Barrier coverage by sensors with adjustable ranges

One of the most fundamental tasks of wireless sensor networks is to provide coverage of the deployment region. We study the coverage of a line interval with a set of wireless sensors with adjustable coverage ranges. Each coverage range of a sensor is an interval centered at that sensor whose length is decided by the power the sensor chooses. 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, whereas in the continuous variant, each sensor can choose power from a given interval. For the discrete variant of the problem, a polynomial-time exact algorithm is designed. For the continuous variant of the problem, NP-hardness of the problem is proved and followed by an ILP formulation. Then, constant-approximation algorithms are designed when the cost for all sensors is proportional to r^κfor some constant κ ≥ 1, where r is the covering radius corresponding to the chosen power. Specifically, if κ = 1, we give a 1.25-approximation algorithm and a fully polynomial-time approximation scheme; if κ > 1, we give a 2-approximation algorithm. We also show that the approximation analyses are tight.