Minimum-Cost Linear Coverage by Sensors with Adjustable Ranges

One of the most fundamental tasks of wireless sensor networks is to provide coverage of the deployment region. In this paper, we study the coverage of a line segment with a set of wireless sensors with adjustable coverage ranges. Each coverage range of a sensor is an interval centered at that sensor. The objective is to find a range assignment with the minimum cost. There are two variants of the optimization problem. In the discrete variant, each sensor can only choose from a finite set of powers while in the continuous variant, each sensor can choose power from a given interval. For the discrete variant of the problem, we present a polynomial-time exact algorithm. For the continuous variant of the problem, we develop constant-approximation algorithms when the cost for all sensors is proportional to r^κ for some constant κ 1, where r is the covering radius corresponding to the chosen power. Specifically, if κ = 1, we give a simple 1.25-approximation algorithm and a polynomial-time approximation scheme (PTAS); if κ > 1, we give a simple 2-approximation algorithm.