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Random Bichromatic Matchings

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Abstract

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 non-traditional canonical paths that can backtrack. We show that this chain can be used to sample matchings in the 2-dimensional toroidal lattice of any fixed size ℓ with k Red edges, where the horizontal edges are Red and the vertical edges are Blue.

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Authors and Affiliations

  1. College of Computing, Georgia Institute of Technology, 801 Atlantic Drive, Atlanta, GA, 30332-0280, USA

    Nayantara Bhatnagar, Dana Randall, Vijay V. Vazirani & Eric Vigoda

Authors
  1. Nayantara Bhatnagar
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  2. Dana Randall
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  3. Vijay V. Vazirani
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  4. Eric Vigoda
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Corresponding author

Correspondence to Nayantara Bhatnagar.

Additional information

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 CCR-0515105 and DMS-0505505.

V.V. Vazirani’s research was supported in part by NSF grants 0311541, 0220343 and CCR-0515186.

N. Bhatnagar’s and E. Vigoda’s research was supported in part by NSF grant CCR-0455666.

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Bhatnagar, N., Randall, D., Vazirani, V.V. et al. Random Bichromatic Matchings. Algorithmica 50, 418–445 (2008). https://doi.org/10.1007/s00453-007-9096-4

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  • DOI: https://doi.org/10.1007/s00453-007-9096-4

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