Range assignment of base-stations maximizing coverage area without interference

0534821 - ÚI 2021 NL eng J - Journal Article
Acharyya, Ankush - De, M. - Nandy, S. C. - Roy, B.
Range assignment of base-stations maximizing coverage area without interference.
Theoretical Computer Science. Roč. 804 (2020), s. 81-97. ISSN 0304-3975. E-ISSN 1879-2294
Keywords : time approximation schemes * packing * Quadratic programming * Discrete packing * Range assignment in wireless communication * NP-hardness * Approximation algorithm * ptas
Impact factor: 0.827, year: 2020

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.
Permanent Link: http://hdl.handle.net/11104/0312983