## 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 [Johnson 1982] and the best previous practical solution is a 38-approximation algorithm by Carmi et al. [Carmi 2007]. 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. [Carmi 2007] results in an O(m

^{2}n

^{4}) time 22-approximate solution to the discrete unit disk cover problem.