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Start-up and the Results of the Volunteer Computing Project RakeSearch

  • Maxim Manzyuk
  • Natalia NikitinaEmail author
  • Eduard Vatutin
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 1129)

Abstract

In this paper we describe the experience of setting up a computational infrastructure based on BOINC middleware and running a volunteer computing project on its basis. The project is aimed at characterizing the space of diagonal Latin squares of order 9 in the form of an ensemble of orthogonality graphs, previously not addressed. We implement the search for row-permutational squares orthogonal to an initial one, which allows to reconstruct the full graphs. We provide the developed application to search for orthogonal pairs of the squares and describe the obtained results. The results prove the efficiency of volunteer computing in unveiling the structure of the space of diagonal Latin squares.

Keywords

Desktop Grid Volunteer computing BOINC Orthogonal diagonal Latin squares Orthogonality graph 

Notes

Acknowledgments

We would like to thank all volunteers who provided their computers to the project. We thank Daniel (BOINC@Poland team) for developing an optimized search application that allowed to save a lot of computational resources and time. Discussions and advice on the project forum were greatly appreciated too.

This work was supported by the Russian Foundation for Basic Research [grant numbers 18-07-00628_a, 18-37-00094_mol_a and 17-07-00317_a].

References

  1. 1.
    Colbourn, C.J., Dinitz, J.H.: Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications). Chapman & Hall/CRC, Boca Raton (2006)Google Scholar
  2. 2.
    Bolshakova, N.S.: About one another application of Latin squares. Vestnik of MSTU 8(1), 170–173 (2005). (in Russian)Google Scholar
  3. 3.
    Thomas, P.R., Morgan, J.P.: Modern experimental design. Stat. Theory Pract. 1(3–4), 501–506 (2007)zbMATHGoogle Scholar
  4. 4.
    Anderson, I.: Combinatorial Designs and Tournaments, vol. 6. Oxford University Press, Oxford (1997)zbMATHGoogle Scholar
  5. 5.
    Cooper, J., Donovan, D., Seberry, J.: Secret sharing schemes arising from Latin squares. Bull. Inst. Comb. Appl. 12, 33–43 (1994)MathSciNetzbMATHGoogle Scholar
  6. 6.
    MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error-Correcting Codes. North Holland Publishing Co., Amsterdam (1977)zbMATHGoogle Scholar
  7. 7.
    Zaikin, O., Zhuravlev, A., Kochemazov, S., Vatutin, E.: On the construction of triples of diagonal Latin squares of order 10. Electron. Notes Discrete Math. 54, 307–312 (2016)CrossRefGoogle Scholar
  8. 8.
    Afanasiev, A.P., Bychkov, I.V., Manzyuk, M.O., Posypkin, M.A., Semenov, A.A., Zaikin, O.S.: Technology for integrating idle computing cluster resources into volunteer computing projects. In: Proceedings of the 5th International Workshop on Computer Science and Engineering, Moscow, Russia, pp. 109–114 (2015)Google Scholar
  9. 9.
    Anderson, D.P.: BOINC: a platform for volunteer computing. J Grid Computing (2019)Google Scholar
  10. 10.
    Parker, E.T.: Computer investigation of orthogonal Latin squares of order ten. In: Proceeding of Symposia in Applied Mathematics, vol. 15, pp. 73–81 (1963)Google Scholar
  11. 11.
    McKay, B.D., Rogoyski, E.: Latin squares of order 10. Electron. J. Comb. 2(3), 1–4 (1995)MathSciNetzbMATHGoogle Scholar
  12. 12.
    McKay, B.D., Wanless, I.M.: On the number of Latin squares. Ann. Comb. 9(3), 335–344 (2005)MathSciNetCrossRefGoogle Scholar
  13. 13.
    McKay, B.D., Meynert, A., Myrvold, W.: Small Latin squares, quasigroups, and loops. J. Comb. Des. 15(2), 98–119 (2007)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Egan, J., Wanless, I.: Enumeration of MOLS of small order. Math. Comput. 85(298), 799–824 (2016)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Lin, H.-H., Wu, I-C.: Solving the minimum sudoku poblem. In: 2010 International Conference on Technologies and Applications of Artificial Intelligence, pp. 456–461. IEEE (2010)Google Scholar
  16. 16.
    Vatutin, E.I., Zaikin, O.S., Kochemazov, S.E., Valyaev, S.Y.: Using volunteer computing to study some features of diagonal Latin squares. Open Eng. 7(1), 453–460 (2017)Google Scholar
  17. 17.
    Vatutin, E.I., Kochemazov, S.E., Zaikin, O.S.: Applying volunteer and parallel computing for enumerating diagonal Latin squares of order 9. In: Sokolinsky, L., Zymbler, M. (eds.) PCT 2017. CCIS, vol. 753, pp. 114–129. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-67035-5_9CrossRefGoogle Scholar
  18. 18.
    Vatutin, E., Belyshev, A., Kochemazov, S., Zaikin, O., Nikitina, N.: Enumeration of isotopy classes of diagonal Latin squares of small order using volunteer computing. In: Voevodin, V., Sobolev, S. (eds.) RuSCDays 2018. CCIS, vol. 965, pp. 578–586. Springer, Cham (2019).  https://doi.org/10.1007/978-3-030-05807-4_49CrossRefGoogle Scholar
  19. 19.
    Zaikin, O., Kochemazov, S.: The search for systems of diagonal Latin squares using the SAT@home project. Int. J. Open Inf. Technol. 3(11), 4–9 (2015)Google Scholar
  20. 20.
    Vatutin, E., Zaikin, O., Kochemazov, S., Valyaev, S.: Using volunteer computing to study some features of diagonal Latin square. Open Eng. 7, 453–460 (2017)Google Scholar
  21. 21.
    RakeSearch. https://rake.boincfast.ru/rakesearch. Accessed 23 June 2019
  22. 22.
    Center for Collective Use of Karelian Research Center of the Russian Academy of Sciences. http://cluster.krc.karelia.ru/index.php?plang=e. Accessed 23 June 2019
  23. 23.
    Nikitina, N.N., Manzyuk, M.O., Vatutin, E.I.: Employment of distributed computing to search and explore orthogonal diagonal Latin squares of rank 9. In: Proceedings of the XI(1) All-Russian Research and Practice Conference on Digital Technologies in Education, Science, Society, pp. 97–100, November 2017. (in Russian)Google Scholar
  24. 24.
    Bammel, S.E., Rothstein, J.: The number of \(9\times 9\) Latin squares. Discrete Math. 11(1), 93–95 (1975)MathSciNetCrossRefGoogle Scholar
  25. 25.
    GitHub - Nevecie/RakeSearch: Rake search of Diagonal Latin Squares. https://github.com/Nevecie/RakeSearch. Accessed 23 June 2019
  26. 26.
    Formula BOINC. http://formula-boinc.org/. Accessed 23 June 2019
  27. 27.
    Vatutin, E.I., Kochemazov, S.E., Zaikin, O.S., Manzuk, M.O., Nikitina, N.N., Titov, V.S.: Properties of central symmetry for diagonal Latin squares (in Russian). High-Perform. Comput. Syst. Technol. 8, 74–78 (2018)Google Scholar
  28. 28.
    Bastian, M., Heymann, S., Jacomy, M.: Gephi: an open source software for exploring and manipulating networks. In: International AAAI Conference on Weblogs and Social Media, pp. 1–2 (2009)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Maxim Manzyuk
    • 1
  • Natalia Nikitina
    • 2
    Email author
  • Eduard Vatutin
    • 3
  1. 1.Internet portal BOINC.ruMoscowRussia
  2. 2.Institute of Applied Mathematical ResearchKarelian Research Center of the Russian Academy of SciencesPetrozavodskRussia
  3. 3.Southwest State UniversityKurskRussia

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