Integer and Constraint Programming Revisited for Mutually Orthogonal Latin Squares (Student Abstract)

Abstract

We use integer programming (IP) and constraint programming (CP) to search for sets of mutually orthogonal latin squares (MOLS). We improve the performance of the solvers by formulating an extended symmetry breaking method and provide an alternative CP encoding which performs much better in practice. Using state-of-the-art solvers we are able to quickly find pairs of MOLS (or prove their nonexistence) in all orders up to and including eleven. We also analyze the effectiveness of using CP and IP solvers to search for triples of MOLS and estimate the running time of using this approach to resolve the longstanding open problem of determining the existence of a triple of MOLS of order ten.