Unit Disk Cover Problem [article]

Rashmisnata Acharyya, Manjanna B., Gautam K. Das
2012 arXiv   pre-print
Given a set D of unit disks in the Euclidean plane, we consider (i) the discrete unit disk cover (DUDC) problem and (ii) the rectangular region cover (RRC) problem. In the DUDC problem, for a given set P of points the objective is to select minimum cardinality subset D^* ⊆ D such that each point in P is covered by at least one disk in D^*. On the other hand, in the RRC problem the objective is to select minimum cardinality subset D^**⊆ D such that each point of a given rectangular region R is
more » ... vered by a disk in D^**. For the DUDC problem, we propose an (9+ϵ)-factor (0 < ϵ≤ 6) approximation algorithm. The previous best known approximation factor was 15 FL12. For the RRC problem, we propose (i) an (9 + ϵ)-factor (0 < ϵ≤ 6) approximation algorithm, (ii) an 2.25-factor approximation algorithm in reduce radius setup, improving previous 4-factor approximation result in the same setup FKKLS07. The solution of DUDC problem is based on a PTAS for the subproblem LSDUDC, where all the points in P are on one side of a line and covered by the disks centered on the other side of that line.
arXiv:1209.2951v1 fatcat:knrkk5vwvjezxny2677ygodth4