Coloring Fast with Broadcasts

Abstract

We provide a O(log 6 log n)-round randomized algorithm for distance-2 coloring in CONGEST with ∆ 2 +1 colors. For ∆ ≫ poly log n, this improves exponentially on the O(log ∆+poly log log n) algorithm of [Halldórsson, Kuhn, Maus, Nolin, DISC'20].Our study is motivated by the ubiquity and hardness of local reductions in CONGEST. For instance, algorithms for the Local Lovász Lemma [Moser, Tardos, JACM'10; Fischer, Ghaffari, DISC'17; Davies, SODA'23] usually assume communication on the conflict graph, which can be simulated in LOCAL with only constant overhead, while this may be prohibitively expensive in CONGEST. We hope our techniques help tackle in CONGEST other coloring problems defined by local relations.