Fast parallel algorithms for coloring random graphs
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(log4n/ 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.
the class of all k-colorable graphs, uniformly chosen. We present a parallel algorithm which actually constructs the coloring in expected parallel time O(log2n), 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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