We describe efficient deterministic techniques for breaking symmetry in parallel. The techniques work well on rooted trees and graphs of constant degree or genus. Our primary technique allows us to t-color a rooted tree in O(lg'n) time on an EREW PRAM using a linear number of processors. We apply these techniques to construct fast linear processor algorithms for several problems, including (A + I)-coloring constant-degree graphs, 5-coloring planar graphs, and finding depth-first-search trees in planar graphs. We also prove lower bounds for a-coloring directed lists and for finding maximal independent sets in arbitrary graphs.
Goldberg et al. REF describe an algorithm for finding a greedy coloring of O(1)-degree graphs in O(lg n) time in the EREW PRAM model using a linear number of processors.
Parallel symmetry-breaking in sparse graphs
STOC '87
Mathematics Computer Science