Using Volunteer Computing to Study Some Features of Diagonal Latin Squares-Reference-Cited by-同舟云学术

Using Volunteer Computing to Study Some Features of Diagonal Latin Squares

Published:2017-12-29 Issue:1 Volume:7 Page:453-460
ISSN:2391-5439
Container-title:Open Engineering
language:
Short-container-title:

Author:

Vatutin Eduard¹,Zaikin Oleg²,Kochemazov Stepan²,Valyaev Sergey³

Affiliation:

1. Southwest State University, Kursk, Russia

2. Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences, Irkutsk, Russia

3. Internet-portal BOINC.ru, Moscow, Russia

Abstract

AbstractIn this research, the study concerns around several features of diagonal Latin squares (DLSs) of small order. Authors of the study suggest an algorithm for computing minimal and maximal numbers of transversals of DLSs. According to this algorithm, all DLSs of a particular order are generated, and for each square all its transversals and diagonal transversals are constructed. The algorithm was implemented and applied to DLSs of order at most 7 on a personal computer. The experiment for order 8 was performed in the volunteer computing project Gerasim@home. In addition, the problem of finding pairs of orthogonal DLSs of order 10 was considered and reduced to Boolean satisfiability problem. The obtained problem turned out to be very hard, therefore it was decomposed into a family of subproblems. In order to solve the problem, the volunteer computing project SAT@home was used. As a result, several dozen pairs of described kind were found.

Publisher

Walter de Gruyter GmbH

Subject

Electrical and Electronic Engineering,Mechanical Engineering,Aerospace Engineering,General Materials Science,Civil and Structural Engineering,Environmental Engineering

Link

https://www.degruyter.com/document/doi/10.1515/eng-2017-0052/pdf

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