Abstract
We provide several algorithms for the exact, uniform random sampling of Latin squares and Sudoku matrices via probabilistic divide-and-conquer (PDC). Our approach divides the sample space into smaller pieces, samples each separately, and combines them in a manner which yields an exact sample from the target distribution. We demonstrate, in particular, a version of PDC in which one of the pieces is sampled using a brute force approach, which we dub almost deterministic second half, as it is a generalization to a previous application of PDC for which one of the pieces is uniquely determined given the others.
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Notes
This number can be simplified to 71 after taking more symmetries into account [18].
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The author would like to acknowledge helpful conversations with James Zhao and Edo Liberty, and also helpful comments from an anonymous reviewer.
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DeSalvo, S. Exact Sampling Algorithms for Latin Squares and Sudoku Matrices via Probabilistic Divide-and-Conquer. Algorithmica 79, 742–762 (2017). https://doi.org/10.1007/s00453-016-0223-y
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DOI: https://doi.org/10.1007/s00453-016-0223-y