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Approximately counting bases of bicircular matroids

Part of: Algorithms - Computer Science Graph theory Markov processes

Published online by Cambridge University Press:  06 August 2020

Heng Guo  and
Mark Jerrum
Heng Guo*
Affiliation:
School of Informatics, University of Edinburgh, Informatics Forum, Edinburgh EH8 9AB, UK
Mark Jerrum
Affiliation:
School ofMathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, UK
*
*Corresponding author. Email: hguo@inf.ed.ac.uk
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Abstract

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We give a fully polynomial-time randomized approximation scheme (FPRAS) for the number of bases in 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.

MSC classification

Primary: 68W20: Randomized algorithms 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 05C31: Graph polynomials

Information

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 30 , Issue 1 , January 2021 , pp. 124 - 135
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

Footnotes

†

The work described here was supported by the EPSRC research grant EP/N004221/1 ‘Algorithms that Count’.

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