Decentralized Distributed Graph Coloring: Cluster Graphs

TL;DR

This paper introduces a sub-logarithmic distributed algorithm for coloring cluster graphs, significantly improving the efficiency of graph coloring in distributed systems, especially for graphs with polylogarithmic degree.

Contribution

It presents the first $O( ext{log}^* n)$-round algorithm for $( ext{Delta}+1)$-coloring of cluster graphs with polylogarithmic degree, advancing distributed graph coloring techniques.

Findings

Achieved sub-logarithmic coloring algorithm for cluster graphs

Extended results to the CONGEST model

Demonstrated rapid solutions for decentralized distributed graph problems

Abstract

Graph coloring is fundamental to distributed computing. We give the first sub-logarithmic distributed algorithm for coloring cluster graphs. These graphs are obtained from the underlying communication network by contracting nodes and edges, and they appear frequently as components in the study of distributed algorithms. In particular, we give a $O(\log^* n)$-round algorithm to $(\Delta+1)$-color cluster graphs of at least polylogarithmic degree. The previous best bound known was $\operatorname{poly}(\log n)$ [Flin et al., SODA'24]. This properly generalizes results in the CONGEST model and shows that distributed graph problems can be solved quickly even when the node itself is decentralized.