In Search of Balance: The Challenge of Generating Balanced Latin Rectangles
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Spatially Balanced Latin Squares are combinatorial structures of great importance for experimental design. From a computational perspective they present a challenging problem and there is a need for efficient methods to generate them. Motivated by a real-world application, we consider a natural extension to this problem, balanced Latin Rectangles. Balanced Latin Rectangles appear to be even more defiant than balanced Latin Squares, to such an extent that perfect balance may not be feasible for Latin rectangles. Nonetheless, for real applications, it is still valuable to have well balanced Latin rectangles. In this work, we study some of the properties of balanced Latin rectangles, prove the nonexistence of perfect balance for an infinite family of sizes, and present several methods to generate the most balanced solutions.
KeywordsLatin Rectangles Experimental design Local search Constraint satisfaction problem Mixed-integer programming
This work was supported by the National Science Foundation (NSF Expeditions in Computing awards for Computational Sustainability, grants CCF-1522054 and CNS-0832782, NSF Computing research infrastructure for Computational Sustainability, grant CNS-1059284).
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