Polynomial Time Construction for Spatially Balanced Latin Squares
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Le Bras, Ronan; Perrault, Andrew; Gomes, Carla P.
In this paper we propose a construction that generates spatially balanced Latin squares (SBLSs) in polynomial time. These structures are central to the design of agronomic experiments, as they avoid biases that are otherwise unintentionally introduced due to spatial auto-correlation. Previous approaches were able to generate SBLSs of order up to 35 and required about two weeks of computation. Our algorithm runs in O(n2) and generates SBLSs of arbitrary order n where 2n + 1 is prime. For example, this algorithm generates a SBLS of order 999 in a fraction of a second.
National Science Foundation (NSF Expeditions in Computing award for Computational Sustainability, grant 0832782; NSF IIS award, grant 0514429), Intelligent Information Systems Institute, Cornell University (Air Force O ce of Scienti c Research, AFOSR, grant FA9550-04-1-0151), Natural Sciences and Engineering Research Council of Canada (NSERC)
Quasigroup; Latin Square; Spatially Balanced; Combinatorial Design; Agronomic Field Experiments