Exact, Uniform Sampling of Contingency Tables via Probabilistic Divide-and-Conquer

We present a new algorithm for the exact, uniform sampling of contingency tables based on the recently introduced probabilistic divide-and-conquer technique. The algorithm improves upon the rejection sampling algorithm for an $m\times n$ contingency table; in particular, it runs in $O(n^{3/2})$ for the well-studied case of a $2\times n$ table under a homogeneity condition, which is substantially better than existing Markov Chain Monte Carlo (MCMC) techniques. Unlike MCMC, the runtime depends only on the size of the table and not on the size of the average entry, and the algorithm can be extended to exact sampling of real-valued contingency tables.