Distributed Graph Coloring Made Easy

In this paper, we present a deterministic \(\mathsf {CONGEST} \) algorithm to compute an O ( kΔ )-vertex coloring in Δ / k ) + log * n rounds, where is the maximum degree of network graph and ≥ 1 can be freely chosen. The extremely simple: Each node locally computes sequence colors then it tries from batches size . Our subsumes many important results history distributed as special cases, including Linial’s color reduction [Linial, FOCS’87], celebrated iterative [Barenboim, Elkin, Goldenberg, PODC’18], various algorithms defective arbdefective colorings. smoothly scale between several these previous also simplifies state art 1)-coloring algorithm. At cost losing some algorithm’s simplicity provide )-coloring \(O(\sqrt {\Delta /k})+\log ^{*} rounds. We improved for ruling sets, and, additionally, tight characterization 1-round algorithms.