Distributed (Δ+1)-Coloring in Sublogarithmic Rounds [article]

David G. Harris, Johannes Schneider, Hsin-Hao Su
2018 arXiv   pre-print
We give a new randomized distributed algorithm for (Δ+1)-coloring in the LOCAL model, running in O(√(Δ))+ 2^O(√( 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( ( √( n/ n), Δ/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
more » ... f distributed symmetry-breaking techniques by performing a decomposition of graphs into dense and sparse parts.
arXiv:1603.01486v4 fatcat:esqg5746onfyjprhdl2lhoso6i