Skip to main content
Log in

Barrier coverage with wireless sensors

  • Published:
Wireless Networks Aims and scope Submit manuscript


When a sensor network is deployed to detect objects penetrating a protected region, it is not necessary to have every point in the deployment region covered by a sensor. It is enough if the penetrating objects are detected at some point in their trajectory. If a sensor network guarantees that every penetrating object will be detected by at least k distinct sensors before it crosses the barrier of wireless sensors, we say the network provides k-barrier coverage. In this paper, we develop theoretical foundations for k-barrier coverage. We propose efficient algorithms using which one can quickly determine, after deploying the sensors, whether the deployment region is k-barrier covered. Next, we establish the optimal deployment pattern to achieve k-barrier coverage when deploying sensors deterministically. Finally, we consider barrier coverage with high probability when sensors are deployed randomly. The major challenge, when dealing with probabilistic barrier coverage, is to derive critical conditions using which one can compute the minimum number of sensors needed to ensure barrier coverage with high probability. Deriving critical conditions for k-barrier coverage is, however, still an open problem. We derive critical conditions for a weaker notion of barrier coverage, called weak k-barrier coverage.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others


  1. A. Arora, R. Ramnath, E. Ertin, P. Sinha, S. Bapat, V. Naik, V. Kulathumani, H. Zhang, H. Cao, M. Sridhara, S. Kumar, N. Seddon, C. Anderson, T. Herman, N. Trivedi, C. Zhang, M. Gouda, Y.-R. Choi, M. Nesterenko, R. Shah, S. Kulkarni, M. Aramugam, L. Wang, D. Culler, P. Dutta, C. Sharp, G. Tolle, M. Grimmer, B. Ferriera and K. Parker, ExScal: Elements of an extreme scale wireless sensor network, in: Proceedings of the Eleventh IEEE International Conference on Real-Time Computing Systems and Applications (IEEE RTCSA), Hong Kong 2005).

  2. N. Alon and J.H. Spencer, The Probabilistic Method. (John Wiley & Sons, 2000).

  3. Bid to Seal-off US-Mexico Border. B.B.C. News, Nov. 4, 2005.

  4. K. Boroczky, Finite Packing and Covering. (Cambridge University Press, 2004).

  5. H.S.M. Coxeter, Introduction to Geometry. (New York, Wiley, 1969).

    MATH  Google Scholar 

  6. D.W. Gage, Command control for many-robot systems, in: AUVS-92 1992.

  7. C. Gui and P. Mohapatra, Power conservation and quality of surveillance in target tracking sensor networks, in: International Conference on Mobile Computing and Networking (ACM MobiCom), Philadelphia, PA (2004).

  8. P. Hall, Introduction to the Theory of Coverage Processes. (John Wiley & Sons, 1988).

  9. C. Huang and Y. Tseng, The coverage problem in a wireless sensor network, ACM International Workshop on Wireless Sensor Networks and Applications (WSNA), San Diego, CA (2003), pp. 115–121

  10. S. Hynes, Multi-agent simulations (mas) for assessing massive sensor coverage and deployment, Technical report, Master’s Thesis, Naval Postgraduate School (2003).

  11. S. Kumar and A. Arora, Echelon topology for node deployment, Technical report, ExScal Note Series: ExScal-OSU-EN00-2004-01-30, The Ohio State University (2004).

  12. S. Kumar, T.H. Lai, and J. Balogh, On k-coverage in a mostly sleeping sensor network, International Conference on Mobile Computing and Networking (ACM MobiCom), Philadelphia, PA (2004), pp. 144–158.

  13. R.P. Langlands, C. Pichet, P. Pouliot and Y. Saint-Aubin, On the universality of crossing probabilities in two-domensional percolation, Journal of Statistical Physics 67(3/4) (1992), pp. 553–574.

    Article  MATH  Google Scholar 

  14. B. Liu and D. Towsley, On the coverage and detectability of large-scale wireless sensor networks, in: Modeling and Optimization in Mobile, Ad-Hoc and Wireless Networks (2003).

  15. S. Meguerdichian, F. Koushanfar, M. Potkonjak and M. B. Srivastava, Coverage Problems in wireless ad-hoc sensor networks, In IEEE INFOCOM (2001).

  16. S. Meguerdichian, F. Koushanfar, G. Qu and M. Potkonjak, Exposure in wireless ad-hoc sensor networks, in: International Conference on Mobile Computing and Networking (ACM MobiCom), Rome, Italy (2001), pp. 139–150.

  17. B. Mohar and N. Robertson, Disjoint Essential Cycles, Journal of Combinatorial Theory, 68(2):324–349, 1996.

    Article  MATH  Google Scholar 

  18. B. Mohar and C. Thomassen, Graphs on Surfaces (Johns Hopkins University Press, 2001).

  19. D. Peleg, Distributed Computing: A Loaclity-Sensitive Approach (Society for Industrial and Applied Mathematics (SIAM), 2000).

  20. S.M. Ross, Introduction to Probability Models (Academic Press, 2000).

  21. A. Schrijver, Combinatorial Optimization (Springer, 2003).

  22. G. Veltri, Q. Huang, G. Qu and M. Potkonjak, “Minimum and maximal exposure path algorithms for wireless embedded sensor networks, in: ACM Conference on Ebmedded Networked Sensor Systems (SenSys) (2003).

  23. X. Wang, G. Xing, Y. Zhang, C. Lu, R. Pless and C. Gill, Integrated coverage and connectivity configuration in wireless sensor networks, in: ACM Conference on Ebmedded Networked Sensor Systems (SenSys), Los Angeles, CA (2003), pp. 28–39.

  24. D. B. West, Introduction to Graph Theory (Prentice Hall, 2001).

  25. H. Zhang and J. Hou, On deriving the upper bound of α-lifetime for large sensor networks, in: International Symposium on Mobile Ad Hoc Networking and Computing (ACM MobiHoc), Tokyo, Japan (2004), pp. 121–132.

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Santosh Kumar.

Additional information

A preliminary version of this paper appeared in the Eleventh Annual International Conference on Mobile Computing and Networking (ACM MobiCom), August 28–September 2, 2005, Cologne, Germany.

Santosh Kumar is a Ph.D. candidate and SBC Presidential Fellow in Computer Science and Engineering at the Ohio State University. He received his B. Tech. in Computer Science and Engineering from the Institute of Technology, Banaras Hindu University (IT-BHU) at Varanasi, India, in 1998. He received his Masters in Computer and Information Science from the Ohio State University in 2002. His current research focusses on the issues of coverage and connectivity in Wireless Sensor Networks. Starting Fall 2006, he will join the department of Computer Science at the University of Memphis as an Assistant Professor.

Ten H. Lai is a Professor of Computer Science and Engineering at the Ohio State University. A pioneer of Zen Networking, he is interested in the art of applying Zen to the teaching and research of protocol design. He served as the program chair of ICPP’98, the general chair of ICPP’00, the program co-chair of ICDCS’04, and, recently, the general chair of ICDCS’05. He is/was an editor of IEEE Transactions on Parallel and Distributed Systems (TPDS), ACM/Springer Wireless Networks, Academia Sinica’s Journal of Information Science and Engineering (JISE), and International Journal of Ad Hoc and Ubiquitous Computing.

Anish Arora is a Professor of Computer Science and Engineering at the Ohio State University. His research focuses on fault tolerance, security, and timeliness of distributed and networked systems, with special emphasis on wireless sensor networking at large scale. He is an expert in self-stabilization. He has chaired/co-chaired several seminars/conferences in self-stabilization, as well as in distributed computing and computer networking; most recently, Arora has served as program chair of the 25th International Conference on Distributed Computing Systems (ICDCS’05) and the program co-chair of the Second ACM Conference on Embedded Sensor Networks Systems (SENSYS’04). Arora is an editor of the ACM Transactions on Sensor Networks, Real Time Systems, and New Generation Systems. His recent research has been supported by DARPA, NSF, and Microsoft Research Embedded Systems Program. Arora received his B. Tech. Degree from the Indian Institute of Technology at New Delhi and his Master’s and Ph.D. degrees from the University of Texas at Austin, all in computer science.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kumar, S., Lai, T.H. & Arora, A. Barrier coverage with wireless sensors. Wireless Netw 13, 817–834 (2007).

Download citation

  • Published:

  • Issue Date:

  • DOI: