Minimizing the total cost of barrier coverage in a linear domain

Barrier coverage, as one of the most important applications of wireless sensor network (WSNs), is to provide coverage for the boundary of a target region. We study the barrier coverage problem by using a set of n sensors with adjustable coverage radii deployed along a line interval or circle. Our goal is to determine a range assignment of sensors such that the line interval or circle is fully covered and its total cost is minimized. For the line interval case, we formulate the barrier coverage problem of line-based offsets deployment, and present two approximation algorithms to solve it. One is an approximation algorithm of ratio 4 / 3 runs in time, while the other is a fully polynomial time approximation scheme (FPTAS) of computational complexity . For the circle case, we optimally solve it when and present a -approximation algorithm when . Besides, we propose an integer linear programming (ILP) to minimize the total cost of the barrier coverage problem such that each point of the line interval is covered by at least k sensors.