Parallel Symmetry-Breaking in Sparse Graphs

Abstract

This paper describes efficient deterministic techniques for breaking symmetry in parallel. These techniques work well on rooted trees and graphs of constant degree or genus. The primary technique allows us to 3-color a rooted tree in $O( \lg^* n )$ time on an EREW PRAM using a linear number of processors. These techniques are used to construct fast linear processor algorithms for several problems, including the problem of $( \Delta + 1)$-coloring constant-degree graphs and 5-coloring planar graphs. Lower bounds for 2-coloring directed lists and for finding maximal independent sets in arbitrary graphs are also proved.