Integer and Constraint Programming Revisited for Mutually Orthogonal Latin Squares (Student Abstract)

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

AAAI 2022 pp. 13037-13038

doi:10.1609/AAAI.V36I11.21655 /aaai/2022/rubin2022aaai-integer/

Abstract

We use integer programming (IP) and constraint programming (CP) to search for sets of mutually orthogonal latin squares (MOLS). 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 we are able to quickly find pairs of MOLS (or prove their nonexistence) in all orders up to and including eleven. We also analyze the effectiveness of using CP and IP solvers to search for triples of MOLS and estimate the running time of using this approach to resolve the longstanding open problem of determining the existence of a triple of MOLS of order ten.

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Cite

Text

Rubin et al. "Integer and Constraint Programming Revisited for Mutually Orthogonal Latin Squares (Student Abstract)." AAAI Conference on Artificial Intelligence, 2022. doi:10.1609/AAAI.V36I11.21655

Markdown

[Rubin et al. "Integer and Constraint Programming Revisited for Mutually Orthogonal Latin Squares (Student Abstract)." AAAI Conference on Artificial Intelligence, 2022.](https://mlanthology.org/aaai/2022/rubin2022aaai-integer/) doi:10.1609/AAAI.V36I11.21655

BibTeX

@inproceedings{rubin2022aaai-integer,
  title     = {{Integer and Constraint Programming Revisited for Mutually Orthogonal Latin Squares (Student Abstract)}},
  author    = {Rubin, Noah and Bright, Curtis and Stevens, Brett and Cheung, Kevin K. H.},
  booktitle = {AAAI Conference on Artificial Intelligence},
  year      = {2022},
  pages     = {13037-13038},
  doi       = {10.1609/AAAI.V36I11.21655},
  url       = {https://mlanthology.org/aaai/2022/rubin2022aaai-integer/}
}