Improving Integer and Constraint Programming for Graeco-Latin Squares

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Noah Rubin, Curtis Bright, Kevin K. H. Cheung, Brett Stevens

Published: 2021, Last Modified: 07 Nov 2025ICTAI 2021EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: We use integer programming (IP) and constraint programming (CP) to search for graeco-latin squares. We improve the performance of the solvers by formulating an extended symmetry breaking method and provide an alternative CP encoding which performs much better in practice. Using state-of-the-art solvers as black boxes we are able to quickly find graeco-latin squares (or prove their nonexistence) in all orders up to and including eleven.