Sampling contingency tables

We give polynomial time algorithms for random sampling from a set of contingency tables, which is the set of m×n matrices with given row and column sums, provided the row and column sums are sufficiently large with respect to m, n. We use this to approximately count the number of such matrices. These problems are of interest in Statistics and Combinatorics. © 1997 John Wiley & Sons, Inc. Random Struct. Alg., 10 , 487–506, 1997