A fresh look to a randomized massively parallel graph coloring algorithm

TL;DR

This paper provides a new perspective on a parallel graph coloring algorithm inspired by statistical mechanics, analyzing its behavior and phase transition phenomena with increased computational power.

Contribution

It offers a fresh analysis of a randomized, massively parallel graph coloring algorithm, highlighting its behavior and phase transition properties.

Findings

Algorithm can be effectively implemented in massively parallel systems

Phase transition phenomena observed in large-scale analysis

Enhanced understanding of the algorithm's behavior with increased computational resources

Abstract

Petford and Welsh introduced a sequential heuristic algorithm for (approximately) solving the NP-hard graph coloring problem. The algorithm is based on the antivoter model and mimics the behaviour of a physical process based on a multi-particle system of statistical mechanics. It was later shown that the algorithm can be implemented in massively parallel model of computation. The increase of processing power in recent years allow us to perform an extensive analysis of the algorithms on a larger scale, leading to possibility of a more comprehensive understanding of the behaviour of the algorithm including the phase transition phenomena.