscrete Algorithms, pages 735-744. ACM/SIAM, 2001.\n[10] D. Lehmann, L. I. O\"Callaghan, and Y. Shoham. Truth\nRevelation in Approximately Efficient Combinatorial\nAuctions. In Proc. of 1st ACM Conf. on E-Commerce, pages\n96-102. ACM Press, New York, 1999.\n[11] H. Moulin and S. Shenker. Strategyproof Sharing of\nSubmodular Costs: Budget Balance Versus Efficiency.\nEconomic Theory, 18:511-533, 2001.\n[12] R. Myerson. Optimal Auction Design. Mathematics of\nOperations Research, 6:58-73, 1981.\n[13] N. Nisan and A. Ronen. Algorithmic Mechanism Design. In\nProc. of 31st Symp. on Theory of Computing, pages\n129-140. ACM Press, New York, 1999.\n[14] I. Segal. Optimal pricing mechanisms with unknown\ndemand. American Economic Review, 16:50929, 2003.\n[15] W. Vickrey. Counterspeculation, Auctions, and Competitive\nSealed Tenders. J. of Finance, 16:8-37, 1961.\nAPPENDIX\nA. PROOF OF THEOREM 4\nWe wish to prove that \u03a5s,t\n3 , the optimal auction for three bidders\nagainst Gs,t, has competitive ratio at least s2\n+t2\n2t\n. Our proof\nfollows the outline of the proof of Lemma 5 and Theorem 1 from [8];\nhowever, our case is simpler because we only looking for a bound\nwhen n = 3. Define the random bid vector B = (B1, B2, B3)\nwith Pr[Bi > z] = 1/z. We compute EB[Gs,t(B)] by integrating\nPr[Gs,t(B) > z]. Then we use the fact that no auction can have\nexpected profit greater than 3 on B to find a lower bound on the\ncompetitive ratio against Gs,t for any auction.\nFor the input distribution B defined above, let B(i) be the ith\nlargest bid. Define the disjoint events H2 = B(2) \u2265 z/s \u2227 B(3) <\nz/t, and H3 = B(3) \u2265 z/t. Intuitively, H3 corresponds to the\nevent that all three bidders win in Gs,t, while H2 corresponds to\nthe event that only the top two bidders win. Gs,t(B) will be greater\nthan z if either event occurs:\nPr[Gs,t(B) > z] = Pr[H2] + Pr[H3] (5)\n= 3\ns\nz\n2\n1 \u2212\nt\nz\n+\nt\nz\n3\n(6)\nUsing the identity defined for non-negative continuous random\nvariables that E[X] =\n\u221e\n0\nPr[X > x] dx, we have\nEB[Gs,t(B)] = t +\n\u221e\nt\n3\ns\nz\n2\n1 \u2212\nt\nz\n+\nt\nz\n3\ndz (7)\n= 3\ns2\n+ t2\n2t\n(8)\nGiven that, for any auction A, EB[EA[A(B)]] \u2264 3 [8], it is clear\nthat\nEB[Gs,t(B)]\nEB[EA[A(B)]]\n\u2265 s2\n+t2\n2t\n. Therefore, there exists some input b\nfor each auction A such that\nGs,t(b)\nEA[A(b)]\n\u2265 s2+t2\n2t\n.\n182", "keywords": "unlimited supply;ratio;benchmark;bound;distribution;competitive analysis;auction;preference;aggregation auction;mechanism design"}
{"name": "train_J-56", "title": "Robust Solutions for Combinatorial Auctions", "abstract": "Bids submitted in auctions are usually treated as enforceable commitments in most bidding and auction theory literature. In reality bidders often withdraw winning bids before the transaction when it is in their best interests to do so. Given a bid withdrawal in a combinatorial auction, finding an alternative repair solution of adequate revenue without causing undue disturbance to the remaining winning bids in the original solution may be difficult or even impossible. We have called this the Bid-taker\"s Exposure Problem. When faced with such unreliable bidders, it is preferable for the bid-taker to preempt such uncertainty by having a solution that is robust to bid withdrawal and provides a guarantee that possible withdrawals may be repaired easily with a bounded loss in revenue. In this paper, we propose an approach to addressing the Bidtaker\"s Exposure Problem. Firstly, we use the Weighted Super Solutions framework [13], from the field of constraint programming, to solve the problem of finding a robust solution. A weighted super solution guarantees that any subset of bids likely to be withdrawn can be repaired to form a new solution of at least a given revenue by making limited changes. Secondly, we introduce an auction model that uses a form of leveled commitment contract [26, 27], which we have called mutual bid bonds, to improve solution reparability by facilitating backtracking on winning bids by the bid-taker. We then examine the trade-off between robustness and revenue in different economically motivated auction scenarios for different constraints on the revenue of repair solutions. We also demonstrate experimentally that fewer winning bids partake in robust solutions, thereby reducing any associated overhead in dealing with extra bidders. Robust solutions can also provide a means of selectively discriminating against distrusted bidders in a measured manner.", "fulltext": "1. INTRODUCTION\nA combinatorial auction (CA) [5] provides an efficient means of\nallocating multiple distinguishable items amongst bidders whose\nperceived valuations for combinations of items differ. Such\nauctions are gaining in popularity and there is a proliferation in their\nusage across various industries such as telecoms, B2B procurement\nand transportation [11, 19].\nRevenue is the most obvious optimization criterion for such\nauctions, but another desirable attribute is solution robustness. In terms\nof combinatorial auctions, a robust solution is one that can\nwithstand bid withdrawal (a break) by making changes easily to form\na repair solution of adequate revenue. A brittle solution to a CA\nis one in which an unacceptable loss in revenue is unavoidable if\na winning bid is withdrawn. In such situations the bid-taker may\nbe left with a set of items deemed to be of low value by all other\nbidders. These bidders may associate a higher value for these items\nif they were combined with items already awarded to others, hence\nthe bid-taker is left in an undesirable local optimum in which a form\nof backtracking is required to reallocate the items in a manner that\nresults in sufficient revenue. We have called this the Bid-taker\"s\nExposure Problem that bears similarities to the Exposure\nProblem faced by bidders seeking multiple items in separate single-unit\nauctions but holding little or no value for a subset of those items.\nHowever, reallocating items may be regarded as disruptive to a\nsolution in many real-life scenarios. Consider a scenario where\nprocurement for a business is conducted using a CA. It would be\nhighly undesirable to retract contracts from a group of suppliers\nbecause of the failure of a third party. A robust solution that is\ntolerant of such breaks is preferable. Robustness may be regarded as a\npreventative measure protecting against future uncertainty by\nsacrificing revenue in place of solution stability and reparability. We\nassume a probabilistic approach whereby the bid-taker has\nknowledge of the reliability of bidders from which the likelihood of an\nincomplete transaction may be inferred.\nRepair solutions are required for bids that are seen as brittle\n(i.e. likely to break). Repairs may also be required for sets of\nbids deemed brittle. We propose the use of the Weighted Super\n183\nSolutions (WSS) framework [13] for constraint programming, that\nis ideal for establishing such robust solutions. As we shall see,\nthis framework can enforce constraints on solutions so that\npossible breakages are reparable.\nThis paper is organized as follows. Section 2 presents the\nWinner Determination Problem (WDP) for combinatorial auctions,\noutlines some possible reasons for bid withdrawal and shows how\nsimply maximizing expected revenue can lead to intolerable revenue\nlosses for risk-averse bid-takers. This motivates the use of robust\nsolutions and Section 3 introduces a constraint programming (CP)\nframework, Weighted Super Solutions [13], that finds such\nsolutions. We then propose an auction model in Section 4 that enhances\nreparability by introducing mandatory mutual bid bonds, that may\nbe seen as a form of leveled commitment contract [26, 27].\nSection 5 presents an extensive empirical evaluation of the approach\npresented in this paper, in the context of a number of well-known\ncombinatorial auction distributions, with very encouraging results.\nSection 6 discusses possible extensions and questions raised by our\nresearch that deserve future work. Finally, in Section 7 a number\nof concluding remarks are made.\n2. COMBINATORIAL AUCTIONS\nBefore presenting the technical details of our solution to the\nBid-taker\"s Exposure Problem, we shall present a brief survey\nof combinatorial auctions and existing techniques for handling bid\nwithdrawal.\nCombinatorial auctions involve a single bid-taker allocating\nmultiple distinguishable items amongst a group of bidders. The\nbidtaker has a set of m items for sale, M = {1, 2, . . . , m}, and\nbidders submit a set of bids, B = {B1, B2, . . . , Bn}. A bid is a tuple\nBj = Sj, pj where Sj \u2286 M is a subset of the items for sale and\npj \u2265 0 is a price. The WDP for a CA is to label all bids as either\nwinning or losing so as to maximize the revenue from winning bids\nwithout allocating any item to more than one bid. The following is\nthe integer programming formulation for the WDP:\nmax\nn\nj=1\npjxj s.t.\nj|i\u2208Sj\nxj \u2264 1, \u2200i \u2208 {1 . . . m}, xj \u2208 {0, 1}.\nThis problem is NP-complete [23] and inapproximable [25],\nand is otherwise known as the Set Packing Problem. The above\nproblem formulation assumes the notion of free disposal. This\nmeans that the optimal solution need not necessarily sell all of the\nitems. If the auction rules stipulate that all items must be sold, the\nproblem becomes a Set Partition Problem [5]. The WDP has been\nextensively studied in recent years. The fastest search algorithms\nthat find optimal solutions (e.g. CABOB [25]) can, in practice,\nsolve very large problems involving thousands of bids very quickly.\n2.1 The Problem of Bid Withdrawal\nWe assume an auction protocol with a three stage process\ninvolving the submission of bids, winner determination, and finally\na transaction phase. We are interested in bid withdrawals that\noccur between the announcement of winning bids and the end of the\ntransaction phase. All bids are valid until the transaction is\ncomplete, so we anticipate an expedient transaction process1\n.\n1\nIn some instances the transaction period may be so lengthy that\nconsideration of non-winning bids as still being valid may not be\nfair. Breaks that occur during a lengthy transaction phase are more\ndifficult to remedy and may require a subsequent auction. For\nexample, if the item is a service contract for a given period of time and\nthe break occurs after partial fulfilment of this contract, the other\nAn example of a winning bid withdrawal occurred in an FCC\nspectrum auction [32]. Withdrawals, or breaks, may occur for\nvarious reasons. Bid withdrawal may be instigated by the bid-taker\nwhen Quality of Service agreements are broken or payment\ndeadlines are not met. We refer to bid withdrawal by the bid-taker as\nitem withdrawal in this paper to distinguish between the actions\nof a bidder and the bid-taker. Harstad and Rothkopf [8] outlined\nseveral possibilities for breaks in single item auctions that include:\n1. an erroneous initial valuation/bid;\n2. unexpected events outside the winning bidder\"s control;\n3. a desire to have the second-best bid honored;\n4. information obtained or events that occurred after the auction\nbut before the transaction that reduces the value of an item;\n5. the revelation of competing bidders\" valuations infers reduced\nprofitability, a problem known as the Winner\"s Curse.\nKastner et al. [15] examined how to handle perturbations given\na solution whilst minimizing necessary changes to that solution.\nThese perturbations may include bid withdrawals, change of\nvaluation/items of a bid or the submission of a new bid. They looked at\nthe problem of finding incremental solutions to restructure a\nsupply chain whose formation is determined using combinatorial\nauctions [30]. Following a perturbation in the optimal solution they\nproceed to impose involuntary item withdrawals from winning\nbidders. They formulated an incremental integer linear program (ILP)\nthat sought to maximize the valuation of the repair solution whilst\npreserving the previous solution as much as possible.\n2.2 Being Proactive against Bid Withdrawal\nWhen a bid is withdrawn there may be constraints on how the\nsolution can be repaired. If the bid-taker was freely able to revoke\nthe awarding of items to other bidders then the solution could be\nrepaired easily by reassigning all the items to the optimal solution\nwithout the withdrawn bid. Alternatively, the bidder who reneged\nupon a bid may have all his other bids disqualified and the items\ncould be reassigned based on the optimum solution without that\nbidder present. However, the bid-taker is often unable to freely\nreassign the items already awarded to other bidders. When items\ncannot be withdrawn from winning bidders, following the failure of\nanother bidder to honor his bid, repair solutions are restricted to the\nset of bids whose items only include those in the bid(s) that were\nreneged upon. We are free to award items to any of the previously\nunsuccessful bids when finding a repair solution.\nWhen faced with uncertainty over the reliability of bidders a\npossible approach is to maximize expected revenue. This approach\ndoes not make allowances for risk-averse bid-takers who may view\na small possibility of very low revenue as unacceptable.\nConsider the example in Table 1, and the optimal expected\nrevenue in the situation where a single bid may be withdrawn. There\nare three submitted bids for items A and B, the third being a\ncombination bid for the pair of items at a value of 190. The optimal\nsolution has a value of 200, with the first and second bids as\nwinners. When we consider the probabilities of failure, in the fourth\ncolumn, the problem of which solution to choose becomes more\ndifficult.\nComputing the expected revenue for the solution with the first\nand second bids winning the items, denoted 1, 1, 0 , gives:\n(200\u00d70.9\u00d70.9)+(2\u00d7100\u00d70.9\u00d70.1)+(190\u00d70.1\u00d70.1) = 181.90.\nbidders\" valuations for the item may have decreased in a non-linear\nfashion.\n184\nTable 1: Example Combinatorial Auction.\nItems\nBids A B AB Withdrawal prob\nx1 100 0 0 0.1\nx2 0 100 0 0.1\nx3 0 0 190 0.1\nIf a single bid is withdrawn there is probability of 0.18 of a revenue\nof 100, given the fact that we cannot withdraw an item from the\nother winning bidder. The expected revenue for 0, 0, 1 is:\n(190 \u00d7 0.9) + (200 \u00d7 0.1) = 191.00.\nWe can therefore surmise that the second solution is preferable to\nthe first based on expected revenue.\nDetermining the maximum expected revenue in the presence of\nsuch uncertainty becomes computationally infeasible however, as\nthe number of brittle bids grows. A WDP needs to be solved for all\npossible combinations of bids that may fail. The possible loss in\nrevenue for breaks is also not tightly bounded using this approach,\ntherefore a large loss may be possible for a small number of breaks.\nConsider the previous example where the bid amount for x3\nbecomes 175. The expected revenue of 1, 1, 0 (181.75) becomes\ngreater than that of 0, 0, 1 (177.50). There are some bid-takers\nwho may prefer the latter solution because the revenue is never less\nthan 175, but the former solution returns revenue of only 100 with\nprobability 0.18. A risk-averse bid-taker may not tolerate such a\npossibility, preferring to sacrifice revenue for reduced risk.\nIf we modify our repair search so that a solution of at least a\ngiven revenue is guaranteed, the search for a repair solution\nbecomes a satisfiability test rather than an optimization problem. The\napproaches described above are in contrast to that which we\npropose in the next section. Our approach can be seen as preventative\nin that we find an initial allocation of items to bidders which is\nrobust to bid withdrawal. Possible losses in revenue are bounded by\na fixed percentage of the true optimal allocation. Perturbations to\nthe original solution are also limited so as to minimize disruption.\nWe regard this as the ideal approach for real-world combinatorial\nauctions.\nDEFINITION 1 (ROBUST SOLUTION FOR A CA). A robust\nsolution for a combinatorial auction is one where any subset of\nsuccessful bids whose probability of withdrawal is greater than or\nequal to \u03b1 can be repaired by reassigning items at a cost of at most\n\u03b2 to other previously losing bids to form a repair solution.\nConstraints on acceptable revenue, e.g. being a minimum\npercentage of the optimum, are defined in the problem model and are\nthus satisfied by all solutions. The maximum cost of repair, \u03b2, may\nbe a fixed value that may be thought of as a fund for\ncompensating winning bidders whose items are withdrawn from them when\ncreating a repair solution. Alternatively, \u03b2 may be a function of\nthe bids that were withdrawn. Section 4 will give an example of\nsuch a mechanism. In the following section we describe an ideal\nconstraint-based framework for the establishment of such robust\nsolutions.\n3. FINDING ROBUST SOLUTIONS\nIn constraint programming [4] (CP), a constraint satisfaction\nproblem (CSP) is modeled as a set of n variables X = {x1, . . . , xn},\na set of domains D = {D(x1), . . . , D(xn)}, where D(xi) is\nthe set of finite possible values for variable xi and a set C =\n{C1, . . . , Cm} of constraints, each restricting the assignments of\nsome subset of the variables in X. Constraint satisfaction involves\nfinding values for each of the problem variables such that all\nconstraints are satisfied. Its main advantages are its declarative nature\nand flexibility in tackling problems with arbitrary side constraints.\nConstraint optimization seeks to find a solution to a CSP that\noptimizes some objective function. A common technique for solving\nconstraint optimization problems is to use branch-and-bound\ntechniques that avoid exploring sub-trees that are known not to contain\na better solution than the best found so far. An initial bound can be\ndetermined by finding a solution that satisfies all constraints in C\nor by using some heuristic methods.\nA classical super solution (SS) is a solution to a CSP in which,\nif a small number of variables lose their values, repair solutions\nare guaranteed with only a few changes, thus providing solution\nrobustness [9, 10]. It is a generalization of both fault tolerance in\nCP [31] and supermodels in propositional satisfiability (SAT) [7].\nAn (a,b)-super solution is one in which if at most a variables lose\ntheir values, a repair solution can be found by changing at most b\nother variables [10].\nSuper solutions for combinatorial auctions minimize the number\nof bids whose status needs to be changed when forming a repair\nsolution [12]. Only a particular set of variables in the solution may\nbe subject to change and these are said to be members of the\nbreakset. For each combination of brittle assignments in the break-set, a\nrepair-set is required that comprises the set of variables whose\nvalues must change to provide another solution. The cardinality of the\nrepair set is used to measure the cost of repair. In reality,\nchanging some variable assignments in a repair solution incurs a lower\ncost than others thereby motivating the use of a different metric for\ndetermining the legality of repair sets.\nThe Weighted Super Solution (WSS) framework [13] considers\nthe cost of repair required, rather than simply the number of\nassignments modified, to form an alternative solution. For CAs this\nmay be a measure of the compensation penalties paid to winning\nbidders to break existing agreements. Robust solutions are\nparticularly desirable for applications where unreliability is a problem\nand potential breakages may incur severe penalties. Weighted\nsuper solutions offer a means of expressing which variables are\neasily re-assigned and those that incur a heavy cost [13]. Hebrard et\nal. [9] describe how some variables may fail (such as machines in a\njob-shop problem) and others may not. A WSS generalizes this\napproach so that there is a probability of failure associated with each\nassignment and sets of variables whose assignments have\nprobabilities of failure greater than or equal to a threshold value, \u03b1, require\nrepair solutions.\nA WSS measures the cost of repairing, or reassigning, other\nvariables using inertia as a metric. Inertia is a measure of a variable\"s\naversion to change and depends on its current assignment, future\nassignment and the breakage variable(s).\nIt may be desirable to reassign items to different bidders in order\nto find a repair solution of satisfactory revenue. Compensation may\nhave to be paid to bidders who lose items during the formation of a\nrepair solution. The inertia of a bid reflects the cost of changing its\nstate. For winning bids this may reflect the necessary compensation\npenalty for the bid-taker to break the agreement (if such breaches\nare permitted), whereas for previously losing bids this is a free\noperation. The total amount of compensation payable to bidders may\ndepend upon other factors, such as the cause of the break. There is\na limit to how much these overall repair costs should be, and this is\ngiven by the value \u03b2. This value may not be known in advance and\n185\nAlgorithm 1: WSS(int level, double \u03b1, double \u03b2):Boolean\nbegin\nif level > number of variables then return true\nchoose unassigned variable x\nforeach value v in the domain of x do\nassign x : v\nif problem is consistent then\nforeach combination of brittle assignments, A do\nif \u00acreparable(A, \u03b2) then return false;\nif WSS(level+1) then return true\nunassign x\nreturn false\nend\nmay depend upon the break. Therefore, \u03b2 may be viewed as the\nfund used to compensate winning bidders for the unilateral\nwithdrawal of their bids by the bid-taker. In summary, an (\u03b1,\u03b2)-WSS\nallows any set of variables whose probability of breaking is greater\nthan or equal to \u03b1 be repaired with changes to the original robust\nsolution with a cost of at most \u03b2.\nThe depth-first search for a WSS (see pseudo-code description\nin Algorithm 1) maintains arc-consistency [24] at each node of the\ntree. As search progresses, the reparability of each previous\nassignment is verified at each node by extending a partial repair\nsolution to the same depth as the current partial solution. This may\nbe thought of as maintaining concurrent search trees for repairs.\nA repair solution is provided for every possible set of break\nvariables, A. The WSS algorithm attempts to extend the current partial\nassignment by choosing a variable and assigning it a value.\nBacktracking may then occur for one of two reasons: we cannot extend\nthe assignment to satisfy the given constraints, or the current\npartial assignment cannot be associated with a repair solution whose\ncost of repair is less than \u03b2 should a break occur. The procedure\nreparable searches for partial repair solutions using\nbacktracking and attempts to extend the last repair found, just as in\n(1,b)super solutions [9]; the differences being that a repair is provided\nfor a set of breakage variables rather than a single variable and the\ncost of repair is considered. A summation operator is used to\ndetermine the overall cost of repair. If a fixed bound upon the size of\nany potential break-set can be formed, the WSS algorithm is\nNPcomplete. For a more detailed description of the WSS search\nalgorithm, the reader is referred to [13], since a complete description of\nthe algorithm is beyond the scope of this paper.\nEXAMPLE 1. We shall step through the example given in\nTable 1 when searching for a WSS. Each bid is represented by a\nsingle variable with domain values of 0 and 1, the former representing\nbid-failure and the latter bid-success. The probability of failure of\nthe variables are 0.1 when they are assigned to 1 and 0.0\notherwise. The problem is initially solved using an ILP solver such as\nlp_solve [3] or CPLEX, and the optimal revenue is found to be\n200. A fixed percentage of this revenue can be used as a threshold\nvalue for a robust solution and its repairs. The bid-taker wishes to\nhave a robust solution so that if a single winning bid is withdrawn,\na repair solution can be formed without withdrawing items from\nany other winning bidder. This example may be seen as searching\nfor a (0.1,0)-weighted super solution, \u03b2 is 0 because no funds are\navailable to compensate the withdrawal of items from winning\nbidders. The bid-taker is willing to compromise on revenue, but only\nby 5%, say, of the optimal value.\nBids 1 and 3 cannot both succeed, since they both require item\nA, so a constraint is added precluding the assignment in which both\nvariables take the value 1. Similarly, bids 2 and 3 cannot both win\nso another constraint is added between these two variables.\nTherefore, in this example the set of CSP variables is V = {x1, x2, x3},\nwhose domains are all {0, 1}. The constraints are x1 + x3 \u2264 1,\nx2 + x3 \u2264 1 and xi\u2208V aixi \u2265 190, where ai reflects the\nrelevant bid-amounts for the respective bid variables. In order to find a\nrobust solution of optimal revenue we seek to maximize the sum of\nthese amounts, max xi\u2208V aixi.\nWhen all variables are set to 0 (see Figure 1(a) branch 3), this is\nnot a solution because the minimum revenue of 190 has not been\nmet, so we try assigning bid3 to 1 (branch 4). This is a valid\nsolution but this variable is brittle because there is a 10% chance that\nthis bid may be withdrawn (see Table 1). Therefore we need to\ndetermine if a repair can be formed should it break. The search for a\nrepair begins at the first node, see Figure 1(b). Notice that value 1\nhas been removed from bid3 because this search tree is simulating\nthe withdrawal of this bid. When bid1 is set to 0 (branch 4.1), the\nmaximum revenue solution in the remaining subtree has revenue of\nonly 100, therefore search is discontinued at that node of the tree.\nBid1 and bid2 are both assigned to 1 (branches 4.2 and 4.4) and\nthe total cost of both these changes is still 0 because no\ncompensation needs to be paid for bids that change from losing to winning.\nWith bid3 now losing (branch 4.5), this gives a repair solution of\n200. Hence 0, 0, 1 is reparable and therefore a WSS. We continue\nour search in Figure 1(a) however, because we are seeking a robust\nsolution of optimal revenue.\nWhen bid1 is assigned to 1 (branch 6) we seek a partial repair\nfor this variable breaking (branch 5 is not considered since it offers\ninsufficient revenue). The repair search sets bid1 to 0 in a separate\nsearch tree, (not shown), and control is returned to the search for\na WSS. Bid2 is set to 0 (branch 7), but this solution would not\nproduce sufficient revenue so bid2 is then set to 1 (branch 8). We\nthen attempt to extend the repair for bid1 (not shown). This fails\nbecause the repair for bid1 cannot assign bid2 to 0 because the\ncost of repairing such an assignment would be \u221e, given that the\nauction rules do not permit the withdrawal of items from winning\nbids. A repair for bid1 breaking is therefore not possible because\nitems have already been awarded to bid2. A repair solution with\nbid2 assigned to 1 does not produce sufficient revenue when bid1\nis assigned to 0. The inability to withdraw items from winning bids\nimplies that 1, 1, 0 is an irreparable solution when the minimum\ntolerable revenue is greater than 100. The italicized comments and\ndashed line in Figure 1(a) illustrate the search path for a WSS if\nboth of these bids were deemed reparable.\nSection 4 introduces an alternative auction model that will allow\nthe bid-taker to receive compensation for breakages and in turn use\nthis payment to compensate other bidders for withdrawal of items\nfrom winning bids. This will enable the reallocation of items and\npermit the establishment of 1, 1, 0 as a second WSS for this\nexample.\n4. MUTUAL BID BONDS: A\nBACKTRACKING MECHANISM\nSome auction solutions are inherently brittle and it may be\nimpossible to find a robust solution. If we can alter the rules of an\nauction so that the bid-taker can retract items from winning\nbidders, then the reparability of solutions to such auctions may be\nimproved. In this section we propose an auction model that permits\nbid and item withdrawal by the bidders and bid-taker, respectively.\nWe propose a model that incorporates mutual bid bonds to enable\nsolution reparability for the bid-taker, a form of insurance against\n186\n0\n0\n0\n0\n0 0 0\n1\n1 1\n1 1 1 1\nInsufficient\nrevenue\nFind repair solution\nfor bid 3 breakage\nFind partial repair for\nbid 1 breakage\nInsufficient\nrevenue\n(a) Extend partial repair\nfor bid 1 breakage\n(b) Find partial repair\nfor bid 2 breakage\nBid 1\nBid 2\nBid 3\nFind repair solutions for\nbid 1 & 2 breakages\n[0] [190] [100] [100] [200]\n1\n2\n3 4\n5\n6\n7 8\n9\nInsufficient\nrevenue\n(a) Search for WSS.\n0\n0\n0\n0\n0 0 0\n1\n1 1\n1 1 1 1\nInsufficient\nrevenue\nInsufficient\nrevenue\nBid 1\nBid 2\nBid 3\ninertia=0\ninertia=0\ninertia=0\n4.1 4.2\n4.3 4.4\n4.5\n(b) Search for a repair for bid 3 breakage.\nFigure 1: Search Tree for a WSS without item withdrawal.\nthe winner\"s curse for the bidder whilst also compensating bidders\nin the case of item withdrawal from winning bids. We propose that\nsuch Winner\"s Curse & Bid-taker\"s Exposure insurance comprise\na fixed percentage, \u03ba, of the bid amount for all bids. Such mutual\nbid bonds are mandatory for each bid in our model2\n. The conditions\nattached to the bid bonds are that the bid-taker be allowed to annul\nwinning bids (item withdrawal) when repairing breaks elsewhere\nin the solution. In the interests of fairness, compensation is paid\nto bidders from whom items are withdrawn and is equivalent to the\npenalty that would have been imposed on the bidder should he have\nwithdrawn the bid.\nCombinatorial auctions impose a heavy computational burden\non the bidder so it is important that the hedging of risk should be\na simple and transparent operation for the bidder so as not to\nfurther increase this burden unnecessarily. We also contend that it\nis imperative that the bidder knows the potential penalty for\nwithdrawal in advance of bid submission. This information is essential\nfor bidders when determining how aggressive they should be in\ntheir bidding strategy. Bid bonds are commonplace in procurement\nfor construction projects. Usually they are mandatory for all bids,\nare a fixed percentage, \u03ba, of the bid amount and are unidirectional\nin that item withdrawal by the bid-taker is not permitted. Mutual\nbid bonds may be seen as a form of leveled commitment contract\nin which both parties may break the contract for the same fixed\npenalty. Such contracts permit unilateral decommitment for\nprespecified penalties. Sandholm et al. showed that this can increase\nthe expected payoffs of all parties and enables deals that would be\nimpossible under full commitment [26, 28, 29].\nIn practice a bid bond typically ranges between 5 and 20% of the\n2\nMaking the insurance optional may be beneficial in some\ninstances. If a bidder does not agree to the insurance, it may be\ninferred that he may have accurately determined the valuation for the\nitems and therefore less likely to fall victim to the winner\"s curse.\nThe probability of such a bid being withdrawn may be less, so a\nrepair solution may be deemed unnecessary for this bid. On the other\nhand it decreases the reparability of solutions.\nbid amount [14, 18]. If the decommitment penalties are the same\nfor both parties in all bids, \u03ba does not influence the reparability of\na given set of bids. It merely influences the levels of penalties and\ncompensation transacted by agents. Low values of \u03ba incur low bid\nwithdrawal penalties and simulate a dictatorial bid-taker who does\nnot adequately compensate bidders for item withdrawal. Andersson\nand Sandholm [1] found that myopic agents reach a higher social\nwelfare quicker if they act selfishly rather than cooperatively when\npenalties in leveled commitment contracts are low. Increased levels\nof bid withdrawal are likely when the penalties are low also.\nHigh values of \u03ba tend towards full-commitment and reduce the\nadvantages of such Winner\"s Curse & Bid-taker\"s Exposure\ninsurance. The penalties paid are used to fund a reassignment of\nitems to form a repair solution of sufficient revenue by\ncompensating previously successful bidders for withdrawal of the items from\nthem.\nEXAMPLE 2. Consider the example given in Table 1 once more,\nwhere the bids also comprise a mutual bid bond of 5% of the bid\namount. If a bid is withdrawn, the bidder forfeits this amount and\nthe bid-taker can then compensate winning bidders whose items are\nwithdrawn when trying to form a repair solution later. The search\nfor repair solutions for breaks to bid1 and bid2 appear in Figures\n2(a) and 2(b), respectively3\n.\nWhen bid1 breaks, there is a compensation penalty paid to the\nbid-taker equal to 5 that can be used to fund a reassignment of the\nitems. We therefore set \u03b2 to 5 and this becomes the maximum\nexpenditure allowed to withdraw items from winning bidders. \u03b2\nmay also be viewed as the size of the fund available to facilitate\nbacktracking by the bid-taker. When we extend the partial repair\nfor bid1 so that bid2 loses an item (branch 8.1), the overall cost of\nrepair increases to 5, due to this item withdrawal by the bid-taker,\n3\nThe actual implementation of WSS search checks previous\nsolutions to see if they can repair breaks before searching for a new\nrepair solution. 0, 0, 1 is a solution that has already been found\nso the search for a repair in this example is not strictly necessary\nbut is described for pedagogical reasons.\n187\n0\n0\n0\n1\n1\nBid 1\nBid 2\nBid 3\nInsufficient revenue\ninertia=5\n=5\ninertia=0\n=5\ninertia=5\n=5\n1\n6.1\n8.1\n9.1\n9.2\n(a) Search for a repair for bid 1 breakage.\n0\n0\n0\n1\n1\nBid 1\nBid 2\nBid 3\nInsufficient revenue\ninertia=10\n=10\ninertia=10\n=10\ninertia=10\n=10\n1\n8.2\n8.3\n9.3\n9.4\n(b) Search for a repair for bid 2 breakage.\nFigure 2: Repair Search Tree for breaks 1 and 2, \u03ba = 0.05.\nand is just within the limit given by \u03b2. In Figure 1(a) the search path\nfollows the dashed line and sets bid3 to be 0 (branch 9). The repair\nsolutions for bids 1 and 2 can be extended further by assigning bid3\nto 1 (branches 9.2 and 9.4). Therefore, 1, 1, 0 may be considered\na robust solution. Recall, that previously this was not the case.\nUsing mutual bid bonds thus increases reparability and allows a\nrobust solution of revenue 200 as opposed to 190, as was previously\nthe case.\n5. EXPERIMENTS\nWe have used the Combinatorial Auction Test Suite (CATS) [16]\nto generate sample auction data. We generated 100 instances of\nproblems in which there are 20 items for sale and 100-2000 bids\nthat may be dominated in some instances4\n. Such dominated bids\ncan participate in repair solutions although they do not feature in\noptimal solutions. CATS uses economically motivated bidding\npatterns to generate auction data in various scenarios. To motivate the\nresearch presented in this paper we use sensitivity analysis to\nexamine the brittleness of optimal solutions and hence determine the\ntypes of auctions most likely to benefit from a robust solution. We\nthen establish robust solutions for CAs using the WSS framework.\n5.1 Sensitivity Analysis for the WDP\nWe have performed sensitivity analysis of the following four\ndistributions: airport take-off/landing slots (matching), electronic\ncomponents (arbitrary), property/spectrum-rights (regions)\nand transportation (paths). These distributions were chosen\nbecause they describe a broad array of bidding patterns in different\napplication domains.\nThe method used is as follows. We first of all determined the\noptimal solution using lp_solve, a mixed integer linear program\nsolver [3]. We then simulated a single bid withdrawal and re-solved\nthe problem with the other winning bids remaining fixed, i.e. there\nwere no involuntary dropouts. The optimal repair solution was\nthen determined. This process is repeated for all winning bids in\nthe overall optimal solution, thus assuming that all bids are brittle.\nFigure 3 shows the average revenue of such repair solutions as a\npercentage of the optimum. Also shown is the average worst-case\nscenario over 100 auctions. We also implemented an auction rule\nthat disallows bids from the reneging bidder participate in a repair5\n.\nFigure 3(a) illustrates how the paths distribution is inherently\nthe most robust distribution since when any winning bid is\nwithdrawn the solution can be repaired to achieve over 98.5% of the\n4\nThe CATS flags included int prices with the bid alpha parameter\nset to 1000.\n5\nWe assumed that all bids in a given XOR bid with the same\ndummy item were from the same bidder.\noptimal revenue on average for auctions with more than 250 bids.\nThere are some cases however when such withdrawals result in\nsolutions whose revenue is significantly lower than optimum. Even\nin auctions with as many as 2000 bids there are occasions when a\nsingle bid withdrawal can result in a drop in revenue of over 5%,\nalthough the average worst-case drop in revenue is only 1%.\nFigure 3(b) shows how the matching distribution is more brittle on\naverage than paths and also has an inferior worst-case revenue on\naverage. This trend continues as the regions-npv (Figure 3(c))\nand arbitrary-npv (Figure 3(d)) distributions are more\nbrittle still. These distributions are clearly sensitive to bid withdrawal\nwhen no other winning bids in the solution may be involuntarily\nwithdrawn by the bid-taker.\n5.2 Robust Solutions using WSS\nIn this section we focus upon both the arbitrary-npv and\nregions-npv distributions because the sensitivity analysis\nindicated that these types of auctions produce optimal solutions that\ntend to be most brittle, and therefore stand to benefit most from\nsolution robustness. We ignore the auctions with 2000 bids because\nthe sensitivity analysis has indicated that these auctions are\ninherently robust with a very low average drop in revenue following a bid\nwithdrawal. They would also be very computationally expensive,\ngiven the extra complexity of finding robust solutions.\nA pure CP approach needs to be augmented with global\nconstraints that incorporate operations research techniques to increase\npruning sufficiently so that thousands of bids may be examined.\nGlobal constraints exploit special-purpose filtering algorithms to\nimprove performance [21]. There are a number of ways to speed\nup the search for a weighted super solution in a CA, although this\nis not the main focus of our current work. Polynomial matching\nalgorithms may be used in auctions whose bid length is short, such\nas those for airport landing/take-off slots for example. The integer\nprogramming formulation of the WDP stipulates that a bid either\nloses or wins. If we relax this constraint so that bids can partially\nwin, this corresponds to the linear relaxation of the problem and is\nsolvable in polynomial time. At each node of the search tree we\ncan quickly solve the linear relaxation of the remaining problem in\nthe subtree below the current node to establish an upper bound on\nremaining revenue. If this upper bound plus revenue in the parent\ntree is less than the current lower bound on revenue, search at that\nnode can cease. The (continuous) LP relaxation thus provides a\nvital speed-up in the search for weighted super solutions, which we\nhave exploited in our implementation. The LP formulation is as\nfollows:\nmax\nxi\u2208V\naixi\n188\n100\n95\n90\n85\n80\n75\n250 500 750 1000 1250 1500 1750 2000\nRevenue(%ofoptimum)\nBids\nAverage Repair Solution Revenue\nWorst-case Repair Solution Revenue\n(a) paths\n100\n95\n90\n85\n80\n75\n250 500 750 1000 1250 1500 1750 2000\nRevenue(%ofoptimum)\nBids\nAverage Repair Solution Revenue\nWorst-case Repair Solution Revenue\n(b) matching\n100\n95\n90\n85\n80\n75\n250 500 750 1000 1250 1500 1750 2000\nRevenue(%ofoptimum)\nBids\nAverage Repair Solution Revenue\nWorst-case Repair Solution Revenue\n(c) regions-npv\n100\n95\n90\n85\n80\n75\n250 500 750 1000 1250 1500 1750 2000\nRevenue(%ofoptimum)\nBids\nAverage Repair Solution Revenue\nWorst-case Repair Solution Revenue\n(d) arbitrary-npv\nFigure 3: Sensitivity of bid distributions to single bid withdrawal.\ns.t.\nj|i\u2208Sj\nxj \u2264 1, \u2200i \u2208 {1 . . . m}, xj \u2265 0, xj \u2208 R.\nAdditional techniques, that are outlined in [25], can aid the\nscalability of a CP approach but our main aim in these experiments is\nto examine the robustness of various auction distributions and\nconsider the tradeoff between robustness and revenue. The WSS solver\nwe have developed is an extension of the super solution solver\npresented in [9, 10]. This solver is, in turn, based upon the EFC\nconstraint solver [2].\nCombinatorial auctions are easily modeled as a constraint\noptimization problems. We have chosen the branch-on-bids\nformulation because in tests it worked faster than a branch-on-items\nformulation for the arbitrary-npv and regions-npv\ndistributions. All variables are binary and our search mechanism uses a\nreverse lexicographic value ordering heuristic. This complements our\ndynamic variable ordering heuristic that selects the most promising\nunassigned variable as the next one in the search tree. We use the\nproduct of the solution of the LP relaxation and the degree of a\nvariable to determine the likelihood of its participation in a robust\nsolution. High values in the LP solution are a strong indication of\nvariables most likely to form a high revenue solution whilst the a\nvariable\"s degree reflects the number of other bids that overlap in\nterms of desired items. Bids for large numbers of items tend to be\nmore robust, which is why we weight our robust solution search in\nthis manner. We found this heuristic to be slightly more effective\nthan the LP solution alone. As the number of bids in the auction\nincreases however, there is an increase in the inherent robustness\nof solutions so the degree of a variable loses significance as the\nauction size increases.\n5.3 Results\nOur experiments simulate three different constraints on repair\nsolutions. The first is that no winning bids are withdrawn by the\nbid-taker and a repair solution must return a revenue of at least 90%\nof the optimal overall solution. Secondly, we relaxed the revenue\nconstraint to 85% of optimum. Thirdly, we allowed backtracking\nby the bid-taker on winning bids using mutual bid bonds but\nmaintaining the revenue constraint at 90% of optimum.\nPrior to finding a robust solution we solved the WDP optimally\nusing lp_solve [3]. We then set the minimum tolerable revenue\nfor a solution to be 90% (then 85%) of the revenue of this\noptimal solution. We assumed that all bids were brittle, thus a repair\nsolution is required for every bid in the solution. Initially we\nassume that no backtracking was permitted on assignments of items\nto other winning bids given a bid withdrawal elsewhere in the\nsolution. Table 2 shows the percentage of optimal solutions that are\nrobust for minimum revenue constraints for repair solutions of 90%\nand 85% of optimal revenue. Relaxing the revenue constraint on\nrepair solutions to 85% of the optimum revenue greatly increases the\nnumber of optimal solutions that are robust. We also conducted\nexperiments on the same auctions in which backtracking by the\nbid-taker is permitted using mutual bid bonds. This significantly\nimproves the reparability of optimal solutions whilst still\nmaintaining repair solutions of 90% of optimum. An interesting feature\nof the arbitrary-npv distribution is that optimal solutions can\nbecome more brittle as the number of bids increases. The reason\nfor this is that optimal solutions for larger auctions have more\nwinning bids. Some of the optimal solutions for the smallest auctions\nwith 100 bids have only one winning bidder. If this bid is\nwithdrawn it is usually easy to find a new repair solution within 90% of\nthe previous optimal revenue. Also, repair solutions for bids that\ncontain a small number of items may be made difficult by the fact\nthat a reduced number of bids cover only a subset of those items. A\nmitigating factor is that such bids form a smaller percentage of the\nrevenue of the optimal solution on average.\nWe also implemented a rule stipulating that any losing bids from\n189\nTable 2: Optimal Solutions that are Inherently Robust (%).\n#Bids\nMin Revenue 100 250 500 1000 2000\narbitrary-npv\nrepair \u2265 90% 21 5 3 37 93\nrepair \u2265 85% 26 15 40 87 100\nMBB & repair \u2265 90% 41 35 60 94 \u2265 93\nregions-npv\nrepair \u2265 90% 30 33 61 91 98\nrepair \u2265 85% 50 71 95 100 100\nMBB & repair \u2265 90% 60 78 96 99 \u2265 98\nTable 3: Occurrence of Robust Solutions (%).\n#Bids\nMin Revenue 100 250 500 1000\narbitrary-npv\nrepair \u2265 90% 58 39 51 98\nrepair \u2265 85% 86 88 94 99\nMBB & repair \u2265 90% 78 86 98 100\nregions-npv\nrepair \u2265 90% 61 70 97 100\nrepair \u2265 85% 89 99 99 100\nMBB & repair \u2265 90% 83 96 100 100\na withdrawing bidder cannot participate in a repair solution. This\nacts as a disincentive for strategic withdrawal and was also used\npreviously in the sensitivity analysis. In some auctions, a robust\nsolution may not exist. Table 3 shows the percentage of auctions that\nsupport robust solutions for the arbitrary-npv and regions\n-npv distributions. It is clear that finding robust solutions for the\nformer distribution is particularly difficult for auctions with 250 and\n500 bids when revenue constraints are 90% of optimum. This\ndifficulty was previously alluded to by the low percentage of optimal\nsolutions that were robust for these auctions. Relaxing the revenue\nconstraint helps increase the percentage of auctions in which robust\nsolutions are achievable to 88% and 94%, respectively. This\nimproves the reparability of all solutions thereby increasing the\naverage revenue of the optimal robust solution. It is somewhat\ncounterintuitive to expect a reduction in reparability of auction solutions as\nthe number of bids increases because there tends to be an increased\nnumber of solutions above a revenue threshold in larger auctions.\nThe MBB auction model performs very well however, and ensures\nthat robust solutions are achievable for such inherently brittle\nauctions without sacrificing over 10% of optimal revenue to achieve\nrepair solutions.\nFigure 4 shows the average revenue of the optimal robust\nsolution as a percentage of the overall optimum. Repair solutions found\nfor a WSS provide a lower bound on possible revenue following a\nbid withdrawal. Note that in some instances it is possible for a\nrepair solution to have higher revenue than the original solution.\nWhen backtracking on winning bids by the bid-taker is disallowed,\nthis can only happen when the repair solution includes two or more\nbids that were not in the original. Otherwise the repair bids would\nparticipate in the optimal robust solution in place of the bid that\nwas withdrawn. A WSS guarantees minimum levels of revenue for\nrepair solutions but this is not to say that repair solutions cannot be\nimproved upon. It is possible to use an incremental algorithm to\n100\n98\n96\n94\n92\n250 500 750 1000 1250 1500 1750 2000\nRevenue(%ofoptimum)\nBids\nRepair Revenue: Min 90% Optimal\nRepair Revenue: Min 85% Optimal\nMBB: Repair Revenue: Min 90% Optimal\n(a) regions-npv\n100\n98\n96\n94\n92\n250 500 750 1000 1250 1500 1750 2000\nRevenue(%ofoptimum)\nBids\nRepair Revenue: Min 90% Optimal\nRepair Revenue: Min 85% Optimal\nMBB: Repair Revenue: Min 90% Optimal\n(b) arbitrary-npv\nFigure 4: Revenue of optimal robust solutions.\ndetermine an optimal repair solution following a break, whilst safe\nin the knowledge that in advance of any possible bid withdrawal\nwe can establish a lower bound on the revenue of a repair. Kastner\net al. have provided such an incremental ILP formulation [15].\nMutual bid bonds facilitate backtracking by the bid-taker on\nalready assigned items. This improves the reparability of all\npossible solutions thus increasing the revenue of the optimal robust\nsolution on average. Figure 4 shows the increase in revenue of\nrobust solutions in such instances. The revenues of repair\nsolutions are bounded by at least 90% of the optimum in our\nexperiments thereby allowing a direct comparison with robust solutions\nalready found using the same revenue constraint but not providing\nfor backtracking. It is immediately obvious that such a mechanism\ncan significantly increase revenue whilst still maintaining solution\nrobustness.\nTable 4 shows the number of winning bids participating in\noptimal and optimal robust solutions given the three different\nconstraints on repairing solutions listed at the beginning of this\nsection. As the number of bids increases, more of the optimal overall\nsolutions are robust. This leads to a convergence in the number of\nwinning bids. The numbers in brackets are derived from the\nsensitivity analysis of optimal solutions that reveals the fact that almost\nall optimal solutions for auctions of 2000 bids are robust. We can\ntherefore infer that the average number of winning bids in\nrevenuemaximizing robust solutions converges towards that of the optimal\noverall solutions.\nA notable side-effect of robust solutions is that fewer bids\nparticipate in the solutions. It can be clearly seen from Table 4 that when\nrevenue constraints on repair solutions are tight, there are fewer\nwinning bids in the optimal robust solution on average. This is\nparticularly pronounced for smaller auctions in both distributions.\nThis can win benefits for the bid-taker such as reduced overheads in\ndealing with fewer suppliers. Although MBBs aid solution\nrepara190\nTable 4: Number of winning bids.\n#Bids\nSolution 100 250 500 1000 2000\narbitrary-npv\nOptimal 3.31 5.60 7.17 9.31 10.63\nRepair \u2265 90% 1.40 2.18 6.10 9.03 (\u2248 10.63)\nRepair \u2265 85% 1.65 3.81 6.78 9.31 (10.63)\nMBB (\u2265 90%) 2.33 5.49 7.33 9.34 (\u2248 10.63)\nregions-npv\nOptimal 4.34 7.05 9.10 10.67 12.76\nRepair \u2265 90% 3.03 5.76 8.67 10.63 (\u2248 12.76)\nRepair \u2265 85% 3.45 6.75 9.07 (10.67) (12.76)\nMBB (\u2265 90%) 3.90 6.86 9.10 10.68 (\u2248 12.76)\nbility, the number of bids in the solutions increases on average.\nThis is to be expected because a greater fraction of these solutions\nare in fact optimal, as we saw in Table 2.\n6. DISCUSSION AND FUTURE WORK\nBidding strategies can become complex in\nnon-incentive-compatible mechanisms where winner determination is no longer\nnecessarily optimal. The perceived reparability of a bid may influence the\nbid amount, with reparable bids reaching a lower equilibrium point\nand perceived irreparable bids being more aggressive.\nPenalty payments for bid withdrawal also create an incentive for\nmore aggressive bidding by providing a form of insurance against\nthe winner\"s curse [8]. If a winning bidder\"s revised valuation for\na set of items drops by more than the penalty for withdrawal of\nthe bid, then it is in his best interests to forfeit the item(s) and pay\nthe penalty. Should the auction rules state that the bid-taker will\nrefuse to sell the items to any of the remaining bidders in the event\nof a withdrawal, then insurance against potential losses will\nstimulate more aggressive bidding. However, in our case we are seeking\nto repair the solution with the given bids. A side-effect of such a\npolicy is to offset the increased aggressiveness by incentivizing\nreduced valuations in expectation that another bidder\"s successful bid\nis withdrawn. Harstad and Rothkopf [8] examined the conditions\nrequired to ensure an equilibrium position in which bidding was at\nleast as aggressive as if no bid withdrawal was permitted, given this\ncountervailing incentive to under-estimate a valuation. Three\nmajor results arose from their study of bid withdrawal in a single item\nauction:\n1. Equilibrium bidding is more aggressive with withdrawal for\nsufficiently small probabilities of an award to the second\nhighest bidder in the event of a bid withdrawal;\n2. Equilibrium bidding is more aggressive with withdrawal if\nthe number of bidders is large enough;\n3. For many distributions of costs and estimates, equilibrium\nbidding is more aggressive with withdrawal if the variability\nof the estimating distribution is sufficiently large.\nIt is important that mutual bid bonds do not result in depressed\nbidding in equilibrium. An analysis of the resultant behavior of\nbidders must incorporate the possibility of a bidder winning an item\nand having it withdrawn in order for the bid-taker to formulate a\nrepair solution after a break elsewhere. Harstad and Rothkopf have\nanalyzed bidder aggressiveness [8] using a strictly game-theoretic\nmodel in which the only reason for bid withdrawal is the winner\"s\ncurse. They assumed all bidders were risk-neutral, but surmised\nthat it is entirely possible for the bid-taker to collect a risk premium\nfrom risk-averse bidders with the offer of such insurance.\nCombinatorial auctions with mutual bid bonds add an extra incentive to\nbid aggressively because of the possibility of being compensated\nfor having a winning bid withdrawn by a bid-taker. This is militated\nagainst by the increased probability of not having items withdrawn\nin a repair solution. We leave an in-depth analysis of the sufficient\nconditions for more aggressive bidding for future work.\nWhilst the WSS framework provides ample flexibility and\nexpressiveness, scalability becomes a problem for larger auctions.\nAlthough solutions to larger auctions tend to be naturally more\nrobust, some bid-takers in such auctions may require robustness. A\npossible extension of our work in this paper may be to examine the\nfeasibility of reformulating integer linear programs so that the\nsolutions are robust. Hebrard et al. [10] examined reformulation of\nCSPs for finding super solutions. Alternatively, it may be\npossible to use a top-down approach by looking at the k-best solutions\nsequentially, in terms of revenue, and performing sensitivity\nanalysis upon each solution until a robust one is found. In procurement\nsettings the principle of free disposal is often discounted and all\nitems must be sold. This reduces the number of potential solutions\nand thereby reduces the reparability of each solution. The impact\nof such a constraint on revenue of robust solutions is also left for\nfuture work.\nThere is another interesting direction this work may take, namely\nrobust mechanism design. Porter et al. introduced the notion of\nfault tolerant mechanism design in which agents have private\ninformation regarding costs for task completion, but also their\nprobabilities of failure [20]. When the bid-taker has combinatorial\nvaluations for task completions it may be desirable to assign the same\ntask to multiple agents to ensure solution robustness. It is desirable\nto minimize such potentially redundant task assignments but not to\nthe detriment of completed task valuations. This problem could be\nmodeled using the WSS framework in a similar manner to that of\ncombinatorial auctions.\nIn the case where no robust solutions are found, it is possible\nto optimize robustness, instead of revenue, by finding a solution\nof at least a given revenue that minimizes the probability of an\nirreparable break. In this manner the least brittle solution of adequate\nrevenue may be chosen.\n7. CONCLUSION\nFairness is often cited as a reason for choosing the optimal\nsolution in terms of revenue only [22]. Robust solutions militate against\nbids deemed brittle, therefore bidders must earn a reputation for\nbeing reliable to relax the reparability constraint attached to their\nbids. This may be seen as being fair to long-standing business\npartners whose reliability is unquestioned. Internet-based auctions\nare often seen as unwelcome price-gouging exercises by suppliers\nin many sectors [6, 17]. Traditional business partnerships are\nbeing severed by increased competition amongst suppliers. Quality\nof Service can suffer because of the increased focus on short-term\nprofitability to the detriment of the bid-taker in the long-term.\nRobust solutions can provide a means of selectively discriminating\nagainst distrusted bidders in a measured manner. As\ncombinatorial auction deployment moves from large value auctions with a\nsmall pool of trusted bidders (e.g. spectrum-rights sales) towards\nlower value auctions with potentially unknown bidders (e.g.\nSupply Chain Management [30]), solution robustness becomes more\nrelevant. As well as being used to ensure that the bid-taker is not\nleft vulnerable to bid withdrawal, it may also be used to cement\nrelationships with preferred, possibly incumbent, suppliers.\n191\nWe have shown that it is possible to attain robust solutions for\nCAs with only a small loss in revenue. We have also illustrated\nhow such solutions tend to have fewer winning bids than overall\noptimal solutions, thereby reducing any overheads associated with\ndealing with more bidders. We have also demonstrated that\nintroducing mutual bid bonds, a form of leveled commitment contract,\ncan significantly increase the revenue of optimal robust solutions\nby improving reparability. We contend that robust solutions\nusing such a mechanism can allow a bid-taker to offer the possibility\nof bid withdrawal to bidders whilst remaining confident about\npostrepair revenue and also facilitating increased bidder aggressiveness.\n8. REFERENCES\n[1] Martin Andersson and Tuomas Sandholm. Leveled\ncommitment contracts with myopic and strategic agents.\nJournal of Economic Dynamics and Control, 25:615-640,\n2001. Special issue on Agent-Based Computational\nEconomics.\n[2] Fahiem Bacchus and George Katsirelos. EFC solver.\nwww.cs.toronto.edu/\u02dcgkatsi/efc/efc.html.\n[3] Michael Berkelaar, Kjell Eikland, and Peter Notebaert.\nlp solve version 5.0.10.0.\nhttp://groups.yahoo.com/group/lp_solve/.\n[4] Rina Dechter. Constraint Processing. Morgan Kaufmann,\n2003.\n[5] Sven DeVries and Rakesh Vohra. Combinatorial auctions: A\nsurvey. INFORMS Journal on Computing, pages 284-309,\n2003.\n[6] Jim Ericson. Reverse auctions: Bad idea. Line 56, Sept 2001.\n[7] Matthew L. Ginsberg, Andrew J. Parkes, and Amitabha Roy.\nSupermodels and Robustness. In Proceedings of AAAI-98,\npages 334-339, Madison, WI, 1998.\n[8] Ronald M. Harstad and Michael H. Rothkopf. Withdrawable\nbids as winner\"s curse insurance. Operations Research,\n43(6):982-994, November-December 1995.\n[9] Emmanuel Hebrard, Brahim Hnich, and Toby Walsh. Robust\nsolutions for constraint satisfaction and optimization. In\nProceedings of the European Conference on Artificial\nIntelligence, pages 186-190, 2004.\n[10] Emmanuel Hebrard, Brahim Hnich, and Toby Walsh. Super\nsolutions in constraint programming. In Proceedings of\nCP-AI-OR 2004, pages 157-172, 2004.\n[11] Gail Hohner, John Rich, Ed Ng, Grant Reid, Andrew J.\nDavenport, Jayant R. Kalagnanam, Ho Soo Lee, and Chae\nAn. Combinatorial and quantity-discount procurement\nauctions benefit Mars Incorporated and its suppliers.\nInterfaces, 33(1):23-35, 2003.\n[12] Alan Holland and Barry O\"Sullivan. Super solutions for\ncombinatorial auctions. In Ercim-Colognet Constraints\nWorkshop (CSCLP 04). Springer LNAI, Lausanne,\nSwitzerland, 2004.\n[13] Alan Holland and Barry O\"Sullivan. Weighted super\nsolutions for constraint programs, December 2004. Technical\nReport: No. UCC-CS-2004-12-02.\n[14] Selective Insurance. Business insurance.\nhttp://www.selectiveinsurance.com/psApps\n/Business/Ins/bonds.asp?bc=13.16.127.\n[15] Ryan Kastner, Christina Hsieh, Miodrag Potkonjak, and\nMajid Sarrafzadeh. On the sensitivity of incremental\nalgorithms for combinatorial auctions. In WECWIS, pages\n81-88, June 2002.\n[16] Kevin Leyton-Brown, Mark Pearson, and Yoav Shoham.\nTowards a universal test suite for combinatorial auction\nalgorithms. In ACM Conference on Electronic Commerce,\npages 66-76, 2000.\n[17] Associated General Contractors of America. Associated\ngeneral contractors of America white paper on reverse\nauctions for procurement of construction.\nhttp://www.agc.org/content/public/pdf\n/Member_Resources/\nReverseAuctionWhitePaper.pdf, 2003.\n[18] National Society of Professional Engineers. A basic guide to\nsurety bonds. http://www.nspe.org/pracdiv\n/76-02surebond.asp.\n[19] Martin Pesendorfer and Estelle Cantillon. Combination\nbidding in multi-unit auctions. Harvard Business School\nWorking Draft, 2003.\n[20] Ryan Porter, Amir Ronen, Yoav Shoham, and Moshe\nTennenholtz. Mechanism design with execution uncertainty.\nIn Proceedings of UAI-02, pages 414-421, 2002.\n[21] Jean-Charles R\u00b4egin. Global constraints and filtering\nalgorithms. In Constraint and Integer\nProgrammingTowards a Unified Methodology, chapter 4, pages 89-129.\nKluwer Academic Publishers, 2004.\n[22] Michael H. Rothkopf and Aleksandar Peke\u02d8c. Combinatorial\nauction design. Management Science, 4(11):1485-1503,\nNovember 2003.\n[23] Michael H. Rothkopf, Aleksandar Peke\u02d8c, and Ronald M.\nHarstad. Computationally manageable combinatorial\nauctions. Management Science, 44(8):1131-1147, 1998.\n[24] Daniel Sabin and Eugene C. Freuder. Contradicting\nconventional wisdom in constraint satisfaction. In A. Cohn,\neditor, Proceedings of ECAI-94, pages 125-129, 1994.\n[25] Tuomas Sandholm. Algorithm for optimal winner\ndetermination in combinatorial auctions. Artificial\nIntelligence, 135(1-2):1-54, 2002.\n[26] Tuomas Sandholm and Victor Lesser. Leveled Commitment\nContracts and Strategic Breach. Games and Economic\nBehavior, 35:212-270, January 2001.\n[27] Tuomas Sandholm and Victor Lesser. Leveled commitment\ncontracting: A backtracking instrument for multiagent\nsystems. AI Magazine, 23(3):89-100, 2002.\n[28] Tuomas Sandholm, Sandeep Sikka, and Samphel Norden.\nAlgorithms for optimizing leveled commitment contracts. In\nProceedings of the IJCAI-99, pages 535-541. Morgan\nKaufmann Publishers Inc., 1999.\n[29] Tuomas Sandholm and Yunhong Zhou. Surplus equivalence\nof leveled commitment contracts. Artificial Intelligence,\n142:239-264, 2002.\n[30] William E. Walsh, Michael P. Wellman, and Fredrik Ygge.\nCombinatorial auctions for supply chain formation. In ACM\nConference on Electronic Commerce, pages 260-269, 2000.\n[31] Rainier Weigel and Christian Bliek. On reformulation of\nconstraint satisfaction problems. In Proceedings of ECAI-98,\npages 254-258, 1998.\n[32] Margaret W. Wiener. Access spectrum bid withdrawal.\nhttp://wireless.fcc.gov/auctions/33\n/releases/da011719.pdf, July 2001.\n192", "keywords": "bid;bid withdrawal;winner determination problem;mutual bid bond;robustness;mandatory mutual bid bond;constraint programming;combinatorial auction;bid-taker's exposure problem;set partition problem;weighted super solution;constraint program;exposure problem;enforceable commitment;weight super solution"}
{"name": "train_J-57", "title": "Marginal Contribution Nets: A Compact Representation Scheme for Coalitional Games", "abstract": "We present a new approach to representing coalitional games based on rules that describe the marginal contributions of the agents. This representation scheme captures characteristics of the interactions among the agents in a natural and concise manner. We also develop efficient algorithms for two of the most important solution concepts, the Shapley value and the core, under this representation. The Shapley value can be computed in time linear in the size of the input. The emptiness of the core can be determined in time exponential only in the treewidth of a graphical interpretation of our representation.", "fulltext": "1. INTRODUCTION\nAgents can often benefit by coordinating their actions.\nCoalitional games capture these opportunities of\ncoordination by explicitly modeling the ability of the agents to take\njoint actions as primitives. As an abstraction, coalitional\ngames assign a payoff to each group of agents in the game.\nThis payoff is intended to reflect the payoff the group of\nagents can secure for themselves regardless of the actions\nof the agents not in the group. These choices of primitives\nare in contrast to those of non-cooperative games, of which\nagents are modeled independently, and their payoffs depend\ncritically on the actions chosen by the other agents.\n1.1 Coalitional Games and E-Commerce\nCoalitional games have appeared in the context of\ne-commerce. In [7], Kleinberg et al. use coalitional games to study\nrecommendation systems. In their model, each individual\nknows about a certain set of items, is interested in learning\nabout all items, and benefits from finding out about them.\nThe payoffs to groups of agents are the total number of\ndistinct items known by its members. Given this coalitional\ngame setting, Kleinberg et al. compute the value of the\nprivate information of the agents is worth to the system using\nthe solution concept of the Shapley value (definition can be\nfound in section 2). These values can then be used to\ndetermine how much each agent should receive for participating\nin the system.\nAs another example, consider the economics behind\nsupply chain formation. The increased use of the Internet as a\nmedium for conducting business has decreased the costs for\ncompanies to coordinate their actions, and therefore\ncoalitional game is a good model for studying the supply chain\nproblem. Suppose that each manufacturer purchases his raw\nmaterials from some set of suppliers, and that the suppliers\noffer higher discount with more purchases. The decrease in\ncommunication costs will let manufacturers find others\ninterested in the same set of suppliers cheaper, and facilitates\nformation of coalitions to bargain with the suppliers.\nDepending on the set of suppliers and how much from each\nsupplier each coalition purchases, we can assign payoffs to\nthe coalitions depending on the discount it receives. The\nresulting game can be analyzed using coalitional game\ntheory, and we can answer questions such as the stability of\ncoalitions, and how to fairly divide the benefits among the\nparticipating manufacturers. A similar problem,\ncombinatorial coalition formation, has previously been studied in [8].\n1.2 Evaluation Criteria for Coalitional Game\nRepresentation\nTo capture the coalitional games described above and\nperform computations on them, we must first find a\nrepresentation for these games. The na\u00a8\u0131ve solution is to enumerate\nthe payoffs to each set of agents, therefore requiring space\n193\nexponential in the number of agents in the game. For the\ntwo applications described, the number of agents in the\nsystem can easily exceed a hundred; this na\u00a8\u0131ve approach will\nnot be scalable to such problems. Therefore, it is critical to\nfind good representation schemes for coalitional games.\nWe believe that the quality of a representation scheme\nshould be evaluated by four criteria.\nExpressivity: the breadth of the class of coalitional games\ncovered by the representation.\nConciseness: the space requirement of the representation.\nEfficiency: the efficiency of the algorithms we can develop\nfor the representation.\nSimplicity: the ease of use of the representation by users\nof the system.\nThe ideal representation should be fully expressive, i.e., it\nshould be able to represent any coalitional games, use as\nlittle space as possible, have efficient algorithms for\ncomputation, and be easy to use. The goal of this paper is to\ndevelop a representation scheme that has properties close to\nthe ideal representation.\nUnfortunately, given that the number of degrees of\nfreedom of coalitional games is O(2n\n), not all games can be\nrepresented concisely using a single scheme due to information\ntheoretic constraints. For any given class of games, one may\nbe able to develop a representation scheme that is tailored\nand more compact than a general scheme. For example, for\nthe recommendation system game, a highly compact\nrepresentation would be one that simply states which agents know\nof which products, and let the algorithms that operate on\nthe representation to compute the values of coalitions\nappropriately. For some problems, however, there may not be\nefficient algorithms for customized representations. By\nhaving a general representation and efficient algorithms that go\nwith it, the representation will be useful as a prototyping\ntool for studying new economic situations.\n1.3 Previous Work\nThe question of coalitional game representation has only\nbeen sparsely explored in the past [2, 3, 4]. In [4], Deng\nand Papadimitriou focused on the complexity of different\nsolution concepts on coalitional games defined on graphs.\nWhile the representation is compact, it is not fully\nexpressive. In [2], Conitzer and Sandholm looked into the problem\nof determining the emptiness of the core in superadditive\ngames. They developed a compact representation scheme\nfor such games, but again the representation is not fully\nexpressive either. In [3], Conitzer and Sandholm developed a\nfully expressive representation scheme based on\ndecomposition. Our work extends and generalizes the representation\nschemes in [3, 4] through decomposing the game into a set of\nrules that assign marginal contributions to groups of agents.\nWe will give a more detailed review of these papers in section\n2.2 after covering the technical background.\n1.4 Summary of Our Contributions\n\u2022 We develop the marginal contribution networks\nrepresentation, a fully expressive representation scheme\nwhose size scales according to the complexity of the\ninteractions among the agents. We believe that the\nrepresentation is also simple and intuitive.\n\u2022 We develop an algorithm for computing the Shapley\nvalue of coalitional games under this representation\nthat runs in time linear in the size of the input.\n\u2022 Under the graphical interpretation of the\nrepresentation, we develop an algorithm for determining the\nwhether a payoff vector is in the core and the emptiness\nof the core in time exponential only in the treewidth\nof the graph.\n2. PRELIMINARIES\nIn this section, we will briefly review the basics of\ncoalitional game theory and its two primary solution concepts,\nthe Shapley value and the core.1\nWe will also review\nprevious work on coalitional game representation in more detail.\nThroughout this paper, we will assume that the payoff to\na group of agents can be freely distributed among its\nmembers. This assumption is often known as the transferable\nutility assumption.\n2.1 Technical Background\nWe can represent a coalition game with transferable utility\nby the pair N, v , where\n\u2022 N is the set of agents; and\n\u2022 v : 2N\n\u2192 R is a function that maps each group of\nagents S \u2286 N to a real-valued payoff.\nThis representation is known as the characteristic form. As\nthere are exponentially many subsets, it will take space\nexponential in the number of agents to describe a coalitional\ngame.\nAn outcome in a coalitional game specifies the utilities\nthe agents receive. A solution concept assigns to each\ncoalitional game a set of reasonable outcomes. Different\nsolution concepts attempt to capture in some way outcomes\nthat are stable and/or fair. Two of the best known solution\nconcepts are the Shapley value and the core.\nThe Shapley value is a normative solution concept. It\nprescribes a fair way to divide the gains from cooperation\nwhen the grand coalition (i.e., N) is formed. The division\nof payoff to agent i is the average marginal contribution of\nagent i over all possible permutations of the agents.\nFormally, let \u03c6i(v) denote the Shapley value of i under\ncharacteristic function v, then2\n\u03c6i(v) =\nS\u2282N\ns!(n \u2212 s \u2212 1)!\nn!\n(v(S \u222a {i}) \u2212 v(S)) (1)\nThe Shapley value is a solution concept that satisfies many\nnice properties, and has been studied extensively in the\neconomic and game theoretic literature. It has a very useful\naxiomatic characterization.\nEfficiency (EFF) A total of v(N) is distributed to the\nagents, i.e., i\u2208N \u03c6i(v) = v(N).\nSymmetry (SYM) If agents i and j are interchangeable,\nthen \u03c6i(v) = \u03c6j(v).\n1\nThe materials and terminology are based on the textbooks\nby Mas-Colell et al. [9] and Osborne and Rubinstein [11].\n2\nAs a notational convenience, we will use the lower-case\nletter to represent the cardinality of a set denoted by the\ncorresponding upper-case letter.\n194\nDummy (DUM) If agent i is a dummy player, i.e., his\nmarginal contribution to all groups S are the same,\n\u03c6i(v) = v({i}).\nAdditivity (ADD) For any two coalitional games v and\nw defined over the same set of agents N, \u03c6i(v + w) =\n\u03c6i(v) + \u03c6i(w) for all i \u2208 N, where the game v + w is\ndefined as (v + w)(S) = v(S) + w(S) for all S \u2286 N.\nWe will refer to these axioms later in our proof of correctness\nof the algorithm for computing the Shapley value under our\nrepresentation in section 4.\nThe core is another major solution concept for coalitional\ngames. It is a descriptive solution concept that focuses on\noutcomes that are stable. Stability under core means that\nno set of players can jointly deviate to improve their payoffs.\nFormally, let x(S) denote i\u2208S xi. An outcome x \u2208 Rn\nis\nin the core if\n\u2200S \u2286 N x(S) \u2265 v(S) (2)\nThe core was one of the first proposed solution concepts\nfor coalitional games, and had been studied in detail. An\nimportant question for a given coalitional game is whether\nthe core is empty. In other words, whether there is any\noutcome that is stable relative to group deviation. For a\ngame to have a non-empty core, it must satisfy the property\nof balancedness, defined as follows. Let 1S \u2208 Rn\ndenote the\ncharacteristic vector of S given by\n(1S)i =\n1 if i \u2208 S\n0 otherwise\nLet (\u03bbS)S\u2286N be a set of weights such that each \u03bbS is in the\nrange between 0 and 1. This set of weights, (\u03bbS)S\u2286N , is a\nbalanced collection if for all i \u2208 N,\nS\u2286N\n\u03bbS(1S)i = 1\nA game is balanced if for all balanced collections of weights,\nS\u2286N\n\u03bbSv(S) \u2264 v(N) (3)\nBy the Bondereva-Shapley theorem, the core of a\ncoalitional game is non-empty if and only if the game is\nbalanced. Therefore, we can use linear programming to\ndetermine whether the core of a game is empty.\nmaximize\n\u03bb\u2208R2n S\u2286N \u03bbSv(S)\nsubject to S\u2286N \u03bbS1S = 1 \u2200i \u2208 N\n\u03bbS \u2265 0 \u2200S \u2286 N\n(4)\nIf the optimal value of (4) is greater than the value of the\ngrand coalition, then the core is empty. Unfortunately, this\nprogram has an exponential number of variables in the\nnumber of players in the game, and hence an algorithm that\noperates directly on this program would be infeasible in practice.\nIn section 5.4, we will describe an algorithm that answers\nthe question of emptiness of core that works on the dual of\nthis program instead.\n2.2 Previous Work Revisited\nDeng and Papadimitriou looked into the complexity of\nvarious solution concepts on coalitional games played on\nweighted graphs in [4]. In their representation, the set of\nagents are the nodes of the graph, and the value of a set of\nagents S is the sum of the weights of the edges spanned by\nthem. Notice that this representation is concise since the\nspace required to specify such a game is O(n2\n). However,\nthis representation is not general; it will not be able to\nrepresent interactions among three or more agents. For example,\nit will not be able to represent the majority game, where a\ngroup of agents S will have value of 1 if and only if s > n/2.\nOn the other hand, there is an efficient algorithm for\ncomputing the Shapley value of the game, and for determining\nwhether the core is empty under the restriction of positive\nedge weights. However, in the unrestricted case,\ndetermining whether the core is non-empty is coNP-complete.\nConitzer and Sandholm in [2] considered coalitional games\nthat are superadditive. They described a concise\nrepresentation scheme that only states the value of a coalition if the\nvalue is strictly superadditive. More precisely, the semantics\nof the representation is that for a group of agents S,\nv(S) = max\n{T1,T2,...,Tn}\u2208\u03a0\ni\nv(Ti)\nwhere \u03a0 is the set of all possible partitions of S. The value\nv(S) is only explicitly specified for S if v(S) is greater than\nall partitioning of S other than the trivial partition ({S}).\nWhile this representation can represent all games that are\nsuperadditive, there are coalitional games that it cannot\nrepresent. For example, it will not be able to represent any\ngames with substitutability among the agents. An\nexample of a game that cannot be represented is the unit game,\nwhere v(S) = 1 as long as S = \u2205. Under this\nrepresentation, the authors showed that determining whether the core\nis non-empty is coNP-complete. In fact, even determining\nthe value of a group of agents is NP-complete.\nIn a more recent paper, Conitzer and Sandholm described\na representation that decomposes a coalitional game into a\nnumber of subgames whose sum add up to the original game\n[3]. The payoffs in these subgames are then represented by\ntheir respective characteristic functions. This scheme is fully\ngeneral as the characteristic form is a special case of this\nrepresentation. For any given game, there may be multiple\nways to decompose the game, and the decomposition may\ninfluence the computational complexity. For computing the\nShapley value, the authors showed that the complexity is\nlinear in the input description; in particular, if the largest\nsubgame (as measured by number of agents) is of size n and\nthe number of subgames is m, then their algorithm runs\nin O(m2n\n) time, where the input size will also be O(m2n\n).\nOn the other hand, the problem of determining whether a\ncertain outcome is in the core is coNP-complete.\n3. MARGINAL CONTRIBUTION NETS\nIn this section, we will describe the Marginal Contribution\nNetworks representation scheme. We will show that the idea\nis flexible, and we can easily extend it to increase its\nconciseness. We will also show how we can use this scheme to\nrepresent the recommendation game from the introduction.\nFinally, we will show that this scheme is fully expressive,\nand generalizes the representation schemes in [3, 4].\n3.1 Rules and MarginalContributionNetworks\nThe basic idea behind marginal contribution networks\n(MC-nets) is to represent coalitional games using sets of\nrules. The rules in MC-nets have the following syntactic\n195\nform:\nPattern \u2192 value\nA rule is said to apply to a group of agents S if S meets\nthe requirement of the Pattern. In the basic scheme, these\npatterns are conjunctions of agents, and S meets the\nrequirement of the given pattern if S is a superset of it. The\nvalue of a group of agents is defined to be the sum over the\nvalues of all rules that apply to the group. For example, if\nthe set of rules are\n{a \u2227 b} \u2192 5\n{b} \u2192 2\nthen v({a}) = 0, v({b}) = 2, and v({a, b}) = 5 + 2 = 7.\nMC-nets is a very flexible representation scheme, and can\nbe extended in different ways. One simple way to extend\nit and increase its conciseness is to allow a wider class of\npatterns in the rules. A pattern that we will use throughout\nthe remainder of the paper is one that applies only in the\nabsence of certain agents. This is useful for expressing\nconcepts such as substitutability or default values. Formally,\nwe express such patterns by\n{p1 \u2227 p2 \u2227 . . . \u2227 pm \u2227 \u00acn1 \u2227 \u00acn2 \u2227 . . . \u2227 \u00acnn}\nwhich has the semantics that such rule will apply to a group\nS only if {pi}m\ni=1 \u2208 S and {nj}n\nj=1 /\u2208 S. We will call\nthe {pi}m\ni=1 in the above pattern the positive literals, and\n{nj}n\nj=1 the negative literals. Note that if the pattern of\na rule consists solely of negative literals, we will consider\nthat the empty set of agents will also satisfy such pattern,\nand hence v(\u2205) may be non-zero in the presence of negative\nliterals.\nTo demonstrate the increase in conciseness of\nrepresentation, consider the unit game described in section 2.2. To\nrepresent such a game without using negative literals, we\nwill need 2n\nrules for n players: we need a rule of value 1\nfor each individual agent, a rule of value \u22121 for each pair of\nagents to counter the double-counting, a rule of value 1 for\neach triplet of agents, etc., similar to the inclusion-exclusion\nprinciple. On the other hand, using negative literals, we\nonly need n rules: value 1 for the first agent, value 1 for the\nsecond agent in the absence of the first agent, value 1 for the\nthird agent in the absence of the first two agents, etc. The\nrepresentational savings can be exponential in the number\nof agents.\nGiven a game represented as a MC-net, we can interpret\nthe set of rules that make up the game as a graph. We call\nthis graph the agent graph. The nodes in the graph will\nrepresent the agents in the game, and for each rule in the\nMCnet, we connect all the agents in the rule together and assign\na value to the clique formed by the set of agents. Notice that\nto accommodate negative literals, we will need to annotate\nthe clique appropriately. This alternative view of MC-nets\nwill be useful in our algorithm for Core-Membership in\nsection 5.\nWe would like to end our discussion of the representation\nscheme by mentioning a trade-off between the\nexpressiveness of patterns and the space required to represent them.\nTo represent a coalitional game in characteristic form, one\nwould need to specify all 2n\n\u2212 1 values. There is no\noverhead on top of that since there is a natural ordering of the\ngroups. For MC-nets, however, specification of the rules\nrequires specifying both the patterns and the values. The\npatterns, if not represented compactly, may end up\noverwhelming the savings from having fewer values to specify.\nThe space required for the patterns also leads to a\ntradeoff between the expressiveness of the allowed patterns and\nthe simplicity of representing them. However, we believe\nthat for most naturally arising games, there should be\nsufficient structure in the problem such that our representation\nachieves a net saving over the characteristic form.\n3.2 Example: Recommendation Game\nAs an example, we will use MC-net to represent the\nrecommendation game discussed in the introduction. For each\nproduct, as the benefit of knowing about the product will\ncount only once for each group, we need to capture\nsubstitutability among the agents. This can be captured by a\nscaled unit game. Suppose the value of the knowledge about\nproduct i is vi, and there are ni agents, denoted by {xj\ni },\nwho know about the product, the game for product i can\nthen be represented as the following rules:\n{x1\ni } \u2192 vi\n{x2\ni \u2227 \u00acx1\ni } \u2192 vi\n...\n{xni\ni \u2227 \u00acxni\u22121\ni \u2227 \u00b7 \u00b7 \u00b7 \u2227 \u00acx1\ni } \u2192 vi\nThe entire game can then be built up from the sets of rules\nof each product. The space requirement will be O(mn\u2217\n),\nwhere m is the number of products in the system, and n\u2217\nis the maximum number of agents who knows of the same\nproduct.\n3.3 Representation Power\nWe will discuss the expressiveness and conciseness of our\nrepresentation scheme and compare it with the previous\nworks in this subsection.\nProposition 1. Marginal contribution networks\nconstitute a fully expressive representation scheme.\nProof. Consider an arbitrary coalitional game N, v in\ncharacteristic form representation. We can construct a set\nof rules to describe this game by starting from the singleton\nsets and building up the set of rules. For any singleton set\n{i}, we create a rule {i} \u2192 v(i). For any pair of agents {i, j},\nwe create a rule {i \u2227 j} \u2192 v({i, j}) \u2212 v({i}) \u2212 v({j}. We\ncan continue to build up rules in a manner similar to the\ninclusion-exclusion principle. Since the game is arbitrary,\nMC-nets are fully expressive.\nUsing the construction outlined in the proof, we can show\nthat our representation scheme can simulate the multi-issue\nrepresentation scheme of [3] in almost the same amount of\nspace.\nProposition 2. Marginal contribution networks use at\nmost a linear factor (in the number of agents) more space\nthan multi-issue representation for any game.\nProof. Given a game in multi-issue representation, we\nstart by describing each of the subgames, which are\nrepresented in characteristic form in [3], with a set of rules.\n196\nWe then build up the grand game by including all the rules\nfrom the subgames. Note that our representation may\nrequire a space larger by a linear factor due to the need to\ndescribe the patterns for each rule. On the other hand, our\napproach may have fewer than exponential number of rules\nfor each subgame, depending on the structure of these\nsubgames, and therefore may be more concise than multi-issue\nrepresentation.\nOn the other hand, there are games that require\nexponentially more space to represent under the multi-issue scheme\ncompared to our scheme.\nProposition 3. Marginal contribution networks are\nexponentially more concise than multi-issue representation for\ncertain games.\nProof. Consider a unit game over all the agents N. As\nexplained in 3.1, this game can be represented in linear space\nusing MC-nets with negative literals. However, as there is\nno decomposition of this game into smaller subgames, it will\nrequire space O(2n\n) to represent this game under the\nmultiissue representation.\nUnder the agent graph interpretation of MC-nets, we can\nsee that MC-nets is a generalization of the graphical\nrepresentation in [4], namely from weighted graphs to weighted\nhypergraphs.\nProposition 4. Marginal contribution networks can\nrepresent any games in graphical form (under [4]) in the same\namount of space.\nProof. Given a game in graphical form, G, for each edge\n(i, j) with weight wij in the graph, we create a rule {i, j} \u2192\nwij. Clearly this takes exactly the same space as the size of\nG, and by the additive semantics of the rules, it represents\nthe same game as G.\n4. COMPUTING THE SHAPLEY VALUE\nGiven a MC-net, we have a simple algorithm to compute\nthe Shapley value of the game. Considering each rule as a\nseparate game, we start by computing the Shapley value of\nthe agents for each rule. For each agent, we then sum up\nthe Shapley values of that agent over all the rules. We first\nshow that this final summing process correctly computes the\nShapley value of the agents.\nProposition 5. The Shapley value of an agent in a marginal\ncontribution network is equal to the sum of the Shapley\nvalues of that agent over each rule.\nProof. For any group S, under the MC-nets\nrepresentation, v(S) is defined to be the sum over the values of all the\nrules that apply to S. Therefore, considering each rule as a\ngame, by the (ADD) axiom discussed in section 2, the\nShapley value of the game created from aggregating all the rules\nis equal to the sum of the Shapley values over the rules.\nThe remaining question is how to compute the Shapley\nvalues of the rules. We can separate the analysis into two\ncases, one for rules with only positive literals and one for\nrules with mixed literals.\nFor rules that have only positive literals, the Shapley value\nof the agents is v/m, where v is the value of the rule and\nm is the number of agents in the rule. This is a direct\nconsequence of the (SYM) axiom of the Shapley value, as\nthe agents in a rule are indistinguishable from each other.\nFor rules that have both positive and negative literals, we\ncan consider the positive and the negative literals separately.\nFor a given positive literal i, the rule will apply only if i\noccurs in a given permutation after the rest of the positive\nliterals but before any of the negative literals. Formally, let\n\u03c6i denote the Shapley value of i, p denote the cardinality of\nthe positive set, and n denote the cardinality of the negative\nset, then\n\u03c6i =\n(p \u2212 1)!n!\n(p + n)!\nv =\nv\np p+n\nn\nFor a given negative literal j, j will be responsible for\ncancelling the application of the rule if all positive literals come\nbefore the negative literals in the ordering, and j is the first\namong the negative literals. Therefore,\n\u03c6j =\np!(n \u2212 1)!\n(p + n)!\n(\u2212v) =\n\u2212v\nn p+n\np\nBy the (SYM) axiom, all positive literals will have the value\nof \u03c6i and all negative literals will have the value of \u03c6j.\nNote that the sum over all agents in rules with mixed\nliterals is 0. This is to be expected as these rules contribute\n0 to the grand coalition. The fact that these rules have no\neffect on the grand coalition may appear odd at first. But\nthis is because the presence of such rules is to define the\nvalues of coalitions smaller than the grand coalition.\nIn terms of computational complexity, given that the\nShapley value of any agent in a given rule can be computed in\ntime linear in the pattern of the rule, the total running time\nof the algorithm for computing the Shapley value of the\ngame is linear in the size of the input.\n5. ANSWERING CORE-RELATED\nQUESTIONS\nThere are a few different but related computational\nproblems associated with the solution concept of the core. We\nwill focus on the following two problems:\nDefinition 1. (Core-Membership) Given a coalitional game\nand a payoff vector x, determine if x is in the core.\nDefinition 2. (Core-Non-Emptiness) Given a coalitional\ngame, determine if the core is non-empty.\nIn the rest of the section, we will first show that these\ntwo problems are coNP-complete and coNP-hard\nrespectively, and discuss some complexity considerations about\nthese problems. We will then review the main ideas of tree\ndecomposition as it will be used extensively in our algorithm\nfor Core-Membership. Next, we will present the algorithm\nfor Core-Membership, and show that the algorithm runs\nin polynomial time for graphs of bounded treewidth. We end\nby extending this algorithm to answer the question of\nCoreNon-Emptiness in polynomial time for graphs of bounded\ntreewidth.\n5.1 Computational Complexity\nThe hardness of Core-Membership and\nCore-NonEmptiness follows directly from the hardness results of games\nover weighted graphs in [4].\n197\nProposition 6. Core-Membership for games represented\nas marginal contribution networks is coNP-complete.\nProof. Core-Membership in MC-nets is in the class\nof coNP since any set of agents S of which v(S) > x(S)\nwill serve as a certificate to show that x does not belong to\nthe core. As for its hardness, given any instance of\nCoreMembership for a game in graphical form of [4], we can\nencode the game in exactly the same space using MC-net\ndue to Proposition 4. Since Core-Membership for games\nin graphical form is coNP-complete, Core-Membership in\nMC-nets is coNP-hard.\nProposition 7. Core-Non-Emptiness for games\nrepresented as marginal contribution networks is coNP-hard.\nProof. The same argument for hardness between games\nin graphical frm and MC-nets holds for the problem of\nCoreNon-Emptiness.\nWe do not know of a certificate to show that\nCore-NonEmptiness is in the class of coNP as of now. Note that\nthe obvious certificate of a balanced set of weights based\non the Bondereva-Shapley theorem is exponential in size. In\n[4], Deng and Papadimitriou showed the coNP-completeness\nof Core-Non-Emptiness via a combinatorial\ncharacterization, namely that the core is non-empty if and only if\nthere is no negative cut in the graph. In MC-nets, however,\nthere need not be a negative hypercut in the graph for the\ncore to be empty, as demonstrated by the following game\n(N = {1, 2, 3, 4}):\nv(S) =\n\uf8f1\n\uf8f4\uf8f2\n\uf8f4\uf8f3\n1 if S = {1, 2, 3, 4}\n3/4 if S = {1, 2}, {1, 3}, {1, 4}, or {2, 3, 4}\n0 otherwise\n(5)\nApplying the Bondereva-Shapley theorem, if we let \u03bb12 =\n\u03bb13 = \u03bb14 = 1/3, and \u03bb234 = 2/3, this set of weights\ndemonstrates that the game is not balanced, and hence the core\nis empty. On the other hand, this game can be represented\nwith MC-nets as follows (weights on hyperedges):\nw({1, 2}) = w({1, 3}) = w({1, 4}) = 3/4\nw({1, 2, 3}) = w({1, 2, 4}) = w({1, 3, 4}) = \u22126/4\nw({2, 3, 4}) = 3/4\nw({1, 2, 3, 4}) = 10/4\nNo matter how the set is partitioned, the sum over the\nweights of the hyperedges in the cut is always non-negative.\nTo overcome the computational hardness of these\nproblems, we have developed algorithms that are based on tree\ndecomposition techniques. For Core-Membership, our\nalgorithm runs in time exponential only in the treewidth of the\nagent graph. Thus, for graphs of small treewidth, such as\ntrees, we have a tractable solution to determine if a payoff\nvector is in the core. By using this procedure as a\nseparation oracle, i.e., a procedure for returning the inequality\nviolated by a candidate solution, to solving a linear\nprogram that is related to Core-Non-Emptiness using the\nellipsoid method, we can obtain a polynomial time algorithm\nfor Core-Non-Emptiness for graphs of bounded treewidth.\n5.2 Review of Tree Decomposition\nAs our algorithm for Core-Membership relies heavily\non tree decomposition, we will first briefly review the main\nideas in tree decomposition and treewidth.3\nDefinition 3. A tree decomposition of a graph G = (V, E)\nis a pair (X, T), where T = (I, F) is a tree and X = {Xi | i \u2208\nI} is a family of subsets of V , one for each node of T, such\nthat\n\u2022 i\u2208I Xi = V ;\n\u2022 For all edges (v, w) \u2208 E, there exists an i \u2208 I with\nv \u2208 Xi and w \u2208 Xi; and\n\u2022 (Running Intersection Property) For all i, j, k \u2208 I: if j\nis on the path from i to k in T, then Xi \u2229 Xk \u2286 Xj.\nThe treewidth of a tree decomposition is defined as the\nmaximum cardinality over all sets in X, less one. The treewidth\nof a graph is defined as the minimum treewidth over all tree\ndecompositions of the graph.\nGiven a tree decomposition, we can convert it into a nice\ntree decomposition of the same treewidth, and of size linear\nin that of T.\nDefinition 4. A tree decomposition T is nice if T is rooted\nand has four types of nodes:\nLeaf nodes i are leaves of T with |Xi| = 1.\nIntroduce nodes i have one child j such that Xi = Xj \u222a\n{v} of some v \u2208 V .\nForget nodes i have one child j such that Xi = Xj \\ {v}\nfor some v \u2208 Xj.\nJoin nodes i have two children j and k with Xi = Xj =\nXk.\nAn example of a (partial) nice tree decomposition together\nwith a classification of the different types of nodes is in\nFigure 1. In the following section, we will refer to nodes in the\ntree decomposition as nodes, and nodes in the agent graph\nas agents.\n5.3 Algorithm for Core Membership\nOur algorithm for Core-Membership takes as an input\na nice tree decomposition T of the agent graph and a payoff\nvector x. By definition, if x belongs to the core, then for\nall groups S \u2286 N, x(S) \u2265 v(S). Therefore, the difference\nx(S)\u2212v(S) measures how close the group S is to violating\nthe core condition. We call this difference the excess of group\nS.\nDefinition 5. The excess of a coalition S, e(S), is defined\nas x(S) \u2212 v(S).\nA brute-force approach to determine if a payoff vector\nbelongs to the core will have to check that the excesses of all\ngroups are non-negative. However, this approach ignores the\nstructure in the agent graph that will allow an algorithm to\ninfer that certain groups have non-negative excesses due to\n3\nThis is based largely on the materials from a survey paper\nby Bodlaender [1].\n198\ni\nj\nk l\nnm\nIntroduce Node:\nXj = {1, 4}\nXk = {1, 4}\nForget Node:\nXl = {1, 4}\nIntroduce Node:\nXm = {1, 2, 4} Xn = {4}\nLeaf Node:\nJoin Node:\nXi = {1, 3, 4}\nJoin Node:\nFigure 1: Example of a (partial) nice tree\ndecomposition\nthe excesses computed elsewhere in the graph. Tree\ndecomposition is the key to take advantage of such inferences in a\nstructured way.\nFor now, let us focus on rules with positive literals.\nSuppose we have already checked that the excesses of all sets\nR \u2286 U are non-negative, and we would like to check if the\naddition of an agent i to the set U will create a group with\nnegative excess. A na\u00a8\u0131ve solution will be to compute the\nexcesses of all sets that include i. The excess of the group\n(R \u222a {i}) for any group R can be computed as follows\ne(R \u222a {i}) = e(R) + xi \u2212 v(c) (6)\nwhere c is the cut between R and i, and v(c) is the sum of\nthe weights of the edges in the cut.\nHowever, suppose that from the tree decomposition, we\nknow that i is only connected to a subset of U, say S, which\nwe will call the entry set to U. Ideally, because i does not\nshare any edges with members of \u00afU = (U \\ S), we would\nhope that an algorithm can take advantage of this structure\nby checking only sets that are subsets of (S \u222a {i}). This\ncomputational saving may be possible since (xi \u2212v(c)) in the\nupdate equation of (6) does not depend on \u00afU. However, we\ncannot simply ignore \u00afU as members of \u00afU may still influence\nthe excesses of groups that include agent i through group\nS. Specifically, if there exists a group T \u2283 S such that\ne(T) < e(S), then even when e(S \u222a {i}) has non-negative\nexcess, e(T \u222a{i}) may have negative excess. In other words,\nthe excess available at S may have been drained away due\nto T. This motivates the definition of the reserve of a group.\nDefinition 6. The reserve of a coalition S relative to a\ncoalition U is the minimum excess over all coalitions between\nS and U, i.e., all T : S \u2286 T \u2286 U. We denote this value by\nr(S, U). We will refer to the group T that has the minimum\nexcess as arg r(S, U). We will also call U the limiting set of\nthe reserve and S the base set of the reserve.\nOur algorithm works by keeping track of the reserves of\nall non-empty subsets that can be formed by the agents of a\nnode at each of the nodes of the tree decomposition. Starting\nfrom the leaves of the tree and working towards the root,\nat each node i, our algorithm computes the reserves of all\ngroups S \u2286 Xi, limited by the set of agents in the subtree\nrooted at i, Ti, except those in (Xi\\S). The agents in (Xi\\S)\nare excluded to ensure that S is an entry set. Specifically,\nS is the entry set to ((Ti \\ Xi) \u222a S).\nTo accomodate for negative literals, we will need to make\ntwo adjustments. Firstly, the cut between an agent m and a\nset S at node i now refers to the cut among agent m, set S,\nand set \u00ac(Xi \\ S), and its value must be computed\naccordingly. Also, when an agent m is introduced to a group at an\nintroduce node, we will also need to consider the change in\nthe reserves of groups that do not include m due to possible\ncut involving \u00acm and the group.\nAs an example of the reserve values we keep track of at a\ntree node, consider node i of the tree in Figure 1. At node\ni, we will keep track of the following:\nr({1}, {1, 2, . . .})\nr({3}, {2, 3, . . .})\nr({4}, {2, 4, . . .})\nr({1, 3}, {1, 2, 3, . . .})\nr({1, 4}, {1, 2, 4, . . .})\nr({3, 4}, {2, 3, 4, . . .})\nr({1, 3, 4}, {1, 2, 3, 4, . . .}\nwhere the dots . . . refer to the agents rooted under node m.\nFor notational use, we will use ri(S) to denote r(S, U) at\nnode i where U is the set of agents in the subtree rooted at\nnode i excluding agents in (Xi \\ S). We sometimes refer to\nthese values as the r-values of a node. The details of the\nr-value computations are in Algorithm 1.\nTo determine if the payoff vector x is in the core, during\nthe r-value computation at each node, we can check if all of\nthe r-values are non-negative. If this is so for all nodes in\nthe tree, the payoff vector x is in the core. The correctness\nof the algorithm is due to the following proposition.\nProposition 8. The payoff vector x is not in the core if\nand only if the r-values at some node i for some group S is\nnegative.\nProof. (\u21d0) If the reserve at some node i for some group\nS is negative, then there exists a coalition T for which\ne(T) = x(T) \u2212 v(T) < 0, hence x is not in the core.\n(\u21d2) Suppose x is not in the core, then there exists some\ngroup R\u2217\nsuch that e(R\u2217\n) < 0. Let Xroot be the set of nodes\nat the root. Consider any set S \u2208 Xroot, rroot(S) will have\nthe base set of S and the limiting set of ((N \\ Xroot) \u222a S).\nThe union over all of these ranges includes all sets U for\nwhich U \u2229 Xroot = \u2205. Therefore, if R\u2217\nis not disjoint from\nXroot, the r-value for some group in the root is negative.\nIf R\u2217\nis disjoint from U, consider the forest {Ti} resulting\nfrom removal of all tree nodes that include agents in Xroot.\n199\nAlgorithm 1 Subprocedures for Core Membership\nLeaf-Node(i)\n1: ri(Xi) \u2190 e(Xi)\nIntroduce-Node(i)\n2: j \u2190 child of i\n3: m \u2190 Xi \\ Xj {the introduced node}\n4: for all S \u2286 Xj, S = \u2205 do\n5: C \u2190 all hyperedges in the cut of m, S, and \u00ac(Xi \\ S)\n6: ri(S \u222a {x}) \u2190 rj(S) + xm \u2212 v(C)\n7: C \u2190 all hyperedges in the cut of \u00acm, S, and \u00ac(Xi \\S)\n8: ri(S) \u2190 rj(S) \u2212 v(C)\n9: end for\n10: r({m}) \u2190 e({m})\nForget-Node(i)\n11: j \u2190 child of i\n12: m \u2190 Xj \\ Xi {the forgotten node}\n13: for all S \u2286 Xi, S = \u2205 do\n14: ri(S) = min(rj(S), rj(S \u222a {m}))\n15: end for\nJoin-Node(i)\n16: {j, k} \u2190 {left, right} child of i\n17: for all S \u2286 Xi, S = \u2205 do\n18: ri(S) \u2190 rj(S) + rk(S) \u2212 e(S)\n19: end for\nBy the running intersection property, the sets of nodes in\nthe trees Ti\"s are disjoint. Thus, if the set R\u2217\n= i Si for\nsome Si \u2208 Ti, e(R\u2217\n) = i e(Si) < 0 implies some group\nS\u2217\ni has negative excess as well. Therefore, we only need to\ncheck the r-values of the nodes on the individual trees in the\nforest.\nBut for each tree in the forest, we can apply the same\nargument restricted to the agents in the tree. In the base\ncase, we have the leaf nodes of the original tree\ndecomposition, say, for agent i. If R\u2217\n= {i}, then r({i}) = e({i}) < 0.\nTherefore, by induction, if e(R\u2217\n) < 0, some reserve at some\nnode would be negative.\nWe will next explain the intuition behind the correctness\nof the computations for the r-values in the tree nodes. A\ndetailed proof of correctness of these computations can be\nfound in the appendix under Lemmas 1 and 2.\nProposition 9. The procedure in Algorithm 1 correctly\ncompute the r-values at each of the tree nodes.\nProof. (Sketch) We can perform a case analysis over\nthe four types of tree nodes in a nice tree decomposition.\nLeaf nodes (i) The only reserve value to be computed is\nri(Xi), which equals r(Xi, Xi), and therefore it is just\nthe excess of group Xi.\nForget nodes (i with child j) Let m be the forgotten node.\nFor any subset S \u2286 Xi, arg ri(S) must be chosen\nbetween the groups of S and S \u222a {m}, and hence we\nchoose between the lower of the two from the r-values\nat node j.\nIntroduce nodes (i with child j) Let m be the introduced\nnode. For any subset T \u2286 Xi that includes m, let S\ndenote (T \\ {m}). By the running intersection\nproperty, there are no rules that involve m and agents of\nthe subtree rooted at node i except those involving\nm and agents in Xi. As both the base set and the\nlimiting set of the r-values of node j and node i\ndiffer by {m}, for any group V that lies between the\nbase set and the limiting set of node i, the excess of\ngroup V will differ by a constant amount from the\ncorresponding group (V \\ {m}) at node j. Therefore,\nthe set arg ri(T) equals the set arg rj(S) \u222a {m}, and\nri(T) = rj(S) + xm \u2212 v(cut), where v(cut) is the value\nof the rules in the cut between m and S. For any\nsubset S \u2282 Xi that does not include m, we need to\nconsider the values of rules that include \u00acm as a literal\nin the pattern. Also, when computing the reserve, the\npayoff xm will not contribute to group S. Therefore,\ntogether with the running intersection property as\nargued above, we can show that ri(S) = rj(S) \u2212 v(cut).\nJoin nodes (i with left child j and right child k) For any\ngiven set S \u2286 Xi, consider the r-values of that set\nat j and k. If arg rj(S) or arg rk(S) includes agents\nnot in S, then argrj(S) and argrk(S) will be\ndisjoint from each other due to the running intersection\nproperty. Therefore, we can decompose arg ri(S) into\nthree sets, (arg rj(S) \\ S) on the left, S in the middle,\nand (arg rk(S) \\ S) on the right. The reserve rj(S)\nwill cover the excesses on the left and in the middle,\nwhereas the reserve rk(S) will cover those on the right\nand in the middle, and so the excesses in the middle is\ndouble-counted. We adjust for the double-counting by\nsubtracting the excesses in the middle from the sum\nof the two reserves rj(S) and rk(S).\nFinally, note that each step in the computation of the\nrvalues of each node i takes time at most exponential in the\nsize of Xi, hence the algorithm runs in time exponential only\nin the treewidth of the graph.\n5.4 Algorithm for Core Non-emptiness\nWe can extend the algorithm for Core-Membership into\nan algorithm for Core-Non-Emptiness. As described in\nsection 2, whether the core is empty can be checked using\nthe optimization program based on the balancedness\ncondition (3). Unfortunately, that program has an exponential\nnumber of variables. On the other hand, the dual of the\nprogram has only n variables, and can be written as follows:\nminimize\nx\u2208Rn\nn\ni=1 xi\nsubject to x(S) \u2265 v(S), \u2200S \u2286 N\n(7)\nBy strong duality, optimal value of (7) is equal to\noptimal value of (4), the primal program described in section\n2. Therefore, by the Bondereva-Shapley theorem, if the\noptimal value of (7) is greater than v(N), the core is empty.\nWe can solve the dual program using the ellipsoid method\nwith Core-Membership as a separation oracle, i.e., a\nprocedure for returning a constraint that is violated. Note that\na simple extension to the Core-Membership algorithm will\nallow us to keep track of the set T for which e(T) < 0\nduring the r-values computation, and hence we can return the\ninequality about T as the constraint violated. Therefore,\nCore-Non-Emptiness can run in time polynomial in the\nrunning time of Core-Membership, which in turn runs in\n200\ntime exponential only in the treewidth of the graph. Note\nthat when the core is not empty, this program will return\nan outcome in the core.\n6. CONCLUDING REMARKS\nWe have developed a fully expressive representation scheme\nfor coalitional games of which the size depends on the\ncomplexity of the interactions among the agents. Our focus\non general representation is in contrast to the approach\ntaken in [3, 4]. We have also developed an efficient\nalgorithm for the computation of the Shapley values for this\nrepresentation. While Core-Membership for MC-nets is\ncoNP-complete, we have developed an algorithm for\nCoreMembership that runs in time exponential only in the treewidth\nof the agent graph. We have also extended the algorithm\nto solve Core-Non-Emptiness. Other than the algorithm\nfor Core-Non-Emptiness in [4] under the restriction of\nnon-negative edge weights, and that in [2] for\nsuperadditive games when the value of the grand coalition is given,\nwe are not aware of any explicit description of algorithms\nfor core-related problems in the literature.\nThe work in this paper is related to a number of areas\nin computer science, especially in artificial intelligence. For\nexample, the graphical interpretation of MC-nets is closely\nrelated to Markov random fields (MRFs) of the Bayes nets\ncommunity. They both address the issue of of conciseness\nof representation by using the combinatorial structure of\nweighted hypergraphs. In fact, Kearns et al. first apply\nthese idea to games theory by introducing a representation\nscheme derived from Bayes net to represent non-cooperative\ngames [6]. The representational issues faced in coalitional\ngames are closely related to the problem of expressing\nvaluations in combinatorial auctions [5, 10]. The OR-bid\nlanguage, for example, is strongly related to superadditivity.\nThe question of the representation power of different\npatterns is also related to Boolean expression complexity [12].\nWe believe that with a better understanding of the\nrelationships among these related areas, we may be able to develop\nmore efficient representations and algorithms for coalitional\ngames.\nFinally, we would like to end with some ideas for\nextending the work in this paper. One direction to increase the\nconciseness of MC-nets is to allow the definition of\nequivalent classes of agents, similar to the idea of extending Bayes\nnets to probabilistic relational models. The concept of\nsymmetry is prevalent in games, and the use of classes of agents\nwill allow us to capture symmetry naturally and concisely.\nThis will also address the problem of unpleasing assymetric\nrepresentations of symmetric games in our representation.\nAlong the line of exploiting symmetry, as the agents within\nthe same class are symmetric with respect to each other, we\ncan extend the idea above by allowing functional description\nof marginal contributions. More concretely, we can specify\nthe value of a rule as dependent on the number of agents\nof each relevant class. The use of functions will allow\nconcise description of marginal diminishing returns (MDRs).\nWithout the use of functions, the space needed to describe\nMDRs among n agents in MC-nets is O(n). With the use\nof functions, the space required can be reduced to O(1).\nAnother idea to extend MC-nets is to augment the\nsemantics to allow constructs that specify certain rules cannot be\napplied simultaneously. This is useful in situations where a\ncertain agent represents a type of exhaustible resource, and\ntherefore rules that depend on the presence of the agent\nshould not apply simultaneously. For example, if agent i in\nthe system stands for coal, we can either use it as fuel for\na power plant or as input to a steel mill for making steel,\nbut not for both at the same time. Currently, to represent\nsuch situations, we have to specify rules to cancel out the\neffects of applications of different rules. The augmented\nsemantics can simplify the representation by specifying when\nrules cannot be applied together.\n7. ACKNOWLEDGMENT\nThe authors would like to thank Chris Luhrs, Bob\nMcGrew, Eugene Nudelman, and Qixiang Sun for fruitful\ndiscussions, and the anonymous reviewers for their helpful\ncomments on the paper.\n8. REFERENCES\n[1] H. L. Bodlaender. Treewidth: Algorithmic techniques\nand results. In Proc. 22nd Symp. on Mathematical\nFoundation of Copmuter Science, pages 19-36.\nSpringer-Verlag LNCS 1295, 1997.\n[2] V. Conitzer and T. Sandholm. Complexity of\ndetermining nonemptiness of the core. In Proc. 18th\nInt. Joint Conf. on Artificial Intelligence, pages\n613-618, 2003.\n[3] V. Conitzer and T. Sandholm. Computing Shapley\nvalues, manipulating value division schemes, and\nchecking core membership in multi-issue domains. In\nProc. 19th Nat. Conf. on Artificial Intelligence, pages\n219-225, 2004.\n[4] X. Deng and C. H. Papadimitriou. On the complexity\nof cooperative solution concepts. Math. Oper. Res.,\n19:257-266, May 1994.\n[5] Y. Fujishima, K. Leyton-Brown, and Y. Shoham.\nTaming the computational complexity of\ncombinatorial auctions: Optimal and approximate\napproaches. In Proc. 16th Int. Joint Conf. on\nArtificial Intelligence, pages 548-553, 1999.\n[6] M. Kearns, M. L. Littman, and S. Singh. Graphical\nmodels for game theory. In Proc. 17th Conf. on\nUncertainty in Artificial Intelligence, pages 253-260,\n2001.\n[7] J. Kleinberg, C. H. Papadimitriou, and P. Raghavan.\nOn the value of private information. In Proc. 8th\nConf. on Theoretical Aspects of Rationality and\nKnowledge, pages 249-257, 2001.\n[8] C. Li and K. Sycara. Algoirthms for combinatorial\ncoalition formation and payoff division in an electronic\nmarketplace. Technical report, Robotics Insititute,\nCarnegie Mellon University, November 2001.\n[9] A. Mas-Colell, M. D. Whinston, and J. R. Green.\nMicroeconomic Theory. Oxford University Press, New\nYork, 1995.\n[10] N. Nisan. Bidding and allocation in combinatorial\nauctions. In Proc. 2nd ACM Conf. on Electronic\nCommerce, pages 1-12, 2000.\n[11] M. J. Osborne and A. Rubinstein. A Course in Game\nTheory. The MIT Press, Cambridge, Massachusetts,\n1994.\n[12] I. Wegener. The Complexity of Boolean Functions.\nJohn Wiley & Sons, New York, October 1987.\n201\nAPPENDIX\nWe will formally show the correctness of the r-value\ncomputation in Algorithm 1 of introduce nodes and join nodes.\nLemma 1. The procedure for computing the r-values of\nintroduce nodes in Algorithm 1 is correct.\nProof. Let node m be the newly introduced agent at i.\nLet U denote the set of agents in the subtree rooted at i.\nBy the running intersection property, all interactions (the\nhyperedges) between m and U must be in node i. For all\nS \u2286 Xi : m \u2208 S, let R denote (U \\ Xi) \u222a S), and Q denote\n(R \\ {m}).\nri(S) = r(S, R)\n= min\nT :S\u2286T \u2286R\ne(T)\n= min\nT :S\u2286T \u2286R\nx(T) \u2212 v(T)\n= min\nT :S\u2286T \u2286R\nx(T \\ {m}) + xm \u2212 v(T \\ {m}) \u2212 v(cut)\n= min\nT :S\\{m}\u2286T \u2286Q\ne(T ) + xm \u2212 v(cut)\n= rj(S) + xm \u2212 v(cut)\nThe argument for sets S \u2286 Xi : m /\u2208 S is symmetric except\nxm will not contribute to the reserve due to the absence of\nm.\nLemma 2. The procedure for computing the r-values of\njoin nodes in Algorithm 1 is correct.\nProof. Consider any set S \u2286 Xi. Let Uj denote the\nsubtree rooted at the left child, Rj denote ((Uj \\ Xj) \u222a S),\nand Qj denote (Uj \\ Xj). Let Uk, Rk, and Qk be defined\nanalogously for the right child. Let R denote (U \\ Xi) \u222a S).\nri(S) = r(S, R)\n= min\nT :S\u2286T \u2286R\nx(T) \u2212 v(T)\n= min\nT :S\u2286T \u2286R\nx(S) + x(T \u2229 Qj) + x(T \u2229 Qk)\n\u2212 v(S) \u2212 v(cut(S, T \u2229 Qj) \u2212 v(cut(S, T \u2229 Qk)\n= min\nT :S\u2286T \u2286R\nx(T \u2229 Qj) \u2212 v(cut(S, T \u2229 Qj))\n+ min\nT :S\u2286T \u2286R\nx(T \u2229 Qk) \u2212 v(cut(S, T \u2229 Qk))\n+ (x(S) \u2212 v(S)) (*)\n= min\nT :S\u2286T \u2286R\nx(T \u2229 Qj) + x(S) \u2212 v(cut(S, T \u2229 Qj)) \u2212 v(S)\n+ min\nT :S\u2286T \u2286R\nx(T \u2229 Qk) + x(S) \u2212 v(cut(S, T \u2229 Qk)) \u2212 v(S)\n\u2212 (x(S) \u2212 v(S))\n= min\nT :S\u2286T \u2286R\ne(T \u2229 Rj) + min\nT :S\u2286T \u2286R\ne(T \u2229 Rk) \u2212 e(S)\n= min\nT :S\u2286T \u2286Rj\ne(T ) + min\nT :S\u2286T \u2286Rk\ne(T ) \u2212 e(S)\n= rj(S) + rk(S) \u2212 e(S)\nwhere (*) is true as T \u2229 Qj and T \u2229 Qk are disjoint due\nto the running intersection property of tree decomposition,\nand hence the minimum of the sum can be decomposed into\nthe sum of the minima.\n202", "keywords": "marginal contribution;mc-net;coalitional game theory;coalitional game;treewidth;coremembership;agent;markov random field;shapley value;representation;interaction;core;marginal diminishing return;compact representation scheme"}
{"name": "train_J-58", "title": "Towards Truthful Mechanisms for Binary Demand Games: A General Framework", "abstract": "The family of Vickrey-Clarke-Groves (VCG) mechanisms is arguably the most celebrated achievement in truthful mechanism design. However, VCG mechanisms have their limitations. They only apply to optimization problems with a utilitarian (or affine) objective function, and their output should optimize the objective function. For many optimization problems, finding the optimal output is computationally intractable. If we apply VCG mechanisms to polynomial-time algorithms that approximate the optimal solution, the resulting mechanisms may no longer be truthful. In light of these limitations, it is useful to study whether we can design a truthful non-VCG payment scheme that is computationally tractable for a given allocation rule O. In this paper, we focus our attention on binary demand games in which the agents\" only available actions are to take part in the a game or not to. For these problems, we prove that a truthful mechanism M = (O, P) exists with a proper payment method P iff the allocation rule O satisfies a certain monotonicity property. We provide a general framework to design such P. We further propose several general composition-based techniques to compute P efficiently for various types of output. In particular, we show how P can be computed through or/and combinations, round-based combinations, and some more complex combinations of the outputs from subgames.", "fulltext": "1. INTRODUCTION\nIn recent years, with the rapid development of the Internet, many\nprotocols and algorithms have been proposed to make the Internet\nmore efficient and reliable. The Internet is a complex distributed\nsystem where a multitude of heterogeneous agents cooperate to\nachieve some common goals, and the existing protocols and\nalgorithms often assume that all agents will follow the prescribed rules\nwithout deviation. However, in some settings where the agents are\nselfish instead of altruistic, it is more reasonable to assume these\nagents are rational - maximize their own profits - according to the\nneoclassic economics, and new models are needed to cope with the\nselfish behavior of such agents.\nTowards this end, Nisan and Ronen [14] proposed the framework\nof algorithmic mechanism design and applied VCG mechanisms to\nsome fundamental problems in computer science, including\nshortest paths, minimum spanning trees, and scheduling on unrelated\nmachines. The VCG mechanisms [5, 11, 21] are applicable to\nmechanism design problems whose outputs optimize the\nutilitarian objective function, which is simply the sum of all agents\"\nvaluations. Unfortunately, some objective functions are not utilitarian;\neven for those problems with a utilitarian objective function,\nsometimes it is impossible to find the optimal output in polynomial time\nunless P=NP. Some mechanisms other than VCG mechanism are\nneeded to address these issues.\nArcher and Tardos [2] studied a scheduling problem where it\nis NP-Hard to find the optimal output. They pointed out that a\ncertain monotonicity property of the output work load is a\nnecessary and sufficient condition for the existence of a truthful\nmechanism for their scheduling problem. Auletta et al. [3] studied a\nsimilar scheduling problem. They provided a family of\ndeterministic truthful (2 + )-approximation mechanisms for any fixed\nnumber of machines and several (1 + )-truthful mechanisms for some\nNP-hard restrictions of their scheduling problem. Lehmann et al.\n[12] studied the single-minded combinatorial auction and gave a\u221a\nm-approximation truthful mechanism, where m is the number of\ngoods. They also pointed out that a certain monotonicity in the\nallocation rule can lead to a truthful mechanism. The work of Mu\"alem\nand Nisan [13] is the closest in spirit to our work. They\ncharacterized all truthful mechanisms based on a certain monotonicity\nproperty in a single-minded auction setting. They also showed how to\nused MAX and IF-THEN-ELSE to combine outputs from\nsubproblems. As shown in this paper, the MAX and IF-THEN-ELSE\ncombinations are special cases of the composition-based techniques\nthat we present in this paper for computing the payments in\npolynomial time under mild assumptions.\nMore generally, we study how to design truthful mechanisms for\nbinary demand games where the allocation of an agent is either\nselected or not selected. We also assume that the valuations\n213\nof agents are uncorrelated, i.e., the valuation of an agent only\ndepends on its own allocation and type. Recall that a mechanism\nM = (O, P) consists of two parts, an allocation rule O and a\npayment scheme P. Previously, it is often assumed that there is an\nobjective function g and an allocation rule O, that either optimizes\ng exactly or approximately. In contrast to the VCG mechanisms,\nwe do not require that the allocation should optimize the objective\nfunction. In fact, we do not even require the existence of an\nobjective function. Given any allocation rule O for a binary demand\ngame, we showed that a truthful mechanism M = (O, P) exists\nfor the game if and only if O satisfies a certain monotonicity\nproperty. The monotonicity property only guarantees the existence of a\npayment scheme P such that (O, P) is truthful. We complement\nthis existence theorem with a general framework to design such a\npayment scheme P. Furthermore, we present general techniques\nto compute the payment when the output is a composition of the\noutputs of subgames through the operators or and and; through\nround-based combinations; or through intermediate results, which\nmay be themselves computed from other subproblems.\nThe remainder of the paper is organized as follows. In Section\n2, we discuss preliminaries and previous works, define binary\ndemand games and discuss the basic assumptions about binary\ndemand games. In Section 3, we show that O satisfying a certain\nmonotonicity property is a necessary and sufficient condition for\nthe existence of a truthful mechanism M = (O, P). A framework\nis then proposed in Section 4 to compute the payment P in\npolynomial time for several types of allocation rules O. In Section 5, we\nprovide several examples to demonstrate the effectiveness of our\ngeneral framework. We conclude our paper in Section 6 with some\npossible future directions.\n2. PRELIMINARIES\n2.1 Mechanism Design\nAs usually done in the literatures about the designing of\nalgorithms or protocols with inputs from individual agents, we adopt\nthe assumption in neoclassic economics that all agents are rational,\ni.e., they respond to well-defined incentives and will deviate from\nthe protocol only if the deviation improves their gain.\nA standard model for mechanism design is as follows. There\nare n agents 1, . . . , n and each agent i has some private\ninformation ti, called its type, only known to itself. For example, the type\nti can be the cost that agent i incurs for forwarding a packet in\na network or can be a payment that the agent is willing to pay\nfor a good in an auction. The agents\" types define the type\nvector t = (t1, t2, . . . , tn). Each agent i has a set of strategies Ai\nfrom which it can choose. For each input vector a = (a1, . . . , an)\nwhere agent i plays strategy ai \u2208 Ai, the mechanism M = (O, P)\ncomputes an output o = O(a) and a payment vector p(a) =\n(p1(a), . . . , pn(a)). Here the payment pi(\u00b7) is the money given to\nagent i and depends on the strategies used by the agents. A game\nis defined as G = (S, M), where S is the setting for the game\nG. Here, S consists the parameters of the game that are set before\nthe game starts and do not depend on the players\" strategies. For\nexample, in a unicast routing game [14], the setting consists of the\ntopology of the network, the source node and the destination node.\nThroughout this paper, unless explicitly mentioned otherwise, the\nsetting S of the game is fixed and we are only interested in how to\ndesign P for a given allocation rule O.\nA valuation function v(ti, o) assigns a monetary amount to agent\ni for each possible output o. Everything about a game S, M ,\nincluding the setting S, the allocation rule O and the payment scheme\nP, is public knowledge except the agent i\"s actual type ti, which\nis private information to agent i. Let ui(ti, o) denote the utility of\nagent i at the outcome of the game o, given its preferences ti. Here,\nfollowing a common assumption in the literature, we assume the\nutility for agent i is quasi-linear, i.e., ui(ti, o) = v(ti, o) + Pi(a).\nLet a|i\nai = (a1, \u00b7 \u00b7 \u00b7 , ai\u22121, ai, ai+1, \u00b7 \u00b7 \u00b7 , an), i.e., each agent\nj = i plays an action aj except that the agent i plays ai. Let a\u2212i =\n(a1, \u00b7 \u00b7 \u00b7 , ai\u22121, ai+1, \u00b7 \u00b7 \u00b7 , an) denote the actions of all agents\nexcept i. Sometimes, we write (a\u2212i, bi) as a|i\nbi. An action ai is\ncalled dominant for i if it (weakly) maximizes the utility of i for all\npossible strategies b\u2212i of other agents, i.e., ui(ti, O(b\u2212i, ai)) \u2265\nui(ti, O(b\u2212i, ai)) for all ai = ai and b\u2212i.\nA direct-revelation mechanism is a mechanism in which the only\nactions available to each agent are to report its private type either\ntruthfully or falsely to the mechanism. An incentive compatible\n(IC) mechanism is a direct-revelation mechanism in which if an\nagent reports its type ti truthfully, then it will maximize its\nutility. Then, in a direct-revelation mechanism satisfying IC, the\npayment scheme should satisfy the property that, for each agent i,\nv(ti, O(t)) + pi(t) \u2265 v(ti, O(t|i\nti)) + pi(t|i\nti). Another\ncommon requirement in the literature for mechanism design is so called\nindividual rationality or voluntary participation: the agent\"s utility\nof participating in the output of the mechanism is not less than the\nutility of the agent of not participating. A direct-revelation\nmechanism is strategproof if it satisfies both IC and IR properties.\nArguably the most important positive result in mechanism\ndesign is the generalized Vickrey-Clarke-Groves (VCG) mechanism\nby Vickrey [21], Clarke [5], and Groves [11]. The VCG\nmechanism applies to (affine) maximization problems where the\nobjective function is utilitarian g(o, t) =\nP\ni v(ti, o) (i.e., the sum of\nall agents\" valuations) and the set of possible outputs is assumed\nto be finite. A direct revelation mechanism M = (O(t), P(t))\nbelongs to the VCG family if (1) the allocation O(t) maximizesP\ni v(ti, o), and (2) the payment to agent i is pi(t) =\nP\nj=i vj(tj, O(t))+\nhi\n(t\u2212i), where hi\n() is an arbitrary function of t\u2212i. Under mild\nassumptions, VCG mechanisms are the only truthful implementations\nfor utilitarian problems [10].\nThe allocation rule of a VCG mechanism is required to\nmaximize the objective function in the range of the allocation function.\nThis makes the mechanism computationally intractable in many\ncases. Furthermore, replacing an optimal algorithm for\ncomputing the output with an approximation algorithm usually leads to\nuntruthful mechanisms if a VCG payment scheme is used. In this\npaper, we study how to design a truthful mechanism that does not\noptimize a utilitarian objective function.\n2.2 Binary Demand Games\nA binary demand game is a game G = (S, M), where M =\n(O, P) and the range of O is {0, 1}n\n. In other words, the\noutput is a n-tuple vector O(t) = (O1(t), O2(t), . . . , On(t)), where\nOi(t) = 1 (respectively, 0) means that agent i is (respectively, is\nnot) selected. Examples of binary demand games include: unicast\n[14, 22, 9] and multicast [23, 24, 8] (generally subgraph\nconstruction by selecting some links/nodes to satisfy some property),\nfacility location [7], and a certain auction [12, 2, 13].\nHereafter, we make the following further assumptions.\n1. The valuation of the agents are not correlated, i.e., v(ti, o) is\na function of v(ti, oi) only is denoted as v(ti, oi).\n2. The valuation v(ti, oi) is a publicly known value and is\nnormalized to 0. This assumption is needed to guarantee the IR\nproperty.\nThus, throughout his paper, we only consider these direct-revelation\nmechanisms in which every agent only needs to reveal its valuation\nvi = v(ti, 1).\n214\nNotice that in applications where agents providing service and\nreceiving payment, e.g., unicast and job scheduling, the valuation\nvi of an agent i is usually negative. For the convenience of\npresentation, we define the cost of agent as ci = \u2212v(ti, 1), i.e., it costs\nagent i ci to provide the service. Throughout this paper, we will\nuse ci instead of vi in our analysis. All our results can apply to\nthe case where the agents receive the service rather than provide by\nsetting ci to negative, as in auction.\nIn a binary demand game, if we want to optimize an\nobjective function g(o, t), then we call it a binary optimization demand\ngame. The main differences between the binary demand games and\nthose problems that can be solved by VCG mechanisms are:\n1. The objective function is utilitarian (or affine maximization\nproblem) for a problem solvable by VCG while there is no\nrestriction on the objective function for a binary demand game.\n2. The allocation rule O studied here does not necessarily\noptimize an objective function, while a VCG mechanism only\nuses the output that optimizes the objective function. We\neven do not require the existence of an objective function.\n3. We assume that the agents\" valuations are not correlated in\na binary demand game, while the agents\" valuations may be\ncorrelated in a VCG mechanism.\nIn this paper, we assume for technical convenience that the\nobjective function g(o, c), if exists, is continuous with respect to the\ncost ci, but most of our results are directly applicable to the discrete\ncase without any modification.\n2.3 Previous Work\nLehmann et al. [12] studied how to design an efficient truthful\nmechanism for single-minded combinatorial auction. In a\nsingleminded combinatorial auction, each agent i (1 \u2264 i \u2264 n) only wants\nto buy a subset Si \u2286 S with private price ci. A single-minded\nbidder i declares a bid bi = Si, ai with Si \u2286 S and ai \u2208 R+\n.\nIn [12], it is assumed that the set of goods allocated to an agent\ni is either Si or \u2205, which is known as exactness. Lehmann et al.\ngave a greedy round-based allocation algorithm, based on the rank\nai\n|Si|1/2 , that has an approximation ratio\n\u221a\nm, where m is the\nnumber of goods in S. Based on the approximation algorithm, they\ngave a truthful payment scheme. For an allocation rule satisfying\n(1) exactness: the set of goods allocated to an agent i is either Si or\n\u2205; (2) monotonicity: proposing more money for fewer goods\ncannot cause a bidder to lose its bid, they proposed a truthful payment\nscheme as follows: (1) charge a winning bidder a certain amount\nthat does not depend on its own bidding; (2) charge a losing\nbidder 0. Notice the assumption of exactness reveals that the single\nminded auction is indeed a binary demand game. Their payment\nscheme inspired our payment scheme for binary demand game.\nIn [1], Archer et al. studied the combinatorial auctions where\nmultiple copies of many different items are on sale, and each\nbidder i desires only one subset Si. They devised a randomized\nrounding method that is incentive compatible and gave a truthful\nmechanism for combinatorial auctions with single parameter agents that\napproximately maximizes the social value of the auction. As they\npointed out, their method is strongly truthful in sense that it is\ntruthful with high probability 1 \u2212 , where is an error probability. On\nthe contrary, in this paper, we study how to design a deterministic\nmechanism that is truthful based on some given allocation rules.\nIn [2], Archer and Tardos showed how to design truthful\nmechanisms for several combinatorial problems where each agent\"s\nprivate information is naturally expressed by a single positive real\nnumber, which will always be the cost incurred per unit load. The\nmechanism\"s output could be arbitrary real number but their\nvaluation is a quasi-linear function t \u00b7 w, where t is the private per\nunit cost and w is the work load. Archer and Tardos characterized\nthat all truthful mechanism should have decreasing work curves\nw and that the truthful payment should be Pi(bi) = Pi(0) +\nbiwi(bi) \u2212\nR bi\n0\nwi(u)du Using this model, Archer and Tardos\ndesigned truthful mechanisms for several scheduling related\nproblems, including minimizing the span, maximizing flow and\nminimizing the weighted sum of completion time problems. Notice\nwhen the load of the problems is w = {0, 1}, it is indeed a binary\ndemand game. If we apply their characterization of the truthful\nmechanism, their decreasing work curves w implies exactly the\nmonotonicity property of the output. But notice that their proof\nis heavily based on the assumption that the output is a continuous\nfunction of the cost, thus their conclusion can\"t directly apply to\nbinary demand games.\nThe paper of Ahuva Mu\"alem and Noam Nisan [13] is closest\nin spirit to our work. They clearly stated that we only discussed a\nlimited class of bidders, single minded bidders, that was introduced\nby [12]. They proved that all truthful mechanisms should have\na monotonicity output and their payment scheme is based on the\ncut value. With a simple generalization, we get our conclusion for\ngeneral binary demand game. They proposed several combination\nmethods including MAX, IF-THEN-ELSE construction to perform\npartial search. All of their methods required the welfare function\nassociated with the output satisfying bitonic property.\nDistinction between our contributions and previous results:\nIt has been shown in [2, 6, 12, 13] that for the single minded\ncombinatorial auction, there exists a payment scheme which\nresults in a truthful mechanism if the allocation rule satisfies a certain\nmonotonicity property. Theorem 4 also depends on the\nmonotonicity property, but it is applicable to a broader setting than the\nsingle minded combinatorial auction. In addition, the binary demand\ngame studied here is different from the traditional packing IP\"s: we\nonly require that the allocation to each agent is binary and the\nallocation rule satisfies a certain monotonicity property; we do not put\nany restrictions on the objective function. Furthermore, the main\nfocus of this paper is to design some general techniques to find the\ntruthful payment scheme for a given allocation rule O satisfying a\ncertain monotonicity property.\n3. GENERAL APPROACHES\n3.1 Properties of Strategyproof Mechanisms\nWe discuss several properties that mechanisms need to satisfy in\norder to be truthful.\nTHEOREM 1. If a mechanism M = (O, P) satisfies IC, then\n\u2200i, if Oi(t|i\nti1 ) = Oi(t|i\nti2 ), then pi(t|i\nti1 ) = pi(t|i\nti2 ).\nCOROLLARY 2. For any strategy-proof mechanism for a binary\ndemand game G with setting S, if we fix the cost c\u2212i of all agents\nother than i, the payment to agent i is a constant p1\ni if Oi(c) = 1,\nand it is another constant p0\ni if Oi(c) = 0.\nTHEOREM 3. Fixed the setting S for a binary demand game,\nif mechanism M = (O, P) satisfies IC, then mechanism M =\n(O, P ) with the same output method O and pi(c) = pi(c) \u2212\n\u03b4i(c\u2212i) for any function \u03b4i(c\u2212i) also satisfies IC.\nThe proofs of above theorems are straightforward and thus\nomitted due to space limit. This theorem implies that for the binary\ndemand games we can always normalize the payment to an agent\ni such that the payment to the agent is 0 when it is not selected.\nHereafter, we will only consider normalized payment schemes.\n215\n3.2 Existence of Strategyproof Mechanisms\nNotice, given the setting S, a mechanism design problem is\ncomposed of two parts: the allocation rule O and a payment scheme P.\nIn this paper, given an allocation rule O we focus our attention\non how to design a truthful payment scheme based on O. Given\nan allocation rule O for a binary demand game, we first present\na sufficient and necessary condition for the existence of a truthful\npayment scheme P.\nDEFINITION 1 (MONOTONE NON-INCREASING PROPERTY (MP)).\nAn output method O is said to satisfy the monotone non-increasing\nproperty if for every agent i and two of its possible costs ci1 < ci2 ,\nOi(c|i\nci2 ) \u2264 Oi(c|i\nci1 ).\nThis definition is not restricted only to binary demand games.\nFor binary demand games, this definition implies that if Oi(c|i\nci2 ) =\n1 then Oi(c|i\nci1 ) = 1.\nTHEOREM 4. Fix the setting S, c\u2212i in a binary demand game\nG with the allocation rule O, the following three conditions are\nequivalent:\n1. There exists a value \u03bai(O, c\u2212i)(which we will call a cut value,\nsuch that Oi(c) = 1 if ci < \u03bai(O, c\u2212i) and Oi(c) = 0 if\nci > \u03bai(O, c\u2212i). When ci = \u03bai(O, c\u2212i), Oi(c) can be\neither 0 or 1 depending on the tie-breaker of the allocation rule\nO. Hereafter, we will not consider the tie-breaker scenario\nin our proofs.\n2. The allocation rule O satisfies MP.\n3. There exists a truthful payment scheme P for this binary\ndemand game.\nPROOF. The proof that Condition 2 implies Condition is\nstraightforward and is omitted here.\nWe then show Condition 3 implies Condition 2. The proof of\nthis is similar to a proof in [13]. To prove this direction, we assume\nthere exists an agent i and two valuation vectors c|i\nci1 and c|i\nci2 ,\nwhere ci1 < ci2 , Oi(c|i\nci2 ) = 1 and Oi(c|i\nci1 ) = 0. From\ncorollary 2, we know that pi(c|i\nci1 ) = p0\ni and pi(c|i\nci2 ) = p1\ni .\nNow fix c\u2212i, the utility for i when ci = ci1 is ui(ci1 ) = p0\ni .\nWhen agent i lies its valuation to ci2 , its utility is p1\ni \u2212 ci1 . Since\nM = (O, P) is truthful, we have p0\ni > p1\ni \u2212 ci1 .\nNow consider the scenario when the actual valuation of agent i\nis ci = ci2 . Its utility is p1\ni \u2212 ci2 when it reports its true valuation.\nSimilarly, if it lies its valuation to ci1 , its utility is p0\ni . Since M =\n(O, P) is truthful, we have p0\ni < p1\ni \u2212 ci2 .\nConsequently, we have p1\ni \u2212ci2 > p0\ni > p1\ni \u2212ci1 . This inequality\nimplies that ci1 > ci2 , which is a contradiction.\nWe then show Condition 1 implies Condition 3. We prove this\nby constructing a payment scheme and proving that this payment\nscheme is truthful. The payment scheme is: If Oi(c) = 1, then\nagent i gets payment pi(c) = \u03bai(O, c\u2212i); else it gets payment\npi(c) = 0.\nFrom condition 1, if Oi(c) = 1 then ci > \u03bai(O, c\u2212i). Thus,\nits utility is \u03bai(O, c\u2212i) \u2212 ci > 0, which implies that the payment\nscheme satisfies the IR. In the following we prove that this payment\nscheme also satisfies IC property. There are two cases here.\nCase 1: ci < \u03ba(O, c\u2212i). In this case, when i declares its true\ncost ci, its utility is \u03bai(O, c\u2212i) \u2212 ci > 0. Now consider the\nsituation when i declares a cost di = ci. If di < \u03bai(O, c\u2212i), then\ni gets the same payment and utility since it is still selected. If\ndi > \u03bai(O, c\u2212i), then its utility becomes 0 since it is not selected\nanymore. Thus, it has no incentive to lie in this case.\nCase 2: ci \u2265 \u03ba(O, c\u2212i). In this case, when i reveals its true\nvaluation, its payment is 0 and the utility is 0. Now consider the\nsituation when i declares a valuation di = ci. If di > \u03bai(O, c\u2212i),\nthen i gets the same payment and utility since it is still not selected.\nIf di \u2264 \u03bai(O, c\u2212i), then its utility becomes \u03bai(O, c\u2212i) \u2212 ci \u2264 0\nsince it is selected now. Thus, it has no incentive to lie.\nThe equivalence of the monotonicity property of the allocation\nrule O and the existence of a truthful mechanism using O can be\nextended to games beyond binary demand games. The details are\nomitted here due to space limit. We now summarize the process to\ndesign a truthful payment scheme for a binary demand game based\non an output method O.\nGeneral Framework 1 Truthful mechanism design for a binary\ndemand game\nStage 1: Check whether the allocation rule O satisfies MP. If it\ndoes not, then there is no payment scheme P such that mechanism\nM = (O, P) is truthful. Otherwise, define the payment scheme P\nas follows.\nStage 2: Based on the allocation rule O, find the cut value\n\u03bai(O, c\u2212i) for agent i such that Oi(c|i\ndi) = 1 when di <\n\u03bai(O, c\u2212i), and Oi(c|i\ndi) = 0 when di > \u03bai(O, c\u2212i).\nStage 3: The payment for agent i is 0 if Oi(c) = 0; the payment is\n\u03bai(O, c\u2212i) if Oi(c) = 1.\nTHEOREM 5. The payment defined by our general framework\nis minimum among all truthful payment schemes using O as output.\n4. COMPUTING CUT VALUE FUNCTIONS\nTo find the truthful payment scheme by using General\nFramework 1, the most difficult stage seems to be the stage 2. Notice\nthat binary search does not work generally since the valuations of\nagents may be continuous. We give some general techniques that\ncan help with finding the cut value function under certain\ncircumstances. Our basic approach is as follows. First, we decompose the\nallocation rule into several allocation rules. Next find the cut value\nfunction for each of these new allocation rules. Then, we compute\nthe original cut value function by combining these cut value\nfunctions of the new allocation rules.\n4.1 Simple Combinations\nIn this subsection, we introduce techniques to compute the cut\nvalue function by combining multiple allocation rules with\nconjunctions or disconjunctions. For simplicity, given an allocation\nrule O, we will use \u03ba(O, c) to denote a n-tuple vector\n(\u03ba1(O, c\u22121), \u03ba2(O, c\u22122), . . . , \u03ban(O, c\u2212n)).\nHere, \u03bai(O, c\u2212i) is the cut value for agent i when the allocation\nrule is O and the costs c\u2212i of all other agents are fixed.\nTHEOREM 6. With a fixed setting S of a binary demand game,\nassume that there are m allocation rules O1\n, O2\n, \u00b7 \u00b7 \u00b7 , Om\n\nsatisfying the monotonicity property, and \u03ba(Oi\n, c) is the cut value vector\nfor Oi\n. Then the allocation rule O(c) =\nWm\ni=1 Oi\n(c) satisfies the\nmonotonicity property. Moreover, the cut value for O is \u03ba(O, c) =\nmaxm\ni=1{\u03ba(Oi\n, c)} Here \u03ba(O, c) = maxm\ni=1{\u03ba(Oi\n, c)} means,\n\u2200j \u2208 [1, n], \u03baj(O, c\u2212j) = maxm\ni=1{\u03baj(Oi\n, c\u2212j)} and O(c) =Wm\ni=1 Oi\n(c) means, \u2200j \u2208 [1, n], Oj(c) = O1\nj (c) \u2228 O2\nj (c) \u2228 \u00b7 \u00b7 \u00b7 \u2228\nOm\nj (c).\nPROOF. Assume that ci > ci and Oi(c) = 1. Without loss\nof generality, we assume that Ok\ni (c) = 1 for some k, 1 \u2264 k \u2264\nm. From the assumption that Ok\ni (c) satisfies MP, we obtain that\n216\nOk\ni (c|i\nci) = 1. Thus, Oi(c|i\nci) =\nWm\nj=1 Oj\n(c) = 1. This proves\nthat O(c) satisfies MP. The correctness of the cut value function\nfollows directly from Theorem 4.\nMany algorithms indeed fall into this category. To demonstrate\nthe usefulness of Theorem 6, we discuss a concrete example here.\nIn a network, sometimes we want to deliver a packet to a set of\nnodes instead of one. This problem is known as multicast. The\nmost commonly used structure in multicast routing is so called\nshortest path tree (SPT). Consider a network G = (V, E, c), where\nV is the set of nodes, and vector c is the actual cost of the nodes\nforwarding the data. Assume that the source node is s and the\nreceivers are Q \u2282 V . For each receiver qi \u2208 Q, we compute the\nshortest path (least cost path), denoted by LCP(s, qi, d), from the\nsource s to qi under the reported cost profile d. The union of all\nsuch shortest paths forms the shortest path tree. We then use\nGeneral Framework 1 to design the truthful payment scheme P when\nthe SPT structure is used as the output for multicast, i.e., we\ndesign a mechanism M = (SPT, P). Notice that VCG mechanisms\ncannot be applied here since SPT is not an affine maximization.\nWe define LCP(s,qi)\nas the allocation corresponds to the path\nLCP(s, qi, d), i.e., LCP\n(s,qi)\nk (d) = 1 if and only if node vk is in\nLCP(s, qi, d). Then the output SPT is defined as\nW\nqi\u2208Q LCP(s,qi)\n.\nIn other words, SPTk(d) = 1 if and only if qk is selected in\nsome LCP(s, qi, d). The shortest path allocation rule is a\nutilitarian and satisfies MP. Thus, from Theorem 6, SPT also satisfies\nMP, and the cut value function vector for SPT can be calculated as\n\u03ba(SPT, c) = maxqi\u2208Q \u03ba(LCP(s,qi)\n, c), where \u03ba(LCP(s,qi)\n, c)\nis the cut value function vector for the shortest path LCP(s, qi, c).\nConsequently, the payment scheme above is truthful and the\nminimum among all truthful payment schemes when the allocation rule\nis SPT.\nTHEOREM 7. Fixed the setting S of a binary demand game,\nassume that there are m output methods O1\n, O2\n, \u00b7 \u00b7 \u00b7 , Om\n\nsatisfying MP, and \u03ba(Oi\n, c) are the cut value functions respectively for\nOi\nwhere i = 1, 2, \u00b7 \u00b7 \u00b7 , m. Then the allocation rule O(c) =Vm\ni=1 Oi\n(c) satisfies MP. Moreover, the cut value function for O\nis \u03ba(O, c) = minm\ni=1{\u03ba(Oi\n, c)}.\nWe show that our simple combination generalizes the\nIF-THENELSE function defined in [13]. For an agent i, assume that there\nare two allocation rules O1\nand O2\nsatisfying MP. Let \u03bai(O1\n, c\u2212i),\n\u03bai(O2\n, c\u2212i) be the cut value functions for O1\n, O2\nrespectively.\nThen the IF-THEN-ELSE function Oi(c) is actually Oi(c) = [(ci \u2264\n\u03bai(O1\n, c\u2212i) + \u03b41(c\u2212i)) \u2227 O2\n(c\u2212i, ci)] \u2228 (ci < \u03bai(O1\n, c\u2212i) \u2212\n\u03b42(c\u2212i)) where \u03b41(c\u2212i) and \u03b42(c\u2212i) are two positive functions. By\napplying Theorems 6 and 7, we know that the allocation rule O\nsatisfies MP and consequently \u03bai(O, c\u2212i) = max{min(\u03bai(O1\n, c\u2212i)+\n\u03b41(c\u2212i), \u03bai(O2\n, c\u2212i)), \u03bai(O1\n, c\u2212i) \u2212 \u03b42(c\u2212i))}.\n4.2 Round-Based Allocations\nSome approximation algorithms are round-based, where each\nround of an algorithm selects some agents and updates the setting\nand the cost profile if necessary. For example, several\napproximation algorithms for minimum weight vertex cover [19], maximum\nweight independent set, minimum weight set cover [4], and\nminimum weight Steiner [18] tree fall into this category.\nAs an example, we discuss the minimum weighted vertex cover\nproblem (MWVC) [16, 15] to show how to compute the cut value\nfor a round-based output. Given a graph G = (V, E), where the\nnodes v1, v2, . . . , vn are the agents and each agent vi has a weight\nci, we want to find a node set V \u2286 V such that for every edge\n(u, v) \u2208 E at least one of u and v is in V . Such V is called a\nvertex cover of G. The valuation of a node i is \u2212ci if it is selected;\notherwise its valuation is 0. For a subset of nodes V \u2208 V , we\ndefine its weight as c(V ) =\nP\ni\u2208V ci.\nWe want to find a vertex cover with the minimum weight. Hence,\nthe objective function to be implemented is utilitarian. To use the\nVCG mechanism, we need to find the vertex cover with the\nminimum weight, which is NP-hard [16]. Since we are interested in\nmechanisms that can be computed in polynomial time, we must\nuse polynomial-time computable allocation rules. Many algorithms\nhave been proposed in the literature to approximate the optimal\nsolution. In this paper, we use a 2-approximation algorithm given\nin [16]. For the sake of completeness, we briefly review this\nalgorithm here. The algorithm is round-based. Each round selects\nsome vertices and discards some vertices. For each node i, w(i)\nis initialized to its weight ci, and when w(i) drops to 0, i is\nincluded in the vertex cover. To make the presentation clear, we say\nan edge (i1, j1) is lexicographically smaller than edge (i2, j2) if\n(1) min(i1, j1) < min(i2, j2), or (2) min(i1, j1) = min(i2, j2)\nand max(i1, j1) < max(i2, j2).\nAlgorithm 2 Approximate Minimum Weighted Vertex Cover\nInput: A node weighted graph G = (V, E, c).\nOutput: A vertex cover V .\n1: Set V = \u2205. For each i \u2208 V , set w(i) = ci.\n2: while V is not a vertex cover do\n3: Pick an uncovered edge (i, j) with the least lexicographic\norder among all uncovered edges.\n4: Let m = min(w(i), w(j)).\n5: Update w(i) to w(i) \u2212 m and w(j) to w(j) \u2212 m.\n6: If w(i) = 0, add i to V . If w(j) = 0, add j to V .\nNotice, selecting an edge using the lexicographic order is\ncrutial to guarantee the monotonicity property. Algorithm 2 outputs\na vertex cover V whose weight is within 2 times of the optimum.\nFor convenience, we use VC(c) to denote the vertex cover\ncomputed by Algorithm 2 when the cost vector of vertices is c. Below\nwe generalize Algorithm 2 to a more general scenario. Typically, a\nround-based output can be characterized as follows (Algorithm 3).\nDEFINITION 2. An updating rule Ur\nis said to be\ncrossingindependent if, for any agent i not selected in round r, (1) Sr+1\nand cr+1\n\u2212i do not depend on cr\nj (2) for fixed cr\n\u2212i, cr\ni1\n\u2264 cr\ni2\nimplies\nthat cr+1\ni1\n\u2264 cr+1\ni2\n.\nWe have the following theorem about the existence of a truthful\npayment using a round based allocation rule A.\nTHEOREM 8. A round-based output A, with the framework\ndefined in Algorithm 3, satisfies MP if the output methods Or\nsatisfy\nMP and all updating rules Ur\nare crossing-independent.\nPROOF. Consider an agent i and fixed c\u2212i. We prove that when\nan agent i is selected with cost ci, then it is also selected with cost\ndi < ci. Assume that i is selected in round r with cost ci. Then\nunder cost di, if agent i is selected in a round before r, our claim\nholds. Otherwise, consider in round r. Clearly, the setting Sr\nand\nthe costs of all other agents are the same as what if agent i had cost\nci since i is not selected in the previous rounds due to the\ncrossindependent property. Since i is selected in round r with cost ci, i\nis also selected in round r with di < ci due to the reason that Or\nsatisfies MP. This finishes the proof.\n217\nAlgorithm 3 A General Round-Based Allocation Rule A\n1: Set r = 0, c0\n= c, and G0\n= G initially.\n2: repeat\n3: Compute an output or\nusing a deterministic algorithm\nOr\n: Sr\n\u00d7 cr\n\u2192 {0, 1}n\n.\nHere Or\n, cr\nand Sr\nare allocation rule, cost vector and game\nsetting in game Gr\n, respectively.\nRemark: Or\nis often a simple greedy algorithm such as\nselecting the agents that minimize some utilitarian function.\nFor the example of vertex cover, Or\nwill always select the\nlight-weighted node on the lexicographically least\nuncovered edge (i, j).\n4: Let r = r + 1. Update the game Gr\u22121\nto obtain a new game\nGr\nwith setting Sr\nand cost vector cr\naccording to some rule\nUr\n: Or\u22121\n\u00d7 (Sr\u22121\n, cr\u22121\n) \u2192 (Sr\n, cr\n).\nHere we updates the cost and setting of the game.\nRemark: For the example of vertex cover, the\nupdating rule will decrease the weight of vertices i and j by\nmin(w(i), w(j)).\n5: until a valid output is found\n6: Return the union of the set of selected players of each round as\nthe final output. For the example of vertex cover, it is the union\nof nodes selected in all rounds.\nAlgorithm 4 Compute Cut Value for Round-Based Algorithms\nInput: A round-based output A, a game G1\n= G, and a updating\nfunction vector U.\nOutput: The cut value x for agent k.\n1: Set r = 0 and ck = \u03b6. Recall that \u03b6 is a value that can\nguarantee Ak = 0 when an agent reports the cost \u03b6.\n2: repeat\n3: Compute an output or\nusing a deterministic algorithm based\non setting Sr\nusing allocation rule Or\n: Sr\n\u00d7cr\n\u2192 {0, 1}n\n.\n4: Find the cut value for agent k based on the allocation rule\nOr\nfor costs cr\n\u2212k. Let r = \u03bak(Or\n, cr\n\u2212k) be the cut value.\n5: Set r = r + 1 and obtain a new game Gr from Gr\u22121\nand or\naccording to the updating rule Ur\n.\n6: Let cr\nbe the new cost vector for game Gr\n.\n7: until a valid output is found.\n8: Let gi(x) be the cost of ci\nk when the original cost vector is\nc|k\nx.\n9: Find the minimum value x such that\n8\n>>>>><\n>>>>>:\ng1(x) \u2265 1;\ng2(x) \u2265 2;\n...\ngt\u22121(x) \u2265 t\u22121;\ngt(x) \u2265 t.\nHere, t is the total number of rounds.\n10: Output the value x as the cut value.\nIf the round-based output satisfies monotonicity property, the\ncut-value always exists. We then show how to find the cut value\nfor a selected agent k in Algorithm 4.\nThe correctness of Algorithm 4 is straightforward. To compute\nthe cut value, we assume that (1) the cut value r for each round r\ncan be computed in polynomial time; (2) we can solve the equation\ngr(x) = r to find x in polynomial time when the cost vector c\u2212i\nand b are given.\nNow we consider the vertex cover problem. For each round r,\nwe select a vertex with the least weight and that is incident on the\nlexicographically least uncovered edge. The output satisfies MP.\nFor agent i, we update its cost to cr\ni \u2212 cr\nj iff edge (i, j) is selected.\nIt is easy to verify this updating rule is crossing-independent, thus\nwe can apply Algorithm 4 to compute the cut value for the set cover\ngame as shown in Algorithm 5.\nAlgorithm 5 Compute Cut Value for MVC.\nInput: A node weighted graph G = (V, E, c) and a node k\nselected by Algorithm 2.\nOutput: The cut value \u03bak(V C, c\u2212k).\n1: For each i \u2208 V , set w(i) = ci.\n2: Set w(k) = \u221e, pk = 0 and V = \u2205.\n3: while V is not a vertex cover do\n4: Pick an uncovered edge (i, j) with the least lexicographic\norder among all uncovered edges.\n5: Set m = min(w(i), w(j)).\n6: Update w(i) = w(i) \u2212 m and w(j) = w(j) \u2212 m.\n7: If w(i) = 0, add i to V ; else add j to V .\n8: If i == k or j == k then set pk = pk + m.\n9: Output pk as the cut value \u03bak(V C, c\u2212k).\n4.3 Complex Combinations\nIn subsection 4.1, we discussed how to find the cut value function\nwhen the output of the binary demand game is a simple\ncombination of some outputs, whose cut values can be computed through\nother means (typically VCG). However, some algorithms cannot\nbe decomposed in the way described in subsection 4.1.\nNext we present a more complex way to combine allocation\nrules, and as we may expected, the way to find the cut value is\nalso more complicated. Assume that there are n agents 1 \u2264 i \u2264 n\nwith cost vector c, and there are m binary demand games Gi with\nobjective functions fi(o, c), setting Si and allocation rule \u03c8i\nwhere\ni = 1, 2, \u00b7 \u00b7 \u00b7 , m. There is another binary demand game with\nsetting S and allocation rule O, whose input is a cost vector d =\n(d1, d2, \u00b7 \u00b7 \u00b7 , dm). Let f be the function vector (f1, f2, \u00b7 \u00b7 \u00b7 , fm),\n\u03c8 be the allocation rule vector (\u03c81\n, \u03c82\n, \u00b7 \u00b7 \u00b7 , \u03c8m\n) and \u222b be the\nsetting vector (S1, S2, \u00b7 \u00b7 \u00b7 , Sm). For notation simplicity, we\ndefine Fi(c) = fi(\u03c8i\n(c), c), for each 1 \u2264 i \u2264 m, and F(c) =\n(F1(c), F2(c), \u00b7 \u00b7 \u00b7 , Fm(c)).\nLet us see a concrete example of these combinations. Consider\na link weighted graph G = (V, E, c), and a subset of q nodes Q \u2286\nV . The Steiner tree problem is to find a set of links with minimum\ntotal cost to connect Q. One way to find an approximation of the\nSteiner tree is as follows: (1) we build a virtual complete graph H\nusing Q as its vertices, and the cost of each edge (i, j) is the cost\nof LCP(i, j, c) in graph G; (2) build the minimum spanning tree\nof H, denoted as MST(H); (3) an edge of G is selected iff it is\nselected in some LCP(i, j, c) and edge (i, j) of H is selected to\nMST(H).\nIn this game, we define q(q \u2212 1)/2 games Gi,j, where i, j \u2208\nQ, with objective functions fi,j(o, c) being the minimum cost of\n218\nconnecting i and j in graph G, setting Si being the original graph\nG and allocation rule is LCP(i, j, c). The game G corresponds to\nthe MST game on graph H. The cost of the pair-wise q(q \u2212 1)/2\nshortest paths defines the input vector d = (d1, d2, \u00b7 \u00b7 \u00b7 , dm) for\ngame MST. More details will be given in Section 5.2.\nDEFINITION 3. Given an allocation rule O and setting S, an\nobjective function vector f, an allocation rule vector \u03c8 and setting\nvector \u222b, we define a compound binary demand game with setting\nS and output O \u25e6 F as (O \u25e6 F)i(c) =\nWm\nj=1(Oj(F(c)) \u2227 \u03c8j\ni (c)).\nThe allocation rule of the above definition can be interpreted as\nfollows. An agent i is selected if and only if there is a j such that\n(1) i is selected in \u03c8j\n(c), and (2) the allocation rule O will select\nindex j under cost profile F(c). For simplicity, we will use O \u25e6 F\nto denote the output of this compound binary demand game.\nNotice that a truthful payment scheme using O \u25e6 F as output\nexists if and only if it satisfies the monotonicity property. To study\nwhen O \u25e6F satisfies MP, several necessary definitions are in order.\nDEFINITION 4. Function Monotonicity Property (FMP) Given\nan objective function g and an allocation rule O, a function H(c) =\ng(O(c), c) is said to satisfy the function monotonicity property, if,\ngiven fixed c\u2212i, it satisfies:\n1. When Oi(c) = 0, H(c) does not increase over ci.\n2. When Oi(c) = 1, H(c) does not decrease over ci.\nDEFINITION 5. Strong Monotonicity Property (SMP) An\nallocation rule O is said to satisfy the strong monotonicity property\nif O satisfies MP, and for any agent i with Oi(c) = 1 and agent\nj = i, Oi(c|j\ncj) = 1 if cj \u2265 cj or Oj(c|j\ncj) = 0.\nLEMMA 1. For a given allocation rule O satisfying SMP and\ncost vectors c, c with ci = ci, if Oi(c) = 1 and Oi(c ) = 0, then\nthere must exist j = i such that cj < cj and Oj(c ) = 1.\nFrom the definition of the strong monotonicity property, we have\nLemma 1 directly. We now can give a sufficient condition when\nO \u25e6 F satisfies the monotonicity property.\nTHEOREM 9. If \u2200i \u2208 [1, m], Fi satisfies FMP, \u03c8i\nsatisfies MP,\nand the output O satisfies SMP, then O \u25e6 F satisfies MP.\nPROOF. Assuming for cost vector c we have (O \u25e6 F)i(c) =\n1, we should prove for any cost vector c = c|i\nci with ci < ci,\n(O \u25e6 F)i(c ) = 1. Noticing that (O \u25e6 F)i(c) = 1, without loss\nof generality, we assume that Ok(F(c)) = 1 and \u03c8k\ni (c) = 1 for\nsome index 1 \u2264 k \u2264 m.\nNow consider the output O with the cost vector F(c )|k\nFk(c).\nThere are two scenarios, which will be studied one by one as\nfollows.\nOne scenario is that index k is not chosen by the output function\nO. From Lemma 1, there must exist j = k such that\nFj(c ) < Fj(c) (1)\nOj(F(c )|k\nFk(c)) = 1 (2)\nWe then prove that agent i will be selected in the output \u03c8j\n(c ),\ni.e., \u03c8j\ni (c ) = 1. If it is not, since \u03c8j\n(c) satisfies MP, we have\n\u03c8j\ni (c) = \u03c8j\ni (c ) = 0 from ci < ci. Since Fj satisfies FMP, we\nknow Fj(c ) \u2265 Fj(c), which is a contradiction to the inequality\n(1). Consequently, we have \u03c8j\ni (c ) = 1. From Equation (2), the\nfact that index k is not selected by allocation rule O and the\ndefinition of SMP, we have Oj(F(c )) = 1, Thus, agent i is selected by\nO \u25e6 F because of Oj(F(c )) = 1 and \u03c8j\ni (c ) = 1.\nThe other scenario is that index k is chosen by the output\nfunction O. First, agent i is chosen in \u03c8k\n(c ) since the output \u03c8k\n(c)\nsatisfies the monotonicity property and ci < ci and \u03c8k\ni (c) = 1.\nSecondly, since the function Fk satisfies FMP, we know that Fk(c ) \u2264\nFk(c). Remember that output O satisfies the SMP, thus we can\nobtain Ok(F(c )) = 1 from the fact that Ok(F(c )|k\nFk(c)) = 1\nand Fk(c ) \u2264 Fk(c). Consequently, agent i will also be selected\nin the final output O \u25e6 F. This finishes our proof.\nThis theorem implies that there is a cut value for the compound\noutput O \u25e6 F. We then discuss how to find the cut value for this\noutput. Below we will give an algorithm to calculate \u03bai(O \u25e6 F)\nwhen (1) O satisfies SMP, (2) \u03c8j\nsatisfies MP, and (3) for fixed c\u2212i,\nFj(c) is a constant, say hj, when \u03c8j\ni (c) = 0, and Fj(c) increases\nwhen \u03c8j\ni (c) = 1. Notice that here hj can be easily computed by\nsetting ci = \u221e since \u03c8j\nsatisfies the monotonicity property. When\ngiven i and fixed c\u2212i, we define (Fi\nj )\u22121\n(y) as the smallest x such\nthat Fj(c|i\nx) = y. For simplicity, we denote (Fi\nj )\u22121\nas F\u22121\nj if\nno confusion is caused when i is a fixed agent. In this paper, we\nassume that given any y, we can find such x in polynomial time.\nAlgorithm 6 Find Cut Value for Compound Method O \u25e6 F\nInput: allocation rule O, objective function vector F and inverse\nfunction vector F\u22121\n= {F\u22121\n1 , \u00b7 \u00b7 \u00b7 , F\u22121\nm }, allocation rule vector\n\u03c8 and fixed c\u2212i.\nOutput: Cut value for agent i based on O \u25e6 F.\n1: for 1 \u2264 j \u2264 m do\n2: Compute the outputs \u03c8j\n(ci).\n3: Compute hj = Fj(c|i\n\u221e).\n4: Use h = (h1, h2, \u00b7 \u00b7 \u00b7 , hm) as the input for the output\nfunction O. Denote \u03c4j = \u03baj(O, h\u2212j) as the cut value function of\noutput O based on input h.\n5: for 1 \u2264 j \u2264 m do\n6: Set \u03bai,j = F\u22121\nj (min{\u03c4j, hj}).\n7: The cut value for i is \u03bai(O \u25e6 F, c\u2212i) = maxm\nj=1 \u03bai,j.\nTHEOREM 10. Algorithm 6 computes the correct cut value for\nagent i based on the allocation rule O \u25e6 F.\nPROOF. In order to prove the correctness of the cut value\nfunction calculated by Algorithm 6, we prove the following two cases.\nFor our convenience, we will use \u03bai to represent \u03bai(O \u25e6 F, c\u2212i) if\nno confusion caused.\nFirst, if di < \u03bai then (O \u25e6 F)i(c|i\ndi) = 1. Without loss of\ngenerality, we assume that \u03bai = \u03bai,j for some j. Since function Fj\nsatisfies FMP and \u03c8j\ni (c|i\ndi) = 1, we have Fj(c|i\ndi) < Fj(\u03bai).\nNotice di < \u03bai,j, from the definition of \u03bai,j = F\u22121\nj (min{\u03c4j, hj})\nwe have (1) \u03c8j\ni (c|i\ndi) = 1, (2) Fj(c|i\ndi) < \u03c4j due to the fact that\nFj(x) is a non-decreasing function when j is selected. Thus, from\nthe monotonicity property of O and \u03c4j is the cut value for output\nO, we have\nOj(h|j\nFj(c|i\ndi)) = 1. (3)\nIf Oj(F(c|i\ndi)) = 1 then (O\u25e6F)i(c|i\ndi) = 1. Otherwise, since\nO satisfies SMP, Lemma 1 and equation 3 imply that there exists\nat least one index k such that Ok(F(c|i\ndi)) = 1 and Fk(c|i\ndi) <\nhk. Note Fk(c|i\ndi) < hk implies that i is selected in \u03c8k\n(c|i\ndi)\nsince hk = Fk(ci|i\n\u221e). In other words, agent i is selected in O\u25e6F.\n219\nSecond, if di \u2265 \u03bai(O \u25e6 F, c\u2212i) then (O \u25e6 F)i(c|i\ndi) = 0.\nAssume for the sake of contradiction that (O \u25e6 F)i(c|i\ndi) = 1. Then\nthere exists an index 1 \u2264 j \u2264 m such that Oj(F(c|i\ndi)) = 1 and\n\u03c8j\ni (c|i\ndi) = 1. Remember that hk \u2265 Fk(c|i\ndi) for any k. Thus,\nfrom the fact that O satisfies SMP, when changing the cost vector\nfrom F(c|i\ndi) to h|j\nFj(c|i\ndi), we still have Oj(h|j\nFj(c|i\ndi)) =\n1. This implies that\nFj(c|i\ndi) < \u03c4j.\nCombining the above inequality and the fact that Fj(c|i\nc|i\ndi) <\nhj, we have Fj(c|i\ndi) < min{hj, \u03c4j}. This implies\ndi < F\u22121\nj (min{hj, \u03c4j}) = \u03bai,j < \u03bai(O \u25e6 F, c\u2212i).\nwhich is a contradiction. This finishes our proof.\nIn most applications, the allocation rule \u03c8j\nimplements the\nobjective function fj and fj is utilitarian. Thus, we can compute\nthe inverse of F\u22121\nj efficiently. Another issue is that it seems the\nconditions when we can apply Algorithm 6 are restrictive.\nHowever, lots of games in practice satisfy these properties and here we\nshow how to deduct the MAX combination in [13]. Assume A1\nand A2 are two allocation rules for single minded combinatorial\nauction, then the combination MAX(A1, A2) returns the\nallocation with the larger welfare. If algorithm A1 and A2 satisfy MP and\nFMP, the operation max(x, y) which returns the larger element of\nx and y satisfies SMP. From Theorem 9 we obtain that\ncombination MAX(A1, A2) also satisfies MP. Further, the cut value of the\nMAX combination can be found by Algorithm 6. As we will show\nin Section 5, the complex combination can apply to some more\ncomplicated problems.\n5. CONCRETE EXAMPLES\n5.1 Set Cover\nIn the set cover problem, there is a set U of m elements needed\nto be covered, and each agent 1 \u2264 i \u2264 n can cover a subset of\nelements Si with a cost ci. Let S = {S1, S2, \u00b7 \u00b7 \u00b7 , Sn} and c =\n(c1, c2, \u00b7 \u00b7 \u00b7 , cn). We want to find a subset of agents D such that\nU \u2286\nS\ni\u2208D Si. The selected subsets is called the set cover for\nU. The social efficiency of the output D is defined as\nP\ni\u2208D ci,\nwhich is the objective function to be minimized. Clearly, this is\na utilitarian and thus VCG mechanism can be applied if we can\nfind the subset of S that covers U with the minimum cost. It is\nwell-known that finding the optimal solution is NP-hard. In [4], an\nalgorithm of approximation ratio of Hm has been proposed and it\nhas been proved that this is the best ratio possible for the set cover\nproblem. For the completeness of presentation, we review their\nmethod here.\nAlgorithm 7 Greedy Set Cover (GSC)\nInput: Agent i\"s subset Si covered and cost ci. (1 \u2264 i \u2264 n).\nOutput: A set of agents that can cover all elements.\n1: Initialize r = 1, T0 = \u2205, and R = \u2205.\n2: while R = U do\n3: Find the set Sj with the minimum density\ncj\n|Sj \u2212Tr|\n.\n4: Set Tr+1 = Tr\nS\nSj and R = R\nS\nj.\n5: r = r + 1\n6: Output R.\nLet GSC(S) be the sets selected by the Algorithm 7.Notice that\nthe output set is a function of S and c. Some works assume that\nthe type of an agent could be ci, i.e., Si is assumed to be a\npublic knowledge. Here, we consider a more general case in which\nthe type of an agent is (Si, ci). In other words, we assume that\nevery agent i can not only lie about its cost ci but also can lie about\nthe set Si. This problem now looks similar to the combinatorial\nauction with single minded bidder studied in [12], but with the\nfollowing differences: in the set cover problem we want to cover all\nthe elements and the sets chosen can have some overlap while in\ncombinatorial auction the chosen sets are disjoint.\nWe can show that the mechanism M = (GSC, PV CG\n), using\nAlgorithm 7 to find a set cover and apply VCG mechanism to\ncompute the payment to the selected agents, is not truthful. Obviously,\nthe set cover problem is a binary demand game. For the moment,\nwe assume that agent i won\"t be able to lie about Si. We will drop\nthis assumption later. We show how to design a truthful mechanism\nby applying our general framework.\n1. Check the monotonicity property: The output of\nAlgorithm 7 is a round-based output. Thus, for an agent i, we\nfirst focus on the output of one round r. In round r, if i is\nselected by Algorithm 7, then it has the minimum ratio ci\n|Si\u2212Tr|\namong all remaining agents. Now consider the case when i\nlies its cost to ci < ci, obviously\nci\n|Si\u2212Tr|\nis still minimum\namong all remaining agents. Consequently, agent i is still\nselected in round r, which means the output of round r satisfies\nMP. Now we look into the updating rules. For every round,\nwe only update the Tr+1 = Tr\nS\nSj and R = R\nS\nj, which\nis obviously cross-independent. Thus, by applying Theorem\n8, we know the output by Algorithm 7 satisfies MP.\n2. Find the cut value: To calculate the cut value for agent i\nwith fixed cost vector c\u2212i, we follow the steps in Algorithm\n4. First, we set ci = \u221e and apply Algorithm 7. Let ir be the\nagent selected in round r and T\u2212i\nr+1 be the corresponding set.\nThen the cut value of round r is\nr =\ncir\n|Sir \u2212 T\u2212i\nr |\n\u00b7 |Si \u2212 T\u2212i\nr |.\nRemember the updating rule only updates the game setting\nbut not the cost of the agent, thus we have gr(x) = x \u2265 r\nfor 1 \u2264 r \u2264 t. Therefore, the final cut value for agent i is\n\u03bai(GSC, c\u2212i) = max\nr\n{\ncir\n|Sir \u2212 T\u2212i\nr |\n\u00b7 |Si \u2212 T\u2212i\nr |}\nThe payment to an agent i is \u03bai if i is selected; otherwise its\npayment is 0.\nWe now consider the scenario when agent i can lie about Si.\nAssume that agent i cannot lie upward, i.e., it can only report a set\nSi \u2286 Si. We argue that agent i will not lie about its elements Si.\nNotice that the cut value computed for round r is r\n=\ncir\n|Sir \u2212T \u2212i\nr |\n\u00b7\n|Si \u2212 T\u2212i\nr |. Obviously |Si \u2212 T\u2212i\nr | \u2264 |Si \u2212 T\u2212i\nr | for any Si \u2286 Si.\nThus, lying its set as Si will not increase the cut value for each\nround. Thus lying about Si will not improve agent i\"s utility.\n5.2 Link Weighted Steiner Trees\nConsider any link weighted network G = (V, E, c), where E =\n{e1, e2, \u00b7 \u00b7 \u00b7 , em} are the set of links and ci is the weight of the link\nei. The link weighted Steiner tree problem is to find a tree rooted at\nsource node s spanning a given set of nodes Q = {q1, q2, \u00b7 \u00b7 \u00b7 , qk} \u2282\nV . For simplicity, we assume that qi = vi, for 1 \u2264 i \u2264 k. Here\nthe links are agents. The total cost of links in a graph H \u2286 G is\ncalled the weight of H, denoted as \u03c9(H). It is NP-hard to find the\nminimum cost multicast tree when given an arbitrary link weighted\n220\ngraph G [17, 20]. The currently best polynomial time method has\napproximation ratio 1 + ln 3\n2\n[17]. Here, we review and discuss the\nfirst approximation method by Takahashi and Matsuyama [20].\nAlgorithm 8 Find LinkWeighted SteinerTree (LST)\nInput: Network G = (V, E, c) where c is the cost vector for link\nset E. Source node s and receiver set Q.\nOutput: A tree LST rooted at s and spanned all receivers.\n1: Set r = 1, G1 = G, Q1\n= Q and s1\n= s.\n2: repeat\n3: In graph Gr, find the receiver, say qi, that is closest to the\nsource s, i.e., LCP(s, qi, c) has the least cost among the\nshortest paths from s to all receivers in Qr\n.\n4: Select all links on LCP(s, qi, c) as relay links and set their\ncost to 0. The new graph is denoted as Gr+1.\n5: Set tr as qi and Pr = LCP(s, qi, c).\n6: Set Qr+1\n= Qr\n\\qi and r = r + 1.\n7: until all receivers are spanned.\nHereafter, let LST(G) be the final tree constructed using the\nabove method. It is shown in [24] that mechanism M = (LST, pV CG\n)\nis not truthful, where pV CG\nis the payment calculated based on\nVCG mechanism.\nWe then show how to design a truthful payment scheme\nusing our general framework. Observe that the output Pr, for any\nround r, satisfies MP, and the update rule for every round\nsatisfies crossing-independence. Thus, from Theorem 8, the\nroundbased output LST satisfies MP. In round r, the cut value for a\nlink ei can be obtained by using the VCG mechanism. Now we\nset ci = \u221e and execute Algorithm 8. Let w\u2212i\nr (ci) be the cost of\nthe path Pr(ci) selected in the rth round and \u03a0i\nr(ci) be the\nshortest path selected in round r if the cost of ci is temporarily set to\n\u2212\u221e. Then the cut value for round r is r = wi\nr(c\u2212i) \u2212 |\u03a0i\nr(c\u2212i)|\nwhere |\u03a0i\nr(c\u2212i)| is the cost of the path \u03a0i\nr(c\u2212i) excluding node\nvi. Using Algorithm 4, we obtain the final cut value for agent i:\n\u03bai(LST, c\u2212i) = maxr{ r}. Thus, the payment to a link ei is\n\u03bai(LST, c\u2212i) if its reported cost is di < \u03bai(LST, d\u2212i);\notherwise, its payment is 0.\n5.3 Virtual Minimal Spanning Trees\nTo connect the given set of receivers to the source node, besides\nthe Steiner tree constructed by the algorithms described before, a\nvirtual minimum spanning tree is also often used. Assume that Q is\nthe set of receivers, including the sender. Assume that the nodes in\na node-weighted graph are all agents. The virtual minimum\nspanning tree is constructed as follows.\nAlgorithm 9 Construct VMST\n1: for all pairs of receivers qi, qj \u2208 Q do\n2: Calculate the least cost path LCP(qi, qj, d).\n3: Construct a virtual complete link weighted graph K(d)\nusing Q as its node set, where the link qiqj corresponds to the\nleast cost path LCP(qi, qj, d), and its weight is w(qiqj) =\n|LCP(qi, qj, d)|.\n4: Build the minimum spanning tree on K(d), denoted as\nV MST(d).\n5: for every virtual link qiqj in V MST(d) do\n6: Find the corresponding least cost path LCP(qi, qj, d) in the\noriginal network.\n7: Mark the agents on LCP(qi, qj, d) selected.\nThe mechanism M = (V MST, pV CG\n) is not truthful [24],\nwhere the payment pV CG\nto a node is based on the VCG\nmechanism. We then show how to design a truthful mechanism based on\nthe framework we described.\n1. Check the monotonicity property: Remember that in the\ncomplete graph K(d), the weight of a link qiqj is |LCP(qi, qj, d)|.\nIn other words, we implicitly defined |Q|(|Q| \u2212 1)/2\nfunctions fi,j, for all i < j and qi \u2208 Q and qj \u2208 Q, with\nfi,j(d) = |LCP(qi, qj, d)|. We can show that the function\nfi,j(d) = |LCP(qi, qj, d)| satisfies FMP, LCP satisfies MP,\nand the output MST satisfies SMP. From Theorem 9, the\nallocation rule VMST satisfies the monotonicity property.\n2. Find the cut value: Notice VMST is the combination of\nMST and function fi,j, so cut value for VMST can be\ncomputed based on Algorithm 6 as follows.\n(a) Given a link weighted complete graph K(d) on Q, we\nshould find the cut value function for edge ek = (qi, qj)\nbased on MST. Given a spanning tree T and a pair of\nterminals p and q, clearly there is a unique path\nconnecting them on T. We denote this path as \u03a0T (p, q),\nand the edge with the maximum length on this path as\nLE(p, q, T). Thus, the cut value can be represented as\n\u03bak(MST, d) = LE(qi, qj, MST(d|k\n\u221e))\n(b) We find the value-cost function for LCP. Assume vk \u2208\nLCP(qi, qj, d), then the value-cost function is xk =\nyk \u2212 |LCPvk (qi, qj, d|k\n0)|. Here, LCPvk (qi, qj, d) is\nthe least cost path between qi and qj with node vk on\nthis path.\n(c) Remove vk and calculate the value K(d|k\n\u221e). Set h(i,j) =\n|LCP(qi, qj, d|\u221e\n))| for every pair of node i = j and\nlet h = {h(i,j)} be the vector. Then it is easy to\nshow that \u03c4(i,j) = |LE(qi, qj, MST(h|(i,j)\n\u221e))| is\nthe cut value for output VMST. It easy to verify that\nmin{h(i,j), \u03c4(i,j)} = |LE(qi, qj, MST(h)|. Thus,\nwe know \u03ba\n(i,j)\nk (V MST, d) is |LE(qi, qj, MST(h)|\u2212\n|LCPvk (qi, qj, d|k\n0)|. The cut value for agent k is\n\u03bak(V MST, d\u2212k) = max0\u2264i,j\u2264r \u03baij\nk (V MST, d\u2212k).\n3. We pay agent k \u03bak(V MST, d\u2212k) if and only if k is selected\nin V MST(d); else we pay it 0.\n5.4 Combinatorial Auctions\nLehmann et al. [12] studied how to design an efficient truthful\nmechanism for single-minded combinatorial auction. In a\nsingleminded combinatorial auction, there is a set of items S to be sold\nand there is a set of agents 1 \u2264 i \u2264 n who wants to buy some of\nthe items: agent i wants to buy a subset Si \u2286 S with maximum\nprice mi. A single-minded bidder i declares a bid bi = Si, ai\nwith Si \u2286 S and ai \u2208 R+\n. Two bids Si, ai and Sj, aj conflict\nif Si \u2229 Sj = \u2205. Given the bids b1, b2, \u00b7 \u00b7 \u00b7 , bn, they gave a greedy\nround-based algorithm as follows. First the bids are sorted by some\ncriterion ( ai\n|Si|1/2 is used in[12]) in an increasing order and let L be\nthe list of sorted bids. The first bid is granted. Then the algorithm\nexams each bid of L in order and grants the bid if it does not conflict\nwith any of the bids previously granted. If it does, it is denied. They\nproved that this greedy allocation scheme using criterion ai\n|Si|1/2\napproximates the optimal allocation within a factor of\n\u221a\nm, where\nm is the number of goods in S.\nIn the auction settings, we have ci = \u2212ai. It is easy to verify the\noutput of the greedy algorithm is a round-based output.\nRemember after bidder j is selected for round r, every bidder has conflict\n221\nwith j will not be selected in the rounds after. This equals to\nupdate the cost of every bidder having conflict with j to 0, which\nsatisfies crossing-independence. In addition, in any round, if\nbidder i is selected with ai then it will still be selected when it\ndeclares ai > ai. Thus, for every round, it satisfies MP and the\ncut value is |Si|1/2\n\u00b7\najr\n|Sjr |1/2 where jr is the bidder selected in\nround r if we did not consider the agent i at all. Notice\najr\n|Sjr |1/2\ndoes not increase when round r increases, so the final cut value\nis |Si|1/2\n\u00b7\naj\n|Sj |1/2 where bj is the first bid that has been denied\nbut would have been selected were it not only for the presence\nof bidder i. Thus, the payment by agent i is |Si|1/2\n\u00b7\naj\n|Sj |1/2 if\nai \u2265 |Si|1/2\n\u00b7\naj\n|Sj |1/2 , and 0 otherwise. This payment scheme is\nexactly the same as the payment scheme in [12].\n6. CONCLUSIONS\nIn this paper, we have studied how to design a truthful\nmechanism M = (O, P) for a given allocation rule O for a binary\ndemand game. We first showed that the allocation rule O\nsatisfying the MP is a necessary and sufficient condition for a truthful\nmechanism M to exist. We then formulate a general framework\nfor designing payment P such that the mechanism M = (O, P) is\ntruthful and computable in polynomial time. We further presented\nseveral general composition-based techniques to compute P\nefficiently for various allocation rules O. Several concrete examples\nwere discussed to demonstrate our general framework for\ndesigning P and for composition-based techniques of computing P in\npolynomial time.\nIn this paper, we have concentrated on how to compute P in\npolynomial time. Our algorithms do not necessarily have the\noptimal running time for computing P given O. It would be of interest\nto design algorithms to compute P in optimal time. We have made\nsome progress in this research direction in [22] by providing an\nalgorithm to compute the payments for unicast in a node weighted\ngraph in optimal O(n log n + m) time.\nAnother research direction is to design an approximation\nallocation rule O satisfying MP with a good approximation ratio for a\ngiven binary demand game. Many works [12, 13] in the mechanism\ndesign literature are in this direction. We point out here that the\ngoal of this paper is not to design a better allocation rule for a\nproblem, but to design an algorithm to compute the payments efficiently\nwhen O is given. It would be of significance to design allocation\nrules with good approximation ratios such that a given binary\ndemand game has a computationally efficient payment scheme.\nIn this paper, we have studied mechanism design for binary\ndemand games. However, some problems cannot be directly\nformulated as binary demand games. The job scheduling problem in [2]\nis such an example. For this problem, a truthful payment scheme P\nexists for an allocation rule O if and only if the workload assigned\nby O is monotonic in a certain manner. It wound be of interest to\ngeneralize our framework for designing a truthful payment scheme\nfor a binary demand game to non-binary demand games. Towards\nthis research direction, Theorem 4 can be extended to a general\nallocation rule O, whose range is R+\n. The remaining difficulty is\nthen how to compute the payment P under mild assumptions about\nthe valuations if a truthful mechanism M = (O, P) does exist.\nAcknowledgements\nWe would like to thank Rakesh Vohra, Tuomas Sandholm, and\nanonymous reviewers for helpful comments and discussions.\n7. REFERENCES\n[1] A. ARCHER, C. PAPADIMITRIOU, K. T., AND TARDOS, E. An\napproximate truthful mechanism for combinatorial auctions with\nsingle parameter agents. In ACM-SIAM SODA (2003), pp. 205-214.\n[2] ARCHER, A., AND TARDOS, E. Truthful mechanisms for\none-parameter agents. In Proceedings of the 42nd IEEE FOCS\n(2001), IEEE Computer Society, p. 482.\n[3] AULETTA, V., PRISCO, R. D., PENNA, P., AND PERSIANO, P.\nDeterministic truthful approximation schemes for scheduling related\nmachines.\n[4] CHVATAL, V. A greedy heuristic for the set covering problem.\nMathematics of Operations Research 4, 3 (1979), 233-235.\n[5] CLARKE, E. H. Multipart pricing of public goods. Public Choice\n(1971), 17-33.\n[6] R. Muller, and R. V. Vohra. On Dominant Strategy Mechanisms.\nWorking paper, 2003.\n[7] DEVANUR, N. R., MIHAIL, M., AND VAZIRANI, V. V.\nStrategyproof cost-sharing mechanisms for set cover and facility\nlocation games. In ACM Electronic Commerce (EC03) (2003).\n[8] FEIGENBAUM, J., KRISHNAMURTHY, A., SAMI, R., AND\nSHENKER, S. Approximation and collusion in multicast cost sharing\n(abstract). In ACM Economic Conference (2001).\n[9] FEIGENBAUM, J., PAPADIMITRIOU, C., SAMI, R., AND SHENKER,\nS. A BGP-based mechanism for lowest-cost routing. In Proceedings\nof the 2002 ACM Symposium on Principles of Distributed\nComputing. (2002), pp. 173-182.\n[10] GREEN, J., AND LAFFONT, J. J. Characterization of satisfactory\nmechanisms for the revelation of preferences for public goods.\nEconometrica (1977), 427-438.\n[11] GROVES, T. Incentives in teams. Econometrica (1973), 617-631.\n[12] LEHMANN, D., OCALLAGHAN, L. I., AND SHOHAM, Y. Truth\nrevelation in approximately efficient combinatorial auctions. Journal\nof ACM 49, 5 (2002), 577-602.\n[13] MU\"ALEM, A., AND NISAN, N. Truthful approximation\nmechanisms for restricted combinatorial auctions: extended abstract.\nIn 18th National Conference on Artificial intelligence (2002),\nAmerican Association for Artificial Intelligence, pp. 379-384.\n[14] NISAN, N., AND RONEN, A. Algorithmic mechanism design. In\nProc. 31st Annual ACM STOC (1999), pp. 129-140.\n[15] E. Halperin. Improved approximation algorithms for the vertex cover\nproblem in graphs and hypergraphs. In Proceedings of the 11th\nAnnual ACM-SIAM Symposium on Discrete Algorithms, pages\n329-337, 2000.\n[16] R. Bar-Yehuda and S. Even. A local ratio theorem for approximating\nthe weighted vertex cover problem. Annals of Discrete Mathematics,\nVolume 25: Analysis and Design of Algorithms for Combinatorial\nProblems, pages 27-46, 1985. Editor: G. Ausiello and M. Lucertini\n[17] ROBINS, G., AND ZELIKOVSKY, A. Improved steiner tree\napproximation in graphs. In Proceedings of the 11th annual\nACM-SIAM SODA (2000), pp. 770-779.\n[18] A. Zelikovsky. An 11/6-approximation algorithm for the network\nSteiner problem. Algorithmica, 9(5):463-470, 1993.\n[19] D. S. Hochbaum. Efficient bounds for the stable set, vertex cover, and\nset packing problems, Discrete Applied Mathematics, 6:243-254,\n1983.\n[20] TAKAHASHI, H., AND MATSUYAMA, A. An approximate solution\nfor the steiner problem in graphs. Math. Japonica 24 (1980),\n573-577.\n[21] VICKREY, W. Counterspeculation, auctions and competitive sealed\ntenders. Journal of Finance (1961), 8-37.\n[22] WANG, W., AND LI, X.-Y. Truthful low-cost unicast in selfish\nwireless networks. In 4th IEEE Transactions on Mobile Computing\n(2005), to appear.\n[23] WANG, W., LI, X.-Y., AND SUN, Z. Design multicast protocols for\nnon-cooperative networks. IEEE INFOCOM 2005, to appear.\n[24] WANG, W., LI, X.-Y., AND WANG, Y. Truthful multicast in selfish\nwireless networks. ACM MobiCom, 2005.\n222", "keywords": "mechanism design;cut value function;objective function;monotonicity property;selfish wireless network;price;selfish agent;composition-based technique;demand game;truthful mechanism;pricing;vickrey-clarke-grove;combination;binary demand game"}
{"name": "train_J-59", "title": "Cost Sharing in a Job Scheduling Problem Using the Shapley Value", "abstract": "A set of jobs need to be served by a single server which can serve only one job at a time. Jobs have processing times and incur waiting costs (linear in their waiting time). The jobs share their costs through compensation using monetary transfers. We characterize the Shapley value rule for this model using fairness axioms. Our axioms include a bound on the cost share of jobs in a group, efficiency, and some independence properties on the the cost share of a job.", "fulltext": "1. INTRODUCTION\nA set of jobs need to be served by a server. The server can\nprocess only one job at a time. Each job has a finite\nprocessing time and a per unit time waiting cost. Efficient ordering\nof this queue directs us to serve the jobs in increasing\norder of the ratio of per unit time waiting cost and processing\ntime. To compensate for waiting by jobs, monetary\ntransfers to jobs are allowed. How should the jobs share the cost\nequitably amongst themselves (through transfers)?\nThe problem of fair division of costs among agents in a\nqueue has many practical applications. For example,\ncomputer programs are regularly scheduled on servers, data are\nscheduled to be transmitted over networks, jobs are\nscheduled in shop-floor on machines, and queues appear in many\npublic services (post offices, banks). Study of queueing\nproblems has attracted economists for a long time [7, 17].\nCost sharing is a fundamental problem in many settings\non the Internet. Internet can be seen as a common resource\nshared by many users and the cost incured by using the\nresource needs to be shared in an equitable manner. The\ncurrent surge in cost sharing literature from computer\nscientists validate this claim [8, 11, 12, 6, 24]. Internet has many\nsettings in which our model of job scheduling appears and\nthe agents waiting in a queue incur costs (jobs scheduled on\nservers, queries answered from a database, data scheduled\nto be transmitted over a fixed bandwidth network etc.). We\nhope that our analysis will give new insights on cost sharing\nproblems of this nature.\nRecently, there has been increased interest in cost\nsharing methods with submodular cost functions [11, 12, 6, 24].\nWhile many settings do have submodular cost functions (for\nexample, multi-cast transmission games [8]), while the cost\nfunction of our game is supermodular. Also, such literature\ntypically does not assume budget-balance (transfers adding\nup to zero), while it is an inherent feature of our model.\nA recent paper by Maniquet [15] is the closest to our model\nand is the motivation behind our work 1\n. Maniquet [15]\nstudies a model where he assumes all processing times are\nunity. For such a model, he characterizes the Shapley value\nrule using classical fairness axioms. Chun [1] interprets the\nworth of a coalition of jobs in a different manner for the same\nmodel and derives a reverse rule. Chun characterizes this\nrule using similar fairness axioms. Chun [2] also studies the\nenvy properties of these rules. Moulin [22, 21] studies the\nqueueing problem from a strategic point view when per unit\nwaiting costs are unity. Moulin introduces new concepts in\nthe queueing settings such as splitting and merging of jobs,\nand ways to prevent them.\nAnother stream of literature is on sequencing games,\nfirst introduced by Curiel et al. [4]. For a detailed survey,\nrefer to Curiel et al. [3]. Curiel et al. [4] defined sequencing\ngames similar to our model, but in which an initial ordering\nof jobs is given. Besides, their notion of worth of a coalition\nis very different from the notions studied in Maniquet [15]\nand Chun [1] (these are the notions used in our work too).\nThe particular notion of the worth of a coalition makes the\nsequencing game of Curiel et al. [4] convex, whereas our\ngame is not convex and does not assume the presence of\nany initial order. In summary, the focus of this stream of\n1\nThe authors thank Fran\u00b8cois Maniquet for several fruitful\ndiscussions.\n232\nresearch is how to share the savings in costs from the\ninitial ordering to the optimal ordering amongst jobs (also see\nHamers et al. [9], Curiel et al. [5]). Recently, Klijn and\nS\u00b4anchez [13, 14] considered sequencing games without any\ninitial ordering of jobs. They take two approaches to define\nthe worth of coalitions. One of their approaches, called the\ntail game, is related to the reverse rule of Chun [1]. In the\ntail game, jobs in a coalition are served after the jobs not in\nthe coalition are served. Klijn and S\u00b4anchez [14] showed that\nthe tail game is balanced. Further, they provide expressions\nfor the Shapley value in tail game in terms of marginal\nvectors and reversed marginal vectors. We provide a simpler\nexpression of the Shapley value in the tail game,\ngeneralizing the result in Chun [1]. Klijn and S\u00b4anchez [13] study the\ncore of this game in detail.\nStrategic aspects of queueing problems have also been\nresearched. Mitra [19] studies the first best implementation\nin queueing models with generic cost functions. First best\nimplementation means that there exists an efficient\nmechanism in which jobs in the queue have a dominant strategy\nto reveal their true types and their transfers add up to zero.\nSuijs [27] shows that if waiting costs of jobs are linear then\nfirst best implementation is possible. Mitra [19] shows that\namong a more general class of queueing problems first best\nimplementation is possible if and only if the cost is linear.\nFor another queueing model, Mitra [18] shows that first best\nimplementation is possible if and only if the cost function\nsatisfies a combinatorial property and an independence\nproperty. Moulin [22, 21] studies strategic concepts such as\nsplitting and merging in queueing problems with unit per unit\nwaiting costs.\nThe general cost sharing literature is vast and has a long\nhistory. For a good survey, we refer to [20]. From the\nseminal work of Shapley [25] to recent works on cost sharing in\nmulti-cast transmission and optimization problems [8, 6, 23]\nthis area has attracted economists, computer scientists, and\noperations researchers.\n1.1 Our Contribution\nOurs is the first model which considers cost sharing when\nboth processing time and per unit waiting cost of jobs are\npresent. We take a cooperative game theory approach and\napply the classical Shapley value rule to the problem. We\nshow that the Shapley value rule satisfies many intuitive\nfairness axioms. Due to two dimensional nature of our model\nand one dimensional nature of Maniquet\"s model [15], his\naxioms are insufficient to characterize the Shapley value in\nour setting. We introduce axioms such as independece of\npreceding jobs\" unit waiting cost and independence of following\njobs\" processing time. A key axiom that we introduce gives\nus a bound on cost share of a job in a group of jobs which\nhave the same ratio of unit time waiting cost and\nprocessing time (these jobs can be ordered in any manner between\nthemseleves in an efficient ordering). If such a group consists\nof just one job, then the axiom says that such a job should\nat least pay his own processing cost (i.e., the cost it would\nhave incurred if it was the only job in the queue). If there\nare multiple jobs in such a group, the probability of any two\njobs from such a group inflicting costs on each other is same\n(1\n2\n) in an efficient ordering. Depending on the ordering\nselected, one job inflicts cost on the other. Our fairness axiom\nsays that each job should at least bear such expected costs.\nWe characterize the Shapley value rule using these fairness\naxioms. We also extend the envy results in [2] to our setting\nand discuss a class of reasonable cost sharing mechanisms.\n2. THE MODEL\nThere are n jobs that need to be served by one server\nwhich can process only one job at a time. The set of jobs\nare denoted as N = {1, . . . , n}. \u03c3 : N \u2192 N is an ordering of\njobs in N and \u03c3i denotes the position of job i in the ordering\n\u03c3. Given an ordering \u03c3, define Fi(\u03c3) = {j \u2208 N : \u03c3i < \u03c3j}\nand Pi(\u03c3) = {j \u2208 N : \u03c3i > \u03c3j}.\nEvery job i is identified by two parameters: (pi, \u03b8i). pi\nis the processing time and \u03b8i is the cost per unit waiting\ntime of job i. Thus, a queueing problem is defined by a list\nq = (N, p, \u03b8) \u2208 Q, where Q is the set of all possible lists. We\nwill denote \u03b3i = \u03b8i\npi\n. Given an ordering of jobs \u03c3, the cost\nincurred by job i is given by\nci(\u03c3) = pi\u03b8i + \u03b8i\n\nj\u2208Pi(\u03c3)\npj.\nThe total cost incurred by all jobs due to an ordering \u03c3\ncan be written in two ways: (i) by summing the cost incurred\nby every job and (ii) by summing the costs inflicted by a job\non other jobs with their own processing cost.\nC(N, \u03c3) =\n\ni\u2208N\nci(\u03c3) =\n\ni\u2208N\npi\u03b8i +\n\ni\u2208N\n\u00a1\u03b8i\n\nj\u2208Pi(\u03c3)\npj\u00a2.\n=\n\ni\u2208N\npi\u03b8i +\n\ni\u2208N\n\u00a1pi\n\nj\u2208Fi(\u03c3)\n\u03b8j\u00a2.\nAn efficient ordering \u03c3\u2217\nis the one which minimizes the\ntotal cost incurred by all jobs. So, C(N, \u03c3\u2217\n) \u2264 C(N, \u03c3) \u2200 \u03c3 \u2208\n\u03a3. To achieve notational simplicity, we will write the total\ncost in an efficient ordering of jobs from N as C(N)\nwhenever it is not confusing. Sometimes, we will deal with only\na subset of jobs S \u2286 N. The ordering \u03c3 will then be\ndefined on jobs in S only and we will write the total cost from\nan efficient ordering of jobs in S as C(S). The following\nlemma shows that jobs are ordered in decreasing \u03b3 in an\nefficient ordering. This is also known as the weighted shortest\nprocessing time rule, first introduced by Smith [26].\nLemma 1. For any S \u2286 N, let \u03c3\u2217\nbe an efficient ordering\nof jobs in S. For every i = j, i, j \u2208 S, if \u03c3\u2217\ni > \u03c3\u2217\nj , then\n\u03b3i \u2264 \u03b3j.\nProof. Assume for contradiction that the statment of\nthe lemma is not true. This means, we can find two\nconsecutive jobs i, j \u2208 S (\u03c3\u2217\ni = \u03c3\u2217\nj + 1) such that \u03b3i > \u03b3j.\nDefine a new ordering \u03c3 by interchanging i and j in \u03c3\u2217\n.\nThe costs to jobs in S \\ {i, j} is not changed from \u03c3\u2217\nto \u03c3.\nThe difference between total costs in \u03c3\u2217\nand \u03c3 is given by,\nC(S, \u03c3) \u2212 C(S, \u03c3\u2217\n) = \u03b8jpi \u2212 \u03b8ipj. From efficiency we get\n\u03b8jpi \u2212 \u03b8ipj \u2265 0. This gives us \u03b3j \u2265 \u03b3i, which is a\ncontradiction.\nAn allocation for q = (N, p, \u03b8) \u2208 Q has two components:\nan ordering \u03c3 and a transfer ti for every job i \u2208 N. ti\ndenotes the payment received by job i. Given a transfer ti\nand an ordering \u03c3, the cost share of job i is defined as,\n\u03c0i = ci(\u03c3) \u2212 ti = \u03b8i\n\nj\u2208N:\u03c3j \u2264\u03c3i\npj \u2212 ti.\n233\nAn allocation (\u03c3, t) is efficient for q = (N, p, \u03b8) whenever\n\u03c3 is an efficient ordering and \u00a3i\u2208N ti = 0. The set of\nefficient orderings of q is denoted as \u03a3\u2217\n(q) and \u03c3\u2217\n(q) will be\nused to refer to a typical element of the set. The following\nstraightforward lemma says that for two different efficient\norderings, the cost share in one efficient allocation is\npossible to achieve in the other by appropriately modifying the\ntransfers.\nLemma 2. Let (\u03c3, t) be an efficient allocation and \u03c0 be the\nvector of cost shares of jobs from this allocation. If \u03c3\u2217\n= \u03c3\nbe an efficient ordering and t\u2217\ni = ci(\u03c3\u2217\n) \u2212 \u03c0i \u2200 i \u2208 N, then\n(\u03c3\u2217\n, t\u2217\n) is also an efficient allocation.\nProof. Since (\u03c3, t) is efficient, \u00a3i\u2208N ti = 0. This gives\n\u00a3i\u2208N \u03c0i = C(N). Since \u03c3\u2217\nis an efficient ordering, \u00a3i\u2208N ci(\u03c3\u2217\n) =\nC(N). This means, \u00a3i\u2208N t\u2217\ni = \u00a3i\u2208N [ci(\u03c3\u2217\n) \u2212 \u03c0i] = 0. So,\n(\u03c3\u2217\n, t\u2217\n) is an efficient allocation.\nDepending on the transfers, the cost shares in different\nefficient allocations may differ. An allocation rule \u03c8 associates\nwith every q \u2208 Q a non-empty subset \u03c8(q) of allocations.\n3. COST SHARING USING THE SHAPLEY\nVALUE\nIn this section, we define the coalitional cost of this game\nand analyze the solution proposed by the Shapley value.\nGiven a queue q \u2208 Q, the cost of a coalition of S \u2286 N jobs\nin the queue is defined as the cost incurred by jobs in S if\nthese are the only jobs served in the queue using an efficient\nordering. Formally, the cost of a coalition S \u2286 N is,\nC(S) =\n\ni\u2208S\n\nj\u2208S:\u03c3\u2217\nj \u2264\u03c3\u2217\ni\n\u03b8jpj,\nwhere \u03c3\u2217\n= \u03c3\u2217\n(S) is an efficient ordering considering jobs\nfrom S only. The worth of a coalition of S jobs is just\n\u2212C(S). Maniquet [15] observes another equivalent way to\ndefine the worth of a coalition is using the dual function of\nthe cost function C(\u00b7). Other interesting ways to define the\nworth of a coalition in such games is discussed by Chun [1],\nwho assume that a coalition of jobs are served after the jobs\nnot in the coalition are served.\nThe Shapley value (or cost share) of a job i is defined as,\nSVi =\n\nS\u2286N\\{i}\n|S|!(|N| \u2212 |S| \u2212 1)!\n|N|!\n\u00a1C(S\u222a{i})\u2212C(S)\u00a2. (1)\nThe Shapley value allocation rule says that jobs are ordered\nusing an efficient ordering and transfers are assigned to jobs\nsuch that the cost share of job i is given by Equation 1.\nLemma 3. Let \u03c3\u2217\nbe an efficient ordering of jobs in set\nN. For all i \u2208 N, the Shapley value is given by,\nSVi = pi\u03b8i +\n1\n2\n\u00a1Li + Ri\u00a2,\nwhere Li = \u03b8i \u00a3j\u2208Pi(\u03c3\u2217) pj and Ri = pi \u00a3j\u2208Fi(\u03c3\u2217) \u03b8j.\nProof. Another way to write the Shapley value formula\nis the following [10],\nSVi =\n\nS\u2286N:i\u2208S\n\u2206(S)\n|S|\n,\nwhere \u2206(S) = C(S) if |S| = 1 and \u2206(S) = C(S)\u2212\u00a3T S \u2206(T).\nThis gives \u2206({i}) = C({i}) = pi\u03b8i \u2200i \u2208 N. For any i, j \u2208 N\nwith i = j, we have\n\u2206({i, j}) = C({i, j}) \u2212 C({i}) \u2212 C({j})\n= min(pi\u03b8i + pj\u03b8j + pj\u03b8i, pi\u03b8i + pj\u03b8j + pi\u03b8j)\n\u2212 pi\u03b8i \u2212 pj\u03b8j\n= min(pj\u03b8i, pi\u03b8j).\nWe will show by induction that \u2206(S) = 0 if |S| > 2. For\n|S| = 3, let S = {i, j, k}. Without loss of generality, assume\n\u03b8i\npi\n\u2265\n\u03b8j\npj\n\u2265 \u03b8k\npk\n. So, \u2206(S) = C(S) \u2212 \u2206({i, j}) \u2212 \u2206({j, k}) \u2212\n\u2206({i, k})\u2212\u2206({i})\u2212\u2206({j})\u2212\u2206({k}) = C(S)\u2212pi\u03b8j \u2212pj\u03b8k \u2212\npi\u03b8k \u2212 pi\u03b8i \u2212 pj\u03b8j \u2212 pk\u03b8k = C(S) \u2212 C(S) = 0.\nNow, assume for T S, \u2206(T) = 0 if |T| > 2. Without\nloss of generality assume that \u03c3 to be the identity mapping.\nNow,\n\u2206(S) = C(S) \u2212\n\nT S\n\u2206(T)\n= C(S) \u2212\n\ni\u2208S\n\nj\u2208S:j<i\n\u2206({i, j}) \u2212\n\ni\u2208S\n\u2206({i})\n= C(S) \u2212\n\ni\u2208S\n\nj\u2208S:j<i\npj\u03b8i \u2212\n\ni\u2208S\npi\u03b8i\n= C(S) \u2212 C(S) = 0.\nThis proves that \u2206(S) = 0 if |S| > 2. Using the Shapley\nvalue formula now,\nSVi =\n\nS\u2286N:i\u2208S\n\u2206(S)\n|S|\n= \u2206({i}) +\n1\n2\n\nj\u2208N:j=i\n\u2206({i, j})\n= pi\u03b8i +\n1\n2\n\u00a1\nj<i\n\u2206({i, j}) +\n\nj>i\n\u2206({i, j})\u00a2\n= pi\u03b8i +\n1\n2\n\u00a1\nj<i\npj\u03b8i +\n\nj>i\npi\u03b8j\u00a2= pi\u03b8i +\n1\n2\n\u00a1Li + Ri\u00a2.\n4. AXIOMATICCHARACTERIZATIONOF\nTHE SHAPLEY VALUE\nIn this section, we will define serveral axioms on fairness\nand characterize the Shapley value using them. For a given\nq \u2208 Q, we will denote \u03c8(q) as the set of allocations from\nallocation rule \u03c8. Also, we will denote the cost share vector\nassociated with an allocation rule (\u03c3, t) as \u03c0 and that with\nallocation rule (\u03c3 , t ) as \u03c0 etc.\n4.1 The Fairness Axioms\nWe will define three types of fairness axioms: (i) related\nto efficiency, (ii) related to equity, and (iii) related to\nindependence.\nEfficiency Axioms\nWe define two types of efficiency axioms. One related to\nefficiency which states that an efficient ordering should be\nselected and the transfers of jobs should add up to zero\n(budget balance).\nDefinition 1. An allocation rule \u03c8 satisfies efficiency if\nfor every q \u2208 Q and (\u03c3, t) \u2208 \u03c8(q), (\u03c3, t) is an efficient\nallocation.\n234\nThe second axiom related to efficiency says that the\nallocation rule should not discriminate between two allocations\nwhich are equivalent to each other in terms of cost shares of\njobs.\nDefinition 2. An allocation rule \u03c8 satisfies Pareto\nindifference if for every q \u2208 Q, (\u03c3, t) \u2208 \u03c8(q), and (\u03c3 , t ) \u2208 \u03a3(q),\nwe have\n\u00a1\u03c0i = \u03c0i \u2200 i \u2208 N\u00a2\u21d2\n\u00a1(\u03c3 , t ) \u2208 \u03c8(q)\u00a2.\nAn implication of Pareto indifference axiom and Lemma\n2 is that for every efficient ordering there is some set of\ntransfers of jobs such that it is part of an efficient rule and\nthe cost share of a job in all these allocations are same.\nEquity Axioms\nHow should the cost be shared between two jobs if the jobs\nhave some kind of similarity between them? Equity axioms\nprovide us with fairness properties which help us answer\nthis question. We provide five such axioms. Some of these\naxioms (for example anonymity, equal treatment of equals)\nare standard in the literature, while some are new.\nWe start with a well known equity axiom called anonymity.\nDenote \u03c1 : N \u2192 N as a permutation of elements in N. Let\n\u03c1(\u03c3, t) denote the allocation obtained by permuting elements\nin \u03c3 and t according to \u03c1. Similarly, let \u03c1(p, \u03b8) denote the\nnew list of (p, \u03b8) obtained by permuting elements of p and \u03b8\naccording to \u03c1. Our first equity axiom states that allocation\nrules should be immune to such permutation of data.\nDefinition 3. An allocation rule \u03c8 satisfies anonymity if\nfor all q \u2208 Q, (\u03c3, t) \u2208 \u03c8(q) and every permutation \u03c1, we then\n\u03c1(\u03c3, t) \u2208 \u03c8(N, \u03c1(q)).\nThe next equity axiom is classical in literature and says\nthat two similar jobs should be compensated such that their\ncost shares are equal. This implies that if all the jobs are of\nsame type, then jobs should equally share the total system\ncost.\nDefinition 4. An allocation rule \u03c8 satisfies equal\ntreatment of equals (ETE) if for all q \u2208 Q, (\u03c3, t) \u2208 \u03c8(q),\ni, j \u2208 N, then\n\u00a1pi = pj; \u03b8i = \u03b8j\u00a2\u21d2\n\u00a1\u03c0i = \u03c0j\u00a2.\nETE directs us to share costs equally between jobs if they\nare of the same per unit waiting cost and processing time.\nBut it is silent about the cost shares of two jobs i and j\nwhich satisfy \u03b8i\npi\n=\n\u03b8j\npj\n. We introduce a new axiom for this.\nIf an efficient rule chooses \u03c3 such that \u03c3i < \u03c3j for some\ni, j \u2208 N, then job i is inflicting a cost of pi\u03b8j on job j\nand job j is inflicting zero cost on job i. Define for some\n\u03b3 \u2265 0, S(\u03b3) = {i \u2208 N : \u03b3i = \u03b3}. In an efficient rule, the\nelements in S(\u03b3) can be ordered in any manner (in |S(\u03b3)|!\nways). If i, j \u2208 S(\u03b3) then we have pj\u03b8i = pi\u03b8j. Probability\nof \u03c3i < \u03c3j is 1\n2\nand so is the probability of \u03c3i > \u03c3j. The\nexpected cost i inflicts on j is 1\n2\npi\u03b8j and j inflicts on i is\n1\n2\npj\u03b8i. Our next fairness axiom says that i and j should\neach be responsible for their own processing cost and this\nexpected cost they inflict on each other. Arguing for every\npair of jobs i, j \u2208 S(\u03b3), we establish a bound on the cost\nshare of jobs in S(\u03b3). We impose this as an equity axiom\nbelow.\nDefinition 5. An allocation rule satisfies expected cost\nbound (ECB) if for all q \u2208 Q, (\u03c3, t) \u2208 \u03c8(q) with \u03c0 being the\nresulting cost share, for any \u03b3 \u2265 0, and for every i \u2208 S(\u03b3),\nwe have\n\u03c0i \u2265 pi\u03b8i +\n1\n2\n\u00a1\nj\u2208S(\u03b3):\u03c3j <\u03c3i\npj\u03b8i +\n\nj\u2208S(\u03b3):\u03c3j >\u03c3i\npi\u03b8j\u00a2.\nThe central idea behind this axiom is that of expected\ncost inflicted. If an allocation rule chooses multiple\nallocations, we can assign equal probabilities of selecting one of\nthe allocations. In that case, the expected cost inflicted by\na job i on another job j in the allocation rule can be\ncalculated. Our axiom says that the cost share of a job should\nbe at least its own processing cost and the total expected\ncost it inflicts on others. Note that the above bound poses\nno constraints on how the costs are shared among different\ngroups. Also observe that if S(\u03b3) contains just one job, ECB\nsays that job should at least bear its own processing cost.\nA direct consequence of ECB is the following lemma.\nLemma 4. Let \u03c8 be an efficient rule which satisfies ECB.\nFor a q \u2208 Q if S(\u03b3) = N, then for any (\u03c3, t) \u2208 \u03c8(q) which\ngives a cost share of \u03c0, \u03c0i = pi\u03b8i + 1\n2\n\u00a1Li + Ri\u00a2\u2200 i \u2208 N.\nProof. From ECB, we get \u03c0i \u2265 pi\u03b8i+1\n2\n\u00a1Li+Ri\u00a2\u2200 i \u2208 N.\nAssume for contradiction that there exists j \u2208 N such that\n\u03c0j > pj\u03b8j + 1\n2\n\u00a1Li + Ri\u00a2. Using efficiency and the fact\nthat \u00a3i\u2208N Li = \u00a3i\u2208N Ri, we get \u00a3i\u2208N \u03c0i = C(N) >\n\u00a3i\u2208N pi\u03b8i + 1\n2\n\u00a3i\u2208N\n\u00a1Li + Ri\u00a2 = C(N). This gives us a\ncontradiction.\nNext, we introduce an axiom about sharing the transfer\nof a job between a set of jobs. In particular, if the last\njob quits the system, then the ordering need not change.\nBut the transfer to the last job needs to be shared between\nthe other jobs. This should be done in proportion to their\nprocessing times because every job influenced the last job\nbased on its processing time.\nDefinition 6. An allocation rule \u03c8 satisfies\nproportionate responsibility of p (PRp) if for all q \u2208 Q, for all\n(\u03c3, t) \u2208 \u03c8(q), k \u2208 N such that \u03c3k = |N|, q = (N \\\n{k}, p , \u03b8 ) \u2208 Q, such that for all i \u2208 N\\{k}: \u03b8i = \u03b8i, pi = pi,\nthere exists (\u03c3 , t ) \u2208 \u03c8(q ) such that for all i \u2208 N \\ {k}:\n\u03c3i = \u03c3i and\nti = ti + tk\npi\n\u00a3j=k pj\n.\nAn analogous fairness axiom results if we remove the job\nfrom the beginning of the queue. Since the presence of the\nfirst job influenced each job depending on their \u03b8 values, its\ntransfer needs to be shared in proportion to \u03b8 values.\nDefinition 7. An allocation rule \u03c8 satisfies\nproportionate responsibility of \u03b8 (PR\u03b8) if for all q \u2208 Q, for all\n(\u03c3, t) \u2208 \u03c8(q), k \u2208 N such that \u03c3k = 1, q = (N \\{k}, p , \u03b8 ) \u2208\nQ, such that for all i \u2208 N \\{k}: \u03b8i = \u03b8i, pi = pi, there exists\n(\u03c3 , t ) \u2208 \u03c8(q ) such that for all i \u2208 N \\ {k}: \u03c3i = \u03c3i and\nti = ti + tk\n\u03b8i\n\u00a3j=k \u03b8j\n.\nThe proportionate responsibility axioms are\ngeneralizations of equal responsibility axioms introduced by\nManiquet [15].\n235\nIndependence Axioms\nThe waiting cost of a job does not depend on the per unit\nwaiting cost of its preceding jobs. Similarly, the waiting cost\ninflicted by a job to its following jobs is independent of the\nprocessing times of the following jobs. These independence\nproperties should be carried over to the cost sharing rules.\nThis gives us two independence axioms.\nDefinition 8. An allocation rule \u03c8 satisfies independence\nof preceding jobs\" \u03b8 (IPJ\u03b8) if for all q = (N, p, \u03b8), q =\n(N, p , \u03b8 ) \u2208 Q, (\u03c3, t) \u2208 \u03c8(q), (\u03c3 , t ) \u2208 \u03c8(q ), if for all\ni \u2208 N \\ {k}: \u03b8i = \u03b8i, pi = pi and \u03b3k < \u03b3k, pk = pk,\nthen for all j \u2208 N such that \u03c3j > \u03c3k: \u03c0j = \u03c0j, where \u03c0 is\nthe cost share in (\u03c3, t) and \u03c0 is the cost share in (\u03c3 , t ).\nDefinition 9. An allocation rule \u03c8 satisfies independence\nof following jobs\" p (IFJp) if for all q = (N, p, \u03b8), q =\n(N, p , \u03b8 ) \u2208 Q, (\u03c3, t) \u2208 \u03c8(q), (\u03c3 , t ) \u2208 \u03c8(q ), if for all\ni \u2208 N \\ {k}: \u03b8i = \u03b8i, pi = pi and \u03b3k > \u03b3k, \u03b8k = \u03b8k,\nthen for all j \u2208 N such that \u03c3j < \u03c3k: \u03c0j = \u03c0j, where \u03c0 is\nthe cost share in (\u03c3, t) and \u03c0 is the cost share in (\u03c3 , t ).\n4.2 The Characterization Results\nHaving stated the fairness axioms, we propose three\ndifferent ways to characterize the Shapley value rule using\nthese axioms. All our characterizations involve efficiency\nand ECB. But if we have IPJ\u03b8, we either need IFJp or PRp.\nSimilarly if we have IFJp, we either need IPJ\u03b8 or PR\u03b8.\nProposition 1. Any efficient rule \u03c8 that satisfies ECB,\nIPJ\u03b8, and IFJp is a rule implied by the Shapley value rule.\nProof. Define for any i, j \u2208 N, \u03b8i\nj = \u03b3ipj and pi\nj =\n\u03b8j\n\u03b3i\n. Assume without loss of generality that \u03c3 is an efficient\nordering with \u03c3i = i \u2200 i \u2208 N.\nConsider the following q = (N, p , \u03b8 ) corresponding to\njob i with pj = pj if j \u2264 i and pj = pi\nj if j > i, \u03b8j = \u03b8i\nj if\nj < i and \u03b8j = \u03b8j if j \u2265 i. Observe that all jobs have the\nsame \u03b3: \u03b3i. By Lemma 2 and efficiency, (\u03c3, t ) \u2208 \u03c8(q ) for\nsome set of transfers t . Using Lemma 4, we get cost share of\ni from (\u03c3, t ) as \u03c0i = pi\u03b8i + 1\n2\n\u00a1Li + Ri\u00a2. Now, for any j < i,\nif we change \u03b8j to \u03b8j without changing processing time, the\nnew \u03b3 of j is \u03b3j \u2265 \u03b3i. Applying IPJ\u03b8, the cost share of job i\nshould not change. Similarly, for any job j > i, if we change\npj to pj without changing \u03b8j, the new \u03b3 of j is \u03b3j \u2264 \u03b3i.\nApplying IFJp, the cost share of job i should not change.\nApplying this procedure for every j < i with IPJ\u03b8 and for\nevery j > i with IFJp, we reach q = (N, p, \u03b8) and the payoff\nof i does not change from \u03c0i. Using this argument for every\ni \u2208 N and using the expression for the Shapley value in\nLemma 3, we get the Shapley value rule.\nIt is possible to replace one of the independence axioms\nwith an equity axiom on sharing the transfer of a job. This\nis shown in Propositions 2 and 3.\nProposition 2. Any efficient rule \u03c8 that satisfies ECB,\nIPJ\u03b8, and PRp is a rule implied by the Shapley value rule.\nProof. As in the proof of Proposition 1, define \u03b8i\nj =\n\u03b3ipj \u2200 i, j \u2208 N. Assume without loss of generality that \u03c3 is\nan efficient ordering with \u03c3i = i \u2200 i \u2208 N.\nConsider a queue with jobs in set K = {1, . . . , i, i + 1},\nwhere i < n. Define q = (K, p, \u03b8 ), where \u03b8j = \u03b8i+1\nj \u2200 j \u2208\nK. Define \u03c3j = \u03c3j \u2200 j \u2208 K. \u03c3 is an efficient ordering\nfor q . By ECB and Lemma 4 the cost share of job i +\n1 in any allocation rule in \u03c8 must be \u03c0i+1 = pi+1\u03b8i+1 +\n1\n2\n\u00a1\u00a3j<i+1 pj\u03b8i+1\u00a2. Now, consider q = (K, p, \u03b8 ) such that\n\u03b8j = \u03b8i\nj \u2200 j \u2264 i and \u03b8i+1 = \u03b8i+1. \u03c3 remains an efficient\nordering in q and by IPJ\u03b8 the cost share of i + 1 remains\n\u03c0i+1. In q = (K \\ {i + 1}, p, \u03b8 ), we can calculate the\ncost share of job i using ECB and Lemma 4 as \u03c0i = pi\u03b8i +\n1\n2\n\u00a3j<i pj\u03b8i. So, using PRp we get the new cost share of job\ni in q as \u03c0i = \u03c0i + ti+1\npi\nj<i+1 pj\n= pi\u03b8i + 1\n2\n\u00a1\u00a3j<i pj\u03b8i +\npi\u03b8i+1\u00a2.\nNow, we can set K = K \u222a {i + 2}. As before, we can\nfind cost share of i + 2 in this queue as \u03c0i+2 = pi+2\u03b8i+2 +\n1\n2\n\u00a1\u00a3j<i+2 pj\u03b8i+2\u00a2. Using PRp we get the new cost share\nof job i in the new queue as \u03c0i = pi\u03b8i + 1\n2\n\u00a1\u00a3j<i pj\u03b8i +\npi\u03b8i+1 + pi\u03b8i+2\u00a2. This process can be repeated till we add\njob n at which point cost share of i is pi\u03b8i + 1\n2\n\u00a1\u00a3j<i pj\u03b8i +\n\u00a3j>i pi\u03b8j\u00a2. Then, we can adjust the \u03b8 of preceding jobs of\ni to their original value and applying IPJ\u03b8, the payoffs of\njobs i through n will not change. This gives us the Shapley\nvalues of jobs i through n. Setting i = 1, we get cost shares\nof all the jobs from \u03c8 as the Shapley value.\nProposition 3. Any efficient rule \u03c8 that satisfies ECB,\nIFJp, and PR\u03b8 is a rule implied by the Shapley value rule.\nProof. The proof mirrors the proof of Proposition 2. We\nprovide a short sketch. Analogous to the proof of\nProposition 2, \u03b8s are kept equal to original data and processing times\nare initialized to pi+1\nj . This allows us to use IFJp. Also,\ncontrast to Proposition 2, we consider K = {i, i + 1, . . . , n} and\nrepeatedly add jobs to the beginning of the queue\nmaintaining the same efficient ordering. So, we add the cost\ncomponents of preceding jobs to the cost share of jobs in each\niteration and converge to the Shapley value rule.\nThe next proposition shows that the Shapley value rule\nsatisfies all the fairness axioms discussed.\nProposition 4. The Shapley value rule satisfies efficiency,\npareto indifference, anonymity, ETE, ECB, IPJ\u03b8, IFJp, PRp,\nand PR\u03b8.\nProof. The Shapley value rule chooses an efficient\nordering and by definition the payments add upto zero. So, it\nsatisfies efficiency.\nThe Shapley value assigns same cost share to a job\nirrespective of the efficient ordering chosen. So, it is pareto\nindifferent.\nThe Shapley value is anonymous because the particular\nindex of a job does not effect his ordering or cost share.\nFor ETE, consider two jobs i, j \u2208 N such that pi = pj\nand \u03b8i = \u03b8j. Without loss of generality assume the efficient\nordering to be 1, . . . , i, . . . , j, . . . , n. Now, the Shapley value\nof job i is\n236\nSVi = pi\u03b8i +\n1\n2\n\u00a1Li + Ri\u00a2(From Lemma 3)\n= pj\u03b8j +\n1\n2\n\u00a1Lj + Rj\u00a2\u2212\n1\n2\n\u00a1Li \u2212 Lj + Ri \u2212 Rj\u00a2\n= SVj \u2212\n1\n2\n\u00a1\ni<k\u2264j\npi\u03b8k \u2212\n\ni\u2264k<j\npk\u03b8i\u00a2\n= SVj \u2212\n1\n2\n\ni<k\u2264j\n(pi\u03b8k \u2212 pk\u03b8i) (Using pi = pj and \u03b8i = \u03b8j)\n= SVj (Using\n\u03b8k\npk\n=\n\u03b8i\npi\nfor all i \u2264 k \u2264 j).\nThe Shapley value satisfies ECB by its expression in Lemma\n3.\nConsider any job i, in an efficient ordering \u03c3, if we increase\nthe value of \u03b3j for some j = i such that \u03c3j > \u03c3i, then\nthe set Pi ( preceding jobs) does not change in the new\nefficient ordering. If \u03b3j is changed such that pj remains the\nsame, then the expression \u00a3j\u2208Pi\n\u03b8ipj is unchanged. If (p, \u03b8)\nvalues of no other jobs are changed, then the Shapley value\nis unchanged by increasing \u03b3j for some j \u2208 Pi while keeping\npj unchanged. Thus, the Shapley value rule satisfies IPJ\u03b8.\nAn analogous argument shows that the Shapley value rule\nsatisfies IFJp.\nFor PRp, assume without loss of generality that jobs are\nordered 1, . . . , n in an efficient ordering. Denote the transfer\nof job i = n due to the Shapley value with set of jobs N and\nset of jobs N \\ {n} as ti and ti respectively. Transfer of last\njob is tn = 1\n2\n\u03b8n \u00a3j<n pj. Now,\nti =\n1\n2\n\u00a1\u03b8i\n\nj<i\npj \u2212 pi\n\nj>i\n\u03b8j\u00a2\n=\n1\n2\n\u00a1\u03b8i\n\nj<i\npj \u2212 pi\n\nj>i:j=n\n\u03b8j\u00a2\u2212\n1\n2\npi\u03b8n\n= ti \u2212\n1\n2\n\u03b8n\n\nj<n\npj\npi\n\u00a3j<n pj\n= ti \u2212 tn\npi\n\u00a3j<n pj\n.\nA similar argument shows that the Shapley value rule\nsatisfies PR\u03b8.\nThese series of propositions lead us to our main result.\nTheorem 1. Let \u03c8 be an allocation rule. The following\nstatements are equivalent:\n1) For each q \u2208 Q, \u03c8(q) selects all the allocation assigning\njobs cost shares implied by the Shapley value.\n2) \u03c8 satisfies efficiency, ECB, IFJp, and IPJ\u03b8.\n3) \u03c8 satisfies efficiency, ECB, IFJp, and PR\u03b8.\n4) \u03c8 satisfies efficiency, ECB, PRp, and IPJ\u03b8.\nProof. The proof follows from Propositions 1, 2, 3, and\n4.\n5. DISCUSSIONS\n5.1 A Reasonable Class of Cost Sharing\nMechanisms\nIn this section, we will define a reasonable class of cost\nsharing mechanisms. We will show how these reasonable\nmechanisms lead to the Shapley value mechanism.\nDefinition 10. An allocation rule \u03c8 is reasonable if for\nall q \u2208 Q and (\u03c3, t) \u2208 \u03c8(q) we have for all i \u2208 N,\nti = \u03b1\n\u00a1\u03b8i\n\nj\u2208Pi(\u03c3)\npj \u2212 pi\n\nj\u2208Fi(\u03c3)\n\u03b8j\u00a2\u2200 i \u2208 N,\nwhere 0 \u2264 \u03b1 \u2264 1.\nThe reasonable cost sharing mechanism says that every\njob should be paid a constant fraction of the difference\nbetween the waiting cost he incurs and the waiting cost he\ninflicts on other jobs. If \u03b1 = 0, then every job bears its\nown cost. If \u03b1 = 1, then every job gets compensated for its\nwaiting cost but compensates others for the cost he inflicts\non others. The Shapley value rule comes as a result of ETE\nas shown in the following proposition.\nProposition 5. Any efficient and reasonable allocation\nrule \u03c8 that satisfies ETE is a rule implied by the Shapley\nvalue rule.\nProof. Consider a q \u2208 Q in which pi = pj and \u03b8i = \u03b8j.\nLet (\u03c3, t) \u2208 \u03c8(q) and \u03c0 be the resulting cost shares. From\nETE, we get,\n\u03c0i = \u03c0j\n\u21d2 ci(\u03c3) \u2212 ti = cj(\u03c3) \u2212 tj\n\u21d2 pi\u03b8i + (1 \u2212 \u03b1)Li + \u03b1Ri = pj\u03b8j + (1 \u2212 \u03b1)Lj + \u03b1Rj\n(Since \u03c8 is efficient and reasonable)\n\u21d2 (1 \u2212 \u03b1)(Li \u2212 Lj) = \u03b1(Rj \u2212 Ri)\n(Using pi = pj, \u03b8i = \u03b8j)\n\u21d2 1 \u2212 \u03b1 = \u03b1\n(Using Li \u2212 Lj = Rj \u2212 Ri = 0)\n\u21d2 \u03b1 =\n1\n2\n.\nThis gives us the Shapley value rule by Lemma 3.\n5.2 Results on Envy\nChun [2] discusses a fariness condition called no-envy for\nthe case when processing times of all jobs are unity.\nDefinition 11. An allocation rule satisfies no-envy if for\nall q \u2208 Q, (\u03c3, t) \u2208 \u03c8(q), and i, j \u2208 N, we have \u03c0i \u2264 ci(\u03c3ij\n) \u2212\ntj, where \u03c0 is the cost share from allocation rule (\u03c3, t) and\n\u03c3ij\nis the ordering obtaining by swapping i and j.\nFrom the result in [2], the Shapley value rule does not\nsatisfy no-envy in our model also. To overcome this, Chun [2]\nintroduces the notion of adjusted no-envy, which he shows\nis satisfied in the Shapley value rule when processing times\nof all jobs are unity. Here, we show that adjusted envy\ncontinues to hold in the Shapley value rule in our model (when\nprocessing times need not be unity).\nAs before denote \u03c3ij\nbe an ordering where the position\nof i and j is swapped from an ordering \u03c3. For adjusted\nnoenvy, if (\u03c3, t) is an allocation for some q \u2208 Q, let tij\nbe the\n237\ntransfer of job i when the transfer of i is calculated with\nrespect to ordering \u03c3ij\n. Observe that an allocation may not\nallow for calculation of tij\n. For example, if \u03c8 is efficient,\nthen tij\ncannot be calculated if \u03c3ij\nis also not efficient. For\nsimplicity, we state the definition of adjusted no-envy to\napply to all such rules.\nDefinition 12. An allocation rule satisfies adjusted\nnoenvy if for all q \u2208 Q, (\u03c3, t) \u2208 \u03c8(q), and i, j \u2208 N, we have\n\u03c0i \u2264 ci(\u03c3ij\n) \u2212 tij\ni .\nProposition 6. The Shapley value rule satisfies adjusted\nno-envy.\nProof. Without loss of generality, assume efficient\nordering of jobs is: 1, . . . , n. Consider two jobs i and i + k.\nFrom Lemma 3,\nSVi = pi\u03b8i +\n1\n2\n\u00a1\nj<i\n\u03b8ipj +\n\nj>i\n\u03b8jpi\u00a2.\nLet \u02c6\u03c0i be the cost share of i due to adjusted transfer tii+k\ni\nin the ordering \u03c3ii+k\n.\n\u02c6\u03c0i = ci(\u03c3ii+k\n) \u2212 tii+k\ni\n= pi\u03b8i +\n1\n2\n\u00a1\nj<i\n\u03b8ipj + \u03b8ipi+k +\n\ni<j<i+k\n\u03b8ipj\n+\n\nj>i\n\u03b8jpi \u2212 \u03b8i+kpi \u2212\n\ni<j<i+k\n\u03b8jpi\u00a2\n= SVi +\n1\n2\n\ni<j\u2264i+k\n\u00a1\u03b8ipj \u2212 \u03b8jpi\u00a2\n\u2265 SVi (Using the fact that\n\u03b8i\npi\n\u2265\n\u03b8j\npj\nfor i < j).\n6. CONCLUSION\nWe studied the problem of sharing costs for a job\nscheduling problem on a single server, when jobs have processing\ntimes and unit time waiting costs. We took a cooperative\ngame theory approach and show that the famous the\nShapley value rule satisfies many nice fairness properties. We\ncharacterized the Shapley value rule using different intuitive\nfairness axioms.\nIn future, we plan to further simplify some of the fairness\naxioms. Some initial simplifications already appear in [16],\nwhere we provide an alternative axiom to ECB and also\ndiscuss the implication of transfers between jobs (in stead of\ntransfers from jobs to a central server). We also plan to look\nat cost sharing mechanisms other than the Shapley value.\nInvestigating the strategic power of jobs in such mechanisms\nis another line of future research.\n7. REFERENCES\n[1] Youngsub Chun. A Note on Maniquet\"s\nCharacterization of the Shapley Value in Queueing\nProblems. Working Paper, Rochester University, 2004.\n[2] Youngsub Chun. No-envy in Queuing Problems.\nWorking Paper, Rochester University, 2004.\n[3] Imma Curiel, Herbert Hamers, and Flip Klijn.\nSequencing Games: A Survey. In Peter Borm and\nHans Peters, editors, Chapter in Game Theory.\nTheory and Decision Library, Kulwer Academic\nPublishers, 2002.\n[4] Imma Curiel, Giorgio Pederzoli, and Stef Tijs.\nSequencing Games. European Journal of Operational\nResearch, 40:344-351, 1989.\n[5] Imma Curiel, Jos Potters, Rajendra Prasad, Stef Tijs,\nand Bart Veltman. Sequencing and Cooperation.\nOperations Research, 42(3):566-568, May-June 1994.\n[6] Nikhil R. Devanur, Milena Mihail, and Vijay V.\nVazirani. Strategyproof Cost-sharing Mechanisms for\nSet Cover and Facility Location Games. In\nProceedings of Fourth Annual ACM Conferece on\nElectronic Commerce, 2003.\n[7] Robert J. Dolan. Incentive Mechanisms for Priority\nQueueing Problems. Bell Journal of Economics,\n9:421-436, 1978.\n[8] Joan Feigenbaum, Christos Papadimitriou, and Scott\nShenker. Sharing the Cost of Multicast Transmissions.\nIn Proceedings of Thirty-Second Annual ACM\nSymposium on Theory of Computing, 2000.\n[9] Herbert Hamers, Jeroen Suijs, Stef Tijs, and Peter\nBorm. The Split Core for Sequencing Games. Games\nand Economic Behavior, 15:165-176, 1996.\n[10] John C. Harsanyi. Contributions to Theory of Games\nIV, chapter A Bargaining Model for Cooperative\nn-person Games. Princeton University Press, 1959.\nEditors: A. W. Tucker, R. D. Luce.\n[11] Kamal Jain and Vijay Vazirani. Applications of\nApproximate Algorithms to Cooperative Games. In\nProceedings of 33rd Symposium on Theory of\nComputing (STOC \"01), 2001.\n[12] Kamal Jain and Vijay Vazirani. Equitable Cost\nAllocations via Primal-Dual Type Algorithms. In\nProceedings of 34th Symposium on Theory of\nComputing (STOC \"02), 2002.\n[13] Flip Klijn and Estela S\u00b4anchez. Sequencing Games\nwithout a Completely Specified Initial Order. Report\nin Statistics and Operations Research, pages 1-17,\n2002. Report 02-04.\n[14] Flip Klijn and Estela S\u00b4anchez. Sequencing Games\nwithout Initial Order. Working Paper, Universitat\nAut\u00b4onoma de Barcelona, July 2004.\n[15] Franois Maniquet. A Characterization of the Shapley\nValue in Queueing Problems. Journal of Economic\nTheory, 109:90-103, 2003.\n[16] Debasis Mishra and Bharath Rangarajan. Cost\nsharing in a job scheduling problem. Working Paper,\nCORE, 2005.\n[17] Manipushpak Mitra. Essays on First Best\nImplementable Incentive Problems. Ph.D. Thesis,\nIndian Statistical Institute, New Delhi, 2000.\n[18] Manipushpak Mitra. Mechanism design in queueing\nproblems. Economic Theory, 17(2):277-305, 2001.\n[19] Manipushpak Mitra. Achieving the first best in\nsequencing problems. Review of Economic Design,\n7:75-91, 2002.\n[20] Herv\u00b4e Moulin. Handbook of Social Choice and\nWelfare, chapter Axiomatic Cost and Surplus Sharing.\nNorth-Holland, 2002. Publishers: Arrow, Sen,\nSuzumura.\n[21] Herv\u00b4e Moulin. On Scheduling Fees to Prevent\n238\nMerging, Splitting and Transferring of Jobs. Working\nPaper, Rice University, 2004.\n[22] Herv\u00b4e Moulin. Split-proof Probabilistic Scheduling.\nWorking Paper, Rice University, 2004.\n[23] Herv\u00b4e Moulin and Rakesh Vohra. Characterization of\nAdditive Cost Sharing Methods. Economic Letters,\n80:399-407, 2003.\n[24] Martin P\u00b4al and \u00b4Eva Tardos. Group Strategyproof\nMechanisms via Primal-Dual Algorithms. In\nProceedings of the 44th Annual IEEE Symposium on\nthe Foundations of Computer Science (FOCS \"03),\n2003.\n[25] Lloyd S. Shapley. Contributions to the Theory of\nGames II, chapter A Value for n-person Games, pages\n307-317. Annals of Mathematics Studies, 1953.\nEdiors: H. W. Kuhn, A. W. Tucker.\n[26] Wayne E. Smith. Various Optimizers for Single-Stage\nProduction. Naval Research Logistics Quarterly,\n3:59-66, 1956.\n[27] Jeroen Suijs. On incentive compatibility and budget\nbalancedness in public decision making. Economic\nDesign, 2, 2002.\n239", "keywords": "job scheduling;cooperative game theory approach;unit waiting cost;processing time;expected cost bound;agent;monetary transfer;queueing problem;shapley value;job schedule;queue problem;fairness axiom;cost sharing;allocation rule;cost share"}
{"name": "train_J-60", "title": "On Decentralized Incentive Compatible Mechanisms for Partially Informed Environments", "abstract": "Algorithmic Mechanism Design focuses on Dominant Strategy Implementations. The main positive results are the celebrated Vickrey-Clarke-Groves (VCG) mechanisms and computationally efficient mechanisms for severely restricted players (single-parameter domains). As it turns out, many natural social goals cannot be implemented using the dominant strategy concept [35, 32, 22, 20]. This suggests that the standard requirements must be relaxed in order to construct general-purpose mechanisms. We observe that in many common distributed environments computational entities can take advantage of the network structure to collect and distribute information. We thus suggest a notion of partially informed environments. Even if the information is recorded with some probability, this enables us to implement a wider range of social goals, using the concept of iterative elimination of weakly dominated strategies. As a result, cooperation is achieved independent of agents\" belief. As a case study, we apply our methods to derive Peer-to-Peer network mechanism for file sharing.", "fulltext": "1. INTRODUCTION\nRecently, global networks have attracted widespread study.\nThe emergence of popular scalable shared networks with\nself-interested entities - such as peer-to-peer systems over\nthe Internet and mobile wireless communication ad-hoc\nnetworks - poses fundamental challenges.\nNaturally, the study of such giant decentralized systems\ninvolves aspects of game theory [32, 34]. In particular, the\nsubfield of Mechanism Design deals with the construction\nof mechanisms: for a given social goal the challenge is to\ndesign rules for interaction such that selfish behavior of the\nagents will result in the desired social goal [23, 33].\nAlgorithmic Mechanism Design (AMD) focuses on\nefficiently computable constructions [32]. Distributed\nAlgorithmic Mechanism Design (DAMD) studies mechanism design\nin inherently decentralized settings [30, 12]. The standard\nmodel assumes rational agents with quasi-linear utilities and\nprivate information, playing dominant strategies.\nThe solution concept of dominant strategies - in which\neach player has a best response strategy regardless of the\nstrategy played by any other player - is well suited to the\nassumption of private information, in which each player is\nnot assumed to have knowledge or beliefs regarding the other\nplayers. The appropriateness of this set-up stems from the\nstrength of the solution concept, which complements the\nweak information assumption. Many mechanisms have been\nconstructed using this set-up, e.g., [1, 4, 6, 11, 14, 22]. Most\nof these apply to severely-restricted cases (e.g., single-item\nauctions with no externalities) in which a player\"s\npreference is described by only one parameter (single-parameter\ndomains).\nTo date, Vickrey-Clarke-Groves (VCG) mechanisms are\nthe only known general method for designing dominant\nstrategy mechanisms for general domains of preferences.\nHowever, in distributed settings without available subsidies from\noutside sources, VCG mechanisms cannot be accepted as\nvalid solutions due to a serious lack of budget balance.\nAdditionally, for some domains of preferences, VCG mechanisms\nand weighted VCG mechanisms are faced with\ncomputational hardness [22, 20]. Further limitations of the set-up\nare discussed in subsection 1.3.\nIn most distributed environments, players can take\nadvantage of the network structure to collect and distribute\ninformation about other players. This paper thus studies\nthe effects of relaxing the private information assumption.\n240\nOne model that has been extensively studied recently is\nthe Peer-to-Peer (P2P) network. A P2P network is a\ndistributed network with no centralized authority, in which the\nparticipants share their individual resources (e.g.,\nprocessing power, storage capacity, bandwidth and content). The\naggregation of such resources provides inexpensive\ncomputational platforms. The most popular P2P networks are\nthose for sharing media files, such as Napster, Gnutella, and\nKazaa. Recent work on P2P Incentives include\nmicropayment methods [15] and reputation-based methods [9, 13].\nThe following description of a P2P network scenario\nillustrates the relevance of our relaxed informational assumption.\nExample 1. Consider a Peer-to-Peer network for file\nsharing. Whenever agent B uploads a file from agent A, all peers\nalong the routing path know that B has loaded the file. They\ncan record this information about agent B. In addition, they\ncan distribute this information.\nHowever, it is impossible to record all the information\neverywhere. First, such duplication induces huge costs.\nSecond, as agents dynamically enter and exit from the network,\nthe information might not be always available. And so it is\nseems natural to consider environments in which the\ninformation is locally recorded, that is, the information is recorded\nin the closest neighborhood with some probability p.\nIn this paper we shall see that if the information is\navailable with some probability, then this enables us to\nimplement a wider range of social goals. As a result, cooperation\nis achieved independent of agents\" belief. This demonstrates\nthat in some computational contexts our approach is far less\ndemanding than the Bayesian approach (that assumes that\nplayers\" types are drawn according to some identified\nprobability density function).\n1.1 Implementations in Complete Information\nSet-ups\nIn complete information environments, each agent is\ninformed about everyone else. That is, each agent observes his\nown preference and the preferences of all other agents.\nHowever, no outsider can observe this information. Specifically,\nneither the mechanism designer nor the court. Many\npositive results were shown for such arguably realistic settings.\nFor recent surveys see [25, 27, 18].\nMoore and Repullo implement a large class of social goals\nusing sequential mechanisms with a small number of rounds\n[28]. The concept they used is subgame-perfect\nimplementations (SPE).\nThe SPE-implementability concept seems natural for the\nfollowing reasons: the designed mechanisms usually have\nnon-artificial constructs and a small strategy space. As\na result, it is straightforward for a player to compute his\nstrategy.1\nSecond, sequential mechanisms avoid\nsimultaneous moves, and thus can be considered for distributed\nnetworks. Third, the constructed mechanisms are often\ndecentralized (i.e., lacking a centralized authority or designer)\n1\nInterestingly, in real life players do not always use their\nsubgame perfect strategies. One such widely studied case is the\nUltimatum Bargaining 2-person game. In this simple game,\nthe proposer first makes an offer of how to divide a certain\nknown sum of money, and the responder either agrees or\nrefuses, in the latter case both players earn zero. Somewhat\nsurprisingly, experiments show that the responder often\nrejects the suggested offer, even if it is bounded away from\nzero and the game is played only once (see e.g. [38]).\nand budget-balanced (i.e., transfers always sum up to zero).\nThis happens essentially if there are at least three players,\nand a direct network link between any two agents. Finally,\nMoore and Repullo observed that they actually use a\nrelaxed complete information assumption: it is only required\nthat for every player there exists only one other player who\nis informed about him.\n1.2 Implementations in Partially Informed\nSet-ups and Our Results\nThe complete information assumption is realistic for small\ngroups of players, but not in general. In this paper we\nconsider players that are informed about each other with\nsome probability. More formally, we say that agent B is\np-informed about agent A, if B knows the type of A with\nprobability p.\nFor such partially-informed environments, we show how to\nuse the solution concept of iterative elimination of weakly\ndominated strategies. We demonstrate this concept through\nsome motivating examples that (i) seem natural in distributed\nsettings and (ii) cannot be implemented in dominant\nstrategies even if there is an authorized center with a direct\nconnection to every agent or even if players have single-parameter\ndomains.\n1. We first show how the subgame perfect techniques of\nMoore and Repullo [28] can be applied to p-informed\nenvironments and further adjusted to the concept of\niterative elimination of weakly dominated strategies\n(for large enough p).\n2. We then suggest a certificate based challenging method\nthat is more natural in computerized p-informed\nenvironments and different from the one introduced by\nMoore and Repullo [28] (for p \u2208 (0, 1]).\n3. We consider implementations in various network\nstructures.\nAs a case study we apply our methods to derive: (1)\nSimplified Peer-to-Peer network for file sharing with no\npayments in equilibrium. Our approach is (agent, file)-specific.\n(2) Web-cache budget-balanced and economically efficient\nmechanism.\nOur mechanisms use reasonable punishments that inversely\ndepend on p. And so, if the fines are large then small p is\nenough to induce cooperation. Essentially, large p implies a\nlarge amount of recorded information.\n1.2.1 Malicious Agents\nDecentralized mechanisms often utilize punishing outcomes.\nAs a result, malicious players might cause severe harm to\nothers. We suggest a quantified notion of malicious player,\nwho benefits from his own gained surplus and from harm\ncaused to others. [12] suggests several categories to classify\nnon-cooperating players. Our approach is similar to [7] (and\nthe references therein), who considered independently such\nplayers in different context. We show a simple\ndecentralized mechanism in which q-malicious players cooperate and\nin particular, do not use their punishing actions in\nequilibrium.\n241\n1.3 Dominant Strategy Implementations\nIn this subsection we shall refer to some recent results\ndemonstrating that the set-up of private information with\nthe concept of dominant strategies is restrictive in general.\nFirst, Roberts\" classical impossibility result shows that if\nplayers\" preferences are not restricted and there are at least\n3 different outcomes, then every dominant-strategy\nmechanism must be weighted VCG (with the social goal that\nmaximizes the weighted welfare) [35]. For slightly-restricted\npreference domains, it is not known how to turn efficiently\ncomputable algorithms into dominant strategy mechanisms.\nThis was observed and analyzed in [32, 22, 31]. Recently [20]\nextends Roberts\" result to some leading examples. They\nshowed that under mild assumptions any dominant\nstrategy mechanism for variety of Combinatorial Auctions over\nmulti-dimensional domains must be almost weighted VCG.\nAdditionally, it turns out that the dominant strategy\nrequirement implies that the social goal must be monotone\n[35, 36, 22, 20, 5, 37]. This condition is very restrictive, as\nmany desired natural goals are non-monotone2\n.\nSeveral recent papers consider relaxations of the dominant\nstrategy concept: [32, 1, 2, 19, 16, 17, 26, 21]. However, most\nof these positive results either apply to severely restricted\ncases (e.g., single-parameter, 2 players) or amount to VCG\nor almost VCG mechanisms (e.g., [19]). Recently, [8, 3]\nconsidered implementations for generalized single-parameter\nplayers.\nOrganization of this paper: In section 2 we illustrate\nthe concepts of subgame perfect and iterative elimination\nof weakly dominated strategies in completely-informed and\npartially-informed environments. In section 3 we show a\nmechanism for Peer-to-Peer file sharing networks. In section\n4 we apply our methods to derive a web cache mechanism.\nFuture work is briefly discussed in section 5.\n2. MOTIVATING EXAMPLES\nIn this section we examine the concepts of subgame perfect\nand iterative elimination of weakly dominated strategies for\ncompletely informed and p-informed environments. We also\npresent the notion of q-maliciousness and some other related\nconsiderations through two illustrative examples.\n2.1 The Fair Assignment Problem\nOur first example is an adjustment to computerized\ncontext of an ancient procedure to ensure that the wealthiest\nman in Athens would sponsor a theatrical production known\nas the Choregia [27]. In the fair assignment problem, Alice\nand Bob are two workers, and there is a new task to be\nperformed. Their goal is to assign the task to the least loaded\nworker without any monetary transfers. The informational\nassumption is that Alice and Bob know both loads and the\nduration of the new task.3\n2\nE.g., minimizing the makespan within a factor of 2 [32] and\nRawls\" Rule over some multi-dimensional domains [20].\n3\nIn first glance one might ask why the completely informed\nagents could not simply sign a contract, specifying the\ndesired goal. Such a contract is sometimes infeasible due to\nfact that the true state cannot be observed by outsiders,\nespecially not the court.\nClaim 1. The fair assignment goal cannot be implemented\nin dominant strategies.4\n2.1.1 Basic Mechanism\nThe following simple mechanism implements this goal in\nsubgame perfect equilibrium.\n\u2022 Stage 1: Alice either agrees to perform the new task\nor refuses.\n\u2022 Stage 2: If she refuses, Bob has to choose between:\n- (a) Performing the task himself.\n- (b) Exchanging his load with Alice and\nperforming the new task as well.\nLet LT\nA, LT\nB be the true loads of Alice and Bob, and let\nt > 0 be the load of the new task. Assume that load\nexchanging takes zero time and cost. We shall see that the\nbasic mechanism achieves the goal in a subgame perfect\nequilibrium. Intuitively this means that in equilibrium each\nplayer will choose his best action at each point he might\nreach, assuming similar behavior of others, and thus every\nSPE is a Nash equilibrium.\nClaim 2. ([27]) The task is assigned to the least loaded\nworker in subgame perfect equilibrium.\nProof. By backward induction argument (look forward\nand reason backward), consider the following cases:\n1. LT\nB \u2264 LT\nA. If stage 2 is reached then Bob will not\nexchange.\n2. LT\nA < LT\nB < LT\nA + t. If stage 2 is reached Bob will\nexchange, and this is what Alice prefers.\n3. LT\nA + t \u2264 LT\nB. If stage 2 is reached then Bob would\nexchange, as a result it is strictly preferable by Alice\nto perform the task.\nNote that the basic mechanism does not use monetary\ntransfers at all and is decentralized in the sense that no third\nparty is needed to run the procedure. The goal is achieved in\nequilibrium (ties are broken in favor of Alice). However, in\nthe second case exchange do occur in an equilibrium point.\nRecall the unrealistic assumption that load exchange takes\nzero time and cost. Introducing fines, the next mechanism\novercomes this drawback.\n2.1.2 Elicitation Mechanism\nIn this subsection we shall see a centralized mechanism for\nthe fair assignment goal without load exchange in\nequilibrium. The additional assumptions are as follows. The cost\nperforming a load of duration d is exactly d. We assume\nthat the duration t of the new task is < T. The payoffs\n4\nproof: Assume that there exists a mechanism that\nimplements this goal in dominant strategies. Then by the\nRevelation Principle [23] there exists a mechanism that implements\nthis goal for which the dominant strategy of each player is\nto report his true load. Clearly, truthfully reporting cannot\nbe a dominant strategy for this goal (if monetary transfers\nare not available), as players would prefer to report higher\nloads.\n242\nof the utility maximizers agents are quasilinear. The\nfollowing mechanism is an adaptation of Moore and Repullo\"s\nelicitation mechanism [28]5\n.\n\u2022 Stage 1: (Elicitation of Alice\"s load)\nAlice announces LA.\nBob announces LA \u2264 LA.\nIf LA = LA (Bob agrees) goto the next Stage.\nOtherwise (Bob challenges), Alice is assigned the\ntask.\nShe then has to choose between:\n- (a) Transferring her original load to Bob and\npaying him LA \u2212 0.5 \u00b7 min{ , LA \u2212 LA}.\nAlice pays to the mechanism.\nBob pays the fine of T + to the mechanism.\n- (b) No load transfer. Alice pays to Bob. STOP.\n\u2022 Stage 2: The elicitation of Bob\"s load is similar to\nStage 1 (switching the roles of Alice and Bob).\n\u2022 Stage 3: If LA < LB Alice is assigned the task,\notherwise Bob. STOP.\nObserve that Alice is assigned the task and fined with\nwhenever Bob challenges. We shall see that the bonus of\nis paid to a challenging player only in out of equilibria cases.\nClaim 3. If the mechanism stops at Stage 3, then the\npayoff of each agent is at least \u2212t and at most 0.\nProposition 1. It is a subgame perfect equilibrium of the\nelicitation mechanism to report the true load, and to\nchallenge with the true load only if the other agent overreports.\nProof. Assume w.l.o.g that the elicitation of Alice\"s load\nis done after Bob\"s, and that Stage 2 is reached. If Alice\ntruly reports LA = LT\nA, Bob strictly prefers to agree.\nOtherwise, if Bob challenges, Alice would always strictly prefer\nto transfer (as in this case Bob would perform her load for\nsmaller cost), as a result Bob would pay T + to the\nmechanism. This punishing outcome is less preferable than the\nnormal outcome of Stage 3 achieved had he agreed.\nIf Alice misreports LA > LT\nA, then Bob can ensure himself\nthe bonus (which is always strictly preferable than reaching\nStage 3) by challenging with LA = LT\nA, and so whenever\nBob gets the bonus Alice gains the worst of all payoffs.\nReporting a lower load LA < LT\nA is not beneficial for Alice.\nIn this case, Bob would strictly prefer to agree (and not to\nannounce LA < LA, as he limited to challenge with a smaller\nload than what she announces). Thus such misreporting can\nonly increase the possibility that she is assigned the task.\nAnd so there is no incentive for Alice to do so.\nAll together, Alice would prefer to report the truth in this\nstage. And so Stage 2 would not abnormally end by STOP,\nand similarly Stage 1.\nObserve that the elicitation mechanism is almost balanced:\nin all outcomes no money comes in or out, except for the\nnon-equilibrium outcome (a), in which both players pay to\nthe mechanism.\n5\nIn [28], if an agent misreport his type then it is always\nbeneficial to the other agent to challenge. In particular,\neven if the agent reports a lower load.\n2.1.3 Elicitation Mechanism for Partially Informed\nAgents\nIn this subsection we consider partially informed agents.\nFormally:\nDefinition 1. An agent A is p-informed about agent B,\nif A knows the type of B with probability p (independently\nof what B knows).\nIt turns out that a version of the elicitation mechanism\nworks for this relaxed information assumption, if we use the\nconcept of iterative elimination of weakly dominated\nstrategies6\n. We replace the fixed fine of in the elicitation\nmechanism with the fine:\n\u03b2p = max{L,\n1 \u2212 p\n2p \u2212 1\nT} + ,\nand assume the bounds LT\nA, LT\nB \u2264 L.\nProposition 2. If all agents are p-informed, p > 0.5,\nthe elicitation mechanism(\u03b2p) implements the fair\nassignment goal with the concept of iterative elimination of weakly\ndominated strategies. The strategy of each player is to report\nthe true load and to challenge with the true load if the other\nagent overreport.\nProof. Assume w.l.o.g that the elicitation of Alice\"s load\nis done after Bob\"s, and that Stage 2 is reached. First\nobserve that underreporting the true value is a dominated\nstrategy, whether Bob is not informed and mistakenly\nchallenges with a lower load (as \u03b2p \u2265 L) or not, or even\nif t is very small. Now we shall see that overreporting her\nvalue is a dominated strategy, as well.\nAlice\"s expected payoff gained by misreporting \u2264\np (payoff if she lies and Bob is informed) +(1 \u2212 p) (max\npayoff if Bob is not informed) \u2264\np (\u2212t \u2212 \u03b2p) < p (\u2212t) + (1 \u2212 p) (\u2212t \u2212 \u03b2p) \u2264\np (min payoff of true report if Bob is informed) + (1 \u2212 p)\n(min payoff if Bob is not informed) \u2264\nAlice\"s expected payoff if she truly reports.\nThe term (\u2212t\u2212\u03b2p) in the left hand side is due to the fact\nthat if Bob is informed he will always prefer to challenge.\nIn the right hand side, if he is informed, then challenging is\na dominated strategy, and if he is not informed the worst\nharm he can make is to challenge. Thus in stage 2 Alice will\nreport her true load. This implies that challenging without\nbeing informed is a dominated strategy for Bob.\nThis argument can be reasoned also for the first stage,\nwhen Bob reports his value. Bob knows the maximum payoff\nhe can gain is at most zero since he cannot expect to get the\nbonus in the next stage.\n2.1.4 Extensions\nThe elicitation mechanism for partially informed agents is\nrather general. As in [28], we need the capability to judge\nbetween two distinct declarations in the elicitation rounds,\n6\nA strategy si of player i is weakly dominated if there exists\nsi such that (i) the payoff gained by si is at least as high as\nthe payoff gained by si, for all strategies of the other players\nand all preferences, and (ii) there exist a preference and a\ncombination of strategies for the other players such that the\npayoff gained by si is strictly higher than the payoff gained\nby si.\n243\nand upper and lower bounds based on the possible payoffs\nderived from the last stage. In addition, for p-informed\nenvironments, some structure is needed to ensure that\nunderbidding is a dominated strategy.\nThe Choregia-type mechanisms can be applied to more\nthan 2 players with the same number of stages: the player in\nthe first stage can simply points out the name of the\nwealthiest agent. Similarly, the elicitation mechanisms can be\nextended in a straightforward manner. These mechanisms can\nbe budget-balanced, as some player might replace the role\nof the designer, and collect the fines, as observed in [28].\nOpen Problem 1. Design a decentralized budget balanced\nmechanism with reasonable fines for independently p-informed\nn players, where p \u2264 1 \u2212 1/2\n1\nn\u22121 .\n2.2 Seller and Buyer Scenario\nA player might cause severe harm to others by choosing a\nnon-equilibrium outcome. In the mechanism for the fair\nassignment goal, an agent might maliciously challenge even\nif the other agent truly reports his load. In this subsection\nwe consider such malicious scenarios. For the ease of\nexposition we present a second example. We demonstrate that\nequilibria remain unchanged even if players are malicious.\nIn the seller-buyer example there is one item to be traded\nand two possible future states. The goal is to sell the item for\nthe average low price pl = ls+lb\n2\nin state L, and the higher\nprice ph = hs+hb\n2\nin the other state H, where ls is seller\"s\ncost and lb is buyer\"s value in state L, and similarly hs, hb in\nH. The players fix the prices without knowing what will be\nthe future state. Assume that ls < hs < lb < hb, and that\ntrade can occur in both prices (that is, pl, ph \u2208 (hs, lb)).\nOnly the players can observe the realization of the true\nstate. The payoffs are of the form ub = xv\u2212tb, us = ts \u2212xvs,\nwhere the binary variable x indicates if trade occurred, and\ntb, ts are the transfers. Consider the following decentralized\ntrade mechanism.\n\u2022 Stage 1: If seller reports H goto Stage 2. Otherwise,\ntrade at the low price pl. STOP.\n\u2022 Stage 2: The buyer has to choose between:\n- (a) Trade at the high price ph.\n- (b) No trade and seller pays \u2206 to the buyer.\nClaim 4. Let \u2206 = lb\u2212ph+ . The unique subgame perfect\nequilibrium of the trade mechanism is to report the true state\nin Stage 1 and trading if Stage 2 is reached.\nNote that the outcome (b) is never chosen in equilibrium.\n2.2.1 Trade Mechanism for Malicious Agents\nThe buyer might maliciously punish the seller by\nchoosing the outcome (b) when the true state is H. The following\nnotion quantifies the consideration that a player is not\nindifferent to the private surpluses of others.\nDefinition 2. A player is q-malicious if his payoff equals:\n(1 \u2212 q) (his private surplus) \u2212 q (summation of others\nsurpluses), q \u2208 [0, 1].\nThis definition appeared independently in [7] in different\ncontext. We shall see that the traders would avoid such bad\nbehavior if they are q-malicious, where q < 0.5, that is if\ntheir non-indifference impact is bounded by 0.5.\nEquilibria outcomes remain unchanged, and so cooperation is\nachieved as in the original case of non-malicious players.\nConsider the trade mechanism with pl = (1 \u2212 q) hs + q lb ,\nph = q hs + (1 \u2212 q) lb , \u2206 = (1 \u2212 q) (hb \u2212 lb \u2212 ). Note that\npl < ph for q < 0.5.\nClaim 5. If q < 0.5, then the unique subgame perfect\nequilibrium for q-malicious players remains unchanged.\nProof. By backward induction we consider two cases.\nIn state H, the q-malicious buyer would prefer to trade if\n(1 \u2212 q)(hb \u2212 ph) + q(hs \u2212 ph) > (1 \u2212 q)\u2206 + q(\u2206). Indeed,\n(1 \u2212 q)hb + qhs > \u2206 + ph. Trivially, the seller prefers to\ntrade at the higher price, (1 \u2212 q)(pl \u2212 hs) + q(pl \u2212 hb) <\n(1 \u2212 q)(ph \u2212 hs) + q(ph \u2212 hb).\nIn state L the buyer prefers the no trade outcome, as\n(1\u2212q)(lb \u2212ph)+q(ls \u2212ph) < \u2206. The seller prefers to trade\nat a low price, as (1 \u2212 q)(pl \u2212 ls) + q(pl \u2212 lb) > 0 > \u2212\u2206.\n2.2.2 Discussion\nNo mechanism can Nash-implement this trading goal if\nthe only possible outcomes are trade at pl and trade at ph.\nTo see this, it is enough to consider normal forms (as any\nextensive form mechanism can be presented as a normal one).\nConsider a matrix representation, where the seller is the row\nplayer and the buyer is the column player, in which every\nentry includes an outcome. Suppose there is equilibrium entry\nfor the state L. The associate column must be all pl,\notherwise the seller would have an incentive to deviate. Similarly,\nthe associate row of the H equilibrium entry must be all ph\n(otherwise the buyer would deviate), a contradiction. 7 8\nThe buyer prefers pl and seller ph, and so the preferences\nare identical in both states. Hence reporting preferences\nover outcomes is not enough - players must supply\nadditional information. This is captured by outcome (b) in\nthe trade mechanism.\nIntuitively, if a goal is not Nash-implementable we need\nto add more outcomes. The drawback is that some new\nadditional equilibria must be ruled out. E.g., additional\nNash equilibrium for the trade mechanism is (trade at pl,\n(b)). That is, the seller chooses to trade at low price at either\nstates, and the buyer always chooses the no trade option that\nfines the seller, if the second stage is reached. Such buyer\"s\nthreat is not credible, because if the mechanism is played\nonly once, and Stage 2 is reached in state H, the buyer would\nstrictly decrease his payoff if he chooses (b). Clearly, this is\nnot a subgame perfect equilibrium. Although each extensive\ngame-form is strategically equivalent to a normal form one,\nthe extensive form representation places more structure and\nso it seems plausible that the subgame perfect equilibrium\nwill be played.9\n7\nFormally, this goal is not Maskin monotonic, a necessary\ncondition for Nash-implementability [24].\n8\nA similar argument applies for the Fair Assignment\nProblem.\n9\nInterestingly, it is a straight forward to construct a\nsequential mechanism with unique SPE, and additional NE with a\nstrictly larger payoff for every player.\n244\n3. PEER-TO-PEER NETWORKS\nIn this section we describe a simplified Peer-to-Peer\nnetwork for file sharing, without payments in equilibrium, using\na certificate-based challenging method. In this challenging\nmethod - as opposed to [28] - an agent that challenges cannot\nharm other agents, unless he provides a valid certificate.\nIn general, if agent B copied a file f from agent A, then\nagent A knows that agent B holds a copy of the file. We\ndenote such information as a certificate(B, f) (we shall omit\ncryptographic details). Such a certificate can be recorded\nand distributed along the network, and so we can treat each\nagent holding the certificate as an informed agent.\nAssumptions: We assume an homogeneous system with\nfiles of equal size. The benefit each agent gains by holding\na copy of any file is V . The only cost each agent has is\nthe uploading cost C (induced while transferring a file to\nan immediate neighbor). All other costs are negligible (e.g.,\nstoring the certificates, forwarding messages, providing\nacknowledgements, digital signatures, etc). Let upA, downA\nbe the numbers of agent A uploads and downloads if he\nalways cooperates. We assume that each agent A enters the\nsystem if upA \u00b7 C < downA \u00b7 V .\nEach agent has a quasilinear utility and only cares about\nhis current bandwidth usage. In particular, he ignores future\nscenarios (e.g., whether forwarding or dropping of a packet\nmight affect future demand).\n3.1 Basic Mechanism\nWe start with a mechanism for a network with 3 p-informed\nagents: B, A1, A2. We assume that B is directly connected\nto A1 and A2.\nIf B has the certificate(A1, f), then he can apply directly\nto A1 and request the file (if he refuses, then B can go to\ncourt). The following basic sequential mechanism is\napplicable whenever agent B is not informed and still would like to\ndownload the file if it exists in the network. Note that this\ngoal cannot be implemented in dominant strategies\nwithout payments (similar to Claim 1, when the type of each\nagent here is the set of files he holds). Define tA,B to be the\nmonetary amount that agent A should transfer to B.\n\u2022 Stage 1: Agent B requests the file f from A1.\n- If A1 replies yes then B downloads the file from\nA1. STOP.\n- Otherwise, agent B sends A1s no reply to agent\nA2.\n\u2217 If A2 declares agree then goto the next stage.\n\u2217 Else, A2 sends a certificate(A1, f) to agent B.\n\u00b7 If the certificate is correct then tA1,A2 =\n\u03b2p. STOP.\n\u00b7 Else tA2,A1 = |C| + . STOP.\nStage 2: Agent B requests the file f from A2. Switch\nthe roles of the agents A1, A2.\nClaim 6. The basic mechanism is budget-balanced\n(transfers always sum to zero) and decentralized.\nTheorem 1. Let \u03b2p = |C|\np\n+ , p \u2208 (0, 1]. A strategy that\nsurvives iterative elimination of weakly dominated strategies\nis to reply yes if Ai holds the file, and to challenge only\nwith a valid certificate. As a result, B downloads the file if\nsome agent holds it, in equilibrium. There are no payments\nor transfers in equilibrium.\nProof. Clearly if the mechanism ends without\nchallenging: \u2212C \u2264 u(Ai) \u2264 0. And so, challenging with an invalid\ncertificate is always a dominated strategy. Now, when Stage\n2 is reached, A2 is the last to report if he has the file. If A2\nhas the file it is a weakly undominated strategy to misreport,\nwhether A1 is informed or not:\nA2\"s expected payoff gained by misreporting no \u2264\np \u00b7 (\u2212\u03b2p) + (1 \u2212 p) \u00b7 0 < \u2212C \u2264 A2\"s payoff if she reports\nyes.\nThis argument can be reasoned also for Stage 1, when\nA1 reports whether he has the file. A1 knows that A2 will\nreport yes if and only if she has the file in the next stage,\nand so the maximum payoff he can gain is at most zero since\nhe cannot expect to get a bonus.\n3.2 Chain Networks\nIn a chain network, agent B is directly connected to A1,\nand Ai is directly connected to agent Ai+1. Assume that we\nhave an acknowledgment protocol to confirm the receipt of\na particular message. To avoid message dropping, we add\nthe fine (\u03b2p +2 ) to be paid by an agent who hasn\"t properly\nforwarded a message. The chain mechanism follows:\n\u2022 Stage i: Agent B forwards a request for the file f to\nAi (through {Ak}k\u2264i).\n\u2022 If Ai reports yes, then B downloads f from Ai.\nSTOP.\n\u2022 Otherwise Ai reports no.\nIf Aj sends a certificate(Ak, f) to B, ( j, k \u2264 i), then\n- If certificate(Ak, f) is correct, then t(Ak, Aj) =\n\u03b2p. STOP.\n- Else, t(Aj, Ak) = C + . STOP.\nIf Ai reports that he has no copy of the file, then any agent\nin between might challenge. Using digital signatures and\nacknowledgements, observe that every agent must forward\neach message, even if it contains a certificate showing that\nhe himself has misreported.\nWe use the same fine, \u03b2p, as in the basic mechanism,\nbecause the protocol might end at stage 1 (clearly, the former\nanalysis still applies, since the actual p increases with the\nnumber of players).\n3.3 Network Mechanism\nIn this subsection we consider general network structures.\nWe need the assumption that there is a ping protocol that\nchecks whether a neighbor agent is on-line or not (that is,\nan on-line agent cannot hide himself). To limit the amount\nof information to be recorded, we assume that an agent is\ncommitted to keep any downloaded file to at least one hour,\nand so certificates are valid for a limited amount of time. We\nassume that each agent has a digitally signed listing of his\ncurrent immediate neighbors. As in real P2P file sharing\napplications, we restrict each request for a file to be forwarded\nat most r times (that is, downloads are possible only inside\na neighborhood of radius r).\n245\nThe network mechanism utilizes the chain mechanism in\nthe following way: When agent B requests a file from agent\nA (at most r \u2212 1 far), then A sends to B the list of his\nneighbors and the output of the ping protocol to all of these\nneighbors. As a result, B can explore the network.\nRemark: In this mechanism we assumed that the\nenvironment is p-informed. An important design issue that it\nis not addressed here is the incentives for the information\npropagation phase.\n4. WEB CACHE\nWeb caches are widely used tool to improve overall\nsystem efficiency by allowing fast local access. They were listed\nin [12] as a challenging application of Distributed\nAlgorithmic Mechanism Design.\nNisan [30] considered a single cache shared by strategic\nagents. In this problem, agent i gains the value vT\ni if a\nparticular item is loaded to the local shared cache. The\nefficient goal is to load the item if and only if \u03a3vT\ni \u2265 C,\nwhere C is the loading cost. This goal reduces to the public\nproject problem analyzed by Clarke [10]. However, it is well\nknown that this mechanism is not budget-balanced (e.g., if\nthe valuation of each player is C, then everyone pays zero).\nIn this section we suggest informational and\nenvironmental assumptions for which we describe a decentralized\nbudgetbalanced efficient mechanism. We consider environments\nfor which future demand of each agent depends on past\ndemand. The underlying informational and environmental\nrequirements are as follows.\n1. An agent can read the content of a message only if he\nis the target node (even if he has to forward the\nmessage as an intermediate node of some routing path).\nAn agent cannot initiate a message on behalf of other\nagents.\n2. An acknowledgement protocol is available, so that\nevery agent can provide a certificate indicating that he\nhandled a certain message properly.\n3. Negligible costs: we assume p-informed agents, where\np is such that the agent\"s induced cost for keeping\nrecords of information is negligible. We also assume\nthat the cost incurred by sending and forwarding\nmessages is negligible.\n4. Let qi(t) denotes the number of loading requests agent\ni initiated for the item during the time slot t. We\nassume that vT\ni (t), the value for caching the item in\nthe beginning of slot t depends only on most recent\nslot, formally vT\ni (t) = max{Vi(qi(t \u2212 1)), C}, where\nVi(\u00b7) is a non-decreasing real function. In addition,\nVi(\u00b7) is a common knowledge among the players.\n5. The network is homogeneous in the sense that if\nagent j happens to handle k requests initiated by agent\ni during the time slot t, then qi(t) = k\u03b1, where \u03b1\ndepends on the routing protocol and the environment\n(\u03b1 might be smaller than 1, if each request is flooded\nseveral times). We assume that the only way agent i\ncan affect the true qi(t) is by superficially increasing\nhis demand for the cached item, but not the other way\n(that is, agent\"s loss, incurred by giving up a necessary\nrequest for the item, is not negligible).\nThe first requirement is to avoid free riding, and also to\navoid the case that an agent superficially increases the\ndemand of others and as a result decreases his own demand.\nThe second requirement is to avoid the case that an agent\nwho gets a routing request for the item, records it and then\ndrops it. The third is to ensure that the environment stays\nwell informed. In addition, if the forwarding cost is\nnegligible each agent cooperates and forwards messages as he would\nnot like to decrease the future demand (that monotonically\ndepends on the current time slot, as assumed in the forth\nrequirement) of some other agent. Given that the payments\nare increasing with the declared values, the forth and fifth\nrequirements ensure that the agent would not increase his\ndemand superficially and so qi(t) is the true demand.\nThe following Web-Cache Mechanism implements the\nefficient goal that shares the cost proportionally. For simplicity\nit is described for two players and w.l.o.g vT\ni (t) equals the\nnumber of requests initiated by i and observed by any\ninformed j (that is, \u03b1 = 1 and Vi(qi(t \u2212 1)) = qi(t \u2212 1)).\n\u2022 Stage 1: (Elicitation of vT\nA(t))\nAlice announces vA.\nBob announces vA \u2265 vA. If vA = vA goto the next\nStage. Otherwise (Bob challenges):\n- If Bob provides vA valid records then Alice pays C\nto finance the loading of the item into the cache.\nShe also pays \u03b2p to Bob. STOP.\n- Otherwise, Bob finances the loading of the item\ninto the cache. STOP.\n\u2022 Stage 2: The elicitation of vT\nB(t) is done analogously.\n\u2022 Stage 3: If vA + vB < C, then STOP.\nOtherwise, load the item to the cache, Alice pays pA =\nvA\nvA+vB\n\u00b7 C, and Bob pays pB = vB\nvA+vB\n\u00b7 C.\nClaim 7. It is a dominated strategy to overreport the true\nvalue.\nProof. Let vT\nA < VA. There are two cases to consider:\n\u2022 If vT\nA + vB < C and vA + vB \u2265 C.\nWe need to show that if the mechanism stops normally\nAlice would pay more than vT\nA, that is: vA\nvA+vB\n\u00b7C > vT\nA.\nIndeed, vA C > vA (vT\nA + vB) > vT\nA (vA + vB).\n\u2022 If vT\nA + vB \u2265 C, then clearly, vA\nvA+vB\n>\nvT\nA\nvT\nA\n+vB\n.\nTheorem 2. Let \u03b2p = max{0, 1\u22122p\np\n\u00b7 C} + , p \u2208\n(0, 1]. A strategy that survives iterative elimination of weakly\ndominated strategies is to report the truth and to challenge\nonly when the agent is informed. The mechanism is efficient,\nbudget-balanced, exhibits consumer sovereignty, no positive\ntransfer and individual rationality10\n.\nProof. Challenging without being informed (that is,\nwithout providing enough valid records) is always dominated\nstrategy in this mechanism. Now, assume w.l.o.g. Alice is\n10\nSee [29] or [12] for exact definitions.\n246\nthe last to report her value. Alice\"s expected payoff gained\nby underreporting \u2264\np \u00b7 (\u2212C \u2212 \u03b2p) + (1 \u2212 p) \u00b7 C < p \u00b7 0 + (1 \u2212 p) \u00b7 0 \u2264 Alice\"s\nexpected payoff if she honestly reports.\nThe right hand side equals zero as the participation costs\nare negligible. Reasoning back, Bob cannot expect to get\nthe bonus and so misreporting is dominated strategy for\nhim.\n5. CONCLUDING REMARKS\nIn this paper we have seen a new partial informational\nassumption, and we have demonstrated its suitability to\nnetworks in which computational agents can easily collect\nand distribute information. We then described some\nmechanisms using the concept of iterative elimination of weakly\ndominated strategies. Some issues for future work include:\n\u2022 As we have seen, the implementation issue in p-informed\nenvironments is straightforward - it is easy to construct\nincentive compatible mechanisms even for\nnon-singleparameter cases. The challenge is to find more realistic\nscenarios in which the partial informational\nassumption is applicable.\n\u2022 Mechanisms for information propagation and\nmaintenance. In our examples we choose p such that the\nmaintenance cost over time is negligible. However,\nthe dynamics of the general case is delicate: an agent\ncan use the recorded information to eliminate data\nthat is not likely to be needed, in order to decrease\nhis maintenance costs. As a result, the probability\nthat the environment is informed decreases, and\nselfish agents would not cooperate. Incentives for\ninformation propagation should be considered as well (e.g.,\nfor P2P networks for file sharing).\n\u2022 It seems that some social choice goals cannot be\nimplemented if each player is at least 1/n-malicious (where\nn is the number of players). It would be interesting to\nidentify these cases.\nAcknowledgements\nWe thank Meitav Ackerman, Moshe Babaioff, Liad\nBlumrozen, Michal Feldman, Daniel Lehmann, Noam Nisan, Motty\nPerry and Eyal Winter for helpful discussions.\n6. REFERENCES\n[1] A. Archer and E. Tardos. Truthful mechanisms for\none-parameter agents. 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Annales D\" Economie et De Statistique,\n61, 2001.\n248", "keywords": "iterative elimination of weakly dominated strategy;cooperation;distribute algorithmic mechanism design;p-informed environment;partially informed environment;weakly dominated strategy iterative elimination;agent;dominant strategy implementation;decentralized incentive compatible mechanism;distributed algorithmic mechanism design;peer-to-peer;vickrey-clarke-grove;distributed environment;computational entity"}
{"name": "train_J-61", "title": "ICE: An Iterative Combinatorial Exchange", "abstract": "We present the first design for an iterative combinatorial exchange (ICE). The exchange incorporates a tree-based bidding language that is concise and expressive for CEs. Bidders specify lower and upper bounds on their value for different trades. These bounds allow price discovery and useful preference elicitation in early rounds, and allow termination with an efficient trade despite partial information on bidder valuations. All computation in the exchange is carefully optimized to exploit the structure of the bid-trees and to avoid enumerating trades. A proxied interpretation of a revealedpreference activity rule ensures progress across rounds. A VCG-based payment scheme that has been shown to mitigate opportunities for bargaining and strategic behavior is used to determine final payments. The exchange is fully implemented and in a validation phase.", "fulltext": "1. INTRODUCTION\nCombinatorial exchanges combine and generalize two\ndifferent mechanisms: double auctions and combinatorial\nauctions. In a double auction (DA), multiple buyers and sellers\ntrade units of an identical good [20]. In a combinatorial\nauction (CA), a single seller has multiple heterogeneous items\nup for sale [11]. Buyers may have complementarities or\nsubstitutabilities between goods, and are provided with an\nexpressive bidding language. A common goal in both market\ndesigns is to determine the efficient allocation, which is the\nallocation that maximizes total value.\nA combinatorial exchange (CE) [24] is a combinatorial\ndouble auction that brings together multiple buyers and\nsellers to trade multiple heterogeneous goods. For example, in\nan exchange for wireless spectrum, a bidder may declare that\nshe is willing to pay $1 million for a trade where she obtains\nlicenses for New York City, Boston, and Philadelphia, and\nloses her license for Washington DC. Thus, unlike a DA, a\nCE allows all participants to express complex valuations via\nexpressive bids. Unlike a CA, a CE allows for fragmented\nownership, with multiple buyers and sellers and agents that\nare both buying and selling.\nCEs have received recent attention both in the context of\nwireless spectrum allocation [18] and for airport takeoff and\nlanding slot allocation [3]. In both of these domains there\nare incumbents with property rights, and it is important\nto facilitate a complex multi-way reallocation of resources.\nAnother potential application domain for CEs is to resource\nallocation in shared distributed systems, such as PlanetLab\n[13]. The instantiation of our general purpose design to\nspecific domains is a compelling next step in our research.\nThis paper presents the first design for an iterative\ncombinatorial exchange (ICE). The genesis of this project was a\nclass, CS 286r Topics at the Interface between Economics\nand Computer Science, taught at Harvard University in\nSpring 2004.1\nThe entire class was dedicated to the design\nand prototyping of an iterative CE.\nThe ICE design problem is multi-faceted and quite hard.\nThe main innovation in our design is an expressive yet\nconcise tree-based bidding language (which generalizes known\nlanguages such as XOR/OR [23]), and the tight coupling\nof this language with efficient algorithms for price-feedback\nto guide bidding, winner-determination to determine trades,\nand revealed-preference activity rules to ensure progress\nacross rounds. The exchange is iterative: bidders express\nupper and lower valuations on trades by annotating their\nbid-tree, and then tighten these bounds in response to price\nfeedback in each round. The Threshold payment rule,\nintroduced by Parkes et al. [24], is used to determine final\npayments.\nThe exchange has a number of interesting theoretical\nproperties. For instance, when there exist linear prices we\nestablish soundness and completeness: for straightforward\nbidders that adjust their bounds to meet activity rules while\nkeeping their true value within the bounds, the exchange\nwill terminate with the efficient allocation. In addition, the\n1\nhttp://www.eecs.harvard.edu/\u223cparkes/cs286r/ice.html\n249\nTruth Agent Act Rule WD ACC\nFAIR\nBALClosing RuleVickreyThreshold\nDONE\n! DONE\n2,2\n+A\n+10\n+B\n+10\nBUYER\n2,2\n-A\n-5\n-B\n-5\nSELLER\n2,2\n+A\n+15\n+8\n+B\n+15\n+8\nBUYER\n2,2\n-A\n-2\n-6\n-B\n-2\n-6\nSELLER\nBUYER, buy AB\nSELLER, sell AB\n12 < PA+PB < 16\nPA+PB=14\nPA=PB=7\nPBUYER = 16 - (4-0) = 12\nPSELLER = -12 - (4-0) = -16\nPBUYER = 14\nPSELLER = -14\nPessim\nistic\nO\nptim\nistic = 1\nFigure 1: ICE System Flow of Control\nefficient allocation can often be determined without bidders\nrevealing, or even knowing, their exact value for all trades.\nThis is essential in complex domains where the valuation\nproblem can itself be very challenging for a participant [28].\nWhile we cannot claim that straightforward bidding is an\nequilibrium of the exchange (and indeed, should not expect\nto by the Myerson-Satterthwaite impossibility theorem [22]),\nthe Threshold payment rule minimizes the ex post incentive\nto manipulate across all budget-balanced payment rules.\nThe exchange is implemented in Java and is currently in\nvalidation. In describing the exchange we will first provide\nan overview of the main components and introduce several\nworking examples. Then, we introduce the basic\ncomponents for a simple one-shot variation in which bidders state\ntheir exact values for trades in a single round. We then\ndescribe the full iterative exchange, with upper and lower\nvalues, price-feedback, activity rules, and termination\nconditions. We state some theoretical properties of the exchange,\nand end with a discussion to motivate our main design\ndecisions, and suggest some next steps.\n2. AN OVERVIEW OF THE ICE DESIGN\nThe design has four main components, which we will\nintroduce in order through the rest of the paper:\n\u2022 Expressive and concise tree-based bidding language.\nThe language describes values for trades, such as my value\nfor selling AB and buying C is $100, or my value for selling\nABC is -$50, with negative values indicating that a bidder\nmust receive a payment for the trade to be acceptable. The\nlanguage allows bidders to express upper and lower bounds\non value, which can be tightened across rounds.\n\u2022 Winner Determination. Winner-determination (WD)\nis formulated as a mixed-integer program (MIP), with the\nstructure of the bid-trees captured explicitly in the\nformulation. Comparing the solution at upper and lower values\nallows for a determination to be made about termination,\nwith progress in intermediate rounds driven by an\nintermediate valuation and the lower values adopted on termination.\n\u2022 Payments. Payments are computed using the Threshold\npayment rule [24], with the intermediate valuations adopted\nin early rounds and lower values adopted on termination.\n\u2022 Price feedback. An approximate price is computed\nfor each item in the exchange in each round, in terms of\nthe intermediate valuations and the provisional trade. The\nprices are optimized to approximate competitive equilibrium\nprices, and further optimized to best approximate the\ncurrent Threshold payments with remaining ties broken to favor\nprices that are balanced across different items. In computing\nthe prices, we adopt the methods of constraint-generation to\nexploit the structure of the bidding language and avoid\nenumerating all feasible trades. The subproblem to generate\nnew constraints is a variation of the WD problem.\n\u2022 Activity rule. A revealed-preference activity rule [1]\nensures progress across rounds. In order to remain active, a\nbidder must tighten bounds so that there is enough\ninformation to define a trade that maximizes surplus at the current\nprices. Another variation on the WD problem is formulated,\nboth to verify that the activity rule is met and also to\nprovide feedback to a bidder to explain how to meet the rule.\nAn outline of the ICE system flow of control is provided\nin Figure 1. We will return to this example later in the\npaper. For now, just observe in this two-agent example that\nthe agents state lower and upper bounds that are checked in\nthe activity rule, and then passed to winner-determination\n(WD), and then through three stages of pricing (accuracy,\nfairness, balance). On passing the closing rule (in which\nparameters \u03b1eff\nand \u03b1thresh\nare checked for convergence of the\ntrade and payments), the exchange goes to a last-and-final\nround. At the end of this round, the trade and payments\nare finally determined, based on the lower valuations.\n2.1 Related Work\nMany ascending-price one-sided CAs are known in the\nliterature [10, 25, 29]. Direct elicitation approaches have also\nbeen proposed for one-sided CAs in which agents respond to\nexplicit queries about their valuations [8, 14, 19]. A number\nof ascending CAs are designed to work with simple prices\non items [12, 17]. The price generation methods that we use\nin ICE generalize the methods in these earlier papers.\nParkes et al. [24] studied sealed-bid combinatorial\nexchanges and introduced the Threshold payment rule.\nSubsequently, Krych [16] demonstrated experimentally that the\nThreshold rule promotes efficient allocations. We are not\naware of any previous studies of iterative CEs. Dominant\nstrategy DAs are known for unit demand [20] and also for\nsingle-minded agents [2]. No dominant strategy mechanisms\nare known for the general CE problem.\nICE is a hybrid auction design, in that it couples\nsimple item prices to drive bidding in early rounds with\ncombinatorial WD and payments, a feature it shares with the\nclock-proxy design of Ausubel et al. [1] for one-sided CAs.\nWe adopt a variation on the clock-proxy auctions\"s\nrevealedpreference activity rule.\nThe bidding language shares some structural elements\nwith the LGB language of Boutilier and Hoos [7], but has\nvery different semantics. Rothkopf et al. [27] also describe a\nrestricted tree-based bidding language. In LGB, the\nsemantics are those of propositional logic, with the same items\nin an allocation able to satisfy a tree in multiple places.\nAlthough this can make LGB especially concise in some\nsettings, the semantics that we propose appear to provide\nuseful locality, so that the value of one component in a tree\ncan be understood independently from the rest of the tree.\nThe idea of capturing the structure of our bidding language\nexplicitly within a mixed-integer programming formulation\nfollows the developments in Boutilier [6].\n3. PRELIMINARIES\nIn our model, we consider a set of goods, indexed {1, . . . ,\nm} and a set of bidders, indexed {1, . . . , n}. The initial\nallocation of goods is denoted x0\n= (x0\n1, . . . , x0\nn), with x0\ni =\n(x0\ni1, . . . , x0\nim) and x0\nij \u2265 0 for good j indicating the number\n250\nof units of good j held by bidder i. A trade \u03bb = (\u03bb1, . . . , \u03bbn)\ndenotes the change in allocation, with \u03bbi = (\u03bbi1, . . . , \u03bbim)\nwhere \u03bbij \u2208\n\nis the change in the number of units of item\nj to bidder i. So, the final allocation is x1\n= x0\n+ \u03bb.\nEach bidder has a value vi(\u03bbi) \u2208 \u00a1 for a trade \u03bbi. This\nvalue can be positive or negative, and represents the change\nin value between the final allocation x0\ni +\u03bbi and the initial\nallocation x0\ni . Utility is quasi-linear, with ui(\u03bbi, p) = vi(\u03bbi)\u2212p\nfor trade \u03bbi and payment p \u2208 \u00a1 . Price p can be negative,\nindicating the bidder receives a payment for the trade. We\nuse the term payoff interchangeably with utility.\nOur goal in the ICE design is to implement the efficient\ntrade. The efficient trade, \u03bb\u2217\n, maximizes the total increase\nin value across bidders.\nDefinition 1 (Efficient trade). The efficient trade\n\u03bb\u2217\nsolves\nmax\n(\u03bb1,...,\u03bbn)\n\u00a2\ni\nvi(\u03bbi)\ns.t. \u03bbij + x0\nij \u2265 0, \u2200i, \u2200j (1)\n\u00a2\ni\n\u03bbij \u2264 0, \u2200j (2)\n\u03bbij \u2208\n\n(3)\nConstraints (1) ensure that no agent sells more items than\nit has in its initial allocation. Constraints (2) provide free\ndisposal, and allows feasible trades to sell more items than\nare purchased (but not vice versa).\nLater, we adopt Feas(x0\n) to denote the set of feasible\ntrades, given these constraints and given an initial\nallocation x0\n= (x0\n1, . . . , x0\nn).\n3.1 Working Examples\nIn this section, we provide three simple examples of\ninstances that we will use to illustrate various components of\nthe exchange. All three examples have only one seller, but\nthis is purely illustrative.\nExample 1. One seller and one buyer, two goods {A, B},\nwith the seller having an initial allocation of AB. Changes\nin values for trades:\nseller buyer\nAND(\u2212A, \u2212B) AND(+A, +B)\n-10 +20\nThe AND indicates that both the buyer and the seller\nare only interested in trading both goods as a bundle. Here,\nthe efficient (value-maximizing) trade is for the seller to sell\nAB to the buyer, denoted \u03bb\u2217\n= ([\u22121, \u22121], [+1, +1]).\nExample 2. One seller and four buyers, four goods {A, B,\nC, D}, with the seller having an initial allocation of ABCD.\nChanges in values for trades:\nseller buyer1 buyer 2 buyer 3 buyer 4\nOR(\u2212A, \u2212B, AND(+A, XOR(+A, AND(+C, XOR(+C,\n\u2212C, \u2212D) +B) +B) +D) +D)\n0 +6 +4 +3 +2\nThe OR indicates that the seller is willing to sell any\nnumber of goods. The XOR indicates that buyers 2 and\n4 are willing to buy at most one of the two goods in which\nthey are interested. The efficient trade is for bundle AB\nto go to buyer 1 and bundle CD to buyer 3, denoted \u03bb\u2217\n=\n([\u22121, \u22121, \u22121, \u22121], [+1, +1, 0, 0], [0, 0, 0, 0], [0, 0, +1, +1],\n[0, 0, 0, 0]).\n2,2\n+A\n+10\n+B\n+10\nBUYER\n2,2\n-A\n-5\n-B\n-5\nSELLER\nExample 1: Example 3:\n2,2\n+C +D\nBUYER 2\n2,2\n+A +B\nBUYER 1\n+11 +84,4\n-B\nSELLER\n-A -C -D\nExample 2:\n1,1\n+A +B\nBUYER 2\n2,2\n+A +B\nBUYER 1\n+6 +40,4\n-B\nSELLER\n-C -D-A\n1,1\n+C +D\nBUYER 4\n2,2\n+C +D\n+3 +2\nBUYER 3\n-18\nFigure 2: Example Bid Trees.\nExample 3. One seller and two buyers, four goods {A, B,\nC, D}, with the seller having an initial allocation of ABCD.\nChanges in values for trades:\nseller buyer1 buyer 2\nAND(\u2212A, \u2212B, \u2212C, \u2212D) AND(+A, +B) AND(+C, +D)\n-18 +11 +8\nThe efficient trade is for bundle AB to go to buyer 1 and\nbundle CD to go to buyer 2, denoted \u03bb\u2217\n= ([\u22121, \u22121, \u22121, \u22121],\n[+1, +1, 0, 0], [0, 0, +1, +1]).\n4. A ONE-SHOT EXCHANGE DESIGN\nThe description of ICE is broken down into two sections:\none-shot (sealed-bid) and iterative. In this section we\nabstract away the iterative aspect and introduce a\nspecialization of the tree-based language that supports only exact\nvalues on nodes.\n4.1 Tree-Based Bidding Language\nThe bidding language is designed to be expressive and\nconcise, entirely symmetric with respect to buyers and\nsellers, and to extend to capture bids from mixed buyers and\nsellers, ranging from simple swaps to highly complex trades.\nBids are expressed as annotated bid trees, and define a\nbidder\"s value for all possible trades.\nThe language defines changes in values on trades, with\nleaves annotated with traded items and nodes annotated\nwith changes in values (either positive or negative). The\nmain feature is that it has a general interval-choose\nlogical operator on internal nodes, and that it defines careful\nsemantics for propagating values within the tree. We\nillustrate the language on each of Examples 1-3 in Figure 2.\nThe language has a tree structure, with trades on items\ndefined on leaves and values annotated on nodes and leaves.\nThe nodes have zero values where no value is indicated.\nInternal nodes are also labeled with interval-choose (IC)\nranges. Given a trade, the semantics of the language define\nwhich nodes in the tree can be satisfied, or switched-on.\nFirst, if a child is on then its parent must be on. Second, if\na parent node is on, then the number of children that are on\nmust be within the IC range on the parent node. Finally,\nleaves in which the bidder is buying items can only be on if\nthe items are provided in the trade.\nFor instance, in Example 2 we can consider the efficient\ntrade, and observe that in this trade all nodes in the trees of\nbuyers 1 and 3 (and also the seller), but none of the nodes in\nthe trees of buyers 2 and 4, can be on. On the other hand, in\n251\nthe trade in which A goes to buyer 2 and D to buyer 4, then\nthe root and appropriate leaf nodes can be on for buyers 2\nand 4, but no nodes can be on for buyers 1 and 3. Given a\ntrade there is often a number of ways to choose the set of\nsatisfied nodes. The semantics of the language require that\nthe nodes that maximize the summed value across satisfied\nnodes be activated.\nConsider bid tree Ti from bidder i. This defines nodes \u03b2 \u2208\nTi, of which some are leaves, Leaf (i) \u2286 Ti. Let Child(\u03b2) \u2286\nTi denote the children of a node \u03b2 (that is not itself a leaf).\nAll nodes except leaves are labeled with the interval-choose\noperator [IC x\ni (\u03b2), ICy\ni (\u03b2)]. Every node is also labeled with a\nvalue, vi\u03b2 \u2208 \u00a1 . Each leaf \u03b2 is labeled with a trade, qi\u03b2 \u2208\n\nm\n(i.e., leaves can define a bundled trade on more than one\ntype of item.)\nGiven a trade \u03bbi to bidder i, the interval-choose operators\nand trades on leaves define which nodes can be satisfied.\nThere will often be a choice. Ties are broken to maximize\nvalue. Let sati\u03b2 \u2208 {0, 1} denote whether node \u03b2 is satisfied.\nSolution sati is valid given tree Ti and trade \u03bbi, written\nsati \u2208 valid(Ti, \u03bbi), if and only if:\n\u00a2\n\u03b2\u2208Leaf (i)\nqi\u03b2j \u00b7 sati\u03b2 \u2264 \u03bbij , \u2200i, \u2200j (4)\nICx\ni (\u03b2)sati\u03b2 \u2264\n\u00a2\n\u03b2 \u2208Child(\u03b2)\nsati\u03b2 \u2264 ICy\ni (\u03b2)sati\u03b2, \u2200\u03b2 /\u2208 Leaf (i) (5)\nIn words, a set of leaves can only be considered satisfied\ngiven trade \u03bbi if the total increase in quantity summed across\nall such leaves is covered by the trade, for all goods (Eq. 4).\nThis works for sellers as well as buyers: for sellers a trade\nis negative and this requires that the total number of items\nindicated sold in the tree is at least the total number sold as\ndefined in the trade. We also need upwards-propagation:\nany time a node other than the root is satisfied then its\nparent must be satisfied (by\n\u03b2 \u2208Child(\u03b2) sati\u03b2 \u2264 ICy\ni (\u03b2)sati\u03b2\nin Eq. 5). Finally, we need downwards-propagation: any\ntime an internal node is satisfied then the appropriate\nnumber of children must also be satisfied (Eq. 5). The total\nvalue of trade \u03bbi, given bid-tree Ti, is defined as:\nvi(Ti, \u03bbi) = max\nsat\u2208valid(Ti,\u03bbi)\n\u00a2\n\u03b2\u2208T\nv\u03b2 \u00b7 sat\u03b2 (6)\nThe tree-based language generalizes existing languages.\nFor instance: IC(2, 2) on a node with 2 children is equivalent\nto an AND operator; IC(1, 3) on a node with 3 children is\nequivalent to an OR operator; and IC(1, 1) on a node with\n2 children is equivalent to an XOR operator. Similarly, the\nXOR/OR bidding languages can be directly expressed as a\nbid tree in our language.2\n4.2 Winner Determination\nThis section defines the winner determination problem,\nwhich is formulated as a MIP and solved in our\nimplementation with a commercial solver.3\nThe solver uses\nbranchand-bound search with dynamic cut generation and\nbranching heuristics to solve large MIPs in economically feasible\nrun times.\n2\nThe OR* language is the OR language with dummy items\nto provide additional structure. OR* is known to be\nexpressive and concise. However, it is not known whether OR*\ndominates XOR/OR in terms of conciseness [23].\n3\nCPLEX, www.ilog.com\nIn defining the MIP representation we are careful to avoid\nan XOR-based enumeration of all bundles. A variation on\nthe WD problem is reused many times within the exchange,\ne.g. for column generation in pricing and for checking\nrevealed preference.\nGiven bid trees T = (T1, . . . , Tn) and initial allocation x0\n,\nthe mixed-integer formulation for WD is:\nWD(T, x0\n) : max\n\u03bb,sat\n\u00a2\ni\n\u00a2\n\u03b2\u2208Ti\nvi\u03b2 \u00b7 sati\u03b2\ns.t. (1), (2), sati\u03b2 \u2208 {0, 1}, \u03bbij \u2208\n\nsati \u2208 valid(Ti, \u03bbi), \u2200i\nSome goods may go unassigned because free disposal is\nallowed within the clearing rules of winner determination.\nThese items can be allocated back to agents that sold the\nitems, i.e. for which \u03bbij < 0.\n4.3 Computing Threshold Payments\nThe Threshold payment rule is based on the payments\nin the Vickrey-Clarke-Groves (VCG) mechanism [15], which\nitself is truthful and efficient but does not satisfy budget\nbalance. Budget-balance requires that the total payments\nto the exchange are equal to the total payments made by\nthe exchange. In VCG, the payment paid by agent i is\npvcg,i = \u02c6v(\u03bb\u2217\ni ) \u2212 (V \u2217\n\u2212 V\u2212i) (7)\nwhere \u03bb\u2217\nis the efficient trade, V \u2217\nis the reported value of\nthis trade, and V\u2212i is the reported value of the efficient\ntrade that would be implemented without bidder i. We\ncall \u2206vcg,i = V \u2217\n\u2212 V\u2212i the VCG discount. For instance,\nin Example 1 pvcg,seller = \u221210 \u2212 (+10 \u2212 0) = \u221220 and\npvcg,buyer = +20 \u2212 (+10 \u2212 0) = 10, and the exchange would\nrun at a budget deficit of \u221220 + 10 = \u221210.\nThe Threshold payment rule [24] determines\nbudgetbalanced payments to minimize the maximal error across all\nagents to the VCG outcome.\nDefinition 2. The Threshold payment scheme implements\nthe efficient trade \u03bb\u2217\ngiven bids, and sets payments pthresh,i =\n\u02c6vi(\u03bb\u2217\ni ) \u2212 \u2206i, where \u2206 = (\u22061, . . . , \u2206n) is set to minimize\nmaxi(\u2206vcg,i \u2212 \u2206i) subject to \u2206i \u2264 \u2206vcg,i and\ni \u2206i \u2264 V \u2217\n(this gives budget-balance).\nExample 4. In Example 2, the VCG discounts are (9, 2,\n0, 1, 0) to the seller and four buyers respectively, VCG\npayments are (\u22129, 4, 0, 2, 0) and the exchange runs at a deficit\nof -3. In Threshold, the discounts are (8, 1, 0, 0, 0) and the\npayments are (\u22128, 5, 0, 3, 0). This minimizes the worst-case\nerror to VCG discounts across all budget-balanced payment\nschemes.\nThreshold payments are designed to minimize the\nmaximal ex post incentive to manipulate. Krych [16] confirmed\nthat Threshold promotes allocative efficiency in restricted\nand approximate Bayes-Nash equilibrium.\n5. THE ICE DESIGN\nWe are now ready to introduce the iterative\ncombinatorial exchange (ICE) design. Several new components are\nintroduced, relative to the design for the one-shot exchange.\nRather than provide precise valuations, bidders can provide\nlower and upper valuations and revise this bid information\nacross rounds. The exchange provides price-based feedback\n252\nto guide bidders in this process, and terminates with an\nefficient (or approximately-efficient) trade with respect to\nreported valuations.\nIn each round t \u2208 {0, 1, . . .} the current lower and upper\nbounds, vt\nand vt\n, are used to define a provisional\nvaluation profile v\u03b1\n(the \u03b1-valuation), together with a provisional\ntrade \u03bbt\nand provisional prices pt\n= (pt\n1, . . . , pt\nm) on items.\nThe \u03b1-valuation is a linear combination of the current\nupper and lower valuations, with \u03b1EFF\n\u2208 [0, 1] chosen\nendogenously based on the closeness of the optimistic trade (at\nv) and the pessimistic trade (at v). Prices pt\nare used to\ninform an activity rule, and drive progress towards an efficient\ntrade.\n5.1 Upper and Lower Valuations\nThe bidding language is extended to allow a bidder i to\nreport a lower and upper value (vi\u03b2, vi\u03b2) on each node. These\ntake the place of the exact value vi\u03b2 defined in Section 4.1.\nBased on these labels, we can define the valuation functions\nvi(Ti, \u03bbi) and vi(Ti, \u03bbi), using the exact same semantics as\nin Eq. (6). We say that such a bid-tree is well-formed if\nvi\u03b2 \u2264 vi\u03b2 for all nodes. The following lemma is useful:\nLemma 1. Given a well-formed tree, T, then vi(Ti, \u03bbi) \u2264\nvi(Ti, \u03bbi) for all trades.\nProof. Suppose there is some \u03bbi for which vi(Ti, \u03bbi) >\nvi(Ti, \u03bbi). Then, maxsat\u2208valid(Ti,\u03bbi)\n\u03b2\u2208Ti\nvi\u03b2 \u00b7 sat\u03b2 >\nmaxsat\u2208valid(Ti,\u03bbi)\n\u03b2\u2208Ti\nvi\u03b2 \u00b7 sat\u03b2. But, this is a\ncontradiction because the trade \u03bb that defines vi(Ti, \u03bbi) is still\nfeasible with upper bounds vi, and vi\u03b2 \u2265 vi\u03b2 for all nodes\n\u03b2 in a well-formed tree.\n5.2 Price Feedback\nIn each round, approximate competitive-equilibrium (CE)\nprices, pt\n= (pt\n1, . . . , pt\nm), are determined. Given these\nprovisional prices, the price on trade \u03bbi for bidder i is pt\n(\u03bbi) =\n\nj\u2264m pt\nj \u00b7 \u03bbij.\nDefinition 3 (CE prices). Prices p\u2217\nare competitive\nequilibrium prices if the efficient trade \u03bb\u2217\nis supported at\nprices p\u2217\n, so that for each bidder:\n\u03bb\u2217\ni \u2208 arg max\n\u03bb\u2208Feas(x0)\n{vi(\u03bbi) \u2212 p\u2217\n(\u03bbi)} (8)\nCE prices will not always exist and we will often need to\ncompute approximate prices [5]. We extend ideas due to\nRassenti et al. [26], Kwasnica et al. [17] and Dunford et al.\n[12], and select approximate prices as follows:\nI: Accuracy. First, we compute prices that minimize the\nmaximal error in the best-response constraints across\nall bidders.\nII: Fairness. Second, we break ties to prefer prices that\nminimize the maximal deviation from Threshold\npayments across all bidders.\nIII: Balance. Third, we break ties to prefer prices that\nminimize the maximal price across all items.\nTaken together, these steps are designed to promote the\ninformativeness of the prices in driving progress across rounds.\nIn computing prices, we explain how to compute\napproximate (or otherwise) prices for structured bidding languages,\nand without enumerating all possible trades. For this, we\nadopt constraint generation to efficient handle an\nexponential number of constraints. Each step is described in detail\nbelow.\nI: Accuracy. We adopt a definition of price accuracy that\ngeneralizes the notions adopted in previous papers for\nunstructured bidding languages. Let \u03bbt\ndenote the current\nprovisional trade and suppose the provisional valuation is\nv\u03b1\n. To compute accurate CE prices, we consider:\nmin\np,\u03b4\n\u03b4 (9)\ns.t. v\u03b1\ni (\u03bb) \u2212 p(\u03bb) \u2264 v\u03b1\ni (\u03bbt\ni) \u2212 p(\u03bbt\ni) + \u03b4, \u2200i, \u2200\u03bb (10)\n\u03b4 \u2265 0,pj \u2265 0, \u2200j.\nThis linear program (LP) is designed to find prices that\nminimize the worst-case error across all agents.\nFrom the definition of CE prices, it follows that CE prices\nwould have \u03b4 = 0 as a solution to (9), at which point trade\n\u03bbt\ni would be in the best-response set of every agent (with\n\u03bbt\ni = \u2205, i.e. no trade, for all agents with no surplus for trade\nat the prices.)\nExample 5. We can illustrate the formulation (9) on\nExample 2, assuming for simplicity that v\u03b1\n= v (i.e. truth).\nThe efficient trade allocates AB to buyer 1 and CD to buyer\n3. Accuracy will seek prices p(A), p(B), p(C) and p(D) to\nminimize the \u03b4 \u2265 0 required to satisfy constraints:\np(A) + p(B) + p(C) + p(D) \u2265 0 (seller)\np(A) + p(B) \u2264 6 + \u03b4 (buyer 1)\np(A) + \u03b4 \u2265 4, p(B) + \u03b4 \u2265 4 (buyer 2)\np(C) + p(D) \u2264 3 (buyer 3)\np(C) + \u03b4 \u2265 2, p(D) + \u03b4 \u2265 2 (buyer 4)\nAn optimal solution requires p(A) = p(B) = 10/3, with\n\u03b4 = 2/3, with p(C) and p(D) taking values such as p(C) =\np(D) = 3/2.\nBut, (9) has an exponential number of constraints (Eq. 10).\nRather than solve it explicitly we use constraint\ngeneration [4] and dynamically generate a sufficient subset of\nconstraints. Let\ni denote a manageable subset of all possible\nfeasible trades to bidder i. Then, a relaxed version of (9)\n(written ACC) is formulated by substituting (10) with\nv\u03b1\ni (\u03bb) \u2212 p(\u03bb) \u2264 v\u03b1\ni (\u03bbt\ni) \u2212 p(\u03bbt\ni) + \u03b4, \u2200i, \u2200\u03bb \u2208\ni , (11)\nwhere\ni is a set of trades that are feasible for bidder i\ngiven the other bids. Fixing the prices p\u2217\n, we then solve n\nsubproblems (one for each bidder),\nmax\n\u03bb\nv\u03b1\ni (\u03bbi) \u2212 p\u2217\n(\u03bbi) [R-WD(i)]\ns.t. \u03bb \u2208 Feas(x0\n), (12)\nto check whether solution (p\u2217\n, \u03b4\u2217\n) to ACC is feasible in\nproblem (9). In R-WD(i) the objective is to determine a most\npreferred trade for each bidder at these prices. Let \u02c6\u03bbi denote\nthe solution to R-WD(i). Check condition:\nv\u03b1\ni (\u02c6\u03bbi) \u2212 p\u2217\n(\u02c6\u03bb) \u2264 v\u03b1\ni (\u03bbt\ni) \u2212 p\u2217\n(\u03bbt\ni) + \u03b4\u2217\n, (13)\nand if this condition holds for all bidders i, then solution\n(p\u2217\n, \u03b4\u2217\n) is optimal for problem (9). Otherwise, trade \u02c6\u03bbi is\nadded to\ni for all bidders i for which this constraint is\n253\nviolated and we re-solve the LP with the new set of\nconstraints.4\nII: Fairness. Second, we break remaining ties to prefer fair\nprices: choosing prices that minimize the worst-case error\nwith respect to Threshold payoffs (i.e. utility to bidders with\nThreshold payments), but without choosing prices that are\nless accurate.5\nExample 6. For example, accuracy in Example 1\n(depicted in Figure 1) requires 12 \u2264 pA +pB \u2264 16 (for v\u03b1\n= v).\nAt these valuations the Threshold payoffs would be 2 to both\nthe seller and the buyer. This can be exactly achieved in\npricing with pA + pB = 14.\nThe fairness tie-breaking method is formulated as the\nfollowing LP:\nmin\np,\u03c0\n\u03c0 [FAIR]\ns.t. v\u03b1\ni (\u03bb) \u2212 p(\u03bb) \u2264 v\u03b1\ni (\u03bbt\ni) \u2212 p(\u03bbt\ni) + \u03b4\u2217\ni , \u2200i, \u2200\u03bb \u2208\ni (14)\n\u03c0 \u2265 \u03c0vcg,i \u2212 (v\u03b1\ni (\u03bbt\ni) \u2212 p(\u03bbt\ni)), \u2200i (15)\n\u03c0 \u2265 0,pj \u2265 0, \u2200j,\nwhere \u03b4\u2217\nrepresents the error in the optimal solution, from\nACC. The objective here is the same as in the Threshold\npayment rule (see Section 4.3): minimize the maximal\nerror between bidder payoff (at v\u03b1\n) for the provisional trade\nand the VCG payoff (at v\u03b1\n). Problem FAIR is also solved\nthrough constraint generation, using R-WD(i) to add\nadditional violated constraints as necessary.\nIII: Balance. Third, we break remaining ties to prefer\nbalanced prices: choosing prices that minimize the maximal\nprice across all items. Returning again to Example 1,\ndepicted in Figure 1, we see that accuracy and fairness require\np(A) + p(B) = 14. Finally, balance sets p(A) = p(B) = 7.\nBalance is justified when, all else being equal, items are\nmore likely to have similar than dissimilar values.6\nThe LP\nfor balance is formulated as follows:\nmin\np,Y\nY [BAL]\ns.t. v\u03b1\ni (\u03bb) \u2212 p(\u03bb) \u2264 v\u03b1\ni (\u03bbt\ni) \u2212 p(\u03bbt\ni) + \u03b4\u2217\ni , \u2200i, \u2200\u03bb \u2208\ni (16)\n\u03c0\u2217\ni \u2265 \u03c0vcg,i \u2212 (v\u03b1\ni (\u03bbt\ni) \u2212 p(\u03bbt\ni)), \u2200i, (17)\nY \u2265 pj, \u2200j (18)\nY \u2265 0, pj \u2265 0, \u2200j,\nwhere \u03b4\u2217\nrepresents the error in the optimal solution from\nACC and \u03c0\u2217\nrepresents the error in the optimal solution\nfrom FAIR. Constraint generation is also used to solve BAL,\ngenerating new trades for\ni as necessary.\n4\nProblem R-WD(i) is a specialization of the WD problem,\nin which the objective is to maximize the payoff of a single\nbidder, rather than the total value across all bidders. It is\nsolved as a MIP, by rewriting the objective in WD(T, x0\n)\nas max{vi\u03b2 \u00b7 sati\u03b2 \u2212\nj p\u2217\nj \u00b7 \u03bbij } for agent i. Thus, the\nstructure of the bid-tree language is exploited in generating\nnew constraints, because this is solved as a concise MIP.\nThe other bidders are kept around in the MIP (but do not\nappear in the objective), and are used to define the space of\nfeasible trades.\n5\nThe methods of Dunford et al. [12], that use a nucleolus\napproach, are also closely related.\n6\nThe use of balance was advocated by Kwasnica et al. [17].\nDunford et al. [12] prefer to smooth prices across rounds.\nComment 1: Lexicographical Refinement. For all\nthree sub-problems we also perform lexicographical\nrefinement (with respect to bidders in ACC and FAIR, and with\nrespect to goods in BAL). For instance, in ACC we\nsuccessively minimize the maximal error across all bidders. Given\nan initial solution we first pin down the error on all\nbidders for whom a constraint (11) is binding. For such a bidder\ni, the constraint is replaced with\nv\u03b1\ni (\u03bb) \u2212 p(\u03bb) \u2264 v\u03b1\ni (\u03bbt\ni) \u2212 p(\u03bbt\ni) + \u03b4\u2217\ni , \u2200\u03bb \u2208\ni , (19)\nand the error to bidder i no longer appears explicitly in\nthe objective. ACC is then re-solved, and makes progress\nby further minimizing the maximal error across all bidders\nyet to be pinned down. This continues, pinning down any\nnew bidders for whom one of constraints (11) is binding,\nuntil the error is lexicographically optimized for all\nbidders.7\nThe exact same process is repeated for FAIR and\nBAL, with bidders pinned down and constraints (15)\nreplaced with \u03c0\u2217\ni \u2265 \u03c0vcg,i \u2212 (v\u03b1\ni (\u03bbt\ni) \u2212 p(\u03bbt\ni)), \u2200\u03bb \u2208\ni , (where\n\u03c0\u2217\ni is the current objective) in FAIR, and items pinned down\nand constraints (18) replaced with p\u2217\nj \u2265 pj (where p\u2217\nj\nrepresents the target for the maximal price on that item) in\nBAL.\nComment 2: Computation. All constraints in\ni are\nretained, and this set grows across all stages and across all\nrounds of the exchange. Thus, the computational effort in\nconstraint generation is re-used. In implementation we are\ncareful to address a number of  -issues that arise due to\nfloating-point issues. We prefer to err on the side of being\nconservative in determining whether or not to add another\nconstraint in performing check (13). This avoids later\ninfeasibility issues. In addition, when pinning-down bidders for\nthe purpose of lexicographical refinement we relax the\nassociated bidder-constraints with a small > 0 on the\nrighthand side.\n5.3 Revealed-Preference Activity Rules\nThe role of activity rules in the auction is to ensure both\nconsistency and progress across rounds [21]. Consistency in\nour exchange requires that bidders tighten bounds as the\nexchange progresses. Activity rules ensure that bidders are\nactive during early rounds, and promote useful elicitation\nthroughout the exchange.\nWe adopt a simple revealed-preference (RP) activity rule.\nThe idea is loosely based around the RP-rule in Ausubel et\nal. [1], where it is used for one-sided CAs. The motivation\nis to require more than simply consistency: we need bidders\nto provide enough information for the system to be able to\nto prove that an allocation is (approximately) efficient.\nIt is helpful to think about the bidders interacting with\nproxy agents that will act on their behalf in responding\nto provisional prices pt\u22121\ndetermined at the end of round\nt \u2212 1. The only knowledge that such a proxy has of the\nvaluation of a bidder is through the bid-tree. Suppose a\nproxy was queried by the exchange and asked which trade\nthe bidder was most interested in at the provisional prices.\nThe RP rule says the following: the proxy must have enough\n7\nFor example, applying this to accuracy on Example 2 we\nsolve once and find bidders 1 and 2 are binding, for error\n\u03b4\u2217\n= 2/3. We pin these down and then minimize the error\nto bidders 3 and 4. Finally, this gives p(A) = p(B) = 10/3\nand p(C) = p(D) = 5/3, with accuracy 2/3 to bidders 1 and\n2 and 1/3 to bidders 3 and 4.\n254\ninformation to be able to determine this surplus-maximizing\ntrade at current prices. Consider the following examples:\nExample 7. A bidder has XOR(+A, +B) and a value of\n+5 on the leaf +A and a value range of [5,10] on leaf +B.\nSuppose prices are currently 3 for each of A and B. The RP\nrule is satisfied because the proxy knows that however the\nremaining value uncertainty on +B is resolved the bidder\nwill always (weakly) prefer +B to +A.\nExample 8. A bidder has XOR(+A, +B) and value\nbounds [5, 10] on the root node and a value of 1 on leaf +A.\nSuppose prices are currently 3 for each of A and B. The RP\nrule is satisfied because the bidder will always prefer +A to\n+B at equal prices, whichever way the uncertain value on\nthe root node is ultimately resolved.\nOverloading notation, let vi \u2208 Ti denote a valuation that\nis consistent with lower and upper valuations in bid tree Ti.\nDefinition 4. Bid tree Ti satisfies RP at prices pt\u22121\nif\nand only if there exists some feasible trade L\u2217\nfor which,\nvi(L\u2217\ni ) \u2212 pt\u22121\n(L\u2217\ni ) \u2265 max\n\u03bb\u2208Feas(x0)\nvi(\u03bbi) \u2212 pt\u22121\n(\u03bbi), \u2200vi \u2208 Ti.\n(20)\nTo make this determination for bidder i we solve a\nsequence of problems, each of which is a variation on the WD\nproblem. First, we construct a candidate lower-bound trade,\nwhich is a feasible trade that solves:\nmax\n\u03bb\nvi(\u03bbi) \u2212 pt\u22121\n(\u03bbi) [RP1(i)]\ns.t. \u03bb \u2208 Feas(x0\n), (21)\nThe solution \u03c0\u2217\nl to RP1(i) represents the maximal payoff\nthat bidder i can achieve across all feasible trades, given its\npessimistic valuation.\nSecond, we break ties to find a trade with maximal value\nuncertainty across all possible solutions to RP1(i):\nmax\n\u03bb\nvi(\u03bbi) \u2212 vi(\u03bbi) [RP2(i)]\ns.t. \u03bb \u2208 Feas(x0\n) (22)\nvi(\u03bbi) \u2212 pt\u22121\n(\u03bbi) \u2265 \u03c0\u2217\nl (23)\nWe adopt solution L\u2217\ni as our candidate for the trade that\nmay satisfy RP. To understand the importance of this\ntiebreaking rule consider Example 7. The proxy can prove +B\nbut not +A is a best-response for all vi \u2208 Ti, and should\nchoose +B as its candidate. Notice that +B is a\ncounterexample to +A, but not the other way round.\nNow, we construct a modified valuation \u02dcvi, by setting\n\u02dcvi\u03b2 =\n\nvi\u03b2 , if \u03b2 \u2208 sat(L\u2217\ni )\nvi\u03b2 , otherwise.\n(24)\nwhere sat(L\u2217\ni ) is the set of nodes that are satisfied in the\nlower-bound tree for trade L\u2217\ni . Given this modified\nvaluation, we find U\u2217\nto solve:\nmax\n\u03bb\n\u02dcvi(\u03bbi) \u2212 pt\u22121\n(\u03bbi) [RP3(i)]\ns.t. \u03bb \u2208 Feas(x0\n) (25)\nLet \u03c0\u2217\nu denote the payoff from this optimal trade at modified\nvalues \u02dcv. We call trade U\u2217\ni the witness trade. We show in\nProposition 1 that the RP rule is satisfied if and only if\n\u03c0\u2217\nl \u2265 \u03c0\u2217\nu.\nConstructing the modified valuation as \u02dcvi recognizes that\nthere is shared uncertainty across trades that satisfy the\nsame nodes in a bid tree. Example 8 helps to illustrate this.\nJust using vi in RP3(i), we would find L\u2217\ni is buy A with\npayoff \u03c0\u2217\nl = 3 but then find U\u2217\ni is buy B with \u03c0\u2217\nu = 7 and\nfail RP. We must recognize that however the uncertainty on\nthe root node is resolved it will affect +A and +B in exactly\nthe same way. For this reason, we set \u02dcvi\u03b2 = vi\u03b2 = 5 on the\nroot node, which is exactly the same value that was adopted\nin determining \u03c0\u2217\nl . Then, RP3(i) applied to U\u2217\ni gives buy\nA and the RP test is judged to be passed.\nProposition 1. Bid tree Ti satisfies RP given prices pt\u22121\nif and only if any lower-bound trade L\u2217\ni that solves RP1(i)\nand RP2(i) satisfies:\nvi(Ti, L\u2217\ni ) \u2212 pt\u22121\n(L\u2217\ni ) \u2265 \u02dcvi(Ti, U\u2217\ni ) \u2212 pt\u22121\n(U\u2217\ni ), (26)\nwhere \u02dcvi is the modified valuation in Eq. (24).\nProof. For sufficiency, notice that the difference in\npayoff between trade L\u2217\ni and another trade \u03bbi is unaffected by\nthe way uncertainty is resolved on any node that is satisfied\nin both L\u2217\ni and \u03bbi. Fixing the values in \u02dcvi on nodes satisfied\nin L\u2217\ni has the effect of removing this consideration when a\ntrade U\u2217\ni is selected that satisfies one of these nodes. On\nthe other hand, fixing the values on these nodes has no\neffect on trades considered in RP3(i) that do not share a node\nwith L\u2217\ni . For the necessary direction, we first show that any\ntrade that satisfies RP must solve RP1(i). Suppose\notherwise, that some \u03bbi with payoff greater than \u03c0\u2217\nl satisfies RP.\nBut, valuation vi \u2208 Ti together with L\u2217\ni presents a\ncounterexample to RP (Eq. 20). Now, suppose (for\ncontradiction) that some \u03bbi with maximal payoff \u03c0\u2217\nl but uncertainty\nless than L\u2217\ni satisfies RP. Proceed by case analysis. Case\na): only one solution to RP1(i) has uncertain value and so\n\u03bbi has certain value. But, this cannot satisfy RP because\nL\u2217\ni with uncertain value would be a counterexample to RP\n(Eq. 20). Case b): two or more solutions to RP1(i) have\nuncertain value. Here, we first argue that one of these trades\nmust satisfy a (weak) superset of all the nodes with\nuncertain value that are satisfied by all other trades in this set.\nThis is by RP. Without this, then for any choice of trade\nthat solves RP1(i), there is another trade with a disjoint set\nof uncertain but satisfied nodes that provides a\ncounterexample to RP (Eq. 20). Now, consider the case that some\ntrade contains a superset of all the uncertain satisfied nodes\nof the other trades. Clearly RP2(i) will choose this trade,\nL\u2217\ni , and \u03bbi must satisfy a subset of these nodes (by\nassumption). But, we now see that \u03bbi cannot satisfy RP because\nL\u2217\ni would be a counterexample to RP.\nFailure to meet the activity rule must have some\nconsequence. In the current rules, the default action we choose\nis to set the upper bounds in valuations down to the\nmaximal value of the provisional price on a node8\nand the\nlowerbound value on that node.9\nSuch a bidder can remain active\n8\nThe provisional price on a node is defined as the minimal\ntotal price across all feasible trades for which the subtree\nrooted at the tree is satisfied.\n9\nThis is entirely analogous to when a bidder in an ascending\nclock auction stops bidding at a price: she is not permitted\nto bid at a higher price again in future rounds.\n255\nwithin the exchange, but only with valuations that are\nconsistent with these new bounds.\n5.4 Bidder Feedback\nIn each round, our default design provides every bidder\nwith the provisional trade and also with the current\nprovisional prices. See 7 for an additional discussion. We also\nprovide guidance to help a bidder meet the RP rule. Let\nsat(L\u2217\ni ) and sat(U\u2217\ni ) denote the nodes that are satisfied in\ntrades L\u2217\ni and U\u2217\ni , as computed in RP1-RP3.\nLemma 2. When RP fails, a bidder must increase a lower\nbound on at least one node in sat(L\u2217\ni ) \\ sat(U\u2217\ni ) or decrease\nan upper bound on at least one node in sat(U\u2217\ni ) \\ sat(L\u2217\ni ) in\norder to meet the activity rule.\nProof. Changing the upper- or lower- values on nodes\nthat are not satisfied by either trade does not change L\u2217\ni or\nU\u2217\ni , and does not change the payoff from these trades. Thus,\nthe RP condition will continue to fail. Similarly, changing\nthe bounds on nodes that are satisfied in both trades has\nno effect on revealed preference. A change to a lower bound\non a shared node affects both L\u2217\ni and U\u2217\ni identically because\nof the use of the modified valuation to determine U\u2217\ni . A\nchange to an upper bound on a shared node has no effect in\ndetermining either L\u2217\ni or U\u2217\ni .\nNote that when sat(U\u2217\ni ) = sat(L\u2217\ni ) then condition (26) is\nalways trivially satisfied, and so the guidance in the lemma\nis always well-defined when RP fails. This is an elegant\nfeedback mechanism because it is adaptive. Once a bidder\nmakes some changes on some subset of these nodes, the\nbidder can query the exchange. The exchange can then respond\nyes, or can revise the set of nodes sat(\u03bb\u2217\nl ) and sat(\u03bb\u2217\nu) as\nnecessary.\n5.5 Termination Conditions\nOnce each bidder has committed its new bids (and either\nmet the RP rule or suffered the penalty) then round t closes.\nAt this point, the task is to determine the new \u03b1-valuation,\nand in turn the provisional allocation \u03bbt\nand provisional\nprices pt\n. A termination condition is also checked, to\ndetermine whether to move the exchange to a last-and-final\nround. To define the \u03b1-valuation we compute the following\ntwo quantities:\nPessimistic at Pessimistic (PP) Determine an efficient\ntrade, \u03bb\u2217\nl , at pessimistic values, i.e. to solve\nmax\u03bb\ni vi(\u03bbi), and set PP=\ni vi(\u03bb\u2217\nli).\nPessimistic at Optimistic (PO) Determine an efficient\ntrade, \u03bb\u2217\nu, at optimistic values, i.e. to solve\nmax\u03bb\ni vi(\u03bbi), and set PO=\ni vi(\u03bb\u2217\nui).\nFirst, note that PP \u2265 PO and PP \u2265 0 by definition,\nfor all bid-trees, although PO can be negative (because the\nright trade at v is not currently a useful trade at v).\nRecognizing this, define\n\u03b3eff\n(PP, PO) = 1 +\nPP \u2212 PO\nPP\n, (27)\nwhen PP > 0, and observe that \u03b3eff\n(PP, PO) \u2265 1 when\nthis is defined, and that \u03b3eff\n(PP, PO) will start large and\nthen trend towards 1 as the optimistic allocation converges\ntowards the pessimistic allocation. In each round, we define\n\u03b1eff\n\u2208 [0, 1] as:\n\u03b1eff\n=\n\n0 when PP is 0\n1/\u03b3eff\notherwise\n(28)\nwhich is 0 while PP is 0 and then trends towards 1 once\nPP> 0 in some round. This is used to define \u03b1-valuation\nv\u03b1\ni = \u03b1eff\nvi + (1 \u2212 \u03b1eff\n)vi, \u2200i, (29)\nwhich is used to define the provisional allocation and\nprovisional prices. The effect is to endogenously define a\nschedule for moving from optimistic to pessimistic values across\nrounds, based on how close the trades are to one another.\nTermination Condition. In moving to the last-and-final\nround, and finally closing, we also care about the\nconvergence of payments, in addition to the convergence towards\nan efficient trade. For this we introduce another parameter,\n\u03b1thresh\n\u2208 [0, 1], that trends from 0 to 1 as the Threshold\npayments at lower and upper valuations converge. Consider\nthe following parameter:\n\u03b3thresh\n= 1 +\n||pthresh(v) \u2212 pthresh(v)||2\n(PP/Nactive)\n, (30)\nwhich is defined for PP > 0, where pthresh(v) denotes the\nThreshold payments at valuation profile v, Nactive is the\nnumber of bidders that are actively engaged in trade in the\nPP trade, and || \u00b7 ||2 is the L2-norm. Note that \u03b3thresh\nis\ndefined for payments and not payoffs. This is appropriate\nbecause it is the accuracy of the outcome of the exchange\nthat matters: i.e. the trade and the payments. Given this,\nwe define\n\u03b1thresh\n=\n\n0 when PP is 0\n1/\u03b3thresh\notherwise\n(31)\nwhich is 0 while PP is 0 and then trends towards 1 as\nprogress is made.\nDefinition 5 (termination). ICE transitions to a\nlastand-final round when one of the following holds:\n1. \u03b1eff\n\u2265 CUTOFFeff and \u03b1thresh\n\u2265 CUTOFFthresh,\n2. there is no trade at the optimistic values,\nwhere CUTOFFeff , CUTOFFthresh \u2208 (0, 1] determine the\naccuracy required for termination.\nAt the end of the last-and-final round v\u03b1\n= v is used to\ndefine the final trade and the final Threshold payments.\nExample 9. Consider again Example 1, and consider the\nupper and lower bounds as depicted in Figure 1. First, if the\nseller\"s bounds were [\u221220, \u22124] then there is an optimistic\ntrade but no pessimistic trade, and PO = \u22124 and PP = 0,\nand \u03b1eff\n= 0. At the bounds depicted, both the optimistic\nand the pessimistic trades occur and PO = PP = 4 and\n\u03b1eff\n= 1. However, we can see the Threshold payments are\n(17, \u221217) at v but (14, \u221214) at v. Evaluating \u03b3thresh\n, we\nhave \u03b3thresh\n= 1 +\n\u221a\n1/2(32+32)\n(4/2)\n= 5/2, and \u03b1thresh\n= 2/5.\nFor CUTOFFthresh < 2/5 the exchange would remain open.\nOn the other hand, if the buyer\"s value for +AB was\nbetween [18, 24] and the seller\"s value for \u2212AB was between\n[\u221212, \u22126], the Threshold payments are (15, \u221215) at both\nupper and lower bounds, and \u03b1thresh\n= 1.\n256\nComponent Purpose Lines\nAgent. Captures strategic behavior and information revelation decisions 762\nModel Support Provides XML support to load goods and valuations into world 200\nWorld Keeps track of all agent, good, and valuation details 998\nExchange Driver & Communication Controls exchange, and coordinates remote agent behavior 585\nBidding Language Implements the tree-based bidding language 1119\nActivity Rule Engine Implements the revealed preference rule with range support 203\nClosing Rule Engine Checks if auction termination condition reached 137\nWD Engine Provides WD-related logic 377\nPricing Engine Provides Pricing-related logic 460\nMIP Builders Translates logic used by engines into our general optimizer formulation 346\nPricing Builders Used by three pricing stages 256\nWinner Determination Builders Used by WD, activity rule, closing rule, and pricing constraint generation 365\nFramework Support code; eases modular replacement of above components 510\nTable 1: Exchange Component and Code Breakdown.\n6. SYSTEMS INFRASTRUCTURE\nICE is approximately 6502 lines of Java code, broken up\ninto the functional packages described in Table 1.10\nThe prototype is modular so that researchers may easily\nreplace components for experimentation. In addition to the\ncore exchange discussed in this paper, we have developed\nan agent component that allows a user to simulate the\nbehavior and knowledge of other players in the system, better\nallowing a user to formulate their strategy in advance of\nactual play. A user specifies a valuation model in an\nXMLinterpretation of our bidding language, which is revealed to\nthe exchange via the agent\"s strategy.\nMajor exchange tasks are handled by engines that\ndictate the non-optimizer specific logic. These engines drive\nthe appropriate MIP/LP builders. We realized that all of\nour optimization formulations boil down to two classes of\noptimization problem. The first, used by winner\ndetermination, activity rule, closing rule, and constraint generation\nin pricing, is a MIP that finds trades that maximize value,\nholding prices and slacks constant. The second, used by the\nthree pricing stages, is an LP that holds trades constant,\nseeking to minimize slack, profit, or prices. We take\nadvantage of the commonality of these problems by using common\nLP/MIP builders that differ only by a few functional hooks\nto provide the correct variables for optimization.\nWe have generalized our back-end optimization solver\ninterface11\n(we currently support CPLEX and the LGPL-\nlicensed LPSolve), and can take advantage of the load-balancing\nand parallel MIP/LP solving capability that this library\nprovides.\n7. DISCUSSION\nThe bidding language was defined to allow for perfect\nsymmetry between buyers and sellers and provide expressiveness\nin an exchange domain, for instance for mixed bidders\ninterested in executing trades such as swaps. This proved\nespecially challenging. The breakthrough came when we\nfocused on changes in value for trades rather than providing\nabsolute values for allocations. For simplicity, we require the\nsame tree structure for both the upper and lower valuations.\n10\nCode size is measured in physical source line of code\n(SLOC), as generated using David A. Wheeler\"s SLOC\nCount. The total of 6502 includes 184 for instrumentation\n(not shown in the table). The JOpt solver interface is\nanother 1964 lines, and Castor automatically generates around\n5200 lines of code for XML file manipulation.\n11\nhttp://econcs.eecs.harvard.edu/jopt\nThis allows the language itself to ensure consistency (with\nthe upper value at least the lower value on all trades) and\nenforce monotonic tightening of these bounds for all trades\nacross rounds. It also provides for an efficient method to\ncheck the RP activity rule, because it makes it simple to\nreason about shared uncertainty between trades.\nThe decision to adopt a direct and proxied approach\nin which bidders express their upper and lower values to a\ntrusted proxy agent that interacts with the exchange was\nmade early in the design process. In many ways this is\nthe clearest and most immediate way to generalize the\ndesign in Parkes et al. [24] and make it iterative. In addition,\nthis removes much opportunity for strategic manipulation:\nbidders are restricted to making (incremental) statements\nabout their valuations. Another advantage is that it makes\nthe activity rule easy to explain: bidders can always meet\nthe activity rule by tightening bounds such that their true\nvalue remains in the support.12\nPerhaps most importantly,\nhaving explicit information on upper and lower values\npermits progress in early rounds, even while there is no efficient\ntrade at pessimistic values.\nUpper and lower bound information also provides\nguidance about when to terminate. Note that taken by itself,\nPP = PO does not imply that the current provisional trade\nis efficient with respect to all values consistent with current\nvalue information. The difference in values between\ndifferent trades, aggregated across all bidders, could be similar at\nlower and upper bounds but quite different at intermediate\nvalues (including truth). Nevertheless, we conjecture that\nPP = PO will prove an excellent indicator of efficiency in\npractical settings where the shape of the upper and lower\nvaluations does convey useful information. This is worthy of\nexperimental investigation. Moreover, the use of price and\nRP activity provides additional guarantees.\nWe adopted linear prices (prices on individual items) rather\nthan non-linear prices (with prices on a trade not equal to\nthe sum of the prices on the component items) early in the\ndesign process. The conciseness of this price representation\nis very important for computational tractability within the\nexchange and also to promote simplicity and transparency\nfor bidders. The RP activity rule was adopted later, and is\na good choice because of its excellent theoretical properties\nwhen coupled with CE prices. The following can be easily\nestablished: given exact CE prices pt\u22121\nfor provisional trade\n12\nThis is in contrast to indirect price-based approaches, such\nas clock-proxy [1], in which bidders must be able to reason\nabout the RP-constraints implied by bids in each round.\n257\n\u03bbt\u22121\nat valuations v\u03b1\n, then if the upper and lower values at\nthe start of round t already satisfy the RP rule (and without\nthe need for any tie-breaking), the provisional trade is\nefficient for all valuations consistent with the current bid trees.\nWhen linear CE prices exist, this provides for a soundness\nand completeness statement: if PP = PO, linear CE prices\nexist, and the RP rule is satisfied, the provisional trade is\nefficient (soundness); if prices are exact CE prices for the\nprovisional trade at v\u03b1\n, but the trade is inefficient with\nrespect to some valuation profile consistent with the current\nbid trees, then at least one bidder must fail RP with her\ncurrent bid tree and progress will be made (completeness).\nFuture work must study convergence experimentally, and\nextend this theory to allow for approximate prices.\nSome strategic aspects of our ICE design deserve\ncomment, and further study. First, we do not claim that\ntruthfully responding to the RP rule is an ex post equilibrium.13\nHowever, the exchange is designed to mimic the Threshold\nrule in its payment scheme, which is known to have\nuseful incentive properties [16]. We must be careful, though.\nFor instance we do not suggest to provide \u03b1eff\nto bidders,\nbecause as \u03b1eff\napproaches 1 it would inform bidders that\nbid values are becoming irrelevant to determining the trade\nbut merely used to determine payments (and bidders would\nbecome increasingly reluctant to increase their lower\nvaluations). Also, no consideration has been given in this work\nto collusion by bidders. This is an issue that deserves some\nattention in future work.\n8. CONCLUSIONS\nIn this work we designed and prototyped a scalable and\nhighly-expressive iterative combinatorial exchange. The\ndesign includes many interesting features, including: a new\nbid-tree language for exchanges, a new method to construct\napproximate linear prices from expressive languages, and a\nproxied elicitation method with optimistic and pessimistic\nvaluations with a new method to evaluate a revealed-\npreference activity rule. The exchange is fully implemented in\nJava and is in a validation phase.\nThe next steps for our work are to allow bidders to refine\nthe structure of the bid tree in addition to values on the\ntree. We intend to study the elicitation properties of the\nexchange and we have put together a test suite of exchange\nproblem instances. In addition, we are beginning to engage\nin collaborations to apply the design to airline takeoff and\nlanding slot scheduling and to resource allocation in\nwidearea network distributed computational systems.\nAcknowledgments\nWe would like to dedicate this paper to all of the participants\nin CS 286r at Harvard University in Spring 2004. This work\nis supported in part by NSF grant IIS-0238147.\n9. REFERENCES\n[1] L. Ausubel, P. Cramton, and P. Milgrom. The clock-proxy\nauction: A practical combinatorial auction design. In Cramton\net al. [9], chapter 5.\n[2] M. Babaioff, N. Nisan, and E. Pavlov. Mechanisms for a\nspatially distributed market. In Proc. 5th ACM Conf. on\nElectronic Commerce, pages 9-20. ACM Press, 2001.\n13\nGiven the Myerson-Satterthwaite impossibility\ntheorem [22] and the method by which we determine the trade\nwe should not expect this.\n[3] M. Ball, G. Donohue, and K. Hoffman. Auctions for the safe,\nefficient, and equitable allocation of airspace system resources.\nIn S. Cramton, Shoham, editor, Combinatorial Auctions.\n2004. Forthcoming.\n[4] D. Bertsimas and J. Tsitsiklis. Introduction to Linear\nOptimization. Athena Scientific, 1997.\n[5] S. Bikhchandani and J. M. Ostroy. The package assignment\nmodel. Journal of Economic Theory, 107(2):377-406, 2002.\n[6] C. Boutilier. A pomdp formulation of preference elicitation\nproblems. In Proc. 18th National Conference on Artificial\nIntelligence (AAAI-02), 2002.\n[7] C. Boutilier and H. Hoos. Bidding languages for combinatorial\nauctions. In Proc. 17th International Joint Conference on\nArtificial Intelligence (IJCAI-01), 2001.\n[8] W. Conen and T. Sandholm. Preference elicitation in\ncombinatorial auctions. In Proc. 3rd ACM Conf. on\nElectronic Commerce (EC-01), pages 256-259. ACM Press,\nNew York, 2001.\n[9] P. Cramton, Y. Shoham, and R. Steinberg, editors.\nCombinatorial Auctions. MIT Press, 2004.\n[10] S. de Vries, J. Schummer, and R. V. Vohra. On ascending\nVickrey auctions for heterogeneous objects. Technical report,\nMEDS, Kellogg School, Northwestern University, 2003.\n[11] S. de Vries and R. V. Vohra. Combinatorial auctions: A\nsurvey. Informs Journal on Computing, 15(3):284-309, 2003.\n[12] M. Dunford, K. Hoffman, D. Menon, R. Sultana, and\nT. Wilson. Testing linear pricing algorithms for use in\nascending combinatorial auctions. Technical report, SEOR,\nGeorge Mason University, 2003.\n[13] Y. Fu, J. Chase, B. Chun, S. Schwab, and A. Vahdat. Sharp:\nan architecture for secure resource peering. In Proceedings of\nthe nineteenth ACM symposium on Operating systems\nprinciples, pages 133-148. ACM Press, 2003.\n[14] B. Hudson and T. Sandholm. Effectiveness of query types and\npolicies for preference elicitation in combinatorial auctions. In\nProc. 3rd Int. Joint. Conf. on Autonomous Agents and Multi\nAgent Systems, pages 386-393, 2004.\n[15] V. Krishna. Auction Theory. Academic Press, 2002.\n[16] D. Krych. Calculation and analysis of Nash equilibria of\nVickrey-based payment rules for combinatorial exchanges,\nHarvard College, April 2003.\n[17] A. M. Kwasnica, J. O. Ledyard, D. Porter, and C. DeMartini.\nA new and improved design for multi-object iterative auctions.\nManagement Science, 2004. To appear.\n[18] E. Kwerel and J. Williams. A proposal for a rapid transition to\nmarket allocation of spectrum. Technical report, FCC Office of\nPlans and Policy, Nov 2002.\n[19] S. M. Lahaie and D. C. Parkes. Applying learning algorithms\nto preference elicitation. In Proc. ACM Conf. on Electronic\nCommerce, pages 180-188, 2004.\n[20] R. P. McAfee. A dominant strategy double auction. J. of\nEconomic Theory, 56:434-450, 1992.\n[21] P. Milgrom. Putting auction theory to work: The simultaneous\nascending auction. J.Pol. Econ., 108:245-272, 2000.\n[22] R. B. Myerson and M. A. Satterthwaite. Efficient mechanisms\nfor bilateral trading. Journal of Economic Theory,\n28:265-281, 1983.\n[23] N. Nisan. Bidding and allocation in combinatorial auctions. In\nProc. 2nd ACM Conf. on Electronic Commerce (EC-00),\npages 1-12, 2000.\n[24] D. C. Parkes, J. R. Kalagnanam, and M. Eso. Achieving\nbudget-balance with Vickrey-based payment schemes in\nexchanges. In Proc. 17th International Joint Conference on\nArtificial Intelligence (IJCAI-01), pages 1161-1168, 2001.\n[25] D. C. Parkes and L. H. Ungar. Iterative combinatorial\nauctions: Theory and practice. In Proc. 17th National\nConference on Artificial Intelligence (AAAI-00), pages\n74-81, July 2000.\n[26] S. J. Rassenti, V. L. Smith, and R. L. Bulfin. A combinatorial\nmechanism for airport time slot allocation. Bell Journal of\nEconomics, 13:402-417, 1982.\n[27] M. H. Rothkopf, A. Peke\u02c7c, and R. M. Harstad.\nComputationally manageable combinatorial auctions.\nManagement Science, 44(8):1131-1147, 1998.\n[28] T. Sandholm and C. Boutilier. Preference elicitation in\ncombinatorial auctions. In Cramton et al. [9], chapter 10.\n[29] P. R. Wurman and M. P. Wellman. AkBA: A progressive,\nanonymous-price combinatorial auction. In Second ACM\nConference on Electronic Commerce, pages 21-29, 2000.\n258", "keywords": "winner-determination;double auction;combinatorial auction;price;combinatorial exchange;vcg;bidding;threshold payment;tree-based bidding language;trade;preference elicitation;iterative combinatorial exchange;buyer and seller"}
{"name": "train_J-62", "title": "Weak Monotonicity Suffices for Truthfulness on Convex Domains", "abstract": "Weak monotonicity is a simple necessary condition for a social choice function to be implementable by a truthful mechanism. Roberts [10] showed that it is sufficient for all social choice functions whose domain is unrestricted. Lavi, Mu\"alem and Nisan [6] proved the sufficiency of weak monotonicity for functions over order-based domains and Gui, Muller and Vohra [5] proved sufficiency for order-based domains with range constraints and for domains defined by other special types of linear inequality constraints. Here we show the more general result, conjectured by Lavi, Mu\"alem and Nisan [6], that weak monotonicity is sufficient for functions defined on any convex domain.", "fulltext": "1. INTRODUCTION\nSocial choice theory centers around the general problem of\nselecting a single outcome out of a set A of alternative\noutcomes based on the individual preferences of a set P of\nplayers. A method for aggregating player preferences to select\none outcome is called a social choice function. In this paper\nwe assume that the range A is finite and that each player\"s\npreference is expressed by a valuation function which\nassigns to each possible outcome a real number representing\nthe benefit the player derives from that outcome. The\nensemble of player valuation functions is viewed as a\nvaluation matrix with rows indexed by players and columns by\noutcomes.\nA major difficulty connected with social choice functions\nis that players can not be required to tell the truth about\ntheir preferences. Since each player seeks to maximize his\nown benefit, he may find it in his interest to misrepresent\nhis valuation function. An important approach for dealing\nwith this problem is to augment a given social choice\nfunction with a payment function, which assigns to each player\na (positive or negative) payment as a function of all of the\nindividual preferences. By carefully choosing the payment\nfunction, one can hope to entice each player to tell the truth.\nA social choice function augmented with a payment function\nis called a mechanism 1\nand the mechanism is said to\nimplement the social choice function. A mechanism is truthful\n(or to be strategyproof or to have a dominant strategy) if\neach player\"s best strategy, knowing the preferences of the\nothers, is always to declare his own true preferences. A\nsocial choice function is truthfully implementable, or truthful\nif it has a truthful implementation. (The property of\ntruthful implementability is sometimes called dominant strategy\nincentive compatibility). This framework leads naturally to\nthe question: which social choice functions are truthful?\nThis question is of the following general type: given a\nclass of functions (here, social choice functions) and a\nproperty that holds for some of them (here, truthfulness),\ncharacterize the property. The definition of the property itself\nprovides a characterization, so what more is needed? Here\nare some useful notions of characterization:\n\u2022 Recognition algorithm. Give an algorithm which, given\nan appropriate representation of a function in the class,\ndetermines whether the function has the property.\n\u2022 Parametric representation. Give an explicit parametrized\nfamily of functions and show that each function in the\n1\nThe usual definition of mechanism is more general than this\n(see [8] Chapter 23.C or [9]); the mechanisms we consider\nhere are usually called direct revelation mechanisms.\n286\nfamily has the property, and that every function with\nthe property is in the family.\nA third notion applies in the case of hereditary properties\nof functions. A function g is a subfunction of function f, or\nf contains g, if g is obtained by restricting the domain of\nf. A property P of functions is hereditary if it is preserved\nunder taking subfunctions. Truthfulness is easily seen to be\nhereditary.\n\u2022 Sets of obstructions. For a hereditary property P, a\nfunction g that does not have the property is an\nobstruction to the property in the sense that any function\ncontaining g doesn\"t have the property. An obstruction\nis minimal if every proper subfunction has the\nproperty. A set of obstructions is complete if every function\nthat does not have the property contains one of them\nas a subfunction. The set of all functions that don\"t\nsatisfy P is a complete (but trivial and uninteresting)\nset of obstructions; one seeks a set of small (ideally,\nminimal) obstructions.\nWe are not aware of any work on recognition algorithms\nfor the property of truthfulness, but there are significant\nresults concerning parametric representations and obstruction\ncharacterizations of truthfulness. It turns out that the\ndomain of the function, i.e., the set of allowed valuation\nmatrices, is crucial. For functions with unrestricted domain, i.e.,\nwhose domain is the set of all real matrices, there are very\ngood characterizations of truthfulness. For general domains,\nhowever, the picture is far from complete. Typically, the\ndomains of social choice functions are specified by a system of\nconstraints. For example, an order constraint requires that\none specified entry in some row be larger than another in\nthe same row, a range constraint places an upper or lower\nbound on an entry, and a zero constraint forces an entry to\nbe 0. These are all examples of linear inequality constraints\non the matrix entries.\nBuilding on work of Roberts [10], Lavi, Mu\"alem and\nNisan [6] defined a condition called weak monotonicity\n(WMON). (Independently, in the context of multi-unit\nauctions, Bikhchandani, Chatterji and Sen [3] identified the\nsame condition and called it nondecreasing in marginal\nutilities (NDMU).) The definition of W-MON can be formulated\nin terms of obstructions: for some specified simple set F of\nfunctions each having domains of size 2, a function satisfies\nW-MON if it contains no function from F. The functions\nin F are not truthful, and therefore W-MON is a\nnecessary condition for truthfulness. Lavi, Mu\"alem and Nisan\n[6] showed that W-MON is also sufficient for truthfulness\nfor social choice functions whose domain is order-based, i.e.,\ndefined by order constraints and zero constraints, and Gui,\nMuller and Vohra [5] extended this to other domains. The\ndomain constraints considered in both papers are special\ncases of linear inequality constraints, and it is natural to\nask whether W-MON is sufficient for any domain defined by\nsuch constraints. Lavi, Mu\"alem and Nisan [6] conjectured\nthat W-MON suffices for convex domains. The main result\nof this paper is an affirmative answer to this conjecture:\nTheorem 1. For any social choice function having\nconvex domain and finite range, weak monotonicity is necessary\nand sufficient for truthfulness.\nUsing the interpretation of weak monotonicity in terms\nof obstructions each having domain size 2, this provides a\ncomplete set of minimal obstructions for truthfulness within\nthe class of social choice functions with convex domains.\nThe two hypotheses on the social choice function, that\nthe domain is convex and that the range is finite, can not\nbe omitted as is shown by the examples given in section 7.\n1.1 Related Work\nThere is a simple and natural parametrized set of\ntruthful social choice functions called affine maximizers. Roberts\n[10] showed that for functions with unrestricted domain,\nevery truthful function is an affine maximizer, thus providing\na parametrized representation for truthful functions with\nunrestricted domain. There are many known examples of\ntruthful functions over restricted domains that are not affine\nmaximizers (see [1], [2], [4], [6] and [7]). Each of these\nexamples has a special structure and it seems plausible that\nthere might be some mild restrictions on the class of all\nsocial choice functions such that all truthful functions obeying\nthese restrictions are affine maximizers. Lavi, Mu\"alem and\nNisan [6] obtained a result in this direction by showing that\nfor order-based domains, under certain technical\nassumptions, every truthful social choice function is almost an\naffine maximizer.\nThere are a number of results about truthfulness that\ncan be viewed as providing obstruction characterizations,\nalthough the notion of obstruction is not explicitly discussed.\nFor a player i, a set of valuation matrices is said to be\ni-local if all of the matrices in the set are identical except for\nrow i. Call a social choice function i-local if its domain is\nilocal and call it local if it is i-local for some i. The following\neasily proved fact is used extensively in the literature:\nProposition 2. The social choice function f is truthful\nif and only if every local subfunction of f is truthful.\nThis implies that the set of all local non-truthful functions\ncomprises a complete set of obstructions for truthfulness.\nThis set is much smaller than the set of all non-truthful\nfunctions, but is still far from a minimal set of obstructions.\nRochet [11], Rozenshtrom [12] and Gui, Muller and Vohra\n[5] identified a necessary and sufficient condition for\ntruthfulness (see lemma 3 below) called the nonnegative cycle\nproperty. This condition can be viewed as providing a\nminimal complete set of non-truthful functions. As is required\nby proposition 2, each function in the set is local.\nFurthermore it is one-to-one. In particular its domain has size at\nmost the number of possible outcomes |A|.\nAs this complete set of obstructions consists of minimal\nnon-truthful functions, this provides the optimal obstruction\ncharacterization of non-truthful functions within the class of\nall social choice functions. But by restricting attention to\ninteresting subclasses of social choice functions, one may hope\nto get simpler sets of obstructions for truthfulness within\nthat class.\nThe condition of weak monotonicity mentioned earlier can\nbe defined by a set of obstructions, each of which is a local\nfunction of domain size exactly 2. Thus the results of Lavi,\nMu\"alem and Nisan [6], and of Gui, Muller and Vohra [5]\ngive a very simple set of obstructions for truthfulness within\ncertain subclasses of social choice functions. Theorem 1\nextends these results to a much larger subclass of functions.\n287\n1.2 Weak Monotonicity and the Nonnegative\nCycle Property\nBy proposition 2, a function is truthful if and only if each\nof its local subfunctions is truthful. Therefore, to get a set\nof obstructions for truthfulness, it suffices to obtain such a\nset for local functions.\nThe domain of an i-local function consists of matrices that\nare fixed on all rows but row i. Fix such a function f and\nlet D \u2286 RA\nbe the set of allowed choices for row i. Since\nf depends only on row i and row i is chosen from D, we\ncan view f as a function from D to A. Therefore, f is a\nsocial choice function having one player; we refer to such a\nfunction as a single player function.\nAssociated to any single player function f with domain D\nwe define an edge-weighted directed graph Hf whose vertex\nset is the image of f. For convenience, we assume that f\nis surjective and so this image is A. For each a, b \u2208 A,\nx \u2208 f\u22121\n(a) there is an edge ex(a, b) from a to b with weight\nx(a) \u2212 x(b). The weight of a set of edges is just the sum of\nthe weights of the edges. We say that f satisfies:\n\u2022 the nonnegative cycle property if every directed cycle\nhas nonnegative weight.\n\u2022 the nonnegative two-cycle property if every directed\ncycle between two vertices has nonnegative weight.\nWe say a local function g satisfies nonnegative cycle\nproperty/nonnegative two-cycle property if its associated single\nplayer function f does.\nThe graph Hf has a possibly infinite number of edges\nbetween any two vertices. We define Gf to be the\nedgeweighted directed graph with exactly one edge from a to b,\nwhose weight \u03b4ab is the infimum (possibly \u2212\u221e) of all of the\nedge weights ex(a, b) for x \u2208 f\u22121\n(a). It is easy to see that Hf\nhas the nonnegative cycle property/nonnegative two-cycle\nproperty if and only if Gf does. Gf is called the outcome\ngraph of f.\nThe weak monotonicity property mentioned earlier can\nbe defined for arbitrary social choice functions by the\ncondition that every local subfunction satisfies the nonnegative\ntwo-cycle property. The following result was obtained by\nRochet [11] in a slightly different form and rediscovered by\nRozenshtrom [12] and Gui, Muller and Vohra [5]:\nLemma 3. A local social choice function is truthful if and\nonly if it has the nonnegative cycle property. Thus a social\nchoice function is truthful if and only if every local\nsubfunction satisfies the nonnegative cycle property.\nIn light of this, theorem 1 follows from:\nTheorem 4. For any surjective single player function f :\nD \u2212\u2192 A where D is a convex subset of RA\nand A is finite,\nthe nonnegative two-cycle property implies the nonnegative\ncycle property.\nThis is the result we will prove.\n1.3 Overview of the Proof of Theorem 4\nLet D \u2286 RA\nbe convex and let f : D \u2212\u2192 A be a single\nplayer function such that Gf has no negative two-cycles. We\nwant to conclude that Gf has no negative cycles. For two\nvertices a, b, let \u03b4\u2217\nab denote the minimum weight of any path\nfrom a to b. Clearly \u03b4\u2217\nab \u2264 \u03b4ab. Our proof shows that the\n\u03b4\u2217\n-weight of every cycle is exactly 0, from which theorem 4\nfollows.\nThere seems to be no direct way to compute \u03b4\u2217\nand so we\nproceed indirectly. Based on geometric considerations, we\nidentify a subset of paths in Gf called admissible paths and\na subset of admissible paths called straight paths. We prove\nthat for any two outcomes a, b, there is a straight path from\na to b (lemma 8 and corollary 10), and all straight paths\nfrom a to b have the same weight, which we denote \u03c1ab\n(theorem 12). We show that \u03c1ab \u2264 \u03b4ab (lemma 14) and that\nthe \u03c1-weight of every cycle is 0. The key step to this proof\nis showing that the \u03c1-weight of every directed triangle is 0\n(lemma 17).\nIt turns out that \u03c1 is equal to \u03b4\u2217\n(corollary 20), although\nthis equality is not needed in the proof of theorem 4.\nTo expand on the above summary, we give the definitions\nof an admissible path and a straight path. These are\nsomewhat technical and rely on the geometry of f. We first\nobserve that, without loss of generality, we can assume that\nD is (topologically) closed (section 2). In section 3, for each\na \u2208 A, we enlarge the set f\u22121\n(a) to a closed convex set\nDa \u2286 D in such a way that for a, b \u2208 A with a = b, Da and\nDb have disjoint interiors. We define an admissible path to\nbe a sequence of outcomes (a1, . . . , ak) such that each of the\nsets Ij = Daj \u2229 Daj+1 is nonempty (section 4). An\nadmissible path is straight if there is a straight line that meets one\npoint from each of the sets I1, . . . , Ik\u22121 in order (section 5).\nFinally, we mention how the hypotheses of convex domain\nand finite range are used in the proof. Both hypotheses are\nneeded to show: (1) the existence of a straight path from a\nto b for all a, b (lemma 8). (2) that the \u03c1-weight of a directed\ntriangle is 0 (lemma 17). The convex domain hypothesis is\nalso needed for the convexity of the sets Da (section 3). The\nfinite range hypothesis is also needed to reduce theorem 4 to\nthe case that D is closed (section 2) and to prove that every\nstraight path from a to b has the same \u03b4-weight (theorem\n12).\n2. REDUCTION TO CLOSED DOMAIN\nWe first reduce the theorem to the case that D is closed.\nWrite DC\nfor the closure of D. Since A is finite, DC\n=\n\u222aa\u2208A(f\u22121\n(a))C\n. Thus for each v \u2208 DC\n\u2212 D, there is an\na = a(v) \u2208 A such that v \u2208 (f\u22121\n(a))C\n. Extend f to the\nfunction g on DC\nby defining g(v) = a(v) for v \u2208 DC\n\u2212\nD and g(v) = f(v) for v \u2208 D. It is easy to check that\n\u03b4ab(g) = \u03b4ab(f) for all a, b \u2208 A and therefore it suffices to\nshow that the nonnegative two-cycle property for g implies\nthe nonnegative cycle property for g.\nHenceforth we assume D is convex and closed.\n3. A DISSECTION OF THE DOMAIN\nIn this section, we construct a family of closed convex sets\n{Da : a \u2208 A} with disjoint interiors whose union is D and\nsatisfying f\u22121\n(a) \u2286 Da for each a \u2208 A.\nLet Ra = {v : \u2200b \u2208 A, v(a) \u2212 v(b) \u2265 \u03b4ab}. Ra is a closed\npolyhedron containing f\u22121\n(a). The next proposition\nimplies that any two of these polyhedra intersect only on their\nboundary.\nProposition 5. Let a, b \u2208 A. If v \u2208 Ra \u2229Rb then v(a)\u2212\nv(b) = \u03b4ab = \u2212\u03b4ba.\n288\nDa\nDb\nDc\nDd\nDe\nv\nw\nx\ny\nz\nu\np\nFigure 1: A 2-dimensional domain with 5 outcomes.\nProof. v \u2208 Ra implies v(a) \u2212 v(b) \u2265 \u03b4ab and v \u2208 Rb\nimplies v(b)\u2212v(a) \u2265 \u03b4ba which, by the nonnegative two-cycle\nproperty, implies v(a) \u2212 v(b) \u2264 \u03b4ab. Thus v(a) \u2212 v(b) = \u03b4ab\nand by symmetry v(b) \u2212 v(a) = \u03b4ba.\nFinally, we restrict the collection of sets {Ra : a \u2208 A}\nto the domain D by defining Da = Ra \u2229 D for each a \u2208\nA. Clearly, Da is closed and convex, and contains f\u22121\n(a).\nTherefore\nS\na\u2208A Da = D. Also, by proposition 5, any point\nv in Da \u2229 Db satisfies v(a) \u2212 v(b) = \u03b4ab = \u2212\u03b4ba.\n4. PATHS AND D-SEQUENCES\nA path of size k is a sequence \u2212\u2192a = (a1, . . . , ak) with each\nai \u2208 A (possibly with repetition). We call \u2212\u2192a an (a1,\nak)path. For a path \u2212\u2192a , we write |\u2212\u2192a | for the size of \u2212\u2192a . \u2212\u2192a is\nsimple if the ai\"s are distinct.\nFor b, c \u2208 A we write Pbc for the set of (b, c)-paths and\nSPbc for the set of simple (b, c)-paths. The \u03b4-weight of path\n\u2212\u2192a is defined by\n\u03b4(\u2212\u2192a ) =\nk\u22121X\ni=1\n\u03b4aiai+1 .\nA D-sequence of order k is a sequence \u2212\u2192u = (u0, . . . , uk)\nwith each ui \u2208 D (possibly with repetition). We call \u2212\u2192u a\n(u0, uk)-sequence. For a D-sequence \u2212\u2192u , we write ord(u) for\nthe order of \u2212\u2192u . For v, w \u2208 D we write Svw\nfor the set of\n(v, w)-sequences.\nA compatible pair is a pair (\u2212\u2192a , \u2212\u2192u ) where \u2212\u2192a is a path\nand \u2212\u2192u is a D-sequence satisfying ord(\u2212\u2192u ) = |\u2212\u2192a | and for\neach i \u2208 [k], both ui\u22121 and ui belong to Dai .\nWe write C(\u2212\u2192a ) for the set of D-sequences \u2212\u2192u that are\ncompatible with \u2212\u2192a . We say that \u2212\u2192a is admissible if C(\u2212\u2192a )\nis nonempty. For \u2212\u2192u \u2208 C(\u2212\u2192a ) we define\n\u2206\u2212\u2192a (\u2212\u2192u ) =\n|\u2212\u2192a |\u22121\nX\ni=1\n(ui(ai) \u2212 ui(ai+1)).\nFor v, w \u2208 D and b, c \u2208 A, we define Cvw\nbc to be the set of\ncompatible pairs (\u2212\u2192a , \u2212\u2192u ) such that \u2212\u2192a \u2208 Pbc and \u2212\u2192u \u2208 Svw\n.\nTo illustrate these definitions, figure 1 gives the\ndissection of a domain, a 2-dimensional plane, into five regions\nDa, Db, Dc, Dd, De. D-sequence (v, w, x, y, z) is compatible\nwith both path (a, b, c, e) and path (a, b, d, e); D-sequence\n(v, w, u, y, z) is compatible with a unique path (a, b, d, e).\nD-sequence (x, w, p, y, z) is compatible with a unique path\n(b, a, d, e). Hence (a, b, c, e), (a, b, d, e) and (b, a, d, e) are\nadmissible paths. However, path (a, c, d) or path (b, e) is not\nadmissible.\nProposition 6. For any compatible pair (\u2212\u2192a , \u2212\u2192u ), \u2206\u2212\u2192a (\u2212\u2192u ) =\n\u03b4(\u2212\u2192a ).\nProof. Let k = ord(\u2212\u2192u ) = |\u2212\u2192a |. By the definition of a\ncompatible pair, ui \u2208 Dai \u2229 Dai+1 for i \u2208 [k \u2212 1]. ui(ai) \u2212\nui(ai+1) = \u03b4aiai+1 from proposition 5. Therefore,\n\u2206\u2212\u2192a (\u2212\u2192u ) =\nk\u22121X\ni=1\n(ui(ai) \u2212 ui(ai+1)) =\nk\u22121X\ni=1\n\u03b4aiai+1 = \u03b4(\u2212\u2192a ).\nLemma 7. Let b, c \u2208 A and let \u2212\u2192a , \u2212\u2192a \u2208 Pbc. If C(\u2212\u2192a ) \u2229\nC(\u2212\u2192a ) = \u2205 then \u03b4(\u2212\u2192a ) = \u03b4(\u2212\u2192a ).\nProof. Let \u2212\u2192u be a D-sequence in C(\u2212\u2192a ) \u2229 C(\u2212\u2192a ). By\nproposition 6, \u03b4(\u2212\u2192a ) = \u2206\u2212\u2192a (\u2212\u2192u ) and \u03b4(\u2212\u2192a ) = \u2206\u2212\u2192a (\u2212\u2192u ), it\nsuffices to show \u2206\u2212\u2192a (\u2212\u2192u ) = \u2206\u2212\u2192a (\u2212\u2192u ).\nLet k = ord(\u2212\u2192u ) = |\u2212\u2192a | = |\u2212\u2192a |. Since\n\u2206\u2212\u2192a (\u2212\u2192u ) =\nk\u22121X\ni=1\n(ui(ai) \u2212 ui(ai+1))\n= u1(a1) +\nk\u22121X\ni=2\n(ui(ai) \u2212 ui\u22121(ai)) \u2212 uk\u22121(ak)\n= u1(b) +\nk\u22121X\ni=2\n(ui(ai) \u2212 ui\u22121(ai)) \u2212 uk\u22121(c),\n\u2206\u2212\u2192a (\u2212\u2192u ) \u2212 \u2206\u2212\u2192a (\u2212\u2192u )\n=\nk\u22121X\ni=2\n((ui(ai) \u2212 ui\u22121(ai)) \u2212 (ui(ai) \u2212 ui\u22121(ai)))\n=\nk\u22121X\ni=2\n((ui(ai) \u2212 ui(ai)) \u2212 (ui\u22121(ai) \u2212 ui\u22121(ai))).\nNoticing both ui\u22121 and ui belong to Dai \u2229 Dai\n, we have by\nproposition 5\nui\u22121(ai) \u2212 ui\u22121(ai) = \u03b4aiai\n= ui(ai) \u2212 ui(ai).\nHence \u2206\u2212\u2192a (\u2212\u2192u ) \u2212 \u2206\u2212\u2192a (\u2212\u2192u ) = 0.\n5. LINEAR D-SEQUENCES AND STRAIGHT\nPATHS\nFor v, w \u2208 D we write vw for the (closed) line segment\njoining v and w.\nA D-sequence \u2212\u2192u of order k is linear provided that there\nis a sequence of real numbers 0 = \u03bb0 \u2264 \u03bb1 \u2264 . . . \u2264 \u03bbk = 1\nsuch that ui = (1 \u2212 \u03bbi)u0 + \u03bbiuk. In particular, each ui\nbelongs to u0uk. For v, w \u2208 D we write Lvw\nfor the set of\nlinear (v, w)-sequences.\nFor b, c \u2208 A and v, w \u2208 D we write LCvw\nbc for the set of\ncompatible pairs (\u2212\u2192a , \u2212\u2192u ) such that \u2212\u2192a \u2208 Pbc and \u2212\u2192u \u2208 Lvw\n.\nFor a path \u2212\u2192a , we write L(\u2212\u2192a ) for the set of linear\nsequences compatible with \u2212\u2192a . We say that \u2212\u2192a is straight if\nL(\u2212\u2192a ) = \u2205.\nFor example, in figure 1, D-sequence (v, w, x, y, z) is\nlinear while (v, w, u, y, z), (x, w, p, y, z), and (x, v, w, y, z) are\nnot. Hence path (a, b, c, e) and (a, b, d, e) are both straight.\nHowever, path (b, a, d, e) is not straight.\n289\nLemma 8. Let b, c \u2208 A and v \u2208 Db, w \u2208 Dc. There is\na simple path \u2212\u2192a and D-sequence \u2212\u2192u such that (\u2212\u2192a , \u2212\u2192u ) \u2208\nLCvw\nbc . Furthermore, for any such path \u2212\u2192a , \u03b4(\u2212\u2192a ) \u2264 v(b) \u2212\nv(c).\nProof. By the convexity of D, any sequence of points on\nvw is a D-sequence.\nIf b = c, singleton path \u2212\u2192a = (b) and D-sequence \u2212\u2192u =\n(v, w) are obviously compatible. \u03b4(\u2212\u2192a ) = 0 = v(b) \u2212 v(c).\nSo assume b = c. If Db \u2229Dc \u2229vw = \u2205, we pick an arbitrary\nx from this set and let \u2212\u2192a = (b, c) \u2208 SPbc, \u2212\u2192u = (v, x, w) \u2208\nLvw\n. Again it is easy to check the compatibility of (\u2212\u2192a , \u2212\u2192u ).\nSince v \u2208 Db, v(b) \u2212 v(c) \u2265 \u03b4bc = \u03b4(\u2212\u2192a ).\nFor the remaining case b = c and Db \u2229Dc \u2229vw = \u2205, notice\nv = w otherwise v = w \u2208 Db \u2229 Dc \u2229 vw. So we can define\n\u03bbx for every point x on vw to be the unique number in [0, 1]\nsuch that x = (1 \u2212 \u03bbx)v + \u03bbxw. For convenience, we write\nx \u2264 y for \u03bbx \u2264 \u03bby.\nLet Ia = Da \u2229 vw for each a \u2208 A. Since D = \u222aa\u2208ADa, we\nhave vw = \u222aa\u2208AIa. Moreover, by the convexity of Da and\nvw, Ia is a (possibly trivial) closed interval.\nWe begin by considering the case that Ib and Ic are each\na single point, that is, Ib = {v} and Ic = {w}.\nLet S be a minimal subset of A satisfying \u222as\u2208SIs = vw.\nFor each s \u2208 S, Is is maximal, i.e., not contained in any\nother It, for t \u2208 S. In particular, the intervals {Is : s \u2208\nS} have all left endpoints distinct and all right endpoints\ndistinct and the order of the left endpoints is the same as\nthat of the right endpoints. Let k = |S| + 2 and index S\nas a2, . . . , ak\u22121 in the order defined by the right endpoints.\nDenote the interval Iai by [li, ri]. Thus l2 < l3 < . . . < lk\u22121,\nr2 < r3 < . . . < rk\u22121 and the fact that these intervals cover\nvw implies l2 = v, rk\u22121 = w and for all 2 \u2264 i \u2264 k \u2212 2,\nli+1 \u2264 ri which further implies li < ri. Now we define\nthe path \u2212\u2192a = (a1, a2, . . . , ak\u22121, ak) with a1 = b, ak = c\nand a2, a3, . . . , ak\u22121 as above. Define the linear D-sequence\n\u2212\u2192u = (u0, u1, . . . , uk) by u0 = u1 = v, uk = w and for\n2 \u2264 i \u2264 k\u22121, ui = ri. It follows immediately that (\u2212\u2192a , \u2212\u2192u ) \u2208\nLCvw\nbc . Neither b nor c is in S since lb = rb and lc = rc. Thus\n\u2212\u2192a is simple.\nFinally to show \u03b4(\u2212\u2192a ) \u2264 v(b) \u2212 v(c), we note\nv(b) \u2212 v(c) = v(a1) \u2212 v(ak) =\nk\u22121X\ni=1\n(v(ai) \u2212 v(ai+1))\nand\n\u03b4(\u2212\u2192a ) = \u2206\u2212\u2192a (\u2212\u2192u ) =\nk\u22121X\ni=1\n(ui(ai) \u2212 ui(ai+1))\n= v(a1) \u2212 v(a2) +\nk\u22121X\ni=2\n(ri(ai) \u2212 ri(ai+1)).\nFor two outcomes d, e \u2208 A, let us define fde(z) = z(d)\u2212z(e)\nfor all z \u2208 D. It suffices to show faiai+1 (ri) \u2264 faiai+1 (v) for\n2 \u2264 i \u2264 k \u2212 1.\nFact 9. For d, e \u2208 A, fde(z) is a linear function of z.\nFurthermore, if x \u2208 Dd and y \u2208 De with x = y, then\nfde(x) = x(d) \u2212 x(e) \u2265 \u03b4de \u2265 \u2212\u03b4ed \u2265 \u2212(y(e) \u2212 y(d)) =\nfde(y). Therefore fde(z) is monotonically nonincreasing along\nthe line\n\u2190\u2192\nxy as z moves in the direction from x to y.\nApplying this fact with d = ai, e = ai+1, x = li and y = ri\ngives the desired conclusion. This completes the proof for\nthe case that Ib = {v} and Ic = {w}.\nFor general Ib, Ic, rb < lc otherwise Db \u2229 Dc \u2229 vw = Ib \u2229\nIc = \u2205. Let v = rb and w = lc. Clearly we can apply the\nabove conclusion to v \u2208 Db, w \u2208 Dc and get a compatible\npair (\u2212\u2192a , \u2212\u2192u ) \u2208 LCv w\nbc with \u2212\u2192a simple and \u03b4(\u2212\u2192a ) \u2264 v (b) \u2212\nv (c). Define the linear D-sequence \u2212\u2192u by u0 = v, uk = w\nand ui = ui for i \u2208 [k \u2212 1]. (\u2212\u2192a , \u2212\u2192u ) \u2208 LCvw\nbc is evident.\nMoreover, applying the above fact with d = b, e = c, x = v\nand y = w, we get v(b) \u2212 v(c) \u2265 v (b) \u2212 v (c) \u2265 \u03b4(\u2212\u2192a ).\nCorollary 10. For any b, c \u2208 A there is a straight (b,\nc)path.\nThe main result of this section (theorem 12) says that for\nany b, c \u2208 A, every straight (b, c)-path has the same \u03b4-weight.\nTo prove this, we first fix v \u2208 Db and w \u2208 Dc and show\n(lemma 11) that every straight (b, c)-path compatible with\nsome linear (v, w)-sequence has the same \u03b4-weight \u03c1bc(v, w).\nWe then show in theorem 12 that \u03c1bc(v, w) is the same for\nall choices of v \u2208 Db and w \u2208 Dc.\nLemma 11. For b, c \u2208 A, there is a function \u03c1bc : Db \u00d7\nDc \u2212\u2192 R satisfying that for any (\u2212\u2192a , \u2212\u2192u ) \u2208 LCvw\nbc , \u03b4(\u2212\u2192a ) =\n\u03c1bc(v, w).\nProof. Let (\u2212\u2192a , \u2212\u2192u ), (\u2212\u2192a , \u2212\u2192u ) \u2208 LCvw\nbc . It suffices to\nshow \u03b4(\u2212\u2192a ) = \u03b4(\u2212\u2192a ). To do this we construct a linear\n(v, w)-sequence \u2212\u2192u and paths \u2212\u2192a \u2217\n, \u2212\u2192a \u2217\u2217\n\u2208 Pbc, both\ncompatible with \u2212\u2192u , satisfying \u03b4(\u2212\u2192a \u2217\n) = \u03b4(\u2212\u2192a ) and \u03b4(\u2212\u2192a \u2217\u2217\n) = \u03b4(\u2212\u2192a ).\nLemma 7 implies \u03b4(\u2212\u2192a \u2217\n) = \u03b4(\u2212\u2192a \u2217\u2217\n), which will complete the\nproof.\nLet |\u2212\u2192a | = ord(\u2212\u2192u ) = k and |\u2212\u2192a | = ord(\u2212\u2192u ) = l. We\nselect \u2212\u2192u to be any linear (v, w)-sequence (u0, u1, . . . , ut) such\nthat \u2212\u2192u and \u2212\u2192u are both subsequences of \u2212\u2192u , i.e., there\nare indices 0 = i0 < i1 < \u00b7 \u00b7 \u00b7 < ik = t and 0 = j0 <\nj1 < \u00b7 \u00b7 \u00b7 < jl = t such that \u2212\u2192u = (ui0 , ui1 , . . . , uik ) and\n\u2212\u2192u = (uj0 , uj1 , . . . , ujl ). We now construct a (b, c)-path\n\u2212\u2192a \u2217\ncompatible with \u2212\u2192u such that \u03b4(\u2212\u2192a \u2217\n) = \u03b4(\u2212\u2192a ). (An\nanalogous construction gives \u2212\u2192a \u2217\u2217\ncompatible with \u2212\u2192u such\nthat \u03b4(\u2212\u2192a \u2217\u2217\n) = \u03b4(\u2212\u2192a ).) This will complete the proof.\n\u2212\u2192a \u2217\nis defined as follows: for 1 \u2264 j \u2264 t, a\u2217\nj = ar where\nr is the unique index satisfying ir\u22121 < j \u2264 ir. Since both\nuir\u22121 = ur\u22121 and uir = ur belong to Dar\n, uj \u2208 Dar\nfor\nir\u22121 \u2264 j \u2264 ir by the convexity of Dar\n. The compatibility of\n(\u2212\u2192a \u2217\n, \u2212\u2192u ) follows immediately. Clearly, a\u2217\n1 = a1 = b and a\u2217\nt =\nak = c, so \u2212\u2192a \u2217\n\u2208 Pbc. Furthermore, as \u03b4a\u2217\nj a\u2217\nj+1\n= \u03b4arar\n= 0\nfor each r \u2208 [k], ir\u22121 < j < ir,\n\u03b4(\u2212\u2192a \u2217\n) =\nk\u22121X\nr=1\n\u03b4a\u2217\nir\na\u2217\nir+1\n=\nk\u22121X\nr=1\n\u03b4arar+1\n= \u03b4(\u2212\u2192a ).\nWe are now ready for the main theorem of the section:\nTheorem 12. \u03c1bc is a constant map on Db \u00d7 Dc. Thus\nfor any b, c \u2208 A, every straight (b, c)-path has the same\n\u03b4weight.\nProof. For a path \u2212\u2192a , (v, w) is compatible with \u2212\u2192a if\nthere is a linear (v, w)-sequence compatible with \u2212\u2192a . We\nwrite CP(\u2212\u2192a ) for the set of pairs (v, w) compatible with\n\u2212\u2192a . \u03c1bc is constant on CP(\u2212\u2192a ) because for each (v, w) \u2208\nCP(\u2212\u2192a ), \u03c1bc(v, w) = \u03b4(\u2212\u2192a ). By lemma 8, we also haveS\n\u2212\u2192a \u2208SPbc\nCP(\u2212\u2192a ) = Db \u00d7Dc. Since A is finite, SPbc, the set\nof simple paths from b to c, is finite as well.\n290\nNext we prove that for any path \u2212\u2192a , CP(\u2212\u2192a ) is closed.\nLet ((vn\n, wn\n) : n \u2208 N) be a convergent sequence in CP(\u2212\u2192a )\nand let (v, w) be the limit. We want to show that (v, w) \u2208\nCP(\u2212\u2192a ). For each n \u2208 N, since (vn\n, wn\n) \u2208 CP(\u2212\u2192a ), there is\na linear (vn\n, wn\n)-sequence un\ncompatible with \u2212\u2192a , i.e., there\nare 0 = \u03bbn\n0 \u2264 \u03bbn\n1 \u2264 . . . \u2264 \u03bbn\nk = 1 (k = |\u2212\u2192a |) such that\nun\nj = (1 \u2212 \u03bbn\nj )vn\n+ \u03bbn\nj wn\n(j = 0, 1, . . . , k). Since for each\nn, \u03bbn\n= (\u03bbn\n0 , \u03bbn\n1 , . . . , \u03bbn\nk ) belongs to the closed bounded set\n[0, 1]k+1\nwe can choose an infinite subset I \u2286 N such that the\nsequence (\u03bbn\n: n \u2208 I) converges. Let \u03bb = (\u03bb0, \u03bb1, . . . , \u03bbk) be\nthe limit. Clearly 0 = \u03bb0 \u2264 \u03bb1 \u2264 \u00b7 \u00b7 \u00b7 \u2264 \u03bbk = 1.\nDefine the linear (v, w)-sequence \u2212\u2192u by uj = (1 \u2212 \u03bbj )v +\n\u03bbj w (j = 0, 1, . . . , k). Then for each j \u2208 {0, . . . , k}, uj is\nthe limit of the sequence (un\nj : n \u2208 I). For j > 0, each un\nj\nbelongs to the closed set Daj , so uj \u2208 Daj . Similarly, for j <\nk each un\nj belongs to the closed set Daj+1 , so uj \u2208 Daj+1 .\nHence (\u2212\u2192a , \u2212\u2192u ) is compatible, implying (v, w) \u2208 CP(\u2212\u2192a ).\nNow we have Db \u00d7 Dc covered by finitely many closed\nsubsets on each of them \u03c1bc is a constant.\nSuppose for contradiction that there are (v, w), (v , w ) \u2208\nDb \u00d7 Dc such that \u03c1bc(v, w) = \u03c1bc(v , w ).\nL = {((1 \u2212 \u03bb)v + \u03bbv , (1 \u2212 \u03bb)w + \u03bbw ) : \u03bb \u2208 [0, 1]}\nis a line segment in Db \u00d7Dc by the convexity of Db, Dc. Let\nL1 = {(x, y) \u2208 L : \u03c1bc(x, y) = \u03c1bc(v, w)}\nand L2 = L \u2212 L1. Clearly (v, w) \u2208 L1, (v , w ) \u2208 L2. Let\nP = {\u2212\u2192a \u2208 SPbc : \u03b4(\u2212\u2192a ) = \u03c1bc(v, w)}.\nL1 =\n`S\n\u2212\u2192a \u2208P CP(\u2212\u2192a )\n\u00b4\n\u2229 L, L2 =\nS\n\u2212\u2192a \u2208SPbc\u2212P CP(\u2212\u2192a )\n\n\u2229 L\nare closed by the finiteness of P. This is a contradiction,\nsince it is well known (and easy to prove) that a line segment\ncan not be expressed as the disjoint union of two nonempty\nclosed sets.\nSummarizing corollary 10, lemma 11 and theorem 12, we\nhave\nCorollary 13. For any b, c \u2208 A, there is a real number\n\u03c1bc with the property that (1) There is at least one straight\n(b, c)-path of \u03b4-weight \u03c1bc and (2) Every straight (b, c)-path\nhas \u03b4-weight \u03c1bc.\n6. PROOF OF THEOREM 4\nLemma 14. \u03c1bc \u2264 \u03b4bc for all b, c \u2208 A.\nProof. For contradiction, suppose \u03c1bc \u2212 \u03b4bc = > 0.\nBy the definition of \u03b4bc, there exists v \u2208 f\u22121\n(b) \u2286 Db with\nv(b) \u2212 v(c) < \u03b4bc + = \u03c1bc. Pick an arbitrary w \u2208 Dc.\nBy lemma 8, there is a compatible pair (\u2212\u2192a , \u2212\u2192u ) \u2208 LCvw\nbc\nwith \u03b4(\u2212\u2192a ) \u2264 v(b) \u2212 v(c). Since \u2212\u2192a is a straight (b, c)-path,\n\u03c1bc = \u03b4(\u2212\u2192a ) \u2264 v(b) \u2212 v(c), leading to a contradiction.\nDefine another edge-weighted complete directed graph Gf\non vertex set A where the weight of arc (a, b) is \u03c1ab.\nImmediately from lemma 14, the weight of every directed cycle in\nGf is bounded below by its weight in Gf . To prove theorem\n4, it suffices to show the zero cycle property of Gf , i.e.,\nevery directed cycle has weight zero. We begin by considering\ntwo-cycles.\nLemma 15. \u03c1bc + \u03c1cb = 0 for all b, c \u2208 A.\nProof. Let \u2212\u2192a be a straight (b, c)-path compatible with\nlinear sequence \u2212\u2192u . let \u2212\u2192a be the reverse of \u2212\u2192a and \u2212\u2192u the\nreverse of \u2212\u2192u . Obviously, (\u2212\u2192a , \u2212\u2192u ) is compatible as well and\nthus \u2212\u2192a is a straight (c, b)-path. Therefore,\n\u03c1bc + \u03c1cb = \u03b4(\u2212\u2192a ) + \u03b4(\u2212\u2192a ) =\nk\u22121X\ni=1\n\u03b4aiai+1 +\nk\u22121X\ni=1\n\u03b4ai+1ai\n=\nk\u22121X\ni=1\n(\u03b4aiai+1 + \u03b4ai+1ai ) = 0,\nwhere the final equality uses proposition 5.\nNext, for three cycles, we first consider those compatible\nwith linear triples.\nLemma 16. If there are collinear points u \u2208 Da, v \u2208 Db,\nw \u2208 Dc (a, b, c \u2208 A), \u03c1ab + \u03c1bc + \u03c1ca = 0.\nProof. First, we prove for the case where v is between u\nand w. From lemma 8, there are compatible pairs (\u2212\u2192a , \u2212\u2192u ) \u2208\nLCuv\nab , (\u2212\u2192a , \u2212\u2192u ) \u2208 LCvw\nbc . Let |\u2212\u2192a | = ord(\u2212\u2192u ) = k and\n|\u2212\u2192a | = ord(\u2212\u2192u ) = l. We paste \u2212\u2192a and \u2212\u2192a together as\n\u2212\u2192a = (a = a1, a2, . . . , ak\u22121, ak, a1 , . . . , al = c),\n\u2212\u2192u and \u2212\u2192u as\n\u2212\u2192u = (u = u0, u1, . . . , uk = v = u0 , u1 , . . . , ul = w).\nClearly (\u2212\u2192a , \u2212\u2192u ) \u2208 LCuw\nac and\n\u03b4(\u2212\u2192a ) =\nk\u22121X\ni=1\n\u03b4aiai+1\n+ \u03b4ak\na1\n+\nl\u22121X\ni=1\n\u03b4ai ai+1\n= \u03b4(\u2212\u2192a ) + \u03b4bb + \u03b4(\u2212\u2192a )\n= \u03b4(\u2212\u2192a ) + \u03b4(\u2212\u2192a ).\nTherefore, \u03c1ac = \u03b4(\u2212\u2192a ) = \u03b4(\u2212\u2192a ) + \u03b4(\u2212\u2192a ) = \u03c1ab + \u03c1bc.\nMoreover, \u03c1ac = \u2212\u03c1ca by lemma 15, so we get \u03c1ab + \u03c1bc +\n\u03c1ca = 0.\nNow suppose w is between u and v. By the above\nargument, we have \u03c1ac + \u03c1cb + \u03c1ba = 0 and by lemma 15,\n\u03c1ab + \u03c1bc + \u03c1ca = \u2212\u03c1ba \u2212 \u03c1cb \u2212 \u03c1ac = 0.\nThe case that u is between v and w is similar.\nNow we are ready for the zero three-cycle property:\nLemma 17. \u03c1ab + \u03c1bc + \u03c1ca = 0 for all a, b, c \u2208 A.\nProof. Let S = {(a, b, c) : \u03c1ab + \u03c1bc + \u03c1ca = 0} and\nfor contradiction, suppose S = \u2205. S is finite. For each\na \u2208 A, choose va \u2208 Da arbitrarily and let T be the convex\nhull of {va : a \u2208 A}. For each (a, b, c) \u2208 S, let Rabc =\nDa \u00d7 Db \u00d7 Dc \u2229 T3\n. Clearly, each Rabc is nonempty and\ncompact. Moreover, by lemma 16, no (u, v, w) \u2208 Rabc is\ncollinear.\nDefine f : D3\n\u2192 R by f(u, v, w) = |v\u2212u|+|w\u2212v|+|u\u2212w|.\nFor (a, b, c) \u2208 S, the restriction of f to the compact set Rabc\nattains a minimum m(a, b, c) at some point (u, v, w) \u2208 Rabc\nby the continuity of f, i.e., there exists a triangle \u2206uvw of\nminimum perimeter within T with u \u2208 Da, v \u2208 Db, w \u2208 Dc.\nChoose (a\u2217\n, b\u2217\n, c\u2217\n) \u2208 S so that m(a\u2217\n, b\u2217\n, c\u2217\n) is minimum\nand let (u\u2217\n, v\u2217\n, w\u2217\n) \u2208 Ra\u2217b\u2217c\u2217 be a triple achieving it. Pick\nan arbitrary point p in the interior of \u2206u\u2217\nv\u2217\nw\u2217\n. By the\nconvexity of domain D, there is d \u2208 A such that p \u2208 Dd.\n291\nConsider triangles \u2206u\u2217\npw\u2217\n, \u2206w\u2217\npv\u2217\nand \u2206v\u2217\npu\u2217\n. Since\neach of them has perimeter less than that of \u2206u\u2217\nv\u2217\nw\u2217\nand\nall three triangles are contained in T, by the minimality of\n\u2206u\u2217\nv\u2217\nw\u2217\n, (a\u2217\n, d, c\u2217\n), (c\u2217\n, d, b\u2217\n), (b\u2217\n, d, a\u2217\n) \u2208 S. Thus\n\u03c1a\u2217d + \u03c1dc\u2217 + \u03c1c\u2217a\u2217 = 0,\n\u03c1c\u2217d + \u03c1db\u2217 + \u03c1b\u2217c\u2217 = 0,\n\u03c1b\u2217d + \u03c1da\u2217 + \u03c1a\u2217b\u2217 = 0.\nSumming up the three equalities,\n(\u03c1a\u2217d + \u03c1dc\u2217 + \u03c1c\u2217d + \u03c1db\u2217 + \u03c1b\u2217d + \u03c1da\u2217 )\n+(\u03c1c\u2217a\u2217 + \u03c1b\u2217c\u2217 + \u03c1a\u2217b\u2217 ) = 0,\nwhich yields a contradiction\n\u03c1a\u2217b\u2217 + \u03c1b\u2217c\u2217 + \u03c1c\u2217a\u2217 = 0.\nWith the zero two-cycle and three-cycle properties, the\nzero cycle property of Gf is immediate. As noted earlier,\nthis completes the proof of theorem 4.\nTheorem 18. Every directed cycle of Gf has weight zero.\nProof. Clearly, zero two-cycle and three-cycle properties\nimply triangle equality \u03c1ab +\u03c1bc = \u03c1ac for all a, b, c \u2208 A. For\na directed cycle C = a1a2 . . . aka1, by inductively applying\ntriangle equality, we have\nPk\u22121\ni=1 \u03c1aiai+1 = \u03c1a1ak . Therefore,\nthe weight of C is\nk\u22121X\ni=1\n\u03c1aiai+1 + \u03c1aka1 = \u03c1a1ak + \u03c1aka1 = 0.\nAs final remarks, we note that our result implies the\nfollowing strengthenings of theorem 12:\nCorollary 19. For any b, c \u2208 A, every admissible (b,\nc)path has the same \u03b4-weight \u03c1bc.\nProof. First notice that for any b, c \u2208 A, if Db \u2229Dc = \u2205,\n\u03b4bc = \u03c1bc. To see this, pick v \u2208 Db \u2229 Dc arbitrarily.\nObviously, path \u2212\u2192a = (b, c) is compatible with linear sequence\n\u2212\u2192u = (v, v, v) and is thus a straight (b, c)-path. Hence\n\u03c1bc = \u03b4(\u2212\u2192a ) = \u03b4bc.\nNow for any b, c \u2208 A and any (b, c)-path \u2212\u2192a with C(\u2212\u2192a ) =\n\u2205, let \u2212\u2192u \u2208 C(\u2212\u2192a ). Since ui \u2208 Dai \u2229 Dai+1 for i \u2208 [|\u2212\u2192a | \u2212 1],\n\u03b4(\u2212\u2192a ) =\n|\u2212\u2192a |\u22121\nX\ni=1\n\u03b4aiai+1 =\n|\u2212\u2192a |\u22121\nX\ni=1\n\u03c1aiai+1 ,\nwhich by theorem 18, = \u2212\u03c1a|\u2212\u2192a |a1 = \u03c1a1a|\u2212\u2192a |\n= \u03c1bc.\nCorollary 20. For any b, c \u2208 A, \u03c1bc is equal to \u03b4\u2217\nbc, the\nminimum \u03b4-weight over all (b, c)-paths.\nProof. Clearly \u03c1bc \u2265 \u03b4\u2217\nbc by corollary 13. On the other\nhand, for every (b, c)-path \u2212\u2192a = (b = a1, a2, . . . , ak = c), by\nlemma 14,\n\u03b4(\u2212\u2192a ) =\nk\u22121X\ni=1\n\u03b4aiai+1 \u2265\nk\u22121X\ni=1\n\u03c1aiai+1 ,\nwhich by theorem 18, = \u2212\u03c1aka1 = \u03c1a1ak = \u03c1bc. Hence \u03c1bc \u2264\n\u03b4\u2217\nbc, which completes the proof.\n7. COUNTEREXAMPLES TO STRONGER\nFORMS OF THEOREM 4\nTheorem 4 applies to social choice functions with convex\ndomain and finite range. We now show that neither of these\nhypotheses can be omitted. Our examples are single player\nfunctions.\nThe first example illustrates that convexity can not be\nomitted. We present an untruthful single player social choice\nfunction with three outcomes a, b, c satisfying W-MON on a\npath-connected but non-convex domain. The domain is the\nboundary of a triangle whose vertices are x = (0, 1, \u22121), y =\n(\u22121, 0, 1) and z = (1, \u22121, 0). x and the open line segment\nzx is assigned outcome a, y and the open line segment xy\nis assigned outcome b, and z and the open line segment\nyz is assigned outcome c. Clearly, \u03b4ab = \u2212\u03b4ba = \u03b4bc =\n\u2212\u03b4cb = \u03b4ca = \u2212\u03b4ac = \u22121, W-MON (the nonnegative\ntwocycle property) holds. Since there is a negative cycle \u03b4ab +\n\u03b4bc + \u03b4ca = \u22123, by lemma 3, this is not a truthful choice\nfunction.\nWe now show that the hypothesis of finite range can not\nbe omitted. We construct a family of single player social\nchoice functions each having a convex domain and an infinite\nnumber of outcomes, and satisfying weak monotonicity but\nnot truthfulness.\nOur examples will be specified by a positive integer n and\nan n \u00d7 n matrix M satisfying the following properties: (1)\nM is non-singular. (2) M is positive semidefinite. (3) There\nare distinct i1, i2, . . . , ik \u2208 [n] satisfying\nk\u22121X\nj=1\n(M(ij, ij) \u2212 M(ij , ij+1)) + (M(ik, ik) \u2212 M(ik, i1)) < 0.\nHere is an example matrix with n = 3 and (i1, i2, i3) =\n(1, 2, 3):\n0\n@\n0 1 \u22121\n\u22121 0 1\n1 \u22121 0\n1\nA\nLet e1, e2, . . . , en denote the standard basis of Rn\n. Let\nSn denote the convex hull of {e1, e2 . . . , en}, which is the\nset of vectors in Rn\nwith nonnegative coordinates that sum\nto 1. The range of our social choice function will be the\nset Sn and the domain D will be indexed by Sn, that is\nD = {y\u03bb : \u03bb \u2208 Sn}, where y\u03bb is defined below. The function\nf maps y\u03bb to \u03bb.\nNext we specify y\u03bb. By definition, D must be a set of\nfunctions from Sn to R. For \u03bb \u2208 Sn, the domain element\ny\u03bb : Sn \u2212\u2192 R is defined by y\u03bb(\u03b1) = \u03bbT\nM\u03b1. The\nnonsingularity of M guarantees that y\u03bb = y\u00b5 for \u03bb = \u00b5 \u2208 Sn.\nIt is easy to see that D is a convex subset of the set of all\nfunctions from Sn to R.\nThe outcome graph Gf is an infinite graph whose vertex\nset is the outcome set A = Sn. For outcomes \u03bb, \u00b5 \u2208 A, the\nedge weight \u03b4\u03bb\u00b5 is equal to\n\u03b4\u03bb\u00b5 = inf{v(\u03bb) \u2212 v(\u00b5) : f(v) = \u03bb}\n= y\u03bb(\u03bb) \u2212 y\u03bb(\u00b5) = \u03bbT\nM\u03bb \u2212 \u03bbT\nM\u00b5 = \u03bbT\nM(\u03bb \u2212 \u00b5).\nWe claim that Gf satisfies the nonnegative two-cycle\nproperty (W-MON) but has a negative cycle (and hence is not\ntruthful).\nFor outcomes \u03bb, \u00b5 \u2208 A,\n\u03b4\u03bb\u00b5 +\u03b4\u00b5\u03bb = \u03bbT\nM(\u03bb\u2212\u00b5)+\u00b5T\nM(\u00b5\u2212\u03bb) = (\u03bb\u2212\u00b5)T\nM(\u03bb\u2212\u00b5),\n292\nwhich is nonnegative since M is positive semidefinite. Hence\nthe nonnegative two-cycle property holds. Next we show\nthat Gf has a negative cycle. Let i1, i2, . . . , ik be a\nsequence of indices satisfying property 3 of M. We claim\nei1 ei2 . . . eik ei1 is a negative cycle. Since\n\u03b4eiej = eT\ni M(ei \u2212 ej) = M(i, i) \u2212 M(i, j)\nfor any i, j \u2208 [k], the weight of the cycle\nk\u22121X\nj=1\n\u03b4eij\neij+1\n+ \u03b4eik\nei1\n=\nk\u22121X\nj=1\n(M(ij , ij ) \u2212 M(ij, ij+1)) + (M(ik, ik) \u2212 M(ik, i1)) < 0,\nwhich completes the proof.\nFinally, we point out that the third property imposed on\nthe matrix M has the following interpretation. Let R(M) =\n{r1, r2, . . . , rn} be the set of row vectors of M and let hM be\nthe single player social choice function with domain R(M)\nand range {1, 2, . . . , n} mapping ri to i. Property 3 is\nequivalent to the condition that the outcome graph GhM has a\nnegative cycle. By lemma 3, this is equivalent to the\ncondition that hM is untruthful.\n8. FUTURE WORK\nAs stated in the introduction, the goal underlying the\nwork in this paper is to obtain useful and general\ncharacterizations of truthfulness.\nLet us say that a set D of P \u00d7 A real valuation matrices\nis a WM-domain if any social choice function on D\nsatisfying weak monotonicity is truthful. In this paper, we showed\nthat for finite A, any convex D is a WM-domain. Typically,\nthe domains of social choice functions considered in\nmechanism design are convex, but there are interesting examples\nwith non-convex domains, e.g., combinatorial auctions with\nunknown single-minded bidders. It is intriguing to find the\nmost general conditions under which a set D of real\nmatrices is a WM-domain. We believe that convexity is the main\npart of the story, i.e., a WM-domain is, after excluding some\nexceptional cases, essentially a convex set.\nTurning to parametric representations, let us say a set\nD of P \u00d7 A matrices is an AM-domain if any truthful\nsocial choice function with domain D is an affine maximizer.\nRoberts\" theorem says that the unrestricted domain is an\nAM-domain. What are the most general conditions under\nwhich a set D of real matrices is an AM-domain?\nAcknowledgments\nWe thank Ron Lavi for helpful discussions and the two\nanonymous referees for helpful comments.\n9. REFERENCES\n[1] A. Archer and E. Tardos. Truthful mechanisms for\none-parameter agents. In IEEE Symposium on\nFoundations of Computer Science, pages 482-491, 2001.\n[2] Y. Bartal, R. Gonen, and N. Nisan. Incentive\ncompatible multi unit combinatorial auctions. In\nTARK \"03: Proceedings of the 9th conference on\nTheoretical aspects of rationality and knowledge, pages\n72-87. ACM Press, 2003.\n[3] S. Bikhchandani, S. Chatterjee, and A. Sen. Incentive\ncompatibility in multi-unit auctions. Technical report,\nUCLA Department of Economics, Dec. 2004.\n[4] A. Goldberg, J. Hartline, A. Karlin, M. Saks and\nA. Wright. Competitive Auctions, 2004.\n[5] H. Gui, R. Muller, and R. Vohra. Dominant strategy\nmechanisms with multidimensional types. Technical\nReport 047, Maastricht: METEOR, Maastricht\nResearch School of Economics of Technology and\nOrganization, 2004. available at\nhttp://ideas.repec.org/p/dgr/umamet/2004047.html.\n[6] R. Lavi, A. Mu\"alem, and N. Nisan. Towards a\ncharacterization of truthful combinatorial auctions. In\nFOCS \"03: Proceedings of the 44th Annual IEEE\nSymposium on Foundations of Computer Science, page\n574. IEEE Computer Society, 2003.\n[7] D. Lehmann, L. O\"Callaghan, and Y. Shoham. Truth\nrevelation in approximately efficient combinatorial\nauctions. J. ACM, 49(5):577-602, 2002.\n[8] A. Mas-Colell, M. Whinston, and J. Green.\nMicroeconomic Theory. Oxford University Press, 1995.\n[9] N. Nisan. Algorithms for selfish agents. Lecture Notes\nin Computer Science, 1563:1-15, 1999.\n[10] K. Roberts. The characterization of implementable\nchoice rules. Aggregation and Revelation of Preferences,\nJ-J. Laffont (ed.), North Holland Publishing Company.\n[11] J.-C. Rochet. A necessary and sufficient condition for\nrationalizability in a quasi-linear context. Journal of\nMathematical Economics, 16:191-200, 1987.\n[12] I. Rozenshtrom. Dominant strategy implementation\nwith quasi-linear preferences. Master\"s thesis, Dept. of\nEconomics, The Hebrew University, Jerusalem, Israel,\n1999.\n293", "keywords": "truthful implementation;weak monotonicity;non-truthful function;strategyproof;individual preference;social choice function;truthful;truthfulness;dominant strategy;recognition algorithm;affine maximizer;convex domain;nonnegative cycle property;mechanism design"}
{"name": "train_J-63", "title": "Negotiation-Range Mechanisms: Exploring the Limits of Truthful Efficient Markets", "abstract": "This paper introduces a new class of mechanisms based on negotiation between market participants. This model allows us to circumvent Myerson and Satterthwaite\"s impossibility result and present a bilateral market mechanism that is efficient, individually rational, incentive compatible and budget balanced in the single-unit heterogeneous setting. The underlying scheme makes this combination of desirable qualities possible by reporting a price range for each buyer-seller pair that defines a zone of possible agreements, while the final price is left open for negotiation.", "fulltext": "1. INTRODUCTION\nIn this paper we introduce the concept of negotiation\nbased mechanisms in the context of the theory of efficient\ntruthful markets. A market consists of multiple buyers and\nsellers who wish to exchange goods. The market\"s main\nobjective is to produce an allocation of sellers\" goods to buyers\nas to maximize the total gain from trade.\nA commonly studied model of participant behavior is taken\nfrom the field of economic mechanism design [3, 4, 11]. In\nthis model each player has a private valuation function that\nassigns real values to each possible allocation. The\nalgorithm motivates players to participate truthfully by handing\npayments to them.\nThe mechanism in an exchange collects buyer bids and\nseller bids and clears the exchange by computing:(i) a set of\ntrades, and (ii) the payments made and received by players.\nIn designing a mechanism to compute trades and payments\nwe must consider the bidding strategies of self-interested\nplayers, i.e. rational players that follow expected-utility\nmaximizing strategies. We set allocative efficiency as our\nprimary goal. That is the mechanism must compute a set\nof trades that maximizes gain from trade. In addition we\nrequire individual rationality (IR) so that all players have\npositive expected utility to participate, budget balance (BB)\nso that the exchange does not run at a loss, and incentive\ncompatibility (IC) so that reporting the truth is a dominant\nstrategy for each player.\nUnfortunately, Myerson and Satterthwaite\"s (1983) well\nknown result demonstrates that in bilateral trade it is\nimpossible to simultaneously achieve perfect efficiency, BB, and\nIR using an IC mechanism [10]. A unique approach to\novercome Myerson and Satterthwaite\"s impossibility result was\nattempted by Parkes, Kalagnanam and Eso [12]. This result\ndesigns both a regular and a combinatorial bilateral trade\nmechanism (which imposes BB and IR) that approximates\ntruth revelation and allocation efficiency.\nIn this paper we circumvent Myerson and Satterthwaite\"s\nimpossibility result by introducing a new model of\nnegotiationrange markets. A negotiation-range mechanism does not\nproduce payment prices for the market participants. Rather,\nis assigns each buyer-seller pair a price range, called Zone\nOf Possible Agreements (ZOPA). The buyer is provided with\nthe high end of the range and the seller with the low end\nof the range. This allows the trading parties to engage in\nnegotiation over the final price with guarantee that the deal\nis beneficial for both of them. The negotiation process is not\nconsidered part of the mechanism but left up to the\ninterested parties, or to some external mechanism to perform. In\neffect a negotiation-range mechanism operates as a mediator\nbetween the market participants, offering them the grounds\nto be able to finalize the terms of the trade by themselves.\nThis concept is natural to many real-world market\nenvironments such as the real estate market.\n1\nWe focus on the single-unit heterogeneous setting: n\nsellers offer one unique good each by placing sealed bids\nspecifying their willingness to sell, and m buyers, interested in\nbuying a single good each, placing sealed bids specifying\ntheir willingness to pay for each good they may be\ninterested in.\nOur main result is a single-unit heterogeneous bilateral\ntrade negotiation-range mechanism (ZOPAS) that is\nefficient, individually rational, incentive compatible and budget\nbalanced.\nOur result does not contradict Myerson and\nSatterthwaite\"s important theorem. Myerson-Satterthwaite\"s proof\nrelies on a theorem assuring that in two different efficient\nIC markets; if the sellers have the same upper bound utility\nthen they will receive the same prices in each market and\nif the buyers have the same lower bound utility then they\nwill receive the same prices in each market. Our single-unit\nheterogeneous mechanism bypasses Myerson and\nSatterthwaite\"s theorem by producing a price range, defined by a\nseller\"s floor and a buyer\"s ceiling, for each pair of matched\nplayers. In our market mechanism the seller\"s upper bound\nutility may be the same while the seller\"s floor is different\nand the buyer\"s lower bound utility may be the same while\nthe buyer\"s ceiling is different. Moreover, the final price is\nnot fixed by the mechanism at all. Instead, it is determined\nby an independent negotiation between the buyer and seller.\nMore specifically, in a negotiation-range mechanism, the\nrange of prices each matched pair is given is resolved by a\nnegotiation stage where a final price is determined. This\nnegotiation stage is crucial for our mechanism to be IC.\nIntuitively, a negotiation range mechanism is incentive\ncompatible if truth telling promises the best ZOPA from the\npoint of view of the player in question. That is, he would\ntell the truth if this strategy maximizes the upper and lower\nbounds on his utility as expressed by the ZOPA boundaries.\nYet, when carefully examined it turns out that it is\nimpossible (by [10]) that this goal will always hold. This is simply\nbecause such a mechanism could be easily modified to\ndetermine final prices for the players (e.g. by taking the average of\nthe range\"s boundaries). Here, the negotiation stage come\ninto play. We show that if the above utility maximizing\ncondition does not hold then it is the case that the player\ncannot influence the negotiation bound that is assigned to\nhis deal partner no matter what value he declares. This\nmeans that the only thing that he may achieve by reporting\na false valuation is modifying his own negotiation bound,\nsomething that he could alternatively achieve by reporting\nhis true valuation and incorporating the effect of the\nmodified negotiation bound into his negotiation strategy. This\neliminates the benefit of reporting false valuations and\nallows our mechanism to compute the optimal gain from trade\naccording to the players\" true values.\nThe problem of computing the optimal allocation which\nmaximizes gain from trade can be conceptualized as the\nproblem of finding the maximum weighted matching in a\nweighted bipartite graph connecting buyers and sellers, where\neach edge in the graph is assigned a weight equal to the\ndifference between the respective buyer bid and seller bid. It\nis well known that this problem can be solved efficiently in\npolynomial time.\nVCG IC payment schemes [2, 7, 13] support efficient and\nIR bilateral trade but not simultaneously BB. Our particular\napproach adapts the VCG payment scheme to achieve\nbudget balance. The philosophy of the VCG payment schemes\nin bilateral trade is that the buyer pays the seller\"s\nopportunity cost of not selling the good to another buyer and not\nkeeping the good to herself. The seller is paid in addition to\nthe buyer\"s price a compensation for the damage the\nmechanism did to the seller by not extracting the buyer\"s full\nbid. Our philosophy is a bit different: The seller is paid at\nleast her opportunity cost of not selling the good to another\nbuyer and not keeping the good for herself. The buyer pays\nat most his alternate seller\"s opportunity cost of not selling\nthe good to another buyer and not keeping the alternate\ngood for herself.\nThe rest of this paper is organized as follows. In\nSection 2 we describe our model and definitions. In section 3\nwe present the single-unit heterogeneous negotiation-range\nmechanism and show that it is efficient, IR, IC and BB.\nFinally, we conclude with a discussion in Section 4.\n2. NEGOTIATION MARKETS\nPRELIMINARIES\nLet \u03a0 denote the set of players, N the set of n\nselling players, and M the set of m buying players, where\n\u03a0 = N \u222a M. Let \u03a8 = {1, ..., t} denote the set of goods.\nLet Ti \u2208 {\u22121, 0, 1}t\ndenote an exchange vector for a trade,\nsuch that player i buys goods {A \u2208 \u03a8|Ti (A) = 1} and sells\ngoods {A \u2208 \u03a8|Ti (A) = \u22121}. Let T = (T1, ..., T|\u03a0|) denote\nthe complete trade between all players. We view T as\ndescribing the allocation of goods by the mechanism to the\nbuyers and sellers.\nIn the single-unit heterogeneous setting every good\nbelongs to specific seller, and every buyer is interested in\nbuying one good. The buyer may bid for several or all goods.\nAt the end of the auction every good is either assigned to\none of the buyers who bid for it or kept unsold by the seller.\nIt is convenient to assume the sets of buyers and sellers are\ndisjoint (though it is not required), i.e. N \u2229 M = \u2205. Each\nseller i is associated with exactly one good Ai, for which she\nhas true valuation ci which expresses the price at which it\nis beneficial for her to sell the good. If the seller reports a\nfalse valuation at an attempt to improve the auction results\nfor her, this valuation is denoted \u02c6ci. A buyer has a\nvaluation vector describing his valuation for each of the goods\naccording to their owner. Specifically, vj(k) denotes buyer\nj\"s valuation for good Ak. Similarly, if he reports a false\nvaluation it is denoted \u02c6vj(k).\nIf buyer j is matched by the mechanism with seller i then\nTi(Ai) = \u22121 and Tj(Ai) = 1. Notice, that in our setting for\nevery k = i, Ti(Ak) = 0 and Tj(Ai) = 0 and also for every\nz = j, Tz(Ai) = 0.\nFor a matched buyer j - seller i pair, the gain from trade\non the deal is defined as vj(i) \u2212 ci. Given and allocation T,\nthe gain from trade associated with T is\nV =\nj\u2208M,i\u2208N\n(vj(i) \u2212 ci) \u00b7 Tj(Ai).\nLet T\u2217\ndenote the optimal allocation which maximizes the\ngain from trade, computed according to the players\" true\nvaluations. Let V \u2217\ndenote the optimal gain from trade\nassociated with this allocation.\nWhen players\" report false valuations we use \u02c6T\u2217\nand \u02c6V \u2217\nto\ndenote the optimal allocation and gain from trade,\nrespectively, when computed according to the reported valuations.\n2\nWe are interested in the design of negotiation-range\nmechanisms. In contrast to a standard auction mechanism where\nthe buyer and seller are provided with the prices they should\npay, the goal of a negotiation-range mechanism is to provide\nthe player\"s with a range of prices within which they can\nnegotiate the final terms of the deal by themselves. The\nmechanism would provide the buyer with the upper bound\non the range and the seller with the lower bound on the\nrange. This gives each of them a promise that it will be\nbeneficial for them to close the deal, but does not provide\ninformation about the other player\"s terms of negotiation.\nDefinition 1. Negotiation Range: Zone Of Possible\nAgreements, ZOPA, between a matched buyer and seller. The\nZOPA is a range, (L, H), 0 \u2264 L \u2264 H, where H is an upper\nbound (ceiling) price for the buyer and L is a lower bound\n(floor) price for the seller.\nDefinition 2. Negotiation-Range Mechanism: A\nmechanism that computes a ZOPA, (L, H), for each matched buyer\nand seller in T\u2217\n, and provides the buyer with the upper bound\nH and the seller with the lower bound L.\nThe basic assumption is that participants in the auction\nare self-interested players. That is their main goal is to\nmaximize their expected utility. The utility for a buyer who\ndoes not participate in the trade is 0. If he does win some\ngood, his utility is the surplus between his valuation for that\ngood and the price he pays. For a seller, if she keeps the good\nunsold, her utility is just her valuation of the good, and the\nsurplus is 0. If she gets to sell it, her utility is the price she\nis paid for it, and the surplus is the difference between this\nprice and her valuation.\nSince negotiation-range mechanisms assign bounds on the\nrange of prices rather than the final price, it is useful to\ndefine the upper and lower bounds on the player\"s utilities\ndefined by the range\"s limits.\nDefinition 3. Consider a buyer j - seller i pair matched\nby a negotiation-range mechanism and let (L, H) be their\nassociated negotiation range.\n\u2022 The buyer\"s top utility is: vj(i) \u2212 L, and the buyer\"s\nbottom utility is vj(i) \u2212 H.\n\u2022 The seller\"s top utility is H, with surplus H \u2212 ci, and\nthe seller\"s bottom utility is L, with surplus L \u2212 ci.\n3. THE SINGLE-UNIT HETEROGENEOUS\nMECHANISM (ZOPAS)\n3.1 Description of the Mechanism\nZOPAS is a negotiation-range mechanism, it finds the\noptimal allocation T\u2217\nand uses it to define a ZOPA for each\nbuyer-seller pair.\nThe first stage in applying the mechanism is for the buyers\nand sellers to submit their sealed bids. The mechanism then\nallocates buyers to sellers by computing the allocation T \u2217\n,\nwhich results in the optimal gain from trade V \u2217\n, and defines\na ZOPA for each buyer-seller pair. Finally, buyers and sellers\nuse the ZOPA to negotiate a final price.\nComputing T\u2217\ninvolves solving the maximum weighted\nbipartite matching problem for the complete bipartite graph\nKn,m constructed by placing the buyers on one side of the\nFind the optimal allocation T \u2217\nCompute the maximum weighted bipartite\nmatching for the bipartite graph\nof buyers and sellers, and edge weights\nequal to the gain from trade.\nCalculate Sellers\" Floors\nFor every buyer j, allocated good Ai\nFind the optimal allocation (T\u2212j)\u2217\nLi = vj(i) + (V\u2212j)\u2217\n\u2212 V \u2217\nCalculate Buyers\" Ceilings\nFor every buyer j, allocated good Ai\nFind the optimal allocation (T \u2212i\n)\u2217\nFind the optimal allocation (T \u2212i\n\u2212j )\u2217\nHj = vj(i) + (V \u2212i\n\u2212j )\u2217\n\u2212 (V \u2212i\n)\u2217\nNegotiation Phase\nFor every buyer j\nand every seller i of good Ai\nReport to seller i her floor Li\nand identify her matched buyer j\nReport to buyer j his ceiling Hj\nand identify his matched seller i\ni, j negotiate the good\"s final price\nFigure 1: The ZOPAS mechanism\ngraph, the seller on another and giving the edge between\nbuyer j and seller i weight equal to vj(i) \u2212 ci. The\nmaximum weighted matching problem in solvable in polynomial\ntime (e.g., using the Hungarian Method). This results in\na matching between buyers and sellers that maximizes gain\nfrom trade.\nThe next step is to compute for each buyer-seller pair a\nseller\"s floor, which provides the lower bound of the ZOPA\nfor this pair, and assigns it to the seller.\nA seller\"s floor is computed by calculating the difference\nbetween the total gain from trade when the buyer is excluded\nand the total gain from trade of the other participants when\nthe buyer is included (the VCG principle).\nLet (T\u2212j)\u2217\ndenote the gain from trade of the optimal\nallocation when buyer j\"s bids are discarded. Denote by (V\u2212j)\u2217\nthe total gain from trade in the allocation (T\u2212j)\u2217\n.\nDefinition 4. Seller Floor: The lowest price the seller\nshould expect to receive, communicated to the seller by the\nmechanism. The seller floor for player i who was matched\nwith buyer j on good Ai, i.e., Tj(Ai) = 1, is computed as:\nLi = vj(i) + (V\u2212j)\u2217\n\u2212 V \u2217\n.\nThe seller is instructed not to accept less than this price from\nher matched buyer.\nNext, the mechanism computes for each buyer-seller pair a\nbuyer ceiling, which provides the upper bound of the ZOPA\nfor this pair, and assigns it to the buyer.\nEach buyer\"s ceiling is computed by removing the buyer\"s\nmatched seller and calculating the difference between the\ntotal gain from trade when the buyer is excluded and the\ntotal gain from trade of the other participants when the\n3\nbuyer is included. Let (T\u2212i\n)\u2217\ndenote the gain from trade\nof the optimal allocation when seller i is removed from the\ntrade. Denote by (V \u2212i\n)\u2217\nthe total gain from trade in the\nallocation (T\u2212i\n)\u2217\n.\nLet (T\u2212i\n\u2212j )\u2217\ndenote the gain from trade of the optimal\nallocation when seller i is removed from the trade and buyer j\"s\nbids are discarded. Denote by (V \u2212i\n\u2212j )\u2217\nthe total gain from\ntrade in the allocation (T \u2212i\n\u2212j )\u2217\n.\nDefinition 5. Buyer Ceiling: The highest price the seller\nshould expect to pay, communicated to the buyer by the\nmechanism. The buyer ceiling for player j who was matched with\nseller i on good Ai, i.e., Tj(Ai) = 1, is computed as:\nHj = vj(i) + (V \u2212i\n\u2212j )\u2217\n\u2212 (V \u2212i\n)\u2217\n.\nThe buyer is instructed not to pay more than this price to\nhis matched seller.\nOnce the negotiation range lower bound and upper bound\nare computed for every matched pair, the mechanism reports\nthe lower bound price to the seller and the upper bound price\nto the buyer. At this point each buyer-seller pair negotiates\non the final price and concludes the deal.\nA schematic description the ZOPAS mechanism is given\nin Figure 3.1.\n3.2 Analysis of the Mechanism\nIn this section we analyze the properties of the ZOPAS\nmechanism.\nTheorem 1. The ZOPAS market negotiation-range\nmechanism is an incentive-compatible bilateral trade\nmechanism that is efficient, individually rational and budget\nbalanced.\nClearly ZOPAS is an efficient polynomial time mechanism.\nLet us show it satisfies the rest of the properties in the\ntheorem.\nClaim 1. ZOPAS is individually rational, i.e., the\nmechanism maintains nonnegative utility surplus for all\nparticipants.\nProof. If a participant does not trade in the optimal\nallocation then his utility surplus is zero by definition.\nConsider a pair of buyer j and seller i which are matched in the\noptimal allocation T \u2217\n. Then the buyer\"s utility is at least\nvj(i) \u2212 Hj. Recall that Hj = vj(i) + (V \u2212i\n\u2212j )\u2217\n\u2212 (V \u2212i\n)\u2217\n, so\nthat vj(i) \u2212 Hj = (V \u2212i\n)\u2217\n\u2212 (V \u2212i\n\u2212j )\u2217\n. Since the optimal gain\nfrom trade which includes j is higher than that which does\nnot, we have that the utility is nonnegative: vj(i) \u2212 Hj \u2265 0.\nNow, consider the seller i. Her utility surplus is at least\nLi \u2212 ci. Recall that Li = vj(i) + (V\u2212j)\u2217\n\u2212 V \u2217\n. If we\nremoved from the optimal allocation T \u2217\nthe contribution of\nthe buyer j - seller i pair, we are left with an allocation\nwhich excludes j, and has value V \u2217\n\u2212 (vj(i) \u2212 ci). This\nimplies that (V\u2212j)\u2217\n\u2265 V \u2217\n\u2212 vj(i) + ci, which implies that\nLi \u2212 ci \u2265 0.\nThe fact that ZOPAS is a budget-balanced mechanism\nfollows from the following lemma which ensures the validity\nof the negotiation range, i.e., that every seller\"s floor is below\nher matched buyer\"s ceiling. This ensures that they can close\nthe deal at a final price which lies in this range.\nLemma 1. For every buyer j- seller i pair matched by the\nmechanism: Li \u2264 Hj.\nProof. Recall that Li = vj(i) + (V\u2212j)\u2217\n\u2212 V \u2217\nand Hj =\nvj(i)+(V \u2212i\n\u2212j )\u2217\n\u2212(V \u2212i\n)\u2217\n. To prove that Li \u2264 Hj it is enough\nto show that\n(V \u2212i\n)\u2217\n+ (V\u2212j)\u2217\n\u2264 V \u2217\n+ (V \u2212i\n\u2212j )\u2217\n. (1)\nThe proof of (1) is based on a method which we apply\nseveral times in our analysis. We start with the\nallocations (T\u2212i\n)\u2217\nand (T\u2212j)\u2217\nwhich together have value equal\nto (V \u2212i\n)\u2217\n+ (V\u2212j)\u2217\n. We now use them to create a pair of\nnew valid allocations, by using the same pairs that were\nmatched in the original allocations. This means that the\nsum of values of the new allocations is the same as the\noriginal pair of allocations. We also require that one of the new\nallocations does not include buyer j or seller i. This means\nthat the sum of values of these new allocations is at most\nV \u2217\n+ (V \u2212i\n\u2212j )\u2217\n, which proves (1).\nLet G be the bipartite graph where the nodes on one side\nof G represent the buyers and the nodes on the other side\nrepresent the sellers, and edge weights represent the gain\nfrom trade for the particular pair. The different allocations\nrepresent bipartite matchings in G. It will be convenient for\nthe sake of our argument to think of the edges that belong\nto each of the matchings as being colored with a specific\ncolor representing this matching.\nAssign color 1 to the edges in the matching (T \u2212i\n)\u2217\nand\nassign color 2 to the edges in the matching (T\u2212j)\u2217\n. We claim\nthat these edges can be recolored using colors 3 and 4 so that\nthe new coloring represents allocations T (represented by\ncolor 3) and (T\u2212i\n\u2212j ) (represented by color 4). This implies\nthe that inequality (1) holds. Figure 2 illustrates the graph\nG and the colorings of the different matchings.\nDefine an alternating path P starting at j. Let S1 be\nthe seller matched to j in (T \u2212i\n)\u2217\n(if none exists then P is\nempty). Let B1 be the buyer matched to S1 in (T\u2212j)\u2217\n, S2 be\nthe seller matched to B1 in (T\u2212i\n)\u2217\n, B2 be the buyer matched\nto S2 in (T\u2212j)\u2217\n, and so on. This defines an alternating\npath P, starting at j, whose edges\" colors alternate between\ncolors 1 and 2 (starting with 1). This path ends either in a\nseller who is not matched in (T\u2212j)\u2217\nor in a buyer who is not\nmatched in (T\u2212i\n)\u2217\n. Since all sellers in this path are matched\nin (T\u2212i\n)\u2217\n, we have that seller i does not belong to P. This\nensures that edges in P may be colored by alternating colors\n3 and 4 (starting with 3). Since except for the first edge, all\nothers do not involve i or j and thus may be colored 4 and\nbe part of an allocation (T \u2212i\n\u2212j ) .\nWe are left to recolor the edges that do not belong to P.\nSince none of these edges includes j we have that the edges\nthat were colored 1, which are part of (T \u2212i\n)\u2217\n, may now be\ncolored 4, and be included in the allocation (T \u2212i\n\u2212j ) . It is\nalso clear that the edges that were colored 2, which are part\nof (T\u2212j)\u2217\n, may now be colored 3, and be included in the\nallocation T . This completes the proof of the lemma.\n3.3 Incentive Compatibility\nThe basic requirement in mechanism design is for an\nexchange mechanism to be incentive compatible. This means\nthat its payment structure enforces that truth-telling is the\nplayers\" weakly dominant strategy, that is that the\nstrategy by which the player is stating his true valuation results\n4\n...\njS1\nS2 B1\nS3 B2\nB3S4\nS5 B4\nS6 B5\nS8 B7\nS7 B6\n...\nFigure 2: Alternating path argument for Lemma 1\n(Validity of the Negotiation Range) and Claim 2\n(part of Buyer\"s IC proof)\nColors\nBidders\n1 32 4\nUnmatchedMatched\nFigure 3: Key to Figure 2\nin bigger or equal utility as any other strategy. The\nutility surplus is defined as the absolute difference between the\nplayer\"s bid and his price.\nNegotiation-range mechanisms assign bounds on the range\nof prices rather than the final price and therefore the player\"s\nvaluation only influences the minimum and maximum bounds\non his utility. For a buyer the minimum (bottom) utility\nwould be based on the top of the negotiation range\n(ceiling), and the maximum (top) utility would be based on the\nbottom of the negotiation range (floor). For a seller it\"s the\nother way around. Therefore the basic natural requirement\nfrom negotiation-range mechanisms would be that stating\nthe player\"s true valuation results in both the higher\nbottom utility and higher top utility for the player, compared\nwith other strategies. Unfortunately, this requirement is\nstill too strong and it is impossible (by [10]) that this will\nalways hold. Therefore we slightly relax it as follows: we\nrequire this holds when the false valuation based strategy\nchanges the player\"s allocation. When the allocation stays\nunchanged we require instead that the player would not be\nable to change his matched player\"s bound (e.g. a buyer\ncannot change the seller\"s floor). This means that the only\nthing he can influence is his own bound, something that he\ncan alternatively achieve through means of negotiation.\nThe following formally summarizes our incentive\ncompatibility requirements from the negotiation-range mechanism.\nBuyer\"s incentive compatibility:\n\u2022 Let j be a buyer matched with seller i by the\nmechanism according to valuation vj and the\nnegotiationrange assigned is (Li, Hj). Assume that when the\nmechanism is applied according to valuation \u02c6vj, seller\nk = i is matched with j and the negotiation-range\nassigned is (\u02c6Lk, \u02c6Hj). Then\nvj(i) \u2212 Hj \u2265 vj(k) \u2212 \u02c6Hj. (2)\nvj(i) \u2212 Li \u2265 vj(k) \u2212 \u02c6Lk. (3)\n\u2022 Let j be a buyer not matched by the mechanism\naccording to valuation vj. Assume that when the\nmechanism is applied according to valuation \u02c6vj, seller k = i\nis matched with j and the negotiation-range assigned\nis (\u02c6Lk, \u02c6Hj). Then\nvj(k) \u2212 \u02c6Hj \u2264 vj(k) \u2212 \u02c6Lk \u2264 0. (4)\n\u2022 Let j be a buyer matched with seller i by the\nmechanism according to valuation vj and let the assigned\nbottom of the negotiation range (seller\"s floor) be Li.\nAssume that when the mechanism is applied according\nto valuation \u02c6vj, the matching between i and j remains\nunchanged and let the assigned bottom of the\nnegotiation range (seller\"s floor) be \u02c6Li. Then,\n\u02c6Li = Li. (5)\nNotice that the first inequality of (4) always holds for a valid\nnegotiation range mechanism (Lemma 1).\nSeller\"s incentive compatibility:\n\u2022 Let i be a seller not matched by the mechanism\naccording to valuation ci. Assume that when the mechanism\n5\nis applied according to valuation \u02c6ci, buyer z = j is\nmatched with i and the negotiation-range assigned is\n(\u02c6Li, \u02c6Hz). Then\n\u02c6Li \u2212 ci \u2264 \u02c6Hz \u2212 ci \u2264 0. (6)\n\u2022 Let i be a buyer matched with buyer j by the\nmechanism according to valuation ci and let the assigned top\nof the negotiation range (buyer\"s ceiling) be Hj.\nAssume that when the mechanism is applied according\nto valuation \u02c6ci, the matching between i and j remains\nunchanged and let the assigned top of the negotiation\nrange (buyer\"s ceiling) be \u02c6Hj. Then,\n\u02c6Hj = Hj. (7)\nNotice that the first inequality of (6) always holds for a valid\nnegotiation range mechanism (Lemma 1).\nObserve that in the case of sellers in our setting, the case\nexpressed by requirement (6) is the only case in which the\nseller may change the allocation to her benefit. In particular,\nit is not possible for seller i who is matched in T \u2217\nto change\nher buyer by reporting a false valuation. This fact simply\nfollows from the observation that reducing the seller\"s\nvaluation increases the gain from trade for the current allocation\nby at least as much than any other allocation, whereas\nincreasing the seller\"s valuation decreases the gain from trade\nfor the current allocation by exactly the same amount as any\nother allocation in which it is matched. Therefore, the only\ncase the optimal allocation may change is when in the new\nallocation i is not matched in which case her utility surplus\nis 0.\nTheorem 2. ZOPAS is an incentive compatible\nnegotiationrange mechanism.\nProof. We begin with the incentive compatibility for\nbuyers.\nConsider a buyer j who is matched with seller i according\nto his true valuation v. Consider that j is reporting instead\na false valuation \u02c6v which results in a different allocation in\nwhich j is matched with seller k = i. The following claim\nshows that a buyer j which changed his allocation due to\na false declaration of his valuation cannot improve his top\nutility.\nClaim 2. Let j be a buyer matched to seller i in T \u2217\n, and\nlet k = i be the seller matched to j in \u02c6T\u2217\n. Then,\nvj(i) \u2212 Hj \u2265 vj(k) \u2212 \u02c6Hj. (8)\nProof. Recall that Hj = vj(i) + (V \u2212i\n\u2212j )\u2217\n\u2212 (V \u2212i\n)\u2217\nand\n\u02c6Hj = \u02c6vj(k) + ( \u02c6V \u2212k\n\u2212j )\u2217\n\u2212 ( \u02c6V \u2212k\n)\u2217\n. Therefore, vj(i) \u2212 Hj =\n(V \u2212i\n)\u2217\n\u2212 (V \u2212i\n\u2212j )\u2217\nand vj(k) \u2212 \u02c6Hj = vj(k) \u2212 \u02c6vj(k) + ( \u02c6V \u2212k\n)\u2217\n\u2212\n( \u02c6V \u2212k\n\u2212j )\u2217\n.\nIt follows that in order to prove (8) we need to show\n( \u02c6V \u2212k\n)\u2217\n+ (V \u2212i\n\u2212j )\u2217\n\u2264 (V \u2212i\n)\u2217\n+ ( \u02c6V \u2212k\n\u2212j )\u2217\n+ \u02c6vj(k) \u2212 vj(k). (9)\nConsider first the case were j is matched to i in ( \u02c6T\u2212k\n)\u2217\n. If\nwe remove this pair and instead match j with k we obtain\na matching which excludes i, if the gain from trade on the\nnew pair is taken according to the true valuation then we\nget\n( \u02c6V \u2212k\n)\u2217\n\u2212 (\u02c6vj(i) \u2212 ci) + (vj(k) \u2212 ck) \u2264 (V \u2212i\n)\u2217\n.\nNow, since the optimal allocation \u02c6T\u2217\nmatches j with k rather\nthan with i we have that\n(V \u2212i\n\u2212j )\u2217\n+ (\u02c6vj(i) \u2212 ci) \u2264 \u02c6V \u2217\n= ( \u02c6V \u2212k\n\u2212j )\u2217\n+ (\u02c6vj(k) \u2212 ck),\nwhere we have used that ( \u02c6V \u2212i\n\u2212j )\u2217\n= (V \u2212i\n\u2212j )\u2217\nsince these\nallocations exclude j. Adding up these two inequalities implies\n(9) in this case.\nIt is left to prove (9) when j is not matched to i in ( \u02c6T\u2212k\n)\u2217\n.\nIn fact, in this case we prove the stronger inequality\n( \u02c6V \u2212k\n)\u2217\n+ (V \u2212i\n\u2212j )\u2217\n\u2264 (V \u2212i\n)\u2217\n+ ( \u02c6V \u2212k\n\u2212j )\u2217\n. (10)\nIt is easy to see that (10) indeed implies (9) since it follows\nfrom the fact that k is assigned to j in \u02c6T\u2217\nthat \u02c6vj(k) \u2265\nvj(k). The proof of (10) works as follows. We start with the\nallocations ( \u02c6T\u2212k\n)\u2217\nand (T\u2212i\n\u2212j )\u2217\nwhich together have value\nequal to ( \u02c6V \u2212k\n)\u2217\n+ (V \u2212i\n\u2212j )\u2217\n. We now use them to create a\npair of new valid allocations, by using the same pairs that\nwere matched in the original allocations. This means that\nthe sum of values of the new allocations is the same as the\noriginal pair of allocations. We also require that one of the\nnew allocations does not include seller i and is based on the\ntrue valuation v, while the other allocation does not include\nbuyer j or seller k and is based on the false valuation \u02c6v. This\nmeans that the sum of values of these new allocations is at\nmost (V \u2212i\n)\u2217\n+ ( \u02c6V \u2212k\n\u2212j )\u2217\n, which proves (10).\nLet G be the bipartite graph where the nodes on one side\nof G represent the buyers and the nodes on the other side\nrepresent the sellers, and edge weights represent the gain\nfrom trade for the particular pair. The different allocations\nrepresent bipartite matchings in G. It will be convenient for\nthe sake of our argument to think of the edges that belong\nto each of the matchings as being colored with a specific\ncolor representing this matching.\nAssign color 1 to the edges in the matching ( \u02c6T\u2212k\n)\u2217\nand\nassign color 2 to the edges in the matching (T \u2212i\n\u2212j )\u2217\n. We claim\nthat these edges can be recolored using colors 3 and 4 so that\nthe new coloring represents allocations (T \u2212i\n) (represented\nby color 3) and ( \u02c6T\u2212k\n\u2212j ) (represented by color 4). This implies\nthe that inequality (10) holds. Figure 2 illustrates the graph\nG and the colorings of the different matchings.\nDefine an alternating path P starting at j. Let S1 = i be\nthe seller matched to j in ( \u02c6T\u2212k\n)\u2217\n(if none exists then P is\nempty). Let B1 be the buyer matched to S1 in (T\u2212i\n\u2212j )\u2217\n, S2 be\nthe seller matched to B1 in ( \u02c6T\u2212k\n)\u2217\n, B2 be the buyer matched\nto S2 in (T\u2212i\n\u2212j )\u2217\n, and so on. This defines an alternating\npath P, starting at j, whose edges\" colors alternate between\ncolors 1 and 2 (starting with 1). This path ends either in\na seller who is not matched in (T \u2212i\n\u2212j )\u2217\nor in a buyer who\nis not matched in ( \u02c6T\u2212k\n)\u2217\n. Since all sellers in this path are\nmatched in ( \u02c6T\u2212k\n)\u2217\n, we have that seller k does not belong to\nP. Since in this case S1 = i and the rest of the sellers in P\nare matched in (T\u2212i\n\u2212j )\u2217\nwe have that seller i as well does not\nbelong to P. This ensures that edges in P may be colored\nby alternating colors 3 and 4 (starting with 3). Since S1 = i,\nwe may use color 3 for the first edge and thus assign it to\nthe allocation (T\u2212i\n) . All other edges, do not involve i, j\nor k and thus may be either colored 4 and be part of an\nallocation ( \u02c6T\u2212k\n\u2212j ) or colored 3 and be part of an allocation\n(T\u2212i\n) , in an alternating fashion.\nWe are left to recolor the edges that do not belong to P.\nSince none of these edges includes j we have that the edges\n6\nthat were colored 1, which are part of ( \u02c6T\u2212k\n)\u2217\n, may now be\ncolored 4, and be included in the allocation ( \u02c6T\u2212k\n\u2212j ) . It is\nalso clear that the edges that were colored 2, which are part\nof (T\u2212i\n\u2212j )\u2217\n, may now be colored 3, and be included in the\nallocation (T\u2212i\n) . This completes the proof of (10) and the\nclaim.\nThe following claim shows that a buyer j which changed\nhis allocation due to a false declaration of his valuation\ncannot improve his bottom utility. The proof is basically the\nstandard VCG argument.\nClaim 3. Let j be a buyer matched to seller i in T \u2217\n, and\nk = i be the seller matched to j in \u02c6T\u2217\n. Then,\nvj(i) \u2212 Li \u2265 vj(k) \u2212 \u02c6Lk. (11)\nProof. Recall that Li = vj(i) + (V\u2212j)\u2217\n\u2212 V \u2217\n, and \u02c6Lk =\n\u02c6vj(k) + ( \u02c6V\u2212j)\u2217\n\u2212 \u02c6V \u2217\n= \u02c6vj(k) + (V\u2212j)\u2217\n\u2212 \u02c6V \u2217\n. Therefore,\nvj(i) \u2212 Li = V \u2217\n\u2212 (V\u2212j)\u2217\nand vj(k) \u2212 \u02c6Lk = vj(k) \u2212 \u02c6vj(k) +\n\u02c6V \u2217\n\u2212 (V\u2212j)\u2217\n.\nIt follows that in order to prove (11) we need to show\nV \u2217\n\u2265 vj(k) \u2212 \u02c6vj(k) + \u02c6V \u2217\n. (12)\nThe scenario of this claim occurs when j understates his\nvalue for Ai or overstated his value for Ak. Consider these\ntwo cases:\n\u2022 \u02c6vj(k) > vj(k): Since Ak was allocated to j in the\nallocation \u02c6T\u2217\nwe have that using the allocation of \u02c6T\u2217\naccording to the true valuation gives an allocation of\nvalue U satisfying \u02c6V \u2217\n\u2212 \u02c6vj(k) + vj(k) \u2264 U \u2264 V \u2217\n.\n\u2022 \u02c6vj(k) = vj(k) and \u02c6vj(i) < vj(i): In this case (12)\nreduces to V \u2217\n\u2265 \u02c6V \u2217\n. Since j is not allocated i in \u02c6T\u2217\nwe have that \u02c6T\u2217\nis an allocation that uses only true\nvaluations. From the optimality of T \u2217\nwe conclude\nthat V \u2217\n\u2265 \u02c6V \u2217\n.\nAnother case in which a buyer may try to improve his\nutility is when he does not win any good by stating his true\nvaluation. He may give a false valuation under which he\nwins some good. The following claim shows that doing this\nis not beneficial to him.\nClaim 4. Let j be a buyer not matched in T \u2217\n, and\nassume seller k is matched to j in \u02c6T\u2217\n. Then,\nvj(k) \u2212 \u02c6Lk \u2264 0.\nProof. The scenario of this claim occurs if j did not\nbuy in the truth-telling allocation and overstates his value\nfor Ak, \u02c6vj(k) > vj(k) in his false valuation. Recall that\n\u02c6Lk = \u02c6vj(k) + ( \u02c6V\u2212j)\u2217\n\u2212 \u02c6V \u2217\n. Thus we need to show that\n0 \u2265 vj(k) \u2212 \u02c6vj(k) + \u02c6V \u2217\n\u2212 (V\u2212j)\u2217\n. Since j is not allocated\nin T\u2217\nthen (V\u2212j)\u2217\n= V \u2217\n. Since j is allocated Ak in \u02c6T\u2217\nwe have that using the allocation of \u02c6T\u2217\naccording to the\ntrue valuation gives an allocation of value U satisfying \u02c6V \u2217\n\u2212\n\u02c6vj(k) + vj(k) \u2264 U \u2264 V \u2217\n. Thus we can conclude that 0 \u2265\nvj(k) \u2212 \u02c6vj(k) + \u02c6V \u2217\n\u2212 (V\u2212j)\u2217\n.\nFinally, the following claim ensures that a buyer cannot\ninfluence the floor bound of the ZOPA for the good he wins.\nClaim 5. Let j be a buyer matched to seller i in T \u2217\n, and\nassume that \u02c6T\u2217\n= T\u2217\n, then \u02c6Li = Li.\nProof. Recall that Li = vj(i) + (V\u2212j)\u2217\n\u2212 V \u2217\n, and \u02c6Li =\n\u02c6vj(i) + ( \u02c6V\u2212j)\u2217\n\u2212 \u02c6V \u2217\n= \u02c6vj(i) + (V\u2212j)\u2217\n\u2212 \u02c6V \u2217\n. Therefore we\nneed to show that \u02c6V \u2217\n= V \u2217\n+ \u02c6vj(i) \u2212 vj(i).\nSince j is allocated Ai in T\u2217\n, we have that using the\nallocation of T\u2217\naccording to the false valuation gives an allocation\nof value U satisfying V \u2217\n\u2212 vj(i) + \u02c6vj(i) \u2264 U \u2264 \u02c6V \u2217\n.\nSimilarly since j is allocated Ai in \u02c6T\u2217\n, we have that using the\nallocation of \u02c6T\u2217\naccording to the true valuation gives an\nallocation of value U satisfying \u02c6V \u2217\n\u2212 \u02c6vj(i)+vj(i) \u2264 U \u2264 V \u2217\n,\nwhich together with the previous inequality completes the\nproof.\nThis completes the analysis of the buyer\"s incentive\ncompatibility. We now turn to prove the seller\"s incentive\ncompatibility properties of our mechanism.\nThe following claim handles the case where a seller that\nwas not matched in T \u2217\nfalsely understates her valuation such\nthat she gets matched n \u02c6T\u2217\n.\nClaim 6. Let i be a seller not matched in T \u2217\n, and assume\nbuyer z is matched to i in \u02c6T\u2217\n. Then,\n\u02c6Hz \u2212 ci \u2264 0.\nProof. Recall that \u02c6Hz = vz(i) + ( \u02c6V \u2212i\n\u2212z )\u2217\n\u2212 ( \u02c6V \u2212i\n)\u2217\n.\nSince i is not matched in T \u2217\nand ( \u02c6T\u2212i\n)\u2217\ninvolves only true\nvaluations we have that ( \u02c6V \u2212i\n)\u2217\n= V \u2217\n. Since i is matched\nwith z in \u02c6T\u2217\nit can be obtained by adding the buyer z - seller\ni pair to ( \u02c6T\u2212i\n\u2212z)\u2217\n. It follows that \u02c6V \u2217\n= ( \u02c6V \u2212i\n\u2212z )\u2217\n+ vz(i) \u2212 \u02c6ci.\nThus, we have that \u02c6Hz = \u02c6V \u2217\n+ \u02c6ci \u2212 V \u2217\n. Now, since i is\nmatched in \u02c6T\u2217\n, using this allocation according to the true\nvaluation gives an allocation of value U satisfying \u02c6V \u2217\n+ \u02c6ci \u2212\nci \u2264 U \u2264 V \u2217\n. Therefore \u02c6Hz \u2212ci = \u02c6V \u2217\n+\u02c6ci \u2212V \u2217\n\u2212ci \u2264 0.\nFinally, the following simple claim ensures that a seller\ncannot influence the ceiling bound of the ZOPA for the good\nshe sells.\nClaim 7. Let i be a seller matched to buyer j in T \u2217\n, and\nassume that \u02c6T\u2217\n= T\u2217\n, then \u02c6Hj = Hj.\nProof. Since ( \u02c6V \u2212i\n\u2212j )\u2217\n= (V \u2212i\n\u2212j )\u2217\nand ( \u02c6V \u2212i\n)\u2217\n= (V \u2212i\n)\u2217\nit\nfollows that\n\u02c6Hj = vj(i)+( \u02c6V \u2212i\n\u2212j )\u2217\n\u2212( \u02c6V \u2212i\n)\u2217\n= vj(i)+(V \u2212i\n\u2212j )\u2217\n\u2212(V \u2212i\n)\u2217\n= Hj.\n4. CONCLUSIONS AND EXTENSIONS\nIn this paper we suggest a way to deal with the\nimpossibility of producing mechanisms which are efficient,\nindividually rational, incentive compatible and budget balanced.\nTo this aim we introduce the concept of negotiation-range\nmechanisms which avoid the problem by leaving the final\ndetermination of prices to a negotiation between the buyer\nand seller. The goal of the mechanism is to provide the\ninitial range (ZOPA) for negotiation in a way that it will be\nbeneficial for the participants to close the proposed deals.\nWe present a negotiation range mechanism that is efficient,\nindividually rational, incentive compatible and budget\nbalanced. The ZOPA produced by our mechanism is based\n7\non a natural adaptation of the VCG payment scheme in a\nway that promises valid negotiation ranges which permit a\nbudget balanced allocation.\nThe basic question that we aimed to tackle seems very\nexciting: which properties can we expect a market\nmechanism to achieve ? Are there different market models and\nrequirements from the mechanisms that are more feasible\nthan classic mechanism design goals ?\nIn the context of our negotiation-range model, is\nnatural to further study negotiation based mechanisms in more\ngeneral settings. A natural extension is that of a\ncombinatorial market. Unfortunately, finding the optimal allocation\nin a combinatorial setting is NP-hard, and thus the problem\nof maintaining BB is compounded by the problem of\nmaintaining IC when efficiency is approximated [1, 5, 6, 9, 11].\nApplying the approach in this paper to develop\nnegotiationrange mechanisms for combinatorial markets, even in\nrestricted settings, seems a promising direction for research.\n5. REFERENCES\n[1] Y. Bartal, R. Gonen, and N. Nisan. Incentive\nCompatible Multi-Unit Combinatorial Auctions.\nProceeding of 9th TARK 2003, pp. 72-87, June 2003.\n[2] E. H. Clarke. Multipart Pricing of Public Goods. In\njournal Public Choice 1971, volume 2, pages 17-33.\n[3] J.Feigenbaum, C. Papadimitriou, and S. Shenker.\nSharing the Cost of Multicast Transmissions. Journal\nof Computer and System Sciences, 63(1),2001.\n[4] A. Fiat, A. Goldberg, J. Hartline, and A. Karlin.\nCompetitive Generalized Auctions. Proceeding of 34th\nACM Symposium on Theory of Computing,2002.\n[5] R. Gonen, and D. Lehmann. Optimal Solutions for\nMulti-Unit Combinatorial Auctions: Branch and\nBound Heuristics. Proceeding of ACM Conference on\nElectronic Commerce EC\"00, pages 13-20, October\n2000.\n[6] R. Gonen, and D. Lehmann. Linear Programming\nhelps solving Large Multi-unit Combinatorial\nAuctions. In Proceeding of INFORMS 2001,\nNovember, 2001.\n[7] T. Groves. Incentives in teams. In journal\nEconometrica 1973, volume 41, pages 617-631.\n[8] R. Lavi, A. Mu\"alem and N. Nisan. Towards a\nCharacterization of Truthful Combinatorial Auctions.\nProceeding of 44th Annual IEEE Symposium on\nFoundations of Computer Science,2003.\n[9] D. Lehmann, L. I. O\"Callaghan, and Y. Shoham.\nTruth revelation in rapid, approximately efficient\ncombinatorial auctions. In Proceedings of the First\nACM Conference on Electronic Commerce, pages\n96-102, November 1999.\n[10] R. Myerson, M. Satterthwaite. Efficient Mechanisms\nfor Bilateral Trading. Journal of Economic Theory,\n28, pages 265-81, 1983.\n[11] N. Nisan and A. Ronen. Algorithmic Mechanism\nDesign. In Proceeding of 31th ACM Symposium on\nTheory of Computing, 1999.\n[12] D.C. Parkes, J. Kalagnanam, and M. Eso. Achieving\nBudget-Balance with Vickrey-Based Payment Schemes\nin Exchanges. Proceeding of 17th International Joint\nConference on Artificial Intelligence, pages 1161-1168,\n2001.\n[13] W. Vickrey. Counterspeculation, Auctions and\nCompetitive Sealed Tenders. In Journal of Finance\n1961, volume 16, pages 8-37.\n8", "keywords": "negotiation-range mechanism;real-world market environment;efficient market;impossibility result;negotiationrange market;zone of possible agreement;negotiation based mechanism;incentive compatibility;utility;efficient truthful market;individual rationality;good exchange;possible agreement zone;buyer and seller;mechanism design"}
{"name": "train_J-65", "title": "Privacy in Electronic Commerce and the Economics of Immediate Gratification", "abstract": "Dichotomies between privacy attitudes and behavior have been noted in the literature but not yet fully explained. We apply lessons from the research on behavioral economics to understand the individual decision making process with respect to privacy in electronic commerce. We show that it is unrealistic to expect individual rationality in this context. Models of self-control problems and immediate gratification offer more realistic descriptions of the decision process and are more consistent with currently available data. In particular, we show why individuals who may genuinely want to protect their privacy might not do so because of psychological distortions well documented in the behavioral literature; we show that these distortions may affect not only \u2018na\u00a8\u0131ve\" individuals but also \u2018sophisticated\" ones; and we prove that this may occur also when individuals perceive the risks from not protecting their privacy as significant.", "fulltext": "1. PRIVACY AND ELECTRONIC\nCOMMERCE\nPrivacy remains an important issue for electronic\ncommerce. A PriceWaterhouseCoopers study in 2000 showed\nthat nearly two thirds of the consumers surveyed would\nshop more online if they knew retail sites would not do\nanything with their personal information [15]. A Federal Trade\nCommission study reported in 2000 that sixty-seven\npercent of consumers were very concerned about the privacy\nof the personal information provided on-line [11]. More\nrecently, a February 2002 Harris Interactive survey found that\nthe three biggest consumer concerns in the area of on-line\npersonal information security were: companies trading\npersonal data without permission, the consequences of insecure\ntransactions, and theft of personal data [19]. According to\na Jupiter Research study in 2002, $24.5 billion in on-line\nsales will be lost by 2006 - up from $5.5 billion in 2001.\nOnline retail sales would be approximately twenty-four percent\nhigher in 2006 if consumers\" fears about privacy and\nsecurity were addressed effectively [21]. Although the media\nhype has somewhat diminished, risks and costs have\nnotas evidenced by the increasing volumes of electronic spam\nand identity theft [16].\nSurveys in this field, however, as well as experiments and\nanecdotal evidence, have also painted a different picture.\n[36, 10, 18, 21] have found evidence that even privacy\nconcerned individuals are willing to trade-off privacy for\nconvenience, or bargain the release of very personal information in\nexchange for relatively small rewards. The failure of several\non-line services aimed at providing anonymity for Internet\nusers [6] offers additional indirect evidence of the reluctance\nby most individuals to spend any effort in protecting their\npersonal information.\nThe dichotomy between privacy attitudes and behavior\nhas been highlighted in the literature. Preliminary\ninterpretations of this phenomenon have been provided [2, 38,\n33, 40]. Still missing are: an explanation grounded in\neconomic or psychological theories; an empirical validation of\nthe proposed explanation; and, of course, the answer to the\nmost recurring question: should people bother at all about\nprivacy?\nIn this paper we focus on the first question: we formally\nanalyze the individual decision making process with respect\nto privacy and its possible shortcomings. We focus on\nindividual (mis)conceptions about their handling of risks they\nface when revealing private information. We do not address\nthe issue of whether people should actually protect\nthemselves. We will comment on that in Section 5, where we will\nalso discuss strategies to empirically validate our theory.\nWe apply lessons from behavioral economics. Traditional\neconomics postulates that people are forward-looking and\nbayesian updaters: they take into account how current\nbehavior will influence their future well-being and preferences.\nFor example, [5] study rational models of addiction. This\napproach can be compared to those who see in the decision\n21\nnot to protect one\"s privacy a rational choice given the\n(supposedly) low risks at stake. However, developments in the\narea of behavioral economics have highlighted various forms\nof psychological inconsistencies (self-control problems,\nhyperbolic discounting, present-biases, etc.) that clash with\nthe fully rational view of the economic agent. In this\npaper we draw from these developments to reach the following\nconclusions:\n\u2022 We show that it is unlikely that individuals can act\nrationally in the economic sense when facing privacy\nsensitive decisions.\n\u2022 We show that alternative models of personal behavior\nand time-inconsistent preferences are compatible with\nthe dichotomy between attitudes and behavior and can\nbetter match current data. For example, they can\nexplain the results presented by [36] at the ACM EC\n\"01 conference. In their experiment, self-proclaimed\nprivacy advocates were found to be willing to reveal\nvarying amounts of personal information in exchange\nfor small rewards.\n\u2022 In particular, we show that individuals may have a\ntendency to under-protect themselves against the privacy\nrisks they perceive, and over-provide personal\ninformation even when wary of (perceived) risks involved.\n\u2022 We show that the magnitude of the perceived costs of\nprivacy under certain conditions will not act as\ndeterrent against behavior the individual admits is risky.\n\u2022 We show, following similar studies in the economics of\nimmediate gratification [31], that even \u2018sophisticated\"\nindividuals may under certain conditions become\n\u2018privacy myopic.\"\nOur conclusion is that simply providing more\ninformation and awareness in a self-regulative environment is not\nsufficient to protect individual privacy. Improved\ntechnologies, by lowering costs of adoption and protection, certainly\ncan help. However, more fundamental human behavioral\nresponses must also be addressed if privacy ought to be\nprotected.\nIn the next section we propose a model of rational agents\nfacing privacy sensitive decisions. In Section 3 we show the\ndifficulties that hinder any model of privacy decision\nmaking based on full rationality. In Section 4 we show how\nbehavioral models based on immediate gratification bias can\nbetter explain the attitudes-behavior dichotomy and match\navailable data. In Section 5 we summarize and discuss our\nconclusions.\n2. A MODEL OF RATIONALITY IN\nPRIVACY DECISION MAKING\nSome have used the dichotomy between privacy attitudes\nand behavior to claim that individuals are acting rationally\nwhen it comes to privacy. Under this view, individuals may\naccept small rewards for giving away information because\nthey expect future damages to be even smaller (when\ndiscounted over time and with their probability of occurrence).\nHere we want to investigate what underlying assumptions\nabout personal behavior would support the hypothesis of\nfull rationality in privacy decision making.\nSince [28, 37, 29] economists have been interested in\nprivacy, but only recently formal models have started\nappearing [3, 7, 39, 40]. While these studies focus on market\ninteractions between one agent and other parties, here we are\ninterested in formalizing the decision process of the single\nindividual. We want to see if individuals can be\neconomically rational (forward-lookers, bayesian updaters, utility\nmaximizers, and so on) when it comes to protect their own\npersonal information.\nThe concept of privacy, once intended as the right to be\nleft alone [41], has transformed as our society has become\nmore information oriented. In an information society the self\nis expressed, defined, and affected through and by\ninformation and information technology. The boundaries between\nprivate and public become blurred. Privacy has therefore\nbecome more a class of multifaceted interests than a single,\nunambiguous concept. Hence its value may be discussed (if\nnot ascertained) only once its context has also been\nspecified. This most often requires the study of a network of\nrelations between a subject, certain information (related to\nthe subject), other parties (that may have various linkages\nof interest or association with that information or that\nsubject), and the context in which such linkages take place.\nTo understand how a rational agent could navigate through\nthose complex relations, in Equation 1 we abstract the\ndecision process of an idealized rational economic agent who\nis facing privacy trade-offs when completing a certain\ntransaction.\nmax\nd\nUt = \u03b4 vE (a) , pd\n(a) + \u03b3 vE (t) , pd\n(t) \u2212 cd\nt (1)\nIn Equation 1, \u03b4 and \u03b3 are unspecified functional forms\nthat describe weighted relations between expected payoffs\nfrom a set of events v and the associated probabilities of\noccurrence of those events p. More precisely, the utility U of\ncompleting a transaction t (the transaction being any action\n- not necessarily a monetary operation - possibly involving\nexposure of personal information) is equal to some function\nof the expected payoff vE (a) from maintaining (or not)\ncertain information private during that transaction, and the\nprobability of maintaining [or not maintaining] that\ninformation private when using technology d, pd\n(a) [1 \u2212 pd\n(a)];\nplus some function of the expected payoff vE (t) from\ncompleting (or non completing) the transaction (possibly\nrevealing personal information), and the probability of completing\n[or not completing] that transaction with a certain\ntechnology d, pd\n(t) [1 \u2212 pd\n(t)]; minus the cost of using the\ntechnology t: cd\nt .1\nThe technology d may or may not be privacy enhancing.\nSince the payoffs in Equation 1 can be either positive or\nnegative, Equation 1 embodies the duality implicit in privacy\nissues: there are both costs and benefits gained from\nrevealing or from protecting personal information, and the costs\nand benefits from completing a transaction, vE (t), might be\ndistinct from the costs and benefits from keeping the\nassociated information private, vE (a). For instance, revealing\none\"s identity to an on-line bookstore may earn a discount.\nViceversa, it may also cost a larger bill, because of price\ndiscrimination. Protecting one\"s financial privacy by not\ndivulging credit card information on-line may protect against\nfuture losses and hassles related to identity theft. But it may\n1\nSee also [1].\n22\nmake one\"s on-line shopping experience more cumbersome,\nand therefore more expensive.\nThe functional parameters \u03b4 and \u03b3 embody the variable\nweights and attitudes an individual may have towards\nkeeping her information private (for example, her privacy\nsensitivity, or her belief that privacy is a right whose respect\nshould be enforced by the government) and completing\ncertain transactions. Note that vE and p could refer to sets of\npayoffs and the associated probabilities of occurrence. The\npayoffs are themselves only expected because, regardless of\nthe probability that the transaction is completed or the\ninformation remains private, they may depend on other sets of\nevents and their associated probabilities. vE() and pd\n(), in\nother words, can be read as multi-variate parameters inside\nwhich are hidden several other variables, expectations, and\nfunctions because of the complexity of the privacy network\ndescribed above.\nOver time, the probability of keeping certain information\nprivate, for instance, will not only depend on the chosen\ntechnology d but also on the efforts by other parties to\nappropriate that information. These efforts may be function,\namong other things, of the expected value of that\ninformation to those parties. The probability of keeping\ninformation private will also depend on the environment in which\nthe transaction is taking place. Similarly, the expected\nbenefit from keeping information private will also be a\ncollection over time of probability distributions dependent on\nseveral parameters. Imagine that the probability of keeping\nyour financial transactions private is very high when you\nuse a bank in Bermuda: still, the expected value from\nkeeping your financial information confidential will depend on a\nnumber of other factors.\nA rational agent would, in theory, choose the technology\nd that maximizes her expected payoff in Equation 1. Maybe\nshe would choose to complete the transaction under the\nprotection of a privacy enhancing technology. Maybe she would\ncomplete the transaction without protection. Maybe she\nwould not complete the transaction at all (d = 0). For\nexample, the agent may consider the costs and benefits of\nsending an email through an anonymous MIX-net system\n[8] and compare those to the costs and benefits of sending\nthat email through a conventional, non-anonymous\nchannel. The magnitudes of the parameters in Equation 1 will\nchange with the chosen technology. MIX-net systems may\ndecrease the expected losses from privacy intrusions.\nNonanonymous email systems may promise comparably higher\nreliability and (possibly) reduced costs of operations.\n3. RATIONALITY AND PSYCHOLOGICAL\nDISTORTIONS IN PRIVACY\nEquation 1 is a comprehensive (while intentionally generic)\nroad-map for navigation across privacy trade-offs that no\nhuman agent would be actually able to use.\nWe hinted to some difficulties as we noted that several\nlayers of complexities are hidden inside concepts such as the\nexpected value of maintaining certain information private,\nand the probability of succeeding doing so. More precisely,\nan agent will face three problems when comparing the\ntradeoffs implicit in Equation 1: incomplete information about all\nparameters; bounded power to process all available\ninformation; no deviation from the rational path towards\nutilitymaximization. Those three problems are precisely the same\nissues real people have to deal with on an everyday basis as\nthey face privacy-sensitive decisions. We discuss each\nproblem in detail.\n1. Incomplete information. What information has the\nindividual access to as she prepares to take privacy sensitive\ndecisions? For instance, is she aware of privacy invasions and\nthe associated risks? What is her knowledge of the existence\nand characteristics of protective technologies?\nEconomic transactions are often characterized by\nincomplete or asymmetric information. Different parties involved\nmay not have the same amount of information about the\ntransaction and may be uncertain about some important\naspects of it [4]. Incomplete information will affect almost all\nparameters in Equation 1, and in particular the estimation\nof costs and benefits. Costs and benefits associated with\nprivacy protection and privacy intrusions are both\nmonetary and immaterial. Monetary costs may for instance\ninclude adoption costs (which are probably fixed) and usage\ncosts (which are variable) of protective technologies - if the\nindividual decides to protect herself. Or they may include\nthe financial costs associated to identity theft, if the\nindividual\"s information turns out not to have been adequately\nprotected. Immaterial costs may include learning costs of\na protective technology, switching costs between different\napplications, or social stigma when using anonymizing\ntechnologies, and many others. Likewise, the benefits from\nprotecting (or not protecting) personal information may also be\neasy to quantify in monetary terms (the discount you receive\nfor revealing personal data) or be intangible (the feeling of\nprotection when you send encrypted emails).\nIt is difficult for an individual to estimate all these\nvalues. Through information technology, privacy invasions can\nbe ubiquitous and invisible. Many of the payoffs associated\nwith privacy protection or intrusion may be discovered or\nascertained only ex post through actual experience. Consider,\nfor instance, the difficulties in using privacy and encrypting\ntechnologies described in [43].\nIn addition, the calculations implicit in Equation 1 depend\non incomplete information about the probability\ndistribution of future events. Some of those distributions may be\npredicted after comparable data - for example, the\nprobability that a certain credit card transaction will result in fraud\ntoday could be calculated using existing statistics. The\nprobability distributions of other events may be very\ndifficult to estimate because the environment is too\ndynamicfor example, the probability of being subject to identity theft\n5 years in the future because of certain data you are\nreleasing now. And the distributions of some other events may be\nalmost completely subjective - for example, the probability\nthat a new and practical form of attack on a currently\nsecure cryptosystem will expose all of your encrypted personal\ncommunications a few years from now.\nThis leads to a related problem: bounded rationality.\n2. Bounded rationality. Is the individual able to\ncalculate all the parameters relevant to her choice? Or is she\nlimited by bounded rationality?\nIn our context, bounded rationality refers to the inability\nto calculate and compare the magnitudes of payoffs\nassociated with various strategies the individual may choose in\nprivacy-sensitive situations. It also refers to the inability to\nprocess all the stochastic information related to risks and\nprobabilities of events leading to privacy costs and benefits.\n23\nIn traditional economic theory, the agent is assumed to\nhave both rationality and unbounded \u2018computational\" power\nto process information. But human agents are unable to\nprocess all information in their hands and draw accurate\nconclusions from it [34]. In the scenario we consider, once\nan individual provides personal information to other parties,\nshe literally loses control of that information. That loss of\ncontrol propagates through other parties and persists for\nunpredictable spans of time. Being in a position of\ninformation asymmetry with respect to the party with whom she\nis transacting, decisions must be based on stochastic\nassessments, and the magnitudes of the factors that may affect\nthe individual become very difficult to aggregate, calculate,\nand compare.2\nBounded rationality will affect the\ncalculation of the parameters in Equation 1, and in particular \u03b4,\n\u03b3, vE(), and pt(). The cognitive costs involved in trying to\ncalculate the best strategy could therefore be so high that\nthe individual may just resort to simple heuristics.\n3. Psychological distortions. Eventually, even if an\nindividual had access to complete information and could\nappropriately compute it, she still may find it difficult to\nfollow the rational strategy presented in Equation 1. A vast\nbody of economic and psychological literature has by now\nconfirmed the impact of several forms of psychological\ndistortions on individual decision making. Privacy seems to\nbe a case study encompassing many of those distortions:\nhyperbolic discounting, under insurance, self-control\nproblems, immediate gratification, and others. The traditional\ndichotomy between attitude and behavior, observed in\nseveral aspects of human psychology and studied in the social\npsychology literature since [24] and [13], may also appear in\nthe privacy space because of these distortions.\nFor example, individuals have a tendency to discount\n\u2018hyperbolically\" future costs or benefits [31, 27]. In economics,\nhyperbolic discounting implies inconsistency of personal\npreferences over time - future events may be discounted at\ndifferent discount rates than near-term events. Hyperbolic\ndiscounting may affect privacy decisions, for instance when we\nheavily discount the (low) probability of (high) future risks\nsuch as identity theft.3\nRelated to hyperbolic discounting\nis the tendency to underinsure oneself against certain risks\n[22].\nIn general, individuals may put constraints on future\nbehavior that limit their own achievement of maximum utility:\npeople may genuinely want to protect themselves, but\nbecause of self-control bias, they will not actually take those\nsteps, and opt for immediate gratification instead.\nPeople tend to underappreciate the effects of changes in their\nstates, and hence falsely project their current preferences\nover consumption onto their future preferences. Far more\nthan suggesting merely that people mispredict future tastes,\nthis projection bias posits a systematic pattern in these\nmispredictions which can lead to systematic errors in\ndynamicchoice environments [25, p. 2].\n2\nThe negative utility coming from future potential\nmisuses of somebody\"s personal information could be a random\nshock whose probability and scope are extremely variable.\nFor example, a small and apparently innocuous piece of\ninformation might become a crucial asset or a dangerous\nliability in the right context.\n3\nA more rigorous description and application of hyperbolic\ndiscounting is provided in Section 4.\nIn addition, individuals suffer from optimism bias [42],\nthe misperception that one\"s risks are lower than those of\nother individuals under similar conditions. Optimism bias\nmay lead us to believe that we will not be subject to privacy\nintrusions.\nIndividuals encounter difficulties when dealing with\ncumulative risks. [35], for instance, shows that while young\nsmokers appreciate the long term risks of smoking, they do not\nfully realize the cumulative relation between the low risks of\neach additional cigarette and the slow building up of a\nserious danger. Difficulties with dealing with cumulative risks\napply to privacy, because our personal information, once\nreleased, can remain available over long periods of time. And\nsince it can be correlated to other data, the \u2018anonymity sets\"\n[32, 14] in which we wish to remain hidden get smaller. As\na result, the whole risk associated with revealing different\npieces of personal information is more than the sum of the\nindividual risks associated with each piece of data.\nAlso, it is easier to deal with actions and effects that\nare closer to us in time. Actions and effects that are in\nthe distant future are difficult to focus on given our limited\nforesight perspective. As the foresight changes, so does\nbehavior, even when preferences remain the same [20]. This\nphenomenon may also affects privacy decisions, since the\ncosts of privacy protection may be immediate, but the\nrewards may be invisible (absence of intrusions) and spread\nover future periods of time.\nTo summarize: whenever we face privacy sensitive\ndecisions, we hardly have all data necessary for an informed\nchoice. But even if we had, we would be likely unable to\nprocess it. And even if we could process it, we may still end\nbehaving against our own better judgment. In what follows,\nwe present a model of privacy attitudes and behavior based\non some of these findings, and in particular on the plight of\nimmediate gratification.\n4. PRIVACY AND THE ECONOMICS OF\nIMMEDIATE GRATIFICATION\nThe problem of immediate gratification (which is related\nto the concepts of time inconsistency, hyperbolic\ndiscounting, and self-control bias) is so described by O\"Donoghue and\nRabin [27, p. 4]: A person\"s relative preference for\nwellbeing at an earlier date over a later date gets stronger as the\nearlier date gets closer. [...] [P]eople have self-control\nproblems caused by a tendency to pursue immediate gratification\nin a way that their \u2018long-run selves\" do not appreciate. For\nexample, if you were given only two alternatives, on Monday\nyou may claim you will prefer working 5 hours on Saturday\nto 5 hours and half on Sunday. But as Saturday comes, you\nwill be more likely to prefer postponing work until Sunday.\nThis simple observation has rather important consequences\nin economic theory, where time-consistency of preferences is\nthe dominant model. Consider first the traditional model\nof utility that agents derive from consumption: the model\nstates that utility discounts exponentially over time:\nUt =\nT\n\u03c4=t\n\u03b4\u03c4\nu\u03c4 (2)\nIn Equation 2, the cumulative utility U at time t is the\ndiscounted sum of all utilities from time t (the present) until\ntime T (the future). \u03b4 is the discount factor, with a value\n24\nPeriod 1 Period 2 Period 3 Period 4\nBenefits from selling period 1 2 0 0 0\nCosts from selling period 1 0 1 1 1\nBenefits from selling period 2 0 2 0 0\nCosts from selling period 2 0 0 1 1\nBenefits from selling period 3 0 0 2 0\nCosts from selling period 3 0 0 0 1\nTable 1: (Fictional) expected payoffs from joining loyalty program.\nbetween 0 and 1. A value of 0 would imply that the\nindividual discounts so heavily that the utility from future periods\nis worth zero today. A value of 1 would imply that the\nindividual is so patient she does not discount future utilities.\nThe discount factor is used in economics to capture the fact\nthat having (say) one dollar one year from now is valuable,\nbut not as much as having that dollar now. In Equation 2,\nif all u\u03c4 were constant - for instance, 10 - and \u03b4 was 0.9,\nthen at time t = 0 (that is, now) u0 would be worth 10, but\nu1 would be worth 9.\nModifying the traditional model of utility discounting, [23]\nand then [31] have proposed a model which takes into\naccount possible time-inconsistency of preferences. Consider\nEquation 3:\nUt(ut, ut+1, ..., uT ) = \u03b4t\nut + \u03b2\nT\n\u03c4=t+1\n\u03b4\u03c4\nu\u03c4 (3)\nAssume that \u03b4, \u03b2 \u2208 [0, 1]. \u03b4 is the discount factor for\nintertemporal utility as in Equation 2. \u03b2 is the parameter\nthat captures an individual\"s tendency to gratify herself\nimmediately (a form of time-inconsistent preferences). When\n\u03b2 is 1, the model maps the traditional time-consistent\nutility model, and Equation 3 is identical to Equation 2. But\nwhen \u03b2 is zero, the individual does not care for anything but\ntoday. In fact, any \u03b2 smaller than 1 represents self-control\nbias.\nThe experimental literature has convincingly proved that\nhuman beings tend to have self-control problems even when\nthey claim otherwise: we tend to avoid and postpone\nundesirable activities even when this will imply more effort\ntomorrow; and we tend to over-engage in pleasant activities\neven though this may cause suffering or reduced utility in\nthe future.\nThis analytical framework can be applied to the study\nof privacy attitudes and behavior. Protecting your privacy\nsometimes means protecting yourself from a clear and present\nhassle (telemarketers, or people peeping through your\nwindow and seeing how you live - see [33]); but sometimes it\nrepresents something akin to getting an insurance against\nfuture and only uncertain risks. In surveys completed at\ntime t = 0, subjects asked about their attitude towards\nprivacy risks may mentally consider some costs of protecting\nthemselves at a later time t = s and compare those to the\navoided costs of privacy intrusions in an even more distant\nfuture t = s + n. Their alternatives at survey time 0 are\nrepresented in Equation 4.\nmin\nwrt x\nDU0 = \u03b2[(E(cs,p)\u03b4s\nx) + (E(cs+n,i)\u03b4s+n\n(1 \u2212 x))] (4)\nx is a dummy variable that can take values 0 or 1. It\nrepresents the individual\"s choice - which costs the\nindividual opts to face: the expected cost of protecting herself at\ntime s, E(cs,p) (in which case x = 1), or the expected costs\nof being subject to privacy intrusions at a later time s + n,\nE(cs+n,i).\nThe individual is trying to minimize the disutility DU of\nthese costs with respect to x. Because she discounts the\ntwo future events with the same discount factor (although\nat different times), for certain values of the parameters the\nindividual may conclude that paying to protect herself is\nworthy. In particular, this will happen when:\nE(cs,p)\u03b4s\n< E(cs+n,i)\u03b4s+n\n(5)\nNow, consider what happens as the moment t = s comes.\nNow a real price should be paid in order to enjoy some form\nof protection (say, starting to encrypt all of your emails to\nprotect yourself from future intrusions). Now the individual\nwill perceive a different picture:\nmin\nwrt x\nDUs = \u03b4E(cs,p)x + \u03b2E(cn,i)\u03b4n\n(1 \u2212 x)] (6)\nNote that nothing has changed in the equation (certainly\nnot the individual\"s perceived risks) except time. If \u03b2 (the\nparameter indicating the degree of self-control problems) is\nless than one, chances are that the individual now will\nactually choose not to protect herself. This will in fact happen\nwhen:\n\u03b4E(cs,p) > \u03b2E(cn,i)\u03b4n\n(7)\nNote that Disequalities 5 and 7 may be simultaneously\nmet for certain \u03b2 < 1. At survey time the individual\nhonestly claimed she wanted to protect herself in\nprinciplethat is, some time in the future. But as she is asked to\nmake an effort to protect herself right now, she chooses to\nrun the risk of privacy intrusion.\nSimilar mathematical arguments can be made for the\ncomparison between immediate costs with immediate benefits\n(subscribing to a \u2018no-call\" list to stop telemarketers from\nharassing you at dinner), and immediate costs with only\nfuture expected rewards (insuring yourself against identity\ntheft, or protecting yourself from frauds by never using your\ncredit card on-line), particularly when expected future\nrewards (or avoided risks) are also intangible: the immaterial\nconsequences of living (or not) in a dossier society, or the\nchilling effects (or lack thereof) of being under surveillance.\nThe reader will have noticed that we have focused on\nperceived (expected) costs E(c), rather than real costs. We\ndo not know the real costs and we do not claim that the\n25\nindividual does. But we are able to show that under\ncertain conditions even costs perceived as very high (as during\nperiods of intense privacy debate) will be ignored.\nWe can provide some fictional numerical examples to make\nthe analysis more concrete. We present some scenarios\ninspired by the calculations in [31].\nImagine an economy with just 4 periods (Table 1). Each\nindividual can enroll in a supermarket\"s loyalty program by\nrevealing personal information. If she does so, the individual\ngets a discount of 2 during the period of enrollment, only to\npay one unit each time thereafter because of price\ndiscrimination based on the information she revealed (we make no\nattempt at calibrating the realism of this obviously abstract\nexample; the point we are focusing on is how time\ninconsistencies may affect individual behavior given the expected\ncosts and benefits of certain actions).4\nDepending on which\nperiod the individual chooses for \u2018selling\" her data, we have\nthe undiscounted payoffs represented in Table 1.\nImagine that the individual is contemplating these\noptions and discounting them according to Equation 3.\nSuppose that \u03b4 = 1 for all types of individuals (this means that\nfor simplicity we do not consider intertemporal discounting)\nbut \u03b2 = 1/2 for time-inconsistent individuals and \u03b2 = 1 for\neverybody else. The time-consistent individual will choose\nto join the program at the very last period and rip off a\nbenefit of 2-1=1. The individual with immediate\ngratification problems, for whom \u03b2 = 1/2, will instead perceive the\nbenefits from joining now or in period 3 as equivalent (0.5),\nand will join the program now, thus actually making herself\nworse off.\n[31] also suggest that, in addition to the distinction\nbetween time-consistent individuals and individuals with\ntimeinconsistent preferences, we should also distinguish\ntimeinconsistent individuals who are na\u00a8\u0131ve from those who are\nsophisticated. Na\u00a8\u0131ve time-inconsistent individuals are not\naware of their self-control problems - for example, they are\nthose who always plan to start a diet next week.\nSophisticated time-inconsistent individuals suffer of immediate\ngratification bias, but are at least aware of their inconsistencies.\nPeople in this category choose their behavior today correctly\nestimating their future time-inconsistent behavior.\nNow consider how this difference affects decisions in\nanother scenario, represented in Table 2. An individual is\nconsidering the adoption of a certain privacy enhancing\ntechnology. It will cost her some money both to protect herself\nand not to protect herself. If she decides to protect herself,\nthe cost will be the amount she pays - for example - for some\ntechnology that shields her personal information. If she\ndecides not to protect herself, the cost will be the expected\nconsequences of privacy intrusions.\nWe assume that both these aggregate costs increase over\ntime, although because of separate dynamics. As time goes\nby, more and more information about the individual has\nbeen revealed, and it becomes more costly to be protected\nagainst privacy intrusions. At the same time, however,\nintrusions become more frequent and dangerous.\n4\nOne may claim that loyalty cards keep on providing\nbenefits over time. Here we make the simplifying assumption\nthat such benefits are not larger than the future costs\nincurred after having revealed one\"s tastes. We also assume\nthat the economy ends in period 4 for all individuals,\nregardless of when they chose to join the loyalty program.\nIn period 1, the individual may protect herself by spending\n5, or she may choose to face a risk of privacy intrusion the\nfollowing period, expected to cost 7. In the second period,\nassuming that no intrusion has yet taken place, she may\nonce again protect herself by spending a little more, 6; or\nshe may choose to face a risk of privacy intrusion the next\n(third) period, expected to cost 9. In the third period she\ncould protect herself for 8 or face an expected cost of 15 in\nthe following last period.\nHere too we make no attempt at calibrating the values in\nTable 2. Again, we focus on the different behavior driven by\nheterogeneity in time-consistency and sophistication versus\nna\u00a8\u0131vete. We assume that \u03b2 = 1 for individuals with no\nself control problems and \u03b2 = 1/2 for everybody else. We\nassume for simplicity that \u03b4 = 1 for all.\nThe time-consistent individuals will obviously choose to\nprotect themselves as soon as possible.\nIn the first period, na\u00a8\u0131ve time-inconsistent individuals will\ncompare the costs of protecting themselves then or face a\nprivacy intrusion in the second period. Because 5 > 7 \u2217\n(1/2), they will prefer to wait until the following period to\nprotect themselves. But in the second period they will be\ncomparing 6 > 9 \u2217 (1/2) - and so they will postpone their\nprotection again. They will keep on doing so, facing higher\nand higher risks. Eventually, they will risk to incur the\nhighest perceived costs of privacy intrusions (note again that\nwe are simply assuming that individuals believe there are\nprivacy risks and that they increase over time; we will come\nback to this concept later on).\nTime-inconsistent but sophisticated individuals, on the\nother side, will adopt a protective technology in period 2\nand pay 6. By period 2, in fact, they will (correctly) realize\nthat if they wait till period 3 (which they are tempted to\ndo, because 6 > 9 \u2217 (1/2)), their self-control bias will lead\nthem to postpone adopting the technology once more\n(because 8 > 15 \u2217 (1/2)). Therefore they predict they would\nincur the expected cost 15 \u2217 (1/2), which is larger than\n6the cost of protecting oneself in period 2. In period 1,\nhowever, they correctly predict that they will not wait to protect\nthemselves further than period 2. So they wait till period\n2, because 5 > 6 \u2217 (1/2), at which time they will adopt a\nprotective technology (see also [31]).\nTo summarize, time-inconsistent people tend not to fully\nappreciate future risks and, if na\u00a8\u0131ve, also their inability to\ndeal with them. This happens even if they are aware of those\nrisks and they are aware that those risks are increasing. As\nwe learnt from the second scenario, time inconsistency can\nlead individuals to accept higher and higher risks.\nIndividuals may tend to downplay the fact that single actions present\nlow risks, but their repetition forms a huge liability: it is a\ndeceiving aspect of privacy that its value is truly\nappreciated only after privacy itself is lost. This dynamics captures\nthe essence of privacy and the so-called anonymity sets [32,\n14], where each bit of information we reveal can be linked to\nothers, so that the whole is more than the sum of the parts.\nIn addition, [31] show that when costs are immediate,\ntime-inconsistent individuals tend to procrastinate; when\nbenefits are immediate, they tend to preoperate. In our\ncontext things are even more interesting because all privacy\ndecisions involve at the same time costs and benefits. So\nwe opt against using eCash [9] in order to save us the costs\nof switching from credit cards. But we accept the risk that\nour credit card number on the Internet could be used\nma26\nPeriod 1 Period 2 Period 3 Period 4\nProtection costs 5 6 8 .\nExpected intrusion costs . 7 9 15\nTable 2: (Fictional) costs of protecting privacy and expected costs of privacy intrusions over time.\nliciously. And we give away our personal information to\nsupermarkets in order to gain immediate discounts - which\nwill likely turn into price discrimination in due time [3, 26].\nWe have shown in the second scenario above how\nsophisticated but time-inconsistent individuals may choose to\nprotect their information only in period 2. Sophisticated\npeople with self-control problems may be at a loss, sometimes\neven when compared to na\u00a8\u0131ve people with time\ninconsistency problems (how many privacy advocates do use\nprivacy enhancing technologies all the time?). The reasoning\nis that sophisticated people are aware of their self-control\nproblems, and rather than ignoring them, they incorporate\nthem into their decision process. This may decrease their\nown incentive to behave in the optimal way now.\nSophisticated privacy advocates might realize that protecting\nthemselves from any possible privacy intrusion is unrealistic, and\nso they may start misbehaving now (and may get used to\nthat, a form of coherent arbitrariness). This is consistent\nwith the results by [36] presented at the ACM EC \"01\nconference. [36] found that privacy advocates were also willing\nto reveal personal information in exchange for monetary\nrewards.\nIt is also interesting to note that these inconsistencies are\nnot caused by ignorance of existing risks or confusion about\navailable technologies. Individuals in the abstract scenarios\nwe described are aware of their perceived risks and costs.\nHowever, under certain conditions, the magnitude of those\nliabilities is almost irrelevant. The individual will take very\nslowly increasing risks, which become steps towards huge\nliabilities.\n5. DISCUSSION\nApplying models of self-control bias and immediate\ngratification to the study of privacy decision making may offer\na new perspective on the ongoing privacy debate. We have\nshown that a model of rational privacy behavior is\nunrealistic, while models based on psychological distortions offer\na more accurate depiction of the decision process. We have\nshown why individuals who genuinely would like to protect\ntheir privacy may not do so because of psychological\ndistortions well documented in the behavioral economics\nliterature. We have highlighted that these distortions may affect\nnot only na\u00a8\u0131ve individuals but also sophisticated ones.\nSurprisingly, we have also found that these inconsistencies may\noccur when individuals perceive the risks from not\nprotecting their privacy as significant.\nAdditional uncertainties, risk aversion, and varying\nattitudes towards losses and gains may be confounding elements\nin our analysis. Empirical validation is necessary to calibrate\nthe effects of different factors.\nAn empirical analysis may start with the comparison of\navailable data on the adoption rate of privacy technologies\nthat offer immediate refuge from minor but pressing privacy\nconcerns (for example, \u2018do not call\" marketing lists), with\ndata on the adoption of privacy technologies that offer less\nobviously perceivable protection from more dangerous but\nalso less visible privacy risks (for example, identity theft\ninsurances). However, only an experimental approach over\ndifferent periods of time in a controlled environment may\nallow us to disentangle the influence of several factors. Surveys\nalone cannot suffice, since we have shown why survey-time\nattitudes will rarely match decision-time actions. An\nexperimental verification is part of our ongoing research agenda.\nThe psychological distortions we have discussed may be\nconsidered in the ongoing debate on how to deal with the\nprivacy problem: industry self-regulation, users\" self protection\n(through technology or other strategies), or government\"s\nintervention. The conclusions we have reached suggest that\nindividuals may not be trusted to make decisions in their\nbest interests when it comes to privacy. This does not mean\nthat privacy technologies are ineffective. On the contrary,\nour results, by aiming at offering a more realistic model of\nuser-behavior, could be of help to technologists in their\ndesign of privacy enhancing tools. However, our results also\nimply that technology alone or awareness alone may not\naddress the heart of the privacy problem. Improved\ntechnologies (with lower costs of adoption and protection) and\nmore information about risks and opportunities certainly\ncan help. However, more fundamental human behavioral\nmechanisms must also be addressed. Self-regulation, even\nin presence of complete information and awareness, may not\nbe trusted to work for the same reasons. A combination of\ntechnology, awareness, and regulative policies - calibrated\nto generate and enforce liabilities and incentives for the\nappropriate parties - may be needed for privacy-related welfare\nincrease (as in other areas of an economy: see on a related\nanalysis [25]).\nObserving that people do not want to pay for privacy or do\nnot care about privacy, therefore, is only a half truth. People\nmay not be able to act as economically rational agents when\nit comes to personal privacy. And the question whether do\nconsumers care? is a different question from does privacy\nmatter? Whether from an economic standpoint privacy\nought to be protected or not, is still an open question. It is\na question that involves defining specific contexts in which\nthe concept of privacy is being invoked. But the value of\nprivacy eventually goes beyond the realms of economic\nreasoning and cost benefit analysis, and ends up relating to one\"s\nviews on society and freedom. Still, even from a purely\neconomic perspective, anecdotal evidence suggest that the costs\nof privacy (from spam to identity theft, lost sales, intrusions,\nand the like [30, 12, 17, 33, 26]) are high and increasing.\n6. ACKNOWLEDGMENTS\nThe author gratefully acknowledges Carnegie Mellon\nUniversity\"s Berkman Development Fund, that partially\nsupported this research. The author also wishes to thank Jens\nGrossklags, Charis Kaskiris, and three anonymous referees\nfor their helpful comments.\n27\n7. REFERENCES\n[1] A. Acquisti, R. Dingledine, and P. Syverson. On the\neconomics of anonymity. In Financial\nCryptographyFC \"03, pages 84-102. Springer Verlag, LNCS 2742,\n2003.\n[2] A. Acquisti and J. Grossklags. 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Towards an information\ntheoretic metric for anonymity. In P. Syverson and\nR. Dingledine, editors, Privacy Enhancing\nTechnologies - PET \"02. Springer Verlag, LNCS 2482,\n2002.\n[33] A. Shostack. Paying for privacy: Consumers and\ninfrastructures. In 2nd Annual Workshop on\nEconomics and Information Security - WEIS \"03,\n2003.\n[34] H. A. Simon. Models of bounded rationality. The MIT\nPress, Cambridge, MA, 1982.\n28\n[35] P. Slovic. What does it mean to know a cumulative\nrisk? Adolescents\" perceptions of short-term and\nlong-term consequences of smoking. Journal of\nBehavioral Decision Making, 13:259-266, 2000.\n[36] S. Spiekermann, J. Grossklags, and B. Berendt.\nE-privacy in 2nd generation e-commerce: Privacy\npreferences versus actual behavior. In 3rd ACM\nConference on Electronic Commerce - EC \"01, pages\n38-47, 2002.\n[37] G. J. Stigler. An introduction to privacy in economics\nand politics. Journal of Legal Studies, 9:623-644, 1980.\n[38] P. Syverson. The paradoxical value of privacy. In 2nd\nAnnual Workshop on Economics and Information\nSecurity - WEIS \"03, 2003.\n[39] C. R. Taylor. Private demands and demands for\nprivacy: Dynamic pricing and the market for customer\ninformation. Department of Economics, Duke\nUniversity, Duke Economics Working Paper 02-02,\n2002.\n[40] T. Vila, R. Greenstadt, and D. Molnar. Why we can\"t\nbe bothered to read privacy policies: Models of\nprivacy economics as a lemons market. In 2nd Annual\nWorkshop on Economics and Information\nSecurityWEIS \"03, 2003.\n[41] S. Warren and L. Brandeis. The right to privacy.\nHarvard Law Review, 4:193-220, 1890.\n[42] N. D. Weinstein. Optimistic biases about personal\nrisks. Science, 24:1232-1233, 1989.\n[43] A. Whitten and J. D. Tygar. Why Johnny can\"t\nencrypt: A usability evaluation of PGP 5.0. In 8th\nUSENIX Security Symposium, 1999.\n29", "keywords": "privacy;financial privacy;electronic commerce;psychological inconsistency;personal information protection;rationality;hyperbolic discounting;time-inconsistent preference;individual decision making process;privacy enhancing technology;psychological distortion;self-control problem;immediate gratification;privacy sensitive decision;anonymity;hyperbolic discount"}
{"name": "train_J-66", "title": "Expressive Negotiation over Donations to Charities\u2217", "abstract": "When donating money to a (say, charitable) cause, it is possible to use the contemplated donation as negotiating material to induce other parties interested in the charity to donate more. Such negotiation is usually done in terms of matching offers, where one party promises to pay a certain amount if others pay a certain amount. However, in their current form, matching offers allow for only limited negotiation. For one, it is not immediately clear how multiple parties can make matching offers at the same time without creating circular dependencies. Also, it is not immediately clear how to make a donation conditional on other donations to multiple charities, when the donator has different levels of appreciation for the different charities. In both these cases, the limited expressiveness of matching offers causes economic loss: it may happen that an arrangement that would have made all parties (donators as well as charities) better off cannot be expressed in terms of matching offers and will therefore not occur. In this paper, we introduce a bidding language for expressing very general types of matching offers over multiple charities. We formulate the corresponding clearing problem (deciding how much each bidder pays, and how much each charity receives), and show that it is NP-complete to approximate to any ratio even in very restricted settings. We give a mixed-integer program formulation of the clearing problem, and show that for concave bids, the program reduces to a linear program. We then show that the clearing problem for a subclass of concave bids is at least as hard as the decision variant of linear programming. Subsequently, we show that the clearing problem is much easier when bids are quasilinear-for surplus, the problem decomposes across charities, and for payment maximization, a greedy approach is optimal if the bids are concave (although this latter problem is weakly NP-complete when the bids are not concave). For the quasilinear setting, we study the mechanism design question. We show that an ex-post efficient mechanism is impossible even with only one charity and a very restricted class of bids. We also show that there may be benefits to linking the charities from a mechanism design standpoint.", "fulltext": "1. INTRODUCTION\nWhen money is donated to a charitable (or other) cause\n(hereafter referred to as charity), often the donating party\ngives unconditionally: a fixed amount is transferred from\nthe donator to the charity, and none of this transfer is\ncontingent on other events-in particular, it is not contingent\non the amount given by other parties. Indeed, this is\ncurrently often the only way to make a donation, especially for\nsmall donating parties such as private individuals. However,\nwhen multiple parties support the same charity, each of them\nwould prefer to see the others give more rather than less to\nthis charity. In such scenarios, it is sensible for a party to\nuse its contemplated donation as negotiating material to\ninduce the others to give more. This is done by making the\ndonation conditional on the others\" donations. The\nfollowing example will illustrate this, and show that the donating\nparties as well as the charitable cause may simultaneously\nbenefit from the potential for such negotiation.\nSuppose we have two parties, 1 and 2, who are both\nsupporters of charity A. To either of them, it would be worth\n$0.75 if A received $1. It follows neither of them will be\nwilling to give unconditionally, because $0.75 < $1. However, if\nthe two parties draw up a contract that says that they will\neach give $0.5, both the parties have an incentive to accept\nthis contract (rather than have no contract at all): with the\ncontract, the charity will receive $1 (rather than $0\nwithout a contract), which is worth $0.75 to each party, which\nis greater than the $0.5 that that party will have to give.\nEffectively, each party has made its donation conditional on\nthe other party\"s donation, leading to larger donations and\ngreater happiness to all parties involved.\n51\nOne method that is often used to effect this is to make\na matching offer. Examples of matching offers are: I will\ngive x dollars for every dollar donated., or I will give x\ndollars if the total collected from other parties exceeds y.\nIn our example above, one of the parties can make the offer\nI will donate $0.5 if the other party also donates at least\nthat much, and the other party will have an incentive to\nindeed donate $0.5, so that the total amount given to the\ncharity increases by $1. Thus this matching offer implements\nthe contract suggested above. As a real-world example, the\nUnited States government has authorized a donation of up to\n$1 billion to the Global Fund to fight AIDS, TB and Malaria,\nunder the condition that the American contribution does not\nexceed one third of the total-to encourage other countries\nto give more [23].\nHowever, there are several severe limitations to the simple\napproach of matching offers as just described.\n1. It is not clear how two parties can make matching\noffers where each party\"s offer is stated in terms of the\namount that the other pays. (For example, it is not\nclear what the outcome should be when both parties\noffer to match the other\"s donation.) Thus, matching\noffers can only be based on payments made by\nparties that are giving unconditionally (not in terms of a\nmatching offer)-or at least there can be no circular\ndependencies.1\n2. Given the current infrastructure for making matching\noffers, it is impractical to make a matching offer\ndepend on the amounts given to multiple charities. For\ninstance, a party may wish to specify that it will pay\n$100 given that charity A receives a total of $1000,\nbut that it will also count donations made to charity\nB, at half the rate. (Thus, a total payment of $500 to\ncharity A combined with a total payment of $1000 to\ncharity B would be just enough for the party\"s offer to\ntake effect.)\nIn contrast, in this paper we propose a new approach\nwhere each party can express its relative preferences for\ndifferent charities, and make its offer conditional on its own\nappreciation for the vector of donations made to the\ndifferent charities. Moreover, the amount the party offers to\ndonate at different levels of appreciation is allowed to vary\narbitrarily (it does need to be a dollar-for-dollar (or\nn-dollarfor-dollar) matching arrangement, or an arrangement where\nthe party offers a fixed amount provided a given (strike)\ntotal has been exceeded). Finally, there is a clear\ninterpretation of what it means when multiple parties are making\nconditional offers that are stated in terms of each other.\nGiven each combination of (conditional) offers, there is a\n(usually) unique solution which determines how much each\nparty pays, and how much each charity is paid.\nHowever, as we will show, finding this solution (the\nclearing problem) requires solving a potentially difficult\noptimization problem. A large part of this paper is devoted to\nstudying how difficult this problem is under different assumptions\non the structure of the offers, and providing algorithms for\nsolving it.\n1\nTypically, larger organizations match offers of private\nindividuals. For example, the American Red Cross Liberty\nDisaster Fund maintains a list of businesses that match their\ncustomers\" donations [8].\nTowards the end of the paper, we also study the\nmechanism design problem of motivating the bidders to bid\ntruthfully.\nIn short, expressive negotiation over donations to charities\nis a new way in which electronic commerce can help the\nworld. A web-based implementation of the ideas described\nin this paper can facilitate voluntary reallocation of wealth\non a global scale. Aditionally, optimally solving the clearing\nproblem (and thereby generating the maximum economic\nwelfare) requires the application of sophisticated algorithms.\n2. COMPARISON TO COMBINATORIAL\nAUCTIONS AND EXCHANGES\nThis section discusses the relationship between expressive\ncharity donation and combinatorial auctions and exchanges.\nIt can be skipped, but may be of interest to the reader with\na background in combinatorial auctions and exchanges.\nIn a combinatorial auction, there are m items for sale,\nand bidders can place bids on bundles of one or more items.\nThe auctioneer subsequently labels each bid as winning or\nlosing, under the constraint that no item can be in more\nthan one winning bid, to maximize the sum of the values of\nthe winning bids. (This is known as the clearing problem.)\nVariants include combinatorial reverse auctions, where the\nauctioneer is seeking to procure a set of items; and\ncombinatorial exchanges, where bidders can both buy and and sell\nitems (even within the same bid). Other extensions include\nallowing for side constraints, as well as the specification of\nattributes of the items in bids. Combinatorial auctions and\nexchanges have recently become a popular research topic [20,\n21, 17, 22, 9, 18, 13, 3, 12, 26, 19, 25, 2].\nThe problems of clearing expressive charity donation\nmarkets and clearing combinatorial auctions or exchanges are\nvery different in formulation. Nevertheless, there are\ninteresting parallels. One of the main reasons for the interest\nin combinatorial auctions and exchanges is that it allows\nfor expressive bidding. A bidder can express exactly how\nmuch each different allocation is worth to her, and thus the\nglobally optimal allocation may be chosen by the\nauctioneer. Compare this to a bidder having to bid on two different\nitems in two different (one-item) auctions, without any way\nof expressing that (for instance) one item is worthless if the\nother item is not won. In this scenario, the bidder may win\nthe first item but not the second (because there was another\nhigh bid on the second item that she did not anticipate),\nleading to economic inefficiency.\nExpressive bidding is also one of the main benefits of the\nexpressive charity donation market. Here, bidders can\nexpress exactly how much they are willing to donate for every\nvector of amounts donated to charities. This may allow\nbidders to negotiate a complex arrangement of who gives\nhow much to which charity, which is beneficial to all\nparties involved; whereas no such arrangement may have been\npossible if the bidders had been restricted to using simple\nmatching offers on individual charities. Again, expressive\nbidding is necessary to achieve economic efficiency.\nAnother parallel is the computational complexity of the\nclearing problem. In order to achieve the full economic\nefficiency allowed by the market\"s expressiveness (or even come\nclose to it), hard computational problems must be solved\nin combinatorial auctions and exchanges, as well as in the\ncharity donation market (as we will see).\n52\n3. DEFINITIONS\nThroughout this paper, we will refer to the offers that the\ndonating parties make as bids, and to the donating parties\nas bidders. In our bidding framework, a bid will specify,\nfor each vector of total payments made to the charities, how\nmuch that bidder is willing to contribute. (The contribution\nof this bidder is also counted in the vector of\npaymentsso, the vector of total payments to the charities represents\nthe amount given by all donating parties, not just the ones\nother than this bidder.) The bidding language is expressive\nenough that no bidder should have to make more than one\nbid. The following definition makes the general form of a\nbid in our framework precise.\nDefinition 1. In a setting with m charities c1, c2, . . . , cm,\na bid by bidder bj is a function vj : Rm\n\u2192 R. The\ninterpretation is that if charity ci receives a total amount of \u03c0ci , then\nbidder j is willing to donate (up to) vj(\u03c0c1 , \u03c0c2 , . . . , \u03c0cm ).\nWe now define possible outcomes in our model, and which\noutcomes are valid given the bids that were made.\nDefinition 2. An outcome is a vector of payments made\nby the bidders (\u03c0b1 , \u03c0b2 , . . . , \u03c0bn ), and a vector of payments\nreceived by the charities (\u03c0c1 , \u03c0c2 , . . . , \u03c0cm ). A valid\noutcome is an outcome where\n1.\nn\nj=1\n\u03c0bj \u2265\nm\ni=1\n\u03c0ci (at least as much money is collected\nas is given away);\n2. For all 1 \u2264 j \u2264 n, \u03c0bj \u2264 vj(\u03c0c1 , \u03c0c2 , . . . , \u03c0cm ) (no\nbidder gives more than she is willing to).\nOf course, in the end, only one of the valid outcomes can\nbe chosen. We choose the valid outcome that maximizes the\nobjective that we have for the donation process.\nDefinition 3. An objective is a function from the set of\nall outcomes to R.2\nAfter all bids have been collected, a valid\noutcome will be chosen that maximizes this objective.\nOne example of an objective is surplus, given by\nn\nj=1\n\u03c0bj \u2212\nm\ni=1\n\u03c0ci . The surplus could be the profits of a company\nmanaging the expressive donation marketplace; but,\nalternatively, the surplus could be returned to the bidders, or\ngiven to the charities. Another objective is total amount\ndonated, given by\nm\ni=1\n\u03c0ci . (Here, different weights could also\nbe placed on the different charities.)\nFinding the valid outcome that maximizes the objective\nis a (nontrivial) computational problem. We will refer to it\nas the clearing problem. The formal definition follows.\nDefinition 4 (DONATION-CLEARING). We are\ngiven a set of n bids over charities c1, c2, . . . , cm.\nAdditionally, we are given an objective function. We are asked to\nfind an objective-maximizing valid outcome.\nHow difficult the DONATION-CLEARING problem is\ndepends on the types of bids used and the language in which\nthey are expressed. This is the topic of the next section.\n2\nIn general, the objective function may also depend on the\nbids, but the objective functions under consideration in this\npaper do not depend on the bids. The techniques presented\nin this paper will typically generalize to objectives that take\nthe bids into account directly.\n4. A SIMPLIFIED BIDDING LANGUAGE\nSpecifying a general bid in our framework (as defined\nabove) requires being able to specify an arbitrary real-valued\nfunction over Rm\n. Even if we restricted the possible total\npayment made to each charity to the set {0, 1, 2, . . . , s}, this\nwould still require a bidder to specify (s+1)m\nvalues. Thus,\nwe need a bidding language that will allow the bidders to\nat least specify some bids more concisely. We will specify a\nbidding language that only represents a subset of all possible\nbids, which can be described concisely.3\nTo introduce our bidding language, we will first describe\nthe bidding function as a composition of two functions; then\nwe will outline our assumptions on each of these functions.\nFirst, there is a utility function uj : Rm\n\u2192 R, specifying how\nmuch bidder j appreciates a given vector of total donations\nto the charities. (Note that the way we define a bidder\"s\nutility function, it does not take the payments the bidder\nmakes into account.) Then, there is a donation willingness\nfunction wj : R \u2192 R, which specifies how much bidder j is\nwilling to pay given her utility for the vector of donations\nto the charities. We emphasize that this function does not\nneed to be linear, so that utilities should not be thought of as\nexpressible in dollar amounts. (Indeed, when an individual\nis donating to a large charity, the reason that the individual\ndonates only a bounded amount is typically not decreasing\nmarginal value of the money given to the charity, but rather\nthat the marginal value of a dollar to the bidder herself\nbecomes larger as her budget becomes smaller.) So, we have\nwj(uj(\u03c0c1 , \u03c0c2 , . . . , \u03c0cm )) = vj(\u03c0c1 , \u03c0c2 , . . . , \u03c0cm ), and we\nlet the bidder describe her functions uj and wj separately.\n(She will submit these functions as her bid.)\nOur first restriction is that the utility that a bidder\nderives from money donated to one charity is independent of\nthe amount donated to another charity. Thus,\nuj(\u03c0c1 , \u03c0c2 , . . . , \u03c0cm ) =\nm\ni=1\nui\nj(\u03c0ci ). (We observe that this\ndoes not imply that the bid function vj decomposes\nsimilarly, because of the nonlinearity of wj.) Furthermore, each\nui\nj must be piecewise linear. An interesting special case\nwhich we will study is when each ui\nj is a line: ui\nj(\u03c0ci ) =\nai\nj\u03c0ci . This special case is justified in settings where the\nscale of the donations by the bidders is small relative to the\namounts the charities receive from other sources, so that the\nmarginal use of a dollar to the charity is not affected by the\namount given by the bidders.\nThe only restriction that we place on the payment\nwillingness functions wj is that they are piecewise linear. One\ninteresting special case is a threshold bid, where wj is a step\nfunction: the bidder will provide t dollars if her utility\nexceeds s, and otherwise 0. Another interesting case is when\nsuch a bid is partially acceptable: the bidder will provide t\ndollars if her utility exceeds s; but if her utility is u < s, she\nis still willing to provide ut\ns\ndollars.\nOne might wonder why, if we are given the bidders\" utility\nfunctions, we do not simply maximize the sum of the\nutilities rather than surplus or total donated. There are several\nreasons. First, because affine transformations do not affect\nutility functions in a fundamental way, it would be\npossi3\nOf course, our bidding language can be trivially extended\nto allow for fully expressive bids, by also allowing bids from\na fully expressive bidding language, in addition to the bids\nin our bidding language.\n53\nble for a bidder to inflate her utility by changing its units,\nthereby making her bid more important for utility\nmaximization purposes. Second, a bidder could simply give a\npayment willingness function that is 0 everywhere, and have\nher utility be taken into account in deciding on the outcome,\nin spite of her not contributing anything.\n5. AVOIDING INDIRECT PAYMENTS\nIn an initial implementation, the approach of having\ndonations made out to a center, and having a center forward\nthese payments to charities, may not be desirable. Rather, it\nmay be preferable to have a partially decentralized solution,\nwhere the donating parties write out checks to the charities\ndirectly according to a solution prescribed by the center. In\nthis scenario, the center merely has to verify that parties are\ngiving the prescribed amounts. Advantages of this include\nthat the center can keep its legal status minimal, as well\nas that we do not require the donating parties to trust the\ncenter to transfer their donations to the charities (or require\nsome complicated verification protocol). It is also a step\ntowards a fully decentralized solution, if this is desirable.\nTo bring this about, we can still use the approach\ndescribed earlier. After we clear the market in the manner\ndescribed before, we know the amount that each donator is\nsupposed to give, and the amount that each charity is\nsupposed to receive. Then, it is straightforward to give some\nspecification of who should give how much to which charity,\nthat is consistent with that clearing. Any greedy algorithm\nthat increases the cash flow from any bidder who has not\nyet paid enough, to any charity that has not yet received\nenough, until either the bidder has paid enough or the\ncharity has received enough, will provide such a specification.\n(All of this is assuming that\nbj\n\u03c0bj =\nci\n\u03c0ci . In the case\nwhere there is nonzero surplus, that is,\nbj\n\u03c0bj >\nci\n\u03c0ci , we\ncan distribute this surplus across the bidders by not\nrequiring them to pay the full amount, or across the charities by\ngiving them more than the solution specifies.)\nNevertheless, with this approach, a bidder may have to\nwrite out a check to a charity that she does not care for at\nall. (For example, an environmental activist who was using\nthe system to increase donations to a wildlife preservation\nfund may be required to write a check to a group\nsupporting a right-wing political party.) This is likely to lead to\ncomplaints and noncompliance with the clearing. We can\naddress this issue by letting each bidder specify explicitly\n(before the clearing) which charities she would be willing\nto make a check out to. These additional constraints, of\ncourse, may change the optimal solution. In general,\nchecking whether a given centralized solution (with zero surplus)\ncan be accomplished through decentralized payments when\nthere are such constraints can be modeled as a MAX-FLOW\nproblem. In the MAX-FLOW instance, there is an edge from\nthe source node s to each bidder bj, with a capacity of \u03c0bj\n(as specified in the centralized solution); an edge from each\nbidder bj to each charity ci that the bidder is willing to\ndonate money to, with a capacity of \u221e; and an edge from each\ncharity ci to the target node t with capacity \u03c0ci (as specified\nin the centralized solution).\nIn the remainder of this paper, all our hardness results\napply even to the setting where there is no constraint on which\nbidders can pay to which charity (that is, even the problem\nas it was specified before this section is hard). We also\ngeneralize our clearing algorithms to the partially decentralized\ncase with constraints.\n6. HARDNESS OF CLEARING THE\nMARKET\nIn this section, we will show that the clearing problem is\ncompletely inapproximable, even when every bidder\"s utility\nfunction is linear (with slope 0 or 1 in each charity\"s\npayments), each bidder cares either about at most two charities\nor about all charities equally, and each bidder\"s payment\nwillingness function is a step function. We will reduce from\nMAX2SAT (given a formula in conjunctive normal form\n(where each clause has two literals) and a target number of\nsatisfied clauses T, does there exist an assignment of truth\nvalues to the variables that makes at least T clauses true?),\nwhich is NP-complete [7].\nTheorem 1. There exists a reduction from MAX2SAT\ninstances to DONATION-CLEARING instances such that\n1. If the MAX2SAT instance has no solution, then the\nonly valid outcome is the zero outcome (no bidder pays\nanything and no charity receives anything); 2. Otherwise, there\nexists a solution with positive surplus. Additionally, the\nDONATION-CLEARING instances that we reduce to have\nthe following properties: 1. Every ui\nj is a line; that is, the\nutility that each bidder derives from any charity is linear; 2.\nAll the ui\nj have slope either 0 or 1; 3. Every bidder either\nhas at most 2 charities that affect her utility (with slope 1),\nor all charities affect her utility (with slope 1); 4. Every bid\nis a threshold bid; that is, every bidder\"s payment willingness\nfunction wj is a step function.\nProof. The problem is in NP because we can\nnondeterministically choose the payments to be made and received,\nand check the validity and objective value of this outcome.\nIn the following, we will represent bids as follows:\n({(ck, ak)}, s, t) indicates that uk\nj (\u03c0ck ) = ak\u03c0ck (this\nfunction is 0 for ck not mentioned in the bid), and wj(uj) = t\nfor uj \u2265 s, wj(uj) = 0 otherwise.\nTo show NP-hardness, we reduce an arbitrary MAX2SAT\ninstance, given by a set of clauses K = {k} = {(l1\nk, l2\nk)}\nover a variable set V together with a target number of\nsatisfied clauses T, to the following DONATION-CLEARING\ninstance. Let the set of charities be as follows. For every\nliteral l \u2208 L, there is a charity cl. Then, let the set of\nbids be as follows. For every variable v, there is a bid bv =\n({(c+v, 1), (c\u2212v, 1)}, 2, 1 \u2212 1\n4|V |\n). For every literal l, there is\na bid bl = ({(cl, 1)}, 2, 1). For every clause k = {l1\nk, l2\nk} \u2208 K,\nthere is a bid bk = ({(cl1\nk\n, 1), (cl2\nk\n, 1)}, 2, 1\n8|V ||K|\n). Finally,\nthere is a single bid that values all charities equally: b0 =\n({(c1, 1), (c2, 1), . . . , (cm, 1)}, 2|V |+ T\n8|V ||K|\n, 1\n4\n+ 1\n16|V ||K|\n). We\nshow the two instances are equivalent.\nFirst, suppose there exists a solution to the MAX2SAT\ninstance. If in this solution, l is true, then let \u03c0cl = 2 +\nT\n8|V |2|K|\n; otherwise \u03c0cl = 0. Also, the only bids that are\nnot accepted (meaning the threshold is not met) are the bl\nwhere l is false, and the bk such that both of l1\nk, l2\nk are false.\nFirst we show that no bidder whose bid is accepted pays\nmore than she is willing to. For each bv, either c+v or c\u2212v\nreceives at least 2, so this bidder\"s threshold has been met.\n54\nFor each bl, either l is false and the bid is not accepted, or l\nis true, cl receives at least 2, and the threshold has been met.\nFor each bk, either both of l1\nk, l2\nk are false and the bid is not\naccepted, or at least one of them (say li\nk) is true (that is, k\nis satisfied) and cli\nk\nreceives at least 2, and the threshold has\nbeen met. Finally, because the total amount received by the\ncharities is 2|V | + T\n8|V ||K|\n, b0\"s threshold has also been met.\nThe total amount that can be extracted from the accepted\nbids is at least |V |(1\u2212 1\n4|V |\n)+|V |+T 1\n8|V ||K|\n+ 1\n4\n+ 1\n16|V ||K|\n) =\n2|V |+ T\n8|V ||K|\n+ 1\n16|V ||K|\n> 2|V |+ T\n8|V ||K|\n, so there is positive\nsurplus. So there exists a solution with positive surplus to\nthe DONATION-CLEARING instance.\nNow suppose there exists a nonzero outcome in the\nDONATION-CLEARING instance. First we show that it\nis not possible (for any v \u2208 V ) that both b+v and b\u2212v are\naccepted. For, this would require that \u03c0c+v + \u03c0c\u2212v \u2265 4.\nThe bids bv, b+v, b\u2212v cannot contribute more than 3, so\nwe need another 1 at least. It is easily seen that for any\nother v , accepting any subset of {bv , b+v , b\u2212v } would\nrequire that at least as much is given to c+v and c\u2212v as\ncan be extracted from these bids, so this cannot help.\nFinally, all the other bids combined can contribute at most\n|K| 1\n8|V ||K|\n+ 1\n4\n+ 1\n16|V ||K|\n< 1. It follows that we can\ninterpret the outcome in the DONATION-CLEARING instance\nas a partial assignment of truth values to variables: v is set\nto true if b+v is accepted, and to false if b\u2212v is accepted. All\nthat is left to show is that this partial assignment satisfies\nat least T clauses.\nFirst we show that if a clause bid bk is accepted, then\neither bl1\nk\nor bl2\nk\nis accepted (and thus either l1\nk or l2\nk is set\nto true, hence k is satisfied). If bk is accepted, at least one\nof cl1\nk\nand cl2\nk\nmust be receiving at least 1; without loss of\ngenerality, say it is cl1\nk\n, and say l1\nk corresponds to variable\nv1\nk (that is, it is +v1\nk or \u2212v1\nk). If cl1\nk\ndoes not receive at\nleast 2, bl1\nk\nis not accepted, and it is easy to check that\nthe bids bv1\nk\n, b+v1\nk\n, b\u2212v1\nk\ncontribute (at least) 1 less than is\npaid to c+v1\nk\nand c+v1\nk\n. But this is the same situation that\nwe analyzed before, and we know it is impossible. All that\nremains to show is that at least T clause bids are accepted.\nWe now show that b0 is accepted. Suppose it is not; then\none of the bv must be accepted. (The solution is nonzero by\nassumption; if only some bk are accepted, the total payment\nfrom these bids is at most |K| 1\n8|V ||K|\n< 1, which is not\nenough for any bid to be accepted; and if one of the bl is\naccepted, then the threshold for the corresponding bv is also\nreached.) For this v, bv1\nk\n, b+v1\nk\n, b\u2212v1\nk\ncontribute (at least)\n1\n4|V |\nless than the total payments to c+v and c\u2212v. Again,\nthe other bv and bl cannot (by themselves) help to close this\ngap; and the bk can contribute at most |K| 1\n8|V ||K|\n< 1\n4|V |\n.\nIt follows that b0 is accepted.\nNow, in order for b0 to be accepted, a total of 2|V |+ T\n8|V ||K|\nmust be donated. Because is not possible (for any v \u2208 V )\nthat both b+v and b\u2212v are accepted, it follows that the total\npayment by the bv and the bl can be at most 2|V | \u2212 1\n4\n.\nAdding b0\"s payment of 1\n4\n+ 1\n16|V ||K|\nto this, we still need\nT \u2212 1\n2\n8|V ||K|\nfrom the bk. But each one of them contributes at\nmost 1\n8|V ||K|\n, so at least T of them must be accepted.\nCorollary 1. Unless P=NP, there is no polynomial-time\nalgorithm for approximating DONATION-CLEARING (with\neither the surplus or the total amount donated as the\nobjective) within any ratio f(n), where f is a nonzero function of\nthe size of the instance. This holds even if the\nDONATIONCLEARING structures satisfy all the properties given in\nTheorem 1.\nProof. Suppose we had such a polynomial time\nalgorithm, and applied it to the DONATION-CLEARING\ninstances that were reduced from MAX2SAT instances in\nTheorem 1. It would return a nonzero solution when the\nMAX2SAT instance has a solution, and a zero solution\notherwise. So we can decide whether arbitrary MAX2SAT\ninstances are satisfiable this way, and it would follow that\nP=NP.\n(Solving the problem to optimality is NP-complete in many\nother (noncomparable or even more restricted) settings as\nwell-we omit such results because of space constraint.)\nThis should not be interpreted to mean that our approach is\ninfeasible. First, as we will show, there are very expressive\nfamilies of bids for which the problem is solvable in\npolynomial time. Second, NP-completeness is often overcome in\npractice (especially when the stakes are high). For instance,\neven though the problem of clearing combinatorial auctions\nis NP-complete [20] (even to approximate [21]), they are\ntypically solved to optimality in practice.\n7. MIXED INTEGER PROGRAMMING\nFORMULATION\nIn this section, we give a mixed integer programming\n(MIP) formulation for the general problem. We also discuss\nin which special cases this formulation reduces to a linear\nprogramming (LP) formulation. In such cases, the problem\nis solvable in polynomial time, because linear programs can\nbe solved in polynomial time [11].\nThe variables of the MIP defining the final outcome are\nthe payments made to the charities, denoted by \u03c0ci , and\nthe payments extracted from the bidders, \u03c0bj . In the case\nwhere we try to avoid direct payments and let the bidders\npay the charities directly, we add variables \u03c0ci,bj indicating\nhow much bj pays to ci, with the constraints that for each\nci, \u03c0ci \u2264\nbj\n\u03c0ci,bj ; and for each bj, \u03c0bj \u2265\nci\n\u03c0ci,bj .\nAdditionally, there is a constraint \u03c0ci,bj = 0 whenever bidder bj\nis unwilling to pay charity ci. The rest of the MIP can be\nphrased in terms of the \u03c0ci and \u03c0bj .\nThe objectives we have discussed earlier are both linear:\nsurplus is given by\nn\nj=1\n\u03c0bj \u2212\nm\ni=1\n\u03c0ci , and total amount\ndonated is given by\nm\ni=1\n\u03c0ci (coefficients can be added to\nrepresent different weights on the different charities in the\nobjective).\nThe constraint that the outcome should be valid (no deficit)\nis given simply by:\nn\nj=1\n\u03c0bj \u2265\nm\ni=1\n\u03c0ci .\nFor every bidder, for every charity, we define an additional\nutility variable ui\nj indicating the utility that this bidder\nderives from the payment to this charity. The bidder\"s total\n55\nutility is given by another variable uj, with the constraint\nthat uj =\nm\ni=1\nui\nj.\nEach ui\nj is given as a function of \u03c0ci by the (piecewise\nlinear) function provided by the bidder. In order to\nrepresent this function in the MIP formulation, we will merely\nplace upper bounding constraints on ui\nj, so that it cannot\nexceed the given functions. The MIP solver can then push\nthe ui\nj variables all the way up to the constraint, in order\nto extract as much payment from this bidder as possible.\nIn the case where the ui\nj are concave, this is easy: if (sl, tl)\nand (sl+1, tl+1) are endpoints of a finite linear segment in the\nfunction, we add the constraint that ui\nj \u2264 tl +\n\u03c0ci\n\u2212sl\nsl+1\u2212sl\n(tl+1 \u2212\ntl). If the final (infinite) segment starts at (sk, tk) and has\nslope d, we add the constraint that ui\nj \u2264 tk + d(\u03c0ci \u2212 sk).\nUsing the fact that the function is concave, for each value of\n\u03c0ci , the tightest upper bound on ui\nj is the one corresponding\nto the segment above that value of \u03c0ci , and therefore these\nconstraints are sufficient to force the correct value of ui\nj.\nWhen the function is not concave, we require (for the first\ntime) some binary variables. First, we define another point\non the function: (sk+1, tk+1) = (sk + M, tk + dM), where\nd is the slope of the infinite segment and M is any upper\nbound on the \u03c0cj . This has the effect that we will never be\non the infinite segment again. Now, let xi,j\nl be an indicator\nvariable that should be 1 if \u03c0ci is below the lth segment of\nthe function, and 0 otherwise. To effect this, first add a\nconstraint\nk\nl=0\nxi,j\nl = 1. Now, we aim to represent \u03c0ci as a\nweighted average of its two neighboring si,j\nl . For 0 \u2264 l \u2264\nk + 1, let \u03bbi,j\nl be the weight on si,j\nl . We add the constraint\nk+1\nl=0\n\u03bbi,j\nl = 1. Also, for 0 \u2264 l \u2264 k + 1, we add the constraint\n\u03bbi,j\nl \u2264 xl\u22121 +xl (where x\u22121 and xk+1 are defined to be zero),\nso that indeed only the two neighboring si,j\nl have nonzero\nweight. Now we add the constraint \u03c0ci =\nk+1\nl=0\nsi,j\nl \u03bbi,j\nl , and\nnow the \u03bbi,j\nl must be set correctly. Then, we can set ui\nj =\nk+1\nl=0\nti,j\nl \u03bbi,j\nl . (This is a standard MIP technique [16].)\nFinally, each \u03c0bj is bounded by a function of uj by the\n(piecewise linear) function provided by the bidder (wj).\nRepresenting this function is entirely analogous to how we\nrepresented ui\nj as a function of \u03c0ci . (Again we will need binary\nvariables only if the function is not concave.)\nBecause we only use binary variables when either a\nutility function ui\nj or a payment willingness function wj is not\nconcave, it follows that if all of these are concave, our MIP\nformulation is simply a linear program-which can be solved\nin polynomial time. Thus:\nTheorem 2. If all functions ui\nj and wj are concave (and\npiecewise linear), the DONATION-CLEARING problem can\nbe solved in polynomial time using linear programming.\nEven if some of these functions are not concave, we can\nsimply replace each such function by the smallest upper\nbounding concave function, and use the linear programming\nformulation to obtain an upper bound on the\nobjectivewhich may be useful in a search formulation of the general\nproblem.\n8. WHY ONE CANNOT DO MUCH\nBETTER THAN LINEAR\nPROGRAMMING\nOne may wonder if, for the special cases of the\nDONATIONCLEARING problem that can be solved in polynomial time\nwith linear programming, there exist special purpose\nalgorithms that are much faster than linear programming\nalgorithms. In this section, we show that this is not the case.\nWe give a reduction from (the decision variant of) the\ngeneral linear programming problem to (the decision variant\nof) a special case of the DONATION-CLEARING problem\n(which can be solved in polynomial time using linear\nprogramming). (The decision variant of an optimization\nproblem asks the binary question: Can the objective value\nexceed o?) Thus, any special-purpose algorithm for solving\nthe decision variant of this special case of the\nDONATIONCLEARING problem could be used to solve a decision\nquestion about an arbitrary linear program just as fast. (And\nthus, if we are willing to call the algorithm a logarithmic\nnumber of times, we can solve the optimization version of\nthe linear program.)\nWe first observe that for linear programming, a decision\nquestion about the objective can simply be phrased as\nanother constraint in the LP (forcing the objective to exceed\nthe given value); then, the original decision question\ncoincides with asking whether the resulting linear program has\na feasible solution.\nTheorem 3. The question of whether an LP (given by a\nset of linear constraints4\n) has a feasible solution can be\nmodeled as a DONATION-CLEARING instance with payment\nmaximization as the objective, with 2v charities and v + c\nbids (where v is the number of variables in the LP, and c is\nthe number of constraints). In this model, each bid bj has\nonly linear ui\nj functions, and is a partially acceptable\nthreshold bid (wj(u) = tj for u \u2265 sj, otherwise wj(u) =\nutj\nsj\n). The\nv bids corresponding to the variables mention only two\ncharities each; the c bids corresponding to the constraints mention\nonly two times the number of variables in the corresponding\nconstraint.\nProof. For every variable xi in the LP, let there be two\ncharities, c+xi and c\u2212xi . Let H be some number such that\nif there is a feasible solution to the LP, there is one in which\nevery variable has absolute value at most H.\nIn the following, we will represent bids as follows:\n({(ck, ak)}, s, t) indicates that uk\nj (\u03c0ck ) = ak\u03c0ck (this\nfunction is 0 for ck not mentioned in the bid), and wj(uj) = t\nfor uj \u2265 s, wj(uj) =\nuj t\ns\notherwise.\nFor every variable xi in the LP, let there be a bid bxi =\n({(c+xi , 1), (c\u2212xi , 1)}, 2H, 2H \u2212 c\nv\n). For every constraint\ni\nrj\ni xi \u2264 sj in the linear program, let there be a bid bj =\n({(c\u2212xi , rj\ni )}i:r\nj\ni >0\n\u222a {(c+xi , \u2212rj\ni )}i:r\nj\ni <0\n, (\ni\n|rj\ni |)H \u2212 sj, 1).\nLet the target total amount donated be 2vH.\nSuppose there is a feasible solution (x\u2217\n1, x\u2217\n2, . . . , x\u2217\nv) to the\nLP. Without loss of generality, we can suppose that |x\u2217\ni | \u2264 H\nfor all i. Then, in the DONATION-CLEARING instance,\n4\nThese constraints must include bounds on the variables\n(including nonnegativity bounds), if any.\n56\nfor every i, let \u03c0c+xi\n= H + x\u2217\ni , and let \u03c0c\u2212xi\n= H \u2212 x\u2217\ni\n(for a total payment of 2H to these two charities). This\nallows us to extract the maximum payment from the bids\nbxi -a total payment of 2vH \u2212 c. Additionally, the utility\nof bidder bj is now\ni:r\nj\ni >0\nrj\ni (H \u2212 x\u2217\ni ) +\ni:r\nj\ni <0\n\u2212rj\ni (H + x\u2217\ni ) =\n(\ni\n|rj\ni |)H \u2212\ni\nrj\ni x\u2217\ni \u2265 (\ni\n|rj\ni |)H \u2212 sj (where the last\ninequality stems from the fact that constraint j must be\nsatisfied in the LP solution), so it follows we can extract the\nmaximum payment from all the bidders bj, for a total\npayment of c. It follows that we can extract the required 2vH\npayment from the bidders, and there exists a solution to\nthe DONATION-CLEARING instance with a total amount\ndonated of at least 2vH.\nNow suppose there is a solution to the\nDONATIONCLEARING instance with a total amount donated of at\nleast vH. Then the maximum payment must be extracted\nfrom each bidder. From the fact that the maximum payment\nmust be extracted from each bidder bxi , it follows that for\neach i, \u03c0c+xi\n+ \u03c0c\u2212xi\n\u2265 2H. Because the maximum\nextractable total payment is 2vH, it follows that for each i,\n\u03c0c+xi\n+ \u03c0c\u2212xi\n= 2H. Let x\u2217\ni = \u03c0c+xi\n\u2212 H = H \u2212 \u03c0c\u2212xi\n.\nThen, from the fact that the maximum payment must be\nextracted from each bidder bj, it follows that (\ni\n|rj\ni |)H \u2212\nsj \u2264\ni:r\nj\ni >0\nrj\ni \u03c0c\u2212xi\n+\ni:r\nj\ni <0\n\u2212rj\ni \u03c0c+xi\n=\ni:r\nj\ni >0\nrj\ni (H \u2212 x\u2217\ni ) +\ni:r\nj\ni <0\n\u2212rj\ni (H + x\u2217\ni ) = (\ni\n|rj\ni |)H \u2212\ni\nrj\ni x\u2217\ni . Equivalently,\ni\nrj\ni x\u2217\ni \u2264 sj. It follows that the x\u2217\ni constitute a feasible\nsolution to the LP.\n9. QUASILINEAR BIDS\nAnother class of bids of interest is the class of quasilinear\nbids. In a quasilinear bid, the bidder\"s payment willingness\nfunction is linear in utility: that is, wj = uj. (Because the\nunits of utility are arbitrary, we may as well let them\ncorrespond exactly to units of money-so we do not need a\nconstant multiplier.) In most cases, quasilinearity is an\nunreasonable assumption: for example, usually bidders have a\nlimited budget for donations, so that the payment\nwillingness will stop increasing in utility after some point (or at\nleast increase slower in the case of a softer budget\nconstraint). Nevertheless, quasilinearity may be a reasonable\nassumption in the case where the bidders are large\norganizations with large budgets, and the charities are a few small\nprojects requiring relatively little money. In this setting,\nonce a certain small amount has been donated to a charity,\na bidder will derive no more utility from more money\nbeing donated from that charity. Thus, the bidders will never\nreach a high enough utility for their budget constraint (even\nwhen it is soft) to take effect, and thus a linear\napproximation of their payment willingness function is reasonable.\nAnother reason for studying the quasilinear setting is that\nit is the easiest setting for mechanism design, which we will\ndiscuss shortly. In this section, we will see that the clearing\nproblem is much easier in the case of quasilinear bids.\nFirst, we address the case where we are trying to maximize\nsurplus (which is the most natural setting for mechanism\ndesign). The key observation here is that when bids are\nquasilinear, the clearing problem decomposes across charities.\nLemma 1. Suppose all bids are quasilinear, and surplus\nis the objective. Then we can clear the market optimally by\nclearing the market for each charity individually. That is,\nfor each bidder bj, let \u03c0bj =\nci\n\u03c0bi\nj\n. Then, for each charity\nci, maximize (\nbj\n\u03c0bi\nj\n) \u2212 \u03c0ci , under the constraint that for\nevery bidder bj, \u03c0bi\nj\n\u2264 ui\nj(\u03c0ci ).\nProof. The resulting solution is certainly valid: first of\nall, at least as much money is collected as is given away,\nbecause\nbj\n\u03c0bj \u2212\nci\n\u03c0ci =\nbj ci\n\u03c0bi\nj\n\u2212\nci\n\u03c0ci =\nci\n((\nbj\n\u03c0bi\nj\n) \u2212\n\u03c0ci )-and the terms of this summation are the objectives of\nthe individual optimization problems, each of which can be\nset at least to 0 (by setting all the variables are set to 0),\nso it follows that the expression is nonnegative. Second, no\nbidder bj pays more than she is willing to, because uj \u2212\u03c0bj =\nci\nui\nj(\u03c0ci )\u2212\nci\n\u03c0bi\nj\n=\nci\n(ui\nj(\u03c0ci )\u2212\u03c0bi\nj\n)-and the terms of this\nsummation are nonnegative by the constraints we imposed\non the individual optimization problems.\nAll that remains to show is that the solution is\noptimal. Because in an optimal solution, we will extract as\nmuch payment from the bidders as possible given the \u03c0ci ,\nall we need to show is that the \u03c0ci are set optimally by\nthis approach. Let \u03c0\u2217\nci\nbe the amount paid to charity \u03c0ci\nin some optimal solution. If we change this amount to \u03c0ci\nand leave everything else unchanged, this will only affect\nthe payment that we can extract from the bidders because\nof this particular charity, and the difference in surplus will\nbe\nbj\nui\nj(\u03c0ci\n) \u2212 ui\nj(\u03c0\u2217\nci\n) \u2212 \u03c0ci\n+ \u03c0\u2217\nci\n. This expression is, of\ncourse, 0 if \u03c0ci\n= \u03c0\u2217\nci\n. But now notice that this expression\nis maximized as a function of \u03c0ci\nby the decomposed\nsolution for this charity (the terms without \u03c0ci\nin them do not\nmatter, and of course in the decomposed solution we always\nset \u03c0bi\nj\n= ui\nj(\u03c0ci )). It follows that if we change \u03c0ci to the\ndecomposed solution, the change in surplus will be at least\n0 (and the solution will still be valid). Thus, we can change\nthe \u03c0ci one by one to the decomposed solution without ever\nlosing any surplus.\nTheorem 4. When all bids are quasilinear and surplus\nis the objective, DONATION-CLEARING can be done in\nlinear time.\nProof. By Lemma 1, we can solve the problem\nseparately for each charity. For charity ci, this amounts to\nmaximizing (\nbj\nui\nj(\u03c0ci )) \u2212 \u03c0ci as a function of \u03c0ci . Because all\nits terms are piecewise linear functions, this whole function\nis piecewise linear, and must be maximized at one of the\npoints where it is nondifferentiable. It follows that we need\nonly check all the points at which one of the terms is\nnondifferentiable.\nUnfortunately, the decomposing lemma does not hold for\npayment maximization.\nProposition 1. When the objective is payment\nmaximization, even when bids are quasilinear, the solution obtained\nby decomposing the problem across charities is in general not\noptimal (even with concave bids).\n57\nProof. Consider a single bidder b1 placing the following\nquasilinear bid over two charities c1 and c2: u1\n1(\u03c0c1 ) = 2\u03c0ci\nfor 0 \u2264 \u03c0ci \u2264 1, u1\n1(\u03c0c1 ) = 2 +\n\u03c0ci\n\u22121\n4\notherwise; u2\n1(\u03c0c2 ) =\n\u03c0ci\n2\n. The decomposed solution is \u03c0c1 = 7\n3\n, \u03c0c2 = 0, for a\ntotal donation of 7\n3\n. But the solution \u03c0c1 = 1, \u03c0c2 = 2 is\nalso valid, for a total donation of 3 > 7\n3\n.\nIn fact, when payment maximization is the objective,\nDONATION-CLEARING remains (weakly) NP-complete in\ngeneral. (In the remainder of the paper, proofs are omitted\nbecause of space constraint.)\nTheorem 5. DONATION-CLEARING is (weakly)\nNPcomplete when payment maximization is the objective, even\nwhen every bid is concerns only one charity (and has a\nstepfunction utility function for this charity), and is quasilinear.\nHowever, when the bids are also concave, a simple greedy\nclearing algorithm is optimal.\nTheorem 6. Given a DONATION-CLEARING instance\nwith payment maximization as the objective where all bids\nare quasilinear and concave, consider the following\nalgorithm. Start with \u03c0ci = 0 for all charities. Then, letting\n\u03b3ci =\nd\nbj\nui\nj (\u03c0ci\n)\nd\u03c0ci\n(at nondifferentiable points, these\nderivatives should be taken from the right), increase \u03c0c\u2217\ni\n(where\nc\u2217\ni \u2208 arg maxci \u03b3ci ), until either \u03b3c\u2217\ni\nis no longer the highest\n(in which case, recompute c\u2217\ni and start increasing the\ncorresponding payment), or\nbj\nuj =\nci\n\u03c0ci and \u03b3c\u2217\ni\n< 1. Finally,\nlet \u03c0bj = uj.\n(A similar greedy algorithm works when the objective is\nsurplus and the bids are quasilinear and concave, with as\nonly difference that we stop increasing the payments as soon\nas \u03b3c\u2217\ni\n< 1.)\n10. INCENTIVE COMPATIBILITY\nUp to this point, we have not discussed the bidders\"\nincentives for bidding any particular way. Specifically, the bids\nmay not truthfully reflect the bidders\" preferences over\ncharities because a bidder may bid strategically, misrepresenting\nher preferences in order to obtain a result that is better to\nherself. This means the mechanism is not strategy-proof.\n(We will show some concrete examples of this shortly.) This\nis not too surprising, because the mechanism described so\nfar is, in a sense, a first-price mechanism, where the\nmechanism will extract as much payment from a bidder as her bid\nallows. Such mechanisms (for example, first-price auctions,\nwhere winners pay the value of their bids) are typically not\nstrategy-proof: if a bidder reports her true valuation for an\noutcome, then if this outcome occurs, the payment the\nbidder will have to make will offset her gains from the outcome\ncompletely. Of course, we could try to change the rules of\nthe game-which outcome (payment vector to charities) do\nwe select for which bid vector, and which bidder pays how\nmuch-in order to make bidding truthfully beneficial, and\nto make the outcome better with regard to the bidders\" true\npreferences. This is the field of mechanism design. In this\nsection, we will briefly discuss the options that mechanism\ndesign provides for the expressive charity donation problem.\n10.1 Strategic bids under the first-price\nmechanism\nWe first point out some reasons for bidders to misreport\ntheir preferences under the first-price mechanism described\nin the paper up to this point. First of all, even when there is\nonly one charity, it may make sense to underbid one\"s true\nvaluation for the charity. For example, suppose a bidder\nwould like a charity to receive a certain amount x, but does\nnot care if the charity receives more than that. Additionally,\nsuppose that the other bids guarantee that the charity will\nreceive at least x no matter what bid the bidder submits\n(and the bidder knows this). Then the bidder is best off not\nbidding at all (or submitting a utility for the charity of 0),\nto avoid having to make any payment. (This is known in\neconomics as the free rider problem [14].\nWith multiple charities, another kind of manipulation may\noccur, where the bidder attempts to steer others\" payments\ntowards her preferred charity. Suppose that there are two\ncharities, and three bidders. The first bidder bids u1\n1(\u03c0c1 ) =\n1 if \u03c0c1 \u2265 1, u1\n1(\u03c0c1 ) = 0 otherwise; u2\n1(\u03c0c2 ) = 1 if \u03c0c2 \u2265 1,\nu2\n1(\u03c0c2 ) = 0 otherwise; and w1(u1) = u1 if u1 \u2264 1, w1(u1) =\n1+ 1\n100\n(u1 \u22121) otherwise. The second bidder bids u1\n2(\u03c0c1 ) =\n1 if \u03c0c1 \u2265 1, u1\n1(\u03c0c1 ) = 0 otherwise; u2\n2(\u03c0c2 ) = 0 (always);\nw2(u2) = 1\n4\nu2 if u2 \u2264 1, w2(u2) = 1\n4\n+ 1\n100\n(u2 \u22121) otherwise.\nNow, the third bidder\"s true preferences are accurately\nrepresented5\nby the bid u1\n3(\u03c0c1 ) = 1 if \u03c0c1 \u2265 1, u1\n3(\u03c0c1 ) = 0\notherwise; u2\n3(\u03c0c2 ) = 3 if \u03c0c2 \u2265 1, u2\n3(\u03c0c1 ) = 0 otherwise;\nand w3(u3) = 1\n3\nu3 if u3 \u2264 1, w3(u3) = 1\n3\n+ 1\n100\n(u3 \u2212 1)\notherwise. Now, it is straightforward to check that, if the third\nbidder bids truthfully, regardless of whether the objective is\nsurplus maximization or total donated, charity 1 will receive\nat least 1, and charity 2 will receive less than 1. The same is\ntrue if bidder 3 does not place a bid at all (as in the previous\ntype of manipulation); hence bidder 2\"s utility will be 1 in\nthis case. But now, if bidder 3 reports u1\n3(\u03c0c1 ) = 0\neverywhere; u2\n3(\u03c0c2 ) = 3 if \u03c0c2 \u2265 1, u2\n3(\u03c0c2 ) = 0 otherwise (this\npart of the bid is truthful); and w3(u3) = 1\n3\nu3 if u3 \u2264 1,\nw3(u3) = 1\n3\notherwise; then charity 2 will receive at least\n1, and bidder 3 will have to pay at most 1\n3\n. Because up to\nthis amount of payment, one unit of money corresponds to\nthree units of utility to bidder 3, it follows his utility is now\nat least 3 \u2212 1 = 2 > 1. We observe that in this case, the\nstrategic bidder is not only affecting how much the bidders\npay, but also how much the charities receive.\n10.2 Mechanism design in the quasilinear\nsetting\nThere are four reasons why the mechanism design\napproach is likely to be most successful in the setting of\nquasilinear preferences. First, historically, mechanism design has\nbeen been most successful when the quasilinear assumption\ncould be made. Second, because of this success, some very\ngeneral mechanisms have been discovered for the\nquasilinear setting (for instance, the VCG mechanisms [24, 4, 10],\nor the dAGVA mechanism [6, 1]) which we could apply\ndirectly to the expressive charity donation problem. Third, as\nwe saw in Section 9, the clearing problem is much easier in\n5\nFormally, this means that if the bidder is forced to pay\nthe full amount that his bid allows for a particular vector of\npayments to charities, the bidder is indifferent between this\nand not participating in the mechanism at all. (Compare\nthis to bidding truthfully in a first-price auction.)\n58\nthis setting, and thus we are less likely to run into\ncomputational trouble for the mechanism design problem. Fourth, as\nwe will show shortly, the quasilinearity assumption in some\ncases allows for decomposing the mechanism design problem\nover the charities (as it did for the simple clearing problem).\nMoreover, in the quasilinear setting (unlike in the general\nsetting), it makes sense to pursue social welfare (the sum\nof the utilities) as the objective, because now 1) units of\nutility correspond directly to units of money, so that we do\nnot have the problem of the bidders arbitrarily scaling their\nutilities; and 2) it is no longer possible to give a payment\nwillingness function of 0 while still affecting the donations\nthrough a utility function.\nBefore presenting the decomposition result, we introduce\nsome terms from game theory. A type is a preference profile\nthat a bidder can have and can report (thus, a type report\nis a bid). Incentive compatibility (IC) means that bidders\nare best off reporting their preferences truthfully; either\nregardless of the others\" types (in dominant strategies), or in\nexpectation over them (in Bayes-Nash equilibrium).\nIndividual rationality (IR) means agents are at least as well off\nparticipating in the mechanism as not participating; either\nregardless of the others\" types (ex-post), or in expectation\nover them (ex-interim). A mechanism is budget balanced\nif there is no flow of money into or out of the system-in\ngeneral (ex-post), or in expectation over the type reports\n(ex-ante). A mechanism is efficient if it (always) produces\nthe efficient allocation of wealth to charities.\nTheorem 7. Suppose all agents\" preferences are\nquasilinear. Furthermore, suppose that there exists a single-charity\nmechanism M that, for a certain subclass P of (quasilinear)\npreferences, under a given solution concept S\n(implementation in dominant strategies or Bayes-Nash equilibrium) and\na given notion of individual rationality R (ex post, ex\ninterim, or none), satisfies a certain notion of budget balance\n(ex post, ex ante, or none), and is ex-post efficient. Then\nthere exists such a mechanism for any number of charities.\nTwo mechanisms that satisfy efficiency (and can in fact be\napplied directly to the multiple-charity problem without use\nof the previous theorem) are the VCG (which is incentive\ncompatible in dominant strategies) and dAGVA (which is\nincentive compatible only in Bayes-Nash equilibrium)\nmechanisms. Each of them, however, has a drawback that would\nprobably make it impractical in the setting of donations to\ncharities. The VCG mechanism is not budget balanced. The\ndAGVA mechanism does not satisfy ex-post individual\nrationality. In the next subsection, we will investigate if we\ncan do better in the setting of donations to charities.\n10.3 Impossibility of efficiency\nIn this subsection, we show that even in a very restricted\nsetting, and with minimal requirements on IC and IR\nconstraints, it is impossible to create a mechanism that is\nefficient.\nTheorem 8. There is no mechanism which is ex-post\nbudget balanced, ex-post efficient, and ex-interim individually\nrational with Bayes-Nash equilibrium as the solution concept\n(even with only one charity, only two quasilinear bidders,\nwith identical type distributions (uniform over two types,\nwith either both utility functions being step functions or both\nutility functions being concave piecewise linear functions)).\nThe case of step-functions in this theorem corresponds\nexactly to the case of a single, fixed-size, nonexcludable public\ngood (the public good being that the charity receives the\ndesired amount)-for which such an impossibility result is\nalready known [14]. Many similar results are known,\nprobably the most famous of which is the Myerson-Satterthwaite\nimpossibility result, which proves the impossibility of\nefficient bilateral trade under the same requirements [15].\nTheorem 7 indicates that there is no reason to decide on\ndonations to multiple charities under a single mechanism\n(rather than a separate one for each charity), when an\nefficient mechanism with the desired properties exists for the\nsingle-charity case. However, because under the\nrequirements of Theorem 8, no such mechanism exists, there may\nbe a benefit to bringing the charities under the same\numbrella. The next proposition shows that this is indeed the\ncase.\nProposition 2. There exist settings with two charities\nwhere there exists no ex-post budget balanced, ex-post\nefficient, and ex-interim individually rational mechanism with\nBayes-Nash equilibrium as the solution concept for either\ncharity alone; but there exists an ex-post budget balanced,\nex-post efficient, and ex-post individually rational\nmechanism with dominant strategies as the solution concept for\nboth charities together. (Even when the conditions are the\nsame as in Theorem 8, apart from the fact that there are\nnow two charities.)\n11. CONCLUSION\nWe introduced a bidding language for expressing very\ngeneral types of matching offers over multiple charities. We\nformulated the corresponding clearing problem (deciding how\nmuch each bidder pays, and how much each charity receives),\nand showed that it is NP-complete to approximate to any\nratio even in very restricted settings. We gave a mixed-integer\nprogram formulation of the clearing problem, and showed\nthat for concave bids (where utility functions and payment\nwillingness function are concave), the program reduces to a\nlinear program and can hence be solved in polynomial time.\nWe then showed that the clearing problem for a subclass of\nconcave bids is at least as hard as the decision variant of\nlinear programming, suggesting that we cannot do much better\nthan a linear programming implementation for such bids.\nSubsequently, we showed that the clearing problem is much\neasier when bids are quasilinear (where payment willingness\nfunctions are linear)-for surplus, the problem decomposes\nacross charities, and for payment maximization, a greedy\napproach is optimal if the bids are concave (although this\nlatter problem is weakly NP-complete when the bids are not\nconcave). For the quasilinear setting, we studied the\nmechanism design question of making the bidders report their\npreferences truthfully rather than strategically. We showed\nthat an ex-post efficient mechanism is impossible even with\nonly one charity and a very restricted class of bids. We\nalso showed that even though the clearing problem\ndecomposes over charities in the quasilinear setting, there may be\nbenefits to linking the charities from a mechanism design\nstandpoint.\nThere are many directions for future research. One is to\nbuild a web-based implementation of the (first-price)\nmechanism proposed in this paper. Another is to study the\ncomputational scalability of our MIP/LP approach. It is also\n59\nimportant to identify other classes of bids (besides concave\nones) for which the clearing problem is tractable. Much\ncrucial work remains to be done on the mechanism design\nproblem. Finally, are there good iterative mechanisms for\ncharity donation?6\n12. REFERENCES\n[1] K. Arrow. The property rights doctrine and demand\nrevelation under incomplete information. In\nM. Boskin, editor, Economics and human welfare.\nNew York Academic Press, 1979.\n[2] L. M. Ausubel and P. Milgrom. Ascending auctions\nwith package bidding. Frontiers of Theoretical\nEconomics, 1, 2002. No. 1, Article 1.\n[3] Y. Bartal, R. Gonen, and N. Nisan. Incentive\ncompatible multi-unit combinatorial auctions. In\nTheoretical Aspects of Rationality and Knowledge\n(TARK IX), Bloomington, Indiana, USA, 2003.\n[4] E. H. Clarke. Multipart pricing of public goods. Public\nChoice, 11:17-33, 1971.\n[5] V. Conitzer and T. Sandholm. Complexity of\nmechanism design. In Proceedings of the 18th Annual\nConference on Uncertainty in Artificial Intelligence\n(UAI-02), pages 103-110, Edmonton, Canada, 2002.\n[6] C. d\"Aspremont and L. A. G\u00b4erard-Varet. Incentives\nand incomplete information. Journal of Public\nEconomics, 11:25-45, 1979.\n[7] M. R. Garey, D. S. Johnson, and L. Stockmeyer. Some\nsimplified NP-complete graph problems. Theoretical\nComputer Science, 1:237-267, 1976.\n[8] D. Goldburg and S. McElligott. Red cross statement\non official donation locations. 2001. Press release,\nhttp://www.redcross.org/press/disaster/ds pr/\n011017legitdonors.html.\n[9] R. Gonen and D. Lehmann. Optimal solutions for\nmulti-unit combinatorial auctions: Branch and bound\nheuristics. In Proceedings of the ACM Conference on\nElectronic Commerce (ACM-EC), pages 13-20,\nMinneapolis, MN, Oct. 2000.\n[10] T. Groves. Incentives in teams. Econometrica,\n41:617-631, 1973.\n[11] L. Khachiyan. A polynomial algorithm in linear\nprogramming. Soviet Math. Doklady, 20:191-194,\n1979.\n[12] R. Lavi, A. Mu\"Alem, and N. Nisan. Towards a\ncharacterization of truthful combinatorial auctions. In\nProceedings of the Annual Symposium on Foundations\nof Computer Science (FOCS), 2003.\n[13] D. Lehmann, L. I. O\"Callaghan, and Y. Shoham.\nTruth revelation in rapid, approximately efficient\ncombinatorial auctions. Journal of the ACM,\n49(5):577-602, 2002. Early version appeared in\nACMEC-99.\n6\nCompare, for example, iterative mechanisms in the\ncombinatorial auction setting [19, 25, 2].\n[14] A. Mas-Colell, M. Whinston, and J. R. Green.\nMicroeconomic Theory. Oxford University Press, 1995.\n[15] R. Myerson and M. Satterthwaite. Efficient\nmechanisms for bilateral trading. Journal of Economic\nTheory, 28:265-281, 1983.\n[16] G. L. Nemhauser and L. A. Wolsey. Integer and\nCombinatorial Optimization. John Wiley & Sons,\n1999. Section 4, page 11.\n[17] N. Nisan. Bidding and allocation in combinatorial\nauctions. In Proceedings of the ACM Conference on\nElectronic Commerce (ACM-EC), pages 1-12,\nMinneapolis, MN, 2000.\n[18] N. Nisan and A. Ronen. Computationally feasible\nVCG mechanisms. In Proceedings of the ACM\nConference on Electronic Commerce (ACM-EC),\npages 242-252, Minneapolis, MN, 2000.\n[19] D. C. Parkes. iBundle: An efficient ascending price\nbundle auction. In Proceedings of the ACM Conference\non Electronic Commerce (ACM-EC), pages 148-157,\nDenver, CO, Nov. 1999.\n[20] M. H. Rothkopf, A. Peke\u02c7c, and R. M. Harstad.\nComputationally manageable combinatorial auctions.\nManagement Science, 44(8):1131-1147, 1998.\n[21] T. Sandholm. Algorithm for optimal winner\ndetermination in combinatorial auctions. Artificial\nIntelligence, 135:1-54, Jan. 2002. Conference version\nappeared at the International Joint Conference on\nArtificial Intelligence (IJCAI), pp. 542-547,\nStockholm, Sweden, 1999.\n[22] T. Sandholm, S. Suri, A. Gilpin, and D. Levine.\nCABOB: A fast optimal algorithm for combinatorial\nauctions. In Proceedings of the Seventeenth\nInternational Joint Conference on Artificial\nIntelligence (IJCAI), pages 1102-1108, Seattle, WA,\n2001.\n[23] J. Tagliabue. Global AIDS Funds Is Given Attention,\nbut Not Money. The New York Times, June 1, 2003.\nReprinted on\nhttp://www.healthgap.org/press releases/a03/\n060103 NYT HGAP G8 fund.html.\n[24] W. Vickrey. Counterspeculation, auctions, and\ncompetitive sealed tenders. Journal of Finance,\n16:8-37, 1961.\n[25] P. R. Wurman and M. P. Wellman. AkBA: A\nprogressive, anonymous-price combinatorial auction.\nIn Proceedings of the ACM Conference on Electronic\nCommerce (ACM-EC), pages 21-29, Minneapolis,\nMN, Oct. 2000.\n[26] M. Yokoo. The characterization of strategy/false-name\nproof combinatorial auction protocols: Price-oriented,\nrationing-free protocol. In Proceedings of the\nEighteenth International Joint Conference on Artificial\nIntelligence (IJCAI), Acapulco, Mexico, Aug. 2003.\n60", "keywords": "bidding language;linear programming;expressive negotiation;supporter of charity;combinatorial auction;economic efficiency;charity supporter;expressive charity donation;threshold bid;incentive compatibility;market clear;concave bid;donation to charity;payment willingness function;negotiating material;quasilinearity;bidding framework;donation-clearing;mechanism design"}
{"name": "train_J-67", "title": "Mechanism Design for Online Real-Time Scheduling", "abstract": "For the problem of online real-time scheduling of jobs on a single processor, previous work presents matching upper and lower bounds on the competitive ratio that can be achieved by a deterministic algorithm. However, these results only apply to the non-strategic setting in which the jobs are released directly to the algorithm. Motivated by emerging areas such as grid computing, we instead consider this problem in an economic setting, in which each job is released to a separate, self-interested agent. The agent can then delay releasing the job to the algorithm, inflate its length, and declare an arbitrary value and deadline for the job, while the center determines not only the schedule, but the payment of each agent. For the resulting mechanism design problem (in which we also slightly strengthen an assumption from the non-strategic setting), we present a mechanism that addresses each incentive issue, while only increasing the competitive ratio by one. We then show a matching lower bound for deterministic mechanisms that never pay the agents.", "fulltext": "1. INTRODUCTION\nWe consider the problem of online scheduling of jobs on\na single processor. Each job is characterized by a release\ntime, a deadline, a processing time, and a value for successful\ncompletion by its deadline. The objective is to maximize the\nsum of the values of the jobs completed by their respective\ndeadlines. The key challenge in this online setting is that\nthe schedule must be constructed in real-time, even though\nnothing is known about a job until its release time.\nCompetitive analysis [6, 10], with its roots in [12], is a\nwell-studied approach for analyzing online algorithms by\ncomparing them against the optimal o\ufb04ine algorithm, which\nhas full knowledge of the input at the beginning of its\nexecution. One interpretation of this approach is as a game\nbetween the designer of the online algorithm and an adversary.\nFirst, the designer selects the online algorithm. Then, the\nadversary observes the algorithm and selects the sequence of\njobs that maximizes the competitive ratio: the ratio of the\nvalue of the jobs completed by an optimal o\ufb04ine algorithm\nto the value of those completed by the online algorithm.\nTwo papers paint a complete picture in terms of\ncompetitive analysis for this setting, in which the algorithm is\nassumed to know k, the maximum ratio between the value\ndensities (value divided by processing time) of any two jobs.\nFor k = 1, [4] presents a 4-competitive algorithm, and proves\nthat this is a lower bound on the competitive ratio for\ndeterministic algorithms. The same paper also generalizes the\nlower bound to (1 +\n\u221a\nk)2\nfor any k \u2265 1, and [15] then\npresents a matching (1 +\n\u221a\nk)2\n-competitive algorithm.\nThe setting addressed by these papers is completely\nnonstrategic, and the algorithm is assumed to always know the\ntrue characteristics of each job upon its release. However,\nin domains such as grid computing (see, for example, [7,\n8]) this assumption is invalid, because buyers of processor\ntime choose when and how to submit their jobs.\nFurthermore, sellers not only schedule jobs but also determine\nthe amount that they charge buyers, an issue not addressed\nin the non-strategic setting.\nThus, we consider an extension of the setting in which\neach job is owned by a separate, self-interested agent.\nInstead of being released to the algorithm, each job is now\nreleased only to its owning agent. Each agent now has four\ndifferent ways in which it can manipulate the algorithm: it\ndecides when to submit the job to the algorithm after the\ntrue release time, it can artificially inflate the length of the\njob, and it can declare an arbitrary value and deadline for\nthe job. Because the agents are self-interested, they will\nchoose to manipulate the algorithm if doing so will cause\n61\ntheir job to be completed; and, indeed, one can find\nexamples in which agents have incentive to manipulate the\nalgorithms presented in [4] and [15].\nThe addition of self-interested agents moves the problem\nfrom the area of algorithm design to that of mechanism\ndesign [17], the science of crafting protocols for self-interested\nagents. Recent years have seen much activity at the\ninterface of computer science and mechanism design (see, e.g.,\n[9, 18, 19]). In general, a mechanism defines a protocol for\ninteraction between the agents and the center that\nculminates with the selection of an outcome. In our setting, a\nmechanism will take as input a job from each agent, and\nreturn a schedule for the jobs, and a payment to be made by\neach agent to the center. A basic solution concept of\nmechanism design is incentive compatibility, which, in our setting,\nrequires that it is always in each agent\"s best interests to\nimmediately submit its job upon release, and to truthfully\ndeclare its value, length, and deadline.\nIn order to evaluate a mechanism using competitive\nanalysis, the adversary model must be updated. In the new\nmodel, the adversary still determines the sequence of jobs,\nbut it is the self-interested agents who determine the\nobserved input of the mechanism. Thus, in order to achieve a\ncompetitive ratio of c, an online mechanism must both be\nincentive compatible, and always achieve at least 1\nc\nof the\nvalue that the optimal o\ufb04ine mechanism achieves on the\nsame sequence of jobs.\nThe rest of the paper is structured as follows. In\nSection 2, we formally define and review results from the\noriginal, non-strategic setting. After introducing the incentive\nissues through an example, we formalize the mechanism\ndesign setting in Section 3. In Section 4 we present our first\nmain result, a ((1 +\n\u221a\nk)2\n+ 1)-competitive mechanism, and\nformally prove incentive compatibility and the competitive\nratio. We also show how we can simplify this mechanism for\nthe special case in which k = 1 and each agent cannot alter\nthe length of its job. Returning the general setting, we show\nin Section 5 that this competitive ratio is a lower bound for\ndeterministic mechanisms that do not pay agents. Finally,\nin Section 6, we discuss related work other than the directly\nrelevant [4] and [15], before concluding with Section 7.\n2. NON-STRATEGIC SETTING\nIn this section, we formally define the original, non-strategic\nsetting, and recap previous results.\n2.1 Formulation\nThere exists a single processor on which jobs can execute,\nand N jobs, although this number is not known beforehand.\nEach job i is characterized by a tuple \u03b8i = (ri, di, li, vi),\nwhich denotes the release time, deadline, length of\nprocessing time required, and value, respectively. The space \u0398i of\npossible tuples is the same for each job and consists of all\n\u03b8i such that ri, di, li, vi \u2208 + (thus, the model of time is\ncontinuous). Each job is released at time ri, at which point\nits three other characteristics are known. Nothing is known\nabout the job before its arrival. Each deadline is firm (or,\nhard), which means that no value is obtained for a job that\nis completed after its deadline. Preemption of jobs is\nallowed, and it takes no time to switch between jobs. Thus,\njob i is completed if and only if the total time it executes\non the processor before di is at least li.\nLet \u03b8 = (\u03b81, . . . , \u03b8N ) denote the vector of tuples for all\njobs, and let \u03b8\u2212i = (\u03b81, . . . , \u03b8i\u22121, \u03b8i+1, . . . , \u03b8N ) denote the\nsame vector without the tuple for job i. Thus, (\u03b8i, \u03b8\u2212i)\ndenotes a complete vector of tuples.\nDefine the value density \u03c1i = vi\nli\nof job i to be the ratio of\nits value to its length. For an input \u03b8, denote the maximum\nand minimum value densities as \u03c1min = mini \u03c1i and \u03c1max =\nmaxi \u03c1i. The importance ratio is then defined to be \u03c1max\n\u03c1min\n,\nthe maximal ratio of value densities between two jobs. The\nalgorithm is assumed to always know an upper bound k on\nthe importance ratio. For simplicity, we normalize the range\nof possible value densities so that \u03c1min = 1.\nAn online algorithm is a function f : \u03981 \u00d7 . . . \u00d7 \u0398N \u2192\nO that maps the vector of tuples (for any number N) to\nan outcome o. An outcome o \u2208 O is simply a schedule of\njobs on the processor, recorded by the function S : + \u2192\n{0, 1, . . . , N}, which maps each point in time to the active\njob, or to 0 if the processor is idle.\nTo denote the total elapsed time that a job has spent on\nthe processor at time t, we will use the function ei(t) =\nt\n0\n\u00b5(S(x) = i)dx, where \u00b5(\u00b7) is an indicator function that\nreturns 1 if the argument is true, and zero otherwise. A\njob\"s laxity at time t is defined to be di \u2212 t \u2212 li + ei(t) ,\nthe amount of time that it can remain inactive and still be\ncompleted by its deadline. A job is abandoned if it cannot\nbe completed by its deadline (formally, if di \u2212t+ei(t) < li).\nAlso, overload S(\u00b7) and ei(\u00b7) so that they can also take a\nvector \u03b8 as an argument. For example, S(\u03b8, t) is shorthand\nfor the S(t) of the outcome f(\u03b8), and it denotes the active\njob at time t when the input is \u03b8.\nSince a job cannot be executed before its release time, the\nspace of possible outcomes is restricted in that S(\u03b8, t) = i\nimplies ri \u2264 t. Also, because the online algorithm must\nproduce the schedule over time, without knowledge of future\ninputs, it must make the same decision at time t for inputs\nthat are indistinguishable at this time. Formally, let \u03b8(t)\ndenote the subset of the tuples in \u03b8 that satisfy ri \u2264 t. The\nconstraint is then that \u03b8(t) = \u03b8 (t) implies S(\u03b8, t) = S(\u03b8 , t).\nThe objective function is the sum of the values of the jobs\nthat are completed by their respective deadlines: W(o, \u03b8) =\ni vi \u00b7 \u00b5(ei(\u03b8, di) \u2265 li) . Let W\u2217\n(\u03b8) = maxo\u2208O W(o, \u03b8)\ndenote the maximum possible total value for the profile \u03b8.\nIn competitive analysis, an online algorithm is evaluated\nby comparing it against an optimal o\ufb04ine algorithm.\nBecause the o\ufb04ine algorithm knows the entire input \u03b8 at time\n0 (but still cannot start each job i until time ri), it\nalways achieves W\u2217\n(\u03b8). An online algorithm f(\u00b7) is (strictly)\nc-competitive if there does not exist an input \u03b8 such that\nc \u00b7 W(f(\u03b8), \u03b8) < W\u2217\n(\u03b8). An algorithm that is c-competitive\nis also said to achieve a competitive ratio of c.\nWe assume that there does not exist an overload period\nof infinite duration. A period of time [ts\n, tf\n] is overloaded\nif the sum of the lengths of the jobs whose release time and\ndeadline both fall within the time period exceeds the\nduration of the interval (formally, if tf\n\u2212ts\n\u2264 i|(ts\u2264ri,di\u2264tf ) li).\nWithout such an assumption, it is not possible to achieve a\nfinite competitive ratio [15].\n2.2 Previous Results\nIn the non-strategic setting, [4] presents a 4-competitive\nalgorithm called TD1 (version 2) for the case of k = 1, while\n[15] presents a (1+\n\u221a\nk)2\n-competitive algorithm called Dover\nfor the general case of k \u2265 1. Matching lower bounds for\ndeterministic algorithms for both of these cases were shown\n62\nin [4]. In this section we provide a high-level description of\nTD1 (version 2) using an example.\nTD1 (version 2) divides the schedule into intervals, each\nof which begins when the processor transitions from idle to\nbusy (call this time tb\n), and ends with the completion of\na job. The first active job of an interval may have laxity;\nhowever, for the remainder of the interval, preemption of the\nactive job is only considered when some other job has zero\nlaxity. For example, when the input is the set of jobs listed\nin Table 1, the first interval is the complete execution of\njob 1 over the range [0.0, 0.9]. No preemption is considered\nduring this interval, because job 2 has laxity until time 1.5.\nThen, a new interval starts at tb\n= 0.9 when job 2 becomes\nactive. Before job 2 can finish, preemption is considered at\ntime 4.8, when job 3 is released with zero laxity.\nIn order to decide whether to preempt the active job, TD1\n(version 2) uses two more variables: te\nand p loss. The\nformer records the latest deadline of a job that would be\nabandoned if the active job executes to completion (or, if\nno such job exists, the time that the active job will finish\nif it is not preempted). In this case, te\n= 17.0. The value\nte\n\u2212tb\nrepresents the an upper bound on the amount of\npossible execution time lost to the optimal o\ufb04ine algorithm\ndue to the completion of the active job. The other variable,\np loss, is equal to the length of the first active job of the\ncurrent interval. Because in general this job could have\nlaxity, the o\ufb04ine algorithm may be able to complete it outside\nof the range [tb\n, te\n].1\nIf the algorithm completes the active\njob and this job\"s length is at least te\n\u2212tb\n+p loss\n4\n, then the\nalgorithm is guaranteed to be 4-competitive for this\ninterval (note that k = 1 implies that all jobs have the same\nvalue density and thus that lengths can used to compute\nthe competitive ratio). Because this is not case at time 4.8\n(since te\n\u2212tb\n+p loss\n4\n= 17.0\u22120.9+4.0\n4\n> 4.0 = l2), the algorithm\npreempts job 2 for job 3, which then executes to completion.\nJob ri di li vi\n1 0.0 0.9 0.9 0.9\n2 0.5 5.5 4.0 4.0\n3 4.8 17.0 12.2 12.2\n01 5 17\n6\n?\n6\n?\n6\n?\nTable 1: Input used to recap TD1 (version 2) [4].\nThe up and down arrows represent ri and di,\nrespectively, while the length of the box equals li.\n3. MECHANISM DESIGN SETTING\nHowever, false information about job 2 would cause TD1\n(version 2) to complete this job. For example, if job 2\"s\ndeadline were declared as \u02c6d2 = 4.7, then it would have zero laxity\nat time 0.7. At this time, the algorithm would preempt job\n1 for job 2, because te\n\u2212tb\n+p loss\n4\n= 4.7\u22120.0+1.0\n4\n> 0.9 = l1.\nJob 2 would then complete before the arrival of job 3.2\n1\nWhile it would be easy to alter the algorithm to recognize\nthat this is not possible for the jobs in Table 1, our example\ndoes not depend on the use of p loss.\n2\nWhile we will not describe the significantly more complex\nIn order to address incentive issues such as this one, we\nneed to formalize the setting as a mechanism design\nproblem. In this section we first present the mechanism design\nformulation, and then define our goals for the mechanism.\n3.1 Formulation\nThere exists a center, who controls the processor, and\nN agents, where the value of N is unknown by the center\nbeforehand. Each job i is owned by a separate agent i. The\ncharacteristics of the job define the agent\"s type \u03b8i \u2208 \u0398i.\nAt time ri, agent i privately observes its type \u03b8i, and has\nno information about job i before ri. Thus, jobs are still\nreleased over time, but now each job is revealed only to the\nowning agent.\nAgents interact with the center through a direct\nmechanism \u0393 = (\u03981, . . . , \u0398N , g(\u00b7)), in which each agent declares a\njob, denoted by \u02c6\u03b8i = (\u02c6ri, \u02c6di, \u02c6li, \u02c6vi), and g : \u03981\u00d7. . .\u00d7\u0398N \u2192 O\nmaps the declared types to an outcome o \u2208 O. An outcome\no = (S(\u00b7), p1, . . . , pN ) consists of a schedule and a payment\nfrom each agent to the mechanism.\nIn a standard mechanism design setting, the outcome is\nenforced at the end of the mechanism. However, since the\nend is not well-defined in this online setting, we choose to\nmodel returning the job if it is completed and collecting a\npayment from each agent i as occurring at \u02c6di, which,\naccording to the agent\"s declaration, is the latest relevant point of\ntime for that agent. That is, even if job i is completed before\n\u02c6di, the center does not return the job to agent i until that\ntime. This modelling decision could instead be viewed as a\ndecision by the mechanism designer from a larger space of\npossible mechanisms. Indeed, as we will discuss later, this\ndecision of when to return a completed job is crucial to our\nmechanism.\nEach agent\"s utility, ui(g(\u02c6\u03b8), \u03b8i) = vi \u00b7 \u00b5(ei(\u02c6\u03b8, di) \u2265 li) \u00b7\n\u00b5( \u02c6di \u2264 di) \u2212 pi(\u02c6\u03b8), is a quasi-linear function of its value for\nits job (if completed and returned by its true deadline) and\nthe payment it makes to the center. We assume that each\nagent is a rational, expected utility maximizer.\nAgent declarations are restricted in that an agent cannot\ndeclare a length shorter than the true length, since the center\nwould be able to detect such a lie if the job were completed.\nOn the other hand, in the general formulation we will allow\nagents to declare longer lengths, since in some settings it\nmay be possible add unnecessary work to a job. However,\nwe will also consider a restricted formulation in which this\ntype of lie is not possible. The declared release time \u02c6ri\nis the time that the agent chooses to submit job i to the\ncenter, and it cannot precede the time ri at which the job\nis revealed to the agent. The agent can declare an arbitrary\ndeadline or value. To summarize, agent i can declare any\ntype \u02c6\u03b8i = (\u02c6ri, \u02c6di, \u02c6li, \u02c6vi) such that \u02c6li \u2265 li and \u02c6ri \u2265 ri.\nWhile in the non-strategic setting it was sufficient for the\nalgorithm to know the upper bound k on the ratio \u03c1max\n\u03c1min\n,\nin the mechanism design setting we will strengthen this\nassumption so that the mechanism also knows \u03c1min (or,\nequivalently, the range [\u03c1min, \u03c1max] of possible value densities).3\nDover\n, we note that it is similar in its use of intervals and\nits preference for the active job. Also, we note that the\nlower bound we will show in Section 5 implies that false\ninformation can also benefit a job in Dover\n.\n3\nNote that we could then force agent declarations to satisfy\n\u03c1min \u2264 \u02c6vi\n\u02c6li\n\u2264 \u03c1max. However, this restriction would not\n63\nWhile we feel that it is unlikely that a center would know k\nwithout knowing this range, we later present a mechanism\nthat does not depend on this extra knowledge in a restricted\nsetting.\nThe restriction on the schedule is now that S(\u02c6\u03b8, t) = i\nimplies \u02c6ri \u2264 t, to capture the fact that a job cannot be\nscheduled on the processor before it is declared to the mechanism.\nAs before, preemption of jobs is allowed, and job switching\ntakes no time.\nThe constraints due to the online mechanism\"s lack of\nknowledge of the future are that \u02c6\u03b8(t) = \u02c6\u03b8 (t) implies S(\u02c6\u03b8, t) =\nS(\u02c6\u03b8 , t), and \u02c6\u03b8( \u02c6di) = \u02c6\u03b8 ( \u02c6di) implies pi(\u02c6\u03b8) = pi(\u02c6\u03b8 ) for each\nagent i. The setting can then be summarized as follows.\n1Overview of the Setting:\nfor all t do\nThe center instantiates S(\u02c6\u03b8, t) \u2190 i, for some i s.t. \u02c6ri \u2264 t\nif \u2203i, (ri = t) then\n\u03b8i is revealed to agent i\nif \u2203i, (t \u2265 ri) and agent i has not declared a job then\nAgent i can declare any job \u02c6\u03b8i, s.t. \u02c6ri = t and \u02c6li \u2265 li\nif \u2203i, ( \u02c6di = t) \u2227 (ei(\u02c6\u03b8, t) \u2265 li) then\nCompleted job i is returned to agent i\nif \u2203i, ( \u02c6di = t) then\nCenter sets and collects payment pi(\u02c6\u03b8) from agent i\n3.2 Mechanism Goals\nOur aim as mechanism designer is to maximize the value\nof completed jobs, subject to the constraints of incentive\ncompatibility and individual rationality.\nThe condition for (dominant strategy) incentive\ncompatibility is that for each agent i, regardless of its true type\nand of the declared types of all other agents, agent i cannot\nincrease its utility by unilaterally changing its declaration.\nDefinition 1. A direct mechanism \u0393 satisfies incentive\ncompatibility (IC) if \u2200i, \u03b8i, \u03b8i, \u02c6\u03b8\u2212i :\nui(g(\u03b8i, \u02c6\u03b8\u2212i), \u03b8i) \u2265 ui(g(\u03b8i, \u02c6\u03b8\u2212i), \u03b8i)\nFrom an agent perspective, dominant strategies are\ndesirable because the agent does not have to reason about either\nthe strategies of the other agents or the distribution from\nthe which other agent\"s types are drawn. From a\nmechanism designer perspective, dominant strategies are\nimportant because we can reasonably assume that an agent who\nhas a dominant strategy will play according to it. For these\nreasons, in this paper we require dominant strategies, as\nopposed to a weaker equilibrium concept such as Bayes-Nash,\nunder which we could improve upon our positive results.4\ndecrease the lower bound on the competitive ratio.\n4\nA possible argument against the need for incentive\ncompatibility is that an agent\"s lie may actually improve the\nschedule. In fact, this was the case in the example we showed\nfor the false declaration \u02c6d2 = 4.7. However, if an agent lies\ndue to incorrect beliefs over the future input, then the lie\ncould instead make the schedule the worse (for example, if\njob 3 were never released, then job 1 would have been\nunnecessarily abandoned). Furthermore, if we do not know the\nbeliefs of the agents, and thus cannot predict how they will\nlie, then we can no longer provide a competitive guarantee\nfor our mechanism.\nWhile restricting ourselves to incentive compatible direct\nmechanisms may seem limiting at first, the Revelation\nPrinciple for Dominant Strategies (see, e.g., [17]) tells us that if\nour goal is dominant strategy implementation, then we can\nmake this restriction without loss of generality.\nThe second goal for our mechanism, individual rationality,\nrequires that agents who truthfully reveal their type never\nhave negative utility. The rationale behind this goal is that\nparticipation in the mechanism is assumed to be voluntary.\nDefinition 2. A direct mechanism \u0393 satisfies individual\nrationality (IR) if \u2200i, \u03b8i, \u02c6\u03b8\u2212i, ui(g(\u03b8i, \u02c6\u03b8\u2212i), \u03b8i) \u2265 0.\nFinally, the social welfare function that we aim to\nmaximize is the same as the objective function of the non-strategic\nsetting: W(o, \u03b8) = i vi \u00b7 \u00b5(ei(\u03b8, di) \u2265 li) . As in the\nnonstrategic setting, we will evaluate an online mechanism using\ncompetitive analysis to compare it against an optimal o\ufb04ine\nmechanism (which we will denote by \u0393offline). An o\ufb04ine\nmechanism knows all of the types at time 0, and thus can\nalways achieve W\u2217\n(\u03b8).5\nDefinition 3. An online mechanism \u0393 is (strictly)\nccompetitive if it satisfies IC and IR, and if there does not\nexist a profile of agent types \u03b8 such that c\u00b7W(g(\u03b8), \u03b8) < W\u2217\n(\u03b8).\n4. RESULTS\nIn this section, we first present our main positive result: a\n(1+\n\u221a\nk)2\n+1 -competitive mechanism (\u03931). After providing\nsome intuition as to why \u03931 satisfies individual rationality\nand incentive compatibility, we formally prove first these two\nproperties and then the competitive ratio. We then consider\na special case in which k = 1 and agents cannot lie about the\nlength of their job, which allows us to alter this mechanism\nso that it no longer requires either knowledge of \u03c1min or the\ncollection of payments from agents.\nUnlike TD1 (version 2) and Dover\n, \u03931 gives no\npreference to the active job. Instead, it always executes the\navailable job with the highest priority: (\u02c6vi +\n\u221a\nk \u00b7 ei(\u02c6\u03b8, t) \u00b7 \u03c1min).\nEach agent whose job is completed is then charged the\nlowest value that it could have declared such that its job still\nwould have been completed, holding constant the rest of its\ndeclaration.\nBy the use of a payment rule similar to that of a\nsecondprice auction, \u03931 satisfies both IC with respect to values\nand IR. We now argue why it satisfies IC with respect to\nthe other three characteristics. Declaring an improved job\n(i.e., declaring an earlier release time, a shorter length, or\na later deadline) could possibly decrease the payment of an\nagent. However, the first two lies are not possible in our\nsetting, while the third would cause the job, if it is completed,\nto be returned to the agent after the true deadline. This is\nthe reason why it is important to always return a completed\njob at its declared deadline, instead of at the point at which\nit is completed.\n5\nAnother possibility is to allow only the agents to know\ntheir types at time 0, and to force \u0393offline to be incentive\ncompatible so that agents will truthfully declare their types\nat time 0. However, this would not affect our results, since\nexecuting a VCG mechanism (see, e.g., [17]) at time 0 both\nsatisfies incentive compatibility and always maximizes social\nwelfare.\n64\nMechanism 1 \u03931\nExecute S(\u02c6\u03b8, \u00b7) according to Algorithm 1\nfor all i do\nif ei(\u02c6\u03b8, \u02c6di) \u2265 \u02c6li {Agent i\"s job is completed} then\npi(\u02c6\u03b8) \u2190 arg minvi\u22650(ei(((\u02c6ri, \u02c6di, \u02c6li, vi), \u02c6\u03b8\u2212i), \u02c6di) \u2265 \u02c6li)\nelse\npi(\u02c6\u03b8) \u2190 0\nAlgorithm 1\nfor all t do\nAvail \u2190 {i|(t \u2265 \u02c6ri)\u2227(ei(\u02c6\u03b8, t) < \u02c6li)\u2227(ei(\u02c6\u03b8, t)+ \u02c6di\u2212t \u2265 \u02c6li)}\n{Set of all released, non-completed, non-abandoned jobs}\nif Avail = \u2205 then\nS(\u02c6\u03b8, t) \u2190 arg maxi\u2208Avail(\u02c6vi +\n\u221a\nk \u00b7 ei(\u02c6\u03b8, t) \u00b7 \u03c1min)\n{Break ties in favor of lower \u02c6ri}\nelse\nS(\u02c6\u03b8, t) \u2190 0\nIt remains to argue why an agent does not have incentive\nto worsen its job. The only possible effects of an inflated\nlength are delaying the completion of the job and causing it\nto be abandoned, and the only possible effects of an earlier\ndeclared deadline are causing to be abandoned and causing\nit to be returned earlier (which has no effect on the agent\"s\nutility in our setting). On the other hand, it is less obvious\nwhy agents do not have incentive to declare a later release\ntime. Consider a mechanism \u03931 that differs from \u03931 in that\nit does not preempt the active job i unless there exists\nanother job j such that (\u02c6vi +\n\u221a\nk\u00b7li(\u02c6\u03b8, t)\u00b7\u03c1min) < \u02c6vj. Note that\nas an active job approaches completion in \u03931, its condition\nfor preemption approaches that of \u03931.\nHowever, the types in Table 2 for the case of k = 1 show\nwhy an agent may have incentive to delay the arrival of its\njob under \u03931. Job 1 becomes active at time 0, and job 2\nis abandoned upon its release at time 6, because 10 + 10 =\nv1 +l1 > v2 = 13. Then, at time 8, job 1 is preempted by job\n3, because 10 + 10 = v1 + l1 < v3 = 22. Job 3 then executes\nto completion, forcing job 1 to be abandoned. However, job\n2 had more weight than job 1, and would have prevented\njob 3 from being executed if it had been the active job at\ntime 8, since 13 + 13 = v2 + l2 > v3 = 22. Thus, if agent\n1 had falsely declared \u02c6r1 = 20, then job 3 would have been\nabandoned at time 8, and job 1 would have completed over\nthe range [20, 30].\nJob ri di li vi\n1 0 30 10 10\n2 6 19 13 13\n3 8 30 22 22\n0 6 10 20 30\n6\n?\n6\n?\n6\n?\nTable 2: Jobs used to show why a slightly altered\nversion of \u03931 would not be incentive compatible with\nrespect to release times.\nIntuitively, \u03931 avoids this problem because of two\nproperties. First, when a job becomes active, it must have a greater\npriority than all other available jobs. Second, because a job\"s\npriority can only increase through the increase of its elapsed\ntime, ei(\u02c6\u03b8, t), the rate of increase of a job\"s priority is\nindependent of its characteristics. These two properties together\nimply that, while a job is active, there cannot exist a time\nat which its priority is less than the priority that one of\nthese other jobs would have achieved by executing on the\nprocessor instead.\n4.1 Proof of Individual Rationality and\nIncentive Compatibility\nAfter presenting the (trivial) proof of IR, we break the\nproof of IC into lemmas.\nTheorem 1. Mechanism \u03931 satisfies individual\nrationality.\nProof. For arbitrary i, \u03b8i, \u02c6\u03b8\u2212i, if job i is not completed,\nthen agent i pays nothing and thus has a utility of zero;\nthat is, pi(\u03b8i, \u02c6\u03b8\u2212i) = 0 and ui(g(\u03b8i, \u02c6\u03b8\u2212i), \u03b8i) = 0. On the\nother hand, if job i is completed, then its value must\nexceed agent i\"s payment. Formally, ui(g(\u03b8i, \u02c6\u03b8\u2212i), \u03b8i) = vi \u2212\narg minvi\u22650(ei(((ri, di, li, vi), \u02c6\u03b8\u2212i), di) \u2265 li) \u2265 0 must hold,\nsince vi = vi satisfies the condition.\nTo prove IC, we need to show that for an arbitrary agent\ni, and an arbitrary profile \u02c6\u03b8\u2212i of declarations of the other\nagents, agent i can never gain by making a false declaration\n\u02c6\u03b8i = \u03b8i, subject to the constraints that \u02c6ri \u2265 ri and \u02c6li \u2265 li.\nWe start by showing that, regardless of \u02c6vi, if truthful\ndeclarations of ri, di, and li do not cause job i to be completed,\nthen worse declarations of these variables (that is,\ndeclarations that satisfy \u02c6ri \u2265 ri, \u02c6li \u2265 li and \u02c6di \u2264 di) can never\ncause the job to be completed. We break this part of the\nproof into two lemmas, first showing that it holds for the\nrelease time, regardless of the declarations of the other\nvariables, and then for length and deadline.\nLemma 2. In mechanism \u03931, the following condition holds\nfor all i, \u03b8i, \u02c6\u03b8\u2212i: \u2200 \u02c6vi, \u02c6li \u2265 li, \u02c6di \u2264 di, \u02c6ri \u2265 ri,\nei ((\u02c6ri, \u02c6di, \u02c6li, \u02c6vi), \u02c6\u03b8\u2212i), \u02c6di \u2265 \u02c6li =\u21d2\nei ((ri, \u02c6di, \u02c6li, \u02c6vi), \u02c6\u03b8\u2212i), \u02c6di \u2265 \u02c6li\nProof. Assume by contradiction that this condition does\nnot hold- that is, job i is not completed when ri is truthfully\ndeclared, but is completed for some false declaration \u02c6ri \u2265\nri. We first analyze the case in which the release time is\ntruthfully declared, and then we show that job i cannot be\ncompleted when agent i delays submitting it to the center.\nCase I: Agent i declares \u02c6\u03b8i = (ri, \u02c6di, \u02c6li, \u02c6vi).\nFirst, define the following three points in the execution of\njob i.\n\u2022 Let ts\n= arg mint S((\u02c6\u03b8i, \u02c6\u03b8\u2212i), t) = i be the time that\njob i first starts execution.\n\u2022 Let tp\n= arg mint>ts S((\u02c6\u03b8i, \u02c6\u03b8\u2212i), t) = i be the time\nthat job i is first preempted.\n\u2022 Let ta\n= arg mint ei((\u02c6\u03b8i, \u02c6\u03b8\u2212i), t) + \u02c6di \u2212 t < \u02c6li be the\ntime that job i is abandoned.\n65\nIf ts\nand tp\nare undefined because job i never becomes\nactive, then let ts\n= tp\n= ta\n.\nAlso, partition the jobs declared by other agents before ta\ninto the following three sets.\n\u2022 X = {j|(\u02c6rj < tp\n) \u2227 (j = i)} consists of the jobs (other\nthan i) that arrive before job i is first preempted.\n\u2022 Y = {j|(tp\n\u2264 \u02c6rj \u2264 ta\n)\u2227(\u02c6vj > \u02c6vi +\n\u221a\nk\u00b7ei((\u02c6\u03b8i, \u02c6\u03b8\u2212i), \u02c6rj)}\nconsists of the jobs that arrive in the range [tp\n, ta\n] and\nthat when they arrive have higher priority than job i\n(note that we are make use of the normalization).\n\u2022 Z = {j|(tp\n\u2264 \u02c6rj \u2264 ta\n)\u2227(\u02c6vj \u2264 \u02c6vi +\n\u221a\nk \u00b7ei((\u02c6\u03b8i, \u02c6\u03b8\u2212i), \u02c6rj)}\nconsists of the jobs that arrive in the range [tp\n, ta\n] and\nthat when they arrive have lower priority than job i.\nWe now show that all active jobs during the range (tp\n, ta\n]\nmust be either i or in the set Y . Unless tp\n= ta\n(in which case\nthis property trivially holds), it must be the case that job i\nhas a higher priority than an arbitrary job x \u2208 X at time tp\n,\nsince at the time just preceding tp\njob x was available and job\ni was active. Formally, \u02c6vx +\n\u221a\nk \u00b7 ex((\u02c6\u03b8i, \u02c6\u03b8\u2212i), tp\n) < \u02c6vi +\n\u221a\nk \u00b7\nei((\u02c6\u03b8i, \u02c6\u03b8\u2212i), tp\n) must hold.6\nWe can then show that, over the\nrange [tp\n, ta\n], no job x \u2208 X runs on the processor. Assume\nby contradiction that this is not true. Let tf\n\u2208 [tp\n, ta\n] be\nthe earliest time in this range that some job x \u2208 X is active,\nwhich implies that ex((\u02c6\u03b8i, \u02c6\u03b8\u2212i), tf\n) = ex((\u02c6\u03b8i, \u02c6\u03b8\u2212i), tp\n). We\ncan then show that job i has a higher priority at time tf\nas\nfollows: \u02c6vx+\n\u221a\nk\u00b7ex((\u02c6\u03b8i, \u02c6\u03b8\u2212i), tf\n) = \u02c6vx+\n\u221a\nk\u00b7ex((\u02c6\u03b8i, \u02c6\u03b8\u2212i), tp\n) <\n\u02c6vi +\n\u221a\nk \u00b7 ei((\u02c6\u03b8i, \u02c6\u03b8\u2212i), tp\n) \u2264 \u02c6vi +\n\u221a\nk \u00b7 ei((\u02c6\u03b8i, \u02c6\u03b8\u2212i), tf\n),\ncontradicting the fact that job x is active at time tf\n.\nA similar argument applies to an arbitrary job z \u2208 Z,\nstarting at it release time \u02c6rz > tp\n, since by definition job i\nhas a higher priority at that time. The only remaining jobs\nthat can be active over the range (tp\n, ta\n] are i and those in\nthe set Y .\nCase II: Agent i declares \u02c6\u03b8i = (\u02c6ri, \u02c6di, \u02c6li, \u02c6vi), where \u02c6ri > ri.\nWe now show that job i cannot be completed in this case,\ngiven that it was not completed in case I. First, we can\nrestrict the range of \u02c6ri that we need to consider as follows.\nDeclaring \u02c6ri \u2208 (ri, ts\n] would not affect the schedule, since\nts\nwould still be the first time that job i executes. Also,\ndeclaring \u02c6ri > ta\ncould not cause the job to be completed,\nsince di \u2212 ta\n< \u02c6li holds, which implies that job i would be\nabandoned at its release. Thus, we can restrict consideration\nto \u02c6ri \u2208 (ts\n, ta\n].\nIn order for declaring \u02c6\u03b8i to cause job i to be completed, a\nnecessary condition is that the execution of some job yc\n\u2208 Y\nmust change during the range (tp\n, ta\n], since the only jobs\nother than i that are active during that range are in Y .\nLet tc\n= arg mint\u2208(tp,ta][\u2203yc\n\u2208 Y, (S((\u02c6\u03b8i, \u02c6\u03b8\u2212i), t) = yc\n) \u2227\n(S((\u02c6\u03b8i, \u02c6\u03b8\u2212i), t) = yc\n)] be the first time that such a change\noccurs. We will now show that for any \u02c6ri \u2208 (ts\n, ta\n], there\ncannot exist a job with higher priority than yc\nat time tc\n,\ncontradicting (S((\u02c6\u03b8i, \u02c6\u03b8\u2212i), t) = yc\n).\nFirst note that job i cannot have a higher priority, since\nthere would have to exist a t \u2208 (tp\n, tc\n) such that \u2203y \u2208\n6\nFor simplicity, when we give the formal condition for a job x\nto have a higher priority than another job y, we will assume\nthat job x\"s priority is strictly greater than job y\"s, because,\nin the case of a tie that favors x, future ties would also be\nbroken in favor of job x.\nY, (S((\u02c6\u03b8i, \u02c6\u03b8\u2212i), t) = y) \u2227 (S((\u02c6\u03b8i, \u02c6\u03b8\u2212i), t) = i), contradicting\nthe definition of tc\n.\nNow consider an arbitrary y \u2208 Y such that y = yc\n. In case\nI, we know that job y has lower priority than yc\nat time tc\n;\nthat is, \u02c6vy +\n\u221a\nk\u00b7ey((\u02c6\u03b8i, \u02c6\u03b8\u2212i), tc\n) < \u02c6vyc +\n\u221a\nk\u00b7eyc ((\u02c6\u03b8i, \u02c6\u03b8\u2212i), tc\n).\nThus, moving to case II, job y must replace some other job\nbefore tc\n. Since \u02c6ry \u2265 tp\n, the condition is that there must\nexist some t \u2208 (tp\n, tc\n) such that \u2203w \u2208 Y \u222a{i}, (S((\u02c6\u03b8i, \u02c6\u03b8\u2212i), t) =\nw) \u2227 (S((\u02c6\u03b8i, \u02c6\u03b8\u2212i), t) = y). Since w \u2208 Y would contradict the\ndefinition of tc\n, we know that w = i. That is, the job that y\nreplaces must be i. By definition of the set Y , we know that\n\u02c6vy > \u02c6vi +\n\u221a\nk \u00b7 ei((\u02c6\u03b8i, \u02c6\u03b8\u2212i), \u02c6ry). Thus, if \u02c6ry \u2264 t, then job i\ncould not have executed instead of y in case I. On the other\nhand, if \u02c6ry > t, then job y obviously could not execute at\ntime t, contradicting the existence of such a time t.\nNow consider an arbitrary job x \u2208 X. We know that\nin case I job i has a higher priority than job x at time\nts\n, or, formally, that \u02c6vx +\n\u221a\nk \u00b7 ex((\u02c6\u03b8i, \u02c6\u03b8\u2212i), ts\n) < \u02c6vi +\n\u221a\nk \u00b7\nei((\u02c6\u03b8i, \u02c6\u03b8\u2212i), ts\n). We also know that \u02c6vi +\n\u221a\nk\u00b7ei((\u02c6\u03b8i, \u02c6\u03b8\u2212i), tc\n) <\n\u02c6vyc +\n\u221a\nk \u00b7 eyc ((\u02c6\u03b8i, \u02c6\u03b8\u2212i), tc\n). Since delaying i\"s arrival will\nnot affect the execution up to time ts\n, and since job x\ncannot execute instead of a job y \u2208 Y at any time t \u2208\n(tp\n, tc\n] by definition of tc\n, the only way for job x\"s\npriority to increase before tc\nas we move from case I to II\nis to replace job i over the range (ts\n, tc\n]. Thus, an\nupper bound on job x\"s priority when agent i declares \u02c6\u03b8i is:\n\u02c6vx+\n\u221a\nk\u00b7 ex((\u02c6\u03b8i, \u02c6\u03b8\u2212i), ts\n)+ei((\u02c6\u03b8i, \u02c6\u03b8\u2212i), tc\n)\u2212ei((\u02c6\u03b8i, \u02c6\u03b8\u2212i), ts\n) <\n\u02c6vi +\n\u221a\nk\u00b7 ei((\u02c6\u03b8i, \u02c6\u03b8\u2212i), ts\n)+ei((\u02c6\u03b8i, \u02c6\u03b8\u2212i), tc\n)\u2212ei((\u02c6\u03b8i, \u02c6\u03b8\u2212i), ts\n) =\n\u02c6vi +\n\u221a\nk \u00b7 ei((\u02c6\u03b8i, \u02c6\u03b8\u2212i), tc\n) < \u02c6vyc +\n\u221a\nk \u00b7 eyc ((\u02c6\u03b8i, \u02c6\u03b8\u2212i), tc\n).\nThus, even at this upper bound, job yc\nwould execute\ninstead of job x at time tc\n. A similar argument applies to\nan arbitrary job z \u2208 Z, starting at it release time \u02c6rz. Since\nthe sets {i}, X, Y, Z partition the set of jobs released before\nta\n, we have shown that no job could execute instead of job\nyc\n, contradicting the existence of tc\n, and completing the\nproof.\nLemma 3. In mechanism \u03931, the following condition holds\nfor all i, \u03b8i, \u02c6\u03b8\u2212i: \u2200 \u02c6vi, \u02c6li \u2265 li, \u02c6di \u2264 di,\nei ((ri, \u02c6di, \u02c6li, \u02c6vi), \u02c6\u03b8\u2212i), \u02c6di \u2265 \u02c6li =\u21d2\nei ((ri, di, li, \u02c6vi), \u02c6\u03b8\u2212i), \u02c6di \u2265 li\nProof. Assume by contradiction there exists some\ninstantiation of the above variables such that job i is not\ncompleted when li and di are truthfully declared, but is\ncompleted for some pair of false declarations \u02c6li \u2265 li and\n\u02c6di \u2264 di.\nNote that the only effect that \u02c6di and \u02c6li have on the\nexecution of the algorithm is on whether or not i \u2208 Avail.\nSpecifically, they affect the two conditions: (ei(\u02c6\u03b8, t) < \u02c6li)\nand (ei(\u02c6\u03b8, t) + \u02c6di \u2212 t \u2265 \u02c6li). Because job i is completed when\n\u02c6li and \u02c6di are declared, the former condition (for\ncompletion) must become false before the latter. Since truthfully\ndeclaring li \u2264 \u02c6li and di \u2265 \u02c6di will only make the former\ncondition become false earlier and the latter condition become\nfalse later, the execution of the algorithm will not be\naffected when moving to truthful declarations, and job i will\nbe completed, a contradiction.\nWe now use these two lemmas to show that the payment\nfor a completed job can only increase by falsely declaring\nworse \u02c6li, \u02c6di, and \u02c6ri.\n66\nLemma 4. In mechanism \u03931, the following condition holds\nfor all i, \u03b8i, \u02c6\u03b8\u2212i: \u2200 \u02c6li \u2265 li, \u02c6di \u2264 di, \u02c6ri \u2265 ri,\narg min\nvi\u22650\nei ((\u02c6ri, \u02c6di, \u02c6li, vi), \u02c6\u03b8\u2212i), \u02c6di \u2265 \u02c6li \u2265\narg min\nvi\u22650\nei ((ri, di, li, vi), \u02c6\u03b8\u2212i), di \u2265 li\nProof. Assume by contradiction that this condition does\nnot hold. This implies that there exists some value vi such\nthat the condition (ei(((\u02c6ri, \u02c6di, \u02c6li, vi), \u02c6\u03b8\u2212i), \u02c6di) \u2265 \u02c6li) holds,\nbut (ei(((ri, di, li, vi), \u02c6\u03b8\u2212i), di) \u2265 li) does not. Applying\nLemmas 2 and 3: (ei(((\u02c6ri, \u02c6di, \u02c6li, vi), \u02c6\u03b8\u2212i), \u02c6di) \u2265 \u02c6li) =\u21d2\n(ei(((ri, \u02c6di, \u02c6li, vi), \u02c6\u03b8\u2212i), \u02c6di) \u2265 \u02c6li) =\u21d2\n(ei(((ri, di, li, vi), \u02c6\u03b8\u2212i), di) \u2265 li), a contradiction.\nFinally, the following lemma tells us that the completion\nof a job is monotonic in its declared value.\nLemma 5. In mechanism \u03931, the following condition holds\nfor all i, \u02c6\u03b8i, \u02c6\u03b8\u2212i: \u2200 \u02c6vi \u2265 \u02c6vi,\nei ((\u02c6ri, \u02c6di, \u02c6li, \u02c6vi), \u02c6\u03b8\u2212i), \u02c6di \u2265 \u02c6li =\u21d2\nei ((\u02c6ri, \u02c6di, \u02c6li, \u02c6vi), \u02c6\u03b8\u2212i), \u02c6di \u2265 \u02c6li\nThe proof, by contradiction, of this lemma is omitted\nbecause it is essentially identical to that of Lemma 2 for \u02c6ri. In\ncase I, agent i declares (\u02c6ri, \u02c6di, \u02c6li, \u02c6vi) and the job is not\ncompleted, while in case II he declares (\u02c6ri, \u02c6di, \u02c6li, \u02c6vi) and the job\nis completed. The analysis of the two cases then proceeds as\nbefore- the execution will not change up to time ts\nbecause\nthe initial priority of job i decreases as we move from case\nI to II; and, as a result, there cannot be a change in the\nexecution of a job other than i over the range (tp\n, ta\n].\nWe can now combine the lemmas to show that no\nprofitable deviation is possible.\nTheorem 6. Mechanism \u03931 satisfies incentive\ncompatibility.\nProof. For an arbitrary agent i, we know that \u02c6ri \u2265 ri\nand \u02c6li \u2265 li hold by assumption. We also know that agent\ni has no incentive to declare \u02c6di > di, because job i would\nnever be returned before its true deadline. Then, because\nthe payment function is non-negative, agent i\"s utility could\nnot exceed zero. By IR, this is the minimum utility it would\nachieve if it truthfully declared \u03b8i. Thus, we can restrict\nconsideration to \u02c6\u03b8i that satisfy \u02c6ri \u2265 ri, \u02c6li \u2265 li, and \u02c6di \u2264 di.\nAgain using IR, we can further restrict consideration to \u02c6\u03b8i\nthat cause job i to be completed, since any other \u02c6\u03b8i yields a\nutility of zero.\nIf truthful declaration of \u03b8i causes job i to be completed,\nthen by Lemma 4 any such false declaration \u02c6\u03b8i could not\ndecrease the payment of agent i. On the other hand, if\ntruthful declaration does not cause job i to be completed,\nthen declaring such a \u02c6\u03b8i will cause agent i to have negative\nutility, since vi < arg minvi\u22650 ei(((ri, di, li, vi), \u02c6\u03b8\u2212i), \u02c6di) \u2265\nli \u2264 arg minvi\u22650 ei(((\u02c6ri, \u02c6di, \u02c6li, vi), \u02c6\u03b8\u2212i), \u02c6di) \u2265 \u02c6li holds by\nLemmas 5 and 4, respectively.\n4.2 Proof of Competitive Ratio\nThe proof of the competitive ratio, which makes use of\ntechniques adapted from those used in [15], is also broken\ninto lemmas. Having shown IC, we can assume truthful\ndeclaration (\u02c6\u03b8 = \u03b8). Since we have also shown IR, in order\nto prove the competitive ratio it remains to bound the loss\nof social welfare against \u0393offline.\nDenote by (1, 2, . . . , F) the sequence of jobs completed by\n\u03931. Divide time into intervals If = (topen\nf , tclose\nf ], one for\neach job f in this sequence. Set tclose\nf to be the time at\nwhich job f is completed, and set topen\nf = tclose\nf\u22121 for f \u2265 2,\nand topen\n1 = 0 for f = 1. Also, let tbegin\nf be the first time\nthat the processor is not idle in interval If .\nLemma 7. For any interval If , the following inequality\nholds: tclose\nf \u2212 tbegin\nf \u2264 (1 + 1\u221a\nk\n) \u00b7 vf\nProof. Interval If begins with a (possibly zero length)\nperiod of time in which the processor is idle because there is\nno available job. Then, it continuously executes a sequence\nof jobs (1, 2, . . . , c), where each job i in this sequence is\npreempted by job i + 1, except for job c, which is completed\n(thus, job c in this sequence is the same as job f is the global\nsequence of completed jobs). Let ts\ni be the time that job i\nbegins execution. Note that ts\n1 = tbegin\nf .\nOver the range [tbegin\nf , tclose\nf ], the priority (vi+\n\u221a\nk\u00b7ei(\u03b8, t))\nof the active job is monotonically increasing with time,\nbecause this function linearly increases while a job is active,\nand can only increase at a point in time when preemption\noccurs. Thus, each job i > 1 in this sequence begins\nexecution at its release time (that is, ts\ni = ri), because its priority\ndoes not increase while it is not active.\nWe now show that the value of the completed job c\nexceeds the product of\n\u221a\nk and the time spent in the interval\non jobs 1 through c\u22121, or, more formally, that the following\ncondition holds: vc \u2265\n\u221a\nk c\u22121\nh=1(eh(\u03b8, ts\nh+1) \u2212 eh(\u03b8, ts\nh)). To\nshow this, we will prove by induction that the stronger\ncondition vi \u2265\n\u221a\nk i\u22121\nh=1 eh(\u03b8, ts\nh+1) holds for all jobs i in the\nsequence.\nBase Case: For i = 1, v1 \u2265\n\u221a\nk 0\nh=1 eh(\u03b8, ts\nh+1) = 0,\nsince the sum is over zero elements.\nInductive Step: For an arbitrary 1 \u2264 i < c, we assume\nthat vi \u2265\n\u221a\nk i\u22121\nh=1 eh(\u03b8, ts\nh+1) holds. At time ts\ni+1, we\nknow that vi+1 \u2265 vi +\n\u221a\nk \u00b7 ei(\u03b8, ts\ni+1) holds, because ts\ni+1 =\nri+1. These two inequalities together imply that vi+1 \u2265\u221a\nk i\nh=1 eh(\u03b8, ts\nh+1), completing the inductive step.\nWe also know that tclose\nf \u2212 ts\nc \u2264 lc \u2264 vc must hold, by the\nsimplifying normalization of \u03c1min = 1 and the fact that job\nc\"s execution time cannot exceed its length. We can thus\nbound the total execution time of If by: tclose\nf \u2212 tbegin\nf =\n(tclose\nf \u2212ts\nc)+ c\u22121\nh=1(eh(\u03b8, ts\nh+1)\u2212eh(\u03b8, ts\nh)) \u2264 (1+ 1\u221a\nk\n)vf .\nWe now consider the possible execution of uncompleted\njobs by \u0393offline. Associate each job i that is not completed\nby \u03931 with the interval during which it was abandoned. All\njobs are now associated with an interval, since there are no\ngaps between the intervals, and since no job i can be\nabandoned after the close of the last interval at tclose\nF . Because\nthe processor is idle after tclose\nF , any such job i would\nbecome active at some time t \u2265 tclose\nF , which would lead to the\ncompletion of some job, creating a new interval and\ncontradicting the fact that IF is the last one.\n67\nThe following lemma is equivalent to Lemma 5.6 of [15],\nbut the proof is different for our mechanism.\nLemma 8. For any interval If and any job i abandoned\nin If , the following inequality holds: vi \u2264 (1 +\n\u221a\nk)vf .\nProof. Assume by contradiction that there exists a job\ni abandoned in If such that vi > (1 +\n\u221a\nk)vf . At tclose\nf ,\nthe priority of job f is vf +\n\u221a\nk \u00b7 lf < (1 +\n\u221a\nk)vf . Because\nthe priority of the active job monotonically increases over\nthe range [tbegin\nf , tclose\nf ], job i would have a higher priority\nthan the active job (and thus begin execution) at some time\nt \u2208 [tbegin\nf , tclose\nf ]. Again applying monotonicity, this would\nimply that the priority of the active job at tclose\nf exceeds\n(1 +\n\u221a\nk)vf , contradicting the fact that it is (1 +\n\u221a\nk)vf .\nAs in [15], for each interval If , we give \u0393offline the\nfollowing gift: k times the amount of time in the range\n[tbegin\nf , tclose\nf ] that it does not schedule a job. Additionally,\nwe give the adversary vf , since the adversary may be able\nto complete this job at some future time, due to the fact\nthat \u03931 ignores deadlines. The following lemma is Lemma\n5.10 in [15], and its proof now applies directly.\nLemma 9. [15] With the above gifts the total net gain\nobtained by the clairvoyant algorithm from scheduling the jobs\nabandoned during If is not greater than (1 +\n\u221a\nk) \u00b7 vf .\nThe intuition behind this lemma is that the best that\nthe adversary can do is to take almost all of the gift of\nk \u00b7(tclose\nf \u2212tbegin\nf ) (intuitively, this is equivalent to executing\njobs with the maximum possible value density over the time\nthat \u03931 is active), and then begin execution of a job\nabandoned by \u03931 right before tclose\nf . By Lemma 8, the value of\nthis job is bounded by (1 +\n\u221a\nk) \u00b7 vf . We can now combine\nthe results of these lemmas to prove the competitive ratio.\nTheorem 10. Mechanism \u03931 is (1+\n\u221a\nk)2+1 -competitive.\nProof. Using the fact that the way in which jobs are\nassociated with the intervals partitions the entire set of jobs,\nwe can show the competitive ratio by showing that \u03931 is\n(1+\n\u221a\nk)2\n+1 -competitive for each interval in the sequence\n(1, . . . , F). Over an arbitrary interval If , the o\ufb04ine\nalgorithm can achieve at most (tclose\nf \u2212tbegin\nf )\u00b7k+vf +(1+\n\u221a\nk)vf ,\nfrom the two gifts and the net gain bounded by Lemma\n9. Applying Lemma 7, this quantity is then bounded from\nabove by (1+ 1\u221a\nk\n)\u00b7vf \u00b7k+vf +(1+\n\u221a\nk)vf = ((1+\n\u221a\nk)2\n+1)\u00b7vf .\nSince \u03931 achieves vf , the competitive ratio holds.\n4.3 Special Case: Unalterable length and k=1\nWhile so far we have allowed each agent to lie about all\nfour characteristics of its job, lying about the length of the\njob is not possible in some settings. For example, a user\nmay not know how to alter a computational problem in a\nway that both lengthens the job and allows the solution of\nthe original problem to be extracted from the solution to\nthe altered problem. Another restriction that is natural in\nsome settings is uniform value densities (k = 1), which was\nthe case considered by [4]. If the setting satisfies these two\nconditions, then, by using Mechanism \u03932, we can achieve a\ncompetitive ratio of 5 (which is the same competitive ratio\nas \u03931 for the case of k = 1) without knowledge of \u03c1min and\nwithout the use of payments. The latter property may be\nnecessary in settings that are more local than grid\ncomputing (e.g., within a department) but in which the users are\nstill self-interested.7\nMechanism 2 \u03932\nExecute S(\u02c6\u03b8, \u00b7) according to Algorithm 2\nfor all i do\npi(\u02c6\u03b8) \u2190 0\nAlgorithm 2\nfor all t do\nAvail \u2190 {i|(t \u2265 \u02c6ri)\u2227(ei(\u02c6\u03b8, t) < li)\u2227(ei(\u02c6\u03b8, t)+ \u02c6di\u2212t \u2265 li)}\nif Avail = \u2205 then\nS(\u02c6\u03b8, t) \u2190 arg maxi\u2208Avail(li + ei(\u02c6\u03b8, t))\n{Break ties in favor of lower \u02c6ri}\nelse\nS(\u02c6\u03b8, t) \u2190 0\nTheorem 11. When k = 1, and each agent i cannot\nfalsely declare li, Mechanism \u03932 satisfies individual\nrationality and incentive compatibility.\nTheorem 12. When k = 1, and each agent i cannot\nfalsely declare li, Mechanism \u03932 is 5-competitive.\nSince this mechanism is essentially a simplification of \u03931,\nwe omit proofs of these theorems. Basically, the fact that\nk = 1 and \u02c6li = li both hold allows \u03932 to substitute the\npriority (li +ei(\u02c6\u03b8, t)) for the priority used in \u03931; and, since \u02c6vi\nis ignored, payments are no longer needed to ensure incentive\ncompatibility.\n5. COMPETITIVE LOWER BOUND\nWe now show that the competitive ratio of (1 +\n\u221a\nk)2\n+\n1 achieved by \u03931 is a lower bound for deterministic\nonline mechanisms. To do so, we will appeal to third\nrequirement on a mechanism, non-negative payments (NNP),\nwhich requires that the center never pays an agent (formally,\n\u2200i, \u02c6\u03b8, pi(\u02c6\u03b8i) \u2265 0). Unlike IC and IR, this requirement is not\nstandard in mechanism design. We note, however, that both\n\u03931 and \u03932 satisfy it trivially, and that, in the following proof,\nzero only serves as a baseline utility for an agent, and could\nbe replaced by any non-positive function of \u02c6\u03b8\u2212i.\nThe proof of the lower bound uses an adversary argument\nsimilar to that used in [4] to show a lower bound of (1 +\u221a\nk)2\nin the non-strategic setting, with the main novelty\nlying in the perturbation of the job sequence and the related\nincentive compatibility arguments. We first present a lemma\nrelating to the recurrence used for this argument, with the\nproof omitted due to space constraints.\nLemma 13. For any k \u2265 1, for the recurrence defined by\nli+1 = \u03bb \u00b7 li \u2212 k \u00b7 i\nh=1 lh and l1 = 1, where (1 +\n\u221a\nk)2\n\u2212 1 <\n\u03bb < (1 +\n\u221a\nk)2\n, there exists an integer m \u2265 1 such that\nlm+k\u00b7 m\u22121\nh=1\nlh\nlm\n> \u03bb.\n7\nWhile payments are not required in this setting, \u03932 can be\nchanged to collect a payments without affecting incentive\ncompatibility by charging some fixed fraction of li for each\njob i that is completed.\n68\nTheorem 14. There does not exist a deterministic online\nmechanism that satisfies NNP and that achieves a\ncompetitive ratio less than (1 +\n\u221a\nk)2\n+ 1.\nProof. Assume by contradiction that there exists a\ndeterministic online mechanism \u0393 that satisfies NNP and that\nachieves a competitive ratio of c = (1 +\n\u221a\nk)2\n+ 1 \u2212 for\nsome > 0 (and, by implication, satisfies IC and IR as\nwell). Since a competitive ratio of c implies a competitive\nratio of c + x, for any x > 0, we assume without loss of\ngenerality that < 1. First, we will construct a profile of\nagent types \u03b8 using an adversary argument. After possibly\nslightly perturbing \u03b8 to assure that a strictness property is\nsatisfied, we will then use a more significant perturbation of\n\u03b8 to reach a contradiction.\nWe now construct the original profile \u03b8. Pick an \u03b1 such\nthat 0 < \u03b1 < , and define \u03b4 = \u03b1\nck+3k\n. The adversary uses\ntwo sequences of jobs: minor and major. Minor jobs i are\ncharacterized by li = \u03b4, vi = k \u00b7 \u03b4, and zero laxity. The first\nminor job is released at time 0, and ri = di\u22121 for all i > 1.\nThe sequence stops whenever \u0393 completes any job.\nMajor jobs also have zero laxity, but they have the\nsmallest possible value ratio (that is, vi = li). The lengths of the\nmajor jobs that may be released, starting with i = 1, are\ndetermined by the following recurrence relation.\nli+1 = (c \u2212 1 + \u03b1) \u00b7 li \u2212 k \u00b7\ni\nh=1\nlh\nl1 = 1\nThe bounds on \u03b1 imply that (1 +\n\u221a\nk)2\n\u2212 1 < c \u2212 1 + \u03b1 <\n(1+\n\u221a\nk)2\n, which allows us to apply Lemma 13. Let m be the\nsmallest positive number such that\nlm+k\u00b7 m\u22121\nh=1\nlh\nlm\n> c\u22121+\u03b1.\nThe first major job has a release time of 0, and each major\njob i > 1 has a release time of ri = di\u22121 \u2212 \u03b4, just before\nthe deadline of the previous job. The adversary releases\nmajor job i \u2264 m if and only if each major job j < i was\nexecuted continuously over the range [ri, ri+1]. No major\njob is released after job m.\nIn order to achieve the desired competitive ratio, \u0393 must\ncomplete some major job f, because \u0393offline can always at\nleast complete major job 1 (for a value of 1), and \u0393 can\ncomplete at most one minor job (for a value of \u03b1\nc+3\n< 1\nc\n).\nAlso, in order for this job f to be released, the processor\ntime preceding rf can only be spent executing major jobs\nthat are later abandoned. If f < m, then major job f + 1\nwill be released and it will be the final major job. \u0393 cannot\ncomplete job f +1, because rf +lf = df > rf+1. Therefore,\n\u03b8 consists of major jobs 1 through f + 1 (or, f, if f = m),\nplus minor jobs from time 0 through time df .\nWe now possibly perturb \u03b8 slightly. By IR, we know\nthat vf \u2265 pf (\u03b8). Since we will later need this inequality\nto be strict, if vf = pf (\u03b8), then change \u03b8f to \u03b8f , where\nrf = rf , but vf , lf , and df are all incremented by \u03b4 over\ntheir respective values in \u03b8f . By IC, job f must still be\ncompleted by \u0393 for the profile (\u03b8f , \u03b8\u2212f ). If not, then by\nIR and NNP we know that pf (\u03b8f , \u03b8\u2212f ) = 0, and thus that\nuf (g(\u03b8f , \u03b8\u2212f ), \u03b8f ) = 0. However, agent f could then increase\nits utility by falsely declaring the original type of \u03b8f ,\nreceiving a utility of: uf (g(\u03b8f , \u03b8\u2212f ), \u03b8f ) = vf \u2212 pf (\u03b8) = \u03b4 > 0,\nviolating IC. Furthermore, agent f must be charged the same\namount (that is, pf (\u03b8f , \u03b8\u2212f ) = pf (\u03b8)), due to a similar\nincentive compatibility argument. Thus, for the remainder of\nthe proof, assume that vf > pf (\u03b8).\nWe now use a more substantial perturbation of \u03b8 to\ncomplete the proof. If f < m, then define \u03b8f to be identical\nto \u03b8f , except that df = df+1 + lf , allowing job f to be\ncompletely executed after job f + 1 is completed. If f = m,\nthen instead set df = df +lf . IC requires that for the profile\n(\u03b8f , \u03b8\u2212f ), \u0393 still executes job f continuously over the range\n[rf , rf +lf ], thus preventing job f +1 from being completed.\nAssume by contradiction that this were not true. Then, at\nthe original deadline of df , job f is not completed. Consider\nthe possible profile (\u03b8f , \u03b8\u2212f , \u03b8x), which differs from the new\nprofile only in the addition of a job x which has zero laxity,\nrx = df , and vx = lx = max(df \u2212 df , (c + 1) \u00b7 (lf + lf+1)).\nBecause this new profile is indistinguishable from (\u03b8f , \u03b8\u2212f )\nto \u0393 before time df , it must schedule jobs in the same way\nuntil df . Then, in order to achieve the desired competitive\nratio, it must execute job x continuously until its deadline,\nwhich is by construction at least as late as the new deadline\ndf of job f. Thus, job f will not be completed, and, by\nIR and NNP, it must be the case that pf (\u03b8f , \u03b8\u2212f , \u03b8x) =\n0 and uf (g(\u03b8f , \u03b8\u2212f , \u03b8x), \u03b8f ) = 0. Using the fact that \u03b8 is\nindistinguishable from (\u03b8f , \u03b8\u2212f , \u03b8x) up to time df , if agent\nf falsely declared his type to be the original \u03b8f , then its job\nwould be completed by df and it would be charged pf (\u03b8).\nIts utility would then increase to uf (g(\u03b8f , \u03b8\u2212f , \u03b8x), \u03b8f ) =\nvf \u2212 pf (\u03b8) > 0, contradicting IC.\nWhile \u0393\"s execution must be identical for both (\u03b8f , \u03b8\u2212f )\nand (\u03b8f , \u03b8\u2212f ), \u0393offline can take advantage of the change. If\nf < m, then \u0393 achieves a value of at most lf +\u03b4 (the value of\njob f if it were perturbed), while \u0393offline achieves a value of\nat least k\u00b7( f\nh=1 lh \u22122\u03b4)+lf+1 +lf by executing minor jobs\nuntil rf+1, followed by job f +1 and then job f (we subtract\ntwo \u03b4\"s instead of one because the last minor job before rf+1\nmay have to be abandoned). Substituting in for lf+1, the\ncompetitive ratio is then at least:\nk\u00b7(\nf\nh=1\nlh\u22122\u03b4)+lf+1+lf\nlf +\u03b4\n=\nk\u00b7(\nf\nh=1\nlh)\u22122k\u00b7\u03b4+(c\u22121+\u03b1)\u00b7lf \u2212k\u00b7(\nf\nh=1\nlh)+lf\nlf +\u03b4\n=\nc\u00b7lf +(\u03b1\u00b7lf \u22122k\u00b7\u03b4)\nlf +\u03b4\n\u2265\nc\u00b7lf +((ck+3k)\u03b4\u22122k\u00b7\u03b4)\nlf +\u03b4\n> c.\nIf instead f = m, then \u0393 achieves a value of at most lm +\u03b4,\nwhile \u0393offline achieves a value of at least k \u00b7 ( m\nh=1 lh \u2212\n2\u03b4) + lm by completing minor jobs until dm = rm + lm,\nand then completing job m. The competitive ratio is then\nat least:\nk\u00b7( m\nh=1 lh\u22122\u03b4)+lm\nlm+\u03b4\n=\nk\u00b7( m\u22121\nh=1\nlh)\u22122k\u00b7\u03b4+klm+lm\nlm+\u03b4\n>\n(c\u22121+\u03b1)\u00b7lm\u22122k\u00b7\u03b4+klm\nlm+\u03b4\n= (c+k\u22121)\u00b7lm+(\u03b1lm\u22122k\u00b7\u03b4)\nlm+\u03b4\n> c.\n6. RELATED WORK\nIn this section we describe related work other than the\ntwo papers ([4] and [15]) on which this paper is based.\nRecent work related to this scheduling domain has focused on\ncompetitive analysis in which the online algorithm uses a\nfaster processor than the o\ufb04ine algorithm (see, e.g., [13,\n14]). Mechanism design was also applied to a scheduling\nproblem in [18]. In their model, the center owns the jobs\nin an o\ufb04ine setting, and it is the agents who can execute\nthem. The private information of an agent is the time it will\nrequire to execute each job. Several incentive compatible\nmechanisms are presented that are based on approximation\nalgorithms for the computationally infeasible optimization\nproblem. This paper also launched the area of\nalgorithmic mechanism design, in which the mechanism must\nsat69\nisfy computational requirements in addition to the standard\nincentive requirements. A growing sub-field in this area is\nmulticast cost-sharing mechanism design (see, e.g., [1]), in\nwhich the mechanism must efficiently determine, for each\nagent in a multicast tree, whether the agent receives the\ntransmission and the price it must pay. For a survey of\nthis and other topics in distributed algorithmic mechanism\ndesign, see [9].\nOnline execution presents a different type of algorithmic\nchallenge, and several other papers study online algorithms\nor mechanisms in economic settings. For example, [5]\nconsiders an online market clearing setting, in which the\nauctioneer matches buy and sells bids (which are assumed to be\nexogenous) that arrive and expire over time. In [2], a\ngeneral method is presented for converting an online algorithm\ninto an online mechanism that is incentive compatible with\nrespect to values. Truthful declaration of values is also\nconsidered in [3] and [16], which both consider multi-unit online\nauctions. The main difference between the two is that the\nformer considers the case of a digital good, which thus has\nunlimited supply. It is pointed out in [16] that their results\ncontinue to hold when the setting is extended so that bidders\ncan delay their arrival.\nThe only other paper we are aware of that addresses the\nissue of incentive compatibility in a real-time system is [11],\nwhich considers several variants of a model in which the\ncenter allocates bandwidth to agents who declare both their\nvalue and their arrival time. A dominant strategy IC\nmechanism is presented for the variant in which every point in time\nis essentially independent, while a Bayes-Nash IC\nmechanism is presented for the variant in which the center\"s\ncurrent decision affects the cost of future actions.\n7. CONCLUSION\nIn this paper, we considered an online scheduling domain\nfor which algorithms with the best possible competitive\nratio had been found, but for which new solutions were\nrequired when the setting is extended to include self-interested\nagents. We presented a mechanism that is incentive\ncompatible with respect to release time, deadline, length and value,\nand that only increases the competitive ratio by one. We\nalso showed how this mechanism could be simplified when\nk = 1 and each agent cannot lie about the length of its job.\nWe then showed a matching lower bound on the\ncompetitive ratio that can be achieved by a deterministic mechanism\nthat never pays the agents.\nSeveral open problems remain in this setting. One is to\ndetermine whether the lower bound can be strengthened by\nremoving the restriction of non-negative payments. Also,\nwhile we feel that it is reasonable to strengthen the\nassumption of knowing the maximum possible ratio of value\ndensities (k) to knowing the actual range of possible value\ndensities, it would be interesting to determine whether there\nexists a ((1 +\n\u221a\nk)2\n+ 1)-competitive mechanism under the\noriginal assumption. Finally, randomized mechanisms\nprovide an unexplored area for future work.\n8. REFERENCES\n[1] A. Archer, J. Feigenbaum, A. Krishnamurthy,\nR. Sami, and S. Shenker, Approximation and collusion\nin multicast cost sharing, Games and Economic\nBehavior (to appear).\n[2] B. Awerbuch, Y. Azar, and A. Meyerson, Reducing\ntruth-telling online mechanisms to online\noptimization, Proceedings on the 35th Symposium on\nthe Theory of Computing, 2003.\n[3] Z. Bar-Yossef, K. Hildrum, and F. Wu,\nIncentive-compatible online auctions for digital goods,\nProceedings of the 13th Annual ACM-SIAM\nSymposium on Discrete Algorithms, 2002.\n[4] S. Baruah, G. Koren, D. Mao, B. Mishra,\nA. Raghunathan, L. Rosier, D. Shasha, and F. Wang,\nOn the competitiveness of on-line real-time task\nscheduling, Journal of Real-Time Systems 4 (1992),\nno. 2, 125-144.\n[5] A. Blum, T. Sandholm, and M. Zinkevich, Online\nalgorithms for market clearing, Proceedings of the\n13th Annual ACM-SIAM Symposium on Discrete\nAlgorithms, 2002.\n[6] A. Borodin and R. El-Yaniv, Online computation and\ncompetitive analysis, Cambridge University Press,\n1998.\n[7] R. Buyya, D. Abramson, J. Giddy, and H. Stockinger,\nEconomic models for resource management and\nscheduling in grid computing, The Journal of\nConcurrency and Computation: Practice and\nExperience 14 (2002), 1507-1542.\n[8] N. Camiel, S. London, N. Nisan, and O. Regev, The\npopcorn project: Distributed computation over the\ninternet in java, 6th International World Wide Web\nConference, 1997.\n[9] J. Feigenbaum and S. Shenker, Distributed algorithmic\nmechanism design: Recent results and future\ndirections, Proceedings of the 6th International\nWorkshop on Discrete Algorithms and Methods for\nMobile Computing and Communications, 2002,\npp. 1-13.\n[10] A. Fiat and G. Woeginger (editors), Online\nalgorithms: The state of the art, Springer Verlag, 1998.\n[11] E. Friedman and D. Parkes, Pricing wifi at\nstarbucksissues in online mechanism design, EC\"03, 2003.\n[12] R. L. Graham, Bounds for certain multiprocessor\nanomalies, Bell System Technical Journal 45 (1966),\n1563-1581.\n[13] B. Kalyanasundaram and K. Pruhs, Speed is as\npowerful as clairvoyance, Journal of the ACM 47\n(2000), 617-643.\n[14] C. Koo, T. Lam, T. Ngan, and K. To, On-line\nscheduling with tight deadlines, Theoretical Computer\nScience 295 (2003), 251-261.\n[15] G. Koren and D. Shasha, D-over: An optimal on-line\nscheduling algorithm for overloaded real-time systems,\nSIAM Journal of Computing 24 (1995), no. 2,\n318-339.\n[16] R. Lavi and N. Nisan, Competitive analysis of online\nauctions, EC\"00, 2000.\n[17] A. Mas-Colell, M. Whinston, and J. Green,\nMicroeconomic theory, Oxford University Press, 1995.\n[18] N. Nisan and A. Ronen, Algorithmic mechanism\ndesign, Games and Economic Behavior 35 (2001),\n166-196.\n[19] C. 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{"name": "train_J-69", "title": "Robust Incentive Techniques for Peer-to-Peer Networks", "abstract": "Lack of cooperation (free riding) is one of the key problems that confronts today\"s P2P systems. What makes this problem particularly difficult is the unique set of challenges that P2P systems pose: large populations, high turnover, asymmetry of interest, collusion, zero-cost identities, and traitors. To tackle these challenges we model the P2P system using the Generalized Prisoner\"s Dilemma (GPD), and propose the Reciprocative decision function as the basis of a family of incentives techniques. These techniques are fully distributed and include: discriminating server selection, maxflowbased subjective reputation, and adaptive stranger policies. Through simulation, we show that these techniques can drive a system of strategic users to nearly optimal levels of cooperation.", "fulltext": "1. INTRODUCTION\nMany peer-to-peer (P2P) systems rely on cooperation among\nselfinterested users. For example, in a file-sharing system, overall\ndownload latency and failure rate increase when users do not share\ntheir resources [3]. In a wireless ad-hoc network, overall packet\nlatency and loss rate increase when nodes refuse to forward packets\non behalf of others [26]. Further examples are file preservation [25],\ndiscussion boards [17], online auctions [16], and overlay routing\n[6]. In many of these systems, users have natural disincentives to\ncooperate because cooperation consumes their own resources and\nmay degrade their own performance. As a result, each user\"s\nattempt to maximize her own utility effectively lowers the overall\nA\nBC\nFigure 1: Example of asymmetry of interest. A wants service from B,\nB wants service form C, and C wants service from A.\nutility of the system. Avoiding this tragedy of the commons [18]\nrequires incentives for cooperation.\nWe adopt a game-theoretic approach in addressing this problem. In\nparticular, we use a prisoners\" dilemma model to capture the\nessential tension between individual and social utility, asymmetric\npayoff matrices to allow asymmetric transactions between peers,\nand a learning-based [14] population dynamic model to specify the\nbehavior of individual peers, which can be changed continuously.\nWhile social dilemmas have been studied extensively, P2P\napplications impose a unique set of challenges, including:\n\u2022 Large populations and high turnover: A file sharing\nsystem such as Gnutella and KaZaa can exceed 100, 000\nsimultaneous users, and nodes can have an average life-time of the\norder of minutes [33].\n\u2022 Asymmetry of interest: Asymmetric transactions of P2P\nsystems create the possibility for asymmetry of interest. In\nthe example in Figure 1, A wants service from B, B wants\nservice from C, and C wants service from A.\n\u2022 Zero-cost identity: Many P2P systems allow peers to\ncontinuously switch identities (i.e., whitewash).\nStrategies that work well in traditional prisoners\" dilemma games\nsuch as Tit-for-Tat [4] will not fare well in the P2P context.\nTherefore, we propose a family of scalable and robust incentive\ntechniques, based upon a novel Reciprocative decision function, to\naddress these challenges and provide different tradeoffs:\n\u2022 Discriminating Server Selection: Cooperation requires\nfamiliarity between entities either directly or indirectly.\nHowever, the large populations and high turnover of P2P systems\nmakes it less likely that repeat interactions will occur with\na familiar entity. We show that by having each peer keep a\n102\nprivate history of the actions of other peers toward her, and\nusing discriminating server selection, the Reciprocative\ndecision function can scale to large populations and moderate\nlevels of turnover.\n\u2022 Shared History: Scaling to higher turnover and mitigating\nasymmetry of interest requires shared history. Consider the\nexample in Figure 1. If everyone provides service, then the\nsystem operates optimally. However, if everyone keeps only\nprivate history, no one will provide service because B does\nnot know that A has served C, etc. We show that with shared\nhistory, B knows that A served C and consequently will serve\nA. This results in a higher level of cooperation than with\nprivate history. The cost of shared history is a distributed\ninfrastructure (e.g., distributed hash table-based storage) to store\nthe history.\n\u2022 Maxflow-based Subjective Reputation: Shared history\ncreates the possibility for collusion. In the example in Figure 1,\nC can falsely claim that A served him, thus deceiving B into\nproviding service. We show that a maxflow-based algorithm\nthat computes reputation subjectively promotes cooperation\ndespite collusion among 1/3 of the population. The basic idea\nis that B would only believe C if C had already provided\nservice to B. The cost of the maxflow algorithm is its O(V 3\n)\nrunning time, where V is the number of nodes in the system.\nTo eliminate this cost, we have developed a constant mean\nrunning time variation, which trades effectiveness for\ncomplexity of computation. We show that the maxflow-based\nalgorithm scales better than private history in the presence of\ncolluders without the centralized trust required in previous\nwork [9] [20].\n\u2022 Adaptive Stranger Policy: Zero-cost identities allows\nnoncooperating peers to escape the consequences of not\ncooperating and eventually destroy cooperation in the system if not\nstopped. We show that if Reciprocative peers treat strangers\n(peers with no history) using a policy that adapts to the\nbehavior of previous strangers, peers have little incentive to\nwhitewash and whitewashing can be nearly eliminated from\nthe system. The adaptive stranger policy does this without\nrequiring centralized allocation of identities, an entry fee for\nnewcomers, or rate-limiting [13] [9] [25].\n\u2022 Short-term History: History also creates the possibility that\na previously well-behaved peer with a good reputation will\nturn traitor and use his good reputation to exploit other peers.\nThe peer could be making a strategic decision or someone\nmay have hijacked her identity (e.g., by compromising her\nhost). Long-term history exacerbates this problem by\nallowing peers with many previous transactions to exploit that\nhistory for many new transactions. We show that short-term\nhistory prevents traitors from disrupting cooperation.\nThe rest of the paper is organized as follows. We describe the model\nin Section 2 and the reciprocative decision function in Section 3. We\nthen proceed to the incentive techniques in Section 4. In Section 4.1,\nwe describe the challenges of large populations and high turnover\nand show the effectiveness of discriminating server selection and\nshared history. In Section 4.2, we describe collusion and\ndemonstrate how subjective reputation mitigates it. In Section 4.3, we\npresent the problem of zero-cost identities and show how an\nadaptive stranger policy promotes persistent identities. In Section 4.4,\nwe show how traitors disrupt cooperation and how short-term\nhistory deals with them. We discuss related work in Section 5 and\nconclude in Section 6.\n2. MODEL AND ASSUMPTIONS\nIn this section, we present our assumptions about P2P systems and\ntheir users, and introduce a model that aims to capture the behavior\nof users in a P2P system.\n2.1 Assumptions\nWe assume a P2P system in which users are strategic, i.e., they\nact rationally to maximize their benefit. However, to capture some\nof the real-life unpredictability in the behavior of users, we allow\nusers to randomly change their behavior with a low probability (see\nSection 2.4).\nFor simplicity, we assume a homogeneous system in which all peers\nissue and satisfy requests at the same rate. A peer can satisfy any\nrequest, and, unless otherwise specified, peers request service\nuniformly at random from the population.1\n. Finally, we assume that all\ntransactions incur the same cost to all servers and provide the same\nbenefit to all clients.\nWe assume that users can pollute shared history with false\nrecommendations (Section 4.2), switch identities at zero-cost\n(Section 4.3), and spoof other users (Section 4.4). We do not assume\nany centralized trust or centralized infrastructure.\n2.2 Model\nTo aid the development and study of the incentive schemes, in this\nsection we present a model of the users\" behaviors. In particular,\nwe model the benefits and costs of P2P interactions (the game) and\npopulation dynamics caused by mutation, learning, and turnover.\nOur model is designed to have the following properties that\ncharacterize a large set of P2P systems:\n\u2022 Social Dilemma: Universal cooperation should result in\noptimal overall utility, but individuals who exploit the\ncooperation of others while not cooperating themselves (i.e.,\ndefecting) should benefit more than users who do cooperate.\n\u2022 Asymmetric Transactions: A peer may want service from\nanother peer while not currently being able to provide the\nservice that the second peer wants. Transactions should be\nable to have asymmetric payoffs.\n\u2022 Untraceable Defections: A peer should not be able to\ndetermine the identity of peers who have defected on her. This\nmodels the difficulty or expense of determining that a peer\ncould have provided a service, but didn\"t. For example, in the\nGnutella file sharing system [21], a peer may simply ignore\nqueries despite possessing the desired file, thus preventing\nthe querying peer from identifying the defecting peer.\n\u2022 Dynamic Population: Peers should be able to change their\nbehavior and enter or leave the system independently and\ncontinuously.\n1The exception is discussed in Section 4.1.1\n103\nCooperate\nDefect\nCooperate DefectClient\nServer\nsc RR /\nsc ST / sc PP /\nsc TS /\nFigure 2: Payoff matrix for the Generalized Prisoner\"s Dilemma. T, R,\nP, and S stand for temptation, reward, punishment and sucker,\nrespectively.\n2.3 Generalized Prisoner\"s Dilemma\nThe Prisoner\"s Dilemma, developed by Flood, Dresher, and Tucker\nin 1950 [22] is a non-cooperative repeated game satisfying the\nsocial dilemma requirement. Each game consists of two players who\ncan defect or cooperate. Depending how each acts, the players\nreceive a payoff. The players use a strategy to decide how to act.\nUnfortunately, existing work either uses a specific asymmetric payoff\nmatrix or only gives the general form for a symmetric one [4].\nInstead, we use the Generalized Prisoner\"s Dilemma (GPD), which\nspecifies the general form for an asymmetric payoff matrix that\npreserves the social dilemma. In the GPD, one player is the client and\none player is the server in each game, and it is only the decision\nof the server that is meaningful for determining the outome of the\ntransaction. A player can be a client in one game and a server in\nanother. The client and server receive the payoff from a generalized\npayoff matrix (Figure 2). Rc, Sc, Tc, and Pc are the client\"s payoff\nand Rs, Ss, Ts, and Ps are the server\"s payoff. A GPD payoff\nmatrix must have the following properties to create a social dilemma:\n1. Mutual cooperation leads to higher payoffs than mutual\ndefection (Rs + Rc > Ps + Pc).\n2. Mutual cooperation leads to higher payoffs than one player\nsuckering the other (Rs + Rc > Sc + Ts and Rs + Rc >\nSs + Tc).\n3. Defection dominates cooperation (at least weakly) at the\nindividual level for the entity who decides whether to\ncooperate or defect: (Ts \u2265 Rs and Ps \u2265 Ss and (Ts > Rs or\nPs > Ss))\nThe last set of inequalities assume that clients do not incur a cost\nregardless of whether they cooperate or defect, and therefore clients\nalways cooperate. These properties correspond to similar properties\nof the classic Prisoner\"s Dilemma and allow any form of\nasymmetric transaction while still creating a social dilemma.\nFurthermore, one or more of the four possible actions (client\ncooperate and defect, and server cooperate and defect) can be\nuntraceable. If one player makes an untraceable action, the other player\ndoes not know the identity of the first player.\nFor example, to model a P2P application like file sharing or\noverlay routing, we use the specific payoff matrix values shown in\nFigure 3. This satisfies the inequalities specified above, where only the\nserver can choose between cooperating and defecting. In addition,\nfor this particular payoff matrix, clients are unable to trace server\ndefections. This is the payoff matrix that we use in our simulation\nresults.\nRequest\nService\nDon't Request\n7 / -1\n0 / 0\n0 / 0\n0 / 0\nProvide\nService\nIgnore\nRequest\nClient\nServer\nFigure 3: The payoff matrix for an application like P2P file sharing or\noverlay routing.\n2.4 Population Dynamics\nA characteristic of P2P systems is that peers change their\nbehavior and enter or leave the system independently and continuously.\nSeveral studies [4] [28] of repeated Prisoner\"s Dilemma games use\nan evolutionary model [19] [34] of population dynamics. An\nevolutionary model is not suitable for P2P systems because it only\nspecifies the global behavior and all changes occur at discrete times.\nFor example, it may specify that a population of 5 100%\nCooperate players and 5 100% Defect players evolves into a population\nwith 3 and 7 players, respectively. It does not specify which specific\nplayers switched. Furthermore, all the switching occurs at the end\nof a generation instead of continuously, like in a real P2P system. As\na result, evolutionary population dynamics do not accurately model\nturnover, traitors, and strangers.\nIn our model, entities take independent and continuous actions that\nchange the composition of the population. Time consists of rounds.\nIn each round, every player plays one game as a client and one game\nas a server. At the end of a round, a player may: 1) mutate 2) learn,\n3) turnover, or 4) stay the same. If a player mutates, she switches to\na randomly picked strategy. If she learns, she switches to a strategy\nthat she believes will produce a higher score (described in more\ndetail below). If she maintains her identity after switching strategies,\nthen she is referred to as a traitor. If a player suffers turnover, she\nleaves the system and is replaced with a newcomer who uses the\nsame strategy as the exiting player.\nTo learn, a player collects local information about the performance\nof different strategies. This information consists of both her\npersonal observations of strategy performance and the observations of\nthose players she interacts with. This models users communicating\nout-of-band about how strategies perform. Let s be the running\naverage of the performance of a player\"s current strategy per round\nand age be the number of rounds she has been using the strategy. A\nstrategy\"s rating is\nRunningAverage(s \u2217 age)\nRunningAverage(age)\n.\nWe use the age and compute the running average before the ratio to\nprevent young samples (which are more likely to be outliers) from\nskewing the rating. At the end of a round, a player switches to\nhighest rated strategy with a probability proportional to the difference\nin score between her current strategy and the highest rated strategy.\n104\n3. RECIPROCATIVE DECISION\nFUNCTION\nIn this section, we present the new decision function, Reciprocative,\nthat is the basis for our incentive techniques. A decision function\nmaps from a history of a player\"s actions to a decision whether to\ncooperate with or defect on that player. A strategy consists of a\ndecision function, private or shared history, a server selection\nmechanism, and a stranger policy. Our approach to incentives is to\ndesign strategies which maximize both individual and social benefit.\nStrategic users will choose to use such strategies and thereby drive\nthe system to high levels of cooperation. Two examples of\nsimple decision functions are 100% Cooperate and 100% Defect.\n100% Cooperate models a naive user who does not yet realize\nthat she is being exploited. 100% Defect models a greedy user\nwho is intent on exploiting the system. In the absence of incentive\ntechniques, 100% Defect users will quickly dominate the 100%\nCooperate users and destroy cooperation in the system.\nOur requirements for a decision function are that (1) it can use\nshared and subjective history, (2) it can deal with untraceable\ndefections, and (3) it is robust against different patterns of defection.\nPrevious decision functions such as Tit-for-Tat[4] and Image[28]\n(see Section 5) do not satisfy these criteria. For example, Tit-for-Tat\nand Image base their decisions on both cooperations and defections,\ntherefore cannot deal with untraceable defections . In this section\nand the remaining sections we demonstrate how the\nReciprocativebased strategies satisfy all of the requirements stated above.\nThe probability that a Reciprocative player cooperates with a peer\nis a function of its normalized generosity. Generosity measures the\nbenefit an entity has provided relative to the benefit it has\nconsumed. This is important because entities which consume more\nservices than they provide, even if they provide many services, will\ncause cooperation to collapse. For some entity i, let pi and ci be the\nservices i has provided and consumed, respectively. Entity i\"s\ngenerosity is simply the ratio of the service it provides to the service it\nconsumes:\ng(i) = pi/ci. (1)\nOne possibility is to cooperate with a probability equal to the\ngenerosity. Although this is effective in some cases, in other cases, a\nReciprocative player may consume more than she provides (e.g.,\nwhen initially using the Stranger Defect policy in 4.3). This will\ncause Reciprocative players to defect on each other. To prevent this\nsituation, a Reciprocative player uses its own generosity as a\nmeasuring stick to judge its peer\"s generosity. Normalized generosity\nmeasures entity i\"s generosity relative to entity j\"s generosity. More\nconcretely, entity i\"s normalized generosity as perceived by entity\nj is\ngj(i) = g(i)/g(j). (2)\nIn the remainder of this section, we describe our simulation\nframework, and use it to demonstrate the benefits of the baseline\nReciprocative decision function.\nParameter Nominal value Section\nPopulation Size 100 2.4\nRun Time 1000 rounds 2.4\nPayoff Matrix File Sharing 2.3\nRatio using 100% Cooperate 1/3 3\nRatio using 100% Defect 1/3 3\nRatio using Reciprocative 1/3 3\nMutation Probability 0.0 2.4\nLearning Probability 0.05 2.4\nTurnover Probability 0.0001 2.4\nHit Rate 1.0 4.1.1\nTable 1: Default simulation parameters.\n3.1 Simulation Framework\nOur simulator implements the model described in Section 2. We use\nthe asymmetric file sharing payoff matrix (Figure 3) with\nuntraceable defections because it models transactions in many P2P\nsystems like file-sharing and packet forwarding in ad-hoc and overlay\nnetworks. Our simulation study is composed of different scenarios\nreflecting the challenges of various non-cooperative behaviors.\nTable 1 presents the nominal parameter values used in our simulation.\nThe Ratio using rows refer to the initial ratio of the total\npopulation using a particular strategy. In each scenario we vary the value\nrange of a specific parameter to reflect a particular situation or\nattack. We then vary the exact properties of the Reciprocative strategy\nto defend against that situation or attack.\n3.2 Baseline Results\n0\n20\n40\n60\n80\n100\n120\n0\n200\n400\n600\n800\n1000\nPopulation\nTime\n(a) Total Population: 60\n0\n20\n40\n60\n80\n100\n120\n0\n200\n400\n600\n800\n1000\nTime\n(b) Total Population: 120\nDefector\nCooperator\nRecip. Private\nFigure 4: The evolution of strategy populations over time. Time the\nnumber of elapsed rounds. Population is the number of players using\na strategy.\nIn this section, we present the dynamics of the game for the\nbasic scenario presented in Table 1 to familiarize the reader and set\na baseline for more complicated scenarios. Figures 4(a) (60\nplayers) and (b) (120 players) show players switching to higher\nscoring strategies over time in two separate runs of the simulator. Each\npoint in the graph represents the number of players using a\nparticular strategy at one point in time. Figures 5(a) and (b) show the\ncorresponding mean overall score per round. This measures the degree\nof cooperation in the system: 6 is the maximum possible (achieved\nwhen everybody cooperates) and 0 is the minimum (achieved when\neverybody defects). From the file sharing payoff matrix, a net of 6\nmeans everyone is able to download a file and a 0 means that no one\n105\n0\n1\n2\n3\n4\n5\n6\n0\n200\n400\n600\n800\n1000\nMeanOverallScore/Round\nTime\n(a) Total Population: 60\n0\n1\n2\n3\n4\n5\n6\n0\n200\n400\n600\n800\n1000\nTime\n(b) Total Population: 120\nFigure 5: The mean overall per round score over time.\nis able to do so. We use this metric in all later results to evaluate our\nincentive techniques.\nFigure 5(a) shows that the Reciprocative strategy using private\nhistory causes a system of 60 players to converge to a cooperation\nlevel of 3.7, but drops to 0.5 for 120 players. One would expect the\n60 player system to reach the optimal level of cooperation (6)\nbecause all the defectors are eliminated from the system. It does not\nbecause of asymmetry of interest. For example, suppose player B\nis using Reciprocative with private history. Player A may happen to\nask for service from player B twice in succession without\nproviding service to player B in the interim. Player B does not know of the\nservice player A has provided to others, so player B will reject\nservice to player A, even though player A is cooperative. We discuss\nsolutions to asymmetry of interest and the failure of Reciprocative\nin the 120 player system in Section 4.1.\n4. RECIPROCATIVE-BASED INCENTIVE\nTECHNIQUES\nIn this section we present our incentives techniques and evaluate\ntheir behavior by simulation. To make the exposition clear we group\nour techniques by the challenges they address: large populations\nand high turnover (Section 4.1), collusions (Section 4.2), zero-cost\nidentities (Section 4.3), and traitors (Section 4.4).\n4.1 Large Populations and High Turnover\nThe large populations and high turnover of P2P systems makes it\nless likely that repeat interactions will occur with a familiar entity.\nUnder these conditions, basing decisions only on private history\n(records about interactions the peer has been directly involved in)\nis not effective. In addition, private history does not deal well with\nasymmetry of interest. For example, if player B has cooperated with\nothers but not with player A himself in the past, player A has no\nindication of player B\"s generosity, thus may unduly defect on him.\nWe propose two mechanisms to alleviate the problem of few repeat\ntransactions: server-selection and shared history.\n4.1.1 Server Selection\nA natural way to increase the probability of interacting with familiar\npeers is by discriminating server selection. However, the\nasymmetry of transactions challenges selection mechanisms. Unlike in the\nprisoner\"s dilemma payoff matrix, where players can benefit one\nanother within a single transaction, transactions in GPD are\nasymmetric. As a result, a player who selects her donor for the second\ntime without contributing to her in the interim may face a defection.\nIn addition, due to untraceability of defections, it is impossible to\nmaintain blacklists to avoid interactions with known defectors.\nIn order to deal with asymmetric transactions, every player holds\n(fixed size) lists of both past donors and past recipients, and selects\na server from one of these lists at random with equal\nprobabilities. This way, users approach their past recipients and give them a\nchance to reciprocate.\nIn scenarios with selective users we omit the complete availability\nassumption to prevent players from being clustered into a lot of\nvery small groups; thus, we assume that every player can perform\nthe requested service with probability p (for the results presented in\nthis section, p = .3). In addition, in order to avoid bias in favor of\nthe selective players, all players (including the non-discriminative\nones) select servers for games.\nFigure 6 demonstrates the effectiveness of the proposed selection\nmechanism in scenarios with large population sizes. We fix the\ninitial ratio of Reciprocative in the population (33%) while varying\nthe population size (between 24 to 1000) (Notice that while in\nFigures 4(a) and (b), the data points demonstrates the evolution of the\nsystem over time, each data point in this figure is the result of an\nentire simulation for a specific scenario). The figure shows that the\nReciprocative decision function using private history in conjunction\nwith selective behavior can scale to large populations.\nIn Figure 7 we fix the population size and vary the turnover rate.\nIt demonstrates that while selective behavior is effective for low\nturnover rates, as turnover gets higher, selective behavior does not\nscale. This occurs because selection is only effective as long as\nplayers from the past stay alive for long enough such that they can\nbe selected for future games.\n4.1.2 Shared history\nIn order to mitigate asymmetry of interest and scale to higher\nturnover rate, there is a need in shared history. Shared history means\nthat every peer keeps records about all of the interactions that\noccur in the system, regardless of whether he was directly involved\nin them or not. It allows players to leverage off of the experiences\nof others in cases of few repeat transactions. It only requires that\nsomeone has interacted with a particular player for the entire\npopulation to observe it, thus scales better to large populations and high\nturnovers, and also tolerates asymmetry of interest. Some examples\nof shared history schemes are [20] [23] [28].\nFigure 7 shows the effectiveness of shared history under high\nturnover rates. In this figure, we fix the population size and vary the\nturnover rate. While selective players with private history can only\ntolerate a moderate turnover, shared history scales to turnovers of\nup to approximately 0.1. This means that 10% of the players leave\nthe system at the end of each round. In Figure 6 we fix the turnover\nand vary the population size. It shows that shared history causes\nthe system to converge to optimal cooperation and performance,\nregardless of the size of the population.\nThese results show that shared history addresses all three\nchallenges of large populations, high turnover, and asymmetry of\ntransactions. Nevertheless, shared history has two disadvantages. First,\n106\n0\n1\n2\n3\n4\n5\n6\n0\n50\n100\n150\n200\n250\n300\n350\n400\nMeanOverallScore/Round\nNumPlayers\nShared Non-Sel\nPrivate Non-Sel\nPrivate Selective\nFigure 6: Private vs. Shared History as a function of population size.\n0\n1\n2\n3\n4\n5\n6\n0.0001 0.001 0.01 0.1\nMeanOverallScore/Round\nTurnover\nShared Non-Sel\nPrivate Non-Sel\nPrivate Selective\nFigure 7: Performance of selection mechanism under turnover. The\nx-axis is the turnover rate. The y-axis is the mean overall per round\nscore.\nwhile a decentralized implementation of private history is\nstraightforward, implementation of shared-history requires communication\noverhead or centralization. A decentralized shared history can be\nimplemented, for example, on top of a DHT, using a peer-to-peer\nstorage system [36] or by disseminating information to other\nentities in a similar way to routing protocols. Second, and more\nfundamental, shared history is vulnerable to collusion. In the next section\nwe propose a mechanism that addresses this problem.\n4.2 Collusion and Other Shared History\nAttacks\n4.2.1 Collusion\nWhile shared history is scalable, it is vulnerable to collusion.\nCollusion can be either positive (e.g. defecting entities claim that other\ndefecting entities cooperated with them) or negative (e.g. entities\nclaim that other cooperative entities defected on them). Collusion\nsubverts any strategy in which everyone in the system agrees on the\nreputation of a player (objective reputation). An example of\nobjective reputation is to use the Reciprocative decision function with\nshared history to count the total number of cooperations a player\nhas given to and received from all entities in the system; another\nexample is the Image strategy [28]. The effect of collusion is\nmagnified in systems with zero-cost identities, where users can create\nfake identities that report false statements.\nInstead, to deal with collusion, entities can compute reputation\nsubjectively, where player A weighs player B\"s opinions based on how\nmuch player A trusts player B. Our subjective algorithm is based\non maxflow [24] [32]. Maxflow is a graph theoretic problem, which\ngiven a directed graph with weighted edges asks what is the greatest\nrate at which material can be shipped from the source to the target\nwithout violating any capacity constraints. For example, in figure 8\neach edge is labeled with the amount of traffic that can travel on it.\nThe maxflow algorithm computes the maximum amount of traffic\nthat can go from the source (s) to the target (t) without violating the\nconstraints. In this example, even though there is a loop of high\ncapacity edges, the maxflow between the source and the target is only\n2 (the numbers in brackets represent the actual flow on each edge\nin the solution).\n100(0)\n1(1)\n5(1)\ns t\n10(1)\n100(1)\n1(1)\n100(1)\n20(0)\nFigure 8: Each edge in the graph is labeled with its capacity and the\nactual flow it carries in brackets. The maxflow between the source and\nthe target in the graph is 2.\nC\nC\nCCCC\n100100100100\n100\n00\n0\n0\n20\n20\n0\n0\nA\nB\nFigure 9: This graph illustrates the robustness of maxflow in the\npresence of colluders who report bogus high reputation values.\nWe apply the maxflow algorithm by constructing a graph whose\nvertices are entities and the edges are the services that entities have\nreceived from each other. This information can be stored using the\nsame methods as the shared history. A maxflow is the greatest level\nof reputation the source can give to the sink without violating\nreputation capacity constraints. As a result, nodes who dishonestly\nreport high reputation values will not be able to subvert the\nreputation system.\nFigure 9 illustrates a scenario in which all the colluders (labeled\nwith C) report high reputation values for each other. When node A\ncomputes the subjective reputation of B using the maxflow\nalgorithm, it will not be affected by the local false reputation values,\nrather the maxflow in this case will be 0. This is because no service\nhas been received from any of the colluders.\n107\nIn our algorithm, the benefit that entity i has received (indirectly)\nfrom entity j is the maxflow from j to i. Conversely, the benefit that\nentity i has provided indirectly to j is the maxflow from i to j. The\nsubjective reputation of entity j as perceived by i is:\nmin\nmaxflow(j to i)\nmaxflow(i to j)\n, 1 (3)\n0\n1\n2\n3\n4\n5\n6\n0\n100\n200\n300\n400\n500\n600\n700\n800\n900\n1000\nMeanOverallScore/Round\nPopulation\nShared\nPrivate\nSubjective\nFigure 10: Subjective shared history compared to objective shared\nhistory and private history in the presence of colluders.\nAlgorithm 1 CONSTANTTIMEMAXFLOW Bound the mean running time\nof Maxflow to a constant.\nmethod CTMaxflow(self, src, dst)\n1: self.surplus \u2190 self.surplus + self.increment\n{Use the running mean as a prediction.}\n2: if random() > (0.5\u2217self.surplus/self.mean iterations) then\n3: return None {Not enough surplus to run.}\n4: end if\n{Get the flow and number of iterations used from the maxflow alg.}\n5: flow, iterations \u2190 Maxflow(self.G, src, dst)\n6: self.surplus \u2190 self.surplus \u2212 iterations\n{Keep a running mean of the number of iterations used.}\n7: self.mean iterations \u2190 self.\u03b1 \u2217 self.mean iterations + (1 \u2212\nself.\u03b1) \u2217 iterations\n8: return flow\nThe cost of maxflow is its long running time. The standard\npreflowpush maxflow algorithm has a worst case running time of O(V 3\n).\nInstead, we use Algorithm 1 which has a constant mean running\ntime, but sometimes returns no flow even though one exists. The\nessential idea is to bound the mean number of nodes examined\nduring the maxflow computation. This bounds the overhead, but also\nbounds the effectiveness. Despite this, the results below show that\na maxflow-based Reciprocative decision function scales to higher\npopulations than one using private history.\nFigure 10 compares the effectiveness of subjective reputation to\nobjective reputation in the presence of colluders. In these\nscenarios, defectors collude by claiming that other colluders that they\nencounter gave them 100 cooperations for that encounter. Also, the\nparameters for Algorithm 1 are set as follows: increment = 100,\n\u03b1 = 0.9.\nAs in previous sections, Reciprocative with private history results\nin cooperation up to a point, beyond which it fails. The difference\nhere is that objective shared history fails for all population sizes.\nThis is because the Reciprocative players cooperate with the\ncolluders because of their high reputations. However, subjective\nhistory can reach high levels of cooperation regardless of colluders.\nThis is because there are no high weight paths in the cooperation\ngraph from colluders to any non-colluders, so the maxflow from\na colluder to any non-colluder is 0. Therefore, a subjective\nReciprocative player will conclude that that colluder has not provided\nany service to her and will reject service to the colluder. Thus, the\nmaxflow algorithm enables Reciprocative to maintain the\nscalability of shared history without being vulnerable to collusion or\nrequiring centralized trust (e.g., trusted peers). Since we bound the\nrunning time of the maxflow algorithm, cooperation decreases as\nthe population size increases, but the key point is that the subjective\nReciprocative decision function scales to higher populations than\none using private history. This advantage only increases over time\nas CPU power increases and more cycles can be devoted to running\nthe maxflow algorithm (by increasing the increment parameter).\nDespite the robustness of the maxflow algorithm to the simple form\nof collusion described previously, it still has vulnerabilities to more\nsophisticated attacks. One is for an entity (the mole) to provide\nservice and then lie positively about other colluders. The other\ncolluders can then exploit their reputation to receive service. However,\nthe effectiveness of this attack relies on the amount of service that\nthe mole provides. Since the mole is paying all of the cost of\nproviding service and receiving none of the benefit, she has a strong\nincentive to stop colluding and try another strategy. This forces the\ncolluders to use mechanisms to maintain cooperation within their\ngroup, which may drive the cost of collusion to exceed the benefit.\n4.2.2 False reports\nAnother attack is for a defector to lie about receiving or providing\nservice to another entity. There are four possibile actions that can be\nlied about: providing service, not providing service, receiving\nservice, and not receiving service. Falsely claiming to receive service\nis the simple collusion attack described above. Falsely claiming not\nto have provided service provides no benefit to the attacker.\nFalsely claiming to have provided service or not to have received\nit allows an attacker to boost her own reputation and/or lower the\nreputation of another entity. An entity may want to lower another\nentity\"s reputation in order to discourage others from selecting it\nand exclusively use its service. These false claims are clearly\nidentifiable in the shared history as inconsistencies where one entity\nclaims a transaction occurred and another claims it did not. To limit\nthis attack, we modify the maxflow algorithm so that an entity\nalways believes the entity that is closer to him in the flow graph. If\nboth entities are equally distant, then the disputed edge in the flow is\nnot critical to the evaluation and is ignored. This modification\nprevents those cases where the attacker is making false claims about an\nentity that is closer than her to the evaluating entity, which prevents\nher from boosting her own reputation. The remaining possibilities\nare for the attacker to falsely claim to have provided service to or\nnot to have received it from a victim entity that is farther from the\nevalulator than her. In these cases, an attacker can only lower the\nreputation of the victim. The effectiveness of doing this is limited\nby the number of services provided and received by the attacker,\nwhich makes executing this attack expensive.\n108\n4.3 Zero-Cost Identities\nHistory assumes that entities maintain persistent identities.\nHowever, in most P2P systems, identities are zero-cost. This is desirable\nfor network growth as it encourages newcomers to join the system.\nHowever, this also allows misbehaving users to escape the\nconsequences of their actions by switching to new identities (i.e.,\nwhitewashing). Whitewashers can cause the system to collapse if they\nare not punished appropriately. Unfortunately, a player cannot tell\nif a stranger is a whitewasher or a legitimate newcomer. Always\ncooperating with strangers encourages newcomers to join, but at the\nsame time encourages whitewashing behavior. Always defecting on\nstrangers prevents whitewashing, but discourages newcomers from\njoining and may also initiate unfavorable cycles of defection.\nThis tension suggests that any stranger policy that has a fixed\nprobability of cooperating with strangers will fail by either being too\nstingy when most strangers are newcomers or too generous when\nmost strangers are whitewashers. Our solution is the Stranger\nAdaptive stranger policy. The idea is to be generous to strangers\nwhen they are being generous and stingy when they are stingy.\nLet ps and cs be the number of services that strangers have\nprovided and consumed, respectively. The probability that a player\nusing Stranger Adaptive helps a stranger is ps/cs. However, we do\nnot wish to keep these counts permanently (for reasons described in\nSection 4.4). Also, players may not know when strangers defect\nbecause defections are untraceable (as described in Section 2).\nConsequently, instead of keeping ps and cs, we assume that k = ps + cs,\nwhere k is a constant and we keep the running ratio r = ps/cs.\nWhen we need to increment ps or cs, we generate the current\nvalues of ps and cs from k and r:\ncs = k/(1 + r)\nps = cs \u2217 r\nWe then compute the new r as follows:\nr = (ps + 1)/cs , if the stranger provided service\nr = ps/(cs + 1) , if the stranger consumed service\nThis method allows us to keep a running ratio that reflects the\nrecent generosity of strangers without knowing when strangers have\ndefected.\n0\n1\n2\n3\n4\n5\n6\n0.0001 0.001 0.01 0.1 1\nMeanOverallScore/Round\nTurnover\nStranger Cooperate\nStranger Defect\nStranger Adaptive\nFigure 11: Different stranger policies for Reciprocative with shared\nhistory. The x-axis is the turnover rate on a log scale. The y-axis is the\nmean overall per round score.\nFigures 11 and 12 compare the effectiveness of the\nReciprocative strategy using different policies toward strangers. Figure 11\n0\n1\n2\n3\n4\n5\n6\n0.0001 0.001 0.01 0.1 1\nMeanOverallScore/Round\nTurnover\nStranger Cooperate\nStranger Defect\nStranger Adaptive\nFigure 12: Different stranger policies for Reciprocative with private\nhistory. The x-axis is the turnover rate on a log scale. The y-axis is the\nmean overall per round score.\ncompares different stranger policies for Reciprocative with shared\nhistory, while Figure 12 is with private history. In both figures,\nthe players using the 100% Defect strategy change their\nidentity (whitewash) after every transaction and are indistinguishable\nfrom legitimate newcomers. The Reciprocative players using the\nStranger Cooperate policy completely fail to achieve cooperation.\nThis stranger policy allows whitewashers to maximize their payoff\nand consequently provides a high incentive for users to switch to\nwhitewashing.\nIn contrast, Figure 11 shows that the Stranger Defect policy is\neffective with shared history. This is because whitewashers always\nappear to be strangers and therefore the Reciprocative players will\nalways defect on them. This is consistent with previous work [13]\nshowing that punishing strangers deals with whitewashers.\nHowever, Figure 12 shows that Stranger Defect is not effective with\nprivate history. This is because Reciprocative requires some initial\ncooperation to bootstrap. In the shared history case, a Reciprocative\nplayer can observe that another player has already cooperated with\nothers. With private history, the Reciprocative player only knows\nabout the other players\" actions toward her. Therefore, the initial\ndefection dictated by the Stranger Defect policy will lead to later\ndefections, which will prevent Reciprocative players from ever\ncooperating with each other. In other simulations not shown here,\nthe Stranger Defect stranger policy fails even with shared history\nwhen there are no initial 100% Cooperate players.\nFigure 11 shows that with shared history, the Stranger\nAdaptive policy performs as well as Stranger Defect policy until the\nturnover rate is very high (10% of the population turning over after\nevery transaction). In these scenarios, Stranger Adaptive is using\nk = 10 and each player keeps a private r. More importantly, it is\nsignificantly better than Stranger Defect policy with private\nhistory because it can bootstrap cooperation. Although the Stranger\nDefect policy is marginally more effective than Stranger\nAdaptive at very high rates of turnover, P2P systems are unlikely to\noperate there because other services (e.g., routing) also cannot tolerate\nvery high turnover.\nWe conclude that of the stranger policies that we have explored,\nStranger Adaptive is the most effective. By using Stranger\nAdaptive, P2P systems with zero-cost identities and a sufficiently\nlow turnover can sustain cooperation without a centralized\nallocation of identities.\n109\n4.4 Traitors\nTraitors are players who acquire high reputation scores by\ncooperating for a while, and then traitorously turn into defectors before\nleaving the system. They model both users who turn deliberately\nto gain a higher score and cooperators whose identities have been\nstolen and exploited by defectors. A strategy that maintains\nlongterm history without discriminating between old and recent actions\nbecomes highly vulnerable to exploitation by these traitors.\nThe top two graphs in Figure 13 demonstrate the effect of traitors\non cooperation in a system where players keep long-term history\n(never clear history). In these simulations, we run for 2000 rounds\nand allow cooperative players to keep their identities when\nswitching to the 100% Defector strategy. We use the default values for the\nother parameters. Without traitors, the cooperative strategies thrive.\nWith traitors, the cooperative strategies thrive until a cooperator\nturns traitor after 600 rounds. As this cooperator exploits her\nreputation to achieve a high score, other cooperative players notice this\nand follow suit via learning. Cooperation eventually collapses. On\nthe other hand, if we maintain short-term history and/or\ndiscounting ancient history vis-a-vis recent history, traitors can be quickly\ndetected, and the overall cooperation level stays high, as shown in\nthe bottom two graphs in Figure 13.\n0\n20\n40\n60\n80\n100\n1K 2K\nLong-TermHistory\nNo Traitors\nPopulation\n0\n20\n40\n60\n80\n100\n1K 2K\nTraitors\nDefector\nCooperator\nRecip. Shared\n0\n20\n40\n60\n80\n100\n1K 2K\nShort-TermHistory\nTime\nPopulation\n0\n20\n40\n60\n80\n100\n1K 2K\nTime\nFigure 13: Keeping long-term vs. short-term history both with and\nwithout traitors.\n5. RELATED WORK\nPrevious work has examined the incentive problem as applied to\nsocieties in general and more recently to Internet applications and\npeer-to-peer systems in particular. A well-known phenomenon in\nthis context is the tragedy of the commons [18] where resources\nare under-provisioned due to selfish users who free-ride on the\nsystem\"s resources, and is especially common in large networks [29]\n[3].\nThe problem has been extensively studied adopting a game\ntheoretic approach. The prisoners\" dilemma model provides a\nnatural framework to study the effectiveness of different strategies in\nestablishing cooperation among players. In a simulation\nenvironment with many repeated games, persistent identities, and no\ncollusion, Axelrod [4] shows that the Tit-for-Tat strategy dominates.\nOur model assumes growth follows local learning rather than\nevolutionary dynamics [14], and also allows for more kinds of attacks.\nNowak and Sigmund [28] introduce the Image strategy and\ndemonstrate its ability to establish cooperation among players despite few\nrepeat transactions by the employment of shared history. Players\nusing Image cooperate with players whose global count of\ncooperations minus defections exceeds some threshold. As a result, an\nImage player is either vulnerable to partial defectors (if the\nthreshold is set too low) or does not cooperate with other Image players\n(if the threshold is set too high).\nIn recent years, researchers have used economic mechanism\ndesign theory to tackle the cooperation problem in Internet\napplications. Mechanism design is the inverse of game theory. It asks how\nto design a game in which the behavior of strategic players results\nin the socially desired outcome. Distributed Algorithmic\nMechanism Design seeks solutions within this framework that are both\nfully distributed and computationally tractable [12]. [10] and [11]\nare examples of applying DAMD to BGP routing and multicast cost\nsharing. More recently, DAMD has been also studied in dynamic\nenvironments [38]. In this context, demonstrating the superiority of\na cooperative strategy (as in the case of our work) is consistent with\nthe objective of incentivizing the desired behavior among selfish\nplayers.\nThe unique challenges imposed by peer-to-peer systems inspired\nadditional body of work [5] [37], mainly in the context of packet\nforwarding in wireless ad-hoc routing [8] [27] [30] [35], and file\nsharing [15] [31]. Friedman and Resnick [13] consider the\nproblem of zero-cost identities in online environments and find that in\nsuch systems punishing all newcomers is inevitable. Using a\ntheoretical model, they demonstrate that such a system can converge to\ncooperation only for sufficiently low turnover rates, which our\nresults confirm. [6] and [9] show that whitewashing and collusion can\nhave dire consequences for peer-to-peer systems and are difficult to\nprevent in a fully decentralized system.\nSome commercial file sharing clients [1] [2] provide incentive\nmechanisms which are enforced by making it difficult for the user\nto modify the source code. These mechanisms can be circumvented\nby a skilled user or by a competing company releasing a compatible\nclient without the incentive restrictions. Also, these mechanisms are\nstill vulnerable to zero-cost identities and collusion. BitTorrent [7]\nuses Tit-for-Tat as a method for resource allocation, where a user\"s\nupload rate dictates his download rate.\n6. CONCLUSIONS\nIn this paper we take a game theoretic approach to the\nproblem of cooperation in peer-to-peer networks. Addressing the\nchallenges imposed by P2P systems, including large populations, high\nturnover, asymmetry of interest and zero-cost identities, we propose\na family of scalable and robust incentive techniques, based upon\nthe Reciprocative decision function, to support cooperative\nbehavior and improve overall system performance.\nWe find that the adoption of shared history and discriminating\nserver selection techniques can mitigate the challenge of few repeat\ntransactions that arises due to large population size, high turnover\nand asymmetry of interest. Furthermore, cooperation can be\nestablished even in the presence of zero-cost identities through the use of\nan adaptive policy towards strangers. Finally, colluders and traitors\ncan be kept in check via subjective reputations and short-term\nhistory, respectively.\n110\n7. ACKNOWLEDGMENTS\nWe thank Mary Baker, T.J. Giuli, Petros Maniatis, the\nanonymous reviewer, and our shepherd, Margo Seltzer, for their useful\ncomments that helped improve the paper. This work is supported\nin part by the National Science Foundation under ITR awards\nANI-0085879 and ANI-0331659, and Career award ANI-0133811.\nViews and conclusions contained in this document are those of the\nauthors and should not be interpreted as representing the official\npolicies, either expressed or implied, of NSF, or the U.S.\ngovernment.\n8. REFERENCES\n[1] Kazaa. http://www.kazaa.com.\n[2] Limewire. http://www.limewire.com.\n[3] ADAR, E., AND HUBERMAN, B. A. Free Riding on Gnutella. First\nMonday 5, 10 (October 2000).\n[4] AXELROD, R. The Evolution of Cooperation. Basic Books, 1984.\n[5] BURAGOHAIN, C., AGRAWAL, D., AND SURI, S. A\nGame-Theoretic Framework for Incentives in P2P Systems. In\nInternational Conference on Peer-to-Peer Computing (Sep 2003).\n[6] CASTRO, M., DRUSCHEL, P., GANESH, A., ROWSTRON, A., AND\nWALLACH, D. S. Security for Structured Peer-to-Peer Overlay\nNetworks. In Proceedings of Multimedia Computing and Networking\n2002 (MMCN \"02) (2002).\n[7] COHEN, B. Incentives build robustness in bittorrent. In 1st Workshop\non Economics of Peer-to-Peer Systems (2003).\n[8] CROWCROFT, J., GIBBENS, R., KELLY, F., AND \u02d8 OSTRING, S.\nModeling Incentives for Collaboration in Mobile ad-hoc Networks.\nIn Modeling and Optimization in Mobile, ad-hoc and Wireless\nNetworks (2003).\n[9] DOUCEUR, J. R. The Sybil Attack. In Electronic Proceedings of the\nInternational Workshop on Peer-to-Peer Systems (2002).\n[10] FEIGENBAUM, J., PAPADIMITRIOU, C., SAMI, R., AND SHENKER,\nS. A BGP-based Mechanism for Lowest-Cost Routing. In\nProceedings of the ACM Symposium on Principles of Distributed\nComputing (2002).\n[11] FEIGENBAUM, J., PAPADIMITRIOU, C., AND SHENKER, S. Sharing\nthe Cost of Multicast Transmissions. 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Are Contributions to P2P Technical\nForums Private or Public Goods? - An Empirical Investigation. In 1st\nWorkshop on Economics of Peer-to-Peer Systems (2003).\n[18] HARDIN, G. The Tragedy of the Commons. Science 162 (1968),\n1243-1248.\n[19] JOSEF HOFBAUER AND KARL SIGMUND. Evolutionary Games and\nPopulation Dynamics. Cambridge University Press, 1998.\n[20] KAMVAR, S. D., SCHLOSSER, M. T., AND GARCIA-MOLINA, H.\nThe EigenTrust Algorithm for Reputation Management in P2P\nNetworks. In Proceedings of the Twelfth International World Wide\nWeb Conference (May 2003).\n[21] KAN, G. Peer-to-Peer: Harnessing the Power of Disruptive\nTechnologies, 1st ed. O\"Reilly & Associates, Inc., March 2001,\nch. Gnutella, pp. 94-122.\n[22] KUHN, S. Prisoner\"s Dilemma. In The Stanford Encyclopedia of\nPhilosophy, Edward N. Zalta, Ed., Summer ed. 2003.\n[23] LEE, S., SHERWOOD, R., AND BHATTACHARJEE, B. Cooperative\nPeer Groups in Nice. In Proceedings of the IEEE INFOCOM (2003).\n[24] LEVIEN, R., AND AIKEN, A. Attack-Resistant Trust Metrics for\nPublic Key Certification. In Proceedings of the USENIX Security\nSymposium (1998), pp. 229-242.\n[25] MANIATIS, P., ROUSSOPOULOS, M., GIULI, T. J., ROSENTHAL,\nD. S. H., BAKER, M., AND MULIADI, Y. Preserving Peer Replicas\nby Rate-Limited Sampled Voting. In ACM Symposium on Operating\nSystems Principles (2003).\n[26] MARTI, S., GIULI, T. J., LAI, K., AND BAKER, M. Mitigating\nRouting Misbehavior in Mobile ad-hoc Networks. In Proceedings of\nMobiCom (2000), pp. 255-265.\n[27] MICHIARDI, P., AND MOLVA, R. A Game Theoretical Approach to\nEvaluate Cooperation Enforcement Mechanisms in Mobile ad-hoc\nNetworks. In Modeling and Optimization in Mobile, ad-hoc and\nWireless Networks (2003).\n[28] NOWAK, M. A., AND SIGMUND, K. Evolution of Indirect\nReciprocity by Image Scoring. Nature 393 (1998), 573-577.\n[29] OLSON, M. The Logic of Collective Action: Public Goods and the\nTheory of Groups. Harvard University Press, 1971.\n[30] RAGHAVAN, B., AND SNOEREN, A. Priority Forwarding in ad-hoc\nNetworks with Self-Ineterested Parties. In Workshop on Economics of\nPeer-to-Peer Systems (June 2003).\n[31] RANGANATHAN, K., RIPEANU, M., SARIN, A., AND FOSTER, I.\nTo Share or Not to Share: An Analysis of Incentives to Contribute in\nCollaborative File Sharing Environments. In Workshop on Economics\nof Peer-to-Peer Systems (June 2003).\n[32] REITER, M. K., AND STUBBLEBINE, S. G. Authentication Metric\nAnalysis and Design. ACM Transactions on Information and System\nSecurity 2, 2 (1999), 138-158.\n[33] SAROIU, S., GUMMADI, P. K., AND GRIBBLE, S. D. A\nMeasurement Study of Peer-to-Peer File Sharing Systems. In\nProceedings of Multimedia Computing and Networking 2002\n(MMCN \"02) (2002).\n[34] SMITH, J. M. Evolution and the Theory of Games. Cambridge\nUniversity Press, 1982.\n[35] URPI, A., BONUCCELLI, M., AND GIORDANO, S. Modeling\nCooperation in Mobile ad-hoc Networks: a Formal Description of\nSelfishness. In Modeling and Optimization in Mobile, ad-hoc and\nWireless Networks (2003).\n[36] VISHNUMURTHY, V., CHANDRAKUMAR, S., AND SIRER, E. G.\nKARMA : A Secure Economic Framework for P2P Resource\nSharing. In Workshop on Economics of Peer-to-Peer Networks (2003).\n[37] WANG, W., AND LI, B. To Play or to Control: A Game-based\nControl-Theoretic Approach to Peer-to-Peer Incentive Engineering.\nIn International Workshop on Quality of Service (June 2003).\n[38] WOODARD, C. J., AND PARKES, D. C. Strategyproof mechanisms\nfor ad-hoc network formation. In Workshop on Economics of\nPeer-to-Peer Systems (June 2003).\n111", "keywords": "generosity;prisoner dilemma;p2p system;reputation;free-ride;selfinterested user;peer-to-peer;maxflow-based algorithm;stranger adaptive;cheap pseudonym;game-theoretic approach;reciprocative peer;mutual cooperation;parameter nominal value;adaptive stranger policy;incentive for cooperation;collusion;whitewasher;reciprocative decision function;stranger defect;asymmetric payoff;whitewash;incentive"}
{"name": "train_J-70", "title": "Self-interested Automated Mechanism Design and Implications for Optimal Combinatorial Auctions\u2217", "abstract": "Often, an outcome must be chosen on the basis of the preferences reported by a group of agents. The key difficulty is that the agents may report their preferences insincerely to make the chosen outcome more favorable to themselves. Mechanism design is the art of designing the rules of the game so that the agents are motivated to report their preferences truthfully, and a desirable outcome is chosen. In a recently proposed approach-called automated mechanism design-a mechanism is computed for the preference aggregation setting at hand. This has several advantages, but the downside is that the mechanism design optimization problem needs to be solved anew each time. Unlike the earlier work on automated mechanism design that studied a benevolent designer, in this paper we study automated mechanism design problems where the designer is self-interested. In this case, the center cares only about which outcome is chosen and what payments are made to it. The reason that the agents\" preferences are relevant is that the center is constrained to making each agent at least as well off as the agent would have been had it not participated in the mechanism. In this setting, we show that designing optimal deterministic mechanisms is NP-complete in two important special cases: when the center is interested only in the payments made to it, and when payments are not possible and the center is interested only in the outcome chosen. We then show how allowing for randomization in the mechanism makes problems in this setting computationally easy. Finally, we show that the payment-maximizing AMD problem is closely related to an interesting variant of the optimal (revenuemaximizing) combinatorial auction design problem, where the bidders have best-only preferences. We show that here, too, designing an optimal deterministic auction is NPcomplete, but designing an optimal randomized auction is easy.", "fulltext": "1. INTRODUCTION\nIn multiagent settings, often an outcome must be\nchosen on the basis of the preferences reported by a group of\nagents. Such outcomes could be potential presidents, joint\nplans, allocations of goods or resources, etc. The preference\naggregator generally does not know the agents\" preferences\na priori. Rather, the agents report their preferences to the\ncoordinator. Unfortunately, an agent may have an incentive\nto misreport its preferences in order to mislead the\nmechanism into selecting an outcome that is more desirable to\nthe agent than the outcome that would be selected if the\nagent revealed its preferences truthfully. Such manipulation\nis undesirable because preference aggregation mechanisms\nare tailored to aggregate preferences in a socially desirable\nway, and if the agents reveal their preferences insincerely, a\nsocially undesirable outcome may be chosen.\nManipulability is a pervasive problem across preference\naggregation mechanisms. A seminal negative result, the\nGibbard-Satterthwaite theorem, shows that under any\nnondictatorial preference aggregation scheme, if there are at\nleast 3 possible outcomes, there are preferences under which\nan agent is better off reporting untruthfully [10, 23]. (A\npreference aggregation scheme is called dictatorial if one of\nthe agents dictates the outcome no matter what preferences\nthe other agents report.)\nWhat the aggregator would like to do is design a\npreference aggregation mechanism so that 1) the self-interested\nagents are motivated to report their preferences truthfully,\nand 2) the mechanism chooses an outcome that is desirable\nfrom the perspective of some objective. This is the classic\nsetting of mechanism design in game theory. In this paper,\nwe study the case where the designer is self-interested, that\nis, the designer does not directly care about how the\nout132\ncome relates to the agents\" preferences, but is rather\nconcerned with its own agenda for which outcome should be\nchosen, and with maximizing payments to itself. This is the\nmechanism design setting most relevant to electronic\ncommerce.\nIn the case where the mechanism designer is interested in\nmaximizing some notion of social welfare, the importance\nof collecting the agents\" preferences is clear. It is perhaps\nless obvious why they should be collected when the designer\nis self-interested and hence its objective is not directly\nrelated to the agents\" preferences. The reason for this is that\noften the agents\" preferences impose limits on how the\ndesigner chooses the outcome and payments. The most\ncommon such constraint is that of individual rationality (IR),\nwhich means that the mechanism cannot make any agent\nworse off than the agent would have been had it not\nparticipated in the mechanism. For instance, in the setting\nof optimal auction design, the designer (auctioneer) is only\nconcerned with how much revenue is collected, and not per\nse with how well the allocation of the good (or goods)\ncorresponds to the agents\" preferences. Nevertheless, the\ndesigner cannot force an agent to pay more than its valuation\nfor the bundle of goods allocated to it. Therefore, even a\nself-interested designer will choose an outcome that makes\nthe agents reasonably well off. On the other hand, the\ndesigner will not necessarily choose a social welfare\nmaximizing outcome. For example, if the designer always chooses\nan outcome that maximizes social welfare with respect to\nthe reported preferences, and forces each agent to pay the\ndifference between the utility it has now and the utility it\nwould have had if it had not participated in the mechanism,\nit is easy to see that agents may have an incentive to\nmisreport their preferences-and this may actually lead to less\nrevenue being collected. Indeed, one of the counterintuitive\nresults of optimal auction design theory is that sometimes\nthe good is allocated to nobody even when the auctioneer\nhas a reservation price of 0.\nClassical mechanism design provides some general\nmechanisms, which, under certain assumptions, satisfy some\nnotion of nonmanipulability and maximize some objective. The\nupside of these mechanisms is that they do not rely on\n(even probabilistic) information about the agents\"\npreferences (e.g., the Vickrey-Clarke-Groves (VCG) mechanism [24,\n4, 11]), or they can be easily applied to any probability\ndistribution over the preferences (e.g., the dAGVA\nmechanism [8, 2], the Myerson auction [18], and the Maskin-Riley\nmulti-unit auction [17]). However, the general mechanisms\nalso have significant downsides:\n\u2022 The most famous and most broadly applicable general\nmechanisms, VCG and dAGVA, only maximize social\nwelfare. If the designer is self-interested, as is the case\nin many electronic commerce settings, these\nmechanisms do not maximize the designer\"s objective.\n\u2022 The general mechanisms that do focus on a\nselfinterested designer are only applicable in very restricted\nsettings-such as Myerson\"s expected revenue\nmaximizing auction for selling a single item, and Maskin\nand Riley\"s expected revenue maximizing auction for\nselling multiple identical units of an item.\n\u2022 Even in the restricted settings in which these\nmechanisms apply, the mechanisms only allow for payment\nmaximization. In practice, the designer may also be\ninterested in the outcome per se. For example, an\nauctioneer may care which bidder receives the item.\n\u2022 It is often assumed that side payments can be used\nto tailor the agents\" incentives, but this is not always\npractical. For example, in barter-based electronic\nmarketplaces-such as Recipco, firstbarter.com,\nBarterOne, and Intagio-side payments are not\nallowed. Furthermore, among software agents, it might\nbe more desirable to construct mechanisms that do not\nrely on the ability to make payments, because many\nsoftware agents do not have the infrastructure to make\npayments.\nIn contrast, we follow a recent approach where the\nmechanism is designed automatically for the specific problem at\nhand. This approach addresses all of the downsides listed\nabove. We formulate the mechanism design problem as an\noptimization problem. The input is characterized by the\nnumber of agents, the agents\" possible types (preferences),\nand the aggregator\"s prior distributions over the agents\"\ntypes. The output is a nonmanipulable mechanism that is\noptimal with respect to some objective. This approach is\ncalled automated mechanism design.\nThe automated mechanism design approach has four\nadvantages over the classical approach of designing general\nmechanisms. First, it can be used even in settings that\ndo not satisfy the assumptions of the classical mechanisms\n(such as availability of side payments or that the objective\nis social welfare). Second, it may allow one to circumvent\nimpossibility results (such as the Gibbard-Satterthwaite\ntheorem) which state that there is no mechanism that is\ndesirable across all preferences. When the mechanism is designed\nfor the setting at hand, it does not matter that it would\nnot work more generally. Third, it may yield better\nmechanisms (in terms of stronger nonmanipulability guarantees\nand/or better outcomes) than classical mechanisms because\nthe mechanism capitalizes on the particulars of the setting\n(the probabilistic information that the designer has about\nthe agents\" types). Given the vast amount of information\nthat parties have about each other today, this approach is\nlikely to lead to tremendous savings over classical\nmechanisms, which largely ignore that information. For example,\nimagine a company automatically creating its procurement\nmechanism based on statistical knowledge about its\nsuppliers, rather than using a classical descending procurement\nauction. Fourth, the burden of design is shifted from\nhumans to a machine.\nHowever, automated mechanism design requires the\nmechanism design optimization problem to be solved anew for\neach setting. Hence its computational complexity becomes\na key issue. Previous research has studied this question for\nbenevolent designers-that wish to maximize, for example,\nsocial welfare [5, 6]. In this paper we study the\ncomputational complexity of automated mechanism design in the\ncase of a self-interested designer. This is an important\nsetting for automated mechanism design due to the shortage\nof general mechanisms in this area, and the fact that in\nmost e-commerce settings the designer is self-interested. We\nalso show that this problem is closely related to a particular\noptimal (revenue-maximizing) combinatorial auction design\nproblem.\n133\nThe rest of this paper is organized as follows. In\nSection 2, we justify the focus on nonmanipulable mechanisms.\nIn Section 3, we define the problem we study. In Section 4,\nwe show that designing an optimal deterministic mechanism\nis NP-complete even when the designer only cares about the\npayments made to it. In Section 5, we show that designing\nan optimal deterministic mechanism is also NP-complete\nwhen payments are not possible and the designer is only\ninterested in the outcome chosen. In Section 6, we show that\nan optimal randomized mechanism can be designed in\npolynomial time even in the general case. Finally, in Section 7,\nwe show that for designing optimal combinatorial auctions\nunder best-only preferences, our results on AMD imply that\nthis problem is NP-complete for deterministic auctions, but\neasy for randomized auctions.\n2. JUSTIFYING THE FOCUS ON\nNONMANIPULABLE MECHANISMS\nBefore we define the computational problem of automated\nmechanism design, we should justify our focus on\nnonmanipulable mechanisms. After all, it is not immediately\nobvious that there are no manipulable mechanisms that, even\nwhen agents report their types strategically and hence\nsometimes untruthfully, still reach better outcomes (according to\nwhatever objective we use) than any nonmanipulable\nmechanism. This does, however, turn out to be the case: given\nany mechanism, we can construct a nonmanipulable\nmechanism whose performance is identical, as follows. We build\nan interface layer between the agents and the original\nmechanism. The agents report their preferences (or types) to\nthe interface layer; subsequently, the interface layer inputs\ninto the original mechanism the types that the agents would\nhave strategically reported to the original mechanism, if their\ntypes were as declared to the interface layer. The resulting\noutcome is the outcome of the new mechanism. Since the\ninterface layer acts strategically on each agent\"s behalf,\nthere is never an incentive to report falsely to the interface\nlayer; and hence, the types reported by the interface layer\nare the strategic types that would have been reported\nwithout the interface layer, so the results are exactly as they\nwould have been with the original mechanism. This\nargument is known in the mechanism design literature as the\nrevelation principle [16]. (There are computational difficulties\nwith applying the revelation principle in large combinatorial\noutcome and type spaces [7, 22]. However, because here we\nfocus on flatly represented outcome and type spaces, this is\nnot a concern here.) Given this, we can focus on truthful\nmechanisms in the rest of the paper.\n3. DEFINITIONS\nWe now formalize the automated mechanism design\nsetting.\nDefinition 1. In an automated mechanism design\nsetting, we are given:\n\u2022 a finite set of outcomes O;\n\u2022 a finite set of N agents;\n\u2022 for each agent i,\n1. a finite set of types \u0398i,\n2. a probability distribution \u03b3i over \u0398i (in the case of\ncorrelated types, there is a single joint distribution\n\u03b3 over \u03981 \u00d7 . . . \u00d7 \u0398N ), and\n3. a utility function ui : \u0398i \u00d7 O \u2192 R; 1\n\u2022 An objective function whose expectation the designer\nwishes to maximize.\nThere are many possible objective functions the designer\nmight have, for example, social welfare (where the designer\nseeks to maximize the sum of the agents\" utilities), or the\nminimum utility of any agent (where the designer seeks to\nmaximize the worst utility had by any agent). In both\nof these cases, the designer is benevolent, because the\ndesigner, in some sense, is pursuing the agents\" collective\nhappiness. However, in this paper, we focus on the case of\na self-interested designer. A self-interested designer cares\nonly about the outcome chosen (that is, the designer does\nnot care how the outcome relates to the agents\" preferences,\nbut rather has a fixed preference over the outcomes), and\nabout the net payments made by the agents, which flow to\nthe designer.\nDefinition 2. A self-interested designer has an objective\nfunction given by g(o) +\nN\ni=1\n\u03c0i, where g : O \u2192 R indicates\nthe designer\"s own preference over the outcomes, and \u03c0i is\nthe payment made by agent i. In the case where g = 0\neverywhere, the designer is said to be payment maximizing.\nIn the case where payments are not possible, g constitutes\nthe objective function by itself.\nWe now define the kinds of mechanisms under study. By\nthe revelation principle, we can restrict attention to\ntruthful, direct revelation mechanisms, where agents report their\ntypes directly and never have an incentive to misreport them.\nDefinition 3. We consider the following kinds of\nmechanism:\n\u2022 A deterministic mechanism without payments consists\nof an outcome selection function o : \u03981 \u00d7 \u03982 \u00d7 . . . \u00d7\n\u0398N \u2192 O.\n\u2022 A randomized mechanism without payments consists\nof a distribution selection function p : \u03981 \u00d7 \u03982 \u00d7 . . . \u00d7\n\u0398N \u2192 P(O), where P(O) is the set of probability\ndistributions over O.\n\u2022 A deterministic mechanism with payments consists of\nan outcome selection function o : \u03981 \u00d7\u03982 \u00d7. . .\u00d7\u0398N \u2192\nO and for each agent i, a payment selection function\n\u03c0i : \u03981 \u00d7 \u03982 \u00d7 . . . \u00d7 \u0398N \u2192 R, where \u03c0i(\u03b81, . . . , \u03b8N )\ngives the payment made by agent i when the reported\ntypes are \u03b81, . . . , \u03b8N .\n1\nThough this follows standard game theory notation [16],\nthe fact that the agent has both a utility function and a type\nis perhaps confusing. The types encode the various possible\npreferences that the agent may turn out to have, and the\nagent\"s type is not known to the aggregator. The utility\nfunction is common knowledge, but because the agent\"s type\nis a parameter in the agent\"s utility function, the aggregator\ncannot know what the agent\"s utility is without knowing the\nagent\"s type.\n134\n\u2022 A randomized mechanism with payments consists of\na distribution selection function p : \u03981 \u00d7 \u03982 \u00d7 . . . \u00d7\n\u0398N \u2192 P(O), and for each agent i, a payment selection\nfunction \u03c0i : \u03981 \u00d7 \u03982 \u00d7 . . . \u00d7 \u0398N \u2192 R.2\nThere are two types of constraint on the designer in\nbuilding the mechanism.\n3.1 Individual rationality (IR) constraints\nThe first type of constraint is the following. The utility of\neach agent has to be at least as great as the agent\"s fallback\nutility, that is, the utility that the agent would receive if it\ndid not participate in the mechanism. Otherwise that agent\nwould not participate in the mechanism-and no agent\"s\nparticipation can ever hurt the mechanism designer\"s\nobjective because at worst, the mechanism can ignore an agent\nby pretending the agent is not there. (Furthermore, if no\nsuch constraint applied, the designer could simply make the\nagents pay an infinite amount.) This type of constraint is\ncalled an IR (individual rationality) constraint. There are\nthree different possible IR constraints: ex ante, ex interim,\nand ex post, depending on what the agent knows about its\nown type and the others\" types when deciding whether to\nparticipate in the mechanism. Ex ante IR means that the\nagent would participate if it knew nothing at all (not even\nits own type). We will not study this concept in this paper.\nEx interim IR means that the agent would always\nparticipate if it knew only its own type, but not those of the others.\nEx post IR means that the agent would always participate\neven if it knew everybody\"s type. We will define the\nlatter two notions of IR formally. First, we need to formalize\nthe concept of the fallback outcome. We assume that each\nagent\"s fallback utility is zero for each one of its types. This\nis without loss of generality because we can add a constant\nterm to an agent\"s utility function (for a given type),\nwithout affecting the decision-making behavior of that expected\nutility maximizing agent [16].\nDefinition 4. In any automated mechanism design\nsetting with an IR constraint, there is a fallback outcome o0 \u2208\nO where, for any agent i and any type \u03b8i \u2208 \u0398i, we have\nui(\u03b8i, o0) = 0. (Additionally, in the case of a self-interested\ndesigner, g(o0) = 0.)\nWe can now to define the notions of individual rationality.\nDefinition 5. Individual rationality (IR) is defined by:\n\u2022 A deterministic mechanism is ex interim IR if for any\nagent i, and any type \u03b8i \u2208 \u0398i, we have\nE(\u03b81,..,\u03b8i\u22121,\u03b8i+1,..,\u03b8N )|\u03b8i\n[ui(\u03b8i, o(\u03b81, .., \u03b8N ))\u2212\u03c0i(\u03b81, .., \u03b8N )]\n\u2265 0.\nA randomized mechanism is ex interim IR if for any\nagent i, and any type \u03b8i \u2208 \u0398i, we have\nE(\u03b81,..,\u03b8i\u22121,\u03b8i+1,..,\u03b8N )|\u03b8i\nEo|\u03b81,..,\u03b8n [ui(\u03b8i, o)\u2212\u03c0i(\u03b81, .., \u03b8N )]\n\u2265 0.\n\u2022 A deterministic mechanism is ex post IR if for any\nagent i, and any type vector (\u03b81, . . . , \u03b8N ) \u2208 \u03981 \u00d7 . . . \u00d7\n\u0398N , we have ui(\u03b8i, o(\u03b81, . . . , \u03b8N )) \u2212 \u03c0i(\u03b81, . . . , \u03b8N ) \u2265\n0.\n2\nWe do not randomize over payments because as long as\nthe agents and the designer are risk neutral with respect to\npayments, that is, their utility is linear in payments, there\nis no reason to randomize over payments.\nA randomized mechanism is ex post IR if for any agent\ni, and any type vector (\u03b81, . . . , \u03b8N ) \u2208 \u03981 \u00d7 . . . \u00d7 \u0398N ,\nwe have Eo|\u03b81,..,\u03b8n [ui(\u03b8i, o) \u2212 \u03c0i(\u03b81, .., \u03b8N )] \u2265 0.\nThe terms involving payments can be left out in the case\nwhere payments are not possible.\n3.2 Incentive compatibility (IC) constraints\nThe second type of constraint says that the agents should\nnever have an incentive to misreport their type (as justified\nabove by the revelation principle). For this type of\nconstraint, the two most common variants (or solution concepts)\nare implementation in dominant strategies, and\nimplementation in Bayes-Nash equilibrium.\nDefinition 6. Given an automated mechanism design\nsetting, a mechanism is said to implement its outcome and\npayment functions in dominant strategies if truthtelling is\nalways optimal even when the types reported by the other\nagents are already known. Formally, for any agent i, any\ntype vector (\u03b81, . . . , \u03b8i, . . . , \u03b8N ) \u2208 \u03981 \u00d7 . . . \u00d7 \u0398i \u00d7 . . . \u00d7 \u0398N ,\nand any alternative type report \u02c6\u03b8i \u2208 \u0398i, in the case of\ndeterministic mechanisms we have\nui(\u03b8i, o(\u03b81, . . . , \u03b8i, . . . , \u03b8N )) \u2212 \u03c0i(\u03b81, . . . , \u03b8i, . . . , \u03b8N ) \u2265\nui(\u03b8i, o(\u03b81, . . . , \u02c6\u03b8i, . . . , \u03b8N )) \u2212 \u03c0i(\u03b81, . . . , \u02c6\u03b8i, . . . , \u03b8N ).\nIn the case of randomized mechanisms we have\nEo|\u03b81,..,\u03b8i,..,\u03b8n [ui(\u03b8i, o) \u2212 \u03c0i(\u03b81, . . . , \u03b8i, . . . , \u03b8N )] \u2265\nEo|\u03b81,.., \u02c6\u03b8i,..,\u03b8n\n[ui(\u03b8i, o) \u2212 \u03c0i(\u03b81, . . . , \u02c6\u03b8i, . . . , \u03b8N )].\nThe terms involving payments can be left out in the case\nwhere payments are not possible.\nThus, in dominant strategies implementation, truthtelling\nis optimal regardless of what the other agents report. If it\nis optimal only given that the other agents are truthful, and\ngiven that one does not know the other agents\" types, we\nhave implementation in Bayes-Nash equilibrium.\nDefinition 7. Given an automated mechanism design\nsetting, a mechanism is said to implement its outcome and\npayment functions in Bayes-Nash equilibrium if truthtelling\nis always optimal to an agent when that agent does not yet\nknow anything about the other agents\" types, and the other\nagents are telling the truth. Formally, for any agent i, any\ntype \u03b8i \u2208 \u0398i, and any alternative type report \u02c6\u03b8i \u2208 \u0398i, in the\ncase of deterministic mechanisms we have\nE(\u03b81,..,\u03b8i\u22121,\u03b8i+1,..,\u03b8N )|\u03b8i\n[ui(\u03b8i, o(\u03b81, . . . , \u03b8i, . . . , \u03b8N ))\u2212\n\u03c0i(\u03b81, . . . , \u03b8i, . . . , \u03b8N )] \u2265\nE(\u03b81,..,\u03b8i\u22121,\u03b8i+1,..,\u03b8N )|\u03b8i\n[ui(\u03b8i, o(\u03b81, . . . , \u02c6\u03b8i, . . . , \u03b8N ))\u2212\n\u03c0i(\u03b81, . . . , \u02c6\u03b8i, . . . , \u03b8N )].\nIn the case of randomized mechanisms we have\nE(\u03b81,..,\u03b8i\u22121,\u03b8i+1,..,\u03b8N )|\u03b8i\nEo|\u03b81,..,\u03b8i,..,\u03b8n [ui(\u03b8i, o)\u2212\n\u03c0i(\u03b81, . . . , \u03b8i, . . . , \u03b8N )] \u2265\nE(\u03b81,..,\u03b8i\u22121,\u03b8i+1,..,\u03b8N )|\u03b8i\nEo|\u03b81,.., \u02c6\u03b8i,..,\u03b8n\n[ui(\u03b8i, o)\u2212\n\u03c0i(\u03b81, . . . , \u02c6\u03b8i, . . . , \u03b8N )].\nThe terms involving payments can be left out in the case\nwhere payments are not possible.\n135\n3.3 Automated mechanism design\nWe can now define the computational problem we study.\nDefinition 8. (AUTOMATED-MECHANISM-DESIGN\n(AMD)) We are given:\n\u2022 an automated mechanism design setting,\n\u2022 an IR notion (ex interim, ex post, or none),\n\u2022 a solution concept (dominant strategies or Bayes-Nash),\n\u2022 whether payments are possible,\n\u2022 whether randomization is possible,\n\u2022 (in the decision variant of the problem) a target value\nG.\nWe are asked whether there exists a mechanism of the\nspecified kind (in terms of payments and randomization) that\nsatisfies both the IR notion and the solution concept, and\ngives an expected value of at least G for the objective.\nAn interesting special case is the setting where there is\nonly one agent. In this case, the reporting agent always\nknows everything there is to know about the other agents\"\ntypes-because there are no other agents. Since ex post and\nex interim IR only differ on what an agent is assumed to\nknow about other agents\" types, the two IR concepts\ncoincide here. Also, because implementation in dominant\nstrategies and implementation in Bayes-Nash equilibrium only\ndiffer on what an agent is assumed to know about other agents\"\ntypes, the two solution concepts coincide here. This\nobservation will prove to be a useful tool in proving hardness\nresults: if we prove computational hardness in the\nsingleagent setting, this immediately implies hardness for both\nIR concepts, for both solution concepts, for any number of\nagents.\n4.\nPAYMENT-MAXIMIZINGDETERMINISTIC AMD IS HARD\nIn this section we demonstrate that it is NP-complete\nto design a deterministic mechanism that maximizes the\nexpected sum of the payments collected from the agents.\nWe show that this problem is hard even in the single-agent\nsetting, thereby immediately showing it hard for both IR\nconcepts, for both solution concepts. To demonstrate\nNPhardness, we reduce from the MINSAT problem.\nDefinition 9 (MINSAT). We are given a formula \u03c6\nin conjunctive normal form, represented by a set of Boolean\nvariables V and a set of clauses C, and an integer K (K <\n|C|). We are asked whether there exists an assignment to the\nvariables in V such that at most K clauses in \u03c6 are satisfied.\nMINSAT was recently shown to be NP-complete [14]. We\ncan now present our result.\nTheorem 1. Payment-maximizing deterministic AMD is\nNP-complete, even for a single agent, even with a uniform\ndistribution over types.\nProof. It is easy to show that the problem is in NP.\nTo show NP-hardness, we reduce an arbitrary MINSAT\ninstance to the following single-agent payment-maximizing\ndeterministic AMD instance. Let the agent\"s type set be\n\u0398 = {\u03b8c : c \u2208 C} \u222a {\u03b8v : v \u2208 V }, where C is the set of\nclauses in the MINSAT instance, and V is the set of\nvariables. Let the probability distribution over these types be\nuniform. Let the outcome set be O = {o0} \u222a {oc : c \u2208\nC} \u222a {ol : l \u2208 L}, where L is the set of literals, that is,\nL = {+v : v \u2208 V } \u222a {\u2212v : v \u2208 V }. Let the notation v(l) = v\ndenote that v is the variable corresponding to the literal l,\nthat is, l \u2208 {+v, \u2212v}. Let l \u2208 c denote that the literal l\noccurs in clause c. Then, let the agent\"s utility function\nbe given by u(\u03b8c, ol) = |\u0398| + 1 for all l \u2208 L with l \u2208 c;\nu(\u03b8c, ol) = 0 for all l \u2208 L with l /\u2208 c; u(\u03b8c, oc) = |\u0398| + 1;\nu(\u03b8c, oc ) = 0 for all c \u2208 C with c = c ; u(\u03b8v, ol) = |\u0398| for all\nl \u2208 L with v(l) = v; u(\u03b8v, ol) = 0 for all l \u2208 L with v(l) = v;\nu(\u03b8v, oc) = 0 for all c \u2208 C. The goal of the AMD instance\nis G = |\u0398| + |C|\u2212K\n|\u0398|\n, where K is the goal of the MINSAT\ninstance. We show the instances are equivalent. First, suppose\nthere is a solution to the MINSAT instance. Let the\nassignment of truth values to the variables in this solution be given\nby the function f : V \u2192 L (where v(f(v)) = v for all v \u2208 V ).\nThen, for every v \u2208 V , let o(\u03b8v) = of(v) and \u03c0(\u03b8v) = |\u0398|.\nFor every c \u2208 C, let o(\u03b8c) = oc; let \u03c0(\u03b8c) = |\u0398| + 1 if c\nis not satisfied in the MINSAT solution, and \u03c0(\u03b8c) = |\u0398|\nif c is satisfied. It is straightforward to check that the IR\nconstraint is satisfied. We now check that the agent has no\nincentive to misreport. If the agent\"s type is some \u03b8v, then\nany other report will give it an outcome that is no better,\nfor a payment that is no less, so it has no incentive to\nmisreport. If the agent\"s type is some \u03b8c where c is a satisfied\nclause, again, any other report will give it an outcome that\nis no better, for a payment that is no less, so it has no\nincentive to misreport. The final case to check is where the\nagent\"s type is some \u03b8c where c is an unsatisfied clause. In\nthis case, we observe that for none of the types, reporting it\nleads to an outcome ol for a literal l \u2208 c, precisely because\nthe clause is not satisfied in the MINSAT instance. Because\nalso, no type besides \u03b8c leads to the outcome oc, reporting\nany other type will give an outcome with utility 0, while still\nforcing a payment of at least |\u0398| from the agent. Clearly the\nagent is better off reporting truthfully, for a total utility of\n0. This establishes that the agent never has an incentive to\nmisreport. Finally, we show that the goal is reached. If s is\nthe number of satisfied clauses in the MINSAT solution (so\nthat s \u2264 K), the expected payment from this mechanism\nis |V ||\u0398|+s|\u0398|+(|C|\u2212s)(|\u0398|+1)\n|\u0398|\n\u2265 |V ||\u0398|+K|\u0398|+(|C|\u2212K)(|\u0398|+1)\n|\u0398|\n=\n|\u0398| + |C|\u2212K\n|\u0398|\n= G. So there is a solution to the AMD\ninstance.\nNow suppose there is a solution to the AMD instance,\ngiven by an outcome function o and a payment function\n\u03c0. First, suppose there is some v \u2208 V such that o(\u03b8v) /\u2208\n{o+v, o\u2212v}. Then the utility that the agent derives from\nthe given outcome for this type is 0, and hence, by IR, no\npayment can be extracted from the agent for this type.\nBecause, again by IR, the maximum payment that can be\nextracted for any other type is |\u0398| + 1, it follows that the\nmaximum expected payment that could be obtained is at\nmost (|\u0398|\u22121)(|\u0398|+1)\n|\u0398|\n< |\u0398| < G, contradicting that this is a\nsolution to the AMD instance. It follows that in the solution\nto the AMD instance, for every v \u2208 V , o(\u03b8v) \u2208 {o+v, o\u2212v}.\n136\nWe can interpret this as an assignment of truth values to\nthe variables: v is set to true if o(\u03b8v) = o+v, and to false\nif o(\u03b8v) = o\u2212v. We claim this assignment is a solution to\nthe MINSAT instance. By the IR constraint, the maximum\npayment we can extract from any type \u03b8v is |\u0398|. Because\nthere can be no incentives for the agent to report falsely, for\nany clause c satisfied by the given assignment, the maximum\npayment we can extract for the corresponding type \u03b8c is |\u0398|.\n(For if we extracted more from this type, the agent\"s utility\nin this case would be less than 1; and if v is the variable\nsatisfying c in the assignment, so that o(\u03b8v) = ol where l occurs\nin c, then the agent would be better off reporting \u03b8v instead\nof the truthful report \u03b8c, to get an outcome worth |\u0398|+1 to\nit while having to pay at most |\u0398|.) Finally, for any\nunsatisfied clause c, by the IR constraint, the maximum payment\nwe can extract for the corresponding type \u03b8c is |\u0398| + 1. It\nfollows that the expected payment from our mechanism is\nat most V |\u0398|+s|\u0398|+(|C|\u2212s)(|\u0398|+1)\n\u0398\n, where s is the number of\nsatisfied clauses. Because our mechanism achieves the goal,\nit follows that V |\u0398|+s|\u0398|+(|C|\u2212s)(|\u0398|+1)\n\u0398\n\u2265 G, which by simple\nalgebraic manipulations is equivalent to s \u2264 K. So there is\na solution to the MINSAT instance.\nBecause payment-maximizing AMD is just the special case\nof AMD for a self-interested designer where the designer has\nno preferences over the outcome chosen, this immediately\nimplies hardness for the general case of AMD for a\nselfinterested designer where payments are possible. However,\nit does not yet imply hardness for the special case where\npayments are not possible. We will prove hardness in this\ncase in the next section.\n5. SELF-INTERESTED DETERMINISTIC\nAMD WITHOUT PAYMENTS IS HARD\nIn this section we demonstrate that it is NP-complete to\ndesign a deterministic mechanism that maximizes the\nexpectation of the designer\"s objective when payments are not\npossible. We show that this problem is hard even in the\nsingle-agent setting, thereby immediately showing it hard\nfor both IR concepts, for both solution concepts.\nTheorem 2. Without payments, deterministic AMD for\na self-interested designer is NP-complete, even for a single\nagent, even with a uniform distribution over types.\nProof. It is easy to show that the problem is in NP.\nTo show NP-hardness, we reduce an arbitrary MINSAT\ninstance to the following single-agent self-interested\ndeterministic AMD without payments instance. Let the agent\"s type\nset be \u0398 = {\u03b8c : c \u2208 C} \u222a {\u03b8v : v \u2208 V }, where C is the\nset of clauses in the MINSAT instance, and V is the set of\nvariables. Let the probability distribution over these types\nbe uniform. Let the outcome set be O = {o0} \u222a {oc : c \u2208\nC}\u222a{ol : l \u2208 L}\u222a{o\u2217\n}, where L is the set of literals, that is,\nL = {+v : v \u2208 V } \u222a {\u2212v : v \u2208 V }. Let the notation v(l) = v\ndenote that v is the variable corresponding to the literal l,\nthat is, l \u2208 {+v, \u2212v}. Let l \u2208 c denote that the literal l\noccurs in clause c. Then, let the agent\"s utility function be\ngiven by u(\u03b8c, ol) = 2 for all l \u2208 L with l \u2208 c; u(\u03b8c, ol) = \u22121\nfor all l \u2208 L with l /\u2208 c; u(\u03b8c, oc) = 2; u(\u03b8c, oc ) = \u22121 for\nall c \u2208 C with c = c ; u(\u03b8c, o\u2217\n) = 1; u(\u03b8v, ol) = 1 for all\nl \u2208 L with v(l) = v; u(\u03b8v, ol) = \u22121 for all l \u2208 L with\nv(l) = v; u(\u03b8v, oc) = \u22121 for all c \u2208 C; u(\u03b8v, o\u2217\n) = \u22121. Let\nthe designer\"s objective function be given by g(o\u2217\n) = |\u0398|+1;\ng(ol) = |\u0398| for all l \u2208 L; g(oc) = |\u0398| for all c \u2208 C. The goal\nof the AMD instance is G = |\u0398| + |C|\u2212K\n|\u0398|\n, where K is the\ngoal of the MINSAT instance. We show the instances are\nequivalent. First, suppose there is a solution to the MINSAT\ninstance. Let the assignment of truth values to the variables\nin this solution be given by the function f : V \u2192 L (where\nv(f(v)) = v for all v \u2208 V ). Then, for every v \u2208 V , let\no(\u03b8v) = of(v). For every c \u2208 C that is satisfied in the\nMINSAT solution, let o(\u03b8c) = oc; for every unsatisfied c \u2208 C,\nlet o(\u03b8c) = o\u2217\n. It is straightforward to check that the IR\nconstraint is satisfied. We now check that the agent has no\nincentive to misreport. If the agent\"s type is some \u03b8v, it is\ngetting the maximum utility for that type, so it has no\nincentive to misreport. If the agent\"s type is some \u03b8c where c\nis a satisfied clause, again, it is getting the maximum utility\nfor that type, so it has no incentive to misreport. The final\ncase to check is where the agent\"s type is some \u03b8c where c is\nan unsatisfied clause. In this case, we observe that for none\nof the types, reporting it leads to an outcome ol for a literal\nl \u2208 c, precisely because the clause is not satisfied in the\nMINSAT instance. Because also, no type leads to the outcome\noc, there is no outcome that the mechanism ever selects that\nwould give the agent utility greater than 1 for type \u03b8c, and\nhence the agent has no incentive to report falsely. This\nestablishes that the agent never has an incentive to misreport.\nFinally, we show that the goal is reached. If s is the number\nof satisfied clauses in the MINSAT solution (so that s \u2264 K),\nthen the expected value of the designer\"s objective function\nis |V ||\u0398|+s|\u0398|+(|C|\u2212s)(|\u0398|+1)\n|\u0398|\n\u2265 |V ||\u0398|+K|\u0398|+(|C|\u2212K)(|\u0398|+1)\n|\u0398|\n=\n|\u0398| + |C|\u2212K\n|\u0398|\n= G. So there is a solution to the AMD\ninstance.\nNow suppose there is a solution to the AMD instance,\ngiven by an outcome function o. First, suppose there is\nsome v \u2208 V such that o(\u03b8v) /\u2208 {o+v, o\u2212v}. The only other\noutcome that the mechanism is allowed to choose under the\nIR constraint is o0. This has an objective value of 0, and\nbecause the highest value the objective function ever takes\nis |\u0398| + 1, it follows that the maximum expected value of\nthe objective function that could be obtained is at most\n(|\u0398|\u22121)(|\u0398|+1)\n|\u0398|\n< |\u0398| < G, contradicting that this is a\nsolution to the AMD instance. It follows that in the solution\nto the AMD instance, for every v \u2208 V , o(\u03b8v) \u2208 {o+v, o\u2212v}.\nWe can interpret this as an assignment of truth values to\nthe variables: v is set to true if o(\u03b8v) = o+v, and to false\nif o(\u03b8v) = o\u2212v. We claim this assignment is a solution to\nthe MINSAT instance. By the above, for any type \u03b8v, the\nvalue of the objective function in this mechanism will be\n|\u0398|. For any clause c satisfied by the given assignment,\nthe value of the objective function in the case where the\nagent reports type \u03b8c will be at most |\u0398|. (This is because\nwe cannot choose the outcome o\u2217\nfor such a type, as in\nthis case the agent would have an incentive to report \u03b8v\ninstead, where v is the variable satisfying c in the\nassignment (so that o(\u03b8v) = ol where l occurs in c).) Finally,\nfor any unsatisfied clause c, the maximum value the\nobjective function can take in the case where the agent\nreports type \u03b8c is |\u0398| + 1, simply because this is the largest\nvalue the function ever takes. It follows that the expected\nvalue of the objective function for our mechanism is at most\nV |\u0398|+s|\u0398|+(|C|\u2212s)(|\u0398|+1)\n\u0398\n, where s is the number of satisfied\n137\nclauses. Because our mechanism achieves the goal, it follows\nthat V |\u0398|+s|\u0398|+(|C|\u2212s)(|\u0398|+1)\n\u0398\n\u2265 G, which by simple algebraic\nmanipulations is equivalent to s \u2264 K. So there is a solution\nto the MINSAT instance.\nBoth of our hardness results relied on the constraint that\nthe mechanism should be deterministic. In the next section,\nwe show that the hardness of design disappears when we\nallow for randomization in the mechanism.\n6. RANDOMIZED AMD FOR A\nSELFINTERESTED DESIGNER IS EASY\nWe now show how allowing for randomization over the\noutcomes makes the problem of self-interested AMD tractable\nthrough linear programming, for any constant number of\nagents.\nTheorem 3. Self-interested randomized AMD with a\nconstant number of agents is solvable in polynomial time by\nlinear programming, both with and without payments, both for\nex post and ex interim IR, and both for implementation in\ndominant strategies and for implementation in Bayes-Nash\nequilibrium-even if the types are correlated.\nProof. Because linear programs can be solved in\npolynomial time [13], all we need to show is that the number of\nvariables and equations in our program is polynomial for any\nconstant number of agents-that is, exponential only in N.\nThroughout, for purposes of determining the size of the\nlinear program, let T = maxi{|\u0398i|}. The variables of our linear\nprogram will be the probabilities (p(\u03b81, \u03b82, . . . , \u03b8N ))(o) (at\nmost TN\n|O| variables) and the payments \u03c0i(\u03b81, \u03b82, . . . , \u03b8N )\n(at most NTN\nvariables). (We show the linear program for\nthe case where payments are possible; the case without\npayments is easily obtained from this by simply omitting all the\npayment variables in the program, or by adding additional\nconstraints forcing the payments to be 0.)\nFirst, we show the IR constraints. For ex post IR, we add\nthe following (at most NTN\n) constraints to the LP:\n\u2022 For every i \u2208 {1, 2, . . . , N}, and for every (\u03b81, \u03b82, . . . , \u03b8N )\n\u2208 \u03981 \u00d7 \u03982 \u00d7 . . . \u00d7 \u0398N , we add\n(\no\u2208O\n(p(\u03b81, \u03b82, . . . , \u03b8N ))(o)u(\u03b8i, o)) \u2212 \u03c0i(\u03b81, \u03b82, . . . , \u03b8N ) \u2265 0.\nFor ex interim IR, we add the following (at most NT)\nconstraints to the LP:\n\u2022 For every i \u2208 {1, 2, . . . , N}, for every \u03b8i \u2208 \u0398i, we add\n\u03b81,... ,\u03b8N\n\u03b3(\u03b81, . . . , \u03b8N |\u03b8i)((\no\u2208O\n(p(\u03b81, \u03b82, . . . , \u03b8N ))(o)u(\u03b8i, o))\u2212\n\u03c0i(\u03b81, \u03b82, . . . , \u03b8N )) \u2265 0.\nNow, we show the solution concept constraints. For\nimplementation in dominant strategies, we add the following\n(at most NTN+1\n) constraints to the LP:\n\u2022 For every i \u2208 {1, 2, . . . , N}, for every\n(\u03b81, \u03b82, . . . , \u03b8i, . . . , \u03b8N ) \u2208 \u03981 \u00d7 \u03982 \u00d7 . . . \u00d7 \u0398N , and for every\nalternative type report \u02c6\u03b8i \u2208 \u0398i, we add the constraint\n(\no\u2208O\n(p(\u03b81, \u03b82, . . . , \u03b8i, . . . , \u03b8N ))(o)u(\u03b8i, o)) \u2212\n\u03c0i(\u03b81, \u03b82, . . . , \u03b8i, . . . , \u03b8N ) \u2265\n(\no\u2208O\n(p(\u03b81, \u03b82, . . . , \u02c6\u03b8i, . . . , \u03b8N ))(o)u(\u03b8i, o)) \u2212\n\u03c0i(\u03b81, \u03b82, . . . , \u02c6\u03b8i, . . . , \u03b8N ).\nFinally, for implementation in Bayes-Nash equilibrium, we\nadd the following (at most NT2\n) constraints to the LP:\n\u2022 For every i \u2208 {1, 2, ..., N}, for every \u03b8i \u2208 \u0398i, and for\nevery alternative type report \u02c6\u03b8i \u2208 \u0398i, we add the constraint\n\u03b81,...,\u03b8N\n\u03b3(\u03b81, ..., \u03b8N |\u03b8i)((\no\u2208O\n(p(\u03b81, \u03b82, ..., \u03b8i, ..., \u03b8N ))(o)u(\u03b8i, o))\n\u2212 \u03c0i(\u03b81, \u03b82, ..., \u03b8i, ..., \u03b8N )) \u2265\n\u03b81,...,\u03b8N\n\u03b3(\u03b81, ..., \u03b8N |\u03b8i)((\no\u2208O\n(p(\u03b81, \u03b82, ..., \u02c6\u03b8i, ..., \u03b8N ))(o)u(\u03b8i, o))\n\u2212 \u03c0i(\u03b81, \u03b82, ..., \u02c6\u03b8i, ..., \u03b8N )).\nAll that is left to do is to give the expression the designer\nis seeking to maximize, which is:\n\u2022\n\u03b81,...,\u03b8N\n\u03b3(\u03b81, ..., \u03b8N )((\no\u2208O\n(p(\u03b81, \u03b82, ..., \u03b8i, ..., \u03b8N ))(o)g(o))\n+\nN\ni=1\n\u03c0i(\u03b81, \u03b82, ..., \u03b8N )).\nAs we indicated, the number of variables and constraints\nis exponential only in N, and hence the linear program is of\npolynomial size for constant numbers of agents. Thus the\nproblem is solvable in polynomial time.\n7. IMPLICATIONS FOR AN OPTIMAL\nCOMBINATORIAL AUCTION DESIGN\nPROBLEM\nIn this section, we will demonstrate some interesting\nconsequences of the problem of automated mechanism design\nfor a self-interested designer on designing optimal\ncombinatorial auctions.\nConsider a combinatorial auction with a set S of items\nfor sale. For any bundle B \u2286 S, let ui(\u03b8i, B) be bidder\ni\"s utility for receiving bundle B when the bidder\"s type is\n\u03b8i. The optimal auction design problem is to specify the\nrules of the auction so as to maximize expected revenue to\nthe auctioneer. (By the revelation principle, without loss\nof generality, we can assume the auction is truthful.) The\noptimal auction design problem is solved for the case of a\nsingle item by the famous Myerson auction [18]. However,\ndesigning optimal auctions in combinatorial auctions is a\nrecognized open research problem [3, 25]. The problem is\nopen even if there are only two items for sale. (The\ntwoitem case with a very special form of complementarity and\nno substitutability has been solved recently [1].)\nSuppose we have free disposal-items can be thrown away\nat no cost. Also, suppose that the bidders\" preferences have\nthe following structure: whenever a bidder receives a bundle\nof items, the bidder\"s utility for that bundle is determined\nby the best item in the bundle only. (We emphasize that\n138\nwhich item is the best is allowed to depend on the bidder\"s\ntype.)\nDefinition 10. Bidder i is said to have best-only\npreferences over bundles of items if there exists a function vi :\n\u0398i \u00d7 S \u2192 R such that for any \u03b8i \u2208 \u0398i, for any B \u2286 S,\nui(\u03b8i, B) = maxs\u2208B vi(\u03b8i, s).\nWe make the following useful observation in this setting:\nthere is no sense in awarding a bidder more than one item.\nThe reason is that if the bidder is reporting truthfully, taking\nall but the highest valued item away from the bidder will\nnot hurt the bidder; and, by free disposal, doing so can only\nreduce the incentive for this bidder to falsely report this\ntype, when the bidder actually has another type.\nWe now show that the problem of designing a\ndeterministic optimal auction here is NP-complete, by a reduction\nfrom the payment maximizing AMD problem!\nTheorem 4. Given an optimal combinatorial auction\ndesign problem under best-only preferences (given by a set of\nitems S and for each bidder i, a finite type space \u0398i and a\nfunction vi : \u0398i \u00d7 S \u2192 R such that for any \u03b8i \u2208 \u0398i, for any\nB \u2286 S, ui(\u03b8i, B) = maxs\u2208B vi(\u03b8i, s)), designing the\noptimal deterministic auction is NP-complete, even for a single\nbidder with a uniform distribution over types.\nProof. The problem is in NP because we can\nnondeterministically generate an allocation rule, and then set the\npayments using linear programming.\nTo show NP-hardness, we reduce an arbitrary\npaymentmaximizing deterministic AMD instance, with a single agent\nand a uniform distribution over types, to the following\noptimal combinatorial auction design problem instance with\na single bidder with best-only preferences. For every\noutcome o \u2208 O in the AMD instance (besides the outcome o0),\nlet there be one item so \u2208 S. Let the type space be the\nsame, and let v(\u03b8i, so) = ui(\u03b8i, o) (where u is as specified in\nthe AMD instance). Let the expected revenue target value\nbe the same in both instances. We show the instances are\nequivalent.\nFirst suppose there exists a solution to the AMD instance,\ngiven by an outcome function and a payment function. Then,\nif the AMD solution chooses outcome o for a type, in the\noptimal auction solution, allocate {so} to the bidder for this\ntype. (Unless o = o0, in which case we allocate {} to the\nbidder.) Let the payment functions be the same in both\ninstances. Then, the utility that an agent receives for\nreporting a type (given the true type) in either solution is the\nsame, so we have incentive compatibility in the optimal\nauction solution. Moreover, because the type distribution and\nthe payment function are the same, the expected revenue to\nthe auctioneer/designer is the same. It follows that there\nexists a solution to the optimal auction design instance.\nNow suppose there exists a solution to the optimal auction\ndesign instance. By the at-most-one-item observation, we\ncan assume without loss of generality that the solution never\nallocates more than one item. Then, if the optimal auction\nsolution allocates item so to the bidder for a type, in the\nAMD solution, let the mechanism choose outcome o for that\ntype. If the optimal auction solution allocates nothing to the\nbidder for a type, in the AMD solution, let the mechanism\nchoose outcome o0 for that type. Let the payment functions\nbe the same. Then, the utility that an agent receives for\nreporting a type (given the true type) in either solution is\nthe same, so we have incentive compatibility in the AMD\nsolution. Moreover, because the type distribution and the\npayment function are the same, the expected revenue to the\ndesigner/auctioneer is the same. It follows that there exists\na solution to the AMD instance.\nFortunately, we can also carry through the easiness result\nfor randomized mechanisms to this combinatorial auction\nsetting-giving us one of the few known polynomial-time\nalgorithms for an optimal combinatorial auction design\nproblem.\nTheorem 5. Given an optimal combinatorial auction\ndesign problem under best-only preferences (given by a set of\nitems S and for each bidder i, a finite type space \u0398i and a\nfunction vi : \u0398i \u00d7 S \u2192 R such that for any \u03b8i \u2208 \u0398i, for\nany B \u2286 S, ui(\u03b8i, B) = maxs\u2208B vi(\u03b8i, s)), if the number of\nbidders is a constant k, then the optimal randomized\nauction can be designed in polynomial time. (For any IC and\nIR constraints.)\nProof. By the at-most-one-item observation, we can\nwithout loss of generality restrict ourselves to allocations where\neach bidder receives at most one item. There are fewer than\n(|S| + 1)k\nsuch allocations-that is, a polynomial number\nof allocations. Because we can list the outcomes explicitly,\nwe can simply solve this as a payment-maximizing AMD\ninstance, with linear programming.\n8. RELATED RESEARCH ON\nCOMPLEXITY IN MECHANISM DESIGN\nThere has been considerable recent interest in mechanism\ndesign in computer science. Some of it has focused on\nissues of computational complexity, but most of that work has\nstrived toward designing mechanisms that are easy to\nexecute (e.g. [20, 15, 19, 9, 12]), rather than studying the\ncomplexity of designing the mechanism. The closest piece of\nearlier work studied the complexity of automated mechanism\ndesign by a benevolent designer [5, 6]. Roughgarden has\nstudied the complexity of designing a good network\ntopology for agents that selfishly choose the links they use [21].\nThis is related to mechanism design, but differs significantly\nin that the designer only has restricted control over the rules\nof the game because there is no party that can impose the\noutcome (or side payments). Also, there is no explicit\nreporting of preferences.\n9. CONCLUSIONS AND FUTURE\nRESEARCH\nOften, an outcome must be chosen on the basis of the\npreferences reported by a group of agents. The key difficulty\nis that the agents may report their preferences insincerely\nto make the chosen outcome more favorable to themselves.\nMechanism design is the art of designing the rules of the\ngame so that the agents are motivated to report their\npreferences truthfully, and a desirable outcome is chosen. In a\nrecently emerging approach-called automated mechanism\ndesign-a mechanism is computed for the specific preference\naggregation setting at hand. This has several advantages,\n139\nbut the downside is that the mechanism design optimization\nproblem needs to be solved anew each time. Unlike earlier\nwork on automated mechanism design that studied a\nbenevolent designer, in this paper we studied automated\nmechanism design problems where the designer is\nself-interesteda setting much more relevant for electronic commerce. In\nthis setting, the center cares only about which outcome is\nchosen and what payments are made to it. The reason that\nthe agents\" preferences are relevant is that the center is\nconstrained to making each agent at least as well off as the agent\nwould have been had it not participated in the mechanism.\nIn this setting, we showed that designing an optimal\ndeterministic mechanism is NP-complete in two important\nspecial cases: when the center is interested only in the payments\nmade to it, and when payments are not possible and the\ncenter is interested only in the outcome chosen. These\nhardness results imply hardness in all more general automated\nmechanism design settings with a self-interested designer.\nThe hardness results apply whether the individual\nrationality (participation) constraints are applied ex interim or ex\npost, and whether the solution concept is dominant\nstrategies implementation or Bayes-Nash equilibrium\nimplementation. We then showed that allowing randomization in the\nmechanism makes the design problem in all these settings\ncomputationally easy. Finally, we showed that the\npaymentmaximizing AMD problem is closely related to an interesting\nvariant of the optimal (revenue-maximizing) combinatorial\nauction design problem, where the bidders have best-only\npreferences. We showed that here, too, designing an\noptimal deterministic mechanism is NP-complete even with one\nagent, but designing an optimal randomized mechanism is\neasy.\nFuture research includes studying automated mechanism\ndesign with a self-interested designer in more restricted\nsettings such as auctions (where the designer\"s objective may\ninclude preferences about which bidder should receive the\ngood-as well as payments). We also want to study the\ncomplexity of automated mechanism design in settings where the\noutcome and type spaces have special structure so they can\nbe represented more concisely. 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Hahn, editor, The Economics of\nMissing Markets, Information, and Games,\nchapter 14, pages 312-335. Clarendon Press, Oxford,\n1989.\n[18] R. Myerson. Optimal auction design. Mathematics of\nOperation Research, 6:58-73, 1981.\n[19] N. Nisan and A. Ronen. Computationally feasible\nVCG mechanisms. In Proceedings of the ACM\nConference on Electronic Commerce (ACM-EC),\npages 242-252, Minneapolis, MN, 2000.\n[20] N. Nisan and A. Ronen. Algorithmic mechanism\ndesign. Games and Economic Behavior, 35:166-196,\n2001. Early version in Proceedings of the Annual ACM\nSymposium on Theory of Computing (STOC), 1999.\n[21] T. Roughgarden. Designing networks for selfish users\nis hard. In Proceedings of the Annual Symposium on\nFoundations of Computer Science (FOCS), 2001.\n[22] T. Sandholm. Issues in computational Vickrey\nauctions. International Journal of Electronic\nCommerce, 4(3):107-129, 2000. Special Issue on\n140\nApplying Intelligent Agents for Electronic Commerce.\nA short, early version appeared at the Second\nInternational Conference on Multi-Agent Systems\n(ICMAS), pages 299-306, 1996.\n[23] M. A. Satterthwaite. Strategy-proofness and Arrow\"s\nconditions: existence and correspondence theorems for\nvoting procedures and social welfare functions.\nJournal of Economic Theory, 10:187-217, 1975.\n[24] W. Vickrey. Counterspeculation, auctions, and\ncompetitive sealed tenders. Journal of Finance,\n16:8-37, 1961.\n[25] R. V. Vohra. Research problems in combinatorial\nauctions. Mimeo, version Oct. 29, 2001.\n141", "keywords": "preference aggregator;desirable outcome;statistical knowledge;automated mechanism design;revenue maximization;nonmanipulable mechanism;payment maximizing;complementarity;combinatorial auction;minsat;fallback outcome;manipulability;individual rationality;automate mechanism design;self-interested amd;classical mechanism;mechanism design"}
{"name": "train_J-71", "title": "A Dynamic Pari-Mutuel Market for Hedging, Wagering, and Information Aggregation", "abstract": "I develop a new mechanism for risk allocation and information speculation called a dynamic pari-mutuel market (DPM). A DPM acts as hybrid between a pari-mutuel market and a continuous double auction (CDA), inheriting some of the advantages of both. Like a pari-mutuel market, a DPM offers infinite buy-in liquidity and zero risk for the market institution; like a CDA, a DPM can continuously react to new information, dynamically incorporate information into prices, and allow traders to lock in gains or limit losses by selling prior to event resolution. The trader interface can be designed to mimic the familiar double auction format with bid-ask queues, though with an addition variable called the payoff per share. The DPM price function can be viewed as an automated market maker always offering to sell at some price, and moving the price appropriately according to demand. Since the mechanism is pari-mutuel (i.e., redistributive), it is guaranteed to pay out exactly the amount of money taken in. I explore a number of variations on the basic DPM, analyzing the properties of each, and solving in closed form for their respective price functions.", "fulltext": "1. INTRODUCTION\nA wide variety of financial and wagering mechanisms have\nbeen developed to support hedging (i.e., insuring) against\nexposure to uncertain events and/or speculative trading on\nuncertain events. The dominant mechanism used in\nfinancial circles is the continuous double auction (CDA), or in\nsome cases the CDA with market maker (CDAwMM). The\nprimary mechanism used for sports wagering is a bookie or\nbookmaker, who essentially acts exactly as a market maker.\nHorse racing and jai alai wagering traditionally employ the\npari-mutuel mechanism. Though there is no formal or\nlogical separation between financial trading and wagering, the\ntwo endeavors are socially considered distinct. Recently,\nthere has been a move to employ CDAs or CDAwMMs for\nall types of wagering, including on sports, horse racing,\npolitical events, world news, and many other uncertain events,\nand a simultaneous and opposite trend to use bookie systems\nfor betting on financial markets. These trends highlight the\ninterchangeable nature of the mechanisms and further blur\nthe line between investing and betting. Some companies at\nthe forefront of these movements are growing exponentially,\nwith some industry observers declaring the onset of a\nrevolution in the wagering business.1\nEach mechanism has pros and cons for the market\ninstitution and the participating traders. A CDA only matches\nwilling traders, and so poses no risk whatsoever for the\nmarket institution. But a CDA can suffer from illiquidity in the\nform huge bid-ask spreads or even empty bid-ask queues if\ntrading is light and thus markets are thin. A successful CDA\nmust overcome a chicken-and-egg problem: traders are\nattracted to liquid markets, but liquid markets require a large\nnumber of traders. A CDAwMM and the similar bookie\nmechanism have built-in liquidity, but at a cost: the market\nmaker itself, usually affiliated with the market institution, is\nexposed to significant risk of large monetary losses. Both the\nCDA and CDAwMM offer incentives for traders to leverage\ninformation continuously as soon as that information\nbecomes available. As a result, prices are known to capture\nthe current state of information exceptionally well.\nPari-mutuel markets effectively have infinite liquidity:\nanyone can place a bet on any outcome at any time, without\nthe need for a matching offer from another bettor or a\nmarket maker. Pari-mutuel markets also involve no risk for the\nmarket institution, since they only redistribute money from\nlosing wagers to winning wagers. However, pari-mutuel\nmar1\nhttp://www.wired.com/news/ebiz/0,1272,61051,00.html\n170\nkets are not suitable for situations where information arrives\nover time, since there is a strong disincentive for placing bets\nuntil either (1) all information is revealed, or (2) the market\nis about to close. For this reason, pari-mutuel prices prior\nto the market\"s close cannot be considered a reflection of\ncurrent information. Pari-mutuel market participants\ncannot buy low and sell high: they cannot cash out gains (or\nlimit losses) before the event outcome is revealed. Because\nthe process whereby information arrives continuously over\ntime is the rule rather than the exception, the applicability\nof the standard pari-mutuel mechanism is questionable in a\nlarge number of settings.\nIn this paper, I develop a new mechanism suitable for\nhedging, speculating, and wagering, called a dynamic\nparimutuel market (DPM). A DPM can be thought of as a\nhybrid between a pari-mutuel market and a CDA. A DPM is\nindeed pari-mutuel in nature, meaning that it acts only to\nredistribute money from some traders to others, and so\nexposes the market institution to no volatility (no risk). A\nconstant, pre-determined subsidy is required to start the\nmarket. The subsidy can in principle be arbitrarily small and\nmight conceivably come from traders (via antes or\ntransaction fees) rather than the market institution, though a\nnontrivial outside subsidy may actually encourage trading\nand information aggregation. A DPM has the infinite\nliquidity of a pari-mutuel market: traders can always purchase\nshares in any outcome at any time, at some price\nautomatically set by the market institution. A DPM is also able\nto react to and incorporate information arriving over time,\nlike a CDA. The market institution changes the price for\nparticular outcomes based on the current state of wagering.\nIf a particular outcome receives a relatively large number of\nwagers, its price increases; if an outcome receives relatively\nfew wagers, its price decreases. Prices are computed\nautomatically using a price function, which can differ depending\non what properties are desired. The price function\ndetermines the instantaneous price per share for an infinitesimal\nquantity of shares; the total cost for purchasing n shares\nis computed as the integral of the price function from 0 to\nn. The complexity of the price function can be hidden from\ntraders by communicating only the ask prices for various lots\nof shares (e.g., lots of 100 shares), as is common practice in\nCDAs and CDAwMMs. DPM prices do reflect current\ninformation, and traders can cash out in an aftermarket to lock\nin gains or limit losses before the event outcome is revealed.\nWhile there is always a market maker willing to accept buy\norders, there is not a market maker accepting sell orders,\nand thus no guaranteed liquidity for selling: instead, selling\nis accomplished via a standard CDA mechanism. Traders\ncan always hedge-sell by purchasing the opposite outcome\nthan they already own.\n2. BACKGROUND AND RELATED WORK\n2.1 Pari-mutuel markets\nPari-mutuel markets are common at horse races [1, 22, 24,\n25, 26], dog races, and jai alai games. In a pari-mutuel\nmarket people place wagers on which of two or more mutually\nexclusive and exhaustive outcomes will occur at some time\nin the future. After the true outcome becomes known, all\nof the money that is lost by those who bet on the incorrect\noutcome is redistributed to those who bet on the correct\noutcome, in direct proportion to the amount they wagered.\nMore formally, if there are k mutually exclusive and\nexhaustive outcomes (e.g., k horses, exactly one of which will win),\nand M1, M2, . . . , Mk dollars are bet on each outcome, and\noutcome i occurs, then everyone who bet on an outcome\nj = i loses their wager, while everyone who bet on outcome\ni receives\nPk\nj=1 Mj/Mi dollars for every dollar they wagered.\nThat is, every dollar wagered on i receives an equal share of\nall money wagered. An equivalent way to think about the\nredistribution rule is that every dollar wagered on i is\nrefunded, then receives an equal share of all remaining money\nbet on the losing outcomes, or\nP\nj=i Mj/Mi dollars.\nIn practice, the market institution (e.g., the racetrack)\nfirst takes a certain percent of the total amount wagered,\nusually about 20% in the United States, then redistributes\nwhatever money remains to the winners in proportion to\ntheir amount bet.\nConsider a simple example with two outcomes, A and B.\nThe outcomes are mutually exclusive and exhaustive,\nmeaning that Pr(A \u2227 B) = 0 and Pr(A) + Pr(B) = 1. Suppose\n$800 is bet on A and $200 on B. Now suppose that A\noccurs (e.g., horse A wins the race). People who wagered on\nB lose their money, or $200 in total. People who wagered\non A win and each receives a proportional share of the total\n$1000 wagered (ignoring fees). Specifically, each $1 wager\non A entitles its owner a 1/800 share of the $1000, or $1.25.\nEvery dollar bet in a pari-mutuel market has an equal\npayoff, regardless of when the wager was placed or how much\nmoney was invested in the various outcomes at the time the\nwager was placed. The only state that matters is the final\nstate: the final amounts wagered on all the outcomes when\nthe market closes, and the identity of the correct outcome.\nAs a result, there is a disincentive to place a wager early\nif there is any chance that new information might become\navailable. Moreover, there are no guarantees about the\npayoff rate of a particular bet, except that it will be nonnegative\nif the correct outcome is chosen. Payoff rates can fluctuate\narbitrarily until the market closes. So a second reason not\nto bet early is to wait to get a better sense of the final\npayout rates. This is in contrast to CDAs and CDAwMMs, like\nthe stock market, where incentives exist to invest as soon as\nnew information is revealed.\nPari-mutuel bettors may be allowed to switch their\nchosen outcome, or even cancel their bet, prior to the market\"s\nclose. However, they cannot cash out of the market early,\nto either lock in gains or limit losses, if new information\nfavors one outcome over another, as is possible in a CDA\nor a CDAwMM. If bettors can cancel or change their bets,\nthen an aftermarket to sell existing wagers is not sensible:\nevery dollar wagered is worth exactly $1 up until the\nmarket\"s close-no one would buy at greater than $1 and no one\nwould sell at less than $1. Pari-mutuel bettors must wait\nuntil the outcome is revealed to realize any profit or loss.\nUnlike a CDA, in a pari-mutuel market, anyone can place\na wager of any amount at any time-there is in a sense\ninfinite liquidity for buying. A CDAwMM also has built-in\nliquidity, but at the cost of significant risk for the market\nmaker. In a pari-mutuel market, since money is only\nredistributed among bettors, the market institution itself has no\nrisk. The main drawback of a pari-mutuel market is that\nit is useful only for capturing the value of an uncertain\nasset at some instant in time. It is ill-suited for situations\nwhere information arrives over time, continuously updating\nthe estimated value of the asset-situations common in\nal171\nmost all trading and wagering scenarios. There is no notion\nof buying low and selling high, as occurs in a CDA, where\nbuying when few others are buying (and the price is low) is\nrewarded more than buying when many others are buying\n(and the price is high). Perhaps for this reason, in most\ndynamic environments, financial mechanisms like the CDA\nthat can react in real-time to changing information are more\ntypically employed to facilitate speculating and hedging.\nSince a pari-mutuel market can estimate the value of an\nasset at a single instant in time, a repeated pari-mutuel\nmarket, where distinct pari-mutuel markets are run at\nconsecutive intervals, could in principle capture changing\ninformation dynamics. But running multiple consecutive\nmarkets would likely thin out trading in each individual market.\nAlso, in each individual pari-mutuel market, the incentives\nwould still be to wait to bet until just before the ending\ntime of that particular market. This last problem might\nbe mitigated by instituting a random stopping rule for each\nindividual pari-mutuel market.\nIn laboratory experiments, pari-mutuel markets have shown\na remarkable ability to aggregate and disseminate\ninformation dispersed among traders, at least for a single snapshot\nin time [17]. A similar ability has been recognized at real\nracetracks [1, 22, 24, 25, 26].\n2.2 Financial markets\nIn the financial world, wagering on the outcomes of\nuncertain future propositions is also common. The typical market\nmechanism used is the continuous double auction (CDA).\nThe term securities market in economics and finance\ngenerically encompasses a number of markets where speculating\non uncertain events is possible. Examples include stock\nmarkets like NASDAQ, options markets like the CBOE [13],\nfutures markets like the CME [21], other derivatives markets,\ninsurance markets, political stock markets [6, 7], idea futures\nmarkets [12], decision markets [10] and even market games\n[3, 15, 16]. Securities markets generally have an economic\nand social value beyond facilitating speculation or wagering:\nthey allow traders to hedge risk, or to insure against\nundesirable outcomes. So if a particular outcome has disutility\nfor a trader, he or she can mitigate the risk by wagering\nfor the outcome, to arrange for compensation in case the\noutcome occurs. In this sense, buying automobile insurance\nis effectively a bet that an accident or other covered event\nwill occur. Similarly, buying a put option, which is useful\nas a hedge for a stockholder, is a bet that the underlying\nstock will go down. In practice, agents engage in a mixture\nof hedging and speculating, and there is no clear dividing\nline between the two [14]. Like pari-mutuel markets, often\nprices in financial markets are excellent information\naggregators, yielding very accurate forecasts of future events [5,\n18, 19].\nA CDA constantly matches orders to buy an asset with\norders to sell. If at any time one party is willing to buy\none unit of the asset at a bid price of pbid, while another\nparty is willing to sell one unit of the asset at an ask price of\npask, and pbid is greater than or equal to pask, then the two\nparties transact (at some price between pbid and pask). If\nthe highest bid price is less than the lowest ask price, then no\ntransactions occur. In a CDA, the bid and ask prices rapidly\nchange as new information arrives and traders reassess the\nvalue of the asset. Since the auctioneer only matches willing\nbidders, the auctioneer takes on no risk. However, buyers\ncan only buy as many shares as sellers are willing to sell; for\nany transaction to occur, there must be a counterparty on\nthe other side willing to accept the trade.\nAs a result, when few traders participate in a CDA, it may\nbecome illiquid, meaning that not much trading activity\noccurs. The spread between the highest bid price and the\nlowest ask price may be very large, or one or both queues may\nbe completely empty, discouraging trading.2\nOne way to\ninduce liquidity is to provide a market maker who is willing\nto accept a large number of buy and sell orders at particular\nprices. We call this mechanism a CDA with market maker\n(CDAwMM).3\nConceptually, the market maker is just like\nany other trader, but typically is willing to accept a much\nlarger volume of trades. The market maker may be a\nperson, or may be an automated algorithm. Adding a market\nmaker to the system increases liquidity, but exposes the\nmarket maker to risk. Now, instead of only matching trades, the\nsystem actually takes on risk of its own, and depending on\nwhat happens in the future, may lose considerable amounts\nof money.\n2.3 Wagering markets\nThe typical Las Vegas bookmaker or oddsmaker functions\nmuch like a market maker in a CDA. In this case, the\nmarket institution (the book or house) sets the odds,4\ninitially\naccording to expert opinion, and later in response to the\nrelative level of betting on the various outcomes. Unlike in a\npari-mutuel environment, whenever a wager is placed with\na bookmaker, the odds or terms for that bet are fixed at the\ntime of the bet. The bookmaker profits by offering different\nodds for the two sides of the bet, essentially defining a\nbidask spread. While odds may change in response to changing\ninformation, any bets made at previously set odds remain\nin effect according to the odds at the time of the bet; this\nis precisely in analogy to a CDAwMM. One difference\nbetween a bookmaker and a market maker is that the former\nusually operates in a take it or leave it mode: bettors\ncannot place their own limit orders on a common queue, they\ncan in effect only place market orders at prices defined by\nthe bookmaker. Still, the bookmaker certainly reacts to\nbettor demand. Like a market maker, the bookmaker exposes\nitself to significant risk. Sports betting markets have also\nbeen shown to provide high quality aggregate forecasts [4,\n9, 23].\n2.4 Market scoring rule\nHanson\"s [11] market scoring rule (MSR) is a new\nmechanism for hedging and speculating that shares some\nproperties in common with a DPM. Like a DPM, an MSR can be\nconceptualized as an automated market maker always\nwilling to accept a trade on any event at some price. An MSR\nrequires a patron to subsidize the market. The patron\"s final\nloss is variable, and thus technically implies a degree of risk,\nthough the maximum loss is bounded. An MSR maintains\na probability distribution over all events. At any time any\n2\nThin markets do occur often in practice, and can be\nseen in a variety of the less popular markets available on\nhttp://TradeSports.com, or in some financial options\nmarkets, for example.\n3\nA very clear example of a CDAwMM is the interactive\nbetting market on http://WSEX.com.\n4\nOr, alternatively, the bookmaker sets the game line in order\nto provide even-money odds.\n172\ntrader who believes the probabilities are wrong can change\nany part of the distribution by accepting a lottery ticket that\npays off according to a scoring rule (e.g., the logarithmic\nscoring rule) [27], as long as that trader also agrees to pay\noff the most recent person to change the distribution. In the\nlimit of a single trader, the mechanism behaves like a\nscoring rule, suitable for polling a single agent for its probability\ndistribution. In the limit of many traders, it produces a\ncombined estimate. Since the market essentially always has a\ncomplete set of posted prices for all possible outcomes, the\nmechanism avoids the problem of thin markets or illiquidity.\nAn MSR is not pari-mutuel in nature, as the patron in\ngeneral injects a variable amount of money into the system. An\nMSR provides a two-sided automated market maker, while\na DPM provides a one-sided automated market maker. In\nan MSR, the vector of payoffs across outcomes is fixed at\nthe time of the trade, while in a DPM, the vector of payoffs\nacross outcomes depends both on the state of wagering at\nthe time of the trade and the state of wagering at the\nmarket\"s close. While the mechanisms are quite different-and\nso trader acceptance and incentives may strongly differ-the\nproperties and motivations of DPMs and MSRs are quite\nsimilar.\nHanson shows how MSRs are especially well suited for\nallowing bets on a combinatorial number of outcomes. The\npatron\"s payment for subsidizing trading on all 2n\npossible\ncombinations of n events is no larger than the sum of\nsubsidizing the n event marginals independently. The mechanism\nwas planned for use in the Policy Analysis Market (PAM), a\nfutures market in Middle East related outcomes and funded\nby DARPA [20], until a media firestorm killed the project.5\nAs of this writing, the founders of PAM were considering\nreopening under private control.6\n3. A DYNAMIC PARI-MUTUEL MARKET\n3.1 High-level description\nIn contrast to a standard pari-mutuel market, where each\ndollar always buys an equal share of the payoff, in a DPM\neach dollar buys a variable share in the payoff depending on\nthe state of wagering at the time of purchase. So a wager\non A at a time when most others are wagering on B offers a\ngreater possible profit than a wager on A when most others\nare also wagering on A.\nA natural way to communicate the changing payoff of a\nbet is to say that, at any given time, a certain amount of\nmoney will buy a certain number of shares in one outcome\nthe other. Purchasing a share entitles its owner to an equal\nstake in the winning pot should the chosen outcome occur.\nThe payoff is variable, because when few people are betting\non an outcome, shares will generally be cheaper than at a\ntime when many people are betting that outcome. There\nis no pre-determined limit on the number of shares: new\nshares can be continually generated as trading proceeds.\nFor simplicity, all analyses in this paper consider the\nbinary outcome case; generalizing to multiple discrete\noutcomes should be straightforward. Denote the two outcomes\nA and B. The outcomes are mutually exclusive and\nex5\nSee http://hanson.gmu.edu/policyanalysismarket.html for\nmore information, or http://dpennock.com/pam.html for\ncommentary.\n6\nhttp://www.policyanalysismarket.com/\nhaustive. Denote the instantaneous price per share of A as\np1 and the price per share of B as p2. Denote the payoffs\nper share as P1 and P2, respectively. These four numbers,\np1, p2, P1, P2 are the key numbers that traders must track\nand understand. Note that the price is set at the time of the\nwager; the payoff per share is finalized only after the event\noutcome is revealed.\nAt any time, a trader can purchase an infinitesimal\nquantity of shares of A at price p1 (and similarly for B). However,\nsince the price changes continuously as shares are purchased,\nthe cost of buying n shares is computed as the integral of a\nprice function from 0 to n. The use of continuous functions\nand integrals can be hidden from traders by aggregating the\nautomated market maker\"s sell orders into discrete lots of,\nsay, 100 shares each. These ask orders can be\nautomatically entered into the system by the market institution, so\nthat traders interact with what looks like a more familiar\nCDA; we examine this interface issue in more detail below\nin Section 4.2.\nFor our analysis, we introduce the following additional\nnotation. Denote M1 as the total amount of money wagered\non A, M2 as the total amount of money wagered on B,\nT = M1 + M2 as the total amount of money wagered on\nboth sides, N1 as the total number of shares purchased of\nA, and N2 as the total number of shares purchased of B.\nThere are many ways to formulate the price function.\nSeveral natural price functions are outlined below; each is\nmotivated as the unique solution to a particular constraint on\nprice dynamics.\n3.2 Advantages and disadvantages\nTo my knowledge, a DPM is the only known mechanism\nfor hedging and speculating that exhibits all three of the\nfollowing properties: (1) guaranteed liquidity, (2) no risk\nfor the market institution, and (3) continuous incorporation\nof information. A standard pari-mutuel fails (3). A CDA\nfails (1). A CDAwMM, the bookmaker mechanism, and an\nMSR all fail (2). Even though technically an MSR exposes\nits patron to risk (i.e., a variable future payoff), the\npatron\"s maximum loss is bounded, so the distinction between\na DPM and an MSR in terms of these three properties is\nmore technical than practical.\nDPM traders can cash out of the market early, just like\nstock market traders, to lock in a profit or limit a loss, an\naction that is simply not possible in a standard pari-mutuel.\nA DPM also has some drawbacks. The payoff for a\nwager depends both on the price at the time of the trade, and\non the final payoff per share at the market\"s close. This\ncontrasts with the CDA variants, where the payoff vector\nacross possible future outcomes is fixed at the time of the\ntrade. So a trader\"s strategic optimization problem is\ncomplicated by the need to predict the final values of P1 and\nP2. If P changes according to a random walk, then traders\ncan take the current P as an unbiased estimate of the\nfinal P, greatly decreasing the complexity of their\noptimization. If P does not change according to a random walk,\nthe mechanism still has utility as a mechanism for hedging\nand speculating, though optimization may be difficult, and\ndetermining a measure of the market\"s aggregate opinion of\nthe probabilities of A and B may be difficult. We discuss\nthe implications of random walk behavior further below in\nSection 4.1 in the discussion surrounding Assumption 3.\nA second drawback of a DPM is its one-sided nature.\n173\nWhile an automated market maker always stands ready to\naccept buy orders, there is no corresponding market maker\nto accept sell orders. Traders must sell to each other\nusing a standard CDA mechanism, for example by posting an\nask order at a price at or below the market maker\"s current\nask price. Traders can also always hedge-sell by\npurchasing shares in the opposite outcome from the market maker,\nthereby hedging their bet if not fully liquidating it.\n3.3 Redistribution rule\nIn a standard pari-mutuel market, payoffs can be\ncomputed in either of two equivalent ways: (1) each winning $1\nwager receives a refund of the initial $1 paid, plus an equal\nshare of all losing wagers, or (2) each winning $1 wager\nreceives an equal share of all wagers, winning or losing.\nBecause each dollar always earns an equal share of the payoff,\nthe two formulations are precisely the same:\n$1 +\nMlose\nMwin\n=\nMwin + Mlose\nMwin\n.\nIn a dynamic pari-mutuel market, because each dollar is\nnot equally weighted, the two formulations are distinct, and\nlead to significantly different price functions and\nmechanisms, each with different potentially desirable properties.\nWe consider each case in turn. The next section analyzes\ncase (1), where only losing money is redistributed. Section 5\nexamines case (2), where all money is redistributed.\n4. DPM I: LOSING MONEY\nREDISTRIBUTED\nFor the case where the initial payments on winning bets\nare refunded, and only losing money is redistributed, the\nrespective payoffs per share are simply:\nP1 =\nM2\nN1\nP2 =\nM1\nN2\n.\nSo, if A occurs, shareholders of A receive all of their\ninitial payment back, plus P1 dollars per share owned, while\nshareholders of B lose all money wagered. Similarly, if B\noccurs, shareholders of B receive all of their initial payment\nback, plus P2 dollars per share owned, while shareholders of\nA lose all money wagered.\nWithout loss of generality, I will analyze the market from\nthe perspective of A, deriving prices and payoffs for A only.\nThe equations for B are symmetric.\nThe trader\"s per-share expected value for purchasing an\ninfinitesimal quantity of shares of A is\nE[ shares]\n= Pr(A) \u00b7 E [P1|A] \u2212 (1 \u2212 Pr(A)) \u00b7 p1\nE[ shares]\n= Pr(A) \u00b7 E\n\u00bb\nM2\nN1\n\u02db\n\u02db\n\u02db\n\u02db A\n\n\u2212 (1 \u2212 Pr(A)) \u00b7 p1\nwhere is an infinitesimal quantity of shares of A, Pr(A)\nis the trader\"s belief in the probability of A, and p1 is the\ninstantaneous price per share of A for an infinitesimal\nquantity of shares. E[P1|A] is the trader\"s expectation of the\npayoff per share of A after the market closes and given that\nA occurs. This is a subtle point. The value of P1 does not\nmatter if B occurs, since in this case shares of A are\nworthless, and the current value of P1 does not necessarily matter\nas this may change as trading continues. So, in order to\ndetermine the expected value of shares of A, the trader must\nestimate what he or she expects the payoff per share to be\nin the end (after the market closes) if A occurs.\nIf E[ shares]/ > 0, a risk-neutral trader should purchase\nshares of A. How many shares? This depends on the price\nfunction determining p1. In general, p1 increases as more\nshares are purchased. The risk-neutral trader should\ncontinue purchasing shares until E[ shares]/ = 0. (A\nriskaverse trader will generally stop purchasing shares before\ndriving E[ shares]/ all the way to zero.) Assuming\nriskneutrality, the trader\"s optimization problem is to choose a\nnumber of shares n \u2265 0 of A to purchase, in order to\nmaximize\nE[n shares] = Pr(A)\u00b7n\u00b7E [P1|A]\u2212(1\u2212Pr(A))\u00b7\nZ n\n0\np1(n)dn.\n(1)\nIt\"s easy to see that the same value of n can be solved for by\nfinding the number of shares required to drive E[ shares]/\nto zero. That is, find n \u2265 0 satisfying\n0 = Pr(A) \u00b7 E [P1|A] \u2212 (1 \u2212 Pr(A)) \u00b7 p1(n),\nif such a n exists, otherwise n = 0.\n4.1 Market probability\nAs traders who believe that E[ shares of A]/ > 0\npurchase shares of A and traders who believe that E[ shares\nof B]/ > 0 purchase shares of B, the prices p1 and p2\nchange according to a price function, as prescribed below.\nThe current prices in a sense reflect the market\"s opinion as\na whole of the relative probabilities of A and B.\nAssuming an efficient marketplace, the market as a whole\nconsiders E[ shares]/ = 0, since the mechanisms is a zero sum\ngame. For example, if market participants in aggregate felt\nthat E[ shares]/ > 0, then there would be net demand for\nA, driving up the price of A until E[ shares]/ = 0. Define\nMPr(A) to be the market probability of A, or the\nprobability of A inferred by assuming that E[ shares]/ = 0. We\ncan consider MPr(A) to be the aggregate probability of A\nas judged by the market as a whole. MPr(A) is the solution\nto\n0 = MPr(A) \u00b7 E[P1|A] \u2212 (1 \u2212 MPr(A)) \u00b7 p1.\nSolving we get\nMPr(A) =\np1\np1 + E[P1|A]\n. (2)\nAt this point we make a critical assumption in order to\ngreatly simplify the analysis; we assume that\nE[P1|A] = P1. (3)\nThat is, we assume that the current value for the payoff per\nshare of A is the same as the expected final value of the\npayoff per share of A given that A occurs. This is certainly true\nfor the last (infinitesimal) wager before the market closes.\nIt\"s not obvious, however, that the assumption is true well\nbefore the market\"s close. Basically, we are assuming that\nthe value of P1 moves according to an unbiased random\nwalk: the current value of P1 is the best expectation of\nits future value. I conjecture that there are reasonable\nmarket efficiency conditions under which assumption (3) is true,\nthough I have not been able to prove that it arises naturally\nfrom rational trading. We examine scenarios below in which\n174\nassumption (3) seems especially plausible. Nonetheless, the\nassumption effects our analysis only. Regardless of whether\n(3) is true, each price function derived below implies a\nwelldefined zero-sum game in which traders can play. If traders\ncan assume that (3) is true, then their optimization\nproblem (1) is greatly simplified; however, optimizing (1) does\nnot depend on the assumption, and traders can still optimize\nby strategically projecting the final expected payoff in\nwhatever complicated way they desire. So, the utility of DPM for\nhedging and speculating does not necessarily hinge on the\ntruth of assumption (3). On the other hand, the ability to\neasily infer an aggregate market consensus probability from\nmarket prices does depend on (3).\n4.2 Price functions\nA variety of price functions seem reasonable, each\nexhibiting various properties, and implying differing market\nprobabilities.\n4.2.1 Price function I: Price of A equals payoff of B\nOne natural price function to consider is to set the price\nper share of A equal to the payoff per share of B, and set\nthe price per share of B equal to the payoff per share of A.\nThat is,\np1 = P2\np2 = P1. (4)\nEnforcing this relationship reduces the dimensionality of\nthe system from four to two, simplifying the interface: traders\nneed only track two numbers instead of four. The\nrelationship makes sense, since new information supporting A\nshould encourage purchasing of shares A, driving up both\nthe price of A and the payoff of B, and driving down the\nprice of B and the payoff of A. In this setting, assumption\n(3) seems especially reasonable, since if an efficient market\nhypothesis leads prices to follow a random walk, than payoffs\nmust also follow a random walk.\nThe constraints (4) lead to the following derivation of the\nmarket probability:\nMPr(A)P1 = MPr(B)p1\nMPr(A)P1 = MPr(B)P2\nMPr(A)\nMPr(B)\n=\nP2\nP1\nMPr(A)\nMPr(B)\n=\nM1\nN2\nM2\nN1\nMPr(A)\nMPr(B)\n=\nM1N1\nM2N2\nMPr(A) =\nM1N1\nM1N1 + M2N2\n(5)\nThe constraints (4) specify the instantaneous\nrelationship between payoff and price. From this, we can derive\nhow prices change when (non-infinitesimal) shares are\npurchased. Let n be the number of shares purchased and let m\nbe the amount of money spent purchasing n shares. Note\nthat p1 = dm/dn, the instantaneous price per share, and\nm =\nR n\n0\np1(n)dn. Substituting into equation (4), we get:\np1 = P2\ndm\ndn\n=\nM1 + m\nN2\ndm\nM1 + m\n=\ndn\nN2\nZ\ndm\nM1 + m\n=\nZ\ndn\nN2\nln(M1 + m) =\nn\nN2\n+ C\nm = M1\nh\ne\nn\nN2 \u2212 1\ni\n(6)\nEquation 6 gives the cost of purchasing n shares. The\ninstantaneous price per share as a function of n is\np1(n) =\ndm\ndn\n=\nM1\nN2\ne\nn\nN2 . (7)\nNote that p1(0) = M1/N2 = P2 as required. The derivation\nof the price function p2(n) for B is analogous and the results\nare symmetric.\nThe notion of buying infinitesimal shares, or\nintegrating costs over a continuous function, are probably foreign\nto most traders. A more standard interface can be\nimplemented by discretizing the costs into round lots of shares,\nfor example lots of 100 shares. Then ask orders of 100\nshares each at the appropriate price can be automatically\nplaced by the market institution. For example, the\nmarket institution can place an ask order for 100 shares at\nprice m(100)/100, another ask order for 100 shares at price\n(m(200)\u2212m(100))/100, a third ask for 100 shares at (m(300)\u2212\nm(200))/100, etc. In this way, the market looks more\nfamiliar to traders, like a typical CDA with a number of ask\norders at various prices automatically available. A trader\nbuying less than 100 shares would pay a bit more than if\nthe true cost were computed using (6), but the discretized\ninterface would probably be more intuitive and transparent\nto the majority of traders.\nThe above equations assume that all money that comes in\nis eventually returned or redistributed. In other words, the\nmechanism is a zero sum game, and the market institution\ntakes no portion of the money. This could be generalized so\nthat the market institution always takes a certain amount,\nor a certain percent, or a certain amount per transaction, or\na certain percent per transaction, before money in returned\nor redistributed.\nFinally, note that the above price function is undefined\nwhen the amount bet or the number of shares are zero. So\nthe system must begin with some positive amount on both\nsides, and some positive number of shares outstanding on\nboth sides. These initial amounts can be arbitrarily small in\nprinciple, but the size of the initial subsidy may affect the\nincentives of traders to participate. Also, the smaller the\ninitial amounts, the more each new dollar effects the prices.\nThe initialization amounts could be funded as a subsidy from\nthe market institution or a patron, which I\"ll call a seed\nwager, or from a portion of the fees charged, which I\"ll call\nan ante wager.\n4.2.2 Price function II: Price of A proportional to\nmoney on A\nA second price function can be derived by requiring the\nratio of prices to be equal to the ratio of money wagered.\n175\nThat is,\np1\np2\n=\nM1\nM2\n. (8)\nIn other words, the price of A is proportional to the amount\nof money wagered on A, and similarly for B. This seems like\na particularly natural way to set the price, since the more\nmoney that is wagered on one side, the cheaper becomes a\nshare on the other side, in exactly the same proportion.\nUsing Equation 8, along with (2) and (3), we can derive\nthe implied market probability:\nM1\nM2\n=\np1\np2\n=\nMPr(A)\nMPr(B)\n\u00b7 M2\nN1\nMPr(B)\nMPr(A)\n\u00b7 M1\nN2\n=\n(MPr(A))2\n(MPr(B))2\n\u00b7\nM2N2\nM1N1\n(MPr(A))2\n(MPr(B))2\n=\n(M1)2\nN1\n(M2)2N2\nMPr(A)\nMPr(B)\n=\nM1\n\u221a\nN1\nM2\n\u221a\nN2\nMPr(A) =\nM1\n\u221a\nN1\nM1\n\u221a\nN1 + M2\n\u221a\nN2\n(9)\nWe can solve for the instantaneous price as follows:\np1 =\nMPr(A)\nMPr(B)\n\u00b7 P1\n=\nM1\n\u221a\nN1\nM2\n\u221a\nN2\n\u00b7\nM2\nN1\n=\nM1\n\u221a\nN1N2\n(10)\nWorking from the above instantaneous price, we can\nderive the implied cost function m as a function of the number\nn of shares purchased as follows:\ndm\ndn\n=\nM1 + m\n\u221a\nN1 + n\n\u221a\nN2\nZ\ndm\nM1 + m\n=\nZ\ndn\n\u221a\nN1 + n\n\u221a\nN2\nln(M1 + m) =\n2\nN2\n[(N1 + n)N2]\n1\n2 + C\nm = M1\n\"\ne\n2\nr\nN1+n\nN2\n\u22122\nr\nN1\nN2 \u2212 1\n#\n. (11)\nFrom this we get the price function:\np1(n) =\ndm\ndn\n=\nM1\np\n(N1 + n)N2\ne\n2\nr\nN1+n\nN2\n\u22122\nr\nN1\nN2\n. (12)\nNote that, as required, p1(0) = M1/\n\u221a\nN1N2, and p1(0)/p2(0)\n= M1/M2. If one uses the above price function, then the\nmarket dynamics will be such that the ratio of the\n(instantaneous) prices of A and B always equals the ratio of the\namounts wagered on A and B, which seems fairly natural.\nNote that, as before, the mechanism can be modified to\ncollect transaction fees of some kind. Also note that seed or\nante wagers are required to initialize the system.\n5. DPM II: ALL MONEY REDISTRIBUTED\nAbove we examined the policy of refunding winning\nwagers and redistributing only losing wagers. In this section\nwe consider the second policy mentioned in Section 3.3: all\nmoney from all wagers are collected and redistributed to\nwinning wagers.\nFor the case where all money is redistributed, the\nrespective payoffs per share are:\nP1 =\nM1 + M2\nN1\n=\nT\nN1\nP2 =\nM1 + M2\nN2\n=\nT\nN2\n,\nwhere T = M1 + M2 is the total amount of money wagered\non both sides. So, if A occurs, shareholders of A lose their\ninitial price paid, but receive P1 dollars per share owned;\nshareholders of B simply lose all money wagered. Similarly,\nif B occurs, shareholders of B lose their initial price paid,\nbut receive P2 dollars per share owned; shareholders of A\nlose all money wagered.\nIn this case, the trader\"s per-share expected value for\npurchasing an infinitesimal quantity of shares of A is\nE[ shares]\n= Pr(A) \u00b7 E [P1|A] \u2212 p1. (13)\nA risk-neutral trader optimizes by choosing a number of\nshares n \u2265 0 of A to purchase, in order to maximize\nE[n shares] = Pr(A) \u00b7 n \u00b7 E [P1|A] \u2212\nZ n\n0\np1(n)dn\n= Pr(A) \u00b7 n \u00b7 E [P1|A] \u2212 m (14)\nThe same value of n can be solved for by finding the number\nof shares required to drive E[ shares]/ to zero. That is,\nfind n \u2265 0 satisfying\n0 = Pr(A) \u00b7 E [P1|A] \u2212 p1(n),\nif such a n exists, otherwise n = 0.\n5.1 Market probability\nIn this case MPr(A), the aggregate probability of A as\njudged by the market as a whole, is the solution to\n0 = MPr(A) \u00b7 E[P1|A] \u2212 p1.\nSolving we get\nMPr(A) =\np1\nE[P1|A]\n. (15)\nAs before, we make the simplifying assumption (3) that\nthe expected final payoff per share equals the current payoff\nper share. The assumption is critical for our analysis, but\nmay not be required for a practical implementation.\n5.2 Price functions\nFor the case where all money is distributed, the\nconstraints (4) that keep the price of A equal to the payoff of B,\nand vice versa, do not lead to the derivation of a coherent\nprice function.\nA reasonable price function can be derived from the\nconstraint (8) employed in Section 4.2.2, where we require that\nthe ratio of prices to be equal to the ratio of money wagered.\nThat is, p1/p2 = M1/M2. In other words, the price of A is\nproportional to the amount of money wagered on A, and\nsimilarly for B.\n176\nUsing Equations 3, 8, and 15 we can derive the implied\nmarket probability:\nM1\nM2\n=\np1\np2\n=\nMPr(A)\nMPr(B)\n\u00b7\nT\nN1\n\u00b7\nN2\nT\n=\nMPr(A)\nMPr(B)\n\u00b7\nN2\nN1\nMPr(A)\nMPr(B)\n=\nM1N1\nM2N2\nMPr(A) =\nM1N1\nM1N1 + M2N2\n(16)\nInterestingly, this is the same market probability derived in\nSection 4.2.1 for the case of losing-money redistribution with\nthe constraints that the price of A equal the payoff of B and\nvice versa.\nThe instantaneous price per share for an infinitesimal\nquantity of shares is:\np1 =\n(M1)2\n+ M1M2\nM1N1 + M2N2\n=\nM1 + M2\nN1 + M2\nM1\nN2\nWorking from the above instantaneous price, we can\nderive the number of shares n that can be purchased for m\ndollars, as follows:\ndm\ndn\n=\nM1 + M2 + m\nN1 + n + M2\nM1+m\nN2\ndn\ndm\n=\nN1 + n + M2\nM1+m\nN2\nM1 + M2 + m\n(17)\n\u00b7 \u00b7 \u00b7\nn =\nm(N1 \u2212 N2)\nT\n+\nN2(T + m)\nM2\nln\n\u00bb\nT(M1 + m)\nM1(T + m)\n\n.\nNote that we solved for n(m) rather than m(n). I could not\nfind a closed-form solution for m(n), as was derived for the\ntwo other cases above. Still, n(m) can be used to determine\nhow many shares can be purchased for m dollars, and the\ninverse function can be approximated to any degree\nnumerically. From n(m) we can also compute the price function:\np1(m) =\ndm\ndn\n=\n(M1 + m)M2T\ndenom\n, (18)\nwhere\ndenom = (M1 + m)M2N1 + (M2 \u2212 m)M2N2\n+T(M1 + m)N2 ln\n\u00bb\nT(M1 + m)\nM1(T + m)\n\nNote that, as required, p1(0)/p2(0) = M1/M2. If one uses\nthe above price function, then the market dynamics will be\nsuch that the ratio of the (instantaneous) prices of A and B\nalways equals the ratio of the amounts wagered on A and\nB.\nThis price function has another desirable property: it acts\nsuch that the expected value of wagering $1 on A and\nsimultaneously wagering $1 on B equals zero, assuming (3). That\nis, E[$1 of A + $1 of B] = 0. The derivation is omitted.\n5.3 Comparing DPM I and II\nThe main advantage of refunding winning wagers (DPM\nI) is that every bet on the winning outcome is guaranteed\nto at least break even. The main disadvantage of\nrefunding winning wagers is that shares are not homogenous: each\nshare of A, for example, is actually composed of two distinct\nparts: (1) the refund, or a lottery ticket that pays $p if A\noccurs, where p is the price paid per share, and (2) one share\nof the final payoff ($P1) if A occurs. This complicates the\nimplementation of an aftermarket to cash out of the market\nearly, which we will examine below in Section 7. When all\nmoney is redistributed (DPM II), shares are homogeneous:\neach share entitles its owner to an equal slice of the final\npayoff. Because shares are homogenous, the\nimplementation of an aftermarket is straightforward, as we shall see in\nSection 7. On the other hand, because initial prices paid\nare not refunded for winning bets, there is a chance that, if\nprices swing wildly enough, a wager on the correct outcome\nmight actually lose money. Traders must be aware that if\nthey buy in at an excessively high price that later tumbles\nallowing many others to get in at a much lower price, they\nmay lose money in the end regardless of the outcome. From\ninformal experiments, I don\"t believe this eventuality would\nbe common, but nonetheless it requires care in\ncommunicating to traders the possible risks. One potential fix would be\nfor the market maker to keep track of when the price is going\ntoo low, endangering an investor on the correct outcome. At\nthis point, the market maker could artificially stop lowering\nthe price. Sell orders in the aftermarket might still come in\nbelow the market maker\"s price, but in this way the system\ncould ensure that every wager on the correct outcome at\nleast breaks even.\n6. OTHER VARIATIONS\nA simple ascending price function would set p1 = \u03b1M1\nand p2 = \u03b1M2, where \u03b1 > 0. In this case, prices would only\ngo up. For the case of all money being redistributed, this\nwould eliminate the possibility of losing money on a wager on\nthe correct outcome. Even though the market maker\"s price\nonly rises, the going price may fall well below the market\nmaker\"s price, as ask orders are placed in the aftermarket.\nI have derived price functions for several other cases, using\nthe same methodology above. Each price function may have\nits own desirable properties, but it\"s not clear which is best,\nor even that a single best method exists. Further analyses\nand, more importantly, empirical investigations are required\nto answer these questions.\n7. AFTERMARKETS\nA key advantage of DPM over a standard pari-mutuel\nmarket is the ability to cash out of the market before it\ncloses, in order to take a profit or limit a loss. This is\naccomplished by allowing traders to place ask orders on the\nsame queue as the market maker. So traders can sell the\nshares that they purchased at or below the price set by the\nmarket maker. Or traders can place a limit sell order at any\nprice. Buyers will purchase any existing shares for sale at\nthe lower prices first, before purchasing new shares from the\nmarket maker.\n7.1 Aftermarket for DPM II\nFor the second main case explored above, where all money\n177\nis redistributed, allowing an aftermarket is simple. In fact,\naftermarket may be a poor descriptor: buying and selling\nare both fully integrated into the same mechanism. Every\nshare is worth precisely the same amount, so traders can\nsimply place ask orders on the same queue as the market maker\nin order to sell their shares. New buyers will accept the\nlowest ask price, whether it comes from the market maker or\nanother trader. In this way, traders can cash out early and\nwalk away with their current profit or loss, assuming they\ncan find a willing buyer.\n7.2 Aftermarket for DPM I\nWhen winning wagers are refunded and only losing wagers\nare redistributed, each share is potentially worth a different\namount, depending on how much was paid for it, so it is not\nas simple a matter to set up an aftermarket. However, an\naftermarket is still possible. In fact, much of the complexity\ncan be hidden from traders, so it looks nearly as simple as\nplacing a sell order on the queue.\nIn this case shares are not homogenous: each share of A\nis actually composed of two distinct parts: (1) the refund of\np \u00b7 1A dollars, and (2) the payoff of P1 \u00b7 1A dollars, where p\nis the per-share price paid and 1A is the indicator function\nequalling 1 if A occurs, and 0 otherwise. One can\nimagine running two separate aftermarkets where people can sell\nthese two respective components. However, it is possible to\nautomate the two aftermarkets, by automatically bundling\nthem together in the correct ratio and selling them in the\ncentral DPM. In this way, traders can cash out by placing\nsell orders on the same queue as the DPM market maker,\neffectively hiding the complexity of explicitly having two\nseparate aftermarkets. The bundling mechanism works as\nfollows. Suppose the current price for 1 share of A is p1. A\nbuyer agrees to purchase the share at p1. The buyer pays\np1 dollars and receives p1 \u00b7 1A + P1 \u00b7 1A dollars. If there is\nenough inventory in the aftermarkets, the buyer\"s share is\nconstructed by bundling together p1 \u00b71A from the first\naftermarket, and P1 \u00b71A from the second aftermarket. The seller\nin the first aftermarket receives p1MPr(A) dollars, and the\nseller in the second aftermarket receives p1MPr(B) dollars.\n7.3 Pseudo aftermarket for DPM I\nThere is an alternative pseudo aftermarket that\"s\npossible for the case of DPM I that does not require bundling.\nConsider a share of A purchased for $5. The share is\ncomposed of $5\u00b71A and $P1 \u00b71A. Now suppose the current price\nhas moved from $5 to $10 per share and the trader wants to\ncash out at a profit. The trader can sell 1/2 share at market\nprice (1/2 share for $5), receiving all of the initial $5\ninvestment back, and retaining 1/2 share of A. The 1/2 share is\nworth either some positive amount, or nothing, depending\non the outcome and the final payoff. So the trader is left\nwith shares worth a positive expected value and all of his or\nher initial investment. The trader has essentially cashed out\nand locked in his or her gains. Now suppose instead that\nthe price moves downward, from $5 to $2 per share. The\ntrader decides to limit his or her loss by selling the share for\n$2. The buyer gets the 1 share plus $2\u00b71A (the buyer\"s price\nrefunded). The trader (seller) gets the $2 plus what remains\nof the original price refunded, or $3 \u00b7 1A. The trader\"s loss\nis now limited to $3 at most instead of $5. If A occurs, the\ntrader breaks even; if B occurs, the trader loses $3.\nAlso note that-in either DPM formulation-traders can\nalways hedge sell by buying the opposite outcome without\nthe need for any type of aftermarket.\n8. CONCLUSIONS\nI have presented a new market mechanism for wagering\non, or hedging against, a future uncertain event, called a\ndynamic pari-mutuel market (DPM). The mechanism\ncombines the infinite liquidity and risk-free nature of a\nparimutuel market with the dynamic nature of a CDA, making\nit suitable for continuous information aggregation. To my\nknowledge, all existing mechanisms-including the standard\npari-mutuel market, the CDA, the CDAwMM, the bookie\nmechanism, and the MSR-exhibit at most two of the three\nproperties. An MSR is the closest to a DPM in terms of\nthese properties, if not in terms of mechanics. Given some\nnatural constraints on price dynamics, I have derived in\nclosed form the implied price functions, which encode how\nprices change continuously as shares are purchased. The\ninterface for traders looks much like the familiar CDA, with\nthe system acting as an automated market maker willing\nto accept an infinite number of buy orders at some price.\nI have explored two main variations of a DPM: one where\nonly losing money is redistributed, and one where all money\nis redistributed. Each has its own pros and cons, and each\nsupports several reasonable price functions. I have described\nthe workings of an aftermarket, so that traders can cash out\nof the market early, like in a CDA, to lock in their gains\nor limit their losses, an operation that is not possible in a\nstandard pari-mutuel setting.\n9. FUTURE WORK\nThis paper reports the results of an initial investigation of\nthe concept of a dynamic pari-mutuel market. Many avenues\nfor future work present themselves, including the following:\n\u2022 Random walk conjecture. The most important\nquestion mark in my mind is whether the random walk\nassumption (3) can be proven under reasonable market\nefficiency conditions and, if not, how severely it effects\nthe practicality of the system.\n\u2022 Incentive analysis. Formally, what are the\nincentives for traders to act on new information and when?\nHow does the level of initial subsidy effect trader\nincentives?\n\u2022 Laboratory experiments and field tests. This\npaper concentrated on the mathematics and algorithmics\nof the mechanism. However, the true test of the\nmechanism\"s ability to serve as an instrument for hedging,\nwagering, or information aggregation is to test it with\nreal traders in a realistic environment. In reality, how\ndo people behave when faced with a DPM mechanism?\n\u2022 DPM call market. I have derived the price functions\nto react to wagers on one outcome at a time. The\nmechanism could be generalized to accept orders on\nboth sides, then update the prices wholistically, rather\nthan by assuming a particular sequence on the wagers.\n\u2022 Real-valued variables. I believe the mechanisms in\nthis paper can easily be generalized to multiple discrete\n178\noutcomes, and multiple real-valued outcomes that\nalways sum to some constant value (e.g., multiple\npercentage values that must sum to 100). However, the\ngeneralization to real-valued variables with arbitrary\nrange is less clear, and open for future development.\n\u2022 Compound/combinatorial betting. I believe that\nDPM may be well suited for compound [8, 11] or\ncombinatorial [2] betting, for many of the same reasons\nthat market scoring rules [11] are well suited for the\ntask. DPM may also have some computational\nadvantages over MSR, though this remains to be seen.\nAcknowledgments\nI thank Dan Fain, Gary Flake, Lance Fortnow, and Robin\nHanson.\n10. REFERENCES\n[1] Mukhtar M. Ali. Probability and utility estimates for\nracetrack bettors. Journal of Political Economy,\n85(4):803-816, 1977.\n[2] Peter Bossaerts, Leslie Fine, and John Ledyard.\nInducing liquidity in thin financial markets through\ncombined-value trading mechanisms. European\nEconomic Review, 46:1671-1695, 2002.\n[3] Kay-Yut Chen, Leslie R. Fine, and Bernardo A.\nHuberman. Forecasting uncertain events with small\ngroups. In Third ACM Conference on Electronic\nCommerce (EC\"01), pages 58-64, 2001.\n[4] Sandip Debnath, David M. Pennock, C. Lee Giles, and\nSteve Lawrence. Information incorporation in online\nin-game sports betting markets. In Fourth ACM\nConference on Electronic Commerce (EC\"03), 2003.\n[5] Robert Forsythe and Russell Lundholm. Information\naggregation in an experimental market. Econometrica,\n58(2):309-347, 1990.\n[6] Robert Forsythe, Forrest Nelson, George R. Neumann,\nand Jack Wright. Anatomy of an experimental\npolitical stock market. American Economic Review,\n82(5):1142-1161, 1992.\n[7] Robert Forsythe, Thomas A. Rietz, and Thomas W.\nRoss. Wishes, expectations, and actions: A survey on\nprice formation in election stock markets. Journal of\nEconomic Behavior and Organization, 39:83-110,\n1999.\n[8] Lance Fortnow, Joe Kilian, David M. Pennock, and\nMichael P. Wellman. Betting boolean-style: A\nframework for trading in securities based on logical\nformulas. In Proceedings of the Fourth Annual ACM\nConference on Electronic Commerce, pages 144-155,\n2003.\n[9] John M. Gandar, William H. Dare, Craig R. Brown,\nand Richard A. Zuber. Informed traders and price\nvariations in the betting market for professional\nbasketball games. Journal of Finance,\nLIII(1):385-401, 1998.\n[10] Robin Hanson. Decision markets. IEEE Intelligent\nSystems, 14(3):16-19, 1999.\n[11] Robin Hanson. Combinatorial information market\ndesign. Information Systems Frontiers, 5(1), 2002.\n[12] Robin D. Hanson. Could gambling save science?\nEncouraging an honest consensus. Social\nEpistemology, 9(1):3-33, 1995.\n[13] Jens Carsten Jackwerth and Mark Rubinstein.\nRecovering probability distributions from options\nprices. Journal of Finance, 51(5):1611-1631, 1996.\n[14] Joseph B. Kadane and Robert L. Winkler. Separating\nprobability elicitation from utilities. Journal of the\nAmerican Statistical Association, 83(402):357-363,\n1988.\n[15] David M. Pennock, Steve Lawrence, C. Lee Giles, and\nFinn \u02daArup Nielsen. The real power of artificial\nmarkets. Science, 291:987-988, February 9 2001.\n[16] David M. Pennock, Steve Lawrence, Finn \u02daArup\nNielsen, and C. Lee Giles. Extracting collective\nprobabilistic forecasts from web games. In Seventh\nInternational Conference on Knowledge Discovery and\nData Mining, pages 174-183, 2001.\n[17] C. R. Plott, J. Wit, and W. C. Yang. Parimutuel\nbetting markets as information aggregation devices:\nExperimental results. Technical Report Social Science\nWorking Paper 986, California Institute of\nTechnology, April 1997.\n[18] Charles R. Plott. Markets as information gathering\ntools. Southern Economic Journal, 67(1):1-15, 2000.\n[19] Charles R. Plott and Shyam Sunder. Rational\nexpectations and the aggregation of diverse\ninformation in laboratory security markets.\nEconometrica, 56(5):1085-1118, 1988.\n[20] Charles Polk, Robin Hanson, John Ledyard, and\nTakashi Ishikida. Policy analysis market: An\nelectronic commerce application of a combinatorial\ninformation market. In Proceedings of the Fourth\nAnnual ACM Conference on Electronic Commerce,\npages 272-273, 2003.\n[21] R. Roll. Orange juice and weather. American\nEconomic Review, 74(5):861-880, 1984.\n[22] Richard N. Rosett. Gambling and rationality. Journal\nof Political Economy, 73(6):595-607, 1965.\n[23] Carsten Schmidt and Axel Werwatz. How accurate do\nmarkets predict the outcome of an event? The Euro\n2000 soccer championships experiment. Technical\nReport 09-2002, Max Planck Institute for Research\ninto Economic Systems, 2002.\n[24] Wayne W. Snyder. Horse racing: Testing the efficient\nmarkets model. Journal of Finance, 33(4):1109-1118,\n1978.\n[25] Richard H. Thaler and William T. Ziemba. Anomalies:\nParimutuel betting markets: Racetracks and lotteries.\nJournal of Economic Perspectives, 2(2):161-174, 1988.\n[26] Martin Weitzman. Utility analysis and group\nbehavior: An empirical study. Journal of Political\nEconomy, 73(1):18-26, 1965.\n[27] Robert L. Winkler and Allan H. Murphy. Good\nprobability assessors. J. Applied Meteorology,\n7:751-758, 1968.\n179", "keywords": "trader interface;information speculation;bet;dynamic pari-mutuel market;pari-mutuel market;gamble;dpm;demand;double auction format;risk allocation;hedge;bid-ask queue;price;continuous double auction;combinatorial bet;selling;price function;market institution;loss;gain;event resolution;automated market maker;information aggregation;trade;payoff per share;hybrid;cda;speculate;automate market maker;compound security market;infinite buy-in liquidity;wager;zero risk"}
{"name": "train_J-72", "title": "Applying Learning Algorithms to Preference Elicitation", "abstract": "We consider the parallels between the preference elicitation problem in combinatorial auctions and the problem of learning an unknown function from learning theory. We show that learning algorithms can be used as a basis for preference elicitation algorithms. The resulting elicitation algorithms perform a polynomial number of queries. We also give conditions under which the resulting algorithms have polynomial communication. Our conversion procedure allows us to generate combinatorial auction protocols from learning algorithms for polynomials, monotone DNF, and linear-threshold functions. In particular, we obtain an algorithm that elicits XOR bids with polynomial communication.", "fulltext": "1. INTRODUCTION\nIn a combinatorial auction, agents may bid on bundles of\ngoods rather than individual goods alone. Since there are\nan exponential number of bundles (in the number of goods),\ncommunicating values over these bundles can be\nproblematic. Communicating valuations in a one-shot fashion can\nbe prohibitively expensive if the number of goods is only\nmoderately large. Furthermore, it might even be hard for\nagents to determine their valuations for single bundles [14].\nIt is in the interest of such agents to have auction protocols\nwhich require them to bid on as few bundles as possible.\nEven if agents can efficiently compute their valuations, they\nmight still be reluctant to reveal them entirely in the course\nof an auction, because such information may be valuable to\ntheir competitors. These considerations motivate the need\nfor auction protocols that minimize the communication and\ninformation revelation required to determine an optimal\nallocation of goods.\nThere has been recent work exploring the links between\nthe preference elicitation problem in combinatorial auctions\nand the problem of learning an unknown function from\ncomputational learning theory [5, 19]. In learning theory, the\ngoal is to learn a function via various types of queries, such\nas What is the function\"s value on these inputs? In\npreference elicitation, the goal is to elicit enough partial\ninformation about preferences to be able to compute an optimal\nallocation. Though the goals of learning and preference\nelicitation differ somewhat, it is clear that these problems share\nsimilar structure, and it should come as no surprise that\ntechniques from one field should be relevant to the other.\nWe show that any exact learning algorithm with\nmembership and equivalence queries can be converted into a\npreference elicitation algorithm with value and demand queries.\nThe resulting elicitation algorithm guarantees elicitation in\na polynomial number of value and demand queries. Here\nwe mean polynomial in the number of goods, agents, and\nthe sizes of the agents\" valuation functions in a given\nencoding scheme. Preference elicitation schemes have not\ntraditionally considered this last parameter. We argue that\ncomplexity guarantees for elicitation schemes should allow\ndependence on this parameter. Introducing this parameter\nalso allows us to guarantee polynomial worst-case\ncommunication, which usually cannot be achieved in the number\nof goods and agents alone. Finally, we use our conversion\nprocedure to generate combinatorial auction protocols from\nlearning algorithms for polynomials, monotone DNF, and\nlinear-threshold functions.\nOf course, a one-shot combinatorial auction where agents\nprovide their entire valuation functions at once would also\nhave polynomial communication in the size of the agents\"\nvaluations, and only require one query. The advantage of\nour scheme is that agents can be viewed as black-boxes\nthat provide incremental information about their valuations.\nThere is no burden on the agents to formulate their\nvaluations in an encoding scheme of the auctioneer\"s choosing.\nWe expect this to be an important consideration in practice.\nAlso, with our scheme entire revelation only happens in the\nworst-case.\n180\nFor now, we leave the issue of incentives aside when\nderiving elicitation algorithms. Our focus is on the time and\ncommunication complexity of preference elicitation\nregardless of incentive constraints, and on the relationship between\nthe complexities of learning and preference elicitation.\nRelated work. Zinkevich et al. [19] consider the problem\nof learning restricted classes of valuation functions which can\nbe represented using read-once formulas and Toolbox DNF.\nRead-once formulas can represent certain substitutabilities,\nbut no complementarities, whereas the opposite holds for\nToolbox DNF. Since their work is also grounded in learning\ntheory, they allow dependence on the size of the target\nvaluation as we do (though read-once valuations can always be\nsuccinctly represented anyway). Their work only makes use\nof value queries, which are quite limited in power. Because\nwe allow ourselves demand queries, we are able to derive an\nelicitation scheme for general valuation functions.\nBlum et al. [5] provide results relating the complexities\nof query learning and preference elicitation. They consider\nmodels with membership and equivalence queries in query\nlearning, and value and demand queries in preference\nelicitation. They show that certain classes of functions can be\nefficiently learned yet not efficiently elicited, and vice-versa.\nIn contrast, our work shows that given a more general (yet\nstill quite standard) version of demand query than the type\nthey consider, the complexity of preference elicitation is no\ngreater than the complexity of learning. We will show that\ndemand queries can simulate equivalence queries until we\nhave enough information about valuations to imply a\nsolution to the elicitation problem.\nNisan and Segal [12] study the communication\ncomplexity of preference elicitation. They show that for many rich\nclasses of valuations, the worst-case communication\ncomplexity of computing an optimal allocation is exponential.\nTheir results apply to the black-box model of\ncomputational complexity. In this model algorithms are allowed to\nask questions about agent valuations and receive honest\nresponses, without any insight into how the agents internally\ncompute their valuations. This is in fact the basic\nframework of learning theory. Our work also addresses the issue\nof communication complexity, and we are able to derive\nalgorithms that provide significant communication guarantees\ndespite Nisan and Segal\"s negative results. Their work\nmotivates the need to rely on the sizes of agents\" valuation\nfunctions in stating worst-case results.\n2. THE MODELS\n2.1 Query Learning\nThe query learning model we consider here is called exact\nlearning from membership and equivalence queries,\nintroduced by Angluin [2]. In this model the learning\nalgorithm\"s objective is to exactly identify an unknown target\nfunction f : X \u2192 Y via queries to an oracle. The target\nfunction is drawn from a function class C that is known to\nthe algorithm. Typically the domain X is some subset of\n{0, 1}m\n, and the range Y is either {0, 1} or some subset\nof the real numbers \u00ca. As the algorithm progresses, it\nconstructs a manifest hypothesis \u02dcf which is its current estimate\nof the target function. Upon termination, the manifest\nhypothesis of a correct learning algorithm satisfies \u02dcf(x) = f(x)\nfor all x \u2208 X.\nIt is important to specify the representation that will be\nused to encode functions from C. For example, consider the\nfollowing function from {0, 1}m\nto \u00ca: f(x) = 2 if x\nconsists of m 1\"s, and f(x) = 0 otherwise. This function may\nsimply be represented as a list of 2m\nvalues. Or it may be\nencoded as the polynomial 2x1 \u00b7 \u00b7 \u00b7 xm, which is much more\nsuccinct. The choice of encoding may thus have a significant\nimpact on the time and space requirements of the learning\nalgorithm. Let size(f) be the size of the encoding of f with\nrespect to the given representation class. Most\nrepresentation classes have a natural measure of encoding size. The\nsize of a polynomial can be defined as the number of non-zero\ncoefficients in the polynomial, for example. We will usually\nonly refer to representation classes; the corresponding\nfunction classes will be implied. For example, the representation\nclass of monotone DNF formulae implies the function class\nof monotone Boolean functions.\nTwo types of queries are commonly used for exact\nlearning: membership and equivalence queries. On a membership\nquery, the learner presents some x \u2208 X and the oracle replies\nwith f(x). On an equivalence query, the learner presents\nits manifest hypothesis \u02dcf. The oracle either replies \u2018YES\" if\n\u02dcf = f, or returns a counterexample x such that \u02dcf(x) = f(x).\nAn equivalence query is proper if size( \u02dcf) \u2264 size(f) at the\ntime the manifest hypothesis is presented.\nWe are interested in efficient learning algorithms. The\nfollowing definitions are adapted from Kearns and Vazirani [9]:\nDefinition 1. The representation class C is\npolynomialquery exactly learnable from membership and\nequivalence queries if there is a fixed polynomial p(\u00b7, \u00b7) and an\nalgorithm L with access to membership and equivalence\nqueries of an oracle such that for any target function f \u2208 C, L\noutputs after at most p(size(f), m) queries a function \u02dcf \u2208 C\nsuch that \u02dcf(x) = f(x) for all instances x.\nSimilarly, the representation class C is efficiently\nexactly learnable from membership and equivalence\nqueries if the algorithm L outputs a correct hypothesis in\ntime p(size(f), m), for some fixed polynomial p(\u00b7, \u00b7).\nHere m is the dimension of the domain. Since the target\nfunction must be reconstructed, we also necessarily allow\npolynomial dependence on size(f).\n2.2 Preference Elicitation\nIn a combinatorial auction, a set of goods M is to be\nallocated among a set of agents N so as to maximize the sum of\nthe agents\" valuations. Such an allocation is called efficient\nin the economics literature, but we will refer to it as optimal\nand reserve the term efficient to refer to computational\nefficiency. We let n = |N| and m = |M|. An allocation\nis a partition of the objects into bundles (S1, . . . , Sn), such\nthat Si \u2229 Sj = \u2205 for all distinct i, j \u2208 N. Let \u0393 be the set\nof possible allocations. Each agent i \u2208 N has a valuation\nfunction vi : 2M\n\u2192 \u00ca over the space of possible bundles.\nEach valuation vi is drawn from a known class of valuations\nVi. The valuation classes do not need to coincide.\nWe will assume that all the valuations considered are\nnormalized, meaning v(\u2205) = 0, and that there are no\nexternalities, meaning vi(S1, ..., Sn) = vi(Si), for all agents i \u2208 N,\nfor any allocation (S1, ..., Sn) \u2208 \u0393 (that is, an agent cares\nonly about the bundle allocated to her). Valuations\nsatisfying these conditions are called general valuations.1\nWe\n1\nOften general valuations are made to satisfy the additional\n181\nalso assume that agents have quasi-linear utility functions,\nmeaning that agents\" utilities can be divided into monetary\nand non-monetary components. If an agent i is allocated\nbundle S at price p, it derives utility ui(S, p) = vi(S) \u2212 p.\nA valuation function may be viewed as a vector of 2m\n\u2212 1\nnon-negative real-values. Of course there may also be more\nsuccinct representations for certain valuation classes, and\nthere has been much research into concise bidding languages\nfor various types of valuations [11]. A classic example which\nwe will refer to again later is the XOR bidding language.\nIn this language, the agent provides a list of atomic bids,\nwhich consist of a bundle together with its value. To\ndetermine the value of a bundle S given these bids, one searches\nfor the bundle S of highest value listed in the atomic bids\nsuch that S \u2286 S. It is then the case that v(S) = v(S ).\nAs in the learning theory setting, we will usually only refer\nto bidding languages rather than valuation classes, because\nthe corresponding valuation classes will then be implied. For\nexample, the XOR bidding language implies the class of\nvaluations satisfying free-disposal, which is the condition that\nA \u2286 B \u21d2 v(A) \u2264 v(B).\nWe let size(v1, . . . , vn) =\n\u00c8n\ni=1 size(vi). That is, the size\nof a vector of valuations is the size of the concatenation of\nthe valuations\" representations in their respective encoding\nschemes (bidding languages).\nTo make an analogy to computational learning theory, we\nassume that all representation classes considered are\npolynomially interpretable [11], meaning that the value of a bundle\nmay be computed in polynomial time given the valuation\nfunction\"s representation. More formally, a representation\nclass (bidding language) C is polynomially interpretable if\nthere exists an algorithm that given as input some v \u2208 C\nand an instance x \u2208 X computes the value v(x) in time\nq(size(v), m), for some fixed polynomial q(\u00b7, \u00b7).2\nIn the intermediate rounds of an (iterative) auction, the\nauctioneer will have elicited information about the agents\"\nvaluation functions via various types of queries. She will\nthus have constructed a set of manifest valuations, denoted\n\u02dcv1, . . . , \u02dcvn.3\nThe values of these functions may correspond\nexactly to the true agent values, or they may for example\nbe upper or lower bounds on the true values, depending\non the types of queries made. They may also simply be\ndefault or random values if no information has been acquired\nabout certain bundles. The goal in the preference elicitation\nproblem is to construct a set of manifest valuations such\nthat:\narg max\n(S1,...,Sn)\u2208\u0393\ni\u2208N\n\u02dcvi(Si) \u2286 arg max\n(S1,...,Sn)\u2208\u0393\ni\u2208N\nvi(Si)\nThat is, the manifest valuations provide enough information\nto compute an allocation that is optimal with respect to the\ntrue valuations. Note that we only require one such optimal\nallocation.\ncondition of free-disposal (monotonicity), but we do not\nneed it at this point.\n2\nThis excludes OR\u2217\n, assuming P = NP, because\ninterpreting bids from this language is NP-hard by reduction from\nweighted set-packing, and there is no well-studied\nrepresentation class in learning theory that is clearly analogous to\nOR\u2217\n.\n3\nThis view of iterative auctions is meant to parallel the\nlearning setting. In many combinatorial auctions, manifest\nvaluations are not explicitly maintained but rather simply\nimplied by the history of bids.\nTwo typical queries used in preference elicitation are value\nand demand queries. On a value query, the auctioneer\npresents a bundle S \u2286 M and the agent responds with\nher (exact) value for the bundle v(S) [8]. On a demand\nquery, the auctioneer presents a vector of non-negative prices\np \u2208 \u00ca(2m )\nover the bundles together with a bundle S. The\nagent responds \u2018YES\" if it is the case that\nS \u2208 arg max\nS \u2286M\n\nv(S ) \u2212 p(S )\n\u00a1\nor otherwise presents a bundle S such that\nv(S ) \u2212 p(S ) > v(S) \u2212 p(S)\nThat is, the agent either confirms that the presented bundle\nis most preferred at the quoted prices, or indicates a\nbetter one [15].4\nNote that we include \u2205 as a bundle, so the\nagent will only respond \u2018YES\" if its utility for the proposed\nbundle is non-negative. Note also that communicating\nnonlinear prices does not necessarily entail quoting a price for\nevery possible bundle. There may be more succinct ways of\ncommunicating this vector, as we show in section 5.\nWe make the following definitions to parallel the query\nlearning setting and to simplify the statements of later\nresults:\nDefinition 2. The representation classes V1, . . . , Vn can\nbe polynomial-query elicited from value and demand\nqueries if there is a fixed polynomial p(\u00b7, \u00b7) and an\nalgorithm L with access to value and demand queries of the\nagents such that for any (v1, . . . , vn) \u2208 V1 \u00d7 . . . \u00d7 Vn, L\noutputs after at most p(size(v1, . . . , vn), m) queries an\nallocation (S1, . . . , Sn) \u2208 arg max(S1,...,Sn)\u2208\u0393\n\u00c8\nvi(Si).\nSimilarly, the representation class C can be efficiently\nelicited from value and demand queries if the\nalgorithm L outputs an optimal allocation with communication\np(size(v1, . . . , vn), m), for some fixed polynomial p(\u00b7, \u00b7).\nThere are some key differences here with the query\nlearning definition. We have dropped the term exactly since\nthe valuation functions need not be determined exactly in\norder to compute an optimal allocation. Also, an efficient\nelicitation algorithm is polynomial communication, rather\nthan polynomial time. This reflects the fact that\ncommunication rather than runtime is the bottleneck in elicitation.\nComputing an optimal allocation of goods even when given\nthe true valuations is NP-hard for a wide range of\nvaluation classes. It is thus unreasonable to require polynomial\ntime in the definition of an efficient preference elicitation\nalgorithm. We are happy to focus on the communication\ncomplexity of elicitation because this problem is widely\nbelieved to be more significant in practice than that of winner\ndetermination [11].5\n4\nThis differs slightly from the definition provided by Blum\net al. [5] Their demand queries are restricted to linear prices\nover the goods, where the price of a bundle is the sum of\nthe prices of its underlying goods. In contrast our demand\nqueries allow for nonlinear prices, i.e. a distinct price for\nevery possible bundle. This is why the lower bound in their\nTheorem 2 does not contradict our result that follows.\n5\nThough the winner determination problem is NP-hard for\ngeneral valuations, there exist many algorithms that solve\nit efficiently in practice. These range from special\npurpose algorithms [7, 16] to approaches using off-the-shelf IP\nsolvers [1].\n182\nSince the valuations need not be elicited exactly it is\ninitially less clear whether the polynomial dependence on\nsize(v1, . . . , vn) is justified in this setting. Intuitively, this\nparameter is justified because we must learn valuations\nexactly when performing elicitation, in the worst-case. We\naddress this in the next section.\n3. PARALLELSBETWEEN EQUIVALENCE\nAND DEMAND QUERIES\nWe have described the query learning and preference\nelicitation settings in a manner that highlights their similarities.\nValue and membership queries are clear analogs. Slightly\nless obvious is the fact that equivalence and demand queries\nare also analogs. To see this, we need the concept of Lindahl\nprices. Lindahl prices are nonlinear and non-anonymous\nprices over the bundles. They are nonlinear in the sense\nthat each bundle is assigned a price, and this price is not\nnecessarily the sum of prices over its underlying goods. They\nare non-anonymous in the sense that two agents may face\ndifferent prices for the same bundle of goods. Thus Lindahl\nprices are of the form pi(S), for all S \u2286 M, for all i \u2208 N.\nLindahl prices are presented to the agents in demand\nqueries.\nWhen agents have normalized quasi-linear utility\nfunctions, Bikhchandani and Ostroy [4] show that there always\nexist Lindahl prices such that (S1, . . . , Sn) is an optimal\nallocation if and only if\nSi \u2208 arg max\nSi\n\nvi(Si) \u2212 pi(Si)\n\u00a1\n\u2200i \u2208 N (1)\n(S1, . . . , Sn) \u2208 arg max\n(S1,...,Sn)\u2208\u0393\ni\u2208N\npi(Si) (2)\nCondition (1) states that each agent is allocated a bundle\nthat maximizes its utility at the given prices. Condition (2)\nstates that the allocation maximizes the auctioneer\"s\nrevenue at the given prices. The scenario in which these\nconditions hold is called a Lindahl equilibrium, or often a\ncompetitive equilibrium. We say that the Lindahl prices support\nthe optimal allocation. It is therefore sufficient to announce\nsupporting Lindahl prices to verify an optimal allocation.\nOnce we have found an allocation with supporting Lindahl\nprices, the elicitation problem is solved.\nThe problem of finding an optimal allocation (with respect\nto the manifest valuations) can be formulated as a linear\nprogram whose solutions are guaranteed to be integral [4].\nThe dual variables to this linear program are supporting\nLindahl prices for the resulting allocation. The objective\nfunction to the dual program is:\nmin\npi(S)\n\u03c0s\n+\ni\u2208N\n\u03c0i (3)\nwith \u03c0i = max\nS\u2286M\n(\u02dcvi(S) \u2212 pi(S))\n\u03c0s\n= max\n(S1,...,Sn)\u2208\u0393\ni\u2208N\npi(Si)\nThe optimal values of \u03c0i and \u03c0s\ncorrespond to the maximal\nutility to agent i with respect to its manifest valuation and\nthe maximal revenue to the seller.\nThere is usually a range of possible Lindahl prices\nsupporting a given optimal allocation. The agent\"s manifest\nvaluations are in fact valid Lindahl prices, and we refer to\nthem as maximal Lindahl prices. Out of all possible\nvectors of Lindahl prices, maximal Lindahl prices maximize the\nutility of the auctioneer, in fact giving her the entire\nsocial welfare. Conversely, prices that maximize the\n\u00c8\ni\u2208N \u03c0i\ncomponent of the objective (the sum of the agents\" utilities)\nare minimal Lindahl prices. Any Lindahl prices will do for\nour results, but some may have better elicitation\nproperties than others. Note that a demand query with maximal\nLindahl prices is almost identical to an equivalence query,\nsince in both cases we communicate the manifest valuation\nto the agent. We leave for future work the question of which\nLindahl prices to choose to minimize preference elicitation.\nConsidering now why demand and equivalence queries are\ndirect analogs, first note that given the \u03c0i in some Lindahl\nequilibrium, setting\npi(S) = max{0, \u02dcvi(S) \u2212 \u03c0i} (4)\nfor all i \u2208 N and S \u2286 M yields valid Lindahl prices. These\nprices leave every agent indifferent across all bundles with\npositive price, and satisfy condition (1). Thus demand\nqueries can also implicitly communicate manifest valuations,\nsince Lindahl prices will typically be an additive constant\naway from these by equality (4). In the following lemma we\nshow how to obtain counterexamples to equivalence queries\nthrough demand queries.\nLemma 1. Suppose an agent replies with a preferred\nbundle S when proposed a bundle S and supporting Lindahl\nprices p(S) (supporting with respect to the the agent\"s\nmanifest valuation). Then either \u02dcv(S) = v(S) or \u02dcv(S ) = v(S ).\nProof. We have the following inequalities:\n\u02dcv(S) \u2212 p(S) \u2265 \u02dcv(S ) \u2212 p(S )\n\u21d2 \u02dcv(S ) \u2212 \u02dcv(S) \u2264 p(S ) \u2212 p(S) (5)\nv(S ) \u2212 p(S ) > v(S) \u2212 p(S)\n\u21d2 v(S ) \u2212 v(S) > p(S ) \u2212 p(S) (6)\nInequality (5) holds because the prices support the proposed\nallocation with respect to the manifest valuation. Inequality\n(6) holds because the agent in fact prefers S to S given the\nprices, according to its response to the demand query. If it\nwere the case that \u02dcv(S) = v(S) and \u02dcv(S ) = v(S ), these\ninequalities would represent a contradiction. Thus at least\none of S and S is a counterexample to the agent\"s manifest\nvaluation.\nFinally, we justify dependence on size(v1, . . . , vn) in\nelicitation problems. Nisan and Segal (Proposition 1, [12])\nand Parkes (Theorem 1, [13]) show that supporting Lindahl\nprices must necessarily be revealed in the course of any\npreference elicitation protocol which terminates with an optimal\nallocation. Furthermore, Nisan and Segal (Lemma 1, [12])\nstate that in the worst-case agents\" prices must coincide with\ntheir valuations (up to a constant), when the valuation class\nis rich enough to contain dual valuations (as will be the\ncase with most interesting classes). Since revealing Lindahl\nprices is a necessary condition for establishing an optimal\nallocation, and since Lindahl prices contain the same\ninformation as valuation functions (in the worst-case), allowing\nfor dependence on size(v1, . . . , vn) in elicitation problems is\nentirely natural.\n183\n4. FROM LEARNING TO PREFERENCE\nELICITATION\nThe key to converting a learning algorithm to an\nelicitation algorithm is to simulate equivalence queries with\ndemand and value queries until an optimal allocation is found.\nBecause of our Lindahl price construction, when all agents\nreply \u2018YES\" to a demand query, we have found an optimal\nallocation, analogous to the case where an agent replies \u2018YES\"\nto an equivalence query when the target function has been\nexactly learned. Otherwise, we can obtain a\ncounterexample to an equivalence query given an agent\"s response to a\ndemand query.\nTheorem 1. The representation classes V1, . . . , Vn can\nbe polynomial-query elicited from value and demand queries\nif they can each be polynomial-query exactly learned from\nmembership and equivalence queries.\nProof. Consider the elicitation algorithm in Figure 1.\nEach membership query in step 1 is simulated with a value\nquery since these are in fact identical. Consider step 4. If all\nagents reply \u2018YES\", condition (1) holds. Condition (2) holds\nbecause the computed allocation is revenue-maximizing for\nthe auctioneer, regardless of the agents\" true valuations.\nThus an optimal allocation has been found. Otherwise, at\nleast one of Si or Si is a counterexample to \u02dcvi, by Lemma 1.\nWe identify a counterexample by performing value queries\non both these bundles, and provide it to Ai as a response to\nits equivalence query.\nThis procedure will halt, since in the worst-case all agent\nvaluations will be learned exactly, in which case the\noptimal allocation and Lindahl prices will be accepted by all\nagents. The procedure performs a polynomial number of\nqueries, since A1, . . . , An are all polynomial-query learning\nalgorithms.\nNote that the conversion procedure results in a\npreference elicitation algorithm, not a learning algorithm. That\nis, the resulting algorithm does not simply learn the\nvaluations exactly, then compute an optimal allocation. Rather,\nit elicits partial information about the valuations through\nvalue queries, and periodically tests whether enough\ninformation has been gathered by proposing an allocation to the\nagents through demand queries. It is possible to generate a\nLindahl equilibrium for valuations v1, . . . , vn using an\nallocation and prices derived using manifest valuations \u02dcv1, . . . , \u02dcvn,\nand finding an optimal allocation does not imply that the\nagents\" valuations have been exactly learned. The use of\ndemand queries to simulate equivalence queries enables this\nearly halting. We would not obtain this property with\nequivalence queries based on manifest valuations.\n5. COMMUNICATION COMPLEXITY\nIn this section, we turn to the issue of the\ncommunication complexity of elicitation. Nisan and Segal [12] show\nthat for a variety of rich valuation spaces (such as general\nand submodular valuations), the worst-case communication\nburden of determining Lindahl prices is exponential in the\nnumber of goods, m. The communication burden is\nmeasured in terms of the number of bits transmitted between\nagents and auctioneer in the case of discrete communication,\nor in terms of the number of real numbers transmitted in the\ncase of continuous communication.\nConverting efficient learning algorithms to an elicitation\nalgorithm produces an algorithm whose queries have sizes\npolynomial in the parameters m and size(v1, . . . , vn).\nTheorem 2. The representation classes V1, . . . , Vn can\nbe efficiently elicited from value and demand queries if they\ncan each be efficiently exactly learned from membership and\nequivalence queries.\nProof. The size of any value query is O(m): the\nmessage consists solely of the queried bundle. To communicate\nLindahl prices to agent i, it is sufficient to communicate\nthe agent\"s manifest valuation function and the value \u03c0i, by\nequality (4). Note that an efficient learning algorithm never\nbuilds up a manifest hypothesis of superpolynomial size,\nbecause the algorithm\"s runtime would then also be\nsuperpolynomial, contradicting efficiency. Thus communicating the\nmanifest valuation requires size at most p(size(vi), m), for\nsome polynomial p that upper-bounds the runtime of the\nefficient learning algorithm. Representing the surplus \u03c0i to\nagent i cannot require space greater than q(size(\u02dcvi), m) for\nsome fixed polynomial q, because we assume that the chosen\nrepresentation is polynomially interpretable, and thus any\nvalue generated will be of polynomial size. We must also\ncommunicate to i its allocated bundle, so the total\nmessage size for a demand query is at most p(size(vi), m) +\nq(p(size(vi), m), m)+O(m). Clearly, an agent\"s response to\na value or demand query has size at most q(size(vi), m) +\nO(m). Thus the value and demand queries, and the\nresponses to these queries, are always of polynomial size. An\nefficient learning algorithm performs a polynomial number of\nqueries, so the total communication of the resulting\nelicitation algorithm is polynomial in the relevant parameters.\nThere will often be explicit bounds on the number of\nmembership and equivalence queries performed by a learning\nalgorithm, with constants that are not masked by big-O\nnotation. These bounds can be translated to explicit bounds\non the number of value and demand queries made by the\nresulting elicitation algorithm. We upper-bounded the size\nof the manifest hypothesis with the runtime of the learning\nalgorithm in Theorem 2. We are likely to be able to do\nmuch better than this in practice. Recall that an\nequivalence query is proper if size( \u02dcf) \u2264 size(f) at the time the\nquery is made. If the learning algorithm\"s equivalence\nqueries are all proper, it may then also be possible to provide\ntight bounds on the communication requirements of the\nresulting elicitation algorithm.\nTheorem 2 show that elicitation algorithms that depend\non the size(v1, . . . , vn) parameter sidestep Nisan and\nSegal\"s [12] negative results on the worst-case communication\ncomplexity of efficient allocation problems. They provide\nguarantees with respect to the sizes of the instances of\nvaluation functions faced at any run of the algorithm. These\nalgorithms will fare well if the chosen representation class\nprovides succinct representations for the simplest and most\ncommon of valuations, and thus the focus moves back to one\nof compact yet expressive bidding languages. We consider\nthese issues below.\n6. APPLICATIONS\nIn this section, we demonstrate the application of our\nmethods to particular representation classes for\ncombinatorial valuations. We have shown that the preference\nelicitation problem for valuation classes V1, . . . , Vn can be reduced\n184\nGiven: exact learning algorithms A1, . . . , An for valuations classes V1, . . . , Vn respectively.\nLoop until there is a signal to halt:\n1. Run A1, . . . , An in parallel on their respective agents until each requires a response to an\nequivalence query, or has halted with the agent\"s exact valuation.\n2. Compute an optimal allocation (S1, . . . , Sn) and corresponding Lindahl prices with respect to\nthe manifest valuations \u02dcv1, . . . , \u02dcvn determined so far.\n3. Present the allocation and prices to the agents in the form of a demand query.\n4. If they all reply \u2018YES\", output the allocation and halt. Otherwise there is some agent i that\nhas replied with some preferred bundle Si. Perform value queries on Si and Si to find a\ncounterexample to \u02dcvi, and provide it to Ai.\nFigure 1: Converting learning algorithms to an elicitation algorithm.\nto the problem of finding an efficient learning algorithm for\neach of these classes separately. This is significant because\nthere already exist learning algorithms for a wealth of\nfunction classes, and because it may often be simpler to solve\neach learning subproblem separately than to attack the\npreference elicitation problem directly. We can develop an\nelicitation algorithm that is tailored to each agent\"s valuation,\nwith the underlying learning algorithms linked together at\nthe demand query stages in an algorithm-independent way.\nWe show that existing learning algorithms for\npolynomials, monotone DNF formulae, and linear-threshold functions\ncan be converted into preference elicitation algorithms for\ngeneral valuations, valuations with free-disposal, and\nvaluations with substitutabilities, respectively. We focus on\nrepresentations that are polynomially interpretable, because\nthe computational learning theory literature places a heavy\nemphasis on computational tractability [18].\nIn interpreting the methods we emphasize the\nexpressiveness and succinctness of each representation class. The\nrepresentation class, which in combinatorial auction terms\ndefines a bidding language, must necessarily be expressive\nenough to represent all possible valuations of interest, and\nshould also succinctly represent the simplest and most\ncommon functions in the class.\n6.1 Polynomial Representations\nSchapire and Sellie [17] give a learning algorithm for sparse\nmultivariate polynomials that can be used as the basis for\na combinatorial auction protocol. The equivalence queries\nmade by this algorithm are all proper. Specifically, their\nalgorithm learns the representation class of t-sparse\nmultivariate polynomials over the real numbers, where the variables\nmay take on values either 0 or 1. A t-sparse polynomial\nhas at most t terms, where a term is a product of variables,\ne.g. x1x3x4. A polynomial over the real numbers has\ncoefficients drawn from the real numbers. Polynomials are\nexpressive: every valuation function v : 2M\n\u2192 \u00ca+ can be\nuniquely written as a polynomial [17].\nTo get an idea of the succinctness of polynomials as a\nbidding language, consider the additive and single-item\nvaluations presented by Nisan [11]. In the additive valuation,\nthe value of a bundle is the number of goods the bundle\ncontains. In the single-item valuation, all bundles have value\n1, except \u2205 which has value 0 (i.e. the agent is satisfied as\nsoon as it has acquired a single item). It is not hard to show\nthat the single-item valuation requires polynomials of size\n2m\n\u2212 1, while polynomials of size m suffice for the additive\nvaluation. Polynomials are thus appropriate for valuations\nthat are mostly additive, with a few substitutabilities and\ncomplementarities that can be introduced by adjusting\ncoefficients.\nThe learning algorithm for polynomials makes at most\nmti +2 equivalence queries and at most (mti +1)(t2\ni +3ti)/2\nmembership queries to an agent i, where ti is the sparcity of\nthe polynomial representing vi [17]. We therefore obtain an\nalgorithm that elicits general valuations with a polynomial\nnumber of queries and polynomial communication.6\n6.2 XOR Representations\nThe XOR bidding language is standard in the\ncombinatorial auctions literature. Recall that an XOR bid is\ncharacterized by a set of bundles B \u2286 2M\nand a value function\nw : B \u2192 \u00ca+ defined on those bundles, which induces the\nvaluation function:\nv(B) = max\n{B \u2208B | B \u2286B}\nw(B ) (7)\nXOR bids can represent valuations that satisfy free-disposal\n(and only such valuations), which again is the property that\nA \u2286 B \u21d2 v(A) \u2264 v(B).\nThe XOR bidding language is slightly less expressive than\npolynomials, because polynomials can represent valuations\nthat do not satisfy free-disposal. However, XOR is as\nexpressive as required in most economic settings. Nisan [11] notes\nthat XOR bids can represent the single-item valuation with\nm atomic bids, but 2m\n\u2212 1 atomic bids are needed to\nrepresent the additive valuation. Since the opposite holds for\npolynomials, these two languages are incomparable in\nsuccinctness, and somewhat complementary for practical use.\nBlum et al. [5] note that monotone DNF formulae are the\nanalogs of XOR bids in the learning theory literature. A\nmonotone DNF formula is a disjunction of conjunctions in\nwhich the variables appear unnegated, for example x1x2 \u2228\nx3 \u2228 x2x4x5. Note that such formulae can be represented\nas XOR bids where each atomic bid has value 1; thus XOR\nbids generalize monotone DNF formulae from Boolean to\nreal-valued functions. These insights allow us to generalize\na classic learning algorithm for monotone DNF ([3] Theorem\n6\nNote that Theorem 1 applies even if valuations do not\nsatisfy free-disposal.\n185\n1, [18] Theorem B) to a learning algorithm for XOR bids.7\nLemma 2. An XOR bid containing t atomic bids can be\nexactly learned with t + 1 equivalence queries and at most\ntm membership queries.\nProof. The algorithm will identify each atomic bid in\nthe target XOR bid in turn. Initialize the manifest valuation\n\u02dcv to the bid that is identically zero on all bundles (this is an\nXOR bid containing 0 atomic bids). Present \u02dcv as an\nequivalence query. If the response is \u2018YES\", we are done. Otherwise\nwe obtain a bundle S for which v(S) = \u02dcv(S). Create a\nbundle T as follows. First initialize T = S. For each item i in T,\ncheck via a membership query whether v(T) = v(T \u2212 {i}).\nIf so set T = T \u2212 {i}. Otherwise leave T as is and proceed\nto the next item.\nWe claim that (T, v(T)) is an atomic bid of the target\nXOR bid. For each item i in T, we have v(T) = v(T \u2212 {i}).\nTo see this, note that at some point when generating T, we\nhad a \u00afT such that T \u2286 \u00afT \u2286 S and v( \u00afT) > v( \u00afT \u2212 {i}), so that\ni was kept in \u00afT. Note that v(S) = v( \u00afT) = v(T) because the\nvalue of the bundle S is maintained throughout the process\nof deleting items. Now assume v(T) = v(T \u2212 {i}). Then\nv( \u00afT) = v(T) = v(T \u2212 {i}) > v( \u00afT \u2212 {i})\nwhich contradicts free-disposal, since T \u2212 {i} \u2286 \u00afT \u2212 {i}.\nThus v(T) > v(T \u2212 {i}) for all items i in T. This implies\nthat (T, v(T)) is an atomic bid of v. If this were not the case,\nT would take on the maximum value of its strict subsets, by\nthe definition of an XOR bid, and we would have\nv(T) = max\ni\u2208T\n{ max\nT \u2286T \u2212{i}\nv(T )} = max\ni\u2208T\n{v(T \u2212 {i})} < v(T)\nwhich is a contradiction.\nWe now show that v(T) = \u02dcv(T), which will imply that\n(T, v(T)) is not an atomic bid of our manifest hypothesis by\ninduction. Assume that every atomic bid (R, \u02dcv(R))\nidentified so far is indeed an atomic bid of v (meaning R is indeed\nlisted in an atomic bid of v as having value v(R) = \u02dcv(R)).\nThis assumption holds vacuously when the manifest\nvaluation is initialized. Using the notation from (7), let ( \u02dcB, \u02dcw) be\nour hypothesis, and (B, w) be the target function. We have\n\u02dcB \u2286 B, and \u02dcw(B) = w(B) for B \u2208 \u02dcB by assumption. Thus,\n\u02dcv(S) = max\n{B\u2208 \u02dcB | B\u2286S}\n\u02dcw(B)\n= max\n{B\u2208 \u02dcB | B\u2286S}\nw(B)\n\u2264 max\n{B\u2208B | B\u2286S}\nw(B)\n= v(S) (8)\nNow assume v(T) = \u02dcv(T). Then,\n\u02dcv(T) = v(T) = v(S) = \u02dcv(S) (9)\nThe second equality follows from the fact that the value\nremains constant when we derive T from S. The last\ninequality holds because S is a counterexample to the\nmanifest valuation. From equation (9) and free-disposal, we\n7\nThe cited algorithm was also used as the basis for Zinkevich\net al.\"s [19] elicitation algorithm for Toolbox DNF. Recall\nthat Toolbox DNF are polynomials with non-negative\ncoefficients. For these representations, an equivalence query can\nbe simulated with a value query on the bundle containing\nall goods.\nhave \u02dcv(T) < \u02dcv(S). Then again from equation (9) it\nfollows that v(S) < \u02dcv(S). This contradicts (8), so we in fact\nhave v(T) = \u02dcv(T). Thus (T, v(T)) is not currently in our\nhypothesis as an atomic bid, or we would correctly have\n\u02dcv(T) = v(T) by the induction hypothesis. We add (T, v(T))\nto our hypothesis and repeat the process above,\nperforming additional equivalence queries until all atomic bids have\nbeen identified.\nAfter each equivalence query, an atomic bid is identified\nwith at most m membership queries. Each counterexample\nleads to the discovery of a new atomic bid. Thus we make at\nmost tm membership queries and exactly t + 1 equivalence\nqueries.\nThe number of time steps required by this algorithm is\nessentially the same as the number of queries performed, so\nthe algorithm is efficient. Applying Theorem 2, we therefore\nobtain the following corollary:\nTheorem 3. The representation class of XOR bids can\nbe efficiently elicited from value and demand queries.\nThis contrasts with Blum et al.\"s negative results ([5],\nTheorem 2) stating that monotone DNF (and hence XOR bids)\ncannot be efficiently elicited when the demand queries are\nrestricted to linear and anonymous prices over the goods.\n6.3 Linear-Threshold Representations\nPolynomials, XOR bids, and all languages based on the\nOR bidding language (such as XOR-of-OR, OR-of-XOR,\nand OR\u2217\n) fail to succinctly represent the majority\nvaluation [11]. In this valuation, bundles have value 1 if they\ncontain at least m/2 items, and value 0 otherwise. More\ngenerally, consider the r-of-S family of valuations where bundles\nhave value 1 if they contain at least r items from a specified\nset of items S \u2286 M, and value 0 otherwise. The\nmajority valuation is a special case of the r-of-S valuation with\nr = m/2 and S = M. These valuations are appropriate for\nrepresenting substitutabilities: once a required set of items\nhas been obtained, no other items can add value.\nLetting k = |S|, such valuations are succinctly represented\nby r-of-k threshold functions. These functions take the form\nof linear inequalities:\nxi1 + . . . + xik \u2265 r\nwhere the function has value 1 if the inequality holds, and\n0 otherwise. Here i1, . . . , ik are the items in S. Littlestone\"s\nWINNOW 2 algorithm can learn such functions using\nequivalence queries only, using at most 8r2\n+ 5k + 14kr ln m + 1\nqueries [10]. To provide this guarantee, r must be known to\nthe algorithm, but S (and k) are unknown. The elicitation\nalgorithm that results from WINNOW 2 uses demand\nqueries only (value queries are not necessary here because the\nvalues of counterexamples are implied when there are only\ntwo possible values).\nNote that r-of-k threshold functions can always be\nsuccinctly represented in O(m) space. Thus we obtain an\nalgorithm that can elicit such functions with a polynomial\nnumber of queries and polynomial communication, in the\nparameters n and m alone.\n186\n7. CONCLUSIONS AND FUTURE WORK\nWe have shown that exact learning algorithms with\nmembership and equivalence queries can be used as a basis for\npreference elicitation algorithms with value and demand\nqueries. At the heart of this result is the fact that demand\nqueries may be viewed as modified equivalence queries,\nspecialized to the problem of preference elicitation. Our result\nallows us to apply the wealth of available learning algorithms\nto the problem of preference elicitation.\nA learning approach to elicitation also motivates a\ndifferent approach to designing elicitation algorithms that\ndecomposes neatly across agent types. If the designer knowns\nbeforehand what types of preferences each agent is likely to\nexhibit (mostly additive, many substitutes, etc...), she can\ndesign learning algorithms tailored to each agents\"\nvaluations and integrate them into an elicitation scheme. The\nresulting elicitation algorithm makes a polynomial number\nof queries, and makes polynomial communication if the\noriginal learning algorithms are efficient.\nWe do not require that agent valuations can be learned\nwith value and demand queries. Equivalence queries can\nonly be, and need only be, simulated up to the point where\nan optimal allocation has been computed. This is the\npreference elicitation problem. Theorem 1 implies that elicitation\nwith value and demand queries is no harder than learning\nwith membership and equivalence queries, but it does not\nprovide any asymptotic improvements over the learning\nalgorithms\" complexity. It would be interesting to find\nexamples of valuation classes for which elicitation is easier than\nlearning. Blum et al. [5] provide such an example when\nconsidering membership/value queries only (Theorem 4).\nIn future work we plan to address the issue of\nincentives when converting learning algorithms to elicitation\nalgorithms. In the learning setting, we usually assume that\noracles will provide honest responses to queries; in the\nelicitation setting, agents are usually selfish and will provide\npossibly dishonest responses so as to maximize their utility.\nWe also plan to implement the algorithms for learning\npolynomials and XOR bids as elicitation algorithms, and test\ntheir performance against other established combinatorial\nauction protocols [6, 15]. An interesting question here is:\nwhich Lindahl prices in the maximal to minimal range are\nbest to quote in order to minimize information revelation?\nWe conjecture that information revelation is reduced when\nmoving from maximal to minimal Lindahl prices, namely as\nwe move demand queries further away from equivalence\nqueries. Finally, it would be useful to determine whether the\nOR\u2217\nbidding language [11] can be efficiently learned (and\nhence elicited), given this language\"s expressiveness and\nsuccinctness for a wide variety of valuation classes.\nAcknowledgements\nWe would like to thank Debasis Mishra for helpful\ndiscussions. This work is supported in part by NSF grant\nIIS0238147.\n8. REFERENCES\n[1] A. Andersson, M. Tenhunen, and F. Ygge. Integer\nprogramming for combinatorial auction winner\ndetermination. In Proceedings of the Fourth\nInternational Conference on Multiagent Systems\n(ICMAS-00), 2000.\n[2] D. Angluin. Learning regular sets from queries and\ncounterexamples. Information and Computation,\n75:87-106, November 1987.\n[3] D. Angluin. Queries and concept learning. Machine\nLearning, 2:319-342, 1987.\n[4] S. Bikhchandani and J. Ostroy. The Package\nAssignment Model. Journal of Economic Theory,\n107(2), December 2002.\n[5] A. Blum, J. Jackson, T. Sandholm, and M. Zinkevich.\nPreference elicitation and query learning. In Proc.\n16th Annual Conference on Computational Learning\nTheory (COLT), Washington DC, 2003.\n[6] W. Conen and T. Sandholm. Partial-revelation VCG\nmechanism for combinatorial auctions. In Proc. the\n18th National Conference on Artificial Intelligence\n(AAAI), 2002.\n[7] Y. Fujishima, K. Leyton-Brown, and Y. Shoham.\nTaming the computational complexity of\ncombinatorial auctions: Optimal and approximate\napproaches. In Proc. the 16th International Joint\nConference on Artificial Intelligence (IJCAI), pages\n548-553, 1999.\n[8] B. Hudson and T. Sandholm. Using value queries in\ncombinatorial auctions. In Proc. 4th ACM Conference\non Electronic Commerce (ACM-EC), San Diego, CA,\nJune 2003.\n[9] M. J. Kearns and U. V. Vazirani. An Introduction to\nComputational Learning Theory. MIT Press, 1994.\n[10] N. Littlestone. Learning quickly when irrelevant\nattributes abound: A new linear-threshold algorithm.\nMachine Learning, 2:285-318, 1988.\n[11] N. Nisan. Bidding and allocation in combinatorial\nauctions. In Proc. the ACM Conference on Electronic\nCommerce, pages 1-12, 2000.\n[12] N. Nisan and I. Segal. The communication\nrequirements of efficient allocations and supporting\nLindahl prices. Working Paper, Hebrew University,\n2003.\n[13] D. C. Parkes. Price-based information certificates for\nminimal-revelation combinatorial auctions. In\nPadget et al., editor, Agent-Mediated Electronic\nCommerce IV,LNAI 2531, pages 103-122.\nSpringer-Verlag, 2002.\n[14] D. C. Parkes. Auction design with costly preference\nelicitation. In Special Issues of Annals of Mathematics\nand AI on the Foundations of Electronic Commerce,\nForthcoming (2003).\n[15] D. C. Parkes and L. H. Ungar. Iterative combinatorial\nauctions: Theory and practice. In Proc. 17th National\nConference on Artificial Intelligence (AAAI-00), pages\n74-81, 2000.\n[16] T. Sandholm, S. Suri, A. Gilpin, and D. Levine.\nCABOB: A fast optimal algorithm for combinatorial\nauctions. In Proc. the 17th International Joint\nConference on Artificial Intelligence (IJCAI), pages\n1102-1108, 2001.\n[17] R. Schapire and L. Sellie. Learning sparse multivariate\npolynomials over a field with queries and\ncounterexamples. In Proceedings of the Sixth Annual\nACM Workshop on Computational Learning Theory,\npages 17-26. ACM Press, 1993.\n187\n[18] L. Valiant. A theory of the learnable. Commun. ACM,\n27(11):1134-1142, Nov. 1984.\n[19] M. Zinkevich, A. Blum, and T. Sandholm. On\npolynomial-time preference elicitation with\nvalue-queries. In Proc. 4th ACM Conference on\nElectronic Commerce (ACM-EC), San Diego, CA,\nJune 2003.\n188", "keywords": "xor bid;learning theory;polynomial communication;elicitation algorithm;learning;linear-threshold function;learn;preference elicitation problem;combinatorial auction;monotone dnf;learning algorithm;conversion procedure;preference elicitation algorithm;polynomial;polynomial number of query;parallel;resulting algorithm;preference elicitation;combinatorial auction protocol;query polynomial number"}
{"name": "train_J-73", "title": "Competitive Algorithms for VWAP and Limit Order Trading", "abstract": "We introduce new online models for two important aspects of modern financial markets: Volume Weighted Average Price trading and limit order books. We provide an extensive study of competitive algorithms in these models and relate them to earlier online algorithms for stock trading.", "fulltext": "1. INTRODUCTION\nWhile popular images of Wall Street often depict\nswashbuckling traders boldly making large gambles on just their\nmarket intuitions, the vast majority of trading is actually\nconsiderably more technical and constrained. The constraints\noften derive from a complex combination of business,\nregulatory and institutional issues, and result in certain kinds\nof standard trading strategies or criteria that invite\nalgorithmic analysis.\nOne of the most common activities in modern financial\nmarkets is known as Volume Weighted Average Price, or\nVWAP, trading. Informally, the VWAP of a stock over a\nspecified market period is simply the average price paid per\nshare during that period, so the price of each transaction in\nthe market is weighted by its volume. In VWAP trading,\none attempts to buy or sell a fixed number of shares at a\nprice that closely tracks the VWAP.\nVery large institutional trades constitute one of the main\nmotivations behind VWAP activity. A typical scenario goes\nas follows. Suppose a very large mutual fund holds 3% of\nthe outstanding shares of a large, publicly traded company\n- a huge fraction of the shares - and that this fund\"s\nmanager decides he would like to reduce this holding to 2% over\na 1-month period. (Such a decision might be forced by the\nfund\"s own regulations or other considerations.) Typically,\nsuch a fund manager would be unqualified to sell such a large\nnumber of shares in the open market - it requires a\nprofessional broker to intelligently break the trade up over time,\nand possibly over multiple exchanges, in order to minimize\nthe market impact of such a sizable transaction. Thus, the\nfund manager would approach brokerages for help in selling\nthe 1%.\nThe brokerage will typically alleviate the fund manager\"s\nproblem immediately by simply buying the shares directly\nfrom the fund manager, and then selling them off\nlaterbut what price should the brokerage pay the fund manager?\nPaying the price on the day of the sale is too risky for the\nbrokerage, as they need to sell the shares themselves over an\nextended period, and events beyond their control (such as\nwars) could cause the price to fall dramatically. The usual\nanswer is that the brokerage offers to buy the shares from\nthe fund manager at a per-share price tied to the VWAP\nover some future period - in our example, the brokerage\nmight offer to buy the 1% at a per-share price of the\ncoming month\"s VWAP minus 1 cent. The brokerage now has a\nvery clean challenge: by selling the shares themselves over\nthe next month in a way that exactly matches the VWAP,\na penny per share is earned in profits. If they can beat the\nVWAP by a penny, they make two cents per share. Such\nsmall-margin, high-volume profits can be extremely\nlucrative for a large brokerage. The importance of the VWAP\nhas led to many automated VWAP trading algorithms -\nindeed, every major brokerage has at least one VWAP box,\n189\nPrice Volume Model Order Book Model Macroscopic Distribution Model\nOWT \u0398(log(R)) (From[3]) O(log(R) log(N)) 2E(Pbins\nmaxprice )\n2(1 + )E(Pbins\nmaxprice ) for -approx of Pbins\nmaxprice\n\u0398(log(Q)) (same as above plus...)\nVWAP \u0398(log(R)) O(log(R) log(N)) (from above) 2E(Pbins\nvol )\n\u2126(Q) fixed schedule O(log(Q)) for large N (1 + )2E(Pbins\nvol ) for -approx. of Pbins\nvol\n1 for volume in [N, QN]\nFigure 1: The table summarizes the results presented in this paper. The rows represent results for either the OWT\nor VWAP criterion. The columns represent which model we are working in. The entry in the table is the competitive\nratio between our algorithm and an optimal algorithm, and the closer the ratio is to 1 the better. The parameter R\nrepresents a bound on the maximum to the minimum price fluctuation and the parameter Q represents a bound on the\nmaximum to minimum volume fluctuation in the respective model. (See Section 4 for a description of the Macroscopic\nDistribution Model.) All the results for the OWT trading criterion (which is a stronger criterion) directly translate\nto the VWAP criterion. However, in the VWAP setting, considering a restriction on the maximum to the minimum\nvolume fluctuation Q, leads to an additional class of results which depends on Q.\nand some small companies focus exclusively on proprietary\nVWAP trading technology.\nIn this paper, we provide the first study of VWAP trading\nalgorithms in an online, competitive ratio setting. We first\nformalize the VWAP trading problem in a basic online model\nwe call the price-volume model, which can be viewed as a\ngeneralization of previous theoretical online trading models\nincorporating market volume information. In this model, we\nprovide VWAP algorithms and competitive ratios, and\ncompare this setting with the one-way trading (OWT) problem\nstudied in [3].\nOur most interesting results, however, examine the VWAP\ntrading problem in a new online trading model capturing the\nimportant recent phenomenon of limit order books in\nfinancial markets. Briefly, a limit buy or sell order specifies both\nthe number of shares and the desired price, and will only\nbe executed if there is a matching party on the opposing\nside, according to a well-defined matching procedure used\nby all the major exchanges. While limit order books (the\nlist of limit orders awaiting possible future execution) have\nexisted since the dawn of equity exchanges, only very\nrecently have these books become visible to traders in real\ntime, thus opening the way to trading algorithms of all\nvarieties that attempt to exploit this rich market microstructure\ndata. Such data and algorithms are a topic of great current\ninterest on Wall Street [4].\nWe thus introduce a new online trading model\nincorporating limit order books, and examine both the one-way and\nVWAP trading problems in it. Our results are summarized\nin Figure 1 (see the caption for a summary).\n2. THEPRICE-VOLUMETRADINGMODEL\nWe now present a trading model which includes both price\nand volume information about the sequence of trades. While\nthis model is a generalization of previous formalisms for\nonline trading, it makes an infinite liquidity assumption which\nfails to model the negative market impact that trading a\nlarge number of shares typically has. This will be addressed\nin the order book model studied in the next section.\nA note on terminology: throughout the paper (unless\notherwise specified), we shall use the term market to describe\nall activity or orders other than those of the algorithm\nunder consideration. The setting we consider can be viewed as\na game between our algorithm and the market.\n2.1 The Model\nIn the price-volume trading model, we assume that the\nintraday trading activity in a given stock is summarized by\na discrete sequence of price and volume pairs (pt, vt) for\nt = 1, . . . , T. Here t = 0 corresponds to the day\"s\nmarket open, and t = T to the close. While there is nothing\ntechnically special about the time horizon of a single day, it\nis particularly consistent with limit order book trading on\nWall Street. The pair (pt, vt) represents the fact that a total\nof vt shares were traded at an (average) price per share pt\nin the market between time t \u2212 1 and t. Realistically, we\nshould imagine the number of intervals T being reasonably\nlarge, so that it is sensible to assign a common approximate\nprice to all shares traded within an interval.\nIn the price-volume model, we shall make an infinite\nliquidity assumption for our trading algorithms. More\nprecisely, in this online model, we see the price-volume sequence\none pair at a time. Following the observation of (pt, vt),\nwe are permitted to sell any (possibly fractional) number\nof shares nt at the price pt. Let us assume that our goal\nis to sell N shares over the course of the day. Hence, at\neach time, we must select a (possibly fractional) number of\nshares nt to sell at price pt, subject to the global constraint\nT\nt=1 nt = N. It is thus assumed that if we have left over\nshares to sell after time T \u2212 1, we are forced to sell them at\nthe closing price of the market - that is, nT = N \u2212 T \u22121\nt=1 nt\nis sold at pT . In this way we are certain to sell exactly N\nshares over the course of the day; the only thing an\nalgorithm must do is determine the schedule of selling based on\nthe incoming market price-volume stream.\nAny algorithm which sells fractional volumes can be\nconverted to a randomized algorithm which only sells integral\nvolumes with the same expected number of shares sold. If\nwe keep the hard constraint of selling exactly N shares, we\nmight incur an additional slight loss in the conversion. (Note\nthat we only allow fractional volumes in the price-volume\nmodel, where liquidity is not an issue. In the order book\nmodel to follow, we do not allow fractional volumes.)\nIn VWAP trading, the goal of an online algorithm A which\nsells exactly N shares is not to maximize profits per se, but\nto track the market VWAP. The market VWAP for an\nintraday trading sequence S = (p1, v1), . . . , (pT , vT ) is simply the\naverage price paid per share over the course of the trading\n190\nday, ie\nVWAPM (S) =\nT\nt=1\nptvt /V\nwhere V is the total daily volume, i.e., V = T\nt=1 vt. If on\nthe sequence S, the algorithm A sells its N stocks using the\nvolume sequence n1, . . . nT , then we analogously define the\nVWAP of A on market sequence S by\nVWAPA(S) =\nT\nt=1\nptnt /N .\nNote that the market VWAP does not include the shares\nthat the algorithm sells.\nThe VWAP competitive ratio of A with respect to a set\nof sequences \u03a3 is then\nRVWAP(A) = max\nS\u2208\u03a3\n{VWAPM (S)/VWAPA(S)}\nIn the case that A is randomized, we generalize the definition\nabove by taking an expectation over VWAPA(S) inside the\nmax. We note that unlike on Wall Street, our definition of\nVWAPM does not take our own trading into account. It is\neasy to see that this makes it a more challenging criterion\nto track.\nIn contrast to the VWAP, another common measure of\nthe performance of an online selling algorithm would be its\none-way trading (OWT) competitive ratio [3] with respect\nto a set of sequences \u03a3:\nROWT(A) = max\nS\u2208\u03a3\nmax\n1\u2264t\u2264T\n{pt/VWAPA(S)}\nwhere the algorithms performance is compared to the largest\nindividual price appearing in the sequence S.\nIn both VWAP and OWT, we are comparing the average\nprice per share received by a selling algorithm to some\nmeasure of market performance. In the case of OWT, we\ncompare to the rather ambitious benchmark of the high price of\nthe day, ignoring volumes entirely. In VWAP trading, we\nhave the more modest goal of comparing favorably to the\noverall market average of the day. As we shall see, there are\nsome important commonalities and differences to these two\napproaches. For now we note one simple fact: on any specific\nsequence S, VWAPA(S) may be larger that VWAPM (S).\nHowever, RVWAP(A) cannot be smaller than 1, since on any\nsequence S in which all price pt are identical, it is impossible\nto get a better average share per price. Thus, for all\nalgorithms A, both RVWAP(A) and ROWT(A) are larger than\n1, and the closer to 1 they are, the better A is tracking its\nrespective performance measure.\n2.2 VWAP Results in the Price-Volume Model\nAs in previous work on online trading, it is generally not\npossible to obtain finite bounds on competitive ratios with\nabsolutely no assumptions on the set of sequences\n\u03a3bounds on the maximum variation in price or volume are\nrequired, depending on the exact setting. We thus introduce\nthe following two assumptions.\n2.2.0.1 Volume Variability Assumption..\nLet 0 < Vmin \u2264 Vmax be known positive constants, and\ndefine Q = Vmax /Vmin . For all intraday trading sequences\nS \u2208 \u03a3, the total daily volume V \u2208 [Vmin , Vmax ].\n2.2.0.2 Price Variability Assumption..\nLet 0 < pmin \u2264 pmax be known positive constants, and\ndefine R = pmax/pmin. For all intraday trading sequences S \u2208\n\u03a3, the prices satisfy pt \u2208 [pmin, pmax], for all t = 1, . . . , T.\nCompetitive ratios are generally taken over all sets \u03a3\nconsistent with at least one of these assumptions. To gain some\nintuition consider the two trivial cases of R = 1 and Q = 1.\nIn the case of R = 1 (where there is no fluctuation in price),\nany schedule is optimal. In the case of Q = 1 (where the\ntotal volume V over the trading period is known), we can\ngain a competitive ratio of 1 by selling vt\nV\nN shares after each\ntime period.\nFor the OWT problem in the price-volume model,\nvolumes are irrelevant for the performance criterion, but for\nthe VWAP criterion they are central. For the OWT problem\nunder the price variability assumption, the results of [3]\nestablished that the optimal competitive ratio was \u0398(log(R)).\nOur first result establishes that the optimal competitive\nratio for VWAP under the volume variability assumption is\n\u0398(log(Q)) and is achieved by an algorithm that ignores the\nprice data.\nTheorem 1. In the price-volume model under the volume\nvariability assumption, there exists an online algorithm A\nfor selling N shares achieving competitive ratio RVWAP(A) \u2264\n2 log(Q). In addition, if only the volume variability (and not\nthe price variability) assumption holds, any online algorithm\nA for selling N shares has RVWAP(A) = \u2126(log(Q)).\nProof. (Sketch) For the upper bound, the idea is\nsimilar to the price reservation algorithm of [3] for the OWT\nproblem, and similar in spirit to the general technique of\nclassify and select [1]. Consider algorithms which use a\nparameter \u02c6V , which is interpreted as an estimate for the total\nvolume for the day. Then at each time t, if the market\nprice and volume is (pt, vt), the algorithm sells a fraction\nvt/ \u02c6V of its shares. We consider a family of log(Q) such\nalgorithms, where algorithm Ai uses \u02c6V = Vmin 2i\u22121\n. Clearly,\none of the Ai has a competitive ratio of 2. We can derive an\nO(log(Q)) VWAP competitive ratio by running these\nalgorithms in parallel, and letting each algorithm sell N/ log(Q)\nshares. (Alternatively, we can randomly select one Ai and\nguarantee the same expected competitive ratio.)\nWe now sketch the proof of the lower bound, which\nrelates performance in the VWAP and OWT problems. Any\nalgorithm that is c-competitive in the VWAP setting\n(under fixed Q) is 3c-competitive in the OWT setting with\nR = Q/2. To show this, we take any sequence S of prices\nfor the OWT problem, and convert it into a price-volume\nsequence for the VWAP problem. The prices in the VWAP\nsequence are the same as in S. To construct the volumes in the\nVWAP sequence, we segment the prices in S into log(R)\nintervals [2i\u22121\npmin , 2i\npmin ). Suppose pt \u2208 [2i\u22121\npmin , 2i\npmin ),\nand this is the first time in S that a price has fallen in this\ninterval. Then in the VWAP sequence we set the volume\nvt = 2i\u22121\n. If this is not the first visit to the interval\ncontaining pt, we set vt = 0. Assume that the maximum price\nin S is pmax . The VWAP of our sequence is at least pmax /3.\nSince we had a c competitive algorithm, its average sell is at\nleast pmax /3c. The lower bound now follows using the lower\nbound in [3].\nAn alternative approach to VWAP is to ignore the\nvolumes in favor of prices, and apply an algorithm for the OWT\nproblem. Note that the lower bound in this theorem, unlike\nin the previous one, only assumes a price variation bound.\n191\nTheorem 2. In the price-volume model under the price\nvariability assumption, there exists an online algorithm A\nfor selling N shares achieving competitive ratio RVWAP(A) =\nO(log(R)). In addition, if only the price variability (and not\nthe volume variability) assumption holds, any online A for\nselling N shares has RVWAP(A) = \u2126(log(R)).\nProof. (Sketch) Follows immediately from the results of\n[3] for OWT: the upper bound from the simple fact that for\nany sequence S, VWAPA(S) is less than max1\u2264t\u2264T {pt}, and\nthe lower bound from a reduction to OWT.\nTheorems 1 and 2 demonstrate that one can achieve\nlogarithmic VWAP competitive ratios under the assumption of\neither bounded variability of total volume or bounded\nvariability of maximum price. If both assumptions hold, it is\npossible to give an algorithm accomplishing the minimum\nof log(Q) and log(R). This flexibility of approach derives\nfrom the fact that the VWAP is a quantity in which both\nprices and volumes matter, as opposed to OWT.\n2.3 RelatedResultsinthePrice-VolumeModel\nAll of the VWAP algorithms we have discussed so far\nmake some use of the daily data (pt, vt) as it unfolds,\nusing either the price or volume information. In contrast, a\nfixed schedule VWAP algorithm has a predetermined\ndistribution {f1, f2, . . . fT }, and simply sells ftN shares at time t,\nindependent of (pt, vt). Fixed schedule VWAP algorithms,\nor slight variants of them, are surprisingly common on Wall\nStreet, and the schedule is usually derived from historical\nintraday volume data. Our next result demonstrates that\nsuch algorithms can perform considerably worse than\ndynamically adaptive algorithms in terms of the worst case\ncompetitive ratio.\nTheorem 3. In the price-volume model under both the\nvolume and price variability assumptions, any fixed schedule\nVWAP algorithm A for selling N shares has sell VWAP\ncompetitive ratio RVWAP(A) = \u2126(min(T, R)).\nThe proofs of all the results in this subsection are in the\nAppendix.\nSo far our emphasis has been on VWAP algorithms that\nmust sell exactly N shares. In many realistic circumstances,\nhowever, there is actually some flexibility in the precise\nnumber of shares to be sold. For instance, this is true at\nlarge brokerages, where many separate VWAP trades may\nbe pooled and executed by a common algorithm, and the\nfirm would be quite willing to carry a small position of\nunsold shares overnight if it resulted in better execution prices.\nThe following theorem (which interestingly has no analogue\nfor the OWT problem) demonstrates that this trade-off in\nshares sold and performance can be realized dramatically in\nour model. It states that if we are willing to let the number\nof shares sold vary with Q, we can in fact achieve a VWAP\ncompetitive ratio of 1.\nTheorem 4. In the price-volume model under the volume\nvariability assumption, there exists an algorithm A that\nalways sells between N and QN shares and that the average\nprice per sold share is exactly VWAPM (S).\nIn many online problems, there is a clear distinction\nbetween benefit problems and cost problems [2]. In the\nVWAP setting, selling shares is a benefit problem, and\nbuying shares is a cost problem. The definitions of the\ncompetitive ratios, Rbuy\nVWAP(A) and Rbuy\nOWT(A), for algorithms which\nFigure 2: Sample Island order books for MSFT.\nbuy exactly N shares are maxS\u2208\u03a3{VWAPA(S)/VWAPM (S)}\nand maxS\u2208\u03a3 maxt{VWAPA(S)/pt} respectively. Eventhough\nTheorem 4 also holds for buying, in general, the competitive\nratio of the buy (cost) problem is much higher, as stated in\nthe following theorem.\nTheorem 5. In the price-volume model under the volume\nand price variability assumptions, there exists an online\nalgorithm A for buying N shares achieving buy VWAP\ncompetitive ratio Rbuy\nVWAP(A) = O(min{Q,\n\u221a\nR}). In addition\nany online algorithm A for buying N shares has buy VWAP\ncompetitive ratio Rbuy\nVWAP(A) = \u2126(min{Q,\n\u221a\nR}).\n3. A LIMIT ORDER BOOK TRADING\nMODEL\nBefore we can define our online trading model based on\nlimit order books, we give some necessary background on\nthe detailed mechanics of financial markets, which are\nsometimes referred to as market microstructure. We then provide\nresults and algorithms for both the OWT and VWAP\nproblems.\n192\n3.1 Background on Limit Order Books and\nMarket Microstructure\nA fundamental distinction in stock trading is that between\na limit order and a market order. Suppose we wish to\npurchase 1000 shares of Microsoft (MSFT) stock. In a limit\norder, we specify not only the desired volume (1000 shares),\nbut also the desired price. Suppose that MSFT is currently\ntrading at roughly $24.07 a share (see Figure 2, which shows\nan actual snapshot of a recent MSFT order book on\nIsland (www.island.com), a well-known electronic exchange\nfor NASDAQ stocks), but we are only willing to buy the\n1000 shares at $24.04 a share or lower. We can choose to\nsubmit a limit order with this specification, and our order\nwill be placed in a queue called the buy order book, which\nis ordered by price, with the highest offered unexecuted buy\nprice at the top (often referred to as the bid). If there are\nmultiple limit orders at the same price, they are ordered by\ntime of arrival (with older orders higher in the book). In the\nexample provided by Figure 2, our order would be placed\nimmediately after the extant order for 5,503 shares at $24.04;\nthough we offer the same price, this order has arrived before\nours. Similarly, a sell order book for sell limit orders (for\ninstance, we might want to sell 500 shares of MSFT at $24.10\nor higher) is maintained, this time with the lowest sell price\noffered (often referred to as the ask).\nThus, the order books are sorted from the most\ncompetitive limit orders at the top (high buy prices and low sell\nprices) down to less competitive limit orders. The bid and\nask prices (which again, are simply the prices in the limit\norders at the top of the buy and sell books, respectively)\ntogether are sometimes referred to as the inside market, and\nthe difference between them as the spread. By definition,\nthe order books always consist exclusively of unexecuted\norders - they are queues of orders hopefully waiting for the\nprice to move in their direction.\nHow then do orders get executed? There are two\nmethods. First, any time a market order arrives, it is immediately\nmatched with the most competitive limit orders on the\nopposing book. Thus, a market order to buy 2000 shares is\nmatched with enough volume on the sell order book to fill\nthe 2000 shares. For instance, in the example of Figure 2,\nsuch an order would be filled by the two limit sell orders\nfor 500 shares at $24.069, the 500 shares at $24.07, the 200\nshares at $24.08, and then 300 of the 1981 shares at $24.09.\nThe remaining 1681 shares of this last limit order would\nremain as the new top of the sell limit order book. Second,\nif a buy (sell, respectively) limit order comes in above the\nask (below the bid, respectively) price, then the order is\nmatched with orders on the opposing books. It is important\nto note that the prices of executions are the prices specified\nin the limit orders already in the books, not the prices of the\nincoming order that is immediately executed.\nEvery market or limit order arrives atomically and\ninstantaneously - there is a strict temporal sequence in which\norders arrive, and two orders can never arrive simultaneously.\nThis gives rise to the definition of the last price of the\nexchange, which is simply the last price at which the exchange\nexecuted an order. It is this quantity that is usually meant\nwhen people casually refer to the (ticker) price of a stock.\nNote that a limit buy (sell, respectively) order with a\nprice of infinity (0, respectively) is effectively a market\norder. We shall thus assume without loss of generality that\nall orders are placed as limit order. Although limit orders\nwhich are unexecuted may be removed by the party which\nplaced them, for simplicity, we assume that limit orders are\nnever removed from the books.\nWe refer the reader to [4] for further discussion of modern\nelectronic exchanges and market microstructure.\n3.2 The Model\nThe online order book trading model is intended to capture\nthe realistic details of market microstructure just discussed\nin a competitive ratio setting. In this refined model, a day\"s\nmarket activity is described by a sequence of limit orders\n(pt, vt, bt). Here bt is a bit indicating whether the order is\na buy or sell order, while pt is the limit order price and vt\nthe number of shares desired. Following the arrival of each\nsuch limit order, an online trading algorithm is permitted\nto place its own limit order. These two interleaved sources\n(market and algorithm) of limit orders are then simply\noperated on according to the matching process described in\nSection 3.1. Any limit order that is not immediately\nexecutable according to this process is placed in the appropriate\n(buy or sell) book for possible future execution; arriving\norders that can be partially or fully executed are so executed,\nwith any residual shares remaining on the respective book.\nThe goal of a VWAP or OWT selling algorithm is\nessentially the same as in the price-volume model, but the\ncontext has changed in the following two fundamental ways.\nFirst, the assumption of infinite liquidity in the price-volume\nmodel is eliminated entirely. The number of shares available\nat any given price is restricted to the total volume of limit\norders offering that price. Second, all incoming orders, and\ntherefore the complete limit order books, are assumed to\nbe visible to the algorithm. This is consistent with modern\nelectronic financial exchanges, and indeed is the source of\nmuch current interest on Wall Street [4].\nIn general, the definition of competitive ratios in the order\nbook model is complicated by the fact that now our\nalgorithm\"s activity influences the sequence of executed prices\nand volumes. We thus first define the execution sequence\ndetermined by a limit order sequence (placed by the\nmarket and our algorithm). Let S = (p1, v1, b1), . . . , (pT , vT , bT )\nbe a limit order sequence placed by the market, and let\nS = (p1, v1, b1), . . . , (pT , vT , bT ) be a limit order sequence\nplaced by our algorithm (unless otherwise specified, all bt are\nof the sell type). Let merge(S, S ) be the merged sequence\n(p1, v1, b1), (p1, v1, b1), . . . , (pT , vT , bT ), (pT , vT , bT ), which is\nthe time sequence of orders placed by the market and\nalgorithm. Note that the algorithm has the option of not placing\nan order, which we can view as a zero volume order.\nIf we conducted the order book maintenance and order\nexecution process described in Section 3.1 on the sequence\nmerge(S, S ), at irregular intervals a trade occurs for some\nnumber of shares and some price. In each executed trade,\nthe selling party is either the market or the algorithm. Let\nexecM (S, S ) = (q1, w1), . . . , (qT , wT ) be the sequence of\nexecutions where the market (that is, a party other than\nthe algorithm) was the selling party, where the qt are the\nexecution prices and wt the execution volumes. Similarly,\nwe define execA(S, S ) = (r1, x1), . . . , (rT , xT ) to be the\nsequence of executions in which the algorithm was the selling\nparty. Thus, execA(S, S ) \u222a execM (S, S ) is the set of all\nexecutions. We generally expect T to be (possibly much)\nsmaller than T .\nThe revenue of the algorithm and the market are defined\n193\nas:\nREVM (S, S ) \u2261\nT\nt=1\nqtwt , REVA(S, S ) \u2261\nT\nt=1\nrtxt\nNote that both these quantities are solely determined by the\nexecution sequences execM (S, S ) and execA(S, S ),\nrespectively.\nFor an algorithm A which is constrained to sell exactly N\nshares, we define the OWT competitive ratio of A, ROWT(A),\nas the maximum ratio (under any S \u2208 \u03a3) of the revenue\nobtained by A, as compared to the revenue obtained by an\noptimal o\ufb04ine algorithm A\u2217\n. More formally, for A\u2217\nwhich\nis constrained to sell exactly N shares, we define\nROWT(A) = max\nS\u2208\u03a3\nmax\nA\u2217\nREVA\u2217 (S S\u2217\n)\nREVA(S, S )\nwhere S\u2217\nis the limit order sequence placed by A\u2217\non S. If\nthe algorithm A is randomized then we take the appropriate\nexpectation with respect to S \u223c A.\nWe define the VWAP competitive ratio, RVWAP(A), as\nthe maximum ratio (under any S \u2208 \u03a3) between the market\nand algorithm VWAPs. More formally, define VWAPM (S, S )\nas REVM (S, S )/ T\nt=1 wt, where the denominator is just\nthe total executed volume of orders placed by the\nmarket. Similarly, we define VWAPA(S, S ) as REVA(S, S )/N,\nsince we assume the algorithm sells no more than N shares\n(this definition implicitly assumes that A gets a 0 price for\nunsold shares). The VWAP competitive ratio of A is then:\nRVWAP(A) = max\nS\u2208\u03a3\n{VWAPM (S, S )/VWAPA(S, S )}\nwhere S is the online sequence of limit orders generated by\nA in response to the sequence S.\n3.3 OWT Results in the Order Book Model\nFor the OWT problem in the order book model, we\nintroduce a more subtle version of the price variability\nassumption. This is due to the fact that our algorithm\"s trading\ncan impact the high and low prices of the day. For the\nassumption below, note that execM (S, \u2205) is the sequence of\nexecutions without the interaction of our algorithm.\n3.3.0.3 Order Book Price Variability Assumption..\nLet 0 < pmin \u2264 pmax be known positive constants, and\ndefine R = pmax/pmin. For all intraday trading sequences\nS \u2208 \u03a3, the prices pt in the sequence execM (S, \u2205) satisfy\npt \u2208 [pmin, pmax], for all t = 1, . . . , T.\nNote that this assumption does not imply that the ratios\nof high to low prices under the sequences execM (S, S ) or\nexecA(S, S ) are bounded by R. In fact, the ratio in the\nsequence execA(S, S ) could be infinite if the algorithm ends\nup selling some stocks at a 0 price.\nTheorem 6. In the order book model under the order\nbook price variability assumption, there exists an online\nalgorithm A for selling N shares achieving sell OWT competitive\nratio ROWT(A) = 2 log(R) log(N).\nProof. The algorithm A works by guessing a price p in\nthe set {pmin2i\n: 1 \u2264 i \u2264 log(R)} and placing a sell limit\norder for all N shares at the price p at the beginning of\nthe day. (Alternatively, algorithm A can place log(R) sell\nlimit orders, where the i-th one has price 2i\npmin and volume\nN/ log(R).) By placing an order at the beginning of the day,\nthe algorithm undercuts all sell orders that will be placed\nduring the day for a price of p or higher, meaning the\nalgorithm\"s N shares must be filled first at this price. Hence,\nif there were k shares that would have been sold at price p\nor higher without our activity, then A would sell at least kp\nshares.\nWe define {pj} to be the multiset of prices of\nindividual shares that are either executed or are buy limit order\nshares that remained unexecuted, excluding the activity of\nour algorithm (that is, assuming our algorithm places no\norders). Assume without loss of generality that p1 \u2265 p2 \u2265 . . ..\nConsider guessing the kth highest such price, pk. If an\norder for N shares is placed at the day\"s start at price pk,\nthen we are guaranteed to obtain a return of kpk. Let\nk\u2217\n= argmaxk{kpk}. We can view our algorithm as\nattempting to guess pk\u2217 , and succeeding if the guess p\nsatisfies p \u2208 [pk\u2217 /2, pk\u2217 ]. Hence, we are 2 log(R) competitive\nwith the quantity max1\u2264k\u2264N kpk. Note that\n\u03c1 \u2261\nN\ni=1\npi\n=\nN\ni=1\n1\ni\nipi\n\u2264 max\n1\u2264k\u2264N\nkpk\nN\ni=1\n1\ni\n\u2264 log(N) max\n1\u2264k\u2264N\nkpk\nwhere \u03c1 is defined as the sum of the top N prices pi without\nA\"s involvement.\nSimilarly, let {pj} be the multiset of prices of\nindividual executed shares, or the prices of unexecuted buy order\nshares, but now including the orders placed by some selling\nalgorithm A . We now wish to show that for all algorithms\nA which sell N shares, REVA \u2264 N\ni=1 pi \u2264 \u03c1.\nEssentially, this inequality states the intuitive idea that a selling\nalgorithm can only lower executed or unmatched buy\norder share prices. To prove this, we use induction to show\nthat the removal of the activity of a selling algorithm causes\nthese prices to increase. First, remove the last share in the\nlast sell order placed by either A or the market on an\narbitrary sequence merge(S, S ) - by this we mean, take the\nlast sell order placed by A or the market and decrease its\nvolume by one share. After this modification, the top N\nprices p1 . . . pN will not decrease. This is because either this\nsell order share was not executed, in which case the claim\nis trivially true, or, if it was executed, the removal of this\nsell order share leaves an additional unexecuted buy order\nshare of equal or higher price. For induction, assume that if\nwe remove a share from any sell order that was placed, by\nA or the market, at or after time t then the top N prices\ndo not decrease. We now show that if we remove a share\nfrom the last sell order that was placed by A or the market\nbefore time t, then the top N prices do not decrease. If this\nsell order share was not executed, then the claim is trivially\ntrue. Else, if the sell order share was executed, then claim\nis true because by removing this executed share from the\nsell order either: i) the corresponding buy order share (of\nequal or higher value) is unmatched on the remainder of the\nsequence, in which case the claim is true; or ii) this buy\n194\norder matches some sell order share at an equal or higher\nprice, which has the effect of removing a share from a sell\norder on the remainder of the sequence, and, by the\ninductive assumption, this can only increase prices. Hence, we\nhave proven that for all A which sell N shares REVA \u2264 \u03c1.\nWe have now established that our revenue satisfies\n2 log(R)ES \u223cA[REVA(S, S )] \u2265 max\n1\u2264k\u2264N\n{kpk}\n\u2265 \u03c1/ log(N)\n\u2265 max\nA\n{REVA }/ log(N),\nwhere A performs an arbitrary sequence of N sell limit\norders.\n3.4 VWAP Results in the Order Book Model\nThe OWT algorithm from Theorem 6 can be applied to\nobtain the following VWAP result:\nCorollary 7. In the order book model under the order\nbook price variability assumption, there exists an online\nalgorithm A for selling N shares achieving sell VWAP\ncompetitive ratio RVWAP(A) = O(log(R) log(N)).\nWe now make a rather different assumption on the\nsequences S.\n3.4.0.4 Bounded Order Volume and Max Price\nAssumption.\nThe set of sequences \u03a3 satisfies the following two\nproperties. First, we assume that each order placed by the market\nis of volume less than \u03b3, which we view as a mild assumption\nsince typically single orders on the market are not of high\nvolume (due to liquidity issues). This assumption allows our\nalgorithm to place at least one limit order at a time\ninterleaved with approximately \u03b3 market executions. Second, we\nassume that there is large volume in the sell order books\nbelow the price pmax , which means that no orders placed by\nthe market will be executed above the price pmax . The\nsimplest way to instantiate this latter assumption in the order\nbook model is to assume that each sequence S \u2208 \u03a3 starts\nby placing a huge number of sell orders (more than Vmax )\nat price pmax .\nAlthough this assumption has a maximum price\nparameter, it does not imply that the price ratio R is finite, since\nit does not imply any lower bound on the prices of buy or\nexecuted shares (aside from the trivial one of 0).\nTheorem 8. Consider the order book model under the\nbounded order volume and max price assumption. There\nexists an algorithm A in which after exactly \u03b3N market\nexecutions have occurred, then A has sold at most N shares\nand\nREVA(S, S )\nN\n= VWAPA(S, S )\n\u2265 (1 \u2212 )VWAPM (S, S ) \u2212\npmax\nN\nwhere S is a sequence of N sell limit orders generated by A\nwhen observing S.\nProof. The algorithm divides the trading day into\nvolume intervals whose real-time duration may vary. For each\nperiod i in which \u03b3 shares have been executed in the\nmarket, the algorithm computes the market VWAP of only those\nshares traded in period i; let us denote this by VWAPi.\nFollowing this ith volume interval, the algorithm places a limit\norder to sell exactly one share at a price close to VWAPi.\nMore precisely, the algorithm only places orders at the\ndiscrete prices (1\u2212 )pmax , (1\u2212 )2\npmax , . . .. Following volume\ninterval i, the algorithm places a limit order to sell one share\nat the discretized price that is closest to VWAPi, but which\nis strictly smaller.\nFor the analysis, we begin by noting that if all of the\nalgorithm\"s limit orders are executed during the day, the\ntotal revenue received by the algorithm would be at least\n(1 \u2212 )VWAPM (S, S )N. To see this, it suffices to note that\nVWAPM (S, S ) is a uniform mixture of the VWAPi (since\nby definition they each cover the same amount of market\nvolume); and if all the algorithm\"s limit orders were\nexecuted, they each received more than (1 \u2212 )VWAPi dollars\nfor the interval i they followed.\nWe now count the potential lost revenue of the\nalgorithm due to unexecuted limit orders. By the assumption\nthat individual orders are placed with volume less than \u03b3,\nthen our algorithm is able to place a limit order during every\nblock of \u03b3 shares have been traded. Hence, after \u03b3N market\norders have been executed, A has placed N orders in the\nmarket.\nNote that there can be at most one limit order (and thus,\nat most one share) left unexecuted at each level of the\ndiscretized price ladder defined above. This is because\nfollowing interval i, the algorithm places its limit order strictly\nbelow VWAPi, so if VWAPj \u2265 VWAPi for j > i, this limit\norder must have been executed. Thus unexecuted limit\norders bound the VWAPs of the remainder of the day,\nresulting in at most one unexecuted order per price level.\nA bound on the lost revenue is thus the sum of the\ndiscretized prices: \u221e\ni=1(1 \u2212 )i\npmax \u2264 pmax / . Clearly our\nalgorithm has sold at most N shares.\nNote that as N becomes large, VWAPA approaches 1 \u2212\ntimes the market VWAP. If we knew that the final total\nvolume of the market executions is V , then we can set \u03b3 =\nV/N, assuming that \u03b3 >> 1. If we have only an upper and\nlower bound on V we should be able to guess and incur a\nlogarithmic loss. The following assumption tries to capture\nthe market volume variability.\n3.4.0.5 Order Book Volume Variability Assumption.\nWe now assume that the total volume (which includes\nthe shares executed by both our algorithm and the market)\nis variable within some known region and that the market\nvolume will be greater than our algorithms volume. More\nformally, for all S \u2208 \u03a3, assume that the total volume V\nof shares traded in execM (S, S ), for any sequence S of N\nsell limit orders, satisfies 2N \u2264 Vmin \u2264 V \u2264 Vmax . Let\nQ = Vmax /Vmin .\nThe following corollary is derived using a constant = 1/2\nand observing that if we set \u03b3 such that V \u2264 \u03b3N \u2264 2V then\nour algorithm will place between N and N/2 limit orders.\nCorollary 9. In the order book model, if the bounded\norder volume and max price assumption, and the order book\nvolume variability assumption hold, there exists an online\nalgorithm A for selling at most N shares such that\nVWAPA(S, S ) \u2265\n1\n4 log(Q)\nVWAPM (S, S ) \u2212\n2pmax\nN\n195\n0 2 4 6 8\nx 10\n7\n0\n20\n40\n60\n80\n100\nQQQ: log(Q)=4.71, E=3.77\n0 2 4 6 8 10\nx 10\n6\n0\n20\n40\n60\n80\nJNPR: log(Q)=5.66, E=3.97\n0 0.5 1 1.5 2\nx 10\n6\n0\n10\n20\n30\n40\n50\n60\n70\nMCHP: log(Q)=5.28, E=3.86\n0 2 4 6 8 10\nx 10\n6\n0\n50\n100\n150\n200\n250\nCHKP: log(Q)=6.56, E=4.50\nFigure 3: Here we present bounds from Section 4 based on the empirical volume distributions for four real stocks:\nQQQ, MCHP, JNPR, and CHKP. The plots show histograms for the total daily volumes transacted on Island for\nthese stocks, in the last year and a half, along with the corresponding values of log(Q) and E(Pbins\nvol ) (denoted by \"E\").\nWe assume that the minimum and maximum daily volumes in the data correspond to Vmin and Vmax , respectively.\nThe worst-case competitive ratio bounds (which are twice log(Q)) of our algorithm for those stocks are 9.42, 10.56, 11.32,\nand 13.20, respectively. The corresponding bounds on the competitive ratio performance of our algorithm under the\nvolume distribution model (which are twice E(Pbins\nvol )) are better: 7.54, 7.72, 7.94, and 9.00, respectively (a 20\u221240% relative\nimprovement). Using a finer volume binning along with a slightly more refined bound on the competitive ratio, we can\nconstruct algorithms that, using the empirical volume distribution given as correct, guarantee even better competitive\nratios of 2.76, 2.73, 2.75, and 3.17, respectively for those stocks (details omitted).\n4. MACROSCOPIC DISTRIBUTION\nMODELS\nWe conclude our results with a return to the price-volume\nmodel, where we shall introduce some refined methods of\nanalysis for online trading algorithms. We leave the\ngeneralization of these methods to the order book model for\nfuture work.\nThe competitive ratios defined so far measure performance\nrelative to some baseline criterion in the worst case over all\nmarket sequences S \u2208 \u03a3. It has been observed in many\nonline settings that such worst-case metrics can yield\npessimistic results, and various relaxations have been\nconsidered, such as permitting a probability distribution over the\ninput sequence.\nWe now consider distributional models that are\nconsiderably weaker than assuming a distribution over complete\nmarket sequences S \u2208 \u03a3. In the volume distribution model,\nwe assume only that there exists a distribution Pvol over the\ntotal volume V traded in the market for the day, and then\nexamine the worst-case competitive ratio over sequences\nconsistent with the randomly chosen volume. More precisely,\nwe define\nRVWAP(A, Pvol ) = EV \u223cPvol max\nS\u2208seq(V )\nVWAPM (S)\nVWAPA(S)\n.\nHere V \u223c Pvol denotes that V is chosen with respect to\ndistribution Pvol , and seq(V ) \u2282 \u03a3 is the set of all market\nsequences (p1, v1), . . . , (pT , vT ) satisfying T\nt=1 vt = V .\nSimilarly, for OWT, we can define\nROWT(A, Pmaxprice ) = Ep\u223cPmaxprice max\nS\u2208seq(p)\np\nVWAPA(S)\n.\nHere Pmaxprice is a distribution over just the maximum price\nof the day, and we then examine worst-case sequences\nconsistent with this price (seq(p) \u2282 \u03a3 is the set of all market\nsequences satisfying max1\u2264t\u2264T pt = p). Analogous buy-side\ndefinitions can be given.\nWe emphasize that in these models, only the distribution\nof maximum volume and price is known to the algorithm.\nWe also note that our probabilistic assumptions on S are\nconsiderably weaker than typical statistical finance\nmodels, which would posit a detailed stochastic model for the\nstep-by-step evolution of (pt, vt). Here we instead permit\nonly a distribution over crude, macroscopic measures of the\nentire day\"s market activity, such as the total volume and\nhigh price, and analyze the worst-case performance\nconsistent with these crude measures. For this reason, we refer to\nsuch settings as the macroscopic distribution model.\nThe work of El-Yaniv et al. [3] examines distributional\nassumptions similar to ours, but they emphasize the\nworst196\ncase choices for the distributions as well, and show that this\nleads to results no better than the original worst-case\nanalysis over all sequences. In contrast, we feel that the analysis\nof specific distributions Pvol and Pmaxprice is natural in many\nfinancial contexts and our preliminary experimental results\nshow significant improvements when this rather crude\ndistributional information is taken into account (see Figure 3).\nOur results in the VWAP setting examine the cases where\nthese distributions are known exactly or only approximately.\nSimilar results can be obtained for macroscopic distributions\nof maximum daily price for the one-way trading setting.\n4.1 Results in the Macroscopic Distribution\nModel\nWe begin by noting that the algorithms examined so far\nwork by binning total volumes or maximum prices into bins\nof exponentially increasing size, and then guessing the\nindex of the bin in which the actual quantity falls. It is\nthus natural that the macroscopic distribution model\nperformance of such algorithms (which are common in\ncompetitive analysis) might depend on the distribution of the true\nbin index.\nIn the remaining, we assume that Q is a power of 2 and\nthe base of the logarithm is 2. Let Pvol denote the\ndistribution of total daily market volume. We define the\nrelated distribution Pbins\nvol over bin indices i as follows: for\nall i = 1, . . . , log(Q) \u2212 1, Pbins\nvol (i) is equal to the\nprobability, under Pvol , that the daily volume falls in the interval\n[Vmin 2i\u22121\n, Vmin 2i\n), and Pbins\nvol (log(Q)) is for the last interval\n[Vmax /2, Vmax ] .\nWe define E as\nE(Pbins\nvol ) \u2261 Ei\u223cP bins\nvol\n1/Pbins\nvol (i)\n2\n=\n\uf8eb\n\uf8ed\nlog(Q)\ni=1\nPbins\nvol (i)\n\uf8f6\n\uf8f8\n2\n.\nSince the support of Pbins\nvol has only log(Q) elements, E(Pbins\nvol )\ncan vary from 1 (for distributions Pvol that place all of\ntheir weight in only one of the log(Q) intervals between\nVmin , Vmin 2, Vmin 4, . . . , Vmax ) to log(Q) (for distributions\nPvol in which the total daily volume is equally likely to fall\nin any one of these intervals). Note that distributions Pvol\nof this latter type are far from uniform over the entire range\n[Vmin , Vmax ].\nTheorem 10. In the volume distribution model under the\nvolume variability assumption, there exists an online\nalgorithm A for selling N shares that, using only knowledge of\nthe total volume distribution Pvol , achieves RVWAP(A, Pvol ) \u2264\n2E(Pbins\nvol ).\nAll proofs in this section are provided in the appendix.\nAs a concrete example, consider the case in which Pvol\nis the uniform distribution over [Vmin , Vmax ]. In that case,\nPbins\nvol is exponentially increasing and peaks at the last bin,\nwhich, having the largest width, also has the largest weight.\nIn this case E(Pbins\nvol ) is a constant (i.e., independent of Q),\nleading to a constant competitive ratio. On the other hand,\nif Pvol is exponential, then Pbins\nvol is uniform, leading to an\nO(log(Q)) competitive ratio, just as in the more adversarial\nprice-volume setting discussed earlier. In Figure 3, we\nprovide additional specific bounds obtained for empirical total\ndaily volume distributions computed for some real stocks.\nWe now examine the setting in which Pvol is unknown,\nbut an approximation \u02dcPvol is available. Let us define\nC(Pbins\nvol , \u02dcPbins\nvol ) = log(Q)\nj=1\n\u02dcPbins\nvol (j) log(Q)\ni=1\nP bins\nvol (i)\n\u221a \u02dcP bins\nvol\n(i)\n.\nC is minimized at C(Pbins\nvol , Pbins\nvol ) = E(Pbins\nvol ), and C may\nbe infinite if \u02dcPbins\nvol (i) is 0 when Pbins\nvol (i) > 0.\nTheorem 11. In the volume distribution model under the\nvolume variability assumption, there exists an online\nalgorithm A for selling N shares that using only knowledge of\nan approximation \u02dcPvol of Pvol achieves RVWAP(A, Pvol ) \u2264\n2C(Pbins\nvol , \u02dcPbins\nvol ).\nAs an example of this result, suppose our approximation\nobeys (1/\u03b1)Pbins\nvol (i) \u2264 \u02dcPbins\nvol (i) \u2264 \u03b1Pbins\nvol (i) for all i, for\nsome \u03b1 > 1. Thus our estimated bin index probabilities\nare all within a factor of \u03b1 of the truth. Then it is easy\nto show that C(Pbins\nvol , \u02dcPbins\nvol ) \u2264 \u03b1E(Pbins\nvol ), so according to\nTheorems 10 and 11 our penalty for using the approximate\ndistribution is a factor of \u03b1 in competitive ratio.\n5. REFERENCES\n[1] B. Awerbuch, Y. Bartal, A. Fiat, and A. Ros\u00b4en.\nCompetitive non-preemptive call control. In Proc. 5\"th\nACM-SIAM Symp. on Discrete Algorithms, pages\n312-320, 1994.\n[2] A. Borodin and R. El-Yaniv. Online Computation and\nCompetitive Analysis. Cambridge University Press,\n1998.\n[3] R. El-Yaniv, A. Fiat, R. M. Karp, and G. Turpin.\nOptimal search and one-way trading online algorithms.\nAlgorithmica, 30:101-139, 2001.\n[4] M. Kearns and L. Ortiz. The Penn-Lehman automated\ntrading project. IEEE Intelligent Systems, 2003. To\nappear.\n6. APPENDIX\n6.1 Proofs from Subsection 2.3\nProof. (Sketch of Theorem 3) W.l.o.g., assume that Q =\n1 and the total volume is V . Consider the time t where the\nfixed schedule f sells the least, then ft \u2264 N/T. Consider the\nsequences where at time t we have pt = pmax , vt = V , and\nfor times t = t we have pt = pmin and vt = 0. The VWAP\nis pmax and the fixed schedule average is (N/T)pmax + (N \u2212\nN/T)pmin .\nProof. (Sketch of Theorem 4) The algorithm simply sells\nut = (vt/Vmin )N shares at time t. The total number of\nshares sold U is clearly more than N and\nU =\nt\nut =\nt\n(vt/Vmin )N = (V/Vmin )N \u2264 QN\nThe average price is\nV WAPA(S) = (\nt\nptut)/U =\nt\npt(vt/V ) = V WAPM (S),\nwhere we used the fact that ut/U = vt/V .\n197\nProof. (of Theorem 5) We start with the proof of the\nlower bound. Consider the following scenario. For the first\nT time units we have a price of\n\u221a\nRpmin , and a total volume\nof Vmin . We observe how many shares the online algorithm\nhas bought. If it has bought more than half of the shares,\nthe remaining time steps have price pmin and volume Vmax \u2212\nVmin . Otherwise, the remaining time steps have price pmax\nand negligible volume.\nIn the first case the online has paid at least\n\u221a\nRpmin /2\nwhile the VWAP is at most\n\u221a\nRpmin /Q + pmin . Therefore,\nin this case the competitive ratio is \u2126(Q). In the second case\nthe online has to buy at least half of the shares at pmax , so\nits average cost is at least pmax /2. The market VWAP is\u221a\nRpmin = pmax /\n\u221a\nR, hence the competitive ratio is \u2126(\n\u221a\nR).\nFor the upper bound, we can get a\n\u221a\nR competitive ratio,\nby buying all the shares once the price drops below\n\u221a\nRpmin .\nThe Q upper bound is derive by running an algorithm that\nassumes the volume is Vmin . The online pays a cost of p,\nwhile the VWAP will be at least p/Q.\n6.2 Proofs from Section 4\nProof. (Sketch of Theorem 10) We use the idea of\nguessing the total volume from Theorem 1, but now allow for the\npossibility of an arbitrary (but known) distribution over the\ntotal volume. In particular, consider constructing a\ndistribution Gbins\nvol over a set of volume values using Pvol and use\nit to guess the total volume V . Let the algorithm guess\n\u02c6V = Vmin 2i\nwith probability Gbins\nvol (i). Then note that,\nfor any price-volume sequence S, if V \u2208 [Vmin 2i\u22121\n, Vmin 2i\n],\nVWAPA(S) \u2265 Gbins\nvol (i)VWAPM (S)/2. This implies an\nupper bound on RVWAP(A, Pvol ) in terms of Gbins\nvol . We then\nget that Gbins\nvol (i) \u221d Pbins\nvol (i) minimizes the upper bound,\nwhich leads to the upper bound stated in the theorem.\nProof. (Sketch of Theorem 11) Replace Pvol with \u02dcPvol\nin the expression for Gbins\nvol in the proof sketch for the last\nresult.\n198", "keywords": "share;modern financial market;online algorithm;online trade;sequence of trade;trade sequence;competitive analysis;market order;volume weighted average price trading model;vwap;competitive algorithm;stock trading;online model;limit order book trading model"}
{"name": "train_J-74", "title": "On Cheating in Sealed-Bid Auctions", "abstract": "Motivated by the rise of online auctions and their relative lack of security, this paper analyzes two forms of cheating in sealed-bid auctions. The first type of cheating we consider occurs when the seller spies on the bids of a second-price auction and then inserts a fake bid in order to increase the payment of the winning bidder. In the second type, a bidder cheats in a first-price auction by examining the competing bids before deciding on his own bid. In both cases, we derive equilibrium strategies when bidders are aware of the possibility of cheating. These results provide insights into sealedbid auctions even in the absence of cheating, including some counterintuitive results on the effects of overbidding in a first-price auction.", "fulltext": "1. INTRODUCTION\nAmong the types of auctions commonly used in practice,\nsealed-bid auctions are a good practical choice because they\nrequire little communication and can be completed almost\ninstantly. Each bidder simply submits a bid, and the winner\nis immediately determined. However, sealed-bid auctions\ndo require that the bids be kept private until the auction\nclears. The increasing popularity of online auctions only\nmakes this disadvantage more troublesome. At an auction\nhouse, with all participants present, it is difficult to examine\na bid that another bidder gave directly to the auctioneer.\nHowever, in an online auction the auctioneer is often little\nmore than a server with questionable security; and, since all\nparticipants are in different locations, one can anonymously\nattempt to break into the server. In this paper, we present a\ngame theoretic analysis of how bidders should behave when\nthey are aware of the possibility of cheating that is based on\nknowledge of the bids.\nWe investigate this type of cheating along two dimensions:\nwhether it is the auctioneer or a bidder who cheats, and\nwhich variant (either first or second-price) of the sealed-bid\nauction is used. Note that two of these cases are trivial.\nIn our setting, there is no incentive for the seller to submit\na shill bid in a first price auction, because doing so would\neither cancel the auction or not affect the payment of the\nwinning bidder. In a second-price auction, knowing the\ncompeting bids does not help a bidder because it is dominant\nstrategy to bid truthfully. This leaves us with two cases that\nwe examine in detail.\nA seller can profitably cheat in a second-price auction by\nlooking at the bids before the auction clears and submitting\nan extra bid. This possibility was pointed out as early as\nthe seminal paper [12] that introduced this type of auction.\nFor example, if the bidders in an eBay auction each use a\nproxy bidder (essentially creating a second-price auction),\nthen the seller may be able to break into eBay\"s server,\nobserve the maximum price that a bidder is willing to pay, and\nthen extract this price by submitting a shill bid just below\nit using a false identity. We assume that there is no chance\nthat the seller will be caught when it cheats. However, not\nall sellers are willing to use this power (or, not all sellers can\nsuccessfully cheat). We assume that each bidder knows the\nprobability with which the seller will cheat. Possible\nmotivation for this knowledge could be a recently published expos\u00b4e\non seller cheating in eBay auctions. In this setting, we derive\nan equilibrium bidding strategy for the case in which each\nbidder\"s value for the good is independently drawn from a\ncommon distribution (with no further assumptions except\nfor continuity and differentiability). This result shows how\nfirst and second-price auctions can be viewed as the\nendpoints of a spectrum of auctions.\nBut why should the seller have all the fun? In a first-price\nauction, a bidder must bid below his value for the good (also\ncalled shaving his bid) in order to have positive utility if he\n76\nwins. To decide how much to shave his bid, he must trade off\nthe probability of winning the auction against how much he\nwill pay if he does win. Of course, if he could simply examine\nthe other bids before submitting his own, then his problem\nis solved: bid the minimum necessary to win the auction.\nIn this setting, our goal is to derive an equilibrium bidding\nstrategy for a non-cheating bidder who is aware of the\npossibility that he is competing against cheating bidders. When\nbidder values are drawn from the commonly-analyzed\nuniform distribution, we show the counterintuitive result that\nthe possibility of other bidders cheating has no effect on\nthe equilibrium strategy of an honest bidder. This result\nis then extended to show the robustness of the equilibrium\nof a first-price auction without the possibility of cheating.\nWe conclude this section by exploring other distributions,\nincluding some in which the presence of cheating bidders\nactually induces an honest bidder to lower its bid.\nThe rest of the paper is structured as follows. In Section\n2 we formalize the setting and present our results for the\ncase of a seller cheating in a second price auction. Section\n3 covers the case of bidders cheating in a first-price auction.\nIn Section 4, we quantify the effects that the possibility of\ncheating has on an honest seller in the two settings. We\ndiscuss related work, including other forms of cheating in\nauctions, in Section 5, before concluding with Section 6. All\nproofs and derivations are found in the appendix.\n2. SECOND-PRICE AUCTION,\nCHEATING SELLER\nIn this section, we consider a second-price auction in which\nthe seller may cheat by inserting a shill bid after\nobserving all of the bids. The formulation for this section will be\nlargely reused in the following section on bidders cheating\nin a first-price auction. While no prior knowledge of game\ntheory or auction theory is assumed, good introductions can\nbe found in [2] and [6], respectively.\n2.1 Formulation\nThe setting consists of N bidders, or agents, (indexed by\ni = 1, \u00b7 \u00b7 \u00b7 , n) and a seller. Each agent has a type \u03b8i \u2208\n[0, 1], drawn from a continuous range, which represents the\nagent\"s value for the good being auctioned.2\nEach agent\"s\ntype is independently drawn from a cumulative distribution\nfunction (cdf ) F over [0, 1], where F(0) = 0 and F(1) = 1.\nWe assume that F(\u00b7) is strictly increasing and differentiable\nover the interval [0, 1]. Call the probability density function\n(pdf ) f(\u03b8i) = F (\u03b8i), which is the derivative of the cdf.\nEach agent knows its own type \u03b8i, but only the\ndistribution over the possible types of the other agents. A bidding\nstrategy for an agent bi : [0, 1] \u2192 [0, 1] maps its type to its\nbid.3\nLet \u03b8 = (\u03b81, \u00b7 \u00b7 \u00b7 , \u03b8n) be the vector of types for all agents,\nand \u03b8\u2212i = (\u03b81, \u00b7 \u00b7 \u00b7 , \u03b8i\u22121, \u03b8i+1, \u00b7 \u00b7 \u00b7 \u03b8n) be the vector of all\ntypes except for that of agent i. We can then combine the\nvectors so that \u03b8 = (\u03b8i, \u03b8\u2212i). We also define the vector of\nbids as b(\u03b8) = (b1(\u03b81), . . . , bn(\u03b8n)), and this vector without\n2\nWe can restrict the types to the range [0, 1] without loss\nof generality because any distribution over a different range\ncan be normalized to this range.\n3\nWe thus limit agents to deterministic bidding strategies,\nbut, because of our continuity assumption, there always\nexists a pure strategy equilibrium.\nthe bid of agent i as b\u2212i(\u03b8\u2212i). Let b[1](\u03b8) be the value of the\nhighest bid of the vector b(\u03b8), with a corresponding\ndefinition for b[1](\u03b8\u2212i).\nAn agent obviously wins the auction if its bid is greater\nthan all other bids, but ties complicate the formulation.\nFortunately, we can ignore the case of ties in this paper because\nour continuity assumption will make them a zero probability\nevent in equilibrium. We assume that the seller does not set\na reserve price.4\nIf the seller does not cheat, then the winning agent pays\nthe highest bid by another agent. On the other hand, if\nthe seller does cheat, then the winning agent will pay its\nbid, since we assume that a cheating seller would take full\nadvantage of its power. Let the indicator variable \u00b5c\nbe 1\nif the seller cheats, and 0 otherwise. The probability that\nthe seller cheats, Pc\n, is known by all agents.5\nWe can then\nwrite the payment of the winning agent as follows.\npi(b(\u03b8), \u00b5c\n) = \u00b5c\n\u00b7 bi(\u03b8i) \u2212 (1 \u2212 \u00b5c\n) \u00b7 b[1](\u03b8\u2212i) (1)\nLet \u00b5(\u00b7) be an indicator function that takes an inequality\nas an argument and returns is 1 if it holds, and 0 otherwise.\nThe utility for agent i is zero if it does not win the auction,\nand the difference between its valuation and its price if it\ndoes.\nui(b(\u03b8), \u00b5c\n, \u03b8i) = \u00b5 bi(\u03b8i) > b[1](\u03b8\u2212i) \u00b7 \u03b8i \u2212 pi(b(\u03b8), \u00b5c\n)\n(2)\nWe will be concerned with the expected utility of an agent,\nwith the expectation taken over the types of the other agents\nand over whether or not the seller cheats. By pushing the\nexpectation inward so that it is only over the price\n(conditioned on the agent winning the auction), we can write the\nexpected utility as:\nE\u03b8\u2212i,\u00b5c [ui(b(\u03b8), \u00b5c\n, \u03b8i)] = Prob bi(\u03b8i) > b[1](\u03b8\u2212i) \u00b7\n\u03b8i \u2212 E\u03b8\u2212i,\u00b5c pi(b(\u03b8), \u00b5c\n) | bi(\u03b8i) > b[1](\u03b8\u2212i) (3)\nWe assume that all agents are rational, expected utility\nmaximizers. Because of the uncertainty over the types of\nthe other agents, we will be looking for a Bayes-Nash\nequilibrium. A vector of bidding strategies b\u2217\nis a Bayes-Nash\nequilibrium if for each agent i and each possible type \u03b8i,\nagent i cannot increase its expected utility by using an\nalternate bidding strategy bi, holding the bidding strategies\nfor all other agents fixed. Formally, b\u2217\nis a Bayes-Nash\nequilibrium if:\n\u2200i, \u03b8i, bi E\u03b8\u2212i,\u00b5c ui b\u2217\ni (\u03b8i), b\u2217\n\u2212i(\u03b8\u2212i) , \u00b5c\n, \u03b8i \u2265\nE\u03b8\u2212i,\u00b5c ui bi(\u03b8i), b\u2217\n\u2212i(\u03b8\u2212i) , \u00b5c\n, \u03b8i (4)\n2.2 Equilibrium\nWe first present the Bayes-Nash equilibrium for an\narbitrary distribution F(\u00b7).\n4\nThis simplifies the analysis, but all of our results can be\napplied to the case in which the seller announces a reserve\nprice before the auction begins.\n5\nNote that common knowledge is not necessary for the\nexistence of an equilibrium.\n77\nTheorem 1. In a second-price auction in which the seller\ncheats with probability Pc\n, it is a Bayes-Nash equilibrium for\neach agent to bid according to the following strategy:\nbi(\u03b8i) = \u03b8i \u2212\n\u03b8i\n0\nF( N\u22121\nP c )\n(x)dx\nF( N\u22121\nP c )\n(\u03b8i)\n(5)\nIt is useful to consider the extreme points of Pc\n. Setting\nPc\n= 1 yields the correct result for a first-price auction (see,\ne.g., [10]). In the case of Pc\n= 0, this solution is not defined.\nHowever, in the limit, bi(\u03b8i) approaches \u03b8i as Pc\napproaches\n0, which is what we expect as the auction approaches a\nstandard second-price auction.\nThe position of Pc\nis perhaps surprising. For example, the\nlinear combination bi(\u03b8i) = \u03b8i \u2212 Pc\n\u00b7\n\u03b8i\n0 F (N\u22121)\n(x)dx\nF (N\u22121)(\u03b8i)\nof the\nequilibrium bidding strategies of first and second-price\nauctions would have also given us the correct bidding strategies\nfor the cases of Pc\n= 0 and Pc\n= 1.\n2.3 Continuum of Auctions\nAn alternative perspective on the setting is as a\ncontinuum between first and second-price auctions. Consider a\nprobabilistic sealed-bid auction in which the seller is\nhonest, but the price paid by the winning agent is determined\nby a weighted coin flip: with probability Pc\nit is his bid,\nand with probability 1 \u2212 Pc\nit is the second-highest bid.\nBy adjusting Pc\n, we can smoothly move between a first\nand second-price auction. Furthermore, the fact that this\nprobabilistic auction satisfies the properties required for the\nRevenue Equivalence Theorem (see, e.g., [2]) provides a way\nto verify that the bidding strategy in Equation 5 is the\nsymmetric equilibrium of this auction (see the alternative proof\nof Theorem 1 in the appendix).\n2.4 Special Case: Uniform Distribution\nAnother way to try to gain insight into Equation 5 is by\ninstantiating the distribution of types. We now consider the\noften-studied uniform distribution: F(\u03b8i) = \u03b8i.\nCorollary 2. In a second-price auction in which the\nseller cheats with probability Pc\n, and F(\u03b8i) = \u03b8i, it is a\nBayes-Nash equilibrium for each agent to bid according to\nthe following strategy:\nbi(\u03b8i) =\nN \u2212 1\nN \u2212 1 + Pc\n\u03b8i (6)\nThis equilibrium bidding strategy, parameterized by Pc\n,\ncan be viewed as an interpolation between two well-known\nresults. When Pc\n= 0 the bidding strategy is now\nwelldefined (each agent bids its true type), while when Pc\n= 1\nwe get the correct result for a first-price auction: each agent\nbids according to the strategy bi(\u03b8i) = N\u22121\nN\n\u03b8i.\n3. FIRST-PRICE AUCTION,\nCHEATING AGENTS\nWe now consider the case in which the seller is honest,\nbut there is a chance that agents will cheat and examine the\nother bids before submitting their own (or, alternatively,\nthey will revise their bid before the auction clears). Since\nthis type of cheating is pointless in a second-price auction,\nwe only analyze the case of a first-price auction. After\nrevising the formulation from the previous section, we present a\nfixed point equation for the equilibrium strategy for an\narbitrary distribution F(\u00b7). This equation will be useful for the\nanalysis the uniform distribution, in which we show that the\npossibility of cheating agents does not change the\nequilibrium strategy of honest agents. This result has implications\nfor the robustness of the symmetric equilibrium to\noverbidding in a standard first-price auction. Furthermore, we find\nthat for other distributions overbidding actually induces a\ncompeting agent to shave more off of its bid.\n3.1 Formulation\nIt is clear that if a single agent is cheating, he will bid\n(up to his valuation) the minimum amount necessary to win\nthe auction. It is less obvious, though, what will happen if\nmultiple agents cheat. One could imagine a scenario similar\nto an English auction, in which all cheating agents keep\nrevising their bids until all but one cheater wants the good\nat the current winning bid. However, we are only concerned\nwith how an honest agent should bid given that it is aware\nof the possibility of cheating. Thus, it suffices for an honest\nagent to know that it will win the auction if and only if\nits bid exceeds every other honest agent\"s bid and every\ncheating agent\"s type.\nThis intuition can be formalized as the following\ndiscriminatory auction. In the first stage, each agent\"s payment\nrule is determined. With probability Pa\n, the agent will pay\nthe second highest bid if it wins the auction (essentially,\nhe is a cheater), and otherwise it will have to pay its bid.\nThese selections are recorded by a vector of indicator\nvariables \u00b5a\n= (\u00b5a1\n, . . . , \u00b5an\n), where \u00b5ai\n= 1 denotes that agent\ni pays the second highest bid. Each agent knows the\nprobability Pa\n, but does not know the payment rule for all other\nagents. Otherwise, this auction is a standard, sealed-bid\nauction. It is thus a dominant strategy for a cheater to bid\nits true type, making this formulation strategically\nequivalent to the setting outlined in the previous paragraph. The\nexpression for the utility of an honest agent in this\ndiscriminatory auction is as follows.\nui(b(\u03b8), \u00b5a\n, \u03b8i) = \u03b8i \u2212 bi(\u03b8) \u00b7\nj=i\n\u00b5aj\n\u00b7 \u00b5 bi(\u03b8i) > \u03b8j + (1 \u2212 \u00b5aj\n) \u00b7 \u00b5 bi(\u03b8i) > bj(\u03b8j)\n(7)\n3.2 Equilibrium\nOur goal is to find the equilibrium in which all cheating\nagents use their dominant strategy of bidding truthfully and\nhonest agents bid according to a symmetric bidding strategy.\nSince we have left F(\u00b7) unspecified, we cannot present a\nclosed form solution for the honest agent\"s bidding strategy,\nand instead give a fixed point equation for it.\nTheorem 3. In a first-price auction in which each agent\ncheats with probability Pa\n, it is a Bayes-Nash equilibrium\nfor each non-cheating agent i to bid according to the strategy\nthat is a fixed point of the following equation:\nbi(\u03b8i) = \u03b8i \u2212\n\u03b8i\n0 Pa \u00b7 F(bi(x)) + (1 \u2212 Pa) \u00b7 F(x)\n(N\u22121)\ndx\nPa \u00b7 F(bi(\u03b8i)) + (1 \u2212 Pa) \u00b7 F(\u03b8i)\n(N\u22121)\n(8)\n78\n3.3 Special Case: Uniform Distribution\nSince we could not solve Equation 8 in the general case,\nwe can only see how the possibility of cheating affects the\nequilibrium bidding strategy for particular instances of F(\u00b7).\nA natural place to start is uniform distribution: F(\u03b8i) = \u03b8i.\nRecall the logic behind the symmetric equilibrium strategy\nin a first-price auction without cheating: bi(\u03b8i) = N\u22121\nN\n\u03b8i is\nthe optimal tradeoff between increasing the probability of\nwinning and decreasing the price paid upon winning, given\nthat the other agents are bidding according to the same\nstrategy. Since in the current setting the cheating agents\ndo not shave their bid at all and thus decrease an honest\nagent\"s probability of winning (while obviously not affecting\nthe price that an honest agent pays if he wins), it is\nnatural to expect that an honest agent should compensate by\nincreasing his bid. The idea is that sacrificing some\npotential profit in order to regain some of the lost probability of\nwinning would bring the two sides of the tradeoff back into\nbalance. However, it turns out that the equilibrium bidding\nstrategy is unchanged.\nCorollary 4. In a first-price auction in which each agent\ncheats with probability Pa\n, and F(\u03b8i) = \u03b8i, it is a\nBayesNash equilibrium for each non-cheating agent to bid\naccording to the strategy bi(\u03b8i) = N\u22121\nN\n\u03b8i.\nThis result suggests that the equilibrium of a first-price\nauction is particularly robust when types are drawn from the\nuniform distribution, since the best response is unaffected\nby deviations of the other agents to the strategy of always\nbidding their type. In fact, as long as all other agents shave\ntheir bid by a fraction (which can differ across the agents) no\ngreater than 1\nN\n, it is still a best response for the remaining\nagent to bid according to the equilibrium strategy. Note\nthat this result holds even if other agents are shaving their\nbid by a negative fraction, and are thus irrationally bidding\nabove their type.\nTheorem 5. In a first-price auction where F(\u03b8i) = \u03b8i, if\neach agent j = i bids according a strategy bj(\u03b8j) =\nN\u22121+\u03b1j\nN\n\u03b8j,\nwhere \u03b1j \u2265 0, then it is a best response for the remaining\nagent i to bid according to the strategy bi(\u03b8i) = N\u22121\nN\n\u03b8i.\nObviously, these strategy profiles are not equilibria (unless\neach \u03b1j = 0), because each agent j has an incentive to set\n\u03b1j = 0. The point of this theorem is that a wide range of\npossible beliefs that an agent can hold about the strategies\nof the other agents will all lead him to play the equilibrium\nstrategy. This is important because a common (and valid)\ncriticism of equilibrium concepts such as Nash and\nBayesNash is that they are silent on how the agents converge\non a strategy profile from which no one wants to deviate.\nHowever, if the equilibrium strategy is a best response to a\nlarge set of strategy profiles that are out of equilibrium, then\nit seems much more plausible that the agents will indeed\nconverge on this equilibrium.\nIt is important to note, though, that while this equilibrium\nis robust against arbitrary deviations to strategies that shave\nless, it is not robust to even a single agent shaving more off\nof its bid. In fact, if we take any strategy profile consistent\nwith the conditions of Theorem 5 and change a single agent\nj\"s strategy so that its corresponding \u03b1j is negative, then\nagent i\"s best response is to shave more than 1\nN\noff of its\nbid.\n3.4 Effects of Overbidding for\nOther Distributions\nA natural question is whether the best response bidding\nstrategy is similarly robust to overbidding by competing\nagents for other distributions. It turns out that Theorem\n5 holds for all distributions of the form F(\u03b8i) = (\u03b8i)k\n, where\nk is some positive integer. However, taking a simple linear\ncombination of two such distributions to produce F(\u03b8i) =\n\u03b82\ni +\u03b8i\n2\nyields a distribution in which an agent should\nactually shave its bid more when other agents shave their bids\nless. In the example we present for this distribution (with\nthe details in the appendix), there are only two players and\nthe deviation by one agent is to bid his type. However, it\ncan be generalized to a higher number of agents and to other\ndeviations.\nExample 1. In a first-price auction where F(\u03b8i) =\n\u03b82\ni +\u03b8i\n2\nand N = 2, if agent 2 always bids its type (b2(\u03b82) = \u03b82),\nthen, for all \u03b81 > 0, agent 1\"s best response bidding strategy\nis strictly less than the bidding strategy of the symmetric\nequilibrium.\nWe also note that the same result holds for the normalized\nexponential distribution (F(\u03b8i) = e\u03b8i \u22121\ne\u22121\n).\nIt is certainly the case that distributions can be found\nthat support the intuition given above that agents should\nshave their bid less when other agents are doing likewise.\nExamples include F(\u03b8i) = \u22121\n2\n\u03b82\ni + 3\n2\n\u03b8i (the solution to the\nsystem of equations: F (\u03b8i) = \u22121, F(0) = 0, and F(1) = 1),\nand F(\u03b8i) = e\u2212e(1\u2212\u03b8i)\ne\u22121\n.\nIt would be useful to relate the direction of the change\nin the best response bidding strategy to a general\ncondition on F(\u00b7). Unfortunately, we were not able to find such\na condition, in part because the integral in the symmetric\nbidding strategy of a first-price auction cannot be solved\nwithout knowing F(\u00b7) (or at least some restrictions on it).\nWe do note, however, that the sign of the second\nderivative of F(\u03b8i)/f(\u03b8i) is an accurate predictor for all of the\ndistributions that we considered.\n4. REVENUE LOSS FOR AN\nHONEST SELLER\nIn both of the settings we covered, an honest seller suffers\na loss in expected revenue due to the possibility of cheating.\nThe equilibrium bidding strategies that we derived allow us\nto quantify this loss. Although this is as far as we will take\nthe analysis, it could be applied to more general settings,\nin which the seller could, for example, choose the market\nin which he sells his good or pay a trusted third party to\noversee the auction.\nIn a second-price auction in which the seller may cheat, an\nhonest seller suffers due the fact that the agents will shave\ntheir bids. For the case in which agent types are drawn from\nthe uniform distribution, every agent will shave its bid by\nP c\nN\u22121+P c , which is thus also the fraction by which an honest\nseller\"s revenue decreases due to the possibility of cheating.\nAnalysis of the case of a first-price auction in which agents\nmay cheat is not so straightforward. If Pa\n= 1 (each agent\ncheats with certainty), then we simply have a second-price\nauction, and the seller\"s expected revenue will be unchanged.\nAgain considering the uniform distribution for agent types,\nit is not surprising that Pa\n= 1\n2\ncauses the seller to lose\n79\nthe most revenue. However, even in this worst case, the\npercentage of expected revenue lost is significantly less than\nit is for the second-price auction in which Pc\n= 1\n2\n, as shown\nin Table 1.6\nIt turns out that setting Pc\n= 0.2 would make\nthe expected loss of these two settings comparable. While\nthis comparison between the settings is unlikely to be useful\nfor a seller, it is interesting to note that agent suspicions of\npossible cheating by the seller are in some sense worse than\nagents actually cheating themselves.\nPercentage of Revenue lost for an Honest Seller\nAgents Second-Price Auction First-Price Auction\n(Pc\n= 0.5) (Pa\n= 0.5)\n2 33 12\n5 11 4.0\n10 5.3 1.8\n15 4.0 1.5\n25 2.2 0.83\n50 1.1 0.38\n100 0.50 0.17\nTable 1: The percentage of expected revenue lost\nby an honest seller due to the possibility of cheating\nin the two settings considered in this paper. Agent\nvaluations are drawn from the uniform distribution.\n5. RELATED WORK\nExisting work covers another dimension along which we\ncould analyze cheating: altering the perceived value of N.\nIn this paper, we have assumed that N is known by all\nof the bidders. However, in an online setting this\nassumption is rather tenuous. For example, a bidder\"s only source\nof information about N could be a counter that the seller\nplaces on the auction webpage, or a statement by the seller\nabout the number of potential bidders who have indicated\nthat they will participate. In these cases, the seller could\narbitrarily manipulate the perceived N. In a first-price\nauction, the seller obviously has an incentive to increase the\nperceived value of N in order to induce agents to bid closer\nto their true valuation. However, if agents are aware that\nthe seller has this power, then any communication about\nN to the agents is cheap talk, and furthermore is not\ncredible. Thus, in equilibrium the agents would ignore the\ndeclared value of N, and bid according to their own prior\nbeliefs about the number of agents. If we make the natural\nassumption of a common prior, then the setting reduces to\nthe one tackled by [5], which derived the equilibrium\nbidding strategies of a first-price auction when the number of\nbidders is drawn from a known distribution but not revealed\nto any of the bidders. Of course, instead of assuming that\nthe seller can always exploit this power, we could assume\nthat it can only do so with some probability that is known\nby the agents. The analysis would then proceed in a similar\nmanner as that of our cheating seller model.\nThe other interesting case of this form of cheating is by\nbidders in a first-price auction. Bidders would obviously\nwant to decrease the perceived number of agents in order\nto induce their competition to lower their bids. While it is\n6\nNote that we have not considered the costs of the seller.\nThus, the expected loss in profit could be much greater than\nthe numbers that appear here.\nunreasonable for bidders to be able to alter the perceived\nN arbitrarily, collusion provides an opportunity to decrease\nthe perceived N by having only one of a group of colluding\nagents participate in the auction. While the non-colluding\nagents would account for this possibility, as long as they are\nnot certain of the collusion they will still be induced to shave\nmore off of their bids than they would if the collusion did\nnot take place. This issue is tackled in [7].\nOther types of collusion are of course related to the\ngeneral topic of cheating in auctions. Results on collusion in\nfirst and second-price auctions can be found in [8] and [3],\nrespectively.\nThe work most closely related to our first setting is [11],\nwhich also presents a model in which the seller may cheat in\na second-price auction. In their setting, the seller is a\nparticipant in the Bayesian game who decides between running\na first-price auction (where profitable cheating is never\npossible) or second-price auction. The seller makes this choice\nafter observing his type, which is his probability of having\nthe opportunity and willingness to cheat in a second-price\nauction. The bidders, who know the distribution from which\nthe seller\"s type is drawn, then place their bid. It is shown\nthat, in equilibrium, only a seller with the maximum\nprobability of cheating would ever choose to run a second-price\nauction. Our work differs in that we focus on the agents\"\nstrategies in a second-price auction for a given probability\nof cheating by the seller. An explicit derivation of the\nequilibrium strategies then allows us relate first and second-price\nauctions.\nAn area of related work that can be seen as\ncomplementary to ours is that of secure auctions, which takes the point\nof view of an auction designer. The goals often extend\nwell beyond simply preventing cheating, including\nproperties such as anonymity of the bidders and nonrepudiation of\nbids. Cryptographic methods are the standard weapon of\nchoice here (see [1, 4, 9]).\n6. CONCLUSION\nIn this paper we presented the equilibria of sealed-bid\nauctions in which cheating is possible. In addition to providing\nstrategy profiles that are stable against deviations, these\nresults give us with insights into both first and second-price\nauctions. The results for the case of a cheating seller in a\nsecond-price auction allow us to relate the two auctions as\nendpoints along a continuum. The case of agents cheating in\na first-price auction showed the robustness of the first-price\nauction equilibrium when agent types are drawn from the\nuniform distribution. We also explored the effect of\noverbidding on the best response bidding strategy for other\ndistributions, and showed that even for relatively simple\ndistributions it can be positive, negative, or neutral. Finally,\nresults from both of our settings allowed us to quantify the\nexpected loss in revenue for a seller due to the possibility of\ncheating.\n7. REFERENCES\n[1] M. Franklin and M. Reiter. The Design and\nImplementation of a Secure Auction Service. In Proc.\nIEEE Symp. on Security and Privacy, 1995.\n[2] D. Fudenberg and J. Tirole. Game Theory. MIT\nPress, 1991.\n80\n[3] D. Graham and R. Marshall. Collusive bidder behavior\nat single-object second-price and english auctions.\nJournal of Political Economy, 95:579-599, 1987.\n[4] M. Harkavy, J. D. Tygar, and H. Kikuchi. Electronic\nauctions with private bids. In Proceedings of the 3rd\nUSENIX Workshop on Electronic Commerce, 1998.\n[5] R. Harstad, J. Kagel, and D. Levin. Equilibrium bid\nfunctions for auctions with an uncertain number of\nbidders. Economic Letters, 33:35-40, 1990.\n[6] P. Klemperer. Auction theory: A guide to the\nliterature. Journal of Economic Surveys,\n13(3):227-286, 1999.\n[7] K. Leyton-Brown, Y. Shoham, and M. Tennenholtz.\nBidding clubs in first-price auctions. In AAAI-02.\n[8] R. McAfee and J. McMillan. Bidding rings. The\nAmerican Economic Review, 71:579-599, 1992.\n[9] M. Naor, B. Pinkas, and R. Sumner. Privacy\npreserving auctions and mechanism design. In EC-99.\n[10] J. Riley and W. Samuelson. Optimal auctions.\nAmerican Economic Review, 71(3):381-392, 1981.\n[11] M. Rothkopf and R. Harstad. Two models of bid-taker\ncheating in vickrey auctions. The Journal of Business,\n68(2):257-267, 1995.\n[12] W. Vickrey. Counterspeculations, auctions, and\ncompetitive sealed tenders. Journal of Finance,\n16:15-27, 1961.\nAPPENDIX\nTheorem 1. In a second-price auction in which the seller\ncheats with probability Pc\n, it is a Bayes-Nash equilibrium for\neach agent to bid according to the following strategy:\nbi(\u03b8i) = \u03b8i \u2212\n\u03b8i\n0\nF( N\u22121\nP c )\n(x)dx\nF( N\u22121\nP c )\n(\u03b8i)\n(5)\nProof. To find an equilibrium, we start by guessing that\nthere exists an equilibrium in which all agents bid\naccording to the same function bi(\u03b8i), because the game is\nsymmetric. Further, we guess that bi(\u03b8i) is strictly increasing\nand differentiable over the range [0, 1]. We can also assume\nthat bi(0) = 0, because negative bids are not allowed and\na positive bid is not rational when the agent\"s valuation is\n0. Note that these are not assumptions on the setting- they\nare merely limitations that we impose on our search.\nLet \u03a6i : [0, bi(1)] \u2192 [0, 1] be the inverse function of bi(\u03b8i).\nThat is, it takes a bid for agent i as input and returns the\ntype \u03b8i that induced this bid. Recall Equation 3:\nE\u03b8\u2212i,\u00b5c ui(b(\u03b8), \u00b5c\n, \u03b8i) = Prob bi(\u03b8i) > b[1](\u03b8\u2212i) \u00b7\n\u03b8i \u2212 E\u03b8\u2212i,\u00b5c pi(b(\u03b8), \u00b5c\n) | bi(\u03b8i) > b[1](\u03b8\u2212i)\nThe probability that a single other bid is below that of\nagent i is equal to the cdf at the type that would induce\na bid equal to that of agent i, which is formally written as\nF(\u03a6i(bi(\u03b8i))). Since all agents are independent, the\nprobability that all other bids are below agent i\"s is simply this\nterm raised the (N \u2212 1)-th power.\nThus, we can re-write the expected utility as:\nE\u03b8\u2212i,\u00b5c ui(b(\u03b8), \u00b5c\n, \u03b8i) = FN\u22121\n(\u03a6i(bi(\u03b8i)))\u00b7\n\u03b8i \u2212 E\u03b8\u2212i,\u00b5c pi(b(\u03b8), \u00b5c\n) | bi(\u03b8i) > b[1](\u03b8\u2212i) (9)\nWe now solve for the expected payment. Plugging\nEquation 1 (which gives the price for the winning agent) into the\nterm for the expected price in Equation 9, and then\nsimplifying the expectation yields:\nE\u03b8\u2212i,\u00b5c pi(b(\u03b8), \u00b5c\n) | bi(\u03b8i) > b[1](\u03b8\u2212i)\n= E\u03b8\u2212i,\u00b5c \u00b5c\n\u00b7 bi(\u03b8i) + (1 \u2212 \u00b5c\n) \u00b7 b[1](\u03b8\u2212i) |\nbi(\u03b8i) > b[1](\u03b8\u2212i)\n= Pc\n\u00b7 bi(\u03b8i) + (1 \u2212 Pc\n) \u00b7 E\u03b8\u2212i b[1](\u03b8\u2212i) |\nbi(\u03b8i) > b[1](\u03b8\u2212i)\n= Pc\n\u00b7 bi(\u03b8i) + (1 \u2212 Pc\n) \u00b7\nbi(\u03b8i)\n0\nb[1](\u03b8\u2212i)\u00b7\npdf b[1](\u03b8\u2212i) | bi(\u03b8i) > b[1](\u03b8\u2212i) db[1](\u03b8\u2212i) (10)\nNote that the integral on the last line is taken up to\nbi(\u03b8i) because we are conditioning on the fact that bi(\u03b8i) >\nb[1](\u03b8\u2212i). To derive the pdf of b[1](\u03b8\u2212i) given this condition,\nwe start with the cdf. For a given value b[1](\u03b8\u2212i), the\nprobability that any one agent\"s bid is less than this value is equal\nto F(\u03a6i(b[1](\u03b8\u2212i))). We then condition on the agent\"s bid\nbeing below bi(\u03b8i) by dividing by F(\u03a6i(bi(\u03b8i))). The cdf for\nthe N \u2212 1 agents is then this value raised to the (N \u2212 1)-th\npower.\ncdf b[1](\u03b8\u2212i) | bi(\u03b8i) > b[1](\u03b8\u2212i) =\nFN\u22121\n(\u03a6i(b[1](\u03b8\u2212i)))\nFN\u22121(\u03a6i(bi(\u03b8i)))\nThe pdf is then the derivative of the cdf with respect to\nb[1](\u03b8\u2212i):\npdf b[1](\u03b8\u2212i) | bi(\u03b8i) > b[1](\u03b8\u2212i)\n=\nN \u2212 1\nFN\u22121(\u03a6i(bi(\u03b8i)))\n\u00b7 FN\u22122\n(\u03a6i(b[1](\u03b8\u2212i)))\u00b7\nf(\u03a6i(b[1](\u03b8\u2212i))) \u00b7 \u03a6i(b[1](\u03b8\u2212i))\nSubstituting the pdf into Equation 10 and pulling terms\nout of the integral that do not depend on b[1](\u03b8\u2212i) yields:\nE\u03b8\u2212i,\u00b5c pi(b(\u03b8), \u00b5c\n) | bi(\u03b8i) > b[1](\u03b8\u2212i) = Pc\n\u00b7 bi(\u03b8i)+\n(1 \u2212 Pc\n) \u00b7 (N \u2212 1)\nFN\u22121(\u03a6i(bi(\u03b8i)))\n\u00b7\nbi(\u03b8i)\n0\nb[1](\u03b8\u2212i) \u00b7 FN\u22122\n(\u03a6i(b[1](\u03b8\u2212i)))\u00b7\nf(\u03a6i(b[1](\u03b8\u2212i))) \u00b7 \u03a6i(b[1](\u03b8\u2212i)) db[1](\u03b8\u2212i)\n81\nPlugging the expected price back into the expected utility\nequation (9), and distributing FN\u22121\n(\u03a6i(bi(\u03b8i))), yields:\nE\u03b8\u2212i,\u00b5c ui(b(\u03b8), \u00b5c\n, \u03b8i) = FN\u22121\n(\u03a6i(bi(\u03b8i))) \u00b7 \u03b8i\u2212\nFN\u22121\n(\u03a6i(bi(\u03b8i))) \u00b7 Pc\n\u00b7 bi(\u03b8i)\u2212\n(1 \u2212 Pc\n) \u00b7 (N \u2212 1) \u00b7\nbi(\u03b8i)\n0\nb[1](\u03b8\u2212i) \u00b7 FN\u22122\n(\u03a6i(b[1](\u03b8\u2212i)))\u00b7\nf(\u03a6i(b[1](\u03b8\u2212i))) \u00b7 \u03a6i(b[1](\u03b8\u2212i)) db[1](\u03b8\u2212i)\nWe are now ready to optimize the expected utility by\ntaking the derivative with respect to bi(\u03b8i) and setting it to 0.\nNote that we do not need to solve the integral, because it\nwill disappear when the derivative is taken (by application\nof the Fundamental Theorem of Calculus).\n0 = (N\u22121)\u00b7FN\u22122\n(\u03a6i(bi(\u03b8i)))\u00b7f(\u03a6i(bi(\u03b8i)))\u00b7\u03a6i(bi(\u03b8i))\u00b7\u03b8i\u2212\nFN\u22121\n(\u03a6i(bi(\u03b8i))) \u00b7 Pc\n\u2212\nPc\n\u00b7(N\u22121)\u00b7FN\u22122\n(\u03a6i(bi(\u03b8i)))\u00b7f(\u03a6i(bi(\u03b8i)))\u00b7\u03a6i(bi(\u03b8i))\u00b7bi(\u03b8i)\u2212\n(1\u2212Pc\n)\u00b7(N\u22121)\u00b7 bi(\u03b8i)\u00b7FN\u22122\n(\u03a6i(bi(\u03b8i)))\u00b7f(\u03a6i(bi(\u03b8i)))\u00b7\u03a6i(bi(\u03b8i))\nDividing through by FN\u22122\n(\u03a6i(bi(\u03b8i))) and combining like\nterms yields:\n0 = \u03b8i \u2212 Pc\n\u00b7 bi(\u03b8i) \u2212 (1 \u2212 Pc\n) \u00b7 bi(\u03b8i) \u00b7 (N \u2212 1)\n\u00b7 f(\u03a6i(bi(\u03b8i))) \u00b7 \u03a6i(bi(\u03b8i)) \u2212 Pc\n\u00b7 F(\u03a6i(bi(\u03b8i)))\nSimplifying the expression and rearranging terms produces:\nbi(\u03b8i) = \u03b8i \u2212\nPc\n\u00b7 F(\u03a6i(bi(\u03b8i)))\n(N \u2212 1) \u00b7 f(\u03a6i(bi(\u03b8i))) \u00b7 \u03a6i(bi(\u03b8i))\nTo further simplify, we use the formula f (x) = 1\ng (f(x))\n,\nwhere g(x) is the inverse function of f(x). Plugging in\nfunction from our setting gives us: \u03a6i(bi(\u03b8i)) = 1\nbi(\u03b8i)\n. Applying\nboth this equation and \u03a6i(bi(\u03b8i)) = \u03b8i yields:\nbi(\u03b8i) = \u03b8i \u2212\nPc\n\u00b7 F(\u03b8i) \u00b7 bi(\u03b8i)\n(N \u2212 1) \u00b7 f(\u03b8i)\n(11)\nAttempts at a derivation of the solution from this point\nproved fruitless, but we are at a point now where a guessed\nsolution can be quickly verified. We used the solution for\nthe first-price auction (see, e.g., [10]) as our starting point\nto find the answer:\nbi(\u03b8i) = \u03b8i \u2212\n\u03b8i\n0\nF( N\u22121\nP c )\n(x)dx\nF( N\u22121\nP c )\n(\u03b8i)\n(12)\nTo verify the solution, we first take its derivative:\nbi(\u03b8i) = 1\u2212\nF(2\u00b7 N\u22121\nP c )\n(\u03b8i) \u2212 N\u22121\nP c \u00b7 F( N\u22121\nP c \u22121)\n(\u03b8i) \u00b7 f(\u03b8i) \u00b7\n\u03b8i\n0\nF( N\u22121\nP c )\n(x)dx\nF(2\u00b7 N\u22121\nP c )\n(\u03b8i)\nThis simplifies to:\nbi(\u03b8i) =\nN\u22121\nP c \u00b7 f(\u03b8i) \u00b7\n\u03b8i\n0\nF( N\u22121\nP c )\n(x)dx\nF( N\u22121\nP c +1)\n(\u03b8i)\nWe then plug this derivative into the equation we derived\n(11):\nbi(\u03b8i) = \u03b8i \u2212\nPc\n\u00b7 F(\u03b8i) \u00b7 N\u22121\nP c \u00b7 f(\u03b8i) \u00b7\n\u03b8i\n0\nF( N\u22121\nP c )\n(x)dx\n(N \u2212 1) \u00b7 f(\u03b8i) \u00b7 F( N\u22121\nP c +1)\n(\u03b8i)\nCancelling terms yields Equation 12, verifying that our\nguessed solution is correct.\nAlternative Proof of Theorem 1:\nThe following proof uses the Revenue Equivalence\nTheorem (RET) and the probabilistic auction given as an\ninterpretation of our cheating seller setting.\nIn a first-price auction without the possibility of cheating,\nthe expected payment for an agent with type \u03b8i is simply\nthe product of its bid and the probability that this bid is\nthe highest. For the symmetric equilibrium, this is equal to:\nF(N\u22121)\n(\u03b8i) \u00b7 \u03b8i \u2212\n\u03b8i\n0\nF(N\u22121)\n(x)dx\nF(N\u22121)(\u03b8i)\nFor our probabilistic auction, the expected payment of\nthe winning agent is a weighted average of its bid and the\nsecond highest bid. For the bi(\u00b7) we found in the original\ninterpretation of the setting, it can be written as follows.\nF(N\u22121)\n(\u03b8i) \u00b7 Pc\n\u03b8i \u2212\n\u03b8i\n0\nF( N\u22121\nP c )\n(x)dx\nF( N\u22121\nP c )\n(\u03b8i)\n+\n(1 \u2212 Pc\n)\n1\nF(N\u22121)(\u03b8i)\n\u00b7\n\u03b8i\n0\nx\u2212\nx\n0\nF( N\u22121\nP c )\n(y)dy\nF( N\u22121\nP c )\n(x)\n\u00b7(N \u22121)\u00b7F(N\u22122)\n(x)\u00b7f(x)dx\nBy the RET, the expected payments will be the same\nin the two auctions. Thus, we can verify our equilibrium\nbidding strategy by showing that the expected payment in\nthe two auctions is equal. Since the expected payment is\nzero at \u03b8i = 0 for both functions, it suffices to verify that the\nderivatives of the expected payment functions with respect\nto \u03b8i are equal, for an arbitrary value \u03b8i. Thus, we need to\nverify the following equation:\nF(N\u22121)\n(\u03b8i) + (N \u2212 1) \u00b7 F(N\u22122)\n(\u03b8i) \u00b7 f(\u03b8i) \u00b7 \u03b8i \u2212 F(N\u22121)\n(\u03b8i)\n=\nPc\n\u00b7 F(N\u22121)\n(\u03b8i) \u00b7 1 \u2212 1\u2212\n(N\u22121\nP c ) \u00b7 F( N\u22121\nP c \u22121)\n(\u03b8i) \u00b7 f(\u03b8i) \u00b7\n\u03b8i\n0\nF( N\u22121\nP c )\n(x)dx\nF2( N\u22121\nP c )\n(\u03b8i)\n+\n(N \u2212 1) \u00b7 F(N\u22122)\n(\u03b8i) \u00b7 f(\u03b8i) \u00b7 \u03b8i \u2212\n\u03b8i\n0\nF( N\u22121\nP c )\n(x)dx\nF( N\u22121\nP c )\n(\u03b8i)\n+\n(1\u2212Pc\n) \u03b8i\u2212\n\u03b8i\n0\nF( N\u22121\nP c )\n(y)dy\nF( N\u22121\nP c )\n(\u03b8i)\n\u00b7(N\u22121)\u00b7F(N\u22122)\n(\u03b8i)\u00b7f(\u03b8i)\n82\nThis simplifies to:\n0 = Pc\n\u00b7\n(N\u22121\nP c ) \u00b7 F(N\u22122)\n(\u03b8i) \u00b7 f(\u03b8i) \u00b7\n\u03b8i\n0\nF( N\u22121\nP c )\n(x)dx\nF( N\u22121\nP c )\n(\u03b8i)\n+\n(N \u2212 1) \u00b7 F(N\u22122)\n(\u03b8i) \u00b7 f(\u03b8i) \u00b7 \u2212\n\u03b8i\n0\nF( N\u22121\nP c )\n(x)dx\nF( N\u22121\nP c )\n(\u03b8i)\n+\n(1\u2212Pc\n) \u2212\n\u03b8i\n0\nF( N\u22121\nP c )\n(y)dy\nF( N\u22121\nP c )\n(\u03b8i)\n\u00b7(N\u22121)\u00b7F(N\u22122)\n(\u03b8i)\u00b7f(\u03b8i)\nAfter distributing Pc\n, the right-hand side of this equation\ncancels out, and we have verified our equilibrium bidding\nstrategy.\nCorollary 2. In a second-price auction in which the\nseller cheats with probability Pc\n, and F(\u03b8i) = \u03b8i, it is a\nBayes-Nash equilibrium for each agent to bid according to\nthe following strategy:\nbi(\u03b8i) =\nN \u2212 1\nN \u2212 1 + Pc\n\u03b8i (6)\nProof. Plugging F(\u03b8i) = \u03b8i into Equation 5 (repeated\nas 12), we get:\nbi(\u03b8i) = \u03b8i \u2212\n\u03b8i\n0\nx( N\u22121\nP c )\ndx\n\u03b8i\n( N\u22121\nP c )\n= \u03b8i \u2212\nP c\nN\u22121+P c \u03b8i\n( N\u22121+P c\nP c )\n\u03b8i\n( N\u22121\nP c )\n= \u03b8i \u2212\nPc\nN \u2212 1 + Pc\n\u00b7 \u03b8i =\nN \u2212 1\nN \u2212 1 + Pc\n\u00b7 \u03b8i\nTheorem 3. In a first-price auction in which each agent\ncheats with probability Pa\n, it is a Bayes-Nash equilibrium\nfor each non-cheating agent i to bid according to the strategy\nthat is a fixed point of the following equation:\nbi(\u03b8i) = \u03b8i \u2212\n\u03b8i\n0 Pa \u00b7 F(bi(x)) + (1 \u2212 Pa) \u00b7 F(x)\n(N\u22121)\ndx\nPa \u00b7 F(bi(\u03b8i)) + (1 \u2212 Pa) \u00b7 F(\u03b8i)\n(N\u22121)\n(8)\nProof. We make the same guesses about the equilibrium\nstrategy to aid our search as we did in the proof of Theorem\n1. When simplifying the expectation of this setting\"s\nutility equation (7), we use the fact that the probability that\nagent i will have a higher bid than another honest agent is\nstill F(\u03a6i(bi(\u03b8i))), while the probability is F(bi(\u03b8i)) if the\nother agent cheats. The probability that agent i beats a\nsingle other agent is then a weighted average of these two\nprobabilities. Thus, we can write agent i\"s expected utility\nas:\nE\u03b8\u2212i,\u00b5a ui(b(\u03b8), \u00b5a\n, \u03b8i) = \u03b8i \u2212 bi(\u03b8i) \u00b7\nPa\n\u00b7 F(bi(\u03b8i)) + (1 \u2212 Pa\n) \u00b7 F(\u03a6i(bi(\u03b8i)))\nN\u22121\nAs before, to find the equilibrium bi(\u03b8i), we take the\nderivative and set it to zero:\n0 = \u03b8i \u2212 bi(\u03b8i) \u00b7 (N \u2212 1)\u00b7\nPa\n\u00b7 F(bi(\u03b8i)) + (1 \u2212 Pa\n) \u00b7 F(\u03a6i(bi(\u03b8i)))\nN\u22122\n\u00b7\nPa\n\u00b7 f(bi(\u03b8i)) + (1 \u2212 Pa\n) \u00b7 f(\u03a6i(bi(\u03b8i))) \u00b7 \u03a6i(bi(\u03b8i)) \u2212\nPa\n\u00b7 F(bi(\u03b8i)) + (1 \u2212 Pa\n) \u00b7 F(\u03a6i(bi(\u03b8i)))\nN\u22121\nApplying the equations \u03a6i(bi(\u03b8i)) = 1\nbi(\u03b8i)\nand \u03a6i(bi(\u03b8i)) =\n\u03b8i, and dividing through, produces:\n0 = \u03b8i \u2212 bi(\u03b8i) \u00b7 (N \u2212 1)\u00b7\nPa\n\u00b7 f(bi(\u03b8i)) + (1 \u2212 Pa\n) \u00b7 f(\u03b8i) \u00b7\n1\nbi(\u03b8i)\n\u2212\nPa\n\u00b7 F(bi(\u03b8i)) + (1 \u2212 Pa\n) \u00b7 F(\u03b8i)\nRearranging terms yields:\nbi(\u03b8i) = \u03b8i \u2212\nPa \u00b7 F(bi(\u03b8i)) + (1 \u2212 Pa) \u00b7 F(\u03b8i) \u00b7 bi(\u03b8i)\n(N \u2212 1) \u00b7 Pa \u00b7 f(bi(\u03b8i)) \u00b7 bi(\u03b8i) + (1 \u2212 Pa) \u00b7 f(\u03b8i)\n(13)\nIn this setting, because we leave F(\u00b7) unspecified, we\ncannot present a closed form solution. However, we can simplify\nthe expression by removing its dependence on bi(\u03b8i).\nbi(\u03b8i) = \u03b8i \u2212\n\u03b8i\n0 Pa \u00b7 F(bi(x)) + (1 \u2212 Pa) \u00b7 F(x)\n(N\u22121)\ndx\nPa \u00b7 F(bi(\u03b8i)) + (1 \u2212 Pa) \u00b7 F(\u03b8i)\n(N\u22121)\n(14)\nTo verify Equation 14, first take its derivative:\nbi(\u03b8i) = 1 \u2212 1\u2212\n(N \u2212 1) \u00b7 Pa\n\u00b7 F(bi(\u03b8i)) + (1 \u2212 Pa\n) \u00b7 F(\u03b8i)\n(N\u22122)\n\u00b7\nPa\n\u00b7 f(bi(\u03b8i)) \u00b7 bi(\u03b8i)) + (1 \u2212 Pa\n) \u00b7 f(\u03b8i) \u00b7\n\u03b8i\n0\nPa\n\u00b7 F(bi(x)) + (1 \u2212 Pa\n) \u00b7 F(x)\n(N\u22121)\ndx\nPa \u00b7 F(bi(\u03b8i)) + (1 \u2212 Pa) \u00b7 F(\u03b8i)\n2(N\u22121)\nThis equation simplifies to:\nbi(\u03b8i) = (N \u22121)\u00b7 Pa\n\u00b7f(bi(\u03b8i))\u00b7bi(\u03b8i))+(1\u2212Pa\n)\u00b7f(\u03b8i) \u00b7\n\u03b8i\n0\nPa\n\u00b7 F(bi(x)) + (1 \u2212 Pa\n) \u00b7 F(x)\n(N\u22121)\ndx\nPa \u00b7 F(bi(\u03b8i)) + (1 \u2212 Pa) \u00b7 F(\u03b8i)\nN\nPlugging this equation into the bi(\u03b8i) in the numerator of\nEquation 13 yields Equation 14, verifying the solution.\n83\nCorollary 4. In a first-price auction in which each agent\ncheats with probability Pa\n, and F(\u03b8i) = \u03b8i, it is a\nBayesNash equilibrium for each non-cheating agent to bid\naccording to the strategy bi(\u03b8i) = N\u22121\nN\n\u03b8i.\nProof. Instantiating the fixed point equation (8, and\nrepeated as 14) with F(\u03b8i) = \u03b8i yields:\nbi(\u03b8i) = \u03b8i \u2212\n\u03b8i\n0\nPa\n\u00b7 bi(x) + (1 \u2212 Pa\n) \u00b7 x\n(N\u22121)\ndx\nPa \u00b7 bi(\u03b8i) + (1 \u2212 Pa) \u00b7 \u03b8i\n(N\u22121)\nWe can plug the strategy bi(\u03b8i) = N\u22121\nN\n\u03b8i into this\nequation in order to verify that it is a fixed point.\nbi(\u03b8i) = \u03b8i \u2212\n\u03b8i\n0\nPa\n\u00b7 N\u22121\nN\nx + (1 \u2212 Pa\n) \u00b7 x\n(N\u22121)\ndx\nPa \u00b7 N\u22121\nN\n\u03b8i + (1 \u2212 Pa) \u00b7 \u03b8i\n(N\u22121)\n= \u03b8i \u2212\n\u03b8i\n0\nx(N\u22121)\ndx\n\u03b8\n(N\u22121)\ni\n= \u03b8i \u2212\n1\nN\n\u03b8N\ni\n\u03b8\n(N\u22121)\ni\n=\nN \u2212 1\nN\n\u03b8i\nTheorem 5. In a first-price auction where F(\u03b8i) = \u03b8i, if\neach agent j = i bids according a strategy bj(\u03b8j) =\nN\u22121+\u03b1j\nN\n\u03b8j,\nwhere \u03b1j \u2265 0, then it is a best response for the remaining\nagent i to bid according to the strategy bi(\u03b8i) = N\u22121\nN\n\u03b8i.\nProof. We again use \u03a6j : [0, bj(1)] \u2192 [0, 1] as the inverse\nof bj(\u03b8j). For all j = i in this setting, \u03a6j(x) = N\nN\u22121+\u03b1j\nx.\nThe probability that agent i has a higher bid than a single\nagent j is F(\u03a6j(bi(\u03b8i))) = N\nN\u22121+\u03b1j\nbi(\u03b8i). Note, however,\nthat since \u03a6j(\u00b7) is only defined over the range [0, bj(1)], it\nmust be the case that bi(1) \u2264 bj(1), which is why \u03b1j \u2265\n0 is necessary, in addition to being sufficient. Assuming\nthat bi(\u03b8i) = N\u22121\nN\n\u03b8i, then indeed \u03a6j(bi(\u03b8i)) is always\nwelldefined. We will now show that this assumption is correct.\nThe expected utility for agent i can then be written as:\nE\u03b8\u2212i ui(b(\u03b8), \u03b8i) = \u03a0j=i\nN\nN \u2212 1 + \u03b1j\nbi(\u03b8i) \u00b7 \u03b8i \u2212bi(\u03b8)\n= \u03a0j=i\nN\nN \u2212 1 + \u03b1j\n\u00b7 \u03b8i\u00b7 bi(\u03b8i)\n(N\u22121)\n\u2212 bi(\u03b8i)\nN\nTaking the derivative with respect to bi(\u03b8i), setting it to\nzero, and dividing out \u03a0j=i\nN\nN\u22121+\u03b1j\nyields:\n0 = \u03b8i \u00b7 (N \u2212 1) \u00b7 bi(\u03b8i)\n(N\u22122)\n\u2212 N \u00b7 bi(\u03b8i)\n(N\u22121)\nThis simplifies to the solution: bi(\u03b8i) = N\u22121\nN\n\u03b8i.\nFull Version of Example 1:\nIn a first-price auction where F(\u03b8i) =\n\u03b82\ni +\u03b8i\n2\nand N = 2,\nif agent 2 always bids its type (b2(\u03b82) = \u03b82), then, for all\n\u03b81 > 0, agent 1\"s best response bidding strategy is strictly\nless than the bidding strategy of the symmetric equilibrium.\nAfter calculating the symmetric equilibrium in which both\nagents shave their bid by the same amount, we find the best\nresponse to an agent who instead does not shave its bid.\nWe then show that this best response is strictly less than\nthe equilibrium strategy. To find the symmetric equilibrium\nbidding strategy, we instantiate N = 2 in the general\nformula the equation found in [10], plug in F(\u03b8i) =\n\u03b82\ni +\u03b8i\n2\n, and\nsimplify:\nbi(\u03b8i) = \u03b8i \u2212\n\u03b8i\n0\nF(x)dx\nF(\u03b8i)\n= \u03b8i\u2212\n1\n2\n\u00b7\n\u03b8i\n0\n(x2\n+ x)dx\n1\n2\n\u00b7 (\u03b82\ni + \u03b8i)\n= \u03b8i\u2212\n1\n3\n\u03b83\ni + 1\n2\n\u03b82\ni\n\u03b82\ni + \u03b8i\n=\n2\n3\n\u03b82\ni + 1\n2\n\u03b8i\n\u03b8i + 1\nWe now derive the best response for agent 1 to the\nstrategy b2(\u03b82) = \u03b82, denoting the best response strategy b\u2217\n1(\u03b81)\nto distinguish it from the symmetric case. The\nprobability of agent 1 winning is F(b\u2217\n1(\u03b81)), which is the probability\nthat agent 2\"s type is less than agent 1\"s bid. Thus, agent\n1\"s expected utility is:\nE\u03b82 ui((b\u2217\n1(\u03b81), b2(\u03b82)), \u03b81) = F(b\u2217\n1(\u03b81)) \u00b7 \u03b81 \u2212 b\u2217\n1(\u03b81)\n=\n(b\u2217\n1(\u03b81))2\n+ b\u2217\n1(\u03b81)\n2\n\u00b7 \u03b81 \u2212 b\u2217\n1(\u03b81)\nTaking the derivative with respect to b\u2217\n1(\u03b81), setting it to\nzero, and then rearranging terms gives us:\n0 =\n1\n2\n\u00b7 2 \u00b7 b\u2217\n1(\u03b81) \u00b7 \u03b81 \u2212 3 \u00b7 (b\u2217\n1(\u03b81))2\n+ \u03b81 \u2212 2 \u00b7 b\u2217\n1(\u03b81)\n0 = 3 \u00b7 (b\u2217\n1(\u03b81))2\n+ (2 \u2212 2 \u00b7 \u03b81) \u00b7 b\u2217\n1(\u03b81) \u2212 \u03b81\nOf the two solutions of this equation, one always produces\na negative bid. The other is:\nb\u2217\n1(\u03b81) =\n\u03b81 \u2212 1 + \u03b82\n1 + \u03b81 + 1\n3\nWe now need to show that b1(\u03b81) > b\u2217\n1(\u03b81) holds for all\n\u03b8i > 0. Substituting in for both terms, and then simplifying\nthe inequality gives us:\n2\n3\n\u03b82\n1 + 1\n2\n\u03b81\n\u03b81 + 1\n>\n\u03b81 \u2212 1 + \u03b82\n1 + \u03b81 + 1\n3\n\u03b82\n1 +\n3\n2\n\u03b81 + 1 > (\u03b81 + 1) \u03b82\n1 + \u03b81 + 1\nSince \u03b81 \u2265 0, we can square both sides of the inequality,\nwhich then allows us to verify the inequality for all \u03b81 > 0.\n\u03b84\n1 + 3\u03b83\n1 +\n17\n4\n\u03b82\n1 + 3\u03b81 + 1 > \u03b84\n1 + 3\u03b83\n1 + 4\u03b82\n1 + 3\u03b81 + 1\n1\n4\n\u03b82\n1 > 0\n84", "keywords": "sealed-bid auction;game theory;seller;cheating;first-price auction;sealed-bid;auction;agent;cheat;payment;case;bidsecond-price auction;possibility"}