Distributed domination on sparse graph classes

TL;DR

This paper presents a distributed algorithm that approximates the dominating set problem efficiently on sparse graph classes, extending previous results and improving approximation factors on planar graphs.

Contribution

It introduces a general constant-factor approximation algorithm for dominating sets on sparse graphs in the distributed LOCAL model, and refines it for planar graphs to achieve an (11+ε)-approximation.

Findings

Constant factor approximation in constant rounds for bounded expansion graphs

Extension of previous results to broader sparse graph classes

Improved approximation factor of (11+ε) for planar graphs

Abstract

We show that the dominating set problem admits a constant factor approximation in a constant number of rounds in the LOCAL model of distributed computing on graph classes with bounded expansion. This generalizes a result of Czygrinow et al. for graphs with excluded topological minors to very general classes of uniformly sparse graphs. We demonstrate how our general algorithm can be modified and fine-tuned to compute an ($11+\epsilon$)-approximation (for any $\epsilon>0)$ of a minimum dominating set on planar graphs. This improves on the previously best known approximation factor of 52 on planar graphs, which was achieved by an elegant and simple algorithm of Lenzen et al.