A Constructive Algorithm for Partial Latin Square Extension Problem that Solves Hardest Instances Effectively

  • Kazuya HaraguchiEmail author
Part of the Studies in Computational Intelligence book series (SCI, volume 580)


A partial Latin square (PLS) is a partial assignment of \(n\) symbols to an \(n\times n\) grid such that, in each row and in each column, each symbol appears at most once. The partial Latin square extension (PLSE) problem asks to find such a PLS that is a maximum extension of a given PLS. Recently Haraguchi et al. proposed a heuristic algorithm for the PLSE problem. In this paper, we present its effectiveness especially for the “hardest” instances. We show by empirical studies that, when \(n\) is large to some extent, the instances such that symbols are given in 60–70 % of the \(n^2\) cells are the hardest. For such instances, the algorithm delivers a better solution quickly than IBM ILOG CPLEX, a state-of-the-art optimization solver, that is given a longer time limit. It also outperforms surrogate constraint based heuristics that are originally developed for the maximum independent set problem.


Partial Latin square extension problem Heuristic Constructive algorithm Maximum matching Maximum independent set problem 


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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Faculty of CommerceOtaru University of CommerceOtaruJapan

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