Combinatorica

, Volume 22, Issue 4, pp 523–530 | Cite as

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

Original Paper

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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Copyright information

© János Bolyai Mathematical Society 2002

Authors and Affiliations

  1. 1.Center for Hearing and Communication ResearchKarolinska InstitutetStockholmSweden
  2. 2.Laboratoire de Physique Théorique et Modèles StatistiquesUniversité de Paris-SudOrsayFrance

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