Packing Problem and Random Coverage in Continuous Domain

Abstract

The packing problem is a well known-problem. There are several versions of this problem. In this paper we consider packing or covering of a disc of a given radius r by a number of discs of unit radius. We introduced two types of packing, hexagonal packing and square packing. We show that hexagonal packing is better in the sense that it needs less discs to cover a disc of higher radius. Coverage problem is similar to the packing problem in continuous domain. Coverage is essential in wireless sensor networks. In this paper we also discuss the coverage problem in random deployment scenario.