Journal of Combinatorial Optimization

, Volume 36, Issue 2, pp 434–457 | Cite as

Minimizing the total cost of barrier coverage in a linear domain

  • Xiao Zhang
  • Haosheng Fan
  • Victor C. S. Lee
  • Minming Li
  • Yingchao Zhao
  • Chuang Liu


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


Wireless sensor networks Barrier coverage Range assignment Approximation algorithm 



The work described in this paper was partially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. UGC/FDS11/E04/15) and National Natural Science Foundation of China (No. 61772154).


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computer ScienceCity University of Hong KongHong Kong SARChina
  2. 2.Department of MarketingHong Kong University of Science and TechnologyHong Kong SARChina
  3. 3.Department of Computer ScienceCaritas Institute of Higher EducationHong Kong SARChina
  4. 4.Department of Computer Science and Technology, Harbin Institute of Technology Shenzhen Graduate SchoolShenzhen Key Laboratory of Internet Information CollaborationShenzhenChina

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