Sampling binary contingency tables with a greedy start

We study the problem of counting and randomly sampling binary contingency tables. For given row and column sums, we are interested in approximately counting (or sampling) 0/1 n x m matrices with the specified row/column sums. We present a simulated annealing algorithm with running time O((nm)2D3d max log5(n+m)) for any row/column sums where D is the number of non-zero entries and d max is the maximum row/column sum. This is the first algorithm to directly solve binary contingency tables for all row/column sums. Previous work reduced the problem to the permanent, or restricted attention to row/column sums that are close to regular. The interesting aspect of our simulated annealing algorithm is that it starts at a non-trivial instance, whose solution relies on the existence of short alternating paths in the graph constructed by a particular Greedy algorithm.

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