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Graph coloring with physics-inspired graph neural networks

Schuetz, Martin J. A. and Brubaker, J. Kyle and Zhu, Zhihuai and Katzgraber, Helmut G. (2022) Graph coloring with physics-inspired graph neural networks. Physical Review Research, 4 (4). Art. No. 043131. ISSN 2643-1564. doi:10.1103/physrevresearch.4.043131.

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We show how graph neural networks can be used to solve the canonical graph coloring problem. We frame graph coloring as a multiclass node classification problem and utilize an unsupervised training strategy based on the statistical physics Potts model. Generalizations to other multiclass 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.

Item Type:Article
Related URLs:
URLURL TypeDescription
Schuetz, Martin J. A.0000-0001-5948-6859
Brubaker, J. Kyle0000-0002-6439-5270
Katzgraber, Helmut G.0000-0003-3341-9943
Additional Information:We thank M. Kastoryano, E. Kessler, T. Mullenbach, N. Pancotti, M. Resende, S. Roy, and G. Salton for fruitful discussions.
Group:AWS Center for Quantum Computing
Issue or Number:4
Record Number:CaltechAUTHORS:20230103-818063100.32
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:118630
Deposited By: Research Services Depository
Deposited On:03 Feb 2023 20:51
Last Modified:03 Feb 2023 20:51

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