An approximation algorithm for counting contingency tables

An approximation algorithm for counting contingency tables (2008)

by Alexander Barvinok , Zur Luria , Alexander Samorodnitsky , Alexander Yong

Citations:

2 - 1 self

User correction supplied by mph

Datum	Value	Source
TITLE	An approximation algorithm for counting contingency tables	user correction
AUTHOR NAME	Alexander Barvinok	user correction
AUTHOR NAME	Zur Luria	user correction
AUTHOR NAME	Alexander Samorodnitsky	user correction
AUTHOR NAME	Alexander Yong	user correction
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 N O(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 + √ 5)/2 ≈ 1.618. The algorithm builds on Monte Carlo integration and sampling algorithms for logconcave densities, the matrix scaling algorithm, the permanent approximation algorithm, and an integral representation for the number of contingency tables.	user correction
YEAR	2008	SVM HeaderParse 0.2
CITATIONS	39 found	ParsCit 1.0