Skip to main content
Log in

Approximation for minimum strongly connected dominating and absorbing set with routing-cost constraint in disk digraphs

  • Original Paper
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

The strongly connected dominating and absorbing set (DAS) is used as a virtual backbone in heterogeneous wireless sensor. To reduce routing cost, we introduce a routing-cost constraint and study the problem of computing the minimum strongly connected DAS under routing-cost constraint. An approximation algorithm with guaranteed performance will be presented.

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

Access this article

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

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

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

    Article  MathSciNet  MATH  Google Scholar 

  3. Ding, L., Gao, X., Wu, W., Lee, W., Zhu, X., Du, D.-Z.: Distributed construction of connected dominating sets with minimum routing cost in wireless network. In: The 30th International Conference on Distributed Computing Systems (ICDCS), pp. 448–457 (2010)

  4. Ding, L., Wu, W., Willson, J., Du, H., Lee, W., Du, D.-Z.: Efficient algorithms for topology control problem with minimum routing constraints in wireless networks. In: IEEE Transactions on Parallel and Distributed Systems, vol. 22(10), pp. 1601–1609 (2011)

  5. Ding, L., Gao, X., Weili, W., Wonjun Lee, X., Du Zhu, Ding-Zhu: An exact algorithm for minimum CDS with shortest path constraint in wireless networks. Optim. Lett. 5(2), 297–306 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  6. Du, D.-Z., Graham, R.L., Pardalos, P.M., Wan, P.-J., Wu, W., Zhao, W.: Analysis of greedy approximations with nonsubmodular potential functions. In: Proceedings of the 19th Annual ACM-SIAM Symposium on Dicrete Algorithms (SODA), pp. 167–175, San Francisco, 20–22 January 2008 (2008)

  7. Du, H., Ye, Q., Wu, W., Li, D., Du, D.-Z., Howard, S.: Constant approximation for virtual backbone construction with guaranteed routing cost in wireless sensor networks. In: INFOCOM, pp.1737–1744 (2011)

  8. Du, H., Wu, W., Ye, Q., Li, D., Lee, W., Xu, X.: CDS-based virtual backbone construction with guaranteed routing cost in wireless sensor networks. IEEE Trans. Parallel Distrib. Syst. 24(4), 652–661 (2013)

    Article  Google Scholar 

  9. Gao, X., Wang, W., Zhang, Z., Zhu, S., Weili, W.: A PTAS for minimum d-hop connected dominating set in growth-bounded graphs. Optim. Lett. 4(3), 321–333 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  10. Groemer, H.: Über die Einlagerung von Kreisen in einen konvexen Bereich. Math. Z. 73, 285–294 (1960)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  12. Kim, D., Yiwei, W., Li, Y., Zou, F., Ding-Zhu, D.: Constructing minimum connected dominating sets with bounded diameters in wireless networks. IEEE Trans. Parallel Distrib. Syst. 20(2), 147–157 (2009)

    Article  Google Scholar 

  13. Liu, Q., Zhang, Z., Hong, Y., Wu, W., Du, D.-Z.: A PTAS for weak minimum routing cost connected dominating set of unit disk graph. In: Chinchuluun, A. et al. (eds.) Optimization, Simulation, and Control. Springer Optimization and Its Applications, vol. 76, pp. 131–142 (2013)

  14. Ma, W., Li, D., Zhang, Z.: Algorithms for the minimum weight \(k\)-fold (connected) dominating set problem. J. Comb. Optim. 23(4), 528–540 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  15. Oler, N.: An inequality in the geometry of numbers. Acta Math. 105, 19–48 (1961)

    Article  MathSciNet  MATH  Google Scholar 

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

  17. Weili, W., Gao, X., Pardalos, P.M., Ding-Zhu, D.: Wireless networking, dominating and packing. Optim. Lett. 4(3), 347–358 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  18. Willson, J., Gao, X., Qu, Z., Zhu, Y., Li, Y., Wu, W.: Efficient distributed algorithms for topology control problem with shortest path constraints. Discrete Math. Algorithm Appl. 1(4), 437–462 (2009)

  19. Wu, J., Li, H.: 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)

  20. Zhou, J., Zhang, Z., Weili, W., Xing, K.: A greedy algorithm for the fault-tolerant connected dominating set in a general graph. J. Comb. Optim. 28(1), 310–319 (2014)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ding-Zhu Du.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, Z., Lee, JL., Wu, W. et al. Approximation for minimum strongly connected dominating and absorbing set with routing-cost constraint in disk digraphs. Optim Lett 10, 1393–1401 (2016). https://doi.org/10.1007/s11590-016-1007-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-016-1007-7

Keywords

Navigation