Improved bounds for sampling contingency tables

Authors:
Ben J. Morris
Affiliations:
Statistics Department, University of California, Berkeley, CA
Venue:
Random Structures & Algorithms
Year:
2002

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Abstract

We study the problem of sampling contingency tables (nonnegative integer matrices with specified row and column sums) uniformly at random. We give an algorithm which runs in polynomial time provided that the row sums ri and the column sums cj satisfy ri = Ω(n3/2m log m), and cj = Ω(m3/2n log n). This algorithm is based on a reduction to continuous sampling from a convex set. The same approach was taken by Dyer, Kannan, and Mount in previous work. However, the algorithm we present is simpler and has weaker requirements on the row and column sums.