A Fast Local Search Algorithm for the Latin Square Completion Problem

The Latin square completion (LSC) problem is an important NP-complete with numerous applications. Given its theoretical and practical importance, several algorithms are designed for solving the LSC problem. In this work, to further improve performance, a fast local search algorithm developed based on three main ideas. Firstly, reduction reasoning technique used reduce scale of space. Secondly, we propose novel conflict value selection heuristic, which considers history conflicting information vertices as criterion when more than one vertex have equal values primary scoring function. Thirdly, during phase, record previous then make use these restart candidate solution. Experimental results show that our proposed significantly outperforms state-of-the-art heuristic almost all instances in terms success rate run time.