TY - JOUR

T1 - An approximation algorithm for counting contingency tables

AU - Barvinok, Alexander

AU - Luria, Zur

AU - Samorodnitsky, Alex

AU - Yong, Alexander

PY - 2010/8

Y1 - 2010/8

N2 - 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 quasi-polynomial 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 we√l as between the largest and the smallest column sums are strictly smaller than the golden ratio (1 + √ 5)/2 ≈ 1.618. The algorithm builds on Monte Carlo integration and sampling algorithms for log-concave densities, the matrix scaling algorithm, the permanent approximation algorithm, and an integral representation for the number of contingency tables.

AB - 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 quasi-polynomial 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 we√l as between the largest and the smallest column sums are strictly smaller than the golden ratio (1 + √ 5)/2 ≈ 1.618. The algorithm builds on Monte Carlo integration and sampling algorithms for log-concave densities, the matrix scaling algorithm, the permanent approximation algorithm, and an integral representation for the number of contingency tables.

KW - Contingency tables

KW - Matrix scaling

KW - Permanent approximation

KW - Randomized algorithms

UR - http://www.scopus.com/inward/record.url?scp=77954474566&partnerID=8YFLogxK

U2 - 10.1002/rsa.20301

DO - 10.1002/rsa.20301

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AN - SCOPUS:77954474566

SN - 1042-9832

VL - 37

SP - 25

EP - 66

JO - Random Structures and Algorithms

JF - Random Structures and Algorithms

IS - 1

ER -