基于概率分治的拉丁方和数独矩阵精确采样算法
Exact sampling algorithms for Latin squares and Sudoku matrices via probabilistic divide-and-conquer
摘要：
我们提供了几个算法的精确，均匀随机抽样的拉丁方和数独矩阵通过概率分而治之（PDC）。我们的方法将样本空间划分为更小的块，分别对每个块进行采样，并以从目标分布中产生精确样本的方式将它们组合起来。我们证明，特别是，PDC的一个版本，其中一块是使用蛮力的方法，我们称之为$\textit{almost deterministic second half}$采样，因为它是一个概括以前的应用程序的PDC的一块是唯一确定的其他。
英文摘要：
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 $\textit{almost deterministic second half}$, 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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