Minimum Total Communication Power Connected Dominating Set in Wireless Networks

  • Deying Li
  • Donghyun Kim
  • Qinghua Zhu
  • Lin Liu
  • Weili Wu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7405)


A virtual backbone of a wireless network is a connected subset of nodes responsible for routing messages in the network. A node in the subset is likely to be exhausted much faster than the others due to its heavy duties. This situation can be more aggravated if the node uses higher communication power to form the virtual backbone. In this paper, we introduce the minimum total communication power connected dominating set (MTCPCDS) problem, whose goal is to compute a virtual backbone with minimum total communication power. We show this problem is NP-hard and propose two distributed algorithms. Especially, the first algorithm, MST-MTCPCDS, has a worst case performance guarantee. A simulations is conducted to evaluate the performance of our algorithms.


Wireless Network Minimum Span Tree Message Complexity Grid Graph Unit Disk Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Guha, S., Khuller, S.: Approximation Algorithms for Connected Dominating Sets. Algorithmica 20, 374–387 (1996)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Funke, S., Kesselman, A., Meyer, U., Segal, M.: A Simple Improved Distributed Algorithm for Minimum CDS in Unit Disk Graphs. ACM Transactions on Sensor Networks (TOSN) 2(3), 444–453 (2006)CrossRefGoogle Scholar
  3. 3.
    Li, X., Gao, X., Wu, W.: A Better Theoretical Bound to Approximate Connected Dominating Set in Unit Disk Graph. In: Li, Y., Huynh, D.T., Das, S.K., Du, D.-Z. (eds.) WASA 2008. LNCS, vol. 5258, pp. 162–175. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  4. 4.
    Cheng, X., Huang, X., Li, D., Wu, W., Du, D.-Z.: A Polynomial-Time Approximation Scheme for the Minimum-Connected Dominating Set in Ad Hoc Wireless Networks. Networks 42(4), 202–208 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Wan, P.-J., Alzoubi, K.M., Frieder, O.: Distributed Construction of Connected Dominating Set in Wireless Ad Hoc Networks. ACM Journal on Mobile Networks and Applications (MONET) 9(2), 141–149 (2004)CrossRefGoogle Scholar
  6. 6.
    Wu, J., Dai, F., Gao, M., Stojmenovic, I.: On Calculating Power-Aware Connected Dominating Sets for Efficient Routing in Ad Hoc Wireless Networks. IEEE/KICS Journal of Communications and Networks 4, 59–70 (2002)Google Scholar
  7. 7.
    Kim, D., Wu, Y., Li, Y., Zou, F., Du, D.-Z.: Constructing Minimum Connected Dominating Sets with Bounded Diameters in Wireless Networks. IEEE Transactions on Parallel and Distributed Systems (TPDS) 20(2), 147–157 (2009)CrossRefGoogle Scholar
  8. 8.
    Kim, D., Zhang, Z., Li, X., Wang, W., Wu, W., Du, D.-Z.: A Better Approximation Algorithm For Computing Connected Dominating Sets in Unit Ball Graphs. IEEE Transactions on Mobile Computing (TMC) 9(8), 1108–1118 (2010)CrossRefGoogle Scholar
  9. 9.
    Thai, M.T., Wang, F., Liu, D., Zhu, S., Du, D.-Z.: Connected Dominating Sets in Wireless Networks with Different Transmission Ranges. IEEE Transactions on Mobile Computing (TMC) 6(7), 721–730 (2007)CrossRefGoogle Scholar
  10. 10.
    Guha, S., Khuller, S.: Improved Methods for Approximating Node Weighted Steiner Trees and Connected Dominating Sets. Information and Computation 150(1), 57–74 (1999)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Gao, X., Huang, Y., Zhang, Z., Wu, W.: (6 + ε)-Approximation for Minimum Weight Dominating Set in Unit Disk Graphs. In: Hu, X., Wang, J. (eds.) COCOON 2008. LNCS, vol. 5092, pp. 551–557. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  12. 12.
    Huang, Y., Gao, X., Zhang, Z., Wu, W.: A Better Constant-Factor Approximation for Weighted Dominating Set in Unit Disk Graph. Journal of Combinatorial Optimization (JOCO) 18(2), 179–194 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Dai, D., Yu, C.: A (5 + ε)-Approximation Algorithm for Minimum Weighted Dominating Set in Unit Disk Graph. Theoretical Computer Science (TCS) 41(8-10), 756–765 (2009)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Clementi, A., Crescenzi, P., Penna, P., Rossi, G., Vocca, P.: On the Complexity of Computing Minimum Energy Consumption Broadcast Subgraphs. In: Ferreira, A., Reichel, H. (eds.) STACS 2001. LNCS, vol. 2010, pp. 121–131. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  15. 15.
    Wan, P.J., Calinescu, G., Li, X.Y., Frieder, O.: Minimum-energy Broadcasting in Static Ad Hoc Wireless Networks. Wireless Networks 8(6), 607–617 (2002)zbMATHCrossRefGoogle Scholar
  16. 16.
    Ambühl, C.: An Optimal Bound for the MST Algorithm to Compute Energy Efficient Broadcast Trees in Wireless Networks. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 1139–1150. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  17. 17.
    Flammini, M., Klasing, R., Navarra, A., Perennes, S.: Improved Approximation Results for the Minimum Energy Broadcasting Problem. Algorithmica 49(4), 318–336 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Clark, B.N., Colbourn, C.J., Johnson, D.S.: Unit Disk Graphs. Discrete Mathematics 86, 165–177 (1990)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Carmi, P., Katz, M.J., Segal, M., Shpungin, H.: Fault-Tolerant Power Assignment and Backbone in Wireless Networks. Ad Hoc & Sensor Wireless Networks 4(4), 355–366 (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Deying Li
    • 1
  • Donghyun Kim
    • 2
  • Qinghua Zhu
    • 1
  • Lin Liu
    • 1
  • Weili Wu
    • 3
  1. 1.School of InformationRenmin University of ChinaBeijingChina
  2. 2.Dept. of Mathematics and Computer ScienceNorth Carolina Central UniversityDurhamUSA
  3. 3.Dept. of Computer ScienceUniversity of Texas at DallasRichardsonUSA

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