We study the binary contingency table problem, where our goal is to count the number of n x m binary tables ({0,1}-valued matrices) that satisfy certain given row and column sums. We present a straightforward Markov Chain Monte Carlo (MCMC) algorithm that gives robust estimates for the number of binary contingency tables when the dimension of the matrices is relatively low. We then present the parallel tempering method, which makes use of coupled Markov Chains running at different "temperatures", for approximately counting the number of binary contingency tables. We then discuss the qualitative properties of the parallel tempering method and its advantages with regards to other randomized algorithms such as the splitting algorithm.
Sukurdeep, Yashil,
"Applications of randomized algorithms to counting problems"
(2017).
Summer Research Symposium.
Brown Digital Repository. Brown University Library.
https://doi.org/10.26300/zsx9-v648
Each year, Brown University showcases the research of its undergraduates at the Summer Research Symposium. More than half of the student-researchers are UTRA recipients, while others receive funding from a variety of Brown-administered and national programs and fellowships and go …
