Applying Volunteer and Parallel Computing for Enumerating Diagonal Latin Squares of Order 9

  • Eduard I. Vatutin
  • Stepan E. Kochemazov
  • Oleg S. ZaikinEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 753)


In this paper we design the algorithm aimed at fast enumeration of diagonal Latin squares of small order. This brute force based algorithm uses straightforward representation of a Latin square and greatly depends on the order in which we fill in Latin square cells. Moreover, we greatly improved its effectiveness by careful optimization using bit arithmetic. By applying this algorithm we have enumerated diagonal Latin squares of order 9. This problem was previously unsolved. In order to ensure the accuracy of the obtained result, two separate large-scale experiments were carried out. In the first one a computing cluster was employed. The second one was performed in a BOINC-based volunteer computing project. Each experiment took about 3 months. As a result we obtained two similar numbers.


Combinatorics Latin square Enumeration Bit arithmetic Volunteer computing BOINC Parallel computing 


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Southwest State UniversityKurskRussia
  2. 2.Matrosov Institute for System Dynamics and Control Theory SB RASIrkutskRussia

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