FPRAS Approximation of the Matrix Permanent in Practice
Abstract
The matrix permanent belongs to the complexity class #P-Complete. It is generally believed to be computationally infeasible for large problem sizes, and significant research has been done on approximation algorithms for the matrix permanent. We present an implementation and detailed runtime analysis of one such Markov Chain Monte Carlo (MCMC) based Fully Polynomial Randomized Approximation Scheme (FPRAS) for the matrix permanent, which has previously only been described theoretically and with big-Oh runtime analysis. We demonstrate by analysis and experiment that the constant factors hidden by previous big-Oh analyses result in computational infeasibility.
Cite
@article{arxiv.2012.03367,
title = {FPRAS Approximation of the Matrix Permanent in Practice},
author = {James E. Newman and Moshe Y. Vardi},
journal= {arXiv preprint arXiv:2012.03367},
year = {2020}
}
Comments
This article is based on an MS thesis by the first author, submitted to Rice University on June 12, 2020. Research partially supported by NSF Grant no. IIS-1527668