A parallel algorithmic version of the local lemma

Abstract

The Lovasz local lemma (1975) is a tool that enables one to show that certain events hold with positive, though very small probability. It often yields existence proofs of results without supplying any efficient way of solving the corresponding algorithmic problems. J. Beck has recently found a method for converting some of these existence proofs into efficient algorithmic procedures, at the cost of losing a little in the estimates, but his method does not seem to be parallelizable. His technique is modified to achieve an algorithmic version that can be parallelized, thus providing deterministic NC/sup 1/ algorithms for various interesting algorithmic search problems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>