Paper ID: 2202.01606

Graph Coloring with Physics-Inspired Graph Neural Networks

Martin J. A. Schuetz, J. Kyle Brubaker, Zhihuai Zhu, Helmut G. Katzgraber

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.

Submitted: Feb 3, 2022