Constrained many-to-many point matching in two dimensions
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Published:2024-01-26
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ISSN:1862-4472
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Container-title:Optimization Letters
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language:en
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Short-container-title:Optim Lett
Author:
Caraballo L. E., Castro R. A., Díaz-Báñez J. M., Heredia M. A., Urrutia J., Ventura I.ORCID, Zaragoza F. J.
Abstract
AbstractIn the minimum-weight many-to-many point matching problem, we are given a set R of red points and a set B of blue points in the plane, of total size N, and we want to pair up each point in R to one or more points in B and vice versa so that the sum of distances between the paired points is minimized. This problem can be solved in $$O(N^3)$$
O
(
N
3
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time by using a reduction to the minimum-weight perfect matching problem, and thus, it is not fast enough to be used for on-line systems where a large number of tunes need to be compared. Motivated by similarity problems in music theory, in this paper we study several constrained minimum-weight many-to-many point matching problems in which the allowed pairings are given by geometric restrictions, i.e., a bichromatic pair can be matched if and only if the corresponding points satisfy a specific condition of closeness. We provide algorithms to solve these constrained versions in O(N) time when the sets R and B are given ordered by abscissa.
Funder
HORIZON EUROPE Marie Sklodowska-Curie Actions Ministerio de Ciencia e Innovación Sistema Nacional de Investigadores Universidad Nacional Autónoma de México Universidad de Sevilla
Publisher
Springer Science and Business Media LLC
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