The paper is devoted to discovering new features of diagonal Latin squares of small order. We present an algorithm, based on a special kind of transformations, that constructs a canonical form of a given diagonal Latin square. Each canonical form corresponds to one isotopy class of diagonal Latin squares. The algorithm was implemented and used to enumerate the isotopy classes of diagonal Latin squares of order at most 8. For order 8 the computational experiment was conducted in a volunteer computing project. The algorithm was also used to estimate how long it would take to enumerate the isotopy classes of diagonal Latin squares of order 9 in the same volunteer computing project.

Enumeration of Isotopy Classes of Diagonal Latin Squares of Small Order Using Volunteer Computing

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.

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

The paper describes a discrete event simulation model of a Desktop Grid system. Firstly, we present a stochastic model of a volunteer computing project. We then employ the event simulation approach based on the generalized semi-Markov processes to develop a discrete event simulation model. Finally, using the simulation model, we describe a performance optimization problem aiming to optimize the project runtime as a function of the task size under performance constraints.

Discrete Event Simulation Model of a Desktop Grid System.

/pdf/central-symmetry-properties-for-diagonal-latin-squares-4zm52nwgpj.pdf

Central symmetry properties for diagonal latin squares

We propose an algorithm for enumerating diagonal Latin squares. It relies on specific properties of diagonal Latin squares to employ symmetry breaking techniques.

Enumerating Diagonal Latin Squares of Order Up to 9.

Abstract In 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.

Using Volunteer Computing to Study Some Features of Diagonal Latin Squares

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Using Volunteer Computing to Study Some Features of Diagonal Latin Squares