An approximation algorithm for counting contingency tables

Abstract. We present a randomized approximation algorithm for counting contingency tables, m × n non-negative integer matrices with given row sums R = (r1, . . . , rm) and column sums C = (c1, . . . , cn). We define smooth margins (R, C) in terms of the typical table and prove that for such margins the algorithm has quasipolynomial NO(ln N) complexity, where N = r1 + · · · + rm = c1 + · · · + cn. Various classes of margins are smooth, e.g., when m = O(n), n = O(m) and the ratios between the largest and the smallest row sums as well as between the largest and the smallest column sums are strictly smaller than the golden ratio (1 + √

• Type: Journal
• Year: 2010
• Where: RSA
• Authors: Alexander I. Barvinok, Zur Luria, Alex Samorodnitsky, Alexander Yong
• Keywords: Row Sums, RSA 2010, Smallest Column Sums, Smallest Row Sums