The solution of some random NP-hard problems in polynomial expected time
Journal of Algorithms
The greedy coloring is a bad probabilistic algorithm
Journal of Algorithms
A still better performance guarantee for approximate graph coloring
Information Processing Letters
A spectral technique for coloring random 3-colorable graphs (preliminary version)
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Finding a large hidden clique in a random graph
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Finding and certifying a large hidden clique in a semirandom graph
Random Structures & Algorithms
Spectral Techniques in Graph Algorithms
LATIN '98 Proceedings of the Third Latin American Symposium on Theoretical Informatics
Coloring Random Graphs in Polynomial Expected Time
ISAAC '93 Proceedings of the 4th International Symposium on Algorithms and Computation
Zero Knowledge and the Chromatic Number
CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
Clique is hard to approximate within n1-
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Eigenvalues and graph bisection: An average-case analysis
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Go with the Winners Algorithms for Cliques in Random Graphs
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
Efficient Recognition of Random Unsatisfiable k-SAT Instances by Spectral Methods
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
Strong Refutation Heuristics for Random k-SAT
Combinatorics, Probability and Computing
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The independence number of a graph and its chromatic number are hard to approximate. It is known that, unless coRP = NP, there is no polynomial time algorithm which approximates any of these quantities within a factor of n1-Ɛ for graphs on n vertices. We show that the situation is significantly better for the average case. For every edge probability p = p(n) in the range n-1/2+Ɛ ≤ p ≤ 3/4, we present an approximation algorithm for the independence number of graphs on n vertices, whose approximation ratio is O((np)1/2/log n) and whose expected running time over the probability space G(n,p) is polynomial. An algorithm with similar features is described also for the chromatic number. A key ingredient in the analysis of both algorithms is a new large deviation inequality for eigenvalues of random matrices, obtained through an application of Talagrand's inequality.