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A minimal perfect hash function h for a set S ⊆ U of size n is a function $h\colon U\to \{0,\ldots,n-1\}$ that is one-to-one on S. The complexity measures of interest are storage space for h, evaluation time (which should be constant), and construction time. The talk gives an overview of several recent randomized constructions of minimal perfect hash functions, leading to space-efficient solutions that are fast in practice. A central issue is a method ("split-and-share") that makes it possible to assume that fully random (hash) functions are available. [ABSTRACT FROM AUTHOR]

In this paper we study the support sizes of evolutionary stable strategies (ESS) in random evolutionary games. We prove that, when the elements of the payoff matrix behave either as uniform, or normally distributed independent random variables, almost all ESS have support sizes o(n), where n is the number of possible types for a player. Our arguments are based exclusively on the severity of a stability property that the payoff submatrix indicated by the support of an ESS must satisfy. We then combine our normal-random result with a recent result of McLennan and Berg (2005), concerning the expected number of Nash Equilibria in normal-random bimatrix games, to show that the expected number of ESS is significantly smaller than the expected number of symmetric Nash equilibria of the underlying symmetric bimatrix game. JEL Classification Code: C7 - Game Theory and Bargaining Theory. [ABSTRACT FROM AUTHOR]

Orthogonal variable spreading factor (OVSF) codes are widely used to provide variable data rates for supporting different bandwidth requirements in wideband code division multiple access (WCDMA) systems. Many works in the literature have intensively investigated to find an optimal dynamic code assignment scheme for OVSF codes. Unlike earlier studies, which assign OVSF codes using conventional (CCA) or dynamic (DCA) code allocation schemes, in this paper, stochastic optimization methods which are genetic algorithm (GA) and simulated annealing (SA) were applied which population is adaptively constructed according to existing traffic density in the OVSF code-tree. Also, the influences of the GA (selection, crossover and mutation techniques) and the SA (cooling schedules, number of inner loop) parameters were examined on the dynamic OVSF code allocation problem. Simulation results show that the GA and SA provide reduced code blocking probability and improved spectral efficiency when compared to the CCA and DCA schemes. [ABSTRACT FROM AUTHOR]

Quantum finite automata with mixed states are proved to be super-exponentially more concise rather than quantum finite automata with pure states. It was proved earlier by A.Ambainis and R.Freivalds that quantum finite automata with pure states can have exponentially smaller number of states than deterministic finite automata recognizing the same language. There was a never published "folk theorem" proving that quantum finite automata with mixed states are no more than super-exponentially more concise than deterministic finite automata. It was not known whether the super-exponential advantage of quantum automata is really achievable. We prove that there is an infinite sequence of distinct integers n such that there are languages Ln such that there are quantum finite automata with mixed states with 5n states recognizing the language Ln with probability $\frac{3}{4} $ while any deterministic finite automaton recognizing Ln needs to have at least eO(nlnn) states. Unfortunately, the alphabet for these languages grows with n. In order to prove a similar result for languages in a fixed alphabet we consider a counterpart of Hamming codes for permutations of finite sets, i.e. sets of permutations such that any two distinct permutations in the set have Hamming distance at least d. The difficulty arises from the fact that in the traditional Hamming codes for binary strings positions in the string are independent while positions in a permutation are not independent. For instance, any two permutations of the same set either coinside or their Hamming distance is at least 2. The main combinatorial problem still remains open. [ABSTRACT FROM AUTHOR]

A two-way finite automaton is sweeping if its input head can change direction only on the end-markers. For each n ≥ 2, we exhibit a problem that can be solved by a O(n2)-state sweeping LasVegas automaton, but needs 2Ω(n) states on every sweeping deterministic automaton. [ABSTRACT FROM AUTHOR]

"Hit-and-run is fast and fun" to generate a random point in a high dimensional convex set K (Lovász/Vempala, MSR-TR-2003-05). More precisely, the hit-and-run random walk mixes fast independently of where it is started inside the convex set. To hit-and-run from a point , a line L through is randomly chosen (uniformly over all directions). Subsequently, the walk's next point is sampled from L ∩ K using a membership oracle which tells us whether a point is in K or not. Here the focus is on black-box optimization, however, where the function to be minimized is given as an oracle, namely a black box for f-evaluations. We obtain in an obvious way a direct-search method when we substitute the f-oracle for the K-membership oracle to do a line search over L, and, naturally, we are interested in how fast such a hit-and-run direct-search heuristic converges to the optimum point in the search space . We prove that, even under the assumption of perfect line search, the search converges (at best) linearly at an expected rate larger (worse) than 1 − 1/n. This implies a lower bound of 0.5 n on the expected number of line searches necessary to halve the approximation error. Moreover, we show that 0.4 n line searches suffice to halve the approximation error only with an exponentially small probability of $\exp(-\Omega(n^{1/3}))$. Since each line search requires at least one query to the f-oracle, the lower bounds obtained hold also for the number of f-evaluations. [ABSTRACT FROM AUTHOR]

We introduce a new approach for randomizing the digit sets of binary integer representations used in elliptic curve cryptography, and present a formal analysis of the sparsity of such representations. The motivation is to improve the sparseness of integer representations and to provide a tool for defense against side channel attacks. Existing alternative digit sets D such as D = {0,1, − 1} require a certain non-adjacency property (no two successive digits are non-zero) in order to attain the desired level of sparseness. Our digit sets do not rely on the non-adjacency property, which in any case is only possible for a certain very restricted class of digit sets, but nevertheless achieve better sparsity. For example, we construct a large explicit family of digit sets for which the resulting integer representations consist on average of 74% zeros, which is an improvement over the 67% sparsity available using non-adjacent form representations. Our proof of the sparsity result is novel and is dramatically simpler than the existing analyses of non-adjacent form representations available in the literature, in addition to being more general. We conclude with some performance comparisons and an analysis of the resilience of our implementation against side channel attacks under an attack model called the open representation model. We emphasize that our side channel analysis remains preliminary and that our attack model represents only a first step in devising a formal framework for assessing the security of randomized representations as a side channel attack countermeasure. [ABSTRACT FROM AUTHOR]

Motivated by an application in project portfolio analysis under uncertainty, we develop an algorithm S-VNS for solving stochastic combinatorial optimization (SCO) problems based on the Variable Neighborhood Search (VNS) metaheuristic, and show its theoretical soundness by a mathematical convergence result. S-VNS is the first general-purpose algorithm for SCO problems using VNS. It combines a classical VNS search strategy with a sampling approach with suitably increasing sample size. After the presentation of the algorithm, the considered application problem in project management, which combines a project portfolio decision on an upper level and project scheduling as well as staff assignment decisions on a lower level, is described. Uncertain work times require a treatment as an SCO problem. First experimental results on the application of S-VNS to this problem are outlined. [ABSTRACT FROM AUTHOR]

In the layered-graph query model of network discovery, a query at a node v of an undirected graph G discovers all edges and non-edges whose endpoints have different distance from v. We study the number of queries at randomly selected nodes that are needed for approximate network discovery in Erdős-Rényi random graphs Gn,p. We show that a constant number of queries is sufficient if p is a constant, while Ω(nα) queries are needed if p = nε/n, for arbitrarily small choices of ε = 3 / (6 ·i + 5) with i ∈ ℕ. Note that α> 0 is a constant depending only on ε. Our proof of the latter result yields also a somewhat surprising result on pairwise distances in random graphs which may be of independent interest: We show that for a random graph Gn,p with p = nε/n, for arbitrarily small choices of ε> 0 as above, in any constant cardinality subset of the nodes the pairwise distances are all identical with high probability. [ABSTRACT FROM AUTHOR]

The line-of-sight networks is a network model introduced recently by Frieze et al. It considers wireless networks in which the underlying environment has a large number of obstacles and the communication can only take place between objects that are close in space and are in the line of sight to one another. To capture the main properties of this model, Frieze et al. proposed a new random networks model in which nodes are randomly placed on an n ×n grid and a node can communicate with all the nodes that are in at most a certain fixed distance r and which are in the same row or column. Frieze et al. concentrated their study on basic structural properties of the random line-of-sight networks and in this paper we focus on their communication aspects in the scenario of ad-hoc radio communication networks. We present efficient algorithms for two fundamental communication problems of broadcasting and gossiping in the classical ad-hoc radio communication model adjusted to random line-of-sight networks. [ABSTRACT FROM AUTHOR]

We initiate studying the convergence time to Nash equilibria in player-specific singleton congestion games. We consider simple games that have natural representations as graphs as we assume that each player chooses between two resources. We are not able to present an analysis for general graphs. However, we present first results for interesting classes of graphs. For the class of games that are represented as trees, we show that every best-response schedule terminates after O(n2) steps. We also consider games that are represented as circles. We show that deterministic best response schedules may cycle, whereas the random best response schedule, which selects the next player to play a best response uniformly at random, terminates after O(n2) steps in expectation. These results imply that in player-specific congestion games in which each player chooses between two resources, and each resource is allocated by at most two players, the random best response schedule terminates quickly. Our analysis reveals interesting relationships between random walks on lines and the random best response schedule. [ABSTRACT FROM AUTHOR]

Devices connected wirelessly, in various forms including computers, hand-held devices, ad hoc networks, and embedded systems, are expected to become ubiquitous all around us. Wireless networks pose interesting new challenges, some of which do not arise in standard (wired) networks. This survey discusses some key probabilistic notions - both randomized algorithms and probabilistic analysis - in wireless networking. [ABSTRACT FROM AUTHOR]

We consider applications of probabilistic techniques in the framework of algorithmic game theory. We focus on three distinct case studies: (i) The exploitation of the probabilistic method to demonstrate the existence of approximate Nash equilibria of logarithmic support sizes in bimatrix games; (ii) the analysis of the statistical conflict that mixed strategies cause in network congestion games; (iii) the effect of coalitions in the quality of congestion games on parallel links. [ABSTRACT FROM AUTHOR]

For a given graph with weighted vertices, the goal of the minimum-weight dominating set problem is to compute a vertex subset of smallest weight such that each vertex of the graph is contained in the subset or has a neighbor in the subset. A unit disk graph is a graph in which each vertex corresponds to a unit disk in the plane and two vertices are adjacent if and only if their disks have a non-empty intersection. We present the first constant-factor approximation algorithm for the minimum-weight dominating set problem in unit disk graphs, a problem motivated by applications in wireless ad-hoc networks. The algorithm is obtained in two steps: First, the problem is reduced to the problem of covering a set of points located in a small square using a minimum-weight set of unit disks. Then, a constant-factor approximation algorithm for the latter problem is obtained using enumeration and dynamic programming techniques exploiting the geometry of unit disks. Furthermore, we also show how to obtain a constant-factor approximation algorithm for the minimum-weight connected dominating set problem in unit disk graphs. [ABSTRACT FROM AUTHOR]

Consider a scenario where base stations need to send data to users with wireless devices. Time is discrete and slotted into synchronous rounds. Transmitting a data item from a base station to a user takes one round. A user can receive the data item from any of the base stations. The positions of the base stations and users are modeled as points in Euclidean space. If base station b transmits to user u in a certain round, no other user within distance at most from b can receive data in the same round due to interference phenomena. The goal is to minimize, given the positions of the base stations and users, the number of rounds until all users have their data. We call this problem the Joint Base Station Scheduling Problem (JBS) and consider it on the line (1D-JBS) and in the plane (2D-JBS). For 1D-JBS, we give a 2-approximation algorithm and polynomial optimal algorithms for special cases. We model transmissions from base stations to users as arrows (intervals with a distinguished endpoint) and show that their conflict graphs, which we call arrow graphs, are a subclass of the class of perfect graphs. For 2D-JBS, we prove NP-hardness and discuss an approximation algorithm. [ABSTRACT FROM AUTHOR]

10.1. Deterministic Models 10.1.1. Measuring Structural Equivalence 10.1.2. Multidimensional Scaling 10.1.3. Clustering Based Methods 10.1.4. CONCOR 10.1.5. Computing the Image Matrix 10.1.6. Goodness-of-Fit Indices 10.1.7. Generalized Blockmodeling 10.2. Stochastic Models 10.2.1. The p1 Model 10.2.2. Goodness-of-Fit Indices 10.2.3. Blockmodels and p110.2.4. Posterior Blockmodel Estimation 10.2.5. p* Models 10.3. Chapter Notes [ABSTRACT FROM AUTHOR]

Many models in theoretical computer science allow for computations or representations where the answer is only slightly biased in the right direction. The best-known of these is the complexity class PP, for "probabilistic polynomial time". A language is in PP if there is a randomized polynomial-time Turing machine whose acceptance probability is greater than 1/2 if, and only if, its input is in the language. Most computational complexity classes have an analogous class in communication complexity. The class PP in fact has two, a version with weakly restricted bias called PPcc, and a version with unrestricted bias called UPPcc. Ever since their introduction by Babai, Frankl, and Simon in 1986, it has been open whether these classes are the same. We show that PPcc is strictly included in UPPcc. Our proof combines a query complexity separation due to Beigel with a technique of Razborov that translates the acceptance probability of quantum protocols to polynomials. We will discuss some complexity theoretical consequences of this separation. This presentation is bases on joined work with Nikolay Vereshchagin and Ronald de Wolf. [ABSTRACT FROM AUTHOR]