A Polynomial-Time Approximation Algorithm for a Geometric Dispersion Problem

We consider the problem of placing a set of disks in a region containing obstacles such that no two disks intersect. We are given a bounding polygon P and a set R of possibly intersecting unit disks whose centers are in P . The task is to find a set B of m disks of maximum radius such that no disk in B intersects a disk in B ∪ R, where m is the maximum number of unit disks that can be packed. Baur and Fekete showed that the problem cannot be solved efficiently for radii that exceed 13/14, unless P = NP . In this paper we present a 2/3approximation algorithm.