Fast Algorithm for Enumerating Diagonal Latin Squares of Small Order
Combinatorics
2017-09-11 v1 Distributed, Parallel, and Cluster Computing
Discrete Mathematics
Data Structures and Algorithms
Abstract
In this paper we propose an algorithm for enumerating diagonal Latin squares of small order. It relies on specific properties of diagonal Latin squares to employ symmetry breaking techniques, and on several heuristic optimizations and bit arithmetic techniques to make use of computational power of state-of-the-art CPUs. Using this approach we enumerated diagonal Latin squares of order at most 9, and vertically symmetric diagonal Latin squares of order at most 10.
Keywords
Cite
@article{arxiv.1709.02599,
title = {Fast Algorithm for Enumerating Diagonal Latin Squares of Small Order},
author = {Stepan Kochemazov and Eduard Vatutin and Oleg Zaikin},
journal= {arXiv preprint arXiv:1709.02599},
year = {2017}
}