An O(n2)-Time Algorithm for Computing a Max-Min 3-Dispersion on a Point Set in Convex Position - UCHIZAWA, Kei; NAKANO, Shin-ichi; YAMANAKA, Katsuhisa; YAMAGUCHI, Yutaro; KOBAYASHI, Yasuaki; UNO, Takeaki (IEICE Transactions on Information and Systems, 2022)
Given a set P of n points and an integer k, we wish to place k facilities on points in P so that the minimum distance between facilities is maximized. The problem is called the k-dispersion problem, and the set of such k points is called a k-dispersion of P. Note that the 2-dispersion problem corresponds to the computation of the diameter of P. Thus, the k-dispersion problem is a natural generalization of the diameter problem. In this paper, we consider the case of k=3, which is the 3-dispersion problem, when P is in convex position. We present an O(n2)-time algorithm to compute a 3-dispersion of P.