Vestnik Yuzhno-Ural'skogo Gosudarstvennogo Universiteta. Seriya "Vychislitelnaya Matematika i Informatika"
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Vestnik Yuzhno-Ural'skogo Gosudarstvennogo Universiteta. Seriya "Vychislitelnaya Matematika i Informatika", 2015, Volume 4, Issue 3, Pages 95–108
DOI: https://doi.org/10.14529/cmse150308
(Mi vyurv8)
 

Discrete Mathematics and Mathematical Cybernetics

The search for pairs of orthogonal diagonal latin squares of order 10 in the volunteer computing project SAT@home

O. S. Zaikin, S. E. Kochemazov

Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences (Irkutsk, Russian Federation)
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Abstract: In this paper we consider the approach to search for systems of orthogonal Latin Squares, that is based on reducing the corresponding problems to Boolean Satisfiability problem. We constructed the SAT encoding for finding orthogonal diagonal Latin Squares of order 10. Using this encoding and the resources provided by the volunteer computing project SAT@home we managed to find 17 previously unknown pairs. Based on these 17 pairs and on 3 previously published pairs we constructed the pseudotriples of diagonal Latin Squares of order 10. To construct pseudotriples we employed the computing cluster. The last step required us to make parallel implementation of the algorithm for generating diagonal Latin Squares of order 10.
Keywords: Latin squares, volunteer computing, Boolean satisfiability problem, SAT@home project.
Received: 27.03.2015
Bibliographic databases:
Document Type: Article
UDC: 519.1, 004.832.25
Language: Russian
Citation: O. S. Zaikin, S. E. Kochemazov, “The search for pairs of orthogonal diagonal latin squares of order 10 in the volunteer computing project SAT@home”, Vestn. YuUrGU. Ser. Vych. Matem. Inform., 4:3 (2015), 95–108
Citation in format AMSBIB
\Bibitem{ZaiKoc15}
\by O.~S.~Zaikin, S.~E.~Kochemazov
\paper The search for pairs of orthogonal diagonal latin squares of order 10 in the volunteer computing project SAT@home
\jour Vestn. YuUrGU. Ser. Vych. Matem. Inform.
\yr 2015
\vol 4
\issue 3
\pages 95--108
\mathnet{http://mi.mathnet.ru/vyurv8}
\crossref{https://doi.org/10.14529/cmse150308}
\elib{https://elibrary.ru/item.asp?id=23790227}
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