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 $$\mathbf {R}=({r_{1}},{r_{2}}, \ldots , {r_{n}})$$R=(r1,r2,…,rn) of sensors such that the line interval or circle is fully covered and its total cost $$C(\mathbf {R})=\sum _{i=1}^n {r_{i}}^\alpha $$C(R)=∑i=1nriα 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 $$O(n^{2})$$O(n2) time, while the other is a fully polynomial time approximation scheme (FPTAS) of computational complexity $$O(\frac{n^{2}}{\epsilon })$$O(n2ϵ). For the circle case, we optimally solve it when $$\alpha = 1$$α=1 and present a $$2(\frac{\pi }{2})^\alpha $$2(π2)α-approximation algorithm when $$\alpha > 1$$α>1. 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.