Artikel
Semi-discrete optimal transport: a solution procedure for the unsquared Euclidean distance case
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.
- Language
-
Englisch
- Bibliographic citation
-
Journal: Mathematical Methods of Operations Research ; ISSN: 1432-5217 ; Volume: 92 ; Year: 2020 ; Issue: 1 ; Pages: 133-163 ; Berlin, Heidelberg: Springer
- Classification
-
Wirtschaft
Consumer Protection
Economic History: Financial Markets and Institutions: General, International, or Comparative
- Subject
-
Monge–Kantorovich problem
Spatial resource allocation
Wasserstein metric
Weighted Voronoi tessellation
- Event
-
Geistige Schöpfung
- (who)
-
Hartmann, Valentin
Schuhmacher, Dominic
- Event
-
Veröffentlichung
- (who)
-
Springer
- (where)
-
Berlin, Heidelberg
- (when)
-
2020
- DOI
-
doi:10.1007/s00186-020-00703-z
- Last update
-
10.03.2025, 11:46 AM CET
Data provider
ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften - Leibniz-Informationszentrum Wirtschaft. If you have any questions about the object, please contact the data provider.
Object type
- Artikel
Associated
- Hartmann, Valentin
- Schuhmacher, Dominic
- Springer
Time of origin
- 2020
Other Objects (12)
On distance preserving mapping of Euclidean-like planes
On Clustering Time Series Using Euclidean Distance and Pearson Correlation
Euclidean distance-optimized data transformation for cluster analysis in biomedical data (EDOtrans)
Euclidean sequences
Optimal transport : a semi-discrete approach
On discrete groups of Euclidean isometries: representation theory, harmonic analysis and splitting properties
Euclidean random permutations
Non-Euclidean Geometry.
Semi-discrete unbalanced optimal transport and quantization
A Hashin-Shtrikman type semi-analytical homogenization procedure
Euclidean distance versus travel time in business location: A probabilistic mixture of hurdle-Poisson models
Symbolic coding Euclidean billiards.
On distance preserving mapping of Euclidean-like planes
On Clustering Time Series Using Euclidean Distance and Pearson Correlation
Euclidean distance-optimized data transformation for cluster analysis in biomedical data (EDOtrans)
Euclidean sequences
Optimal transport : a semi-discrete approach
On discrete groups of Euclidean isometries: representation theory, harmonic analysis and splitting properties
Euclidean random permutations
Non-Euclidean Geometry.
Semi-discrete unbalanced optimal transport and quantization
A Hashin-Shtrikman type semi-analytical homogenization procedure
Euclidean distance versus travel time in business location: A probabilistic mixture of hurdle-Poisson models
Symbolic coding Euclidean billiards.
On distance preserving mapping of Euclidean-like planes
On Clustering Time Series Using Euclidean Distance and Pearson Correlation
Euclidean distance-optimized data transformation for cluster analysis in biomedical data (EDOtrans)
Euclidean sequences
Optimal transport : a semi-discrete approach
On discrete groups of Euclidean isometries: representation theory, harmonic analysis and splitting properties
Euclidean random permutations
Non-Euclidean Geometry.
Semi-discrete unbalanced optimal transport and quantization
A Hashin-Shtrikman type semi-analytical homogenization procedure
Euclidean distance versus travel time in business location: A probabilistic mixture of hurdle-Poisson models