Random generation of combinatorial structures from a uniform
Theoretical Computer Science
A random polynomial-time algorithm for approximating the volume of convex bodies
Journal of the ACM (JACM)
A polynomial time algorithm for counting integral points in polyhedra when the dimension is fixed
Mathematics of Operations Research
Random Structures & Algorithms
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Polynomial-time counting and sampling of two-rowed contingency tables
Theoretical Computer Science
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
Combinatorics, Probability and Computing
A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries
Journal of the ACM (JACM)
Counting Integer Flows in Networks
Foundations of Computational Mathematics
Fast Algorithms for Logconcave Functions: Sampling, Rounding, Integration and Optimization
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
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
Markov bases and structural zeros
Journal of Symbolic Computation
Time hierarchies for sampling distributions
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
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We consider the problem of approximately counting integral flows in a network. We show that there is a fully polynomial randomized approximation scheme (FPRAS) based on volume estimation if all capacities are sufficiently large, generalizing a result of Dyer, Kannan, and Mount [Random Structures Algorithms, 10 (1997), pp. 487-506]. We apply this to approximating the number of contingency tables with prescribed cell bounds when the number of rows is constant, but the row sums, column sums, and cell bounds may be arbitrary. We provide an FPRAS for this problem via a combination of dynamic programming and volume estimation. This generalizes an algorithm of Cryan and Dyer [J. Comput. System Sci., 67 (2003), pp. 291-310] for standard contingency tables, but the analysis here is considerably more intricate.