Graph Coloring with Physics-Inspired Graph Neural Networks
This provides a scalable solution for graph coloring and related multi-class problems like scheduling, though it is incremental as it adapts existing methods to a new application.
The paper tackles the graph coloring problem by framing it as multi-class node classification using a physics-inspired graph neural network with an unsupervised Potts model training strategy, achieving performance on par or better than existing solvers and scaling to millions of variables.
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.