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Almost Sure Convergence of the Minimum Bipartite Matching Functional in Euclidean Space

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Let L N = L MBM (X 1, . . .,X N ;Y 1, . . . , Y N ) be the minimum length of a bipartite matching between two sets of points in R d, where X 1,...,X N , . . . and Y 1, . . . , Y N , . . . are random points independently and uniformly distributed in [0, 1]d. We prove that for d ≥ 3, L N /N 1−1/d converges with probability one to a constant β MBM (d) > 0 as N → ∞.

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Authors and Affiliations

  1. Center for Hearing and Communication Research, Karolinska Institutet, 17176, Stockholm, Sweden

    J. H. Boutet de Monvel

  2. Laboratoire de Physique Théorique et Modèles Statistiques, Université de Paris-Sud, 91405, Orsay, France

    O. C. Martin

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  1. J. H. Boutet de Monvel
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  2. O. C. Martin
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Correspondence to J. H. Boutet de Monvel.

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Boutet de Monvel, J.H., Martin, O.C. Almost Sure Convergence of the Minimum Bipartite Matching Functional in Euclidean Space. Combinatorica 22, 523–530 (2002). https://doi.org/10.1007/s00493-002-0004-x

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  • DOI: https://doi.org/10.1007/s00493-002-0004-x

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