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arXiv · 2403.08977

On maximum-sum matchings of bichromatic points

Oscar Chacón-Rivera·Pablo Pérez-Lantero
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Abstract

Huemer et al. (Discrete Math, 2019) proved that for any two finite point sets $R$ and $B$ in the plane with $|R| = |B|$, 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 nonempty common intersection. A pair of matched points induces the disk that has the segment connecting the points as diameter. In this note, we characterize these maximum-sum matchings for some family of continuous (semi-)metrics, focusing on both the Euclidean distance and squared Euclidean distance. Using this characterization, we give a different but simpler proof for the common intersection property proved by Huemer et al..

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Oscar Chacón-Rivera, Pablo Pérez-Lantero. 2024-03-13. On maximum-sum matchings of bichromatic points. https://arxiv.org/abs/2403.08977

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