Random bichromatic matchings

Authors:
Nayantara Bhatnagar;Dana Randall;Vijay V. Vazirani;Eric Vigoda
Affiliations:
College of Computing, Georgia Institute of Technology, Atlanta, GA;College of Computing, Georgia Institute of Technology, Atlanta, GA;College of Computing, Georgia Institute of Technology, Atlanta, GA;College of Computing, Georgia Institute of Technology, Atlanta, GA
Venue:
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Year:
2006

Citing 5
Cited 0

Random generation of combinatorial structures from a uniform

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Matching is as easy as matrix inversion

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SIAM Journal on Computing
Matchings in colored bipartite networks

Discrete Applied Mathematics
A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries

Journal of the ACM (JACM)

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Abstract

Given a graph with edges colored Red and Blue, we wish to sample and approximately count the number of perfect matchings with exactly kRed edges. We study a Markov chain on the space of all matchings of a graph that favors matchings with kRed edges. We show that it is rapidly mixing using non-traditional canonical paths that can backtrack, based on an algorithm for a simple combinatorial problem. We show that this chain can be used to sample dimer configurations on a 2-dimensional toroidal region with kRed edges.