Improved Bounds for Sampling Contingency Tables
This paper addresses the problem of sampling contingency tables (non-negative integer matrices with specified row and column sums) uniformly at random. We give an approximation algorithm which runs in polynomial time provided that the row and column sums satisfy r i =Ω (n 3/2 m log(m)), and c j =Ω (m 3/2 n log(n)). Our algorithm is based on a reduction to continuous sampling from a convex set. This is an approach which was taken by Dyer, Kannan and Mount in previous work. However, the algorithm we present is simpler, and has a greater range of applicability since the requirements on the row and column sums are weaker.
KeywordsContingency Table Integer Point Integer Matrix 25th International Colloquium Improve Bound
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