Distributed Algorithms for Coloring and Domination in Wireless Ad Hoc Networks

  • Srinivasan Parthasarathy
  • Rajiv Gandhi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3328)


We present fast distributed algorithms for coloring and (connected) dominating set construction in wireless ad hoc networks. We present our algorithms in the context of Unit Disk Graphs which are known to realistically model wireless networks. Our distributed algorithms take into account the loss of messages due to contention from simultaneous interfering transmissions in the wireless medium.

We present randomized distributed algorithms for (conflict-free) Distance-2 coloring, dominating set construction, and connected dominating set construction in Unit Disk Graphs. The coloring algorithm has a time complexity of O(Δ log2 n) and is guaranteed to use at most O(1) times the number of colors required by the optimal algorithm. We present two distributed algorithms for constructing the (connected) dominating set; the former runs in time O(Δ log 2 n) and the latter runs in time O(log 2 n). The two algorithms differ in the amount of local topology information available to the network nodes.

Our algorithms are geared at constructing Well Connected Dominating Sets (WCDS) which have certain powerful and useful structural properties such as low size, low stretch and low degree. In this work, we also explore the rich connections between WCDS and routing in ad hoc networks. Specifically, we combine the properties of WCDS with other ideas to obtain the following interesting applications:

  • An online distributed algorithm for collision-free, low latency, low redundancy and high throughput broadcasting.

  • Distributed capacity preserving backbones for unicast routing and scheduling.


Time Slot Channel Assignment Unit Disk Graph Broadcast Algorithm Virtual Backbone 
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.
    Alzoubi, K.M.: Connected dominating set and its induced position-less sparse spanner for mobile ad hoc networks. In: Proceedings of the Eighth IEEE Symposium on Computers and Communications (June 2003)Google Scholar
  2. 2.
    Alzoubi, K.M., Wan, P.-J., Frieder, O.: Distributed heuristics for connected dominating sets in wireless ad hoc networks. IEEE ComSoc/KICS Journal on Communication Networks 4, 22–29 (2002)Google Scholar
  3. 3.
    Alzoubi, K.M., Wan, P.-J., Frieder, O.: Message efficient construction of nontrivial connected dominating sets in wireless ad hoc networks. To appear in Special Issue of ACM Journal of Monet (2002)Google Scholar
  4. 4.
    Alzoubi, K.M., Wan, P.-J., Frieder, O.: Message-optimal connected-dominating-set construction for routing in mobile ad hoc networks. In: Proceedings of the Third ACM International Symposium on Mobile Ad Hoc Networking and Computing (June 2002)Google Scholar
  5. 5.
    Alzoubi, K.M., Wan, P.-J., Frieder, O.: New distributed algorithm for connected dominating set in wireless ad hoc networks. In: IEEE HICSS35 (2002)Google Scholar
  6. 6.
    Cheng, X., Huang, X., Li, D., Du, D.-Z.: Polynomial-time approximation scheme for minimum connected dominating set in ad hoc wireless networks. Technical reportGoogle Scholar
  7. 7.
    Clark, B., Colbourn, C., Johnson, D.: Unit disk graphs. Discrete Mathematics 86, 165–177 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Das, B., Sivakumar, R., Bharghavan, V.: Routing in ad-hoc networks using a virtual backbone. In: 6th International Conference on Computer Communications and Networks IC3N 1997 (September 1997), pp. 1–20 (1997)Google Scholar
  9. 9.
    Das, B., Bharghavan, V.: Routing in ad-hoc networks using minimum connected dominating sets. ICC 1, 376–380 (1997)Google Scholar
  10. 10.
    Gandhi, R., Parthasarathy, S., Mishra, A.: Minimizing broadcast latency and redundancy in ad hoc networks. In: Proceedings of the fourth ACM international symposium on Mobile ad hoc networking and computing, pp. 222–232. ACM Press, New York (2003)CrossRefGoogle Scholar
  11. 11.
    Gupta, P., Kumar, P.R.: The capacity of wireless networks. IEEE Transactions on Information Theory 46(2), 388–404 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Krumke, S.O., Marathe, M.V., Ravi, S.S.: Models and approximation algorithms for channel assignment in radio networks. Wireless Networks 7(6), 575–584 (2001)zbMATHCrossRefGoogle Scholar
  13. 13.
    Anil Kumar, V.S., Marathe, M.V., Parthasarathy, S., Srinivasan, A.: End-to-End Packet Scheduling in Ad Hoc Networks. To appear in ACM SODA (2004)Google Scholar
  14. 14.
    Luby, M.: A simple parallel algorithm for the maximal independent set problem. SIAM Journal on Computing 15(4), 1036–1053 (1986)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Luby, M.: Removing randomness in parallel computation without a processor penalty. Journal of Computer and System Sciences 47(2), 250–286 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Marathe, M.V., Breu, H., Hunt III, H.B., Ravi, S.S., Rosenkrantz, D.J.: Simple heuristics for unit disk graphs. Networks 25, 59–68 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Ramanathan, S.: A unified framework and algorithm for channel assignment in wireless networks. Wireless Networks 5(2), 81–94 (1999)CrossRefGoogle Scholar
  18. 18.
    Ramanathan, S., Lloyd, E.L.: Scheduling algorithms for multihop radio networks. IEEE/ACM Transactions on Networking (TON) 1(2), 166–177 (1993)CrossRefGoogle Scholar
  19. 19.
    Sen, A., Melesinska, E.: On approximation algorithms for radio network scheduling. In: Proceedings of the 35th Allerton Conference on Communication, Control and Computing, pp. 573–582 (1997)Google Scholar
  20. 20.
    Sivakumar, R., Das, B., Bharghavan, V.: Spine routing in ad hoc networks. ACM/Baltzer Cluster Computing Journal (special issue on Mobile Computing) (1998)Google Scholar
  21. 21.
    Wan, P.-J., Alzoubi, K., Frieder, O.: Distributed construction of connnected dominating set in wireless ad hoc networks. In: IEEE INFOCOM (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Srinivasan Parthasarathy
    • 1
  • Rajiv Gandhi
    • 2
  1. 1.Department of Computer ScienceUniversity of MarylandCollege Park
  2. 2.Department of Computer ScienceRutgers UniversityCamden

Personalised recommendations