Three-Dimensional Statistical Data Security Problems
SIAM Journal on Computing
The Markov chain Monte Carlo method: an approach to approximate counting and integration
Approximation algorithms for NP-hard problems
On sampling with Markov chains
Proceedings of the seventh international conference on Random structures and algorithms
Random Structures & Algorithms
Random generation of 2 × n contingency tables
Random Structures & Algorithms
Simple Markov-chain algorithms for generating bipartite graphs and tournaments
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Polynomial-time counting and sampling of two-rowed contingency tables
Theoretical Computer Science
Randomized algorithms: approximation, generation, and counting
Randomized algorithms: approximation, generation, and counting
A polynomial-time approximation algorithm for the permanent of a matrix with non-negative entries
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
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
Path coupling: A technique for proving rapid mixing in Markov chains
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
| Hi-index | 5.23 |
We propose two Markov chains for sampling (m + 1)-dimensional contingency tables indexed by {1, 2}m × {1, 2,..... n}. Stationary distributions of our chains are the uniform distribution and a conditional multinomial distribution (which is equivalent to the hypergeometric distribution if m = 1). Mixing times of our chains are bounded by (½)n(n - 1) ln(N/(2mε)) = (½)n(n - 1) ln(dn/ε), where d is the average of the values in the cells and ε is a given error bound. We use the path coupling method for estimating the mixing times of our chains and showed that our chains mix rapidly.