Journal of Global Optimization

, Volume 75, Issue 4, pp 1111–1131 | Cite as

Online hole healing for sensor coverage

  • Zhao Zhang
  • Zaixin Lu
  • Xianyue Li
  • Xiaohui Huang
  • Ding-Zhu DuEmail author


Many applications of wireless sensor networks require a quality of service including coverage and connectivity. However, both coverage and connectivity may be lost due to failure of sensors, in which case some holes appear. To heal holes, a hybrid wireless sensor system with mobile sensors has been proposed in the literature. Redundant mobile sensors can move to heal holes. Limited by energy supply, the largest distance that a mobile sensor can move cannot be too large. Such a consideration calls for cascade hole healing. This paper studies online cascade hole healing problem in which holes appear online and should be healed immediately without knowing future locations of holes. Two targets are considered, aiming to minimize the total energy consumption and the largest individual energy consumption, respectively. We show that naive greedy strategy does not work well for both targets, having exponentially large competitive ratios in a worst case. Then, we present two online algorithms with theoretically guaranteed tight competitive ratios. Extensive experiments show that our algorithm approximates offline optimal solutions fairly well.


Hole healing Online algorithm Competitive ratio 



We would like to thank the reviewers for their valuable suggestions.

This research work is supported in part by NSFC (11771013, 61751303, 11531011, 61472272), the Zhejiang Provincial Natural Science Foundation of China (LD19A010001, LY19A010018), and NSF under grant 1747818.


  1. 1.
    Bisnik, N., Abouzeid, A., Isler, V.: Stochastic event capture using mobile sensors subject to a quality metric. In: Proceedings of MobiCom’06, pp. 98–109. ACM, New York, NY (2006)Google Scholar
  2. 2.
    Cardei, M., Thai, M.T., Li, Y., Wu, W.: Energy-efficient target coverage in wireless sensor networks. In: INFOCOM, pp. 1976–1984 (2005)Google Scholar
  3. 3.
    Cardei, M., Du, D.-Z.: Improving wireless sensor network lifetime through power aware organization. Wirel. Netw. 11(3), 333–340 (2005)CrossRefGoogle Scholar
  4. 4.
    Chellappan, S., Gu, W., Bai, X., Xuan, D., Ma, B., Zhang, K.: Deploying wireless sensor networks under limited mobility constraints. IEEE Trans. Mob. Comput. 6(10), 1142–1157 (2007)CrossRefGoogle Scholar
  5. 5.
    Cheng, M.X., Ruan, L., Wu, W.: Achieving minimum coverage breach under bandwidth constraints in wireless sensor networks. In: INFOCOM, pp. 2638–2645 (2005)Google Scholar
  6. 6.
    Coman, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 3rd edn. MIT Press, Cambridge (2009)Google Scholar
  7. 7.
    Ding, L., Wu, W., Willson, J., Wu, L., Lu, Z., Lee, W.: Constant-approximation for target coverage problem in wireless sensor networks. In: INFOCOM, pp. 1584–1592 (2012)Google Scholar
  8. 8.
    Ghrist, R., Muhammad, A.: Coverage and hole-detection in sensor networks via homology. In: Proceedings of IPSN’05. IEEE Press, Piscataway, NJ (2005)Google Scholar
  9. 9.
    Goldberg, A.V., Tarjan, R.E.: Finding minimum-cost circulations by successive approximation. Math. Oper. Res. 15(3), 430–466 (1990)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Iyengar, R., Kar, K., Banerjee, S.: Low-coordination topologies for redundancy in sensor networks. In: Proceedings of MobiHoc’05, pp. 332–342. ACM, New York, NY (2005)Google Scholar
  11. 11.
    Li, X., Hunter, D.: Distributed coordinate-free hole recovery. In: IEEE International Conference on Communications Workshops, ICC Workshops’08, pp. 189–194 (2008)Google Scholar
  12. 12.
    Li, X., Santoro, N., Stojmenovic, I.: Mesh-based sensor relocation for coverage maintenance in mobile sensor networks. In: Proceedings of UIC’07, pp. 696–708. Springer, Berlin (2007)Google Scholar
  13. 13.
    Liu, B., Brass, P., Dousse, O., Nain, P., Towsley, D.: Mobility improves coverage of sensor networks. In: Proceedings of MobiHoc’05, pp. 300–308. ACM, New York, NY (2005)Google Scholar
  14. 14.
    Nguyen, D.T., Nguyen, N.P., Thai, M.T., Helal, A.: Optimal and distributed algorithms for coverage hole healing in hybrid sensor networks. Int. J. Sen. Netw. 11(4), 228–240 (2012)CrossRefGoogle Scholar
  15. 15.
    Srinivasan, W.W.V., Chua, K.-C.: Trade-offs between mobility and density for coverage in wireless sensor networks. In: Proceedings of MobiCom’07, pp. 39–50. ACM, New York, NY (2007)Google Scholar
  16. 16.
    Wang, G., Cao, G., La Porta, T., Zhang, W.: Sensor relocation in mobile sensor networks. In: INFOCOM 2005, vol. 4, pp. 2302–2312 (2005)Google Scholar
  17. 17.
    Wang, X., Xing, G., Zhang, Y., Lu, C., Pless, R., Gill, C.: Integrated coverage and connectivity configuration in wireless sensor networks. In: Proceedings of SenSys’03, pp. 28–39. ACM, New York, NY (2003)Google Scholar
  18. 18.
    Wu, L., Du, H., Wu, W., Li, D., Lv, J., Lee, W.: Approximations for minimum connected sensor cover. In: INFOCOM, pp. 1187–1194 (2013)Google Scholar
  19. 19.
    Yilin, S., Dung, T.N., My T.T: Adaptive approximation algorithms for hole healing in hybrid wireless sensor networks. In: INFOCOM, pp. 1178-1186 (2013)Google Scholar
  20. 20.
    Zhang, H., Hou, J.C.: Maintaining sensing coverage and connectivity in large sensor networks. Ad Hoc Sens. Wirel. Netw. 1(1–2), 89–124 (2005)Google Scholar
  21. 21.
    Zhang, Z., Willson, J., Lu, Z., Wu, W., Zhu, X., Du, D.-Z.: Approximating maximum lifetime k-Coverage through minimizing weighted k-cover in homogeneous wireless sensor networks. IEEE/ACM Trans. Netw. 24(6), 3620–3633 (2016)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Zhao Zhang
    • 1
  • Zaixin Lu
    • 2
  • Xianyue Li
    • 3
  • Xiaohui Huang
    • 4
  • Ding-Zhu Du
    • 5
    Email author
  1. 1.College of Mathematics and Computer ScienceZhejiang Normal UniversityJinhuaChina
  2. 2.School of Engineering and Computer ScienceWashington State UniversityVancouverUSA
  3. 3.School of Mathematics and StatisticsLanzhou UniversityLanzhouChina
  4. 4.Library and Information CenterZhejiang Normal UniversityJinhuaChina
  5. 5.Department of Computer ScienceUniversity of Texas at DallasRichardsonUSA

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