On the Complexity of and Algorithms for Min-Max Target Coverage On a Line Boundary

  • Peihuang Huang
  • Wenxing Zhu
  • Longkun GuoEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11436)


Given a set of sensors distributed on the plane and a set of Point of Interests (POIs) on a line segment, a primary task of the mobile wireless sensor network is to schedule a coverage of the POIs by the sensors, such that each POI is monitored by at least one sensor. For balancing the energy consumption, we study the min-max line barrier target coverage (LBTC) problem which aims to minimize the maximum movement of the sensors from their original positions to final positions for the coverage. We first proved that when the radius of the sensors are non-uniform integers, even 1-dimensional LBTC (1D-LBTC), a special case of LBTC in which the sensors are distributed on the line segment instead of the plane, is \(\mathcal{NP}\)-hard. The hardness result is interesting, since the continuous version of LBTC of covering a given line segment instead of the POIs is known polynomial solvable [2]. Then we presented an exact algorithm for LBTC with sensors of uniform radius distributed on the plane, via solving the decision version of LBTC. We showed that our algorithm always finds an optimal solution in time \(O(mn(\log m+ \log n))\) to LBTC when there exists any, where m and n are the numbers of POIs and sensors.


  1. 1.
    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)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Chen, D., Yan, G., Li, J., Wang, H.: Algorithms on minimizing the maximum sensor movement for barrier coverage of a linear domain. Discrete Comput. Geom. 50(2), 374–408 (2013)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Cherry, A., Gudmundsson, J., Mestre, J.: Barrier coverage with uniform radii in 2D. In: Fernández Anta, A., Jurdzinski, T., Mosteiro, M.A., Zhang, Y. (eds.) ALGOSENSORS 2017. LNCS, vol. 10718, pp. 57–69. Springer, Cham (2017). Scholar
  4. 4.
    Czyzowicz, J., et al.: On minimizing the maximum sensor movement for barrier coverage of a line segment. In: Ruiz, P.M., Garcia-Luna-Aceves, J.J. (eds.) ADHOC-NOW 2009. LNCS, vol. 5793, pp. 194–212. Springer, Heidelberg (2009). Scholar
  5. 5.
    Czyzowicz, J., et al.: On minimizing the sum of sensor movements for barrier coverage of a line segment. In: Nikolaidis, I., Wu, K. (eds.) ADHOC-NOW 2010. LNCS, vol. 6288, pp. 29–42. Springer, Heidelberg (2010). Scholar
  6. 6.
    Dobrev, S., et al.: Complexity of barrier coverage with relocatable sensors in the plane. Theor. Comput. Sci. 579, 64–73 (2015)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Gage, D.W.: Command control for many-robot systems. Technical report, Naval Command Control and Ocean Surveillance Center RDT and E Div, San Diego, CA (1992)Google Scholar
  8. 8.
    Kumar, S., Lai, T.H., Arora, A.: Barrier coverage with wireless sensors. In: Proceedings of the 11th Annual International Conference on Mobile Computing and Networking, pp. 284–298. ACM (2005)Google Scholar
  9. 9.
    Li, S., Shen, H.: Minimizing the maximum sensor movement for barrier coverage in the plane. In: IEEE Conference on Computer Communications (INFOCOM), pp. 244–252. IEEE (2015)Google Scholar
  10. 10.
    Li, X., Frey, H., Santoro, N., Stojmenovic, I.: Localized sensor self-deployment with coverage guarantee. ACM SIGMOBILE Mob. Comput. Commun. Rev. 12(2), 50–52 (2008)CrossRefGoogle Scholar
  11. 11.
    Mehrandish, M., Narayanan, L., Opatrny, J.: Minimizing the number of sensors moved on line barriers. In: IEEE Wireless Communications and Networking Conference (WCNC), pp. 653–658. IEEE (2011)Google Scholar
  12. 12.
    Tan, X., Wu, G.: New algorithms for barrier coverage with mobile sensors. In: Lee, D.-T., Chen, D.Z., Ying, S. (eds.) FAW 2010. LNCS, vol. 6213, pp. 327–338. Springer, Heidelberg (2010). Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.College of Physics and Information EngineeringFuzhou UniversityFuzhouChina
  2. 2.College of Mathematics and Computer ScienceFuzhou UniversityFuzhouChina

Personalised recommendations