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We give a fully polynomial-time randomised approximation scheme (FPRAS) for the number of bases in a bicircular matroids.
The number of combinatorial geometries
Mike J. Piff and Dominic J. A. Welsh · 1971
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Matrix generalizations of some theorems on trees, cycles and cocycles in graphs
Stephen B. Maurer · 1976
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Bicircular matroids
Laurence R. Matthews · 1977
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Balanced matroids
Tomás Feder and Milena Mihail · 1992
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Randomized algorithms
Rajeev Motwani and Prabhakar Raghavan · 1995
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Randomised approximation of the number of bases
Laura Chávez Lomelí and Dominic J. A. Welsh · 1996
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Strong convergence and a game of numbers
Kimmo Eriksson · 1996
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Generating random spanning trees more quickly than the cover time
David Bruce Wilson · 1996
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How to get a perfectly random sample from a generic Markov chain and generate a random spanning tree of a directed graph
James G. Propp and David B. Wilson · 1998
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Generating a random sink-free orientation in quadratic time
Henry Cohn, Robin Pemantle, and James G. Propp · 2002
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Counting, sampling and integrating: algorithms and complexity
Mark Jerrum · 2003
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Elementary bounds on Poincaré and log-Sobolev constants for decomposable Markov chains
Mark Jerrum, Jung-Bae Son, Prasad Tetali, and Eric Vigoda · 2004
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On the number of bases of bicircular matroids
Omer Giménez, Anna de Mier, and Marc Noy · 2005
Cited alongside, same era.
On the complexity of computing the Tutte polynomial of bicircular matroids
Omer Giménez and Marc Noy · 2006
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Two remarks concerning balanced matroids
Mark Jerrum · 2006
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Adaptive simulated annealing: A near-optimal connection between sampling and counting
Daniel Štefankovič, Santosh Vempala, and Eric Vigoda · 2009
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Approximation algorithms for the normalizing constant of Gibbs distributions
Mark Huber · 2015
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Learning about critical phenomena from scribbles and sandpiles
Adrien Kassel · 2015
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Random curves on surfaces induced from the Laplacian determinant
Adrien Kassel and Richard Kenyon · 2017
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Tight bounds for popping algorithms
Heng Guo and Kun He · 2018
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A faster approximation algorithm for the Gibbs partition function
Vladimir Kolmogorov · 2018
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Log-concave polynomials II: high-dimensional walks and an FPRAS for counting bases of a matroid
Nima Anari, Kuikui Liu, Shayan Oveis Gharan, and Cynthia Vinzant · 2019
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Moser and Tardos meet Lovász
Kashyap Babu Rao Kolipaka and Mario Szegedy · 2011
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Counting bases of representable matroids
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Generalized loop-erased random walks and approximate reachability
Igor Gorodezky and Igor Pak · 2014
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A polynomial-time approximation algorithm for all-terminal network reliability
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Heng Guo, Mark Jerrum, and Jingcheng Liu · 2019
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