Distributed (Δ + 1)-coloring in sublogarithmic rounds

Abstract

We give a new randomized distributed algorithm for (Δ + 1)-coloring in the LOCAL model, running in O(√ log Δ) + 2O( √ log log n) rounds in a graph of maximum degree Δ. This implies that the (Δ + 1)-coloring problem is easier than the maximal independent set problem and the maximal matching problem, due to their lower bounds of Ω(min(√ log n log log n , log Δ log log Δ )) by Kuhn, Moscibroda, and Wattenhofer [PODC'04]. Our algorithm also extends to list-coloring where the palette of each node contains Δ + 1 colors.We extend the set of distributed symmetry-breaking techniques by performing a decomposition of graphs into dense and sparse parts.