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Local Update Algorithms for Random Graphs

  • Philippe Duchon
  • Romaric Duvignau
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8392)

Abstract

We study the problem of maintaining a given distribution of random graphs under an arbitrary sequence of vertex insertions and deletions. Since our goal is to model the evolution of dynamic logical networks, we work in a local model where we do not have direct access to the list of all vertices. Instead, we assume access to a global primitive that returns a random vertex, chosen uniformly from the whole vertex set. In this preliminary work, we focus on a simple model of uniform directed random graphs where all vertices have a fixed outdegree. We describe and analyze several algorithms for the maintenance task; the most elaborate of our algorithms are asymptotically optimal.

Keywords

random graphs dynamic graphs logical network maintenance randomness preservation 

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References

  1. 1.
    Frankel, J., Pepper, T.: The gnutella project, http://www.gnutelliums.com/
  2. 2.
    Bennett, K., Stef, T., Grothoff, C., Horozov, T., Patrascu, I.: The gnet whitepaper. Technical report, Purdue University (2002)Google Scholar
  3. 3.
    Clarke, I., Sandberg, O., Wiley, B., Hong, T.W.: Freenet: A distributed anonymous information storage and retrieval system. In: Federrath, H. (ed.) Designing Privacy Enhancing Technologies. LNCS, vol. 2009, pp. 46–66. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  4. 4.
    Liben-nowell, D., Balakrishnan, H., Karger, D.: Analysis of the evolution of peer-to-peer systems. In: ACM Symposium on Principles of Distributed Computing, pp. 233–242 (2002)Google Scholar
  5. 5.
    Pandurangan, G., Raghavan, P., Upfal, E.: Building low-diameter p2p networks. In: FOCS, pp. 492–499 (2001)Google Scholar
  6. 6.
    Cooper, C., Dyer, M., Greenhill, C.: Sampling regular graphs and a peer-to-peer network. Comb. Probab. Comput. 16(4), 557–593 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Bourassa, V., Holt, F.B.: Swan: Small-world wide area networks. In: International Conference on Advances in Infracstructure, SSGRR-2003s (2003)Google Scholar
  8. 8.
    Seidel, R., Aragon, C.R.: Randomized search trees. Algorithmica 16(4/5), 464–497 (1996)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Martínez, C., Roura, S.: Randomized binary search trees. J. ACM 45(2), 288–323 (1998)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Pugh, W.: Skip lists: A probabilistic alternative to balanced trees. Commun. ACM 33(6), 668–676 (1990)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Stoica, I., Morris, R., Karger, D., Kaashoek, M.F., Balakrishnan, H.: Chord: A scalable peer-to-peer lookup service for internet applications. SIGCOMM Comput. Commun. Rev. 31(4), 149–160 (2001)CrossRefGoogle Scholar
  12. 12.
    Cooper, C., Klasing, R., Radzik, T.: A randomized algorithm for the joining protocol in dynamic distributed networks. Theor. Comput. Sci. 406(3), 248–262 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Knuth, D.E., Yao, A.C.: The complexity of nonuniform random number generation. In: Proceedings of Symposium on Algorithms and Complexity, pp. 357–428. Academic Press, New York (1976)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Philippe Duchon
    • 1
    • 2
  • Romaric Duvignau
    • 1
    • 2
  1. 1.LaBRI, UMR 5800Univ. BordeauxTalenceFrance
  2. 2.LaBRI, UMR 5800CNRSTalenceFrance

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