Local planar domination revisited

TL;DR

This paper presents a distributed algorithm that computes a 20-approximation of a minimum dominating set in planar graphs within a constant number of rounds, improving the approximation factor significantly over previous methods.

Contribution

It introduces a new distributed algorithm that combines existing techniques to achieve a better approximation ratio for dominating sets in planar graphs.

Findings

Achieves a 20-approximation in constant rounds

Improves the previous approximation factor of 52

Combines ideas from multiple recent algorithms

Abstract

We show how to compute a 20-approximation of a minimum dominating set in a planar graph in a constant number of rounds in the LOCAL model of distributed computing. This improves on the previously best known approximation factor of 52, which was achieved by an elegant and simple algorithm of Lenzen et al. Our algorithm combines ideas from the algorithm of Lenzen et al. with recent work of Czygrinow et al. and Kublenz et al. to reduce to the case of bounded degree graphs, where we can simulate a distributed version of the classical greedy algorithm.