A major difficulty in evaluating incomplete local search style algorithms for constraint satisfaction problems is the need for a source of hard problem instances that are guaranteed to be satisfiable. A standard approach to evaluate incomplete search methods has been to use a general problem generator and a complete search method to filter out the unsatisfiable instances. Unfortunately, this approach cannot be used to create problem instances that are beyond the reach of complete search methods. So far, it has proven to be surprisingly difficult to develop a direct generator for satisfiable instances only. In this paper, we propose a generator that only outputs satisfiable problem instances. We also show how one can finely control the hardness of the satisfiable instances by establishing a connection between problem hardness and a new kind of phase transition phenomenon in the space of problem instances. Finally, we use our problem distribution to show the easy-hard-easy pattern in search complexity for local search procedures, analogous to the previously reported pattern for complete search methods.

We present a novel distributed algorithm for constructing random overlay networks that are composed of d Hamilton cycles. The protocol is completely decentralized as no globally-known server is required. The constructed topologies are expanders with O(log d n) diameter with high probability.

ABSTRACT: We consider the following probabilistic model of a graph on n labeled vertices. First choose a random graph Gn,1�2 Ž., and then choose randomly a subset Q of vertices of size k and force it to be a clique by joining every pair of vertices of Q by an edge. The problem is to give a polynomial time algorithm for finding this hidden clique almost surely for various values of k. This question was posed independently, in various variants, by Jerrum and by Kucera. In this paper we present an efficient algorithm for all k�cn0.5 ˇ, for

We study the algorithmic and structural properties of very large, realistic social contact networks. We consider the social network for the city of Portland, Oregon, USA, developed as a part of the TRANSIMS/EpiSims project at the Los Alamos National Laboratory. The most expressive social contact network is a bipartite graph, with two types of nodes: people and locations; edges represent people visiting locations on a typical day. Three types of results are presented. (i) Our empirical results show that many basic characteristics of the dataset are well-modeled by a random graph approach suggested by Fan Chung Graham and Lincoln Lu (the CL-model), with a power-law degree distribution. (ii) We obtain fast approximation algorithms for computing

Upper bounds on probabilities of large deviations for sums of bounded independent random variables may be extended to handle functions which depend in a limited way on a number of independent random variables. This ‘method of bounded differences’ has over the last dozen or so years had a great impact in probabilistic methods in discrete mathematics and in the mathematics of operational research and theoretical computer science. Recently Talagrand introduced an exciting new method for bounding probabilities of large deviations, which often proves superior to the bounded differences approach. In this paper we

Abstract. We study the Lovász number ϑ along with two further SDP relaxations ϑ1/2, ϑ2 of the independence number and the corresponding relaxations ¯ ϑ, ¯ ϑ1/2, ¯ ϑ2 of the chromatic number on random graphs Gn,p. We prove that ϑ, ϑ1/2, ϑ2(Gn,p) are concentrated about their means, and that ¯ ϑ, ¯ ϑ1/2, ¯ ϑ2(Gn,p) in the case p < n −1/2−ε are concentrated in intervals of constant length. Moreover, extending a result of Juhász [27], we show that ϑ,ϑ1/2, ϑ2(Gn,p) = Θ ( � n/p) and that ¯ ϑ, ¯ ϑ1/2, ¯ ϑ2(Gn,p) = Θ ( √ np) for c0/n ≤ p ≤ 1/2. As an application, we give an improved algorithm for approximating the independence number of Gn,p in polynomial expected time, thereby extending a result of Krivelevich and Vu [33]. We also improve on the analysis of an algorithm of Krivelevich [30] for deciding whether Gn,p is k-colorable. Topics and key words: Lovász number, vector chromatic number, random graphs, maximum independent set problem, graph coloring 1

. In this paper we introduce a general strategy for approximating the solution to minimisation problems in random regular graphs. We describe how the approach can be applied to the minimum vertex cover (MVC), minimum independent dominating set (MIDS) and minimum edge dominating set (MEDS) problems. In almost all cases we are able to improve the best known results for these problems. Results for the MVC problem translate immediately to results for the maximum independent set problem. We also derive lower bounds on the size of an optimal MIDS. 1

Abstract not found

In this paper we survey the work done for graphs on random geometric models. We present some heuristics for the problem of the Minimal Linear Arrangement on [0, 1]² and we conclude with a collection of open problems.

A 2-coloring of a hypergraph is a mapping from its vertices to a set of two colors such that no edge is monochromatic. Let Hk (n; m) be a random k-uniform hypergraph on n vertices formed by picking m edges uniformly, independently and with replacement. It is easy to show that if r rc = 2 ln 2 (ln 2)=2, then with high probability Hk (n; m = rn) is not 2-colorable. We complement this observation by proving that if r rc 1 then with high probability Hk (n; m = rn) is 2-colorable.