Efficient Deterministic Distributed Coloring with Small Bandwidth
Philipp Bamberger, Fabian Kühn, Yannic Maus · 2020
We show that the (degree + 1)-list coloring problem can be solved deterministically in O(D · log n · log2 Δ) rounds in the CONGEST model, where D is the diameter of the graph, n the number of nodes, and Δ the maximum degree. Using the recent polylogarithmic-time deterministic network decomposition algorithm by Rozhoň and Ghaffari [49], this implies the first efficient (i.e., poly log n-time) deterministic CONGEST algorithm for the (Δ + 1)-coloring and the (degree + 1)-list coloring problem. Previously the best known algorithm required [EQUATION] rounds and was not based on network decompositions.