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

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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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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AMS Subject Classification (2000):

  • 60D05