Applications of randomized algorithms to counting problems

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Title
Applications of randomized algorithms to counting problems
Contributors
Sukurdeep, Yashil (creator)
Dupuis, Paul (advisor)
Brown University. Karen T. Romer Undergraduate Teaching and Research Awards (research program)
Doi
10.26300/zsx9-v648
Date Created
2017
Abstract
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.
Keywords
Markov processes
Monte Carlo method
Algorithms
Extent
1 poster

Citation

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

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    Each year, Brown showcases the research of nearly 200 undergraduates at our 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. Presenters include ...

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