Almost sure convergence of the minimum bipartite matching functional in Euclidean space

Details Almost sure convergence of the minimum bipartite matching functional in Euclidean space Almost sure convergence of the minimum bipartite matching functional in Euclidean space

2002-05-13

arxiv.org/abs/math/0205140v1

Combinatorica 22(4):523-530 (2002)

Mathematics

Combinatorics

To appear in Combinatorica

Scientific paper

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 $\mathbf{R}^d$, 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 $d \ge 3$, $L_N/N^{1-1/d}$ converges with probability one to a constant $\beta_{MBM}(d)>0$ as $N\to \infty $.

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