Authentication and Secrecy Codes for Equiprobable Source Probability Distributions

Abstract: We give new combinatorial constructions for codes providing authentication and secrecy for equiprobable source probability distributions. In particular, we construct an infinite class of optimal authentication codes which are multiple-fold secure against spoofing and simultaneously achieve perfect secrecy. Several further new optimal codes satisfying these properties will also be constructed and presented in general tables. Almost all of these appear to be the first authentication codes with these properties.


The mdt algorithm

Abstract: Link state routing protocols such as OSPF or IS-IS currently use only best paths to forward IP packets throughout a domain. The optimality of sub-paths ensures consistency of hop by hop forwarding although paths, calculated using Dijkstra algorithm, are recursively composed. According to the link metric, the diversity of existing paths can be underestimated using only best paths. Hence, it reduces potential benefits of multipath applications such as load balancing and fast rerouting. In this paper, we propose a low time complexity multipath computation algorithm able to calculate at least two paths with a different first hop between all pairs of nodes in the network if such next hops exist. Using real and generated topologies, we evaluate and compare the complexity of our proposition with several techniques. Simulation results suggest that the path diversity achieved with our proposition is approximatively the same that the one obtained using consecutive Dijsktra computations, but with a lower time complexity.


Safe Reasoning Over Ontologies

Abstract: As ontologies proliferate and automatic reasoners become more powerful, the problem of protecting sensitive information becomes more serious. In particular, as facts can be inferred from other facts, it becomes increasingly likely that information included in an ontology, while not itself deemed sensitive, may be able to be used to infer other sensitive information. We first consider the problem of testing an ontology for safeness defined as its not being able to be used to derive any sensitive facts using a given collection of inference rules. We then consider the problem of optimizing an ontology based on the criterion of making as much useful information as possible available without revealing any sensitive facts.


Sublinear Time Algorithms for Earth Mover's Distance

Abstract: We study the problem of estimating the Earth Mover's Distance (EMD) between probability distributions when given access only to samples. We give closeness testers and additive-error estimators over domains in $[0, \Delta]^d$, with sample complexities independent of domain size - permitting the testability even of continuous distributions over infinite domains. Instead, our algorithms depend on other parameters, such as the diameter of the domain space, which may be significantly smaller. We also prove lower bounds showing the dependencies on these parameters to be essentially optimal. Additionally, we consider whether natural classes of distributions exist for which there are algorithms with better dependence on the dimension, and show that for highly clusterable data, this is indeed the case. Lastly, we consider a variant of the EMD, defined over tree metrics instead of the usual L1 metric, and give optimal algorithms.


INFRAWEBS axiom editor - a graphical ontology-driven tool for creating complex logical expressions

Abstract: The current INFRAWEBS European research project aims at developing ICT framework enabling software and service providers to generate and establish open and extensible development platforms for Web Service applications. One of the concrete project objectives is developing a full-life-cycle software toolset for creating and maintaining Semantic Web Services (SWSs) supporting specific applications based on Web Service Modelling Ontology (WSMO) framework. According to WSMO, functional and behavioural descriptions of a SWS may be represented by means of complex logical expressions (axioms). The paper describes a specialized user-friendly tool for constructing and editing such axioms - INFRAWEBS Axiom Editor. After discussing the main design principles of the Editor, its functional architecture is briefly presented. The tool is implemented in Eclipse Graphical Environment Framework and Eclipse Rich Client Platform.


Design, development and implementation of a tool for construction of declarative functional descriptions of semantic web services based on WSMO methodology

Abstract: Semantic web services (SWS) are self-contained, self-describing, semantically marked-up software resources that can be published, discovered, composed and executed across the Web in a semi-automatic way. They are a key component of the future Semantic Web, in which networked computer programs become providers and users of information at the same time. This work focuses on developing a full-life-cycle software toolset for creating and maintaining Semantic Web Services (SWSs) based on the Web Service Modelling Ontology (WSMO) framework. A main part of WSMO-based SWS is service capability - a declarative description of Web service functionality. A formal syntax and semantics for such a description is provided by Web Service Modeling Language (WSML), which is based on different logical formalisms, namely, Description Logics, First-Order Logic and Logic Programming. A WSML description of a Web service capability is represented as a set of complex logical expressions (axioms). We develop a specialized user-friendly tool for constructing and editing WSMO-based SWS capabilities. Since the users of this tool are not specialists in first-order logic, a graphical way for constricting and editing axioms is proposed. The designed process for constructing logical expressions is ontology-driven, which abstracts away as much as possible from any concrete syntax of logical language. We propose several mechanisms to guarantees the semantic consistency of the produced logical expressions. The tool is implemented in Java using Eclipse for IDE and GEF (Graphical Editing Framework) for visualization.


Visual approach for data mining on medical information databases using Fastmap algorithm

Abstract: The rapid development of tools for acquisition and storage of information has lead to the formation of enormous medical databases. The large quantity of data definitely surpasses the abilities of humans for efficient usage without specialized tools for analysis. The situation is described as rich in data, but poor in information. In order to fill this growing gap, different approaches from the field of Data Mining are applied. These methods perform analysis of large sets of observed data in order to find new dependencies or concise representation of the data, which is more meaningful to humans. One of the possible approaches for discovery of dependencies is the visual approach, in which data is processed and visualized in a way suitable for analysis by a domain expert. This work proposes a visual approach, in which data is processed and visualized in a way suitable for analysis by a domain expert. We design and implement a software solution for visualization of multi-dimensional, classified medical data using the FastMap algorithm for graduate reduction of dimensions. The implementation of the graphical user interface is described in detail since it is the most important factor for the ease of use of these tools by non-professionals in data mining.


Incremental Deployment of Network Monitors Based on Group Betweenness Centrality

Abstract: In many applications we are required to increase the deployment of a distributed monitoring system on an evolving network. In this paper we present a new method for finding candidate locations for additional deployment in the network. This method is based on the Group Betweenness Centrality (GBC) measure that is used to estimate the influence of a group of nodes over the information flow in the network. The new method assists in finding the location of k additional monitors in the evolving network, such that the portion of additional traffic covered is at least (1-1/e) of the optimal.


What Do Family Caregivers of Alzheimer's Disease Patients Desire in Smart Home Technologies?

Abstract: Objectives - The authors' aim was to investigate the representations, wishes, and fears of family caregivers (FCs) regarding 14 innovative technologies (IT) for care aiding and burden alleviation, given the severe physical and psychological stress induced by dementia care, and the very slow uptake of these technologies in our society. Methods - A cluster sample survey based on a self-administered questionnaire was carried out on data collected from 270 families of patients with Alzheimer's disease or related disorders, located in the greater Paris area. Multiple Correspondence Analysis was used in addition to usual statistical tests to identify homogenous FCs clusters concerning the appreciation or rejection of the considered technologies. Results - Two opposite clusters were clearly defined: FCs in favor of a substantial use of technology, and those rather or totally hostile. Furthermore the distributions of almost all the answers of appreciations were U shaped. Significant relations were demonstrated between IT appreciation and FC's family or gender statuses (e.g., female FCs appreciated more than male FCs a tracking device for quick recovering of wandering patients: p=0.0025, N=195). Conclusions - The study provides further evidence of the contrasted perception of technology in dementia care at home, and suggests the development of public debates based on rigorous assessment of practices and a strict ethical aim to protect against misuse.


Theory of Carry Value Transformation (CVT) and its Application in Fractal formation

Abstract: In this paper the theory of Carry Value Transformation (CVT) is designed and developed on a pair of n-bit strings and is used to produce many interesting patterns. One of them is found to be a self-similar fractal whose dimension is same as the dimension of the Sierpinski triangle. Different construction procedures like L-system, Cellular Automata rule, Tilling for this fractal are obtained which signifies that like other tools CVT can also be used for the formation of self-similar fractals. It is shown that CVT can be used for the production of periodic as well as chaotic patterns. Also, the analytical and algebraic properties of CVT are discussed. The definition of CVT in two-dimension is slightly modified and its mathematical properties are highlighted. Finally, the extension of CVT and modified CVT (MCVT) are done in higher dimensions.


Time Hopping technique for faster reinforcement learning in simulations

Abstract: This preprint has been withdrawn by the author for revision


Eligibility Propagation to Speed up Time Hopping for Reinforcement Learning

Abstract: A mechanism called Eligibility Propagation is proposed to speed up the Time Hopping technique used for faster Reinforcement Learning in simulations. Eligibility Propagation provides for Time Hopping similar abilities to what eligibility traces provide for conventional Reinforcement Learning. It propagates values from one state to all of its temporal predecessors using a state transitions graph. Experiments on a simulated biped crawling robot confirm that Eligibility Propagation accelerates the learning process more than 3 times.


The Derivational Complexity Induced by the Dependency Pair Method

Abstract: We study the derivational complexity induced by the dependency pair method, enhanced with standard refinements. We obtain upper bounds on the derivational complexity induced by the dependency pair method in terms of the derivational complexity of the base techniques employed. In particular we show that the derivational complexity induced by the dependency pair method based on some direct technique, possibly refined by argument filtering, the usable rules criterion, or dependency graphs, is primitive recursive in the derivational complexity induced by the direct method. This implies that the derivational complexity induced by a standard application of the dependency pair method based on traditional termination orders like KBO, LPO, and MPO is exactly the same as if those orders were applied as the only termination technique.


Efficient Description Logic Reasoning in Prolog: The DLog system

Abstract: This paper describes a resolution based Description Logic reasoning system called DLog. DLog transforms Description Logic axioms into a Prolog program and uses the standard Prolog execution for efficiently answering instance retrieval queries. From the Description Logic point of view, DLog is an ABox reasoning engine for the full SHIQ language. The DLog approach makes it possible to store the individuals in a database instead of memory, which results in better scalability and helps using description logic ontologies directly on top of existing information sources. To appear in Theory and Practice of Logic Programming (TPLP).


Fuzzy Linguistic Logic Programming and its Applications

Abstract: The paper introduces fuzzy linguistic logic programming, which is a combination of fuzzy logic programming, introduced by P. Vojtas, and hedge algebras in order to facilitate the representation and reasoning on human knowledge expressed in natural languages. In fuzzy linguistic logic programming, truth values are linguistic ones, e.g., VeryTrue, VeryProbablyTrue, and LittleFalse, taken from a hedge algebra of a linguistic truth variable, and linguistic hedges (modifiers) can be used as unary connectives in formulae. This is motivated by the fact that humans reason mostly in terms of linguistic terms rather than in terms of numbers, and linguistic hedges are often used in natural languages to express different levels of emphasis. The paper presents: (i) the language of fuzzy linguistic logic programming; (ii) a declarative semantics in terms of Herbrand interpretations and models; (iii) a procedural semantics which directly manipulates linguistic terms to compute a lower bound to the truth value of a query, and proves its soundness; (iv) a fixpoint semantics of logic programs, and based on it, proves the completeness of the procedural semantics; (v) several applications of fuzzy linguistic logic programming; and (vi) an idea of implementing a system to execute fuzzy linguistic logic programs.


Performing Nonlinear Blind Source Separation with Signal Invariants

Abstract: Given a time series of multicomponent measurements x(t), the usual objective of nonlinear blind source separation (BSS) is to find a "source" time series s(t), comprised of statistically independent combinations of the measured components. In this paper, the source time series is required to have a density function in (s,ds/dt)-space that is equal to the product of density functions of individual components. This formulation of the BSS problem has a solution that is unique, up to permutations and component-wise transformations. Separability is shown to impose constraints on certain locally invariant (scalar) functions of x, which are derived from local higher-order correlations of the data's velocity dx/dt. The data are separable if and only if they satisfy these constraints, and, if the constraints are satisfied, the sources can be explicitly constructed from the data. The method is illustrated by using it to separate two speech-like sounds recorded with a single microphone.


Settling the Complexity of Arrow-Debreu Equilibria in Markets with Additively Separable Utilities

Abstract: We prove that the problem of computing an Arrow-Debreu market equilibrium is PPAD-complete even when all traders use additively separable, piecewise-linear and concave utility functions. In fact, our proof shows that this market-equilibrium problem does not have a fully polynomial-time approximation scheme unless every problem in PPAD is solvable in polynomial time.


Evolvability need not imply learnability

Abstract: We show that Boolean functions expressible as monotone disjunctive normal forms are PAC-evolvable under a uniform distribution on the Boolean cube if the hypothesis size is allowed to remain fixed. We further show that this result is insufficient to prove the PAC-learnability of monotone Boolean functions, thereby demonstrating a counter-example to a recent claim to the contrary. We further discuss scenarios wherein evolvability and learnability will coincide as well as scenarios under which they differ. The implications of the latter case on the prospects of learning in complex hypothesis spaces is briefly examined.


Privacy in Search Logs

Abstract: Search engine companies collect the "database of intentions", the histories of their users' search queries. These search logs are a gold mine for researchers. Search engine companies, however, are wary of publishing search logs in order not to disclose sensitive information. In this paper we analyze algorithms for publishing frequent keywords, queries and clicks of a search log. We first show how methods that achieve variants of $k$-anonymity are vulnerable to active attacks. We then demonstrate that the stronger guarantee ensured by $\epsilon$-differential privacy unfortunately does not provide any utility for this problem. We then propose an algorithm ZEALOUS and show how to set its parameters to achieve $(\epsilon,\delta)$-probabilistic privacy. We also contrast our analysis of ZEALOUS with an analysis by Korolova et al. [17] that achieves $(\epsilon',\delta')$-indistinguishability. Our paper concludes with a large experimental study using real applications where we compare ZEALOUS and previous work that achieves $k$-anonymity in search log publishing. Our results show that ZEALOUS yields comparable utility to $k-$anonymity while at the same time achieving much stronger privacy guarantees.


About the impossibility to prove P=NP and the pseudo-randomness in NP

Abstract: The relationship between the complexity classes P and NP is an unsolved question in the field of theoretical computer science. In this paper, we look at the link between the P - NP question and the "Deterministic" versus "Non Deterministic" nature of a problem, and more specifically at the temporal nature of the complexity within the NP class of problems. Let us remind that the NP class is called the class of "Non Deterministic Polynomial" languages. Using the meta argument that results in Mathematics should be "time independent" as they are reproducible, the paper shows that the P!=NP assertion is impossible to prove in the a-temporal framework of Mathematics. In a previous version of the report, we use a similar argument based on randomness to show that the P = NP assertion was also impossible to prove, but this part of the paper was shown to be incorrect. So, this version deletes it. In fact, this paper highlights the time dependence of the complexity for any NP problem, linked to some pseudo-randomness in its heart.


Moveable objects and applications, based on them

Abstract: The inner views of all our applications are predetermined by the designers; only some non-significant variations are allowed with the help of adaptive interface. In several programs you can find some moveable objects, but it is an extremely rare thing. However, the design of applications on the basis of moveable and resizable objects opens an absolutely new way of programming; such applications are much more effective in users' work, because each user can adjust an application to his purposes. Programs, using adaptive interface, only implement the designer's ideas of what would be the best reaction to any of the users' doings or commands. Applications on moveable elements do not have such predetermined system of rules; they are fully controlled by the users. This article describes and demonstrates the new way of applications' design.


Optimal Tableau Decision Procedures for PDL

Abstract: We reformulate Pratt's tableau decision procedure of checking satisfiability of a set of formulas in PDL. Our formulation is simpler and more direct for implementation. Extending the method we give the first EXPTIME (optimal) tableau decision procedure not based on transformation for checking consistency of an ABox w.r.t. a TBox in PDL (here, PDL is treated as a description logic). We also prove the new result that the data complexity of the instance checking problem in PDL is coNP-complete.


(Meta) Kernelization

Abstract: In a parameterized problem, every instance I comes with a positive integer k. The problem is said to admit a polynomial kernel if, in polynomial time, one can reduce the size of the instance I to a polynomial in k, while preserving the answer. In this work we give two meta-theorems on kernelzation. The first theorem says that all problems expressible in Counting Monadic Second Order Logic and satisfying a coverability property admit a polynomial kernel on graphs of bounded genus. Our second result is that all problems that have finite integer index and satisfy a weaker coverability property admit a linear kernel on graphs of bounded genus. These theorems unify and extend all previously known kernelization results for planar graph problems.


Effect of cell residence time variance on the performance of an advanced paging algorithm

Abstract: The use of advanced sequential paging algorithms has been suggested as a means to reduce the signaling cost in future mobile cellular networks. In a proposed algorithm (Koukoutsidis and Theologou, 2003), the system can use the additional information of the last interaction cell combined with a mobility model to predict the short-term location probabilities at the time of an incoming call arrival. The short-term location probabilities reduce the uncertainty in mobile user position and thus greatly improve the search. In this paper, an analytical model is derived that allows for a general distribution of cell residence times. By considering a Gamma distribution, we study the effect of the variance of cell residence times and derive useful results on the performance of the algorithm.


Evaluating and Optimising Models of Network Growth

Abstract: This paper presents a statistically sound method for measuring the accuracy with which a probabilistic model reflects the growth of a network, and a method for optimising parameters in such a model. The technique is data-driven, and can be used for the modeling and simulation of any kind of evolving network. The overall framework, a Framework for Evolving Topology Analysis (FETA), is tested on data sets collected from the Internet AS-level topology, social networking websites and a co-authorship network. Statistical models of the growth of these networks are produced and tested using a likelihood-based method. The models are then used to generate artificial topologies with the same statistical properties as the originals. This work can be used to predict future growth patterns for a known network, or to generate artificial models of graph topology evolution for simulation purposes. Particular application examples include strategic network planning, user profiling in social networks or infrastructure deployment in managed overlay-based services.


Stability Analysis and Learning Bounds for Transductive Regression Algorithms

Abstract: This paper uses the notion of algorithmic stability to derive novel generalization bounds for several families of transductive regression algorithms, both by using convexity and closed-form solutions. Our analysis helps compare the stability of these algorithms. It also shows that a number of widely used transductive regression algorithms are in fact unstable. Finally, it reports the results of experiments with local transductive regression demonstrating the benefit of our stability bounds for model selection, for one of the algorithms, in particular for determining the radius of the local neighborhood used by the algorithm.


Approximability of Sparse Integer Programs

Abstract: The main focus of this paper is a pair of new approximation algorithms for certain integer programs. First, for covering integer programs {min cx: Ax >= b, 0 <= x <= d} where A has at most k nonzeroes per row, we give a k-approximation algorithm. (We assume A, b, c, d are nonnegative.) For any k >= 2 and eps>0, if P != NP this ratio cannot be improved to k-1-eps, and under the unique games conjecture this ratio cannot be improved to k-eps. One key idea is to replace individual constraints by others that have better rounding properties but the same nonnegative integral solutions; another critical ingredient is knapsack-cover inequalities. Second, for packing integer programs {max cx: Ax <= b, 0 <= x <= d} where A has at most k nonzeroes per column, we give a (2k^2+2)-approximation algorithm. Our approach builds on the iterated LP relaxation framework. In addition, we obtain improved approximations for the second problem when k=2, and for both problems when every A_{ij} is small compared to b_i. Finally, we demonstrate a 17/16-inapproximability for covering integer programs with at most two nonzeroes per column.


Boosting the Accuracy of Differentially-Private Histograms Through Consistency

Abstract: We show that it is possible to significantly improve the accuracy of a general class of histogram queries while satisfying differential privacy. Our approach carefully chooses a set of queries to evaluate, and then exploits consistency constraints that should hold over the noisy output. In a post-processing phase, we compute the consistent input most likely to have produced the noisy output. The final output is differentially-private and consistent, but in addition, it is often much more accurate. We show, both theoretically and experimentally, that these techniques can be used for estimating the degree sequence of a graph very precisely, and for computing a histogram that can support arbitrary range queries accurately.


Color Dipole Moments for Edge Detection

Abstract: Dipole and higher moments are physical quantities used to describe a charge distribution. In analogy with electromagnetism, it is possible to define the dipole moments for a gray-scale image, according to the single aspect of a gray-tone map. In this paper we define the color dipole moments for color images. For color maps in fact, we have three aspects, the three primary colors, to consider. Associating three color charges to each pixel, color dipole moments can be easily defined and used for edge detection.


Dependency Pairs and Polynomial Path Orders

Abstract: We show how polynomial path orders can be employed efficiently in conjunction with weak innermost dependency pairs to automatically certify polynomial runtime complexity of term rewrite systems and the polytime computability of the functions computed. The established techniques have been implemented and we provide ample experimental data to assess the new method.


Approche conceptuelle par un processus d'annotation pour la repr\'esentation et la valorisation de contenus informationnels en intelligence \'economique (IE)

Abstract: In the era of the information society, the impact of the information systems on the economy of material and immaterial is certainly perceptible. With regards to the information resources of an organization, the annotation involved to enrich informational content, to track the intellectual activities on a document and to set the added value on information for the benefit of solving a decision-making problem in the context of economic intelligence. Our contribution is distinguished by the representation of an annotation process and its inherent concepts to lead the decisionmaker to an anticipated decision: the provision of relevant and annotated information. Such information in the system is made easy by taking into account the diversity of resources and those that are well annotated so formally and informally by the EI actors. A capital research framework consist of integrating in the decision-making process the annotator activity, the software agent (or the reasoning mechanisms) and the information resources enhancement.


A Program to Determine the Exact Competitive Ratio of List s-Batching with Unit Jobs

Abstract: We consider the online list s-batch problem, where all the jobs have processing time 1 and we seek to minimize the sum of the completion times of the jobs. We give a Java program which is used to verify that the competitiveness of this problem is 619/583.


5-axis High Speed Milling Optimisation

Abstract: Manufacturing of free form parts relies on the calculation of a tool path based on a CAD model, on a machining strategy and on a given numerically controlled machine tool. In order to reach the best possible performances, it is necessary to take into account a maximum of constraints during tool path calculation. For this purpose, we have developed a surface representation of the tool paths to manage 5-axis High Speed Milling, which is the most complicated case. This model allows integrating early in the step of tool path computation the machine tool geometrical constraints (axis ranges, part holder orientation), kinematical constraints (speed and acceleration on the axes, singularities) as well as gouging issues between the tool and the part. The aim of the paper is to optimize the step of 5-axis HSM tool path calculation with a bi-parameter surface representation of the tool path. We propose an example of integration of the digital process for tool path computation, ensuring the required quality and maximum productivity


Usinage de poches en UGV - Aide au choix de strat\'egies

Abstract: The paper deals with associating the optimal machining strategy to a given pocket geometry, within the context of High-Speed Machining (HSM) of aeronautical pockets. First we define different classes of pocket features according to geometrical criteria. Following, we propose a method allowing to associate a set of capable tools to the features. Each capable tool defines a machined zone with a specific geometry. The last part of the paper is thus dedicated to associate the optimal machining strategy to a given geometry within the context of HSM. Results highlight that analyses must be conducted in a dynamical as well as a geometrical viewpoint. In particular, it becomes necessary to integrate dynamical specifities associated to the behavior of the couple machine/NC unit in the tool path calculation.


On formal verification of arithmetic-based cryptographic primitives

Abstract: Cryptographic primitives are fundamental for information security: they are used as basic components for cryptographic protocols or public-key cryptosystems. In many cases, their security proofs consist in showing that they are reducible to computationally hard problems. Those reductions can be subtle and tedious, and thus not easily checkable. On top of the proof assistant Coq, we had implemented in previous work a toolbox for writing and checking game-based security proofs of cryptographic primitives. In this paper we describe its extension with number-theoretic capabilities so that it is now possible to write and check arithmetic-based cryptographic primitives in our toolbox. We illustrate our work by machine checking the game-based proofs of unpredictability of the pseudo-random bit generator of Blum, Blum and Shub, and semantic security of the public-key cryptographic scheme of Goldwasser and Micali.


k-Means has Polynomial Smoothed Complexity

Abstract: The k-means method is one of the most widely used clustering algorithms, drawing its popularity from its speed in practice. Recently, however, it was shown to have exponential worst-case running time. In order to close the gap between practical performance and theoretical analysis, the k-means method has been studied in the model of smoothed analysis. But even the smoothed analyses so far are unsatisfactory as the bounds are still super-polynomial in the number n of data points. In this paper, we settle the smoothed running time of the k-means method. We show that the smoothed number of iterations is bounded by a polynomial in n and 1/\sigma, where \sigma is the standard deviation of the Gaussian perturbations. This means that if an arbitrary input data set is randomly perturbed, then the k-means method will run in expected polynomial time on that input set.


A New Key-Agreement-Protocol

Abstract: A new 4-pass Key-Agreement Protocol is presented. The security of the protocol mainly relies on the existence of a (polynomial-computable) One-Way-Function and the supposed computational hardness of solving a specific system of equations.


Learning convex bodies is hard

Abstract: We show that learning a convex body in $\RR^d$, given random samples from the body, requires $2^{\Omega(\sqrt{d/\eps})}$ samples. By learning a convex body we mean finding a set having at most $\eps$ relative symmetric difference with the input body. To prove the lower bound we construct a hard to learn family of convex bodies. Our construction of this family is very simple and based on error correcting codes.


The Distribution and Deposition Algorithm for Multiple Sequences Sets

Abstract: Sequences set is a mathematical model used in many applications. As the number of the sequences becomes larger, single sequence set model is not appropriate for the rapidly increasing problem sizes. For example, more and more text processing applications separate a single big text file into multiple files before processing. For these applications, the underline mathematical model is multiple sequences sets (MSS). Though there is increasing use of MSS, there is little research on how to process MSS efficiently. To process multiple sequences sets, sequences are first distributed to different sets, and then sequences for each set are processed. Deriving effective algorithm for MSS processing is both interesting and challenging. In this paper, we have defined the cost functions and performance ratio for analysis of the quality of synthesis sequences. Based on these, the problem of Process of Multiple Sequences Sets (PMSS) is formulated. We have first proposed two greedy algorithms for the PMSS problem, which are based on generalization of algorithms for single sequences set. Then based on the analysis of the characteristics of multiple sequences sets, we have proposed the Distribution and Deposition (DDA) algorithm and DDA* algorithm for PMSS problem. In DDA algorithm, the sequences are first distributed to multiple sets according to their alphabet contents; then sequences in each set are deposited by the deposition algorithm. The DDA* algorithm differs from the DDA algorithm in that the DDA* algorithm distributes sequences by clustering based on sequence profiles. Experiments show that DDA and DDA* always output results with smaller costs than other algorithms, and DDA* outperforms DDA in most instances. The DDA and DDA* algorithms are also efficient both in time and space.


Maximizing the number of accepted flows in TDMA-based wireless ad hoc networks is APX-complete

Abstract: Full exploitation of the bandwidth resources of Wireless Networks is challenging because of the sharing of the radio medium among neighboring nodes. Practical algorithms and distributed schemes that tries to optimising the use of the network radio resources. In this technical report we present the proof that maximising the network capacity is is an APX Complete problem (not approximable within 1/(1 - 2^(-k)) - eps for eps > 0).


An Investigation Report on Auction Mechanism Design

Abstract: Auctions are markets with strict regulations governing the information available to traders in the market and the possible actions they can take. Since well designed auctions achieve desirable economic outcomes, they have been widely used in solving real-world optimization problems, and in structuring stock or futures exchanges. Auctions also provide a very valuable testing-ground for economic theory, and they play an important role in computer-based control systems. Auction mechanism design aims to manipulate the rules of an auction in order to achieve specific goals. Economists traditionally use mathematical methods, mainly game theory, to analyze auctions and design new auction forms. However, due to the high complexity of auctions, the mathematical models are typically simplified to obtain results, and this makes it difficult to apply results derived from such models to market environments in the real world. As a result, researchers are turning to empirical approaches. This report aims to survey the theoretical and empirical approaches to designing auction mechanisms and trading strategies with more weights on empirical ones, and build the foundation for further research in the field.


Theoretical framework for constructing matching algorithms in biometric authentication systems

Abstract: In this paper, we propose a theoretical framework to construct matching algorithms for any biometric authentication systems. Conventional matching algorithms are not necessarily secure against strong intentional impersonation attacks such as wolf attacks. The wolf attack is an attempt to impersonate a genuine user by presenting a "wolf" to a biometric authentication system without the knowledge of a genuine user's biometric sample. A wolf is a sample which can be accepted as a match with multiple templates. The wolf attack probability (WAP) is the maximum success probability of the wolf attack, which was proposed by Une, Otsuka, Imai as a measure for evaluating security of biometric authentication systems. We present a principle for construction of secure matching algorithms against the wolf attack for any biometric authentication systems. The ideal matching algorithm determines a threshold for each input value depending on the entropy of the probability distribution of the (Hamming) distances. Then we show that if the information about the probability distribution for each input value is perfectly given, then our matching algorithm is secure against the wolf attack. Our generalized matching algorithm gives a theoretical framework to construct secure matching algorithms. How lower WAP is achievable depends on how accurately the entropy is estimated. Then there is a trade-off between the efficiency and the achievable WAP. Almost every conventional matching algorithm employs a fixed threshold and hence it can be regarded as an efficient but insecure instance of our theoretical framework. Daugman's IrisCode recognition algorithm proposed can also be regarded as a non-optimal instance of our framework.


On the perfect matching index of bridgeless cubic graphs

Abstract: If $G$ is a bridgeless cubic graph, Fulkerson conjectured that we can find 6 perfect matchings $M_1,...,M_6$ of $G$ with the property that every edge of $G$ is contained in exactly two of them and Berge conjectured that its edge set can be covered by 5 perfect matchings. We define $\tau(G)$ as the least number of perfect matchings allowing to cover the edge set of a bridgeless cubic graph and we study this parameter. The set of graphs with perfect matching index 4 seems interesting and we give some informations on this class.


On the Parameterised Intractability of Monadic Second-Order Logic

Abstract: One of Courcelle's celebrated results states that if C is a class of graphs of bounded tree-width, then model-checking for monadic second order logic is fixed-parameter tractable on C by linear time parameterised algorithms. An immediate question is whether this is best possible or whether the result can be extended to classes of unbounded tree-width. In this paper we show that in terms of tree-width, the theorem can not be extended much further. More specifically, we show that if C is a class of graphs which is closed under colourings and satisfies certain constructibility conditions such that the tree-width of C is not bounded by log^{16}(n) then MSO_2-model checking is not fixed-parameter tractable unless the satisfiability problem SAT for propositional logic can be solved in sub-exponential time. If the tree-width of C is not poly-logarithmically bounded, then MSO_2-model checking is not fixed-parameter tractable unless all problems in the polynomial-time hierarchy, and hence in particular all problems in NP, can be solved in sub-exponential time.


A Unified Approach to Ranking in Probabilistic Databases

Abstract: The dramatic growth in the number of application domains that naturally generate probabilistic, uncertain data has resulted in a need for efficiently supporting complex querying and decision-making over such data. In this paper, we present a unified approach to ranking and top-k query processing in probabilistic databases by viewing it as a multi-criteria optimization problem, and by deriving a set of features that capture the key properties of a probabilistic dataset that dictate the ranked result. We contend that a single, specific ranking function may not suffice for probabilistic databases, and we instead propose two parameterized ranking functions, called PRF-w and PRF-e, that generalize or can approximate many of the previously proposed ranking functions. We present novel generating functions-based algorithms for efficiently ranking large datasets according to these ranking functions, even if the datasets exhibit complex correlations modeled using probabilistic and/xor trees or Markov networks. We further propose that the parameters of the ranking function be learned from user preferences, and we develop an approach to learn those parameters. Finally, we present a comprehensive experimental study that illustrates the effectiveness of our parameterized ranking functions, especially PRF-e, at approximating other ranking functions and the scalability of our proposed algorithms for exact or approximate ranking.


Reducibility Among Fractional Stability Problems

Abstract: In this paper, we resolve the computational complexity of a number of outstanding open problems with practical applications. Here is the list of problems we show to be PPAD-complete, along with the domains of practical significance: Fractional Stable Paths Problem (FSPP) [21] - Internet routing; Core of Balanced Games [41] - Economics and Game theory; Scarf's Lemma [41] - Combinatorics; Hypergraph Matching [1]- Social Choice and Preference Systems; Fractional Bounded Budget Connection Games (FBBC) [30] - Social networks; and Strong Fractional Kernel [2]- Graph Theory. In fact, we show that no fully polynomial-time approximation schemes exist (unless PPAD is in FP). This paper is entirely a series of reductions that build in nontrivial ways on the framework established in previous work. In the course of deriving these reductions, we created two new concepts - preference games and personalized equilibria. The entire set of new reductions can be presented as a lattice with the above problems sandwiched between preference games (at the "easy" end) and personalized equilibria (at the "hard" end). Our completeness results extend to natural approximate versions of most of these problems. On a technical note, we wish to highlight our novel "continuous-to-discrete" reduction from exact personalized equilibria to approximate personalized equilibria using a linear program augmented with an exponential number of "min" constraints of a specific form. In addition to enhancing our repertoire of PPAD-complete problems, we expect the concepts and techniques in this paper to find future use in algorithmic game theory.


Towards an explanatory and computational theory of scientific discovery

Abstract: We propose an explanatory and computational theory of transformative discoveries in science. The theory is derived from a recurring theme found in a diverse range of scientific change, scientific discovery, and knowledge diffusion theories in philosophy of science, sociology of science, social network analysis, and information science. The theory extends the concept of structural holes from social networks to a broader range of associative networks found in science studies, especially including networks that reflect underlying intellectual structures such as co-citation networks and collaboration networks. The central premise is that connecting otherwise disparate patches of knowledge is a valuable mechanism of creative thinking in general and transformative scientific discovery in particular.


Computing Stuttering Simulations

Abstract: Stuttering bisimulation is a well-known behavioral equivalence that preserves CTL-X, namely CTL without the next-time operator X. Correspondingly, the stuttering simulation preorder induces a coarser behavioral equivalence that preserves the existential fragment ECTL-{X,G}, namely ECTL without the next-time X and globally G operators. While stuttering bisimulation equivalence can be computed by the well-known Groote and Vaandrager's [1990] algorithm, to the best of our knowledge, no algorithm for computing the stuttering simulation preorder and equivalence is available. This paper presents such an algorithm for finite state systems.


Online prediction of ovarian cancer

Abstract: In this paper we apply computer learning methods to diagnosing ovarian cancer using the level of the standard biomarker CA125 in conjunction with information provided by mass-spectrometry. We are working with a new data set collected over a period of 7 years. Using the level of CA125 and mass-spectrometry peaks, our algorithm gives probability predictions for the disease. To estimate classification accuracy we convert probability predictions into strict predictions. Our algorithm makes fewer errors than almost any linear combination of the CA125 level and one peak's intensity (taken on the log scale). To check the power of our algorithm we use it to test the hypothesis that CA125 and the peaks do not contain useful information for the prediction of the disease at a particular time before the diagnosis. Our algorithm produces $p$-values that are better than those produced by the algorithm that has been previously applied to this data set. Our conclusion is that the proposed algorithm is more reliable for prediction on new data.


On the closed-form solution of the rotation matrix arising in computer vision problems

Abstract: We show the closed-form solution to the maximization of trace(A'R), where A is given and R is unknown rotation matrix. This problem occurs in many computer vision tasks involving optimal rotation matrix estimation. The solution has been continuously reinvented in different fields as part of specific problems. We summarize the historical evolution of the problem and present the general proof of the solution. We contribute to the proof by considering the degenerate cases of A and discuss the uniqueness of R.


Mathematical and Statistical Opportunities in Cyber Security

Abstract: The role of mathematics in a complex system such as the Internet has yet to be deeply explored. In this paper, we summarize some of the important and pressing problems in cyber security from the viewpoint of open science environments. We start by posing the question "What fundamental problems exist within cyber security research that can be helped by advanced mathematics and statistics?" Our first and most important assumption is that access to real-world data is necessary to understand large and complex systems like the Internet. Our second assumption is that many proposed cyber security solutions could critically damage both the openness and the productivity of scientific research. After examining a range of cyber security problems, we come to the conclusion that the field of cyber security poses a rich set of new and exciting research opportunities for the mathematical and statistical sciences.


Fuzzy inference based mentality estimation for eye robot agent

Abstract: Household robots need to communicate with human beings in a friendly fashion. To achieve better understanding of displayed information, an importance and a certainty of the information should be communicated together with the main information. The proposed intent expression system aims to convey this additional information using an eye robot. The eye motions are represented as states in a pleasure-arousal space model. Change of the model state is calculated by fuzzy inference according to the importance and certainty of the displayed information. This change influences the arousal-sleep coordinate in the space which corresponds to activeness in communication. The eye robot provides a basic interface for the mascot robot system which is an easy to understand information terminal for home environments in a humatronics society.


Self-Assembly of a Statistically Self-Similar Fractal

Abstract: We demonstrate existence of a tile assembly system that self-assembles the statistically self-similar Sierpinski Triangle in the Winfree-Rothemund Tile Assembly Model. This appears to be the first paper that considers self-assembly of a random fractal, instead of a deterministic fractal or a finite, bounded shape. Our technical contributions include a way to remember, and use, unboundedly-long prefixes of an infinite coding sequence at each stage of fractal construction; a tile assembly mechanism for nested recursion; and a definition of "almost-everywhere local determinism," to describe a tileset whose assembly is locally determined, conditional upon a zeta-dimension zero set of (infinitely many) "input" tiles. This last is similar to the definition of randomized computation for Turing machines, in which an algorithm is deterministic relative to an oracle sequence of coin flips that provides advice but does not itself compute. Keywords: tile self-assembly, statistically self-similar Sierpinski Triangle.


Intent expression using eye robot for mascot robot system

Abstract: An intent expression system using eye robots is proposed for a mascot robot system from a viewpoint of humatronics. The eye robot aims at providing a basic interface method for an information terminal robot system. To achieve better understanding of the displayed information, the importance and the degree of certainty of the information should be communicated along with the main content. The proposed intent expression system aims at conveying this additional information using the eye robot system. Eye motions are represented as the states in a pleasure-arousal space model. Changes in the model state are calculated by fuzzy inference according to the importance and degree of certainty of the displayed information. These changes influence the arousal-sleep coordinates in the space that corresponds to levels of liveliness during communication. The eye robot provides a basic interface for the mascot robot system that is easy to be understood as an information terminal for home environments in a humatronics society.


CP-logic: A Language of Causal Probabilistic Events and Its Relation to Logic Programming

Abstract: This papers develops a logical language for representing probabilistic causal laws. Our interest in such a language is twofold. First, it can be motivated as a fundamental study of the representation of causal knowledge. Causality has an inherent dynamic aspect, which has been studied at the semantical level by Shafer in his framework of probability trees. In such a dynamic context, where the evolution of a domain over time is considered, the idea of a causal law as something which guides this evolution is quite natural. In our formalization, a set of probabilistic causal laws can be used to represent a class of probability trees in a concise, flexible and modular way. In this way, our work extends Shafer's by offering a convenient logical representation for his semantical objects. Second, this language also has relevance for the area of probabilistic logic programming. In particular, we prove that the formal semantics of a theory in our language can be equivalently defined as a probability distribution over the well-founded models of certain logic programs, rendering it formally quite similar to existing languages such as ICL or PRISM. Because we can motivate and explain our language in a completely self-contained way as a representation of probabilistic causal laws, this provides a new way of explaining the intuitions behind such probabilistic logic programs: we can say precisely which knowledge such a program expresses, in terms that are equally understandable by a non-logician. Moreover, we also obtain an additional piece of knowledge representation methodology for probabilistic logic programs, by showing how they can express probabilistic causal laws.


Undirected Graphs of Entanglement 3

Abstract: Entanglement is a complexity measure of digraphs that origins in fixed-point logics. Its combinatorial purpose is to measure the nested depth of cycles in digraphs. We address the problem of characterizing the structure of graphs of entanglement at most $k$. Only partial results are known so far: digraphs for $k=1$, and undirected graphs for $k=2$. In this paper we investigate the structure of undirected graphs for $k=3$. Our main tool is the so-called \emph{Tutte's decomposition} of 2-connected graphs into cycles and 3-connected components into a tree-like fashion. We shall give necessary conditions on Tutte's tree to be a tree decomposition of a 2-connected graph of entanglement 3.


The Star Height Hierarchy Vs. The Variable Hierarchy

Abstract: The star height hierarchy (resp. the variable hierarchy) results in classifying $\mu$-terms into classes according to the nested depth of fixed point operators (resp. to the number of bound variables). We prove, under some assumptions, that the variable hierarchy is a proper refinement of the star height hierarchy. We mean that the non collapse of the variable hierarchy implies the non collapse of the star height hierarchy. The proof relies on the combinatorial characterization of the two hierarchies.


Closure Under Minors of Undirected Entanglement

Abstract: Entanglement is a digraph complexity measure that origins in fixed-point theory. Its purpose is to count the nested depth of cycles in digraphs. In this paper we prove that the class of undirected graphs of entanglement at most $k$, for arbitrary fixed $k \in \mathbb{N}$, is closed under taking minors. Our proof relies on the game theoretic characterization of entanglement in terms of Robber and Cops games.


Bounded Max-Colorings of Graphs

Abstract: In a bounded max-coloring of a vertex/edge weighted graph, each color class is of cardinality at most $b$ and of weight equal to the weight of the heaviest vertex/edge in this class. The bounded max-vertex/edge-coloring problems ask for such a coloring minimizing the sum of all color classes' weights. In this paper we present complexity results and approximation algorithms for those problems on general graphs, bipartite graphs and trees. We first show that both problems are polynomial for trees, when the number of colors is fixed, and $H_b$ approximable for general graphs, when the bound $b$ is fixed. For the bounded max-vertex-coloring problem, we show a 17/11-approximation algorithm for bipartite graphs, a PTAS for trees as well as for bipartite graphs when $b$ is fixed. For unit weights, we show that the known 4/3 lower bound for bipartite graphs is tight by providing a simple 4/3 approximation algorithm. For the bounded max-edge-coloring problem, we prove approximation factors of $3-2/\sqrt{2b}$, for general graphs, $\min\{e, 3-2/\sqrt{b}\}$, for bipartite graphs, and 2, for trees. Furthermore, we show that this problem is NP-complete even for trees. This is the first complexity result for max-coloring problems on trees.


Joint Opportunistic Scheduling in Multi-Cellular Systems

Abstract: We address the problem of multiuser scheduling with partial channel information in a multi-cell environment. The scheduling problem is formulated jointly with the ARQ based channel learning process and the intercell interference mitigating cell breathing protocol. The optimal joint scheduling policy under various system constraints is established. The general problem is posed as a generalized Restless Multiarmed Bandit process and the notion of indexability is studied. We conjecture, with numerical support, that the multicell multiuser scheduling problem is indexable and obtain a partial structure of the index policy.


On polynomial growth functions of D0L-systems

Abstract: The aim of this paper is to prove that every polynomial function that maps the natural integers to the positive integers is the growth function of some D0L-system.


Opportunistic Multiuser Scheduling in a Three State Markov-modeled Downlink

Abstract: We consider the downlink of a cellular system and address the problem of multiuser scheduling with partial channel information. In our setting, the channel of each user is modeled by a three-state Markov chain. The scheduler indirectly estimates the channel via accumulated Automatic Repeat Request (ARQ) feedback from the scheduled users and uses this information in future scheduling decisions. Using a Partially Observable Markov Decision Process (POMDP), we formulate a throughput maximization problem that is an extension of our previous work where the channels were modeled using two states. We recall the greedy policy that was shown to be optimal and easy to implement in the two state case and study the implementation structure of the greedy policy in the considered downlink. We classify the system into two types based on the channel statistics and obtain round robin structures for the greedy policy for each system type. We obtain performance bounds for the downlink system using these structures and study the conditions under which the greedy policy is optimal.


Exact Join Detection for Convex Polyhedra and Other Numerical Abstractions

Abstract: Deciding whether the union of two convex polyhedra is itself a convex polyhedron is a basic problem in polyhedral computations; having important applications in the field of constrained control and in the synthesis, analysis, verification and optimization of hardware and software systems. In such application fields though, general convex polyhedra are just one among many, so-called, numerical abstractions, which range from restricted families of (not necessarily closed) convex polyhedra to non-convex geometrical objects. We thus tackle the problem from an abstract point of view: for a wide range of numerical abstractions that can be modeled as bounded join-semilattices --that is, partial orders where any finite set of elements has a least upper bound--, we show necessary and sufficient conditions for the equivalence between the lattice-theoretic join and the set-theoretic union. For the case of closed convex polyhedra --which, as far as we know, is the only one already studied in the literature-- we improve upon the state-of-the-art by providing a new algorithm with a better worst-case complexity. The results and algorithms presented for the other numerical abstractions are new to this paper. All the algorithms have been implemented, experimentally validated, and made available in the Parma Polyhedra Library.


On Fodor on Darwin on Evolution

Abstract: Jerry Fodor argues that Darwin was wrong about "natural selection" because (1) it is only a tautology rather than a scientific law that can support counterfactuals ("If X had happened, Y would have happened") and because (2) only minds can select. Hence Darwin's analogy with "artificial selection" by animal breeders was misleading and evolutionary explanation is nothing but post-hoc historical narrative. I argue that Darwin was right on all counts.


First Person Singular

Abstract: Brian Rotman argues that (one) "mind" and (one) "god" are only conceivable, literally, because of (alphabetic) literacy, which allowed us to designate each of these ghosts as an incorporeal, speaker-independent "I" (or, in the case of infinity, a notional agent that goes on counting forever). I argue that to have a mind is to have the capacity to feel. No one can be sure which organisms feel, hence have minds, but it seems likely that one-celled organisms and plants do not, whereas animals do. So minds originated before humans and before language --hence, a fortiori, before writing, whether alphabetic or ideographic.


On Distributed Model Checking of MSO on Graphs

Abstract: We consider distributed model-checking of Monadic Second-Order logic (MSO) on graphs which constitute the topology of communication networks. The graph is thus both the structure being checked and the system on which the distributed computation is performed. We prove that MSO can be distributively model-checked with only a constant number of messages sent over each link for planar networks with bounded diameter, as well as for networks with bounded degree and bounded tree-length. The distributed algorithms rely on nontrivial transformations of linear time sequential algorithms for tree decompositions of bounded tree-width graphs.


Logical locality entails frugal distributed computation over graphs

Abstract: First-order logic is known to have limited expressive power over finite structures. It enjoys in particular the locality property, which states that first-order formulae cannot have a global view of a structure. This limitation ensures on their low sequential computational complexity. We show that the locality impacts as well on their distributed computational complexity. We use first-order formulae to describe the properties of finite connected graphs, which are the topology of communication networks, on which the first-order formulae are also evaluated. We show that over bounded degree networks and planar networks, first-order properties can be frugally evaluated, that is, with only a bounded number of messages, of size logarithmic in the number of nodes, sent over each link. Moreover, we show that the result carries over for the extension of first-order logic with unary counting.


Feasibility of Motion Planning on Acyclic and Strongly Connected Directed Graphs

Abstract: Motion planning is a fundamental problem of robotics with applications in many areas of computer science and beyond. Its restriction to graphs has been investigated in the literature for it allows to concentrate on the combinatorial problem abstracting from geometric considerations. In this paper, we consider motion planning over directed graphs, which are of interest for asymmetric communication networks. Directed graphs generalize undirected graphs, while introducing a new source of complexity to the motion planning problem: moves are not reversible. We first consider the class of acyclic directed graphs and show that the feasibility can be solved in time linear in the product of the number of vertices and the number of arcs. We then turn to strongly connected directed graphs. We first prove a structural theorem for decomposing strongly connected directed graphs into strongly biconnected components.Based on the structural decomposition, we give an algorithm for the feasibility of motion planning on strongly connected directed graphs, and show that it can also be decided in time linear in the product of the number of vertices and the number of arcs.


Seidel Minor, Permutation Graphs and Combinatorial Properties

Abstract: A permutation graph is an intersection graph of segments lying between two parallel lines. A Seidel complementation of a finite graph at one of it vertex $v$ consists to complement the edges between the neighborhood and the non-neighborhood of $v$. Two graphs are Seidel complement equivalent if one can be obtained from the other by a successive application of Seidel complementation. In this paper we introduce the new concept of Seidel complementation and Seidel minor, we then show that this operation preserves cographs and the structure of modular decomposition. The main contribution of this paper is to provide a new and succinct characterization of permutation graphs i.e. A graph is a permutation graph \Iff it does not contain the following graphs: $C_5$, $C_7$, $XF_{6}^{2}$, $XF_{5}^{2n+3}$, $C_{2n}, n\geqslant6$ and their complement as Seidel minor. In addition we provide a $O(n+m)$-time algorithm to output one of the forbidden Seidel minor if the graph is not a permutation graph.


Personalized Recommendation via Integrated Diffusion on User-Item-Tag Tripartite Graphs

Abstract: Personalized recommender systems are confronting great challenges of accuracy, diversification and novelty, especially when the data set is sparse and lacks accessorial information, such as user profiles, item attributes and explicit ratings. Collaborative tags contain rich information about personalized preferences and item contents, and are therefore potential to help in providing better recommendations. In this paper, we propose a recommendation algorithm based on an integrated diffusion on user-item-tag tripartite graphs. We use three benchmark data sets, Del.icio.us, MovieLens and BibSonomy, to evaluate our algorithm. Experimental results demonstrate that the usage of tag information can significantly improve accuracy, diversification and novelty of recommendations.


Simplicial Databases

Abstract: In this paper, we define a category DB, called the category of simplicial databases, whose objects are databases and whose morphisms are data-preserving maps. Along the way we give a precise formulation of the category of relational databases, and prove that it is a full subcategory of DB. We also prove that limits and colimits always exist in DB and that they correspond to queries such as select, join, union, etc. One feature of our construction is that the schema of a simplicial database has a natural geometric structure: an underlying simplicial set. The geometry of a schema is a way of keeping track of relationships between distinct tables, and can be thought of as a system of foreign keys. The shape of a schema is generally intuitive (e.g. the schema for round-trip flights is a circle consisting of an edge from $A$ to $B$ and an edge from $B$ to $A$), and as such, may be useful for analyzing data. We give several applications of our approach, as well as possible advantages it has over the relational model. We also indicate some directions for further research.


Stochastic Service Guarantee Analysis Based on Time-Domain Models

Abstract: Stochastic network calculus is a theory for stochastic service guarantee analysis of computer communication networks. In the current stochastic network calculus literature, its traffic and server models are typically based on the cumulative amount of traffic and cumulative amount of service respectively. However, there are network scenarios where the applicability of such models is limited, and hence new ways of modeling traffic and service are needed to address this limitation. This paper presents time-domain models and results for stochastic network calculus. Particularly, we define traffic models, which are based on probabilistic lower-bounds on cumulative packet inter-arrival time, and server models, which are based on probabilistic upper-bounds on cumulative packet service time. In addition, examples demonstrating the use of the proposed time-domain models are provided. On the basis of the proposed models, the five basic properties of stochastic network calculus are also proved, which implies broad applicability of the proposed time-domain approach.


A new Protocol for 1-2 Oblivious Transfer

Abstract: A new protocol for 1-2 (String) Oblivious Transfer is proposed. The protocol uses 5 rounds of message exchange.


A Near-Optimal Algorithm for L1-Difference

Abstract: We give the first L_1-sketching algorithm for integer vectors which produces nearly optimal sized sketches in nearly linear time. This answers the first open problem in the list of open problems from the 2006 IITK Workshop on Algorithms for Data Streams. Specifically, suppose Alice receives a vector x in {-M,...,M}^n and Bob receives y in {-M,...,M}^n, and the two parties share randomness. Each party must output a short sketch of their vector such that a third party can later quickly recover a (1 +/- eps)-approximation to ||x-y||_1 with 2/3 probability given only the sketches. We give a sketching algorithm which produces O(eps^{-2}log(1/eps)log(nM))-bit sketches in O(n*log^2(nM)) time, independent of eps. The previous best known sketching algorithm for L_1 is due to [Feigenbaum et al., SICOMP 2002], which achieved the optimal sketch length of O(eps^{-2}log(nM)) bits but had a running time of O(n*log(nM)/eps^2). Notice that our running time is near-linear for every eps, whereas for sufficiently small values of eps, the running time of the previous algorithm can be as large as quadratic. Like their algorithm, our sketching procedure also yields a small-space, one-pass streaming algorithm which works even if the entries of x,y are given in arbitrary order.


Cloud Networking Formation in CogMesh Environment

Abstract: As radio spectrum usage paradigm moving from the traditional command and control allocation scheme to the open spectrum allocation scheme, wireless networks meet new opportunities and challenges. In this article we introduce the concept of cognitive wireless mesh (CogMesh) networks and address the unique problem in such a network. CogMesh is a self-organized distributed network architecture combining cognitive technologies with the mesh structure in order to provide a uniform service platform over a wide range of networks. It is based on dynamic spectrum access (DSA) and featured by self-organization, self-configuration and self-healing. The unique problem in CogMesh is the common control channel problem, which is caused by the opportunistic spectrum sharing nature of secondary users (SU) in the network. More precisely, since the channels of SUs are fluctuating according to the radio environment, it is difficult to find always available global common control channels. This puts a significant challenge on the network design. We develop the control cloud based control channel selection and cluster based network formation techniques to tackle this problem. Moreover, we show in this article that the swarm intelligence is a good candidate to deal with the control channel problem in CogMesh. Since the study of cognitive wireless networks (CWN) is still in its early phase, the ideas provided in this article act as a catalyst to inspire new solutions in this field.


Boosting through Optimization of Margin Distributions

Abstract: Boosting has attracted much research attention in the past decade. The success of boosting algorithms may be interpreted in terms of the margin theory. Recently it has been shown that generalization error of classifiers can be obtained by explicitly taking the margin distribution of the training data into account. Most of the current boosting algorithms in practice usually optimizes a convex loss function and do not make use of the margin distribution. In this work we design a new boosting algorithm, termed margin-distribution boosting (MDBoost), which directly maximizes the average margin and minimizes the margin variance simultaneously. This way the margin distribution is optimized. A totally-corrective optimization algorithm based on column generation is proposed to implement MDBoost. Experiments on UCI datasets show that MDBoost outperforms AdaBoost and LPBoost in most cases.


The Power of Depth 2 Circuits over Algebras

Abstract: We study the problem of polynomial identity testing (PIT) for depth 2 arithmetic circuits over matrix algebra. We show that identity testing of depth 3 (Sigma-Pi-Sigma) arithmetic circuits over a field F is polynomial time equivalent to identity testing of depth 2 (Pi-Sigma) arithmetic circuits over U_2(F), the algebra of upper-triangular 2 x 2 matrices with entries from F. Such a connection is a bit surprising since we also show that, as computational models, Pi-Sigma circuits over U_2(F) are strictly `weaker' than Sigma-Pi-Sigma circuits over F. The equivalence further shows that PIT of depth 3 arithmetic circuits reduces to PIT of width-2 planar commutative Algebraic Branching Programs (ABP). Thus, identity testing for commutative ABPs is interesting even in the case of width-2. Further, we give a deterministic polynomial time identity testing algorithm for a Pi-Sigma circuit over any constant dimensional commutative algebra over F. While over commutative algebras of polynomial dimension, identity testing is at least as hard as that of Sigma-Pi-Sigma circuits over F.


Complementary cooperation, minimal winning coalitions, and power indices

Abstract: We introduce a new simple game, which is referred to as the complementary weighted multiple majority game (C-WMMG for short). C-WMMG models a basic cooperation rule, the complementary cooperation rule, and can be taken as a sister model of the famous weighted majority game (WMG for short). In this paper, we concentrate on the two dimensional C-WMMG. An interesting property of this case is that there are at most $n+1$ minimal winning coalitions (MWC for short), and they can be enumerated in time $O(n\log n)$, where $n$ is the number of players. This property guarantees that the two dimensional C-WMMG is more handleable than WMG. In particular, we prove that the main power indices, i.e. the Shapley-Shubik index, the Penrose-Banzhaf index, the Holler-Packel index, and the Deegan-Packel index, are all polynomially computable. To make a comparison with WMG, we know that it may have exponentially many MWCs, and none of the four power indices is polynomially computable (unless P=NP). Still for the two dimensional case, we show that local monotonicity holds for all of the four power indices. In WMG, this property is possessed by the Shapley-Shubik index and the Penrose-Banzhaf index, but not by the Holler-Packel index or the Deegan-Packel index. Since our model fits very well the cooperation and competition in team sports, we hope that it can be potentially applied in measuring the values of players in team sports, say help people give more objective ranking of NBA players and select MVPs, and consequently bring new insights into contest theory and the more general field of sports economics. It may also provide some interesting enlightenments into the design of non-additive voting mechanisms. Last but not least, the threshold version of C-WMMG is a generalization of WMG, and natural variants of it are closely related with the famous airport game and the stable marriage/roommates problem.


Selfish Bin Covering

Abstract: In this paper, we address the selfish bin covering problem, which is greatly related both to the bin covering problem, and to the weighted majority game. What we mainly concern is how much the lack of coordination harms the social welfare. Besides the standard PoA and PoS, which are based on Nash equilibrium, we also take into account the strong Nash equilibrium, and several other new equilibria. For each equilibrium, the corresponding PoA and PoS are given, and the problems of computing an arbitrary equilibrium, as well as approximating the best one, are also considered.


On stratified regions

Abstract: Type and effect systems are a tool to analyse statically the behaviour of programs with effects. We present a proof based on the so called reducibility candidates that a suitable stratification of the type and effect system entails the termination of the typable programs. The proof technique covers a simply typed, multi-threaded, call-by-value lambda-calculus, equipped with a variety of scheduling (preemptive, cooperative) and interaction mechanisms (references, channels, signals).


A Distributed Software Architecture for Collaborative Teleoperation based on a VR Platform and Web Application Interoperability

Abstract: Augmented Reality and Virtual Reality can provide to a Human Operator (HO) a real help to complete complex tasks, such as robot teleoperation and cooperative teleassistance. Using appropriate augmentations, the HO can interact faster, safer and easier with the remote real world. In this paper, we present an extension of an existing distributed software and network architecture for collaborative teleoperation based on networked human-scaled mixed reality and mobile platform. The first teleoperation system was composed by a VR application and a Web application. However the 2 systems cannot be used together and it is impossible to control a distant robot simultaneously. Our goal is to update the teleoperation system to permit a heterogeneous collaborative teleoperation between the 2 platforms. An important feature of this interface is based on different Mobile platforms to control one or many robots.


Colorful Strips

Abstract: Given a planar point set and an integer $k$, we wish to color the points with $k$ colors so that any axis-aligned strip containing enough points contains all colors. The goal is to bound the necessary size of such a strip, as a function of $k$. We show that if the strip size is at least $2k{-}1$, such a coloring can always be found. We prove that the size of the strip is also bounded in any fixed number of dimensions. In contrast to the planar case, we show that deciding whether a 3D point set can be 2-colored so that any strip containing at least three points contains both colors is NP-complete. We also consider the problem of coloring a given set of axis-aligned strips, so that any sufficiently covered point in the plane is covered by $k$ colors. We show that in $d$ dimensions the required coverage is at most $d(k{-}1)+1$. Lower bounds are given for the two problems. This complements recent impossibility results on decomposition of strip coverings with arbitrary orientations. Finally, we study a variant where strips are replaced by wedges.


Crossing-Optimal Acyclic HP-Completion for Outerplanar st-Digraphs

Abstract: Given an embedded planar acyclic digraph G, we define the problem of acyclic hamiltonian path completion with crossing minimization (Acyclic-HPCCM) to be the problem of determining a hamiltonian path completion set of edges such that, when these edges are embedded on G, they create the smallest possible number of edge crossings and turn G to a hamiltonian acyclic digraph. Our results include: 1. We provide a characterization under which a planar st-digraph G is hamiltonian. 2. For an outerplanar st-digraph G, we define the st-polygon decomposition of G and, based on its properties, we develop a linear-time algorithm that solves the Acyclic-HPCCM problem. 3. For the class of planar st-digraphs, we establish an equivalence between the Acyclic-HPCCM problem and the problem of determining an upward 2-page topological book embedding with minimum number of spine crossings. We infer (based on this equivalence) for the class of outerplanar st-digraphs an upward topological 2-page book embedding with minimum number of spine crossings. To the best of our knowledge, it is the first time that edge-crossing minimization is studied in conjunction with the acyclic hamiltonian completion problem and the first time that an optimal algorithm with respect to spine crossing minimization is presented for upward topological book embeddings.


On the Cooperation of the Constraint Domains H, R and FD in CFLP

Abstract: This paper presents a computational model for the cooperation of constraint domains and an implementation for a particular case of practical importance. The computational model supports declarative programming with lazy and possibly higher-order functions, predicates, and the cooperation of different constraint domains equipped with their respective solvers, relying on a so-called Constraint Functional Logic Programming (CFLP) scheme. The implementation has been developed on top of the CFLP system TOY, supporting the cooperation of the three domains H, R and FD, which supply equality and disequality constraints over symbolic terms, arithmetic constraints over the real numbers, and finite domain constraints over the integers, respectively. The computational model has been proved sound and complete w.r.t. the declarative semantics provided by the $CFLP$ scheme, while the implemented system has been tested with a set of benchmarks and shown to behave quite efficiently in comparison to the closest related approach we are aware of. To appear in Theory and Practice of Logic Programming (TPLP)


Inferring Dynamic Bayesian Networks using Frequent Episode Mining

Abstract: Motivation: Several different threads of research have been proposed for modeling and mining temporal data. On the one hand, approaches such as dynamic Bayesian networks (DBNs) provide a formal probabilistic basis to model relationships between time-indexed random variables but these models are intractable to learn in the general case. On the other, algorithms such as frequent episode mining are scalable to large datasets but do not exhibit the rigorous probabilistic interpretations that are the mainstay of the graphical models literature. Results: We present a unification of these two seemingly diverse threads of research, by demonstrating how dynamic (discrete) Bayesian networks can be inferred from the results of frequent episode mining. This helps bridge the modeling emphasis of the former with the counting emphasis of the latter. First, we show how, under reasonable assumptions on data characteristics and on influences of random variables, the optimal DBN structure can be computed using a greedy, local, algorithm. Next, we connect the optimality of the DBN structure with the notion of fixed-delay episodes and their counts of distinct occurrences. Finally, to demonstrate the practical feasibility of our approach, we focus on a specific (but broadly applicable) class of networks, called excitatory networks, and show how the search for the optimal DBN structure can be conducted using just information from frequent episodes. Application on datasets gathered from mathematical models of spiking neurons as well as real neuroscience datasets are presented. Availability: Algorithmic implementations, simulator codebases, and datasets are available from our website at http://neural-code.cs.vt.edu/dbn


A Weakly-Robust PTAS for Minimum Clique Partition in Unit Disk Graphs

Abstract: We consider the problem of partitioning the set of vertices of a given unit disk graph (UDG) into a minimum number of cliques. The problem is NP-hard and various constant factor approximations are known, with the current best ratio of 3. Our main result is a {\em weakly robust} polynomial time approximation scheme (PTAS) for UDGs expressed with edge-lengths, it either (i) computes a clique partition or (ii) gives a certificate that the graph is not a UDG; for the case (i) that it computes a clique partition, we show that it is guaranteed to be within $(1+\eps)$ ratio of the optimum if the input is UDG; however if the input is not a UDG it either computes a clique partition as in case (i) with no guarantee on the quality of the clique partition or detects that it is not a UDG. Noting that recognition of UDG's is NP-hard even if we are given edge lengths, our PTAS is a weakly-robust algorithm. Our algorithm can be transformed into an $O(\frac{\log^* n}{\eps^{O(1)}})$ time distributed PTAS. We consider a weighted version of the clique partition problem on vertex weighted UDGs that generalizes the problem. We note some key distinctions with the unweighted version, where ideas useful in obtaining a PTAS breakdown. Yet, surprisingly, it admits a $(2+\eps)$-approximation algorithm for the weighted case where the graph is expressed, say, as an adjacency matrix. This improves on the best known 8-approximation for the {\em unweighted} case for UDGs expressed in standard form.


The equality problem for infinite words generated by primitive morphisms

Abstract: We study the equality problem for infinite words obtained by iterating morphisms. In particular, we give a practical algorithm to decide whether or not two words generated by primitive morphisms are equal.


A Comprehensive study of a New Multipath Energy Aware Routing Protocol for Mobile Ad-hoc Networks

Abstract: Maximizing network lifetime is a very challenging issue in routing protocol design for Mobile Ad-hoc NETworks (MANETs), since mobile nodes are powered by limited-capacity batteries. Furthermore, replacing or recharging batteries is often impossible in critical environments (e.g. battlefields, disaster areas, etc.) The proposed MEA-DSR (Multipath Energy-Aware on Demand Source Routing) protocol uses a load distribution policy in order to maximize network lifetime. The simulation results have shown the efficiency of the proposed protocol in comparison to DSR routing protocol in many difficult scenarios


On irreversible dynamic monopolies in general graphs

Abstract: Consider the following coloring process in a simple directed graph $G(V,E)$ with positive indegrees. Initially, a set $S$ of vertices are white, whereas all the others are black. Thereafter, a black vertex is colored white whenever more than half of its in-neighbors are white. The coloring process ends when no additional vertices can be colored white. If all vertices end up white, we call $S$ an irreversible dynamic monopoly (or dynamo for short) under the strict-majority scenario. An irreversible dynamo under the simple-majority scenario is defined similarly except that a black vertex is colored white when at least half of its in-neighbors are white. We derive upper bounds of $(2/3)\,|\,V\,|$ and $|\,V\,|/2$ on the minimum sizes of irreversible dynamos under the strict and the simple-majority scenarios, respectively. For the special case when $G$ is an undirected connected graph, we prove the existence of an irreversible dynamo with size at most $\lceil |\,V\,|/2 \rceil$ under the strict-majority scenario. Let $\epsilon>0$ be any constant. We also show that, unless $\text{NP}\subseteq \text{TIME}(n^{O(\ln \ln n)}),$ no polynomial-time, $((1/2-\epsilon)\ln |\,V\,|)$-approximation algorithms exist for finding the minimum irreversible dynamo under either the strict or the simple-majority scenario. The inapproximability results hold even for bipartite graphs with diameter at most 8.


Exact and Approximation Algorithms for Geometric and Capacitated Set Cover Problems with Applications

Abstract: First, we study geometric variants of the standard set cover motivated by assignment of directional antenna and shipping with deadlines, providing the first known polynomial-time exact solutions. Next, we consider the following general capacitated set cover problem. There is given a set of elements with real weights and a family S of sets of elements. One can use a set if it is a subset of one of the sets on our lists and the sum of weights is at most one. The goal is to cover all the elements with the allowed sets.<br>We show that any polynomial-time algorithm that approximates the un-capacitated version of the set cover problem with ratio r can be converted to an approximation algorithm for the capacitated version with ratio r + 1.357.In particular, the composition of these two results yields a polynomial-time approximation algorithm for the problem of covering a set of customers represented by a weighted n-point set with a minimum number of antennas of variable angular range and fixed capacity with ratio 2.357. Finally, we provide a PTAS for the dual problem where the number of sets (e.g., antennas) to use is fixed and the task is to minimize the maximum set load, in case the sets correspond to line intervals or arcs.


Why Global Performance is a Poor Metric for Verifying Convergence of Multi-agent Learning

Abstract: Experimental verification has been the method of choice for verifying the stability of a multi-agent reinforcement learning (MARL) algorithm as the number of agents grows and theoretical analysis becomes prohibitively complex. For cooperative agents, where the ultimate goal is to optimize some global metric, the stability is usually verified by observing the evolution of the global performance metric over time. If the global metric improves and eventually stabilizes, it is considered a reasonable verification of the system's stability. The main contribution of this note is establishing the need for better experimental frameworks and measures to assess the stability of large-scale adaptive cooperative systems. We show an experimental case study where the stability of the global performance metric can be rather deceiving, hiding an underlying instability in the system that later leads to a significant drop in performance. We then propose an alternative metric that relies on agents' local policies and show, experimentally, that our proposed metric is more effective (than the traditional global performance metric) in exposing the instability of MARL algorithms.


Explicit fairness in testing semantics

Abstract: In this paper we investigate fair computations in the pi-calculus. Following Costa and Stirling's approach for CCS-like languages, we consider a method to label process actions in order to filter out unfair computations. We contrast the existing fair-testing notion with those that naturally arise by imposing weak and strong fairness. This comparison provides insight about the expressiveness of the various `fair' testing semantics and about their discriminating power.


Pricing Randomized Allocations

Abstract: Randomized mechanisms, which map a set of bids to a probability distribution over outcomes rather than a single outcome, are an important but ill-understood area of computational mechanism design. We investigate the role of randomized outcomes (henceforth, "lotteries") in the context of a fundamental and archetypical multi-parameter mechanism design problem: selling heterogeneous items to unit-demand bidders. To what extent can a seller improve her revenue by pricing lotteries rather than items, and does this modification of the problem affect its computational tractability? Our results show that the answers to these questions hinge on whether consumers can purchase only one lottery (the buy-one model) or purchase any set of lotteries and receive an independent sample from each (the buy-many model). In the buy-one model, there is a polynomial-time algorithm to compute the revenue-maximizing envy-free prices (thus overcoming the inapproximability of the corresponding item pricing problem) and the revenue of the optimal lottery system can exceed the revenue of the optimal item pricing by an unbounded factor as long as the number of item types exceeds 4. In the buy-many model with n item types, the profit achieved by lottery pricing can exceed item pricing by a factor of O(log n) but not more, and optimal lottery pricing cannot be approximated within a factor of O(n^eps) for some eps>0, unless NP has subexponential-time randomized algorithms. Our lower bounds rely on a mixture of geometric and algebraic techniques, whereas the upper bounds use a novel rounding scheme to transform a mechanism with randomized outcomes into one with deterministic outcomes while losing only a bounded amount of revenue.


Effective Bounds for P-Recursive Sequences

Abstract: We describe an algorithm that takes as input a complex sequence $(u_n)$ given by a linear recurrence relation with polynomial coefficients along with initial values, and outputs a simple explicit upper bound $(v_n)$ such that $|u_n| \leq v_n$ for all $n$. Generically, the bound is tight, in the sense that its asymptotic behaviour matches that of $u_n$. We discuss applications to the evaluation of power series with guaranteed precision.


Subshifts, Languages and Logic

Abstract: We study the Monadic Second Order (MSO) Hierarchy over infinite pictures, that is tilings. We give a characterization of existential MSO in terms of tilings and projections of tilings. Conversely, we characterise logic fragments corresponding to various classes of infinite pictures (subshifts of finite type, so?c subshifts).


One-Counter Markov Decision Processes

Abstract: We study the computational complexity of central analysis problems for One-Counter Markov Decision Processes (OC-MDPs), a class of finitely-presented, countable-state MDPs. OC-MDPs are equivalent to a controlled extension of (discrete-time) Quasi-Birth-Death processes (QBDs), a stochastic model studied heavily in queueing theory and applied probability. They can thus be viewed as a natural ``adversarial'' version of a classic stochastic model. Alternatively, they can also be viewed as a natural probabilistic/controlled extension of classic one-counter automata. OC-MDPs also subsume (as a very restricted special case) a recently studied MDP model called ``solvency games'' that model a risk-averse gambling scenario. Basic computational questions about these models include ``termination'' questions and ``limit'' questions, such as the following: does the controller have a ``strategy'' (or ``policy'') to ensure that the counter (which may for example count the number of jobs in the queue) will hit value 0 (the empty queue) almost surely (a.s.)? Or that it will have infinite limsup value, a.s.? Or, that it will hit value 0 in selected terminal states, a.s.? Or, in case these are not satisfied a.s., compute the maximum (supremum) such probability over all strategies. We provide new upper and lower bounds on the complexity of such problems. For some of them we present a polynomial-time algorithm, whereas for others we show PSPACE- or BH-hardness and give an EXPTIME upper bound. Our upper bounds combine techniques from the theory of MDP reward models, the theory of random walks, and a variety of automata-theoretic methods.


Universal Structures and the logic of Forbidden Patterns

Abstract: Forbidden Patterns Problems (FPPs) are a proper generalisation of Constraint Satisfaction Problems (CSPs). However, we show that when the input is connected and belongs to a class which has low tree-depth decomposition (e.g. structure of bounded degree, proper minor closed class and more generally class of bounded expansion) any FPP becomes a CSP. This result can also be rephrased in terms of expressiveness of the logic MMSNP, introduced by Feder and Vardi in relation with CSPs. Our proof generalises that of a recent paper by Nesetril and Ossona de Mendez. Note that our result holds in the general setting of problems over arbitrary relational structures (not just for graphs).


What does Newcomb's paradox teach us?

Abstract: In Newcomb's paradox you choose to receive either the contents of a particular closed box, or the contents of both that closed box and another one. Before you choose though, an antagonist uses a prediction algorithm to deduce your choice, and fills the two boxes based on that deduction. Newcomb's paradox is that game theory's expected utility and dominance principles appear to provide conflicting recommendations for what you should choose. A recent extension of game theory provides a powerful tool for resolving paradoxes concerning human choice, which formulates such paradoxes in terms of Bayes nets. Here we apply this to ol to Newcomb's scenario. We show that the conflicting recommendations in Newcomb's scenario use different Bayes nets to relate your choice and the algorithm's prediction. These two Bayes nets are incompatible. This resolves the paradox: the reason there appears to be two conflicting recommendations is that the specification of the underlying Bayes net is open to two, conflicting interpretations. We then show that the accuracy of the prediction algorithm in Newcomb's paradox, the focus of much previous work, is irrelevant. We similarly show that the utility functions of you and the antagonist are irrelevant. We end by showing that Newcomb's paradox is time-reversal invariant; both the paradox and its resolution are unchanged if the algorithm makes its `prediction' \emph{after} you make your choice rather than before.


Disproof of the Neighborhood Conjecture with Implications to SAT

Abstract: We study a Maker/Breaker game described by Beck. As a result we disprove a conjecture of Beck on positional games, establish a connection between this game and SAT and construct an unsatisfiable k-CNF formula with few occurrences per variable, thereby improving a previous result by Hoory and Szeider and showing that the bound obtained from the Lovasz Local Lemma is tight up to a constant factor. The Maker/Breaker game we study is as follows. Maker and Breaker take turns in choosing vertices from a given n-uniform hypergraph F, with Maker going first. Maker's goal is to completely occupy a hyperedge and Breaker tries to avoid this. Beck conjectures that if the maximum neighborhood size of F is at most 2^(n-1) then Breaker has a winning strategy. We disprove this conjecture by establishing an n-uniform hypergraph with maximum neighborhood size 3*2^(n - 3) where Maker has a winning strategy. Moreover, we show how to construct an n-uniform hypergraph with maximum degree (2^(n-1))/n where maker has a winning strategy. Finally, we establish a connection between SAT and the Maker/Breaker game we study. We can use this connection to derive new results in SAT. Kratochvil, Savicky and Tuza showed that for every k >= 3 there is an integer f(k) such that every (k,f(k))-formula is satisfiable, but (k,f(k) + 1)-SAT is already NP-complete (it is not known whether f(k) is computable). Kratochvil, Savicky and Tuza also gave the best known lower bound f(k) = Omega(2^k/k), which is a consequence of the Lovasz Local Lemma. We prove that, in fact, f(k) = Theta(2^k/k), improving upon the best known upper bound O((log k) * 2^k/k) by Hoory and Szeider.


Geodesic Paths On 3D Surfaces: Survey and Open Problems

Abstract: This survey gives a brief overview of theoretically and practically relevant algorithms to compute geodesic paths and distances on three-dimensional surfaces. The survey focuses on polyhedral three-dimensional surfaces.


PTAS for k-tour cover problem on the plane for moderately large values of k

Abstract: Let P be a set of n points in the Euclidean plane and let O be the origin point in the plane. In the k-tour cover problem (called frequently the capacitated vehicle routing problem), the goal is to minimize the total length of tours that cover all points in P, such that each tour starts and ends in O and covers at most k points from P. The k-tour cover problem is known to be NP-hard. It is also known to admit constant factor approximation algorithms for all values of k and even a polynomial-time approximation scheme (PTAS) for small values of k, i.e., k=O(log n / log log n). We significantly enlarge the set of values of k for which a PTAS is provable. We present a new PTAS for all values of k <= 2^{log^{\delta}n}, where \delta = \delta(\epsilon). The main technical result proved in the paper is a novel reduction of the k-tour cover problem with a set of n points to a small set of instances of the problem, each with O((k/\epsilon)^O(1)) points.