A Convex-Hull Based Algorithm to Connect the Maximal Independent Set in Unit-Disk Graphs

  • Dechang Chen
  • Xilong Mao
  • Xia Fei
  • Kai Xing
  • Fang Liu
  • Min Song
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4138)


In this paper we propose and analyze a localized convex-hull based algorithm to connect a maximal independent set. The cardinality of the resultant connected dominating set is at most 76 Open image in new window opt +19, where opt is the size of a minimum connected dominating set. To our knowledge, this is a dramatic improvement compared to the best published results in the same context [1,6] . Our algorithm plays an important rule in efficiently constructing a virtual backbone for ad hoc and sensor networks.


Ad hoc and sensor networks maximal independent set connected dominating set 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alzoubi, K.M., Wan, P.-J., Frieder, O.: Message-Optimal Connected Dominating Sets in Mobile Ad Hoc Networks. In: MOBIHOC, EPFL Lausanne, Switzerland (2002)Google Scholar
  2. 2.
    Alzoubi, K.M., Wan, P.-J., Frieder, O.: New Distributed Algorithm for Connected Dominating Set in Wireleess Ad Hoc Networks. In: Proceedings of the 35th Hawaii International Conference on System Sciences, Big Island, Hawaii (2002)Google Scholar
  3. 3.
    Alzoubi, K.M., Wan, P.-J., Frieder, O.: Distributed Heuristics for Connected Dominating Sets in Wireless Ad Hoc Networks. Journal of Communications and Networks 4(1) (March 2002)Google Scholar
  4. 4.
    Blum, J., Ding, M., Thaeler, A., Cheng, X.: Connected Dominating Sets in Sensor Networks and MANETs. In: Du, D.-Z., Pardalos, P. (eds.) Handbook of Combinatorial Optimization, pp. 329–369 (2004)Google Scholar
  5. 5.
    Cheng, X., Huang, X., Li, D., Wu, W., Du, D.-Z.: Polynomial-Time Approximation Scheme for Minimum Connected Dominating Set in Ad Hoc Wireless Networks. Networks 42(4), 202–208 (2003)CrossRefMathSciNetzbMATHGoogle Scholar
  6. 6.
    Cheng, X., Ding, M., Du, D.H., Jia, X.: On The Construction of Connected Dominating Set in Ad Hoc Wireless Networks. Wireless Communications and Mobile Computing 6, 183–190 (2006)CrossRefGoogle Scholar
  7. 7.
    Cheng, X.: Routing Issues in Ad Hoc Wireless Networks, PhD Thesis, Department of Computer Science, University of Minnesota (2002)Google Scholar
  8. 8.
    Cidon, I., Mokryn, O.: Propagation and Leader Election in Multihop Broadcast Environment. In: Proc. 12th Int. Symp. Distr. Computing, Greece, pp. 104–119 (1998)Google Scholar
  9. 9.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. Mc Graw Hill, New York (2001)zbMATHGoogle Scholar
  10. 10.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A guide to the theory of NP-completeness. Freeman, San Francisco (1978)Google Scholar
  11. 11.
    Guha, S., Khuller, S.: Approximation algorithms for connected dominating sets. Algorithmica 20(4), 374–387 (1998)CrossRefMathSciNetzbMATHGoogle Scholar
  12. 12.
    Min, M., Du, H., Jia, X., Huang, C.X., Huang, S.C.-H., Wu, W.: Improving Construction for Connected Dominating Set with Steiner Tree in Wireless Sensor Networks. Journal of Global Optimization 35(1), 111–119 (2006)CrossRefMathSciNetzbMATHGoogle Scholar
  13. 13.
    Sivakumar, R., Sinha, P., Bharghavan, V.: CEDAR: a core-extraction distributed ad hoc routing algorithm. IEEE Journal on Selected Areas in Communications 17(8), 1454–1465 (1999)CrossRefGoogle Scholar
  14. 14.
    Wan, P.-J., Alzoubi, K.M., Frieder, O.: Distributed Construction of Connected Dominating Set in Wireless Ad Hoc Networks. In: IEEE INFOCOM, pp. 1597–1604 (2002)Google Scholar
  15. 15.
    Wu, J., Dai, F., Gao, M., Stojmenovic, I.: On Calculating Power- Aware Connected Dominating Set for Ecient Routing in Ad Hoc Wireless Networks. Journal of Communications and Networks 5(2), 169–178 (2002)Google Scholar
  16. 16.
    Xu, Y., Heidemann, J., Estrin, D.: Geography-informed energy conservation for Ad Hoc routing. In: MobiCom 2001, pp. 70–84 (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Dechang Chen
    • 1
  • Xilong Mao
    • 2
  • Xia Fei
    • 3
  • Kai Xing
    • 4
  • Fang Liu
    • 4
  • Min Song
    • 5
  1. 1.Uniformed Services University of the Health SciencesBethesdaUSA
  2. 2.School of ComputerNational University of Defense TechnologyChangsha, HunanP.R. China
  3. 3.Rizhao Geotechical Investigation and SurveyingInstitute of Urban and Rural ConstructionRizhao, ShandongP.R. China
  4. 4.Department of Computer ScienceThe George Washington UniversityWashingtonUSA
  5. 5.Department of Electrical and Computer EngineeringOld Dominion UniversityNorfolkUSA

Personalised recommendations