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Date:
27 Oct 2007
Random Bichromatic Matchings
 Nayantara Bhatnagar,
 Dana Randall,
 Vijay V. Vazirani,
 Eric Vigoda
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Given a graph with edges colored Red and Blue, we study the problem of sampling and approximately counting the number of matchings with exactly k Red edges. We solve the problem of estimating the number of perfect matchings with exactly k Red edges for dense graphs. We study a Markov chain on the space of all matchings of a graph that favors matchings with k Red edges. We show that it is rapidly mixing using nontraditional canonical paths that can backtrack. We show that this chain can be used to sample matchings in the 2dimensional toroidal lattice of any fixed size ℓ with k Red edges, where the horizontal edges are Red and the vertical edges are Blue.
An extended abstract appeared in J.R. Correa, A. Hevia and M.A. Kiwi (eds.) Proceedings of the 7th Latin American Theoretical Informatics Symposium, LNCS 3887, pp. 190–201, Springer, 2006.
N. Bhatnagar’s and D. Randall’s research was supported in part by NSF grants CCR0515105 and DMS0505505.
V.V. Vazirani’s research was supported in part by NSF grants 0311541, 0220343 and CCR0515186.
N. Bhatnagar’s and E. Vigoda’s research was supported in part by NSF grant CCR0455666.
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 Title
 Random Bichromatic Matchings
 Journal

Algorithmica
Volume 50, Issue 4 , pp 418445
 Cover Date
 20080401
 DOI
 10.1007/s0045300790964
 Print ISSN
 01784617
 Online ISSN
 14320541
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Markov chains
 Matchings
 Sampling
 Approximate counting
 Industry Sectors
 Authors

 Nayantara Bhatnagar ^{(1)}
 Dana Randall ^{(1)}
 Vijay V. Vazirani ^{(1)}
 Eric Vigoda ^{(1)}
 Author Affiliations

 1. College of Computing, Georgia Institute of Technology, 801 Atlantic Drive, Atlanta, GA, 303320280, USA