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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
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