Greedy Randomized Adaptive Search and Variable Neighbourhood Search for the minimum labelling spanning tree problem This paper studies heuristics for the minimum labelling spanning tree (MLST) problem. The purpose is to find a spanning tree using edges that are as similar as possible. Given an undirected labelled connected graph, the minimum labelling spanning tree problem seeks a spanning tree whose edges have the smallest number of distinct labels. This problem has been shown to be NP-hard. A Greedy Randomized Adaptive Search Procedure (GRASP) and a Variable Neighbourhood Search (VNS) are proposed in this paper. They are compared with other algorithms recommended in the literature: the Modified Genetic Algorithm and the Pilot Method. Nonparametric statistical tests show that the heuristics based on GRASP and VNS outperform the other algorithms tested. Furthermore, a comparison with the results provided by an exact approach shows that we may quickly obtain optimal or near-optimal solutions with the proposed heuristics. Many combinatorial optimisation problems can be formulated on a graph where the possible solutions are spanning trees. These problems consist of finding spanning trees that are optimal with respect to some measure and have been extensively studied in graph theory (Avis et al., 2005) . Typical measures include the total length or the diameter of the tree. Many real-life combinatorial optimisation problems belong to this class of problems and consequently there is a large and growing interest in both theoretical and practical aspects. For some of these problems there are polynomial-time algorithms, while most are NP-hard. Thus, it is not possible to guarantee that an exact solution to the problem can be found within an acceptable timeframe and one has to settle for heuristics and approximate solution approaches with performance guarantees.. The minimum labelling spanning tree (MLST) problem is an NP-hard problem in which, given a graph with labelled edges, one seeks a spanning tree with the least number of labels. Such a model can represent many real-world problems in telecommunications networks, power networks, and multimodal transportation networks. For example, in telecommunications networks, there are many different types of communications media, such as optical fibre, coaxial cable, microwave, and telephone line (Tanenbaum, 2003) . A communications node may communicate with different nodes by choosing different types of communications media. Given a set of communications network nodes, the problem is to find a spanning tree (a connected communications network) that uses as few communications types as possible. This spanning tree will reduce the construction cost and the complexity of the network.. The MLST problem can be formulated as a network or graph problem. We are given a labelled connected undirected graph G = (V, E, L), where V is the set of n nodes, E is the set of m edges, and L is the set of labels. In the telecommunications example (Tanenbaum, 2003) , the vertices represent communications nodes, the edges communications links, and the labels communications types. Each edge in E has a label in a finite set L that identifies the communications type. The objective is to find a spanning tree that uses the smallest number of different types of edges. Define L T to be the set of different labels of the edges in a spanning tree T . The labelling can be represented by a function f L : E → L for all edges e ∈ E or by a partition P L of the edge set; the sets of the partitions are those consisting of the edges with the same label.. Another example is given by multimodal transportation networks ( Van-Nes, 2002) . In such problems, it is desirable to provide a complete service using the minimum number of companies. The multimodal transportation network is represented by a graph where each edge is assigned a label, denoting a different company managing that edge. The aim is to find a spanning tree of the graph using the minimum number of labels. The interpretation is that all terminal nodes are connected without cycles, using the minimum number of companies.. The minimum labelling spanning tree problem is formally defined as follows:. MLST problem: Given a labelled graph G = (V, E, L), where V is the set of n nodes, E is the set of m edges, and L is the set of labels, find a spanning tree T of G such that |L T | is minimized, where L T is the set of labels used in T .. Although a solution to the MLST problem is a spanning tree, we first consider connected subgraphs. A feasible solution is defined as a set of labels C ⊆ L, such that all the edges with labels in C represent a connected subgraph of G and span all the nodes in G. If C is a feasible solution, then any spanning tree of C has at most |C| labels. Moreover, if C is an optimal solution, then any spanning tree of C is a minimum labelling spanning tree. Thus, in order to solve the MLST problem we seek a feasible solution with the least number of labels (Xiong et al., 2005a) .. The upper left graph of Figure 1 is an example of an input graph with the optimal solution shown on the upper right. The lower part of Figure 1 shows examples of feasible solutions.. -INSERT FIGURE 1 -The rest of the paper is organised as follows. In the next section, we review the literature of the problem. In section three we present the details of the heuristics considered in this paper: ones recommended in the literature (the Modified Genetic Algorithm of Xiong et al. (2006) , and the Pilot Method of Cerulli et al. (2005) ), and some new approaches to the MLST problem (a Greedy Randomized Adaptive Search Procedure, and a basic Variable Neighbourhood Search). Section four includes the experimental analysis of the comparison of these metaheuristics, and the paper ends with some conclusions. For a survey on the basic concepts of metaheuristics and combinatorial optimisation, the reader is referred to Glover and Kochenberger, 2003) .

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


Document annotation and ontology population from linguistic extractions In this paper, we present a workbench for semi-automatic ontology population from textual documents. It provides an environment for mapping the linguistic extractions with the domain ontology thanks to knowledge acquisition rules. Those rules are activated when a pertinent linguistic tag is reached. Those linguistic tags are then mapped to a concept, one of its attributes or even a semantic relation between several concepts. The rules instantiate these concepts, attributes and relations in the knowledge base constrained by the domain ontology. This paper deals with the underlying knowledge capture process and presents the first experiments realized on a real client application from the legal publishing domain. From the publishing industry to the competitive intelligence business, important volumes of data from various sources have to be processed daily and analyzed by professional users. First, they must select the most relevant documents with regards to their applications needs. Second, they must manually capture the pertinent knowledge contained in each selected resource. That knowledge is used to annotate the document by a set of descriptors (terms from the thesaurus like 'divorce' and named entities like 'Mr. Bouscharain') and to enrich the knowledge base (with named entities, attributes of these named entities and semantic relations between these named entities).. In the Semantic Web context, the content of a document can be described and annotated using knowledge representation languages such as RDF, XTM and OWL. RDF, the Resource Description Framework [15] , is a formalism of knowledge representation from the semantic networks field. It is mainly used to describe resources, such as an electronic web document, by a set of metadata (author, date, source, etc.) and of descriptors. Those metadatas are composed of triples : (subject, verb, object) or (object 1, relation, object 2) or (resource, property, value) according to the needed description type.. Topic Maps are another formalism of knowledge representation [16] . Topic Maps define a set of topics linked to the same domain and constituting a semantic map of the knowledge. A topic represents everything that can be described or thought of by a human. It can participate in one or many relations, called associations, in which it plays a specific role. The topics have at least a name and intrinsic properties, called occurrences. This language allows a great flexibility in knowledge representation, especially with regards to modeling complex n-ary semantic relations.. OWL, Web Ontology Language [10] , is used to formalize an ontology [8] , or more generally some ontological and terminological resources [3] , by defining concepts used to represent a domain of knowledge. Each concept is described by a set of properties, relations and constraints. The OWL formalism comes from some of description logic.. In our projects, we use RDF to describe the content of a resource, OWL to model the ontology which will represent an applicative or a functional vision of the domain and Topic Maps to implement the knowledge base that will contain the instances of the concepts, properties and relations described in the domain ontology. The pertinent knowledge of the domain, contained in the documents will be captured to instantiate the knowledge base and to create semantic annotations of these texts. The semantic annotations can then be interpret-able by the machine to be later shared, published, queried or more generally used [13] .. Semantic annotation and ontology population are greatly dependent of the knowledge captured in the documents by the professional users. Manual processing of documents is extremely expensive in time and resources. The entire process involves productivity and quality issues. For all those reasons, companies are more and more looking for implementing solutions based on the use of linguistic tools that semiautomatically capture the pertinent information from textual documents.. Those natural language processing technologies should be tightly integrated into the future Semantic web applications and shall even become essential to the development, acceptance and use of the Semantic Web [2] . Thanks to the functionalities offered by the natural language processing technologies, and mainly those of Information Extraction, solutions adapted to the specific needs of Semantic Web might be developed such as:. • The semi-automatic construction of terminologies/vocabularies of a domain from a representative corpus as well as their maintenance [3] .. • The semi-automatic enrichment of knowledge bases by named entities and semantic relationships extracted from textual documents [12] .. • Semantic annotation of resources [11] [9] [17] .. Contrary to the researches previously cited, we noticed in our own projects that the linguistic tools and the ontology of the client domain are independently modeled from one another. That's why we decided to implement a gateway between the concepts of the ontology and the semantic annotations produced by the linguistic tools that will capture the pertinent knowledge of the studied domain.. In this article, we present an innovative workbench for document annotation and knowledge acquisition. In the next section of this paper, we will describe the implementation of our solution. Then, we will present the results of the first experiments from a project in the legal publishing field. This project will be used throughout the paper to illustrate our work. Finally, we will sum up the results in order to develop a new hypothesis and conclude on the future perspectives of our research.

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Decomposing bent functions Abstract -T h i s work is a contribution to t h e classification of bent functions. We notably point o u t that t h e bent functions m a y differ on t h e properties of t h e i r decompositions into 4 functions.We denote by L?, the set of all Boolean functions of m variables. For any a E FT, ' For any f E L?, and any V c FY, the restriction off t o V is the function f+v, the usual product in L?, of f with the indicator of V ( & ( x ) = 1 if and only if x E V). When V is a &dimensional subspace of FT, the restriction of f to V can obviously be identified with a function of IC variables. Similarly, for any coset a + V of V, we identify f cjba+v with h E BI, as follows: Recall that the derivative of f E B, with respect to V, is the function defined by DV f ( x ) = xVEv f ( x +U). We first prove a general result, linking f&.to D v f . Now, we consider the decompositions of f into four functions, i.e., IC = m -2 in the previous theorem. Applying Theorem 2, it appears (for instance) that any bent function which is quadratic or which has a cubic dual admits at least one decomposition into four bent functions. But this property does not hold in general, providing a suitable tool for the classification of bent functions. We study the main classes of bent functions. We notably prove that the two following classes do not admit such a decomposition.

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A loop accelerator for low power embedded VLIW processors The high transistor density afforded by modern VLSI processes have enabled the design of embedded processors that use clustered execution units to deliver high levels of performance. However, delivering data to the execution resources in a timely manner remains a major problem that limits ILP. It is particularly significant for embedded systems where memory and power budgets are limited. A distributed address generation and loop acceleration architecture for VLIW processors is presented. This decentralized onchip memory architecture uses multiple SRAMs to provide high intra-processor bandwidth. Each SRAM has an associated stream address generator capable of implementing a variety of addressing modes in conjunction with a shared loop accelerator.The architecture is extremely useful for generating application specific embedded processors, particularly for processing input data which is organized as a stream. The idea is evaluated in the context of a fine grain VLIW architecture executing complex perception algorithms such as speech and visual feature recognition. Transistor level Spice simulations are used to demonstrate a 159x improvement in the energy delay product when compared to conventional architectures executing the same applications. Traditionally, embedded computing was synonymous with the use of highly energy efficient, but low performance processors and micro-controllers for control and monitoring applications. The emergence of super DSPs with ever increasing BDTI scores introduces a new category of compute intensive embedded workloads. Sophisticated applications such as speech recognition, visual feature recognition, secure wireless networking, and general media processing will define the architecture and performance requirements of future mobile embedded environments. The need to deliver high performance at low energy levels has resulted in increased special- Common tactics include static extraction of ILP using VLIW techniques, specialization of the on-chip memory system, software managed scratch pad memory systems, cache banks which can be locked down under software control, bit-reversed and auto increment addressing modes, etc. Two important themes have emerged: a) improving the throughput of execution resources and b) improving data delivery to those execution resources. This paper will address the architecture of an on-chip memory system which significantly improves the capacity to deliver data to execution resources in a timely manner. It provides addressing mechanisms which generalize the auto increment or vector oriented addressing modes commonly used in processors. The strategy results in radical performance improvements in loop intensive algorithms.. A set of ten algorithms from the speech recognition, computer vision, encryption and signal processing domains are used to evaluate this work. These algorithms tend to be stream oriented with a large number of 2D array and vector accesses per elementary operation. Hardware performance counter based measurements on a MIPS R14K processor showed that 32.5% (Geometric mean) of the executed instructions were loads and stores. Since this RISC processor does not have auto increment addressing mode, assuming that there is at least one address calculation instruction for each load and store, it may be seen that 65% of the instructions are related to array accesses in one form or another. Amdhal's law therefore argues in favor of accelerating these patterns. Figure 1 shows the internal organization of a VLIW processor used to evaluate this research. It consists of a set of clock gated function units, a loop unit, multiple software managed dual ported SRAMs and associated address generators (one for each SRAM port), local bypass paths between neighboring function units as well as a cluster wide interconnect. Adding a distributed address generation and loop acceleration mechanism to a VLIW processor has been shown to have considerable benefit both in terms of power and energy consumption. The architecture has been evaluated for important classes of future embedded applications like speech recognition, vision and cryptography. This approach has a number of advantages: the approach provides performance and energy efficiency that is close to an ASIC while avoiding the costs of an ASIC and retaining most of the generality of a general purpose processor approach;, it achieves an energy-delay product that is 159 times better than an idealized Intel The loop accelerator and scratch-pad memory design focused on the need to provide high operand flow to the function units. This improves function unit utilization and IPC. Figure 5 shows the IPC of the cluster compared against the IPC measured using performance counters on a MIPS R14K CPU. Our VLIW processor vastly outperforms the the out of order processor and the highly optimizing SGI MIPSPro compiler. The mean 1 IPC of the processor is 3.3 times that of the competition. A large fraction of this performance advantage is due to the on-chip memory subsystem.. Sufficient throughput to meet real time performance is important for stream computations. Figure 6 shows the throughput of the various implementations. Throughput is defined as the number of input packets processed per second. The numbers are normalized to the throughput of the Pentium 4. Our VLIW architecture outperforms the Pentium 4 by a factor of 1.75 and achieves 41.4% of the ASIC's performance. The real advantage of the architecture becomes apparent in Figure 7 where it may be seen that this throughput is achieved at energy levels that are on average 13.5 times better than the XScale. Figure 8 shows that the cluster architecture improves the energy delay product over the Xscale on average by 159 times and is only 12 times worse than an ASIC implementation. Note that the last three graphs use a log scale for the Y axis. The radical improvements in energy and performance suggests that when high performance, programmability and low energy levels are crucial, a loop accelerated VLIW architecture is an attractive alternative to general purpose processors and ASICs. Banakar et al. have demonstrated the advantages of scratchpad memories as a power saving mechanism [1] . Processors like the IBM Elite DSP include vector extensions that can operate on disjoint data, but do not possess the level of autonomy our distributed address generation mechanism provides. The Reconfigurable Streaming Vector Processor targeted at low power multimedia systems implements hardware acceleration for base-stride vectors [2] . Vector register files possess a limited amount of autonomy in address generation, but the scheduling is completely done in hardware and is therefore inflexible. Our method is not only more general than vector processing, but also amenable to compiler instruction scheduling since we use enhanced scalar loads in conjunction with a VLIW architecture. High performance DSP processors provide bit-reversed addressing modes and auto increment instructions. The methods described in this paper are significantly more general in the access patterns they can deal with.

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


Validation of Nearest Neighbor Classifiers We develop a probabilistic bound on the error rate of the nearest neighbor classi er formed from a set of labelled examples. The bound is computed using only the examples in the set. A subset of the examples is used as a validation set to bound the error rate of the classi er formed from the remaining examples. Then a bound is computed for the di erence in error rates between the original classi er and the reduced classi er. This bound is computed by partitioning the validation set and using each subset to compute bounds for the error rate di erence due to the other subsets. Let Ln be the underlying error rate. Let Rn be the average of Ln over all size n in-sample data sets drawn from the input distribution. While this paper focuses on Ln, the error rate of the classi er at hand, much work in the past has focused on Rn, the average error rate over classi ers formed from randomly drawn examples. Cover and Hart 5] proved that under mild continuity assumptions R1 is no more than twice the Bayes (optimal) error rate. Cover 3] showed that the average error rate of using the remaining examples to classify each example in the in-sample set is an unbiased estimate of Rn?1. This paper develops the following method to bound Ln. Some insample examples are removed from the in-sample set to form a validation set. The remaining in-sample examples form a reduced classi er. Since the validation examples are independent of the reduced classi er, the validation examples can be used to obtain an error bound for the reduced classi er. To produce an error bound for the original classi er, we must also bound the di erence in error rates between the original classi er and the reduced classi er. To do this, we partition the validation examples into subsets. Since the examples in each subset are independent of the examples in the other subsets, we can use each subset to obtain a bound for the di erence in error rates due to the other subsets. We combine these bounds using truncated inclusion and exclusion to bound the error rate di erence due to the entire validation set, which is the error rate di erence between the original and reduced classi ers.. After developing bounds for the underlying error rate that can be computed using only the in-sample examples, we develop bounds that incorporate independently drawn unlabelled inputs and bounds that incorporate knowledge of the input distribution. Next, we develop bounds for the test error rate, including bounds that incorporate knowledge of test inputs. We have developed methods to bound the underlying error rate and the test error rate of a nearest neighbor classi er. The bounds can be computed using only the examples in the classi er. Thus, all available examples can be employed for the primary purpose of forming the classi er. No examples must be sacri ced for the secondary purpose of computing probabilistic bounds for the error rate on unseen data.. A challenge for the future is to extend the bounds for single classi ers to uniform bounds over multiple classi ers. For nite sets of classi ers, uniform bounds may be developed by summing the probabilities of bound failures for single classi ers to bound the probability of failure in the uniform bound 1]. For example, these bounds apply to sets of classi ers formed by eliminating di erent subsets of examples from the in-sample set. It may be possible to improve these bounds using methods of validation by inference based on rates of agreement among classi ers, as in 2]. For in nite classes of classi ers, it may be possible to develop bounds using the concept of VC dimension 14]. For example, these bounds would apply to all classi ers with a particular set of examples and a metric from some class of metrics. Another challenge is to develop bounds for k nearest neighbor classi ers, in which the output is the result of voting among the k classi er examples with inputs nearest to the test input.

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 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 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 O O O O O O O O O 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 B 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 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Dynamic Defragmentation of Reconfigurable Devices We propose a new method for defragmenting the module layout of a reconfigurable device, enabled by a novel approach for dealing with communication needs between relocated modules and with inhomogeneities found in commonly used FPGAs. Our method is based on dynamic relocation of module positions during runtime, with only very little reconfiguration overhead; the objective is to maximize the length of contiguous free space that is available for new modules. We describe a number of algorithmic aspects of good defragmentation, and present an optimization method based on tabu search. Experimental results indicate that we can improve the quality of module layout by roughly 50% over the static layout. Among other benefits, this improvement avoids unnecessary rejections of modules. In this article, we presented a new approach for defragmenting the module layout on a dynamically reconfigurable device, for example, an FPGA, in a seamless fashion. As the reconfiguration costs continuously decrease with each new generation of reconfigurable devices and a number of techniques for task preemption and relocation at a different positions are conceived (see Koch et al. [2007] for a comparison), task relocation at runtime becomes a new opportunity for improving the performance and efficiency of reconfigurable devices. However, this also poses new challenges, because defragmentation methods developed so far cannot be applied to reconfigurable devices, as they do not take into account their special characteristics. For example, many reconfigurable devices have heterogeneities on their reconfigurable area, such as memory blocks, DSPs, and CPUs. We presented different defragmentation strategies to relocate running modules and achieve a contiguous free space of maximum size.. The presented experiments show in average an increase in the maximal free space by 30% when applying our defragmentation techniques to FPGAs with heterogeneities; on some inputs an increase up to 200% is observed. This additional free space allows earlier execution of later modules, so the total execution time is reduced. This shows that it pays off to prefer a sophisticated heuristic for defragmentation (e.g., tabu search) over a simple heuristic (i.e., greedy), or over no defragmentation at all, provided that the execution times and module sizes are not too extreme (i.e., too large or too small compared to the size of the FPGA).. Obviously, improved algorithmic results can lead to further improvements. One of the possible extensions considers a more controlled overall placement of modules, instead of simply fixing fragmentation. As the necessary algorithmic methods are more involved, we leave this to future work.

O B 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 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 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 B 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 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 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 B 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


Stochastic language models for style-directed layout analysis of document images Abstract-Image segmentation is an important component of any document image analysis system. While many segmentation algorithms exist in the literature, very few i) allow users to specify the physical style, and ii) incorporate user-specified style information into the algorithm's objective function that is to be minimized. We describe a segmentation algorithm that models a document's physical structure as a hierarchical structure where each node describes a region of the document using a stochastic regular grammar. The exact form of the hierarchy and the stochastic language is specified by the user, while the probabilities associated with the transitions are estimated from groundtruth data. We demonstrate the segmentation algorithm on images of bilingual dictionaries. O UR OBJECTIVE is to develop a generic algorithm for segmenting scanned images of printed bilingual dictionaries formatted in various styles, and in various language pairs. The need for such an algorithm arose in a project in which we are developing an end-to-end system that can rapidly create cross-language information retrieval systems for low-density languages (languages for which online text is not readily available). Bilingual dictionaries have translation of words, which is a crucial resource for building cross-language retrieval systems. Furthermore, bilingual dictionaries are also very valuable for creating speech recognition systems for any new language since dictionaries typically have pronunciations of words.. While many segmentation algorithms have been proposed in the past, very few algorithms either i) allow users to specify the physical style of the input documents or ii) use the user-specified style information for segmenting document images to optimize some criterion. A style-directed segmentation algorithm could arguably give a better performance on the class of documents represented by the style than a generic algorithm that is designed for all types of document styles. In this paper we describe a probabilistic physical layout model for representing the physical style of documents. We then use this model to design Manuscript received July 31, 2001; revised December 11, 2002 . The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Aleksandra Mojsilović.. T. Kanungo is with IBM Almaden Research Center, San Jose, CA 95120 USA (e-mail: kanungo@almaden.ibm.com).. S. Mao is with the Communications Engineering Branch, U.S. National Library of Medicine, Bethesda, MD 20894 (e-mail: maosong@cfar.umd.edu; maos@mail.nlm.nih.gov).. Digital Object Identifier 10.1109/TIP. 2003 . 811487 an algorithm for extracting the physical structure of the document from a given image. This paper is organized as follows. In Section II, we provide a survey of related work. In Section III, we introduce a generative stochastic document model and describe the probabilistic physical layout model component in detail. In Section IV, we give the statement of problem and propose a document physical layout analysis algorithm based on our proposed model. A five-step performance evaluation methodology for training and evaluating physical layout analysis algorithms is presented in Section V. In Section VI, an experimental protocol is described for conducting training and evaluating experiments. In Section VII, we present our experimental results and provide a detailed discussion. We use our generative stochastic document model to automatically create large scale synthetic datasets with precise groundtruth and controlled degradation levels. Let be a synthetically generated dataset using our proposed model . The dataset contains document image and groundtruth pairs where denotes the image index and denotes the image degradation level. The steps of our experimental methodology for characterizing the performance of document structure analysis algorithms are as follows.. 1) Use the generative model with a set of parameters to generate a dataset . 2) Randomly partition the dataset into a mutually exclusive training dataset and test dataset . Thus and , where is the empty dataset. Each element in the datasets is an image-groundtruth pair where denotes the image index and denotes the degradation level of the image. We can control the dataset generation by adjusting the model parameter set . Hence, we can perform controlled experiments by generating datasets with different physical layout styles, logical structures and degradation levels. 3) Define a meaningful and computable performance metric where is an document image with index and degradation level , is the groundtruth of , and is the structure analysis result on . 4) For a document structure analysis algorithm , estimate its parameter set using the training dataset with degradation level where . We estimate the algorithm parameter vector on different degradation level . These estimated models are used in step 5 to study the robustness of the algorithm to document noise. 5) Evaluate the algorithm with the estimated parameters using the test dataset over different degradation levels . Let where is a function of the estimated parameter and the performance metric on each document image and groundtruth pair in the test dataset , and is the structure analysis function corresponding to . The function is defined by the user. In our case, which is the average of the performance metric on each document image and groundtruth pair with degradation level in the test dataset . 6) Perform error analysis in different error categories over different degradation levels on both the training and test datasets to identify/hypothesize why the algorithms perform at the respective levels.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 O O O O O O O O O O O O O O O O O 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 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Branching-time logics with path relativisation We define extensions of the full branching-time temporal logic CTL * in which the path quantifiers are relativised by formal languages of infinite words, and consider its natural fragments obtained by extending the logics CTL and CTL + in the same way. This yields a small and two-dimensional hierarchy of temporal logics parametrised by the class of languages used for the path restriction on one hand, and the use of temporal operators on the other. We motivate the study of such logics through two application scenarios: in abstraction and refinement they offer more precise means for the exclusion of spurious traces; and they may be useful in software synthesis where decidable logics without the finite model property are required. We study the relative expressive power of these logics as well as the complexities of their satisfiability and model-checking problems. Branching-time temporal logics are some of the most well-known and used specification languages for reactive systems. The most prominent ones are the logics CTL [12, 15] and CTL * [16] . While CTL has nice algorithmic properties -model checking is p-complete and satisfiability checking is exptime-complete -its expressive power is very weak. CTL * amends this by unifying CTL with the linear-time temporal logic LTL [34] . This way, it can express important properties like fairness which is not possible in CTL. This comes at a certain price, though. Model checking CTL * is naturally at least as expensive as it is for LTL. In fact it is no more expensive either, thus, it is pspace-complete [35] . The additional complexity introduced by merging branching-time with linear-time formalisms shows through in satisfiability checking which is 2-exptime-complete [39, 17] .. Temporal logics in general, and with it such branching-time logics, have become prominent because of the success that model checking -an automatic program verification method for correctness properties specified in temporal logics -has had over the past decades [22] . In particular, model checking was very successful in hardware verification because hardware can be modelled by finite-state systems. Verifying infinite-state systems has become more and more important in the domain of program verification since, and this is mainly due to the growing importance of software in reactive systems. Note that software usually leads to infinite-state systems because of the use of unbounded data structures, recursive functions, etc.. The model-checking complexities mentioned above hold with respect to finite models. Clearly, model-checking infinitestate programs is undecidable in general but it remains decidable for certain classes of infinite-state programs, e.g. pushdown processes, and weak temporal logics like CTL and LTL. It is still just pspace-complete for LTL but exptime-complete for CTL [9, 41] .. Several extensions and variations of such branching-time logics have been considered since, usually with special purposes in mind: Timed CTL has been introduced in order to verify properties in which real-time effects play a crucial role [2] ; action-based CTL considers models with more than one accessibility relation [33] ; Graded CTL adds some possibility of counting [7] ; etc.. Here we consider extensions of branching-time logics in which the path quantifiers can be relativised to traces that belong to a formal language of ω-words. This defines a hierarchy of extensions parametrised by the class of formal languages which can be used for the relativisation. In Section 2 we introduce these logics -based on CTL, CTL * and the lesser known CTL + which is known to be only as expressive as CTL [15] but exponentially more succinct [42, 1, 26] . Section 3 motivates the use of these logics through two scenarios: abstraction and software synthesis. Still, the main focus of this paper are the logics themselves. Here we study the hierarchy of expressive power we obtain from these logics (Section 5) with respect to different classes of formal languages, namely the ω-regular ones, the ω-context-free ones and the ω-visibly pushdown ones. We study their the computational complexity and decidability of their satisfiability problems (Section 6) and of their model-checking problems (Section 7). We motivate the study of path relativised branching-time logics through two scenarios: abstraction and refinement, and software synthesis.

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


Interference Mitigation Through Limited Receiver Cooperation Abstract-Interference is a major issue limiting the performance in wireless networks. Cooperation among receivers can help mitigate interference by forming distributed MIMO systems. The rate at which receivers cooperate, however, is limited in most scenarios. How much interference can one bit of receiver cooperation mitigate? In this paper, we study the two-user Gaussian interference channel with conferencing decoders to answer this question in a simple setting. We identify two regions regarding the gain from receiver cooperation: linear and saturation regions. In the linear region, receiver cooperation is efficient and provides a degrees-of-freedom gain, which is either one cooperation bit buys one over-the-air bit or two cooperation bits buy one over-the-air bit. In the saturation region, receiver cooperation is inefficient and provides a power gain, which is bounded regardless of the rate at which receivers cooperate. The conclusion is drawn from the characterization of capacity region to within two bits/s/Hz, regardless of channel parameters. The proposed strategy consists of two parts: 1) the transmission scheme, where superposition encoding with a simple power split is employed and 2) the cooperative protocol, where one receiver quantize-bin-and-forwards its received signal and the other after receiving the side information decode-bin-and-forwards its received signal.Index Terms-Capacity to within a bounded gap, distributed MIMO system, interference management, receiver cooperation.

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Cultural kinship as a computational system: from bottom-up to top-down forms of social organization Abstract A key change in the evolution of our species from a common ancestor with the chimpanzees was the shift to a field of social interaction no longer dependent upon face-to-face interaction for the maintenance of social coherency. Our hunter-gatherers ancestors made a radical shift to social relations based on a culturally constructed system of kinship relations. Unlike biological kinship that reflects the facts of biological reproduction, cultural kinship is a constructed, computational system that enables symbolic computation of kinship relations that are expressed through the kin terms of a kinship terminology. The system of kin terms is analogous to arithmetic as a computational system for computing quantities with symbols instantiated by the counting numbers. The internal logic of a kinship terminology ensures consistency both in kinship relation computations and translation of kin term computations to the perspective of each person who culturally shares the same kinship terminology. The constraint of internal and external consistency does not lead to a single kinship terminology computational system, hence there are a variety of kinship terminology systems across human societies. In this paper I outline a theory for the generative structure of kinship terminology systems and briefly discuss the implications this for explaining structural differences between kinship terminologies and how structure relates to social organization. The evolution of our species, Homo sapiens, from an ancestral species we share with modern-day chimpanzees includes the introduction of a number of social and cognitive abilities that distinguish human societies from those of the non-human primates. One of the key changes was a shift from societies whose organization and internal coherence derives from intensive, face-to-face interaction to societies with relational based forms of social organization. The field of social interaction in non-human primate societies is typically limited to a closed group of individuals interacting with each other on a day-to-day basis. With the development of hunter-gatherer societies in the Upper Paleolithic around 25-45,000 BP, a major shift took place in which the field of social interaction was no longer dependent upon face-to-face interaction and instead was predicated upon a system of culturally constructed (as opposed to biologically determined) kin relations. The social boundary shifted from being based on familiarity gained through face-to-face interaction to one determined by those who were cultural kin to each other. Our hunter-gatherer ancestors put into place a radical shift from a pragmatic social boundary expressed through day-to-day behavior to a conceptual social boundary determined through a culturally constructed system of kin relations.. Unlike biological kinship that simply reflects the facts of reproduction based on who copulated with whom, cultural kinship goes beyond biological kinship. It is by a computational system for symbolically computing conceptually defined kinship relations-expressed through the kin terms in a kinship terminology-that the kinship relation one person has to another is determined, much like arithmetic is a computational system for computing quantities with number symbols instantiated by the counting numbers. As a computational system, a kinship terminology must have an internal logic that both ensures internal consistency in kinship relation computations and external consistency when translating kin term computations to the perspective of each person who culturally shares the same kinship terminology computational system. Unlike arithmetic, though, there is no single kinship computational system satisfying the requirement for internal and external consistency, hence there are a variety of kinship terminology systems across human societies. Kinship terminologies provide, then, a top-down form of organization for the culturally constructed kinship relations that make up a kinship system since their structures do not derive from external conditions but from conceptual constraints such as reciprocity of kinship relations. Terminologies are, therefore, sui generis in the sense that Emile Durkheim used this expression in The Division of Labour in Society (1933 [1893 ) and other publications.

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Optimal Ternary Cyclic Codes From Monomials Abstract-Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. Perfect nonlinear monomials were employed to construct optimal ternary cyclic codes with parameters by Carlet, Ding, and Yuan in 2005. In this paper, almost perfect nonlinear monomials, and a number of other monomials over are used to construct optimal ternary cyclic codes with the same parameters. Nine open problems on such codes are also presented.

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Coordinated scheduling of production and delivery with production window and delivery capacity constraints This paper considers the coordinated production and delivery scheduling problem. We have a planning horizon consisting of z delivery times each with a unique delivery capacity. Suppose we have a set of jobs each with a committed delivery time, processing time, production window, and profit. The company can earn the profit if the job is produced in its production window and delivered before its committed delivery time. From the company point of view, we are interested in picking a subset of jobs to process and deliver so as to maximize the total profit subject to the delivery capacity constraint. We consider both the single delivery time case and the multiple delivery times case.Suppose the given set of jobs are k-disjoint, that is, the jobs can be partitioned into k lists of jobs such that the jobs in each list have disjoint production windows. When k is a constant, we developed a PTAS for the single delivery case. For multiple delivery times case, we also develop a PTAS when the number of delivery times is a constant as well. Under the current competitive manufacturing environment, companies tend to put more emphasis on the coordination of different stages of a supply chain, i.e. suppliers, manufacturers, distributors and customers. Among these four stages, the issue of coordinating production and distribution (delivery) has been widely discussed.. In the stage of distribution (delivery), the company may own transportation vehicles which deliver products at periodic or aperiodic times, or the company may rely on a third party to deliver, which picks up products at regular or irregular times. The products incurred by different orders may be delivered together if the destinations are close to each other, e.g. delivery to same countries by ships, delivery to same states or cities by flights, or delivery to same areas by trucks. The delivery capacity may vary at different delivery times and is always bounded.. In the stage of production, each order may have a non-customer defined production window. For example, the company may rely on another company to complete a sub-process, or may rely on a manufacturer to make the products or semi-products. With some pre-scheduled jobs, the manufacturer can only provide partial production line, or in some cases, it provides a production window for each order where the windows of different orders may overlap. Another example of production window is that the company may have to wait for arrivals of raw materials to start the manufacturing process. If the raw materials are perishable, the company has to start the manufacturing process immediately. Given the arrival schedule of raw materials, the company creates a production window for each order.. In summary, in the production stage, the company has the constraint of production window, and in the delivery stage, the company has the constraint of delivery capacity and promised delivery date. The company has to decide which orders to accept based on these constraints and the potential profit of each order in order to maximize the total profit . This paper addresses the problem faced by the company under the above scenarios. We consider the commit-to-ship model, i.e. if an order is accepted, the company guarantees the products be shipped to the customer before the committed time, we call this time the committed delivery date. We focus on the single machine production environment. We are interested in selecting a subset of orders in order to maximize the total profit. When orders are selected, both production schedule and delivery schedule should be considered simultaneously. Thus we face a "coordinated scheduling problem": generate a coordinated schedule, which consists of a production schedule and a delivery schedule subject to the production window, delivery date, and delivery capacity constraints. Problem definition. Our problem can be formally defined as follows. We have a planning horizon consisting of z delivery times, T = {D 1 , D 2 , · · · , D z }. Each delivery time D j is associated with a delivery capacity C j . We have a set of jobs J = {J 1 , J 2 , · · · , J n }. Each job J i has a promised delivery time d i ∈ T , a processing time p i , a production window [l i , r i ], a size c i , and a profit f i which can be earned if J i is processed at or before r i , and delivered before or at d i . Without loss of generality, we assume that p i ≤ r i − l i and p i ≤ d i for all jobs J i . We also assume r i ≤ d i for all jobs J i . The problem is to select a subset of jobs from J = {J 1 , J 2 , · · · , J n }, and generate a feasible coordinated production and delivery schedule S of these jobs so as to maximize the total profit. A feasible coordinated schedule S consists of a feasible production schedule and a feasible delivery schedule. A production schedule is feasible if all the jobs are processed within their production windows; and a delivery schedule is feasible if all jobs are delivered before the promised delivery time and the delivery capacities at all times are satisfied.

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Np-hardness proof and an approximation algorithm for the minimum vertex ranking spanning tree problem The minimum vertex ranking spanning tree problem (MVRST) is to find a spanning tree of G whose vertex ranking is minimum. In this paper, we show that MVRST is NP-hard. To prove this, we polynomially reduce the 3-dimensional matching problem to MVRST. Moreover, we present a ( D s /2 + 1)/( log 2 (D s + 1) + 1)-approximation algorithm for MVRST where D s is the minimum diameter of spanning trees of G. Consider a simple connected undirected graph G = (V , E). A vertex ranking of G is labeling r from the vertices of G to the positive integers such that for each path between any two vertices u and v, u = v, with r(u) = r(v), there exists at least one vertex w on the path with r(w) > r(u) = r(v). The value r(v) of a vertex v is called the rank of vertex v. A vertex ranking by integers 1, 2, . . . , k is called a k-vertex ranking. A graph G is said to be k-vertex-rankable if it has a k-vertex ranking. A vertex ranking r of G is minimum if the largest rank k assigned by r is the smallest among all rankings of G. Such rank k is called the vertex ranking number of G, denoted by (G). The vertex ranking problem is to find a minimum ranking of given graph G. The vertex ranking problem has interesting applications, e.g., to, communication network design, planning efficient assembly of products in manufacturing systems [5, 6, 12, 17] , and VLSI layout design [9, 16] .. As for the complexity, this problem is NP-hard even when restricted to cobipartite graphs [13] and bipartite graphs [1] , and a number of polynomial time algorithms for this problem have been developed on several subclasses of graphs. Much work has been done in finding the minimum vertex ranking of a tree; a linear time algorithm for trees is proposed Fig. 1 . Graph G and its spanning trees T 1 , T 2 , T 3 with minimum vertex ranking. Note that each spanning tree of G is isomorphic to one of T 1 , T 2 , T 3 , and T 1 is a minimum vertex ranking spanning tree of G.. in [14] . The problem is trivial on split graphs and is solvable in linear time on cographs [15] . Concerning interval graphs, although an O(n 4 ) time algorithm was known, Deogun et al. has given an O(n 3 ) time algorithm recently [3] . They also presented O(n 6 ) algorithms on permutation graphs and on trapezoid graphs, respectively, and showed that a polynomial time algorithm on d-trapezoid graphs exists [3] . Moreover, a polynomial time algorithm on graphs with treewidth at most k was developed [2] .. The problem described above is the ranking with respect to vertices, while a ranking with respect to edges is similarly defined as follows. An edge ranking of G is labeling r from the edges of G to the positive integers such that for each path between any two edges e 1 and e 2 , e 1 = e 2 , with r(e 1 ) = r(e 2 ), there exists at least one edge e 3 on the path with r(e 3 ) > r(e 1 ) = r(e 2 ). The value r(e) of a vertex e is called the rank of edge e. An edge ranking of G is minimum if the largest rank k assigned by r is the smallest among all rankings of G. Such rank k is called the edge ranking number of G, denoted by e (G). The edge ranking problem is to find a minimum ranking of given graph G. Before the proof of this problem to be NP-hard was given, an O(n 3 ) time algorithm for trees was known [17] . By now, a linear time algorithm for trees is shown in [8] . Recently, it has finally been shown that this problem on general graphs is NP-hard [7] .. Makino et al. introduced a minimum edge ranking spanning tree problem (MERST) which is related to the minimum edge ranking problem but is essentially different [10] . MERST is to find a spanning tree of G whose edge ranking is minimum. They proved that MERST is NP-hard and presented an approximation algorithm for MERST. MERST has interesting applications, e.g., to scheduling the parallel assembly of a multipart product from its components and relational databases [10] .. In this paper, we consider the vertex version of MERST, i.e., the minimum vertex ranking spanning tree problem (MVRST). MVRST is to find a spanning tree of G whose vertex ranking is minimum [11] . This problem is related to the minimum vertex ranking problem but is also essentially different as is the case of MERST. An example of a minimum vertex ranking spanning tree is illustrated in Fig. 1 . Note that for each application of the vertex ranking problem introduced previously in this paper, MVRST corresponds to a variation of the problem in that each edge is optional and a solution requires connectivity among vertices. Nakayama et al. presented O(n 3 ) time algorithms on interval graphs [11] . However, the complexity of MVRST on general graphs was left open. In this paper, we show that MVRST is NP-hard for general graphs. To prove this, we polynomially reduce the 3-dimensional matching problem (3DM) to MVRST. Moreover, we present a ( D s /2 + 1)/( log 2 (D s + 1) + 1)-approximation algorithm for MVRST where D s is the minimum diameter of spanning trees of G. In this paper, we showed that MVRST is NP-hard for general graphs and presented a ( D s /2 + 1)/ ( log 2 (D s + 1) + 1)-approximation algorithm for MVRST where D s is the minimum diameter of spanning trees of G.

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Quantum Fingerprints that Keep Secrets We introduce a new type of cryptographic primitive that we call hiding fingerprinting. A (quantum) fingerprinting scheme translates a binary string of length n to d (qu)bits, typically d ≪ n, such that given any string y and a fingerprint of x, one can decide with high accuracy whether x = y. Classical fingerprinting schemes cannot hide information very well: a classical fingerprint of x that guarantees error ≤ ε necessarily reveals Ω(log(1/ε)) bits about x. We call a scheme hiding if it reveals o(log(1/ε)) bits; accordingly, no classical scheme is hiding.For any constant c, we construct two kinds of hiding fingerprinting schemes, both mapping x ∈ {0, 1} n to O(log n) qubits and guaranteeing one-sided error probability at most 1/n c . The first kind uses pure states and leaks at most O(1) bits, and the second kind uses mixed states and leaks at most 1/n c bits, where the "leakage" is bounded via accessible information. The schemes are computationally efficient.Our mixed-state scheme is optimal, as shown via a generic strategy that extracts 1/ poly(n) bits from any fingerprint over O(log n) qubits.Our results have a communication complexity interpretation. We give quantum protocols for the equality problem in the models of one-way communication and simultaneous message passing that have communication cost O(log n) and offer hiding guarantees that cannot be matched by classical protocols of any cost.Some of the technical lemmas in this work might be of independent interest. Cryptography probably is the area that benefits most from replacing classical computers by quantum ones. In particular, the most restricting classical "axiom" of computational cryptography, the one it owes its name to, can be partially removed: With quantum protocols it is no longer true that virtually any interesting cryptographic protocol can be safe only if computational limitations of a potential intruder are assumed.. The famous quantum key distribution protocol by Bennett and Brassard [BB84] is a good example where the assumption that "an intruder is computationally limited" has been replaced by the assumption that quantum mechanics is valid in our physical universe. And if we accept quantum mechanics, it is highly desirable to find more examples of quantum crypto-protocols with unconditional security guarantees: Besides pleasing those of us who prefer to keep their secrets for themselves, such examples might shed more light on the nature of differences between quantum and classical information.. Informally speaking, the possibility to use quantum mechanics in order to achieve unconditional cryptographic security comes from the fact that, in general, quantum states are not "cloneable" (cf. [WZ82] ). Sometimes it can be very challenging to use this property alone (not making any computational assumptions) in order to build a cryptographic primitive; moreover, some very tempting goals are already known to be beyond the reach (cf. [May97] ). It is the quest of quantum cryptography to understand what crypto-goals can be achieved in a universe where the laws of quantum mechanics are valid.

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Volume Preservation of Multiresolution Meshes Geometric constraints have proved to be efficient for enhancing the realism of shape animation. The present paper addresses the computation and the preservation of the volume enclosed by multiresolution meshes. A wavelet based representation allows the mesh to be handled at any level of resolution. The key contribution is the calculation of the volume as a trilinear form with respect to the multiresolution coefficients. Efficiency is reached thanks to the preprocessing of a sparse 3D data structure involving the transposition of the filters while represented as a lifting scheme. A versatile and interactive method for preserving the volume during a deformation process is then proposed. It is based on a quadratic minimization subject to a linearization of the volume constraint. A closed form of the solution is derived. Wavelet based multiresolution (MR) analysis is now established as an efficient tool for modeling and handling curves and surfaces [6, 22] . It provides an efficient representation of complex functions at multiple levels of detail. Thus convenient handling of geometrical objects is possible. It has been extended to semi-regular meshes, and successfully used for level-of-detail visualization [4, 21] and deformation [17] . It has been combined with a local frame encoding and used for mesh compression [13, 19] . Compared to other multiresolution models for meshes [27, 14, 10] , the wavelet approach takes advantage of involving only linear filters that are not geometry dependent. Moreover it is also suitable for smooth surfaces.. Besides, geometric constraints have proved to be useful for deforming curves and surfaces. Linear constraints such as position, tangency, orthogonality, and symmetry [7, 8] are generally related to direct shape manipulation. These constraints offer the advantage of efficient processing, allowing for interactive manipulation of the free form geometry. Satisfying non-linear constraints, in contrast, requires intense computational effort, so that their use for interactive shape manipulation is generally very limited. The volume constraint has been considered for free-form solids [20] , FFD [1, 12] , vector-field based deformation [25] and meshes [3, 16] . When manipulating surfaces, the volume is a global property because it is given by an integral over the surface. Thus one of the main issues is to get a meaningful local preservation of the volume. Botsch and Kobbelt [3] achieve this by building a MR representation based on the encoding of volume elements between levels. The main drawbacks are expensive optimizations, and a very specific representation. Lipman et al. [16] link an approximation of the volume to the curvature of the surface. It is combined with an intrinsic representation of meshes based on the first and second fundamental forms. By way of compensation the handling of the mesh is not very intuitive.. In the context of multiresolution, editing with area constraints has been studied for planar curves [5, 11] . Both methods are designed for real-time deformations with up to a few thousand control points. Yet, a generalization to the volume of MR meshes is not obvious because of the growth of the complexity, and because of a complex topology.. This paper makes two main contributions. First, it provides formulas and an efficient algorithm to compute the volume enclosed by a mesh with respect to a multiresolution basis. The volume of the fine mesh is expressed through all levels of resolution as a trilinear form of the coarse and detail coefficients. It involves the transposition of the MR filters while they are represented as a lifting scheme made up of local masks. Though it is illustrated with a specific scheme, it works for any multiresolution scheme, as long as a lifting scheme representation is available. Second, an algorithm is provided for real-time deformation of the mesh at any MR level while preserving the volume. It is versatile since it doesn't depend on a particular mesh deformation technique: given a target shape, a correction is performed to meet a reference volume. The correction is computed by linearizing the volume constraint and by solving a constrained minimization problem. Efficiency is achieved thanks to a closed form of the solution.. The paper is organized as follows. Section 2 reminds the basics about semi-regular MR meshes and the lifting scheme. In Section 3 we provide a computation of the enclosed volume, including algorithms and data structures. In Section 4 we derive a volume preserving deformation algorithm, whose efficiency is illustrated by a few examples in Section 5. A conclusion is given in Section 6, together with existing and future extensions of this work. We present here several examples that show the effectiveness of our volume preserving algorithm. It is combined with various deformation techniques, which proves the versatility of our method. All examples undergo first a MR analysis in order to obtain a coarse control mesh. The scheme based on the modified Butterfly subdivision is used for the horse and the bunny examples. The scheme based on the Loop subdivision scheme is used for the bouncing ball example. We then apply the deformations to the control mesh while preserving the volume of the fine input mesh. Once the volume coefficients θ e (see Section 3.1) are pre-computed and stored, all deformations and animations can be performed in real-time.. In Figure 6 are shown several deformations of a spiky ball. Thanks to the MR representation (N = 642, n = 3 and e = 0) the details are preserved while the global shape changes. The volume is free in the upper row, and preserved in the lower row. If modeling a soft but non-stretch material, the volume preservation obviously improves the realism of the deformations. Those positions are extracted from an animation of a bouncing ball 1 . The coarse control mesh (an icosahedron) was animated thanks to physical 1D equations.. The Stanford bunny is deformed in Figure 7 .

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Interference decoding for deterministic channels Abstract-An inner bound to the capacity region of a class of three user pair deterministic interference channels is presented. The key idea is to simultaneously decode the combined interference signal and the intended message at each receiver. It is shown that this interference-decoding inner bound strictly contains the inner bound obtained by treating interference as noise, which includes interference alignment for deterministic channels. The gain comes from judicious analysis of the number of combined interference sequences in different regimes of input distributions and message rates. Interference channels with three or more user pairs exhibit the interesting property that decoding at each receiver is impaired by the joint effect of interference from all other senders rather by each sender's signal separately. Consequently, coding schemes that deal directly with the effect of the combined interference signal are expected to achieve higher rates. One such coding scheme is the celebrated interference alignment, e.g., [1] , [2] , whereby the code is designed so that the combined interference signal at each receiver is confined (aligned) to a subset of the receiver signal space. Depending on the specific channel, this alignment may be achieved via linear subspaces, signal scale levels, time delay slots, or numbertheoretic irrational bases. In each case, the subset that contains the combined interference is disregarded, while the desired signal is reconstructed from the complement subset.. An important aspect to note about interference alignment is that the interfering signal is treated as noise, that is, the receivers do not attempt to partially or fully decode it as in the Han-Kobayashi scheme [3] for the two user pair case. Decoding combined interference signals was first considered by Bresler et al. [4] for the many-to-one Gaussian interference channel. The authors argue that with Gaussian codes, decoding the combined interference is tantamount to decoding each interfering sender's codeword, while lattice codes can make the combined interference look essentially like codewords from a single interferer. For channels with inherent linearity such as Gaussian interference channels, it is natural to consider decoding linear combinations of individual interfering codewords. Nazer and Gastpar [5] consider Gaussian relay networks and propose decoding linear functions at intermediate nodes, thus creating a compute-forward relaying architecture.. This work is partially supported by DARPA ITMANET. Bernd Bandemer is supported by an Eric and Illeana Benhamou Stanford Graduate Fellowship. In this paper, we investigate interference decoding for a three receiver deterministic interference channel (3-DIC), which is an extension of the Costa-El Gamal two user pair model [6] and more general than the deterministic class studied in [7] . It consists of three sender-receiver alphabet pairs (X k , Y k ), loss functions g kl , interference combining functions h k , and receiver functions. The channel is depicted in Figure 1 for user pair (X 1 , Y 1 ). We assume that h k and f k become one-to-one when one of their arguments is fixed arbitrarily. For example, for. for every probability mass function (pmf) p(x 11 , s 1 ).. Each sender k ∈ {1, 2, 3} wishes to convey an independent message M k at data rate R k to its corresponding receiver. We define a (2 nR1 , 2 nR2 , 2 nR3 , n) code, probability of error, and achievability of a given rate triple (R 1 , R 2 , R 3 ) in the standard way [8] .. We focus on this class of deterministic channels for several reasons. First, the capacity region for the two user pair version of this class [6] is known and is achieved by the Han-Kobayashi scheme. This gives some hope that an appropriate extension of Han-Kobayashi where the combined interference is decoded partially or fully may be optimal for more than two user pairs. Second, this class includes the finite field deterministic model in [9] , which approximates Gaussian ICs in the high SNR regime [10] . For more than two user pairs, capacity results for this finite field deterministic model are known only in some special cases [11] , [12] , where interference is treated as noise. An interesting question is whether more sophisticated coding schemes can achieve higher rates for this class of channels. Finally, the combined interference signal in our channel takes values from a finite set, and therefore a certain type of alignment can be observed without resorting to complicated structured codes [13] . Of course, structured codes may still achieve even higher rates, but we do not investigate this possibility in this paper.. The main result of the paper is an inner bound to the capacity region of the 3-DIC, which is achieved via interference decoding. In this scheme, each receiver decodes the combined interference signal together with its intended message. We use simple randomly generated point-to-point codes without rate splitting or superposition coding. The key observation is that depending on the input pmfs and the message rates, the number of possible combined interference sequences can be equal to the number of interfering message pairs, the number of typical combined interference sequences, or some combination of the two. In our scheme, each sender does not need to know the other senders' codebooks. However, we use simultaneous decoding, which requires that the receivers know all codebooks. As in the recent characterization of the Han-Kobayashi region [14] , we do not require the interference decoding to be correct with arbitrarily small probability of error. We show that interference decoding strictly outperforms treating interference as noise.. The inner bound is presented in the next section, and examples are given in Section III. Details of the proofs are available in an extended version of this paper posted on Arxiv. Notation and basic definitions follow [8] .. where Q is a time sharing random variable with arbitrary cardinality. Define the region R 1 (Q, X 1 , X 2 , X 3 ) to consist of the rate triples (R 1 , R 2 , R 3 ) such that Interference decoding is a promising middle ground between treating interference as noise and more sophisticated schemes that employ rate splitting and superposition coding. As in treating interference as noise, simple point-to-point codes can be used. However, more sophisticated coding schemes are needed to achieve capacity.

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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 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 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


A note on communicating between information systems based on including degrees In order to study the communication between information systems, Gong and Xiao (2010, International journal of general systems, 39, 189-206) proposed the concept of general relation mappings based on including degrees. Some properties and the extension for fuzzy information systems of the general relation mappings have been investigated there. In this paper, we point out by counterexamples that several assertions (Lemmas 3.1 and 3.2, Theorems 4.1 and 4.3) in the aforementioned work are not true in general.

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