Solving graph coloring problems with the Douglas-Rachford algorithm

TL;DR

This paper demonstrates that the Douglas-Rachford algorithm can effectively solve graph coloring problems by formulating them as feasibility problems, showing promising results across various experiments despite their nonconvex nature.

Contribution

The paper introduces a novel application of the Douglas-Rachford algorithm as a heuristic for graph coloring, addressing nonconvexity in combinatorial optimization.

Findings

Effective heuristic for graph coloring

Successful application despite nonconvexity

Good computational performance

Abstract

We present the Douglas-Rachford algorithm as a successful heuristic for solving graph coloring problems. Given a set of colors, these type of problems consist in assigning a color to each node of a graph, in such a way that every pair of adjacent nodes are assigned with different colors. We formulate the graph coloring problem as an appropriate feasibility problem that can be effectively solved by the Douglas-Rachford algorithm, despite the nonconvexity arising from the combinatorial nature of the problem. Different modifications of the graph coloring problem and applications are also presented. The good performance of the method is shown in various computational experiments.