Practical discrete unit disk cover using an exact line-separable algorithm

Abstract

Given m unit disks and n points in the plane, the discrete unit disk cover problem is to select a minimum subset of the disks to cover the points. This problem is NP-hard [11] and the best previous practical solution is a 38-approximation algorithm by Carmi et al. [4]. We first consider the line-separable discrete unit disk cover problem (the set of disk centres can be separated from the set of points by a line) for which we present an O(m 2 n)-time algorithm that finds an exact solution. Combining our line-separable algorithm with techniques from the algorithm of Carmi et al. [4] results in an O(m 2 n 4) time 22-approximate solution to the discrete unit disk cover problem. © 2009 Springer-Verlag Berlin Heidelberg.