Graph Coloring with Physics-Inspired Graph Neural Networks

TL;DR

This paper introduces a physics-inspired graph neural network approach to solve graph coloring and related multi-class problems, demonstrating competitive performance and scalability to large instances.

Contribution

It presents a novel unsupervised GNN method based on the Potts model for graph coloring, extending to other multi-class problems, and shows scalability and effectiveness in real-world applications.

Findings

Performs on par or better than existing solvers

Scales to problems with millions of variables

Applicable to various multi-class problems

Abstract

We show how graph neural networks can be used to solve the canonical graph coloring problem. We frame graph coloring as a multi-class node classification problem and utilize an unsupervised training strategy based on the statistical physics Potts model. Generalizations to other multi-class problems such as community detection, data clustering, and the minimum clique cover problem are straightforward. We provide numerical benchmark results and illustrate our approach with an end-to-end application for a real-world scheduling use case within a comprehensive encode-process-decode framework. Our optimization approach performs on par or outperforms existing solvers, with the ability to scale to problems with millions of variables.