Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/288281 
Year of Publication: 
2020
Citation: 
[Journal:] Mathematical Methods of Operations Research [ISSN:] 1432-5217 [Volume:] 92 [Issue:] 1 [Publisher:] Springer [Place:] Berlin, Heidelberg [Year:] 2020 [Pages:] 133-163
Publisher: 
Springer, Berlin, Heidelberg
Abstract: 
We consider the problem of finding an optimal transport plan between an absolutely continuous measure and a finitely supported measure of the same total mass when the transport cost is the unsquared Euclidean distance. We may think of this problem as closest distance allocation of some resource continuously distributed over Euclidean space to a finite number of processing sites with capacity constraints. This article gives a detailed discussion of the problem, including a comparison with the much better studied case of squared Euclidean cost. We present an algorithm for computing the optimal transport plan, which is similar to the approach for the squared Euclidean cost by Aurenhammer et al. (Algorithmica 20(1):61–76, 1998) and Mérigot (Comput Graph Forum 30(5):1583–1592, 2011). We show the necessary results to make the approach work for the Euclidean cost, evaluate its performance on a set of test cases, and give a number of applications. The later include goodness-of-fit partitions, a novel visual tool for assessing whether a finite sample is consistent with a posited probability density.
Subjects: 
Monge–Kantorovich problem
Spatial resource allocation
Wasserstein metric
Weighted Voronoi tessellation
JEL: 
D18
N20
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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