On maximum-sum matchings of points
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Published:2022-06-21
Issue:1
Volume:85
Page:111-128
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ISSN:0925-5001
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Container-title:Journal of Global Optimization
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language:en
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Short-container-title:J Glob Optim
Author:
Bereg Sergey, Chacón-Rivera Oscar P., Flores-Peñaloza David, Huemer Clemens, Pérez-Lantero Pablo, Seara CarlosORCID
Abstract
AbstractHuemer et al. (Discrete Mathematics, 2019) proved that for any two point sets R and B with $$|R|=|B|$$
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R
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=
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B
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, the perfect matching that matches points of R with points of B, and maximizes the total squared Euclidean distance of the matched pairs, has the property that all the disks induced by the matching have a common point. Each pair of matched points $$p\in R$$
p
∈
R
and $$q\in B$$
q
∈
B
induces the disk of smallest diameter that covers p and q. Following this research line, in this paper we consider the perfect matching that maximizes the total Euclidean distance. First, we prove that this new matching for R and B does not always ensure the common intersection property of the disks. Second, we extend the study of this new matching for sets of 2n uncolored points in the plane, where a matching is just a partition of the points into n pairs. As the main result, we prove that in this case all disks of the matching do have a common point.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Management Science and Operations Research,Control and Optimization,Computer Science Applications,Business, Management and Accounting (miscellaneous)
Reference22 articles.
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