Coloring Fast with Broadcasts
Maxime Flin, Mohsen Ghaffari, Magnús M. Halldórsson, Fabian Kühn, Alexandre Nolin · 2023
We present an O(log3 log n)-round distributed algorithm for the (Δ + 1)-coloring problem, where each node broadcasts only one O(log n)-bit message per round to its neighbors. Previously, the best such broadcast-based algorithm required O(log n) rounds. If Δ ∈ Ω(log 3 n), our algorithm runs in O(log* n) rounds. Our algorithm's round complexity matches the state-of-the-art in the much more powerful CONGEST model [Halldórsson et al., STOC'21 & PODC'22], where each node sends one different message to each of its neighbors, thus sending up to Θ(n log n) bits per round. This is the best complexity known, even if message sizes are unbounded.