Range assignment of base-stations maximizing coverage area without interference.

We study the problem of assigning non-overlapping geometric objects centered at a given set of points such that the sum of area covered by them is maximized. The problem remains open since 2002, as mentioned in a lecture slide of David Eppstein. In this paper, we have performed an exhaustive study on the problem. We show that, if the points are placed in R 2 then the problem is NP-hard even for simplest type of covering objects like disks or squares. In contrast, Eppstein (2017) [10] proposed a polynomial time algorithm for maximizing the sum of radii (or perimeter) of non-overlapping disks when the points are arbitrarily placed in R 2. We show that Eppstein's algorithm for maximizing sum of perimeter of the disks in R 2 gives a 2-approximation solution for the sum of area maximization problem. We also propose a PTAS for the same problem. Our results can be extended in higher dimensions as well as for a class of centrally symmetric convex objects. [ABSTRACT FROM AUTHOR]