Center of maximum-sum matchings of bichromatic points

01/17/2023

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by   Pablo Pérez-Lantero, et al.

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Let R and B be two disjoint point sets in the plane with |R|=|B|=n. Let ℳ={(r_i,b_i),i=1,2,…,n} be a perfect matching that matches points of R with points of B and maximizes ∑_i=1^nr_i-b_i, the total Euclidean distance of the matched pairs. In this paper, we prove that there exists a point o of the plane (the center of ℳ) such that r_i-o+b_i-o≤√(2) r_i-b_i for all i∈{1,2,…,n}.