# Fast parallel algorithms for coloring random graphs

Conference paper

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## Abstract

We improve here the

*expected*performance of parallel algorithms for graph coloring. This is achieved through new*adaptive*techniques that may be useful for the average-case analysis of many graph algorithms. We apply our techniques to:- (a)
the class

*G*_{ n,p }of random graphs. We present a parallel algorithm which colors the graph with a number of colors at most twice its chromatic number and runs in time O(log^{4}*n/*log log*n*) almost surely, for*p*= Ω((log^{(3)}*n*)^{2}/ log^{(2)}*n*). The number of processors used is O(*m*) where*m*is the number of edges of the graph. - (b)
the class of all

*k*-colorable graphs, uniformly chosen. We present a parallel algorithm which actually*constructs*the coloring in*expected*parallel time O(log^{2}*n*), for constant*k*, by using O(*m*) processors on the average. This problem is not known to have a polynomial time algorithm in the worst case.

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## Copyright information

© Springer-Verlag Berlin Heidelberg 1992