Exact and approximative algorithms for coloring G(n,p)

We investigate the problem of coloring random graphs G(n, p) in polynomial expected time. For the case p ≤ 1.01/n, we present an algorithm that finds an optimal coloring in linear expected time. For p ≫ ln6(n)/n, we give algorithms which approximate the chromatic number within a factor of O( ). We also obtain an O(/ln(np))‐approximation algorithm for the independence number. As an application, we propose an algorithm for deciding satisfiability of random 2k‐SAT formulas over n propositional variables with ≥ ln7(n)nk clauses in polynomial expected time. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004

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