Efficient Parallel Algorithms for (_+1)-coloring and Maximal Indepdendent Set Problems

Abstract

We describe an efficient technique for breaking symmetry in paralle. The technique works especially well on rooted trees and on graphs with a small maximum degree. In particular, we can find a maximal independent set on a constant-degree graph in O(lg*n) time on an EREW PRAM using a linear number of processors. We show how to apply this technique to construct more efficient paralle algorithms for several problems, including coloring of planar graphs and (Δ+1)-coloring of constant-degree graphs. We also prove lower bounds for two related problems.