A New Heuristic for the Minimum Connected Dominating Set Problem on Ad Hoc Wireless Networks

  • Sergiy Butenko
  • Xiuzhen Cheng
  • Carlos A. Oliveira
  • P. M. Pardalos
Part of the Cooperative Systems book series (COSY, volume 3)


Given a graph G = (V, E), a dominating set D is a subset of V such that any vertex not in D is adjacent to at least one vertex in D. Efficient algorithms for computing the minimum connected dominating set (MCDS) are essential for solving many practical problems, such as finding a minimum size backbone in ad hoc networks. Wireless ad hoc networks appear in a wide variety of applications, including mobile commerce, search and discovery, and military battlefield. In this chapter we propose a new efficient heuristic algorithm for the minimum connected dominating set problem. The algorithm starts with a feasible solution containing all vertices of the graph. Then it reduces the size of the CDS by excluding some vertices using a greedy criterion. We also discuss a distributed version of this algorithm. The results of numerical testing show that, despite its simplicity, the proposed algorithm is competitive with other existing approaches.


Cooperative Control Unit Disk Graph Mobile Commerce Breadth First Search Current Vertex 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    K. M. Alzoubi, P.-J. Wan, and O. Frieder. Distributed heuristics for connected dominating set in wireless ad hoc networks. IEEE ComSoc/KICS Journal on Communication Networks, 4 (1): 22–29, 2002.Google Scholar
  2. [2]
    B. Awerbuch and D. Peleg. Network synchronization with polylogarithmic overhead. In Proc. 31st Symp. Found. Computer Science, pages 514–522, 1990.Google Scholar
  3. [3]
    B. S. Baker. Approximation algorithms for NP-complete problems on planar graphs. Journal of the ACM (JACM), 41 (1): 153–180, 1994.MATHCrossRefGoogle Scholar
  4. [4]
    S. Butenko, X. Cheng, D.-Z. Du, and P. M. Pardalos. On the construction of virtual backbone for ad hoc wireless network. In S. Butenko, R. Murphey, and P. M. Pardalos, editors, Cooperative Control: Models, Applications and Algorithms, pages 43–54. Kluwer Academic Publishers, 2002.Google Scholar
  5. [5]
    X. Cheng, X. Huang, D. Li, W. Wu, and D.-Z. Du. Polynomial-time approximation scheme for minimum connected dominating set in ad hoc wireless networks. To appear in Networks, 2003.Google Scholar
  6. [6]
    B. Das and V. Bharghavan. Routing in ad-hoc networks using minimum connected dominating sets. In International Conference on Communications, pages 376–380, 1997.Google Scholar
  7. [7]
    M. R. Garey and D. S. Johnson. Computers and Intractability - A Guide to the Theory of NP-Completeness. W. H. Freeman, San Francisco CA, 1979.MATHGoogle Scholar
  8. [8]
    S. Guha and S. Khuller. Approximation algorithms for connected dominating sets. Algorithmica, 20 (4): 374–387, 1998.MathSciNetMATHCrossRefGoogle Scholar
  9. [9]
    H. B. Hunt III, M.V. Marathe, V. Radhakrishnan, S.S. Ravi, D.J. Rosenkrantz, and R.E. Stearns. NC-approximation schemes for NP- and PSPACE-hard problems for geometric graphs, J. Algorithms, 26: 238–274, 1998.MathSciNetCrossRefGoogle Scholar
  10. [10]
    N. Malpani, J. Welch, and N. Vaidya. Leader election algorithms for mobile ad hoc networks. In Proc. Fourth International Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications, pages 96–103, 2000.Google Scholar
  11. [11]
    M. V. Marathe, H. Breu, H. B. Hunt III, S. S. Ravi, and D. J. Rosenkrantz. Simple heuristics for unit disk graphs. Networks, 25: 59–68, 1995.MathSciNetMATHCrossRefGoogle Scholar
  12. [12]
    L. A. Sanchis. Experimental analysis of heuristic algorithms for the dominating set problem. Algorithmica, 33: 3–18, 2002.MathSciNetMATHCrossRefGoogle Scholar
  13. [13]
    I. Stojmenovic, M. Seddigh, and J. Zunic. Dominating sets and neighbor elimination based broadcasting algorithms in wireless networks. In Proc. IEEE Hawaii Int. Conf on System Sciences, 2001.Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Sergiy Butenko
    • 1
  • Xiuzhen Cheng
    • 2
  • Carlos A. Oliveira
    • 3
  • P. M. Pardalos
    • 4
  1. 1.Department of Industrial EngineeringTexas A & M UniversityUSA
  2. 2.Department of Computer ScienceThe George Washington UniversityUSA
  3. 3.Department of Industrial and Systems EngineeringUniversity of FloridaGainesvilleUSA
  4. 4.Center for Applied Optimization Department of Industrial and Systems EngineeringUniversity of FloridaGainesvilleUSA

Personalised recommendations