Results 1  10
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21
Finding a large hidden clique in a random graph
, 1998
"... 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 polynomia ..."
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Cited by 83 (5 self)
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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
Generating satisfiable problem instances
 In AAAI/IAAI
, 2000
"... 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 generat ..."
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Cited by 80 (9 self)
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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 easyhardeasy pattern in search complexity for local search procedures, analogous to the previously reported pattern for complete search methods.
Distributed Construction of Random Expander Networks
 In IEEE Infocom
, 2003
"... 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 globallyknown server is required. The constructed topologies are expanders with O(log d n) diameter with high probability. ..."
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Cited by 77 (0 self)
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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 globallyknown server is required. The constructed topologies are expanders with O(log d n) diameter with high probability.
Structural and Algorithmic Aspects of Massive Social Networks
 in Proceedings of 15th ACMSIAM Symposium on Discrete Algorithms (SODA 2004), 711720, SIAM
, 2004
"... 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 net ..."
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Cited by 34 (3 self)
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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 wellmodeled by a random graph approach suggested by Fan Chung Graham and Lincoln Lu (the CLmodel), with a powerlaw degree distribution. (ii) We obtain fast approximation algorithms for computing
Concentration
, 1998
"... 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 impac ..."
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Cited by 17 (2 self)
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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
The Lovász Number of Random Graphs
 In Proceedings of the 7th International Workshop on Randomization and Approximation Techniques in Computer Science
, 2003
"... 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, ¯ ..."
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Cited by 16 (0 self)
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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 kcolorable. Topics and key words: Lovász number, vector chromatic number, random graphs, maximum independent set problem, graph coloring 1
The smoothed complexity of edit distance
 In Proc. of ICALP
, 2008
"... Abstract. We initiate the study of the smoothed complexity of sequence alignment, by proposing a semirandom model of edit distance between two input strings, generated as follows. First, an adversary chooses two binary strings of length d and a longest common subsequence A of them. Then, every char ..."
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Cited by 11 (3 self)
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Abstract. We initiate the study of the smoothed complexity of sequence alignment, by proposing a semirandom model of edit distance between two input strings, generated as follows. First, an adversary chooses two binary strings of length d and a longest common subsequence A of them. Then, every character is perturbed independently with probability p, except that A is perturbed in exactly the same way inside the two strings. We design two efficient algorithms that compute the edit distance on smoothed instances up to a constant factor approximation. The first algorithm runs in nearlinear time, namely d 1+ε for any fixed ε> 0. The second one runs in time sublinear in d, assuming the edit distance is not too small. These approximation and runtime guarantees are significantly better then the bounds known for worstcase inputs, e.g. nearlinear time algorithm achieving approximation roughly d 1/3, due to Batu, Ergün, and Sahinalp [SODA 2006]. Our technical contribution is twofold. First, we rely on finding matches between substrings in the two strings, where two substrings are considered a match if their edit distance is relatively small, a prevailing technique in commonly used heuristics, such as PatternHunter of Ma, Tromp and Li [Bioinformatics, 2002]. Second, we effectively reduce the smoothed edit distance to a simpler variant of (worstcase) edit distance, namely, edit distance on permutations (a.k.a. Ulam’s metric). We are thus able to build on algorithms developed for the Ulam metric, whose much better algorithmic guarantees usually do not carry over to general edit distance. 1
Greedy Algorithms for Minimisation Problems in Random Regular Graphs
, 2001
"... . 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) proble ..."
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Cited by 10 (4 self)
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. 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
Random Geometric Problems on [0, 1]²
 RANDOMIZATION AND APPROXIMATION TECHNIQUES IN COMPUTER SCIENCE, NUMBER 1518 IN LECTURE NOTES IN COMPUTER SCIENCE
, 1998
"... 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. ..."
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Cited by 5 (2 self)
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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.