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Searching for Orthogonal Latin Squares via Cells Mapping and BOINC-Based Cube-and-Conquer

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Supercomputing (RuSCDays 2021)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1510))

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Abstract

This study focuses on searching for pairs of orthogonal diagonal Latin squares of order 10. Consider a cells mapping in accordance to which one diagonal Latin square is mapped to another one. Given a certain cells mapping schema, the problem is to find a pair of orthogonal diagonal Latin squares of order 10 such that they match the schema (or to prove that such a pair does not exist). The problem is reduced to the Boolean satisfiability problem (SAT). Three mapping schemes are considered, and for each of them a SAT instance is constructed. If a satisfying assignment is found for an instance, the corresponding pair of orthogonal Latin squares can be easily extracted from it. The Cube-and-Conquer approach is used to solve the instances. The cubing phase is performed on a sequential look-ahead SAT solver, while on the conquer phase an experiment in a BOINC-based volunteer computing project is launched. In the experiment, for two out of three schemes orthogonal pairs are found.

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Notes

  1. 1.

    https://oeis.org/A299784.

  2. 2.

    https://oeis.org/A309210.

  3. 3.

    https://github.com/Nauchnik/SAT-at-home/tree/master/src_boinc_satcmsdls.

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Acknowledgements

Authors thank all RakeSearch and Gerasim@home volunteers, whose computers took part in the experiments. Oleg Zaikin was supported by EPSRC grant EP/S015523/1. Eduard Vatutin was supported by intra-university grant for SWSU development program (Priority 2030) No. PR2030/2021.

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Authors and Affiliations

  1. Southwest State University, Kursk, Russia

    Eduard Vatutin

  2. Swansea University, Swansea, UK

    Oleg Zaikin

  3. Internet portal BOINC.ru, Moscow, Russia

    Maxim Manzyuk

  4. Institute of Applied Mathematical Research, Karelian Research Centre of RAS, Petrozavodsk, Russia

    Natalia Nikitina

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  1. Eduard Vatutin
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  2. Oleg Zaikin
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Correspondence to Oleg Zaikin .

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  1. RCC MSU, Moscow, Russia

    Vladimir Voevodin

  2. RCC MSU, Moscow, Russia

    Sergey Sobolev

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Vatutin, E., Zaikin, O., Manzyuk, M., Nikitina, N. (2021). Searching for Orthogonal Latin Squares via Cells Mapping and BOINC-Based Cube-and-Conquer. In: Voevodin, V., Sobolev, S. (eds) Supercomputing. RuSCDays 2021. Communications in Computer and Information Science, vol 1510. Springer, Cham. https://doi.org/10.1007/978-3-030-92864-3_38

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  • DOI: https://doi.org/10.1007/978-3-030-92864-3_38

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