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Sub-linear Universal Spatial Gossip Protocols

  • Hervé Baumann
  • Pierre Fraigniaud
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5869)

Abstract

Gossip protocols are communication protocols in which, periodically, every node of a network exchanges information with some other node chosen according to some (randomized) strategy. These protocols have recently found various types of applications for the management of distributed systems. Spatial gossip protocols are gossip protocols that use the underlying spatial structure of the network, in particular for achieving the ”closest-first” property. This latter property states that the closer a node is to the source of a message the more likely it is to receive this message within a prescribed amount of time. Spatial gossip protocols find many applications, including the propagation of alarms in sensor networks, and the location of resources in P2P networks. We design a sub-linear spatial gossip protocol for arbitrary graphs metric. More specifically, we prove that, for any graph metric with maximum degree Δ, for any source s and any ball centered at s with size b, new information is spread from s to all nodes in the ball within \(O( (\sqrt {b \log b}\, \log \log b + \Delta) \log b )\) rounds, with high probability. Moreover, when applied to general metrics with uniform density, the same protocol achieves a propagation time of O(log2 bloglogb) rounds.

Keywords

epidemic algorithm information spreading resource location 

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References

  1. 1.
    Demers, A., Greene, D., Hauser, C., Irish, W., Larson, J., Shenker, S., Sturgis, H., Swinehart, D., Terry, D.: Epidemic Algorithms for Replicated Database Maintenance. In: 6th ACM Symposium on Principles of Distributed Computing (PODC), pp. 1–12 (1987)Google Scholar
  2. 2.
    Feige, U., Peleg, D., Raghavan, P., Upfal, E.: Randomized broadcast in networks. In: Asano, T., Imai, H., Ibaraki, T., Nishizeki, T. (eds.) SIGAL 1990. LNCS, vol. 450, pp. 128–137. Springer, Heidelberg (1990)CrossRefGoogle Scholar
  3. 3.
    Fraigniaud, P., Gavoille, C., Kosowski, A., Lebhar, E., Lotker, Z.: Universal Augmentation Schemes for Network Navigability: Overcoming the \(\sqrt{n}\)-Barrier. In: 19th Annual ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pp. 1–7 (2007)Google Scholar
  4. 4.
    Frieze, A., Grimmett, G.: The shortest-path problem for graphs with random arc-lengths. Discrete Applied Math. 10, 57–77 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Gupta, I., Kermarrec, A.-M., Ganesh, A.: Efficient Epidemic-Style Protocols for Reliable and Scalable Multicast. In: 21st Symposium on Reliable Distributed Systems (SRDS), pp. 180–189 (2002)Google Scholar
  6. 6.
    Kempe, D., Dobra, A., Gehrke, J.: Computing Aggregate Information using Gossip. In: 44th Annual IEEE Symposium on Foundations of Computer Science, FOCS (2003)Google Scholar
  7. 7.
    Kempe, D., Kleinberg, J., Demers, A.: Spatial gossip and resource location protocols. In: 33rd ACM Symposium on Theory of Computing, pp. 163–172 (2001)Google Scholar
  8. 8.
    Kempe, D., Kleinberg, J.: Protocols and impossibility results for gossip-based communication mechanisms. In: Proc. 43rd IEEE Symp. on Foundations of Computer Science, pp. 471–480 (2002)Google Scholar
  9. 9.
    Luo, J., Eugster, P., Hubaux, J.-P.: Route driven gossip: probabilistic reliable multicast in ad hoc networks. In: 22nd Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM), pp. 2229–2239 (2003)Google Scholar
  10. 10.
    Pittel, B.: On spreading a rumour. SIAM J. Applied Math. 47, 213–223 (1987)CrossRefzbMATHGoogle Scholar
  11. 11.
    Plaxton, G., Rajaraman, R., Richa, A.: Accessing Nearby Copies of Replicated Objects in a Distributed Environment. In: 9th ACM Symposium on Parallel Algorithms and Architectures (SPAA), pp. 311–320 (1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Hervé Baumann
    • 1
  • Pierre Fraigniaud
    • 1
    • 2
  1. 1.University Paris DiderotFrance
  2. 2.CNRSFrance

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