An O(n2)-Time Algorithm for Computing a Max-Min 3-Dispersion on a Point Set in Convex Position

• Published in: IEICE Transactions on Information and Systems Vol. E105.D; no. 3; pp. 503 - 507
• Main Authors: UCHIZAWA, Kei, NAKANO, Shin-ichi, YAMANAKA, Katsuhisa, YAMAGUCHI, Yutaro, KOBAYASHI, Yasuaki, UNO, Takeaki
• Format: Journal Article
• Language: English
• Published: Tokyo The Institute of Electronics, Information and Communication Engineers 01.03.2022; Japan Science and Technology Agency
• Subjects: Algorithms; Dispersion; dispersion problem; facility location
• ISSN: 0916-8532; 1745-1361; 1745-1361
• DOI: 10.1587/transinf.2021FCP0013

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.