Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network

  Advanced Search  

DIAMETER PARTITIONING School of Computer Science

David Avis
School of Computer Science
McGill University
805 Sherbrooke St. W.
Montreal, Canada, H3A 2K6
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


Source: Avis, David - School of Computer Science, McGill University


Collections: Computer Technologies and Information Sciences