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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 , as it is a generalization to a previous application of PDC for which one of the pieces is uniquely determined given the others.

Exact Sampling Algorithms for Latin Squares and Sudoku Matrices via Probabilistic Divide-and-Conquer