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We provide several algorithms for the exact, uniform random sampling of Latinsquares and Sudoku matrices via probabilistic divide-and-conquer (PDC). Ourapproach divides the sample space into smaller pieces, samples each separately,and combines them in a manner which yields an exact sample from the targetdistribution. We demonstrate, in particular, a version of PDC in which one ofthe pieces is sampled using a brute force approach, which we dub$\textit{almost deterministic second half}$, as it is a generalization to aprevious application of PDC for which one of the pieces is uniquely determinedgiven the others.

Exact sampling algorithms for Latin squares and Sudoku matrices via probabilistic divide-and-conquer