Line sweep coverage in wireless sensor networks

Traditional coverage in wireless sensor networks requires continuous monitoring of target objects or regions. Unlike traditional coverage, periodic monitoring by a set of mobile sensor nodes is sufficient in sweep coverage. The sweep coverage problem for covering a set of points is NP-hard and it cannot be approximated within a factor of 2 [15]. The sweep coverage problem for a given bounded region is also NP-hard [11]. In this paper, we study sweep coverage for covering a set of line segments on a plane. We prove that the problem is NP-hard and cannot be approximated within a factor 2. Our proposed algorithm achieves the best possible approximation factor 2. As an application of line sweep coverage problem we formulate a data gathering problem, where minimum number of data mules periodically collect data from a set of mobile sensor nodes. The mobile sensor nodes arbitrarily move along their paths, which are line segments. We prove that this problem is NP-hard and propose a 3 approximation algorithm to solve it.