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 → ∞.
AMS Subject Classification (2000):60D05
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