An Improved Line-Separable Algorithm for Discrete Unit Disk Cover



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 [D. Johnson, 1982] and the best previous practical solution is a 38-approximation algorithm by [Carmi et al., 2007]. 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., 2007] results in an O(m2 n4) time 22-approximate solution to the discrete unit disk cover problem.

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