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Distributed Maintenance of Anytime Available Spanning Trees in Dynamic Networks

  • Arnaud Casteigts
  • Serge Chaumette
  • Frédéric Guinand
  • Yoann Pigné
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7960)

Abstract

We address the problem of building and maintaining a forest of spanning trees in highly dynamic networks, in which topological events can occur at any time and any rate, and no stable periods can be assumed. In these harsh environments, we strive to preserve some properties such as cycle-freeness or existence of a unique root in each fragment regardless of the events, so as to keep these fragments functioning uninterruptedly to a possible extent. Our algorithm operates at a coarse-grain level, using atomic pairwise interactions akin to population protocol or graph relabeling systems. The algorithm relies on a perpetual alternation of topology-induced splittings and computation-induced mergings of a forest of trees. Each tree in the forest hosts exactly one token (also called root) that performs a random walk inside the tree, switching parent-child relationships as it crosses edges. When two tokens are located on both sides of a same edge, their trees are merged upon this edge and one token disappears. Whenever an edge that belongs to a tree disappears, its child endpoint regenerates a new token instantly. The main features of this approach is that both merging and splitting are purely localized phenomenons. This paper presents the algorithm and establishes its correctness in arbitrary dynamic networks. We also discuss aspects related to the implementation of this general principle in fine-grain models, as well as embryonic elements of analysis. The characterization of the algorithm performance is left open, both analytically and experimentally.

Keywords

Random Walk Span Tree Dynamic Network Mobile Agent Span Tree Problem 
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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References

  1. 1.
    Abbas, S., Mosbah, M., Zemmari, A.: Distributed computation of a spanning tree in a dynamic graph by mobile agents. In: Proc. of IEEE Int. Conference on Engineering of Intelligent Systems (ICEIS), pp. 1–6 (2006)Google Scholar
  2. 2.
    Aldous, D.J.: The random walk construction of uniform spanning trees and uniform labelled trees. SIAM J. Discret. Math. 3(4), 450–465 (1990)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Angluin, D., Aspnes, J., Diamadi, Z., Fischer, M., Peralta, R.: Computation in networks of passively mobile finite-state sensors. Distributed Computing 18(4), 235–253 (2006)CrossRefGoogle Scholar
  4. 4.
    Awerbuch, B., Kutten, S., Mansour, Y., Patt-Shamir, B., Varghese, G.: Time optimal self-stabilizing synchronization. In: Proc. of the 25th ACM Symp. on Theory of Computing (STOC), New York, USA, pp. 652–661 (1993)Google Scholar
  5. 5.
    Baala, H., Flauzac, O., Gaber, J., Bui, M., El-Ghazawi, T.: A self-stabilizing distributed algorithm for spanning tree construction in wireless ad hoc networks. Journal of Parallel and Distributed Computing 63, 97–104 (2003)zbMATHCrossRefGoogle Scholar
  6. 6.
    Burman, J., Kutten, S.: Time optimal asynchronous self-stabilizing spanning tree. In: Pelc, A. (ed.) DISC 2007. LNCS, vol. 4731, pp. 92–107. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  7. 7.
    Cooper, C., Elsässer, R., Ono, H., Radzik, T.: Coalescing random walks and voting on graphs. In: Proc. of the 31st ACM Symp. on Principles of Distributed Computing (PODC), pp. 47–56 (2012)Google Scholar
  8. 8.
    Fall, K.: A delay-tolerant network architecture for challenged internets. In: Proc. of Int. Conf. on Applications, Technologies, Architectures, and Protocols for Computer Communications (SIGCOMM), pp. 27–34 (2003)Google Scholar
  9. 9.
    Ferreira, A.: Building a reference combinatorial model for MANETs. IEEE Network 18(5), 24–29 (2004)CrossRefGoogle Scholar
  10. 10.
    Gaertner, F.C.: A Survey of Self-Stabilizing Spanning-Tree Construction Algorithms. Technical report, EPFL (2003)Google Scholar
  11. 11.
    Litovsky, I., Métivier, Y., Sopena, E.: Graph relabelling systems and distributed algorithms. In: Handbook of Graph Grammars and Computing by Graph Transformation, vol. III, pp. 1–56. World Scientific Publishing (1999)Google Scholar
  12. 12.
    Peleg, D.: Distributed computing: a locality-sensitive approach. Society for Industrial and Applied Mathematics (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Arnaud Casteigts
    • 1
  • Serge Chaumette
    • 1
  • Frédéric Guinand
    • 2
  • Yoann Pigné
    • 2
  1. 1.LaBRIUniversity of BordeauxFrance
  2. 2.LITISUniversity of Le HavreFrance

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