An O(n(2))-Time Algorithm for Computing a Max-Min 3-Dispersion on a Point Set in Convex Position

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(n(2))-time algorithm to compute a 3-dispersion of P.