Skip to main content
SpringerLink
Log in

A PTAS for minimum connected dominating set in 3-dimensional Wireless sensor networks

  • Published:
Journal of Global Optimization Aims and scope Submit manuscript

Abstract

When homogeneous sensors are deployed into a three-dimensional space instead of a plane, the mathematical model for the sensor network is a unit ball graph instead of a unit disk graph. It is known that for the minimum connected dominating set in unit disk graph, there is a polynomial time approximation scheme (PTAS). However, that construction cannot be extended to obtain a PTAS for unit ball graph. In this paper, we will introduce a new construction, which gives not only a PTAS for the minimum connected dominating set in unit ball graph, but also improves running time of PTAS for unit disk graph.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Alzoubi, K.M., Wan, P., Frieder, O.: 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. Lausanne, Switzerland (2002)

  2. Bharghavan, V., Das, B.: Routing in ad hoc networks using minimum connected dominating sets. International Conference on Communication, Montreal, Canada (1997)

  3. Blum, J., Ding, M., Cheng, X.: Applications of Connectd Dominating Sets in Wireless Netwoks. In: Du D.-Z. Pardalos P. (eds.) Handbook of combinatorial Optimization, pp. 329–369. Kluwer Academic Publisher (2004)

  4. Butenko, S., Ursulenko, O.: On minimum connected dominating set problem in unit-ball graphs. (submitted)

  5. Cadei, M., Cheng, M.X., Cheng, X., Du, D.: Connected domination in ad hoc wireless networks. In: Proceedings of the Sixth International Symposium on Mobile ad hoc Networking and Computing, Lausanne, Switzerland (2002)

  6. Cheng X., Huang X., Li D., Wu W., Du D.: A polynomial-time approximation scheme for minimum connected dominating set in ad hoc wireless networks. Networks 42, 202–208 (2003)

    Article  Google Scholar 

  7. Clark B.N., Colbourn C.J., Johnson D.S.: Unit disk graphs. Discrete Math. 86, 165–177 (1990)

    Article  Google Scholar 

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

    Article  Google Scholar 

  9. Hochbaum D.S., Maass W.: Approximation schemes for covering and packing problems in image processing and VLSI. J. ACM. 32, 130–136 (1985)

    Article  Google Scholar 

  10. Min M., Du H., Jia X., Huang C.X., Huang S.C., Wu W.: Improving construction for connected dominating set with Steiner tree in wireless sensor networks. J. Glob. Optim. 35, 111–119 (2006)

    Article  Google Scholar 

  11. Peter Chen, Y., Liestman, A.L.: Approximating minimum size weakly-connected dominating sets for clustering mobile ad hoc networks. In: Proceedings of the third ACM International Symposium on Mobile ad hoc networking and computing. Lausanne, Switzerland (2002)

  12. Ramamurthy, B., Iness, J., Mukherjee, B.: Minimizing the number of optical amplifiers needed to support a multi-wavelength optical LAN/MAN. In: Proceedings of IEEE INFOCOM’97, pp. 261–268 (1997)

  13. Ruan L., Du H., Jia X., Wu W., Li Y., Ko K.: A greedy approximation for minimum connected dominating set. Theor. Comput. Sci. 329, 325–330 (2004)

    Article  Google Scholar 

  14. Salhieh, A., Weinmann, J., Kochha, M., Schwiebert, L.: Power efficient topologies for wireless sensor networks. In: ICPP’2001, pp. 156–163 (2001)

  15. Sivakumar, R., Das, B., Bharghavan, V.: An improved spine-based infrastructure for routing in ad hoc networks. In: IEEE Symposium on Computer and Communications. Athens, Greece (1998)

  16. Stojmenovic, I., Seddigh, M., Zunic, J.: Dominating sets and neighbor elimination based broadcasting algorithms in wireless networks. In: Proceedings of IEEE Hawaii International Conference on System Sciences (2001)

  17. Wan, P., Alzoubi, K.M., Frieder, O.: Distributed construction of connected dominating set in wireless ad hoc networks. In: Proceedings of Infocom’ 2002 (2002)

  18. Wu, J., Li, H.L.: On calculating connected dominating set for efficient routing in ad hoc wireless networks. In: Proceedings of the 3rd ACM International Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications, pp. 7–14 (1999)

  19. Zong C.: Shere packings. Springer, New York (1999)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang, 830046, People’s Republic of China

    Zhao Zhang

  2. Department of Computer Science, University of Texas at Dallas, Richardson, TX, 75080, USA

    Xiaofeng Gao, Weili Wu & Ding-Zhu Du

Authors
  1. Zhao Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaofeng Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Weili Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ding-Zhu Du
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhao Zhang.

Additional information

This work is supported by National Natural Science Foundation of China (60603003), the Key Project of Chinese Ministry of Education (208161), Scientific Research Program of the Higher Education Institution of Xinjiang, funded by the National Science Foundation under grant CCF-0514796 and CNS-0524429. The work was completed when the first author was visiting Department of Computing Science, the University of Texas at Dallas.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, Z., Gao, X., Wu, W. et al. A PTAS for minimum connected dominating set in 3-dimensional Wireless sensor networks. J Glob Optim 45, 451–458 (2009). https://doi.org/10.1007/s10898-008-9384-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10898-008-9384-9

Keywords

Search

Navigation