DIAMETER PARTITIONING School of Computer Science Summary: DIAMETER PARTITIONING David Avis School of Computer Science McGill University 805 Sherbrooke St. W. Montreal, Canada, H3A 2K6 ABSTRACT We discuss the problem of partitioning a set of points into two sub­ sets with certain conditions on the diameters of the subsets and on their cardinalities. For example, we give an O(n 2 log n) algorithm to find the smallest t such that the set can be split into two equal cardinality subsets each of which has diameter at most t. We also give an algorithm that takes two pairs of points (x, y) and (s, t) and decides whether the set can be par­ titioned into two subsets with the respective pairs of points as diameters. Key Words. Computational Geometry, Partitioning, Diameter 1. Introduction Consider a set of communications posts on a large plane. Each post is equipped with a transmitter that can reach some distance t from the post. If all the posts are within dis­ tance t of each other, all can communicate without difficulty. Suppose, however, that some posts are further than t units apart. We would like to know if the posts can be split Collections: Computer Technologies and Information Sciences