Self-stabilizing Wireless Connected Overlays

  • Vadim Drabkin
  • Roy Friedman
  • Maria Gradinariu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4305)

Abstract

We propose the correctness proofs and the complexity analysis for the first self-stabilizing constructions of connected overlays for wireless networks (eg. MANETs, WSN) based on the computation of Connected Dominating Set (CDS). The basic idea is to construct an overlay that contains a small number of nodes, but still obtain full connectivity of the network while only relying on local exchanges of information and knowledge. We adopt two methodologies of construction: the first methodology consists of two parallel tasks, namely, computing a maximal independent set (MIS) and then adding bridge nodes between the MIS nodes. The second methodology computes a connected dominating set using the observation that a dominator is a bridge between nodes that do not share the same neighborhood.

The proposed algorithms are fully decentralized and are designed in a self-stabilizing manner in order to cope with transient faults, mobility and nodes join/leave. In particular, they do not need to be (re)initialized after a fault or a physical topology change. That is, whatever the initial configuration is, the algorithms satisfy their specification after a stabilization period. The convergence time of our algorithms is linear in the size of the network and they use only one extra bit of memory. We also present an optimization of our algorithms that reduces the number of nodes in the cover. However, the optimization increases the convergence time with a constant factor.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alzoubi, K., Peng-Jun, W., Frieder, O.: Weakly connected dominating sets and sparse spanners in wireless adhoc networks. In: ICDCS 2003 Proceedings of the 23rd International Conference on Distributed Computing Systems, pp. 96–104 (2003)Google Scholar
  2. 2.
    Ankur, J., Gupta, A.: A distributed self-stabilizing algorithm for finding a connected dominating set in a graph. In: PDCAT 2005 (2005)Google Scholar
  3. 3.
    Dai, F., Wu, J.: Distributed dominant pruning in ad hoc networks. In: Proceedings of ICC 2003 (2003)Google Scholar
  4. 4.
    Das, B., Bharghavan, V.: Routing in ad-hoc networks using minimum connected dominating sets. In: ICC (1), pp. 376–380 (1997)Google Scholar
  5. 5.
    Das, B., Sivakumar, R., Bharghavan, V.: Routing in ad hoc networks using a spine. In: ICCCN, pp. 34–41 (1997)Google Scholar
  6. 6.
    Datta, A.K., Gradinariu, M., Linga, P., Raipan-Parvéde, P.: Self-stabilizing query covers in sensor networks. In: SRDS (2005)Google Scholar
  7. 7.
    Datta, A.K., Gradinariu, M., Patel, R.: Optimal self* query region covers in sensor networks. In: ISPAN (2005)Google Scholar
  8. 8.
    Datta, A.K., Gradinariu, M., Patel, R.: Dominating-sets based self-stabilizing minimum query covers in sensor networks. Technical Report 1803, IRISA/Universite Rennes 1 (2006)Google Scholar
  9. 9.
    Dijkstra, E.W.: Self stabilizing systems in spite of distributed control. Communications of the Association of the Computing Machinery 17(11), 643–644 (1974)MATHGoogle Scholar
  10. 10.
    Dolev, S.: Self-Stabilization. MIT Press, Cambridge (2000)MATHGoogle Scholar
  11. 11.
    Drabkin, V., Friedman, R., Gradinariu, M.: Self-stabilizing wireless connected overlay. Technical report, LIP6, Universite Paris 6 (2006)Google Scholar
  12. 12.
    Friedman, R., Gradinariu, M., Simon, G.: Locating cache proxies in manets. In: MobiHoc 2004 Proceedings of the Thifth ACM International Symposium on Mobile Ad Hoc Networking and Computing (2004)Google Scholar
  13. 13.
    Gouda, M.G., Herman, T.: Adaptive programming. IEEE Trans. Software Eng. 17(9), 911–921 (1991)CrossRefMathSciNetGoogle Scholar
  14. 14.
    Gradinariu, M., Tixeuil, S.: Self-stabilizing vertex coloring of arbitrary graphs. In: Proceedings of OPODIS 2000, STUDIA INFORMATICA, pp. 55–70 (2000)Google Scholar
  15. 15.
    Herman, T., Tixeuil, S.: A distributed TDMA slot assignment algorithm for wireless sensor networks. In: Nikoletseas, S.E., Rolim, J.D.P. (eds.) ALGOSENSORS 2004. LNCS, vol. 3121, pp. 45–58. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  16. 16.
    Ingelrest, F., Simplot-Ryl, D., Stojmenovic, I.: Smaller connected dominating sets in ad hoc and sensor networks based on coverage by two-hop neighbors. Technical report, Institut National De Recherche En Informatique Et En Automatique (April 2005)Google Scholar
  17. 17.
    Kakugawa, H., Masuzawa, T.: A self-stabilizing minimal dominating set algorithm with safe convergence. In: IEEE Parallel and Distributed Processing Synmposium (IPDPS 2006) (2006)Google Scholar
  18. 18.
    Liu, H., Pan, Y., Cao, J.: An improved distributed algorithm for connected dominating sets in wireless ad hoc networks. In: Cao, J., Yang, L.T., Guo, M., Lau, F. (eds.) ISPA 2004. LNCS, vol. 3358, pp. 340–351. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  19. 19.
    Peng-Jun, W., Alzoubi, K., Frieder, O.: Distributed construction of connected dominating sets in wireless adhoc networks. In: INFOCOM 2002 Proceedings of the Conference on Computer Communications (2002)Google Scholar
  20. 20.
    Theoleyre, F., Valois, F.: About the self-stabilization of a virtual topology for self-organization in ad hoc networks. In: Self-Stabilizing Systems, pp. 214–228 (2005)Google Scholar
  21. 21.
    Wu, J.: Extended dominating-set-based routing in ad hoc wireless networks with unidirectional links. IEEE Transactions on Parallel and Distributed Systems 13(9), 866–881 (2002)CrossRefGoogle Scholar
  22. 22.
    Wu, J., Gao, M., Stojmenovic: On calculating power-aware connected dominating sets for efficient routing in ad hoc wireless networks. In: Proc. of the 30th International Conference on Parallel Processing (ICPP 2001), pp. 346–353 (2001)Google Scholar
  23. 23.
    Wu, J., Li, H.: On calculating connected dominating set for efficient routing in ad hoc wireless networks. In: Proc. of the 3th Int. Workshop on Discrete Algothrithms and Methods for MOBILE Computing and Communications (DialM 1999), pp. 7–14 (1999)Google Scholar
  24. 24.
    Xu, Z., Hedetniemi, S.T., Goddard, W., Srimani, P.K.: A synchronous self-stabilizing minimal domination protocol in an arbitrary network graph. In: IWDC 2003 (2003)Google Scholar
  25. 25.
    Das, S., Zhou, Z., Gupta, H.: Fault tolerant connected sensor cover with variable sensing and transmission. SECON (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Vadim Drabkin
    • 1
  • Roy Friedman
    • 1
  • Maria Gradinariu
    • 2
  1. 1.TechnionIsrael
  2. 2.LIP6, Université Paris 6 (Pierre et Marie Currie) – INRIA 

Personalised recommendations