Efficient parallel algorithms for (5+1)-coloring and maximal independent set problems

An efficient technique for breaking symmetry in parallel is described. The technique works especially well on rooted trees and on graphs with a small maximum degree. In particular, a maximal independent set can be found on a constant-degree graph in O(lg*n) time on an EREW PRAM using a linear number of processors. It is shown how to apply this technique to construct more efficient parallel algorithms for several problems, including coloring of planar graphs and (delta + 1)-coloring of constant-degree graphs. Lower bounds for two related problems are proved.