Skip to main content
Springer Nature Link
Log in

An optimization algorithm for the minimum k-connected m-dominating set problem in wireless sensor networks

  • Published:
Wireless Networks Aims and scope Submit manuscript

Abstract

In wireless sensor networks (WSNs), virtual backbone has been proposed as the routing infra-structure and connected dominating set has been widely adopted as virtual backbone. However, since the sensors in WSNs are prone to failures, recent studies suggest that it is also important to maintain a certain degree of redundancy in the backbone. To construct a robust backbone, so called k-connected m-dominating set has been proposed. In this research, we propose an integer programming formulation and an optimal algorithm for the minimum k-connected m-dominating set problem. To the best of our knowledge, this is the first integer programming formulation for the problem, and extensive computational results show that our optimal algorithm is capable of finding a solution within a reasonable amount of time.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /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.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Alzoubi, K. M., Wan, P. J., & Frieder, O. (2002). Message-optimal connected dominating sets in mobile ad hoc networks. In Proceedings of the 3rd ACM international symposium on mobile ad hoc networking and computing (pp. 157–164). ACM, Lausanne, Switzerland.

  2. Basu, P., & Redi, J. (2004). Movement control algorithms for realization of fault tolerant ad hoc robot networks. IEEE Networks, 18, 36–44.

    Article  Google Scholar 

  3. Bertsimas, D., & Tsitsiklis, J. N. (1997). Introduction to linear optimization. Belmont: Athena Scientific.

    Google Scholar 

  4. Blum, J., Ding, M., Thaeler, A., & Cheng, X. (2004). Connected dominating set in sensor networks and MANETs, handbook of combinatorial optimization. Massachusetts: Kluwer Acacemic Publishers.

    Google Scholar 

  5. Bondy, J. A., & Murty, U. S. R. (2008). Graph theory. Berlin: Springer.

    MATH  Google Scholar 

  6. Bredin, J. L., Demaine, E. D., Hajiaghayi, M., & Rus, D. (2005). Deploying sensor networks with guaranteed capacity and fault tolerance. In Proceedings of the 6th ACM international symposium on mobile ad hoc networking and computing (pp. 309–319). ACM SIGMOBILE, Urbana-Champaign, Illinois.

  7. Dai, F., & Wu, J. (2006). On constructing k-connected k-dominating set in wireless network. Journal of Parallel and Distributed Computing, 66, 947–958.

    Article  MATH  Google Scholar 

  8. Garey, M. R., & Johnson, D. S. (1979). Computers and intractability: A guide to the theory of NP-completeness. San Francisco: W. H. Freeman and Company.

    MATH  Google Scholar 

  9. Guha, S., & Khuller, S. (1998). Approximation algorithms for connected dominating sets. Algorithmica, 20, 374–387.

    Article  MATH  MathSciNet  Google Scholar 

  10. Grotschel, M., Lovasz, L., & Schrijver, A. (1981). The ellipsoid method and its consequences in combinatorial optimization. Combinatorica, 1, 169–197.

    Article  MathSciNet  Google Scholar 

  11. Kim, D., Wang, W., Li, X., Zhang, Z., & Wu, W. (2010). A new constant factor approximation for computing 3-connected m-dominating sets in homogeneous wireless networks. In INFOCOM, IEEE (pp. 1–9). San Diego, CA.

  12. Koskinen, H., & Karvo, J. (2005). On improving connectivity of static ad-hoc networks by adding nodes, 4th annual Mediterranean workshop on ad hoc network. IEEE Communications Society (pp. 169–178). Porquerolles, France.

  13. Kuhn, F., Moscibroda, T., & Wattenhofer, R. (2006). Fault-tolerant clustering in ad hoc and sensor networks. In 26th international conference on distributed computing systems. IEEE Computer Society, Lisboa, Portugal.

  14. Li, Y., Wu, Y., Ai, C., & Neyah, R. (2012). On the construction of k-connected m-dominating sets in wireless networks. Journal of Combinatorial Optimization, 23, 118–139.

    Article  MATH  MathSciNet  Google Scholar 

  15. Ni, S. Y., Tseng, Y. C., Chen, Y. S., & Sheu, J. P. (2002). The broadcast storm problem in a mobile ad hoc network. Wireless Networks, 8, 153–167.

    Article  MATH  Google Scholar 

  16. Papadimitriou, C. H., & Steiglitz, K. (1998). Combinatorial pptimization. Mineola, NY: Dover Publications.

    MATH  Google Scholar 

  17. Ryl, D. S., Stojmenović, I., & Wu, J. (2005). Energy-efficient backbone construction, broadcasting, and area coverage in sensor networks. In I. Stojmenović (Ed.), Handbook of sensor networks (pp. 343–380). Hoboken: Wiley.

    Google Scholar 

  18. Shang, W., Yao, F., Wan, P., & Hu, X. (2007). Algorithms for minimum m-connected k-dominating set problem. Lecture Notes in Computer Science, 4616, 182–190.

    Article  MathSciNet  Google Scholar 

  19. Shang, W., Yao, F., Wan, P., & Hu, X. (2008). On minimum m-connected k-dominating set problem in unit disc graphs. Journal of Combinatorial Optimization, 16, 99–106.

    Article  MATH  MathSciNet  Google Scholar 

  20. Sinha, P., Sivakumar, R., & Bharghavan, V. (2001). Enhancing ad hoc routing with dynamic virtual infrastructures. IN 20th annual joint conference of the IEEE computer and communications societies. Technical Committees on Computer Communications (TCCC) of the Societies (Vol. 3, pp. 1763–1772). Anchorage, Alaska.

  21. Stojmenović, I., & Wu, J. (2005). Mobile ad hoc networking. Hoboken: Wiley

    Google Scholar 

  22. Tarjan, R. E. (1972). Depth first search and linear graph algorithms. SIAM Journal on Computing, 1(2), 146–160.

  23. Thai, M. T., Zhang, N., Tiwari, R., & Xu, X. (2007). On approximation algorithms of k-connected m-dominating sets in disk graphs. Theory of Computation Sc, 385, 49–59.

    Article  MATH  MathSciNet  Google Scholar 

  24. Thulasiraman, K., & Swamy, M. N. S. (1992). Graphs: Theory and algorithms. New York: Wiley.

    MATH  Google Scholar 

  25. Tiwari, R., & Thai, M. T. (2012). On enhancing fault tolerance of virtual backbone in a wireless sensor network with unidirectional links. Sensors: Theory, Algorithms, and Applications, 61, 3–18.

    Google Scholar 

  26. Wang, F., Thai, M. T., & Du, D. Z. (2009). On the construction of 2-connected virtual backbone in wireless network. IEEE Transactions on Wireless Communications, 8, 1230–1237.

    Article  Google Scholar 

  27. Wang, W., Kim, D., An, M. K., Gao, W., Li, X., Zhang, Z., & Wu, W. (2012). On construction of quality fault-tolerant virtual backbone in wireless networks. Networking, IEEE/ACM Transactions, 21(5), 1499–1510.

  28. West, D. B. (2001). Introduction to graph theory. Upper Saddle River: Prentice-Hall.

    Google Scholar 

  29. Wu, Y., Wang, F., Thai, M. T., & Li, Y. (2007). Constructing k-connected m-dominating sets in wireless sensor networks. In Military communications conference. Orlando, FL.

  30. Wu, Y., & Li, Y. (2008) Construction algorithms for k-connected m-dominating sets in wireless sensor networks. In 9th ACM international symposium on mobile ad hoc networking and computing (pp. 83–90). ACM SIGMOBILE, May, Hong Kong.

  31. Yu, J., Wang, N., Wang, G., & Yu, D. (2013). Connected dominating sets in wireless ad hoc and sensor networks—A comprehensive survey. Computer Communications, 36, 121–134.

    Article  Google Scholar 

  32. Zhang, J., Gao, X., & Wu, W. (2009). Algorithms for connected set cover problem and fault-tolerant connected set cover problem. Theoretical Computer Science, 410, 812–817.

    Article  MATH  MathSciNet  Google Scholar 

  33. Zhou, J., Zhang, Z., Wu, W., & Xing, K. (2014). A greedy algorithm for the fault-tolerant connected dominating set in a general graph. Journal of Combinatorial Optimization, 28(1), 310–319.

Download references

Author information

Authors and Affiliations

  1. Defense Agency for Technology and Quality, 420, Dongjin-ro, Jinju-si , Gyeongsangnam-do, 660-031, Republic of Korea

    Namsu Ahn

  2. Department of Industrial and Systems Engineering, KAIST, 291, Daehak-ro, Yuseong-gu, Daejeon-si , 305-701, Republic of Korea

    Sungsoo Park

Authors
  1. Namsu Ahn
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Sungsoo Park
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Sungsoo Park.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ahn, N., Park, S. An optimization algorithm for the minimum k-connected m-dominating set problem in wireless sensor networks. Wireless Netw 21, 783–792 (2015). https://doi.org/10.1007/s11276-014-0819-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11276-014-0819-6

Keywords