Practical Discrete Unit Disk Cover Using an Exact Line-Separable Algorithm ⋆ Francisco Claude 1 , Reza Dorrigiv 1 , Stephane Durocher 2,1 , Robert Fraser 1 , Alejandro L´ opez-Ortiz 1 ⋆⋆ , and Alejandro Salinger 1 1 Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada, {fclaude,rdorrigiv,sdurocher,r3fraser, alopez-o,ajsalinger}@cs.uwaterloo.ca 2 Department of Computer Science, University of Manitoba, Winnipeg, Canada, durocher@cs.umanitoba.ca 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 [Joh82] and the best previ- ous practical solution is a 38-approximation algorithm by Carmi et al. [CKLT07]. 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. [CKLT07] results in an O(m 2 n 4 ) time 22-approximate solution to the discrete unit disk cover problem. 1 Introduction Recent interest in specific geometric set cover problems is partly motivated by ap- plications in wireless networking. In particular, when wireless clients and servers are modelled as points in the plane and the range of wireless transmission is assumed to be constant (say one unit), the resulting region of wireless communi- cation is a disk of unit radius centred on the point representing the corresponding wireless transmitting device. Under this model, sender a successfully transmits a wireless message to receiver b if and only if point b is covered by the unit disk centred at point a. This model applies more generally to a variety of facility location problems for which the Euclidean distance between clients and facilities cannot exceed a given radius, and clients and candidate facility locations are represented by discrete sets of points. Examples include (1) select locations for wireless servers (e.g., gateways) from a set of candidate locations to cover a set of wireless clients, (2) position a fleet of water bombers at airports such that every active forest fire is within a given maximum distance of a water bomber, (3) se- lect a set of weather radar antennae to cover a set of cities, (4)select locations for ⋆ Funding for this project was provided by the NSERC Strategic Grant on Optimal Data Structures for Organization and Retrieval of Spatial Data. ⋆⋆ Part of this work took place while the fifth author was on sabbatical at the Max- Planck-Institut f¨ ur Informatik in Saarbr¨ ucken, Germany.