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Joined: 20 Jul 20
As a result of the SAT-CMS experiment, 29 pairs of orthogonal diagonal Latin squares (ODLS) of order 10 were found. 2 cell mapping schemas (CMS) were used for this purpose. 18 found pairs are based on the first CMS, the remaining 11 pairs are based on the second one. CMS is in fact a relation between 2 Latin square from an orthogonal pair: for each element of the first square it shows where this element should be placed in the second square. Therefore, one can effectively construct the second square from a pair given the first square. The computing application was based on the CDCL algorithm aimed at solving the Boolean satisfiability problem (SAT). For each studied CMS, we first reduced a problem of finding pairs of ODLS of order 10 (that match the CMS) to SAT. Then, the obtained SAT problem was splitted into subproblems which in turn formed workunits. Finally, from found satisfying assignments (solutions of the SAT problems) we constructed the corresponding pairs of ODLS. All the found pairs are listed here. We are very grateful to all the crunchers who took part in the experiment!
Joined: 4 Oct 17
очень интересно ! Уверен, что многие из нас надеются продолжить вместе с новым проектом.
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