Max-Min 3-Dispersion Problems

Abstract

Given a set P of n points on which facilities can be placed and an integer k, we want to place k facilities on some points so that the minimum distance between facilities is maximized. The problem is called the k-dispersion problem. In this paper we consider the 3-dispersion problem when P is a set of points on a plane. Note that the 2-dispersion problem corresponds to the diameter problem. We give an O(n) time algorithm to solve the 3-dispersion problem in the (forumala presented). metric, and an O(n) time algorithm to solve the 3-dispersion problem in the (forumala presented) metric. Also we give an (forumala presented) time algorithm to solve the 3-dispersion problem in the (forumala presented) metric.