Unit Disk Cover Problem

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 covered by a disk in D∗∗. For the DUDC problem, we propose an (9+ǫ)-factor (0 < ǫ ≤ 6) approximation algorithm. The previous best known approximation factor was 15 [12]. For the RRC problem, we propose (i) an (9+ǫ)-factor (0 < ǫ ≤ 6) approximation algorithm, (ii) an 2.25-factor approximation algorithm in reduce radius setup, improving previous 4-factor approximation result in the same setup [11]. 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.