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On maximum-sum matchings of points

Author

Listed:
  • Sergey Bereg

    (University of Texas at Dallas)

  • Oscar P. Chacón-Rivera

    (Universidad de Santiago de Chile (USACH), Las Sophoras n° 173)

  • David Flores-Peñaloza

    (Av. Universidad 3000, Circuito Exterior s/n, Alcaldía Coyoacán, CP 04510, Ciudad Universitaria)

  • Clemens Huemer

    (Universitat Politècnica de Catalunya)

  • Pablo Pérez-Lantero

    (Universidad de Santiago de Chile (USACH), Las Sophoras n° 173)

  • Carlos Seara

    (Universitat Politècnica de Catalunya)

Abstract

Huemer et al. (Discrete Mathematics, 2019) proved that for any two point sets R and B with $$|R|=|B|$$ | R | = | B | , 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.

Suggested Citation

  • Sergey Bereg & Oscar P. Chacón-Rivera & David Flores-Peñaloza & Clemens Huemer & Pablo Pérez-Lantero & Carlos Seara, 2023. "On maximum-sum matchings of points," Journal of Global Optimization, Springer, vol. 85(1), pages 111-128, January.
    • Handle: RePEc:spr:jglopt:v:85:y:2023:i:1:d:10.1007_s10898-022-01199-z
    DOI: 10.1007/s10898-022-01199-z
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    References listed on IDEAS

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    1. L. E. Caraballo & C. Ochoa & P. Pérez-Lantero & J. Rojas-Ledesma, 2017. "Matching colored points with rectangles," Journal of Combinatorial Optimization, Springer, vol. 33(2), pages 403-421, February.
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