Approximation algorithms for deployment of sensors for line segment coverage in wireless sensor networks

The coverage problem in wireless sensor networks deals with the problem of covering a region or parts of it with sensors. In this paper, we address the problem of covering a set of line segments with minimum number of sensors. A line segment ℓ is said to be 1-covered if it intersects the sensing region of at least one among the sensors distributed in a bounded rectangular region R. We assume that the sensing radius of each sensor is uniform. The problem of finding the minimum number of sensors needed to 1-cover each member in a given set of line segments in R is NP-hard. We propose two constant factor approximation algorithms and a PTAS (polynomial time approximation scheme) for the problem for 1-covering a set of axis-parallel line segments. We also show that a PTAS exists for 1-covering a set of arbitrarily oriented line segments in R where the lengths of the line segments are bounded within a constant factor of the sensing radius of each sensor. Finally, we propose a constant factor approximation algorithm for k-covering axis-parallel line segments such that sensors maintain a minimum separation among them.