Almost sure convergence of the minimum bipartite matching functional in Euclidean space
Boutet De Monvel, J. ; Martin, Olivier,
HAL, hal-00003446 / Harvested from HAL
Text on HAL
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 $.
Publié le : 2002-07-05
Classification:  [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO],  [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] 
@article{hal-00003446,
     author = {Boutet De Monvel, J. and Martin, Olivier, },
     title = {Almost sure convergence of the minimum bipartite matching functional in Euclidean space},
     journal = {HAL},
     volume = {2002},
     number = {0},
     year = {2002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00003446}
}

Boutet De Monvel, J.; Martin, Olivier, . Almost sure convergence of the minimum bipartite matching functional in Euclidean space. HAL, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/hal-00003446/