Distributed Delta-Coloring under Bandwidth Limitations

We consider the problem of coloring graphs of maximum degree Δ with Δ colors in the distributed setting with limited bandwidth. Specifically, we give a 𝗉𝗈𝗅𝗒loglog n-round randomized algorithm in the CONGEST model. This is close to the lower bound of Ω(loglog n) rounds from [Brandt et al., STOC '16], which holds also in the more powerful LOCAL model. The core of our algorithm is a reduction to several special instances of the constructive Lovász local lemma (LLL) and the deg+1-list coloring problem.