Random generation of combinatorial structures from a uniform
Theoretical Computer Science
Approximate counting, uniform generation and rapidly mixing Markov chains
Information and Computation
Random Structures & Algorithms
Simple Markov-chain algorithms for generating bipartite graphs and tournaments
Random Structures & Algorithms
Improved bounds for sampling contingency tables
Random Structures & Algorithms
Rapidly Mixing Markov Chains for Sampling Contingency Tables with a Constant Number of Rows
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Approximate counting by dynamic programming
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Journal of Computer and System Sciences - STOC 2002
A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries
Journal of the ACM (JACM)
Approximately counting integral flows and cell-bounded contingency tables
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Sampling binary contingency tables with a greedy start
Random Structures & Algorithms - Proceedings from the 12th International Conference “Random Structures and Algorithms”, August1-5, 2005, Poznan, Poland
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The problems of uniformly sampling and approximately counting contingency tables have been widely studied, but efficient solutions are only known in special cases. One appealing approach is the Diaconis and Gangolli Markov chain which updates the entries of a random 2 ×2 submatrix. This chain is known to be rapidly mixing for cell-bounded tables only when the cell bounds are all 1 and the row and column sums are regular. We demonstrate that the chain can require exponential time to mix in the cell-bounded case, even if we restrict to instances for which the state space is connected. Moreover, we show the chain can be slowly mixing even if we restrict to natural classes of problem instances, including regular instances with cell bounds of either 0 or 1 everywhere, and dense instances where at least a linear number of cells in each row or column have non-zero cell-bounds.