Given a set D of m unit disks and a set P of n points in the plane, the discrete unit disk cover problem is to select a minimum cardinality subset D ⊆ D to cover P. This problem is NP-hard [14] [5] . We first consider the line-separable discrete unit disk cover problem (the set of disk centers can be separated from the set of points by a line) for which we present an O(n(log n+m))-time algorithm that finds an exact solution. Combining our line-separable algorithm with techniques from the algorithm of Carmi et al. [5] results in an O(m 2 n 4 ) time 22-approximate solution to the discrete unit disk cover problem.
In the literature it is known as line-separable discrete unit disk cover (LSDUDC) problem REF .
AN IMPROVED LINE-SEPARABLE ALGORITHM FOR DISCRETE UNIT DISK
Mathematics Computer Science