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Corona: A Stabilizing Deterministic Message-Passing Skip List

  • Rizal Mohd Nor
  • Mikhail Nesterenko
  • Christian Scheideler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6976)

Abstract

We present Corona, a deterministic self-stabilizing algorithm for skip list construction in structured overlay networks. Corona operates in the low-atomicity message-passing asynchronous system model. Corona requires constant process memory space for its operation and, therefore, scales well. We prove the general necessary conditions limiting the initial states from which a self-stabilizing structured overlay network in message-passing system can be constructed. The conditions require that initial state information has to form a weakly connected graph and it should only contain identifiers that are present in the system. We formally describe Corona and rigorously prove that it stabilizes from an arbitrary initial state subject to the necessary conditions. We extend Corona to construct a skip graph.

Keywords

Overlay Network Outgoing Link Arbitrary Initial State Left Neighbor Weak Fairness 
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.
    Alima, L.O., Haridi, S., Ghodsi, A., El-Ansary, S., Brand, P.: Position paper: Self-.properties in distributed k-ary structured overlay networks. In: Proceedings of SELF-STAR: International Workshop on Self-* Properties in Complex Information Systems (May 2004)Google Scholar
  2. 2.
    Andersen, D., Balakrishnan, H., Kaashoek, F., Morris, R.: Resilient overlay networks. In: SOSP 2001: Proceedings of the Eighteenth ACM Symposium on Operating Systems Principles, pp. 131–145. ACM, New York (2001)CrossRefGoogle Scholar
  3. 3.
    Aspnes, J., Shah, G.: Skip graphs. ACM Transactions on Algorithms 3(4), 37:1–37:25 (2007)Google Scholar
  4. 4.
    Awerbuch, B., Scheideler, C.: The hyperring: a low-congestion deterministic data structure for distributed environments. In: SODA 2004: Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 318–327. Society for Industrial and Applied Mathematics, Philadelphia (2004)Google Scholar
  5. 5.
    Berns, A., Ghosh, S., Pemmaraju, S.V.: Brief announcement: a framework for building self-stabilizing overlay networks. In: Proc. of the 29th ACM Symp. on Principles of Distributed Computing (PODC), pp. 398–399 (2010)Google Scholar
  6. 6.
    Bhargava, A., Kothapalli, K., Riley, C., Scheideler, C., Thober, M.: Pagoda: a dynamic overlay network for routing, data management, and multicasting. In: SPAA 2004: Proceedings of the Sixteenth Annual ACM Symposium on Parallelism in Algorithms and Architectures, pp. 170–179. ACM, New York (2004)CrossRefGoogle Scholar
  7. 7.
    Bianchi, S., Datta, A., Felber, P., Gradinariu, M.: Stabilizing peer-to-peer spatial filters. In: ICDCS 2007: Proceedings of the 27th International Conference on Distributed Computing Systems, p. 27. IEEE Computer Society Press, Washington, DC, USA (2007)Google Scholar
  8. 8.
    Caron, E., Desprez, F., Petit, F., Tedeschi, C.: Snap-stabilizing prefix tree for peer-to-peer systems. Parallel Processing Letters 20(1), 15–30 (2010)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Clouser, T., Nesterenko, M., Scheideler, C.: Tiara: A Self-stabilizing Deterministic Skip List. In: Kulkarni, S.S., Schiper, A. (eds.) SSS 2008. LNCS, vol. 5340, pp. 124–140. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  10. 10.
    Cramer, C., Fuhrmann, T.: Self-stabilizing ring networks on connected graphs. Technical Report 2005-5, System Architecture Group, University of Karlsruhe (2005)Google Scholar
  11. 11.
    Dijkstra, E.W.: Self-stabilization in spite of distributed control. Communications of the ACM 17(11), 643–644 (1974)CrossRefMATHGoogle Scholar
  12. 12.
    Gall, D., Jacob, R., Richa, A., Scheideler, C., Schmid, S., Täubig, H.: Time complexity of distributed topological self-stabilization: The case of graph linearization, pp. 294–305 (2010)Google Scholar
  13. 13.
    Harvey, N.J.A., Jones, M.B., Saroiu, S., Theimer, M., Wolman, A.: Skipnet: a scalable overlay network with practical locality properties. In: USITS 2003: Proceedings of the 4th Conference on USENIX Symposium on Internet Technologies and Systems, p. 9. USENIX Association, Berkeley (2003)Google Scholar
  14. 14.
    Hérault, T., Lemarinier, P., Peres, O., Pilard, L., Beauquier, J.: Brief Announcement: Self-stabilizing Spanning Tree Algorithm for Large Scale Systems. In: Datta, A.K., Gradinariu, M. (eds.) SSS 2006. LNCS, vol. 4280, pp. 574–575. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  15. 15.
    Jacob, R., Richa, A., Scheideler, C., Schmid, S., Täubig, H.: A distributed polylogarithmic time algorithm for self-stabilizing skip graphs. In: Proc. of the 28th ACM Symp. on Principles of Distributed Computing (PODC), pp. 131–140 (2009)Google Scholar
  16. 16.
    Malkhi, D., Naor, M., Ratajczak, D.: Viceroy: a scalable and dynamic emulation of the butterfly. In: PODC 2002: Proceedings of the Twenty-First Annual Symposium on Principles of Distributed Computing, pp. 183–192. ACM, New York (2002)CrossRefGoogle Scholar
  17. 17.
    Nor, R., Nesterenko, M., Scheideler, C.: Corona: A stabilizing deterministic message-passing skip list. Technical Report TR-KSU-2011-01, CS Dept., Kent State University (May 2011)Google Scholar
  18. 18.
    Onus, M., Richa, A., Scheideler, C.: Linearization: Locally self-stabilizing sorting in graphs. In: Proc. 9th Workshop on Algorithm Engineering and Experiments (ALENEX). SIAM, Philadelphia (2007)Google Scholar
  19. 19.
    Onus, M., Richa, A., Scheideler, C.: Linearization: Locally self-stabilizing sorting in graphs. In: ALENEX 2007: Proceedings of the Workshop on Algorithm Engineering and Experiments. SIAM, Philadelphia (2007)Google Scholar
  20. 20.
    Pugh, W.: Skip lists: A probabilistic alternative to balanced trees. Communications of the ACM 33(6), 668–676 (1990)CrossRefGoogle Scholar
  21. 21.
    Scheideler, C., Jacob, R., Ritscher, S., Schmid, S.: A self-stabilizing and local delaunay graph construction. In: Dong, Y., Du, D.-Z., Ibarra, O. (eds.) ISAAC 2009. LNCS, vol. 5878, pp. 771–780. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  22. 22.
    Ratnasamy, S., Francis, P., Handley, M., Karp, R., Schenker, S.: A scalable content-addressable network. In: SIGCOMM 2001: Proceedings of the 2001 Conference on Applications, Technologies, Architectures, and Protocols for Computer Communications, pp. 161–172. ACM, New York (2001)CrossRefGoogle Scholar
  23. 23.
    Rowstron, A.I.T., Druschel, P.: Pastry: Scalable, Decentralized Object Location, and Routing for Large-Scale Peer-to-Peer Systems. In: Liu, H. (ed.) Middleware 2001. LNCS, vol. 2218, pp. 329–350. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  24. 24.
    Shaker, A., Reeves, D.S.: Self-stabilizing structured ring topology P2P systems. In: Proc. 5th IEEE International Conference on Peer-to-Peer Computing, pp. 39–46 (2005)Google Scholar
  25. 25.
    Stoica, I., Morris, R., Liben-Nowell, D., Karger, D.R., Kaashoek, M.F., Dabek, F., Balakrishnan, H.: Chord: a scalable peer-to-peer lookup protocol for Internet applications. IEEE / ACM Transactions on Networking 11(1), 17–32 (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Rizal Mohd Nor
    • 1
  • Mikhail Nesterenko
    • 1
  • Christian Scheideler
    • 2
  1. 1.Department of Computer ScienceKent State UniversityKentUSA
  2. 2.Department of Computer ScienceUniversity of PaderbornPaderbornGermany

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