On maximum-sum matchings of bichromatic points
arxiv(2024)
摘要
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 any continuous
(semi)metric, 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..
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要