On Concurrent Detection of Errors in Polynomial Basis Multiplication Abstract-The detection of errors in arithmetic operations is an important issue. This paper discusses the detection of multiple-bit errors due to faults in bit-serial and bit-parallel polynomial basis (PB) multipliers over binary extension fields. Our approach is based on multiple parity bits. Experimental results presented here show that due to an increase in the number of parity bits, the area overhead tends to increase linearly, but the probability of error detection approaches unity fairly quickly, e.g., for eight parity bits. In bit-serial implementation of a (2 163 ) PB multiplier using eight parity bits, the area overhead and the probability of error detection are 10.29% and 0.996, respectively. This is achieved without any increase in the computation time of the (2 163 )Index Terms-Concurrent error detection (CED), finite fields, polynomial basis (PB) multiplication. In this paper, a multiple parity error detection scheme is presented for concurrent detection of errors in polynomial basis multipliers. In this scheme, the probability of error detection for random errors is more than 75% and it quickly approaches unity for approximately eight parity bits. The overhead of our implementation tends to increase linearly as the number of parity bits increases. Results show that the area overhead cost of the bit-serial implementation is lower than that for the bit-parallel one. Both implementations have lower area overheads than the traditional dual modular redundant scheme for a sufficient number of parity bits. Additionally, the average time overhead due to the use of the scheme in bit-parallel implementations is around 25%, while for bit-serial implementations time overheads have been observed to be small to negligible. It is hoped that using the results presented in this paper, one will be able to choose an appropriate number of parity bits for specific applications. Important performance measures for an error detection scheme include error detection capability, area, and time overheads. In this section, the results of our studies on these measures are presented. The results can guide the choice of a proper number of parity bits for design requirements.

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On an implicit assessment of fuzzy volatility in the Black and Scholes environment In this work we suggest a methodology to obtain the membership of a non observable parameter through implicit information. To this aim we profit from the interpretation of membership functions as coherent conditional probabilities. We develop full details for the well known Black and Scholes pricing model where the membership of the volatility parameter is obtained from a sample of either asset prices or market prices for options written on that asset.

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Fundamental methodological issues of syntactic pattern recognition Abstract Fundamental open problems, which are frontiers of syntactic pattern recognition are discussed in the paper. Methodological considerations on crucial issues in areas of string and graph grammar-based syntactic methods are made. As a result, recommendations concerning an enhancement of context-free grammars as well as constructing parsable and inducible classes of graph grammars are formulated. Representing a pattern as a structure of the form of string, tree or graph and a set of structures as a formal language is the main idea of syntactic pattern recognition [6, 24, 27, 42, 55] , which is one of the main approaches in the area of machine recognition. A generation of such a language is made with a formal grammar. An analysis and a recognition of an unknown structure is performed with a formal automaton. If patterns are complex, they are defined in a hierarchical way. Thus, at the bottom of the hierarchy we use elementary patterns in order to build simple substructures (These elementary patterns are called primitives and they are represented with symbols of a language alphabet.). Then, using such simple substructures we construct more complex substructures and so on. Syntactic pattern recognition prevails over ''standard'' pattern recognition approaches (probabilistic, discriminant function-based, NN, etc.) when patterns considered can be characterized better with structural features than vectors of features. What is more, using this approach not only can we make a classification (in a sense of ascribing a pattern to a pre-defined category), but also a (structural) interpretation of an unknown pattern. Therefore, for structurally-oriented recognition problems such as: character recognition, speech recognition, scene analysis, chemical and biological structures analysis, texture analysis, fingerprint recognition, geophysics, a syntactic approach has been applied successfully since its beginning in the early 1960s for the next two decades. A rapid development of syntactic methods has slowed down since 1990s and the experts in this area (see e.g. [26] ) have found this approach stagnating.. Methodological considerations on the issues which have an impact on further development of syntactic methods are made in the paper. Firstly, however, key open problems constituting the frontiers of this research area should be identified. It can be easily noticed in the literature concerning syntactic pattern recognition [6, 24, 27, 42, 55] that in the field of string-based models a lot of efficient methods have been developed for structural patterns that can be generated with regular or context-free grammars. On the other hand, if a set of patterns cannot be represented with context-free languages, i.e. it is of a context-sensitive nature, then defining an efficient recognition method is difficult. It results from a nonpolynomial time complexity of automata analyzing contextsensitive languages. Therefore, defining string grammars generating languages with a polynomial membership problem that are stronger than context-free grammars seems to be still the key open problem in this area.. If a pattern is structurally complex, a linear-like string description is very often too weak for its representation. Then, a graph representation is usually used. It means that one should use a graph grammar for a generation of a set of patterns and a graph automaton (parser) for its analysis. Unfortunately, a problem of parsing of non-trivial graph languages is PSPACE-complete or NP-complete [4, 51, 56] . Therefore, defining graph grammars generating languages with a polynomial membership problem is the second crucial open problem in syntactic pattern recognition.. Before we consider two open key problems identified above in Sects. 3 and 4, respectively, we try to formulate in Sect. 2 some general methodological recommendations concerning a research in syntactic pattern recognition. Our considerations are based on the 20 years research experience in both string-based and graph-based syntactic pattern recognition [12-22, 33, 35] . Hopefully, our recommendations concerning methodological aspects of a research in syntactic pattern recognition launch a discussion on prospects and limitations of a future development of this field. The theory of formal languages (mathematical linguistics) constitutes a formal basis for various research areas in computer science. A specificity of an area determines methodological principles that should be followed during a research. In other words, for various areas various principles are valid. The general principles concerning an application of mathematical linguistics formalisms in a syntactic pattern recognition area have been formulated in the paper.. These principles can be summarized as follows. A syntactic pattern recognition model should include not only an efficient syntax analyzer, but also a grammatical inference algorithm of a polynomial complexity. If the model is to be used for a recognition of real-world objects or phenomena, then it should be enhanced with such techniques as: error-correcting parsing, attributed grammars or stochastic grammars. In order to ensure a computational efficiency of the model, a type of a grammar should be of the smallest generative power yet sufficient to generate all the possible patterns. For context-free grammars enhanced with the help of additional syntactic operators, a construction of a grammatical inference algorithm is easier than for grammars with a control mechanism ''hidden'' in productions. A polynomial complexity of a membership problem is a key issue for a graph grammar-based pattern recognition. In order to define algorithms of: syntax analysis and grammatical inference for graph grammar-based methods one should look for analogical algorithms for string grammars.. Let us remember that they are not necessarily valid in other research areas that make use of formalisms of mathematical linguistics such, as e.g. Natural Language Processing, compiler design.. A syntactic pattern recognition paradigm is primarily an approach in a machine recognition area. However, it relates also strongly to other fields of computer science, like: Artificial Intelligence (a problem of pattern understanding, see e.g. [54] ), a construction of secret sharing techniques (see e.g. [39] ), etc. Therefore, a set of methodological principles presented in the paper will be extended in the future with new ones connected with the AI paradigms.. Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

O O O O B I I O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Security and privacy considerations in digital death Death is an uncomfortable subject for many people, and digital systems are rarely designed to deal with this event. In particular, the wide array of existing digital authentication infrastructure rarely deals with gracefully retiring credentials in a uniform fashion.This research paper highlights an emerging paradigm: gracefully dealing with expired digital identities in a secure, privacypreserving fashion. It examines the confluence of modern browser technology, cloud services, and human factors involved in managing a person's digital footprint while they live and retiring it when they die.We contemplate a potential approach to dealing with credentials after death by using cloud computing. We consider the reasons that such an approach may actually provide an opportunity for enhancing authentication security by frustrating identity stealing attacks.We note that this paper is not aimed at trivializing the real grief and loss that people feel, but rather an attempt to understand how security and privacy concerns are shaped by the end of life, with the ultimate goal of easing this transition for friends and family. This paper considers the security and privacy issues involved in the management of digital identities during and at the end of life, and whether a technological solution exists that can ease management and increase assurance against digital identity theft.. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. NSPW '11, September 12-15, 2011 , Marin County, CA, USA. Copyright 2011 ACM 978-1-4503-1078-9/11/09 ...$10.00.. The focus of this paper is on identifying what kind of changes in authentication technology might more easily support security and privacy goals in passing on control of critical online identity aspects. In short, how do we apply thanatosensitive design (see Section 6) to information security? Many information security paradigms seem to ignore the human element in security problems and scenarios. Even disciplines that take human interaction into account (e.g., HCISec or usable security) seldom examine long-term phenomena.. A good expression of this paradigm is in the eventual shift of large parts of our society and economy into the online realm (e.g., banks that are completely online): it is likely that we will have to deal with organizations electronically.. The accrual of a heterogeneous, distributed digital identity footprint presents unique and interesting authentication, authorization, and privacy issues -particularly related to how such an identity collection should be retired after a person dies. One of the best ways to avoid information disclosure is not to store data in the first place, but such restraint is not common, and proactive deletion of information carries a real cost (time and energy spent to trace information and securely erase it). Traditional authentication technologies present roadblocks to coherently and cleanly retiring a digital footprint in a single fell swoop. How can we better manage authentication credentials from the point of view of preparing for the event of death?. We wish to facilitate discussion at the workshop on the following questions:. 1. Is it possible to design even a single authentication mechanism that gracefully handles the event of death? Setting aside the question of how to federate or manage multiple identities, can a single authentication mechanism gracefully expire credentials or automatically delegate them based on "real world" measurements like the existence of a death certificate? Are "heartbeat" services like deathswitch.com really the best solution?. 2. Do the dead have a right to privacy? It does not appear to be the case, but they may still have property rights; the CNET article "Taking Passwords to the Grave" [17] quotes Marc Rotenberg, executive director of the Electronic Privacy Information Center: "The so-called 'Tort of Privacy' expires upon death, but property interests don't," he said. "Private e-mails are a new category. It's not immediately clear how to treat them, but it's a form of digital property.". 3. Given that the most likely legal framework to apply is that of property rights, How does digital identity information compare with other physical "material" property belonging to the departed?. 4. How large are current digital identity footprints? A welldone user study exploring this data might shed light on the complexity of managing multiple identities.. 5. Do the dead have the right to specify the enforcement of compartmentalization of their digital footprint? It seems clear that users engaging in any form of estate planning should have firm footing to specify how to dispose of their digital identity.. 6. Who "owns" a set of digital credentials: the user or the service they are meant to authenticate to? If a third party generated them (e.g., a browser plugin on behalf of a company or developer), does the third party have any rights? We may be wading into legal murkey waters here (we just don't have the background to know) -but it seems like any comprehensive definition of "identity" (like the one we gave in Section 1.3) would likely include elements that service providers would think of as their property, setting up a conflict over control of these assets. A significant amount of work exists on the topic of authorization and authentication; this subfield is a staple of the information security discipline. This paper deals with the usability of authentication schemes (more precisely, digital identity management schemes). Recently, the topic of usable security -particularly usable authentication schemes -has received a great deal of attention. Graphical password schemes were suggested as an easier-to-remember alternative to traditional weak passwords, but even these schemes have weaknesses suggest Biddle et al. [1] . The PassThoughts [22] paper from NSPW 2005 explored the feasibility of a mentallydriven approach to authentication.

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Approximating Maximum Weight K-Colorable Subgraphs in Chordal Graphs We present a 2-approximation algorithm for the problem of finding the maximum weight K-colorable subgraph in a given chordal graph with node weights. The running time of the algorithm is O(K(n+m)), where n and m are the number of vertices and edges in the given graph. The maximum K-colorable subgraph problem is as follows: the input is a graph G = (V, E) and an integer K ≥ 1 and the goal is to find a maximum cardinality subset V ⊆ V such that the subgraph induced by V is K-colorable. In other words, we wish to color a maximum number of nodes such that no two adjacent vertices receive the same color. When K = 1, this is the same as the maximum independent set problem, which cannot be approximated in polynomial time within a factor of n 1− , for any fixed > 0, unless NP=P [13] . Clearly, the hardness result holds for our problem. The problem has been studied by restricting to special graph classes. For the case of interval graphs, Yannakakis and Gavril [12] showed that the problem can be solved in linear time. They also presented a polynomial time algorithm for the weighted version of the problem (see also [4] ).. We study the problem restricted to chordal graphs. A graph is chordal, if every cycle of length at least four has a chord, that is, an edge which is not part of the cycle but connects two vertices in the cycle. Chordal graphs are an important subclass of perfect graphs and generalize interval graphs [7] . The problem finds applications in register allocation [9] (see also [8, 3] ). We consider the node-weighted version of the problem, wherein each node is associated with a positive real weight and the goal is to maximize the total weight of the chosen subset V . Frank [6] designed a linear time algorithm for the case of K = 1 (i.e., the maximum weight independent set problem). Yannakakis and Gavril [12] showed that the unweighted problem can be solved in polynomial time for any fixed K; however, they showed that the problem is NP-hard for arbitrary K.. To the best of our knowledge, approximation algorithms have not been considered even for the unweighted version of the above problem, when K is arbitrary. We present an algorithm for the weighted version of problem with an approximation ratio of 2. The running time of the algorithm is O(K(n + m)), where n and m are the number of vertices and edges in the graph.. Our algorithm and analysis are inspired from two prior results. First, Farber [5] gave an alternative linear time algorithm for finding a maximum weight independent set in chordal graphs based on the primal-dual approach; this problem is equivalent to the case of K = 1 in our problem. Our algorithm can be seen as extension of his algorithm to the case of arbitrary K. Secondly, we observe that the maximum K-colorable subgraph problem (for arbitrary graphs) reduces to the following problem: the input is a graph G = (V, E) and a partition of V into disjoint sets V 1 , V 2 , . . . , V and the goal is to choose a maximum cardinality set V ⊆ V such that V is an independent set in G and additionally, V includes at most one vertex from each set V j . The reduction is as follows. Let the input to the maximum K-colorable subgraph problem be G = (V, E) on n vertices, given by v 1 , v 2 , . . . , v n . Construct a new graph G = (V , E ) on N = Kn vertices. The vertex set V is given by V = {(v, c) : v ∈ V and 1 ≤ c ≤ K}. Two vertices (v, c) and (v , c ) are adjacent in G , if c = c and (v, v ) ∈ E. The set V is partitioned into = n many disjoint sets corresponding to the vertices of G so that. It is clear that solutions of the maximum K-colorable instance corresponds to solutions of the new problem instance, and vice versa. In the weighted version of the new problem, each vertex is associated with a positive real weight and the aim is to maximize the total weight of the chosen set V . Notice that when each V i contains exactly one vertex, the problem is the same as the maximum weight independent set problem. Motivated by certain scheduling issues, Berman and DasGupta [2] studied the above problem restricted to interval graphs (under the name job interval selection problem-JISP) and presented a 2-approximation algorithm for the weighted version (see also [1] ). We extend the analysis of Berman and DasGupta to the more general case of chordal graphs and obtain an approximation algorithm with the same ratio of 2. By combining the above reduction and the extended algorithm, we get the claimed 2-approximation algorithm for the maximum K-colorable subgraph problem on chordal graphs. In the paper, we present the combined algorithm and analysis. While our algorithm can also be analyzed using a primal-dual argument similar to Farber's, we present a more direct analysis of the algorithm. In this section, we analyze the algorithm presented in the previous section. It is easy to see that the algorithm outputs a proper K-coloring of the vertices in U , namely no two adjacent vertices in U are assigned the same color and a vertex is assigned at most one color. We next discuss the approximation ratio achieved by the algorithm and then consider its time complexity.. Our goal is to show that the algorithm has an approximation ratio of 2. Let X any subset of V such that the subgraph induced by X is K-colorable. We shall prove two claims regarding the given solution X and the solution U computed by the algorithm: (i) 2 × VAL ≥ w(X); (ii) w(U ) ≥ VAL. It follows that 2w(U ) ≥ w(X). Since X was an arbitrary feasible solution, we have that U is a 2-approximate solution. We now describe the claimed 2-approximation algorithm. Let G = (V, E) be the input chordal graph on n vertices and let K be the number of allowed colors. For each v ∈ V , let w(v) denote. For all i ≤ n and j ≤ K, set Marked(i, j) = f alse.

O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Empirical evaluation of hash functions for multipoint measurements A broad spectrum of network measurement applications demand passive multipoint measurements in which data from multiple observation points has to be correlated. Examples are the passive measurement of one-way delay or the observation of the path that a packet takes through a network. Nevertheless, due to high data rates and the need for fine granular measurements, the resource consumption for passive measurements can be immense. Furthermore, the resource consumption depends on the traffic in the network, which usually is highly dynamic. Packet and flow-selection methods provide a solution to reduce and control the resource consumption for passive measurements. In order to apply such techniques to multipoint measurements the selection processes need to be synchronized. Hash-based selection is a deterministic packet selection based on a hash function computed on selected parts of the packet content. This selection decision is consistent throughout the network and enables packet tracing and the measurement of delay between network nodes. Because the selection is based on deterministic function it can introduce bias which leads to wrong estimation of traffic characteristics. In this paper we define a set of quality criteria and select methods to investigate which hash function is most suitable for hash-based packet selection. We analyze 23 non-cryptographic and 2 cryptographic hash functions. Experiments are performed with real traffic traces from different networks. Based on the results we recommend 2 fast hash functions which show low bias and sample a representative subset of the population. Network measurements play a vital role in operating and developing today's Internet. Beyond measuring of bandwidth utilization and packet count at a single measurement point there exists a variety of applications that require multipoint measurements ( [20] , [34] , [22] , [5] ). Service Providers need to validate their delay guarantees from Service Level Agreements. Network research has incentives to track where packets are changed, reordered, lost, or delayed, for instance, in error-prone environments like mobile adhoc networks. Hash-based selection is a passive measurement technique that enables multipoint measurements and packet tracing ( [8] , [29] ). In contrast to active one-way delay measurements ( [23] , [25] , [16] ) no additional traffic needs to be introduced into the measured network and quality statements can be made directly about the customer traffic. Hash-based selection reduces the calculation effort because in contrast to other passive multipoint measurements it does not correlate all packets from the measurement points. Instead, with hash-based selection only a subset of packets at every measurement point is selected and the real traffic characteristics can be estimated. Hash-based selection is realized by the following technique. Parts of the packet content (header and payload) that are invariant between measurement nodes are extracted and used as the hash input for a hash function. The hash function with a digest length of N bits maps the hash input to a value in the hash range R = [0..2 N − 1]. The packet itself is selected if the hash value falls into a predefined selection range S ⊂ R. In order to obtain a certain sample size one can adjust the selection range. The advantage of this technique is that the selection decision for each packet along its path is the same, provided that the selected packet content (hash input), hash function and selection range are the same at the different measurement points. Because of this quality, packets are consistently sampled along their path and can be correlated for delay and loss measurements at a common collector. We analyzed a collection of 25 hash functions on their suitability for hash-based selection. The hash functions were evaluated on 4 criteria: performance, non-linearity, unbiasedness and representativeness. The evaluation of unbiasedness and representativeness were based on real traffic traces. Categorial Results are shown in Tab. 6. Hash funcions on the left are most suitable for hash-based packet selection because they satisfy the quality criteria best.. Cryptographic Hash Function Both cryptographic hash functions SHA and MD5 show perfect avalanche. The MD5 hash function has no rejected independence test whereas SHA shows dependency between sampling decision and the byte value because of one rejected individual test. This may be caused by the trimming to 32bit output values. As shown in the performance evaluation both cryptographic hash functions imply heavy processing time compared to their noncryptographic counterparts. For the short 8 byte hash input configuration SHA is 35 and MD5 20 times slower than BOB or OAAT. Especially for low-resource measurement nodes, MD5 and SHA cannot be recommended because the hash needs to be calculated over each hash packet. It has to be evaluated if hardware based approaches may narrow the performance differences to the non-cryptographic hash functions. Nevertheless it has to be clearly stated, that in an adversarial setting only a cryptographic hash function can be applied to ensure proper sampling.. Emulation of Random Selection Two properties of random selection are important for accurate measurements: unbiasedness and representativeness. We have shown that the tests for biasedness of the selection decision and the representativeness of the selected subset is causal related and can be analyzed with the chi-square independence test. We have shown that BOB, MD5, OAAT, RS and TWMX hash function are able to select an unbiased and representative sample based on our recommended 8 byte configuration. Nevertheless hash-based selection is not a random selection, because it is deterministically based on the packet content. Hence results are trace dependent and we have to be aware that the selection decision of identical packets will be cause bias. In order to validate the results it is necessary to use more traces. Especially IPv6 traces are interesting in order to verify the selection decision quality based on the hash input of IPv6 traces. Unfortunately it is difficult to obtain IPv6 traces with more packet information than the IP header. In our paper we evaluated mostly non-cryptographic hash functions. It has to be assessed if there are cryptographic hash functions. A thorough analysis of which characteristics of cryptographic hash functions are required for hash-based packet selection can lead to cryptographic hash functions that are faster than MD5 and SHA but still provide efficient security. Packet ID generation is an adjacent field to hash-based selection in multipoint measurements. Each packet traversing a measurement point will be assigned a packet ID and timestamp which are exported to a multipoint collector. According to this packet ID the packets observations can be correlated for packet tracing and delay measurements. This packet ID is assigned to each packet after the selection process (e.g. after hash-based selection). In [8] [17] [20] it is proposed to use different hash functions (or a different key respectively initial value) for packet ID generation and hashbased selection. A hash function for packet ID generation requires different qualities than the one used for hash-based selection, essentially only hash functions with a low collision probability are useful. Packet ID collisions are critical, because the trajectories of duplicate packet IDs can be misinterpreted as a trace from single packets which leads to wrong delay measurement results. In future we will analyze our hash function collection on their suitability for packet ID generation in terms of collision probability. Further we will evaluate under which circumstances the hash-based selection hash value can be used as packet ID.

O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O B I O O O O O O O O O O O O B I O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Discovering multirelational structure in social media streams In this article, we present a novel algorithm to discover multirelational structures from social media streams. A media item such as a photograph exists as part of a meaningful interrelationship among several attributes, including time, visual content, users, and actions. Discovery of such relational structures enables us to understand the semantics of human activity and has applications in content organization, recommendation algorithms, and exploratory social network analysis.We are proposing a novel nonnegative matrix factorization framework to characterize relational structures of group photo streams. The factorization incorporates image content features and contextual information. The idea is to consider a cluster as having similar relational patterns; each cluster consists of photos relating to similar content or context. Relations represent different aspects of the photo stream data, including visual content, associated tags, photo owners, and post times. The extracted structures minimize the mutual information of the predicted joint distribution. We also introduce a relational modularity function to determine the structure cost penalty, and hence determine the number of clusters. Extensive experiments on a large Flickr dataset suggest that our approach is able to extract meaningful relational patterns from group photo streams. We evaluate the utility of the discovered structures through a tag prediction task and through a user study. Our results show that our method based on relational structures, outperforms baseline methods, including feature and tag frequency based techniques, by 35%-420%. We have conducted a qualitative user study to evaluate the benefits of our framework in exploring group photo streams. The study indicates that users found the extracted clustering results clearly represent major themes in a group; the clustering results not only reflect how users describe the group data but often lead the users to discover the evolution of the group activity. In this article, we present a novel algorithm to discover multirelational structures from social media streams. In particular, we discover latent structures in the popular online social media site, Flickr. The structure encodes relational semantics pertaining to human activity within such social networks. This latent structure has the potential to enhance content organization, improve recommendation algorithms, and support exploratory social network analysis.. The semantics of human activity on social media sites (including Flickr and YouTube) needs to be understood as a relationship between people, actions, artifacts, and supportive contextual metadata. Today, social media sites have made it easy to upload, share, and interact with content as well as to communicate with other users on the site. Each site provides a diverse range of functionalities, including tagging and commenting on media, as well as direct communication with other users. A shared media item is associated with a variety of information, including the identity of the person who uploaded it, associated tags, identities of people who commented on the item, and the number of times viewed or marked as a "favorite." These user actions (including "upload," "tag," "comment") are additionally associated with a timestamp. A media item such as a photograph on Flickr therefore exists as part of a meaningful interrelationship among several attributes including time, visual content, users, and actions. An example is given in Figure 1 . 1 Relational semantics derived from human activity are distinctly different from media semantics (e.g., "what is the meaning of this photo?"). For example, a Flickr group on "Arizona Travel" may have a lot of posts on Sedona, a popular destination, in July from people who live in Phoenix who travel there to escape the heat. There are fewer posts in December, when it is cold in Sedona. Now, the meaning of the relationship between location (Sedona), time (summer), specific users, and photo colors is not explicit in the data. This relationship may exist because the active members of the group are friends who live in Phoenix, and plan an annual summer retreat together in Sedona. In this case, the relational semantics, while not explicit, are known only to the group members. These relational semantics cannot be easily discovered by accessing the photo stream via a single object or attribute (e.g., photo tags), or through a simple aggregation of attributes. Interestingly, the discovery of relational structure in such social media sites can point to emergent cultural behaviors, which may not even be explicitly identifiable by members of the network. We presented a method for extracting multirelational structure in social media streams. Structure discovery is a fundamental problem with applications in content organization, recommendation systems and exploratory social network analysis. We used a nonnegative joint matrix factorization approach to find a set of soft clusters that reflect various relations in a group photo stream. By leveraging various relations, our method dealt with visual and contextual information, including visual content features, photo tags, owners and post times, in a unified manner. We provided an efficient algorithm to solve the clustering problem that scales linearly with the data size. The discovered structured are interpretable in terms of minimizing the mutual information of the joint distribution. A relational modularity function was proposed to determine model penalty and estimate the optimal number of clusters. Extensive experiments on a Flickr dataset and user study show that (a) our analysis can capture the dynamics of group patterns, and give meaningful summary of group photo streams; (b) compared with baseline methods, our joint analysis performs the highest quality tag prediction. These results indicate the utility of our relational clustering method.. As part of our future work, we plan to extend the current framework to (a) consider different forms of the structures (b) and extend the current matrix factorization framework to tensor based analysis. In this section, we first briefly discuss applications based on structure mining in different domains, and then situate our work within the context of online social media analysis. We further discuss related techniques for analyzing multimodality or multirelational data. Structure mining. Mining structures from data arise naturally in many applications. Xie et al. [2002] propose a hidden Markov models (HMMs) based approach for mining temporal structures in video streams. The structures of interest are repetitive segments that often relate to recurrent events, for instance, plays and breaks in a soccer video. McCowan et al. [2005] propose a framework for extracting the structure of group meeting actions such as monologue, discussion, note-taking, etc. from audiovisual streams. "Topic models" [Blei et al. 2003 ] discover patterns in text corpus by representing the underlying topics with word distributions and the topics are combined to form documents. In addition, dynamic topic models [Blei and Lafferty 2006; Wang and McCallum 2006] are developed to capture the evolution of topics in a sequentially organized corpus of documents. In social network analysis, the structures of interest do not necessarily correspond to explicit semantics and must be interpreted according to the time and context of the observation (e.g., U.S. Supreme Court rulings [Doreian and Fujimoto 2001] ). Such analysis has provided important insights for social functions and processes. In this paper, we are interested in relational structures that deviate from the structure mining within multimedia, moving more towards the goals of structure mining within social networks, which may have emergent or context-bounded semantics. Our idea can be stated in a way analogous to the topic modeling methods; we consider the relational structures as coherent distributions of different types of social media features (e.g., users, tags, visual features) which combine to form the social media streams.. Social media analysis. The popularity of social applications and environments has attracted considerable research interests. In particular, our work relates to two primary directions; namely, studying people's social networking behavior, and improving the search and recommendation of media by exploiting contextual as well as social knowledge. The first direction is often studied based on the statistical properties of online social networks. Backstrom et al. [2006] study how the structural features correlate with changes of social group members. Kumar et al. [2006] study the evolution of the blogosphere in terms of the change of graph characteristics and the community burstiness, where a temporal burst is defined based on hyperlinking occurrences. Palla et al. [2007] extract groups per time slice and then quantifies their evolution based on membership differences. The structure of social interactions among people have also been studied through a unipartite or bipartite graph, in which the community structure can be characterized by clustering methods [Lin et al. 2008; Sun et al. 2007] .. The second direction considers utilizing the media metadata associated with media objects to improve media content retrieval. Existing research on tagging services includes improving tag recommendation [Garg and Weber 2008; Sigurbjörnsson and Van Zwol 2008] , and analyzing usage patterns of tagging systems [Negoescu and Gatica-Perez 2008] . Chen et al. [2008] propose a group and tag recommendation system by using concept detectors trained based on visual features and tags. Negoescu and Gatica-Perez [2008] present a large scale analysis of Flickr groups and propose a topic modeling approach for representing a group based on the cooccurrence of groups and tags. Zunjarward et al. [2007] propose a framework for annotating events in images by exploiting the social networks of annotators. Kennedy et al. [2007] propose a framework for generating knowledge (representative tags) for a location, and for extracting place and event semantics for a tag. Their work suggests that communitygenerated media and tags can improve access to multimedia resources. Similarly, Ahern et al. [2007] propose a system to analyze the tags associated with the geo-referenced images to generate knowledge about a given location in the form of representative tags. These tags can be further utilized to help expose the photo content. Shamma et al. [2007] design and prototype tools for capturing the context in which the media is used, and investigate methods for using the information to organize and index media.. Multirelational learning. As discussed in Li and Anand [2007] , classical propositional clustering methods are limited in dealing with data having various types of entities and different semantic relationships among them. The first-order extensions of classical methods (e.g., RDBC [Kirsten and Wrobel 1998 ]) may not be feasible for large relational data due to the quadratic computational complexity. Recently, relational clustering techniques have been proposed to learn the interrelated structures among various entities and multiple relationships [Banerjee et al. 2007; Bekkerman et al. 2005; Long et al. 2006; Tang et al. 2008; . However, the implementations of these techniques can only handle small-scale datasets and do not take advantage of the sparseness in social network data. In addition, most of the relational clustering techniques consider hard clustering assignment (i.e. each entity can belong to only one cluster), which limits its direct usage in applications such as context-sensitive recommendation in social media.. In multimedia, techniques for combining multimodality in media content analysis have been developed to overcome the semantic gap problem since visual features are unable to represent the image content at the semantic level. Cai et al. [2004] use visual, text, and link information of images to construct a relationship graph of Web images. Tong et al. [2005] propose a graph-based learning approach (both semi-supervised and unsupervised), where different modalities are represented independently as a multiple graphs. Rege et al. [2008] propose a graph theoretical framework for simultaneously integrating visual and textual features for co-clustering a tripartite (feature-image-word) graph. Multigraph mining has also been studied in other contexts. In text mining, Zhu et al. [2007] propose a matrix factorization algorithm combining both the linkage and the document-term matrices to improve the hypertext classification.. This article extends our prior work [Lin et al. 2009a] ; we include formal discussion of the problem, extended solutions, detailed algorithms, proof, and new experiment results. Another related work is [Lin et al. 2009b ], which proposes a framework called JAM for constructing a user-centric summary of their online social activities. Instead of a fixed syntactical structure for representing user activities, that is, correlating users and concepts through different actions, this work considers a generalized relational data model to represent data in social media streams. In addition, the JAM framework extracts one dominate theme at each time, while in this work, multiple relational clusters can co-exist, which allows users to compare or contrast multiple themes.. Our unique contribution. Mining time-evolving relational patterns in social media streams deals with the interrelatedness of media content features as well as contextual and temporal information associated with the media. Our analysis aims to generate an interpretable structural representation of the social media stream and allow the flexible incorporating of various media relations (visual, temporal, etc.) . The structural representation with probabilistic interpretation can be used directly to retrieve different types of representative entities and to summarize different aspects of a social media stream. Our method also takes advantage of the sparseness in social network data, which is able to handle large scale data in social media streams. We provide a solution to the objective defined in Equation (6). Since Equation (6) is not convex in all variables, it is difficult to guarantee a global minima solution. By employing the concavity of the log function given in the KL-divergence, we derive a local minima solution to Equation (6) Algorithm: Relational Soft Clustering Input: data matrices {W (r) } for r ∈ {F, U, Q, T } Output: P, and {Z (r) } Method:. Initialize P, , {Z (r) } Repeat until convergence For each r, update Z (r) by Equation (7) update P and by Equation (7) Z. then normalize such that. where μ. The proof of Theorem 1 is provided in the appendix. This iterative update algorithm is a multimatrices factorization that generalizes the algorithm proposed by Lee and Seung [2001] for solving a single nonnegative matrix factorization problem. Table I summarizes the process for solving P, and {Z (r) }. Interpretation. We determine the relational clusters based on the solution matrices P, and {Z (r) }. Specifically, the soft membership (ref. Section 4.1) of each photo i in community k is determined by the conditional probability P(k|i) = P(i, k)/P(i), where P(i,k) is given by (P ) ik , and the marginal probability P(i) is given by k (P ) ik . The soft membership of a user or a tag can be computed in the same way with corresponding normalized coefficient matrices. Such soft membership not only provides information about the relationship between an object and a cluster; it can also be used to infer the relationship between two entities or two clusters in the relational structure. For example, the joint probability between a photo i and a tag j is computed by P(i, j) = k k P ik Z kj (Q) . The joint probability of two clusters k and l can be determined by the marginal probability P(k, l) = i P(k|i)P(l|i)P(i), where i is the entity index within a particular facet such as photo or tag facet. In some application, for instance, visualization, where hard membership (disjoint clusters) may be used, we can convert soft membership to hard membership by choosing the maximum P(k|i) over k.. Computational complexity. We now investigate the time complexity for each iteration of the updates in Equation (7). The most time-consuming part is to compute (P Z (r) ) ij ∀i, j, r. However, most data matrices W (·) are sparse, i.e. they have few nonzero entries. Hence we only need to compute the corresponding (P Z (r) ) ij for each nonzero entry (i, j) in W (r) , which takes O(K) time with K being the number of clusters. Let n denote the largest number of nonzero entries of all data matrices, the total time complexity is O(nK). If we consider K is bounded by some constants, the time complexity per iteration is linear in O(n), the number of non-zero entries in data matrices. Note that the sparse property might not hold for the photo-feature matrix W (F) ; however, W (F) is typically constructed based on fixed length feature vectors. The number of nonzero entries in W (F) only depends on the number of photos and hence it can be considered to have the same degree of sparseness as other data matrices. This section reports our experimental studies on a Flickr group dataset. We first describe the dataset used in our experiments (Section 6.1), and present case studies on the relational clusters extracted from the data (Section 6.2). Finally we quantitatively evaluate and discuss the quality of the clustering structure through a prediction task (Section 6.3). In the appendix, we evaluate the effectiveness of relational modularity by using synthetic datasets, and we present a qualitative user study to evaluate the benefits of our framework in exploring group photo streams. Figure 4 presents a case study for which clustering results are recognized by the participants in our user study.

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O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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Strong Mediated Equilibrium Providing agents with strategies that will be robust against deviations by coalitions is central to the design of multi-agent agents. However, such strategies, captured by the notion of strong equilibrium, rarely exist. This paper suggests the use of mediators in order to enrich the set of situations where we can obtain stability against deviations by coalitions. A mediator is a reliable entity, which can ask the agents for the right to play on their behalf, and is guaranteed to behave in a prespecified way based on messages received from the agents. However, a mediator can not enforce behavior; that is, agents can play in the game directly without the mediator's help. We prove some general results about mediators, and concentrate on the notion of strong mediated equilibrium; we show that desired behaviors, which are stable against deviations by coalitions, can be obtained using mediators in a rich class of settings. In the recent years there has been much interest in work bridging AI and game theory. This interest is a result of the need to consider agents' incentives in multi-agent systems. Indeed, when considering a prescribed multi-agent behavior, it makes little sense to assume that an agent will stick to its part of that behavior, if deviating from it can increase its payoff. This leads to much interest in the study of equilibrium in games; a Nash equilibrium is a strategy profile for the agents, such that deviation by each single agent is not beneficial for it. The good news is that when agents are allowed to use mixed strategies then a Nash equilibrium always exists; the bad news however is that this concept does not take into account deviations by non-singleton sets of agents. While stability against deviations by subsets of the agents is a most natural requirement, it is well known that obtaining such stability is possible only in extremely rare situations.. In order to tackle this issue we consider in this paper the use of mediators. A mediator is a reliable entity that can interact with the players and perform on their behalf actions in a given game. However, a mediator can not enforce behavior. Indeed, an agent is free to participate in the game without the help of the mediator. This notion is highly natural; in many systems there is some form of reliable party or administrator that can be used as a mediator. Notice that we assume that the multi-agent interaction (formalized as a game) is given, and all the mediator can do is to communicate with the agents and perform actions on behalf of the agents that allow it to do so. The mediator's behavior is pre-specified and depends on the messages received from all agents. This natural setting is different from the one discussed in the theory of mechanism design (see Jackson (2001) for an introduction) where a designer designs a new game from scratch in order to yield some desired behavior. The simplest form of mediator discussed in the game theory literature is captured by the notion of correlated equilibrium (Aumann (1974) ). This notion was generalized to communication equilibrium by Forges (1986) ; Myerson (1986) . Another, more powerful type of mediators is discussed in Monderer & Tennenholtz (2004) . However, in all these settings the mediator can not perform actions on behalf of the agents that allow it to do so.. We find the notion of a mediator as central to the theory of multi-agent systems. As a result, in this paper we develop a rigorous concept of a mediator, and prove its generality. We concentrate on the notion of strong mediated equilibrium, a multi-agent behavior which is robust against deviations by coalitions in a mediated game.. In order to illustrate the power of a reliable mediator as discussed in this paper, consider the famous prisoners dilemma game: In this classical example we get that in the only equilibrium both agents will defect, yielding both of them a payoff of 1. However, this equilibrium, which is also a dominant strategy equilibrium, is inefficient; indeed, if both agents deviate from defection to cooperation then both of them will improve their payoffs. Formally, mutual defection is not a strong equilibrium; it is not stable against deviations by coalitions. Indeed, there is no strong equilibrium in the prisoners dilemma game.. Consider now a reliable mediator who offers the agents the following protocol: if both agents agree to use the mediator services then he will perform cooperate on behalf of both agents. However, if only one agent agrees to use his services then he will perform defect on behalf of that agent. Notice that when accepting the mediator's offer the agent is committed to actual behavior as determined by the above protocol. However, there is no way to enforce the agents to accept the suggested protocol, and each agent is free to cooperate or defect without using the mediator's services. Hence, the mediator's protocol generates a new game, which we call mediated game: The mediated game has a most desirable property: in this game there is a strong equilibrium; that is, equilibrium which is stable against deviations by coalitions. In this equilibrium both agents will use the mediator services, which will lead them to a payoff of 4 each! We call a strong equilibrium in a mediated game: a strong mediated equilibrium. Hence, we get cooperation in the prisoners dilemma game as an outcome of a strong mediated equilibrium. We put the concept of a mediator in the perspective of work in game theory. In particular, the concept of cacceptable strategies introduced in Aumann (1959) is an abstract notion that captures the "reasonable outcomes" obtained when subsets of the set of agents can correlate their activities. Our work introduces an explicit model of the mediation activity. We show that the introduction of an explicit mediator makes a difference; the outcomes that can be obtained using strong mediated equilibria are different from the ones that can be obtained using c-acceptable strategies.. Given the general concept of a mediator, we prove that mediators can indeed significantly increase the set of desired outcomes that can be obtained by multi-agent behaviors which are robust against deviations by coalitions. Namely, we show that any symmetric game possesses a strong mediated equilibrium, which also leads to optimal surplus, iff 1 Bernheim, Peleg, & Whinston (1987) defined and analyzed coalition-proof equilibrium, which is a generalization of strong equilibrium for games in strategic form. This type of equilibrium has been further analyzed in e.g., Einy & Peleg (1995) ; Moreno & Wooders (1996) . This enables one to naturally define "coalitionproof mediated equilibrium". We do not analyze this interesting topic in this paper.. its standard TU core is non-empty. This class includes many natural sub-classes of games. We also show another positive result with regard to deviations of coalitions of size at most k. We show that in any symmetric game with n agents, if k! divides n then there exists a k-strong mediated equilibrium, leading to optimal surplus. However, if k! does not divide n, then one can find a symmetric game (with n agents) where the above property does not hold.. In the last section we discuss the connection between mediators and the notion of program equilibrium (Tennenholtz (2004) ). Most proofs are omitted from this paper due to lack of space.

O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O B O O O O O O B I O O O O O O O O O O O O O B O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O B I O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O B I O O O O O O B I O O O O O O O O O O O O O O O B I O O O O O O B O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Two approaches to the problems of self-attacking arguments and general odd-length cycles of attack The problems that arise from the presence of self-attacking arguments and odd-length cycles of attack within argumentation frameworks are widely recognized in the literature on defeasible argumentation. This paper introduces two simple semantics to capture different intuitions about what kinds of arguments should become justified in such scenarios. These semantics are modeled upon two extensions of argumentation frameworks, which we call sustainable and tolerant. Each one is constructed on the common ground of the powerful concept of admissibility introduced by Dung in [10] . The novelty of this approach consists in viewing the admissibility of a subset of arguments as relative to potentially challenging subsets of arguments. Both sustainable and tolerant semantics are more credulous than preferred semantics (i.e. they justify at least the same arguments, and possibly more). Given certain sufficient conditions they coincide among them as well as with other semantics introduced by Dung. Argument systems are aimed to capture the intuition that actual reasoning proceeds by means of the construction and confrontation of defeasible arguments. A tentative conclusion may be revised if its supporting arguments are attacked by others, leading to new tentative conclusions, and so on. Several formalisms have been proposed to model this idea, each focusing on different details, spanning from the internal structure of arguments to the characterization of the warranted or justified arguments.. Despite their differences, the development of argument systems has led to some common paradoxes or, at least, problematic issues. Some of them where inherited from early approaches to nonmonotonic reasoning, such as the well-known Nixon's Diamond where two arguments attack each other. To solve this problem two intuitions have been invoked, one that postulates that none of the conflicting arguments should be warranted -the "skeptical" view-while the other states that it is right to grant equal warrant to both of them, so that the user of the system can freely select either one -the "credulous" view.. Another kind of problems arose from the process of argumentation itself, namely the occurrence of odd-length cycles of attack. In the most simple case, one argument attacks itself. Pollock ( [16] ) studied a particular instance derived from the lottery paradox, introduced by Kyburg ([12] ) as a problem for reasoning with probabilities. Imagine a fair lottery with 1,000,000 tickets, so that each ticket has one in a million chances of winning. Given a particular ticket, we can tentatively conclude that it will not win, since its probability is very low. But the same can be concluded about every ticket, hence we can conclude that none of them will win. But given that the lottery is fair, one ticket must win. Upon this contradiction Pollock claimed that a further contradiction can be drawn, namely that since none of the tickets will win, the lottery cannot be fair. That is, the argument of the lottery paradox, based upon the premise that the lottery is fair attacks itself, since one of its consequences contradicts its premise. This is what Pollock called the 'lottery paradox paradox' (see fig. 1 ).. Self-attacking arguments are cycles of attack of length one. For odd-length cycles, Dung ([10] ) indicates that arguments in such cycles should be deemed controversial since they both attack and defend, directly or indirectly, some arguments (in particular, themselves). Assume that A attacks B, B attacks C and C attacks A. Since A attacks C's attacker, A defends (i.e. attacks the attacker of) C. Hence, A defends its own attacker, so A indirectly attacks itself. The same happens in any cycle of odd length. This analysis led Dung (and most of the researchers in the field) to try to prevent the occurrence of such arguments within any extension, i.e. set of warranted arguments.. In this paper we propose two semantics for dealing with the problem of self-attacking arguments. We define them upon the methodological artifact of seeing an argumentation process as a strategic interaction between two agents. We do not attach ontological weight to this assumption, since the agents may be the two sides that a single reasoner may take while pondering which arguments should be warranted.. Our first semantics takes up from a wide consensus among researchers in the argument systems' community, who seek to solve the problem of self-attacking arguments by rejecting any justification for arguments in any odd-length cycles of attack. We define a new kind of extension called "sustainable", capturing this lead. The second semantics solves as well the problem of self-attacking arguments, but allows the justification of arguments belonging to longer odd-length cycles of attack. Although this runs against the consensus, some authors are also beginning to pursue similar aims ( [3] , [4] ). The rationality of this semantics, captured by extensions called "tolerant", becomes clear when the attack relation among arguments is seen as embodying a transitive preference relation. Then, as we will show, tolerant semantics exhibit the intended behavior of preferred semantics.. The platform on which our semantics are developed is the argumentation frameworks model of Dung. The main idea introduced there is the admissibility of sets of arguments. This notion defines the way a set of arguments can be defended from external attacks. We build upon this idea, stating that the defense of a set of arguments should not be defined in absolute terms but relative to other possible challenging sets of arguments. In this way we obtain a notion of cogency on which we base both sustainable and tolerant semantics.. The intuition behind is that an acceptable set of arguments is not necessarily one that can be defended against uncoordinated attacks, but one that can be defended against arguments that are firmly supported. Philosophers of science will recognize the similarity of this condition with the one stating that the withdrawal of scientific theories is not due to some contrary evidence, but to the appearance of a better theory that supports that evidence. In this vein, this paper also proposes a game-theoretic counterpart of sustainable and tolerant semantics showing a strategical rationale for adopting them. A strategic argumentation game will be defined as a two-agent game in which each agent has to choose a set of arguments to confront with and defend against the possible choices of the other agent.. The paper is organized as follows. The main features of Dung's system are presented in section 2. In section 3 we introduce the two semantics. In section 4 we show that in well-founded argumentation frameworks (those in which no cycles of attack occur), sustainable, tolerant and preferred semantics are equivalent. In section 5 we argue for the rationality of tolerant semantics by showing that the hypothesis attacks = conflict + preference establishes also a sufficient condition for the equivalence between this and preferred semantics. The game-theoretic counterpart of the semantics is offered in 6, arguing for strategical foundations. In section 7 we analyze and discuss related work, while the main conclusions are summarized in section 8. The appendix provides the proofs of the formal results. In the final section of his paper, Dung recognizes that his approach lacks a solution for the problem of self-attacking arguments ( [10] , p. 351). In this paper we intended to give two alternative semantics, that we deemed sustainable and tolerant extensions, to solve the problems of odd-length cycles of attack while keeping a close contact with Dung's work. We did this using the same basic tool of Dung: the concept of admissibility. The novelty of our approach raises from a strategy-based concept of 'cogency', which basically is a defensibility notion build upon admissibility, albeit slightly weaker than that. This conception builds upon the following ideas:. • a subset of arguments is a possible argumentation strategy of an agent,. • the admissibility of a strategy is relative to the possible strategies of the rival, • the choice consists of the maximal strategies that can be successfully defended against those challenging strategies which in turn can be successfully defended against them (i.e. choosing those strategies that are capable of "shifting the burden of proof").. The resulting semantics were shown to be more credulous (i.e. justifying more arguments) than preferred semantics, while sufficient conditions were established for the equivalence with this and other Dung's semantics. Moreover, a game-theoretic foundation was provided showing the strategical rationale of choosing sustainable and tolerant sets of arguments in a debate.

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