Building Self-stabilizing Overlay Networks with the Transitive Closure Framework

  • Andrew Berns
  • Sukumar Ghosh
  • Sriram V. Pemmaraju
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6976)


Overlay networks are expected to operate in hostile environments, where node and link failures are commonplace. One way to make overlay networks robust is to design self-stabilizing overlay networks, i.e., overlay networks that can handle node and link failures without any external supervision. In this paper, we first describe a simple framework, which we call the Transitive Closure Framework (TCF), for the self-stabilizing construction of an extensive class of overlay networks. Like previous self-stabilizing overlay networks, TCF permits node degrees to grow to Ω(n), independent of the maximum degree of the target overlay network. However, TCF has several advantages over previous work in this area: (i) it is a “framework” and can be used for the construction of a variety of overlay networks, not just a particular network, (ii) it runs in an optimal number of rounds for a variety of overlay networks, and (iii) it can easily be composed with other non-self-stabilizing protocols that can recover from specific bad initial states in a memory-efficient fashion. We demonstrate the power of our framework by deriving from TCF a simple self-stabilizing protocol for constructing Skip+ graphs (Jacob et al., PODC 2009) which presents optimal convergence time from any configuration, and requires only a O(1) factor of extra memory for handling node Joins.


Node Degree Overlay Network Link Failure Virtual Link Linear Network 
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.
    Aspnes, J., Shah, G.: Skip graphs. In: SODA 2003: Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 384–393. Society for Industrial and Applied Mathematics, Philadelphia (2003)Google Scholar
  2. 2.
    Aspnes, J., Wu, Y.: O(logn)-time overlay network construction from graphs with out-degree 1. In: Tovar, E., Tsigas, P., Fouchal, H. (eds.) OPODIS 2007. LNCS, vol. 4878, pp. 286–300. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  3. 3.
    Dijkstra, E.W.: Self-stabilizing systems in spite of distributed control. Commun. ACM 17(11), 643–644 (1974)CrossRefzbMATHGoogle Scholar
  4. 4.
    Jacob, R., Richa, A., Scheideler, C., Schmid, S., Täubig, H.: A distributed polylogarithmic time algorithm for self-stabilizing skip graphs. In: PODC 2009: Proceedings of the 28th ACM Symposium on Principles of Distributed Computing, pp. 131–140. ACM, New York (2009)Google Scholar
  5. 5.
    Kniesburges, S., Scheideler, C., Koutsopoulos, A.: Re-chord: A self-stabilizing chord overlay network. In: SPAA 2011: Proceedings of the 23rd ACM Symposium on Parallelism in Algorithms and Architectures. ACM, New York (2011)Google Scholar
  6. 6.
    Onus, M., Richa, A.W., Scheideler, C.: Linearization: Locally self-stabilizing sorting in graphs. In: ALENEX. SIAM, Philadelphia (2007)Google Scholar
  7. 7.
    Peleg, D.: Distributed computing: a locality-sensitive approach. Society for Industrial and Applied Mathematics, Philadelphia (2000)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Andrew Berns
    • 1
  • Sukumar Ghosh
    • 1
  • Sriram V. Pemmaraju
    • 1
  1. 1.Department of Computer ScienceThe University of IowaIowa CityUSA

Personalised recommendations