Almost Sure Convergence of the Minimum Bipartite Matching Functional in Euclidean Space
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Let LN = LMBM(X1, . . .,XN;Y1, . . . , YN) be the minimum length of a bipartite matching between two sets of points in Rd, where X1,...,XN, . . . and Y1, . . . , YN, . . . are random points independently and uniformly distributed in [0, 1]d. We prove that for d ≥ 3, LN/N1−1/d converges with probability one to a constant βMBM(d) > 0 as N → ∞.
AMS Subject Classification (2000):60D05
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