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Comptes Rendus Mathématique
Volume 348, n° 15-16
pages 901-905 (août 2010)
Doi : 10.1016/j.crma.2010.07.010
Received : 1 December 2009 ;  accepted : 12 July 2010
Local matching indicators for concave transport costs
Indicateurs d'appariement locaux pour le transport en coût concave
 

Julie Delon a , Julien Salomon b , Andreĭ Sobolevskiĭ c, d
a LTCI CNRS, Télécom ParisTech, France 
b Université Paris-Dauphine/CEREMADE, place du Maléchal de Tassigny, 75016 Paris, France 
c A.A. Kharkevich Institute for Information Transmission Problems, Moscow, Russia 
d UMI 2615 CNRS “Laboratoire J.-V. Poncelet”, France 

Abstract

In this Note, we introduce a class of indicators that enable to compute efficiently optimal transport plans associated to arbitrary distributions of N demands and N supplies in R in the case where the cost function is concave. The cost of these indicators is small and independent of N . Using them recursively according to a particular algorithm allows to find an optimal transport plan in less than   evaluations of the cost function.

The full text of this article is available in PDF format.
Résumé

Dans cette Note, nous introduisons une classe d'indicateurs permettant de calculer efficacement des plans de transport optimaux associés à des distributions arbitraires de N sources et de N puits sur la droite réelle dans le cas d'une fonction de coût concave. Ces indicateurs ont un coût de calcul faible et indépendant de N . Leur usage récursif permet, selon un certain algorithme, le calcul d'un plan de transport optimal en au plus   opérations.

The full text of this article is available in PDF format.


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