Center of Maximum-Sum Matchings of Bichromatic Points

Let R and B be two point sets in the plane with |R|=|B|=n. Let M={(r<inf>i</inf>,b<inf>i</inf>),i=1,2,…,n} be a perfect matching that matches points of R with points of B and maximizes ∑<inf>i=1</inf>n‖r<inf>i</inf>−b<inf>i</inf>‖, 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<inf>i</inf>−o‖+‖b<inf>i</inf>−o‖≤2‖r<inf>i</inf>−b<inf>i</inf>‖ for all i∈{1,2,…,n}. © 2023 Elsevier B.V.