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Towards a Universal Approach for Monotonic Searchability in Self-stabilizing Overlay Networks

  • Christian Scheideler
  • Alexander Setzer
  • Thim Strothmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9888)

Abstract

For overlay networks, the ability to recover from a variety of problems like membership changes or faults is a key element to preserve their functionality. In recent years, various self-stabilizing overlay networks have been proposed that have the advantage of being able to recover from any illegal state. However, the vast majority of these networks cannot give any guarantees on its functionality while the recovery process is going on. We are especially interested in searchability, i.e., the functionality that search messages for a specific identifier are answered successfully if a node with that identifier exists in the network. We investigate overlay networks that are not only self-stabilizing but that also ensure that monotonic searchability is maintained while the recovery process is going on, as long as there are no corrupted messages in the system. More precisely, once a search message from node u to another node v is successfully delivered, all future search messages from u to v succeed as well. Monotonic searchability was recently introduced in OPODIS 2015, in which the authors provide a solution for a simple line topology. We present the first universal approach to maintain monotonic searchability that is applicable to a wide range of topologies. As the base for our approach, we introduce a set of primitives for manipulating overlay networks that allows us to maintain searchability and show how existing protocols can be transformed to use theses primitives. We complement this result with a generic search protocol that together with the use of our primitives guarantees monotonic searchability. As an additional feature, searching existing nodes with the generic search protocol is as fast as searching a node with any other fixed routing protocol once the topology has stabilized.

Keywords

Overlay Network Admissible State Legitimate State Search Protocol Search Request 
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.

References

  1. 1.
    Berns, A., Ghosh, S., Pemmaraju, S.V.: Building self-stabilizing overlay networks with the transitive closure framework. Theor. Comput. Sci. 512, 2–14 (2013)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Bui, A., Datta, A.K., Petit, F., Villain, V.: Snap-stabilization and PIF in tree networks. Distrib. Comput. 20(1), 3–19 (2007)MATHGoogle Scholar
  3. 3.
    Delaët, S., Devismes, S., Nesterenko, M., Tixeuil, S.: Snap-stabilization in message-passing systems. J. Parallel Distrib. Comput. 70(12), 1220–1230 (2010)CrossRefMATHGoogle Scholar
  4. 4.
    Dijkstra, E.W.: Self-stabilizing systems in spite of distributed control. Commun. ACM 17(11), 643–644 (1974)CrossRefMATHGoogle Scholar
  5. 5.
    Dolev, S., Herman, T.: Superstabilizing protocols for dynamic distributed systems. Chicago J. Theor. Comput. Sci. 1997 (1997)Google Scholar
  6. 6.
    Dolev, S., Tzachar, N.: Spanders: distributed spanning expanders. Sci. Comput. Program. 78(5), 544–555 (2013)CrossRefMATHGoogle Scholar
  7. 7.
    Gall, D., Jacob, R., Richa, A.W., Scheideler, C., Schmid, S., Täubig, H.: A note on the parallel runtime of self-stabilizing graph linearization. Theory Comput. Syst. 55(1), 110–135 (2014)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Jacob, R., Richa, A.W., Scheideler, C., Schmid, S., Täubig, H.: Skip\({}^{\text{+}}\): a self-stabilizing skip graph. J. ACM 61(6), 36:1–36:26 (2014)Google Scholar
  9. 9.
    Jacob, R., Ritscher, S., Scheideler, C., Schmid, S.: Towards higher-dimensional topological self-stabilization: a distributed algorithm for delaunay graphs. Theor. Comput. Sci. 457, 137–148 (2012)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Johnen, C., Mekhaldi, F.: Robust self-stabilizing construction of bounded size weight-based clusters. In: D’Ambra, P., Guarracino, M., Talia, D. (eds.) Euro-Par 2010, Part I. LNCS, vol. 6271, pp. 535–546. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  11. 11.
    Kakugawa, H., Masuzawa, T.: A self-stabilizing minimal dominating set algorithm with safe convergence. In: 20th International Parallel and Distributed Processing Symposium (IPDPS 2006), Proceedings, 25–29 April 2006. Rhodes, Island, Greece (2006)Google Scholar
  12. 12.
    Kniesburges, S., Koutsopoulos, A., Scheideler, C.: A self-stabilization process for small-world networks. In: 26th IEEE International Parallel and Distributed Processing Symposium, IPDPS 2012, Shanghai, China, 21–25 May 2012, pp. 1261–1271 (2012)Google Scholar
  13. 13.
    Koutsopoulos, A., Scheideler, C., Strothmann, T.: Towards a universal approach for the finite departure problem in overlay networks. In: Pelc, A., Schwarzmann, A.A. (eds.) SSS 2015. LNCS, vol. 9212, pp. 201–216. Springer, Heidelberg (2015)CrossRefGoogle Scholar
  14. 14.
    Nor, R.M., Nesterenko, M., Scheideler, C.: Corona: a stabilizing deterministic message-passing skip list. Theor. Comput. Sci. 512, 119–129 (2013)Google Scholar
  15. 15.
    Onus, M., Richa, A.W., Scheideler, C.: Linearization: locally self-stabilizing sorting in graphs. In: Proceedings of the Nine Workshop on Algorithm Engineering and Experiments, ALENEX 2007, New Orleans, Louisiana, USA, 6 January 2007Google Scholar
  16. 16.
    Scheideler, C., Setzer, A., Strothmann, T.: Towards establishing monotonic searchability in self-stabilizing data structures. In: Principles of Distributed Systems - 19th International Conference, OPODIS 2015, Proceedings (2015)Google Scholar
  17. 17.
    Scheideler, C., Setzer, A., Strothmann, T.: Towards a universal approach for monotonic searchability in self-stabilizing overlay networks (full version). ArXiv e-prints, July 2016Google Scholar
  18. 18.
    Shaker, A., Reeves, D.S.: Self-stabilizing structured ring topology P2P systems. In: Fifth IEEE International Conference on Peer-to-Peer Computing (P2P 2005), 31 August–2 September 2005, Konstanz, Germany, pp. 39–46 (2005)Google Scholar
  19. 19.
    Yamauchi, Y., Tixeuil, S.: Monotonic stabilization. In: Lu, C., Masuzawa, T., Mosbah, M. (eds.) OPODIS 2010. LNCS, vol. 6490, pp. 475–490. Springer, Heidelberg (2010)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Christian Scheideler
    • 1
  • Alexander Setzer
    • 1
  • Thim Strothmann
    • 1
  1. 1.Paderborn UniversityPaderbornGermany

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