Approximately counting bases of bicircular matroids
Heng Guo, Mark Jerrum
TL;DR
This paper presents an efficient randomized algorithm to approximate the number of bases in bicircular matroids, a class where exact counting is computationally hard but approximate counting is feasible.
Contribution
It introduces the first fully polynomial-time randomized approximation scheme for counting bases in bicircular matroids, bridging a gap in computational matroid theory.
Findings
FPRAS for bicircular matroid bases
Approximate counting is efficient despite #P-hardness of exact counting
Advances understanding of computational complexity in matroid theory
Abstract
We give a fully polynomial-time randomised approximation scheme (FPRAS) for the number of bases in a bicircular matroids. This is a natural class of matroids for which counting bases exactly is #P-hard and yet approximate counting can be done efficiently.
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