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We give an algorithm that generates a uniformly random contingency table withspecified marginals, i.e. a matrix with non-negative integer values andspecified row and column sums. Such algorithms are useful in statistics andcombinatorics. When $\Delta^4< M/5$, where $\Delta$ is the maximum of the rowand column sums and $M$ is the sum of all entries of the matrix, our algorithmruns in time linear in $M$ in expectation. Most previously published algorithmsfor this problem are approximate samplers based on Markov chain Monte Carlo,whose provable bounds on the mixing time are typically polynomials with ratherlarge degrees.

Linear-time uniform generation of random sparse contingency tables with specified marginals