Distributed Computing

, Volume 29, Issue 5, pp 361–376 | Cite as

Distributed algorithms for barrier coverage using relocatable sensors

  • Mohsen Eftekhari
  • Evangelos Kranakis
  • Danny Krizanc
  • Oscar Morales-Ponce
  • Lata Narayanan
  • Jaroslav Opatrny
  • Sunil Shende


We study the barrier coverage problem using relocatable sensor nodes. We assume each sensor can sense an intruder or event inside its sensing range. Sensors are initially located at arbitrary positions on the barrier and can move along the barrier. The goal is to find final positions for sensors so that the entire barrier is covered. In recent years, the problem has been studied extensively in the centralized setting. In this paper, we study a barrier coverage problem in the distributed and discrete setting. We assume that we have n identical sensors located at grid positions on the barrier, and that each sensor repeatedly executes a Look-Compute-Move cycle: based on what it sees in its vicinity, it makes a decision on where to move, and moves to its next position. We make two strong but realistic restrictions on the capabilities of sensors: they have a constant visibility range and can move only a constant distance in every cycle. In this model, we give the first two distributed algorithms that achieve barrier coverage for a line segment barrier when there are enough nodes in the network to cover the entire barrier. Our algorithms are synchronous, and local in the sense that sensors make their decisions independently based only on what they see within their constant visibility range. One of our algorithms is oblivious whereas the other uses two bits of memory at each sensor to store the type of move made in the previous step. We show that our oblivious algorithm terminates within \(\varTheta (n^2)\) steps with the barrier fully covered, while the constant-memory algorithm is shown to take \(\varTheta (n)\) steps to terminate in the worst case. Since any algorithm in which a sensor can only move a constant distance in one step requires \(\varOmega (n)\) steps on some inputs, our second algorithm is asymptotically optimal.


Barrier coverage Wireless relocatable sensors Autonomous mobile robots Optimal algorithms Distributed algorithms 



The authors thank the anonymous referees for providing us with many useful suggestions that improved the paper.


  1. 1.
    Ando, H., Suzuki, I., Yamashita, M.: Formation and agreement problems for synchronous mobile robots with limited visibility. In: Proceedings of IEEE international symposium on intelligent control, pp. 453–460 (1995)Google Scholar
  2. 2.
    Balister, P., Bollobas, B., Sarkar, A., Kumar, S.: Reliable density estimates for coverage and connectivity in thin strips of finite length. In: Proceedings of MobiCom’07, pp. 75–86 (2007)Google Scholar
  3. 3.
    Bhattacharya, B., Burmester, M., Hu, Y., Kranakis, E., Shi, Q., Wiese, A.: Optimal movement of mobile sensors for barrier coverage of a planar region. Theor. Comput. Sci. 410(52), 5515–5528 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Chen, D.Z., Gu, Y., Li, J., Wang, H.: Algorithms on minimizing the maximum sensor movement for barrier coverage of a linear domain. In: Proceedings of SWAT’12, pp. 177–188 (2012)Google Scholar
  5. 5.
    Cohen, R., Peleg, D.: Local algorithms for autonomous robots systems. In: Proceedings of SIROCCO’06, LNCS v. 4056, pp. 29–43 (2006)Google Scholar
  6. 6.
    Czyzowicz, J., Gasieniec, L., Pelc, A.: Gathering few fat mobile robots in the plane. Theor. Comput. Sci. 410(6–7), 481–499 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Czyzowicz, J., Kranakis, E., Krizanc, D., Lambadaris, I., Narayanan, L., Opatrny, J., Stacho, L., Urrutia, J., Yazdani, M.: On minimizing the maximum sensor movement for barrier coverage of a line segment. In: Proceedings of ADHOC-NOW, LNCS v. 5793, pp. 194–212 (2009)Google Scholar
  8. 8.
    Czyzowicz, J., Kranakis, E., Krizanc, D., Lambadaris, I., Narayanan, L., Opatrny, J., Stacho, L., Urrutia, J., Yazdani, M.: On minimizing the sum of sensor movements for barrier coverage of a line segment. In: Proceedings of ADHOC-NOW, LNCS v. 6288, pp. 29–42 (2010)Google Scholar
  9. 9.
    Datta, S., Dutta, A., Chaudhuri, S.C., Mukhopadhyaya, K.: Circle formation by asynchronous transparent fat robots. In: Proceedings of ICDCIT’13, pp. 195–207 (2013)Google Scholar
  10. 10.
    Flocchini, P., Prencipe, G., Santoro, N.: Distributed Computing by Oblivious Mobile Robots: Synthesis Lectures on Distributed Computing Theory. Morgan and Claypool Publishers, San Rafael (2012)zbMATHGoogle Scholar
  11. 11.
    Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Gathering of asynchronous mobile robots with limited visibility. In: Proceedings of STACS’01, LNCS v. 2010, pp. 247–258 (2001)Google Scholar
  12. 12.
    Huang, C.F., Tseng, Y.C.: The coverage problem in a wireless sensor network. In: Proceedings of WSNA’03, pp. 115–121 (2003)Google Scholar
  13. 13.
    Kumar, S., Lai, T.H., Arora, A.: Barrier coverage with wireless sensors. In: Proceedings of MobiCom’05, pp. 284–298 (2005)Google Scholar
  14. 14.
    Kumar, S., Lai, T.H., Balogh, J.: On \(k\)-coverage in a mostly sleeping sensor network. In: Proceedings of MobiCom’04, pp. 144–158 (2004)Google Scholar
  15. 15.
    Matarić, M.: Interaction and intelligent behavior. PhD thesis, MIT (1994)Google Scholar
  16. 16.
    Meguerdichian, S., Koushanfar, F., Potkonjak, M., Srivastava, M.B.: Coverage problems in wireless ad-hoc sensor networks. In: Proceedings of IEEE INFOCOM’01, pp. 1380–1387 (2001)Google Scholar
  17. 17.
    Mehrandish, M., Narayanan, L., Opatrny, J.: Minimizing the number of sensors moved on line barriers. In: Proceedings of IEEE WCNC’11, pp. 1464–1469 (2011)Google Scholar
  18. 18.
    Prencipe, G., Santoro, N.: Distributed algorithms for autonomous mobile robots. In: Proceedings 5th IFIP international conference on theoretical computer science (TCS’06), vol 209, pp. 47–62 (2006)Google Scholar
  19. 19.
    Shen, C., Cheng, W., Liao, X., Peng, S.: Barrier coverage with mobile sensors. In: Proceedings of I-SPAN’08, pp. 99–104 (2008)Google Scholar
  20. 20.
    Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots: formation of geometric patterns. SIAM J. Comput. 28(4), 1347–1363 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Yan, G., Qiao, D.: Multi-round sensor deployment for guaranteed barrier coverage. In: Proceedings of IEEE INFOCOM’10, pp. 2462–2470 (2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Mohsen Eftekhari
    • 1
  • Evangelos Kranakis
    • 2
  • Danny Krizanc
    • 3
  • Oscar Morales-Ponce
    • 4
  • Lata Narayanan
    • 1
  • Jaroslav Opatrny
    • 1
  • Sunil Shende
    • 5
  1. 1.Department Computer Science and Software EngineeringConcordia UniversityMontrealCanada
  2. 2.School of Computer ScienceCarleton UniversityOttawaCanada
  3. 3.Department of Mathematics and Computer ScienceWesleyan UniversityMiddletownUSA
  4. 4.Department of Computer ScienceChalmers University of TechnologyGothenburgSweden
  5. 5.Department of Computer ScienceRutgers UniversityCamdenUSA

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