In this paper, we consider constant factor approximation algorithms for a variant of the discrete piercing set problem for unit disks. Here a set of points P is given; the objective is to choose minimum number of points in P to pierce the unit disks centered at all the points in P . We first propose a very simple algorithm that produces 12-approximation result in O(n log n) time. Next, we improve the approximation factor to 4 and then to 3. The worst case running time of these algorithms are O(n 8 log n) and O(n 15 log n) respectively. Apart from the space required for storing the input, the extra work-space requirement of all these algorithms are O(1). Finally, we propose a PTAS for the same problem. Given a positive integer k, it can produce a solution with performance ratio (1 +
Recently, De at al. REF considered the geometric version of MDS problem and proposed 12-factor, 4-factor, and 3-factor approximation algorithms with running time O(n log n), O(n 8 log n), and O(n 15 log n) respectively.
Approximation Algorithms for a Variant of discrete Piercing Set Problem for Unit Disks
Int. J. Comput. Geometry Appl.
Int. J. Comput. Geometry Appl.
Computer Science Mathematics